Determination of Soil Parameters via the Solution of Inverse Problems in Infiltration |
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| Authors: | D Constales J Kačur |
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| Institution: | (1) Department for Mathematical Analysis, Ghent University, Galglaan 2, B-9000 Gent, Belgium;(2) Faculty of Mathematics and Physics, Comenius University Bratislava, Mly'nska dolina, 84215 Bratislava, Slovakia |
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| Abstract: | In this paper, we propose an efficient method for the identification of soil parameters in unsaturated porous media, using measurements from infiltration experiments. The infiltration is governed by Richard's nonlinear equation expressed in terms of effective saturation. The soil retention and hydraulic permeability functions are expressed using the Van Genuchten-Mualem ansatz in terms of the soil parameters. The mathematical algorithm is based on a transformation of Richard's equation to a system of ordinary differential equations completed by the governing equation for the movement of the wetness front. This system can be efficiently solved by specialized packages for the solution of stiff systems of ODE. The unknown parameters are determined using the optimization approach of minimizing a cost functional for the discrepancy between the model output and the measurements. The gradient and Hessian of the solution with respect to soil parameter vector are determined using automatic differentiation. Several numerical experiments are included. |
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