Land surface energy balance
The total land surface energy balance, i.e. surface energy balance for the combined soil-snow-plant system, is calculated as additional variables:
(8.1)
where Rn,tot, HTotal, and LvETotal are the sum of net radiation, sensible heat flux, and latent heat flux for bare soil, snow, and plants, respectively. GTotal is the sum of surface heat flux to soil and snow including the latent heat in precipitation. It is not an output in the model yet, but can be calculated as Rn,tot-HTotal-LvETotal.
Different numerical methods are used to solve the surface energy balance for plants, snow, and bare soil. The dynamic coupling between surface temperature, heat fluxes, and net radiation is only used for the bare soil surface (see section Evaporation from the soil surface) and for the snow surface (see section Snow Dynamics). Evaporation from plants, i.e. transpiration and evaporation of intercepted water, is calculated with the analytical Penman-Monteith equation (see chapter Potential transpiration). Sensible heat flux and corresponding surface temperatures of the vegetation are calculated based on the residual term of the energy balance for the vegetation, assuming that the vegetation has zero heat capacity.
In case of multiple plants, the sensible heat flux from each plant, Hj, is calculated as:
(8.2)
where Rn,j is the net radiation, and LvEj is the latent heat flux corresponding to the sum of actual transpiration and interception evaporation (see sections Water uptake by roots and Interception). The corresponding difference between plant and air temperature ∆Tj is calculated by inverting the bulk aerodynamic equation for sensible heat flux:
(8.3)
where ra,j is the plant aerodynamic resistance and ρa and cp are constants.
The plant surface temperature, Tj, is used for the calculation of net radiation the next time step. To reduce the risk of numerical instability, a recursive filter is applied on the temperature difference before calculating the actual plant temperatures:
(8.4)
(8.5)