Summary:

Numerical Implementation of Canopy Energy Conservation

1. Canopy Energy Conservation Equation:
   - The energy balance equation for the vegetation canopy is given as:
     ∇Sv + Lv(Tv) + Hv(Tv) + λEv(Tv) = 0
   - Where Sv is the solar radiation absorbed, Lv is the net longwave radiation absorbed, Hv is the sensible heat flux, and λEv is the latent heat flux from vegetation.

2. Iterative Solution for Vegetation Temperature:
   - The Newton-Raphson method is used to iteratively solve for the vegetation temperature Tv.
   - The partial derivatives of Lv, Hv, and λEv with respect to Tv are provided.
   - The changes in leaf temperature, sensible heat flux, and latent heat flux are updated at each iteration.

3. Numerical Solution Procedure:
   - Initial values for canopy air temperature and humidity are obtained.
   - An initial guess for wind speed and Monin-Obukhov length is made.
   - An iterative process is followed to calculate various parameters, including:
     - Friction velocity, temperature and humidity scales
     - Aerodynamic and leaf boundary layer resistances
     - Sunlit and shaded stomatal resistances
     - Sensible and latent heat fluxes
   - The iteration continues until convergence criteria are met or a maximum number of iterations is reached.
   - Finally, the momentum fluxes, ground heat and vapor fluxes, and 2-m height air properties are calculated.

The summary provides a concise overview of the numerical implementation of the canopy energy conservation, focusing on the key aspects of the iterative solution for vegetation temperature and the detailed numerical solution procedure.