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Urban drainage modelling typically requires development of highly detailed simulators due to the nature of various underlying surface and drainage processes, which makes them computationally too expensive. Application of such simulators is still challenging in activities such as real-time control (RTC), uncertainty quantification analysis or model calibration in which numerous simulations are required. The focus of this paper is to present a rather simple hybrid surrogate modelling (or emulation) strategy to simplify and accelerate a detailed urban drainage simulator (UDS). The proposed surrogate modelling strategy includes: a) identification of the variables to be emulated; b) development of a simplified conceptual model in which every component contributing to the variables identified in step (a) is replaced by a function; c) definition of these functions, either based on knowledge about the mechanisms of the simulator, or based on the data produced by the simulator; and finally, d) validation of the results produced by the surrogate model in comparison with the original detailed simulator. Herein, a detailed InfoWorks ICM simulator was selected for surrogate modelling. The case study area was a small urban drainage network in Luxembourg. An emulator was developed to map the rainfall time series, as input, to a storage tank volume and combined sewer overflow (CSO) in the case study network. The results showed that the introduced strategy provides a reliable method to simplify the simulator and reduce its run time significantly. For the specific case study, the emulator was approximately 1300 times faster than the original detailed simulator. For quantification of the emulation error, an ensemble of 500 rainfall scenarios with 1 month duration was generated by application of a multivariate autoregressive model for conditional simulation of rainfall time series. The results produced by the emulator were compared to the ones produced by the simulator. Finally, as an indicator of the emulation error, distributions of Nash-Sutcliffe efficiency (NSE) between the emulator and simulator results for prediction of storage tank volume and CSO flow time series were presented. [ABSTRACT FROM AUTHOR]

In this research, we investigated the potential application of deep learning (DL) techniques in data-driven surrogate modelling of urban drainage simulators. Surrogate modelling or emulation is a strategy to accelerate the input-output mapping of computationally expensive simulators in order to facilitate applications such as real-time control, uncertainty analysis, calibration, sensitivity analysis and so forth. In this study, the key research question is to define (a/ the) suitable DL technique(s) to emulate urban drainage simulators to accelerate time series predictions with a low accuracy cost. Over the last few years, Deep Learning has applied to many problems, in many cases, DL outperformed the previous work. To the best of our knowledge, the application of DL as a data-driven surrogate modelling method, in which the inputs and outputs of interest are in multivariate time series format is one of the very few attempts been made in the urban drainage modelling domain. We applied both Recurrent Neural Networks (RNN) and its refined version Long-Short-Term-Memory (LSTM) for sequential data (time series) prediction. A small combined urban drainage network in Luxembourg developed in the InfoWorks ICM® simulator was selected as a case study. One-year-long input and output time series data with 10 minutes resolution were generated by the simulator to be used in training and validation of the deep networks. We focused on surrogate modelling for input-output mapping in a combined sewer overflow (CSO) location in the case study. The inputs were including time series of 1) the rainfall within the catchment; 2) daily dry weather flow and NH4 patterns; and 3) the outflow to downstream by a control pump. The output time series to predict were: 1) total wastewater volume at the CSO location; 2) the emitted CSO volume in case of occurrence; and 3) the NH4 concentration at the storage tank. For the quantification of the emulation error, Nash-Sutcliffe efficiency (NSE) and Volumetric Efficiency (VE) between the simulator and emulator (surrogate model) prediction time series were calculated as the loss function. The results showed that, DL training for wastewater quality prediction (NH4 time series in this case) is more challenging in comparison to wastewater quantity prediction, due to the nonlinearity of the sequential data. Comparing both DL methods, the trained RNN outperformed the LSTM network regarding prediction accuracy and loss values for the specific case study in this research. [ABSTRACT FROM AUTHOR]

In this study, applicability of a data-driven Gaussian Process Emulator (GPE) technique to develop a dynamic surrogate model for a computationally expensive urban drainage simulator is investigated. Considering rainfall time series as the main driving force is a challenge in this regard due to the high dimensionality problem. However, this problem can be less relevant when the focus is only on short-term simulations. The novelty of this research is the consideration of short-term rainfall time series as training parameters for the GPE. Rainfall intensity at each time step is counted as a separate parameter. A method to generate synthetic rainfall events for GPE training purposes is introduced as well. Here, an emulator is developed to predict the upcoming daily time series of the total wastewater volume in a storage tank and the corresponding Combined Sewer Overflow (CSO) volume. Nash-Sutcliffe Efficiency (NSE) and Volumetric Efficiency (VE) are calculated as emulation error indicators. For the case study herein, the emulator is able to speed up the simulations up to 380 times with a low accuracy cost for prediction of the total storage tank volume (medians of NSE = 0.96 and VE = 0.87). CSO events occurrence is detected in 82% of the cases, although with some considerable accuracy cost (medians of NSE = 0.76 and VE = 0.5). Applicability of the emulator for consecutive short-term simulations, based on real observed rainfall time series is also validated with a high accuracy (NSE = 0.97, VE = 0.89). [ABSTRACT FROM AUTHOR]

• Uncertainty based decision making for threshold-based regulatory criteria. • Utilizing detailed information on uncertainties in comparing decision alternatives. • Quantifying the impact of differing risk preferences on investment cost estimates. • Risk-preferences can result in considerable variation in preferred investment. Uncertainty in urban drainage modelling studies presents challenges to decision makers with limited investment resources attempting to achieve regulatory compliance for intermittent discharges from Combined Sewer Overflows. This paper presents the development of a new decision-making approach to address two key challenges encountered when attempting to manage sewer overflows, these are (i) the implications of different risk preferences of individuals for investment decisions; and (ii) how to utilize information on uncertainties in system performance predictions due to input or parameter uncertainty while comparing decision alternatives. The developed decision-making approach uses a multi-objective decision formulation to analyse the trade-off between investment and predicted system performance under uncertainty while accounting for risk preferences of the individual decision maker. The proposed uncertainty based decision-making approach is able to incorporate any threshold-based regulatory criteria for intermittent sewer overflows and is illustrated using a case study catchment in Luxembourg. The results from this case study highlight the significant impact of individuals' risk preferences on the level of investment recommended to comply with threshold-based regulatory criteria. It was demonstrated that differing levels of risk-averseness can result in a substantial increase in investment cost for solutions that are regulatory compliant. This paper demonstrates the need for water companies to rigorously define a corporate risk preference strategy to ensure consistent investment decisions across their operations; otherwise, individual preferences may cause significant over-investment to meet the same regulatory goals. [Display omitted] [ABSTRACT FROM AUTHOR]