Improving the efficiency of Monte Carlo simulation for groundwater transport models

When applied to complicated groundwater models or when used to estimate the probability of exceeding high pollutant concentrations, the Monte Carlo method becomes either imprecise or expensive. Two methods are proposed here that substantially reduce the computational requirements in comparison to Monte Carlo (MC) simulation when the objective is to estimate a given fractile of the output concentration. The methods are general with respect to the probability distribution of the uncertain source and model parameters and with respect to the algorithm that estimates the desired concentration, given such parameters. One of the methods uses a combination of several uncertainty-propagation techniques; the other is an adaptation of the Rackwitz-Riessler algorithm of system reliability analysis. Both methods employ recursive linearization of the mass transport model. The methods have been implemented in a FORTRAN computer code and used to evaluate the 0.9 fractile of downgradient concentration using a semianalytical three-dimensional mass transport model. Results are typically close to direct MC estimates, and the CPU time is about two orders of magnitude less than that required by the MC method. This is an important feature of the proposed methods, especially for the evaluation of exposure through complicated numerical algorithms