Stochastic inverse approaches for variably saturated flow in heterogeneous porous media: Conditional moments

In this paper we describe two stochastic iterative approaches to derive co-conditional mean parameter fields for variably saturated flow in porous media. The first is a direct approach that uses the approximate conditional mean flow equation to derive the co-conditional mean parameters directly. The other is an iterative co-conditional Monte Carlo simulation technique that generates co-conditional realizations of hydrologic parameters. By averaging all the realizations, the co-conditional means of K and phi fields are obtained and co-conditional variances, a measure of uncertainty associated with the estimate, are then calculated. Numerical experiments are carried out to test these two approaches.