Fuzzy-probabilistic calculations of water-balance uncertainty

Hydrogeological systems are often characterized by imprecise, vague, inconsistent, incomplete, or subjective information, which may limit the application of conventional stochastic methods in predicting hydrogeologic conditions and associated uncertainty. Instead, predictions and uncertainty analysis can be made using uncertain input parameters expressed as probability boxes, intervals, and fuzzy numbers. The objective of this paper is to present the theory for, and a case study as an application of, the fuzzy-probabilistic approach, combining probability and possibility theory for simulating soil water balance and assessing associated uncertainty in the components of a simple water-balance equation. The application of this approach is demonstrated using calculations with the RAMAS Risk Calc code, to assess the propagation of uncertainty in calculating potential evapotranspiration, actual evapotranspiration, and infiltration—in a case study at the Hanford site, Washington, USA. Propagation of uncertainty into the results of water-balance calculations was evaluated by changing the types of models of uncertainty incorporated into various input parameters. The results of these fuzzy-probabilistic calculations are compared to the conventional Monte Carlo simulation approach and estimates from field observations at the Hanford site.