A neural network-based method for evaluating a spatially distributed parameter field: An application in groundwater remediation under uncertainty

Uncertainty due to spatial variability of hydraulic conductivity is an important issue in the design of reliable groundwater remediation strategies. Using groundwater management models based on a stochastic approach to groundwater flow, where the log-hydraulic conductivity is represented as a random field, is a frequently studied technique for the design of aquifer remediation in the presence of uncertainty. Such an approach employs the solution of a management model for a large set of equally probable realizations of the hydraulic conductivity. However, only a few critical realizations out of the large set will influence the final design. Incorporation of only a few of the critical realizations in the design procedure would result in a robust design with high reliability level. This reliability level is comparable to those of the designs obtained using many realizations.The spatial distribution of the hydraulic conductivity values in a realization, and the degree of variation of the hydraulic conductivity values within a realization are identified as two important features that determine the level of criticalness of a realization. The association between the hydraulic conductivity pattern and the level of criticalness is not known explicitly and needs to be captured for efficient screening. The screening method presented here utilizes the pattern classification capability of a neural network and its ability to learn from examples. The performance of predicting the critical realizations by this method is evaluated to be versatile in a range of design scenarios. The application of the screening method in a pump-and-treat design problem is illustrated via two examples. In the first example, it is shown that incorporation of as few as 10 critical realizations, as identified by the screening method, in a groundwater management model yields designs with greater than 90% reliability levels. These designs are comparable to those obtained with 100 unscreened realizations. The second example shows that the cost-reliability trade-off obtained with a small set of critical realizations is comparable to that obtained with four times as many realizations. The reduction in the number of realizations incorporated in the management model results in a 80% savings in cpu time for the solution of the management model.U of I OnlyETDs are only available to UIUC Users without author permissio