Urban flood numerical modeling and hydraulic performance of a drainage network: A case study in Algiers, Algeria

Climate change poses a significant global challenge, leading to changing rainfall patterns, increasing urbanization, and population and economic growth in flood-prone areas. This combination of factors raises the risk of urban flooding in various parts of the world (Hemmati et al. 2020). The hydrological cycle has been greatly affected by climate change, population growth, and urban expansion, resulting in the expansion of impervious surfaces (Morita 2011; Lee et al. 2015; Gigović et al. 2017). Urban flooding is a critical issue worldwide due to factors such as intense rainstorms, decreased permeability of urban areas, increased surface catchment volume, and inadequate drainage infrastructure. Consequently, numerous cities experience significant flood-related damages and losses each year (Xu et al. 2023).

Flooding has emerged as a global problem that requires immediate attention due to its harmful impacts on communities and infrastructure (Peña-Guzmán et al. 2017). The study of flood protection and urban water management has gained significant momentum recently, highlighting the importance of effective flood mitigation strategies (Hettiarachchi et al. 2017; Zahmatkesh et al. 2019; Loudyi & Kantoush 2020; Tamiru & Wagari 2021). Arid countries, including Arab countries, are particularly susceptible to frequent and devastating flooding events due to approximately one-third of global land being classified as arid or semiarid and nearly 20% of the world's population residing in these regions (Dahm et al. 2002; Youssef et al. 2015; Ahmed 2019; El-Kholei 2019).

The hydrological cycle has undergone significant changes in Arab countries due to climate change, population growth, and urban expansion, resulting in the proliferation of impervious surfaces (Morita 2011; Lee et al. 2015; Gigović et al. 2017). In these countries, the issue of urban flooding is exacerbated by unsustainable horizontal and vertical densification, which puts additional strain on ageing sewerage networks that were not designed to handle increased flow during extreme events (Abdrabo et al. 2021). Moreover, rapid urban growth and inadequate land-use planning have led to the emergence of impoverished neighborhoods lacking essential housing, infrastructure, and services, making vulnerable populations, especially women and children, more susceptible to flood hazards (Abdrabo et al. 2020, 2022a, 2022b; Saber et al. 2020). The lack of comprehensive knowledge about floods further complicates flood management and forecasting efforts (Abdelkarim et al. 2019; Nkwunonwo et al. 2020; Salazar-Briones et al. 2020).

Algeria, the largest country in Africa with diverse climate zones, including a mild Mediterranean coastal climate, a semiarid zone called the High Plains, and the arid Sahara desert in the south, faces significant natural disaster risks, with floods accounting for the majority of recorded hazards between 1980 and 2010 (World Bank 2014). Floods cause casualties, damage to buildings, and disruptions to roads and urban infrastructure in Algeria (Sardou & Missoum 2016; Hamlat et al. 2021). Flash floods in Algeria are characterized by their short duration, limited spatial extent, and high flood peaks. The country has witnessed major flood events resulting in substantial human and material losses in various regions, such as the devastating floods in Algiers in 2001, the catastrophic floods in the valley of Oued M'zab in 2008, and the floods in Annaba in 2010, as well as more recent floods in Oum el Bouaghi, Constantine, Chlef, Jijel, and Algiers in 2018 and 2021 (Sardou & Missoum 2016).

Traditionally, rainwater management in Algeria relies on recorded extreme events, but accurately predicting sewerage network discharges remains a challenge due to the lack of powerful tools for flood prediction (Zhou et al. 2013). While several modeling studies have been conducted on wadi flooding in Algeria, detailed studies on the sewage system are lacking (Boutaghane et al. 2021). Similarly, research in other arid countries has predominantly focused on river flooding, resulting in limited understanding of urban sewerage systems (Youssef et al. 2015; Lefebvre et al. 2019; El Khalki et al. 2020; Farooq & Alluqmani 2021). Existing network modeling studies often rely on daily data, neglecting sub-hourly variations and real-time monitoring capabilities (Talchabhadel & Man Sharkya 2015; Hermoso et al. 2018; Tamiru & Wagari 2021).

