Multidimensional linearized nonsteady infiltration toward a shallow water table

The Green's function method is used to derive a general analytical model pertaining to multidimensional nonsteady infiltration toward a shallow water table with arbitrary initial conditions, boundary conditions, and root uptake forcing functions and for various simple source geometries. The general Green's function solution allows the derivation of particular analytical solutions pertaining to cases of surface and subsurface irrigation, evaporation, root uptake, and moisture redistribution. The model assumes that the hydraulic conductivity function is an exponential function of the water pressure and a linear function of the moisture content. One-dimensional solutions are obtained for time-dependent distributions of the flux at the land surface and of root uptake in the subsurface. Two- and three-dimensional solutions are also derived for point and line sources in the domain, for a strip, a rectangle, and a disc source at the land surface, and for two- and three-dimensional moisture redistribution and root uptake. Most of the solutions are a product of two terms; one term is a function of depth while the other term is a function of time and the lateral coordinates. Numerical results show the effect of the water table and soil type on the two-dimensional moisture movement from a strip source.