SENSITIVITY ANALYSIS OF FLOW IN UNSATURATED HETEROGENEOUS POROUS-MEDIA - THEORY, NUMERICAL-MODEL, AND ITS VERIFICATION

Sensitivity analysis is one of the tools available for analyzing the effects of parameter uncertainty and soil heterogeneity on the transport of moisture in the unsaturated similar porous media. Direct differentiation of the discretized Richards equation with respect to parameters defining spatial variability leads to linear systems of equations for elementary sensitivities that are readily solved in conjunction with the original equation. These elementary sensitivities can be easily transformed into approximations of functional sensitivities and into sensitivities of boundary fluxes. A numerical implementation of this technique in one space dimension yields results that are consistent with exact analytical solutions and with numerical perturbation calculations. The effects of a given heterogeneity can be modeled adequately provided that the maximum relative change of the scale factor from one grid point to the next not exceed a number on the order of unity. Copyright 1990 by the American Geophysical Union.