A Dynamic Urban Waterlogging Risk Assessment Framework Using RAGA-Optimized Projection Pursuit and Scenario Simulation

Abstract

In response to escalating urban waterlogging crises exacerbated by global warming and accelerated urbanization, an innovative waterlogging risk assessment framework was advanced in this study to bolster urban resilience and promote sustainable urban development. Current methodologies often suffer from subjective bias in weight assignments for evaluation indicators. To overcome this limitation, the projection pursuit (PP) technique was integrated with a real-coded accelerated genetic algorithm (RAGA) to derive objective indicator weights. Focusing on the built-up area of Xiushan County in Chongqing, the InfoWorks ICM was employed to develop a 1D-2D coupled hydrodynamic model for simulating the dynamic spatiotemporal evolution of waterlogging events. Based on three dimensions namely hazard, sensitivity, and vulnerability, an urban waterlogging risk assessment model was developed and ArcGIS was utilized to precisely generate risk distribution maps under rainfall scenarios with return periods of 20 years and 100 years. Additionally, to enhance flood mitigation capabilities in identified high-risk zones, this study proposed implementing stormwater storage tank systems. Simulation results demonstrated that these measures achieve a 50.88% reduction in overflow volumes in critical areas, effectively lowering peak waterlogging depth from 0.74 m to 0.53 m. Key findings revealed that high-risk areas exhibit significant spatial clustering in low-elevation districts characterized by high population density and economic development intensity, where extreme rainfall events amplify water accumulation vulnerabilities, highlighting the importance of sustainable land use planning and climate adaptation strategies. The proposed assessment methodology not only enables objective quantification of urban waterlogging risks but also facilitates evidence-based formulation of targeted mitigation strategies, facilitating the goals of urban sustainability and long-term environmental resilience.

1. Introduction

Against the backdrop of increasingly severe global flood disasters, establishing robust disaster prevention and emergency response mechanisms is crucial for addressing short-term and sudden heavy rainfall events [1,2]. Conducting scientifically grounded urban flood risk assessments and implementing targeted management strategies in high-risk areas are essential steps toward enhancing urban resilience and advancing urban sustainability [3,4,5,6].

Recent advances in flood modeling have shifted from conventional hydraulic models [7,8] toward integrated approaches that couple one-dimensional drainage simulations with two-dimensional overland flow models [9]. These are increasingly supplemented by data-driven techniques, enabling more accurate spatiotemporal predictions of flood dynamics [10]. In the field of urban flood mitigation, recent research and practices have seen continuous innovation in technological approaches. Zhang et al. [11] proposed a “Double E” framework that optimizes land use conversion during urban expansion to minimize both runoff and investment costs, effectively mitigating flood risks. However, this framework is primarily suited for newly developed urban areas, and its application in the redevelopment of densely built-up central districts remains challenging due to higher investment requirements. In a complementary direction, Tian et al. [12] developed a real-time control system based on deep reinforcement learning for urban drainage networks, incorporating new reward functions to enhance system resilience and reduce flooding as well as combined sewer overflow discharges. While such emerging technologies show considerable potential, their practical implementation is often constrained by the limited capacity of aging drainage infrastructure in older urban zones.

Given these limitations, mainstream flood mitigation strategies in built-up urban areas continue to emphasize the construction of sustainable gray-green infrastructure (such as rain gardens [13], permeable pavements [14], and storage tanks [15]) as integral components of holistic risk management frameworks. While early placement methods relied on hydraulic modeling combined with multi-objective optimization [16], they often oversimplified risk distributions. Emerging frameworks now incorporate high-resolution spatial risk assessments to prioritize interventions in critical hotspots [17]. Furthermore, recent studies leverage surrogate modeling and advanced optimization algorithms to efficiently resolve the complex placement problem under multiple constraints [18,19], significantly improving the sustainability and cost-effectiveness of mitigation investments.

To systematically evaluate these risks and inform such strategies, several methodological approaches have been developed. Common approaches to urban flood disaster risk assessment include historical disaster data-based risk evaluation, indicator system-driven evaluation, and high-precision scenario simulation-based risk analysis.

