Flood risk investigation of pedestrians and vehicles in a mountainous city using a coupled coastal ocean and stormwater management model

To examine the attributes, underlying mechanisms, and impacts of rainfall patterns on the vulnerability of pedestrians and vehicles to flood‐induced instability within mountainous urban areas, we introduced an integrated urban flood model that combined the Storm Water Management Model (SWMM) and Finite Volume Coastal Ocean Model (FVCOM). We implemented this model in the Yuelai New Town of Chongqing, China. Our findings indicated that in the case of early peak rainfalls, there was a rapid surge in flood volume during the initial stages of rainfall , while this increase was more gradual when the peak rainfall was delayed. Furthermore, for events with the same return period, flood peaks resulting from later peak rainfalls covered a larger area compared with those from earlier peak rainfalls; however, this effect diminished with increasing return periods. As the return period was extended, the exposed risk area for pedestrians and vehicles expanded. Analysis of instability indices revealed that pedestrians exhibit a lower index compared with vehicles, adults fare better than children, and SUVs outperform sedans. The efficacy of our proposed model framework was demonstrated through its successful application in assessing urban flood risk and evaluating the instability index for pedestrians and vehicles within a mountainous urban setting.


| INTRODUCTION
It is now understood that the interplay of climate change and rapid urbanization has disrupted the natural hydrological cycle, resulting in an upsurge of extreme rainstorm events within urban locales (Fadhel et al., 2018;Zhou et al., 2019).These rainstorms and ensuing waterlogging incidents pose substantial threats to pedestrian safety, vehicle movement, and public infrastructure and have even led to significant casualties and economic losses (Blake et al., 2013;Coulthard & Frostick, 2010;Zhang et al., 2015).
As computer technology and model theories advance, numerical models play an increasingly pivotal role in comprehending urban flood characteristics and the hydrodynamic processes that underlie them.Processbased flood models furnish tools for both retrospective analysis and prospective prediction of flooding, offering spatiotemporal insights into flood dynamics such as distribution, water depth, and duration.These insights hold critical implications for evacuation and flood management.However, the accuracy and efficiency of urban flood models hinge upon diverse factors encompassing integrity and precision of input data, computational domain scale, complexity of drainage systems, and the performance of computational hardware and modeling algorithms.Since the 1960s, several numerical models for urban flood management have surfaced, including onedimensional drainage pipe models like the widely used jStorm Water Management Model (SWMM) developed by the United States Environmental Protection Agency, as well as two-dimensional hydrological and hydrodynamic models such as InfoWorks ICM and MIKE Urban (Yang et al., 2020).The prevalence of open-source accessibility and its low learning curve have positioned SWMM as a widely utilized tool in both academic and industrial circles (Rossman, 2015).On the other hand, despite the higher cost associated with procuring commercial software, InfoWorks ICM and MIKE have attracted significant interest globally due to their comprehensive pre-and postprocessing capabilities, coupled with stable and efficient modeling algorithms.Concurrently, certain scholars have pioneered inventive flood models anchored in hydrodynamic theories and advanced programming paradigms.Noteworthy examples include the work of Hou et al. (2013Hou et al. ( , 2015) ) and Simons et al. (2014) who introduced a suite of surface hydrodynamic numerical models bolstered by GPU acceleration technology.In contrast, some researchers have opted to adapt existing open-source models to their needs.For instance, Wu et al. (2017) explored rain-induced flooding in Dongguan, Guangdong Province, by amalgamating SWMM with the LISFLOOD-FP model.Fahad et al. (2020) proposed a structural damage assessment model using the advanced circulation (ADCIRC) model and two-dimensional unsteady flow (TUFLOW) model.Gori et al. (2020) numerically assessed the compound flood risks due to the interaction of storm surge and rainfall using the ADCIRC model.The application of these models has yielded a series of studies concerning urban flood risk assessment (Xia et al., 2017;Zhang et al., 2021;Zhao et al., 2021), which collectively contribute to the enrichment of urban flood management theory.
Nonetheless, due to inherent heterogeneity between pedestrians and vehicles, assessing their respective floodinduced instability risks solely based on parameters like water depth or velocity distribution is complex.In order to unravel the intricacies of flood instability for pedestrians and vehicles, researchers have explored the forces acting upon them during various flood scenarios, culminating in a set of criteria and formulas for evaluating instability.Walder et al. (2006) formulated an instability assessment formula for determining human slipping during tsunami risk evaluations.Experimental work by Cox et al. (2010) illuminated that human flood instability primarily manifests as slipping and falling, the determinants of which include flow velocity and water depth.Abt et al. (1989) and Karvonen et al. (2000) calibrated formulas for human flood instability through flume experiments.Based on stress analysis, Xia, Falconer, Xiao, et al. (2014) also deduced the incipient velocity formula of human slipping and falling in flood by applying the ergonomic and the sediment incipient motion theory and calibrated the relevant parameters involved in the formula by conducting flume tests using human models.Addressing vehicle instability in flood, Gordon and Stone (1973) and Keller and Mitsch (1993) carried out physical model tests and theoretical analyses, respectively.Xia, Falconer, et al. (2011), Xia, Falconer, Xiao, et al. (2014), and Xia, Teo, et al. (2011) formulated incipient velocity formulas for vehicles based on sediment incipient formula derivation through theoretical and empirical investigations.These studies have significantly advanced the theoretical framework underpinning flood-induced instability risk assessment for pedestrians and vehicles.However, it should be borne in mind that real-world conditions, owing to the intricate interplay of flood processes and the inherent distinctions between pedestrians and vehicles, equating flood risk to the instability risk faced by pedestrians and vehicles during floods might oversimplify the situation.To address this issue, several studies have been performed.For example, Bocanegra and Francés (2021) developed an assessment method to estimate the vehicle instability risk by the statistical integral of the instability hazard and vehicles' vulnerability.Tahvildari et al. (2022) quantified compound flooding across roadway networks driven by storm surges and rainfall using a coupled storm surge and two-dimensional hydrodynamic model.However, existing research often either relies on proprietary models or omits consideration of drainage systems, potentially introducing inaccuracies in urban flood simulations.Therefore, it is necessary to develop a convenient, robust, and accurate method for systematically investigating the similarities and differences between flood characteristics and the instability risk of pedestrians and vehicles, thereby providing more precise guidance for urban traffic safety during floods.
In addition, the spatiotemporal heterogeneity of rainfall in mountainous cities is significant due to the large fluctuations in terrain (Emmanuel et al., 2012).The impact of rainstorms on urban flooding is influenced not solely by rain intensity and duration but also by the specific patterns of rainfall.While research has addressed the former factors to a certain extent, limited attention has been paid to the impact of rainfall patterns (Chen et al., 2018;Luo et al., 2018;Mu et al., 2021).Nevertheless, the intricate relationship between flood characteristics and rainfall patterns remains inadequately elucidated.Consequently, to quantitatively explore the flood-induced instability risk for pedestrians and vehicles while accounting for the effects of rainfall patterns, we have integrated two open-source models, namely SWMM and Finite Volume Coastal Ocean Model (FVCOM) (Chen et al., 2003) and applied them to Yuelai New City in Chongqing, China.This modeling approach facilitated a comprehensive investigation into drainage system performance, flood characteristics, and the ensuing instability risks for typical pedestrians and vehicles (adults, children, SUVs, and sedans).Through numerical analysis, we assessed differences between flood and instability risk distributions for pedestrians and vehicles and explored the influence of rainfall patterns.This devised modeling strategy offers a robust numerical simulation framework and serves as a valuable technical resource to enhance urban flood management practices.

