Convergence analysis for Latin-hypercube lattice-sample selection strategies for 3D correlated random hydraulic-conductivity fields

Abstract

The Monte Carlo technique provides a natural method for evaluating uncertainties. The uncertainty is represented by a probability distribution or by related quantities such as statistical moments. When the groundwater flow and transport governing equations are solved and the hydraulic conductivity field is treated as a random spatial function, the hydraulic head, velocities and concentrations also become random spatial functions. When that is the case, for the stochastic simulation of groundwater flow and transport it is necessary to obtain realizations of the hydraulic conductivity. For this reason, the next question arises, how many hydraulic conductivity realizations are necessary to get a good representation of the quantities relevant in a given problem? Different methods require different number of realizations and it is relevant to work with the one that reduces the computational effort the most. Zhang and Pinder (2003) proposed a specific case of the latin hypercube sampling (LHS) method called the lattice sampling technique for the generation of Monte Carlo realizations that resulted in a reduction in the computational effort required to achieve a reliable random field simulation of groundwater flow and transport. They compared the LHS method with three other random field generation algorithms: sequential Gaussian simulation, turning bands and LU decomposition. To compare the methods they presented a two-dimensional example problem. In this paper we report a test of the LHS method in a three dimensional random hydraulic conductivity field. We present two example problems, in the first problem an exponential covariance function is assumed and in the second problem a spherical covariance one. The LHS is compared with the sequential Gaussian simulation available in GSLIB (Deutsch and Journel, 1998).