Assessment of Object-Level Flood Impact Considering Pump Station Operations in Coastal Urban Areas

Abstract

Flooding increasingly threatens lives and property under climate change and rapid urbanization. Mobile pumping stations offer a practical and cost-effective solution for flood protection in low-lying, densely populated coastal areas. However, previous studies typically used simplified methods to represent pump stations, and few have integrated pump operations into high-resolution simulations of multi-source urban flooding. This study develops a High-Performance Integrated Hydrodynamic Modeling System–Pumping System Model–Flood Impact Assessment Model (i.e., HiPIMS-PSM-FIM) framework to evaluate object-level exposure and quantify the benefits of pumping. In this framework, the PSM is two-way coupled with HiPIMS using a Source Coupling Method to simulate spatiotemporal flood dynamics. The results are then integrated with exposure data through FIM to identify risks and support mitigation strategies. The framework is applied to a multi-source flood in Yuhuan City, Zhejiang Province, China, at 3 m resolution, and shows strong agreement with field surveys. Vulnerability analysis shows Children > Sedans > Adults > SUVs, with educational facilities facing highest risks. Sensitivity results to pumping rates demonstrate that mobile pumping can reduce the affected population by 82% and decrease impacts on key facilities and roads, demonstrating the framework’s robustness and practical value for enhancing urban flood resilience.

1. Introduction

Climate change and rapid urbanization are increasing the frequency and severity of urban floods, amplifying risks in coastal and estuarine regions [1,2]. For example, Hurricane Ida in the United States caused 116 deaths and a direct economic loss of USD 102.3 billion in September 2021, while Depression Bernd in Germany in July 2021 resulted in 196 deaths and EUR 35.99 billion in losses. Projections suggest that global coastal areas could face annual economic damages exceeding USD 1 trillion by the mid-21st century if proactive adaptation measures are not implemented [3]. These figures highlight the urgent need for effective flood risk mitigation strategies to safeguard lives, protect property, and support sustainable development.

Mobile pumping stations have emerged as a cost-effective and flexible measure for mitigating flood impacts, particularly in low-lying areas where fixed hydraulic structures are insufficient. Their ability to rapidly evacuate water provides a critical adaptation option. However, managing mobile pumping stations precisely remains a challenge due to the highly transient nature of urban flooding and the nonlinear interactions among multiple flooding drivers, such as rainfall, tide, and storm surges. Hydrodynamic models provide a valuable means of representing these processes and have become indispensable tools to support flood risk assessment and management [4,5].

Previous attempts to incorporate pumping station effects into hydrodynamic models have often relied on simplified representations, such as kinematic waves and diffusion waves theories to solve simplified shallow water equations (SWEs). Cea, et al. [6] and Costabile, et al. [7] proposed that these two theories are constrained by their assumptions and are unsuitable for complex urban terrain. Dynamic wave theory, with its automatic shock-capturing capability and robustness in solving the fully two-dimensional (2-D) nonlinear SWEs, has since been adopted and has shown great potential for simulating transient urban floods [8,9,10]. In fully 2-D SWEs-based hydrodynamic models, two main approaches exist for representing pumps: boundary condition methods and source/sink term coupling. Commercial software such as MIKE 21 integrates MIKE FLOOD using boundary conditions to represent pumping. Yet, this approach has drawbacks for mobile pump stations, including the need for frequent water level and discharge exchange at each time step, which may introduce significant calculation errors and the risk of numerical instability if boundary conditions are poorly specified.

To better capture the interactions between surface flow dynamics and mobile pump operations, Angeloudis, et al. [11] proposed a source/sink term coupling method that directly represents pumping within a 2-D SWE model. This approach has since been implemented in models such as Infoworks ICM, EFDC, and HEC-RAS. Nonetheless, challenges remain in simulating multi-driver urban floods (e.g., intense rainfall, tidal levels, and storm surges) under complex topography, and in quantifying how pump operations influence flood impacts in coastal and estuarine cities. While source/sink term coupling has been used for fluvial flood simulations, its application in urban multi-source flooding and risk assessment is still limited. Therefore, effective modeling approaches are needed to better understand the drainage mechanisms of mobile pumping stations under compound flooding conditions and to enhance flood resilience in urban environments.

Another challenge lies in assessing urban flood exposure and impacts, which has historically been constrained by sparse data. Recent advances have improved data availability through sources such as OpenStreetMap, Google Earth, global data products, and local archives [12]. These data have enabled the development of various flood risk evaluation metrics for the quantitative assessment of exposed objects. For instance, Wade, et al. [13] proposed a hazard rating method based on flow velocity, depth, and debris presence, while Xia, et al. [14] introduced an algorithm for assessing the flood hazard degree (HD) to people and vehicles, which has since been widely adopted [15]. The Joint Research Centre (JRC) of the European Commission [16] established a global database of flood depth–damage functions for buildings, roads, and agricultural lands. Chen, Zhao, Liang, Maharjan and Joshi [12] applied such functions to assess damage from glacial lake outburst floods. These advances underscore the importance of integrating exposure and impact assessment into urban flood modeling.

