Alternative configurations of quantile regression for estimating predictive uncertainty in water level forecasts for the upper Severn River: a comparison

摘要

The present study comprises an intercomparison of different configurations ofa statistical post-processor that is used to estimate predictive hydrologicaluncertainty. Itbuilds on earlier work by Weerts, Winsemius and Verkade(2011; hereafter referred to as WWV2011), who used thequantile regression technique to estimate predictive hydrologicaluncertainty using a deterministic water level forecastas a predictor. The various configurations are designed to addresstwo issues with the WWV2011 implementation: (i) quantile crossing,which causes non-strictly rising cumulative predictive distributions, and(ii) the use of linear quantile models to describe joint distributions thatmay not be strictly linear. Thus, four configurations were built: (i) a''classical" quantile regression, (ii) a configuration that implements anon-crossing quantile technique, (iii) a configuration where quantile modelsare built in normal space after application of the normal quantiletransformation (NQT) (similar to theimplementation used by WWV2011), and (iv) a configuration thatbuilds quantile model separately on separate domains of the predictor. Usingeach configuration, four reforecasting series of water levels at 14 stationsin the upper Severn River were established. The quality of these four serieswas intercompared using a set of graphical and numerical verificationmetrics. Intercomparison showed that reliability and sharpness vary acrossconfigurations, but in none of the configurations do these two forecastquality aspects improve simultaneously. Further analysis shows that skills interms of the Brier skill score, mean continuous ranked probability skillscore and relative operating characteristic score is very similar across thefour configurations.