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Relative Metrics

Normalized and relative error measures for model evaluation.

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return (np.ma.masked_invalid((mod_arr - obs_arr) / (mod_arr + obs_arr)).mean(axis=axis) * 2.0) * 100.0

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return (np.ma.mean(np.ma.abs(mod_arr - obs_arr) / (mod_arr + obs_arr), axis=axis)) * 2.0 * 100.0

ME(obs, mod, axis=None)

Mean Gross Error (model and obs unit)

Typical Use Cases

  • Quantifying the average magnitude of model errors, regardless of direction.
  • Used in model evaluation to summarize overall error size.

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 Mean gross error value(s).

Examples

import numpy as np obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) ME(obs, mod) 1.0

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]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Mean Gross Error (model and obs unit)

    Typical Use Cases
    -----------------
    - Quantifying the average magnitude of model errors, regardless of direction.
    - Used in model evaluation to summarize overall error size.

    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
        Mean gross error value(s).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> ME(obs, mod)
    1.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = axis
        if isinstance(axis, int):
            dim = obs.dims[axis]
        res = abs(mod - obs).mean(dim=dim)
        return _update_history(res, "Mean Gross Error (ME)")
    else:
        obs_arr = np.asanyarray(obs)
        mod_arr = np.asanyarray(mod)
        return np.mean(np.abs(mod_arr - obs_arr), axis=axis)

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],
    axis: Optional[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 = paxis
        if isinstance(paxis, int):
            pdim = obs.dims[paxis]
        mdim = axis
        if isinstance(axis, int):
            mdim = obs.dims[axis]
        res = (((mod.max(dim=pdim) - obs.max(dim=pdim)) / obs.max(dim=pdim)).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)
        return (
            (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

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],
    axis: Optional[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 = paxis
        if isinstance(paxis, int):
            pdim = obs.dims[paxis]
        mdim = axis
        if isinstance(axis, int):
            mdim = obs.dims[axis]
        res = (abs(mod.max(dim=pdim) - obs.max(dim=pdim)) / obs.max(dim=pdim)).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)
        return (
            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

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return (
            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

MdnE(obs, mod, axis=None)

Median Gross Error (model and obs unit)

Typical Use Cases

  • Evaluating the typical magnitude of model errors, robust to outliers.
  • Used in model evaluation when error distributions are skewed or non-normal.

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 Median gross error value(s).

Examples

import numpy as np obs = np.array([1, 2, 3, 4]) mod = np.array([2, 2, 2, 2]) MdnE(obs, mod) 1.0

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]] = None,
) -> Union[xr.DataArray, np.ndarray, float]:
    """
    Median Gross Error (model and obs unit)

    Typical Use Cases
    -----------------
    - Evaluating the typical magnitude of model errors, robust to outliers.
    - Used in model evaluation when error distributions are skewed or non-normal.

    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
        Median gross error value(s).

    Examples
    --------
    >>> import numpy as np
    >>> obs = np.array([1, 2, 3, 4])
    >>> mod = np.array([2, 2, 2, 2])
    >>> MdnE(obs, mod)
    1.0
    """
    if isinstance(obs, xr.DataArray) and isinstance(mod, xr.DataArray):
        obs, mod = xr.align(obs, mod, join="inner")
        dim = axis
        if isinstance(axis, int):
            dim = obs.dims[axis]
        res = abs(mod - obs).median(dim=dim)
        return _update_history(res, "Median Gross Error (MdnE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        return np.ma.median(np.ma.abs(mod_arr - obs_arr), axis=axis)

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],
    axis: Optional[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 = paxis
        if isinstance(paxis, int):
            pdim = obs.dims[paxis]
        mdim = axis
        if isinstance(axis, int):
            mdim = obs.dims[axis]
        res = ((mod.max(dim=pdim) - obs.max(dim=pdim)) / obs.max(dim=pdim)).median(dim=mdim) * 100.0
        return _update_history(res, "Median Normalized Peak Bias (MdnNPB)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        return (
            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
        )

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],
    axis: Optional[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 = paxis
        if isinstance(paxis, int):
            pdim = obs.dims[paxis]
        mdim = axis
        if isinstance(axis, int):
            mdim = obs.dims[axis]
        res = (abs(mod.max(dim=pdim) - obs.max(dim=pdim)) / obs.max(dim=pdim)).median(dim=mdim) * 100.0
        return _update_history(res, "Median Normalized Peak Error (MdnNPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        return (
            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
        )

