Model Structure Reduction and Robust Experimental Design for Constructing Reliable and Cost-Effective Groundwater Models

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0336952YehMathematical models have become indispensable tools for basin water resources planning, water quality management, pollution source detection and remediation design. After more than 30 years of study, however, the model calibration problem still is not resolved completely. Hydrogeologists may not have sufficient confidence in using their calibrated models for prediction and decision-making purposes. There are two major difficulties in groundwater modeling: (1) the geological structure of a real aquifer usually is very complex and unknown, and (2) the data that can be used for model calibration usually are very limited, in both quantity and quality. These two difficulties are closely interconnected during the model calibration process. A simple model structure may not be able to both fit the observed data and produce reliable predictions. On the other hand, a complex model structure may cause over-parameterization when data are limited, thus rendering a model that contains a large amount of uncertainties. It is well understood that a model that can fit the existing data well may not necessarily be a good model for prediction when it contains significant model error. The following challenging problems thus are presented: can a model be identified that satisfies the accuracy requirement of specified model applications (for example, for use as a decision-making tool) when the data are limited and the model error is significant? Furthermore, can a robust data collection design be found that can provide sufficient information for identifying a reliable model when model structure is highly complex and unknown? This study attempts to address these problems. The overriding objective of this proposal is to perform theoretical analyses to find the quantitative relationships among the reducibility of a model structure, identifiability of a model parameter, reliability of a model application and the robustness of an experimental design. Based on these theoretical results, we will present a new algorithm for calculating the structure error of model reduction. We also will present a new algorithm for robust design when the real structure of the aquifer system is highly complex and unknown. Impact statement: The proposed research attempts to resolve a long-standing problem of model structure identification and experimental design in groundwater modeling. The expected results include the development of a cost-effective and feasible approach for identifying a least complex model that is useful for prediction and decision-making. The developed methodologies can be applied to a variety of simulation models, including groundwater flow, contaminant transport, seawater intrusion and biodegradation. To maximize the immediate applicability of the research results, we have made arrangements with the USGS office in San Diego for collaboration.