The assessment method based on historical disaster data primarily involves conducting statistical analysis of long-term flood events in the study area and constructing a waterlogging disaster database [20]. However, owing to the passage of time and the constraints of past monitoring technologies, obtaining long-term continuous monitoring data has proven to be highly challenging. Moreover, assessments that rely exclusively on historical data often fall short in capturing the intricate changes associated with environmental transformations [21].

The risk indicator-based assessment method integrates three dimensions comprehensively: disaster-causing factor, disaster-pregnant environment, and disaster-affected bodies. This approach transforms natural disaster risk assessment into a multi-factor decision-making problem. By designing and constructing an appropriate indicator system, the method facilitates the development of a disaster risk assessment model. Considering both the natural environment and socio-economic characteristics of the study area, it establishes a comprehensive risk assessment indicator system through the selection of suitable indicator factors [22]. These factors may include various aspects, such as precipitation, topography and landforms, drainage system conditions, population density, and socio-economic status [23], collectively reflecting the probability and potential impact of waterlogging disasters. However, while the indicator system method effectively incorporates the hazardous nature of waterlogging and socio-economic characteristics in urban waterlogging risk assessments, its disaster-causing factor indicators predominantly depend on data such as topography, slope, and historical rainfall records [24]. The accuracy and reliability of these data remain questionable, which limits their ability to precisely depict urban water accumulation patterns. Furthermore, over-reliance on rainfall data without adequately accounting for surface runoff generation and convergence processes undermines the method’s capacity to fully capture the hazard component of waterlogging risk [25].

In contrast, scenario simulation can precisely characterize the spatial distribution of urban waterlogging disasters, effectively addressing the limitations of the indicator system in this aspect. The urban waterlogging risk assessment method based on high-precision scenario simulation is tailored to the specific characteristics of the study area and typically relies on well-established mathematical models for hydrological and hydrodynamic simulations. Numerous studies have been conducted on urban-scale waterlogging risk simulation using hydraulic models, such as SWMM [26,27], MIKE Urban [28,29], and InfoWorks ICM [30]. High-precision scenario simulation models can accurately depict the physical processes of waterlogging and flow dynamics, providing a clear illustration of the affected areas and the severity of waterlogging.

However, most studies rely on methods such as the analytic hierarchy process (AHP) and the entropy method to determine the weights of various indicators. These methods inherently involve a degree of subjectivity [31,32,33], making it challenging to fully capture the randomness and uncertainty associated with risks. Since its inception, the projection pursuit (PP) method has gained widespread application due to its advantages of excellent stability, strong robustness against interference, and high accuracy. It has demonstrated remarkable performance across diverse domains, including remote sensing image recognition [34], image processing [35], risk and disaster assessment [36], and water quality evaluation [37].

This study is structured around addressing two key questions: (i) How can the RAGA-optimized PP (RAGA-PP) method be integrated into a risk assessment framework to mitigate the subjectivity inherent in traditional indicator weighting? (ii) How can scenario simulations and this novel framework be applied to identify high-risk hotspots and evaluate the effectiveness of mitigation measures, such as storage tanks, in a typical mountainous city to support sustainable urban stormwater management? The remainder of this paper is structured as follows. Section 2 outlines the methodology, including the development of the H-S-V indicator system and the integration of the RAGA-PP model for objective weight determination. Section 3 describes the application of the InfoWorks ICM 2021.1 model to simulate urban waterlogging under 20-year and 100-year rainfall return periods. Section 4 presents the results, featuring high-resolution risk maps generated in ArcGIS 10.8 that reveal spatial risk patterns and hotspots. Section 5 proposes and evaluates a targeted mitigation strategy centered on stormwater storage tanks in high-risk areas. Finally, Section 6 provides conclusions and discusses implications for urban flood resilience planning. Through an integrated framework that combines dynamic risk quantification, spatial mapping, and infrastructure optimization, this study establishes a scientific foundation for targeted interventions under resource constraints and facilitates the transition from reactive responses to proactive resilience building, thereby contributing to improved urban safety and the advancement of sustainable development goals in the context of climate-resilient urban planning.

