Autocalibration of hydraulically simplified model for urban drainage systems

Detailed hydrodynamic models like MIKE+ provide accurate representations of the complex behavior of urban drainage systems. Surrogate models simplify this high-resolution representation to minimize the computational cost at the expense of reduced accuracy. As such, they are particularly useful when timely and repetitive simulations are needed.
Physics-based models of urban drainage systems typically include both hydrological (surface runoff) and hydraulic (network collection) components, with the computational cost mostly associated with the latter. The constructed surrogate model retains the hydrological representation of the original MIKE+ model but lumps the hydraulic network to a single collector downstream. This approach caters use cases where the full catchment description is needed.
We apply Muskingum routing to the catchment runoff to emulate the hydraulic routing between the catchment and the collector. The parameters of the routing function (delay and smoothing factor) are defined for each catchment as a function of the distance from the collector. We calibrate two global proxy parameters to optimize the performance of the surrogate: average velocity as a proxy of the individual delay, and smoothing range as a proxy of the individual smoothing factor.
The calibration of the proxy parameters is fully automated, given upper and lower bounds and the number of trials, and utilizes a Bayesian optimization algorithm. The objective of the autocalibration is minimizing the RMSE of the collector discharge for a synthetic rainfall event with 1-year return period.
To validate the calibrated surrogate, we simulated synthetic rainfalls with return periods both lower and higher than the calibration one and compared the modelled discharge with the results of the original model.
Our results for the 1-year rainfall show that the surrogate achieves a 25 times speedup in execution time compared to the original model, while introducing and 0.1% error in the accumulated volume of the event, a 3 minute error in the peak time, and a 5,8 % error in the peak discharge. A similar or better performance was obtained with lower return periods, but the performance of the surrogate quickly degrades with higher return periods.
Further research could focus on testing additional calibration objectives, e.g. timing and magnitude of the peak, as well as investigate methods to extend the validity of the surrogate beyond the calibration return period.