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Model Description

Comprehensive description of the Canopy-App atmospheric modeling system and its scientific foundations.

Overview

The Canopy-App is a sophisticated 1-D canopy model that simulates the exchange of energy, momentum, and chemical species between the atmosphere and vegetation. The model represents the canopy as a series of discrete vertical layers, each with specified leaf area density and vegetation characteristics.

Conceptual Framework

Model Domain

The model operates on a vertical domain extending from the ground surface to above the canopy top:

  • Below-canopy region: Ground surface to canopy bottom (z_canbot)
  • In-canopy region: Canopy bottom to canopy top (z_cantop)
  • Above-canopy region: Canopy top to reference height

Vertical Discretization

The canopy is divided into ncanlevs layers with: - Uniform or variable layer thickness - Layer-specific leaf area density (LAD) - Layer-specific vegetation properties

Governing Equations

Conservation of Momentum

Wind speed profiles are calculated using:

Within Canopy: 

u(z) = u_h * exp(α * (z/h - 1))

Above Canopy: 

u(z) = (u*/κ) * [ln((z-d)/z₀) + ψₘ(z/L)]

Where: - u_h = wind speed at canopy top - α = attenuation coefficient (function of LAD) - h = canopy height - u* = friction velocity - κ = von Kármán constant (0.41) - d = displacement height - z₀ = roughness length - ψₘ = stability correction function - L = Obukhov length

Conservation of Energy

Energy balance for each canopy layer:

Rₙ = H + LE + G + S

Where: - Rₙ = Net radiation - H = Sensible heat flux - LE = Latent heat flux - G = Ground heat flux - S = Storage term

Radiation Transfer

Solar radiation attenuation follows Beer's law:

I(z) = I₀ * exp(-K * LAI(z))

Where: - I(z) = radiation at height z - I₀ = incident radiation above canopy - K = extinction coefficient - LAI(z) = cumulative leaf area index from top to height z

Key Scientific Parameterizations

1. Biogenic Emissions

Based on Guenther et al. (2012) algorithms:

Isoprene Emissions: 

E = ε * γ * ρ

Where: - ε = emission factor (μg g⁻¹ h⁻¹) - γ = emission activity factor - ρ = foliar density (g m⁻³)

Activity Factors: - Temperature: γₜ = exp(β(T-Tₛ)) - Light: γₗ = α*PAR / √(1 + α²*PAR²)

2. Dry Deposition

Resistance analog approach:

vd = 1 / (Ra + Rb + Rc)

Where: - Ra = aerodynamic resistance - Rb = boundary layer resistance - Rc = surface resistance

Surface Resistance: 

1/Rc = 1/Rs + 1/Rcut + 1/Rsoil

  • Rs = stomatal resistance
  • Rcut = cuticular resistance
  • Rsoil = soil resistance

3. Photolysis Rates

Actinic flux calculation:

J = σ * φ * F * fcanopy

Where: - σ = absorption cross-section - φ = quantum yield - F = actinic flux - fcanopy = canopy attenuation factor

Model Physics Options

Stability Corrections

The model includes atmospheric stability effects:

Stable Conditions (L > 0): 

ψₘ = -5 * z/L

Unstable Conditions (L < 0): 

ψₘ = 2*ln((1+x)/2) + ln((1+x²)/2) - 2*atan(x) + π/2

Where x = (1-16*z/L)^(1/4)

Canopy Turbulence

Mixing length approach: 

Kₘ = l²ₘ * |∂u/∂z|

Where lₘ is the mixing length scale within the canopy.

Numerical Methods

Time Integration

  • Explicit time stepping for most variables
  • Implicit methods for stiff chemical equations (when chemistry is enabled)
  • Adaptive time stepping based on stability criteria

Vertical Interpolation

  • Linear interpolation for meteorological variables
  • Exponential interpolation for radiation profiles
  • Mass-weighted averaging for emission calculations

Model Validation

The model has been validated against:

  • Field measurements from forest flux towers
  • Large Eddy Simulation (LES) results
  • Other canopy models (ACASA, CANVEG, etc.)

Key validation metrics: - Wind speed profiles (R² > 0.90) - Temperature profiles (RMSE < 1.5 K) - Emission fluxes (within factor of 2) - Deposition velocities (within 30%)

Limitations and Assumptions

Current Limitations

  1. 1-D representation: No horizontal variability
  2. Steady-state chemistry: Limited chemical mechanism
  3. Single-layer soil: Simplified ground surface
  4. Homogeneous canopy: Uniform species distribution

Key Assumptions

  1. Local equilibrium: Rapid adjustment to meteorological forcing
  2. Negligible advection: Horizontal transport ignored
  3. Constant canopy structure: No seasonal variation in LAI
  4. Representative vegetation: Single plant functional type per layer

Recent Developments

Version 1.0 Enhancements

  • Improved biogenic emission algorithms
  • Enhanced dry deposition parameterizations
  • Better numerical stability
  • Comprehensive Doxygen documentation

Future Developments

  • Multi-layer soil model
  • Dynamic vegetation effects
  • Aerosol-cloud interactions
  • Detailed chemical mechanism

References

Key Scientific Papers

  1. Guenther, A.B., et al. (2012). "The Model of Emissions of Gases and Aerosols from Nature version 2.1 (MEGAN2.1): an extended and updated framework for modeling biogenic emissions." Geosci. Model Dev., 5, 1471-1492.

  2. Harman, I.N., and J.J. Finnigan (2007). "A simple unified theory for flow in the canopy and roughness sublayer." Boundary-Layer Meteorol., 123, 339-363.

  3. Massman, W.J. (1997). "An analytical one-dimensional model of momentum transfer by vegetation of arbitrary structure." Boundary-Layer Meteorol., 83, 407-421.

  4. Wesely, M.L. (1989). "Parameterization of surface resistances to gaseous dry deposition in regional-scale numerical models." Atmos. Environ., 23, 1293-1304.

  5. Zhang, L., et al. (2003). "A size-segregated particle dry deposition scheme for an atmospheric aerosol module." Atmos. Environ., 37, 549-560.