2. Description of Study Area

The research area is located in the built-up area of Xiushan County, Chongqing, China (E 108°43′6″–109°18′58″, N 28°9′43″–28°53′5″), spanning approximately 2371.69 hm² (Figure 1a). Xiushan County features a subtropical humid monsoon climate, with an average annual precipitation of ~1325 mm. Despite having a relatively well-structured separate drainage system, which comprises a stormwater drainage network totaling 74.3 km in length, with pipe diameters ranging from 200 to 2200 mm, the region has faced significant challenges. Specifically, since the initiation of the sponge city pilot project in 2016, three extreme rainfall-induced flood events have occurred, causing substantial economic losses, attributable to limitations in the drainage network’s initial planning phase. The study area is characterized by concentrated monsoonal rainfall, constrained by a separate drainage system, and remains vulnerable to extreme rainfall events despite the implementation of the sponge city pilot project. Therefore, Xiushan County represents a representative case that embodies the common urban waterlogging challenges faced by many built-up areas in Southwest China.

To address these issues, this study utilized InfoWorks ICM (Autodesk, San Francisco, CA, USA) to develop a hydrological model for Xiushan County. A one-dimensional drainage network model was constructed using detailed drainage infrastructure data, incorporating 2349 pipelines, 2384 inspection wells, and 28 drainage outlets. The study area was further divided into seven drainage subzones manually, and Thiessen polygon method [38] was applied to generate 2393 sub-catchments (Figure 1b). Runoff generation and concentration parameters within sub-catchments were calibrated based on land use and surface characteristics. Additionally, a triangulated irregular network (TIN) surface model was developed using elevation point data. Terrain refinement was achieved by rasterizing building and road polygons, with building elevations adjusted to reflect their hydrodynamic obstructive effects on water flow [39]. Building on its representativeness, the “risk identification–scenario evaluation–mitigation strategy” workflow developed in this study demonstrates strong transferability. By leveraging existing data records and practical modeling conditions, the framework can be readily applied and compared across similar urban areas in the region.

3. Methodology

3.1. Development of the Indicator System

This study adopts the “H-S-V” natural disaster risk assessment framework proposed by [23] to evaluate urban waterlogging risks. The framework calculates the risk index using a linear weighting method, aiming to clearly reflect the relative contributions of individual factors, effectively identify key drivers of waterlogging risk, and provide a scientific basis for developing more targeted risk mitigation strategies. The formula is structured as follows:

$$R=w_{1}H+w_{2}S+w_{3}V$$

(1)

where R denotes the comprehensive urban waterlogging risk assessment, H denotes the hazard of disaster-causing factors; S denotes the sensitivity of disaster-pregnant environments; V denotes the vulnerability of disaster-affected bodies; w₁, w₂, and w₃ are the corresponding weights of each index, respectively.

The selection of indicators was guided by a comprehensive literature review [40,41] and three key principles: representativeness, data accessibility, and comprehensiveness. Within the Hazard (H) dimension, indicators such as waterlogging depth and duration were selected due to their direct ability to reflect waterlogging intensity and associated impacts. For Sensitivity (S), topographic factors—including slope and terrain ruggedness—were chosen because they effectively capture the natural propensity of landscapes to generate runoff and influence surface flow conveyance. In the Vulnerability (V) dimension, population density and GDP density were included based on their well-established role in representing socio-economic exposure, as well as their high availability, which enhances data reproducibility across studies. All indicators were derived from reliable and publicly available sources and were preprocessed to a consistent spatial resolution to reduce redundancy and mitigate potential collinearity. The final indicator system is summarized in

Table 1. Indicator system for urban waterlogging risk assessment.

Target Layer	Criterion Layer	Indicator Layer
Urban waterlogging risk	Hazard of disaster-causing factors (H)	Waterlogging depth (m)
		Waterlogging duration (min)
		Waterlogging recession time (min)
		Surface flow velocity (m/s)
	Sensitivity of disaster-pregnant environments (S)	Elevation (m)
		Slope (%)
		Terrain ruggedness index
		Topographic wetness index
		Vegetation coverage
	Vulnerability of disaster-affected bodies (V)	Road density
		Population density (hundred persons/hm2)
		GDP density (million RMB/km2)

.

In summary, the framework for the urban waterlogging disaster assessment indicator system is designed as illustrated in Figure 2, integrating theoretical foundations with empirical data analysis to establish a comprehensive and systematic evaluation structure.

