Population growth and urban expansion, coupled with climate change impacts, are likely to result in an increased pluvial flood risk in urban areas as well as higher discharges through combined sewer overflows (CSOs) (Nilsen et al., 2011). This puts pressure on decision-makers, who will increasingly need to be well-informed in a timely manner to plan and design interventions for alleviating flood risk and CSOs. High-fidelity hydraulic modelling tools, such as InfoWorks ICM (Innovyze, 2021), are widely used to inform wastewater city scale intervention decisions. While these tools are accurate, they are computationally expensive to run because they represent the physical drainage network at high spatial and temporal resolutions (Salvadore et al., 2015). Thus, they are limited in ability to provide modelling support to decision-makers who are trying to simulate drainage network issues over large scales, particularly given the uncertainties associated with future conditions.

One such application in the UK is through introducing a framework for Drainage and Wastewater Management Plans (DWMP). This will require water companies to target investments more effectively and plan interventions in a unified approach for long-term planning (Water UK, 2019). These plans and investments must be supported by hydraulic model simulations able to assess the range of intervention scenarios typically done using design storm concept (Water UK, 2019). However, if hydraulic models are to properly capture the behaviour of wastewater interventions, then they must also use continuous rainfall to drive simulations, as opposed to the traditional design storm approach (Adams and Howard, 1986; Muhandes et al., 2021). These requirements have introduced a severe computational burden on modellers, who cannot accommodate both the uncertainty around future conditions and the requirement for use of continuous storms with a traditional modelling approach. Instead, an approach providing hydraulically based simulations that is accurate enough to provide estimates around flooding and CSOs that can be used in long-term planning, but without the computational burden associated with high-fidelity models, is essential in navigating these future requirements placed on water companies.

In the DWMP context, CSOs have been identified as one of the key indicators used in the risk-based catchment screening in order to establish the vulnerability of the catchment and determine whether it requires more detailed investigations (Water UK, 2019). As CSOs pose a serious risk to the environment and to human health, there is an increased interest to investigate the frequency and the quantity of CSOs on a wastewater catchment/city scale. Designing interventions that reduce CSOs requires simulation under scenarios that characterise potential futures (capturing factors such as climate change, population growth and urban creep) and optimisation or evaluation of plausible options (Claudine and Alain, 2015), both of which require significant computational efficiency.

The state-of-the-art in research has demonstrated that a reduced complexity approach to CSO modelling can be used to create accurate simulations in a fraction of the time (Nielsen et al., 2007; Morales et al., 2017). This enables modelling of CSOs in contexts that require rapid simulations, for example, Lund et al. (2020) use surrogate modelling to control CSO behaviour with optimisation of Model Predictive Control (MPC). These studies all employ some form of spatial aggregation to achieve the reduction in complexity. Even though they are significant simplifications, spatially aggregated modelling approaches can be acceptable by stakeholders when looking at high-level catchment interventions (El Hattab et al., 2020). To reduce the volume and frequency of CSOs, Sustainable Drainage Systems (SuDS) are now recognised as one of the most effective catchment interventions, demonstrated in hydraulic modelling (Riechel et al., 2020) and have become the standard method for surface water management in new developments in the UK (GLA, 2015). However, industry assessments of city-scale SuDS interventions require large scale catchment models to be simulated against design storms using a range of industry recognised storm durations (Singh et al., 2021; Webber et al., 2021). We identify a gap in assessing CSOs in an integrated and fast spatially aggregated model when assessing the benefits of implementing SuDS on CSOs.

A further benefit to reduced complexity modelling is the ability to extend model boundaries beyond drainage systems. Spatially aggregated hydraulic modelling has been used to represent the whole water cycle to inform decisions related to river water quality (Dobson and Mijic, 2020), real-time flood forecasting (Li and Willems, 2020) and supply-sewerage runoff treatment (Coombes et al., 2016). These integrated models were developed with the aim to reveal a wide range of alternative catchment management options without the need to run computationally expensive simulations. Aiming to meet the needs for fast and probabilistic flood modelling, Li and Willems (2020) developed a hybrid modelling approach that integrates spatially aggregated hydrological models that are calibrated to high-fidelity models to predict the occurrence of flooding. They found that the hybrid model can achieve up to 86% accuracy for flood warnings with 96% computational saving compared to the traditional high-fidelity approach. Meanwhile, Dobson and Mijic (2020) presented an integrated model, called CityWat, that represents water supply and wastewater infrastructure to simulate downstream river water quality. The CityWat model (Dobson and Mijic, 2020; Dobson et al., 2021) is an open-source lumped water management model of London water cycle processes. Each process is represented within CityWat at a city scale and the lumping helps with creating efficiency, enabling of sharing parameter information openly without national security concerns and providing the industry with easy-to-understand water management model. The CityWat model has proved to have capability to accurately simulate urban water system at a city scale, however, the model cannot be applied to assess the flood volumes or CSOs as it does not apply a limit on the discharge rate to rivers. Surcharge state, CSOs and flooding only occur when the drainage system is subject to flows/runoff higher than the discharge limit. The importance of the new lumped modelled approach manifests in enabling the industry to assess, develop and run long-term simulations for a wide range of applications such as multi-parameter optimisation, catchment interventions, climate change adaptation and multi-parameter sensitivity analysis with less computational efforts and higher flexibility introduced in the system design. Developing lumped models involves using the physical and spatially distributed hydraulic model parameters which helps enhance the lumped model accuracy.

