We propose and demonstrate a new approach for fast and accurate surrogate modelling of urban drainage system hydraulics based on physics-guided machine learning. The surrogates are trained against a limited set of simulation results from a hydrodynamic (HiFi) model. Our approach reduces simulation times by one to two orders of magnitude compared to a HiFi model. It is thus slower than e.g. conceptual hydrological models, but it enables simulations of water levels, flows and surcharges in all nodes and links of a drainage network and thus largely preserves the level of detail provided by HiFi models. Comparing time series simulated by the surrogate and the HiFi model, R² values in the order of 0.9 are achieved. Surrogate training times are currently in the order of one hour. However, they can likely be reduced through the application of transfer learning and graph neural networks. Our surrogate approach will be useful for interactive workshops in initial design phases of urban drainage systems, as well as for real time applications. In addition, our model formulation is generic and future research should investigate its application for simulating other water systems.

A case study for integrated real-time control (RTC) of an urban drainage system in the city of Wilhelmshaven (Germany) is explained. The fuzzy based RTC strategy combines control of the sewer system and inflow to the waste water treatment plant. The main objective in controlling the sewer system is to reduce the number of overflows and the volume at a combined sewer overflow (CSO), located close to a bathing beach. Based on online measurements, the operation mode of two pumping stations is modified. This approach allows the safe activation of free storage volume in the sewer system without constructive measures. To avoid critical situations in the treatment process, the inflow to the treatment plant is automatically reduced to a defined value if high inflows to the treatment plant occur in combination with unfavorable conditions on the secondary clarifiers during rainfall events. The integrated RTC system has been operational for approximately one year.

Nature-based solutions may actively reduce hydro-meteorological risks in urban areas as a part of climate change adaptation. However, the main reason for the increasing uptake of this type of solution is their many benefits for the local inhabitants, including recreational value. Previous studies on recreational value focus on studies of existing nature sites that are often much larger than what is considered as new NBS for flood adaptation studies in urban areas. We thus prioritized studies with smaller areas and nature types suitable for urban flood adaptation and divided them into four common nature types for urban flood adaptation: sustainable urban drainage systems, city parks, nature areas and rivers. We identified 23 primary valuation studies, including both stated and revealed preference studies, and derived two value transfer functions based on meta-regression analysis on existing areas. We investigated trends between values and variables and found that for the purpose of planning of new NBS the size of NBS and population density were determining factors of recreational value. For existing NBS the maximum travelling distance may be included as well. We find that existing state-of-the-art studies overestimate the recreational with more than a factor of 4 for NBS sizes below 5 ha. Our results are valid in a European context for nature-based solutions below 250 ha and can be applied across different NBS types and sizes.