In this context, the present study develops a high-resolution urban flood modeling framework that integrates mobile pump station operations with impact assessment, leveraging parallelized high-performance computing and multi-source geographic information. The framework quantitatively evaluates pumping effectiveness and provides object-level exposure and impact assessments for real urban environments. Yuhuan City in Zhejiang Province, China, was selected as the case study due to its typical coastal setting and its recent history of severe flood-related economic losses. The remainder of this paper is structured as follows: Section 2 introduces the study area and the proposed modeling framework, Section 3 presents simulation results and validations, Section 4 provides discussion, and Section 5 summarizes the conclusions.

2. Materials and Methods

This section covers the study-area characteristics (Section 2.1), the numerical model configuration—governing equations and coupling method (Section 2.2), the numerical experiment design (Section 2.3), and the evaluation metrics (Section 2.4).

2.1. Study Area

To validate the performance and robustness of the proposed method, HiPIMS-PSM-FIM is used to reproduce the severe urban flood event induced by Typhoon Morakot in Yuhuan City, Zhejiang Province in China (Figure 1). From 29 to 30 September 2009, Typhoon Morakot brought an extreme rainstorm; the average rainfall reached 327.7 mm in Yuhuan City. The rainstorm impacted approximately 320,000 people, damaging almost 3500 hectares of agricultural products and causing direct economic losses of 51 million RMB (USD 7.97 million). The inundation depth in low-lying areas in Damaiyu was reported to exceed 1 m. Many roads, buildings, and agricultural lands were affected by the flooding, resulting in substantial damage.

As shown in Figure 1a, the 53.95 km² computational domain is surrounded by mountains at the north, east, and south, and the independent Qinglan River system is open to the East China Sea to the west. Figure 1b manifests the land use such as roads, buildings, and agricultural lands in the domain. The domain exhibits hydrogeological characteristics that influence flood behavior. Elevation drops sharply from over 300 m in mountainous areas to below 5 m on the coastal plain, promoting rapid runoff concentration. The old town in the city has a shallow groundwater table that restricts subsurface drainage. Tidal influence extends upstream and interacts with channel outfalls, and existing drainage infrastructure provides limited capacity during extreme events. The spatial distribution of the population is displayed in Figure 1c to support the assessment of impacted people during Typhoon Morakot. Field investigations revealed that the extreme rainstorm triggered upstream flooding, resulting in a compound flood event driven by rainstorms, upstream flooding, and high tides in the study area. These factors make the case valuable for validating the proposed modeling framework.

2.2. Numerical Methods

The structure of the proposed modeling framework is illustrated in Figure 2. It integrates the High-Performance Integrated Hydrodynamic Modeling System (HiPIMS) [8], the Pumping System Model (PSM), and an object-level Flood Impact Assessment Model (FIM). HiPIMS is used to simulate flood dynamics and has been widely applied to urban flooding under compound drivers (e.g., rainfall, tidal levels, typhoons), supporting applications in estuarine and coastal cities [12,17,18]. A high-resolution digital elevation model (DEM) is required to set up HiPIMS for flood simulation. Information on the location and operation of hydraulic structures, such as mobile pump stations, is required for the adaptive scheduling module of PSM.

The PSM is coupled with HiPIMS using a two-way source-term coupling method (i.e., SCM). This GPU-accelerated framework efficiently simulates the spatiotemporal evolution of flood dynamics, including inundation depth, velocity, and arrival time. The spatially distributed flood outputs are then combined with exposure datasets (e.g., buildings, roads, and pedestrian distributions) to identify potential exposure to flooding and inform sustainable mitigation solutions in the FIM. Established depth–damage curves, hazard rating formulas, and hazard degree algorithms are applied to quantitatively assess the effectiveness of pumping on exposed objects. The following subsections describe the components and the coupling process of the HiPIMS-PSM-FIM modeling framework.

2.2.1. Hydrodynamic Model

HiPIMS solves the full 2D shallow water equations (SWEs) written in a matrix form as follows [8]:

$${\displaystyle \frac{\partial q}{\partial t}}+{\displaystyle \frac{\partial f}{\partial x}}+{\displaystyle \frac{\partial g}{\partial y}}=s$$

