Postprocessing Ensemble Weather Forecasts for Introducing Multisite and Multivariable Correlations Using Rank Shuffle and Copula Theory

Statistical methods have been widely used to postprocess ensemble weather forecasts for hydrological predictions. However, most of the statistical postprocessing methods apply to a single weather variable at a single location, thus neglecting the intersite and intervariable dependence structures of forecast variables. This study synthesized a multisite and multivariate (MSMV) postprocessing framework that extends the univariate method to the MSMV version by directly rearranging the postprocessed ensemble members (post-reordering strategy) or by rearranging the latent variables used in the univariate method (pre-reordering strategy). Based on the univariate generator-based postprocessing (GPP) method, the two reordering strategies and three dependence reconstruction methods [rank shuffle (RS), Gaussian copula (GC), and empirical copula (EC)] totaling six MSMV methods (RS-Pre, GC-Pre, EC-Pre, RS-Post, GC-Post, and EC-Post) were evaluated in postprocessing ensemble precipitation and temperature forecasts for the Xiangjiang basin in China using the 11-member ensemble forecasts from the Global Ensemble Forecasting System (GEFS). The results showed that raw GEFS forecasts tend to be biased for both the forecast ensembles and the intersite and intervariable dependencies. The univariate method can improve the univariate performance of ensemble mean and spread but misrepresent the intersite and intervariable dependence among the forecast variables. The MSMV framework can well utilize the advantages of the univariate method and also reconstruct the intersite and intervariable dependencies. Among the six methods, RS-Pre, RS-Post, GC-Post, and EC-Post perform better than the others with respect to reproducing the univariate statistics and multivariable dependences. The post-reordering strategy is recommended to combine the univariate method (i.e., GPP) and reconstruction methods.