Improved error modelling for streamflow forecasting at hourly time steps by splitting hydrographs into rising and falling limbs

Abstract Following the development of Error Reduction and Representation In Stages (ERRIS) for daily streamflow forecasting, we extend ERRIS to streamflow forecasting at an hourly time step (ERRIS-h). ERRIS applies a staged error model to reduce errors in hydrological simulations and to quantify prediction uncertainty. ERRIS produces probabilistic predictions, and is capable of propagating errors through multiple lead times to generate ensemble traces. In this study, we identify the need to model the residual distribution differently for rising and falling limbs of hydrographs when applying ERRIS to hourly streamflow forecasting. To address this need, ERRIS-h uses different distribution parameters for the two limbs. We evaluate ERRIS-h on eight rivers in Australia. Hourly streamflow simulations are produced by forcing an initialized GR4H hourly rainfall-runoff model with observed rainfall. We apply ERRIS-h to the streamflow simulations to produce ensemble streamflow predictions with lead times up to 48 h. The ensemble streamflow predictions here can be viewed as forecasts when rainfall forecasts are perfect. In this way, we test the ability of ERRIS-h to update forecasts using the most up-to-date streamflow observations and to generate ensemble traces that reflect hydrological uncertainty. As expected, ERRIS-h is highly effective when applied to the zeroth lead time, dramatically reducing errors in the original GR4H simulations and reliably describing forecast uncertainty. We also show that ERRIS-h ensemble forecasts have smaller errors than deterministic simulations at all lead times and are reliable in ensemble spread even at 48 h lead times.