(1)

where t is the time, x and y represent the Cartesian coordinates, q denotes the vector of flow variables, f and g are the flux vectors in the x- and y-direction, respectively, and s is the source term vector. The vector terms are defined as

$$\begin{array}{l}q={\left[\begin{array}{ccc}\eta & q_x& q_y\end{array}\right]}^{\mathrm{T}}; f={\left[\begin{array}{ccc}{q}_x& u{q}_x+g({\eta }^2-2\eta z_b)/2& u{q}_y\end{array}\right]}^{\mathrm{T}};\\ g={\left[\begin{array}{ccc}{q}_y& v{q}_y& v{q}_y+g({\eta }^2-2\eta z_b)/2\end{array}\right]}^{\mathrm{T}};\\ s={\left[\begin{array}{ccc}R+P& -g\eta \partial z_b/\partial x-{\displaystyle \raisebox{1ex}{${\tau }_{bx}$}\!\left/ \!\raisebox{-1ex}{$\rho $}\right.}& -g\eta \partial z_b/\partial y-{\displaystyle \raisebox{1ex}{${\tau }_{by}$}\!\left/ \!\raisebox{-1ex}{$\rho $}\right.}\end{array}\right]}^{\mathrm{T}}\end{array}$$

(2)

where η = h + z_b represents the water level; h is the water depth; z_b represents the bed elevation above the datum; u and v denote the depth-averaged velocities in the two Cartesian directions; q_x = uh and q_y = vh are the unit-width discharges in the x- and y- directions, respectively; g is the acceleration due to gravity; R = r − i − d represents the rainfall-runoff rate, where r, i, and d denote the rainfall rate, infiltration rate, and drainage loss, the parameters for estimating i using the Green–Ampt model [19,20]; d is valued at a rate of 13 mm/h according to [21]; ρ is the water density; ∂z_b/∂x and ∂z_b/∂y define the bed slope in the two Cartesian directions; and τ_bx and τ_by are the bed friction stresses, calculated using the Manning equation as follows:

$${\tau }_{bx}=\rho C_{f}u\sqrt{u^2+v^2};{\tau }_{by}=\rho C_{f}v\sqrt{u^2+v^2}$$

(3)

where C_f = gn²/h^1/3 is the bed roughness coefficient with n representing the Manning coefficient, P represents the pumping rate, which is newly added to the source/sink term by the source term coupling method (SCM), and the solving method will be introduced in detail in Section 2.2.2.

To improve computational efficiency, the framework is GPU-accelerated with NVIDIA CUDA, enabling street-scale compound-flood simulations [22,23].

2.2.2. Pumping System Model (PSM)

To capture pump effects during the event, the PSM is fully coupled with HiPIMS via a mass-conservative source–sink scheme. This internal source coupling directly resolves localized drawdown and flow redistribution. In the PSM, pump stations can be automatically identified, and the corresponding operational information is systematically stored. As illustrated in Figure 2, the red computational grid corresponds to the source-term pumping unit in Equation (2), while the blue cell denotes its paired sink-term pumping unit. Figure 3 assumed that cells (i + 1, 1) and (i + 2, j − 2) store the pumping information of Pump Station #1 (P1) and Pump Station #2 (P2), functioning as source-term pump station units in Equation (2). And cells (i − 1, j − 2) and (i, j) represent the corresponding sink-term pump station units of P1 and P2. The PSM rigorously maintains mass conservation in the above 2D SWEs and ensures the model’s ability to dynamically represent pump station operations in urban flood modeling.

After automatically identifying the source/sink cell stores profile of the pumping process, the PSM incorporates the designed discharge of pump Station #i as source/sink terms. PSM can be expressed as

$$\begin{array}{l}{P}_{i+1,1}=-q_{P1}/\Delta x;P_{i+2,j-2}=-q_{P2}/\Delta x;\\ P_{i-1,j-2}=-q_{P1}/\Delta x;P_{i,j}=-q_{P2}/\Delta x\end{array}$$

(4)

where $q_{Pi}=Q_{Pi}/{\mathsf{\Omega }}_c$, $Q_{Pi}$ represents the designed discharge of pump station #i, ${\mathsf{\Omega }}_c$ denotes the unit area of the corresponding computational cell, and Δx stands for the edge length of the cell for spatial discretization.

2.2.3. Flood Impact Assessment Model (FIM)

The Flood Impact Model maps hydrodynamic outputs to object-level exposure using depth thresholds and stability/damage functions. Based on the HiPIMS-PSM-predicted physical characteristics including water depth, flow velocities, and flood arrival time, potential exposures to the flood event can be estimated by overlaying the exposure datasets with flood simulation results. Besides flood exposures, quantifying the potential impact of floods is necessary for understanding and adapting the corresponding risk. Estimating flood hazard in individual flood zones can be achieved using the indicator factor, i.e., the hazard rating (HR) [13], as given by $HR=h\times \left(\sqrt{u^2+v^2}+0.5\right)+DF$, in which HR represents flood hazard rating and DF denotes debris factor (valued 0, 0.5, 1 for different debris). Low flood hazard: HR < 0.75; medium flood hazard: 0.75 ≤ HR < 1.25; high flood hazard: 1.25 ≤ HR < 2.0; extreme flood hazard: HR ≥ 2.0. In flood zones, the extent of exposure to people and vehicles could be evaluated by the hazard degree (i.e., $HR=\mathrm{Min}\left(1.0,\sqrt{u^2+v^2}/U_C\right)$) [24,25]; the value for U_c (Figure 4) depends on the category of exposed object (i.e., child, adult, sedan, and SUV) and inundation depth. Assessing the direct damage to buildings, roads, and agricultural lands through depth–damage curves [16,26], d represents inundation depth in Figure 5.

