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API Reference Overview

The Monet Stats API provides a comprehensive collection of statistical metrics and utilities for atmospheric sciences applications. This reference covers all available functions, their parameters, return values, and use cases.

API Structure

Monet Stats is organized into several functional modules:

Core Modules

Import Conventions

Standard Imports

# Import entire library
import monet_stats as ms

# Import specific modules
from monet_stats import contingency_metrics, correlation_metrics

# Import specific functions
from monet_stats import R2, RMSE, POD, FAR

Xarray Accessor (Pangeo Style)

The most recommended way to use Monet Stats with Xarray is via the .monet_stats accessor, which is automatically registered when you import monet_stats.

import monet_stats
import xarray as xr

# Load data
da = xr.open_dataarray("data.nc")

# Use accessor for analysis
climo = da.monet_stats.climatology(freq="month")
mda8 = da.monet_stats.mda8()

import monet_stats as ms
import numpy as np
import xarray as xr

Data Format Support

NumPy Arrays

import numpy as np

obs = np.array([1, 2, 3, 4, 5])
mod = np.array([1.1, 2.1, 2.9, 4.1, 4.8])

r2 = ms.R2(obs, mod)  # Works with 1D arrays
rmse = ms.RMSE(obs, mod)

Multi-dimensional Arrays

# 2D arrays (e.g., spatial fields)
obs_2d = np.random.normal(20, 2, (50, 50))
mod_2d = obs_2d + np.random.normal(0, 1, (50, 50))

fss = ms.FSS(obs_2d, mod_2d, window=5)

Pandas DataFrames

import pandas as pd

df = pd.DataFrame({
    'observed': np.random.normal(20, 2, 100),
    'modeled': np.random.normal(20.5, 2.5, 100),
    'station': ['A'] * 50 + ['B'] * 50
})

# Apply metrics by group
results = df.groupby('station').apply(
    lambda x: pd.Series({
        'RMSE': ms.RMSE(x['observed'], x['modeled']),
        'R2': ms.R2(x['observed'], x['modeled'])
    })
)

XArray DataArrays

import xarray as xr

obs_da = xr.DataArray(
    np.random.normal(20, 2, (10, 10, 365)),
    dims=['lat', 'lon', 'time'],
    coords={
        'lat': range(10),
        'lon': range(10),
        'time': pd.date_range('2020-01-01', periods=365, freq='D')
    }
)

mod_da = obs_da + xr.DataArray(
    np.random.normal(0, 1, (10, 10, 365)),
    dims=['lat', 'lon', 'time'],
    coords=obs_da.coords
)

# Metrics preserve coordinates and dimensions
skill = ms.R2(obs_da, mod_da)  # Returns DataArray with same coordinates

Common Parameters

Core Parameters

Most metrics accept these common parameters:

  • obs: Observed values (array-like)
  • mod: Modeled/predicted values (array-like)
  • axis: Axis along which to compute metrics (int, optional)
  • nan_policy: How to handle NaN values ('omit', 'propagate', 'raise')

Threshold Parameters

Many metrics use threshold parameters for categorical analysis:

  • minval: Minimum threshold for event definition
  • maxval: Maximum threshold for event definition (optional)

Spatial Parameters

Spatial metrics often include:

  • window: Size of spatial window (int)
  • threshold: Event threshold for spatial analysis

Return Value Types

Scalar Values

Most metrics return single scalar values:

r2 = ms.R2(obs, mod)  # float
rmse = ms.RMSE(obs, mod)  # float

Arrays

Some metrics return arrays for multi-dimensional input:

# For 2D spatial data
fss = ms.FSS(obs_2d, mod_2d)  # float

DataArrays (xarray)

When using xarray inputs, metrics return DataArrays:

skill = ms.R2(obs_da, mod_da)  # DataArray with coordinates

Error Handling

Data Shape Validation

try:
    result = ms.R2(obs_1d, mod_2d)  # Will raise ValueError
except ValueError as e:
    print(f"Shape mismatch: {e}")

NaN Handling

# Data with NaN values
obs_with_nan = np.array([1, 2, np.nan, 4])
mod_with_nan = np.array([1.1, 2.1, 3.1, 4.1])

# Functions automatically handle NaN by default
rmse = ms.RMSE(obs_with_nan, mod_with_nan)  # Uses valid pairs only

Type Validation

# Invalid types will raise TypeError
try:
    result = ms.R2("invalid", "data")  # TypeError
except TypeError as e:
    print(f"Invalid data type: {e}")

Performance Considerations

Vectorized Operations

All metrics use NumPy and Xarray vectorized operations for optimal performance. Loop-free implementations ensure maximum speed on modern hardware.

Out-of-Core Processing with Dask

For datasets larger than RAM, monet-stats is fully compatible with Dask. Most metrics are "lazy-aware" and will preserve the Dask computation graph.

# Open large dataset with chunks (Aero Protocol recommended)
ds = xr.open_dataset("large_data.nc", chunks={"time": "auto", "lat": 100, "lon": 100})
obs = xr.open_dataset("obs_data.nc", chunks={"time": "auto", "lat": 100, "lon": 100})

# Metrics stay lazy and don't trigger loading
skill = ms.RMSE(obs.var, ds.var, axis="time")

# Execution only happens on compute()
result = skill.compute()

Scientific Provenance

When using Xarray DataArrays, monet-stats automatically updates the attrs['history'] to track which statistical operations were applied to the data, ensuring scientific reproducibility.

Example Usage Patterns

Basic Error Analysis

import monet_stats as ms
import numpy as np

# Sample data
obs = np.array([1.0, 2.5, 3.2, 4.8, 5.0])
mod = np.array([1.2, 2.3, 3.5, 4.6, 5.2])

# Error metrics
error_analysis = {
    'RMSE': ms.RMSE(obs, mod),
    'MAE': ms.MAE(obs, mod),
    'MB': ms.MB(obs, mod),
    'NMB': ms.NMB(obs, mod),
    'NME': ms.NME(obs, mod)
}

Comprehensive Model Evaluation

def evaluate_model(observed, modeled):
    """Comprehensive model evaluation suite"""

    metrics = {
        # Error measures
        'RMSE': ms.RMSE(observed, modeled),
        'MAE': ms.MAE(observed, modeled),
        'MB': ms.MB(observed, modeled),
        'NMB': ms.NMB(observed, modeled),

        # Skill scores
        'R2': ms.R2(observed, modeled),
        'NSE': ms.NSE(observed, modeled),
        'KGE': ms.KGE(observed, modeled),
        'IOA': ms.IOA(observed, modeled),

        # Relative measures
        'MPE': ms.MPE(observed, modeled),
        'NME': ms.NME(observed, modeled)
    }

    return metrics

# Usage
results = evaluate_model(obs, mod)
for metric, value in results.items():
    print(f"{metric}: {value:.4f}")

Categorical Event Analysis

# Binary event analysis
obs_events = np.array([0, 1, 1, 0, 1, 0, 1, 1, 0, 0])
mod_events = np.array([0, 1, 0, 0, 1, 1, 1, 0, 0, 1])

# Contingency table metrics
contingency_metrics = {
    'POD': ms.POD(obs_events, mod_events, threshold=0.5),
    'FAR': ms.FAR(obs_events, mod_events, threshold=0.5),
    'CSI': ms.CSI(obs_events, mod_events, threshold=0.5),
    'HSS': ms.HSS(obs_events, mod_events, threshold=0.5),
    'ETS': ms.ETS(obs_events, mod_events, threshold=0.5)
}

API Reference

The following sections provide auto-generated documentation for each core module based on docstrings.

Contingency Metrics

BSS_binary(obs, mod, threshold, axis=None)

Binary Brier Skill Score for deterministic forecasts.

Typical Use Cases

  • Evaluating the accuracy of deterministic binary forecasts (e.g., precipitation yes/no).
  • Used in meteorology and environmental modeling to assess forecast skill relative to a reference.

Typical Values and Range

  • Range: -∞ to 1
  • 1: Perfect forecast
  • 0: Same skill as reference forecast
  • Negative: Worse than reference forecast

Parameters

obs : numpy.ndarray or xarray.DataArray Observed binary outcomes or continuous values. mod : numpy.ndarray or xarray.DataArray Forecast binary outcomes or continuous values. threshold : float Threshold value to convert continuous forecasts to binary. axis : int, str, or iterable of such, optional Axis along which to compute the score.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Binary Brier Skill Score.

Examples

import numpy as np from monet_stats.contingency_metrics import BSS_binary obs = np.array([0, 1, 1, 0]) mod = np.array([0, 1, 0, 0]) BSS_binary(obs, mod, threshold=0.5) 0.5

Source code in src/monet_stats/contingency_metrics.py 
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def BSS_binary(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    threshold: float,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Binary Brier Skill Score for deterministic forecasts.

    Typical Use Cases
    -----------------
    - Evaluating the accuracy of deterministic binary forecasts (e.g.,
      precipitation yes/no).
    - Used in meteorology and environmental modeling to assess forecast skill
      relative to a reference.

    Typical Values and Range
    ------------------------
    - Range: -∞ to 1
    - 1: Perfect forecast
    - 0: Same skill as reference forecast
    - Negative: Worse than reference forecast

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed binary outcomes or continuous values.
    mod : numpy.ndarray or xarray.DataArray
        Forecast binary outcomes or continuous values.
    threshold : float
        Threshold value to convert continuous forecasts to binary.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the score.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Binary Brier Skill Score.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.contingency_metrics import BSS_binary
    >>> obs = np.array([0, 1, 1, 0])
    >>> mod = np.array([0, 1, 0, 0])
    >>> BSS_binary(obs, mod, threshold=0.5)
    0.5
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)

        obs_binary = (obs >= threshold).astype(float)
        mod_binary = (mod >= threshold).astype(float)

        bs = ((mod_binary - obs_binary) ** 2).mean(dim=dim)
        # bs_ref is p_bar * (1 - p_bar) where p_bar is the event frequency
        p_bar = obs_binary.mean(dim=dim)
        bs_ref = p_bar * (1.0 - p_bar)

        result = xr.where(bs_ref > 0, 1.0 - (bs / bs_ref), 0.0)
        result.attrs = obs.attrs.copy()
        return _update_history(result, "Binary Brier Skill Score (BSS_binary)")
    else:
        obs_binary = (np.asarray(obs) >= threshold).astype(float)
        mod_binary = (np.asarray(mod) >= threshold).astype(float)

        bs = np.nanmean((mod_binary - obs_binary) ** 2, axis=axis)
        p_bar = np.nanmean(obs_binary, axis=axis)
        bs_ref = p_bar * (1.0 - p_bar)

        with np.errstate(divide="ignore", invalid="ignore"):
            result = np.where(bs_ref > 0, 1.0 - (bs / bs_ref), 0.0)
            return result.item() if np.ndim(result) == 0 else result

CSI(obs, mod, minval, maxval=None, axis=None)

Critical Success Index (CSI).

Typical Use Cases

  • Evaluating forecast skill for rare or binary events (e.g., precipitation, air quality exceedances).
  • Used in meteorology and environmental modeling to assess event prediction accuracy.

Typical Values and Range

  • Range: 0 to 1
  • 1: Perfect forecast
  • 0: No skill (no correct predictions)

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Modeled values. minval : float Minimum threshold value for event detection. maxval : float, optional Maximum threshold value for event detection. axis : int, str, or iterable of such, optional Axis along which to compute the metric.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray CSI value for the given threshold.

Examples

import numpy as np from monet_stats.contingency_metrics import CSI obs = np.array([1, 0, 1, 0]) mod = np.array([1, 1, 0, 0]) CSI(obs, mod, minval=0.5) 0.3333333333333333

Source code in src/monet_stats/contingency_metrics.py 
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def CSI(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval: float,
    maxval: Optional[float] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Critical Success Index (CSI).

    Typical Use Cases
    -----------------
    - Evaluating forecast skill for rare or binary events (e.g., precipitation,
      air quality exceedances).
    - Used in meteorology and environmental modeling to assess event prediction
      accuracy.

    Typical Values and Range
    ------------------------
    - Range: 0 to 1
    - 1: Perfect forecast
    - 0: No skill (no correct predictions)

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Modeled values.
    minval : float
        Minimum threshold value for event detection.
    maxval : float, optional
        Maximum threshold value for event detection.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the metric.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        CSI value for the given threshold.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.contingency_metrics import CSI
    >>> obs = np.array([1, 0, 1, 0])
    >>> mod = np.array([1, 1, 0, 0])
    >>> CSI(obs, mod, minval=0.5)
    0.3333333333333333
    """
    a, b, c, d = _contingency_table(obs, mod, minval, maxval, axis=axis)
    denom = a + b + c
    if isinstance(denom, xr.DataArray):
        result = xr.where(denom > 0, a / denom, np.nan)
        result.attrs = obs.attrs.copy()
        return _update_history(result, "Critical Success Index (CSI)")
    else:
        with np.errstate(divide="ignore", invalid="ignore"):
            result = np.where(denom > 0, a / denom, np.nan)
            return result.item() if np.ndim(result) == 0 else result

CSI_max_threshold(obs, mod, minval_range, maxval_range, step_size=1.0)

Find the threshold that maximizes the Critical Success Index (CSI) over a range.

Vectorized implementation (Aero Protocol).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. minval_range : float Minimum value of threshold range to test. maxval_range : float Maximum value of threshold range to test. step_size : float, optional Step size for testing thresholds. Default is 1.0.

Returns

optimal_threshold : float Threshold value that maximizes CSI. max_csi : float Maximum CSI value achieved.

Source code in src/monet_stats/contingency_metrics.py 
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def CSI_max_threshold(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval_range: float,
    maxval_range: float,
    step_size: float = 1.0,
) -> Tuple[float, float]:
    """
    Find the threshold that maximizes the Critical Success Index (CSI) over a range.

    Vectorized implementation (Aero Protocol).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    minval_range : float
        Minimum value of threshold range to test.
    maxval_range : float
        Maximum value of threshold range to test.
    step_size : float, optional
        Step size for testing thresholds. Default is 1.0.

    Returns
    -------
    optimal_threshold : float
        Threshold value that maximizes CSI.
    max_csi : float
        Maximum CSI value achieved.
    """
    thresholds = np.arange(minval_range, maxval_range, step_size)
    a, b, c, d = _contingency_table(obs, mod, minval=thresholds)

    denom = a + b + c
    with np.errstate(divide="ignore", invalid="ignore"):
        csi_values = np.where(denom > 0, a / denom, np.nan)

    if isinstance(csi_values, xr.DataArray):
        max_idx = csi_values.argmax(dim="threshold").values.item()
        max_val = csi_values.isel(threshold=max_idx).values.item()
    else:
        max_idx = np.nanargmax(csi_values)
        max_val = csi_values[max_idx]

    return float(thresholds[max_idx]), float(max_val)

ETS(obs, mod, minval, maxval=None, axis=None)

Equitable Threat Score (ETS).

Typical Use Cases

  • Evaluating forecast skill for rare events (e.g., precipitation, air quality exceedances).
  • Used in meteorology and environmental modeling to assess binary event prediction accuracy.

Typical Values and Range

  • Range: -1/3 to 1
  • 1: Perfect forecast
  • 0: No skill (random forecast)
  • Negative values: Worse than random

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Modeled values. minval : float Minimum threshold value for event detection. maxval : float, optional Maximum threshold value for event detection. axis : int, str, or iterable of such, optional Axis along which to compute the metric.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray ETS value for the given threshold.

Examples

import numpy as np from monet_stats.contingency_metrics import ETS obs = np.array([1, 0, 1, 0]) mod = np.array([1, 1, 0, 0]) ETS(obs, mod, minval=0.5) -0.2

Source code in src/monet_stats/contingency_metrics.py 
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def ETS(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval: float,
    maxval: Optional[float] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Equitable Threat Score (ETS).

    Typical Use Cases
    -----------------
    - Evaluating forecast skill for rare events (e.g., precipitation, air quality
      exceedances).
    - Used in meteorology and environmental modeling to assess binary event
      prediction accuracy.

    Typical Values and Range
    ------------------------
    - Range: -1/3 to 1
    - 1: Perfect forecast
    - 0: No skill (random forecast)
    - Negative values: Worse than random

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Modeled values.
    minval : float
        Minimum threshold value for event detection.
    maxval : float, optional
        Maximum threshold value for event detection.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the metric.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        ETS value for the given threshold.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.contingency_metrics import ETS
    >>> obs = np.array([1, 0, 1, 0])
    >>> mod = np.array([1, 1, 0, 0])
    >>> ETS(obs, mod, minval=0.5)
    -0.2
    """
    a, b, c, d = _contingency_table(obs, mod, minval, maxval, axis=axis)
    total = a + b + c + d
    random_hits = ((a + b) * (a + c)) / total
    denom = a + b + c - random_hits
    if isinstance(denom, xr.DataArray):
        result = xr.where(denom > 0, (a - random_hits) / denom, np.nan)
        result.attrs = obs.attrs.copy()
        return _update_history(result, "Equitable Threat Score (ETS)")
    else:
        with np.errstate(divide="ignore", invalid="ignore"):
            result = np.where(denom > 0, (a - random_hits) / denom, np.nan)
            return result.item() if np.ndim(result) == 0 else result

ETS_max_threshold(obs, mod, minval_range, maxval_range, step_size=1.0)

Find the threshold that maximizes the Equitable Threat Score (ETS) over a range.

Vectorized implementation (Aero Protocol).

Typical Use Cases

  • Automated tuning of model thresholds to achieve the best possible predictive skill for rare events.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. minval_range : float Minimum value of threshold range to test. maxval_range : float Maximum value of threshold range to test. step_size : float, optional Step size for testing thresholds. Default is 1.0.

Returns

optimal_threshold : float Threshold value that maximizes ETS. max_ets : float Maximum ETS value achieved.

Source code in src/monet_stats/contingency_metrics.py 
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def ETS_max_threshold(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval_range: float,
    maxval_range: float,
    step_size: float = 1.0,
) -> Tuple[float, float]:
    """
    Find the threshold that maximizes the Equitable Threat Score (ETS) over a range.

    Vectorized implementation (Aero Protocol).

    Typical Use Cases
    -----------------
    - Automated tuning of model thresholds to achieve the best possible
      predictive skill for rare events.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    minval_range : float
        Minimum value of threshold range to test.
    maxval_range : float
        Maximum value of threshold range to test.
    step_size : float, optional
        Step size for testing thresholds. Default is 1.0.

    Returns
    -------
    optimal_threshold : float
        Threshold value that maximizes ETS.
    max_ets : float
        Maximum ETS value achieved.
    """
    thresholds = np.arange(minval_range, maxval_range, step_size)
    a, b, c, d = _contingency_table(obs, mod, minval=thresholds)

    total = a + b + c + d
    random_hits = ((a + b) * (a + c)) / total
    denom = a + b + c - random_hits
    with np.errstate(divide="ignore", invalid="ignore"):
        ets_values = np.where(denom > 0, (a - random_hits) / denom, np.nan)

    if isinstance(ets_values, xr.DataArray):
        max_idx = ets_values.argmax(dim="threshold").values.item()
        max_ets = ets_values.isel(threshold=max_idx).values.item()
    else:
        max_idx = np.nanargmax(ets_values)
        max_ets = ets_values[max_idx]

    return float(thresholds[max_idx]), float(max_ets)

FAR(obs, mod, minval, maxval=None, axis=None)

False Alarm Rate (FAR) for a given event threshold.

Typical Use Cases

  • Evaluating the frequency of false alarms in categorical forecasts (e.g., precipitation, air quality events).
  • Used in meteorology and environmental modeling to assess forecast reliability.

Typical Values and Range

  • Range: 0 to 1
  • 0: No false alarms (perfect reliability)
  • 1: All alarms are false (no reliability)

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. minval : float Minimum event threshold. maxval : float, optional Maximum event threshold. axis : int, str, or iterable of such, optional Axis along which to compute the metric.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray False alarm rate.

Examples

import numpy as np from monet_stats.contingency_metrics import FAR obs = np.array([0, 1, 1, 0]) mod = np.array([1, 1, 0, 0]) FAR(obs, mod, minval=0.5) 0.5

Source code in src/monet_stats/contingency_metrics.py 
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def FAR(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval: float,
    maxval: Optional[float] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    False Alarm Rate (FAR) for a given event threshold.

    Typical Use Cases
    -----------------
    - Evaluating the frequency of false alarms in categorical forecasts (e.g.,
      precipitation, air quality events).
    - Used in meteorology and environmental modeling to assess forecast
      reliability.

    Typical Values and Range
    ------------------------
    - Range: 0 to 1
    - 0: No false alarms (perfect reliability)
    - 1: All alarms are false (no reliability)

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    minval : float
        Minimum event threshold.
    maxval : float, optional
        Maximum event threshold.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the metric.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        False alarm rate.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.contingency_metrics import FAR
    >>> obs = np.array([0, 1, 1, 0])
    >>> mod = np.array([1, 1, 0, 0])
    >>> FAR(obs, mod, minval=0.5)
    0.5
    """
    a, b, c, d = _contingency_table(obs, mod, minval, maxval, axis=axis)
    denom = a + c
    if isinstance(denom, xr.DataArray):
        result = xr.where(denom > 0, c / denom, np.nan)
        result.attrs = obs.attrs.copy()
        return _update_history(result, "False Alarm Rate (FAR)")
    else:
        with np.errstate(divide="ignore", invalid="ignore"):
            result = np.where(denom > 0, c / denom, np.nan)
            return result.item() if np.ndim(result) == 0 else result

FAR_min_threshold(obs, mod, minval_range, maxval_range, step_size=1.0)

Find the threshold that minimizes the False Alarm Rate (FAR) over a range.

Vectorized implementation (Aero Protocol).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. minval_range : float Minimum value of threshold range to test. maxval_range : float Maximum value of threshold range to test. step_size : float, optional Step size for testing thresholds. Default is 1.0.

Returns

optimal_threshold : float Threshold value that minimizes FAR. min_far : float Minimum FAR value achieved.

Examples

import numpy as np obs = np.array([1, 2, 3, 4, 5]) mod = np.array([1.5, 2.5, 3.5, 4.5, 5.5]) FAR_min_threshold(obs, mod, 1, 5, 0.5) (1.5, 0.0)

Source code in src/monet_stats/contingency_metrics.py 
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def FAR_min_threshold(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval_range: float,
    maxval_range: float,
    step_size: float = 1.0,
) -> Tuple[float, float]:
    """
    Find the threshold that minimizes the False Alarm Rate (FAR) over a range.

    Vectorized implementation (Aero Protocol).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    minval_range : float
        Minimum value of threshold range to test.
    maxval_range : float
        Maximum value of threshold range to test.
    step_size : float, optional
        Step size for testing thresholds. Default is 1.0.

    Returns
    -------
    optimal_threshold : float
        Threshold value that minimizes FAR.
    min_far : float
        Minimum FAR value achieved.

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4, 5])
    >>> mod = np.array([1.5, 2.5, 3.5, 4.5, 5.5])
    >>> FAR_min_threshold(obs, mod, 1, 5, 0.5)
    (1.5, 0.0)
    """
    thresholds = np.arange(minval_range, maxval_range, step_size)
    a, b, c, d = _contingency_table(obs, mod, minval=thresholds)

    denom = a + c
    with np.errstate(divide="ignore", invalid="ignore"):
        far_values = np.where(denom > 0, c / denom, np.nan)

    if isinstance(far_values, xr.DataArray):
        min_idx = far_values.argmin(dim="threshold").values.item()
        min_val = far_values.isel(threshold=min_idx).values.item()
    else:
        min_idx = np.nanargmin(far_values)
        min_val = far_values[min_idx]

    return float(thresholds[min_idx]), float(min_val)

FBI(obs, mod, minval, maxval=None, axis=None)

Frequency Bias Index (FBI) for a given event threshold.

Typical Use Cases

  • Evaluating whether the model over- or under-predicts the frequency of events.
  • Used in air quality and weather forecasting to assess systematic bias in categorical predictions.

Typical Values and Range

  • Range: 0 to ∞
  • 1: Perfect (events occur with same frequency in model and observations)

  • 1: Over-prediction (model predicts events more often than observed)

  • < 1: Under-prediction (model predicts events less often than observed)

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. minval : float Minimum event threshold. maxval : float, optional Maximum event threshold. axis : int, str, or iterable of such, optional Axis along which to compute the metric.

Returns

fbi : numpy.number, numpy.ndarray, or xarray.DataArray Frequency bias index.

Examples

import numpy as np from monet_stats.contingency_metrics import FBI obs = np.array([0, 1, 1, 0]) mod = np.array([1, 1, 0, 0]) FBI(obs, mod, minval=0.5) 1.0

Source code in src/monet_stats/contingency_metrics.py 
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def FBI(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval: float,
    maxval: Optional[float] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Frequency Bias Index (FBI) for a given event threshold.

    Typical Use Cases
    -----------------
    - Evaluating whether the model over- or under-predicts the frequency of events.
    - Used in air quality and weather forecasting to assess systematic bias in
      categorical predictions.

    Typical Values and Range
    ------------------------
    - Range: 0 to ∞
    - 1: Perfect (events occur with same frequency in model and observations)
    - > 1: Over-prediction (model predicts events more often than observed)
    - < 1: Under-prediction (model predicts events less often than observed)

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    minval : float
        Minimum event threshold.
    maxval : float, optional
        Maximum event threshold.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the metric.

    Returns
    -------
    fbi : numpy.number, numpy.ndarray, or xarray.DataArray
        Frequency bias index.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.contingency_metrics import FBI
    >>> obs = np.array([0, 1, 1, 0])
    >>> mod = np.array([1, 1, 0, 0])
    >>> FBI(obs, mod, minval=0.5)
    1.0
    """
    a, b, c, d = _contingency_table(obs, mod, minval, maxval, axis=axis)
    denom = a + b
    if isinstance(denom, xr.DataArray):
        result = xr.where(denom > 0, (a + c) / denom, np.nan)
        result.attrs = obs.attrs.copy()
        return _update_history(result, "Frequency Bias Index (FBI)")
    else:
        with np.errstate(divide="ignore", invalid="ignore"):
            result = np.where(denom > 0, (a + c) / denom, np.nan)
            return result.item() if np.ndim(result) == 0 else result

HSS(obs, mod, minval, maxval=None, axis=None)

Heidke Skill Score (HSS).

Typical Use Cases

  • Evaluating categorical forecast skill (e.g., precipitation, air quality events).
  • Used in meteorology and environmental modeling to assess binary event prediction accuracy.

Typical Values and Range

  • Range: -∞ to 1
  • 1: Perfect forecast
  • 0: No skill (random forecast)
  • Negative values: Worse than random

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Modeled values. minval : float Minimum threshold value for event detection. maxval : float, optional Maximum threshold value for event detection. axis : int, str, or iterable of such, optional Axis along which to compute the metric.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray HSS value for the given threshold.

Examples

import numpy as np from monet_stats.contingency_metrics import HSS obs = np.array([1, 0, 1, 0]) mod = np.array([1, 1, 0, 0]) HSS(obs, mod, minval=0.5) -0.3333333333333333

Source code in src/monet_stats/contingency_metrics.py 
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def HSS(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval: float,
    maxval: Optional[float] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Heidke Skill Score (HSS).

    Typical Use Cases
    -----------------
    - Evaluating categorical forecast skill (e.g., precipitation, air quality
      events).
    - Used in meteorology and environmental modeling to assess binary event
      prediction accuracy.

    Typical Values and Range
    ------------------------
    - Range: -∞ to 1
    - 1: Perfect forecast
    - 0: No skill (random forecast)
    - Negative values: Worse than random

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Modeled values.
    minval : float
        Minimum threshold value for event detection.
    maxval : float, optional
        Maximum threshold value for event detection.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the metric.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        HSS value for the given threshold.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.contingency_metrics import HSS
    >>> obs = np.array([1, 0, 1, 0])
    >>> mod = np.array([1, 1, 0, 0])
    >>> HSS(obs, mod, minval=0.5)
    -0.3333333333333333
    """
    a, b, c, d = _contingency_table(obs, mod, minval, maxval, axis=axis)
    denom = (a + c) * (c + d) + (a + b) * (b + d)
    if isinstance(denom, xr.DataArray):
        result = xr.where(denom > 0, 2 * (a * d - b * c) / denom, np.nan)
        result.attrs = obs.attrs.copy()
        return _update_history(result, "Heidke Skill Score (HSS)")
    else:
        with np.errstate(divide="ignore", invalid="ignore"):
            result = np.where(denom > 0, 2 * (a * d - b * c) / denom, np.nan)
            return result.item() if np.ndim(result) == 0 else result

HSS_max_threshold(obs, mod, minval_range, maxval_range, step_size=1.0)

Find the threshold that maximizes the Heidke Skill Score (HSS) over a range.

Vectorized implementation (Aero Protocol).

Typical Use Cases

  • Automated tuning of model thresholds to achieve the best possible overall categorical predictive skill.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. minval_range : float Minimum value of threshold range to test. maxval_range : float Maximum value of threshold range to test. step_size : float, optional Step size for testing thresholds. Default is 1.0.

Returns

optimal_threshold : float Threshold value that maximizes HSS. max_hss : float Maximum HSS value achieved.

Examples

import numpy as np obs = np.array([1, 2, 3, 4, 5]) mod = np.array([1.5, 2.5, 3.5, 4.5, 5.5]) HSS_max_threshold(obs, mod, 1, 5, 0.5) (2.5, 1.0)

Source code in src/monet_stats/contingency_metrics.py 
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def HSS_max_threshold(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval_range: float,
    maxval_range: float,
    step_size: float = 1.0,
) -> Tuple[float, float]:
    """
    Find the threshold that maximizes the Heidke Skill Score (HSS) over a range.

    Vectorized implementation (Aero Protocol).

    Typical Use Cases
    -----------------
    - Automated tuning of model thresholds to achieve the best possible
      overall categorical predictive skill.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    minval_range : float
        Minimum value of threshold range to test.
    maxval_range : float
        Maximum value of threshold range to test.
    step_size : float, optional
        Step size for testing thresholds. Default is 1.0.

    Returns
    -------
    optimal_threshold : float
        Threshold value that maximizes HSS.
    max_hss : float
        Maximum HSS value achieved.

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4, 5])
    >>> mod = np.array([1.5, 2.5, 3.5, 4.5, 5.5])
    >>> HSS_max_threshold(obs, mod, 1, 5, 0.5)
    (2.5, 1.0)
    """
    thresholds = np.arange(minval_range, maxval_range, step_size)
    a, b, c, d = _contingency_table(obs, mod, minval=thresholds)

    denom = (a + c) * (c + d) + (a + b) * (b + d)
    with np.errstate(divide="ignore", invalid="ignore"):
        hss_values = np.where(denom > 0, 2 * (a * d - b * c) / denom, np.nan)

    if isinstance(hss_values, xr.DataArray):
        max_idx = hss_values.argmax(dim="threshold").values.item()
        max_hss = hss_values.isel(threshold=max_idx).values.item()
    else:
        max_idx = np.nanargmax(hss_values)
        max_hss = hss_values[max_idx]

    return float(thresholds[max_idx]), float(max_hss)

POD(obs, mod, minval, maxval=None, axis=None)

Probability of Detection (POD) for a given event threshold.

Typical Use Cases

  • Evaluating how well a model detects events above a critical threshold (e.g., pollution exceedances, precipitation events).
  • Used in contingency table analysis for categorical forecast verification.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. minval : float Minimum event threshold. maxval : float, optional Maximum event threshold. axis : int, str, or iterable of such, optional Axis along which to compute the metric.

Returns

pod : numpy.number, numpy.ndarray, or xarray.DataArray Probability of detection.

Examples

import numpy as np from monet_stats.contingency_metrics import POD obs = np.array([0, 1, 1, 0]) mod = np.array([1, 1, 0, 0]) POD(obs, mod, minval=0.5) 0.5

Source code in src/monet_stats/contingency_metrics.py 
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def POD(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval: float,
    maxval: Optional[float] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Probability of Detection (POD) for a given event threshold.

    Typical Use Cases
    -----------------
    - Evaluating how well a model detects events above a critical threshold
      (e.g., pollution exceedances, precipitation events).
    - Used in contingency table analysis for categorical forecast verification.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    minval : float
        Minimum event threshold.
    maxval : float, optional
        Maximum event threshold.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the metric.

    Returns
    -------
    pod : numpy.number, numpy.ndarray, or xarray.DataArray
        Probability of detection.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.contingency_metrics import POD
    >>> obs = np.array([0, 1, 1, 0])
    >>> mod = np.array([1, 1, 0, 0])
    >>> POD(obs, mod, minval=0.5)
    0.5
    """
    a, b, c, d = _contingency_table(obs, mod, minval, maxval, axis=axis)
    denom = a + b
    if isinstance(denom, xr.DataArray):
        result = xr.where(denom > 0, a / denom, np.nan)
        result.attrs = obs.attrs.copy()
        return _update_history(result, "Probability of Detection (POD)")
    else:
        with np.errstate(divide="ignore", invalid="ignore"):
            result = np.where(denom > 0, a / denom, np.nan)
            return result.item() if np.ndim(result) == 0 else result

POD_max_threshold(obs, mod, minval_range, maxval_range, step_size=1.0)

Find the threshold that maximizes the Probability of Detection (POD) over a range.

Vectorized implementation (Aero Protocol).

Typical Use Cases

  • Determining the most sensitive threshold for event detection, prioritizing hits over all other categories.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. minval_range : float Minimum value of threshold range to test. maxval_range : float Maximum value of threshold range to test. step_size : float, optional Step size for testing thresholds. Default is 1.0.

Returns

optimal_threshold : float Threshold value that maximizes POD. max_pod : float Maximum POD value achieved.

Examples

import numpy as np obs = np.array([1, 2, 3, 4, 5]) mod = np.array([1.5, 2.5, 3.5, 4.5, 5.5]) POD_max_threshold(obs, mod, 1, 5, 0.5) (1.0, 1.0)

Source code in src/monet_stats/contingency_metrics.py 
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def POD_max_threshold(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval_range: float,
    maxval_range: float,
    step_size: float = 1.0,
) -> Tuple[float, float]:
    """
    Find the threshold that maximizes the Probability of Detection (POD) over a range.

    Vectorized implementation (Aero Protocol).

    Typical Use Cases
    -----------------
    - Determining the most sensitive threshold for event detection,
      prioritizing hits over all other categories.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    minval_range : float
        Minimum value of threshold range to test.
    maxval_range : float
        Maximum value of threshold range to test.
    step_size : float, optional
        Step size for testing thresholds. Default is 1.0.

    Returns
    -------
    optimal_threshold : float
        Threshold value that maximizes POD.
    max_pod : float
        Maximum POD value achieved.

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4, 5])
    >>> mod = np.array([1.5, 2.5, 3.5, 4.5, 5.5])
    >>> POD_max_threshold(obs, mod, 1, 5, 0.5)
    (1.0, 1.0)
    """
    thresholds = np.arange(minval_range, maxval_range, step_size)
    a, b, c, d = _contingency_table(obs, mod, minval=thresholds)

    denom = a + b
    with np.errstate(divide="ignore", invalid="ignore"):
        pod_values = np.where(denom > 0, a / denom, np.nan)

    if isinstance(pod_values, xr.DataArray):
        max_idx = pod_values.argmax(dim="threshold").values.item()
        max_val = pod_values.isel(threshold=max_idx).values.item()
    else:
        max_idx = np.nanargmax(pod_values)
        max_val = pod_values[max_idx]

    return float(thresholds[max_idx]), float(max_val)

TSS(obs, mod, minval, maxval=None, axis=None)

Hanssen-Kuipers Discriminant (True Skill Statistic, TSS).

Typical Use Cases

  • Assessing the ability of the model to distinguish between event and non-event occurrences.
  • Preferred over other scores for its independence from event frequency (prevalence).

Typical Values and Range

  • Range: -1 to 1
  • 1: Perfect forecast
  • 0: No skill
  • -1: Perfect mis-forecast (always wrong)

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. minval : float Minimum event threshold. maxval : float, optional Maximum event threshold. axis : int, str, or iterable of such, optional Axis along which to compute the metric.

Returns

tss : numpy.number, numpy.ndarray, or xarray.DataArray True skill statistic.

Examples

import numpy as np from monet_stats.contingency_metrics import TSS obs = np.array([0, 1, 1, 0]) mod = np.array([1, 1, 0, 0]) TSS(obs, mod, minval=0.5) 0.0

Source code in src/monet_stats/contingency_metrics.py 
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def TSS(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval: float,
    maxval: Optional[float] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Hanssen-Kuipers Discriminant (True Skill Statistic, TSS).

    Typical Use Cases
    -----------------
    - Assessing the ability of the model to distinguish between event and non-event
      occurrences.
    - Preferred over other scores for its independence from event frequency
      (prevalence).

    Typical Values and Range
    ------------------------
    - Range: -1 to 1
    - 1: Perfect forecast
    - 0: No skill
    - -1: Perfect mis-forecast (always wrong)

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    minval : float
        Minimum event threshold.
    maxval : float, optional
        Maximum event threshold.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the metric.

    Returns
    -------
    tss : numpy.number, numpy.ndarray, or xarray.DataArray
        True skill statistic.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.contingency_metrics import TSS
    >>> obs = np.array([0, 1, 1, 0])
    >>> mod = np.array([1, 1, 0, 0])
    >>> TSS(obs, mod, minval=0.5)
    0.0
    """
    a, b, c, d = _contingency_table(obs, mod, minval, maxval, axis=axis)
    pod_denom = a + b
    pofd_denom = c + d

    if isinstance(pod_denom, xr.DataArray):
        pod = xr.where(pod_denom > 0, a / pod_denom, np.nan)
        pofd = xr.where(pofd_denom > 0, c / pofd_denom, np.nan)
        result = pod - pofd
        result.attrs = obs.attrs.copy()
        return _update_history(result, "True Skill Statistic (TSS)")
    else:
        with np.errstate(divide="ignore", invalid="ignore"):
            pod = np.where(pod_denom > 0, a / pod_denom, np.nan)
            pofd = np.where(pofd_denom > 0, c / pofd_denom, np.nan)
            result = pod - pofd
            return result.item() if np.ndim(result) == 0 else result

TSS_max_threshold(obs, mod, minval_range, maxval_range, step_size=1.0)

Find the threshold that maximizes the True Skill Statistic (TSS) over a range.

Vectorized implementation (Aero Protocol).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. minval_range : float Minimum value of threshold range to test. maxval_range : float Maximum value of threshold range to test. step_size : float, optional Step size for testing thresholds. Default is 1.0.

Returns

optimal_threshold : float Threshold value that maximizes TSS. max_tss : float Maximum TSS value achieved.

Source code in src/monet_stats/contingency_metrics.py 
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def TSS_max_threshold(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval_range: float,
    maxval_range: float,
    step_size: float = 1.0,
) -> Tuple[float, float]:
    """
    Find the threshold that maximizes the True Skill Statistic (TSS) over a range.

    Vectorized implementation (Aero Protocol).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    minval_range : float
        Minimum value of threshold range to test.
    maxval_range : float
        Maximum value of threshold range to test.
    step_size : float, optional
        Step size for testing thresholds. Default is 1.0.

    Returns
    -------
    optimal_threshold : float
        Threshold value that maximizes TSS.
    max_tss : float
        Maximum TSS value achieved.
    """
    thresholds = np.arange(minval_range, maxval_range, step_size)
    a, b, c, d = _contingency_table(obs, mod, minval=thresholds)

    pod_denom = a + b
    pofd_denom = c + d

    if isinstance(a, xr.DataArray):
        pod = xr.where(pod_denom > 0, a / pod_denom, np.nan)
        pofd = xr.where(pofd_denom > 0, c / pofd_denom, np.nan)
        tss_values = pod - pofd
    else:
        with np.errstate(divide="ignore", invalid="ignore"):
            pod = np.where(pod_denom > 0, a / pod_denom, np.nan)
            pofd = np.where(pofd_denom > 0, c / pofd_denom, np.nan)
            tss_values = pod - pofd

    if isinstance(tss_values, xr.DataArray):
        max_idx = tss_values.argmax(dim="threshold").values.item()
        max_val = tss_values.isel(threshold=max_idx).values.item()
    else:
        max_idx = np.nanargmax(tss_values)
        max_val = tss_values[max_idx]

    return float(thresholds[max_idx]), float(max_val)

scores(obs, mod, minval, maxval=None, axis=None)

Calculate the 2x2 contingency table (Aero Protocol).

Typical Use Cases

  • Obtaining the raw counts of hits, misses, false alarms, and correct negatives to compute custom categorical scores.

Parameters

obs : numpy.ndarray or xarray.DataArray Observation values ("truth"). mod : numpy.ndarray or xarray.DataArray Model values ("prediction"). minval : float Minimum threshold for event detection. maxval : float, optional Maximum threshold for event detection. axis : int, str, or iterable of such, optional Axis along which to compute the scores.

Returns

Tuple[Union[np.number, np.ndarray, xr.DataArray], ...] A tuple of (hits, misses, false alarms, correct negatives).

