EULERIAN-LAGRANGIAN ANALYSIS OF TRANSPORT CONDITIONED ON HYDRAULIC DATA .3. SPATIAL MOMENTS, TRAVEL-TIME DISTRIBUTION, MASS-FLOW RATE, AND CUMULATIVE RELEASE ACROSS A COMPLIANCE SURFACE

In paper 1 of this series we described an analytical-numerical approac h to predict deterministically solute transport under uncertainty. The approach allows conditioning such predictions On hydraulic measuremen ts and assessing the corresponding reduction in uncertainty. In paper 2 we examined the effects of log transmissivity and hydraulic head dat a on conditional predictions of concentration due to instantaneous poi nt and nonpoint sources. In this paper we show how the same approach c an be used directly to estimate mass flow rate across a ''compliance s urface,'' cumulative mass release, and the probability distribution of travel times across this surface and the associated uncertainty. Cont rary to some other methods in the literature, our approach requires ne ither a special theory for travel times nor a prior assumption about t heir probability distribution. We also show how one can compute explic itly the second spatial moment of the conditional mean plume about its center of mass, the conditional mean second spatial moment of the act ual plume about its center of mass, and the conditional covariance of the plume center of mass. We illustrate these quantities and the effec t of conditioning on some of them by considering instantaneous point; line, and area sources in a two-dimensional, statistically homogeneous , isotropic, mildly varying log transmissivity field under uniform pri or (unconditional) mean flow.