A GEOSTATISTICAL INVERSE METHOD FOR VARIABLY SATURATED FLOW IN THE VADOSE ZONE

A geostatistical inverse technique utilizing both primary and secondar y information is developed to estimate conditional means of unsaturate d hydraulic conductivity parameters (saturated hydraulic conductivity and pore size distribution parameters) in the vadose zone. Measurement s of saturated hydraulic conductivity and pore size distribution param eters are considered as the primary information, while measurements of steady state flow processes (soil-water pressure head and degree of s aturation) are regarded as the secondary information. This inverse app roach relies on the classical linear predictor (cokriging) theory and takes the advantage of the spatial cross correlation between the soil- water pressure head and each of the following: degree of saturation, s aturated hydraulic conductivity, and a pore size distribution paramete r. Using an approximate perturbation solution for steady, variably sat urated flow under general boundary conditions, the cross covariances b etween the primary and secondary information are derived. The approxim ate solution is formulated on the basis of a first-order Taylor series expansion of a discretized finite element equation. The sensitivity m atrix in the solution is evaluated by an adjoint state sensitivity app roach for flow in heterogeneous media under variably saturated conditi ons. Through several numerical examples the inverse model demonstrates its ability to improve the estimates of the spatial distribution of s aturated hydraulic conductivity and pore size distribution parameters using the secondary information.