This report presents a new methodology to model the time and space evolution of groundwater variables in a system of aquifers when certain components of the model, such as the geohydrologic information, the boundary conditions, the magnitude and variability of the sources or physical parameters are uncertain and defined in stochastic terms. This facilitates a more realistic statistical representation of groundwater flow and groundwater pollution forecasting for either the saturated or the unsaturated zone. The method is based on applications of modern mathematics to the solution of the resulting stochastic transport equations. This procedure exhibits considerable advantages over the existing stochastic modeling techniques. In particular, the semigroup solutions are not restricted to small variances in the stochastic elements (perturbation techniques), unsteady dynamic conditions are specifically considered, time and space randomness may be considered in the sources, the boundary conditions or the parameters, and the methodology reflects a well-posed functional-analytic theory. Several basic example problems are presented in order to illustrate the application of the methodology to the modeling of complex spatially and temporally distributed sources of interest in engineering hydrology today. Further potential applications of the method are very promising, including the modeling of non-conservative contaminants in groundwater systems.
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The work upon which this report is based was supported in part by funds provided by the United States Department of the Interior, Washington, D.C., as authorized by the Water Resources Research Act of 1984. Public Law 98-242.
Serrano, Sergio E., "Modeling Mass Transport in Aquifers: The Distributed Source Problem" (1990). KWRRI Research Reports. 30.