MODCEL-MHUS: a comprehensive multilayer hydrodynamic unified simulation for stormwater, sanitary sewer systems, and urban surface Open Access

Urbanization processes that ignore stormwater dynamics frequently lead to the city occupying flood-prone regions (Rezende et al. 2019). Urban areas in these susceptible spaces more frequently experience precipitation events and face challenges recovering from these socio-natural disasters (Guimarães & Miguez 2020). On the other hand, the occupation of flood-susceptible regions with landfills and soil movements to ensure local safety tends to transfer floods to different areas, where runoff finds places to spread its waters during periods of high-water levels. Furthermore, as urbanization increases and expands, it leads to soil waterproofing, which hinders rainwater infiltration and increases surface runoff. Thus, flooding events become more frequent and severe, causing numerous damages (UNDRR 2019). It is evident, therefore, that there is a direct relationship between city planning, particularly concerning the treatment of urban waters, and its consequent degradation. Also, the interaction between urbanization and climate change has led to an increased frequency of rainfall floods, where the runoff volume exceeds the adequate functioning capacity of stormwater networks (Wałęga et al. 2024). Frequent floods result in the degradation of the built urban environment, impacting various other urban systems, particularly critical infrastructure such as power substations, intermodal terminals, hospitals, and water treatment plants, among others (Oliveira et al. 2022).

The sanitary sewer system (SSS) is strongly associated with the stormwater system (SWS), despite the solution with a separate SSS having guided engineering projects in Brazil since 1912 (Festi 2005). The design of the separate SSS, characterized by absolute physical separation of the networks, adheres to a sanitary logic wherein distinct pathways are established for sanitary and stormwater sewers. This primarily stems from the fact that surface runoff tends to be less contaminated than wastewater. Additionally, the combined sewer system (that collects stormwater runoff, domestic sewage, and industrial wastewater into the same network) becomes challenging during intense rainfall, leading to untreated Combined Sewer Overflow (CSO) (Bertels et al. 2023). Hence, it is important to highlight that CSOs are indeed events with implications for both public health and environmental well-being (Lund et al. 2020). These implications arise not solely from sewage content but also from the presence of stormwater runoff, laden with litter, debris, chemicals, and assorted pollutants (Schneemann 2021).

However, the current scenario observed in Brazilian cities needs to be revised in terms of the collectedness and treatment of sanitary sewage. Data from the Brazilian National Sanitation Information System (SNIS 2021) indicates that only 63.2% of the urban population in Brazil has access to the sewage network, and 50.8% of the collected sewage undergoes treatment. The absence of treatment is a crucial factor in environmental degradation issues. It degrades the urban environment, subjecting it to the consequences of direct interaction with highly polluted rivers and open sewage.

Even in large Brazilian cities that have better sanitation coverage, there are significant things that could be improved in the installed separate SSS. This situation occurs due to the undersizing of the installed SWS or clandestine or irregular sanitary sewer connections to the stormwater network (IRM 2017). There are also cases where ‘parasitic’ stormwater facilities contribute rainwater runoff to the SSS, overloading networks not designed for the flows generated by rainfall. In addition to these operational difficulties, the impact of climate change adds to the challenges. Possible increases in precipitation volumes can exceed the hydraulic capacity of the systems, amplifying overflows from stormwater and sanitary sewer networks (Gogien et al. 2023). Sowby & Jones (2022) highlight that despite SSSs, even when separated from the SWSs, they also receive unwanted surface inflow and infiltration that negatively impact their sizing, economy, and operation. In critical cases, volumes of stormwater contributions to the SSS can impact the pollutant removal efficiency of treatment plants and result in additional costs in sewage management (Sola et al. 2020).

Hence, analyzing the coordinated functioning of these networks becomes crucial for a thorough understanding of the challenges at hand. Consequently, there is an increasing need for tools enabling precise diagnosis and prediction of issues concerning critical urban infrastructures in a unified manner. Over the past four decades, numerous studies have consistently explored unified urban water management. However, limited attention has been given to quantifying the challenges arising from the interaction between separate stormwater and sanitary systems.

Thus, the unified study of urban waters does not necessarily imply two sewage network simulations. Several studies address the simulation of combined sewer systems, which are designed, from their conception, to operate with stormwater and sanitary sewer input in a single network (Saddiqi et al. 2023). Additionally, the concept of CSO events, as discussed in several papers (Botturi et al. 2021), is entirely associated with operating and simulating a single mixed-use network.