3.2. Projection Pursuit Model

The PP methodology, originally proposed by [42] as a mathematical statistical approach, represents a data-driven algorithmic framework operating on sample datasets. Its fundamental concept involves transforming complex, high-dimensional data structures (comprising multiple indicators) into simplified, low-dimensional (typically 1–3 dimensional) subspaces. This dimensional reduction process identifies optimal projection configurations that effectively capture the inherent patterns and characteristics of the original high-dimensional data, facilitating tractable analysis and interpretation. Central to this method is the identification of an optimal projection vector, which quantifies the contribution (or weight) of each data dimension through its projection coefficients. This vector-based feature extraction mechanism serves as the foundation for the development of the PP paradigm [42]. Adopting a micro-urban analytical perspective, this study develops a PP model combined with real-coded accelerated genetic algorithm (RAGA) to establish a specialized urban waterlogging risk assessment system. This hybrid approach facilitates the accurate quantification of risk levels at specific geographic locations within the study area, thereby showcasing significant practical utility in urban flood hazard management.

The following outlines the systematic modeling procedures of the PP model, with Equations (2)–(10) reproduced from Wang et al. [43]:

• Step 1: Data standardization for evaluation indicators

Given the sample matrix of indicator values x*(i, j) (i = 1, 2, 3, …, n; j = 1, 2, 3, …, p), where n denotes the sample size and p denotes the number of indicators, data normalization is implemented to eliminate dimensional discrepancies across indicators. This process accommodates both positively and negatively oriented indicators through distinct normalization formulas:

Positive indicator normalization:

$$x(i,j)={\displaystyle \frac{x^{*}(i,j)-x_{\min }(i,j)}{x_{\max }(j)-x_{\min }(j)}}$$

(2)

Negative indicator normalization:

$$x(i,j)={\displaystyle \frac{x_{\max }(i,j)-x^{*}(i,j)}{x_{\max }(j)-x_{\min }(j)}}$$

(3)

where x_max(j) and x_min(j) represent the maximum and minimum values of the j-th indicator, respectively, while x(i, j) denotes the standardized indicator value sequence.

• Step 2: Projection index function construction

The PP model integrates the p-dimensional data x(i, j) (i = 1, 2, …, n; j = 1, 2, …, p) into a one-dimensional projection value z(i) along the projection direction a = {a(1), a(2), …, a(p)}:

$$z(i)={\displaystyle \sum _{j=1}^{p}a(j)x(i,j)}$$

(4)

where a is a unit-length vector. To enhance local clustering density of projection points, the projection index function Q(a) integrates two components:

$$Q(a)=S_z{D}_z$$

(5)

Standard deviation component:

$$S_z=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{i=1}^n{[z(i)-E(z)]}^2}}{n-1}}}$$

(6)

Local density component:

$$D_z={\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n\{R-r(i,j)u[R-r(i,j)]\}}}$$

(7)

where E(z) is the mean value of the sequence (1, 2, …, n), R is the local density window radius determined experimentally, r(i, j) represents the distance between samples, defined as r(i, j) = |z(i) − z(j)|, and u(t) is a unit step function (u(t) = 1 if t ≥ 0, else u(t) = 0).

• Step 3: Optimize the projection index function

For a fixed sample set, Q(a) depends solely on the projection direction a. The optimal projection direction is identified by maximizing the projection index function:

$$Max:Q(a)=S_z{D}_z$$

(8)

$$s.t.{\displaystyle \sum _{j=1}^p{a}^2(j)=1}$$

(9)

• Step 4: Optimal projection direction and indicator weight calculation

The optimal projection coefficient a = a(a₁, a₂, …, a_p) are determined through optimization. The squared values of these coefficient w_p = (a_p)², represent the weight contributions of individual indicators to the projection.

• Step 5: Component-specific weight allocation

Within each thematic component (hazard, sensitivity, vulnerability), the relative weight W_j of each indicator is calculated as:

$$W_j={\displaystyle \frac{w_p}{{\displaystyle \sum _{j=1}^m{w}_p}}}$$

(10)

where m denotes the number of indicators within the respective component, ensuring normalized weight distribution across indicators within each dimension.

