Schulz, K; Huwe, B: Water flow modeling in the unsaturated zone with imprecise parameters using a fuzzy approach, Journal of Hydrology, 201, 211-229 (1997)
An alternative approach, based on fuzzy set theory, is presented to express imprecision of parameters in a non-probabilistic sense. Imprecision may originate from indirect measurements, estimation routines, subjective interpretation and expert judgement of available information. One dimensional, steady state water flow in the unsaturated zone of homogeneous soils, which is described by the Darcy-Buckingham equation, was chosen to evaluate and to incorporate fuzzy soil hydraulic properties and boundary conditions in the modeling procedure. It is here used to describe soil water pressures with depth, as well as to calculate maximum evapotranspiration rates under steady state conditions. Solving the fuzzy equation for steady state water flow results in minimizing/maximizing procedures, from where resulting membership functions of the dependent variable are calculated. A comparison to a more classical stochastic approach points out the main differences between fuzzy and stochastic concepts to account for uncertainties. Finally, a sensitivity analysis shows the strong impact of different shapes of membership functions of the input parameters on the resulting membership functions of maximum evapotranspiration rates and soil water pressures.
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