Stochastic analysis of the relationship between topography and the spatial distribution of soil moisture

This paper deals with the issue of the spatial horizontal variability of soil moisture in the root zone of a shallow soil at the large scale. The problem of water flow in the unsaturated zone is formulated so that topography appears explicitly as a forcing for the movement and redistribution of soil moisture. This formulation emphasizes the role of the lateral redistribution of water that is induced by topography. A stochastic theory is developed to relate the statistical distribution of soil moisture to that of elevation. This approach will ultimately facilitate the use of the readily available data sets describing topography for the purpose of defining the large‐scale distribution of soil moisture. The steady state horizontal distribution of soil moisture under homogeneous bare soil conditions is regulated by three distinct factors: topography, climate, and soil properties. First, topography, forces a distribution of soil moisture that tends to mimic the elevation field at large scales. The other two factors are the vertical divergence of water in response to the climate forcing (evaporation) and the capillary resistance to water movement. The climate forcing tends to smooth the spatial distribution of soil moisture. However, the capillary forces exerted by the soil matrix tend to resist displacement of water and hence exert adverse effects against the topography and climate forcings. The variance of the soil moisture distribution increases with the variance of the elevation field and decreases with the correlation scale of the elevation field and the magnitude of the climate forcing. The impact of capillary forces on the vertical fluxes of water is more significant than their impact on the topographically induced horizontal fluxes, owing to the larger hydraulic gradient in the vertical direction resulting from the disparity in scale between the vertical and horizontal directions.