2.3. Experiment Design and Scenarios

This study designs a set of controlled numerical experiments to quantify how mobile pumping operations alter compound urban flooding in a coastal city. A high-resolution DEM, which provides the foundation for all hydrodynamic simulations, is shown in Figure 6. The topographic data is corrected to resolve the detected defects through visual inspection based on OSM data, ArcGIS 10.8 Server, and Google Earth. The domain is discretized at a 3 m resolution to resolve street-scale pathways and micro-basins. The Gauge 1–3# is situated at the upper reaches of the Qinglantang River, Liurong River, and Gushun River. The validated filed survey data at Gauge 1#–3# obtained by Zhejiang Institute of Hydraulics & Estuary is 3.9 m, 3.3 m, and 3.8 m, respectively. The values of Manning coefficients in Equation (3) are 0.02 for roads, plazas, and parking spaces; 0.05 for buildings; 0.08 for mountain areas and green fields; and 0.035 for bare grounds and water bodies [27].

The available hydrometeorological data consist chiefly of precipitation and tidal-level measurements, which force the flood in the study domain. Figure 7a illustrates time series of hourly and accumulated rainfall during Typhoon Morakot measured at the rainfall station of Xiaochenao, while Figure 7b presents tidal level at the Qinglan River during the event at the tidal station of Damaiyu. Driven by the spatially varying rainfall and tidal boundary conditions, the simulation is run for 36 h between 10:00 on 29th and 21:00 on 30th September.

Two simulation scenarios are configured to evaluate the effectiveness of mobile pumping interventions. First, a baseline scenario without pumping is established using the topographical and hydrometeorological data described above, following the model configuration in Section 2.2. Second, a mitigation scenario incorporates a mobile pumping station (P1) at the most flood-prone location identified from baseline results. The pump is designed with a drainage capacity of 27 m³/s (pumping rate P = 1 m/s in Equation (2)) and operates under threshold-based activation: pumping initiates when local inundation depth exceeds 0.30 m and ceases otherwise. Additionally, a sensitivity analysis examines five pumping rates (P = 1, 0.1, 0.01, 0.001, and 0.0001 m/s) while maintaining all other parameters constant.

2.4. Model Evaluation Metrics

Model performance is evaluated using the Root Mean Squared Error (RMSE) and the Fit statistic (F). The RMSE measures the average difference between the simulated/predicted results and the observed/field survey data, which is expressed as

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{\left(S_i-O_i\right)}^2}}$$

(5)

where S_i and O_i denote the simulated/predicted and observed/field survey data, respectively, and N denotes the number of comparisons that can be made.

The F reflects is calculated by dividing the variance between groups by the variance within groups, which is defined as

$$F\left(\%\right)={\displaystyle \frac{A-B}{A+B+C}}\times 100$$

(6)

where A represents the number of correctly predicted/simulated flooded cells, B is the number of cells erroneously predicted/simulated as flooded, and C is the number of cells erroneously predicted/simulated as drained.

3. Results

3.1. Hydrodynamic Performance and Validation

This subsection presents hydrodynamic performance and outcomes, including the time series of water levels and flooding processes, validated against observations. Figure 8 illustrates the hydrographs of Gauge 1#–3# (located as shown in Figure 6) during Typhoon Morakot. The arrival time of the maximum water level was determined from hydrographs, which was delayed almost one and a half hours compared to the peak time of rainfall and tidal levels. Results demonstrate a time lag in the propagation of flow peaks during the process of flood wave propagation.

Table 1. Verification of the maximum water level during the event of Typhoon Morakot (RMSE = 0.094).

Gauge	η (m)
	Filed Survey Data	Simulated Results	Relative Error
1#	3.9	4.01	2.8%
2#	3.3	3.29	0.3%
3#	3.8	3.68	3.2%

presents the comparison between the simulation results and observed data for the maximum water level during Typhoon Morakot. Peak levels show minor biases across gauges (≤±0.12 m). The average relative error is less than 3% and RMSE is calculated at 0.094, indicating that the proposed model can effectively reproduce a flood event.

The modeling framework was further applied to simulate and analyze the full evolution of the event under rainfall and tidal level and compared with the surveyed data. Four characteristic stages were examined (Figure 9): tidal level approached the first peak and the rate of change in the slope of the cumulative rainfall curve increased significantly (29th at 16:00), both rainfall and tidal levels are almost approaching their peaks (30th at 00:00), tidal level is at low tide and rainfall intensity shows a declining trend (30th at 03:00), and during the attenuation of both rainfall and tidal levels (30th at 15:00).

