Uncertainty assessment of monthly water balance models based on Incremental Modified Fuzzy Extension Principle method

In this paper, a new method, namely Incremental Modified Fuzzy Extension Principle (IMFEP), is proposed for uncertainty assessment of conceptual water balance models. IMFEP is based on a new modification of fuzzy extension principle using fuzzy approximate. The most important feature of the IMFEP method lies in its realistic superposition of convex fuzzy membership functions of model inputs at different fuzzy α-cuts. To evaluate the IMFEP method, four other fuzzy-based approaches have been used to assess the uncertainties in simulating monthly water balance in basin scale and their results are compared with IMFEP. These approaches, one based on simple fuzzy mathematics, Vertex method, UNcertainty Estimation based on local Errors and Clustering (UNEEC) and Modified Fuzzy Extension Principle (MFEP) have been previously used for uncertainty estimation of water models. The nonlinear monthly water balance models calibrated for the two basins in Iran and France and their outputs with the five aforementioned methods have been compared. For both basins, IMFEP and MFEP methods have shown the best performance followed by UNEEC and Vertex methods (however, the differences in the underlying assumptions of the UNEEC method have to be taken into account). It can be concluded that the IMFEP method shows strong performance of uncertainty propagation in all evaluated fuzzy α-cuts.