Numerical Experiments on Hydraulic Conductivity Estimation Using the Adjoint Method

Abstract

An iterative algorithm based on the adjoint method for the estimation of the saturated hydraulic conductivity k in the unsaturated zone from infiltration experiments is presented. The groundwater flow is assumed to be described by Richards equation and the well-known van Genuchten constitutive model. The cost functional used for the parameter optimization is defined as the L2-error between the calculated pressure head values and the observed data at discrete points in the soil profile during the infiltration process. The exact gradient of the cost functional is obtained by solving an appropriate adjoint problem, which is derived from the equations of the Gateaux derivatives of the pressure head with respect to the parameter k. The a optimization procedure is solved employing a nonlinear conjugate gradient method. A Galerkin finite element procedure is used to obtain approximated solutions of the three differential problems involved in each iteration: the direct and the adjoint problems and the Gateaux derivatives. The algorithm was implemented in one-dimensional domains and used to estimate k in heterogeneous soil profiles using synthetically generated data. Numerical examples show that the proposed algorithm yields very good estimations of the saturated hydraulic conductivity and becomes a promising method for in situ estimation of this parameter.