Uncertainty analysis of transport of water and pesticide in an unsaturated layered soil profile using fuzzy set theory

Incomplete information is notoriously common in planning soil and groundwater remediation. For making decisions groundwater flow and transport models are commonly used. However, uncertainty in prediction arises due to imprecise information on flow and transport parameters like saturated/unsaturated hydraulic conductivity, water retention curve parameters, precipitation and evapo-transpiration rates as well as factors governing the fate of pollutant in soil like dispersion, diffusion, degradation and chemical transformation. Different methods exist for quantifying uncertainty, e.g. first and second order Taylor’s Series and Monte-Carlo method. In this paper, a methodology based on fuzzy set theory is presented to express imprecision of input data, in terms of fuzzy number, to quantify the uncertainty in prediction. The application of the fuzzy set theory is demonstrated through pesticide (endosulfan) transport in an unsaturated layered soil profile. The governing partial differential equation along with fuzzy inputs, results in a non-linear optimization problem. The solution gives complete membership functions for flow (suction head) and pesticide concentration in soil column.