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

这项研究的特点是解决环境工程问题的一个新概念，考虑到土壤介质的异质性。研究的重点是发展和实施新的模拟技术，其成果可以很容易地用于与确保可持续环境有关的决策。特别是，输出将允许非常有效地模拟在统计上一致地实现污染物在地面上的命运。此外，模拟技术将为非均质多孔介质的水力特性采样提供最佳位置。在这种情况下，最优性意味着数学模型在不完全信息下具有良好的预测能力。这个概念取决于将不确定的材料属性表示为其各种尺度乘以随机系数的组合。这将依靠Karhunen-Loeve展开来实现，该展开考虑了场的概率结构，以及定义问题的域的有限范围。求解过程表示为关于这些非均质尺度的非线性泛函展开。这个展开式中的系数是通过求解一个线性代数方程组来计算的。一旦得到这个展开式，预测解的灵敏度将被分析地评估。可以很容易地评估溶液对不同空间位置随机水力参数值的敏感性，并确定样品的最佳位置。这个公式提供了理论上的严谨性，这被认为是在随机水文学领域取得进展和地下水流动系统可靠性所必需的。它允许使用最少数量的随机变量对随机过程进行最佳表示。该研究将补充首席研究员目前在地下水流动随机模型开发方面的工作，并将其应用于决策支持。

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.