Hydraulic conductivity estimation in partially saturated soils using a full-Newton method

An iterative algorithm based on a full-Newton method for the estimation of the saturated hydraulic conductivity k from drainage experiments is presented. The water flow in the unsaturated zone 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 drainage process. The derivative of pressure head with respect to the parameter k is obtained as the solution of a differential equation with appropriate boundary and initial conditions. A Galerkin finite element procedure is used to obtain approximated solutions of the two differential problems involved in each iteration: the direct problem and the derivative of the functional. The algorithm was implemented in one-dimensional domains and used to estimate k in layered soils using both synthetically generated data and observed data from an experimental plot in the Azul River basin (Buenos Aires, Argentina). 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. Copyright © 2007 John Wiley & Sons, Ltd.