Examples

import numpy as np obs = np.array([1, 2, 3, 4]) mod = np.array([1.5, 1.8, 3.2, 3.8]) a, b, c, d = scores(obs, mod, minval=2.5) print(f"Hits: {a}") Hits: 2

Source code in src/monet_stats/contingency_metrics.py 
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def scores(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    minval: float,
    maxval: Optional[float] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Tuple[
    Union[np.number, np.ndarray, xr.DataArray],
    Union[np.number, np.ndarray, xr.DataArray],
    Union[np.number, np.ndarray, xr.DataArray],
    Union[np.number, np.ndarray, xr.DataArray],
]:
    """
    Calculate the 2x2 contingency table (Aero Protocol).

    Typical Use Cases
    -----------------
    - Obtaining the raw counts of hits, misses, false alarms, and correct negatives
      to compute custom categorical scores.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observation values ("truth").
    mod : numpy.ndarray or xarray.DataArray
        Model values ("prediction").
    minval : float
        Minimum threshold for event detection.
    maxval : float, optional
        Maximum threshold for event detection.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the scores.

    Returns
    -------
    Tuple[Union[np.number, np.ndarray, xr.DataArray], ...]
        A tuple of (hits, misses, false alarms, correct negatives).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.5, 1.8, 3.2, 3.8])
    >>> a, b, c, d = scores(obs, mod, minval=2.5)
    >>> print(f"Hits: {a}")
    Hits: 2
    """
    res = _contingency_table(obs, mod, minval, maxval, axis=axis)
    if isinstance(res[0], xr.DataArray):
        return (
            _update_history(res[0], "Hits (a)"),
            _update_history(res[1], "Misses (b)"),
            _update_history(res[2], "False Alarms (c)"),
            _update_history(res[3], "Correct Negatives (d)"),
        )
    return res

Correlation Metrics

Correlation and Agreement Metrics for Model Evaluation

AC(obs, mod, axis=None)

Anomaly Correlation (AC).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Anomaly correlation coefficient (unitless, -1 to 1).

Examples

import numpy as np from monet_stats.correlation_metrics import AC obs = np.array([1, 2, 3, 4]) mod = np.array([1.1, 2.1, 2.9, 4.1]) AC(obs, mod) 0.9922778767136677

Source code in src/monet_stats/correlation_metrics.py 
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def AC(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Anomaly Correlation (AC).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Anomaly correlation coefficient (unitless, -1 to 1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import AC
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.1, 2.1, 2.9, 4.1])
    >>> AC(obs, mod)
    0.9922778767136677
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        obs_bar = obs.mean(dim=dim)
        mod_bar = mod.mean(dim=dim)
        obs_anom = obs - obs_bar
        mod_anom = mod - mod_bar
        p1 = (mod_anom * obs_anom).sum(dim=dim)
        p2 = ((mod_anom**2).sum(dim=dim) * (obs_anom**2).sum(dim=dim)) ** 0.5
        result = p1 / p2
        return _update_history(result, "AC")
    else:
        obs_bar = np.ma.mean(obs, axis=axis)
        mod_bar = np.ma.mean(mod, axis=axis)
        if axis is not None:
            # Need to keep dims for subtraction if axis is not None
            obs_bar_kd = np.ma.mean(obs, axis=axis, keepdims=True)
            mod_bar_kd = np.ma.mean(mod, axis=axis, keepdims=True)
        else:
            obs_bar_kd = obs_bar
            mod_bar_kd = mod_bar
        obs_anom = np.subtract(obs, obs_bar_kd)
        mod_anom = np.subtract(mod, mod_bar_kd)
        p1 = np.ma.sum(np.ma.multiply(mod_anom, obs_anom), axis=axis)
        p2 = np.ma.sqrt(np.ma.multiply(np.ma.sum(obs_anom**2, axis=axis), np.ma.sum(mod_anom**2, axis=axis)))
        result = p1 / p2
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

CCC(obs, mod, axis=None)

Concordance Correlation Coefficient (CCC).

Typical Use Cases

  • Quantifying the agreement between model and observations, accounting for precision and accuracy.
  • Used in model evaluation to assess how well model predictions agree with observations.
  • Measures how far the values deviate from the line of perfect concordance (slope=1, intercept=0).

Typical Values and Range

  • Range: -1 to 1
  • 1: Perfect agreement between model and observations
  • 0: No agreement
  • -1: Perfect negative agreement

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis along which to compute the coefficient.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Concordance correlation coefficient (unitless, -1 to 1).

Examples

import numpy as np from monet_stats.correlation_metrics import CCC obs = np.array([1, 2, 3, 4]) mod = np.array([1.1, 2.1, 2.9, 4.1]) CCC(obs, mod) 0.9984779299847792

Source code in src/monet_stats/correlation_metrics.py 
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def CCC(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Concordance Correlation Coefficient (CCC).

    Typical Use Cases
    -----------------
    - Quantifying the agreement between model and observations, accounting for
      precision and accuracy.
    - Used in model evaluation to assess how well model predictions agree with
      observations.
    - Measures how far the values deviate from the line of perfect concordance
      (slope=1, intercept=0).

    Typical Values and Range
    ------------------------
    - Range: -1 to 1
    - 1: Perfect agreement between model and observations
    - 0: No agreement
    - -1: Perfect negative agreement

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the coefficient.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Concordance correlation coefficient (unitless, -1 to 1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import CCC
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.1, 2.1, 2.9, 4.1])
    >>> CCC(obs, mod)
    0.9984779299847792
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        # Calculate means
        obs_mean = obs.mean(dim=dim)
        mod_mean = mod.mean(dim=dim)

        # Calculate variances and covariance
        obs_var = obs.var(dim=dim)
        mod_var = mod.var(dim=dim)
        covar = ((obs - obs_mean) * (mod - mod_mean)).mean(dim=dim)

        # Calculate CCC
        numerator = 2 * covar
        denominator = obs_var + mod_var + (obs_mean - mod_mean) ** 2
        result = numerator / denominator
        return _update_history(result, "CCC")
    else:
        # Calculate means
        obs_mean = np.nanmean(obs, axis=axis)
        mod_mean = np.nanmean(mod, axis=axis)

        # Calculate variances and covariance
        obs_var = np.nanvar(obs, axis=axis)
        mod_var = np.nanvar(mod, axis=axis)
        if axis is not None:
            obs_mean_kd = np.nanmean(obs, axis=axis, keepdims=True)
            mod_mean_kd = np.nanmean(mod, axis=axis, keepdims=True)
        else:
            obs_mean_kd = obs_mean
            mod_mean_kd = mod_mean
        covar = np.nanmean((obs - obs_mean_kd) * (mod - mod_mean_kd), axis=axis)

        # Calculate CCC
        numerator = 2 * covar
        denominator = obs_var + mod_var + (obs_mean - mod_mean) ** 2
        result = numerator / denominator
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

E1(obs, mod, axis=None)

Modified Coefficient of Efficiency (E1).

Typical Use Cases

  • Quantifying the efficiency of model predictions relative to observed mean, robust to outliers.
  • Used in hydrology, meteorology, and model skill assessment.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Modified coefficient of efficiency (unitless, -inf to 1).

Examples

import numpy as np from monet_stats.correlation_metrics import E1 obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) E1(obs, mod) 0.0

Source code in src/monet_stats/correlation_metrics.py 
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def E1(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Modified Coefficient of Efficiency (E1).

    Typical Use Cases
    -----------------
    - Quantifying the efficiency of model predictions relative to observed mean,
      robust to outliers.
    - Used in hydrology, meteorology, and model skill assessment.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Modified coefficient of efficiency (unitless, -inf to 1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import E1
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> E1(obs, mod)
    0.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        num = abs(obs - mod).sum(dim=dim)
        denom = abs(obs - obs.mean(dim=dim)).sum(dim=dim)
        result = 1.0 - (num / denom)
        result = xr.where((num == 0) & (denom == 0), 1.0, result)
        result = xr.where((num != 0) & (denom == 0), -np.inf, result)

        return _update_history(result, "E1")
    else:
        num = np.ma.abs(np.subtract(obs, mod)).sum(axis=axis)
        mean_obs = np.ma.mean(obs, axis=axis, keepdims=True)
        denom = np.ma.abs(np.subtract(obs, mean_obs)).sum(axis=axis)
        with np.errstate(divide="ignore", invalid="ignore"):
            result = 1.0 - (num / denom)
            result = np.where((num == 0) & (denom == 0), 1.0, result)
            result = np.where((num != 0) & (denom == 0), -np.inf, result)
        return result.item() if np.ndim(result) == 0 else result

E1_prime(obs, mod, axis=None)

Modified Coefficient of Efficiency (E1') - Alternative formulation.

Typical Use Cases

  • Quantifying the efficiency of model predictions relative to observed mean, robust to outliers.
  • Used in hydrology, meteorology, and model skill assessment as an alternative to E1.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Modified coefficient of efficiency (unitless, -inf to 1).

Examples

import numpy as np from monet_stats.correlation_metrics import E1_prime obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) E1_prime(obs, mod) 0.0

Source code in src/monet_stats/correlation_metrics.py 
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def E1_prime(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Modified Coefficient of Efficiency (E1') - Alternative formulation.

    Typical Use Cases
    -----------------
    - Quantifying the efficiency of model predictions relative to observed mean,
      robust to outliers.
    - Used in hydrology, meteorology, and model skill assessment as an
      alternative to E1.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Modified coefficient of efficiency (unitless, -inf to 1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import E1_prime
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> E1_prime(obs, mod)
    0.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        obs_mean = obs.mean(dim=dim)
        num = abs(obs - mod).sum(dim=dim)
        denom = abs(obs - obs_mean).sum(dim=dim)
        # Handle case where denominator is 0
        result = 1.0 - (num / denom)
        result = xr.where((num == 0) & (denom == 0), 1.0, result)
        result = xr.where((num != 0) & (denom == 0), -np.inf, result)

        return _update_history(result, "E1_prime")
    else:
        if axis is None:
            obs_c, mod_c = matchedcompressed(obs, mod)
            obs_mean_kd = np.nanmean(obs_c)
        else:
            obs_c, mod_c = obs, mod
            obs_mean_kd = np.nanmean(obs_c, axis=axis, keepdims=True)

        num = np.nansum(np.abs(obs_c - mod_c), axis=axis)
        denom = np.nansum(np.abs(obs_c - obs_mean_kd), axis=axis)
        with np.errstate(divide="ignore", invalid="ignore"):
            result = 1.0 - (num / denom)
            if np.ndim(result) == 0:
                if num == 0 and denom == 0:
                    result = np.array(1.0)
                elif denom == 0:
                    result = np.array(-np.inf)
            else:
                result = np.where((num == 0) & (denom == 0), 1.0, result)
                result = np.where((num != 0) & (denom == 0), -np.inf, result)
        return result.item() if np.ndim(result) == 0 else result

IOA(obs, mod, axis=None)

Index of Agreement (IOA).

Typical Use Cases

  • Quantifying the agreement between model and observations, normalized by total deviation.
  • Used in model evaluation for skill assessment.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute IOA.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Index of agreement (unitless, 0-1).

Examples

import numpy as np from monet_stats.error_metrics import IOA obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) IOA(obs, mod) 0.8

Source code in src/monet_stats/error_metrics.py 
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def IOA(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Index of Agreement (IOA).

    Typical Use Cases
    -----------------
    - Quantifying the agreement between model and observations, normalized by
      total deviation.
    - Used in model evaluation for skill assessment.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute IOA.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Index of agreement (unitless, 0-1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import IOA
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> IOA(obs, mod)
    0.8
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        obs_mean = obs.mean(dim=dim)
        num = ((obs - mod) ** 2).sum(dim=dim)
        denom = ((abs(mod - obs_mean) + abs(obs - obs_mean)) ** 2).sum(dim=dim)
        result = 1.0 - (num / denom)
        return _update_history(result, "IOA")
    else:
        obs_m = np.ma.masked_invalid(obs)
        mod_m = np.ma.masked_invalid(mod)
        obs_mean = np.ma.mean(obs_m, axis=axis, keepdims=True)
        num = np.ma.sum((obs_m - mod_m) ** 2, axis=axis)
        denom = np.ma.sum((np.ma.abs(mod_m - obs_mean) + np.ma.abs(obs_m - obs_mean)) ** 2, axis=axis)
        with np.errstate(divide="ignore", invalid="ignore"):
            result = 1.0 - (num / denom)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

IOA_prime(obs, mod, axis=None)

Index of Agreement (IOA') - Alternative formulation.

Typical Use Cases

  • Quantifying the agreement between model and observations, normalized by total deviation.
  • Used in model evaluation for skill assessment as an alternative to IOA.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Index of agreement (unitless, 0-1).

Examples

import numpy as np from monet_stats.correlation_metrics import IOA_prime obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) IOA_prime(obs, mod) 0.8

Source code in src/monet_stats/correlation_metrics.py 
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def IOA_prime(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Index of Agreement (IOA') - Alternative formulation.

    Typical Use Cases
    -----------------
    - Quantifying the agreement between model and observations, normalized by
      total deviation.
    - Used in model evaluation for skill assessment as an alternative to IOA.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Index of agreement (unitless, 0-1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import IOA_prime
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> IOA_prime(obs, mod)
    0.8
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        obsmean = obs.mean(dim=dim)
        num = ((obs - mod) ** 2).sum(dim=dim)
        denom = ((abs(mod - obsmean) + abs(obs - obsmean)) ** 2).sum(dim=dim)
        # Handle case where denominator is 0
        result = 1.0 - (num / denom)
        result = xr.where((num == 0) & (denom == 0), 1.0, result)
        result = xr.where((num != 0) & (denom == 0), -np.inf, result)

        return _update_history(result, "IOA_prime")
    else:
        if axis is None:
            obs_c, mod_c = matchedcompressed(obs, mod)
            obsmean_kd = np.nanmean(obs_c)
        else:
            obs_c, mod_c = obs, mod
            obsmean_kd = np.nanmean(obs_c, axis=axis, keepdims=True)

        num = np.nansum((obs_c - mod_c) ** 2, axis=axis)
        denom = np.nansum((np.abs(mod_c - obsmean_kd) + np.abs(obs_c - obsmean_kd)) ** 2, axis=axis)
        with np.errstate(divide="ignore", invalid="ignore"):
            result = 1.0 - (num / denom)
            if np.ndim(result) == 0:
                if num == 0 and denom == 0:
                    result = np.array(1.0)
                elif denom == 0:
                    result = np.array(-np.inf)
            else:
                result = np.where((num == 0) & (denom == 0), 1.0, result)
                result = np.where((num != 0) & (denom == 0), -np.inf, result)
        return result.item() if np.ndim(result) == 0 else result

KGE(obs, mod, axis=None)

Kling-Gupta Efficiency (KGE).

Typical Use Cases

  • Quantifying the overall agreement between model and observations, combining correlation, bias, and variability.
  • Used in hydrology, meteorology, and environmental model evaluation.

Typical Values and Range

  • Range: -∞ to 1
  • 1: Perfect agreement between model and observations
  • 0: Moderate skill
  • Negative values: Poor skill

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis along which to compute KGE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Kling-Gupta efficiency (unitless, -∞ to 1).

Examples

import numpy as np from monet_stats.correlation_metrics import KGE obs = np.array([1, 2, 3]) mod = np.array([1.1, 1.9, 3.2]) KGE(obs, mod) 0.8988771192996924

Source code in src/monet_stats/correlation_metrics.py 
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def KGE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Kling-Gupta Efficiency (KGE).

    Typical Use Cases
    -----------------
    - Quantifying the overall agreement between model and observations,
      combining correlation, bias, and variability.
    - Used in hydrology, meteorology, and environmental model evaluation.

    Typical Values and Range
    ------------------------
    - Range: -∞ to 1
    - 1: Perfect agreement between model and observations
    - 0: Moderate skill
    - Negative values: Poor skill

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute KGE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Kling-Gupta efficiency (unitless, -∞ to 1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import KGE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([1.1, 1.9, 3.2])
    >>> KGE(obs, mod)
    0.8988771192996924
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        r = xr.corr(obs, mod, dim=dim)
        alpha = mod.std(dim=dim) / obs.std(dim=dim)
        beta = mod.mean(dim=dim) / obs.mean(dim=dim)
        result = 1.0 - ((r - 1.0) ** 2 + (alpha - 1.0) ** 2 + (beta - 1.0) ** 2) ** 0.5
        return _update_history(result, "KGE")
    else:
        if axis is None:
            from scipy.stats import pearsonr

            obsc, modc = matchedcompressed(obs, mod)
            if len(obsc) < 2:
                r = 0.0
            else:
                r, _ = pearsonr(obsc, modc)
        else:
            # Manual vectorized correlation for numpy with axis
            obs_mean = np.nanmean(obs, axis=axis, keepdims=True)
            mod_mean = np.nanmean(mod, axis=axis, keepdims=True)
            obs_std = obs - obs_mean
            mod_std = mod - mod_mean
            num = np.nansum(obs_std * mod_std, axis=axis)
            den = np.sqrt(np.nansum(obs_std**2, axis=axis) * np.nansum(mod_std**2, axis=axis))
            with np.errstate(divide="ignore", invalid="ignore"):
                r = num / den
                r = np.where(np.isnan(r), 0.0, r)

        alpha = np.ma.std(mod, axis=axis) / np.ma.std(obs, axis=axis)
        beta = np.ma.mean(mod, axis=axis) / np.ma.mean(obs, axis=axis)
        result = 1.0 - ((r - 1.0) ** 2 + (alpha - 1.0) ** 2 + (beta - 1.0) ** 2) ** 0.5
        return result.item() if np.ndim(result) == 0 else result

R2(obs, mod, axis=None)

Coefficient of Determination (R^2, unitless).

Typical Use Cases

  • Quantifying how well model predictions explain the variance in observations.
  • Used in regression analysis, model skill assessment, and forecast verification.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Coefficient of determination (R^2).

Examples

import numpy as np from monet_stats.correlation_metrics import R2 obs = np.array([1, 2, 3, 4]) mod = np.array([1.1, 1.9, 3.2, 3.8]) R2(obs, mod) 0.9846153846153847

Source code in src/monet_stats/correlation_metrics.py 
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def R2(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Coefficient of Determination (R^2, unitless).

    Typical Use Cases
    -----------------
    - Quantifying how well model predictions explain the variance in observations.
    - Used in regression analysis, model skill assessment, and forecast
      verification.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Coefficient of determination (R^2).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import R2
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.1, 1.9, 3.2, 3.8])
    >>> R2(obs, mod)
    0.9846153846153847
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        if axis is None:
            # Default to all dimensions if None
            dim = obs.dims
        elif isinstance(axis, int):
            dim = obs.dims[axis]
        else:
            dim = axis

        # Use native xarray correlation for speed and laziness (Aero Protocol)
        r = xr.corr(obs, mod, dim=dim)
        result = r**2
        return _update_history(result, "R2")
    else:
        from scipy.stats import pearsonr

        if axis is None:
            obsc, modc = matchedcompressed(obs, mod)
            if len(obsc) < 2 or np.var(obsc) == 0 or np.var(modc) == 0:
                return 0.0
            r_val, _ = pearsonr(obsc, modc)
            if np.isnan(r_val):
                return 0.0
            return r_val**2
        else:
            # Manual vectorized R2
            obs_mean = np.nanmean(obs, axis=axis, keepdims=True)
            mod_mean = np.nanmean(mod, axis=axis, keepdims=True)
            obs_std = obs - obs_mean
            mod_std = mod - mod_mean
            num = np.nansum(obs_std * mod_std, axis=axis)
            den = np.sqrt(np.nansum(obs_std**2, axis=axis) * np.nansum(mod_std**2, axis=axis))
            with np.errstate(divide="ignore", invalid="ignore"):
                r = num / den
                result = np.where(np.isnan(r), 0.0, r**2)
                return result.item() if np.ndim(result) == 0 else result

RMSE(obs, mod, axis=None)

Root Mean Square Error (RMSE).

Typical Use Cases

  • Quantifying the average magnitude of errors between model and observations, accounting for large errors more heavily than MAE.
  • Used in model evaluation, forecast verification, and regression analysis.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute RMSE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Root mean square error.

Examples

import numpy as np from monet_stats.error_metrics import RMSE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) RMSE(obs, mod) 0.816496580927726

Source code in src/monet_stats/error_metrics.py 
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def RMSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Root Mean Square Error (RMSE).

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of errors between model and observations,
      accounting for large errors more heavily than MAE.
    - Used in model evaluation, forecast verification, and regression analysis.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute RMSE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Root mean square error.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import RMSE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> RMSE(obs, mod)
    0.816496580927726
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = ((mod - obs) ** 2).mean(dim=dim, keep_attrs=True) ** 0.5
        return _update_history(result, "RMSE")
    else:
        result = np.ma.sqrt(np.ma.mean((np.subtract(mod, obs)) ** 2, axis=axis))
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

RMSEs(obs, mod, axis=None)

Root Mean Squared Error between observations and regression fit.

(RMSEs, model unit)

Typical Use Cases

  • Quantifying the error between observations and a regression fit to the model predictions.
  • Used in model evaluation to assess how well a regression fit to the model matches the observations.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray, optional Root mean squared error value(s).

Examples

import numpy as np from monet_stats.correlation_metrics import RMSEs obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) RMSEs(obs, mod) 0.7071067811865476

Source code in src/monet_stats/correlation_metrics.py 
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def RMSEs(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray, None]:
    """
    Root Mean Squared Error between observations and regression fit.

    (RMSEs, model unit)

    Typical Use Cases
    -----------------
    - Quantifying the error between observations and a regression fit to the
      model predictions.
    - Used in model evaluation to assess how well a regression fit to the model
      matches the observations.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray, optional
        Root mean squared error value(s).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import RMSEs
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> RMSEs(obs, mod)
    0.7071067811865476
    """
    res = _vectorized_regression_stats(obs, mod, axis=axis, mode="RMSEs")
    return _update_history(res, "RMSEs")

RMSEu(obs, mod, axis=None)

Root Mean Squared Error between regression fit and model predictions.

(RMSEu, model unit)

Typical Use Cases

  • Quantifying the error between a linear regression fit to observations and the model predictions.
  • Used in model evaluation to assess how well a regression fit to obs matches the model output.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray, optional Root mean squared error value(s).

Examples

import numpy as np from monet_stats.correlation_metrics import RMSEu obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) RMSEu(obs, mod) 0.7071067811865476

Source code in src/monet_stats/correlation_metrics.py 
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def RMSEu(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray, None]:
    """
    Root Mean Squared Error between regression fit and model predictions.

    (RMSEu, model unit)

    Typical Use Cases
    -----------------
    - Quantifying the error between a linear regression fit to observations and
      the model predictions.
    - Used in model evaluation to assess how well a regression fit to obs
      matches the model output.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray, optional
        Root mean squared error value(s).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import RMSEu
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> RMSEu(obs, mod)
    0.7071067811865476
    """
    res = _vectorized_regression_stats(obs, mod, axis=axis, mode="RMSEu")
    return _update_history(res, "RMSEu")

WDAC(obs, mod, axis=None)

Wind Direction Anomaly Correlation (WDAC).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed wind direction values (degrees). mod : numpy.ndarray or xarray.DataArray Modeled wind direction values (degrees). axis : int, str, or iterable of such, optional Axis along which to compute the metric.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray WDAC value(s).

Examples

import numpy as np from monet_stats.correlation_metrics import WDAC obs = np.array([350, 10, 20]) mod = np.array([345, 15, 25]) WDAC(obs, mod) 0.9992386127814763

Source code in src/monet_stats/correlation_metrics.py 
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def WDAC(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Wind Direction Anomaly Correlation (WDAC).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed wind direction values (degrees).
    mod : numpy.ndarray or xarray.DataArray
        Modeled wind direction values (degrees).
    axis : int, str, or iterable of such, optional
        Axis along which to compute the metric.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        WDAC value(s).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import WDAC
    >>> obs = np.array([350, 10, 20])
    >>> mod = np.array([345, 15, 25])
    >>> WDAC(obs, mod)
    0.9992386127814763
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        obs_rad = obs * np.pi / 180.0
        mod_rad = mod * np.pi / 180.0
        obs_anom = obs_rad - obs_rad.mean(dim=dim)
        mod_anom = mod_rad - mod_rad.mean(dim=dim)
        numerator = (np.sin(obs_anom) * np.sin(mod_anom)).sum(dim=dim)
        denominator = np.sqrt((np.sin(obs_anom) ** 2).sum(dim=dim) * (np.sin(mod_anom) ** 2).sum(dim=dim))
        result = numerator / denominator
        return _update_history(result, "WDAC")
    else:
        obs_rad = np.deg2rad(obs)
        mod_rad = np.deg2rad(mod)
        if axis is not None:
            obs_bar_rad = np.ma.mean(obs_rad, axis=axis, keepdims=True)
            mod_bar_rad = np.ma.mean(mod_rad, axis=axis, keepdims=True)
        else:
            obs_bar_rad = np.ma.mean(obs_rad)
            mod_bar_rad = np.ma.mean(mod_rad)

        obs_anom = obs_rad - obs_bar_rad
        mod_anom = mod_rad - mod_bar_rad
        numerator = np.ma.sum(np.sin(obs_anom) * np.sin(mod_anom), axis=axis)
        denominator = np.ma.sqrt(
            np.ma.sum(np.sin(obs_anom) ** 2, axis=axis) * np.ma.sum(np.sin(mod_anom) ** 2, axis=axis)
        )
        result = numerator / denominator
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

WDIOA(obs, mod, axis=None)

Wind Direction Index of Agreement (WDIOA).

Standard version.

Typical Use Cases

  • Quantifying the agreement between observed and modeled wind directions, accounting for circularity.
  • Used in wind energy, meteorology, and air quality studies to assess wind direction model performance.

Typical Values and Range

  • Range: 0 to 1
  • 1: Perfect agreement between observed and modeled wind directions
  • 0: No agreement (as bad as using the mean of observations)

Parameters

obs : numpy.ndarray or xarray.DataArray Observed wind direction values (degrees). mod : numpy.ndarray or xarray.DataArray Modeled wind direction values (degrees). axis : int, str, or iterable of such, optional Axis along which to compute the metric.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Wind direction index of agreement (unitless, 0-1).

Examples

import numpy as np from monet_stats.correlation_metrics import WDIOA obs = np.array([350, 10, 20]) mod = np.array([345, 15, 25]) WDIOA(obs, mod) 0.8

Source code in src/monet_stats/correlation_metrics.py 
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def WDIOA(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Wind Direction Index of Agreement (WDIOA).

    Standard version.

    Typical Use Cases
    -----------------
    - Quantifying the agreement between observed and modeled wind directions,
      accounting for circularity.
    - Used in wind energy, meteorology, and air quality studies to assess wind
      direction model performance.

    Typical Values and Range
    ------------------------
    - Range: 0 to 1
    - 1: Perfect agreement between observed and modeled wind directions
    - 0: No agreement (as bad as using the mean of observations)

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed wind direction values (degrees).
    mod : numpy.ndarray or xarray.DataArray
        Modeled wind direction values (degrees).
    axis : int, str, or iterable of such, optional
        Axis along which to compute the metric.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Wind direction index of agreement (unitless, 0-1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import WDIOA
    >>> obs = np.array([350, 10, 20])
    >>> mod = np.array([345, 15, 25])
    >>> WDIOA(obs, mod)
    0.8
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        num = abs(circlebias(obs - mod)).sum(dim=dim)
        mean_obs = obs.mean(dim=dim)
        denom = (abs(circlebias(mod - mean_obs)) + abs(circlebias(obs - mean_obs))).sum(dim=dim)

        result = 1.0 - (num / denom)
        result = xr.where(denom == 0, 1.0, result)

        return _update_history(result, "WDIOA")
    else:
        num = np.ma.sum(np.ma.abs(circlebias(np.subtract(obs, mod))), axis=axis)
        mean_obs = np.ma.mean(obs, axis=axis, keepdims=True)
        denom = np.ma.sum(
            np.ma.abs(circlebias(np.subtract(mod, mean_obs))) + np.ma.abs(circlebias(np.subtract(obs, mean_obs))),
            axis=axis,
        )
        result = np.where(denom == 0, 1.0, 1.0 - (num / denom))
        return result.item() if np.ndim(result) == 0 else result

WDIOA_m(obs, mod, axis=None)

Wind Direction Index of Agreement (WDIOA_m).

Robust to masked arrays.

Typical Use Cases

  • Quantifying the agreement between observed and modeled wind directions, accounting for circularity.
  • Used in wind energy, meteorology, and air quality studies to assess wind direction model performance.

Typical Values and Range

  • Range: 0 to 1
  • 1: Perfect agreement between observed and modeled wind directions
  • 0: No agreement (as bad as using the mean of observations)

Parameters

obs : numpy.ndarray or xarray.DataArray Observed wind direction values (degrees). mod : numpy.ndarray or xarray.DataArray Modeled wind direction values (degrees). axis : int, str, or iterable of such, optional Axis along which to compute the metric.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Wind direction index of agreement (unitless, 0-1).

Examples

import numpy as np from monet_stats.correlation_metrics import WDIOA_m obs = np.array([350, 10, 20]) mod = np.array([345, 15, 25]) WDIOA_m(obs, mod) 0.8

Source code in src/monet_stats/correlation_metrics.py 
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def WDIOA_m(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Wind Direction Index of Agreement (WDIOA_m).

    Robust to masked arrays.

    Typical Use Cases
    -----------------
    - Quantifying the agreement between observed and modeled wind directions,
      accounting for circularity.
    - Used in wind energy, meteorology, and air quality studies to assess wind
      direction model performance.

    Typical Values and Range
    ------------------------
    - Range: 0 to 1
    - 1: Perfect agreement between observed and modeled wind directions
    - 0: No agreement (as bad as using the mean of observations)

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed wind direction values (degrees).
    mod : numpy.ndarray or xarray.DataArray
        Modeled wind direction values (degrees).
    axis : int, str, or iterable of such, optional
        Axis along which to compute the metric.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Wind direction index of agreement (unitless, 0-1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import WDIOA_m
    >>> obs = np.array([350, 10, 20])
    >>> mod = np.array([345, 15, 25])
    >>> WDIOA_m(obs, mod)
    0.8
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        obsmean = obs.mean(dim=dim)
        num = (abs(circlebias_m(obs - mod))).sum(dim=dim)
        denom = (abs(circlebias_m(mod - obsmean)) + abs(circlebias_m(obs - obsmean))).sum(dim=dim)

        result = 1.0 - (num / denom)
        result = xr.where(denom == 0, 1.0, result)

        return _update_history(result, "WDIOA_m")
    else:
        obsmean = np.ma.mean(obs, axis=axis, keepdims=True)
        num = np.ma.sum(np.ma.abs(circlebias_m(np.subtract(obs, mod))), axis=axis)
        denom = np.ma.sum(
            np.ma.abs(circlebias_m(np.subtract(mod, obsmean))) + np.ma.abs(circlebias_m(np.subtract(obs, obsmean))),
            axis=axis,
        )
        result = np.where(denom == 0, 1.0, 1.0 - (num / denom))
        return result.item() if np.ndim(result) == 0 else result

WDRMSE(obs, mod, axis=None)

Wind Direction Root Mean Square Error (WDRMSE, model unit).

Standard version.

Typical Use Cases

  • Quantifying the average magnitude of wind direction errors, accounting for circularity.
  • Used in wind energy, meteorology, and air quality studies to assess wind direction model performance.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed wind direction values (degrees). mod : numpy.ndarray or xarray.DataArray Model predicted wind direction values (degrees). axis : int, str, or iterable of such, optional Axis along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Wind direction root mean square error (degrees).

Examples

import numpy as np from monet_stats.correlation_metrics import WDRMSE obs = np.array([350, 10, 20]) mod = np.array([10, 20, 30]) WDRMSE(obs, mod) 20.0

Source code in src/monet_stats/correlation_metrics.py 
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def WDRMSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Wind Direction Root Mean Square Error (WDRMSE, model unit).

    Standard version.

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of wind direction errors, accounting for
      circularity.
    - Used in wind energy, meteorology, and air quality studies to assess wind
      direction model performance.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed wind direction values (degrees).
    mod : numpy.ndarray or xarray.DataArray
        Model predicted wind direction values (degrees).
    axis : int, str, or iterable of such, optional
        Axis along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Wind direction root mean square error (degrees).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import WDRMSE
    >>> obs = np.array([350, 10, 20])
    >>> mod = np.array([10, 20, 30])
    >>> WDRMSE(obs, mod)
    20.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        result = (circlebias(mod - obs) ** 2).mean(dim=dim, keep_attrs=True) ** 0.5
        return _update_history(result, "WDRMSE")
    else:
        result = np.ma.sqrt(np.ma.mean((circlebias(np.subtract(mod, obs))) ** 2, axis=axis))
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

WDRMSE_m(obs, mod, axis=None)

Wind Direction Root Mean Square Error (WDRMSE, model unit).

Robust to masked arrays.

Typical Use Cases

  • Quantifying the average magnitude of wind direction errors, accounting for circularity, robust to masked arrays.
  • Used in wind energy, meteorology, and air quality studies to assess wind direction model performance.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed wind direction values (degrees). mod : numpy.ndarray or xarray.DataArray Model predicted wind direction values (degrees). axis : int, str, or iterable of such, optional Axis along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Wind direction root mean square error (degrees).

Examples

import numpy as np from monet_stats.correlation_metrics import WDRMSE_m obs = np.array([350, 10, 20]) mod = np.array([10, 20, 30]) WDRMSE_m(obs, mod) 20.0

Source code in src/monet_stats/correlation_metrics.py 
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def WDRMSE_m(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Wind Direction Root Mean Square Error (WDRMSE, model unit).

    Robust to masked arrays.

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of wind direction errors, accounting for
      circularity, robust to masked arrays.
    - Used in wind energy, meteorology, and air quality studies to assess wind
      direction model performance.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed wind direction values (degrees).
    mod : numpy.ndarray or xarray.DataArray
        Model predicted wind direction values (degrees).
    axis : int, str, or iterable of such, optional
        Axis along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Wind direction root mean square error (degrees).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import WDRMSE_m
    >>> obs = np.array([350, 10, 20])
    >>> mod = np.array([10, 20, 30])
    >>> WDRMSE_m(obs, mod)
    20.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        result = (circlebias_m(mod - obs) ** 2).mean(dim=dim, keep_attrs=True) ** 0.5
        return _update_history(result, "WDRMSE_m")
    else:
        result = np.ma.sqrt(np.ma.mean((circlebias_m(np.subtract(mod, obs))) ** 2, axis=axis))
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

d1(obs, mod, axis=None)

Modified Index of Agreement (d1).

Typical Use Cases

  • Quantifying the agreement between model and observations, less sensitive to outliers than IOA.
  • Used in model evaluation for robust skill assessment.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Modified index of agreement (unitless, 0-1).

Examples

import numpy as np from monet_stats.correlation_metrics import d1 obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) d1(obs, mod) 0.5

Source code in src/monet_stats/correlation_metrics.py 
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def d1(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Modified Index of Agreement (d1).

    Typical Use Cases
    -----------------
    - Quantifying the agreement between model and observations, less sensitive
      to outliers than IOA.
    - Used in model evaluation for robust skill assessment.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Modified index of agreement (unitless, 0-1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import d1
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> d1(obs, mod)
    0.5
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        num = abs(obs - mod).sum(dim=dim)
        mean_obs = obs.mean(dim=dim)
        denom = (abs(mod - mean_obs) + abs(obs - mean_obs)).sum(dim=dim)
        result = 1.0 - (num / denom)
        result = xr.where((num == 0) & (denom == 0), 1.0, result)
        result = xr.where((num != 0) & (denom == 0), -np.inf, result)

        return _update_history(result, "d1")
    else:
        num = np.ma.abs(np.subtract(obs, mod)).sum(axis=axis)
        mean_obs = np.ma.mean(obs, axis=axis, keepdims=True)
        denom = (np.ma.abs(np.subtract(mod, mean_obs)) + np.ma.abs(np.subtract(obs, mean_obs))).sum(axis=axis)
        with np.errstate(divide="ignore", invalid="ignore"):
            result = 1.0 - (num / denom)
            result = np.where((num == 0) & (denom == 0), 1.0, result)
            result = np.where((num != 0) & (denom == 0), -np.inf, result)
        return result.item() if np.ndim(result) == 0 else result

kendalltau(obs, mod, axis=None)

Kendall tau correlation coefficient (Aero Protocol: Standardized).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension name along which to compute the coefficient.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Kendall rank correlation coefficient.

Examples

import numpy as np from monet_stats.correlation_metrics import kendalltau obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) kendalltau(obs, mod) 1.0

Source code in src/monet_stats/correlation_metrics.py 
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def kendalltau(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Kendall tau correlation coefficient (Aero Protocol: Standardized).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension name along which to compute the coefficient.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Kendall rank correlation coefficient.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import kendalltau
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> kendalltau(obs, mod)
    1.0
    """
    from scipy.stats import kendalltau as _kendalltau

    # Standardize to DataArray to leverage Xarray's apply_ufunc vectorization
    is_numpy = not isinstance(obs, xr.DataArray)
    if is_numpy:
        obs = xr.DataArray(obs)
        mod = xr.DataArray(mod)
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, Iterable) and not isinstance(axis, str):
                dim = [obs.dims[i] for i in axis]
            else:
                dim = axis
        else:
            dim = obs.dims
    else:
        if isinstance(mod, xr.DataArray):
            obs, mod = xr.align(obs, mod, join="inner")
        if axis is None:
            dim = obs.dims
        elif isinstance(axis, int):
            dim = obs.dims[axis]
        else:
            dim = axis

    if axis is None:
        obsc, modc = matchedcompressed(obs, mod)
        if len(obsc) < 2:
            return np.nan
        return _kendalltau(obsc, modc)[0]

    def _kendalltau_onlytau(a, b):
        a_flat = a.ravel()
        b_flat = b.ravel()
        mask = ~np.isnan(a_flat) & ~np.isnan(b_flat)
        if np.sum(mask) < 2:
            return np.nan
        return _kendalltau(a_flat[mask], b_flat[mask])[0]

    # Use apply_ufunc to eliminate manual loops and support Dask
    icd = [dim] if isinstance(dim, (str, int)) else list(dim)
    result = xr.apply_ufunc(
        _kendalltau_onlytau,
        obs,
        mod,
        input_core_dims=[icd] * 2,
        output_core_dims=[[]],
        vectorize=True,
        dask="parallelized",
        dask_gufunc_kwargs={"allow_rechunk": True},
        output_dtypes=[float],
    )

    if is_numpy:
        return result.values
    return _update_history(result, "kendalltau")

pearsonr(obs, mod, axis=None)

Pearson correlation coefficient.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension name along which to compute the coefficient.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Pearson correlation coefficient.

Examples

import numpy as np from monet_stats.correlation_metrics import pearsonr obs = np.array([1, 2, 3]) mod = np.array([2, 4, 6]) pearsonr(obs, mod) 1.0

Source code in src/monet_stats/correlation_metrics.py 
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def pearsonr(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Pearson correlation coefficient.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension name along which to compute the coefficient.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Pearson correlation coefficient.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import pearsonr
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 4, 6])
    >>> pearsonr(obs, mod)
    1.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        if axis is None:
            dim = obs.dims
        elif isinstance(axis, int):
            dim = obs.dims[axis]
        else:
            dim = axis

        # Use native xarray correlation for speed and laziness (Aero Protocol)
        result = xr.corr(obs, mod, dim=dim)
        return _update_history(result, "pearsonr")
    else:
        from scipy.stats import pearsonr as _pearsonr

        if axis is None:
            obsc, modc = matchedcompressed(obs, mod)
            if len(obsc) < 2 or np.var(obsc) == 0 or np.var(modc) == 0:
                return 0.0
            r_val, _ = _pearsonr(obsc, modc)
            return r_val if not np.isnan(r_val) else 0.0
        else:
            # For numpy with axis, use manual vectorized correlation with pairwise deletion
            obs = np.asanyarray(obs)
            mod = np.asanyarray(mod)
            mask = np.isnan(obs) | np.isnan(mod)
            obs = np.where(mask, np.nan, obs)
            mod = np.where(mask, np.nan, mod)

            obs_mean = np.nanmean(obs, axis=axis, keepdims=True)
            mod_mean = np.nanmean(mod, axis=axis, keepdims=True)
            obs_std = obs - obs_mean
            mod_std = mod - mod_mean
            num = np.nansum(obs_std * mod_std, axis=axis)
            den = np.sqrt(np.nansum(obs_std**2, axis=axis) * np.nansum(mod_std**2, axis=axis))
            with np.errstate(divide="ignore", invalid="ignore"):
                result = num / den
                return result.item() if np.ndim(result) == 0 else result

spearmanr(obs, mod, axis=None)

Spearman rank correlation coefficient (Aero Protocol: Vectorized).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis along which to compute the coefficient.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Spearman rank correlation coefficient.

