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1. Introduction
Because of their ability to depict forecast uncertainties and improve forecast accuracy, ensemble weather and climate forecasts have seen wide applications in hydrologic forecasting, water resources management, and emergency preparedness (Georgakakos et al. 1998; Ajami et al. 2008). Despite substantial improvements made in model physics and data assimilation in recent decades, raw ensemble forecasts from dynamical models remain subject to large systematic and random errors (Hamill and Whitaker 2006). Moreover, downscaling is often required for these forecasts in downstream applications such as hydrologic forecasting. To address these shortcomings, various techniques have been developed and evaluated over the years to postprocess ensemble forecasts (Raftery et al. 2005; Hamill and Whitaker 2006; Schaake et al. 2007; Wu et al. 2011; Cui et al. 2012; Scheuerer and Hamill 2015; Yang et al. 2017).
Natural weather systems possess certain spatiotemporal variability and correlations. Preserving these spatiotemporal properties is necessary for applications in ensemble streamflow predictions and particularly critical for flood forecasting, since the structure of a storm and the direction in which the storm passes over a watershed could determine the timing and magnitude of flood peaks. Characterizing spatiotemporal properties involves multivariate statistical modeling. One approach to ensemble postprocessing in a multivariate setting is by extending conventional parametric methods for univariate ensemble postprocessing. These extensions, however, require the estimation of large numbers of parameters (Gel et al. 2004; Berrocal et al. 2007; Berrocal and Raftery 2008; Pinson 2012; Schuhen et al. 2012), which can severely limit their applicability due to computational constraints. Another approach, instead of using a full parametric modeling strategy, employs an empirical copula framework for postprocessing. This approach has gained popularity in recent years and attracted significant research efforts (Clark et al. 2004; Schaake et al. 2007; Voisin et al. 2010; Robertson et al. 2013; Schefzik et al. 2013; Wilks 2015; Schefzik 2016; Scheuerer et al. 2017). It effectively addresses the dimensionality problem arising from extending conventional parametric methods. In this approach, a rank-based shuffling technique plays a key role. The technique relies on the construction of rank structures from a certain source of forecasts or observations. The precise meaning of a rank structure will be given in section 2b. The original concept of the technique, known as the Schaake Shuffle, is published in...