On the other hand, a separate SSS demonstrates an unplanned combination between the stormwater and sanitary sewage systems, leading to network overflows. Segregating urban water into distinct networks has proven ineffective, particularly in developing countries. Regarding the quantification of stormwater contributing to the separate sewer system, noteworthy is the study by Liu et al. (2021), who proposed a statistical model based on logistic regression to predict the probability of infiltration into the network. However, the study primarily focuses on infiltration from the groundwater. In response to measurements from a case study, Ye et al. (2023) propose a methodology for quantifying surface inflow and infiltration in separate SSSs. Regarding hydrodynamic simulation of separate systems, the work of Mannina & Viviani (2009) stands out. However, the work presents a non-distributed model that cannot simulate contributions in both directions between the networks, limiting its applicability to real cases.

Moreover, Mohammed et al. (2022) highlights the use of SWMM for simulating sewage quality during the leakage of stormwater runoff into the sewage system. However, the case study only presents the simulation of a single network. Additionally, even for a simulation scenario of two separate networks with SWMM, the model shows more significant potential for simulation within traditional hydraulic structures, meaning that the combination of sanitary sewage and stormwater in the urban environment should be conducted externally to the model or in a simplified manner. The authors did not find its application in scientific works. Furthermore, limitations in the hydraulic representation of the selected models prevent interaction and intensification of network overflow by a surface flow layer. In most cases, authors account for the total volume overflow at each connection in a simplified manner (Liao et al. 2015; El Ghazouli et al. 2022).

The primary challenge in developing this type of unified simulation lies in simulating flows in different infrastructures, each with distinct quality parameters for rainwater and sanitary water. Additionally, it is essential to simulate surface flows and water accumulation on streets, buildings, and open spaces. These surface flow simulations are crucial as it is on the surface level that significant interactions between stormwater and sanitary systems occur, such as water input and output through manhole covers or household hydraulic systems during floods. Failures in a separate SSS can arise from the overflow of the SWS, which accumulates water on the surface of the urban area and discharges it onto the SSS. This floodwater can inflow the SSS and lead to overflow at other points. Consequently, this overflow will comprise a blend of untreated stormwater and sanitary sewage. Furthermore, in the context of separate SSSs, considering the various combinations of sanitary sewage and stormwater, the term ‘unforeseen Combined Sewer Overflow’ (uCSO) is more accurate. Subsequently, the uCSO events may flow through the streets and contribute to the SWS at another location, re-entering the subsurface networks.

In this context, the paper's objective is to develop a methodology for the unified simulation of stormwater and SSSs with the urban surface layer for various real-world application cases, considering cross-interferences in the operation of these systems. The methodology utilizes the Urban Flood Cell Model-MODCEL (Miguez et al. 2017), renowned for its capability to simulate hydraulic flows across different layers.

Additionally, the method includes a post-processing model based on the Streeter-Phelps environmental quality model to simulate BOD. A simple and verified methodology tests the post-processing approach and assesses the solution's applicability. To verify the application of the proposed method, the study simulated the sewer network operation of an urban watershed in the western zone of the municipality of Rio de Janeiro (Brazil). This area demonstrates interactions between the sanitary and stormwater sewage systems, primarily due to the accumulation of surface water.

The main novelty of this study is the possibility of assessing the interaction between both systems considering complex urban infrastructure, including standard hydraulic devices and surface flow, and the impacts in terms of water quality and quantity that result from this interaction.

The authors utilized the Urban Flood Cell Model-MODCEL (Miguez et al. 2017) as the simulation system for the developed methodology. Both professional and academic endeavors extensively utilize MODCEL for simulating both natural and urban floods, and it is frequently employed for simulations in stormwater networks (Sousa et al. 2022). It is considered a quasi-bidimensional multilayer cellular model capable of simulating the stormwater network layer with the surface flow layer in a unified way. The application of this model is internationally recognized, being utilized in case studies from Brazil (Rezende et al. 2019; Fraga et al. 2022; Oliveira et al. 2023), Colombia (Oliveira et al. 2019; Pérez-Montiel et al. 2022), United Kingdom (Sousa et al. 2022), Spain (Miguez et al. 2017) and Italy (Scionti et al. 2018; Barbaro et al. 2021).

