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Probabilistic runoff forecasts generated by stochastic greybox models can be notably useful for the improvement of the decision-making process in real-time control setups for urban drainage systems because the prediction risk relationships in these systems are often highly nonlinear. To date, research has primarily focused on one-step-ahead flow predictions for identifying, estimating, and evaluating greybox models. For control purposes, however, stochastic predictions are required for longer forecast horizons and for the prediction of runoff volumes, rather than flows. This article therefore analyzes the quality of multistep ahead forecasts of runoff volume and considers new estimation methods based on scoring rules for k-step-ahead predictions. The study shows that the score-based methods are, in principle, suitable for the estimation of model parameters and can therefore help the identification of models for cases with noisy in-sewer observations. For the prediction of the overflow risk, no improvement was demonstrated through the application of stochastic forecasts instead of point predictions, although this result is thought to be caused by the notably simplified setup used in this analysis. In conclusion, further research must focus on the development of model structures that allow the proper separation of dry and wet weather uncertainties and simulate runoff uncertainties depending on the rainfall input.

Stochastic rainfall-runoff forecasting: parameter estimation, multi-step prediction, and evaluation of overflow risk