摘要：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.
