TRANSIENT GROUNDWATER-FLOW SIMULATION USING A FUZZY SET APPROACH

The expense of characterizing aquifer spatial variability often result s in a lack of available or realistically obtainable direct measuremen t data for ground-water system simulation. As a consequence ground-wat er models that are able to utilize imprecise or ''soft'' information n eed to be developed. In this paper, a methodology based on fuzzy set t heory is developed to incorporate imprecise data into transient ground -water flow simulation. The imprecise model parameters may come from i ndirect measurements, expert judgment, and subjective interpretation o f available information. Fuzzy numbers are used to represent imprecise parameters. They are also used as a measure of the uncertainty associ ated with the hydraulic head due to the imprecision of input data. A f uzzy ground-water flow model is developed by linking the finite-differ ence method with fuzzy number representations. Fuzzy number operations (cy-level cuts) are used to solve the resulting fuzzy ground-water no w model and are extended to consider the dependencies among hydraulic head coefficients. With the fuzzy number inputs, the transient fuzzy g round-water flow model provides a direct measure of hydraulic head unc ertainties in the time domain. The model outputs can be used as the in puts for subsequent risk analysis and decision-making processes. The f uzzy modeling technique can handle imprecise information directly with out generating a large number of realizations. It is also flexible as it can handle different types of membership functions describing fuzzy input parameters. The methodology can be used to combine data with di fferent levels of quality into groundwater flow models and provides a realistic method to handle parameter imprecision, especially expert ju dgment and subjective information. A numerical model based on the meth odology was tested against the Theis analytical solution for a homogen eous aquifer with pumping. The tested model was also applied to two di fferent heterogeneous flow fields to demonstrate the methodology.