The presented study addresses the complex nonlinear optimization problem defined by Equations (7) and (8) through the implementation of an enhanced genetic algorithm known as RAGA. This section outlines the systematic methodology for optimizing the projection function using RAGA, which integrates adaptive mechanisms to significantly improve convergence rates, search efficiency, and solution precision over conventional genetic algorithms [44]. The algorithmic workflow follows the standard RAGA. In this framework, candidate solutions are iteratively refined through crossover and mutation operations to generate successive generations. Specifically, parent solutions are selected based on fitness, and offspring are produced by applying crossover and mutation to effectively explore the solution space. This optimization process is used to efficiently identify the optimal projection direction for the objective function defined in Equations (7) and (8), thereby enabling the derivation of robust indicator weights for the integrated risk assessment.

The algorithmic workflow [45] is structured as follows:

• Step 1: Chromosome representation

Decimal parameters I_j are discretized into an e-bit binary strings {i_a(j, k)| j = 1, 2, …, m; k = 1, 2, …, e} via encoding transformation (Equation (10)). This binary encoding facilitates genetic operations while preserving solution precision.

$$I_j={\displaystyle \sum _{k=1}^e{i}_a(j,k)\times 2^{k-1}}$$

(11)

• Step 2: Population initialization

An initial population matrix {μ(j, i)}of size m × n is generated through stratified random sampling. Each candidate solution undergoes decimal-binary conversion using Equations (10) and (11) to establish the starting population pool.

$$I_j=INT[\mu (j,k)\times 2^e]$$

(12)

• Step 3: Fitness evaluation

The projection function f_i is evaluated for each individual by substituting the i-th group of parameters into the objective functions (Equations (7) and (8)). Fitness scores are inversely proportional to f_i, creating a minimization framework where superior solutions exhibit lower function values.

• Step 4: Adaptive parent selection

A probabilistic selection mechanism employs cumulative distribution thresholds {p_i−1, p_i} to determine parental candidates. Specifically, for the generated set of n random numbers {μ_i|i = 1, 2, …, n}, if μ_i∈(p_i−1, p_i), then the i-th individual is selected to be a parent. This ensures selection pressure dynamically adapts to population diversity, balancing exploration and exploitation.

• Step 5: Crossover operation

Selected parent pairs undergo binary-encoded crossover to produce offspring. The crossover probability is dynamically adjusted based on inter-generational fitness improvements to maintain evolutionary momentum.

• Step 6: Mutation process

Offspring individuals are subjected to bit-flip mutations with adaptive mutation rates. This mechanism prevents premature convergence by introducing controlled genetic diversity, particularly during stagnation phases.

• Step 7: Iterative evolution

The population is cyclically updated using survivor selection. Elitism preservation ensures optimal solutions propagate across generations, with termination triggered when the best-fit individual meets the pre-defined convergence criterion.

• Step 8: Adaptive range acceleration

An innovative acceleration strategy dynamically narrows the search space by focusing on hypercubes surrounding elite individuals. This reduces computational overhead while enhancing local search intensity near promising regions.

The methodology integrates multiple adaptive mechanisms to effectively tackle the “curse of dimensionality” inherent in high-order nonlinear systems. By synergistically combining probabilistic parameter encoding, dynamic operator control, and intelligent search space reduction, the proposed RAGA framework demonstrates superior performance for complex optimization tasks compared to standard evolutionary strategies [46].

3.3. Calibration and Validation of the Waterlogging Model

This study employs the Nash-Sutcliffe efficiency (NSE) coefficient as the primary criterion for evaluating parameter calibration performance. Widely recognized in hydrological modeling, the NSE coefficient quantifies the predictive accuracy of simulation results through the following formulation:

$$NSE=1-{\displaystyle \frac{{\displaystyle \sum _{t=1}^T{\left(Q_{sim}-Q_{obs}\right)}^2}}{{\displaystyle \sum _{t=1}^T{\left(Q_{sim}-\overline{Q_{obs}}\right)}^2}}}$$

(13)

where Q_sim denotes the simulated value at time step i; Q_obs represents the corresponding observed value, and $\overline{Q_{obs}}$ is the mean of observed data series. Following widely accepted guidelines [47], the NSE is categorized as follows: unsatisfactory (NSE < 0.50), satisfactory (0.50 ≤ NSE < 0.65), good (0.65 ≤ NSE < 0.75), and very good (0.75 ≤ NSE ≤ 1.00). In line with our application context, an NSE value of 0.75 or higher is considered operationally acceptable for use in subsequent analyses.