To address these limitations and provide a comprehensive approach to flood management in Algerian urban areas, it is necessary to explore advanced modeling techniques that consider both wadi and sewerage systems. This approach would enable accurate predictions and actionable insights for flood dynamics, leading to effective flood risk management strategies and the resilience of urban areas. In this study, we propose the utilization of the MIKE URBAN MOUSE numerical modeling tool, which leverages actual sub-hourly measurements at the sewerage network level. This approach represents a significant advancement in flood management in Algeria as it considers real-time data and captures the complexities of both wadi and sewerage systems.

The proposed approach offers several unique features and advantages compared to existing methods. Firstly, by integrating sub-hourly measurements, it captures the temporal variability of flow and precipitation, allowing for a more accurate representation of flood dynamics. This real-time monitoring capability enables proactive flood management and timely decision-making. Secondly, the incorporation of the MIKE URBAN MOUSE model, a well-established and widely used tool in previous studies, enhances the credibility and practicality of the proposed modeling approach (Lee et al. 2015; Bisht et al. 2016; Nguyen et al. 2020). The extensive application of this model provides a solid foundation for its implementation in the context of Algerian urban areas.

The proposed approach also addresses the limitations of previous methods by considering both wadi and sewerage systems, providing a more comprehensive understanding of flood dynamics in urban areas. Additionally, the sub-hourly resolution of data enables the identification of rapid fluctuations in flow patterns and their impact on urban infrastructure. This level of detail is crucial for designing and implementing effective flood mitigation strategies tailored to the specific characteristics of Algerian urban areas.

In summary, this research aims to fill existing knowledge gaps and provide a robust framework for flood management in urban areas of Algeria. By utilizing advanced modeling techniques and leveraging sub-hourly measurements, the study seeks to empower stakeholders with the necessary tools and insights to mitigate the impacts of flooding, enhance urban planning practices, and foster sustainable development in the face of increasing climate challenges. The proposed utilization of the MIKE URBAN MOUSE model, based on actual sub-hourly measurements, represents a significant advancement in flood management in Algeria, facilitating the development of a reliable and operable model for proactive decision-making. This research contributes to the field by addressing the limitations of previous methods and providing

The capital city of Algeria has encountered devastating floods characterized by their brief duration and high intensity, which is a common occurrence in Mediterranean regions (Lefebvre et al. 2019; El Khalki et al. 2020; Loudyi & Kantoush 2020; Stefan et al. 2021). Among the numerous flood events in Algeria, the Bab el Oued floods in November 2001 left an indelible mark on the collective memory of Algerians. This catastrophic event resulted in an estimated loss of 900 lives (Boutaghane et al. 2021), prompting the authorities to initiate various flood protection projects and researchers to embark on extensive research endeavors in flood mitigation.

The capital city of Algeria, Algiers, covers an approximate area of 770 km². A significant portion of the rainfall that enters the sewerage system in Algiers originates from the Bouzareah Massif. This massif, though only partially urbanized, comprises multiple wadis that drain the upstream region of the catchment area. Frequently, these wadis join the sewerage collector's downstream, carrying substantial flows. The sewerage network in Algiers primarily consists of unitary types, except for specific areas with separated or pseudo-separated systems, which were established during the colonial era.

The collection network in the Wilaya of Algiers follows a branching pattern and largely relies on gravity flow, owing to the favorable topography. However, the Bab Ezzouar – Dar El Beida sector, situated in a basin that was formerly a marshland, lacks a natural outlet, necessitating the pumping of collected water (both wastewater and rainwater) to the Oued Smar. Conversely, the transfer of sewage to treatment plants typically involves the use of pumping stations.