In this study, MODCEL serves as a hydrodynamic model to simulate the sewage system and its potential interactions with the SWS in a unified manner, integrating with surface flows.

Here, is the flow between neighboring cells i and k; is the water level in the center of cell i; is the water surface area in cell i; is the resulting flow from the rainfall-runoff transformation occurring on cell i; and t is the independent time variable.

Thus, the territory is subdivided into cells, forming a two-dimensional flow network with the potential for flow in various directions, using one-dimensional hydraulic exchange relationships, fulfilling the role of a 1D/2D model. The model includes a predefined base set of cells capable of representing the territory's heterogeneities and predefined types of hydraulic connections. This allows for solving equations for free-surface flow, typical in storm and SSSs design, or pressure flow equations for failures in these systems.

Here, is the water surface area between neighboring cells i and k; is the hydraulic radius between neighboring cells i and k; is the water level in the center of cell k; is the distance between the center of cell i and the center of the cell k.

Here, is the water surface area in cell k; g is the acceleration of gravity.

Here, is the orifice cross-sectional area; is the orifice coefficient; is the orifice outlet bottom elevation.

A key aspect of innovation in the current methodology lies in delineating cell and connection types to simulate the SSS. This system, in turn, must integrate with the other urban systems, already consolidated in the representation of the watershed by flow cells, to establish the basis of a Multilayer Hydrodynamic Unified Simulation with MODCEL (MODCEL-MHUS). By applying MODCEL-MHUS, the main interactions between stormwater and SSSs (through the network or urban surface fails) and their consequences for the territory will be hydrodynamically and environmentally mapped.

For hydrodynamic simulation, three layers of flow simulation in MODCEL-MHUS, described in the following, must be considered. Notably, the three flow layers are simulated in a unified manner, enabling their interaction with the hydraulic system elements and the urban surface.

The first layer represents the surface flow through watercourses, streets, and open spaces in the watershed and accumulation in local depressions and areas with drainage difficulties. This initial layer aligns with the primary goal of cell-type models, widely used for urban flood assessment and extensively documented in the literature (Miguez et al. 2017).

The second layer represents the flows occurring within the SWS elements. Miguez et al. (2017) adapt the representation of the flow cell model to perform this simulation and integrate it with the first layer (surface). This representation occurs similarly to the Dual Drainage (Djordjević et al. 1999) approach. However, it is performed in a unified manner using the same hydrodynamic model, with the possibility of interconnected flows between the surface and subsurface layers at each step. The authors emphasize that the SWS can be represented by defining manholes as flow cells associated with surface cells of streets through connections representing devices such as street inlets and horizontal orifices. Street flow uses the Saint-Venant equation, and flow between manholes uses an equation that also solves the Saint-Venant equation. However, pressure flow can be considered when the manhole is complete and the stormwater pipes start to operate submerged. Additionally, to represent an ideal SWS situation, residential rooftops can be connected directly to manholes through orifice links, simulating building connections to the urban SWS. Figure 2 schematically illustrates the connection between rooftops and manholes for the SWS in a regular scenario.

After constructing the stormwater hydrodynamic model, it should undergo calibration and validation to enhance the reliability of the simulated results. The calibration process involves adjusting the model coefficients to represent reality with a certain degree of precision and accuracy. The calibration of a hydrodynamic model typically uses a heavy rainfall event that has exerted stress on the SWS, as simulating failures is the tool's primary objective. The calibration event should have sufficient records of rainfall, flow rates, and water levels generated by the event. As this is a hydrological and hydrodynamic model, calibration entails adjusting the coefficients to convert rainfall into runoff, thereby calibrating the volume of water in surface runoff (as shown in Equation (1) presented earlier) and adjusting the hydraulic coefficients in the equations between flow cells (Equations (2)–(4)), thus calibrating the flow rates. The validation concept presented by Refsgaard (1997) involves applying the same parameter values set during calibration to another event, known as the validation event. Model validation demonstrates that a model can adequately represent another event with precision and accuracy within acceptable limits without modifying the coefficients used in calibration. Without measured information, one can calibrate (or validate) the model using simplified methods incorporating field campaigns or photographic records of floods (Oliveira et al. 2019).

