Comparison of model predictive control methods that can account for uncertainties in forecasts of flood discharge and storm surge; case study Volkerak-Zoommeer, the Netherlands
Authors: Smoorenburg Maarten , Horváth Klaudia , Vreeken Tjerk , Sinnige Ruben , Nieuwenhuis Stefan , Alvarado-Montero Rodolfo , Piovesan Teresa , Gijsbers Peter 
Published: March 2020

&lt;p&gt;Decision making in operational water management practice is particularly challenging during extreme events. Dealing with extreme events would typically benefit from longer anticipation times, yet forecast uncertainty is often large for extreme events, and grows with lead time. Classical Model Predictive Control (MPC) only considers one deterministic forecast (no uncertainty), making control in anticipation of extreme events highly susceptible to forecast biases. MPC methods that can represent forecast uncertainty through ensemble techniques have been developed, but are rarely used in practice due to the mathematical complexity and computational burden.&lt;br&gt;We set out to test whether newly developed mathematically rigorous implementations of two ensemble based MPC methods could contest this status quo; one method that takes into account that new information comes available in the future and can be acted upon (i.e., the control tree approach of Raso et al., 2014), and one that does not. &amp;#160;We conducted a set of closed-loop experiments with synthetic forecasts of inflow and storm surge, and compared the control results of the ensemble based MPC methods to control with deterministic MPC. We did this for varying degrees of forecast uncertainty and bias. The experiments were conducted for the Volkerak-Zoommeer lake in the Netherlands, a simple example of a water system where water levels should be maintained within a narrow bandwidth by operating drainage works that only allow outflow to sea at low tide. An event with simultaneous high inflows and storm surge at sea can here only be mitigated by timely creation of retention capacity through lowering of the lake level.&lt;br&gt;The control of such an extreme event was mimicked with each MPC method by computing a single optimal control strategy every 12h (but looking 5 days ahead), and simulating the resulting lake level to obtain starting conditions for the next control time in 12h. All models and methods were implemented within the Python-based open source MPC software framework RTC-Tools 2, allowing fast and robust convex optimization of water systems. Since the control of the outlet requires boolean decision variables to account for the flow direction &amp;#8212;typically boosting computation times&amp;#8212;, advanced linearization techniques were needed to keep computation times short enough for operational practice.&lt;br&gt;The experiments showed that the ensemble based MPC methods can more robustly control the lake level than deterministic MPC, which with even mildly underestimating forecasts resulted in worse mitigation of the event. The ensemble method without control tree, known to be more conservative, could provide better control, but, for large forecasts uncertainties, did so by lowering the lake level too much. This illustrates that deciding upon which ensemble method to use requires choices about how conservative the controller should be.&lt;br&gt;The experiments also demonstrate that it is feasible to use ensemble forecasts in combination with ensemble based MPC methods in operational water management practice. This opens doors to including uncertainty information in the operational decision making process in objective ways. More details about the optimization and ensemble techniques are presented in session HS3.3 by Horv&amp;#225;th et al., 2020.&lt;/p&gt;