| Study area and data
The chosen study area for this research is Yuelai New Town, situated in the western region of the Liangjiang New Area in Chongqing, China.The selection of this area is based on its pronounced urbanization and its characteristic mountainous urban topography.Covering an urban construction land area of $6.85 km 2 , the locale encompasses a total of 900 hm 2 (excluding educational institutions, medical facilities, and municipal establishments).Among these, about 250 hm 2 constitutes residential land, with a planned residential population of around 110,000 inhabitants.To facilitate analysis, data pertinent to the drainage pipe system was processed, encompassing details such as pipe network distribution, manhole nodes, and subcatchment areas.
Digital Elevation Model (DEM) data were obtained from geospatial data cloud (https://www.gscloud.cn/),which provides a 30-m resolution elevation dataset.The elevation in the area varies between 200 and 500 m, and the vegetation is well preserved (Figure 1).Due to the lack of measured rainfall data in minutes over the years, the rainstorm intensity formula (Equation 1) of the Yubei District of Chongqing was used for the Chicago design storm method (Keifer & Chu, 1957) defined as Equations ( 2) and (3).The Chicago design storm method delineates the temporal evolution of rainfall intensity both prior to and following the peak rainfall event.This method has found application in numerous investigations (Yang et al., 2020;Yin, Yu, & Wilby, 2016;Yin, Yu, Yin, et al., 2016).Adhering to the guidelines outlined in the Standard for Design of Outdoor Wastewater Engineering (GB50014-2021), a design code in China, and recognizing that the prevailing maximum rainfall return period (typically 100 years) employed in contemporary urban flood management scenarios might fall short in capturing exceedingly severe rain events, we have generated design rainfalls with a duration of 2 h for specific return periods, encompassing 1-, 5-, 20-, 50-, 100-, and 500-year intervals.To investigate the impact of rain patterns on urban flooding, we incorporated a range of design peak coefficients (r), including 0.2, 0.5, and 0.8.The design rainfall hyetograph is shown in Figure 2.
where q is the average rainstorm intensity, L= s Á hm 2 À Á ; P is rainfall return period, year (yr); t is rainfall duration, min.
where i a , i b are the rainfall intensity before and after the rain peak, mm/min; t x , t y are the time intervals before and after the rain peak, min; r is the rain peak coefficient (0 < r < 1); a, b, and c are the local parameters in the rainstorm intensity formula.

