Effective parameters of surface energy balance in heterogeneous landscape

This paper addresses the problem of estimating surface fluxes at large scale over heterogeneous terrain, and the corresponding determination of effective surface parameters. Two kinds of formulation are used to calculate the fluxes of sensible and latent heat: the basic diffusion equations (Ohm's law type) and the Penman-Monteith equations. The strategy explored is based upon the principle of flux conservation, which stipulates that the average flux over a large area is simply the area-weighted mean of the contributions from the different patches making up the area. We show that the application of this strategy leads to different averaging schemes for the surface parameters, depending on the type of flux (latent heat, sensible heat) and on the type of formulation used to express the flux. It appears that the effective value of a given parameter must be appraised for each individual application, because it is not unique, but differs according to the magnitude being conserved and the equation used to express this magnitude. Numerical simulations are carried out to test over contrasted areas the aggregation procedures obtained. The areal fluxes estimated from these effective parameters, together with the areal fluxes calculated by means of a simple areal averaging of the parameters, are compared to the true average fluxes, calculated as area-weighted means of the elementary fluxes. The aggregation procedures obtained prove to be much more accurate for estimating areal fluxes and for closing the energy balance equation than those based upon simple areal averaging of the parameters.