When evaluating the reliability of an ensemble prediction system, it is common to compare the root-mean-square error of the ensemble mean to the average ensemble spread. While this is indeed good practice, two different and inconsistent methodologies have been used over the last few years in the meteorology and hydrology literature to compute the average ensemble spread. In some cases, the square root of average ensemble variance is used, and in other cases, the average of ensemble standard deviation is computed instead. The second option is incorrect. To avoid the perpetuation of practices that are not supported by probability theory, the correct equation for computing the average ensemble spread is obtained and the impact of using the wrong equation is illustrated.

This paper traces two decades of neural network rainfall-runoff and streamflow modelling, collectively termed ‘river forecasting’. The field is now firmly established and the research community involved has much to offer hydrological science. First, however, it will be necessary to converge on more objective and consistent protocols for: selecting and treating inputs prior to model development; extracting physically meaningful insights from each proposed solution; and improving transparency in the benchmarking and reporting of experimental case studies. It is also clear that neural network river forecasting solutions will have limited appeal for operational purposes until confidence intervals can be attached to forecasts. Modular design, ensemble experiments, and hybridization with conventional hydrological models are yielding new tools for decision-making. The full potential for modelling complex hydrological systems, and for characterizing uncertainty, has yet to be realized. Further gains could also emerge from the provision of an agreed set of benchmark data sets and associated development of superior diagnostics for more rigorous intermodel evaluation. To achieve these goals will require a paradigm shift, such that the mass of individual isolated activities, focused on incremental technical refinement, is replaced by a more coordinated, problem-solving international research body.

This paper investigates the temporal transposability of hydrological models under contrasted climate conditions and evaluates the added value of using an ensemble of model structures for flow simulation. This is achieved by applying the Differential Split Sample Test procedure to twenty lumped conceptual models on a catchment in the Province of Québec (Canada) and another one in the State of Bavaria (Germany). First, a calibration/validation procedure was applied on four historical non-continuous periods with contrasted climate conditions. Then, model efficiency was quantified individually (for each model) and collectively (for the model ensemble). The individual analysis evaluated model performance and robustness. The ensemble investigation, based on the average of simulated discharges, focused on the twenty-member ensemble and all possible model subsets. Results showed that using a single model may provide hazardous results when the model is to be applied in contrasted conditions. Overall, some models turned out as a good compromise in terms of performance and robustness, but generally not as much as the twenty-model ensemble. Model subsets offered yet improved performance over the twenty-model ensemble, but at the expanse of spatial transposability (i.e. need of site-specific analysis).