| Modeling strategy
With the rapid development of computing technology and numerical methods, much emphasis has been placed on accurately calculating the flow movement process in the pipe network by solving the complete onedimensional Saint-Venant equation.The diffusion wave, kinematic wave, and dynamic wave methods have the advantages of clear physical meaning and high accuracy.
Among them, the dynamic wave solving process is complete, and the calculation results are the most accurate theoretically.It can simulate various complex flow patterns and complex conditions such as pipe countercurrent, alternating movement of open and full flow, water level jacking, and inlet and outlet losses, and has become the mainstream method of pipe flow simulation.
In the present research, we employed SWMM for runoff generation calculation, as it is widely recognized for its capability to simulate stormwater runoff, sewers, and drainage systems in both urban and rural settings.SWMM divides sub-basins into permeable and impermeable sections, with the impermeable portions further subdivided based on the presence of depression storage capacity.The runoff calculation in SWMM takes into account comprehensive hydrological processes such as depression filling, infiltration, and evaporation, while the convergence process is determined using the nonlinear reservoir method.The drainage system layout in the study area is illustrated in Figure 1b, where the outfall's elevation surpasses that of the downstream water body (Jialing River).In SWMM, the outfall's property is set as free, with the outfall stage determined by the minimum of critical flow depth and normal flow depth in the connecting pipe.
A significant limitation of SWMM is its inability to simulate surface flood processes.To address this limitation, we proposed a loosely coupled approach involving both SWMM and FVCOM.The selection of FVCOM for flood propagation computations in this region was based on several factors.Firstly, FVCOM is open-source and has found successful application in numerous inundation simulation studies, even though the majority have focused on coastal regions (Chen et al., 2014;Liu et al., 2022;Liu & Sasaki, 2019).By employing parallel running mode in high-performance computers, FVCOM can achieve acceptable computational efficiency while maintaining high resolution.One distinct advantage of FVCOM is its inclusion of a complete groundwater input module, which enables users to introduce volume fluxes at the bottom of the model.This particular feature renders it compatible with SWMM via manholes.It is noteworthy, however, that FVCOM's application in urban flood research is relatively uncommon.The groundwater module within FVCOM accounts for changes in volume resulting from groundwater input in the continuity equation.Groundwater fluxes must be specified at mesh nodes corresponding to locations with groundwater sources.As a result, our motivation includes showcasing the model's suitability for flood risk assessment in inland areas, particularly in elevated regions such as mountainous cities.The coupling strategy was implemented by inputting the overflow discharge (nodal flood) at manholes provided by SWMM into FVCOM through the groundwater module.As shown in Figure 3, the hydrodynamics within the pipe network was computed by SWMM, and the time series data (with intervals of 1, 5, or 10 min) representing overflow surcharges from the drainage system's manholes was then utilized as groundwater flux, serving as the boundary condition for FVCOM.