The sewerage network of Algiers comprises three main watersheds: east, center, and west. Our research focuses on studying the central watershed, which requires updates due to frequent overflows. This region has a dense hydrographic network, characterized by numerous secondary tributaries and spanning a linear distance of approximately 600 km. The primary wadi of interest in our study area is Oued El-Harrach. The central region includes several wadis and tributaries that significantly contribute to the sewerage network overflows at their interaction points.

The total length of the sewerage network in Algiers is estimated to be 3,780 km, including 318 km of the main network, with 161 km being visitable (D ≥ 1,500 mm at 1,600 mm). The model used for this study was primarily developed by the Algiers Water and Sewerage Company using the MOUSE software. The model consists of ten storage basins, 357 sub-basins, eight lifting stations, 87 spillways, around 30 outlets, 1,788 maintenance holes, and 1,788 pipes of various shapes.

Hydrological simulation plays a crucial role in predicting flood occurrences for a given return period (Hingray et al. 2014) and quantifying damages by identifying vulnerable areas. The fundamental component for hydrological studies and simulations is rainfall measurement. Typically, rainfall data are presented as a 24-h time series published by meteorological services (Meylan & Musy 1999).

Intensity–Duration–Frequency (IDF) curves have been extensively studied by researchers, who have proposed various mathematical or empirical approaches (Bell 1969; Chen 1983; Chow et al. 1988). IDF curves are essential in the field of flooding as they synthesize data collected over a long period and aid in sizing sewerage network structures, particularly special structures for point flow estimation. Furthermore, IDF curves are used to determine project rainfall, which serves as input data for hydrological modeling (Chocat 1997; Musy & Higy 2010).

Different equations are employed in hydrology, such as Gauss, Gumbel, Galton, and Fréchet (Laborde 2000). The Generalized Extreme Value (GEV) distribution is used to model the Annual Maxima Series (AMS) (Hosking 1997). Various researchers have explained and detailed the different equations used for fitting the GEV law to AMS (e.g., Faridah et al. 2013). Several studies have shown that the GEV distribution is more suitable for developing AMS compared to other commonly used distributions like Gumbel (Faridah et al. 2013). Hence, the GEV distribution was preferred for this study.

In this section, the double triangular project rainfall for the 10-year and 100-year return periods is determined using Montana's law. The parameters of the formula for the 100-year return period are obtained after constructing the IDF curves (Chocat 1997; Bertrand-Krajewski 2006). Two project rainfalls were generated for the simulations, representing rainfall events with return periods of 10 and 100 years. These rainfall events had duration of 4 h, with an intense period of 15 min, as illustrated in Figure 5.

In the central watershed of Algiers, there are approximately 15 height measurement sensors and six rainfall stations. Unfortunately, several sensors were lost during heavy rains, and others have experienced periodic malfunctions, resulting in gaps in the records of water level variations. The availability of data determines the selection of sensors in the central watershed of Algiers. This research focuses on studying the Oued Ouchaih sub catchment, which is known for its sensitivity to extreme rainfall and has a higher number of functioning rain gauges and sensors, ensuring more reliable measurements. Among the six existing stations, the rainfall data from Kouba station were utilized. The records of rainfall-flow variations were captured at a time interval of 15 min.

The presented results below depict a specific sub-watershed in Ain Nadja. This sub-basin serves as an illustrative example for explaining our research strategy, although it represents only a small part of the entire study area. The water flows were measured using sensors that captured the water level variations between November 2015 and January 2020. Events were selected based on continuous functioning of the sensors for a specific period. In our example, out of the five sensors (AN0, AN1, AN2, AN3, and AN4), only AN1 and AN3 provided reliable measurements. The pilot example showcases a main network with a diameter of 1 m and 18 storm overflows (refer to Figure 1).

The choice of using the Kouba rain gauge is justified by its optimal location in relation to the sensors in Ain Nadja (the closest station) and the availability of rainfall records at a 15-min time interval. The selected events along with their cumulative rainfall are presented in Table 1.