Examples

import numpy as np from monet_stats.correlation_metrics import spearmanr obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) spearmanr(obs, mod) 0.8660254037844387

Source code in src/monet_stats/correlation_metrics.py 
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def spearmanr(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Spearman rank correlation coefficient (Aero Protocol: Vectorized).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the coefficient.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Spearman rank correlation coefficient.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import spearmanr
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> spearmanr(obs, mod)
    0.8660254037844387
    """
    # Handle Xarray/NumPy alignment and dimension resolution
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        if axis is None:
            dim = obs.dims
        elif isinstance(axis, int):
            dim = obs.dims[axis]
        else:
            dim = axis
    else:
        dim = axis

    if axis is None:
        obsc, modc = matchedcompressed(obs, mod)
        if len(obsc) < 2:
            return np.nan
        from scipy.stats import spearmanr as _spearmanr

        return _spearmanr(obsc, modc)[0]

    # Spearman is Pearson on ranks. Use rankdata along the axis.
    from scipy.stats import rankdata

    # Apply pairwise masking to ensure ranks are computed on the same set of points
    mask = np.isnan(obs) | np.isnan(mod)
    obs = xr.where(mask, np.nan, obs) if isinstance(obs, xr.DataArray) else np.where(mask, np.nan, obs)
    mod = xr.where(mask, np.nan, mod) if isinstance(mod, xr.DataArray) else np.where(mask, np.nan, mod)

    def _rank_wrapper(data, axis):
        # Handle all-NaN slices to avoid Scipy warnings or errors
        if np.all(np.isnan(data)):
            return np.full(data.shape, np.nan)
        return rankdata(data, axis=axis, nan_policy="omit")

    # Use apply_ufunc for rankdata to support both NumPy and Xarray/Dask
    if isinstance(obs, xr.DataArray):
        icd = [dim] if isinstance(dim, (str, int)) else list(dim)
        obs_ranked = xr.apply_ufunc(
            _rank_wrapper,
            obs,
            input_core_dims=[icd],
            output_core_dims=[icd],
            kwargs={"axis": -1},
            dask="parallelized",
            dask_gufunc_kwargs={"allow_rechunk": True},
            output_dtypes=[float],
            keep_attrs=True,
        )
        mod_ranked = xr.apply_ufunc(
            _rank_wrapper,
            mod,
            input_core_dims=[icd],
            output_core_dims=[icd],
            kwargs={"axis": -1},
            dask="parallelized",
            dask_gufunc_kwargs={"allow_rechunk": True},
            output_dtypes=[float],
            keep_attrs=True,
        )
        return pearsonr(obs_ranked, mod_ranked, axis=dim)
    else:
        obs_ranked = _rank_wrapper(obs, axis=axis)
        mod_ranked = _rank_wrapper(mod, axis=axis)
        return pearsonr(obs_ranked, mod_ranked, axis=axis)

taylor_skill(obs, mod, axis=None)

Taylor Skill Score (TSS).

Typical Use Cases

  • Summarizing model performance in a single skill score for use in Taylor diagrams.
  • Used in climate, weather, and environmental model evaluation.

Typical Values and Range

  • Range: 0 to 1
  • 1: Perfect agreement between model and observations
  • 0: No skill

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis along which to compute the skill score.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Taylor skill score (unitless, 0-1).

Examples

import numpy as np from monet_stats.correlation_metrics import taylor_skill obs = np.array([1, 2, 3]) mod = np.array([1.1, 1.9, 3.2]) taylor_skill(obs, mod) 0.9995574044955781

Source code in src/monet_stats/correlation_metrics.py 
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def taylor_skill(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Taylor Skill Score (TSS).

    Typical Use Cases
    -----------------
    - Summarizing model performance in a single skill score for use in Taylor
      diagrams.
    - Used in climate, weather, and environmental model evaluation.

    Typical Values and Range
    ------------------------
    - Range: 0 to 1
    - 1: Perfect agreement between model and observations
    - 0: No skill

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute the skill score.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Taylor skill score (unitless, 0-1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import taylor_skill
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([1.1, 1.9, 3.2])
    >>> taylor_skill(obs, mod)
    0.9995574044955781
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        std_obs = obs.std(dim=dim)
        std_mod = mod.std(dim=dim)
        corr = xr.corr(obs, mod, dim=dim)

        # Calculate Taylor Skill Score using the common formula
        # S = 4 * (1 + R) / ( (sigma_p/sigma_o + sigma_o/sigma_p)^2 * (1 + R_max) )
        # Assuming R_max = 1.0
        norm_std = std_mod / std_obs
        result = (4.0 * (corr + 1.0)) / ((norm_std + 1.0 / norm_std) ** 2 * 2.0)
        return _update_history(result, "taylor_skill")
    else:
        std_obs = np.ma.std(obs, axis=axis)
        std_mod = np.ma.std(mod, axis=axis)
        from scipy.stats import pearsonr

        if axis is None:
            if np.ma.is_masked(obs):
                corr = pearsonr(obs.compressed(), mod.compressed())[0]
            else:
                corr = pearsonr(obs, mod)[0]
        else:
            # Vectorized correlation over axis for numpy
            obs_mean = np.nanmean(obs, axis=axis, keepdims=True)
            mod_mean = np.nanmean(mod, axis=axis, keepdims=True)
            obs_anom = obs - obs_mean
            mod_anom = mod - mod_mean
            num_corr = np.nansum(obs_anom * mod_anom, axis=axis)
            den_corr = np.sqrt(np.nansum(obs_anom**2, axis=axis) * np.nansum(mod_anom**2, axis=axis))
            with np.errstate(divide="ignore", invalid="ignore"):
                corr = num_corr / den_corr

        norm_std = std_mod / std_obs
        with np.errstate(divide="ignore", invalid="ignore"):
            result = (4.0 * (corr + 1.0)) / ((norm_std + 1.0 / norm_std) ** 2 * 2.0)
            result = np.where(np.isnan(result) | np.isinf(result), 1.0, result)
        return result.item() if np.ndim(result) == 0 else result

Error Metrics

Error Metrics for Model Evaluation

COE(obs, mod, axis=None)

Center of Mass Error (COE).

The COE measures the displacement between the centroids (centers of mass) of two fields. For spatial data, this represents the shift in the center of a feature (e.g., a storm or a pollutant plume).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values (typically 2D spatial field). mod : numpy.ndarray or xarray.DataArray Model or predicted values (typically 2D spatial field). axis : int, str, or iterable of such, optional Axis or dimension(s) over which to compute the centroid. If None, computes over all axes.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Center of mass error (Euclidean distance between centroids).

Examples

import numpy as np from monet_stats.error_metrics import COE obs = np.zeros((5, 5)) obs[2, 2] = 1.0 # Peak at center (2, 2) mod = np.zeros((5, 5)) mod[3, 3] = 1.0 # Peak shifted to (3, 3)

Displacement is sqrt(1^2 + 1^2) = sqrt(2) approx 1.414

np.allclose(COE(obs, mod), np.sqrt(2)) True

Source code in src/monet_stats/error_metrics.py 
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def COE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Center of Mass Error (COE).

    The COE measures the displacement between the centroids (centers of mass)
    of two fields. For spatial data, this represents the shift in the center
    of a feature (e.g., a storm or a pollutant plume).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values (typically 2D spatial field).
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values (typically 2D spatial field).
    axis : int, str, or iterable of such, optional
        Axis or dimension(s) over which to compute the centroid.
        If None, computes over all axes.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Center of mass error (Euclidean distance between centroids).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import COE
    >>> obs = np.zeros((5, 5))
    >>> obs[2, 2] = 1.0  # Peak at center (2, 2)
    >>> mod = np.zeros((5, 5))
    >>> mod[3, 3] = 1.0  # Peak shifted to (3, 3)
    >>> # Displacement is sqrt(1^2 + 1^2) = sqrt(2) approx 1.414
    >>> np.allclose(COE(obs, mod), np.sqrt(2))
    True
    """

    def _get_centroid(da: xr.DataArray, dims: Iterable[str]) -> List[xr.DataArray]:
        """Helper to calculate centroid of a DataArray."""
        total = da.sum(dim=dims)
        # Handle zero sum to avoid division by zero
        total_safe = xr.where(total == 0, 1e-10, total)
        coords_list = []
        for d in dims:
            # Check if coord exists and is numeric
            if d in da.coords and np.issubdtype(da.coords[d].dtype, np.number):
                coord = da.coords[d]
            else:
                # Fallback to dimension indices
                coord = xr.DataArray(np.arange(da.sizes[d]), dims=d, name=d)
            # Weighted mean of coordinate
            c = (da * coord).sum(dim=dims) / total_safe
            coords_list.append(c)
        return coords_list

    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dims = list(obs.dims)
        elif isinstance(dim, str):
            dims = [dim]
        else:
            dims = list(dim)

        c_obs = _get_centroid(obs, dims)
        c_mod = _get_centroid(mod, dims)

        # Euclidean distance
        dist_sq = sum((cm - co) ** 2 for cm, co in zip(c_mod, c_obs))
        result = dist_sq**0.5

        return _update_history(result, "Center of Mass Error (COE)")

    # Fallback to numpy
    obs_arr = np.asanyarray(obs)
    mod_arr = np.asanyarray(mod)

    if axis is None:
        axes = tuple(range(obs_arr.ndim))
    elif isinstance(axis, int):
        axes = (axis,)
    elif isinstance(axis, str):
        # Handle single string axis for consistency with xarray path
        axes = (obs_arr.ndim - 1,)  # Best guess for numpy if only string provided
    else:
        axes = tuple(axis)

    def _get_numpy_centroid(arr: np.ndarray, axes_tuple: Tuple[int, ...]) -> List[np.ndarray]:
        """Helper to calculate centroid of a NumPy array."""
        total = np.sum(arr, axis=axes_tuple)
        total_safe = np.where(total == 0, 1e-10, total)
        c_list = []
        for ax in axes_tuple:
            # Create coordinate array for this axis
            shape = [1] * arr.ndim
            shape[ax] = arr.shape[ax]
            coord = np.arange(arr.shape[ax]).reshape(shape)
            c = np.sum(arr * coord, axis=axes_tuple) / total_safe
            c_list.append(c)
        return c_list

    c_obs_np = _get_numpy_centroid(obs_arr, axes)
    c_mod_np = _get_numpy_centroid(mod_arr, axes)

    dist_sq_np = sum((cm - co) ** 2 for cm, co in zip(c_mod_np, c_obs_np))
    result = dist_sq_np**0.5
    return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

CORR_INDEX(obs, mod, axis=None)

Correlation Index (CORR_INDEX).

Typical Use Cases

  • Measuring the linear relationship between observed and modeled values.
  • Used as a component in model evaluation.
  • Quantifies how well model captures observed patterns.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute correlation index.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Correlation index (unitless, -1 to 1).

Examples

import numpy as np from monet_stats.error_metrics import CORR_INDEX obs = np.array([1, 2, 3, 4]) mod = np.array([2, 4, 6, 8]) CORR_INDEX(obs, mod) 1.0

Source code in src/monet_stats/error_metrics.py 
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def CORR_INDEX(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Correlation Index (CORR_INDEX).

    Typical Use Cases
    -----------------
    - Measuring the linear relationship between observed and modeled values.
    - Used as a component in model evaluation.
    - Quantifies how well model captures observed patterns.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute correlation index.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Correlation index (unitless, -1 to 1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import CORR_INDEX
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 4, 6, 8])
    >>> CORR_INDEX(obs, mod)
    1.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        # Using xarray's built-in correlation function
        result = xr.corr(obs, mod, dim=dim)
        return _update_history(result, "CORR_INDEX")
    else:
        # Fallback to numpy-compatible logic
        obs = np.asarray(obs)
        mod = np.asarray(mod)
        if axis is None:
            from scipy.stats import pearsonr

            result = pearsonr(obs.flatten(), mod.flatten())[0]
            return result.item() if hasattr(result, "item") else float(result)
        else:
            # Manual vectorized correlation over axis for robustness across scipy versions
            obs_mean = np.mean(obs, axis=axis, keepdims=True)
            mod_mean = np.mean(mod, axis=axis, keepdims=True)
            obs_std = obs - obs_mean
            mod_std = mod - mod_mean
            num = np.sum(obs_std * mod_std, axis=axis)
            den = np.sqrt(np.sum(obs_std**2, axis=axis) * np.sum(mod_std**2, axis=axis))
            result = num / den
            return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

CRMSE(obs, mod, axis=None)

Centered Root Mean Square Error (CRMSE).

Typical Use Cases

  • Quantifying the error between anomalies (deviations from mean) of model and observations.
  • Used in Taylor diagrams, model evaluation, and forecast verification.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute CRMSE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Centered root mean square error.

Examples

import numpy as np from monet_stats.error_metrics import CRMSE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) CRMSE(obs, mod) 0.4714045207910317

Source code in src/monet_stats/error_metrics.py 
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def CRMSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Centered Root Mean Square Error (CRMSE).

    Typical Use Cases
    -----------------
    - Quantifying the error between anomalies (deviations from mean) of model
      and observations.
    - Used in Taylor diagrams, model evaluation, and forecast verification.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute CRMSE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Centered root mean square error.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import CRMSE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> CRMSE(obs, mod)
    0.4714045207910317
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        o_ = obs - obs.mean(dim=dim)
        m_ = mod - mod.mean(dim=dim)
        result = ((m_ - o_) ** 2).mean(dim=dim, keep_attrs=True) ** 0.5
        return _update_history(result, "CRMSE")
    else:
        o_ = np.subtract(obs, np.mean(obs, axis=axis, keepdims=True))
        m_ = np.subtract(mod, np.mean(mod, axis=axis, keepdims=True))
        result = (np.ma.abs(m_ - o_) ** 2).mean(axis=axis) ** 0.5
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

IOA(obs, mod, axis=None)

Index of Agreement (IOA).

Typical Use Cases

  • Quantifying the agreement between model and observations, normalized by total deviation.
  • Used in model evaluation for skill assessment.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute IOA.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Index of agreement (unitless, 0-1).

Examples

import numpy as np from monet_stats.error_metrics import IOA obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) IOA(obs, mod) 0.8

Source code in src/monet_stats/error_metrics.py 
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def IOA(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Index of Agreement (IOA).

    Typical Use Cases
    -----------------
    - Quantifying the agreement between model and observations, normalized by
      total deviation.
    - Used in model evaluation for skill assessment.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute IOA.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Index of agreement (unitless, 0-1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import IOA
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> IOA(obs, mod)
    0.8
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        obs_mean = obs.mean(dim=dim)
        num = ((obs - mod) ** 2).sum(dim=dim)
        denom = ((abs(mod - obs_mean) + abs(obs - obs_mean)) ** 2).sum(dim=dim)
        result = 1.0 - (num / denom)
        return _update_history(result, "IOA")
    else:
        obs_m = np.ma.masked_invalid(obs)
        mod_m = np.ma.masked_invalid(mod)
        obs_mean = np.ma.mean(obs_m, axis=axis, keepdims=True)
        num = np.ma.sum((obs_m - mod_m) ** 2, axis=axis)
        denom = np.ma.sum((np.ma.abs(mod_m - obs_mean) + np.ma.abs(obs_m - obs_mean)) ** 2, axis=axis)
        with np.errstate(divide="ignore", invalid="ignore"):
            result = 1.0 - (num / denom)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

LOG_ERROR(obs, mod, axis=None)

Logarithmic Error Metric.

Typical Use Cases

  • Quantifying errors for variables that span several orders of magnitude.
  • Used in atmospheric sciences for concentration data (e.g., pollutants).
  • Helpful when relative rather than absolute errors are important.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values (should be positive). mod : numpy.ndarray or xarray.DataArray Model or predicted values (should be positive). axis : int, str, or iterable of such, optional Axis or dimension along which to compute log error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Logarithmic error metric.

Examples

import numpy as np from monet_stats.error_metrics import LOG_ERROR obs = np.array([1, 100]) mod = np.array([2, 200]) LOG_ERROR(obs, mod) 0.34657359027997264

Source code in src/monet_stats/error_metrics.py 
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def LOG_ERROR(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Logarithmic Error Metric.

    Typical Use Cases
    -----------------
    - Quantifying errors for variables that span several orders of magnitude.
    - Used in atmospheric sciences for concentration data (e.g., pollutants).
    - Helpful when relative rather than absolute errors are important.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values (should be positive).
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values (should be positive).
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute log error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Logarithmic error metric.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import LOG_ERROR
    >>> obs = np.array([1, 100])
    >>> mod = np.array([2, 200])
    >>> LOG_ERROR(obs, mod)
    0.34657359027997264
    """
    # Add small epsilon to avoid log(0) and handle negative values
    epsilon = 1e-10

    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        # Use abs to handle potential negative values, then add epsilon
        obs_safe = abs(obs) + epsilon
        mod_safe = abs(mod) + epsilon
        obs_log = np.log(obs_safe)
        mod_log = np.log(mod_safe)
        result = ((mod_log - obs_log) ** 2).mean(dim=dim, keep_attrs=True) ** 0.5
        return _update_history(result, "LOG_ERROR")
    else:
        # Use abs to handle potential negative values, then add epsilon
        obs_safe = np.abs(obs) + epsilon
        mod_safe = np.abs(mod) + epsilon
        obs_log = np.log(obs_safe)
        mod_log = np.log(mod_safe)

        result = np.sqrt(np.mean((mod_log - obs_log) ** 2, axis=axis))
        # Return 0 for perfect agreement
        if np.array_equal(obs, mod):
            return 0.0
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MAE(obs, mod, axis=None)

Mean Absolute Error (MAE).

Typical Use Cases

  • Quantifying the average magnitude of errors between model and observations, regardless of direction.
  • Used in model evaluation, forecast verification, and regression analysis.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute MAE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean absolute error.

Examples

import numpy as np from monet_stats.error_metrics import MAE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) MAE(obs, mod) 0.6666666666666666

Source code in src/monet_stats/error_metrics.py 
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def MAE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Absolute Error (MAE).

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of errors between model and observations,
      regardless of direction.
    - Used in model evaluation, forecast verification, and regression analysis.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute MAE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean absolute error.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MAE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> MAE(obs, mod)
    0.6666666666666666
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = abs(mod - obs).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "MAE")
    else:
        result = np.ma.abs(np.subtract(mod, obs)).mean(axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MAE_norm(obs, mod, axis=None)

Normalized Mean Absolute Error (MAE_norm).

Normalizes MAE by the range of observations.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute normalized MAE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Normalized mean absolute error (unitless).

Source code in src/monet_stats/error_metrics.py 
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def MAE_norm(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Normalized Mean Absolute Error (MAE_norm).

    Normalizes MAE by the range of observations.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute normalized MAE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Normalized mean absolute error (unitless).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        mae = abs(mod - obs).mean(dim=dim, keep_attrs=True)
        obs_min = obs.min(dim=dim)
        obs_max = obs.max(dim=dim)
        obs_range = obs_max - obs_min
        # Avoid division by zero
        result = xr.where(obs_range == 0, mae, mae / obs_range)
        return _update_history(result, "MAE_norm")
    else:
        mae = np.mean(np.abs(np.subtract(mod, obs)), axis=axis)
        obs_min = np.min(obs, axis=axis)
        obs_max = np.max(obs, axis=axis)
        obs_range = obs_max - obs_min
        # Avoid division by zero
        result = np.where(obs_range == 0, mae, mae / obs_range)
        return result.item() if np.ndim(result) == 0 else result

MAPE(obs, mod, axis=None)

Mean Absolute Percentage Error (MAPE).

Typical Use Cases

  • Quantifying the average relative error between model and observations as a percentage.
  • Used in time series forecasting, regression, and model evaluation for percentage-based error assessment.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute MAPE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean absolute percentage error (in percent).

Examples

import numpy as np from monet_stats.error_metrics import MAPE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) MAPE(obs, mod) 50.0

Source code in src/monet_stats/error_metrics.py 
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def MAPE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Absolute Percentage Error (MAPE).

    Typical Use Cases
    -----------------
    - Quantifying the average relative error between model and observations
      as a percentage.
    - Used in time series forecasting, regression, and model evaluation for
      percentage-based error assessment.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute MAPE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean absolute percentage error (in percent).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MAPE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> MAPE(obs, mod)
    50.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = (100 * abs(mod - obs) / abs(obs)).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "MAPE")
    else:
        result = (100 * np.ma.abs(np.subtract(mod, obs)) / np.ma.abs(obs)).mean(axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MAPE_mod(obs, mod, axis=None)

Modified Mean Absolute Percentage Error (MAPE).

This version handles cases where observations might be zero or near zero by using a small epsilon to avoid division by zero.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute MAPE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean absolute percentage error (in percent).

Source code in src/monet_stats/error_metrics.py 
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def MAPE_mod(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Modified Mean Absolute Percentage Error (MAPE).

    This version handles cases where observations might be zero or near zero
    by using a small epsilon to avoid division by zero.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute MAPE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean absolute percentage error (in percent).
    """
    # Small epsilon to avoid division by zero
    epsilon = 1e-8

    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        # Add epsilon to avoid division by zero
        obs_safe = xr.where(abs(obs) < epsilon, epsilon, obs)
        result = (100 * abs(mod - obs) / abs(obs_safe)).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "MAPE_mod")
    else:
        # Add epsilon to avoid division by zero
        obs_safe = np.where(np.abs(obs) < epsilon, epsilon, obs)
        result = (100 * np.abs(np.subtract(mod, obs)) / np.abs(obs_safe)).mean(axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MASE(obs, mod, axis=None)

Mean Absolute Scaled Error (MASE).

Typical Use Cases

  • Quantifying model error relative to the error of a simple baseline model (e.g., naive forecast).
  • Used in time series forecasting and model evaluation.
  • Provides scale-independent comparison across different datasets.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute MASE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean absolute scaled error (unitless).

Examples

import numpy as np from monet_stats.error_metrics import MASE obs = np.array([1, 2, 3, 4]) mod = np.array([1.1, 2.1, 3.1, 4.1]) MASE(obs, mod) 0.1

Source code in src/monet_stats/error_metrics.py 
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def MASE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Absolute Scaled Error (MASE).

    Typical Use Cases
    -----------------
    - Quantifying model error relative to the error of a simple baseline model
      (e.g., naive forecast).
    - Used in time series forecasting and model evaluation.
    - Provides scale-independent comparison across different datasets.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute MASE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean absolute scaled error (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MASE
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.1, 2.1, 3.1, 4.1])
    >>> MASE(obs, mod)
    0.1
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)

        # Calculate naive forecast error (using previous observation)
        if "time" in obs.dims:
            naive_error = abs(obs - obs.shift(time=1)).mean(dim=dim, skipna=True)
        else:
            # Fallback if time is not named 'time'
            naive_error = abs(obs - obs.shift({obs.dims[0]: 1})).mean(dim=dim, skipna=True)

        model_error = abs(mod - obs).mean(dim=dim, keep_attrs=True)
        result = model_error / naive_error
        return _update_history(result, "MASE")
    else:
        # Calculate naive forecast error (using previous observation)
        if axis is not None:
            naive_diff = np.diff(obs, axis=axis)
            naive_error = np.mean(np.abs(naive_diff), axis=axis)
        else:
            naive_diff = np.diff(obs)
            naive_error = np.mean(np.abs(naive_diff))
        model_error = np.mean(np.abs(np.subtract(mod, obs)), axis=axis)
        result = model_error / naive_error
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MASE_mod(obs, mod, axis=None)

Modified Mean Absolute Scaled Error (MASE).

This version handles cases where the naive forecast error is zero by using a small epsilon to avoid division by zero.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute MASE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean absolute scaled error (unitless).

Source code in src/monet_stats/error_metrics.py 
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def MASE_mod(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Modified Mean Absolute Scaled Error (MASE).

    This version handles cases where the naive forecast error is zero
    by using a small epsilon to avoid division by zero.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute MASE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean absolute scaled error (unitless).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        # Calculate naive forecast error (using previous observation)
        if "time" in obs.dims:
            naive_error = abs(obs - obs.shift(time=1)).mean(dim=dim, skipna=True)
        else:
            naive_error = abs(obs - obs.shift({obs.dims[0]: 1})).mean(dim=dim, skipna=True)

        model_error = abs(mod - obs).mean(dim=dim, keep_attrs=True)
        # Avoid division by zero
        result = xr.where(naive_error == 0, model_error, model_error / naive_error)
        return _update_history(result, "MASE_mod")
    else:
        # Calculate naive forecast error (using previous observation)
        if axis is not None:
            naive_diff = np.diff(obs, axis=axis)
            naive_error = np.mean(np.abs(naive_diff), axis=axis)
        else:
            naive_diff = np.diff(obs)
            naive_error = np.mean(np.abs(naive_diff))
        model_error = np.mean(np.abs(np.subtract(mod, obs)), axis=axis)
        # Avoid division by zero
        result = np.where(naive_error == 0, model_error, model_error / naive_error)
        return result.item() if np.ndim(result) == 0 else result

MASEm(obs, mod, axis=None)

Mean Absolute Scaled Error (MASE) - robust to masked arrays.

Typical Use Cases

  • Quantifying model error relative to the error of a simple baseline model (e.g., naive forecast), robust to masked arrays.
  • Used in time series forecasting and model evaluation with missing data.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute MASE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean absolute scaled error (unitless).

Examples

import numpy as np from monet_stats.error_metrics import MASEm obs = np.array([1, 2, 3, 4]) mod = np.array([1.1, 2.1, 3.1, 4.1]) MASEm(obs, mod) 0.1

Source code in src/monet_stats/error_metrics.py 
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def MASEm(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Absolute Scaled Error (MASE) - robust to masked arrays.

    Typical Use Cases
    -----------------
    - Quantifying model error relative to the error of a simple baseline model
      (e.g., naive forecast), robust to masked arrays.
    - Used in time series forecasting and model evaluation with missing data.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute MASE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean absolute scaled error (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MASEm
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.1, 2.1, 3.1, 4.1])
    >>> MASEm(obs, mod)
    0.1
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        # MASE implementation for xarray already handles NaNs with skipna=True
        return MASE(obs, mod, axis=axis)
    else:
        # Calculate naive forecast error (using previous observation) with masked arrays
        if axis is not None:
            # Use numpy's gradient-like approach for masked arrays
            naive_diff = np.ma.diff(obs, axis=axis)
            naive_error = np.ma.mean(np.ma.abs(naive_diff), axis=axis)
        else:
            naive_diff = np.ma.diff(obs)
            naive_error = np.ma.mean(np.ma.abs(naive_diff))
        model_error = np.ma.mean(np.ma.abs(np.subtract(mod, obs)), axis=axis)
        result = model_error / naive_error
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MB(obs, mod, axis=None)

Mean Bias (MB).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the mean bias.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean bias value(s) = mean(model - observation). Positive values indicate model overestimation.

Source code in src/monet_stats/error_metrics.py 
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def MB(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Bias (MB).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the mean bias.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean bias value(s) = mean(model - observation).
        Positive values indicate model overestimation.
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = (mod - obs).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "MB")
    else:
        result = np.ma.mean(np.subtract(mod, obs), axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MNB(obs, mod, axis=None)

Mean Normalized Bias (%).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the bias.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean normalized bias (percent).

Examples

import numpy as np obs = np.array([1, 2, 3]) mod = np.array([1.1, 2.2, 3.3]) MNB(obs, mod) 10.0

Source code in src/monet_stats/error_metrics.py 
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def MNB(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Normalized Bias (%).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the bias.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean normalized bias (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([1.1, 2.2, 3.3])
    >>> MNB(obs, mod)
    10.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = ((mod - obs) / obs).mean(dim=dim, keep_attrs=True) * 100.0
        return _update_history(result, "MNB")
    else:
        result = np.ma.masked_invalid((mod - obs) / obs).mean(axis=axis) * 100.0
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MNE(obs, mod, axis=None)

Mean Normalized Gross Error (%).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean normalized gross error (percent).

Examples

import numpy as np obs = np.array([1, 2, 3]) mod = np.array([1.1, 1.8, 3.3]) MNE(obs, mod) 10.0

Source code in src/monet_stats/error_metrics.py 
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def MNE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Normalized Gross Error (%).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean normalized gross error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([1.1, 1.8, 3.3])
    >>> MNE(obs, mod)
    10.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = (abs(mod - obs) / obs).mean(dim=dim, keep_attrs=True) * 100.0
        return _update_history(result, "MNE")
    else:
        result = np.ma.masked_invalid(np.ma.abs(mod - obs) / obs).mean(axis=axis) * 100.0
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MO(obs, mod, axis=None)

Mean Error (MO) - Mean of (model - observation).

Typical Use Cases

  • Quantifying the average bias between model predictions and observations.
  • Used in model evaluation to assess systematic errors.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the mean error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean error (model - observation) in observation units. Returns 0.0 for perfect agreement.

Examples

import numpy as np from monet_stats.error_metrics import MO obs = np.array([1, 2, 3, 4, 5]) mod = np.array([1.1, 2.1, 3.1, 4.1, 5.1]) MO(obs, mod) 0.1

Source code in src/monet_stats/error_metrics.py 
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def MO(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Error (MO) - Mean of (model - observation).

    Typical Use Cases
    -----------------
    - Quantifying the average bias between model predictions and observations.
    - Used in model evaluation to assess systematic errors.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the mean error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean error (model - observation) in observation units.
        Returns 0.0 for perfect agreement.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MO
    >>> obs = np.array([1, 2, 3, 4, 5])
    >>> mod = np.array([1.1, 2.1, 3.1, 4.1, 5.1])
    >>> MO(obs, mod)
    0.1
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = (mod - obs).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "MO")
    else:
        result = np.ma.mean(np.ma.masked_invalid(np.subtract(mod, obs)), axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MP(obs=None, mod=None, axis=None)

Mean Predictions (model unit).

Typical Use Cases

  • Calculating the average value of model predictions for baseline or climatological reference.
  • Used in normalization, anomaly calculation, and summary statistics for model output.

Parameters

obs : numpy.ndarray or xarray.DataArray, optional Observed values (not used for MP but included for signature matching). mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the mean.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean of predictions.

Source code in src/monet_stats/error_metrics.py 
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def MP(
    obs: Optional[Union[np.ndarray, xr.DataArray]] = None,
    mod: Union[np.ndarray, xr.DataArray] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Predictions (model unit).

    Typical Use Cases
    -----------------
    - Calculating the average value of model predictions for baseline or
      climatological reference.
    - Used in normalization, anomaly calculation, and summary statistics for
      model output.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray, optional
        Observed values (not used for MP but included for signature matching).
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the mean.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean of predictions.
    """
    if isinstance(mod, xr.DataArray):
        dim = _resolve_axis_to_dim(mod, axis)
        result = mod.mean(dim=dim, keep_attrs=True)
        return _update_history(result, "MP")
    else:
        result = np.ma.mean(np.ma.masked_invalid(mod), axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MSE(obs, mod, axis=None)

Mean Squared Error (MSE).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean squared error.

Examples

import numpy as np from monet_stats.error_metrics import MSE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) MSE(obs, mod) 0.6666666666666666

Source code in src/monet_stats/error_metrics.py 
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def MSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Squared Error (MSE).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean squared error.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MSE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> MSE(obs, mod)
    0.6666666666666666
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = ((mod - obs) ** 2).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "MSE")
    else:
        result = np.ma.mean((np.subtract(mod, obs)) ** 2, axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MdnB(obs, mod, axis=None)

Median Bias (MdnB).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the median bias.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Median bias value(s) = median(model - observation). Positive values indicate model overestimation.

Source code in src/monet_stats/error_metrics.py 
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def MdnB(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Median Bias (MdnB).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the median bias.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Median bias value(s) = median(model - observation).
        Positive values indicate model overestimation.
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff = mod - obs
        if hasattr(diff.data, "chunks"):
            dims_to_chunk = dim if isinstance(dim, (list, tuple)) else [dim]
            diff = diff.chunk({d: -1 for d in dims_to_chunk if d in diff.dims})
        result = diff.quantile(q=0.5, dim=dim, keep_attrs=True).drop_vars("quantile", errors="ignore")
        return _update_history(result, "MdnB")
    else:
        result = np.ma.median(np.subtract(mod, obs), axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MdnNB(obs, mod, axis=None)

Median Normalized Bias (%).

Typical Use Cases

  • Assessing the central tendency of model bias relative to observations, less sensitive to outliers than mean.
  • Useful for robust model evaluation in the presence of skewed or non-normal error distributions.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the bias.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Median normalized bias (percent).

Source code in src/monet_stats/error_metrics.py 
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def MdnNB(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Median Normalized Bias (%).

    Typical Use Cases
    -----------------
    - Assessing the central tendency of model bias relative to observations,
      less sensitive to outliers than mean.
    - Useful for robust model evaluation in the presence of skewed or non-normal
      error distributions.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the bias.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Median normalized bias (percent).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff = (mod - obs) / obs
        if hasattr(diff.data, "chunks"):
            dims_to_chunk = dim if isinstance(dim, (list, tuple)) else [dim]
            diff = diff.chunk({d: -1 for d in dims_to_chunk if d in diff.dims})
        result = diff.quantile(q=0.5, dim=dim, keep_attrs=True).drop_vars("quantile", errors="ignore") * 100.0
        return _update_history(result, "MdnNB")
    else:
        result = np.ma.median(np.ma.masked_invalid((mod - obs) / obs), axis=axis) * 100.0
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MdnNE(obs, mod, axis=None)

Median Normalized Gross Error (%).

Typical Use Cases

  • Evaluating the typical magnitude of model errors relative to observations, robust to outliers.
  • Useful for summarizing error magnitude in non-Gaussian or heavy-tailed error distributions.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Median normalized gross error (percent).

Source code in src/monet_stats/error_metrics.py 
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def MdnNE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Median Normalized Gross Error (%).

    Typical Use Cases
    -----------------
    - Evaluating the typical magnitude of model errors relative to observations,
      robust to outliers.
    - Useful for summarizing error magnitude in non-Gaussian or heavy-tailed
      error distributions.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Median normalized gross error (percent).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff = abs(mod - obs) / obs
        if hasattr(diff.data, "chunks"):
            dims_to_chunk = dim if isinstance(dim, (list, tuple)) else [dim]
            diff = diff.chunk({d: -1 for d in dims_to_chunk if d in diff.dims})
        result = diff.quantile(q=0.5, dim=dim, keep_attrs=True).drop_vars("quantile", errors="ignore") * 100.0
        return _update_history(result, "MdnNE")
    else:
        result = np.ma.median(np.ma.masked_invalid(np.ma.abs(mod - obs) / obs), axis=axis) * 100.0
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MdnO(obs, mod, axis=None)

Median Error (MdnO) - Median of (model - observation).

Typical Use Cases

  • Quantifying the typical bias between model predictions and observations, robust to outliers.
  • Used in robust model evaluation for non-parametric error assessment.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the median error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Median error (model - observation) in observation units. Returns 0.0 for perfect agreement.

Examples

import numpy as np from monet_stats.error_metrics import MdnO obs = np.array([1, 2, 3, 4, 5]) mod = np.array([1.1, 2.1, 3.1, 4.1, 5.1]) MdnO(obs, mod) 0.1

Source code in src/monet_stats/error_metrics.py 
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def MdnO(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Median Error (MdnO) - Median of (model - observation).

    Typical Use Cases
    -----------------
    - Quantifying the typical bias between model predictions and observations,
      robust to outliers.
    - Used in robust model evaluation for non-parametric error assessment.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the median error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Median error (model - observation) in observation units.
        Returns 0.0 for perfect agreement.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MdnO
    >>> obs = np.array([1, 2, 3, 4, 5])
    >>> mod = np.array([1.1, 2.1, 3.1, 4.1, 5.1])
    >>> MdnO(obs, mod)
    0.1
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff = mod - obs
        if hasattr(diff.data, "chunks"):
            dims_to_chunk = dim if isinstance(dim, (list, tuple)) else [dim]
            diff = diff.chunk({d: -1 for d in dims_to_chunk if d in diff.dims})
        result = diff.quantile(q=0.5, dim=dim, keep_attrs=True).drop_vars("quantile", errors="ignore")
        return _update_history(result, "MdnO")
    else:
        result = np.median(np.subtract(mod, obs), axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MdnP(obs, mod, axis=None)

Median Error (MdnP) - Median of (model - observation).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the median error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Median error (model - observation) in model units. Returns 0.0 for perfect agreement.

Source code in src/monet_stats/error_metrics.py 
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def MdnP(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Median Error (MdnP) - Median of (model - observation).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the median error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Median error (model - observation) in model units.
        Returns 0.0 for perfect agreement.
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff = mod - obs
        if hasattr(diff.data, "chunks"):
            dims_to_chunk = dim if isinstance(dim, (list, tuple)) else [dim]
            diff = diff.chunk({d: -1 for d in dims_to_chunk if d in diff.dims})
        result = diff.quantile(q=0.5, dim=dim, keep_attrs=True).drop_vars("quantile", errors="ignore")
        return _update_history(result, "MdnP")
    else:
        result = np.median(np.subtract(mod, obs), axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MedAE(obs, mod, axis=None)

Median Absolute Error (MedAE).

Typical Use Cases

  • Evaluating the typical magnitude of errors, robust to outliers and non-normal error distributions.
  • Used in robust regression, model evaluation, and forecast verification.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute MedAE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Median absolute error.

Examples

import numpy as np from monet_stats.error_metrics import MedAE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) MedAE(obs, mod) 1.0

Source code in src/monet_stats/error_metrics.py 
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def MedAE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Median Absolute Error (MedAE).

    Typical Use Cases
    -----------------
    - Evaluating the typical magnitude of errors, robust to outliers and
      non-normal error distributions.
    - Used in robust regression, model evaluation, and forecast verification.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute MedAE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Median absolute error.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MedAE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> MedAE(obs, mod)
    1.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff_abs = abs(mod - obs)
        if hasattr(diff_abs.data, "chunks"):
            dims_to_chunk = dim if isinstance(dim, (list, tuple)) else [dim]
            diff_abs = diff_abs.chunk({d: -1 for d in dims_to_chunk if d in diff_abs.dims})
        result = diff_abs.quantile(q=0.5, dim=dim, keep_attrs=True).drop_vars("quantile", errors="ignore")
        return _update_history(result, "MedAE")
    else:
        result = np.ma.median(np.ma.abs(np.subtract(mod, obs)), axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NMSE(obs, mod, axis=None)

Normalized Mean Square Error (NMSE).

Typical Use Cases

  • Quantifying the normalized squared error between model and observations.
  • Used in model evaluation to compare performance across different variables or sites with different scales.
  • Provides dimensionless error metric for cross-comparison.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute NMSE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Normalized mean square error (unitless).

Examples

import numpy as np from monet_stats.error_metrics import NMSE obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) NMSE(obs, mod) 0.25

Source code in src/monet_stats/error_metrics.py 
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def NMSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Normalized Mean Square Error (NMSE).

    Typical Use Cases
    -----------------
    - Quantifying the normalized squared error between model and observations.
    - Used in model evaluation to compare performance across different variables
      or sites with different scales.
    - Provides dimensionless error metric for cross-comparison.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute NMSE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Normalized mean square error (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import NMSE
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> NMSE(obs, mod)
    0.25
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        mse = ((mod - obs) ** 2).mean(dim=dim, keep_attrs=True)
        obs_var = obs.var(dim=dim)
        # Handle case where variance is 0 (perfect agreement)
        result = xr.where(obs_var == 0, 0, mse / obs_var)
        return _update_history(result, "NMSE")
    else:
        mse = np.ma.mean(np.ma.masked_invalid(np.subtract(mod, obs)) ** 2, axis=axis)
        obs_var = np.ma.var(np.ma.masked_invalid(obs), axis=axis)
        # Handle case where variance is 0 (perfect agreement)
        result = np.where(obs_var == 0, 0, mse / obs_var)
        return result.item() if np.ndim(result) == 0 else result

NMdnGE(obs, mod, axis=None)

Normalized Median Gross Error (%).

Typical Use Cases

  • Comparing the typical (median) error magnitude, normalized by the mean observation, for robust model evaluation.
  • Useful for inter-comparison of model performance across sites or variables with different scales.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Normalized median gross error (percent).

Examples

import numpy as np from monet_stats.error_metrics import NMdnGE obs = np.array([1, 2, 3, 4, 100]) mod = np.array([1.1, 2.1, 3.1, 4.1, 105]) NMdnGE(obs, mod) 0.45454545454545453

Source code in src/monet_stats/error_metrics.py 
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def NMdnGE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Normalized Median Gross Error (%).

