Uncertainty assessment of hydrological models with fuzzy extension principle: Evaluation of a new arithmetic operator

Abstract

The most important drawback of standard fuzzy arithmetic is unrealistic accumulation of input uncertainties which results in divergence of fuzzy outputs. Some of the currently available methods of simulating fuzzy systems provide the results which tend to naive large values after several time steps of the system simulation. In this paper, a new fuzzy arithmetic operator based on fuzzy extension principle has been proposed for simulation and assessment of uncertainty in hydrological systems. Implementing the concept of fuzzy approximate reasoning in the proposed approach in this study represents acceptable behavior in uncertainty propagation from the parameters and structures of the models to the outputs. To show the efficiency of the proposed fuzzy arithmetic operator in the context of hydrologic modeling, two nonlinear monthly water balance models have been examined and their outputs have been compared with the results obtained by standard fuzzy arithmetic and the Vertex method. One small humid basin in France and a middle size basin in a semiarid region in Iran have been the case studies of this research. In this paper, the lower and upper bounds and the most frequent values of the model parameters inferred from the sampling-simulation procedure have been used to define triangular fuzzy membership functions. Three statistical indicators have been used to evaluate efficiency of the methods based on the bracket observations and coverage of the uncertainty bounds. The estimated values of these indicators have shown that both Vertex and the proposed methods outperform standard fuzzy arithmetic. Also, the proposed method has provided better or roughly equal efficiencies compared with Vertex method over both basins. Key Points Proposing a new fuzzy arithmetic operator Application of fuzzy extension principle with suitable entropy Efficient fuzzy uncertainty assessment versus the presented methods before © 2014. American Geophysical Union. All Rights Reserved.