In this study, we create a novel representation of combined sewer systems that is compatible with an integrated and spatially aggregated urban water model, CityWat (Dobson and Mijic, 2020). This integrated approach enables the representation of the combined sewer discharges into rivers, as well as the foul water overflows at the treatment works. We include a more detailed interaction between surface water, foul water and water supply model components which will improve the assessment of SuDS interventions. We assess and validate the new model (CityWatStorm hereafter) with a focus on flood volume and CSOs by comparing them to InfoWorks ICM simulations driven by continuous rainfall using Norwich city in the UK as a case study. Finally, we assess and compare the effectiveness of modelling SuDS interventions using simulation outputs from CityWatStorm compared to outputs from high-fidelity modelling simulations.

To test the hydraulic performance of the proposed CityWatStorm model and suitability of spatial aggregation, we use the Norwich combined sewer catchment. The Norwich catchment is illustrated in a simplified manner in Figure 3. The sewers in the catchment drain 68.5 km² of foul sub-catchments and 29.9 km² of surface water sub-catchments with 1,300 km of pipes, before discharging into rivers Wensum and Yare at multiple outfall locations. The Norwich case study is ideal for this experiment because it contains a combined sewer network, and it is large enough that running the model using the existing high-fidelity modelling tools for long rainfall timeseries (e.g., years, decades or centuries) is cost prohibitive which makes the case for the computational effort saving. The Norwich catchment and its InfoWorks ICM modelled representation, have been presented in a previous study (Muhandes et al., 2021).

As discussed in the previous sections, the CityWatStorm model captures the interaction between water supply, surface water and foul water. River flows from both Wensum and the Yare are simulated with a maximum abstraction rate (a_cap) introduced to route water through a water supply network reaching the households (N_household) in Norwich which then ends up in the foul sewers as domestic foul flows. Additionally, some sub-catchments have roof runoff that enters the foul network (a roof area shown in the InfoWorks ICM model to be 6.13 km²), in the CityStorm model this runoff also contributes to the simulated foul flow.

As for the surface water component, historical precipitation is modelled over Norwich impermeable area (A_total) generating surface water runoff which is routed through a surface water network and then discharged to rivers according to an allowable discharge limit (Q_limit). Once the flow through the network is throttled because of the allowable discharge limit, a storm-foul water exchange will happen which will lead to flooding once the exchange rate exceeds the foul-stormwater exchange capacity (Cap_exch).

The hydraulic interactions between water supply infrastructure, drainage infrastructure and river flows within CityWatStorm are depicted in Figure 3.

The parameters shown in Table 1 are the ones that dominate the hydraulic behaviour of the CityWatStorm model, while the remaining parameters have been either obtained or scaled down from the original CityWat model (Dobson and Mijic, 2020). The Norwich combined sewer network data from the InfoWorks ICM model was used to inform the choice of most of the parameters. This information, however, could be defined even if only the asset data about the network, rather than the simulation model, were available. Justification for key parameters values selection is given in Table 1.

