A CONCEPTUAL PERTURBATION MODEL OF WATER-MOVEMENT IN STOCHASTICALLY HETEROGENEOUS SOILS

A perturbation model of water movement in heterogeneous soils is prese nted, emphasizing its theoretical features. It is based on the fundame ntal physical concepts of continuity and Darcy's law which hold in sat urated and in unsaturated zones. Soil heterogeneity may be represented by an arbitrary number of spatially varying stochastic parameters. Th e derivation of the model equations leads to a system of functional di fferential equations which describes the average behaviour of a flow p rocess and predicts its stochastic variability. This system will be re duced to the familiar Richards equation, if the soil parameters are as sumed to be known deterministically. For the general stochastic case i t is shown how the deterministic concept of volume conservation is tra nsferred to the conservation of the corresponding distribution moments . Suitable initial and boundary conditions are formulated for means an d covariances of hydraulic head and flux. Finally, the range of applic ability of the new flow model is discussed.