Technical note: Combining quantile forecasts and predictive distributions of streamflows

Abstract

Abstract. The enhanced availability of many different hydro-meteorological modelling and forecasting systems raises the issue of how to optimally combine this great deal of information. Especially the usage of deterministic and probabilistic forecasts with sometimes widely divergent predicted future streamflow values makes it even more complicated for decision makers to sift out the relevant information. In this study multiple streamflow forecast information will be aggregated based on several different predictive distributions, and quantile forecasts. For this combination the Bayesian model averaging (BMA) approach, the nonhomogeneous Gaussian regression (NGR), also known as the ensemble model output statistic (EMOS) techniques, and a novel method called Beta-transformed linear pooling (BLP) will be applied. By the help of the quantile score (QS) and the continuous ranked probability score (CRPS), the combination results for the Sihl River in Switzerland with about 5 years of forecast data will be compared and the differences between the raw and optimally combined forecasts will be highlighted. The results demonstrate the importance of applying proper forecast combination methods for decision makers in the field of flood and water resource management.

A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures

“…Furthermore, an important note is the meaning of the word "probabilities" in the quantitative opinion combination literature. Whilst traditionally, "probabilities" means mass or density functions for the discrete case and continuous case, respectively Clemen (1989), in recent years, there has been some evidence that combining quantiles, first suggested by Vincent (1912), might be at least as good as combining probability densities (see Lichtendahl et al (2013), Busetti (2017), Bansal and Palley (2017), Hora et al (2013), Bogner et al (2017, and Jose et al (2013)), despite some criticism from Colson and Cooke (2017). Quantiles combination was also found to be preferable when individual forecasts are biased; see Bamber et al (2016) and Lichtendahl et al (2013).…”

Machine Learning Techniques for Predicting the Energy Consumption/Production and Its Uncertainties Driven by Meteorological Observations and Forecasts

“…In order to evaluate the monthly forecasts, each of the 51 ensemble members has been taken as input to the energy consumption and production model. For verifying the accuracy, the mean of these 51 forecasts has been calculated and verified with the Nash-Sutcliffe efficiency coefficient, whereas, for the CRPS, the averaged quantiles are used (see [73]). The resulting total predictive uncertainty comprises the uncertainty of the ML model and the NWP based forecast uncertainty, which increases with the lead-time.…”

Sequential Aggregation of Probabilistic Forecasts—Application to Wind Speed Ensemble Forecasts

“…Nowadays, several ensemble forecast systems are available routinely (Bougeault et al., 2010; Descamps et al., 2014). Combining, or ‘aggregating’, several forecasts may improve the predictive performance compared to the any post‐processed ensemble (Allard et al., 2012; Baran & Lerch, 2016; Baudin, 2015; Bogner et al., 2017; Gneiting et al., 2013; Möller & Groß, 2016). The theory of prediction with expert advice (Cesa‐Bianchi et al., 2006; Stoltz, 2010) shows how to efficiently aggregate in real‐time several forecasts based on their respective past performances.…”