Quantification of predictive uncertainty in hydrological modelling by harnessing the wisdom of the crowd: Methodology development and investigation using toy models

We introduce an ensemble learning post-processing methodology for probabilistic hydrological modelling. This methodology generates numerous point predictions by applying a single hydrological model, yet with different parameter values drawn from the respective simulated posterior distribution. We call these predictions “sister predictions”. Each sister prediction extending in the period of interest is converted into a probabilistic prediction using information about the hydrological model's errors. This information is obtained from a preceding period for which observations are available, and is exploited using a flexible quantile regression model. All probabilistic predictions are finally combined via simple quantile averaging to produce the output probabilistic prediction. The idea is inspired by the ensemble learning methods originating from the machine learning literature. The proposed methodology offers larger robustness in performance than basic post-processing methodologies using a single hydrological point prediction. It is also empirically proven to “harness the wisdom of the crowd” in terms of average interval score, i.e., the obtained quantile predictions score no worse –usually better− than the average score of the combined individual predictions. This proof is provided within toy examples, which can be used for gaining insight on how the methodology works and under which conditions it can optimally convert point hydrological predictions to probabilistic ones. A large-scale hydrological application is made in a companion paper.