In recent years, the development of decision support tools that integrate technical and economic designs has gained significant attention (El Khalki et al. 2020). Numerical models have been recognized as effective tools to address engineering and expert challenges. By combining software and other approaches, it becomes possible to quickly predict different trends or scenarios (Peña-Guzmán et al. 2017). In the water field, these models contribute to the formulation of policy strategies (Nguyen et al. 2020) by evaluating various proposed alternatives to solve hydraulic problems (Brendel et al. 2021) and assisting decision-makers in managing urban areas, which are often complex due to the network intricacies in municipalities (Löwe et al. 2017). Several commercially and non-commercially available software packages with varying complexity simulate runoff quantity and quality. Researchers have utilized various models to manage sewer systems, while others have explored the applicability of rainfall and runoff models to urban areas (Bulti & Abebe 2020). Two models are used to describe these different phenomena: hydrological models to generate a hydrograph at the outlet of each sub-basin and hydraulic models to propagate this hydrograph through the sewer system sections (Brendel et al. 2021).

In this study, the coupling of ArcGIS with the MIKE URBAN software developed by the Danish Hydraulic Institute (DHI) is used to model the sewerage network of the Algiers center. This coupling offers a powerful platform for modeling and analyzing urban water systems. The combination of these two software packages enhances geospatial analysis, data integration, and visualization capabilities. The coupling of ArcGIS with MIKE URBAN is implemented in two phases. The first phase involves preparing the data required for the modeling process. ArcGIS is used to create or import geospatial datasets with proper georeferencing. This includes exporting relevant datasets from ArcGIS in a compatible format (Shapefiles) with MIKE URBAN, as well as cleaning and pre-processing the data to ensure compatibility with MIKE URBAN requirements. The second phase occurs after the simulations and focuses on the visualization and analysis of the results. In this phase, the simulation results from MIKE URBAN are imported into ArcGIS for visualization, processing, and analysis. The MIKE URBAN software displays the runoff based on the dimensions of the network inverts, while the runoff processing is carried out according to the Digital Elevation Model (DEM).

MIKE URBAN is powerful hydrological and hydraulic modeling software with a user-friendly interface suitable for sewers of all sizes and types. It is well-suited for analyzing the hydraulic performance of complex looped sewer systems, including overflows, storage basins, and pumping stations. It provides three options for calculating flow depth and velocity: kinematic, diffusive, and dynamic waves (DHI 2017).

The MOUSE software includes all elements constituting the network, such as collectors, junctions (nodes), singularities (storm overflows, drop points, etc.), and lifting stations. These elements play a crucial role in influencing the flow. It is worth noting that network schematization sometimes focuses solely on the main collector to simplify the study. Several bibliographical studies have shown that this simplification does not significantly impact the flow description and system behavior (Kroll et al. 2010). Therefore, for this study, the network simplification was conducted based on the main network schematization only. The specification of upstream and downstream boundary conditions is also performed at the system inlet or outlet (outfall) before commencing the two (02) stages of modeling, namely hydrological and hydraulic modeling (as shown in Supplementary material, Figure S1).

The transfer function utilized in this study is based on the linear reservoir model, which is a simple conceptual model to apply. It only requires one parameter, referred to as ‘k,’ which represents a reservoir that linearly delays the arrival of rainfall.

The coefficient ‘k’ is known as the lag time and represents the storage time in the reservoir. It indicates the temporal shift between the barycenter of the net rainfall hyetograph (rainfall distribution over time) and the hydrograph (flow rate variation over time) at the basin outlet. The linear reservoir model assumes that the storage volume is solely a linear function of the outflow, unlike the nonlinear reservoir model where it depends on both the inflow and outflow in a nonlinear manner. Additionally, the production and transfer functions are assumed to be independent of the initial soil water status. The hydraulic simulation and details of the linear reservoir model are well-described (Chocat 1997).