| Flood instability risk calculation of pedestrians and vehicles
Flood instability in the context of pedestrians and vehicles pertains to situations where the flood surpasses a certain submergence depth and velocity, leading to human slippage and falls, as well as passive starting risks for vehicles parked on roadways.Drawing from prior research (Chanson & Brown, 2015;Martínez-gomariz et al., 2016;Wang et al., 2021;Xia et al., 2016), the flood instability risk of pedestrians can be assessed using incipient velocity formulas (Equations 4 and 5).Pedestrians are further categorized into adults and children, considering their distinct physical attributes.
Fall down : where, U c is the critical velocity at which adults and children begin to become unstable, respectively, m/s; parameters α and β correspond to characteristic attributes of human bodies and experimental water tanks, respectively; ρ is the water density, kg/m 3 ; h f is the flood depth, m; h p and m p are the height (m) and mass (kg) of people, respectively, which can be estimated according to statistical data.These values can be estimated based on statistical data, with the mass values for adults and children derived from prior studies (Foster & Cox, 1973;Yee, 2003); a 1 and b 1 denote the characteristic parameters of individuals, satisfying the condition a 1 þ b 1 ¼ 1 (Drillis et al., 1964;Guo & Wang, 1995;Xia et al., 2016;Xia, Falconer, Wang, et al., 2014); a 2 and b 2 are the linear relation coefficients between human volume and body weight, respectively.The parameter values are presented in Table 1.To accurately simulate real-life scenarios in the assessment, it is assumed that individuals become unstable once the flood depth exceeds their neck height, resulting in either slipping or falling.This assumption considers the combined height of the head and neck as 0.25 m.Consequently, the critical flood depths (or safety depths) for adults and children are taken as 1.39 and 1.01 m, respectively.Figure 4a graphically displays the incipient velocity of individuals at varying flood depths.
Adhering to the principle of assessing flood vulnerability based on the most unfavorable conditions and building upon previous research (Wang et al., 2021;Xia et al., 2016), the minimum velocity of instability (slip or fall) is selected for assessing the risk of pedestrians (see Figure 4b).Thus, the incipient velocity for adults and children is computed using Equations ( 6) and ( 7), respectively.
SUVs and sedans were selected as the typical vehicles since they are commonly used.Adhering to the principle of maximum vulnerability to floods (Xia, Falconer, Xiao, et al., 2014;Xia, Teo, et al., 2011), when vehicles are perpendicular (90 ) to the incoming flood flow, they are at a heightened risk of being carried away.Consequently, the incipient velocity, calculated using Equation (8), serves as the basis for assessing the risk of vehicle instability: where, U c is the critical speed at which vehicles start to become unstable, m/s; α and β are the parameters associated to the vehicle tyre type, appearance, and roughness of the road surface (Xia, Falconer, Xiao, et al., 2014); h c is the vehicle height, m; g is the gravitational acceleration, m/s 2 ; b c is the width of the vehicle, m; ρ c and ρ f are the density of vehicles and flood water, respectively, kg/m 3 ; γ c and γ f are the specific weights of vehicles and water, respectively; h k is the critical depth at which the vehicle begins to float, m.The total weight of vehicles with standard equipment is given in Table 2, and the data were obtained from the official website of the vehicle brand.A sensitivity analysis assessing the impact of mass values on the instability index was conducted, and the findings are discussed in Section 4.3.The parameter values for Equations ( 8) and ( 9) are presented in Table 3.It is assumed that SUVs and sedans start to float in case the flood depth reaches 0.6 and 0.4 m, respectively, according to the experimental studies by Xia, Falconer, Xiao, et al. (2014), where these specific water depths, 0.6 m for SUVs (Audi Q7) and 0.4 m for sedans (Honda Accord), were identified as the thresholds for the onset of floating.Hence, to maintain consistency, the same vehicle types and masses as utilized in their research have been retained for subsequent computations of the instability index for vehicles (Figure 5).

| Instability index of pedestrians and vehicles in flood
The flood instability index (R) of pedestrians and vehicles can be calculated by dividing the flood flow velocity U f by the critical speed (incipient motion speed) U c (Xia, Falconer, et al., 2011).When the resulting index exceeds 1, pedestrians and vehicles become unstable within the Table 4 presents the classification of index levels.

| Water volume balance
To validate the feasibility of the model coupling method, we conducted an analysis of water volume consistency between the coupled model and two other calculation methods under identical computational conditions using an idealized scenario.Within the configuration of the coupled model, the runoff discharge was computed using Equation ( 11) and subsequently utilized as a boundary condition in the FVCOM model for driving the simulation.At each time step, the surface flood volume was computed and compared against the runoff simulations generated by SWMM and the accurate values obtained through the formula method using Equation (11).The computational domain was a square area measuring 100 m in both length and width.The input rainfall is depicted in Figure 6a.The simulation spanned a duration of 4 h.The results of the comparison using various methods are presented in Figure 6b.Notably, the surface flood volume outcomes produced by the coupled model were consistent with the precise runoff computed by the formula method and the runoff simulated by SWMM.
where, Q m is the runoff of the mth calculation unit, m 3 /s; i is the rainfall intensity, mm/min; f is the infiltration rate, mm/h; S m is the area of the mth calculation unit, m 2 .The Horton model (Equation 12; Beven & Robert, 2014;Muleta, 2006;Rossman, 2015Rossman, , 2016;;Vijay, 2017) was adopted to estimate the infiltration rate.
where, f t is the infiltration rate at time t, mm/h; f c is the infiltration rate at steady state, mm/h; f 0 is the initial infiltration rate of soil, mm/h; k is the attenuation coefficient, which is related to the physical properties of the soil, 1/h; t is time, h.