The first aim of this study was to develop and evaluate a spatially aggregated modelling approach to rapidly simulate large urban catchment systems against continuous rainfall timeseries, which will reduce the computational efforts and enable multiple applications such as the optimisation of interventions against various climate projection scenarios. In Figures 4–6 we show that CityWatStorm has been able to capture the total flood volume, total CSO volume and total discharge to rivers volume. The lowest accuracy achieved was 80.6% which is comparable to the 86% accuracy achieved in the investigation conducted by Li and Willems (2020), however the speed improvement of 99.99% is far greater than the improvement of 96% reported in their investigation. A 2-month simulation period in InfoWorks ICM model took 26.7 h to run, whereas the CityWatStorm took 6.5 s to run the same catchment with the Intel(R) Core(TM) i7-8850H CPU @ 2.60 GHz computer. This means that for a 1-year continuous simulation, the CityWatStorm is able to achieve computational effort saving for up to 400 h. Furthermore, the CityWatStorm method does not require calibration against slow high-fidelity models, unlike the model presented in Li and Willems (2020). This suggests that the spatially aggregated approach can be suitable to assess long term system performance under climate projections. It may also be used to quickly assess catchments where no high-fidelity model is available to provide high-level information about the usefulness of SuDS and other wastewater system interventions.

The coefficient of determination values indicate a high variation between CityWatStorm and InfoWorks ICM timeseries, which is mainly due to CityWatStorm rapid response to surface runoff. We expect a further improvement when the CityWatStorm is upgraded to a semi-distributed representation, as is performed in Dobson et al. (2021). However, the results can still provide excellent value-for-effort when running large catchment models especially in the context of designing long-term planning interventions, optimisation against various climate projection scenarios or undertaking uncertainty analysis as the frequency of CSOs. Figures 4–6 show that CityWatStorm captures the main physical behaviour of the system, particularly in capturing the total flood, discharge and CSO volumes. The results from the 2-month simulation are influenced by the initial conditions and we expect a better agreement between CityWatStorm and InfoWorks ICM when running a longer timeseries rainfall (e.g., decades or centuries) with higher magnitude as once the volume available within the network is fully utilised, the time of concentration becomes irrelevant, and the spatially distributed drainage system will have a closer hydraulic behaviour to the spatially aggregated system. In future work approaches such as increasing the spatial resolution of the CityWatStorm model (Dobson et al., 2021) should be tested along with running longer timeseries rainfall.

The second aim of this study was to test the betterment achieved when implementing SuDS on a city scale in both CityWatStorm and InfoWorks ICM. Figures 7, 8 show that CityWatStorm can capture the betterment introduced by implementing SuDS accurately with a 5% higher betterment in CityWatStorm when assessing the total flood volumes and 2% higher when assessing total CSO volumes. The agreement between the SuDS betterment assessment in both CityWatStorm and InfoWorks ICM is due to the ability of the lumped approach to capture the overall runoff reduction regardless of the timing and spatial extent of the SuDS intervention. This means that for the same SuDS uptake percentage, the overall reduction in CSO, flood volumes and river discharge would fall within the same range, but the time-varying results will be different. This makes the case to use CityWatStorm when assessing the SuDS uptake on a city scale.

Muhandes et al. (2021) recommend the use of continuous storms to assess the role of SuDS uptake on a city scale, in this paper, we have used continuous storms and developed a rapid assessment tool to capture the SuDS betterment on a city scale. Future work can include more detailed representations of various SuDS types in a spatially distributed surrogate model of the type presented in Thrysøe et al. (2019), in order to establish the level, spatial extent and the timing of SuDS interventions required to combat climate change adaptation.

The development of the CityWatStorm spatially aggregated tool enabled a wider application of integrated modelling to assess the betterment of implementing SuDS using a continuous rainfall timeseries. The developed CityWatStorm model was shown to be able to capture the SuDS betterment achieving an accuracy of 96.4%, and it was also able to simulate total volumes of flooding, discharge to rivers or CSOs that were comparable to the high-fidelity InfoWorks ICM results. This demonstrates that CityWatStorm can be applied to rapidly undertake detriment/betterment analysis, sensitivity analysis, optimisation scenarios and catchment intervention assessment. We believe that this proposed model can help water companies develop their DWMP and assess their large catchment models against a range of long-term climate projection scenarios.

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author/s.

SM, BD, and AM developed the CityWatStorm model. SM performed code development and analysis of simulation results. AM and BD provided scope and discussion around model evaluation and SuDS impact analysis. All authors contributed to the manuscript writing and plots.

This study received funding from Project Centre Limited. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication. The research reported in this paper was taken as part of the CAMELLIA project (Community Water Management for a Liveable London), funded by the Natural Environment Research Council (NERC) under grant NE/S003495/1.

The views expressed in this paper are those of the authors alone, and not the organisations for which they work.

SM is employed by Project Centre Limited. Project Centre Limited has funded the research and Innovyze has provided the software InfoWorks ICM®. The funding sponsors Project Centre Limited, Innovyze and Imperial College London had no role in the design of the study, in the collection, analysis, or interpretation of data, in the writing of the manuscript, and in the decision to publish the results. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.