In MOUSE, the linear reservoir model is represented by the C model. This runoff model, referred to as Model C, is based on the volume continuity and linear reservoir equations. There are two versions of the C model implemented: C1 used in the Netherlands, and C2 used in France. The difference between these two models, C1 and C2, lies in the estimation equation for the constant C.

where A is the total catchment surface area; TL is the catchment lag time.

Hydrological simulation plays a crucial role in predicting flooding events within a specific return period (Hingray 2014) and assessing the associated damages by identifying vulnerable areas. It serves as the fundamental element for conducting hydrological studies.

The ‘MIKE URBAN’ software offers three options for approximating flow: the dynamic wave approach, diffusive wave approach, and kinematic wave approach. The diffusive and kinematic wave approximations are simplified versions of the complete dynamic descriptions. Hence, the dynamic mode is preferred as it encompasses all scenarios. Dynamic routing utilizes the mechanics equations of the Saint-Venant model, which are derived from the Navier-Stokes equations for flow conditions. It ensures the conservation of mass (continuity equation) and the conservation of momentum (dynamic equation). The general form of these equations is as follows:

The Manning number, denoted as M (or n = 1/M), represents the conduit's wall roughness. In the equations, A refers to the area, and R represents the hydraulic radius. The use of Q|Q| instead of Q² simplifies computations, particularly when dealing with reverse flow scenarios. These equations are applicable to free surface flows. However, they can be generalized to include flows under pressure by incorporating a fictitious space within the pipe. The Preissman gap, implemented in the MIKE URBAN software, is utilized for loaded flows with an unlimited threshold (Chow et al. 1988).

To effectively achieve the primary objective of mitigating flood risks by delineating flood zones using decision support tools, decision-makers should follow the following steps. The initial phase involves collecting comprehensive and up-to-date data on various flood risk factors, including terrain characteristics, hydrology, rainfall patterns, soil conditions, historical flood records, infrastructure, and land use information. This data collection aims to gain a thorough understanding of the area's vulnerability.

The second phase focuses on conducting a flood risk assessment using the decision support tool, specifically the ‘MIKE URBAN’ software, which incorporates hydrological and hydraulic models to simulate water behaviour during flood events. The collected data are analyzed to identify high-risk areas and evaluate the potential extent, depth, and impact of flooding.

The third phase entails utilizing decision support tools such as Geographic Information Systems (GIS) to integrate and analyse spatial data for the delimitation of flood zones. GIS enables decision-makers to visually overlay different layers of information, facilitating the identification of high-risk areas and the delineation of flood zones.

In recent decades, the literature has extensively discussed the calibration of flood models, highlighting various criticisms that limit the acceptance of calibrated flood models (Brendel et al. 2021). These limitations arise from unreliable measurements used in the calibration phase, particularly in developing countries, and the unavailability of other required parameters (Nkwunonwo et al. 2020).

The calibration and validation phases are crucial for the utilization of developed models as they determine the predictive capability of the models. To calibrate the model parameters, we chose an event simulation approach since rain events may not fully capture all the rainfall responsible for critical network overflows (Chocat & Cabane 1999). Manual calibration through trial and error was employed; adjusting the parameters until the observed results closely matched the simulated results (Brendel et al. 2021). The dataset was divided into two parts, allocating 50% for calibration and 50% for validation. This approach ensured the development of a robust model capable of delivering accurate results even under extremely heavy rain conditions. The selection of events for calibration based on peak and duration played a significant role in reducing parameter uncertainty.

Successful modeling also relies on effective model calibration and validation, which ensures that the calculated results reasonably correspond to observed flow data. Calibration and validation are crucial engineering aspects of the modeling process and require careful attention (Moriasi et al. 2015).