The third layer of the flow simulation delineates the infrastructure for the SSS, wherein flow cells symbolize key components such as sanitary sewer manholes and other singularities. The calculated volumes for each cell incorporate the accumulation capacity of the sanitary sewer within every hydraulic structure in the system, encompassing the accumulation within the sanitary sewage pipes. For hydrodynamic simulation, the singularities of the sanitary sewer network are assigned boundary conditions that represent proportional sanitary sewage contributions to each structure's contributing sections. Therefore, unlike the SWS and surface runoff, which initially carry water from rainfall, the sewer flowing through this network originates from sanitary contributions inserted at each manhole. Mapping the origin of each urban water within the model will streamline the water quality calculations presented in a context of connection between the layers.

In their work, Nascimento & Araújo (2013) emphasize that parasitic contributions can occur through the interconnections of residential stormwater networks to sanitary sewage networks and through the openings of sanitary manholes and other singularities. Thus, the unified hydrodynamic simulation process aims to accurately represent the irregular connection of residential SWSs directly to the SSS. The simulation scheme resembles the representation of the SWS, with the difference that the orifice connection, previously linked to the stormwater manhole, becomes obsolete and is replaced by the orifice link connected to the sanitary sewer manhole, as shown in Figure 2. In this case, the percentage of irregular connections is calibrated according to real measurements of uCSO. It is worth noting that this connection is a potential application of unified modeling; however, it will not be applied to the present case study due to the lack of overflow information in the SSS to calibrate the percentage of irregular household contributions.

Considering the potential of MODCEL as a hydrological tool, it becomes necessary to specify the simulated rainfall event. The stress event for the system uses design rainfall associated with return periods of 10, 25, or 50 years, typical for SWSs or based on recorded rains where uCSO has been observed. The choice of the return period (RP) is associated with the design verification of stormwater networks, which need to function without failures for specific probabilities of rainfall events. According to the reference document for stormwater projects in the municipality of Rio de Janeiro (Rio-Águas 2019), new stormwater networks should function appropriately for the 10-year RP, while older networks can be verified for the 5-year RP. When dealing with unlined channels, verification is conducted for the 10-year RP. For lined channels, the 25-year RP is used as a design criterion (with freeboard), and the 50-year RP for verification (without freeboard). According to the reference document, the design rainfall event has a duration equal to the time of concentration of the watershed, and the rainfall intensity is obtained from a series of IDF equations provided for the municipality. The model can also perform long-term simulations to study the system's behavior during dry periods or for low-intensity rainfall. However, this type of simulation will not be explored in the present study.

The application of the hydrodynamic methodology allows for determining the quantitative impacts related to flow rates between systems, providing responses for levels, velocities, and flow rates between cells, considering various interactions, such as:

• (i) impacts of the malfunctioning or absence of the SWS;

• (ii) impacts of the malfunctioning or absence of the SSS;

• (iii) total rainfall entering the sanitary sewage system, as well as its effects on hydraulic overload;

• (iv) locations where stormwater contributes to the sanitary sewage system;

• (v) total uCSOs in separate SSS (or CSOs in combined sewer systems);

• (vi) locations where uCSO or CSO occurs;

• (vii) the estimate of the percentage of clandestine wastewater connections in the SWS;

• (viii) the estimate of the percentage of parasitic stormwater connections in the sanitary sewage system.

In addition to the hydrodynamic model, it is necessary to address the analysis of urban water quality through the interaction between systems to complete the MODCEL-MHUS. This stage involves the development of Environmental Quality Modeling alongside hydrodynamic calculations to assess the water quality in SWSs and receiving bodies. This assessment occurs in a post-processing routine, considering contributions from both the SSS to the SWS and vice versa, as well as their interaction with the surface layer of the flow.