Figure 9c illustrates that the maximum inundation map arrived on 30th September at 03:00. Most of the surveyed flooded objects (e.g., roads, buildings, and agricultural lands) are captured and provided valuable information for validation. As listed in

Table 2. RMSE and F-statistics calculated for exposed objects.

	Objects	Buildings	Roads	Agriculture Lands
Evaluation Metrics
RMSE (m)		0.184	0.189	0.181
F-statistic (%)		72.15	71.02	73.68

, the RMSE and F-statistics are calculated for roads (0.189 and 71.02%), buildings (0.184 and 72.15%), and agricultural lands (0.181 and 73.68%) for quantitative assessment of the robust capability in simulating and predicting flooding in estuarine and coastal regions.

3.2. Object-Level Impact Assessment

In this subsection, the simulated flood characteristics are integrated with the critical objects such as buildings, roads, pedestrians, and vehicles to evaluate their flood hazards, exposures, and potential damage. Specifically, datasets on buildings, roads, and farmlands were extracted from the OpenStreetMap and corrected through sub-meter imagery sourced from ArcGIS Server and Google Earth.

3.2.1. Hazard-Exposure Assessment

Both field surveyed data and simulation results found that the old town in the research domain (i.e., area A1 in Figure 9) suffered severe inundation (maximum inundation depth > 1 m) and has attracted substantial public attention due to its high-density population and intensive road network. Therefore, this study further focuses on the A1 to support a detailed assessment of the flood impact resulting from Typhoon Morakot.

To better understand the flood exposure and damage to low-lying area A1, subsequent figures will incorporate zoomed-in views of area A1, while the whole research area persists in capturing flood dynamics and predicting flood evolution. Nine gauge points (i.e., G1–G9) are laid out, which are key infrastructures such as schools, police offices, and power supply units in area A1. The information on G1–G9 is listed in

Table 3. Information on gauge points at urban critical infrastructures.

Gauge	Location	x (m)	y (m)
G1	Chenyu Middle School	614,101.39	3,110,126.27
G2	Chenyu Kindergarten	614,292.51	3,110,159.02
G3	Chenyu Primary School	614,393.06	3,110,077.03
G4	Modern Educational School	614,585.93	3,110,047.04
G5	Damaiyu Development Individual Tax Office	614,319.29	3,109,739.01
G6	Damaiyu Development Urban Supervision Brigade	614,055.52	3,109,948.37
G7	Yuhuan Lvbo New Energy Co., Ltd.	614,184.76	3,109,703.61
G8	Chenyu Power Supply Bureau	614,088.19	3,109,997.50
G9	Chenyu Power Supply Business Office	614,170.39	3,110,020.58

.

Figure 10 provides spatial and temporal characteristics of the flooding event to assess flood hazard and exposure in the area A1. Figure 10a illustrates the spatial distribution of maximum inundation depth and flood velocity during Typhoon Morakot. Severe flooding (inundation depth exceeds 0.5 m) has been captured at critical roads, such as the cross areas of Jiufeng Road and Shuangfeng Street, Dongsheng Road and Huanfeng Road, and the northwest side of Xingfu Road. Moreover, this situation lasted more than 3 h, which poses a significant flood risk to pedestrians and has substantial impacts on the roadway transportation network, for a water depth of 0.5 m can threaten human standing stability and cause vehicle engines to become vulnerable to hydrostatic lock and stalling [28].

Peak flow discharge (>5 m³/s) occurred at the athletic field of Chenyu Middle School (G1) and along the Xingang West Road. Figure 10b depicts high flood hazard to Chenyu Middle School (G1), Chenyu Kindergarten (G2), and Yuhuan Lvbo New Energy Co., Ltd. (G7); medium flood hazard to Chenyu Power Supply Business Office (G9); and low flood hazard to rest of gauge points, but their HR valued almost 0.75 (HR > 0.75 denotes medium flood hazard). Simulation results indicate that the flood impact pretends to be more dependent on inundation depth than flow velocity.

The revolution of inundation depth during the event at G1–G9 can be shown in Figure 10c. The maximum inundation depths at G1 to G9 occurred sequentially, which is generally consistent with the flow direction indicated by the vectors of flood velocity, and the difference in the time of occurrence was not more than 15 min. The arrival time of maximum inundation depths is postponed compared to the peak time of rainfall and tidal levels, further demonstrating the time lag during flood wave propagation.

To investigate the stability of cars and children on flooded roadways, Figure 11 illustrates the HD associated with various objects on the road at location A1, including children, adults, sedans, and SUVs. It highlights that children present the most significant hazard degree due to their lower U_c (Figure 3), especially on Huabing Road, Dongsheng Road, and the intersection of Xinggang East Road and Liurong Road. The hazard degrees for sedans are higher than those for SUVs and pose a potential effect on road traffic systems as sedans are the main type of vehicle in old town (i.e., area A1) on-site visits. Adults and SUVs exhibit the greatest hazard degrees on Jiufeng Road, Huabing Road, and Dongsheng Road, indicating the requests for proactive flood control interventions on these roads.

