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

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Abstract
The present study comprises an intercomparison of different configurations of a statistical post-processor that is used to estimate predictive hydrological uncertainty. It builds on earlier work by Weerts, Winsemius and Verkade (2011; hereafter referred to as WWV2011), who used the quantile regression technique to estimate predictive hydrological uncertainty using a deterministic water level forecast as a predictor. The various configurations are designed to address two 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 that may not be strictly linear. Thus, four configurations were built: (i) a ''classical" quantile regression, (ii) a configuration that implements a non-crossing quantile technique, (iii) a configuration where quantile models are built in normal space after application of the normal quantile transformation (NQT) (similar to the implementation used by WWV2011), and (iv) a configuration that builds quantile model separately on separate domains of the predictor. Using each configuration, four reforecasting series of water levels at 14 stations in the upper Severn River were established. The quality of these four series was intercompared using a set of graphical and numerical verification metrics. Intercomparison showed that reliability and sharpness vary across configurations, but in none of the configurations do these two forecast quality aspects improve simultaneously. Further analysis shows that skills in terms of the Brier skill score, mean continuous ranked probability skill score and relative operating characteristic score is very similar across the four configurations.
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