    Typical Use Cases
    -----------------
    - Comparing the typical (median) error magnitude, normalized by the mean
      observation, for robust model evaluation.
    - Useful for inter-comparison of model performance across sites or variables
      with different scales.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Normalized median gross error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import NMdnGE
    >>> obs = np.array([1, 2, 3, 4, 100])
    >>> mod = np.array([1.1, 2.1, 3.1, 4.1, 105])
    >>> NMdnGE(obs, mod)
    0.45454545454545453
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff = abs(mod - obs)
        if hasattr(diff.data, "chunks"):
            dims_to_chunk = dim if isinstance(dim, (list, tuple)) else [dim]
            diff = diff.chunk({d: -1 for d in dims_to_chunk if d in diff.dims})
        result = (diff.quantile(q=0.5, dim=dim).drop_vars("quantile", errors="ignore") / obs.mean(dim=dim)) * 100.0
        return _update_history(result, "NMdnGE")
    else:
        result = (
            np.ma.masked_invalid(np.ma.median(np.ma.abs(mod - obs), axis=axis) / np.ma.mean(obs, axis=axis)) * 100.0
        )
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NO(obs, mod=None, axis=None)

N Observations (#).

Typical Use Cases

  • Counting the number of valid (non-masked) observations in a dataset.
  • Used to report sample size for statistical summaries and model evaluation.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray, optional Model predicted values (not used for NO but included for signature matching). axis : int, str, or iterable of such, optional Axis or dimension along which to count.

Returns

int, numpy.ndarray, or xarray.DataArray Number of valid observations.

Source code in src/monet_stats/error_metrics.py 
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def NO(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Optional[Union[np.ndarray, xr.DataArray]] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[int, np.ndarray, xr.DataArray]:
    """
    N Observations (#).

    Typical Use Cases
    -----------------
    - Counting the number of valid (non-masked) observations in a dataset.
    - Used to report sample size for statistical summaries and model evaluation.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray, optional
        Model predicted values (not used for NO but included for signature matching).
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to count.

    Returns
    -------
    int, numpy.ndarray, or xarray.DataArray
        Number of valid observations.
    """
    if isinstance(obs, xr.DataArray):
        dim = _resolve_axis_to_dim(obs, axis)
        return obs.count(dim=dim)
    else:
        result = (~np.ma.getmaskarray(obs)).sum(axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NOP(obs, mod, axis=None)

N Observations/Prediction Pairs (#).

Typical Use Cases

  • Counting the number of valid observation-prediction pairs for paired statistical analysis.
  • Used to ensure sample size consistency in paired model evaluation metrics.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to count.

Returns

int, numpy.ndarray, or xarray.DataArray Number of valid pairs.

Source code in src/monet_stats/error_metrics.py 
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def NOP(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[int, np.ndarray, xr.DataArray]:
    """
    N Observations/Prediction Pairs (#).

    Typical Use Cases
    -----------------
    - Counting the number of valid observation-prediction pairs for paired
      statistical analysis.
    - Used to ensure sample size consistency in paired model evaluation metrics.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to count.

    Returns
    -------
    int, numpy.ndarray, or xarray.DataArray
        Number of valid pairs.
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        # To get pairs where BOTH are not NaN:
        mask = obs.notnull() & mod.notnull()
        return mask.sum(dim=dim)
    else:
        obsc, modc = matchmasks(obs, mod)
        result = (~np.ma.getmaskarray(obsc)).sum(axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NP(obs=None, mod=None, axis=None)

N Predictions (#).

Typical Use Cases

  • Counting the number of valid (non-masked) model predictions in a dataset.
  • Used to report sample size for model output and for filtering invalid predictions.

Parameters

obs : numpy.ndarray or xarray.DataArray, optional Observed values (not used for NP but included for signature matching). mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to count.

Returns

int, numpy.ndarray, or xarray.DataArray Number of valid predictions.

Source code in src/monet_stats/error_metrics.py 
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def NP(
    obs: Optional[Union[np.ndarray, xr.DataArray]] = None,
    mod: Union[np.ndarray, xr.DataArray] = None,
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[int, np.ndarray, xr.DataArray]:
    """
    N Predictions (#).

    Typical Use Cases
    -----------------
    - Counting the number of valid (non-masked) model predictions in a dataset.
    - Used to report sample size for model output and for filtering invalid
      predictions.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray, optional
        Observed values (not used for NP but included for signature matching).
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to count.

    Returns
    -------
    int, numpy.ndarray, or xarray.DataArray
        Number of valid predictions.
    """
    if isinstance(mod, xr.DataArray):
        dim = _resolve_axis_to_dim(mod, axis)
        return mod.count(dim=dim)
    else:
        result = (~np.ma.getmaskarray(mod)).sum(axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NRMSE(obs, mod, axis=None)

Normalized Root Mean Square Error (NRMSE).

Typical Use Cases

  • Quantifying the relative error between model and observations, normalized by the range of observations.
  • Used in model evaluation to compare performance across different variables or sites with different scales.
  • Provides dimensionless error metric for cross-comparison.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute NRMSE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Normalized root mean square error (unitless).

Examples

import numpy as np from monet_stats.error_metrics import NRMSE obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) NRMSE(obs, mod) 0.4714045207910317

Source code in src/monet_stats/error_metrics.py 
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def NRMSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Normalized Root Mean Square Error (NRMSE).

    Typical Use Cases
    -----------------
    - Quantifying the relative error between model and observations, normalized
      by the range of observations.
    - Used in model evaluation to compare performance across different variables
      or sites with different scales.
    - Provides dimensionless error metric for cross-comparison.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute NRMSE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Normalized root mean square error (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import NRMSE
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> NRMSE(obs, mod)
    0.4714045207910317
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        rmse = ((mod - obs) ** 2).mean(dim=dim, keep_attrs=True) ** 0.5
        obs_range = obs.max(dim=dim) - obs.min(dim=dim)
        result = xr.where(obs_range == 0, 0, rmse / obs_range)
        return _update_history(result, "NRMSE")
    else:
        rmse = np.ma.sqrt(np.ma.mean((np.subtract(mod, obs)) ** 2, axis=axis))
        obs_range = np.ma.max(obs, axis=axis) - np.ma.min(obs, axis=axis)
        with np.errstate(divide="ignore", invalid="ignore"):
            result = np.where(obs_range == 0, 0, rmse / obs_range)
            return result.item() if np.ndim(result) == 0 else result

NSC(obs, mod, axis=None)

Nash-Sutcliffe Coefficient (NSC) - Alternative to NSE.

Typical Use Cases

  • Quantifying the predictive power of hydrological models relative to the mean of observations.
  • Used in hydrology, meteorology, and environmental model evaluation.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute NSC.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Nash-Sutcliffe coefficient (unitless).

Examples

import numpy as np from monet_stats.error_metrics import NSC obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) NSC(obs, mod) -0.33333333333333326

Source code in src/monet_stats/error_metrics.py 
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def NSC(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Nash-Sutcliffe Coefficient (NSC) - Alternative to NSE.

    Typical Use Cases
    -----------------
    - Quantifying the predictive power of hydrological models relative to
      the mean of observations.
    - Used in hydrology, meteorology, and environmental model evaluation.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute NSC.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Nash-Sutcliffe coefficient (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import NSC
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> NSC(obs, mod)
    -0.33333333333333326
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        obs_mean = obs.mean(dim=dim)
        numerator = ((obs - mod) ** 2).sum(dim=dim)
        denominator = ((obs - obs_mean) ** 2).sum(dim=dim)
        result = 1.0 - (numerator / denominator)
        return _update_history(result, "NSC")
    else:
        obs_mean = np.mean(obs, axis=axis, keepdims=True)
        numerator = np.sum((obs - mod) ** 2, axis=axis)
        denominator = np.sum((obs - obs_mean) ** 2, axis=axis)
        result = 1.0 - (numerator / denominator)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NSE_alpha(obs, mod, axis=None)

NSE Alpha - Decomposed NSE component measuring ratio of standard deviations.

Typical Use Cases

  • Quantifying the model's ability to capture the variability of observations.
  • Used in model evaluation to assess how well model represents observed variability.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute NSE_alpha.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray NSE alpha component (unitless).

Examples

import numpy as np from monet_stats.error_metrics import NSE_alpha obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) NSE_alpha(obs, mod) 0.0

Source code in src/monet_stats/error_metrics.py 
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def NSE_alpha(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    NSE Alpha - Decomposed NSE component measuring ratio of standard deviations.

    Typical Use Cases
    -----------------
    - Quantifying the model's ability to capture the variability of observations.
    - Used in model evaluation to assess how well model represents observed
      variability.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute NSE_alpha.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        NSE alpha component (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import NSE_alpha
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> NSE_alpha(obs, mod)
    0.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = mod.std(dim=dim) / obs.std(dim=dim)
        return _update_history(result, "NSE_alpha")
    else:
        result = np.std(mod, axis=axis) / np.std(obs, axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NSE_beta(obs, mod, axis=None)

NSE Beta - Decomposed NSE component measuring bias.

Typical Use Cases

  • Quantifying the systematic bias between model and observations.
  • Used in model evaluation to assess mean differences between model and observations.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute NSE_beta.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray NSE beta component (unitless).

Examples

import numpy as np from monet_stats.error_metrics import NSE_beta obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) NSE_beta(obs, mod) 0.5

Source code in src/monet_stats/error_metrics.py 
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def NSE_beta(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    NSE Beta - Decomposed NSE component measuring bias.

    Typical Use Cases
    -----------------
    - Quantifying the systematic bias between model and observations.
    - Used in model evaluation to assess mean differences between model and
      observations.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute NSE_beta.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        NSE beta component (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import NSE_beta
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> NSE_beta(obs, mod)
    0.5
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = mod.mean(dim=dim) / obs.mean(dim=dim)
        return _update_history(result, "NSE_beta")
    else:
        result = np.mean(mod, axis=axis) / np.mean(obs, axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

RM(obs, mod, axis=None)

Root Mean Error (RM) - Root of mean squared error.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Root of mean squared error (observation units). Returns 0.0 for perfect agreement.

Source code in src/monet_stats/error_metrics.py 
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def RM(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Root Mean Error (RM) - Root of mean squared error.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Root of mean squared error (observation units).
        Returns 0.0 for perfect agreement.
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = np.sqrt(((obs - mod) ** 2).mean(dim=dim, keep_attrs=True))
        return _update_history(result, "RM")
    else:
        result = np.sqrt(np.mean((np.subtract(obs, mod)) ** 2, axis=axis))
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

RMSE(obs, mod, axis=None)

Root Mean Square Error (RMSE).

Typical Use Cases

  • Quantifying the average magnitude of errors between model and observations, accounting for large errors more heavily than MAE.
  • Used in model evaluation, forecast verification, and regression analysis.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute RMSE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Root mean square error.

Examples

import numpy as np from monet_stats.error_metrics import RMSE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) RMSE(obs, mod) 0.816496580927726

Source code in src/monet_stats/error_metrics.py 
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def RMSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Root Mean Square Error (RMSE).

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of errors between model and observations,
      accounting for large errors more heavily than MAE.
    - Used in model evaluation, forecast verification, and regression analysis.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute RMSE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Root mean square error.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import RMSE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> RMSE(obs, mod)
    0.816496580927726
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = ((mod - obs) ** 2).mean(dim=dim, keep_attrs=True) ** 0.5
        return _update_history(result, "RMSE")
    else:
        result = np.ma.sqrt(np.ma.mean((np.subtract(mod, obs)) ** 2, axis=axis))
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

RMSE_norm(obs, mod, axis=None)

Normalized Root Mean Square Error (RMSE_norm).

Normalizes RMSE by the range of observations.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute normalized RMSE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Normalized root mean square error (unitless).

Source code in src/monet_stats/error_metrics.py 
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def RMSE_norm(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Normalized Root Mean Square Error (RMSE_norm).

    Normalizes RMSE by the range of observations.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute normalized RMSE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Normalized root mean square error (unitless).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        rmse = ((mod - obs) ** 2).mean(dim=dim, keep_attrs=True) ** 0.5
        obs_min = obs.min(dim=dim)
        obs_max = obs.max(dim=dim)
        obs_range = obs_max - obs_min
        # Avoid division by zero
        result = xr.where(obs_range == 0, rmse, rmse / obs_range)
        return _update_history(result, "RMSE_norm")
    else:
        rmse = np.sqrt(np.mean((np.subtract(mod, obs)) ** 2, axis=axis))
        obs_min = np.min(obs, axis=axis)
        obs_max = np.max(obs, axis=axis)
        obs_range = obs_max - obs_min
        # Avoid division by zero
        result = np.where(obs_range == 0, rmse, rmse / obs_range)
        return result.item() if np.ndim(result) == 0 else result

RMSPE(obs, mod, axis=None)

Root Mean Square Percentage Error (RMSPE).

Typical Use Cases

  • Quantifying the average relative error between model and observations as a percentage, emphasizing larger errors.
  • Used in time series forecasting, regression, and model evaluation for percentage-based error assessment.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute RMSPE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Root mean square percentage error (in percent).

Examples

import numpy as np from monet_stats.error_metrics import RMSPE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) RMSPE(obs, mod) 50.0

Source code in src/monet_stats/error_metrics.py 
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def RMSPE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Root Mean Square Percentage Error (RMSPE).

    Typical Use Cases
    -----------------
    - Quantifying the average relative error between model and observations as
      a percentage, emphasizing larger errors.
    - Used in time series forecasting, regression, and model evaluation for
      percentage-based error assessment.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute RMSPE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Root mean square percentage error (in percent).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import RMSPE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> RMSPE(obs, mod)
    50.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = (100 * ((mod - obs) / obs) ** 2).mean(dim=dim, keep_attrs=True) ** 0.5
        return _update_history(result, "RMSPE")
    else:
        result = 100 * np.ma.sqrt(np.ma.mean(((mod - obs) / obs) ** 2, axis=axis))
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

RMdn(obs, mod, axis=None)

Root Median Error (RMdn) - Root of median squared error.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Root of median squared error (observation units). Returns 0.0 for perfect agreement.

Source code in src/monet_stats/error_metrics.py 
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def RMdn(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Root Median Error (RMdn) - Root of median squared error.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Root of median squared error (observation units).
        Returns 0.0 for perfect agreement.
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff_sq = (obs - mod) ** 2
        if hasattr(diff_sq.data, "chunks"):
            dims_to_chunk = dim if isinstance(dim, (list, tuple)) else [dim]
            diff_sq = diff_sq.chunk({d: -1 for d in dims_to_chunk if d in diff_sq.dims})
        result = np.sqrt(diff_sq.quantile(q=0.5, dim=dim, keep_attrs=True).drop_vars("quantile", errors="ignore"))
        return _update_history(result, "RMdn")
    else:
        squared_errors = (np.subtract(obs, mod)) ** 2
        result = np.sqrt(np.median(squared_errors, axis=axis))
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

STDO(obs, mod, axis=None)

Standard deviation of Observation Errors (obs - mod).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the standard deviation. If None, computes over all axes.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Standard deviation of (observation - model) errors. Returns 0.0 for perfect agreement.

Examples

import numpy as np from monet_stats.error_metrics import STDO obs = np.array([1.0, 2.0, 3.0]) mod = np.array([1.1, 1.9, 3.2]) STDO(obs, mod) 0.1247219128924647

Source code in src/monet_stats/error_metrics.py 
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def STDO(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Standard deviation of Observation Errors (obs - mod).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the standard deviation.
        If None, computes over all axes.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Standard deviation of (observation - model) errors.
        Returns 0.0 for perfect agreement.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import STDO
    >>> obs = np.array([1.0, 2.0, 3.0])
    >>> mod = np.array([1.1, 1.9, 3.2])
    >>> STDO(obs, mod)
    0.1247219128924647
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        errors = obs - mod
        dim = _resolve_axis_to_dim(obs, axis)
        result = errors.std(dim=dim, keep_attrs=True)
        return _update_history(result, "STDO")

    # Fallback to numpy-compatible logic
    errors = np.subtract(obs, mod)
    result = np.ma.std(np.ma.masked_invalid(errors), axis=axis)
    return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

STDP(obs, mod, axis=None)

Standard deviation of Prediction Errors (mod - obs).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the standard deviation. If None, computes over all axes.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Standard deviation of (model - observation) errors. Returns 0.0 for perfect agreement.

Examples

import numpy as np from monet_stats.error_metrics import STDP obs = np.array([1.0, 2.0, 3.0]) mod = np.array([1.1, 1.9, 3.2]) STDP(obs, mod) 0.1247219128924647

Source code in src/monet_stats/error_metrics.py 
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def STDP(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Standard deviation of Prediction Errors (mod - obs).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the standard deviation.
        If None, computes over all axes.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Standard deviation of (model - observation) errors.
        Returns 0.0 for perfect agreement.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import STDP
    >>> obs = np.array([1.0, 2.0, 3.0])
    >>> mod = np.array([1.1, 1.9, 3.2])
    >>> STDP(obs, mod)
    0.1247219128924647
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        errors = mod - obs
        dim = _resolve_axis_to_dim(obs, axis)
        result = errors.std(dim=dim, keep_attrs=True)
        return _update_history(result, "STDP")

    # Fallback to numpy-compatible logic
    errors = np.subtract(mod, obs)
    result = np.ma.std(np.ma.masked_invalid(errors), axis=axis)
    return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

VOLUMETRIC_ERROR(obs, mod, axis=None)

Volumetric Error Metric.

Typical Use Cases

  • Quantifying the volume difference between observed and modeled features.
  • Used in hydrology for flood extent verification.
  • Applied in meteorology for precipitation volume verification.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute volumetric error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Volumetric error metric.

Examples

import numpy as np from monet_stats.error_metrics import VOLUMETRIC_ERROR obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) VOLUMETRIC_ERROR(obs, mod) 0.2

Source code in src/monet_stats/error_metrics.py 
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def VOLUMETRIC_ERROR(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Volumetric Error Metric.

    Typical Use Cases
    -----------------
    - Quantifying the volume difference between observed and modeled features.
    - Used in hydrology for flood extent verification.
    - Applied in meteorology for precipitation volume verification.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute volumetric error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Volumetric error metric.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import VOLUMETRIC_ERROR
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> VOLUMETRIC_ERROR(obs, mod)
    0.2
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        obs_sum = obs.sum(dim=dim)
        mod_sum = mod.sum(dim=dim)
        result = abs(mod_sum - obs_sum) / abs(obs_sum)
        return _update_history(result, "VOLUMETRIC_ERROR")
    else:
        obs_sum = np.sum(obs, axis=axis)
        mod_sum = np.sum(mod, axis=axis)
        result = np.abs(mod_sum - obs_sum) / np.abs(obs_sum)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

WDMB(obs, mod, axis=None)

Wind Direction Mean Bias (WDMB).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed wind direction values (degrees). mod : numpy.ndarray or xarray.DataArray Model predicted wind direction values (degrees). axis : int, str, or iterable of such, optional Axis or dimension along which to compute the mean bias.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean wind direction bias (degrees).

Source code in src/monet_stats/error_metrics.py 
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def WDMB(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Wind Direction Mean Bias (WDMB).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed wind direction values (degrees).
    mod : numpy.ndarray or xarray.DataArray
        Model predicted wind direction values (degrees).
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the mean bias.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean wind direction bias (degrees).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = circlebias(mod - obs).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "WDMB")
    else:
        result = np.ma.mean(circlebias(np.subtract(mod, obs)), axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

WDMdnB(obs, mod, axis=None)

Wind Direction Median Bias (WDMdnB).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed wind direction values (degrees). mod : numpy.ndarray or xarray.DataArray Model predicted wind direction values (degrees). axis : int, str, or iterable of such, optional Axis or dimension along which to compute the median bias.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Median wind direction bias (degrees).

Source code in src/monet_stats/error_metrics.py 
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def WDMdnB(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Wind Direction Median Bias (WDMdnB).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed wind direction values (degrees).
    mod : numpy.ndarray or xarray.DataArray
        Model predicted wind direction values (degrees).
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the median bias.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Median wind direction bias (degrees).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff = circlebias(mod - obs)
        if hasattr(diff.data, "chunks"):
            dims_to_chunk = dim if isinstance(dim, (list, tuple)) else [dim]
            diff = diff.chunk({d: -1 for d in dims_to_chunk if d in diff.dims})
        result = diff.quantile(q=0.5, dim=dim, keep_attrs=True).drop_vars("quantile", errors="ignore")
        return _update_history(result, "WDMdnB")
    else:
        result = np.ma.median(circlebias(np.subtract(mod, obs)), axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

bias_fraction(obs, mod, axis=None)

Bias Fraction (BF).

Quantifies the fraction of total error that is due to systematic bias.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute bias fraction.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Bias fraction (unitless, 0-1).

Source code in src/monet_stats/error_metrics.py 
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def bias_fraction(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Bias Fraction (BF).

    Quantifies the fraction of total error that is due to systematic bias.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute bias fraction.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Bias fraction (unitless, 0-1).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        bias = (mod - obs).mean(dim=dim)
        total_error = np.sqrt(((mod - obs) ** 2).mean(dim=dim, keep_attrs=True))
        # Avoid division by zero
        result = xr.where(total_error == 0, 0, (bias**2) / (total_error**2))
        return _update_history(result, "bias_fraction")
    else:
        bias = np.mean(np.subtract(mod, obs), axis=axis)
        total_error = np.sqrt(np.mean((np.subtract(mod, obs)) ** 2, axis=axis))
        # Avoid division by zero
        result = np.where(total_error == 0, 0, (bias**2) / (total_error**2))
        return result.item() if np.ndim(result) == 0 else result

sMAPE(obs, mod, axis=None)

Symmetric Mean Absolute Percentage Error (sMAPE).

Typical Use Cases

  • Quantifying the average relative error between model and observations, normalized by their mean.
  • Used in time series forecasting, regression, and model evaluation for percentage-based error assessment.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute sMAPE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Symmetric mean absolute percentage error (in percent).

Examples

import numpy as np from monet_stats.error_metrics import sMAPE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) sMAPE(obs, mod) 28.57142857142857

Source code in src/monet_stats/error_metrics.py 
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def sMAPE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Symmetric Mean Absolute Percentage Error (sMAPE).

    Typical Use Cases
    -----------------
    - Quantifying the average relative error between model and observations,
      normalized by their mean.
    - Used in time series forecasting, regression, and model evaluation for
      percentage-based error assessment.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute sMAPE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Symmetric mean absolute percentage error (in percent).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import sMAPE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> sMAPE(obs, mod)
    28.57142857142857
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = (200 * abs(mod - obs) / (abs(mod) + abs(obs))).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "sMAPE")
    else:
        result = (200 * np.ma.abs(np.subtract(mod, obs)) / (np.ma.abs(mod) + np.ma.abs(obs))).mean(axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

Efficiency Metrics

Efficiency Metrics for Model Evaluation (Aero Protocol Compliant).

KGE(obs, mod, axis=None)

Kling-Gupta Efficiency (KGE).

Typical Use Cases

  • Quantifying the overall agreement between model and observations, combining correlation, bias, and variability.
  • Used in hydrology, meteorology, and environmental model evaluation.

Typical Values and Range

  • Range: -∞ to 1
  • 1: Perfect agreement between model and observations
  • 0: Moderate skill
  • Negative values: Poor skill

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis along which to compute KGE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Kling-Gupta efficiency (unitless, -∞ to 1).

Examples

import numpy as np from monet_stats.correlation_metrics import KGE obs = np.array([1, 2, 3]) mod = np.array([1.1, 1.9, 3.2]) KGE(obs, mod) 0.8988771192996924

Source code in src/monet_stats/correlation_metrics.py 
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def KGE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Kling-Gupta Efficiency (KGE).

    Typical Use Cases
    -----------------
    - Quantifying the overall agreement between model and observations,
      combining correlation, bias, and variability.
    - Used in hydrology, meteorology, and environmental model evaluation.

    Typical Values and Range
    ------------------------
    - Range: -∞ to 1
    - 1: Perfect agreement between model and observations
    - 0: Moderate skill
    - Negative values: Poor skill

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis along which to compute KGE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Kling-Gupta efficiency (unitless, -∞ to 1).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.correlation_metrics import KGE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([1.1, 1.9, 3.2])
    >>> KGE(obs, mod)
    0.8988771192996924
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Handle axis vs dim
        if axis is not None:
            if isinstance(axis, int):
                dim = obs.dims[axis]
            elif isinstance(axis, (list, tuple)):
                dim = [obs.dims[d] if isinstance(d, int) else d for d in axis]
            else:
                dim = axis
        else:
            dim = obs.dims

        r = xr.corr(obs, mod, dim=dim)
        alpha = mod.std(dim=dim) / obs.std(dim=dim)
        beta = mod.mean(dim=dim) / obs.mean(dim=dim)
        result = 1.0 - ((r - 1.0) ** 2 + (alpha - 1.0) ** 2 + (beta - 1.0) ** 2) ** 0.5
        return _update_history(result, "KGE")
    else:
        if axis is None:
            from scipy.stats import pearsonr

            obsc, modc = matchedcompressed(obs, mod)
            if len(obsc) < 2:
                r = 0.0
            else:
                r, _ = pearsonr(obsc, modc)
        else:
            # Manual vectorized correlation for numpy with axis
            obs_mean = np.nanmean(obs, axis=axis, keepdims=True)
            mod_mean = np.nanmean(mod, axis=axis, keepdims=True)
            obs_std = obs - obs_mean
            mod_std = mod - mod_mean
            num = np.nansum(obs_std * mod_std, axis=axis)
            den = np.sqrt(np.nansum(obs_std**2, axis=axis) * np.nansum(mod_std**2, axis=axis))
            with np.errstate(divide="ignore", invalid="ignore"):
                r = num / den
                r = np.where(np.isnan(r), 0.0, r)

        alpha = np.ma.std(mod, axis=axis) / np.ma.std(obs, axis=axis)
        beta = np.ma.mean(mod, axis=axis) / np.ma.mean(obs, axis=axis)
        result = 1.0 - ((r - 1.0) ** 2 + (alpha - 1.0) ** 2 + (beta - 1.0) ** 2) ** 0.5
        return result.item() if np.ndim(result) == 0 else result

MAE(obs, mod, axis=None)

Mean Absolute Error (MAE).

Typical Use Cases

  • Quantifying the average magnitude of errors between model and observations, regardless of direction.
  • Used in model evaluation, forecast verification, and regression analysis.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute MAE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean absolute error.

Examples

import numpy as np from monet_stats.error_metrics import MAE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) MAE(obs, mod) 0.6666666666666666

Source code in src/monet_stats/error_metrics.py 
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def MAE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Absolute Error (MAE).

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of errors between model and observations,
      regardless of direction.
    - Used in model evaluation, forecast verification, and regression analysis.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute MAE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean absolute error.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MAE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> MAE(obs, mod)
    0.6666666666666666
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = abs(mod - obs).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "MAE")
    else:
        result = np.ma.abs(np.subtract(mod, obs)).mean(axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MAPE(obs, mod, axis=None)

Mean Absolute Percentage Error (MAPE).

Typical Use Cases

  • Quantifying the average relative error between model and observations as a percentage.
  • Used in time series forecasting, regression, and model evaluation for percentage-based error assessment.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute MAPE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean absolute percentage error (in percent).

Examples

import numpy as np from monet_stats.error_metrics import MAPE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) MAPE(obs, mod) 50.0

Source code in src/monet_stats/error_metrics.py 
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def MAPE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Absolute Percentage Error (MAPE).

    Typical Use Cases
    -----------------
    - Quantifying the average relative error between model and observations
      as a percentage.
    - Used in time series forecasting, regression, and model evaluation for
      percentage-based error assessment.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute MAPE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean absolute percentage error (in percent).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MAPE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> MAPE(obs, mod)
    50.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = (100 * abs(mod - obs) / abs(obs)).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "MAPE")
    else:
        result = (100 * np.ma.abs(np.subtract(mod, obs)) / np.ma.abs(obs)).mean(axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MASE(obs, mod, axis=None)

Mean Absolute Scaled Error (MASE).

Typical Use Cases

  • Quantifying model error relative to the error of a simple baseline model (e.g., naive forecast).
  • Used in time series forecasting and model evaluation.
  • Provides scale-independent comparison across different datasets.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model or predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute MASE.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean absolute scaled error (unitless).

Examples

import numpy as np from monet_stats.error_metrics import MASE obs = np.array([1, 2, 3, 4]) mod = np.array([1.1, 2.1, 3.1, 4.1]) MASE(obs, mod) 0.1

Source code in src/monet_stats/error_metrics.py 
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def MASE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Absolute Scaled Error (MASE).

    Typical Use Cases
    -----------------
    - Quantifying model error relative to the error of a simple baseline model
      (e.g., naive forecast).
    - Used in time series forecasting and model evaluation.
    - Provides scale-independent comparison across different datasets.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model or predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute MASE.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean absolute scaled error (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MASE
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.1, 2.1, 3.1, 4.1])
    >>> MASE(obs, mod)
    0.1
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)

        # Calculate naive forecast error (using previous observation)
        if "time" in obs.dims:
            naive_error = abs(obs - obs.shift(time=1)).mean(dim=dim, skipna=True)
        else:
            # Fallback if time is not named 'time'
            naive_error = abs(obs - obs.shift({obs.dims[0]: 1})).mean(dim=dim, skipna=True)

        model_error = abs(mod - obs).mean(dim=dim, keep_attrs=True)
        result = model_error / naive_error
        return _update_history(result, "MASE")
    else:
        # Calculate naive forecast error (using previous observation)
        if axis is not None:
            naive_diff = np.diff(obs, axis=axis)
            naive_error = np.mean(np.abs(naive_diff), axis=axis)
        else:
            naive_diff = np.diff(obs)
            naive_error = np.mean(np.abs(naive_diff))
        model_error = np.mean(np.abs(np.subtract(mod, obs)), axis=axis)
        result = model_error / naive_error
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MSE(obs, mod, axis=None)

Mean Squared Error (MSE).

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the error.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Mean squared error.

Examples

import numpy as np from monet_stats.error_metrics import MSE obs = np.array([1, 2, 3]) mod = np.array([2, 2, 4]) MSE(obs, mod) 0.6666666666666666

Source code in src/monet_stats/error_metrics.py 
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def MSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Mean Squared Error (MSE).

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the error.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Mean squared error.

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.error_metrics import MSE
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([2, 2, 4])
    >>> MSE(obs, mod)
    0.6666666666666666
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        result = ((mod - obs) ** 2).mean(dim=dim, keep_attrs=True)
        return _update_history(result, "MSE")
    else:
        result = np.ma.mean((np.subtract(mod, obs)) ** 2, axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NSE(obs, mod, axis=None)

Nash-Sutcliffe Efficiency (NSE).

Typical Use Cases

  • Quantifying the predictive power of hydrological models relative to the mean of observations.
  • Used in hydrology, meteorology, and environmental model evaluation.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Nash-Sutcliffe efficiency (unitless).

Examples

import numpy as np from monet_stats.efficiency_metrics import NSE obs = np.array([1, 2, 3, 4]) mod = np.array([1.1, 2.1, 2.9, 4.1]) NSE(obs, mod) 0.992

Source code in src/monet_stats/efficiency_metrics.py 
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def NSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Nash-Sutcliffe Efficiency (NSE).

    Typical Use Cases
    -----------------
    - Quantifying the predictive power of hydrological models relative to the
      mean of observations.
    - Used in hydrology, meteorology, and environmental model evaluation.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Nash-Sutcliffe efficiency (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.efficiency_metrics import NSE
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.1, 2.1, 2.9, 4.1])
    >>> NSE(obs, mod)
    0.992
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)

        obs_mean = obs.mean(dim=dim)
        numerator = ((obs - mod) ** 2).sum(dim=dim)
        denominator = ((obs - obs_mean) ** 2).sum(dim=dim)

        # Handle division by zero
        result = 1.0 - (numerator / denominator)
        result = xr.where((numerator == 0) & (denominator == 0), 1.0, result)
        result = xr.where((numerator != 0) & (denominator == 0), -np.inf, result)

        return _update_history(result, "NSE")
    else:
        obs_mean = np.nanmean(obs, axis=axis, keepdims=True)
        numerator = np.nansum((obs - mod) ** 2, axis=axis)
        denominator = np.nansum((obs - obs_mean) ** 2, axis=axis)

        with np.errstate(divide="ignore", invalid="ignore"):
            result = 1.0 - (numerator / denominator)
            result = np.where((numerator == 0) & (denominator == 0), 1.0, result)
            result = np.where((numerator != 0) & (denominator == 0), -np.inf, result)
        return result.item() if np.ndim(result) == 0 else result

NSElog(obs, mod, axis=None)

Log Nash-Sutcliffe Efficiency (NSElog).

Calculates NSE on logarithmic-transformed data to focus on lower values.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values (positive values only). mod : numpy.ndarray or xarray.DataArray Model predicted values (positive values only). axis : int, str, or iterable of such, optional Axis or dimension along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Log Nash-Sutcliffe efficiency (unitless).

Examples

import numpy as np from monet_stats.efficiency_metrics import NSElog obs = np.array([1, 10, 100]) mod = np.array([1.1, 9.0, 110]) NSElog(obs, mod) 0.988

Source code in src/monet_stats/efficiency_metrics.py 
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def NSElog(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Log Nash-Sutcliffe Efficiency (NSElog).

    Calculates NSE on logarithmic-transformed data to focus on lower values.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values (positive values only).
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values (positive values only).
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Log Nash-Sutcliffe efficiency (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.efficiency_metrics import NSElog
    >>> obs = np.array([1, 10, 100])
    >>> mod = np.array([1.1, 9.0, 110])
    >>> NSElog(obs, mod)
    0.988
    """
    epsilon = 1e-6
    # Avoid double history update by using .data or being careful
    # We apply log first, then call NSE. NSE will handle history if it's a DataArray.
    obs_log = np.log(obs + epsilon)
    mod_log = np.log(mod + epsilon)
    result = NSE(obs_log, mod_log, axis=axis)

    # If it's a DataArray, NSE already updated history to "NSE".
    # We might want to "fix" it to "NSElog".
    if isinstance(result, xr.DataArray):
        # Update history specifically for NSElog
        return _update_history(result, "NSElog")
    return result

NSEm(obs, mod, axis=None)

Nash-Sutcliffe Efficiency (NSE) - robust to masked arrays.

This function is a wrapper for NSE that explicitly handles masked data and NaNs.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Nash-Sutcliffe efficiency (unitless).

Examples

import numpy as np from monet_stats.efficiency_metrics import NSEm obs = np.array([1, 2, np.nan, 4]) mod = np.array([1.1, 2.1, 3.0, 4.1]) NSEm(obs, mod) 0.995

Source code in src/monet_stats/efficiency_metrics.py 
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def NSEm(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Nash-Sutcliffe Efficiency (NSE) - robust to masked arrays.

    This function is a wrapper for NSE that explicitly handles masked data and NaNs.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Nash-Sutcliffe efficiency (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.efficiency_metrics import NSEm
    >>> obs = np.array([1, 2, np.nan, 4])
    >>> mod = np.array([1.1, 2.1, 3.0, 4.1])
    >>> NSEm(obs, mod)
    0.995
    """
    # Standard NSE implementation already handles NaNs if using nan-aware functions
    res = NSE(obs, mod, axis=axis)
    if isinstance(res, xr.DataArray):
        return _update_history(res, "NSEm")
    return res

PC(obs, mod, axis=None, tolerance=0.1)

Percent of Correct (PC).

Calculates the percentage of model predictions that are within a specified tolerance of the observations.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the statistic. tolerance : float, optional Fraction of observed value used as tolerance (default 0.1).

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Percent of correct predictions (0-100%).

Examples

import numpy as np from monet_stats.efficiency_metrics import PC obs = np.array([1, 2, 3, 4]) mod = np.array([1.05, 2.5, 2.95, 4.05]) PC(obs, mod) 75.0

Source code in src/monet_stats/efficiency_metrics.py 
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def PC(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
    tolerance: float = 0.1,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Percent of Correct (PC).

    Calculates the percentage of model predictions that are within a specified
    tolerance of the observations.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the statistic.
    tolerance : float, optional
        Fraction of observed value used as tolerance (default 0.1).

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Percent of correct predictions (0-100%).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.efficiency_metrics import PC
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.05, 2.5, 2.95, 4.05])
    >>> PC(obs, mod)
    75.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)

        tol = tolerance * abs(obs)
        correct = abs(obs - mod) <= tol
        result = (correct.sum(dim=dim) / correct.count(dim=dim)) * 100.0

        return _update_history(result, "PC")
    else:
        obs = np.asanyarray(obs)
        mod = np.asanyarray(mod)
        mask = np.isnan(obs) | np.isnan(mod)

        tol = tolerance * np.abs(obs)
        correct = np.abs(obs - mod) <= tol

        total = np.sum(~mask, axis=axis)
        correct_sum = np.sum(correct & ~mask, axis=axis)

        with np.errstate(divide="ignore", invalid="ignore"):
            result = (correct_sum / total) * 100.0
            result = np.where(total == 0, np.nan, result)

        return result.item() if np.ndim(result) == 0 else result

mNSE(obs, mod, axis=None)

Modified Nash-Sutcliffe Efficiency (mNSE).

Uses absolute differences instead of squared differences.

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values. mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Modified Nash-Sutcliffe efficiency (unitless).

Examples

import numpy as np from monet_stats.efficiency_metrics import mNSE obs = np.array([1, 2, 3, 4]) mod = np.array([1.1, 2.1, 2.9, 4.1]) mNSE(obs, mod) 0.92

Source code in src/monet_stats/efficiency_metrics.py 
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def mNSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Modified Nash-Sutcliffe Efficiency (mNSE).

    Uses absolute differences instead of squared differences.

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values.
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Modified Nash-Sutcliffe efficiency (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.efficiency_metrics import mNSE
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.1, 2.1, 2.9, 4.1])
    >>> mNSE(obs, mod)
    0.92
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)

        obs_mean = obs.mean(dim=dim)
        numerator = abs(obs - mod).sum(dim=dim)
        denominator = abs(obs - obs_mean).sum(dim=dim)

        result = 1.0 - (numerator / denominator)
        result = xr.where((numerator == 0) & (denominator == 0), 1.0, result)
        result = xr.where((numerator != 0) & (denominator == 0), -np.inf, result)

        return _update_history(result, "mNSE")
    else:
        obs_mean = np.nanmean(obs, axis=axis, keepdims=True)
        numerator = np.nansum(np.abs(obs - mod), axis=axis)
        denominator = np.nansum(np.abs(obs - obs_mean), axis=axis)

        with np.errstate(divide="ignore", invalid="ignore"):
            result = 1.0 - (numerator / denominator)
            result = np.where((numerator == 0) & (denominator == 0), 1.0, result)
            result = np.where((numerator != 0) & (denominator == 0), -np.inf, result)
        return result.item() if np.ndim(result) == 0 else result

rNSE(obs, mod, axis=None)

Relative Nash-Sutcliffe Efficiency (rNSE).

Normalizes errors by the magnitude of observed values. Formula: 1 - [ sum( ((obs - mod)/obs)^2 ) / sum( ((obs - mean)/obs)^2 ) ]

Parameters

obs : numpy.ndarray or xarray.DataArray Observed values (should be non-zero for normalization). mod : numpy.ndarray or xarray.DataArray Model predicted values. axis : int, str, or iterable of such, optional Axis or dimension along which to compute the statistic.

Returns

numpy.number, numpy.ndarray, or xarray.DataArray Relative Nash-Sutcliffe efficiency (unitless).

Examples

import numpy as np from monet_stats.efficiency_metrics import rNSE obs = np.array([1, 2, 3, 4]) mod = np.array([1.1, 2.1, 2.9, 4.1]) rNSE(obs, mod) 0.994261721483555

Source code in src/monet_stats/efficiency_metrics.py 
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def rNSE(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Relative Nash-Sutcliffe Efficiency (rNSE).

    Normalizes errors by the magnitude of observed values.
    Formula: 1 - [ sum( ((obs - mod)/obs)^2 ) / sum( ((obs - mean)/obs)^2 ) ]

    Parameters
    ----------
    obs : numpy.ndarray or xarray.DataArray
        Observed values (should be non-zero for normalization).
    mod : numpy.ndarray or xarray.DataArray
        Model predicted values.
    axis : int, str, or iterable of such, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    numpy.number, numpy.ndarray, or xarray.DataArray
        Relative Nash-Sutcliffe efficiency (unitless).