Figure 12 expands the analysis by presenting the HD values for children, adults, sedans, and SUVs at G1–G9, capturing the arrival time at which these objects reach their maximum HD values. The top marginal distribution plot displays the kernel density estimation (KDE) of the variable time and reveals maximum HD values occurred on or around the 30th at 03:00. This juncture coincides with the moment of the maximum inundation map. The right marginal plot shows the histogram of the variable HD. SUV, sedan, adult, and child are represented by purple, red, blue, and green, respectively. Frequency distribution of HD values to SUV, sedan, adult, and child indicates that the values of HD present the flood vulnerability to these objects successively as follows: child > sedan > adult > SUV.

For children, the HD values at G2 (Chenyu Kindergarten), G6 (Damaiyu Development Urban Supervision Brigade), G7–G9 (Yuhuan Lvbo New Energy Co., Ltd., Chenyu Power Supply Bureau and Chenyu Power Supply Business Office) fluctuate around 0.6. Results suggest that flood prevention and mitigation measures should be implemented, particularly at G2, to protect children from flooding, as kindergartens are primary locations where they tend to be concentrated. Although the HD value of SUVs is lower compared to that of children, adults, and sedans, SUVs near G6 (Damaiyu Development Urban Supervision Brigade), G7 (Yuhuan Lvbo New Energy Co., Ltd.), and G9 (Chenyu Power Supply Business Office) still require special attention, as their HD values are close to 0.4.

3.2.2. Damage Assessment

Further work has been put forward to investigate the damage assessment on buildings and roads based on their significant flood hazards using the depth–damage curves introduced in Section 2.2.3, in accordance with the technical manual of the HAZUS Flood model.

Figure 13 presents the maximum damage extents estimated for buildings and roads during Typhoon Morakot. According to the technical manual of the Hazus Flood model [26], 1–10%, 11–50%, and 50–100% of damage is defined as slight, moderate, and substantial damage, respectively.

For buildings, damage percentages below 5% will be represented by hollow black circles to illustrate the simulation results better. Almost 106 buildings (a quarter of the total number of buildings statistically in area A1) suffered from at least moderate damage and substantial damage to XiaLiu Village and Yuhuan ShangYing Machinery Limited Company. This indicates an inevitable impact on the safety of residents and the integrity of facilities.

For road networks, nearly 0.3 km inundated roads were subjected to no less than moderate damage. In particular, the cross areas of Dongsheng Road and Huanfeng Road experienced more than 60% damage (i.e., substantial damage).

3.3. Effectiveness of Mobile Pumping Stations

After systematically exploring the dynamic and impact mechanisms of Typhoon Morakot, area A1 is vulnerable to flooding due to its densely populated and low-lying terrain. This section aims to quantitatively evaluate the effectiveness of a mobile pumping station in mitigating flooding in a timely and cost-efficient manner, providing valuable support for flood adaptation management. Owing to the lack of field pump station data, a mobile pumping station has been assumed for deployment and is labeled as P1 in Figure 14. The drainage capacity of P1 has been designed to be 27 m³/s based on simulation results, achieved by setting a pumping rate of P = 1 m/s in Equation (2). Since the results denote that the flood impact of Typhoon Morakot pretends to be more dependent on inundation depth than flow velocity, P1 will be activated for pumping when the inundation depth exceeds 0.3 m at the Dongsheng–Huanfeng intersection, which has experienced substantial damage. Otherwise, P1 will remain deactivated.

Figure 14 presents the difference in the maximum inundation map before and after pumping by P1 during Typhoon Morakot. Thanks to P1, the inundation depth in the old town (area A1) was decreased by a maximum of 0.96 m. At the same time, the implementation of P1 brings in an average water depth reduction of 0.38 m in the downstream area of Xiaochen Ao Reservoir (area A2). In addition, the inundation depth of agricultural lands adjacent to the Liurong River and Sangu Tang River (area A3) is brought down to 0.1 m, protecting seedlings in croplands from flooding.

4. Discussion

4.1. Model Performance in Coastal Urban Areas

The HiPIMS-PSM-FIM framework demonstrates strong predictive capability, with validation metrics comparable to or exceeding similar high-resolution studies (typically 60–75% F-statistics range). The two-way source coupling method effectively captures pump–flood interactions while maintaining mass conservation. The reproduced multi-driver flooding event reveals complex spatiotemporal dynamics from coupled rainfall, upstream flooding, and tides. The hazard is depth-dominated, with peak water levels lagging external driven conditions underscoring the importance of transient dynamics for early warning systems. These patterns are consistent with findings from compound-flood studies (e.g., Yuan, et al. [29]), which reported timing lags in coastal urban areas. This suggests that in the case of low-gradient coastal storage and backwater effects, the anticipation of evolution should be given more emphasis rather than reaction to current condition.

