Decision Support for Flow in Porous Media: Optimal Sampling for Data Assimilation

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This research features a novel concept for addressing environmental engineering problems that takes into account the heterogeneous nature of the soil medium. The emphasis of the research is on developing and implementing new simulation techniques the output of which can be readily utilized in decision making as related to ensuring a sustainable environment. In particular, the output will permit a very efficient simulation of statistically consistent realizations of fate of pollutants in the ground. Additionally, the simulation technique will provide the optimal location for the sampling of hydraulic properties in a heterogeneous porous medium. Optimality, in this case, is construed to imply good predictive capability of the mathematical model under incomplete information. The concept hinges upon representing uncertain material properties as a combination of their various scales multiplied by random coefficients. This will be achieved by relying on the Karhunen-Loeve expansion that takes into account the probabilistic structure of the field, as well as the finite extent of the domain over which the problem is defined. The solution process is represented as a nonlinear functional expansion with respect to these scales of heterogeneity. The coefficients in this expansion are calculated by solving a linear system of algebraic equations. Once this expansion is obtained, the sensitivity of the predicted solution will be analytically evaluated. The sensitivity of the solution with respect to the values of the random hydraulic parameters at various spatial locations can be readily evaluated, and the optimal location of samples identified. This formulation affords a theoretical rigor which is believed to be essential to progress in the field of stochastic hydrology and reliability of ground-water flow systems. It permits an optimal representation of the random processes involved using a minimum number of random variables. The research will complement current work by the Principal Investigator on stochastic model development for ground water flow and extend its applicability to decision support.