A multiscale approach for estimating solute travel time distributions

This paper uses a multiscale statistical framework to estimate groundwater travel times and to derive conditional travel time probability densities. In the applications of interest here travel time uncertainties depend primarily on uncertainties in hydraulic conductivity. These uncertainties can be reduced if the travel times are conditioned on scattered measurements of hydraulic conductivity and/or hydraulic head. In our approach the spatially discretized log hydraulic conductivity is modeled as a multiscale stochastic process, where each scale describes the process at a di€erent spatial resolution. Related dependent variables such as hydraulic head and travel time are approximated by discrete linear functions of the log conductivity. The linearization makes it possible to incorporate these variables into ecient multiscale estimation and conditional simulation algorithms. We illustrate the application of these algorithms by considering two options for estimating travel time densities: (1) a Monte Carlo technique which only requires linearization of the groundwater ̄ow equation and (2) a Gaussian approximation which also requires linearization of Darcy's law and an implicit particle tracking equation. Both options provide reasonable estimates of the travel time probability density in a synthetic experiment if the underlying log hydraulic conductivity variance is small (0.5). When this variance is increased (to 5.0), the Monte Carlo result is still quite good but the Gaussian approximation is unsatisfactory. The multiscale Monte Carlo option is a very competitive approach for estimating travel time since it provides accurate results over a wide range of conditions and it is more computationally ecient than competing alternatives. Ó 2000 Elsevier Science Ltd. All rights reserved.