This work will address the flow cells representing the surface, stormwater, and sanitary sewer as control volumes where the relevant physical processes for water quality studies occur. The flow cells will be treated as biological reactors. A reactor refers to tanks or generic volumes in which chemical or biological reactions occur (Von Sperling et al. 2020). The mass balance of a reactor depends on the materials that enter or leave, are generated or consumed, and the materials that are accumulated in the analyzed volume (Tchobanoglous & Schroeder 1985). Von Sperling (2014) mentions that locations where flows occur, such as rivers and channels, can be treated as biological reactors. Thus, each flow cell (whether it belongs to the SSS, SWS, or surface flow) will be treated as a biological reactor where these reactions occur. For selecting the hydraulic model of the reactor representing the cells, the authors considered both the flow type and the mixing pattern for each compartment. Given the specific characteristics of urban water interaction problems, we opted for a continuous flow scenario. The authors also considered various aspects of system interaction issues in determining the mixing pattern. These include the favorable geometry for mixing, particularly evident in manholes, the relatively small scale of the problem compared to studies of larger rivers, and the significant energy introduced per unit volume associated with the turbulent kinetic energy of typical free-surface flows. Consequently, the authors chose the complete mixing model to represent the hydraulics in the cells, where incoming particles are promptly dispersed throughout the reactor's interior.

Here, = Flow rates for the M number of output connections of the analyzed cell (l/s); = Concentration at the output after complete mixing in the analyzed cell (mg/l); = Concentration of the accumulated volume in the cell at the beginning of the mixing process (mg/l); V = Volume of water in the flow cell during the time interval t (l – liters); t = Time interval of the simulation (s); = Flow rates for the N number of input connections of the analyzed cell (l/s); = Concentrations of the compound for each of the N input connections in the cell (mg/l); = Production reaction rate of the compound (mg/l.s) – Disregarding for this work; = Consumption reaction rate of the compound (mg/l.s).

Thus, the influent flow of a given flow cell will have the concentration calculated at the end of the respective time interval and will serve as input data for adjacent cells in the next time interval. Initially, the authors developed a post-processing model for the water quality study to represent the parameters of Biochemical Oxygen Demand (BOD) based on considerations of complete mixing reactors in networks. BOD allows for indirectly estimating the amount of organic matter in various accumulation surfaces, including watercourses, stormwater and sanitary sewer networks, and even streets and lots. Thus, the determination of BOD also indicates the consumption of Dissolved Oxygen (DO). In addition, in places with a more significant accumulation of BOD, there is also a greater probability of the existence of pathogens responsible for waterborne diseases. Therefore, BOD, along with Chemical Oxygen Demand (COD), are relevant parameters for determining the degree of pollution of water bodies (Davis 2010).

The θ values for and are 1.047 and 1.024, respectively. The correction for 23.4 °C (average temperature in the case study) results in a Kr of 1.03 ⁠.

Here, L represents the remaining BOD concentration (mg/l); is the initial concentration of BOD at the discharge point (mg/l); is the deoxygenation coefficient (day⁻¹); and t is the time interval.

Finally, the difference between and L over a given simulation time interval (in seconds) will be equal to the consumption reaction rate presented in Equation (5).

The Environmental Quality Modelling of MODCEL-MHUS seeks to elucidate the effects of unplanned interaction between stormwater and SSSs, mainly in a separate SSS. Water level, depths, velocities, and flow data from the hydrodynamic modeling will be input data for a post-processing quality model. Following the outcomes of the unified hydrodynamic model, a post-processing model is employed to simulate water quality, considering various parameters contingent upon the flow source (stormwater or sanitary sewer) and their mixtures and decays. The contaminant concentration values can be modeled in each of the flow cells of the model, whether they are associated with the SSS, stormwater, or cells representing surface areas such as streets, sidewalks, buildings, and open spaces. With the modeling of contaminant concentration over time, it is possible to integrate these values and calculate the total contaminant load flowing through each cell.

With the results of the BOD concentration, it is expected to verify the mixing levels between the systems, seeking to understand the real impact of this type of interaction for scenarios in which the separate SSS does not work correctly. It is possible that, with the confirmation of its applicability, it will be possible to use the tool in a diagnostic manner to estimate the failure rate of the separate SSS in a basin by comparing field data with the modeling results. In this stage, it will be possible to estimate:

• (i) Concentration and load of contaminants in surface layers;

• (ii) Concentration and load of contaminants at key points of the SWS;

• (iii) Concentration and load of contaminants in receiving water bodies;

• (iv) Concentration and load of contaminants flowing into sanitary sewage treatment systems.

It is worth noting that this list corresponds to potential applications of the model. Determining water quality may not be necessary, depending on the problem to be understood and addressed.

