Simple Box-Cox probabilistic models for hourly streamflow predictions

Abstract. The increasing availability of hourly scale hydrological data offers valuable benefits for advancing our scientific understanding of catchment processes and improving operational forecasting capabilities. This work contributes to streamflow predictions at the hourly scale by investigating practical methods for uncertainty quantification using probabilistic predictions. We examine common approaches for representing the heteroscedasticity of streamflow errors using the Box-Cox (BC) transformation and common approaches for representing the persistence of streamflow errors using auto-regressive (AR) models. Case studies based on 7 catchments from Spain, Switzerland and USA that cover humid to semi-arid conditions are reported. The results favor Box-Cox transformations with power parameter values of 0–0.5. Notably the log transformation achieves the best statistical reliability of predictions, while its precision and volumetric bias are not statistically significantly worse than for the BC02 and BC05 transformations respectively. The results also tend to favor the AR2 and AR3 models over the AR1 model in representing persistence of errors, with the addition of moving average terms providing little additional benefit. The study findings are broadly consistent with earlier work with daily data, and provide practical guidance for hourly scale studies in predictive uncertainty quantification that is accessible to a wide range of hydrologists. We also report progress towards "seamless" aggregation from hourly to longer scales, which is a capability that is desirable in many practical operational contexts.