In this research, manual calibration through trial and error was performed to align the measured parameters with the model's predicted values, aiming for the closest possible fit. This was followed by the validation phase, which aimed to test assumptions independent of those used in calibration to verify the model's performance and ensure its realism. The events selected for both calibration and validation stages encompassed medium to high rainfall intensities with durations ranging from 30 min to 24 h.

The increasing frequency of extreme rainfall events due to climate change presents a significant challenge to urban resilience, necessitating changes in the planning, speed, and redundancy of flood-affected communities (Xu et al. 2023). This study proposes a modernized approach to flood management by implementing sensors within the sewage network. Among all the regions in Algeria, Algiers is the only area equipped with hydraulic sensors. The installation of these sensors aims to transfer signals and information to network managers. The crucial information for them includes exceeding specific water levels or predefined thresholds that trigger alerts during exceptional events. In other words, these warning signals serve to protect people from floods during disasters.

Unfortunately, many of the installed sensors were lost during exceptional floods. For the remaining sensors, the lack of understanding among managers regarding the value of the recorded data series poses a challenge. It is essential to utilize this data and employ modeling techniques to predict flow patterns before a flood occurs, rather than relying solely on real-time measurements during a flood. Failure to address this concern could make risk management significantly more challenging in terms of protecting lives and property from this major threat.

The evaluation of model performance is crucial in various fields, including hydrology, climate modeling, and environmental sciences, and it often relies on performance criteria. It is important to note that the choice of performance criteria may vary depending on the specific context and objectives of the modeling study (Moriasi et al. 2015).

Many researchers in flood modeling acknowledge the presence of errors and uncertainties in developed flood models (Moriasi et al. 2015; Nkwunonwo et al. 2020; Tamiru & Wagari 2021). Therefore, assessing the performance of a hydrological or water quality model during the calibration and validation phases is a critical step as it provides valuable insights for selecting appropriate parameters and understanding the phenomenon at hand. In our study, we employed several performance criteria, including NSE, R², RMSE, and PBIAS, to validate the developed model.

Previous studies have demonstrated that as the impermeability coefficient increases, the infiltration capacity decreases, resulting in higher runoff and elevated peak flow rates (Nkwunonwo et al. 2020). Considering this relationship, the calibration process focused on the impermeability coefficient, which represents the portion of the active surface contributing to runoff, as well as the reduction coefficient, which signifies the proportion of runoff effectively entering the network, accounting for initial losses and lag time. Subsequently, the model was calibrated and validated using available in situ measurements to ensure its robustness in replicating the rain-flow transformation in an urban environment.

The following table summarizes the various criteria used to evaluate the performance of our model:

Based on the summary table of performance criteria (Table 2), the findings of this article can be summarized as follows:

Calibration:

• - Nash–Sutcliffe Efficiency (NSE) > 0.67: The NSE value exceeding 0.67 indicates a good fit between the simulated and observed data during the calibration period. It signifies that the model adequately captures the variability of the observed data.

• - R² > 0.75: With an R² value greater than 0.75, the model demonstrates a substantial correlation with the observed data, explaining a significant portion of its variation.

• - RMSE < 6%: The RMSE, which measures the average difference between the simulated and observed data, is less than 6%. This indicates a relatively low level of inaccuracy between the model and the observed data.

• - PBIAS ≤ ±11%: The PBIAS, evaluating the model's bias in predicting observed values, falls within ± 11% during the calibration period. This indicates an acceptable level of bias in the model's predictions.

Validation:

• - NSE > 0.50: Similar to the calibration phase, an NSE value greater than 0.50 signifies a good fit between the model and observed data during the validation period.

• - R² > 063: An R² score higher than 0.63 indicates a reasonably strong correlation between the model and observed data throughout the validation phase.

• - RMSE < 7%: The RMSE value is less than 7%, implying that the model's predictions are relatively accurate compared to the observed data during the validation period.

• - PBIAS ≤ ±10%: The PBIAS value, which measures the model's bias in predictions, is within ± 10%, indicating an acceptable level of bias in the model's performance during the validation period.