    Examples
    --------
    >>> import numpy as np
    >>> from monet_stats.efficiency_metrics import rNSE
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([1.1, 2.1, 2.9, 4.1])
    >>> rNSE(obs, mod)
    0.994261721483555
    """
    epsilon = 1e-8
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)

        obs_mean = obs.mean(dim=dim)
        obs_safe = xr.where(abs(obs) < epsilon, epsilon, obs)

        numerator = (((obs - mod) / obs_safe) ** 2).sum(dim=dim)
        denominator = (((obs - obs_mean) / obs_safe) ** 2).sum(dim=dim)

        result = 1.0 - (numerator / denominator)
        result = xr.where((numerator == 0) & (denominator == 0), 1.0, result)
        result = xr.where((numerator != 0) & (denominator == 0), -np.inf, result)

        return _update_history(result, "rNSE")
    else:
        obs_mean = np.nanmean(obs, axis=axis, keepdims=True)
        obs_safe = np.where(np.abs(obs) < epsilon, epsilon, obs)

        with np.errstate(divide="ignore", invalid="ignore"):
            numerator = np.nansum(((obs - mod) / obs_safe) ** 2, axis=axis)
            denominator = np.nansum(((obs - obs_mean) / obs_safe) ** 2, axis=axis)
            result = 1.0 - (numerator / denominator)
            result = np.where((numerator == 0) & (denominator == 0), 1.0, result)
            result = np.where((numerator != 0) & (denominator == 0), -np.inf, result)
        return result.item() if np.ndim(result) == 0 else result

Relative Metrics

Relative/Percentage Metrics for Model Evaluation (Aero Protocol Compliant)

FB(obs, mod, axis=None)

Fractional Bias (%)

Typical Use Cases

  • Quantifying the average bias as a fraction of the sum of model and observed values.
  • Used in air quality and meteorological model evaluation for normalized bias assessment.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Fractional bias (percent).

Source code in src/monet_stats/relative_metrics.py 
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def FB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Fractional Bias (%)

    Typical Use Cases
    -----------------
    - Quantifying the average bias as a fraction of the sum of model and observed values.
    - Used in air quality and meteorological model evaluation for normalized bias assessment.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Fractional bias (percent).

    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = (((mod - obs) / (mod + obs)).mean(dim=dim) * 2.0) * 100.0
        return _update_history(res, "Fractional Bias (FB)")
    else:
        obs_arr = np.asanyarray(obs)
        mod_arr = np.asanyarray(mod)
        res = (np.ma.masked_invalid((mod_arr - obs_arr) / (mod_arr + obs_arr)).mean(axis=axis) * 2.0) * 100.0
        return res.item() if np.ndim(res) == 0 else res

FE(obs, mod, axis=None)

Fractional Error (%)

Typical Use Cases

  • Quantifying the average magnitude of model errors as a fraction of the sum of model and observed values.
  • Used in air quality and meteorological model evaluation for normalized error assessment.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Fractional error (percent).

Source code in src/monet_stats/relative_metrics.py 
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def FE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Fractional Error (%)

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of model errors as a fraction of the sum of model and observed values.
    - Used in air quality and meteorological model evaluation for normalized error assessment.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Fractional error (percent).

    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = (abs(mod - obs) / (mod + obs)).mean(dim=dim) * 2.0 * 100.0
        return _update_history(res, "Fractional Error (FE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        res = (np.ma.mean(np.ma.abs(mod_arr - obs_arr) / (mod_arr + obs_arr), axis=axis)) * 2.0 * 100.0
        return res.item() if np.ndim(res) == 0 else res

ME(obs, mod, axis=None)

Mean Gross Error (model and obs unit). Alias for MAE.

Source code in src/monet_stats/relative_metrics.py 
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def ME(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Mean Gross Error (model and obs unit). Alias for MAE.
    """
    res = MAE(obs, mod, axis=axis)
    if isinstance(res, (xr.DataArray, xr.Dataset)):
        return _update_history(res, "Mean Gross Error (ME)")
    return res

MNPB(obs, mod, paxis, axis=None)

Mean Normalized Peak Bias (%)

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. paxis : int or str Axis or dimension along which to compute the peak (e.g., time or space). axis : int or str or None, optional Axis or dimension along which to compute the mean of normalized peak bias.

Returns

xarray.DataArray or numpy.ndarray or float Mean normalized peak bias (percent).

Source code in src/monet_stats/relative_metrics.py 
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def MNPB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    paxis: Union[int, str, Iterable[Union[int, str]]],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Mean Normalized Peak Bias (%)

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    paxis : int or str
        Axis or dimension along which to compute the peak (e.g., time or space).
    axis : int or str or None, optional
        Axis or dimension along which to compute the mean of normalized peak bias.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Mean normalized peak bias (percent).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        pdim = _resolve_axis_to_dim(obs, paxis)
        _intermediate = (mod.max(dim=pdim) - obs.max(dim=pdim)) / obs.max(dim=pdim)
        mdim = _resolve_axis_to_dim(_intermediate, axis)
        res = _intermediate.mean(dim=mdim) * 100.0
        return _update_history(res, "Mean Normalized Peak Bias (MNPB)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        res = ((np.ma.max(mod_arr, axis=paxis) - np.ma.max(obs_arr, axis=paxis)) / np.ma.max(obs_arr, axis=paxis)).mean(
            axis=axis
        ) * 100.0
        return res.item() if np.ndim(res) == 0 else res

MNPE(obs, mod, paxis, axis=None)

Mean Normalized Peak Error (MNPE, %)

Typical Use Cases

  • Quantifying the average error in peak values between model and observations, normalized by observed peaks.
  • Used in model evaluation for extreme events, such as air quality exceedances or meteorological extremes.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. paxis : int or str Axis or dimension along which to compute the peak (e.g., time or space). axis : int or str or None, optional Axis or dimension along which to compute the mean of normalized peak error.

Returns

xarray.DataArray or numpy.ndarray or float Mean normalized peak error (percent).

Examples

import numpy as np obs = np.array([[1, 2, 3], [2, 3, 4]]) mod = np.array([[2, 2, 2], [2, 2, 5]]) MNPE(obs, mod, paxis=1) 33.33333333333333

Source code in src/monet_stats/relative_metrics.py 
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def MNPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    paxis: Union[int, str, Iterable[Union[int, str]]],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Mean Normalized Peak Error (MNPE, %)

    Typical Use Cases
    -----------------
    - Quantifying the average error in peak values between model and observations, normalized by observed peaks.
    - Used in model evaluation for extreme events, such as air quality exceedances or meteorological extremes.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    paxis : int or str
        Axis or dimension along which to compute the peak (e.g., time or space).
    axis : int or str or None, optional
        Axis or dimension along which to compute the mean of normalized peak error.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Mean normalized peak error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([[1, 2, 3], [2, 3, 4]])
    >>> mod = np.array([[2, 2, 2], [2, 2, 5]])
    >>> MNPE(obs, mod, paxis=1)
    33.33333333333333
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        pdim = _resolve_axis_to_dim(obs, paxis)
        _intermediate = abs(mod.max(dim=pdim) - obs.max(dim=pdim)) / obs.max(dim=pdim)
        mdim = _resolve_axis_to_dim(_intermediate, axis)
        res = _intermediate.mean(dim=mdim) * 100.0
        return _update_history(res, "Mean Normalized Peak Error (MNPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        res = (
            np.ma.abs(np.ma.max(mod_arr, axis=paxis) - np.ma.max(obs_arr, axis=paxis)) / np.ma.max(obs_arr, axis=paxis)
        ).mean(axis=axis) * 100.0
        return res.item() if np.ndim(res) == 0 else res

MPE(obs, mod, axis=None)

Mean Peak Error (%)

Typical Use Cases

  • Quantifying the average error in peak values between model and observations.
  • Used in model evaluation for extreme events, such as air quality exceedances or meteorological extremes.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the mean of peak error.

Returns

xarray.DataArray or numpy.ndarray or float Mean peak error (percent).

Examples

import numpy as np obs = np.array([[1, 2, 3], [2, 3, 4]]) mod = np.array([[2, 2, 2], [2, 2, 5]]) MPE(obs, mod) 33.33333333

Source code in src/monet_stats/relative_metrics.py 
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def MPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Mean Peak Error (%)

    Typical Use Cases
    -----------------
    - Quantifying the average error in peak values between model and observations.
    - Used in model evaluation for extreme events, such as air quality exceedances
      or meteorological extremes.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the mean of peak error.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Mean peak error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([[1, 2, 3], [2, 3, 4]])
    >>> mod = np.array([[2, 2, 2], [2, 2, 5]])
    >>> MPE(obs, mod)
    33.33333333
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = (abs(mod.max(dim=dim) - obs.max(dim=dim)) / obs.max(dim=dim)).mean() * 100.0
        return _update_history(res, "Mean Peak Error (MPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        res = (
            np.ma.abs(np.ma.max(mod_arr, axis=axis) - np.ma.max(obs_arr, axis=axis)) / np.ma.max(obs_arr, axis=axis)
        ).mean() * 100.0
        return res.item() if np.ndim(res) == 0 else res

MdnE(obs, mod, axis=None)

Median Gross Error (model and obs unit). Alias for MedAE.

Source code in src/monet_stats/relative_metrics.py 
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def MdnE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Median Gross Error (model and obs unit). Alias for MedAE.
    """
    res = MedAE(obs, mod, axis=axis)
    if isinstance(res, (xr.DataArray, xr.Dataset)):
        return _update_history(res, "Median Gross Error (MdnE)")
    return res

MdnNPB(obs, mod, paxis, axis=None)

Median Normalized Peak Bias (%)

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. paxis : int or str Axis or dimension along which to compute the peak (e.g., time or space). axis : int or str or None, optional Axis or dimension along which to compute the median of normalized peak bias.

Returns

xarray.DataArray or numpy.ndarray or float Median normalized peak bias (percent).

Source code in src/monet_stats/relative_metrics.py 
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def MdnNPB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    paxis: Union[int, str, Iterable[Union[int, str]]],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Median Normalized Peak Bias (%)

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    paxis : int or str
        Axis or dimension along which to compute the peak (e.g., time or space).
    axis : int or str or None, optional
        Axis or dimension along which to compute the median of normalized peak bias.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Median normalized peak bias (percent).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        pdim = _resolve_axis_to_dim(obs, paxis)
        _intermediate = (mod.max(dim=pdim) - obs.max(dim=pdim)) / obs.max(dim=pdim)
        mdim = _resolve_axis_to_dim(_intermediate, axis)
        if mdim is None:
            mdim = list(_intermediate.dims)
        if hasattr(_intermediate.data, "chunks"):
            dims_to_chunk = [mdim] if isinstance(mdim, str) else list(mdim)
            _intermediate = _intermediate.chunk({d: -1 for d in dims_to_chunk})
        res = _intermediate.quantile(q=0.5, dim=mdim).drop_vars("quantile", errors="ignore") * 100.0
        return _update_history(res, "Median Normalized Peak Bias (MdnNPB)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        result = (
            np.ma.median(
                ((np.ma.max(mod_arr, axis=paxis) - np.ma.max(obs_arr, axis=paxis)) / np.ma.max(obs_arr, axis=paxis)),
                axis=axis,
            )
            * 100.0
        )
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MdnNPE(obs, mod, paxis, axis=None)

Median Normalized Peak Error (MdnNPE, %)

Typical Use Cases

  • Evaluating the typical error in peak values between model and observations, normalized by observed peaks, robust to outliers.
  • Used in robust model evaluation for extreme events, such as air quality exceedances or meteorological extremes.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. paxis : int or str Axis or dimension along which to compute the peak (e.g., time or space). axis : int or str or None, optional Axis or dimension along which to compute the median of normalized peak error.

Returns

xarray.DataArray or numpy.ndarray or float Median normalized peak error (percent).

Examples

import numpy as np obs = np.array([[1, 2, 3], [2, 3, 4]]) mod = np.array([[2, 2, 2], [2, 2, 5]]) MdnNPE(obs, mod, paxis=1) 33.33333333333333

Source code in src/monet_stats/relative_metrics.py 
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def MdnNPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    paxis: Union[int, str, Iterable[Union[int, str]]],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Median Normalized Peak Error (MdnNPE, %)

    Typical Use Cases
    -----------------
    - Evaluating the typical error in peak values between model and observations,
      normalized by observed peaks, robust to outliers.
    - Used in robust model evaluation for extreme events, such as air quality exceedances
      or meteorological extremes.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    paxis : int or str
        Axis or dimension along which to compute the peak (e.g., time or space).
    axis : int or str or None, optional
        Axis or dimension along which to compute the median of normalized peak error.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Median normalized peak error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([[1, 2, 3], [2, 3, 4]])
    >>> mod = np.array([[2, 2, 2], [2, 2, 5]])
    >>> MdnNPE(obs, mod, paxis=1)
    33.33333333333333
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        pdim = _resolve_axis_to_dim(obs, paxis)
        _intermediate = abs(mod.max(dim=pdim) - obs.max(dim=pdim)) / obs.max(dim=pdim)
        mdim = _resolve_axis_to_dim(_intermediate, axis)
        if mdim is None:
            mdim = list(_intermediate.dims)
        if hasattr(_intermediate.data, "chunks"):
            _intermediate = _intermediate.chunk({d: -1 for d in (mdim if isinstance(mdim, list) else [mdim])})
        res = _intermediate.quantile(q=0.5, dim=mdim).drop_vars("quantile", errors="ignore") * 100.0
        return _update_history(res, "Median Normalized Peak Error (MdnNPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        result = (
            np.ma.median(
                (
                    np.ma.abs(np.ma.max(mod_arr, axis=paxis) - np.ma.max(obs_arr, axis=paxis))
                    / np.ma.max(obs_arr, axis=paxis)
                ),
                axis=axis,
            )
            * 100.0
        )
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

MdnPE(obs, mod, axis=None)

Median Peak Error (%)

Typical Use Cases

  • Evaluating the typical error in peak values between model and observations, robust to outliers.
  • Used in robust model evaluation for extreme events, such as air quality exceedances or meteorological extremes.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the median of peak error.

Returns

xarray.DataArray or numpy.ndarray or float Median peak error (percent).

Examples

import numpy as np obs = np.array([[1, 2, 3], [2, 3, 4]]) mod = np.array([[2, 2, 2], [2, 2, 5]]) MdnPE(obs, mod) 33.333333333

Source code in src/monet_stats/relative_metrics.py 
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def MdnPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Median Peak Error (%)

    Typical Use Cases
    -----------------
    - Evaluating the typical error in peak values between model and observations,
      robust to outliers.
    - Used in robust model evaluation for extreme events, such as air quality
      exceedances or meteorological extremes.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the median of peak error.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Median peak error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([[1, 2, 3], [2, 3, 4]])
    >>> mod = np.array([[2, 2, 2], [2, 2, 5]])
    >>> MdnPE(obs, mod)
    33.333333333
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        _intermediate = abs(mod.max(dim=dim) - obs.max(dim=dim)) / obs.max(dim=dim)
        mdim = list(_intermediate.dims)
        if hasattr(_intermediate.data, "chunks"):
            _intermediate = _intermediate.chunk({d: -1 for d in mdim})
        res = _intermediate.quantile(q=0.5, dim=mdim).drop_vars("quantile", errors="ignore") * 100.0
        return _update_history(res, "Median Peak Error (MdnPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        result = (
            np.ma.median(
                (
                    np.ma.abs(np.ma.max(mod_arr, axis=axis) - np.ma.max(obs_arr, axis=axis))
                    / np.ma.max(obs_arr, axis=axis)
                ),
                axis=axis,
            )
            * 100.0
        )
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NMB(obs, mod, axis=None)

Normalized Mean Bias (%)

Typical Use Cases

  • Comparing model bias across variables or datasets with different units or scales.
  • Common in regulatory and operational air quality model performance reports.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Normalized mean bias (percent).

Examples

import numpy as np obs = np.array([1, 2, 3]) mod = np.array([1.1, 2.2, 3.3]) NMB(obs, mod) 10.0

Source code in src/monet_stats/relative_metrics.py 
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def NMB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Mean Bias (%)

    Typical Use Cases
    -----------------
    - Comparing model bias across variables or datasets with different units or scales.
    - Common in regulatory and operational air quality model performance reports.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized mean bias (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3])
    >>> mod = np.array([1.1, 2.2, 3.3])
    >>> NMB(obs, mod)
    10.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = (mod - obs).sum(dim=dim) / obs.sum(dim=dim) * 100.0
        return _update_history(res, "Normalized Mean Bias (NMB)")
    else:
        obs_arr = np.asanyarray(obs)
        mod_arr = np.asanyarray(mod)
        res = (mod_arr - obs_arr).sum(axis=axis) / obs_arr.sum(axis=axis) * 100.0
        return res.item() if np.ndim(res) == 0 else res

NMB_ABS(obs, mod, axis=None)

Normalized Mean Bias - Absolute of the denominator (%)

Typical Use Cases

  • Quantifying normalized mean bias when the denominator (sum of observations) may be negative or zero.
  • Used for robust model evaluation in cases with possible sign changes in the observed data sum.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Normalized mean bias with absolute denominator (percent).

Source code in src/monet_stats/relative_metrics.py 
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def NMB_ABS(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Mean Bias - Absolute of the denominator (%)

    Typical Use Cases
    -----------------
    - Quantifying normalized mean bias when the denominator (sum of observations) may be negative or zero.
    - Used for robust model evaluation in cases with possible sign changes in the observed data sum.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized mean bias with absolute denominator (percent).
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = (mod - obs).sum(dim=dim) / abs(obs.sum(dim=dim)) * 100.0
        return _update_history(res, "Normalized Mean Bias Absolute (NMB_ABS)")
    else:
        obs_arr = np.asanyarray(obs)
        mod_arr = np.asanyarray(mod)
        res = (mod_arr - obs_arr).sum(axis=axis) / np.abs(obs_arr.sum(axis=axis)) * 100.0
        return res.item() if np.ndim(res) == 0 else res

NME(obs, mod, axis=None)

Normalized Mean Error (%)

Typical Use Cases

  • Quantifying the average magnitude of model errors relative to observations.
  • Used for model evaluation and comparison across variables or datasets with different scales.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Normalized mean error (percent).

Examples

import numpy as np obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) NME(obs, mod) 37.5

Source code in src/monet_stats/relative_metrics.py 
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def NME(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Mean Error (%)

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of model errors relative to observations.
    - Used for model evaluation and comparison across variables or datasets with different scales.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized mean error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> NME(obs, mod)
    37.5
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = (abs(mod - obs).sum(dim=dim) / obs.sum(dim=dim)) * 100
        return _update_history(res, "Normalized Mean Error (NME)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        res = (np.ma.abs(mod_arr - obs_arr).sum(axis=axis) / obs_arr.sum(axis=axis)) * 100
        return res.item() if np.ndim(res) == 0 else res

NME_m(obs, mod, axis=None)

Normalized Mean Error (%) (avoid single block error in np.ma)

Typical Use Cases

  • Quantifying the average magnitude of model errors relative to observations, robust to masked arrays.
  • Used for model evaluation when data may contain masked or missing values.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Normalized mean error (percent).

Examples

import numpy as np obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) NME_m(obs, mod) 37.5

Source code in src/monet_stats/relative_metrics.py 
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def NME_m(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Mean Error (%) (avoid single block error in np.ma)

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of model errors relative to observations, robust to masked arrays.
    - Used for model evaluation when data may contain masked or missing values.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized mean error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> NME_m(obs, mod)
    37.5
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = (abs(mod - obs).sum(dim=dim) / obs.sum(dim=dim)) * 100
        return _update_history(res, "Normalized Mean Error (NME_m)")
    else:
        obs_arr = np.asanyarray(obs)
        mod_arr = np.asanyarray(mod)
        res = (np.abs(mod_arr - obs_arr).sum(axis=axis) / obs_arr.sum(axis=axis)) * 100
        return res.item() if np.ndim(res) == 0 else res

NME_m_ABS(obs, mod, axis=None)

Normalized Mean Error (%) - Absolute of the denominator (avoid single block error in np.ma)

Typical Use Cases

  • Quantifying normalized mean error when the denominator (sum of observations) may be negative or zero, robust to masked arrays.
  • Used for model evaluation with possible sign changes or missing values in observed data.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Normalized mean error with absolute denominator (percent).

Examples

import numpy as np obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) NME_m_ABS(obs, mod) 37.5

Source code in src/monet_stats/relative_metrics.py 
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def NME_m_ABS(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Mean Error (%) - Absolute of the denominator
    (avoid single block error in np.ma)

    Typical Use Cases
    -----------------
    - Quantifying normalized mean error when the denominator (sum of observations)
      may be negative or zero, robust to masked arrays.
    - Used for model evaluation with possible sign changes or missing values in observed data.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized mean error with absolute denominator (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> NME_m_ABS(obs, mod)
    37.5
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = (abs(mod - obs).sum(dim=dim) / abs(obs.sum(dim=dim))) * 100
        return _update_history(res, "Normalized Mean Error Absolute (NME_m_ABS)")
    else:
        obs_arr = np.asanyarray(obs)
        mod_arr = np.asanyarray(mod)
        res = (np.abs(mod_arr - obs_arr).sum(axis=axis) / np.abs(obs_arr.sum(axis=axis))) * 100
        return res.item() if np.ndim(res) == 0 else res

NMPB(obs, mod, paxis, axis=None)

Normalized Mean Peak Bias (NMPB, %)

Typical Use Cases

  • Quantifying the average bias in peak values, normalized by the mean of observed peaks.
  • Used in model evaluation for extreme events, especially when comparing across sites or time periods.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. paxis : int or str Axis or dimension along which to compute the peak (e.g., time or space). axis : int or str or None, optional Axis or dimension along which to compute the mean of normalized peak bias.

Returns

xarray.DataArray or numpy.ndarray or float Normalized mean peak bias (percent).

Examples

import numpy as np obs = np.array([[1, 2, 3], [2, 3, 4]]) mod = np.array([[2, 2, 2], [2, 2, 5]]) NMPB(obs, mod, paxis=1) 33.33333333333333

Source code in src/monet_stats/relative_metrics.py 
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def NMPB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    paxis: Union[int, str, Iterable[Union[int, str]]],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Mean Peak Bias (NMPB, %)

    Typical Use Cases
    -----------------
    - Quantifying the average bias in peak values, normalized by the mean of observed peaks.
    - Used in model evaluation for extreme events, especially when comparing across sites or time periods.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    paxis : int or str
        Axis or dimension along which to compute the peak (e.g., time or space).
    axis : int or str or None, optional
        Axis or dimension along which to compute the mean of normalized peak bias.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized mean peak bias (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([[1, 2, 3], [2, 3, 4]])
    >>> mod = np.array([[2, 2, 2], [2, 2, 5]])
    >>> NMPB(obs, mod, paxis=1)
    33.33333333333333
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        pdim = _resolve_axis_to_dim(obs, paxis)
        _diff_mean = (mod.max(dim=pdim) - obs.max(dim=pdim)).mean(dim=_resolve_axis_to_dim(mod.max(dim=pdim), axis))
        _obs_mean = obs.max(dim=pdim).mean(dim=_resolve_axis_to_dim(obs.max(dim=pdim), axis))
        res = (_diff_mean / _obs_mean) * 100.0
        return _update_history(res, "Normalized Mean Peak Bias (NMPB)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        res = (
            (np.ma.max(mod_arr, axis=paxis) - np.ma.max(obs_arr, axis=paxis)).mean(axis=axis)
            / np.ma.max(obs_arr, axis=paxis).mean(axis=axis)
        ) * 100.0
        return res.item() if np.ndim(res) == 0 else res

NMPE(obs, mod, paxis, axis=None)

Normalized Mean Peak Error (NMPE, %)

Typical Use Cases

  • Quantifying the average error in peak values, normalized by the mean of observed peaks.
  • Used in model evaluation for extreme events, especially when comparing across sites or time periods.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. paxis : int or str Axis or dimension along which to compute the peak (e.g., time or space). axis : int or str or None, optional Axis or dimension along which to compute the mean of normalized peak error.

Returns

xarray.DataArray or numpy.ndarray or float Normalized mean peak error (percent).

Examples

import numpy as np obs = np.array([[1, 2, 3], [2, 3, 4]]) mod = np.array([[2, 2, 2], [2, 2, 5]]) NMPE(obs, mod, paxis=1) 33.33333333333333

Source code in src/monet_stats/relative_metrics.py 
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def NMPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    paxis: Union[int, str, Iterable[Union[int, str]]],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Mean Peak Error (NMPE, %)

    Typical Use Cases
    -----------------
    - Quantifying the average error in peak values, normalized by the mean of observed peaks.
    - Used in model evaluation for extreme events, especially when comparing across sites or time periods.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    paxis : int or str
        Axis or dimension along which to compute the peak (e.g., time or space).
    axis : int or str or None, optional
        Axis or dimension along which to compute the mean of normalized peak error.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized mean peak error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([[1, 2, 3], [2, 3, 4]])
    >>> mod = np.array([[2, 2, 2], [2, 2, 5]])
    >>> NMPE(obs, mod, paxis=1)
    33.33333333333333
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        pdim = _resolve_axis_to_dim(obs, paxis)
        _diff_abs_mean = abs(mod.max(dim=pdim) - obs.max(dim=pdim)).mean(
            dim=_resolve_axis_to_dim(mod.max(dim=pdim), axis)
        )
        _obs_mean = obs.max(dim=pdim).mean(dim=_resolve_axis_to_dim(obs.max(dim=pdim), axis))
        res = (_diff_abs_mean / _obs_mean) * 100.0
        return _update_history(res, "Normalized Mean Peak Error (NMPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        res = (
            np.ma.abs(np.ma.max(mod_arr, axis=paxis) - np.ma.max(obs_arr, axis=paxis)).mean(axis=axis)
            / np.ma.max(obs_arr, axis=paxis).mean(axis=axis)
        ) * 100.0
        return res.item() if np.ndim(res) == 0 else res

NMdnB(obs, mod, axis=None)

Normalized Median Bias (%)

Typical Use Cases

  • Assessing the central tendency of normalized bias, robust to outliers and non-normal distributions.
  • Used for robust model evaluation across variables or sites with different scales.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Normalized median bias (percent).

Examples

import numpy as np obs = np.array([1, 2, 3, 4, 100]) # 100 is an outlier mod = np.array([1.1, 2.2, 3.3, 4.4, 105]) NMdnB(obs, mod) 10.0

Source code in src/monet_stats/relative_metrics.py 
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def NMdnB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Median Bias (%)

    Typical Use Cases
    -----------------
    - Assessing the central tendency of normalized bias, robust to outliers and non-normal distributions.
    - Used for robust model evaluation across variables or sites with different scales.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized median bias (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4, 100])  # 100 is an outlier
    >>> mod = np.array([1.1, 2.2, 3.3, 4.4, 105])
    >>> NMdnB(obs, mod)
    10.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff = mod - obs
        if hasattr(diff.data, "chunks"):
            dims_to_chunk = [dim] if isinstance(dim, str) else list(dim)
            diff = diff.chunk({d: -1 for d in dims_to_chunk})
            obs = obs.chunk({d: -1 for d in dims_to_chunk})
        res = (
            diff.quantile(q=0.5, dim=dim).drop_vars("quantile", errors="ignore")
            / obs.quantile(q=0.5, dim=dim).drop_vars("quantile", errors="ignore")
            * 100.0
        )
        return _update_history(res, "Normalized Median Bias (NMdnB)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        result = np.ma.median(mod_arr - obs_arr, axis=axis) / np.ma.median(obs_arr, axis=axis) * 100.0
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NMdnE(obs, mod, axis=None)

Normalized Median Error (%)

Typical Use Cases

  • Evaluating the typical magnitude of model errors relative to observations, robust to outliers.
  • Used for robust model evaluation and comparison across variables or datasets with different scales.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Normalized median error (percent).

Examples

import numpy as np obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) NMdnE(obs, mod) 33.33333333333333

Source code in src/monet_stats/relative_metrics.py 
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def NMdnE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Median Error (%)

    Typical Use Cases
    -----------------
    - Evaluating the typical magnitude of model errors relative to observations, robust to outliers.
    - Used for robust model evaluation and comparison across variables or datasets with different scales.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized median error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> NMdnE(obs, mod)
    33.33333333333333
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        diff_abs = abs(mod - obs)
        if hasattr(diff_abs.data, "chunks"):
            dims_to_chunk = [dim] if isinstance(dim, str) else list(dim)
            diff_abs = diff_abs.chunk({d: -1 for d in dims_to_chunk})
            obs = obs.chunk({d: -1 for d in dims_to_chunk})
        res = (
            diff_abs.quantile(q=0.5, dim=dim).drop_vars("quantile", errors="ignore")
            / obs.quantile(q=0.5, dim=dim).drop_vars("quantile", errors="ignore")
            * 100
        )
        return _update_history(res, "Normalized Median Error (NMdnE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        result = np.ma.median(np.ma.abs(mod_arr - obs_arr), axis=axis) / np.ma.median(obs_arr, axis=axis) * 100
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NMdnPB(obs, mod, paxis, axis=None)

Normalized Median Peak Bias (NMdnPB, %)

Typical Use Cases

  • Evaluating the typical bias in peak values, normalized by the median of observed peaks, robust to outliers.
  • Used in robust model evaluation for extreme events, especially when comparing across sites or time periods.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. paxis : int or str Axis or dimension along which to compute the peak (e.g., time or space). axis : int or str or None, optional Axis or dimension along which to compute the median of normalized peak bias.

Returns

xarray.DataArray or numpy.ndarray or float Normalized median peak bias (percent).

Examples

import numpy as np obs = np.array([[1, 2, 3], [2, 3, 4]]) mod = np.array([[2, 2, 2], [2, 2, 5]]) NMdnPB(obs, mod, paxis=1) 33.33333333333333

Source code in src/monet_stats/relative_metrics.py 
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def NMdnPB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    paxis: Union[int, str, Iterable[Union[int, str]]],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Median Peak Bias (NMdnPB, %)

    Typical Use Cases
    -----------------
    - Evaluating the typical bias in peak values, normalized by the median of observed peaks, robust to outliers.
    - Used in robust model evaluation for extreme events, especially when comparing across sites or time periods.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    paxis : int or str
        Axis or dimension along which to compute the peak (e.g., time or space).
    axis : int or str or None, optional
        Axis or dimension along which to compute the median of normalized peak bias.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized median peak bias (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([[1, 2, 3], [2, 3, 4]])
    >>> mod = np.array([[2, 2, 2], [2, 2, 5]])
    >>> NMdnPB(obs, mod, paxis=1)
    33.33333333333333
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        pdim = _resolve_axis_to_dim(obs, paxis)
        _diff = mod.max(dim=pdim) - obs.max(dim=pdim)
        _obs_max = obs.max(dim=pdim)
        mdim = _resolve_axis_to_dim(_diff, axis)
        if mdim is None:
            mdim = list(_diff.dims)
        if hasattr(_diff.data, "chunks"):
            dims_to_chunk = [mdim] if isinstance(mdim, str) else list(mdim)
            _diff = _diff.chunk({d: -1 for d in dims_to_chunk})
            _obs_max = _obs_max.chunk({d: -1 for d in dims_to_chunk})
        res = (
            _diff.quantile(q=0.5, dim=mdim).drop_vars("quantile", errors="ignore")
            / _obs_max.quantile(q=0.5, dim=mdim).drop_vars("quantile", errors="ignore")
            * 100.0
        )
        return _update_history(res, "Normalized Median Peak Bias (NMdnPB)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        result = (
            np.ma.median(np.ma.max(mod_arr, axis=paxis) - np.ma.max(obs_arr, axis=paxis), axis=axis)
            / np.ma.median(np.ma.max(obs_arr, axis=paxis), axis=axis)
        ) * 100.0
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

NMdnPE(obs, mod, paxis, axis=None)

Normalized Median Peak Error (NMdnPE, %)

Typical Use Cases

  • Evaluating the typical error in peak values, normalized by the median of observed peaks, robust to outliers.
  • Used in robust model evaluation for extreme events, especially when comparing across sites or time periods.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. paxis : int or str Axis or dimension along which to compute the peak (e.g., time or space). axis : int or str or None, optional Axis or dimension along which to compute the median of normalized peak error.

Returns

xarray.DataArray or numpy.ndarray or float Normalized median peak error (percent).

Examples

import numpy as np obs = np.array([[1, 2, 3], [2, 3, 4]]) mod = np.array([[2, 2, 2], [2, 2, 5]]) NMdnPE(obs, mod, paxis=1) 33.33333333333333

Source code in src/monet_stats/relative_metrics.py 
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def NMdnPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    paxis: Union[int, str, Iterable[Union[int, str]]],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Normalized Median Peak Error (NMdnPE, %)

    Typical Use Cases
    -----------------
    - Evaluating the typical error in peak values, normalized by the median of observed peaks, robust to outliers.
    - Used in robust model evaluation for extreme events, especially when comparing across sites or time periods.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    paxis : int or str
        Axis or dimension along which to compute the peak (e.g., time or space).
    axis : int or str or None, optional
        Axis or dimension along which to compute the median of normalized peak error.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized median peak error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([[1, 2, 3], [2, 3, 4]])
    >>> mod = np.array([[2, 2, 2], [2, 2, 5]])
    >>> NMdnPE(obs, mod, paxis=1)
    33.33333333333333
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        pdim = _resolve_axis_to_dim(obs, paxis)
        _diff_abs = abs(mod.max(dim=pdim) - obs.max(dim=pdim))
        _obs_max = obs.max(dim=pdim)
        mdim = _resolve_axis_to_dim(_diff_abs, axis)
        if mdim is None:
            mdim = list(_diff_abs.dims)
        if hasattr(_diff_abs.data, "chunks"):
            dims_to_chunk = [mdim] if isinstance(mdim, str) else list(mdim)
            _diff_abs = _diff_abs.chunk({d: -1 for d in dims_to_chunk})
            _obs_max = _obs_max.chunk({d: -1 for d in dims_to_chunk})
        res = (
            _diff_abs.quantile(q=0.5, dim=mdim).drop_vars("quantile", errors="ignore")
            / _obs_max.quantile(q=0.5, dim=mdim).drop_vars("quantile", errors="ignore")
            * 100.0
        )
        return _update_history(res, "Normalized Median Peak Error (NMdnPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        result = (
            np.ma.median(
                np.ma.abs(np.ma.max(mod_arr, axis=paxis) - np.ma.max(obs_arr, axis=paxis)),
                axis=axis,
            )
            / np.ma.median(np.ma.max(obs_arr, axis=paxis), axis=axis)
        ) * 100.0
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

PSUTMNPB(obs, mod, axis=None)

Paired Space/Unpaired Time Mean Normalized Peak Bias (PSUTMNPB, %)

Wrapper for MNPB with paxis=0, axis=None.

Source code in src/monet_stats/relative_metrics.py 
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def PSUTMNPB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Paired Space/Unpaired Time Mean Normalized Peak Bias (PSUTMNPB, %)

    Wrapper for MNPB with paxis=0, axis=None.
    """
    return MNPB(obs, mod, paxis=0, axis=None)

PSUTMNPE(obs, mod, axis=None)

Paired Space/Unpaired Time Mean Normalized Peak Error (PSUTMNPE, %)

Wrapper for MNPE with paxis=0, axis=None.

Source code in src/monet_stats/relative_metrics.py 
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def PSUTMNPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Paired Space/Unpaired Time Mean Normalized Peak Error (PSUTMNPE, %)

    Wrapper for MNPE with paxis=0, axis=None.
    """
    return MNPE(obs, mod, paxis=0, axis=None)

PSUTMdnNPB(obs, mod, axis=None)

Paired Space/Unpaired Time Median Normalized Peak Bias (PSUTMdnNPB, %)

Wrapper for MdnNPB with paxis=0, axis=None.

Source code in src/monet_stats/relative_metrics.py 
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def PSUTMdnNPB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Paired Space/Unpaired Time Median Normalized Peak Bias (PSUTMdnNPB, %)

    Wrapper for MdnNPB with paxis=0, axis=None.
    """
    return MdnNPB(obs, mod, paxis=0, axis=None)

PSUTMdnNPE(obs, mod, axis=None)

Paired Space/Unpaired Time Median Normalized Peak Error (PSUTMdnNPE, %)

Wrapper for MdnNPE with paxis=0, axis=None.

Source code in src/monet_stats/relative_metrics.py 
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def PSUTMdnNPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Paired Space/Unpaired Time Median Normalized Peak Error (PSUTMdnNPE, %)

    Wrapper for MdnNPE with paxis=0, axis=None.
    """
    return MdnNPE(obs, mod, paxis=0, axis=None)

PSUTNMPB(obs, mod, axis=None)

Paired Space/Unpaired Time Normalized Mean Peak Bias (PSUTNMPB, %)

Wrapper for NMPB with paxis=0, axis=None.

Source code in src/monet_stats/relative_metrics.py 
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def PSUTNMPB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Paired Space/Unpaired Time Normalized Mean Peak Bias (PSUTNMPB, %)

    Wrapper for NMPB with paxis=0, axis=None.
    """
    return NMPB(obs, mod, paxis=0, axis=None)

PSUTNMPE(obs, mod, axis=None)

Paired Space/Unpaired Time Normalized Mean Peak Error (PSUTNMPE, %)

Wrapper for NMPE with paxis=0, axis=None.

Source code in src/monet_stats/relative_metrics.py 
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def PSUTNMPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Paired Space/Unpaired Time Normalized Mean Peak Error (PSUTNMPE, %)

    Wrapper for NMPE with paxis=0, axis=None.
    """
    return NMPE(obs, mod, paxis=0, axis=None)

PSUTNMdnPB(obs, mod, axis=None)

Paired Space/Unpaired Time Normalized Median Peak Bias (PSUTNMdnPB, %)

Typical Use Cases

  • Evaluating the normalized median peak bias for spatially paired, temporally unpaired datasets, robust to outliers.
  • Used in robust model evaluation for spatial ensemble or multi-time analysis.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the median of normalized peak bias.

Returns

xarray.DataArray or numpy.ndarray or float Normalized median peak bias (percent).

Examples

import numpy as np obs = np.array([[1, 2, 3], [2, 3, 4]]) mod = np.array([[2, 2, 2], [2, 2, 5]]) PSUTNMdnPB(obs, mod) 33.33333333333333

Source code in src/monet_stats/relative_metrics.py 
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def PSUTNMdnPB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Paired Space/Unpaired Time Normalized Median Peak Bias (PSUTNMdnPB, %)

    Typical Use Cases
    -----------------
    - Evaluating the normalized median peak bias for spatially paired, temporally unpaired datasets, robust to outliers.
    - Used in robust model evaluation for spatial ensemble or multi-time analysis.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the median of normalized peak bias.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized median peak bias (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([[1, 2, 3], [2, 3, 4]])
    >>> mod = np.array([[2, 2, 2], [2, 2, 5]])
    >>> PSUTNMdnPB(obs, mod)
    33.33333333333333
    """
    return NMdnPB(obs, mod, paxis=0, axis=None)

PSUTNMdnPE(obs, mod, axis=None)

Paired Space/Unpaired Time Normalized Median Peak Error (PSUTNMdnPE, %)

Typical Use Cases

  • Evaluating the normalized median peak error for spatially paired, temporally unpaired datasets, robust to outliers.
  • Used in robust model evaluation for spatial ensemble or multi-time analysis.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the median of normalized peak error.

Returns

xarray.DataArray or numpy.ndarray or float Normalized median peak error (percent).

Examples

import numpy as np obs = np.array([[1, 2, 3], [2, 3, 4]]) mod = np.array([[2, 2, 2], [2, 2, 5]]) PSUTNMdnPE(obs, mod) 33.33333333333333

Source code in src/monet_stats/relative_metrics.py 
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def PSUTNMdnPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Paired Space/Unpaired Time Normalized Median Peak Error (PSUTNMdnPE, %)

    Typical Use Cases
    -----------------
    - Evaluating the normalized median peak error for spatially paired, temporally unpaired
      datasets, robust to outliers.
    - Used in robust model evaluation for spatial ensemble or multi-time analysis.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the median of normalized peak error.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Normalized median peak error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([[1, 2, 3], [2, 3, 4]])
    >>> mod = np.array([[2, 2, 2], [2, 2, 5]])
    >>> PSUTNMdnPE(obs, mod)
    33.33333333333333
    """
    return NMdnPE(obs, mod, paxis=0, axis=None)

USUTPB(obs, mod, axis=None)

Unpaired Space/Unpaired Time Peak Bias (%)

Typical Use Cases

  • Assessing the bias in peak values between model and observations, regardless of spatial or temporal pairing.
  • Used in event-based or extreme value model evaluation, especially for air quality and meteorological extremes.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Peak bias (percent).

Examples

import numpy as np obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 5]) USUTPB(obs, mod) 25.0

Source code in src/monet_stats/relative_metrics.py 
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def USUTPB(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Unpaired Space/Unpaired Time Peak Bias (%)

    Typical Use Cases
    -----------------
    - Assessing the bias in peak values between model and observations, regardless of spatial or temporal pairing.
    - Used in event-based or extreme value model evaluation, especially for air quality and meteorological extremes.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Peak bias (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 5])
    >>> USUTPB(obs, mod)
    25.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = ((mod.max(dim=dim) - obs.max(dim=dim)) / obs.max(dim=dim)) * 100.0
        return _update_history(res, "Unpaired Space/Unpaired Time Peak Bias (USUTPB)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        res = ((np.ma.max(mod_arr, axis=axis) - np.ma.max(obs_arr, axis=axis)) / np.ma.max(obs_arr, axis=axis)) * 100.0
        return res.item() if np.ndim(res) == 0 else res

USUTPE(obs, mod, axis=None)

Unpaired Space/Unpaired Time Peak Error (%)

Typical Use Cases

  • Quantifying the error in peak values between model and observations, regardless of spatial or temporal pairing.
  • Used in event-based or extreme value model evaluation, especially for air quality and meteorological extremes.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed values. mod : xarray.DataArray or numpy.ndarray Model predicted values. axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Peak error (percent).

