The quantile mapping method is a bias correction method that leads to a good performance in terms of precipitation. Selecting an appropriate probability distribution model is essential for the successful implementation of quantile mapping. Probability distribution models with two shape parameters have proved that they are fit for precipitation modeling because of their flexibility. Hence, the application of a two-shape parameter distribution will improve the performance of the quantile mapping method in the bias correction of precipitation data. In this study, the applicability and appropriateness of two-shape parameter distribution models are examined in quantile mapping, for a bias correction of simulated precipitation data from a climate model under a climate change scenario. Additionally, the impacts of distribution selection on the frequency analysis of future extreme precipitation from climate are investigated. Generalized Lindley, Burr XII, and Kappa distributions are used, and their fits and appropriateness are compared to those of conventional distributions in a case study. Applications of two-shape parameter distributions do lead to better performances in reproducing the statistical characteristics of observed precipitation, compared to those of conventional distributions. The Kappa distribution is considered the best distribution model, as it can reproduce reliable spatial dependences of the quantile corresponding to a 100-year return period, unlike the gamma distribution.Eden et al. [6] attempted to identify any sources of climate model error, and reported that precipitation data corrected by a statistical correction method can be a good predictor for the observed data set at a global scale. Teng et al. [7] assessed the performances of several bias correction methods for precipitation data, and evaluated their impact on a runoff model. They reported that the quantile mapping (QM) and two-state gamma distribution mapping methods provide good performance. The QM method shows better performance than a simpler bias correction for the mean and variation in the precipitation data [8][9][10]. Themeßl et al. [11] reported that QM leads to the best performance for precipitation, particularly to large amounts of quantiles. While the QM method provides a good performance for the bias correction of stationary data, it leads to less reliable results for nonstationary data, such as simulation data under a climate change scenario. To address this drawback, Cannon et al. [12] suggested the quantile delta mapping (QDM) method which explicitly preserves relative changes in all of the quantiles of the distribution. They claimed that the QDM method is superior to the traditional QM method and the detrended quantile mapping (DQM) method, which considers trends in the mean.The QM method assumes that the distribution of simulated or estimated data preserves the distribution of any observed data. In QM, simulated data corresponding to a given probability is replaced by an observed quantile corresponding to the same probabili...

An important problem in frequency analysis is the selection of an appropriate probability distribution for a given sample data. This selection is generally based on goodness-of-fit tests. The goodness-of-fit method is an effective means of examining how well a sample data agrees with an assumed probability distribution as its population. However, the goodness of fit test based on empirical distribution functions gives equal weight to differences between empirical and theoretical distribution functions corresponding to all observations. To overcome this drawback, the modified Anderson-Darling test was suggested by Ahmad et al. (1988b). In this study, the critical values of the modified Anderson-Darling test statistics are revised using simulation experiments with extensions of the shape parameters for the GEV and GLO distributions, and a power study is performed to test the performance of the modified Anderson-Darling test. The results of the power study show that the modified Anderson-Darling test is more powerful than traditional tests such as the v 2 , Kolmogorov-Smirnov, and Cramer von Mises tests. In addition, to compare the results of these goodness-of-fit tests, the modified Anderson-Darling test is applied to the annual maximum rainfall data in Korea.

Abstract:In this study, NSGA-II is applied to multireservoir system optimization. Here, a four-dimensional multireservoir system in the Han River basin was formulated. Two objective functions and three cases having different constraint conditions are used to achieve nondominated solutions. NSGA-II effectively determines these solutions without being subject to any user-defined penalty function, as it is applied to a multireservoir system optimization having a number of constraints (here, 246), multi-objectives, and infeasible initial solutions. Most research by multi-objective genetic algorithms only reveals a trade-off in the objective function space present, and thus the decision maker must reanalyse this trade-off relationship in order to obtain information on the decision variable. Contrastingly, this study suggests a method for identifying the best solutions among the nondominated ones by analysing the relation between objective function values and decision variables. Our conclusions demonstrated that NSGA-II performs well in multireservoir system optimization having multi-objectives.

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