Probability Distributions for a Quantile Mapping Technique for a Bias Correction of Precipitation Data: A Case Study to Precipitation Data Under Climate Change

Abstract

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...

Performance Evaluation of Bias Correction Methods for Climate Change Monthly Precipitation Projections over Costa Rica

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