An iterative stochastic inverse approach for steady-state flow in heterogeneous, variably saturated porous media.

摘要

An iterative stochastic inverse technique utilizing both primary and secondary information is developed to estimate conditional means of unsaturated hydraulic conductivity parameters (saturated hydraulic conductivity and pore-size distribution parameters) in the vadose zone. Measurements of unsaturated hydraulic conductivity parameters are considered as the primary information, while measurements of flow processes (soil-water pressure head and degree of saturation) are regarded as the secondary information. This inverse approach is similar to the classical geostatistical method, which utilizing a linear estimator that depends upon the (cross-)covariance functions of primary and secondary information. The linear estimator is, however, improved by solving the governing flow equation and by updating the residual (cross-)covariance functions, in an iterative manner. Using first-order Taylor series expansion of a discretized finite element equation, the (cross-)covariance functions of the primary and secondary information are derived. The sensitivity matrices in Taylor series expansion are evaluated by an adjoint sensitivity analysis. As a result, the nonlinear relations between unsaturated hydraulic conductivity parameters and flow processes are incorporated in the estimation. Through some numerical examples, the iterative inverse model demonstrates its ability to improve the estimates of unsaturated hydraulic conductivity parameters compared to the classical geostatistical inverse approach. In addition, the inconsistency problem existing in classical geostatistical inverse approach is alleviated. The estimated fields of unsaturated hydraulic conductivity parameters and flow fields not only retain their observed values at sample locations, but satisfy the governing flow equation as well.