A FULL-NEWTON ALGORITHM FOR PARAMETER ESTIMATION IN

Abstract

An iterative algorithm based on a full-Newton method for the estimation of the saturated hydraulic
conductivity k in the unsaturated zone from drainage experiments is presented. The groundwater
ow 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 dened as the L2-error between the
calculated pressure head values and the observed data at discrete points in the soil prole 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 nite
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 soil 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.