Probabilistic forecasting of rainfall response in a Danish stormwater tunnel

Abstract

• Development of a non-linear SDE-model of rainfall response in a stormwater tunnel. • A modified maximum-likelihood estimation of the non-linear SDE-model. • Probabilistic l -step forecasting with the non-linear SDE-model. • Evaluation of the uncertainty in rainfall response forecasts. Sustainable urban drainage is an economically expensive necessity, partially due to the operation of water pumps. Reliable forecasting of stormwater response following a rainfall event has the potential to reduce those expenses, because it can be used in model predictive control schemes that optimize the energy consumption of pumps significantly better than the commonly applied real-time control systems. Urban drainage systems are traditionally designed around highly complex, deterministic models where an assessment of the uncertainty of the stormwater forecast is either absent or relies on computation–heavy simulations. With offset in a Danish stormwater tunnel, we propose a much faster, but reliable, non-linear continuous-discrete-time state-space model based on stochastic differential equations which can generate probabilistic forecasts that contain complete information about the distribution of uncertainty. We explain step-by-step how the model structure is built from simple physical assumptions, then how the parameters are estimated from maximum likelihood principles and finally we demonstrate the forecasting capabilities of the model. We believe this model would be well-suited for a subsequent model predictive control scheme.