The one-dimensional model in InfoWorks ICM was initially validated using water level data from manhole monitoring point No. 5 during the 22 October 2019 rainfall event (Figure S1a). The computed NSE coefficient of 0.83 (>0.75) confirmed the calibration effectiveness, with optimized parameter values presented in Table S1 of Supplementary Materials.

To assess model transferability, two independent rainfall events on 12 September and 10 October 2019 were selected for validation. Both validation exercises achieved NSE values above the 0.75 threshold (classified as “very good” performance) (Figure S1b,c). These results demonstrate the calibrated one-dimensional model’s robustness in InfoWorks ICM, establishing a credible foundation for subsequent 1D-2D coupled hydrodynamic simulations.

The measured rainfall data from 11 August 2020, was employed as the input scenario, with specific rainfall characteristics visualized in Figure S2a. Concurrently, we obtained the geographical distribution and field-measured water depths of ponding locations across the study area during this precipitation event. To evaluate the coupled model’s predictive capability, a comparative analysis was conducted between simulated and observed water depths at these ponding points. The relative error metric (R_E) was computed using the following formula:

$$R_E=\left|{\displaystyle \frac{d_{\mathrm{sim}}-d_{\mathrm{obs}}}{d_{\mathrm{obs}}}}\right|\times 100\%$$

(14)

where d_sim represents the simulated water depth and d_obs denotes the corresponding measured value. This quantitative assessment provided critical insights into the model’s accuracy in replicating real-world hydrological responses under extreme rainfall conditions.

In compliance with the GB/T 22482-2008 [48], simulation results are considered acceptable when relative errors fall below 20%. As shown in Table S2, all calculated R_E values meet this criterion, confirming the model’s satisfactory reliability and precision. This consistency across validation points, including both calibration and verification locations for the 1D–2D coupled hydrodynamic model (as illustrated in Figure S2b), strongly supports the appropriateness of parameter configurations. These validated outcomes support the model’s applicability for subsequent hydrological risk assessment studies, where accurate representation of urban flooding dynamics is critical for infrastructure resilience planning.

3.4. Urban Waterlogging Scenario Design

In this study, scenario simulations are based on different rainfall return periods and other relevant parameters (e.g., topography and drainage systems), and the dynamic processes of rainfall-runoff, drainage, and flood propagation are simulated using the calibrated hydrological and hydrodynamic model InfoWorks ICM to enable dynamic urban waterlogging scenario modeling. This process allows for the derivation of key parameters such as ponding depth, inundation duration, and spatial distribution across the study area, with simulation results presented in Figure 3.

According to the Water Security Assurance Plan of Xiushan Tujia and Miao Autonomous County for the 14th Five-Year Plan, the urban waterlogging prevention system adopts a 20-year return period (20 a) rainstorm scenario as the core design standard. Through application of the storm intensity formula and designed rainfall pattern calculations, both 20 a and 100 a rainfall magnitudes and temporal distributions were analytically determined. The inclusion of the 100-year return period scenario serves to validate the collaborative redundancy capacity of integrated flood prevention infrastructure, specifically examining the synergistic performance of drainage networks, storage facilities, and surface flow pathways under extreme conditions. System resilience to exceedance rainfall events is evaluated through dynamic response analysis under these extreme scenarios. The designed rainfall parameters, including total amounts and temporal distribution patterns, are shown in Figure S3.

4. Urban Waterlogging Risk Assessment

4.1. Risk Level Threshold for Urban Waterlogging

The urban waterlogging risk assessment framework integrates 12 indicators across three categories: natural information factors, socio-economic parameters, and infrastructure-related data. A 30 m × 30 m grid serves as the fundamental evaluation unit, accounting for spatial variability in risk characteristics. The indicators exhibit heterogeneity in magnitude, dimensionality, and directional impact on waterlogging risks. To ensure consistency in the interpretation of indicator correlations and to standardize the direction of risk impacts, the threshold ranges for disaster-inducing factors are derived from the T/CUWA 40058-2025 [49] and are reasonably classified by considering the evolutionary patterns of waterlogging and the distinct risk characteristics of mountainous cities, based on prior engineering projects and field investigations. For all other indicators, excluding disaster-inducing factors, standardization is performed using the GIS Natural Breaks classification method [50]. This method categorizes each indicator into five ordinal risk levels: Low, Relatively Low, Moderate, Relatively High, and High. Through GIS reclassification tools, these qualitative levels were converted to numerical scores from 1 (Low) to 5 (High), as detailed in

Table 2. Risk level threshold classification schema for each indicator.