Examples

import numpy as np obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 5]) USUTPE(obs, mod) 25.0

Source code in src/monet_stats/relative_metrics.py 
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def USUTPE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Unpaired Space/Unpaired Time Peak Error (%)

    Typical Use Cases
    -----------------
    - Quantifying the error in peak values between model and observations, regardless of spatial or temporal pairing.
    - Used in event-based or extreme value model evaluation, especially for air quality and meteorological extremes.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    mod : xarray.DataArray or numpy.ndarray
        Model predicted values.
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Peak error (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 5])
    >>> USUTPE(obs, mod)
    25.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = (abs(mod.max(dim=dim) - obs.max(dim=dim)) / obs.max(dim=dim)) * 100.0
        return _update_history(res, "Unpaired Space/Unpaired Time Peak Error (USUTPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        res = (
            np.ma.abs(np.ma.max(mod_arr, axis=axis) - np.ma.max(obs_arr, axis=axis)) / np.ma.max(obs_arr, axis=axis)
        ) * 100.0
        return res.item() if np.ndim(res) == 0 else res

WDME(obs, mod, axis=None)

Wind Direction Mean Gross Error (model and obs unit)

Typical Use Cases

  • Quantifying the average magnitude of wind direction errors, regardless of direction.
  • Used in wind energy, meteorology, and air quality studies to assess wind direction model performance.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed wind direction values (degrees). mod : xarray.DataArray or numpy.ndarray Model predicted wind direction values (degrees). axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Mean gross error in wind direction (degrees).

Examples

import numpy as np obs = np.array([350, 10, 20]) mod = np.array([10, 20, 30]) WDME(obs, mod) 20.0

Source code in src/monet_stats/relative_metrics.py 
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def WDME(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Wind Direction Mean Gross Error (model and obs unit)

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of wind direction errors, regardless of direction.
    - Used in wind energy, meteorology, and air quality studies to assess wind direction model performance.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed wind direction values (degrees).
    mod : xarray.DataArray or numpy.ndarray
        Model predicted wind direction values (degrees).
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Mean gross error in wind direction (degrees).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([350, 10, 20])
    >>> mod = np.array([10, 20, 30])
    >>> WDME(obs, mod)
    20.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = abs(circlebias(mod - obs)).mean(dim=dim)
        return _update_history(res, "Wind Direction Mean Gross Error (WDME)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        res = np.ma.mean(np.ma.abs(circlebias(mod_arr - obs_arr)), axis=axis)
        return res.item() if np.ndim(res) == 0 else res

WDME_m(obs, mod, axis=None)

Wind Direction Mean Gross Error (model and obs unit) (avoid single block error in np.ma)

Typical Use Cases

  • Quantifying the average magnitude of wind direction errors, regardless of direction.
  • Used in wind energy, meteorology, and air quality studies to assess wind direction model performance.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed wind direction values (degrees). mod : xarray.DataArray or numpy.ndarray Model predicted wind direction values (degrees). axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Mean gross error in wind direction (degrees).

Examples

import numpy as np obs = np.array([350, 10, 20]) mod = np.array([10, 20, 30]) WDME_m(obs, mod) 20.0

Source code in src/monet_stats/relative_metrics.py 
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def WDME_m(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Wind Direction Mean Gross Error (model and obs unit)
    (avoid single block error in np.ma)

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of wind direction errors, regardless of direction.
    - Used in wind energy, meteorology, and air quality studies to assess wind direction model performance.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed wind direction values (degrees).
    mod : xarray.DataArray or numpy.ndarray
        Model predicted wind direction values (degrees).
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Mean gross error in wind direction (degrees).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([350, 10, 20])
    >>> mod = np.array([10, 20, 30])
    >>> WDME_m(obs, mod)
    20.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        res = abs(circlebias_m(mod - obs)).mean(dim=dim)
        return _update_history(res, "Wind Direction Mean Gross Error (WDME_m)")
    else:
        obs_arr = np.asanyarray(obs)
        mod_arr = np.asanyarray(mod)
        res = np.abs(circlebias_m(mod_arr - obs_arr)).mean(axis=axis)
        return res.item() if np.ndim(res) == 0 else res

WDMdnE(obs, mod, axis=None)

Wind Direction Median Gross Error (model and obs unit)

Typical Use Cases

  • Evaluating the typical magnitude of wind direction errors, robust to outliers.
  • Used in wind energy and meteorological applications for robust wind direction model evaluation.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed wind direction values (degrees). mod : xarray.DataArray or numpy.ndarray Model predicted wind direction values (degrees). axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Median gross error in wind direction (degrees).

Examples

import numpy as np obs = np.array([350, 10, 20]) mod = np.array([10, 20, 30]) WDMdnE(obs, mod) 10.0

Source code in src/monet_stats/relative_metrics.py 
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def WDMdnE(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Wind Direction Median Gross Error (model and obs unit)

    Typical Use Cases
    -----------------
    - Evaluating the typical magnitude of wind direction errors, robust to outliers.
    - Used in wind energy and meteorological applications for robust wind direction model evaluation.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed wind direction values (degrees).
    mod : xarray.DataArray or numpy.ndarray
        Model predicted wind direction values (degrees).
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Median gross error in wind direction (degrees).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([350, 10, 20])
    >>> mod = np.array([10, 20, 30])
    >>> WDMdnE(obs, mod)
    10.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        if dim is None:
            dim = list(obs.dims)
        cb = abs(circlebias(mod - obs))
        if hasattr(cb.data, "chunks"):
            dims_to_chunk = [dim] if isinstance(dim, str) else list(dim)
            cb = cb.chunk({d: -1 for d in dims_to_chunk})
        res = cb.quantile(q=0.5, dim=dim).drop_vars("quantile", errors="ignore")
        return _update_history(res, "Wind Direction Median Gross Error (WDMdnE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        cb = circlebias(mod_arr - obs_arr)
        result = np.ma.median(np.ma.abs(cb), axis=axis)
        return result.item() if hasattr(result, "item") and np.ndim(result) == 0 else result

WDNMB_m(obs, mod, axis=None)

Wind Direction Normalized Mean Bias (%) (avoid single block error in np.ma)

Typical Use Cases

  • Comparing the average wind direction bias, normalized by observed wind direction, across sites or time periods.
  • Used in wind energy and meteorological model evaluation for directionally normalized performance.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed wind direction values (degrees). mod : xarray.DataArray or numpy.ndarray Model predicted wind direction values (degrees). axis : int or str or None, optional Axis or dimension along which to compute the statistic.

Returns

xarray.DataArray or numpy.ndarray or float Wind direction normalized mean bias (percent).

Examples

import numpy as np obs = np.array([350, 10, 20]) mod = np.array([345, 15, 25]) WDNMB_m(obs, mod) -5.0

Source code in src/monet_stats/relative_metrics.py 
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def WDNMB_m(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Wind Direction Normalized Mean Bias (%) (avoid single block error in np.ma)

    Typical Use Cases
    -----------------
    - Comparing the average wind direction bias, normalized by observed wind direction, across sites or time periods.
    - Used in wind energy and meteorological model evaluation for directionally normalized performance.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed wind direction values (degrees).
    mod : xarray.DataArray or numpy.ndarray
        Model predicted wind direction values (degrees).
    axis : int or str or None, optional
        Axis or dimension along which to compute the statistic.

    Returns
    -------
    xarray.DataArray or numpy.ndarray or float
        Wind direction normalized mean bias (percent).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([350, 10, 20])
    >>> mod = np.array([345, 15, 25])
    >>> WDNMB_m(obs, mod)
    -5.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = _resolve_axis_to_dim(obs, axis)
        diff = mod - obs
        cb = circlebias_m(diff)
        res = cb.sum(dim=dim) / obs.sum(dim=dim) * 100.0
        return _update_history(res, "Wind Direction Normalized Mean Bias (WDNMB_m)")
    else:
        obs_arr = np.asanyarray(obs)
        mod_arr = np.asanyarray(mod)
        diff = mod_arr - obs_arr
        res = circlebias_m(diff).sum(axis=axis) / obs_arr.sum(axis=axis) * 100.0
        return res.item() if np.ndim(res) == 0 else res

Spatial & Ensemble Metrics

Spatial and Ensemble Metrics for Atmospheric Sciences (Aero Protocol Compliant)

BSS(obs, mod, threshold, dim=None, axis=None)

Brier Skill Score (BSS) for probabilistic forecasts (Aero Protocol).

Typical Use Cases

  • Evaluating the accuracy of probabilistic binary forecasts relative to climatology.
  • Common in meteorological verification for event occurrence.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed binary outcomes (0 or 1) or continuous values (will be binarized). mod : xarray.DataArray or numpy.ndarray Forecast probabilities (0 to 1) or continuous values (will be binarized). threshold : float Threshold for converting values to binary events. dim : str or iterable of str, optional Dimension(s) along which to compute the score (xarray only). axis : int or iterable of int, optional Axis or axes along which to compute the score (numpy only).

Returns

xarray.DataArray, numpy.ndarray, or float Brier Skill Score.

Source code in src/monet_stats/spatial_ensemble_metrics.py 
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def BSS(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    threshold: float,
    dim: Optional[Union[str, Iterable[str]]] = None,
    axis: Optional[Union[int, Iterable[int]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Brier Skill Score (BSS) for probabilistic forecasts (Aero Protocol).

    Typical Use Cases
    -----------------
    - Evaluating the accuracy of probabilistic binary forecasts relative to climatology.
    - Common in meteorological verification for event occurrence.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed binary outcomes (0 or 1) or continuous values (will be binarized).
    mod : xarray.DataArray or numpy.ndarray
        Forecast probabilities (0 to 1) or continuous values (will be binarized).
    threshold : float
        Threshold for converting values to binary events.
    dim : str or iterable of str, optional
        Dimension(s) along which to compute the score (xarray only).
    axis : int or iterable of int, optional
        Axis or axes along which to compute the score (numpy only).

    Returns
    -------
    xarray.DataArray, numpy.ndarray, or float
        Brier Skill Score.
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        # Binarize if not already
        o_bin = (obs >= threshold).astype(float)
        m_prob = (mod >= threshold).astype(float)

        bs = ((m_prob - o_bin) ** 2).mean(dim=dim)
        obs_clim = o_bin.mean(dim=dim)
        bs_ref = ((obs_clim - o_bin) ** 2).mean(dim=dim)

        res = xr.where(bs_ref != 0, 1.0 - (bs / bs_ref), 0.0)
        return _update_history(res, "Brier Skill Score (BSS)")

    o = np.asarray(obs)
    m = np.asarray(mod)
    o_bin = (o >= threshold).astype(float)
    m_prob = (m >= threshold).astype(float)

    bs = np.nanmean((m_prob - o_bin) ** 2, axis=axis)
    obs_clim = np.nanmean(o_bin, axis=axis)
    if axis is not None:
        # Keep dimensions for subtraction
        obs_clim_kd = np.nanmean(o_bin, axis=axis, keepdims=True)
    else:
        obs_clim_kd = obs_clim

    bs_ref = np.nanmean((obs_clim_kd - o_bin) ** 2, axis=axis)

    with np.errstate(divide="ignore", invalid="ignore"):
        res = np.where(bs_ref != 0, 1.0 - (bs / bs_ref), 0.0)
        return res.item() if np.ndim(res) == 0 else res

CRPS(ensemble, obs, axis=0)

Continuous Ranked Probability Score (CRPS) for ensemble forecasts.

Supports lazy evaluation via Xarray/Dask.

Parameters

ensemble : xarray.DataArray or numpy.ndarray Ensemble forecasts. If DataArray, should have an ensemble dimension. obs : xarray.DataArray or numpy.ndarray Observed values. axis : int or str, optional Axis or dimension corresponding to ensemble members. Default is 0.

Returns

xarray.DataArray or numpy.ndarray CRPS values.

Examples

import numpy as np ens = np.array([[1, 2], [2, 3], [3, 4]]) obs = np.array([2, 3]) CRPS(ens, obs, axis=0) array([0.22222222, 0.22222222])

Source code in src/monet_stats/spatial_ensemble_metrics.py 
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def CRPS(
    ensemble: Union[xr.DataArray, np.ndarray],
    obs: Union[xr.DataArray, np.ndarray],
    axis: Union[int, str] = 0,
) -> Union[xr.DataArray, np.ndarray]:
    """
    Continuous Ranked Probability Score (CRPS) for ensemble forecasts.

    Supports lazy evaluation via Xarray/Dask.

    Parameters
    ----------
    ensemble : xarray.DataArray or numpy.ndarray
        Ensemble forecasts. If DataArray, should have an ensemble dimension.
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    axis : int or str, optional
        Axis or dimension corresponding to ensemble members. Default is 0.

    Returns
    -------
    xarray.DataArray or numpy.ndarray
        CRPS values.

    Examples
    --------
    >>> import numpy as np
    >>> ens = np.array([[1, 2], [2, 3], [3, 4]])
    >>> obs = np.array([2, 3])
    >>> CRPS(ens, obs, axis=0)
    array([0.22222222, 0.22222222])
    """

    def _crps_numpy(ens, observation, ens_axis=0):
        ens_sorted = np.sort(ens, axis=ens_axis)
        n = ens.shape[ens_axis]
        # Compute empirical CDFs
        cdf_ens = np.arange(1, n + 1) / n
        shape = [1] * ens.ndim
        shape[ens_axis] = n
        cdf_ens = np.reshape(cdf_ens, shape)
        # Broadcast obs for comparison
        obs_broadcast = np.expand_dims(observation, ens_axis)
        cdf_obs = (ens_sorted >= obs_broadcast).astype(float)
        return np.sum((cdf_ens - cdf_obs) ** 2, axis=ens_axis)

    if isinstance(ensemble, xr.DataArray) and isinstance(obs, xr.DataArray):
        # Determine core dimension
        if isinstance(axis, int):
            ens_dim = ensemble.dims[axis]
        else:
            ens_dim = axis

        res = xr.apply_ufunc(
            _crps_numpy,
            ensemble,
            obs,
            input_core_dims=[[ens_dim], []],
            output_core_dims=[[]],
            kwargs={"ens_axis": -1},
            dask="parallelized",
            output_dtypes=[float],
            dask_gufunc_kwargs={"allow_rechunk": True},
        )
        return _update_history(res, "Continuous Ranked Probability Score (CRPS)")

    return _crps_numpy(np.asarray(ensemble), np.asarray(obs), ens_axis=axis)

EDS(obs, mod, threshold, dim=None, axis=None)

Extreme Dependency Score (EDS) for rare event detection (Aero Protocol).

Typical Use Cases

  • Assessing model performance for rare extreme events (e.g., heavy precipitation).
  • Used when traditional scores like CSI or ETS go to zero as the event becomes rarer.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed field. mod : xarray.DataArray or numpy.ndarray Model field. threshold : float Event threshold to define the extreme event. dim : str or iterable of str, optional Dimension(s) along which to compute the score (xarray only). If None, reduces over all dimensions. axis : int or iterable of int, optional Axis or axes along which to compute the score (numpy only).

Returns

xarray.DataArray, numpy.ndarray, or float Extreme Dependency Score.

Examples

import numpy as np obs = np.zeros((10, 10)); obs[5, 5] = 1 mod = np.zeros((10, 10)); mod[5, 5] = 1 EDS(obs, mod, threshold=0.5) 1.0

Source code in src/monet_stats/spatial_ensemble_metrics.py 
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def EDS(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    threshold: float,
    dim: Optional[Union[str, Iterable[str]]] = None,
    axis: Optional[Union[int, Iterable[int]]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Extreme Dependency Score (EDS) for rare event detection (Aero Protocol).

    Typical Use Cases
    -----------------
    - Assessing model performance for rare extreme events (e.g., heavy precipitation).
    - Used when traditional scores like CSI or ETS go to zero as the event becomes rarer.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed field.
    mod : xarray.DataArray or numpy.ndarray
        Model field.
    threshold : float
        Event threshold to define the extreme event.
    dim : str or iterable of str, optional
        Dimension(s) along which to compute the score (xarray only).
        If None, reduces over all dimensions.
    axis : int or iterable of int, optional
        Axis or axes along which to compute the score (numpy only).

    Returns
    -------
    xarray.DataArray, numpy.ndarray, or float
        Extreme Dependency Score.

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.zeros((10, 10)); obs[5, 5] = 1
    >>> mod = np.zeros((10, 10)); mod[5, 5] = 1
    >>> EDS(obs, mod, threshold=0.5)
    1.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        obs_bin = obs >= threshold
        mod_bin = mod >= threshold

        mask = obs.notnull() & mod.notnull()
        obs_bin = obs_bin & mask
        mod_bin = mod_bin & mask

        hits = (obs_bin & mod_bin).sum(dim=dim)
        n_obs = obs_bin.sum(dim=dim)
        n_mod = mod_bin.sum(dim=dim)
        n = mask.sum(dim=dim)

        # EDS = log(hits/n) / log(n_obs*n_mod / n^2)
        # Avoid log(0) and division by zero
        # p = n_obs / n, q = n_mod / n
        with np.errstate(divide="ignore", invalid="ignore"):
            eds = xr.where(
                (hits > 0) & (n_obs > 0) & (n_mod > 0), np.log(hits / n) / np.log((n_obs / n) * (n_mod / n)), np.nan
            )

        return _update_history(eds, "Extreme Dependency Score (EDS)")

    # NumPy path
    obs_arr = np.asarray(obs)
    mod_arr = np.asarray(mod)
    mask = ~np.isnan(obs_arr) & ~np.isnan(mod_arr)

    obs_bin = (obs_arr >= threshold) & mask
    mod_bin = (mod_arr >= threshold) & mask

    hits = np.sum(obs_bin & mod_bin, axis=axis)
    n_obs = np.sum(obs_bin, axis=axis)
    n_mod = np.sum(mod_bin, axis=axis)
    n = np.sum(mask, axis=axis)

    with np.errstate(divide="ignore", invalid="ignore"):
        res = np.where(
            (hits > 0) & (n_obs > 0) & (n_mod > 0), np.log(hits / n) / np.log((n_obs / n) * (n_mod / n)), np.nan
        )
        return res.item() if np.ndim(res) == 0 else res

SAL(obs, mod, threshold=None, lat_dim='lat', lon_dim='lon')

Structure-Amplitude-Location (SAL) score for spatial verification (Aero Protocol).

This implementation is vectorized over non-spatial dimensions using xarray.apply_ufunc and supports lazy evaluation for dimensions other than the spatial ones.

Parameters

obs : xarray.DataArray or numpy.ndarray Observed field. Should be 2D (lat, lon) or multi-dimensional. mod : xarray.DataArray or numpy.ndarray Model field. threshold : float, optional Threshold for object identification. If None, uses mean of observations per slice (Lazy-friendly). lat_dim : str, optional Name of the latitude dimension. Default is 'lat'. lon_dim : str, optional Name of the longitude dimension. Default is 'lon'.

Returns

S, A, L : xarray.DataArray, numpy.ndarray, or float Structure, Amplitude, and Location components.

Examples

import xarray as xr import numpy as np obs = xr.DataArray(np.random.rand(10, 10, 10), dims=['time', 'lat', 'lon']) mod = xr.DataArray(np.random.rand(10, 10, 10), dims=['time', 'lat', 'lon']) S, A, L = SAL(obs, mod)

Source code in src/monet_stats/spatial_ensemble_metrics.py 
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def SAL(
    obs: Union[xr.DataArray, np.ndarray],
    mod: Union[xr.DataArray, np.ndarray],
    threshold: Optional[float] = None,
    lat_dim: str = "lat",
    lon_dim: str = "lon",
) -> Union[
    Tuple[xr.DataArray, xr.DataArray, xr.DataArray],
    Tuple[np.ndarray, np.ndarray, np.ndarray],
    Tuple[float, float, float],
]:
    """
    Structure-Amplitude-Location (SAL) score for spatial verification (Aero Protocol).

    This implementation is vectorized over non-spatial dimensions using `xarray.apply_ufunc`
    and supports lazy evaluation for dimensions other than the spatial ones.

    Parameters
    ----------
    obs : xarray.DataArray or numpy.ndarray
        Observed field. Should be 2D (lat, lon) or multi-dimensional.
    mod : xarray.DataArray or numpy.ndarray
        Model field.
    threshold : float, optional
        Threshold for object identification. If None, uses mean of observations
        per slice (Lazy-friendly).
    lat_dim : str, optional
        Name of the latitude dimension. Default is 'lat'.
    lon_dim : str, optional
        Name of the longitude dimension. Default is 'lon'.

    Returns
    -------
    S, A, L : xarray.DataArray, numpy.ndarray, or float
        Structure, Amplitude, and Location components.

    Examples
    --------
    >>> import xarray as xr
    >>> import numpy as np
    >>> obs = xr.DataArray(np.random.rand(10, 10, 10), dims=['time', 'lat', 'lon'])
    >>> mod = xr.DataArray(np.random.rand(10, 10, 10), dims=['time', 'lat', 'lon'])
    >>> S, A, L = SAL(obs, mod)
    """
    is_xr = isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray)

    if is_xr:
        obs, mod = xr.align(obs, mod, join="inner")
        # Determine spatial dimensions
        if lat_dim not in obs.dims or lon_dim not in obs.dims:
            # Fallback to last two dimensions if lat/lon not found
            spatial_dims = [obs.dims[-2], obs.dims[-1]]
        else:
            spatial_dims = [lat_dim, lon_dim]
    else:
        # For numpy, assume last two dimensions are spatial
        spatial_dims = [-2, -1]

    def _sal_wrapper(o: np.ndarray, m: np.ndarray, t: Optional[float]) -> Tuple[float, float, float]:
        """
        Wrapper for _sal_numpy to be used with xarray.apply_ufunc.

        Parameters
        ----------
        o : numpy.ndarray
            Observed field slice.
        m : numpy.ndarray
            Model field slice.
        t : float, optional
            Threshold.

        Returns
        -------
        Tuple[float, float, float]
            S, A, L components.

        Examples
        --------
        >>> import numpy as np
        >>> o = np.random.rand(10, 10)
        >>> m = np.random.rand(10, 10)
        >>> _sal_wrapper(o, m, 0.5)
        """
        return _sal_numpy(o, m, t)

    res_s, res_a, res_l = xr.apply_ufunc(
        _sal_wrapper,
        obs,
        mod,
        threshold,
        input_core_dims=[spatial_dims, spatial_dims, []],
        output_core_dims=[[], [], []],
        vectorize=True,
        dask="parallelized",
        output_dtypes=[float, float, float],
    )

    if is_xr:
        res_s = _update_history(res_s, "SAL: Structure component")
        res_a = _update_history(res_a, "SAL: Amplitude component")
        res_l = _update_history(res_l, "SAL: Location component")

    return res_s, res_a, res_l

ensemble_mean(ensemble, axis=0)

Calculate the ensemble mean.

Parameters

ensemble : xarray.DataArray or numpy.ndarray Ensemble forecasts. axis : int or str, optional Axis or dimension corresponding to ensemble members. Default is 0.

Returns

xarray.DataArray or numpy.ndarray Ensemble mean.

Source code in src/monet_stats/spatial_ensemble_metrics.py 
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def ensemble_mean(
    ensemble: Union[xr.DataArray, np.ndarray],
    axis: Union[int, str] = 0,
) -> Union[xr.DataArray, np.ndarray]:
    """
    Calculate the ensemble mean.

    Parameters
    ----------
    ensemble : xarray.DataArray or numpy.ndarray
        Ensemble forecasts.
    axis : int or str, optional
        Axis or dimension corresponding to ensemble members. Default is 0.

    Returns
    -------
    xarray.DataArray or numpy.ndarray
        Ensemble mean.
    """
    if isinstance(ensemble, xr.DataArray):
        dim = axis
        if isinstance(axis, int):
            dim = ensemble.dims[axis]
        res = ensemble.mean(dim=dim)
        return _update_history(res, "Ensemble Mean")
    return np.mean(ensemble, axis=axis)

ensemble_std(ensemble, axis=0)

Calculate the ensemble standard deviation.

Parameters

ensemble : xarray.DataArray or numpy.ndarray Ensemble forecasts. axis : int or str, optional Axis or dimension corresponding to ensemble members. Default is 0.

Returns

xarray.DataArray or numpy.ndarray Ensemble standard deviation.

Source code in src/monet_stats/spatial_ensemble_metrics.py 
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def ensemble_std(
    ensemble: Union[xr.DataArray, np.ndarray],
    axis: Union[int, str] = 0,
) -> Union[xr.DataArray, np.ndarray]:
    """
    Calculate the ensemble standard deviation.

    Parameters
    ----------
    ensemble : xarray.DataArray or numpy.ndarray
        Ensemble forecasts.
    axis : int or str, optional
        Axis or dimension corresponding to ensemble members. Default is 0.

    Returns
    -------
    xarray.DataArray or numpy.ndarray
        Ensemble standard deviation.
    """
    if isinstance(ensemble, xr.DataArray):
        dim = axis
        if isinstance(axis, int):
            dim = ensemble.dims[axis]
        res = ensemble.std(dim=dim)
        return _update_history(res, "Ensemble Standard Deviation")
    return np.std(ensemble, axis=axis)

rank_histogram(ensemble, obs, axis=0)

Calculate the rank histogram counts.

Parameters

ensemble : xarray.DataArray or numpy.ndarray Ensemble forecasts. obs : xarray.DataArray or numpy.ndarray Observed values. axis : int or str, optional Axis or dimension corresponding to ensemble members. Default is 0.

Returns

xarray.DataArray or numpy.ndarray Rank histogram counts.

Examples

import numpy as np ens = np.array([[1, 2], [2, 3], [3, 4]]) obs = np.array([2, 3]) rank_histogram(ens, obs, axis=0) array([0., 0., 2., 0.])

Source code in src/monet_stats/spatial_ensemble_metrics.py 
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def rank_histogram(
    ensemble: Union[xr.DataArray, np.ndarray],
    obs: Union[xr.DataArray, np.ndarray],
    axis: Union[int, str] = 0,
) -> Union[xr.DataArray, np.ndarray]:
    """
    Calculate the rank histogram counts.

    Parameters
    ----------
    ensemble : xarray.DataArray or numpy.ndarray
        Ensemble forecasts.
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    axis : int or str, optional
        Axis or dimension corresponding to ensemble members. Default is 0.

    Returns
    -------
    xarray.DataArray or numpy.ndarray
        Rank histogram counts.

    Examples
    --------
    >>> import numpy as np
    >>> ens = np.array([[1, 2], [2, 3], [3, 4]])
    >>> obs = np.array([2, 3])
    >>> rank_histogram(ens, obs, axis=0)
    array([0., 0., 2., 0.])
    """

    def _rank_numpy(ens, observation, ens_axis=0):
        o_exp = np.expand_dims(observation, ens_axis)
        full_ensemble = np.concatenate([ens, o_exp], axis=ens_axis)
        ranks = np.argsort(full_ensemble, axis=ens_axis)
        obs_rank = np.argmax(ranks == ens.shape[ens_axis], axis=ens_axis)
        n_ens = ens.shape[ens_axis]
        hist, _ = np.histogram(obs_rank, bins=np.arange(n_ens + 2))
        return hist.astype(float)

    if isinstance(ensemble, xr.DataArray) and isinstance(obs, xr.DataArray):
        if isinstance(axis, int):
            ens_dim = ensemble.dims[axis]
        else:
            ens_dim = axis

        def _rank_ufunc(ens, observation):
            o_exp = np.expand_dims(observation, -1)
            full_ensemble = np.concatenate([ens, o_exp], axis=-1)
            ranks = np.argsort(full_ensemble, axis=-1)
            return np.argmax(ranks == ens.shape[-1], axis=-1)

        obs_rank = xr.apply_ufunc(
            _rank_ufunc,
            ensemble,
            obs,
            input_core_dims=[[ens_dim], []],
            output_core_dims=[[]],
            dask="parallelized",
            output_dtypes=[int],
        )

        n_ens = ensemble.sizes[ens_dim]
        bins = np.arange(n_ens + 2)
        if hasattr(obs_rank.data, "dask"):
            import dask.array as da

            hist, _ = da.histogram(obs_rank.data, bins=bins)
            res = xr.DataArray(hist, dims="rank", coords={"rank": np.arange(n_ens + 1)})
        else:
            hist, _ = np.histogram(obs_rank.values, bins=bins)
            res = xr.DataArray(hist, dims="rank", coords={"rank": np.arange(n_ens + 1)})
        return _update_history(res, "Rank Histogram")

    return _rank_numpy(np.asarray(ensemble), np.asarray(obs), ens_axis=axis)

spread_error(ensemble, obs, axis=0, dim=None, reduce_axis=None)

Spread-Error Relationship for ensemble forecasts (Aero Protocol).

Typical Use Cases

  • Assessing if the ensemble spread is a good proxy for the forecast error.
  • Ideally, mean spread should equal RMSE of the ensemble mean.

Parameters

ensemble : xarray.DataArray or numpy.ndarray Ensemble forecasts. obs : xarray.DataArray or numpy.ndarray Observed values. axis : int or str, optional Axis or dimension corresponding to ensemble members. Default is 0. dim : str or iterable of str, optional Dimension(s) along which to compute the mean spread and error (xarray only). If None, reduces over all dimensions. reduce_axis : int or iterable of int, optional Axis or axes along which to compute the mean spread and error (numpy only).

Returns

mean_spread : float, numpy.ndarray, or xarray.DataArray Mean ensemble spread. mean_error : float, numpy.ndarray, or xarray.DataArray Mean absolute error of ensemble mean vs. obs.

Source code in src/monet_stats/spatial_ensemble_metrics.py 
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def spread_error(
    ensemble: Union[xr.DataArray, np.ndarray],
    obs: Union[xr.DataArray, np.ndarray],
    axis: Union[int, str] = 0,
    dim: Optional[Union[str, Iterable[str]]] = None,
    reduce_axis: Optional[Union[int, Iterable[int]]] = None,
) -> Tuple[Any, Any]:
    """
    Spread-Error Relationship for ensemble forecasts (Aero Protocol).

    Typical Use Cases
    -----------------
    - Assessing if the ensemble spread is a good proxy for the forecast error.
    - Ideally, mean spread should equal RMSE of the ensemble mean.

    Parameters
    ----------
    ensemble : xarray.DataArray or numpy.ndarray
        Ensemble forecasts.
    obs : xarray.DataArray or numpy.ndarray
        Observed values.
    axis : int or str, optional
        Axis or dimension corresponding to ensemble members. Default is 0.
    dim : str or iterable of str, optional
        Dimension(s) along which to compute the mean spread and error (xarray only).
        If None, reduces over all dimensions.
    reduce_axis : int or iterable of int, optional
        Axis or axes along which to compute the mean spread and error (numpy only).

    Returns
    -------
    mean_spread : float, numpy.ndarray, or xarray.DataArray
        Mean ensemble spread.
    mean_error : float, numpy.ndarray, or xarray.DataArray
        Mean absolute error of ensemble mean vs. obs.
    """
    if isinstance(ensemble, xr.DataArray) and isinstance(obs, xr.DataArray):
        # Resolve ensemble dimension
        e_dim = axis
        if isinstance(axis, int):
            e_dim = ensemble.dims[axis]

        spread_field = ensemble.std(dim=e_dim)
        ens_mean_field = ensemble.mean(dim=e_dim)
        error_field = abs(ens_mean_field - obs)

        # Average over specified dimensions (or all remaining)
        m_spread = spread_field.mean(dim=dim)
        m_error = error_field.mean(dim=dim)

        return _update_history(m_spread, "Mean Ensemble Spread"), _update_history(m_error, "Mean Ensemble Error")

    # NumPy path
    ens = np.asarray(ensemble)
    observation = np.asarray(obs)

    # Calculate spread and ensemble mean
    spread_f = np.std(ens, axis=axis)
    ens_m_f = np.mean(ens, axis=axis)
    error_f = np.abs(ens_m_f - observation)

    # Average over specified axes
    m_spread = np.nanmean(spread_f, axis=reduce_axis)
    m_error = np.nanmean(error_f, axis=reduce_axis)

    if np.ndim(m_spread) == 0:
        return float(m_spread), float(m_error)
    return m_spread, m_error

Xarray Accessor

Xarray accessors for the MONET Stats package (Aero Protocol Compliant).

MonetDataArrayAccessor

Accessor for xarray.DataArray to provide MONET statistical methods.

Source code in src/monet_stats/accessor.py 
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@xr.register_dataarray_accessor("monet_stats")
class MonetDataArrayAccessor:
    """
    Accessor for xarray.DataArray to provide MONET statistical methods.
    """

    def __init__(self, xarray_obj: xr.DataArray) -> None:
        self._obj = xarray_obj

    def climatology(self, freq: str = "season", method: str = "mean", dim: str = "time") -> xr.DataArray:
        """
        Compute climatological statistics.

        Parameters
        ----------
        freq : str, optional
            Climatology frequency ('season', 'month', 'dayofyear', 'hour').
            Default is 'season'.
        method : str, optional
            Statistical method to apply ('mean', 'std', 'min', 'max', 'median').
            Default is 'mean'.
        dim : str, optional
            Dimension along which to compute climatology. Default is 'time'.

        Returns
        -------
        xarray.DataArray
            Climatological statistics.
        """
        return analysis.climatology(self._obj, freq=freq, method=method, dim=dim)

    def resample_data(self, freq: str = "MS", method: str = "mean", dim: str = "time", **kwargs: Any) -> xr.DataArray:
        """
        Resample data to a new temporal frequency.

        Parameters
        ----------
        freq : str, optional
            Resampling frequency (e.g., 'MS', 'W', 'D'). Default is 'MS'.
        method : str, optional
            Statistical method to apply ('mean', 'sum', 'min', 'max', 'std', 'median').
            Default is 'mean'.
        dim : str, optional
            Dimension along which to resample. Default is 'time'.
        **kwargs : Any
            Additional keyword arguments passed to the resample method.

        Returns
        -------
        xarray.DataArray
            Resampled data.
        """
        return analysis.resample_data(self._obj, freq=freq, method=method, dim=dim, **kwargs)

    def kz_filter(self, m: int, k: int, dim: str = "time") -> xr.DataArray:
        """
        Apply Kolmogorov-Zurbenko (KZ) filter.

        Parameters
        ----------
        m : int
            Window size for the moving average.
        k : int
            Number of iterations.
        dim : str, optional
            Dimension along which to apply the filter. Default is 'time'.

        Returns
        -------
        xarray.DataArray
            Filtered data.
        """
        return analysis.kz_filter(self._obj, m=m, k=k, dim=dim)

    def diurnal_cycle(self, method: str = "mean", dim: str = "time") -> xr.DataArray:
        """
        Compute the diurnal cycle (average hourly profile).

        Parameters
        ----------
        method : str, optional
            Statistical method to apply ('mean', 'median', 'std'). Default is 'mean'.
        dim : str, optional
            Dimension along which to compute the cycle. Default is 'time'.

        Returns
        -------
        xarray.DataArray
            Diurnal cycle.
        """
        return analysis.diurnal_cycle(self._obj, method=method, dim=dim)

    def rolling_mean_8h(self, dim: str = "time", min_periods: int = 6, center: bool = True) -> xr.DataArray:
        """
        Compute rolling 8-hour mean.

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute the mean. Default is 'time'.
        min_periods : int, optional
            Minimum number of observations in window. Default is 6.
        center : bool, optional
            If True, set the labels at the center of the window. Default is True.

        Returns
        -------
        xarray.DataArray
            Rolling 8-hour mean.
        """
        return analysis.rolling_mean_8h(self._obj, dim=dim, min_periods=min_periods, center=center)

    def rolling_mean_24h(self, dim: str = "time", min_periods: int = 18, center: bool = True) -> xr.DataArray:
        """
        Compute rolling 24-hour mean.

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute the mean. Default is 'time'.
        min_periods : int, optional
            Minimum number of observations in window. Default is 18.
        center : bool, optional
            If True, set the labels at the center of the window. Default is True.

        Returns
        -------
        xarray.DataArray
            Rolling 24-hour mean.
        """
        return analysis.rolling_mean_24h(self._obj, dim=dim, min_periods=min_periods, center=center)

    def mda1(self, dim: str = "time") -> xr.DataArray:
        """
        Compute Maximum Daily 1-hour Average (MDA1).

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute. Default is 'time'.

        Returns
        -------
        xarray.DataArray
            MDA1 values.
        """
        return analysis.mda1(self._obj, dim=dim)

    def mda8(self, dim: str = "time", min_periods: int = 6, center: bool = False) -> xr.DataArray:
        """
        Compute Maximum Daily 8-hour Average (MDA8).

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute. Default is 'time'.
        min_periods : int, optional
            Minimum number of observations for the 8-hour rolling mean. Default is 6.
        center : bool, optional
            Whether to center the 8-hour rolling window. Default is False.

        Returns
        -------
        xarray.DataArray
            MDA8 values.
        """
        return analysis.mda8(self._obj, dim=dim, min_periods=min_periods, center=center)

    def exceedance_count(self, threshold: float, dim: str = "time") -> xr.DataArray:
        """
        Count exceedances of a threshold.

        Parameters
        ----------
        threshold : float
            Value above which an exceedance is counted.
        dim : str, optional
            Dimension along which to count exceedances. Default is 'time'.

        Returns
        -------
        xarray.DataArray
            Number of exceedances.
        """
        return analysis.exceedance_count(self._obj, threshold=threshold, dim=dim)

    def percentile(self, q: Union[float, List[float], np.ndarray], dim: str = "time", **kwargs: Any) -> xr.DataArray:
        """
        Compute percentiles.

        Parameters
        ----------
        q : float or list of float
            Percentile(s) to compute (0-100).
        dim : str, optional
            Dimension over which to compute percentiles. Default is 'time'.
        **kwargs : Any
            Additional keyword arguments passed to xarray.quantile.

        Returns
        -------
        xarray.DataArray
            Computed percentiles.
        """
        return analysis.percentile(self._obj, q=q, dim=dim, **kwargs)

    def peak_timing(self, dim: str = "time") -> xr.DataArray:
        """
        Identify the coordinate value of the maximum.

        Parameters
        ----------
        dim : str, optional
            Dimension along which to find the peak. Default is 'time'.

        Returns
        -------
        xarray.DataArray
            Coordinate values where the maximum occurs.
        """
        return analysis.peak_timing(self._obj, dim=dim)

    def weighted_spatial_mean(
        self,
        lat_dim: str = "lat",
        lon_dim: str = "lon",
        weights: Optional[Union[xr.DataArray, np.ndarray]] = None,
    ) -> xr.DataArray:
        """
        Compute area-weighted spatial mean.

        Parameters
        ----------
        lat_dim : str, optional
            Name of the latitude dimension. Default is 'lat'.
        lon_dim : str, optional
            Name of the longitude dimension. Default is 'lon'.
        weights : xarray.DataArray or numpy.ndarray, optional
            Custom weights for the mean.

        Returns
        -------
        xarray.DataArray
            Area-weighted spatial mean.
        """
        return analysis.weighted_spatial_mean(self._obj, lat_dim=lat_dim, lon_dim=lon_dim, weights=weights)

    def fft_analysis(self, dim: str = "time", output: str = "psd") -> xr.DataArray:
        """
        Perform Fast Fourier Transform (FFT) analysis.

        Parameters
        ----------
        dim : str, optional
            Dimension along which to perform FFT. Default is 'time'.
        output : str, optional
            Type of output to return ('psd', 'magnitude', 'complex'). Default is 'psd'.

        Returns
        -------
        xarray.DataArray
            FFT results.
        """
        return analysis.fft_analysis(self._obj, dim=dim, output=output)

    def power_spectrum(
        self,
        dim: str = "time",
        fs: float = 1.0,
        window: str = "hann",
        nperseg: Optional[int] = None,
        **kwargs: Any,
    ) -> xr.DataArray:
        """
        Compute power spectrum using Welch's method.

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute the spectrum. Default is 'time'.
        fs : float, optional
            Sampling frequency. Default is 1.0.
        window : str, optional
            Desired window to use. Default is 'hann'.
        nperseg : int, optional
            Length of each segment.
        **kwargs : Any
            Additional keyword arguments passed to scipy.signal.welch.

        Returns
        -------
        xarray.DataArray
            Power spectral density.
        """
        return analysis.power_spectrum(self._obj, dim=dim, fs=fs, window=window, nperseg=nperseg, **kwargs)

    def seasonal_mean(self, dim: str = "time", weighted: bool = True) -> xr.DataArray:
        """
        Compute seasonal mean (DJF, MAM, JJA, SON).

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute the mean. Default is 'time'.
        weighted : bool, optional
            If True, weight by days in month. Default is True.

