Application of Multi Criteria Analysis to Select the Best Fit Flood Frequency Distribution (Case Study of Mahabad River)

To select a statistical distribution to describe a set of data, there are several criteria that can be used. Rather than the selection of a criterion according to traditional methods, the combination of two or more criteria may be used to achieve the best choice. But when more than two criteria are applied to find out the best model, selection becomes more difficult. In these cases, the use of multi-criteria decision making (MCDM) is essential. This study compares eleven commonly used distributions in hydrology based on five selection criteria. These selection criteria are: The Kolmogorov-Smirnov test, the errors in skewness and kurtosis, the errors in cumulative distribution function, the errors in probability distribution function and the root mean square error. Three MCDM methods, namely, simple additive weighting, weighted product method and fuzzy majority approach, are employed. In the present study, we examine the sensitivity of the results of MCDM by changing the weights and number of criteria. The methods are applied to a case study of Mahabad River, a major river flowing into Lake Urmia in northwestern of Iran. Results of this study have shown that three-parameter Weibull, three-parameter Weibull and generalized extreme value distributions have the best fit for peak flow, volume and duration of Mahabad River flood data, respectively. The result of this study can be used to improve the flood frequency analysis.