Based on the validation results obtained with the selected events, the criteria indicate a good and satisfactory fit for the pilot area. The observed and simulated curves for the two sensors generally exhibit the same pattern. Considering these representations and the validation results of NSE, R², RMSE, and PBIAS, it can be concluded that the model developed for this sub-watershed is reliable for practical use.

These performance criteria provide a comprehensive assessment of the model's accuracy and reliability in capturing observed data. Meeting or exceeding these criteria indicates that the model performs well in both calibration and validation, demonstrating its potential for credible flood risk predictions and simulations.

The main sewerage network under study is characterized by a diameter of 1 m and varying slopes, including low, medium, and very high slopes (refer to Supplementary material, Figure S2). For a 100-year return period, approximately 90% of the studied section exhibits flow velocities exceeding 4 m/s (see Supplementary material, Figure S8). In contrast, for the 10-year return period, only 15% of the network experiences flow velocities exceeding 4 m/s (see Supplementary material, Figure S7). Notably, along a linear stretch constituting 20% of the total, the flow velocities result in a flow rate exceeding 3 m³/s for the 100-year return period, as depicted in Supplementary material, Figures S9 and S10.

Supplementary material (Figures A3 and A4) indicates that flow within the network accounts for approximately 30% during the 10-year return period and nearly 50% during the 100-year return period. Consequently, the assurance of free surface flow is not guaranteed. In terms of overflows occurring outside the sewerage network through storm overflows, 10% of the storm overflows are characterized by overflow heights of less than 0.3 m (see Supplementary material, Figure S5). However, for the 100-year return period, 30% of the spillways experience water heights exceeding 0.5 m at spillway No. 6 (refer to Supplementary material, Figure S6). Thus, it is evident that the main network in the study area is incapable of effectively handling rainfall corresponding to either a 10-year return period or a 100-year return period flood event. Through our comprehensive analysis, we have identified 300 overflow points in the Algiers sewerage network during simulations conducted with a 10-year rainfall event, and 400 points during simulations conducted with a 100-year rainfall event.

In this study, the drainage network of Algiers, Algeria, was modeled and the hydraulic performance of the system was evaluated. The research utilized real-time sub-hourly observations from the sewage network to enhance flood control through numerical modeling. The development of a valid and effective model for urban flood control will be beneficial to decision-makers and urban planners.

During model validation, performance metrics such as NSE, R², RMSE, and PBIAS were used. The results showed that NSE was greater than 0.50, R² was approximately 0.63, RMSE was 7%, and PBIAS was 10%, indicating the model's reliability. By utilizing preferred flow axes, the major overflow points were identified, and water levels for different flood scenarios (annual, 10-year return period, and 100-year return period) were calculated.

The mapping of major flood zones in Algiers and the identification of high overflow areas resulting from exceptional rainfall (exceeding 0.5 m) provide valuable information for disaster mitigation. The model's performance allows decision-makers and managers to predict flow behaviour in the sewer system and estimate overflow rates based on precipitation forecasts.

However, there are certain limitations to this study. It focused solely on urban catchments and modeled only main storm sewer pipes, neglecting auxiliary storm sewer conduits that could have improved the model's estimated hydrological responses. Additionally, model validation relied on extreme event simulations rather than continuous simulations, and groundwater-related processes were not simulated. The number of sensors placed on the sewage network was limited, which could have impacted the calculation efficiency and introduced uncertainties in the model's results.

To address these limitations, it is recommended to consider additional sensors in the pluvial drainage network to decrease uncertainties and enhance the model's reliability. Moreover, incorporating auxiliary storm sewer conduits and simulating groundwater-related processes would further improve the accuracy of the model. Each urban sub-basin may exhibit different characteristics, such as soil use, drainage systems, and pluviometry, which should be taken into account to obtain reliable results.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.