Copula based post-processing for improving the NMME precipitation forecasts

Abstract

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.

Statistical refinement of the North American Multi-Model Ensemble precipitation forecasts over Karoon basin, Iran

“…Figure 2 presents the proposed three-step postprocessing approach based on the Copula-Bayesian method. As mentioned in the studies by Khajehei et al (2018) and Yazdandoost et al (2021), the proposed approach is based on the presence of a general association between the historical raw forecast and observational data. In the first step, the data are prepared to obtain fitted distributions of forecast and observational time series.…”

“…Then, the obtained time series containing monthly precipitation data (with the annual time steps for each 1°cell) are used to prepare a marginal distribution. Later, the marginal distribution functions are separately estimated for historical observations and the model in the analyses period based on the normal kernel density distribution, which has been shown to be efficient in previous studies (Yazdandoost et al 2020;Yazdandoost et al 2021). The marginal distribution and kernel Copula function are set based on the historical period from 1982 to 2010.…”

“…The process mentioned earlier for creating CPDF (as CPDF f ) will be carried out for each specific raw forecast data. We encourage readers to further explore the topic by referring to Sklar (1959) and Yazdandoost et al (2021).…”

Waves and Storm Surges of Tropical Cyclones Over the Arabian Sea: Future Projections and Uncertainty Analysis

“…Warder et al (2021) also computed the rise of uncertainty level by bathymetry and bottom friction, which is negligible compared to the meteorological input. On the other hand, there are other studies (e.g., Yazdandoost et al, 2021) that attempted to improve forecasting, using the statistical approach, disregarding the uncertainty sources.…”

Probabilistic drought forecasting using copula and satellite rainfall based PERSIANN‐CDR and MSWEP datasets

“…Recently, multivariate copula functions have been widely used in hydrology and drought assessment (Shiau, 2006;Shiau et al 2007;Shiau and Modarres, 2009;Wong et al 2010;Reddy and Ganguli, 2011;Kwak et al, 2012;Khedun et al, 2014;Sadri and Burn, 2014;Madadgar and Moradkhani, 2014;Borgomeo et al, 2015;Hamdi et al, 2016;She et al, 2016). Furthermore, copula-based forecasting is recently applied using gridded datasets, such as global simulation model (GSM; Ballarin et al, 2021), and North American Multi-Model Ensemble (NMME; Yazdandoost et al, 2021), newly introduced for drought and rainfall forecasting, respectively. Although the copulas are widely used for multivariate drought analysis using in situ datasets, copula functions' potential for drought forecasting is not adequately investigated, especially using SREs.…”