The sensible and latent heat fluxes at the surface can be written in a generic form :
Depending on the type of closure chosen by the land surface scheme the flux will be computed with variables at time t or t+1. For surface sensible heat ( ) flux the following correspondences are used :
where is the temperature at the first atmospheric level, p is the pressure at this level, pressure at some reference level, is surface temperature, is surface transfer coefficient for heat and moisture (Assumed to be same here.), is the density and is the wind speed at the first level. Equation 20 yields evaporation ( ) if the following definitions are used :
where is the water vapor mixing ratio at the first atmospheric level, is the saturated humidity for the surface temperature and is the aridity coefficient. is defined as the ratio between actual and potential evaporation.
Computing these fluxes is the responsibility of the land surface scheme and our aim is to derive an equation for using as sole information from the surface. This ensures to the land surface scheme a maximum of freedom in the choice of the numerical scheme used for solving the surface energy balance equation. Inserting equation 20 into equation 15 yields :
Thus the only knowledge required for computing and iterating equation 16 from l=2 to the top are the old values of potential enthalpy and humidity at the lowest atmospheric level, the surface fluxes and finally the values of and for obtained during the descent.