Solution Methodology and Validation of Physics-based Stochastic Subsurface Solute Transport Equations
This research project addresses the Quantification of the risks due to contaminant (solute) concentrations in field-scale soils as contaminants migrate under various pollution loadings at the soil surface (boundary conditions), starting with initial contaminant plumes existing within the soil medium prior to the beginning of loadings (initial conditions). The field-scale soils are considered heterogeneous with stationary fluctuations of soil hydraulic properties in the horizontal direction but nonstationary fluctuations of these properties in the vertical direction due to statistical heterogeneity of the soil profile. For the quantification of soil contamination risks, first, almost exact ensemble probability distribution functions of solute travel time for stochastic vertical convective solute transport within above-described heterogeneous field scale soils under both deterministic and stochastic water application rates and unsteady-nonuniform moisture flows were derived directly from the convective transport stochastic partial differential equation (PDE) under general depth-varying initial and time-varying boundary conditions. Secondly, almost exact ensemble pdfs of solute concentrations as function of time and soil depth for stochastic vertical convective solute transport within above-described field-scale, heterogeneous soils under both deterministic and stochastic water application rates were derived directly from the convective transport stochastic PDE under various depth-varying initial and time-varying boundary conditions. Field data from the water and solute transport experiments at U.C. Davis field site showed that the approximation, used in the above ensemble pdfs, is exact for the particular field site. The derived ensemble pdfs for solute concentrations were verified by Monte Carlo simulation solutions of the convective transport stochastic PDE. The derived ensemble pdfs unify the Eulerian and Lagrangian components of transport in one single framework since they contain explicitly the influence of both initial and boundary conditions. They also show that the derived pdfs for both solute travel times and solute concentrations are non-Gaussian under the influence of initial and boundary conditions.