Transient ground-water flow simulation using a fuzzy set approach

The expense of characterizing aquifer spatial variability often results in a lack of available or realistically obtainable direct measurement data for ground-water system simulation. As a consequence ground-water models that are able to utilize imprecise or ''soft'' information need to be developed. In this paper, a methodology based on fuzzy set theory is developed to incorporate imprecise data into transient ground-water flow simulation. The imprecise model parameters may come from indirect measurements, expert judgment, and subjective interpretation of available information. Fuzzy numbers are used to represent imprecise parameters. They are also used as a measure of the uncertainty associated with the hydraulic head due to the imprecision of input data. A fuzzy ground-water flow model is developed by linking the finite-difference method with fuzzy number representations. Fuzzy number operations (cy-level cuts) are used to solve the resulting fuzzy ground-water now model and are extended to consider the dependencies among hydraulic head coefficients. With the fuzzy number inputs, the transient fuzzy ground-water flow model provides a direct measure of hydraulic head uncertainties in the time domain. The model outputs can be used as the inputs for subsequent risk analysis and decision-making processes. The fuzzy modeling technique can handle imprecise information directly without 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 different levels of quality into groundwater flow models and provides a realistic method to handle parameter imprecision, especially expert judgment and subjective information. A numerical model based on the methodology was tested against the Theis analytical solution for a homogeneous aquifer with pumping. The tested model was also applied to two different heterogeneous flow fields to demonstrate the methodology.