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[axis]
        res = (abs(mod.max(dim=dim) - obs.max(dim=dim)) / obs.max(dim=dim)).median() * 100.0
        return _update_history(res, "Median Peak Error (MdnPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        return (
            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
        )

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]] = 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")
        # Ensure we use dimension name if axis is int
        dim = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return (mod_arr - obs_arr).sum(axis=axis) / obs_arr.sum(axis=axis) * 100.0

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return (mod_arr - obs_arr).sum(axis=axis) / np.abs(obs_arr.sum(axis=axis)) * 100.0

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return (np.ma.abs(mod_arr - obs_arr).sum(axis=axis) / obs_arr.sum(axis=axis)) * 100

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return (np.abs(mod_arr - obs_arr).sum(axis=axis) / obs_arr.sum(axis=axis)) * 100

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return (np.abs(mod_arr - obs_arr).sum(axis=axis) / np.abs(obs_arr.sum(axis=axis))) * 100

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],
    axis: Optional[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 = paxis
        if isinstance(paxis, int):
            pdim = obs.dims[paxis]
        mdim = axis
        if isinstance(axis, int):
            mdim = obs.dims[axis]
        res = ((mod.max(dim=pdim) - obs.max(dim=pdim)).mean(dim=mdim) / obs.max(dim=pdim).mean(dim=mdim)) * 100.0
        return _update_history(res, "Normalized Mean Peak Bias (NMPB)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        return (
            (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

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],
    axis: Optional[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 = paxis
        if isinstance(paxis, int):
            pdim = obs.dims[paxis]
        mdim = axis
        if isinstance(axis, int):
            mdim = obs.dims[axis]
        res = (abs(mod.max(dim=pdim) - obs.max(dim=pdim)).mean(dim=mdim) / obs.max(dim=pdim).mean(dim=mdim)) * 100.0
        return _update_history(res, "Normalized Mean Peak Error (NMPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        return (
            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

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[axis]
        res = (mod - obs).median(dim=dim) / obs.median(dim=dim) * 100.0
        return _update_history(res, "Normalized Median Bias (NMdnB)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        return np.ma.median(mod_arr - obs_arr, axis=axis) / np.ma.median(obs_arr, axis=axis) * 100.0

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[axis]
        res = abs(mod - obs).median(dim=dim) / obs.median(dim=dim) * 100
        return _update_history(res, "Normalized Median Error (NMdnE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        return np.ma.median(np.ma.abs(mod_arr - obs_arr), axis=axis) / np.ma.median(obs_arr, axis=axis) * 100

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],
    axis: Optional[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 = paxis
        if isinstance(paxis, int):
            pdim = obs.dims[paxis]
        mdim = axis
        if isinstance(axis, int):
            mdim = obs.dims[axis]
        res = (mod.max(dim=pdim) - obs.max(dim=pdim)).median(dim=mdim) / obs.max(dim=pdim).median(dim=mdim) * 100.0
        return _update_history(res, "Normalized Median Peak Bias (NMdnPB)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        return (
            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

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],
    axis: Optional[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 = paxis
        if isinstance(paxis, int):
            pdim = obs.dims[paxis]
        mdim = axis
        if isinstance(axis, int):
            mdim = obs.dims[axis]
        res = (abs(mod.max(dim=pdim) - obs.max(dim=pdim))).median(dim=mdim) / obs.max(dim=pdim).median(dim=mdim) * 100.0
        return _update_history(res, "Normalized Median Peak Error (NMdnPE)")
    else:
        obs_arr = np.ma.asanyarray(obs)
        mod_arr = np.ma.asanyarray(mod)
        return (
            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

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]] = 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]] = 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]] = 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]] = 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]] = 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]] = 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]] = 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]] = 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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return ((np.ma.max(mod_arr, axis=axis) - np.ma.max(obs_arr, axis=axis)) / np.ma.max(obs_arr, axis=axis)) * 100.0

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return (
            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

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return np.ma.mean(np.ma.abs(circlebias(mod_arr - obs_arr)), axis=axis)

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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)
        return np.abs(circlebias_m(mod_arr - obs_arr)).mean(axis=axis)

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[axis]
        cb = circlebias(mod - obs)
        res = abs(cb).median(dim=dim)
        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)
        return np.ma.median(np.ma.abs(cb), axis=axis)

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]] = 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 = axis
        if isinstance(axis, int):
            dim = obs.dims[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
        return circlebias_m(diff).sum(axis=axis) / obs_arr.sum(axis=axis) * 100.0