Efficient uncertainty analysis in an anisotropic three dimensional hydrogeological model of flow and transport

Abstract

In three dimensional (3D) hydrogeological investigations involving heterogeneous porous media, 3D realizations of saturated hydraulic conductivity are often input to physically-based simulators of flow and transport in a Monte Carlo framework to evaluate the uncertainty in the spatial distribution of solute concentration due to the uncertainty in the spatial distribution of hydraulic conductivity. Realistic uncertainty analysis requires a large number of simulated conductivity realizations. When such conductivity grids are generated via simple random (SR) sampling, uncertainty analysis quickly becomes extremely expensive in terms of both time and computer resources. A more efficient alternative to SR sampling is Latin hypercube (LH) sampling, a form of stratified random sampling, which often yields a more representative distribution of simulated parameter values (in terms of smaller sampling variability of their statistics) with fewer realizations. This work compares the performance of LH sampling to SR sampling in the context of an anisotropic 3D hydrogeological model involving flow and transport. More specifically, 3D lognormal fields of hydraulic conductivity are generated via SR and LH sampling, and are then input to a hydrogeological model to compute the corresponding 3D fields of solute concentration. The sampling methods adopted are evaluated in terms of the reproduction of ensemble statistics of hydraulic conductivity and solute concentration computed from a very large ensemble set generated via SR sampling. The results show that LH sampling is more efficient than SR sampling, in that it can overall reproduce to a similar extent statistics of the conductivity and concentration fields, yet with smaller sampling variability than the latter.