Regarding stormwater and SSSs, there are strong indications that the region interacts with both systems. Urban water contributions to the Prata do Cabuçu River are observed from the SSS, even in dry weather. Sanitary sewer pipes in the study case were discharged directly into the Cabuçu Prata River. The SSS is not yet connected to the local Wastewater Treatment Plant (WWTP). Furthermore, there are several sewage manholes located near stormwater manholes. While this scenario does not indicate an interaction between the systems, given the other evidence, there is a likelihood that these points establish a connection between the systems. Additionally, there are indications of a direct contribution from buildings with domestic sewage to the SWS, as evidenced by covered storm structures. The covered structures suggest unpleasant odors in this area due to the irregular contribution of the SSS. Finally, it is essential to highlight that residents in the area report that during intense rainfall events, the region experiences flooding and water overflow through the manholes of the SSS, indicating irregular stormwater contributions to this system.

The preliminary diagnosis justifies the need to implement the methodology developed in this study. Considering the preliminary diagnosis conducted, the interaction possibilities outlined in the methodology will be partially employed for this case study. Faced with the challenge of estimating households irregularly connecting to public stormwater and SSSs, the authors initially restricted the study to simulate the contribution between the systems via surface runoff. The initiation of this interaction occurs due to the failure of the SWS, leading to water accumulation in areas not prepared to handle it. The remaining potential applications of the methodology may be outlined during the tool's implementation in a future case study. Concerning the unified hydrodynamic simulation, the following will be identified:

• impacts of the malfunctioning of the SWS;

• locations where stormwater contributes to the sanitary sewage system;

• locations where uCSO occurs.

Using water quality modeling, the following outcomes will be identified considering the parameter of BOD:

• concentration of BOD in the surface layer;

• concentration of BOD in receiving water bodies.

It is noteworthy that this hypothetical scenario may not precisely reflect real-world conditions. However, it illustrates the potential of the unified modeling strategy.

The methodology begins with the region's topographic information, and the authors divide the territory into flow cells to represent surface runoff. These cells simulate urban stormwater flows through streets, buildings, and open spaces within the watershed and the flow in the main river.

To incorporate the subsurface layer of stormwater network simulation in MODCEL-MHUS, the authors needed to estimate a SWS for the region of interest. This occurred due to the absence of a municipal registry of the network. Thus, field visits were conducted on-site to identify the layout of the stormwater network. Stormwater devices were identified on virtually all streets within the study area; however, these were old structures in poor condition. To replicate the SWS as closely as possible, technical recommendations for sizing old systems from the municipality of Rio de Janeiro were utilized, considering a design for a recurrence period of 5 years. Additionally, the Manning coefficients used in the MODCEL equations were adjusted due to the lack of maintenance of hydraulic structures. In total, 55 manholes were estimated for the SWS connected to the streets using orifice equations to represent the storm drain inlets.

The sewage network in the region also lacks municipal registration. The network estimation was conducted based on field visits and the assumption that the sanitary sewage system was designed according to Brazilian standards for this system, which have been valid since 1986. While these estimates may not precisely reflect the reality of the networks, they help apply and validate the model, demonstrating its ability to simulate various systems and surface runoff in a unified manner.

The methodology outlines that the model can represent SWS failure, wherein water flows onto streets and may accumulate on the urban surface. In this case study, water accumulating on the surface can enter the SSS through manhole covers or household connections. Floodwater entering the SSS, due to its flow rate exceeding the capacity of the system's networks, may also overflow onto the surface through manhole covers and household connections. This water is a mixture of stormwater and domestic sewage (uCSO). The model maintains control over the volumes of each contribution, thereby facilitating subsequent water quality modeling (It discerns the percentage of stormwater and sanitary sewage in each mixture).

Here, i is the rainfall intensity (mm/h); RP is the RP or recurrence interval (years); and t is the duration of precipitation (min).

Table 1 presents the rainfall used for unified simulation and verification of potential interactions between the simulated systems.

It is worth highlighting that the sewage network assists in draining part of the flooding in the northern region of the watershed, where there are topographic depressions in the terrain. The impoverished area population typically uses the sewage system to drain floods by opening the lids of sanitary sewer manholes. However, this practice is unnecessary for floods to contribute to the sewage system, as the accumulation of water in the streets above the lids of sanitary sewer manholes already facilitates interaction between the systems. After flood levels exceed those of houses, the contribution of stormwater through inspection chambers is also expected, often implemented improvised by untrained individuals.

