Management of diffuse pollution in groundwater under imprecise conditions using fuzzy models

Abstract

This paper presents a framework for evaluation of nitrate control strategies that use spatially variable nitrogen input in the presence of imprecise information. The research stems from the fact that diffuse pollution has caused water consumers to be concerned with reducing the risk posed by contaminated water supplies. An important element in quantifying risk reduction is the use of simulation modeling to predict the transport and fate of contaminants under variable rate application as employed in a wellhead protection area strategy. Specifically, a groundwater model is linked with an unsaturated zone transport (and crop production) model which provides the nutrient and recharge loading rates to the saturated zone. To consider uncertainty stemming from the unsaturated zone model output, in addition to aquifer parameters, a new groundwater modeling technique is developed in which fuzzy set theory is combined with finite-difference modeling methods. The groundwater model incorporates imprecise parameters (i.e., transmissivity) into the modelling process through the use of fuzzy set theory. Imprecision has been encoded directly into the finite-difference equations using fuzzy numbers as input, and level-set operations combined with non-linear optimization are used to solve the system of equations. The resulting fuzzy output can be interpreted as the level of imprecision associated with the model. A case study is presented to illustrate the methodology.