| Real drainage cases
To further assess the performance of the coupled model in real flood scenarios, we selected two recorded rainfall events that occurred in the study area on July 14, 2017, and September 1, 2017.These events were chosen for verification purposes.The measured runoff at Outfall II and Outfall III was compared with the simulated since the monitoring data at the two outfalls were more T A B L E 3 Parameter values of vehicles (Shu et al., 2008(Shu et al., , 2011;;Wang et al., 2021;Xia, Falconer, Xiao, et al., 2014).continuous and stable compared with others.The Nash-Sutcliffe efficiency coefficient (ENS) was employed as a measure to evaluate the degree of agreement between the model outcomes and the observed data.As illustrated in Figure 7, the simulated runoff and the actual measurements taken at the outfalls exhibited strong alignment.
The ENS values for these two events were 0.82 and 0.86, respectively, which indicates a high level of reliability and consistency of the coupled model.

| Effect of the rain pattern on flood characteristics
The flood dynamics within the study area were determined by inputting varying rainfall hyetographs with distinct return periods and peak coefficients into the coupled model.When assessing the influence of rain patterns, three key flood characteristics-namely, flood area, flood volume, and peak flood area-were chosen due to their widespread use as indicators in urban flood risk assessment (Zeng et al., 2022).As shown in Figure 8, it can be found that the variation in flood areas closely mirrors the corresponding rainfall hyetographs.Specifically, an increase in the rainfall return period resulted in a corresponding enlargement of the flood area.Furthermore, the timing of the rain peak plays a pivotal role: an earlier occurrence of the rain peak correlates with an earlier manifestation of the peak flood area, and vice versa.Notably, in cases of later peak rainfalls (e.g., r = 0.5 and r = 0.8), a pronounced period of rapid flood area expansion was observed during the initial stages of rainfall, especially during time intervals of $300-900 s, as observed in Figure 8b,c rapid expansion stage, the rate of flood area increment increased as the rainfall return period increased.Thus, in the case of rainstorms characterized by delayed peak times and longer return periods, it becomes imperative to not only monitor changes in flood levels before and after the peak rainfall but also pay close attention to the rapid expansion of flood areas at the onset of the rainfall.Taking proactive measures during this initial phase is crucial to prevent potential escalation of the situation.
The quantification of water accumulation in floodprone regions can be achieved through the evaluation of flood volume.Figure 9 presents the computation of the water accumulation process across the study area under differing rainfall conditions.A clear trend was observed: an increase in rainfall return period was paralleled by increase in accumulated flood volume.In situations of earlier peak rainfalls, the flood volume experienced a rapid surge during the initial rain stages.Conversely, as the rain peak was postponed, the period of rapid flood volume augmentation also experienced a delay.Notably, changes in the occurrence time of the rain peak did not significantly impact the final flood volume.Analysis of flood area fluctuations revealed that for earlier peak rainfalls, both flood areas and volumes experienced rapid expansion, thereby leaving a limited window for emergency response and disaster mitigation preparation.In contrast, for later peak rainfalls, despite a rapid initial flood area escalation, the increase in flood volume was relatively more gradual compared with earlier peak scenarios.Consequently, this phase offers a critical opportunity to undertake measures aimed at mitigating such flood occurrences.The occurrence of floods remains constant; however, the timing of the flood peak-which often correlates with the most severe impacts during an event-can differ, leading to diverse response strategies.In cases of early peak rainfall, taking action before the onset of rain is a natural approach.On the other hand, for later peak rains, it becomes evident that proactive attention (and requisite actions) should also be focused on reducing flood risks during that stage.In essence, the timing of emergency response might need to be advanced for this specific scenario.
Upon scrutinizing the peak flood areas under various rainfall scenarios, as displayed in Figure 10a, we found that for rainfall events with return periods smaller than 100 years, the peak flood area experienced rapid growth as the return period increased, with the impact of rain peak timing being relatively minor.However, for events with return periods surpassing 100 years, the growth in peak flood areas was more gradual.Under equal rainfall return periods, peak flood areas resulting from later peak rainfalls were larger than those resulting from earlier peak rainfalls.This difference diminished as the rainfall return periods increased.Interestingly, for a rainfall event with a return period of 500 years, variations in peak flood areas due to differing rainfall peak conditions were less apparent.In Figure 10b, where the total rainfall remained constant (e.g., 52.4 mm for P = 1 yr, regardless of r values), the peak flood areas occurred at varying times due to r and generally exhibited a time lag compared with the rain peak (e.g., in Figure 8, the peak flood areas of the rainfall events with r = 0.2, 0.5, and 0.8 occurred at around 2000, 4100, and 6200 s, respectively, while the corresponding rain peaks occurred at 1440, 3600, and 5760 s, respectively).As indicated by the reddotted line shown in Figure 10b, for earlier peak rainfalls, for example, r = 0.2, the accumulated rain at the rain peak time was about 9.7 mm, lower than that of later peak rainfalls (e.g., r = 0.5 with accumulated rain of about 25.3 mm and r = 0.8 with accumulated rainfall of about 40.9 mm).This discrepancy could largely be attributed to the different water (rain) volumes responsible for causing the peak flood areas, resulting in varied peak flood areas for distinct r values.Consequently, later peak rain events tended to exhibit larger peak flood areas than their earlier peak counterparts.This assertion aligns with observations made when analyzing the change in flood volume, as portrayed in Figure 9, as the system did not incur water losses (infiltration is not considered during flood propagation).

