Copula based post-processing for improving the NMME precipitation forecasts

Using reliable and timely precipitation forecasts on a monthly or seasonal scale could be useful in many water resources management planning, especially in countries facing drought challenges. Amongst many, the North American Multi-Model Ensemble (NMME) is one of the most well-known models. In this study, a Bayesian method based on Copula functions has been applied to improve NMME precipitation forecasts. This method is based on the existence of a correlation between the raw forecast and observational data. Two main factors affect the results of rainfall improvement based on the selected method. This research has presented innovative methods in these regards namely; 1) the approach of selecting the appropriate statistical distribution for variables and 2) the selection method of improved data according to the conditional probability distribution functions (CPDF). To evaluate the effectiveness of the statistical distribution, firstly the precipitation forecast improvement model has been developed based on the application of parametric (Exponential, Normal, Gamma, LogNormal and General Exreteme Value (GEV)) and non-parametric distributions (Standard Normal Kernel). Then the novel mixed distribution function based on GEV parametric distribution and Standard Normal Kernel (non-parametric distribution) has been suggested. As the second aim, a new method for selecting improved data based on the center of mass of estimated CPDF is presented. The evaluation of the proposed method for estimating the statistical distribution of data and improving the forecast precipitation by the NMME model has been performed in Sistan and Baluchestan province in Iran. In this regard, the data of 1982-2010 for the calibration period and the data of 2012-2016 for the validation of the results have been used. According to the results, the non-parametric distribution best fitted with the data in the time series and selecting the appropriate bandwidth increased the efficiency of this distribution. Besides, due to the weakness of non-parametric distributions in the boundaries, the use of GEV distribution with a high ability to estimate boundary conditions as semi-parametric distribution, led to improved performance of the proposed distribution. Finally, the selection of the improved data based on the center of the mass method has efficiently provided much improvement compared to the maximum likelihood method commonly used.