        Returns
        -------
        xarray.DataArray
            Seasonal means.
        """
        return analysis.seasonal_mean(self._obj, dim=dim, weighted=weighted)

    def monthly_climatology(self, dim: str = "time", method: str = "mean") -> xr.DataArray:
        """
        Compute monthly climatology.

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute the climatology. Default is 'time'.
        method : str, optional
            Statistical method to apply. Default is 'mean'.

        Returns
        -------
        xarray.DataArray
            Monthly climatology.
        """
        return analysis.monthly_climatology(self._obj, dim=dim, method=method)

    def anomalies(self, freq: str = "month", dim: str = "time") -> xr.DataArray:
        """
        Compute anomalies by subtracting the climatology.

        Parameters
        ----------
        freq : str, optional
            Climatology frequency ('season', 'month', 'dayofyear', 'hour').
            Default is 'month'.
        dim : str, optional
            Dimension along which to compute the anomalies. Default is 'time'.

        Returns
        -------
        xarray.DataArray
            Anomalies.
        """
        return analysis.anomalies(self._obj, freq=freq, dim=dim)

    def detrend(self, method: str = "linear", dim: str = "time") -> xr.DataArray:
        """
        Remove trend from data.

        Parameters
        ----------
        method : str, optional
            Detrending method ('linear', 'constant'). Default is 'linear'.
        dim : str, optional
            Dimension along which to detrend. Default is 'time'.

        Returns
        -------
        xarray.DataArray
            Detrended data.
        """
        return analysis.detrend(self._obj, method=method, dim=dim)

    def optimize(self, target_mb: float = 100.0) -> xr.DataArray:
        """
        Optimize performance by ensuring laziness and recommended chunks (Aero Protocol).

        Parameters
        ----------
        target_mb : float, optional
            Target size for each chunk in Megabytes. Default is 100.0.

        Returns
        -------
        xarray.DataArray
            Optimized DataArray.
        """
        from .utils_stats import _update_history

        if not performance._has_dask():
            return _update_history(self._obj, "Optimization skipped (Dask not installed)")

        # Ensure data is lazy
        res = performance.apply_lazy_threshold(self._obj, threshold_mb=0.1)
        # Always calculate and apply recommended chunks for the target size
        recommendation = performance.get_chunk_recommendation(res, target_mb=target_mb)
        res = res.chunk(recommendation)

        return _update_history(res, f"Optimized for performance (target={target_mb}MB)")

    def rechunk(self, chunks: Optional[dict] = None) -> xr.DataArray:
        """
        Apply new chunks to the DataArray (Aero Protocol provenance tracking).

        Parameters
        ----------
        chunks : dict, optional
            New chunk sizes. If None, uses optimal recommendations (~100MB).

        Returns
        -------
        xarray.DataArray
            Rechunked DataArray.
        """
        from .utils_stats import _update_history

        if not performance._has_dask():
            return _update_history(self._obj, "Rechunking skipped (Dask not installed)")

        if chunks is None:
            chunks = performance.get_chunk_recommendation(self._obj)

        res = self._obj.chunk(chunks)

        return _update_history(res, f"Rechunked with {chunks}")

    def taylor_statistics(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.Dataset:
        """
        Calculate components required for a Taylor diagram (Aero Protocol).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values (reference).
        dim : str or list of str, optional
            Dimension(s) along which to compute the statistics.

        Returns
        -------
        xarray.Dataset
            Dataset containing:
            - std_obs: Standard deviation of observations.
            - std_mod: Standard deviation of model predictions.
            - correlation: Pearson correlation coefficient.
        """
        obs, mod = xr.align(obs, self._obj, join="inner")
        from .utils_stats import _resolve_axis_to_dim, _update_history

        d = _resolve_axis_to_dim(obs, dim)

        res = xr.Dataset(
            {
                "std_obs": obs.std(dim=d),
                "std_mod": mod.std(dim=d),
                "correlation": correlation_metrics.pearsonr(obs, mod, axis=dim),
            }
        )
        return _update_history(res, "Taylor statistics components")

    def mae(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Mean Absolute Error (MAE).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Mean absolute error.
        """
        return error_metrics.MAE(obs, self._obj, axis=dim)

    def rmse(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Root Mean Square Error (RMSE).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Root mean square error.
        """
        return error_metrics.RMSE(obs, self._obj, axis=dim)

    def mb(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Mean Bias (MB).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Mean bias.
        """
        return error_metrics.MB(obs, self._obj, axis=dim)

    def ioa(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Index of Agreement (IOA).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Index of agreement.
        """
        return error_metrics.IOA(obs, self._obj, axis=dim)

    def crmse(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Centered Root Mean Square Error (CRMSE).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Centered root mean square error.
        """
        return error_metrics.CRMSE(obs, self._obj, axis=dim)

    def mdnb(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Median Bias (MdnB).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Median bias.
        """
        return error_metrics.MdnB(obs, self._obj, axis=dim)

    def nmse(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Normalized Mean Square Error (NMSE).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Normalized mean square error.
        """
        return error_metrics.NMSE(obs, self._obj, axis=dim)

    def pearsonr(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Pearson correlation coefficient.

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Pearson correlation coefficient.
        """
        return correlation_metrics.pearsonr(obs, self._obj, axis=dim)

    def r2(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Coefficient of Determination (R^2).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Coefficient of determination.
        """
        return correlation_metrics.R2(obs, self._obj, axis=dim)

    def kge(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Kling-Gupta Efficiency (KGE).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Kling-Gupta efficiency.
        """
        return correlation_metrics.KGE(obs, self._obj, axis=dim)

    def ccc(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Concordance Correlation Coefficient (CCC).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Concordance correlation coefficient.
        """
        return correlation_metrics.CCC(obs, self._obj, axis=dim)

    def nmb(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Normalized Mean Bias (NMB).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Normalized mean bias.
        """
        return relative_metrics.NMB(obs, self._obj, axis=dim)

    def fb(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Fractional Bias (FB).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Fractional bias.
        """
        return relative_metrics.FB(obs, self._obj, axis=dim)

    def mnb(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Mean Normalized Bias (MNB).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Mean normalized bias.
        """
        return error_metrics.MNB(obs, self._obj, axis=dim)

    def mne(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Mean Normalized Gross Error (MNE).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Mean normalized gross error.
        """
        return error_metrics.MNE(obs, self._obj, axis=dim)

    def nse(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
        """
        Compute Nash-Sutcliffe Efficiency (NSE).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metric.

        Returns
        -------
        xarray.DataArray
            Nash-Sutcliffe efficiency.
        """
        return efficiency_metrics.NSE(obs, self._obj, axis=dim)

    def verify(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.Dataset:
        """
        Calculate a bundle of common evaluation metrics (Aero Protocol).

        Parameters
        ----------
        obs : xarray.DataArray
            Observed values.
        dim : str or list of str, optional
            Dimension(s) along which to compute the metrics.

        Returns
        -------
        xarray.Dataset
            Dataset containing: MAE, RMSE, MB, R, IOA, NMB, MNB, MNE, NSE, and R2.
        """
        metrics = {
            "MAE": error_metrics.MAE(obs, self._obj, axis=dim),
            "RMSE": error_metrics.RMSE(obs, self._obj, axis=dim),
            "MB": error_metrics.MB(obs, self._obj, axis=dim),
            "R": correlation_metrics.pearsonr(obs, self._obj, axis=dim),
            "IOA": error_metrics.IOA(obs, self._obj, axis=dim),
            "NMB": relative_metrics.NMB(obs, self._obj, axis=dim),
            "MNB": error_metrics.MNB(obs, self._obj, axis=dim),
            "MNE": error_metrics.MNE(obs, self._obj, axis=dim),
            "NSE": efficiency_metrics.NSE(obs, self._obj, axis=dim),
            "R2": correlation_metrics.R2(obs, self._obj, axis=dim),
        }
        res = xr.Dataset(metrics)
        from .utils_stats import _update_history

        return _update_history(res, "Verification metrics bundle (verify)")

    def plot_spatial(
        self,
        method: str = "matplotlib",
        lat_dim: str = "lat",
        lon_dim: str = "lon",
        title: Optional[str] = None,
        cmap: str = "viridis",
        **kwargs: Any,
    ) -> Any:
        """
        Plot spatial data following the Aero Protocol's Two-Track Rule.

        Parameters
        ----------
        method : str, optional
            Plotting track: 'matplotlib' (Track A) or 'hvplot' (Track B).
            Default is 'matplotlib'.
        lat_dim : str, optional
            Latitude dimension name. Default is 'lat'.
        lon_dim : str, optional
            Longitude dimension name. Default is 'lon'.
        title : str, optional
            Plot title.
        cmap : str, optional
            Colormap. Default is 'viridis'.
        **kwargs : Any
            Additional keyword arguments.

        Returns
        -------
        Any
            The plot object.
        """
        from .visualize import plot_spatial

        return plot_spatial(
            self._obj,
            method=method,
            lat_dim=lat_dim,
            lon_dim=lon_dim,
            title=title,
            cmap=cmap,
            **kwargs,
        )

anomalies(freq='month', dim='time')

Compute anomalies by subtracting the climatology.

Parameters

freq : str, optional Climatology frequency ('season', 'month', 'dayofyear', 'hour'). Default is 'month'. dim : str, optional Dimension along which to compute the anomalies. Default is 'time'.

Returns

xarray.DataArray Anomalies.

Source code in src/monet_stats/accessor.py 
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def anomalies(self, freq: str = "month", dim: str = "time") -> xr.DataArray:
    """
    Compute anomalies by subtracting the climatology.

    Parameters
    ----------
    freq : str, optional
        Climatology frequency ('season', 'month', 'dayofyear', 'hour').
        Default is 'month'.
    dim : str, optional
        Dimension along which to compute the anomalies. Default is 'time'.

    Returns
    -------
    xarray.DataArray
        Anomalies.
    """
    return analysis.anomalies(self._obj, freq=freq, dim=dim)

ccc(obs, dim=None)

Compute Concordance Correlation Coefficient (CCC).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Concordance correlation coefficient.

Source code in src/monet_stats/accessor.py 
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def ccc(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Concordance Correlation Coefficient (CCC).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Concordance correlation coefficient.
    """
    return correlation_metrics.CCC(obs, self._obj, axis=dim)

climatology(freq='season', method='mean', dim='time')

Compute climatological statistics.

Parameters

freq : str, optional Climatology frequency ('season', 'month', 'dayofyear', 'hour'). Default is 'season'. method : str, optional Statistical method to apply ('mean', 'std', 'min', 'max', 'median'). Default is 'mean'. dim : str, optional Dimension along which to compute climatology. Default is 'time'.

Returns

xarray.DataArray Climatological statistics.

Source code in src/monet_stats/accessor.py 
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def climatology(self, freq: str = "season", method: str = "mean", dim: str = "time") -> xr.DataArray:
    """
    Compute climatological statistics.

    Parameters
    ----------
    freq : str, optional
        Climatology frequency ('season', 'month', 'dayofyear', 'hour').
        Default is 'season'.
    method : str, optional
        Statistical method to apply ('mean', 'std', 'min', 'max', 'median').
        Default is 'mean'.
    dim : str, optional
        Dimension along which to compute climatology. Default is 'time'.

    Returns
    -------
    xarray.DataArray
        Climatological statistics.
    """
    return analysis.climatology(self._obj, freq=freq, method=method, dim=dim)

crmse(obs, dim=None)

Compute Centered Root Mean Square Error (CRMSE).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Centered root mean square error.

Source code in src/monet_stats/accessor.py 
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def crmse(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Centered Root Mean Square Error (CRMSE).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Centered root mean square error.
    """
    return error_metrics.CRMSE(obs, self._obj, axis=dim)

detrend(method='linear', dim='time')

Remove trend from data.

Parameters

method : str, optional Detrending method ('linear', 'constant'). Default is 'linear'. dim : str, optional Dimension along which to detrend. Default is 'time'.

Returns

xarray.DataArray Detrended data.

Source code in src/monet_stats/accessor.py 
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def detrend(self, method: str = "linear", dim: str = "time") -> xr.DataArray:
    """
    Remove trend from data.

    Parameters
    ----------
    method : str, optional
        Detrending method ('linear', 'constant'). Default is 'linear'.
    dim : str, optional
        Dimension along which to detrend. Default is 'time'.

    Returns
    -------
    xarray.DataArray
        Detrended data.
    """
    return analysis.detrend(self._obj, method=method, dim=dim)

diurnal_cycle(method='mean', dim='time')

Compute the diurnal cycle (average hourly profile).

Parameters

method : str, optional Statistical method to apply ('mean', 'median', 'std'). Default is 'mean'. dim : str, optional Dimension along which to compute the cycle. Default is 'time'.

Returns

xarray.DataArray Diurnal cycle.

Source code in src/monet_stats/accessor.py 
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def diurnal_cycle(self, method: str = "mean", dim: str = "time") -> xr.DataArray:
    """
    Compute the diurnal cycle (average hourly profile).

    Parameters
    ----------
    method : str, optional
        Statistical method to apply ('mean', 'median', 'std'). Default is 'mean'.
    dim : str, optional
        Dimension along which to compute the cycle. Default is 'time'.

    Returns
    -------
    xarray.DataArray
        Diurnal cycle.
    """
    return analysis.diurnal_cycle(self._obj, method=method, dim=dim)

exceedance_count(threshold, dim='time')

Count exceedances of a threshold.

Parameters

threshold : float Value above which an exceedance is counted. dim : str, optional Dimension along which to count exceedances. Default is 'time'.

Returns

xarray.DataArray Number of exceedances.

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def exceedance_count(self, threshold: float, dim: str = "time") -> xr.DataArray:
    """
    Count exceedances of a threshold.

    Parameters
    ----------
    threshold : float
        Value above which an exceedance is counted.
    dim : str, optional
        Dimension along which to count exceedances. Default is 'time'.

    Returns
    -------
    xarray.DataArray
        Number of exceedances.
    """
    return analysis.exceedance_count(self._obj, threshold=threshold, dim=dim)

fb(obs, dim=None)

Compute Fractional Bias (FB).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Fractional bias.

Source code in src/monet_stats/accessor.py 
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def fb(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Fractional Bias (FB).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Fractional bias.
    """
    return relative_metrics.FB(obs, self._obj, axis=dim)

fft_analysis(dim='time', output='psd')

Perform Fast Fourier Transform (FFT) analysis.

Parameters

dim : str, optional Dimension along which to perform FFT. Default is 'time'. output : str, optional Type of output to return ('psd', 'magnitude', 'complex'). Default is 'psd'.

Returns

xarray.DataArray FFT results.

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def fft_analysis(self, dim: str = "time", output: str = "psd") -> xr.DataArray:
    """
    Perform Fast Fourier Transform (FFT) analysis.

    Parameters
    ----------
    dim : str, optional
        Dimension along which to perform FFT. Default is 'time'.
    output : str, optional
        Type of output to return ('psd', 'magnitude', 'complex'). Default is 'psd'.

    Returns
    -------
    xarray.DataArray
        FFT results.
    """
    return analysis.fft_analysis(self._obj, dim=dim, output=output)

ioa(obs, dim=None)

Compute Index of Agreement (IOA).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Index of agreement.

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def ioa(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Index of Agreement (IOA).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Index of agreement.
    """
    return error_metrics.IOA(obs, self._obj, axis=dim)

kge(obs, dim=None)

Compute Kling-Gupta Efficiency (KGE).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Kling-Gupta efficiency.

Source code in src/monet_stats/accessor.py 
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def kge(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Kling-Gupta Efficiency (KGE).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Kling-Gupta efficiency.
    """
    return correlation_metrics.KGE(obs, self._obj, axis=dim)

kz_filter(m, k, dim='time')

Apply Kolmogorov-Zurbenko (KZ) filter.

Parameters

m : int Window size for the moving average. k : int Number of iterations. dim : str, optional Dimension along which to apply the filter. Default is 'time'.

Returns

xarray.DataArray Filtered data.

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def kz_filter(self, m: int, k: int, dim: str = "time") -> xr.DataArray:
    """
    Apply Kolmogorov-Zurbenko (KZ) filter.

    Parameters
    ----------
    m : int
        Window size for the moving average.
    k : int
        Number of iterations.
    dim : str, optional
        Dimension along which to apply the filter. Default is 'time'.

    Returns
    -------
    xarray.DataArray
        Filtered data.
    """
    return analysis.kz_filter(self._obj, m=m, k=k, dim=dim)

mae(obs, dim=None)

Compute Mean Absolute Error (MAE).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Mean absolute error.

Source code in src/monet_stats/accessor.py 
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def mae(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Mean Absolute Error (MAE).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Mean absolute error.
    """
    return error_metrics.MAE(obs, self._obj, axis=dim)

mb(obs, dim=None)

Compute Mean Bias (MB).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Mean bias.

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def mb(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Mean Bias (MB).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Mean bias.
    """
    return error_metrics.MB(obs, self._obj, axis=dim)

mda1(dim='time')

Compute Maximum Daily 1-hour Average (MDA1).

Parameters

dim : str, optional Dimension along which to compute. Default is 'time'.

Returns

xarray.DataArray MDA1 values.

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def mda1(self, dim: str = "time") -> xr.DataArray:
    """
    Compute Maximum Daily 1-hour Average (MDA1).

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute. Default is 'time'.

    Returns
    -------
    xarray.DataArray
        MDA1 values.
    """
    return analysis.mda1(self._obj, dim=dim)

mda8(dim='time', min_periods=6, center=False)

Compute Maximum Daily 8-hour Average (MDA8).

Parameters

dim : str, optional Dimension along which to compute. Default is 'time'. min_periods : int, optional Minimum number of observations for the 8-hour rolling mean. Default is 6. center : bool, optional Whether to center the 8-hour rolling window. Default is False.

Returns

xarray.DataArray MDA8 values.

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def mda8(self, dim: str = "time", min_periods: int = 6, center: bool = False) -> xr.DataArray:
    """
    Compute Maximum Daily 8-hour Average (MDA8).

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute. Default is 'time'.
    min_periods : int, optional
        Minimum number of observations for the 8-hour rolling mean. Default is 6.
    center : bool, optional
        Whether to center the 8-hour rolling window. Default is False.

    Returns
    -------
    xarray.DataArray
        MDA8 values.
    """
    return analysis.mda8(self._obj, dim=dim, min_periods=min_periods, center=center)

mdnb(obs, dim=None)

Compute Median Bias (MdnB).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Median bias.

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def mdnb(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Median Bias (MdnB).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Median bias.
    """
    return error_metrics.MdnB(obs, self._obj, axis=dim)

mnb(obs, dim=None)

Compute Mean Normalized Bias (MNB).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Mean normalized bias.

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def mnb(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Mean Normalized Bias (MNB).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Mean normalized bias.
    """
    return error_metrics.MNB(obs, self._obj, axis=dim)

mne(obs, dim=None)

Compute Mean Normalized Gross Error (MNE).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Mean normalized gross error.

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def mne(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Mean Normalized Gross Error (MNE).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Mean normalized gross error.
    """
    return error_metrics.MNE(obs, self._obj, axis=dim)

monthly_climatology(dim='time', method='mean')

Compute monthly climatology.

Parameters

dim : str, optional Dimension along which to compute the climatology. Default is 'time'. method : str, optional Statistical method to apply. Default is 'mean'.

Returns

xarray.DataArray Monthly climatology.

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def monthly_climatology(self, dim: str = "time", method: str = "mean") -> xr.DataArray:
    """
    Compute monthly climatology.

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute the climatology. Default is 'time'.
    method : str, optional
        Statistical method to apply. Default is 'mean'.

    Returns
    -------
    xarray.DataArray
        Monthly climatology.
    """
    return analysis.monthly_climatology(self._obj, dim=dim, method=method)

nmb(obs, dim=None)

Compute Normalized Mean Bias (NMB).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Normalized mean bias.

Source code in src/monet_stats/accessor.py 
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def nmb(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Normalized Mean Bias (NMB).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Normalized mean bias.
    """
    return relative_metrics.NMB(obs, self._obj, axis=dim)

nmse(obs, dim=None)

Compute Normalized Mean Square Error (NMSE).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Normalized mean square error.

Source code in src/monet_stats/accessor.py 
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def nmse(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Normalized Mean Square Error (NMSE).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Normalized mean square error.
    """
    return error_metrics.NMSE(obs, self._obj, axis=dim)

nse(obs, dim=None)

Compute Nash-Sutcliffe Efficiency (NSE).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Nash-Sutcliffe efficiency.

Source code in src/monet_stats/accessor.py 
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def nse(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Nash-Sutcliffe Efficiency (NSE).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Nash-Sutcliffe efficiency.
    """
    return efficiency_metrics.NSE(obs, self._obj, axis=dim)

optimize(target_mb=100.0)

Optimize performance by ensuring laziness and recommended chunks (Aero Protocol).

Parameters

target_mb : float, optional Target size for each chunk in Megabytes. Default is 100.0.

Returns

xarray.DataArray Optimized DataArray.

Source code in src/monet_stats/accessor.py 
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def optimize(self, target_mb: float = 100.0) -> xr.DataArray:
    """
    Optimize performance by ensuring laziness and recommended chunks (Aero Protocol).

    Parameters
    ----------
    target_mb : float, optional
        Target size for each chunk in Megabytes. Default is 100.0.

    Returns
    -------
    xarray.DataArray
        Optimized DataArray.
    """
    from .utils_stats import _update_history

    if not performance._has_dask():
        return _update_history(self._obj, "Optimization skipped (Dask not installed)")

    # Ensure data is lazy
    res = performance.apply_lazy_threshold(self._obj, threshold_mb=0.1)
    # Always calculate and apply recommended chunks for the target size
    recommendation = performance.get_chunk_recommendation(res, target_mb=target_mb)
    res = res.chunk(recommendation)

    return _update_history(res, f"Optimized for performance (target={target_mb}MB)")

peak_timing(dim='time')

Identify the coordinate value of the maximum.

Parameters

dim : str, optional Dimension along which to find the peak. Default is 'time'.

Returns

xarray.DataArray Coordinate values where the maximum occurs.

Source code in src/monet_stats/accessor.py 
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def peak_timing(self, dim: str = "time") -> xr.DataArray:
    """
    Identify the coordinate value of the maximum.

    Parameters
    ----------
    dim : str, optional
        Dimension along which to find the peak. Default is 'time'.

    Returns
    -------
    xarray.DataArray
        Coordinate values where the maximum occurs.
    """
    return analysis.peak_timing(self._obj, dim=dim)

pearsonr(obs, dim=None)

Compute Pearson correlation coefficient.

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Pearson correlation coefficient.

Source code in src/monet_stats/accessor.py 
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def pearsonr(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Pearson correlation coefficient.

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Pearson correlation coefficient.
    """
    return correlation_metrics.pearsonr(obs, self._obj, axis=dim)

percentile(q, dim='time', **kwargs)

Compute percentiles.

Parameters

q : float or list of float Percentile(s) to compute (0-100). dim : str, optional Dimension over which to compute percentiles. Default is 'time'. **kwargs : Any Additional keyword arguments passed to xarray.quantile.

Returns

xarray.DataArray Computed percentiles.

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def percentile(self, q: Union[float, List[float], np.ndarray], dim: str = "time", **kwargs: Any) -> xr.DataArray:
    """
    Compute percentiles.

    Parameters
    ----------
    q : float or list of float
        Percentile(s) to compute (0-100).
    dim : str, optional
        Dimension over which to compute percentiles. Default is 'time'.
    **kwargs : Any
        Additional keyword arguments passed to xarray.quantile.

    Returns
    -------
    xarray.DataArray
        Computed percentiles.
    """
    return analysis.percentile(self._obj, q=q, dim=dim, **kwargs)

plot_spatial(method='matplotlib', lat_dim='lat', lon_dim='lon', title=None, cmap='viridis', **kwargs)

Plot spatial data following the Aero Protocol's Two-Track Rule.

Parameters

method : str, optional Plotting track: 'matplotlib' (Track A) or 'hvplot' (Track B). Default is 'matplotlib'. lat_dim : str, optional Latitude dimension name. Default is 'lat'. lon_dim : str, optional Longitude dimension name. Default is 'lon'. title : str, optional Plot title. cmap : str, optional Colormap. Default is 'viridis'. **kwargs : Any Additional keyword arguments.

Returns

Any The plot object.

Source code in src/monet_stats/accessor.py 
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def plot_spatial(
    self,
    method: str = "matplotlib",
    lat_dim: str = "lat",
    lon_dim: str = "lon",
    title: Optional[str] = None,
    cmap: str = "viridis",
    **kwargs: Any,
) -> Any:
    """
    Plot spatial data following the Aero Protocol's Two-Track Rule.

    Parameters
    ----------
    method : str, optional
        Plotting track: 'matplotlib' (Track A) or 'hvplot' (Track B).
        Default is 'matplotlib'.
    lat_dim : str, optional
        Latitude dimension name. Default is 'lat'.
    lon_dim : str, optional
        Longitude dimension name. Default is 'lon'.
    title : str, optional
        Plot title.
    cmap : str, optional
        Colormap. Default is 'viridis'.
    **kwargs : Any
        Additional keyword arguments.

    Returns
    -------
    Any
        The plot object.
    """
    from .visualize import plot_spatial

    return plot_spatial(
        self._obj,
        method=method,
        lat_dim=lat_dim,
        lon_dim=lon_dim,
        title=title,
        cmap=cmap,
        **kwargs,
    )

power_spectrum(dim='time', fs=1.0, window='hann', nperseg=None, **kwargs)

Compute power spectrum using Welch's method.

Parameters

dim : str, optional Dimension along which to compute the spectrum. Default is 'time'. fs : float, optional Sampling frequency. Default is 1.0. window : str, optional Desired window to use. Default is 'hann'. nperseg : int, optional Length of each segment. **kwargs : Any Additional keyword arguments passed to scipy.signal.welch.

Returns

xarray.DataArray Power spectral density.

Source code in src/monet_stats/accessor.py 
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def power_spectrum(
    self,
    dim: str = "time",
    fs: float = 1.0,
    window: str = "hann",
    nperseg: Optional[int] = None,
    **kwargs: Any,
) -> xr.DataArray:
    """
    Compute power spectrum using Welch's method.

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute the spectrum. Default is 'time'.
    fs : float, optional
        Sampling frequency. Default is 1.0.
    window : str, optional
        Desired window to use. Default is 'hann'.
    nperseg : int, optional
        Length of each segment.
    **kwargs : Any
        Additional keyword arguments passed to scipy.signal.welch.

    Returns
    -------
    xarray.DataArray
        Power spectral density.
    """
    return analysis.power_spectrum(self._obj, dim=dim, fs=fs, window=window, nperseg=nperseg, **kwargs)

r2(obs, dim=None)

Compute Coefficient of Determination (R^2).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Coefficient of determination.

Source code in src/monet_stats/accessor.py 
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def r2(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Coefficient of Determination (R^2).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Coefficient of determination.
    """
    return correlation_metrics.R2(obs, self._obj, axis=dim)

rechunk(chunks=None)

Apply new chunks to the DataArray (Aero Protocol provenance tracking).

Parameters

chunks : dict, optional New chunk sizes. If None, uses optimal recommendations (~100MB).

Returns

xarray.DataArray Rechunked DataArray.

Source code in src/monet_stats/accessor.py 
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def rechunk(self, chunks: Optional[dict] = None) -> xr.DataArray:
    """
    Apply new chunks to the DataArray (Aero Protocol provenance tracking).

    Parameters
    ----------
    chunks : dict, optional
        New chunk sizes. If None, uses optimal recommendations (~100MB).

    Returns
    -------
    xarray.DataArray
        Rechunked DataArray.
    """
    from .utils_stats import _update_history

    if not performance._has_dask():
        return _update_history(self._obj, "Rechunking skipped (Dask not installed)")

    if chunks is None:
        chunks = performance.get_chunk_recommendation(self._obj)

    res = self._obj.chunk(chunks)

    return _update_history(res, f"Rechunked with {chunks}")

resample_data(freq='MS', method='mean', dim='time', **kwargs)

Resample data to a new temporal frequency.

Parameters

freq : str, optional Resampling frequency (e.g., 'MS', 'W', 'D'). Default is 'MS'. method : str, optional Statistical method to apply ('mean', 'sum', 'min', 'max', 'std', 'median'). Default is 'mean'. dim : str, optional Dimension along which to resample. Default is 'time'. **kwargs : Any Additional keyword arguments passed to the resample method.

Returns

xarray.DataArray Resampled data.

Source code in src/monet_stats/accessor.py 
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def resample_data(self, freq: str = "MS", method: str = "mean", dim: str = "time", **kwargs: Any) -> xr.DataArray:
    """
    Resample data to a new temporal frequency.

    Parameters
    ----------
    freq : str, optional
        Resampling frequency (e.g., 'MS', 'W', 'D'). Default is 'MS'.
    method : str, optional
        Statistical method to apply ('mean', 'sum', 'min', 'max', 'std', 'median').
        Default is 'mean'.
    dim : str, optional
        Dimension along which to resample. Default is 'time'.
    **kwargs : Any
        Additional keyword arguments passed to the resample method.

    Returns
    -------
    xarray.DataArray
        Resampled data.
    """
    return analysis.resample_data(self._obj, freq=freq, method=method, dim=dim, **kwargs)

rmse(obs, dim=None)

Compute Root Mean Square Error (RMSE).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metric.

Returns

xarray.DataArray Root mean square error.

Source code in src/monet_stats/accessor.py 
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def rmse(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.DataArray:
    """
    Compute Root Mean Square Error (RMSE).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metric.

    Returns
    -------
    xarray.DataArray
        Root mean square error.
    """
    return error_metrics.RMSE(obs, self._obj, axis=dim)

rolling_mean_24h(dim='time', min_periods=18, center=True)

Compute rolling 24-hour mean.

Parameters

dim : str, optional Dimension along which to compute the mean. Default is 'time'. min_periods : int, optional Minimum number of observations in window. Default is 18. center : bool, optional If True, set the labels at the center of the window. Default is True.

Returns

xarray.DataArray Rolling 24-hour mean.

Source code in src/monet_stats/accessor.py 
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def rolling_mean_24h(self, dim: str = "time", min_periods: int = 18, center: bool = True) -> xr.DataArray:
    """
    Compute rolling 24-hour mean.

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute the mean. Default is 'time'.
    min_periods : int, optional
        Minimum number of observations in window. Default is 18.
    center : bool, optional
        If True, set the labels at the center of the window. Default is True.

    Returns
    -------
    xarray.DataArray
        Rolling 24-hour mean.
    """
    return analysis.rolling_mean_24h(self._obj, dim=dim, min_periods=min_periods, center=center)

rolling_mean_8h(dim='time', min_periods=6, center=True)

Compute rolling 8-hour mean.

Parameters

dim : str, optional Dimension along which to compute the mean. Default is 'time'. min_periods : int, optional Minimum number of observations in window. Default is 6. center : bool, optional If True, set the labels at the center of the window. Default is True.

Returns

xarray.DataArray Rolling 8-hour mean.

Source code in src/monet_stats/accessor.py 
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def rolling_mean_8h(self, dim: str = "time", min_periods: int = 6, center: bool = True) -> xr.DataArray:
    """
    Compute rolling 8-hour mean.

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute the mean. Default is 'time'.
    min_periods : int, optional
        Minimum number of observations in window. Default is 6.
    center : bool, optional
        If True, set the labels at the center of the window. Default is True.

    Returns
    -------
    xarray.DataArray
        Rolling 8-hour mean.
    """
    return analysis.rolling_mean_8h(self._obj, dim=dim, min_periods=min_periods, center=center)

seasonal_mean(dim='time', weighted=True)

Compute seasonal mean (DJF, MAM, JJA, SON).

Parameters

dim : str, optional Dimension along which to compute the mean. Default is 'time'. weighted : bool, optional If True, weight by days in month. Default is True.

Returns

xarray.DataArray Seasonal means.

Source code in src/monet_stats/accessor.py 
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def seasonal_mean(self, dim: str = "time", weighted: bool = True) -> xr.DataArray:
    """
    Compute seasonal mean (DJF, MAM, JJA, SON).

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute the mean. Default is 'time'.
    weighted : bool, optional
        If True, weight by days in month. Default is True.

    Returns
    -------
    xarray.DataArray
        Seasonal means.
    """
    return analysis.seasonal_mean(self._obj, dim=dim, weighted=weighted)

taylor_statistics(obs, dim=None)

Calculate components required for a Taylor diagram (Aero Protocol).

Parameters

obs : xarray.DataArray Observed values (reference). dim : str or list of str, optional Dimension(s) along which to compute the statistics.

Returns

xarray.Dataset Dataset containing: - std_obs: Standard deviation of observations. - std_mod: Standard deviation of model predictions. - correlation: Pearson correlation coefficient.

Source code in src/monet_stats/accessor.py 
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def taylor_statistics(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.Dataset:
    """
    Calculate components required for a Taylor diagram (Aero Protocol).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values (reference).
    dim : str or list of str, optional
        Dimension(s) along which to compute the statistics.

    Returns
    -------
    xarray.Dataset
        Dataset containing:
        - std_obs: Standard deviation of observations.
        - std_mod: Standard deviation of model predictions.
        - correlation: Pearson correlation coefficient.
    """
    obs, mod = xr.align(obs, self._obj, join="inner")
    from .utils_stats import _resolve_axis_to_dim, _update_history

    d = _resolve_axis_to_dim(obs, dim)

    res = xr.Dataset(
        {
            "std_obs": obs.std(dim=d),
            "std_mod": mod.std(dim=d),
            "correlation": correlation_metrics.pearsonr(obs, mod, axis=dim),
        }
    )
    return _update_history(res, "Taylor statistics components")

verify(obs, dim=None)

Calculate a bundle of common evaluation metrics (Aero Protocol).

Parameters

obs : xarray.DataArray Observed values. dim : str or list of str, optional Dimension(s) along which to compute the metrics.

Returns

xarray.Dataset Dataset containing: MAE, RMSE, MB, R, IOA, NMB, MNB, MNE, NSE, and R2.

Source code in src/monet_stats/accessor.py 
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def verify(self, obs: xr.DataArray, dim: Optional[Union[str, List[str]]] = None) -> xr.Dataset:
    """
    Calculate a bundle of common evaluation metrics (Aero Protocol).

    Parameters
    ----------
    obs : xarray.DataArray
        Observed values.
    dim : str or list of str, optional
        Dimension(s) along which to compute the metrics.

    Returns
    -------
    xarray.Dataset
        Dataset containing: MAE, RMSE, MB, R, IOA, NMB, MNB, MNE, NSE, and R2.
    """
    metrics = {
        "MAE": error_metrics.MAE(obs, self._obj, axis=dim),
        "RMSE": error_metrics.RMSE(obs, self._obj, axis=dim),
        "MB": error_metrics.MB(obs, self._obj, axis=dim),
        "R": correlation_metrics.pearsonr(obs, self._obj, axis=dim),
        "IOA": error_metrics.IOA(obs, self._obj, axis=dim),
        "NMB": relative_metrics.NMB(obs, self._obj, axis=dim),
        "MNB": error_metrics.MNB(obs, self._obj, axis=dim),
        "MNE": error_metrics.MNE(obs, self._obj, axis=dim),
        "NSE": efficiency_metrics.NSE(obs, self._obj, axis=dim),
        "R2": correlation_metrics.R2(obs, self._obj, axis=dim),
    }
    res = xr.Dataset(metrics)
    from .utils_stats import _update_history

    return _update_history(res, "Verification metrics bundle (verify)")

weighted_spatial_mean(lat_dim='lat', lon_dim='lon', weights=None)

Compute area-weighted spatial mean.

Parameters

lat_dim : str, optional Name of the latitude dimension. Default is 'lat'. lon_dim : str, optional Name of the longitude dimension. Default is 'lon'. weights : xarray.DataArray or numpy.ndarray, optional Custom weights for the mean.

Returns

xarray.DataArray Area-weighted spatial mean.

Source code in src/monet_stats/accessor.py 
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def weighted_spatial_mean(
    self,
    lat_dim: str = "lat",
    lon_dim: str = "lon",
    weights: Optional[Union[xr.DataArray, np.ndarray]] = None,
) -> xr.DataArray:
    """
    Compute area-weighted spatial mean.

    Parameters
    ----------
    lat_dim : str, optional
        Name of the latitude dimension. Default is 'lat'.
    lon_dim : str, optional
        Name of the longitude dimension. Default is 'lon'.
    weights : xarray.DataArray or numpy.ndarray, optional
        Custom weights for the mean.

    Returns
    -------
    xarray.DataArray
        Area-weighted spatial mean.
    """
    return analysis.weighted_spatial_mean(self._obj, lat_dim=lat_dim, lon_dim=lon_dim, weights=weights)

MonetDatasetAccessor

Accessor for xarray.Dataset to provide MONET statistical methods.

Source code in src/monet_stats/accessor.py 
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@xr.register_dataset_accessor("monet_stats")
class MonetDatasetAccessor:
    """
    Accessor for xarray.Dataset to provide MONET statistical methods.
    """

    def __init__(self, xarray_obj: xr.Dataset) -> None:
        self._obj = xarray_obj

    def stats(
        self,
        obs_name: str = "Obs",
        mod_name: str = "Mod",
        threshold: float = 0.0,
        minval: Optional[float] = None,
        maxval: Optional[float] = None,
    ) -> dict:
        """
        Calculate summary statistics for observations and model results.

        Parameters
        ----------
        obs_name : str, optional
            Name of observation variable. Default is 'Obs'.
        mod_name : str, optional
            Name of model variable. Default is 'Mod'.
        threshold : float, optional
            Threshold for contingency scores. Default is 0.0.
        minval : float, optional
            Minimum value for filtering.
        maxval : float, optional
            Maximum value for filtering.

        Returns
        -------
        dict
            Dictionary of calculated statistics.
        """
        from . import stats

        return stats(
            self._obj,
            obs_name=obs_name,
            mod_name=mod_name,
            threshold=threshold,
            minval=minval,
            maxval=maxval,
        )

    def climatology(self, freq: str = "season", method: str = "mean", dim: str = "time") -> xr.Dataset:
        """
        Compute climatological statistics.

        Parameters
        ----------
        freq : str, optional
            Climatology frequency. Default is 'season'.
        method : str, optional
            Statistical method. Default is 'mean'.
        dim : str, optional
            Dimension along which to compute. Default is 'time'.

        Returns
        -------
        xarray.Dataset
            Climatological statistics.
        """
        return analysis.climatology(self._obj, freq=freq, method=method, dim=dim)

    def resample_data(self, freq: str = "MS", method: str = "mean", dim: str = "time", **kwargs: Any) -> xr.Dataset:
        """
        Resample data to a new temporal frequency.

        Parameters
        ----------
        freq : str, optional
            Resampling frequency. Default is 'MS'.
        method : str, optional
            Statistical method. Default is 'mean'.
        dim : str, optional
            Dimension along which to resample. Default is 'time'.
        **kwargs : Any
            Additional keyword arguments.

        Returns
        -------
        xarray.Dataset
            Resampled data.
        """
        return analysis.resample_data(self._obj, freq=freq, method=method, dim=dim, **kwargs)

    def kz_filter(self, m: int, k: int, dim: str = "time") -> xr.Dataset:
        """
        Apply Kolmogorov-Zurbenko (KZ) filter.

        Parameters
        ----------
        m : int
            Window size.
        k : int
            Number of iterations.
        dim : str, optional
            Dimension along which to apply. Default is 'time'.

        Returns
        -------
        xarray.Dataset
            Filtered data.
        """
        return analysis.kz_filter(self._obj, m=m, k=k, dim=dim)

    def diurnal_cycle(self, method: str = "mean", dim: str = "time") -> xr.Dataset:
        """
        Compute the diurnal cycle.

        Parameters
        ----------
        method : str, optional
            Statistical method. Default is 'mean'.
        dim : str, optional
            Dimension along which to compute. Default is 'time'.

        Returns
        -------
        xarray.Dataset
            Diurnal cycle.
        """
        return analysis.diurnal_cycle(self._obj, method=method, dim=dim)

    def rolling_mean_8h(self, dim: str = "time", min_periods: int = 6, center: bool = True) -> xr.Dataset:
        """
        Compute rolling 8-hour mean.

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute. Default is 'time'.
        min_periods : int, optional
            Minimum number of observations. Default is 6.
        center : bool, optional
            If True, center the labels. Default is True.

        Returns
        -------
        xarray.Dataset
            Rolling 8-hour mean.
        """
        return analysis.rolling_mean_8h(self._obj, dim=dim, min_periods=min_periods, center=center)

    def rolling_mean_24h(self, dim: str = "time", min_periods: int = 18, center: bool = True) -> xr.Dataset:
        """
        Compute rolling 24-hour mean.

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute. Default is 'time'.
        min_periods : int, optional
            Minimum number of observations. Default is 18.
        center : bool, optional
            If True, center the labels. Default is True.

        Returns
        -------
        xarray.Dataset
            Rolling 24-hour mean.
        """
        return analysis.rolling_mean_24h(self._obj, dim=dim, min_periods=min_periods, center=center)

    def mda1(self, dim: str = "time") -> xr.Dataset:
        """
        Compute Maximum Daily 1-hour Average (MDA1).

