Iterative coconditional Monte Carlo simulation method for steady-state flow in aquifers

An iterative coconditional Monte Carlo simulation method is developed to estimate coconditional means and variances of transmissivity (T) and head (φ) distributions based on some T and φ measurements in heterogeneous aquifers under steady state condition. This method uses the classical coconditional Monte Carlo simulation technique, and a successive linear estimator to produce realizations of random T and φ fields that preserve measurements of T and φ at sampling locations. In addition, it ensures these random fields to be consistent with the governing flow equation. As a result, the iterative coconditional Monte Carlo simulation method alleviates problems associated with the classical coconditional Monte Carlo simulation method by incorporating the nonlinear relationship between T and φ. The averages of all the coconditional realizations then yields the coconditional means of T and φ fields, and the variances around the means become coconditional variances of T and φ. These variances can be utilized as a measure of the reduction in estimation uncertainty due to T and φ observations.