Determination of soil parameters via the solution of inverse problems in infiltration

In this paper, we propose an efficient method for the identification of soi l parameters in unsaturated porous media, using measurements from infiltrat ion experiments. The infiltration is governed by Richard's nonlinear equati on expressed in terms of effective saturation. The soil retention and hydra ulic permeability functions are expressed using the Van Genuchten-Mualem an satz in terms of the soil parameters. The mathematical algorithm is based o n a transformation of Richard's equation to a system of ordinary differenti al equations completed by the governing equation for the movement of the we tness front. This system can be efficiently solved by specialized packages for the solution of stiff systems of ODE. The unknown parameters are determ ined using the optimization approach of minimizing a cost functional for th e discrepancy between the model output and the measurements. The gradient a nd Hessian of the solution with respect to soil parameter vector are determ ined using automatic differentiation. Several numerical experiments are inc luded.