| Performance of drainage systems and the resultant flood
Next, we assessed the performance of drainage systems and the resultant flood under earlier peak rainfalls.Figure 11a reveals the distribution of overflow manholes across distinct rainfall return periods.Overflow manholes were primarily concentrated in regions characterized by low and level terrain.An example is the eastern side of Yuelai Avenue, where the steep mountain slope could lead to a rapid convergence of runoff even under minor return periods.This convergence overwhelmed the pipe drainage system, prompting overflow at downstream manholes.Notably, the local topography permitted the excess surface runoff from community blocks near the Jialing River to flow into the river channels, mitigating the severity of overflow.Low-lying areas in the northwest, near the Jialing River, were also vulnerable to manhole overflow during substantial return periods.Conversely, due to the elevated terrain and limited manholes along Yuecheng Road, overflow incidents were absent.Specifically, overflow manholes were prevalent in areas characterized by lower terrain on the eastern side.The presence of a river channel connecting to the Jialing River in the southwest contributed to surface runoff reduction, thereby mitigating overflow even during highreturn-period rainfalls.
Figure 11b reveals the rapid escalation in the number of overflow manholes across the study area under minor rainfall return periods, especially when the return period was below 5 years.In the case of a 1-year return period, only a few manholes experienced overflow, predominantly along Yuelai Avenue.For P = 5 yr, the number of overflow manholes was 510, accounting for 15.1% of the total manholes, with the majority distributed along Yuelai Avenue, Xinyue Road, and Yuecheng Road.For P = 100 yr, the number of overflow manholes increased to 740, with new overflow points primarily situated on Tongmao Avenue, Yuerong Road, and Jinshan Avenue.For an extended return period of 500 years (P = 500 yr), the overflow manholes escalated to 820, accounting for 24.3% of the total manholes.
According to the Standard for Design of Outdoor Wastewater Engineering (GB50014-2021) and the Technical Standard for Waterlogging Prevention and Control in Mountainous Cities (DBJ50/T-427-2022, a design code of Chongqing, China), the minimum design standard for rainwater pipes in the central urban areas of megacities was set at a 3-year return period.Importantly, the drainage capacity of the study area's pipe network was slightly below these prescribed standards.Therefore, emphasis should be placed on pipe renovation, particularly in vulnerable areas such as Yuelai Avenue.In the context of mountainous cities, the design of drainage systems must