The old town’s high vulnerability stems from converging factors: low-lying topography with dense development limiting drainage pathways, flow path convergence at key intersections creating accumulation hotspots, and aging infrastructure insufficient for compound flooding. These findings highlight elevated risks in legacy urban districts where dense population and critical facilities coincide with inadequate protection—a pattern likely repeated globally in coastal cities, in line with Kreimer, et al. [30].

Mobile pumping stations demonstrate substantial mitigation potential, with dramatic reductions in affected population and impacted facilities. Spatial benefits extend beyond immediate pumping locations to downstream and adjacent areas, indicating watershed-scale relief rather than merely local protection. Adaptive scheduling proves effective in maintaining water levels below critical thresholds while avoiding unnecessary operation, distinguishing mobile pumping from passive infrastructure through dynamic response capability and efficient resource utilization.

Figure 15 compares the inundation process at point A1-P1 simulated by HiPIMS-PSM (with pumping, green polygon) and HiPIMS (without pumping, orange polygon). The blue-filled area represents the difference in inundation depth between the two scenarios. At the initial stage of the event, the difference between HiPIMS-PSM and HiPIMS remains minimal. This result is consistent with the pump activation criteria: P1 does not activate when inundation depth is below 0.3 m. Once the threshold is exceeded, pump station P1 activates and the blue-filled area shows a sharp divergence, indicating significant pumping effects. The HiPIMS-PSM simulation successfully maintains depths below 0.3 m throughout the critical period (green polygon), demonstrating effective flood control.

These results validate both the scheduling strategy and the robustness of the source term coupling method in capturing real-time pump–flood interactions. The adaptive threshold-based operation optimizes pumping efficiency while maintaining water levels below critical thresholds.

4.2. Sensitivity to Pumping Rates

Further simulations are conducted on different pumping rates P of P1 to investigate the effect of the pump station on the simulation results, and five different P (1 m/s, 0.1 m/s, 0.01 m/s, 0.001 m/s, and 0.0001 m/s) are considered. The inundation process at point A1-P1 (Figure 14) simulated for five different pumping rates in HiPIMS-PSM is shown and compared in Figure 16. The results demonstrate that higher pumping rates significantly reduce inundation depth. During the periods when both rainfall and tidal levels are approaching their peaks (i.e., 00:00 to 05:00 on 30th), the inundation depth would exceed 0.3 m when the P = 0.1 m/s. These results indicate a threshold near 0.1 m s⁻¹: rates below this are insufficient for mitigation, whereas gains beyond it are marginal under the tested scenarios, consistent with the phenomena reported in Yazdi, et al. [31] and Li, et al. [32]. And the differences in the manifestations of the full inundation process with pumping rates of 0.01 m/s, 0.001 m/s, and 0.0001 m/s are almost negligible.

A quantitative assessment for flood mitigation to multiple objects identified through improved exposure data is provided in

Table 4. Quantitative Assessment of Flood Mitigation for Multiple Objects under Different Pumping Scenarios.

Object		P (m/s)
		0	0.01	0.1	1
Population counts		1952	856	253	36
Agricultural (km2)		5.95	4.36	3.29	1.78
Road (km)		39.01	26.22	7.57	5.91
Building		587	393	79	16
Public facility	School	8	6	2	1
	Police	1	1	0	0
	Park	3	3	1	0
	Community	4	3	0	0
	Cultural Center	1	0	0	0
Health facility	Hospital	1	1	1	0
	Pharmacy	3	2	1	1
Traffic facility	Bus station	1	1	0	1
	Gas station	2	2	1	0
Commercial facility	Convenience store	15	13	5	2
	Bank	3	2	2	1
	Restaurant	19	15	6	2
	Hotel	2	2	1	0

. Four different pumping scenarios (P = 0 m/s, 1 m/s, 0.1 m/s, 0.01 m/s) are considered to estimate the potential exposed objects. Owing to the negligible differences observed in inundation processes, scenarios corresponding to pumping rates of P = 0.001 m/s and 0.0001 m/s would be excluded from further analysis.

While 1952 people may be potentially affected without implementing P1, the suffering population can be reduced by 82% after pumping at a pump rating of P = 1 m/s. As pump rating decreases, the resulting floods will affect an increasing size of the population. For example, the affected population becomes 856 when the pump rating of P = 0.01 m/s. Similarly, the exposure of roads and agricultural lands to different pumping scenarios can also be spatially identified, with 39.01 km of roads and 5.95 km² of agricultural lands inundated when P1’s pump rating P valued at 1 m/s.

Similarly, the object-level exposure analysis is also applied to the key public, health, traffic, commercial, and other facilities to identify the individual facilities being affected and their spatial locations. From Table 4, pump rating P valued at 0 m/s may hit 17 public facilities, 4 health facilities, 3 traffic facilities, and 39 commercial and other facilities. These impacted facilities include some key public buildings and infrastructure may avoid suffering from Typhoon Morakot if pump rating of P = 1 m/s; only one public facility, one health facility, one traffic facility, and five commercial facilities should be given special attention in developing mitigation strategies. These fully quantitative assessments of key objects are crucial for developing fit-for-purpose strategies to mitigate urban flood risk.

