Assessing Uncertainty Associated with Groundwater and Watershed Problems Using Fuzzy Mathematics and Generalized Regression Neural Networks

When trying to represent an environmental process using mathematical models, uncertainty is an integral part of numerical representation. Physically-based parameters are required by such models in order to forecast or make predictions. Typically, when the uncertainty inherent in models is addressed, only aleatory uncertainty (irreducible uncertainty) is considered. This type of uncertainty is amenable to analysis using probability theory. However, uncertainty due to lack of knowledge about the system, or epistemic uncertainty, should also be considered. Fuzzy set theory and fuzzy measure theory are tools that can be used to better assess epistemic, as well as aleatory, uncertainty in the mathematical representation of the environment. In this work, four applications of fuzzy mathematics and generalized regression neural networks (GRNN) are presented. In the first, Dempster-Shafer theory (DST) is used to account for uncertainty that surrounds permeability measurements and is typically lost in data analysis. The theory is used to combine multiple sources of subjective information from two expert hydrologists and is applied to three different data collection techniques: drill-stem, core, and pump-test analysis. In the second, a modification is made to the fuzzy least-squares regression model and is used to account for uncertainty involved in using the Cooper-Jacob method to determine transmissivity and the storage coefficient. A third application, involves the development of a GRNN to allow for the use of fuzzy numbers. A small example using stream geomorphic condition assessments conducted in the state of Vermont is provided. Ultimately, this fuzzy GRNN will be used to better understand the relationship between the geomorphic and habitat conditions of stream reaches and their corresponding biological health. Finally, an application of the GRNN algorithm to explore links between physical stream geomorphic and habitat conditions and biological health of stream reaches is provided. The GRNN proves useful; however, physical and biological data collected concurrently is needed to enhance accuracy