| Flood instability of pedestrians and vehicles
The distribution of flood instability risk for children, adults, sedans, and SUVs across various rainfall return periods is depicted in Figure 13.The analysis revealed that the range of extreme risk for sedans exhibited the broadest distribution, followed by SUVs, while the extreme risk areas for children and adults were comparatively smaller and pertained to vehicles.Notably, the areas of extreme risk for SUVs and sedans predominantly occupied main roads, whereas those for children and adults were primarily concentrated in the southern valley region.
Upon comparing Figure 12 with Figure 13, we found that areas characterized by shallow flood depths (e.g., <0.1 m) were consistent with minor risk zones for pedestrians and vehicles.Given that the critical value h f for children to experience slippage, as defined in Equation ( 7), was 0.16 m, even a slight inundation exposed children to slipping hazards.Furthermore, the flood flow velocities in regions marked by depths ranging from 0.1 to 0.9 m fluctuated between 0.6 and 1.8 m/s.In select locales, the maximum flood velocity exceeded 3 m/s.The instability risks for pedestrians and vehicles were subject to substantial variation based on the flood's hydrodynamic processes, which, in turn, were influenced by topography and drainage system performance.Figure 14 illustrates that the gradient of incipient velocity concerning flood depth was more pronounced for vehicles compared with pedestrians.This suggests that the instability index of vehicles demonstrated heightened sensitivity  Figure 15 outlines the incipient velocity of pedestrians and vehicles at varying masses and flood depths.As mass values increased, the incipient velocity escalated for both pedestrians and vehicles.For children, the incipient velocity displayed heightened sensitivity to masses when flood depth spanned 0.1-0.5 m, a range below the safety depth of 1.01 m.Adults, on the other hand, exhibited sensitivity between flood depths of 0.2 and 0.6 m.Notably, for SUVs and sedans, the sensitivity of the incipient velocity to masses increased as flood depth approached critical levels (0.6 m for SUVs and 0.4 m for sedans).This indicated that heavier vehicles possessed a greater capacity to resist instability prior to flood reaching critical depth.For pedestrians, increased mass only contributed to safety when flood depth substantially remained below the safety threshold.
Figure 16 presents a comprehensive overview of risk areas concerning sedans, SUVs, children, and adults.Notably, the expansion of risk areas for both pedestrians and vehicles was directly correlated with increased rainfall return periods, with a swift expansion observable under smaller return periods.Across both pedestrians and vehicles, the predominant presence was in the realm of minor risk areas.Comparable between adults and children, the minor risk area size exceeded that of sedans and SUVs.However, within the same return period, the extreme risk area for children slightly exceeded that of adults.In terms of vehicles, within the same return period, the minor risk area of sedans was marginally smaller than that of SUVs, yet the extreme risk area was comparatively larger.Importantly, the no-risk areas for pedestrians and vehicles exhibited minimal variation across distinct return periods attributed to their predominant location in elevated terrains, rendering them less susceptible to flooding.Besides, the low-and moderaterisk areas for pedestrians and vehicles were relatively compact and gradually increased in extent beyond the 100-year return period, experiencing a slight reduction for the 500-year return period attributed to the transformation of certain low-and moderate-risk zones into areas of extreme risk.

| CONCLUSIONS
In the context of climate change and rapid urbanization, the occurrence of urban floods triggered by extreme rainstorms has become increasingly frequent, presenting a significant menace to urban traffic safety.In order to assess the attributes and mechanisms of flood instability risk for pedestrians and vehicles, alongside the influence of precipitation patterns, a novel integrated flood model combining SWMM and FVCOM was introduced and employed within Chongqing's Yuelai New Town, China.
For rainstorms with later peak timings (such as r = 0.5 and 0.8), a notable surge in flood area was witnessed during the initial stages of precipitation.Consequently, when dealing with later peak rainstorms characterized by lengthy return periods, it is imperative not only to focus on the water accumulation prior to and following the peak rainfall but also to give heed to the swift escalation phase of flood areas during the onset of rainfall.Conversely, for rainstorms with earlier peaks, the flood volume displayed a rapid escalation at the inception of rainfall, with the rapid expansion phase of flood volume also deferred as the rainfall peak was postponed.In scenarios where the rainfall return period remained below 100 years, the peak flood area exhibited swift augmentation with increasing return periods, with the influence of rainfall peaks being relatively inconsequential.Across comparable return periods, rainstorms featuring later peaks prompted larger peak flood areas, although this influence waned with escalated rainfall return periods.
Among the studied elements, sedans exhibited the most widespread extreme risk areas, succeeded by SUVs, while the extreme risk zones for children and adults were relatively smaller in comparison.Predominantly situated on main thoroughfares, the extreme risk areas for SUVs and sedans were concentrated, whereas those for children and adults were more prominent in the southern valley.The susceptibility of pedestrians and vehicles to instability risks can manifest considerable variability based on the hydrodynamic processes of flooding, notably influenced by topography and the efficiency of drainage systems.
The proposed modeling method offers a numerical simulation that can serve as a valuable technical resource for urban flood management and disaster mitigation strategies.