The contribution of stormwater in these areas overloads the SSS, which is designed for significantly lower magnitude flows. The sanitary sewer networks have diameters ranging from 0.10 to 0.15 m, while for stormwater networks, the pipe diameters reach 1.5 m. This situation induces a system operation with pressurized flow in various sections, leading to overflows in other regions that previously did not have water accumulation, particularly noticeable in the middle area of the watershed. It is essential to observe that this water accumulation is a mixture of stormwater and domestic sewage, posing severe health problems due to waterborne diseases.

Another important outcome of this simulation lies in analyzing the influent flows to the discharge point of the SSS. WWTPs and sewer pumping stations (or lift stations) in separate systems are designed to receive a sewage contribution and only a portion of infiltration water from the subsurface. The contribution of stormwater can impact the treatment in WWTPs by diluting the contributing sewage or, in more extreme situations, contributing flows so high that they can overwhelm the structures of WWTPs and lift stations. Sizing spill structures can mitigate problems of excessive water input into the sewer system during rainy periods, but it does not address the core of the problem. Furthermore, spill structures are associated with contributions to receiving water bodies, generating negative environmental impacts.

Besides the environmental impact, improperly discharging stormwater into SSS is detrimental to sanitation services' regulation and quality control. The increased flow at the WWTPs can create a false indicator of attendance, hiding the real situation of population coverage and organic matter removal of the sewage collection and treatment service. Applying the methodology proposed in this study can help identify the critical points of contamination by the SWS and calculate the volume of this improper input. Thus, the method can be a valuable tool for correctly regulating and evaluating the efficiency of sanitary sewage systems, resulting in operational benefits for the sanitation system and economic and public health benefits for the population attended.

In areas where uCSO occurs, the population is directly exposed to combined waters, defining critical points in the system that require priority in decision-making. In these locations, the authors recommend the implementation of overflow control structures and reservoirs to mitigate the population's exposure to combined waters. After rainfall, these structures would facilitate the proper treatment of effluents.

In terms of volume, the unified simulation results provide insight into both the total inflow volume entering the SSS and the total uCSO for the simulated events. Specifically, we observed 734 m³ for the 10-year RP and 875 m³ for the 25-year RP inflow. Concerning uCSO, we noted 278 m³ for the 10-year RP and 282 m³ for the 25-year RP. The disparity between inflow and uCSO arises from the capacity of the separate SSS to convey a portion of the inflow stormwater without overflow.

Regarding the water quality modeling, as described in the method chapter, the simulation result for BOD is presented for the interaction between the flow cells corresponding to each of the simulated layers.

Von Sperling (2007) suggested a value of 350 mg/L for domestic sewage BOD.

Weibel et al. (1964) considered the publication for stormwater, which establishes different BOD values for stormwater, considering different rainfall durations. Higher values are assigned to the initial runoff. The values used can be seen in Table 2.

The irregular connection between the sanitary sewer and SWSs can be perceived after the rainfall event and the overflow between systems. This connection contributes to the untreated sanitary sewers in the analyzed water body (Prata do Cabuçu River), causing an increase in BOD after the event that caused the uCSO. This contribution to extreme events can cause acute contamination in the water body, leading to the classic consequences of contamination by sanitary sewers in rivers, such as deoxygenation and harm to local biota. In addition, since it occurs in events of heavy rainfall, in the event of a flood, the connection between the urban water systems could expose the population of the flooded region to pathogens found in the sanitary sewers, representing a risk to local public health.

A relevant impact on the separate SSS arising from cross-contamination between SWSs is the reduction in the concentration of organic matter that arrives at the WWTPs (although the system is not currently connected in the plant). Considering the RP 10 rainfall event contributing to a dysfunctional SWS, there is a 70% reduction in BOD of outflows of the SSS. WWTPs with biological treatment technology depend on a minimum organic load for proper functioning. BOD values affluent to the stations below may compromise the health of these treatments, both for aerobic and anaerobic reactors.

