Towards achieving reliable probabilistic hydrological predictions at the hourly scale

Floods are among Earth's most widespread, frequent, and destructive natural hazards. In highly responsivecatchments, daily streamflow predictions will underestimate flood hazards. For example, peak flows occurringon sub-daily timescales caused hundreds of fatalities and billions of Euros in damages in the devastating floodsin Germany in 2021 and Spain in 2024. Particularly in small and mesoscale catchments: 1) peak flows maylast only a few hours, so forecasts of daily flows can greatly underestimate flood peaks ; 2) A landscape'sresponsiveness to precipitation depends critically on how wet it is; thus, it is essential to accurately model thewetting and drying of the catchment, and hourly streamflow is needed to capture and understand thehydrological processes in the rising limb of the hydrograph; and 3) the dominant processes affecting shorttermpredictions are not necessarily the same as those affecting streamflow at longer time scales. For example,over longer time scales, predictions become more a question of mass balance, rather than dynamics and routing,while the opposite is true for short-term predictions.Thus, reliably assessing flood hazards requires understanding hydrologic responses at hourly time scales. Butparadoxically, hourly predictions have received relatively less focus. In this work we use a conceptualhydrological model to obtain deterministic hourly predictions and estimate its uncertainty using a residual errormodel. Case study catchments include hydrologically diverse catchments in Europe and the USA. We considerbias, heteroscedasticity and autocorrelation by employing the Box-Cox transformation, autoregressive (AR)and moving average models (ARMA) models. The log transformation was in general the most recommendedoption, in combination with an AR3 model.This work advances streamflow prediction by developing statistically rigorous methods for postprocessing theresiduals of conceptual models at the hourly time scale.