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I G U R E 1 The topography of the study area and the drainage system: (a) Digital Elevation Model; (b): the drainage system.

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I G U R E 3 The model framework.DEM, Digital Elevation Model; FVCOM, Finite Volume Coastal Ocean Model; SWMM, Storm Water Management Model.

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I G U R E 4 The incipient velocity of people (a) for different instability types (slip down or fall down); (b) adhering to the principle of the most unfavorable condition.T A B L E 2 The mass of vehicles with standard equipment.facilitate a clear representation of the instability index distributions, instances where the index value surpasses 1 have been standardized to 1.25.This adjustment expands the index range to [0, +1.25].
. During this F I G U R E 6 (a) Rainfall input for the idealized case and (b) water volume comparison using different methods.SWMM, Storm Water Management Model.F I G U R E 7 Comparison of the simulated runoff using the coupled model and the measured (a) at Outfall II for the rainfall on July 14, 2017; (b) at Outfall III for the rainfall on September 1, 2017.ENS, Nash-Sutcliffe efficiency coefficient.

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I G U R E 8 Variations of flood areas with time (a) r = 0.2; (b) r = 0.5; (c) r = 0.8.

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I G U R E 9 Variations of flood volume with time (a) r = 0.2; (b) r = 0.5; (c) r = 0.8.

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I G U R E 1 0 (a) Variations of peak flood areas under different rain conditions; (b) The designed rainfall hyetograph and the accumulated rain (r = 0.2, 0.5, and 0.8) for P = 1 yr.fully account for local terrain factors.Additionally, the drainage capacity of the designed pipe system should undergo validation using numerical flood models.The flood depth and velocity distributions are shown in Figure 12a,b, respectively.Across all scenarios, areas with a flood depth of <0.1 m were F I G U R E 1 1 The distribution (a) and the number (b) of overflow manholes under different rainfall return periods.predominant, characterized by modest flow velocities.Under scenarios with minor rainfall return periods (e.g., P = 1 yr), flooding primarily affected main roads and low-lying regions.A return period of 5 years (P = 5 yr) led to a substantial expansion of flood areas characterized by low water depth (<0.1 m).As return periods increased, the flood area gradually enlarged.Notably, regions with substantial flood depth (>0.9 m) were concentrated in the southern valley areas.Areas with flood depths ranging between 0.1 and 0.9 m exhibited relatively high flow velocities, primarily found along Xinyue Road, Tongmao Avenue, and Guobo Avenue, areas characterized by low terrain and steep slopes.Due to pronounced topographical variations, flow velocities in the southern region exceeded those in other areas, potentially elevating flood instability risks for pedestrians and vehicles.According to the Technical Code for Urban Flooding Prevention and Control (GB51222-2017, a technical code of China), when the flood depth remained below 0.15 m, the threat to pedestrians and vehicles was relatively low and fell under the category of low risk.However, a flood depth exceeding 0.15 m could trigger pedestrian instability or vehicle stalling.Further, if the flood depth exceeded 0.35 m, vehicles could face the risk of floating or being washed away.

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I G U R E 1 2 The maximum flood depth distribution (a) and flow velocity distribution; (b) under different rainfall return periods.
to changes in flood depth relative to pedestrians.Under conditions where h f >0.31 m and flood flow velocity v > 2.71 m/s, SUVs exhibited low risks of instability, and adults and sedans faced extreme risks.In scenarios where h f >0.39 m and flood flow velocity v > 1.56 m/s, SUVs and adults encountered low risks and moderate risks, respectively, and sedans and children faced extreme risks.With h f >0.47 m and flood flow velocity v > 2.0 m/s, SUVs and

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I G U R E 1 3 Instability risk distributions under different rainfall return periods (a) sedans; (b) SUVs; (c) children; (d) adults.adults were exposed to extreme risks.If h f >0.59 m and flood flow velocity v > 1.08 m/s, adults faced moderate risks, and SUVs and children confronted extreme risks.

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I G U R E 1 4 The comparison of vehicles and pedestrians on the incipient velocity.F I G U R E 1 5 The incipient velocity of (a) pedestrians and (b) vehicles for different masses.

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I G U R E 1 6 Risk areas of pedestrians and vehicles under different rainfall return periods (a) Sedans; (b) SUVs; (c) children; (d) adults.