A geostatistically based inverse model for three-dimensional variably saturated flow

We present a geostatistically based inverse model for characterizing hetero geneity in parameters of unsaturated hydraulic conductivity for three-dimen sional flow. Pressure and moisture content are related to perturbations in hydraulic parameters through cross-covariances, which are calculated to fir st-order. Sensitivities needed for covariance calculations are derived usin g the adjoint state sensitivity method. Approximations of the conditional m ean parameter fields are then obtained from the cokriging estimator. Correl ation between parameters and pressure - moisture content perturbations is s een to be strongly dependent on mean pressure or moisture content. High cor relation between parameters and pressure data was obtained under saturated or near saturated flow conditions, providing accurate estimation of saturat ed hydraulic conductivity, while moisture content measurements provided acc urate estimation of the pore size distribution parameter under unsaturated flow conditions.