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute. Default is 'time'.

        Returns
        -------
        xarray.Dataset
            MDA1 values.
        """
        return analysis.mda1(self._obj, dim=dim)

    def mda8(self, dim: str = "time", min_periods: int = 6, center: bool = False) -> xr.Dataset:
        """
        Compute Maximum Daily 8-hour Average (MDA8).

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute. Default is 'time'.
        min_periods : int, optional
            Minimum number of observations. Default is 6.
        center : bool, optional
            Whether to center the window. Default is False.

        Returns
        -------
        xarray.Dataset
            MDA8 values.
        """
        return analysis.mda8(self._obj, dim=dim, min_periods=min_periods, center=center)

    def exceedance_count(self, threshold: float, dim: str = "time") -> xr.Dataset:
        """
        Count exceedances of a threshold.

        Parameters
        ----------
        threshold : float
            Threshold value.
        dim : str, optional
            Dimension along which to count. Default is 'time'.

        Returns
        -------
        xarray.Dataset
            Number of exceedances.
        """
        return analysis.exceedance_count(self._obj, threshold=threshold, dim=dim)

    def percentile(self, q: Union[float, List[float], np.ndarray], dim: str = "time", **kwargs: Any) -> xr.Dataset:
        """
        Compute percentiles.

        Parameters
        ----------
        q : float or list of float
            Percentile(s) (0-100).
        dim : str, optional
            Dimension over which to compute. Default is 'time'.
        **kwargs : Any
            Additional keyword arguments.

        Returns
        -------
        xarray.Dataset
            Computed percentiles.
        """
        return analysis.percentile(self._obj, q=q, dim=dim, **kwargs)

    def peak_timing(self, dim: str = "time") -> xr.Dataset:
        """
        Identify the coordinate value of the maximum.

        Parameters
        ----------
        dim : str, optional
            Dimension along which to find peak. Default is 'time'.

        Returns
        -------
        xarray.Dataset
            Coordinate values.
        """
        return analysis.peak_timing(self._obj, dim=dim)

    def weighted_spatial_mean(
        self,
        lat_dim: str = "lat",
        lon_dim: str = "lon",
        weights: Optional[Union[xr.DataArray, np.ndarray]] = None,
    ) -> xr.Dataset:
        """
        Compute area-weighted spatial mean.

        Parameters
        ----------
        lat_dim : str, optional
            Latitude dimension name. Default is 'lat'.
        lon_dim : str, optional
            Longitude dimension name. Default is 'lon'.
        weights : xarray.DataArray or numpy.ndarray, optional
            Custom weights.

        Returns
        -------
        xarray.Dataset
            Area-weighted spatial mean.
        """
        return analysis.weighted_spatial_mean(self._obj, lat_dim=lat_dim, lon_dim=lon_dim, weights=weights)

    def seasonal_mean(self, dim: str = "time", weighted: bool = True) -> xr.Dataset:
        """
        Compute seasonal mean (DJF, MAM, JJA, SON).

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute. Default is 'time'.
        weighted : bool, optional
            Weight by days in month. Default is True.

        Returns
        -------
        xarray.Dataset
            Seasonal means.
        """
        return analysis.seasonal_mean(self._obj, dim=dim, weighted=weighted)

    def monthly_climatology(self, dim: str = "time", method: str = "mean") -> xr.Dataset:
        """
        Compute monthly climatology.

        Parameters
        ----------
        dim : str, optional
            Dimension along which to compute. Default is 'time'.
        method : str, optional
            Statistical method. Default is 'mean'.

        Returns
        -------
        xarray.Dataset
            Monthly climatology.
        """
        return analysis.monthly_climatology(self._obj, dim=dim, method=method)

    def anomalies(self, freq: str = "month", dim: str = "time") -> xr.Dataset:
        """
        Compute anomalies by subtracting the climatology.

        Parameters
        ----------
        freq : str, optional
            Climatology frequency ('season', 'month', 'dayofyear', 'hour').
            Default is 'month'.
        dim : str, optional
            Dimension along which to compute the anomalies. Default is 'time'.

        Returns
        -------
        xarray.Dataset
            Anomalies.
        """
        return analysis.anomalies(self._obj, freq=freq, dim=dim)

    def detrend(self, method: str = "linear", dim: str = "time") -> xr.Dataset:
        """
        Remove trend from data.

        Parameters
        ----------
        method : str, optional
            Detrending method ('linear', 'constant'). Default is 'linear'.
        dim : str, optional
            Dimension along which to detrend. Default is 'time'.

        Returns
        -------
        xarray.Dataset
            Detrended data.
        """
        return analysis.detrend(self._obj, method=method, dim=dim)

    def optimize(self, target_mb: float = 100.0) -> xr.Dataset:
        """
        Optimize performance by ensuring laziness and recommended chunks (Aero Protocol).

        Parameters
        ----------
        target_mb : float, optional
            Target size for each chunk in Megabytes. Default is 100.0.

        Returns
        -------
        xarray.Dataset
            Optimized Dataset.
        """
        from .utils_stats import _update_history

        if not performance._has_dask():
            return _update_history(self._obj, "Optimization skipped (Dask not installed)")

        # Ensure data is lazy
        res = performance.apply_lazy_threshold(self._obj, threshold_mb=0.1)
        # Always calculate and apply recommended chunks for the target size
        recommendation = performance.get_chunk_recommendation(res, target_mb=target_mb)
        res = res.chunk(recommendation)

        return _update_history(res, f"Optimized for performance (target={target_mb}MB)")

    def rechunk(self, chunks: Optional[dict] = None) -> xr.Dataset:
        """
        Apply new chunks to the Dataset (Aero Protocol provenance tracking).

        Parameters
        ----------
        chunks : dict, optional
            New chunk sizes. If None, uses optimal recommendations (~100MB).

        Returns
        -------
        xarray.Dataset
            Rechunked Dataset.
        """
        from .utils_stats import _update_history

        if not performance._has_dask():
            return _update_history(self._obj, "Rechunking skipped (Dask not installed)")

        if chunks is None:
            chunks = performance.get_chunk_recommendation(self._obj)

        res = self._obj.chunk(chunks)

        return _update_history(res, f"Rechunked with {chunks}")

anomalies(freq='month', dim='time')

Compute anomalies by subtracting the climatology.

Parameters

freq : str, optional Climatology frequency ('season', 'month', 'dayofyear', 'hour'). Default is 'month'. dim : str, optional Dimension along which to compute the anomalies. Default is 'time'.

Returns

xarray.Dataset Anomalies.

Source code in src/monet_stats/accessor.py 
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def anomalies(self, freq: str = "month", dim: str = "time") -> xr.Dataset:
    """
    Compute anomalies by subtracting the climatology.

    Parameters
    ----------
    freq : str, optional
        Climatology frequency ('season', 'month', 'dayofyear', 'hour').
        Default is 'month'.
    dim : str, optional
        Dimension along which to compute the anomalies. Default is 'time'.

    Returns
    -------
    xarray.Dataset
        Anomalies.
    """
    return analysis.anomalies(self._obj, freq=freq, dim=dim)

climatology(freq='season', method='mean', dim='time')

Compute climatological statistics.

Parameters

freq : str, optional Climatology frequency. Default is 'season'. method : str, optional Statistical method. Default is 'mean'. dim : str, optional Dimension along which to compute. Default is 'time'.

Returns

xarray.Dataset Climatological statistics.

Source code in src/monet_stats/accessor.py 
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def climatology(self, freq: str = "season", method: str = "mean", dim: str = "time") -> xr.Dataset:
    """
    Compute climatological statistics.

    Parameters
    ----------
    freq : str, optional
        Climatology frequency. Default is 'season'.
    method : str, optional
        Statistical method. Default is 'mean'.
    dim : str, optional
        Dimension along which to compute. Default is 'time'.

    Returns
    -------
    xarray.Dataset
        Climatological statistics.
    """
    return analysis.climatology(self._obj, freq=freq, method=method, dim=dim)

detrend(method='linear', dim='time')

Remove trend from data.

Parameters

method : str, optional Detrending method ('linear', 'constant'). Default is 'linear'. dim : str, optional Dimension along which to detrend. Default is 'time'.

Returns

xarray.Dataset Detrended data.

Source code in src/monet_stats/accessor.py 
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def detrend(self, method: str = "linear", dim: str = "time") -> xr.Dataset:
    """
    Remove trend from data.

    Parameters
    ----------
    method : str, optional
        Detrending method ('linear', 'constant'). Default is 'linear'.
    dim : str, optional
        Dimension along which to detrend. Default is 'time'.

    Returns
    -------
    xarray.Dataset
        Detrended data.
    """
    return analysis.detrend(self._obj, method=method, dim=dim)

diurnal_cycle(method='mean', dim='time')

Compute the diurnal cycle.

Parameters

method : str, optional Statistical method. Default is 'mean'. dim : str, optional Dimension along which to compute. Default is 'time'.

Returns

xarray.Dataset Diurnal cycle.

Source code in src/monet_stats/accessor.py 
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def diurnal_cycle(self, method: str = "mean", dim: str = "time") -> xr.Dataset:
    """
    Compute the diurnal cycle.

    Parameters
    ----------
    method : str, optional
        Statistical method. Default is 'mean'.
    dim : str, optional
        Dimension along which to compute. Default is 'time'.

    Returns
    -------
    xarray.Dataset
        Diurnal cycle.
    """
    return analysis.diurnal_cycle(self._obj, method=method, dim=dim)

exceedance_count(threshold, dim='time')

Count exceedances of a threshold.

Parameters

threshold : float Threshold value. dim : str, optional Dimension along which to count. Default is 'time'.

Returns

xarray.Dataset Number of exceedances.

Source code in src/monet_stats/accessor.py 
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def exceedance_count(self, threshold: float, dim: str = "time") -> xr.Dataset:
    """
    Count exceedances of a threshold.

    Parameters
    ----------
    threshold : float
        Threshold value.
    dim : str, optional
        Dimension along which to count. Default is 'time'.

    Returns
    -------
    xarray.Dataset
        Number of exceedances.
    """
    return analysis.exceedance_count(self._obj, threshold=threshold, dim=dim)

kz_filter(m, k, dim='time')

Apply Kolmogorov-Zurbenko (KZ) filter.

Parameters

m : int Window size. k : int Number of iterations. dim : str, optional Dimension along which to apply. Default is 'time'.

Returns

xarray.Dataset Filtered data.

Source code in src/monet_stats/accessor.py 
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def kz_filter(self, m: int, k: int, dim: str = "time") -> xr.Dataset:
    """
    Apply Kolmogorov-Zurbenko (KZ) filter.

    Parameters
    ----------
    m : int
        Window size.
    k : int
        Number of iterations.
    dim : str, optional
        Dimension along which to apply. Default is 'time'.

    Returns
    -------
    xarray.Dataset
        Filtered data.
    """
    return analysis.kz_filter(self._obj, m=m, k=k, dim=dim)

mda1(dim='time')

Compute Maximum Daily 1-hour Average (MDA1).

Parameters

dim : str, optional Dimension along which to compute. Default is 'time'.

Returns

xarray.Dataset MDA1 values.

Source code in src/monet_stats/accessor.py 
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def mda1(self, dim: str = "time") -> xr.Dataset:
    """
    Compute Maximum Daily 1-hour Average (MDA1).

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute. Default is 'time'.

    Returns
    -------
    xarray.Dataset
        MDA1 values.
    """
    return analysis.mda1(self._obj, dim=dim)

mda8(dim='time', min_periods=6, center=False)

Compute Maximum Daily 8-hour Average (MDA8).

Parameters

dim : str, optional Dimension along which to compute. Default is 'time'. min_periods : int, optional Minimum number of observations. Default is 6. center : bool, optional Whether to center the window. Default is False.

Returns

xarray.Dataset MDA8 values.

Source code in src/monet_stats/accessor.py 
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def mda8(self, dim: str = "time", min_periods: int = 6, center: bool = False) -> xr.Dataset:
    """
    Compute Maximum Daily 8-hour Average (MDA8).

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute. Default is 'time'.
    min_periods : int, optional
        Minimum number of observations. Default is 6.
    center : bool, optional
        Whether to center the window. Default is False.

    Returns
    -------
    xarray.Dataset
        MDA8 values.
    """
    return analysis.mda8(self._obj, dim=dim, min_periods=min_periods, center=center)

monthly_climatology(dim='time', method='mean')

Compute monthly climatology.

Parameters

dim : str, optional Dimension along which to compute. Default is 'time'. method : str, optional Statistical method. Default is 'mean'.

Returns

xarray.Dataset Monthly climatology.

Source code in src/monet_stats/accessor.py 
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def monthly_climatology(self, dim: str = "time", method: str = "mean") -> xr.Dataset:
    """
    Compute monthly climatology.

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute. Default is 'time'.
    method : str, optional
        Statistical method. Default is 'mean'.

    Returns
    -------
    xarray.Dataset
        Monthly climatology.
    """
    return analysis.monthly_climatology(self._obj, dim=dim, method=method)

optimize(target_mb=100.0)

Optimize performance by ensuring laziness and recommended chunks (Aero Protocol).

Parameters

target_mb : float, optional Target size for each chunk in Megabytes. Default is 100.0.

Returns

xarray.Dataset Optimized Dataset.

Source code in src/monet_stats/accessor.py 
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def optimize(self, target_mb: float = 100.0) -> xr.Dataset:
    """
    Optimize performance by ensuring laziness and recommended chunks (Aero Protocol).

    Parameters
    ----------
    target_mb : float, optional
        Target size for each chunk in Megabytes. Default is 100.0.

    Returns
    -------
    xarray.Dataset
        Optimized Dataset.
    """
    from .utils_stats import _update_history

    if not performance._has_dask():
        return _update_history(self._obj, "Optimization skipped (Dask not installed)")

    # Ensure data is lazy
    res = performance.apply_lazy_threshold(self._obj, threshold_mb=0.1)
    # Always calculate and apply recommended chunks for the target size
    recommendation = performance.get_chunk_recommendation(res, target_mb=target_mb)
    res = res.chunk(recommendation)

    return _update_history(res, f"Optimized for performance (target={target_mb}MB)")

peak_timing(dim='time')

Identify the coordinate value of the maximum.

Parameters

dim : str, optional Dimension along which to find peak. Default is 'time'.

Returns

xarray.Dataset Coordinate values.

Source code in src/monet_stats/accessor.py 
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def peak_timing(self, dim: str = "time") -> xr.Dataset:
    """
    Identify the coordinate value of the maximum.

    Parameters
    ----------
    dim : str, optional
        Dimension along which to find peak. Default is 'time'.

    Returns
    -------
    xarray.Dataset
        Coordinate values.
    """
    return analysis.peak_timing(self._obj, dim=dim)

percentile(q, dim='time', **kwargs)

Compute percentiles.

Parameters

q : float or list of float Percentile(s) (0-100). dim : str, optional Dimension over which to compute. Default is 'time'. **kwargs : Any Additional keyword arguments.

Returns

xarray.Dataset Computed percentiles.

Source code in src/monet_stats/accessor.py 
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def percentile(self, q: Union[float, List[float], np.ndarray], dim: str = "time", **kwargs: Any) -> xr.Dataset:
    """
    Compute percentiles.

    Parameters
    ----------
    q : float or list of float
        Percentile(s) (0-100).
    dim : str, optional
        Dimension over which to compute. Default is 'time'.
    **kwargs : Any
        Additional keyword arguments.

    Returns
    -------
    xarray.Dataset
        Computed percentiles.
    """
    return analysis.percentile(self._obj, q=q, dim=dim, **kwargs)

rechunk(chunks=None)

Apply new chunks to the Dataset (Aero Protocol provenance tracking).

Parameters

chunks : dict, optional New chunk sizes. If None, uses optimal recommendations (~100MB).

Returns

xarray.Dataset Rechunked Dataset.

Source code in src/monet_stats/accessor.py 
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def rechunk(self, chunks: Optional[dict] = None) -> xr.Dataset:
    """
    Apply new chunks to the Dataset (Aero Protocol provenance tracking).

    Parameters
    ----------
    chunks : dict, optional
        New chunk sizes. If None, uses optimal recommendations (~100MB).

    Returns
    -------
    xarray.Dataset
        Rechunked Dataset.
    """
    from .utils_stats import _update_history

    if not performance._has_dask():
        return _update_history(self._obj, "Rechunking skipped (Dask not installed)")

    if chunks is None:
        chunks = performance.get_chunk_recommendation(self._obj)

    res = self._obj.chunk(chunks)

    return _update_history(res, f"Rechunked with {chunks}")

resample_data(freq='MS', method='mean', dim='time', **kwargs)

Resample data to a new temporal frequency.

Parameters

freq : str, optional Resampling frequency. Default is 'MS'. method : str, optional Statistical method. Default is 'mean'. dim : str, optional Dimension along which to resample. Default is 'time'. **kwargs : Any Additional keyword arguments.

Returns

xarray.Dataset Resampled data.

Source code in src/monet_stats/accessor.py 
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def resample_data(self, freq: str = "MS", method: str = "mean", dim: str = "time", **kwargs: Any) -> xr.Dataset:
    """
    Resample data to a new temporal frequency.

    Parameters
    ----------
    freq : str, optional
        Resampling frequency. Default is 'MS'.
    method : str, optional
        Statistical method. Default is 'mean'.
    dim : str, optional
        Dimension along which to resample. Default is 'time'.
    **kwargs : Any
        Additional keyword arguments.

    Returns
    -------
    xarray.Dataset
        Resampled data.
    """
    return analysis.resample_data(self._obj, freq=freq, method=method, dim=dim, **kwargs)

rolling_mean_24h(dim='time', min_periods=18, center=True)

Compute rolling 24-hour mean.

Parameters

dim : str, optional Dimension along which to compute. Default is 'time'. min_periods : int, optional Minimum number of observations. Default is 18. center : bool, optional If True, center the labels. Default is True.

Returns

xarray.Dataset Rolling 24-hour mean.

Source code in src/monet_stats/accessor.py 
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def rolling_mean_24h(self, dim: str = "time", min_periods: int = 18, center: bool = True) -> xr.Dataset:
    """
    Compute rolling 24-hour mean.

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute. Default is 'time'.
    min_periods : int, optional
        Minimum number of observations. Default is 18.
    center : bool, optional
        If True, center the labels. Default is True.

    Returns
    -------
    xarray.Dataset
        Rolling 24-hour mean.
    """
    return analysis.rolling_mean_24h(self._obj, dim=dim, min_periods=min_periods, center=center)

rolling_mean_8h(dim='time', min_periods=6, center=True)

Compute rolling 8-hour mean.

Parameters

dim : str, optional Dimension along which to compute. Default is 'time'. min_periods : int, optional Minimum number of observations. Default is 6. center : bool, optional If True, center the labels. Default is True.

Returns

xarray.Dataset Rolling 8-hour mean.

Source code in src/monet_stats/accessor.py 
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def rolling_mean_8h(self, dim: str = "time", min_periods: int = 6, center: bool = True) -> xr.Dataset:
    """
    Compute rolling 8-hour mean.

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute. Default is 'time'.
    min_periods : int, optional
        Minimum number of observations. Default is 6.
    center : bool, optional
        If True, center the labels. Default is True.

    Returns
    -------
    xarray.Dataset
        Rolling 8-hour mean.
    """
    return analysis.rolling_mean_8h(self._obj, dim=dim, min_periods=min_periods, center=center)

seasonal_mean(dim='time', weighted=True)

Compute seasonal mean (DJF, MAM, JJA, SON).

Parameters

dim : str, optional Dimension along which to compute. Default is 'time'. weighted : bool, optional Weight by days in month. Default is True.

Returns

xarray.Dataset Seasonal means.

Source code in src/monet_stats/accessor.py 
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def seasonal_mean(self, dim: str = "time", weighted: bool = True) -> xr.Dataset:
    """
    Compute seasonal mean (DJF, MAM, JJA, SON).

    Parameters
    ----------
    dim : str, optional
        Dimension along which to compute. Default is 'time'.
    weighted : bool, optional
        Weight by days in month. Default is True.

    Returns
    -------
    xarray.Dataset
        Seasonal means.
    """
    return analysis.seasonal_mean(self._obj, dim=dim, weighted=weighted)

stats(obs_name='Obs', mod_name='Mod', threshold=0.0, minval=None, maxval=None)

Calculate summary statistics for observations and model results.

Parameters

obs_name : str, optional Name of observation variable. Default is 'Obs'. mod_name : str, optional Name of model variable. Default is 'Mod'. threshold : float, optional Threshold for contingency scores. Default is 0.0. minval : float, optional Minimum value for filtering. maxval : float, optional Maximum value for filtering.

Returns

dict Dictionary of calculated statistics.

Source code in src/monet_stats/accessor.py 
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def stats(
    self,
    obs_name: str = "Obs",
    mod_name: str = "Mod",
    threshold: float = 0.0,
    minval: Optional[float] = None,
    maxval: Optional[float] = None,
) -> dict:
    """
    Calculate summary statistics for observations and model results.

    Parameters
    ----------
    obs_name : str, optional
        Name of observation variable. Default is 'Obs'.
    mod_name : str, optional
        Name of model variable. Default is 'Mod'.
    threshold : float, optional
        Threshold for contingency scores. Default is 0.0.
    minval : float, optional
        Minimum value for filtering.
    maxval : float, optional
        Maximum value for filtering.

    Returns
    -------
    dict
        Dictionary of calculated statistics.
    """
    from . import stats

    return stats(
        self._obj,
        obs_name=obs_name,
        mod_name=mod_name,
        threshold=threshold,
        minval=minval,
        maxval=maxval,
    )

weighted_spatial_mean(lat_dim='lat', lon_dim='lon', weights=None)

Compute area-weighted spatial mean.

Parameters

lat_dim : str, optional Latitude dimension name. Default is 'lat'. lon_dim : str, optional Longitude dimension name. Default is 'lon'. weights : xarray.DataArray or numpy.ndarray, optional Custom weights.

Returns

xarray.Dataset Area-weighted spatial mean.

Source code in src/monet_stats/accessor.py 
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def weighted_spatial_mean(
    self,
    lat_dim: str = "lat",
    lon_dim: str = "lon",
    weights: Optional[Union[xr.DataArray, np.ndarray]] = None,
) -> xr.Dataset:
    """
    Compute area-weighted spatial mean.

    Parameters
    ----------
    lat_dim : str, optional
        Latitude dimension name. Default is 'lat'.
    lon_dim : str, optional
        Longitude dimension name. Default is 'lon'.
    weights : xarray.DataArray or numpy.ndarray, optional
        Custom weights.

    Returns
    -------
    xarray.Dataset
        Area-weighted spatial mean.
    """
    return analysis.weighted_spatial_mean(self._obj, lat_dim=lat_dim, lon_dim=lon_dim, weights=weights)

Utility Functions

Utility Functions for Statistics (Aero Protocol Compliant).

angular_difference(angle1, angle2, units='degrees')

Calculate the smallest angular difference between two angles (Aero Protocol).

Backend-agnostic (supports NumPy and Xarray/Dask).

Parameters

angle1 : ArrayLike First angle(s). angle2 : ArrayLike Second angle(s). units : str, optional Units of angles ('degrees' or 'radians'). Default is 'degrees'.

Returns

Any Smallest angular difference between the two angles.

Source code in src/monet_stats/utils_stats.py 
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def angular_difference(angle1: ArrayLike, angle2: ArrayLike, units: str = "degrees") -> Any:
    """
    Calculate the smallest angular difference between two angles (Aero Protocol).

    Backend-agnostic (supports NumPy and Xarray/Dask).

    Parameters
    ----------
    angle1 : ArrayLike
        First angle(s).
    angle2 : ArrayLike
        Second angle(s).
    units : str, optional
        Units of angles ('degrees' or 'radians'). Default is 'degrees'.

    Returns
    -------
    Any
        Smallest angular difference between the two angles.
    """
    if units == "degrees":
        max_val = 360.0
    elif units == "radians":
        max_val = 2 * np.pi
    else:
        raise ValueError("units must be 'degrees' or 'radians'")

    if isinstance(angle1, (xr.DataArray, xr.Dataset)) or isinstance(angle2, (xr.DataArray, xr.Dataset)):
        if isinstance(angle1, (xr.DataArray, xr.Dataset)) and isinstance(angle2, (xr.DataArray, xr.Dataset)):
            angle1, angle2 = xr.align(angle1, angle2, join="inner")

        diff = abs(angle1 - angle2)
        result = xr.where(diff > max_val / 2, max_val - diff, diff)
        return _update_history(result, "angular_difference")

    angle1_arr = np.asanyarray(angle1)
    angle2_arr = np.asanyarray(angle2)
    diff = np.abs(angle1_arr - angle2_arr)
    return np.minimum(diff, max_val - diff)

circlebias(b)

Circular bias (wrapped to [-180, 180] degrees) (Aero Protocol).

Handles both dense and masked arrays, as well as Xarray/Dask objects.

Parameters

b : ArrayLike Difference between two wind directions (degrees).

Returns

Any Circularly wrapped difference (degrees).

Examples

circlebias(190) -170 circlebias(-190) 170

Source code in src/monet_stats/utils_stats.py 
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def circlebias(b: ArrayLike) -> Any:
    """
    Circular bias (wrapped to [-180, 180] degrees) (Aero Protocol).

    Handles both dense and masked arrays, as well as Xarray/Dask objects.

    Parameters
    ----------
    b : ArrayLike
        Difference between two wind directions (degrees).

    Returns
    -------
    Any
        Circularly wrapped difference (degrees).

    Examples
    --------
    >>> circlebias(190)
    -170
    >>> circlebias(-190)
    170
    """
    if isinstance(b, (xr.DataArray, xr.Dataset)):
        res = (b + 180) % 360 - 180
        return _update_history(res, "circlebias")

    # Handle both dense and masked numpy arrays
    b_arr = np.ma.masked_invalid(b)
    res_arr = (b_arr + 180) % 360 - 180

    if not np.ma.is_masked(res_arr) and not isinstance(b, np.ma.MaskedArray):
        if np.issubdtype(res_arr.dtype, np.floating):
            return res_arr.filled(np.nan)
        return np.ma.getdata(res_arr)

    return res_arr

circlebias_m(b)

Robust circular bias for wind direction (Alias for circlebias).

Parameters

b : ArrayLike Difference between two wind directions (degrees).

Returns

Any Circularly wrapped difference.

Source code in src/monet_stats/utils_stats.py 
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def circlebias_m(b: ArrayLike) -> Any:
    """
    Robust circular bias for wind direction (Alias for circlebias).

    Parameters
    ----------
    b : ArrayLike
        Difference between two wind directions (degrees).

    Returns
    -------
    Any
        Circularly wrapped difference.
    """
    return circlebias(b)

correlation(x, y, axis=None)

Calculate Pearson correlation coefficient (Alias for correlation_metrics.pearsonr).

Parameters

x : Union[np.ndarray, xr.DataArray] First variable. y : Union[np.ndarray, xr.DataArray] Second variable. axis : Union[int, str, Iterable], optional Axis along which to compute correlation.

Returns

Union[np.number, np.ndarray, xr.DataArray] Pearson correlation coefficient.

Raises

ValueError If input arrays are empty.

Source code in src/monet_stats/utils_stats.py 
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def correlation(
    x: Union[np.ndarray, xr.DataArray],
    y: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Calculate Pearson correlation coefficient (Alias for correlation_metrics.pearsonr).

    Parameters
    ----------
    x : Union[np.ndarray, xr.DataArray]
        First variable.
    y : Union[np.ndarray, xr.DataArray]
        Second variable.
    axis : Union[int, str, Iterable], optional
        Axis along which to compute correlation.

    Returns
    -------
    Union[np.number, np.ndarray, xr.DataArray]
        Pearson correlation coefficient.

    Raises
    ------
    ValueError
        If input arrays are empty.
    """
    if hasattr(x, "size") and x.size == 0:
        raise ValueError("Input arrays cannot be empty")
    if hasattr(y, "size") and y.size == 0:
        raise ValueError("Input arrays cannot be empty")

    from .correlation_metrics import pearsonr

    res = pearsonr(x, y, axis=axis)
    if isinstance(res, (xr.DataArray, xr.Dataset)):
        return _update_history(res, "correlation")
    return res

mae(obs, mod, axis=None)

Calculate Mean Absolute Error (Alias for error_metrics.MAE).

Parameters

obs : Union[np.ndarray, xr.DataArray] Observed values. mod : Union[np.ndarray, xr.DataArray] Model or predicted values. axis : Union[int, str, Iterable], optional Axis along which to compute MAE.

Returns

Union[np.number, np.ndarray, xr.DataArray] Mean absolute error.

Source code in src/monet_stats/utils_stats.py 
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def mae(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Calculate Mean Absolute Error (Alias for error_metrics.MAE).

    Parameters
    ----------
    obs : Union[np.ndarray, xr.DataArray]
        Observed values.
    mod : Union[np.ndarray, xr.DataArray]
        Model or predicted values.
    axis : Union[int, str, Iterable], optional
        Axis along which to compute MAE.

    Returns
    -------
    Union[np.number, np.ndarray, xr.DataArray]
        Mean absolute error.
    """
    from .error_metrics import MAE

    res = MAE(obs, mod, axis=axis)
    if isinstance(res, (xr.DataArray, xr.Dataset)):
        return _update_history(res, "mae")
    return res

matchedcompressed(a1, a2)

Return compressed (non-masked) values from two matched arrays.

Note: For Xarray DataArrays, this function will trigger a computation if the data is Dask-backed, as it returns NumPy ndarrays. For lazy operations, prefer using Xarray-native methods with skipna=True.

Parameters

a1 : ArrayLike First input array. a2 : ArrayLike Second input array.

Returns

Tuple[np.ndarray, np.ndarray] Tuple of (a1_compressed, a2_compressed), both 1D arrays of valid values.

Examples

import numpy as np a = np.array([1, np.nan, 3]) b = np.array([4, 5, 6]) matchedcompressed(a, b) (array([1., 3.]), array([4., 6.]))

Source code in src/monet_stats/utils_stats.py 
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def matchedcompressed(a1: ArrayLike, a2: ArrayLike) -> Tuple[np.ndarray, np.ndarray]:
    """
    Return compressed (non-masked) values from two matched arrays.

    Note: For Xarray DataArrays, this function will trigger a computation if
    the data is Dask-backed, as it returns NumPy ndarrays. For lazy operations,
    prefer using Xarray-native methods with `skipna=True`.

    Parameters
    ----------
    a1 : ArrayLike
        First input array.
    a2 : ArrayLike
        Second input array.

    Returns
    -------
    Tuple[np.ndarray, np.ndarray]
        Tuple of (a1_compressed, a2_compressed), both 1D arrays of valid values.

    Examples
    --------
    >>> import numpy as np
    >>> a = np.array([1, np.nan, 3])
    >>> b = np.array([4, 5, 6])
    >>> matchedcompressed(a, b)
    (array([1., 3.]), array([4., 6.]))
    """
    # Handle Xarray objects by extracting values (triggers computation for Dask)
    if isinstance(a1, (xr.DataArray, xr.Dataset)):
        if hasattr(a1, "data") and hasattr(a1.data, "chunks"):
            warnings.warn(
                "matchedcompressed triggered computation on Dask-backed array. "
                "Consider using backend-agnostic xarray operations instead.",
                UserWarning,
                stacklevel=2,
            )
        a1 = a1.values
    if isinstance(a2, (xr.DataArray, xr.Dataset)):
        if hasattr(a2, "data") and hasattr(a2.data, "chunks"):
            warnings.warn(
                "matchedcompressed triggered computation on Dask-backed array. "
                "Consider using backend-agnostic xarray operations instead.",
                UserWarning,
                stacklevel=2,
            )
        a2 = a2.values

    # Convert to masked arrays to handle existing masks and NaNs
    a1_m = np.ma.masked_invalid(a1)
    a2_m = np.ma.masked_invalid(a2)

    # Handle mismatched shapes by truncating both to the minimum size
    if a1_m.shape != a2_m.shape:
        min_size = min(a1_m.size, a2_m.size)
        a1_m = a1_m.flat[:min_size]
        a2_m = a2_m.flat[:min_size]

    mask = np.ma.getmaskarray(a1_m) | np.ma.getmaskarray(a2_m)
    a1_matched = np.ma.masked_where(mask, a1_m)
    a2_matched = np.ma.masked_where(mask, a2_m)

    return a1_matched.compressed(), a2_matched.compressed()

matchmasks(a1, a2)

Match and combine masks from two arrays or align Xarray objects (Aero Protocol).

Parameters

a1 : Any First input array or DataArray. a2 : Any Second input array or DataArray.

Returns

Tuple[Any, Any] Tuple of (a1_matched, a2_matched).

Source code in src/monet_stats/utils_stats.py 
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def matchmasks(a1: Any, a2: Any) -> Tuple[Any, Any]:
    """
    Match and combine masks from two arrays or align Xarray objects (Aero Protocol).

    Parameters
    ----------
    a1 : Any
        First input array or DataArray.
    a2 : Any
        Second input array or DataArray.

    Returns
    -------
    Tuple[Any, Any]
        Tuple of (a1_matched, a2_matched).
    """
    if isinstance(a1, (xr.DataArray, xr.Dataset)) and isinstance(a2, (xr.DataArray, xr.Dataset)):
        return xr.align(a1, a2, join="inner")

    a1_arr = np.asanyarray(a1)
    a2_arr = np.asanyarray(a2)

    # Unify mask handling for numpy
    a1_m = np.ma.masked_invalid(a1_arr)
    a2_m = np.ma.masked_invalid(a2_arr)

    common_mask = np.ma.getmaskarray(a1_m) | np.ma.getmaskarray(a2_m)
    return np.ma.masked_where(common_mask, a1_m), np.ma.masked_where(common_mask, a2_m)

rmse(obs, mod, axis=None)

Calculate Root Mean Square Error (Alias for error_metrics.RMSE).

Parameters

obs : Union[np.ndarray, xr.DataArray] Observed values. mod : Union[np.ndarray, xr.DataArray] Model or predicted values. axis : Union[int, str, Iterable], optional Axis along which to compute RMSE.

Returns

Union[np.number, np.ndarray, xr.DataArray] Root mean square error.

Source code in src/monet_stats/utils_stats.py 
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def rmse(
    obs: Union[np.ndarray, xr.DataArray],
    mod: Union[np.ndarray, xr.DataArray],
    axis: Optional[Union[int, str, Iterable[Union[int, str]]]] = None,
) -> Union[np.number, np.ndarray, xr.DataArray]:
    """
    Calculate Root Mean Square Error (Alias for error_metrics.RMSE).

    Parameters
    ----------
    obs : Union[np.ndarray, xr.DataArray]
        Observed values.
    mod : Union[np.ndarray, xr.DataArray]
        Model or predicted values.
    axis : Union[int, str, Iterable], optional
        Axis along which to compute RMSE.

    Returns
    -------
    Union[np.number, np.ndarray, xr.DataArray]
        Root mean square error.
    """
    from .error_metrics import RMSE

    res = RMSE(obs, mod, axis=axis)
    if isinstance(res, (xr.DataArray, xr.Dataset)):
        return _update_history(res, "rmse")
    return res

Visualization

Visualization utilities for the MONET Stats package (Aero Protocol Compliant).

This module implements the "Two-Track Rule" for scientific visualization: - Track A (Publication): Static quality using Matplotlib and Cartopy. - Track B (Exploration): Interactive exploration using HvPlot and GeoViews.

plot_spatial(da, method='matplotlib', lat_dim='lat', lon_dim='lon', title=None, cmap='viridis', **kwargs)

Plot spatial data following the Aero Protocol's Two-Track Rule.

Parameters

da : xarray.DataArray The spatial data to plot. Must have latitude and longitude coordinates. method : str, optional The plotting track to use: - 'matplotlib' (Track A): Static publication quality. - 'hvplot' (Track B): Interactive exploration. Default is 'matplotlib'. lat_dim : str, optional Name of the latitude dimension/coordinate. Default is 'lat'. lon_dim : str, optional Name of the longitude dimension/coordinate. Default is 'lon'. title : str, optional Title for the plot. cmap : str, optional Colormap to use. Default is 'viridis'. **kwargs : Any Additional keyword arguments passed to the underlying plotting function. For 'matplotlib', these are passed to da.plot(). For 'hvplot', these are passed to da.hvplot.quadmesh().

Returns

Any The plot object (matplotlib.axes.Axes or holoviews.element.Element).

Raises

ValueError If an unknown method is specified. ImportError If the required libraries for the chosen track are missing.

Examples

import xarray as xr import numpy as np da = xr.DataArray(np.random.rand(10, 10), ... coords={'lat': np.arange(10), 'lon': np.arange(10)}, ... dims=('lat', 'lon'))

Track A (Static)

ax = plot_spatial(da, method='matplotlib')

Track B (Interactive)

plot = plot_spatial(da, method='hvplot')

Source code in src/monet_stats/visualize.py 
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def plot_spatial(
    da: xr.DataArray,
    method: str = "matplotlib",
    lat_dim: str = "lat",
    lon_dim: str = "lon",
    title: Optional[str] = None,
    cmap: str = "viridis",
    **kwargs: Any,
) -> Any:
    """
    Plot spatial data following the Aero Protocol's Two-Track Rule.

    Parameters
    ----------
    da : xarray.DataArray
        The spatial data to plot. Must have latitude and longitude coordinates.
    method : str, optional
        The plotting track to use:
        - 'matplotlib' (Track A): Static publication quality.
        - 'hvplot' (Track B): Interactive exploration.
        Default is 'matplotlib'.
    lat_dim : str, optional
        Name of the latitude dimension/coordinate. Default is 'lat'.
    lon_dim : str, optional
        Name of the longitude dimension/coordinate. Default is 'lon'.
    title : str, optional
        Title for the plot.
    cmap : str, optional
        Colormap to use. Default is 'viridis'.
    **kwargs : Any
        Additional keyword arguments passed to the underlying plotting function.
        For 'matplotlib', these are passed to `da.plot()`.
        For 'hvplot', these are passed to `da.hvplot.quadmesh()`.

    Returns
    -------
    Any
        The plot object (matplotlib.axes.Axes or holoviews.element.Element).

    Raises
    ------
    ValueError
        If an unknown method is specified.
    ImportError
        If the required libraries for the chosen track are missing.

    Examples
    --------
    >>> import xarray as xr
    >>> import numpy as np
    >>> da = xr.DataArray(np.random.rand(10, 10),
    ...                   coords={'lat': np.arange(10), 'lon': np.arange(10)},
    ...                   dims=('lat', 'lon'))
    >>> # Track A (Static)
    >>> ax = plot_spatial(da, method='matplotlib')
    >>> # Track B (Interactive)
    >>> plot = plot_spatial(da, method='hvplot')
    """
    if method == "matplotlib":
        try:
            import cartopy.crs as ccrs
            import matplotlib.pyplot as plt
        except ImportError:
            raise ImportError(
                "Track A (matplotlib) requires 'matplotlib' and 'cartopy'. "
                "Install them with 'pip install monet-stats[viz]'."
            )

        # Ensure projection is set in kwargs or defaults to PlateCarree
        projection = kwargs.pop("projection", ccrs.PlateCarree())
        transform = kwargs.pop("transform", ccrs.PlateCarree())

        if "ax" not in kwargs:
            fig = plt.figure(figsize=kwargs.pop("figsize", (10, 6)))
            ax = fig.add_subplot(1, 1, 1, projection=projection)
            kwargs["ax"] = ax
        else:
            ax = kwargs["ax"]

        plot = da.plot(transform=transform, cmap=cmap, **kwargs)

        if hasattr(ax, "coastlines"):
            ax.coastlines()
        if hasattr(ax, "gridlines"):
            ax.gridlines(draw_labels=True)

        if title:
            ax.set_title(title)

        _update_history(da, f"Plotted spatial data using Track A (matplotlib, projection={projection})")
        return ax

    elif method == "hvplot":
        try:
            import hvplot.xarray  # noqa: F401
        except ImportError:
            raise ImportError(
                "Track B (hvplot) requires 'hvplot' and 'geoviews'. Install them with 'pip install monet-stats[viz]'."
            )

        # Aero Protocol mandatory for large grids
        rasterize = kwargs.pop("rasterize", True)
        geo = kwargs.pop("geo", True)

        plot = da.hvplot.quadmesh(
            x=lon_dim,
            y=lat_dim,
            geo=geo,
            rasterize=rasterize,
            cmap=cmap,
            title=title,
            **kwargs,
        )

        _update_history(da, "Plotted spatial data using Track B (hvplot, rasterize=True)")
        return plot

    else:
        raise ValueError(f"Unknown plotting method: {method}. Must be 'matplotlib' or 'hvplot'.")

Contributing to API Documentation

If you find issues with the API documentation or would like to suggest improvements:

  1. Check the GitHub Issues
  2. Submit new issues with clear descriptions
  3. Consider contributing improvements via pull requests

For development documentation, see the Contributing Guide.