A methodology based on fuzzy set theory is presented to express imprecision of input data in a non-probabilitic sense. Imprecision may originate from indirect measurements, estimation routines, subjective interpretation, and expert judgement of available information. A numerical finite difference solution scheme was chosen to solve one-dimensional steady-state water flow in the unsaturated zone of a layered soil profile. To extend the solution algorithm to operate with fuzzy soil-hydraulic properties and boundary conditions, it is necessary to incorporate the scheme into a nonlinear optimisation routine from where resulting membership functions of soil water pressures with depths can be calculated. By subsequently considering the different imprecise parameters in the calculations and analysing their impact, it is concluded that resulting imprecision not only depends on the degree of imprecision and the number of uncertain parameters but also very much on the system context (e.g. boundary conditions and spatial distribution). The comparison with a closed form solution to solve the fuzzy water flow problem show the potential of that method to be extended towards transient, two- and three-dimensional process descriptions.
Uncertainty and sensitivity analysis of water transport modelling in a layered soil profile using fuzzy set theory
Karsten Schulz, Bernd Huwe; Uncertainty and sensitivity analysis of water transport modelling in a layered soil profile using fuzzy set theory. Journal of Hydroinformatics 1 October 1999; 1 (2): 127–138. doi: https://doi.org/10.2166/hydro.1999.0011
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