4.3. Framework Advantages and Limitations

The HiPIMS-PSM-FIM framework advances existing approaches through computational and methodological innovations. GPU acceleration on NVIDIA Tesla K80 achieves a runtime less than 50% of event duration, enabling near-real-time forecasting essential for operational emergency response rather than post-event analysis. The high spatial resolution (3 m) enables detailed urban terrain representation and object-level impact assessment, providing actionable information for targeted mitigation planning versus conventional aggregated district-scale estimates. This granularity proves particularly valuable for prioritizing emergency resources and designing localized protection measures.

Traditional pump representation methods using boundary condition coupling or simplified parameterizations may introduce numerical instability or fail to capture dynamic interactions [33,34]. The two-way source term coupling directly incorporates pumping within 2D shallow water equations, ensuring mass conservation and stability while naturally accommodating time-varying operations without boundary reconfiguration at each time step. This proves particularly suitable for mobile pumps with adaptive scheduling. Framework integration of hydrodynamic modeling, pump representation, and impact assessment enables efficient scenario analysis without separate models and manual data transfer, supporting both planning and real-time decision-making.

Several limitations should be noted. First, pump parameters are hypothetical and have not been field tested. The PSM assumes fixed pump capacity without modeling head–discharge curves or clogging effects. Actual performance may vary with inlet conditions, mechanical issues, and power availability. Second, the depth–damage functions are based on regional databases, which may not reflect local building practices or economic conditions. The damage inventory may also be incomplete, and threshold choices can also affect results. Third, input parameters of the HiPIMS, such as Manning roughness and infiltration rates, may carry uncertainties, leading to discrepancies between model results and actual conditions. Further probabilistic analysis could help quantify these effects and support decision-making.

Future research directions include (1) optimizing multi-pump configurations with coordinated schedules; (2) integrating real-time forecasting with numerical weather predictions and data assimilation; (3) evaluating long-term risk under climate change scenarios; and (4) applying the framework to diverse coastal cities to assess transferability. Additionally, incorporating human behavior during floods and coupling with economic models for indirect losses would provide more comprehensive assessments. User-friendly interfaces and decision support tools would facilitate practitioner adoption for real-world applications.

5. Conclusions

This study developed and validated a High-Performance Integrated Hydrodynamic Modeling System–Pumping System Model–Flood Impact Assessment Model (HiPIMS-PSM-FIM) framework to simulate compound urban flooding and assess object-level exposure in coastal areas. The framework explicitly integrates mobile pump station operations through a two-way source term coupling method and evaluates impacts on buildings, roads, populations, and critical facilities. Applied to Typhoon Morakot in Yuhuan City at 3 m resolution, the framework demonstrates strong predictive capability for flood risk assessment. GPU-accelerated computation (runtime < 50% of event duration) enables near-real-time forecasting, making the framework operationally viable for emergency response rather than limited to post-event analysis.

Model validation shows excellent agreement with observations, as RMSE is 0.094 for maximum water levels and F-statistics are 71–74% for spatial inundation patterns. Flood impact assessment reveals that severe inundation (depth > 0.5 m) persisted over 3 h at key intersections, consistent with field surveys. The old town’s high vulnerability stems from low-lying topography, dense development, and inadequate drainage infrastructure—a pattern common in legacy coastal districts globally. Vulnerability analysis shows children > sedans > adults > SUVs, with educational facilities facing highest risks (HD ≈ 0.6). Approximately 106 buildings (25% of total) and 0.3 km of critical roads experienced moderate to substantial damage. The mitigation strategy is then detected, and the maximum inundation depth was reduced by up to 0.96 m after introducing pump station P1 (P = 1 m/s).

Four scenarios with different pumping rates are further analyzed to check the sensitivity (P = 0 m/s, 1 m/s, 0.1 m/s, 0.01 m/s). Pumping substantially reduced facility exposure across all categories. Without intervention, 63 facilities were at risk (17 public, 4 health, 3 traffic, 39 commercial); pumping at P = 1 m/s decreased this to 8 facilities (1 public, 1 health, 1 traffic, 5 commercial), achieving an 87% overall reduction. Sensitivity analysis confirms pumping rates ≥0.1 m/s are necessary for effective extreme event mitigation. The two-way source term coupling ensures mass conservation and numerical stability while naturally accommodating adaptive threshold-based operations.

Overall, the HiPIMS-PSM-FIM framework demonstrates strong potential for high-resolution urban flood risk assessment and management. By explicitly accounting for mobile pumping operations and object-level impacts, the framework provides a robust and practical tool to support flood resilience planning in coastal cities.