Groundwater flow and solute transport simulation with imprecise parameters

This dissertation develops a methodology to incorporate imprecise parameters into groundwater flow and solute transport modeling. The approach and methodology are developed based on fuzzy set theory coupled with fuzzy number arithmetic operations. The fuzzy set modeling technique is first applied to groundwater flow problems in which the finite-difference technique is combined with fuzzy number representations of transmissivity input. Both steady-state and transient flow conditions are considered. In both situations, the numerical models based on the fuzzy sets approach are verified by comparing them to the corresponding fuzzy analytical solutions. For the steady-state flow case, the fuzzy numerical model is demonstrated using a two-dimensional heterogeneous transmissivity field. The transient flow case is applied to two different heterogeneous flow fields with pumping wells. In solute transport modeling, the fuzzy set modeling technique is used to consider the uncertainty (imprecision) in velocity and dispersivity in the calculation of solute concentration. Both one- and two-dimensional homogeneous uniform flow fields with constant sources of contamination are considered for case studies. Two solution methods, the vertex method and fuzzy-numerical method, are used to solve the fuzzy numerical model of solute transport, which is an explicit function of the fuzzy variables. The resulting fuzzy concentration can be used as a measure of uncertainty in the output due to imprecise parameter input. To consider the imprecision in the nonpoint source leaching to the saturated zone, the MOC groundwater flow and transport model developed by USGS is combined with fuzzy arithmetic to compute the solute concentration at a water supply well in the presence of a conservative solute. A case study is presented to illustrate the methodology. The effects of three different nonpoint source management practices are examined: conventional agricultural production, variable rate application, and well head protection area. In reality, a lack of precise model parameters often occurs in regional groundwater flow and transport modeling. In this case, subjective judgement is essential. One of the distinctive advantages of the fuzzy set approach is the utilization of expert knowledge which may be readily available and important for real situations. The methodology proposed in this study provides an important tool for dealing with imprecise or incomplete and subjective information in groundwater flow systems