An Analytical Hydrological Model for the Study of Scaling Issues in Land Surface Modeling

Abstract

Besides the atmospheric forcing such as solar radiation input and precipitation, the heterogeneity of the surface cover also plays an important role, especially in the distribution characteristics of the latent heat flux (LE). In this study, scaling issues are discussed based on an analytical hydrological model that describes the transpiration and diffusion processes of soil water. The solution of this analytical model is composed of a transient part that depends primarily on initial conditions and a steady part that depends on the boundary conditions. To know how sensitive the different averaging approaches are to the initial conditions, three initial profiles are chosen that cover the prevailing soil moisture regimes. After analyzing its solution, the study shows that 1) upon reaching the steady state, directly taking an average of soil properties will cause systematic overestimation in the calculation of area-averaged LE. For an initially very dry condition, averaging of a sandy soil and a clay soil can cause a percentage error as large as 40%. 2) For vegetation growing on sandy soils, a direct averaging of the transpiration rate results in persistent overestimation of LE. For vegetation growing on clay soil, however, even after reaching the steady state, averaging of two water extraction weights can be either an overestimation or an underestimation, depending on which two vegetation types are involved. 3) During the interim stage of drying down, averaging of the soil/vegetation properties can lead to either an overestimation or an underestimation, depending on the evolving stage of the soil moisture profile. 4) The initial soil moisture condition matters during the transient stage of drying down. Different initial soil moisture conditions yield different scenarios of underestimation and overestimation patterns and a differing severity of errors. The simplicity of the analytical model and the heuristic initial soil profiles make the generalization easier than using sophisticated numerical models and make the causality mechanism clearer for physical interpretations.