Another significant impact on the SSS is the increase in flow that can generate a false service indicator for the sewage basin. If the system operator is contractually regulated based on the population served, an indicator used in Brazil, the two parameters used to compose the indicator are network coverage and influent flow in the WWTPs. If the network is installed, but buildings are not connected to the network in a functional separate SSS, the deficit would be mapped due to the low flow in the treatment plant. In a defective system, where there is stormwater flow in the SSS, the flow of more clean water can mask this data, generating extreme cases where there is the possibility of the service indicator being completely met and no sewage flow being treated. Thus, the methodology can also be used to observe these potential distortions in sanitation indicators.

This paper presents the MODCEL-MHUS as a crucial tool for addressing the unified aspects of urban stormwater and SSSs in countries or regions that have chosen to implement independent network projects. In such cases, there is evidence that the uCSO is caused by a lack of integrated management between the systems.

Additionally, as the method incorporates a surface layer, non-traditional solutions outside urban water networks can be collaboratively addressed, such as implementing reservoirs and constructed wetlands. This corresponds to an innovative approach and makes the tool applicable to countries and regions that have opted to implement a combined sewer system, where CSOs are a source of urban and environmental degradation.

The hydrodynamic simulations presented in this study correspond to a scenario in which an undersized SWS collapsed due to a lack of maintenance and could not safely capture and convey stormwater to the discharge point. The choice of this scenario considered the criticality of stormwater contributions to the SSS and their overflows onto surface layers, recognizing it as a situation with the potential for the most significant negative impact. The authors selected this scenario to emphasize the potential severity of the issue.

The results presented for this failure scenario reveal significant impacts on the SSS, primarily regarding the increased flow at the discharge point caused by the contribution of stormwater to the sanitary sewage network. Additionally, several sewer manhole overflows are observed in the area, degrading the built environment and increasing the likelihood of waterborne disease proliferation. The authors highlight these outcomes as indicative of the adverse consequences resulting from the scenario. The presented results pertain to official design rainfall for SWSs, serving as examples of the model's application, which is deterministic. A more thorough assessment to achieve a design configuration should entail an uncertainty evaluation for enhanced result reliability.

Applying the water quality model to this scenario allowed the authors to observe the criticality of BOD concentrations in the various simulated layers. The natural drainage system is also impacted in this scenario due to the occurrence of uCSO. The Prata do Cabuçu River, which receives the contribution from the SWS, experiences an increase in BOD concentrations during the rainfall event. The authors note the impact of this scenario on the natural drainage system and the consequent rise in BOD concentrations in the Prata do Cabuçu River.

Additionally, it is noteworthy to emphasize the utility of the tool for mapping contaminant concentrations in the territory in a spatially explicit manner, using a tool based on a flow cell model, which is easier to apply even for scenarios with a lack of data, characteristic of the reality of developing countries like Brazil and others in similar situations. The representation considers the main physical phenomena involved in simulating pollutants, highlighting the possibility of integrating initially contaminated waters with various concentrations, such as river waters, domestic (and industrial) sewage, the first flush, and the change in concentration throughout the event.

Therefore, assessing the methodology's potential using the pilot watershed allows the authors to consider that the tool is innovative and helpful in simulating the interaction process among different urban waters and their pollutant concentrations. This particularly applies to regions that have chosen to manage urban sewers from a separate perspective but, in practice, have interactions.

It is worth noting that the unified simulation begins with the initial approach to the problem. The shift in the paradigm of individualized network treatment must be addressed by obtaining data for the modeling process and from the conceptual modeling of the problem.

Practical issues in urban engineering demonstrate that the interaction between urban waters, particularly stormwater and sanitary sewage, is a constant reality and urgently requires attention. However, separately sizing the networks and individually verifying their hydrodynamic functioning do not allow authors to observe the entire problem. Moreover, considering open spaces in the watershed and their incorporation into solutions for both systems' issues must be considered, given the increasing need to explore external solutions beyond the network, considering the entire territory.

Finally, the MODCEL-MHUS method emerges as a robust tool for supporting the unified operation of stormwater and SSSs, whether combined or separated.

This study was conducted with Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Processes 142284/2018-1. We want to express our special appreciation to the students and professors involved in the extension project titled ‘Multicriteria Evaluation of Flood Resilience to Support Territory Planning and Social Construction Process of Risk Perception’ at the Universidade Federal do Rio de Janeiro (UFRJ). Additionally, we extend our gratitude to the UNESCO Chair on Urban Drainage in Regions of Coastal Lowlands hosted at UFRJ.

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

The authors declare there is no conflict.