Multidimensional quasi-linear steady infiltration toward a shallow water table

The present work explores further a class of analytical solutions of moisture movement in unsaturated porous media, characterized by an exponential dependence of the hydraulic conductivity on water pressure. The Green's function method is used to derive a general analytical model pertaining to multidimensional steady infiltration to a shallow water table with arbitrary boundary conditions and arbitrary root-uptake forcing functions and for various simple source geometry. The general solution is expressed in integral form from which particular analytical solutions pertaining to cases of surface and subsurface irrigation, evaporation, and root-uptake in the presence of a shallow water table can be easily deduced from the general analytical model. New solutions include the one-dimensional infiltration subject to discrete extraction functions, the two-dimensional infiltration from a strip source with a uniform exponential and a periodic flux distribution, and the three-dimensional infiltration from a rectangular source at the land surface. Particular solutions have also been obtained for infiltration from a periodic series of point, line, and strip sources. Algebraic equations for the parameter estimation of the hydraulic conductivity function were also derived from the simple one-dimensional solution. The proposed model offers the analyst significant flexibility in deriving results and analyzing infiltration phenomena of practical interest and provides a basis upon which parameter estimation can be effected.