ENERGY-BALANCE OF HETEROGENEOUS TERRAIN - AVERAGING THE CONTROLLING PARAMETERS

We address the problem of averaging surface fluxes of sensible and latent heat at a regional scale. We assume that surface temperature can be expressed, at this scale, as a simple areal averaging of the temperature of each surface making up the region. A theoretical development, based on the diffusion equations and the energy balance equation, allows us to derive a simple averaging process. The controlling parameters of surface fluxes, such as aerodynamic resistance, resistance to latent heat transfer and albedo, must be weighted by the relative area of each component multiplied by what we call an omega coefficient. This coefficient, specific to each component surface, is defined in terms of aerodynamic resistance, surface resistance and also involves air temperature. A numerical simulation is carried out. Three cases are examined in which the whole area is divided into two contrasting components. The averaging process based on the omega coefficients is tested against the real values of energy fluxes directly obtained by averaging the local fluxes. It is shown that the omega coefficients substantially improve the estimates of the regional fluxes with respect to a simple areal averaging of the controlling parameters.