Steady State Groundwater Flow Simulation With Imprecise Parameters

A methodology based on fuzzy set theory is developed to incorporate imprecise parameters into steady state groundwater flow models. In this case, fuzzy numbers are used to represent parameter imprecision. As such, they are also used as a measure for the uncertainty associated with the hydraulic heads due to the imprecision in the input parameters. The imprecise input parameters may come from indirect measurements, subjective interpretation, and expert judgment of available information. In the methodology, a finite difference method is combined with level set operations to formulate the fuzzy groundwater flow model. This fuzzy modeling technique can handle imprecise parameters in a direct way without generating a large number of realizations. Two numerical solution methods are used to solve the fuzzy groundwater flow model: the groundwater model operator method proposed in this methodology and the iterative algorithm based on conventional interval arithmetics. The iterative method is simple but may overestimate the uncertainty of hydraulic heads. The groundwater model operator method not only provides the hull of the solution set for the hydraulic heads but also considers the dependence of hydraulic head coefficients which are functions of imprecise parameters. Sensitivity analysis shows that the dependence of hydraulic head coefficients has a critical impact on the model results, and neglecting this dependence may result in significant overestimation of the uncertainty of hydraulic heads. A numerical model based on the methodology is tested by comparing it with the analytical solution for a homogeneous radial flow problem. It is also applied to a simplified two-dimensional heterogeneous flow case to demonstrate the methodology.