Computational Geosciences 5: 25–46, 2001.  2001 Kluwer Academic Publishers. Printed in the Netherlands. Determination of soil parameters via the solution of inverse problems in infiltration D. Constales a and J. Kaˇ cur b a Ghent University, Department for Mathematical Analysis, Galglaan 2, B-9000 Gent, Belgium E-mail: dcons@world.std.com b Faculty of Mathematics and Physics, Comenius University Bratislava, Mly’nska dolina, 84215 Bratislava, Slovakia E-mail: kacur@fmph.uniba.sk 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 effi- ciently 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 differen- tiation. Several numerical experiments are included. 1. Introduction Unsaturated flow in porous media is modelled by the Richards equation ∂ t θ = div ( k(ψ) grad φ ) , (1) where θ is volumetric water content, ψ is the matric potential head and φ is the total head, given by φ = ψ + z with z (i.e., height) the gravitational potential. The function k(ψ) is the hydraulic conductivity. We denote by u the quotient (θ - θ r )/(θ s - θ r ), where θ s is the volumetric water content at saturation and θ r is the residual volumetric water content; u is also called the effective saturation. Van Genuchten [13] derived an empirical relationship between u (or, equiva- lently, θ ) and ψ in the form u = 1 (1 + (αψ) n ) m ,n = 1 1 - m ,α =- 1 h b ( 2 1/m - 1 ) 1-m , (2) where h b is the bubbling pressure. The hydraulic conductivity at effective saturation u in the unsaturated medium is modelled by the relationship k(u) = k s u 1/2 ( 1 - ( 1 - u 1/m ) m ) 2 , (3)