Risk Level Thresholds	1	2	3	4	5
Waterlogging depth (m)	[0, 0.05]	(0.05, 0.15]	(0.15, 0.3]	(0.3, 0.5]	(0.5, ∞)
Waterlogging duration (min)	[0, 30]	(30, 60]	(60, 90]	(90, 120]	(120, ∞)
Waterlogging recession time (min)	[0, 15]	(15, 30]	(30, 45]	(45, 60]	(60, ∞)
Surface flow velocity (m/s)	[0, 0.05]	(0.05, 0.15]	(0.15, 0.3]	(0.3, 0.5]	(0.5, ∞)
Elevation (m)	(389, 451]	(369, 389]	(358, 369]	(347, 358]	[297, 347]
Slope (%)	(14.35, 21.6]	(7.48, 14.35]	(3.98, 7.48]	(1.69, 3.98]	[0, 1.69]
Terrain ruggedness index	(27, 47]	(15, 27]	(8, 15]	(4, 8]	[0, 4]
Topographic wetness index	(14.3, 19.46]	(11.3, 14.3]	(8.9, 11.3]	(7.1, 8.9]	[0, 7.1]
Vegetation coverage	(0.67, 1]	(0.61, 0.67]	(0.56, 0.61]	(0.5, 0.56]	[0, 0.5]
Road density	[0, 0.027]	(0.027, 0.085]	(0.085, 0.131]	(0.131, 0.165]	(0.165, 0.200]
Population density (hundred persons/hm2)	[0, 1.47]	(1.47, 3.29]	(3.29, 5.73]	(5.73, 8.56]	(8.56, 12.39]
GDP Density (million RMB/km2)	[0, 136]	(136, 262]	(262, 417]	(417, 603]	(603, 924]

. The resulting risk level distributions for each indicator are spatially visualized in Figure 3.

4.2. Indicator Weighting System for Urban Waterlogging Risk

The RAGA-PP model was employed to determine indicator weights for the urban waterlogging risk assessment. Following standardized data preprocessing, the RAGA-PP model was implemented in MATLAB 2020b (MathWorks, Natick, MA, USA) with parameters settings: population size (N = 400), crossover probability (P_c = 0.9), mutation probability (P_m = 0.1), number of optimization variables (n = 12), mutation direction parameter (M = 10), acceleration iterations (C_i = 10), and adaptive search depth (DaiNo = 2 with ads = 1) [51]. Through iterative optimization, the model identified the optimal direction vector (a) and projection index function. The magnitude of each element in vector a quantifies the indicator’s contribution to the system, with larger values indicating greater significance. Under the constraint that the squared sub-vectors sum to unity, indicator weights were derived as shown in

Table 3. Indicator weighting results.

Indicator Name	Optimal Projection Direction (wp)	Weight (Wj)
Waterlogging depth (h1)	0.335	0.112
Waterlogging duration (h2)	0.292	0.085
Waterlogging recession time (h3)	0.336	0.113
Surface flow velocity (h4)	0.255	0.065
Elevation (s1)	0.272	0.074
Slope (s2)	0.338	0.114
Terrain ruggedness index (s3)	0.351	0.123
Topographic wetness index (s4)	0.249	0.062
Vegetation coverage (s5)	0.205	0.042
Road density (v1)	0.155	0.024
Population Density (v2)	0.345	0.119
GDP density (v3)	0.259	0.067

.

The risk assessment framework decomposes waterlogging risk (R) into three components: Hazard (H), which represents the danger level of a grid cell due to disaster-causing factors (Equation (15)); Sensitivity (S), which reflects the environmental susceptibility under disaster-pregnant conditions (Equation (16)); and Vulnerability (V), which indicates socio-economic exposure to disaster-affected elements (Equation (17)).

$$H=0.299h_1+0.227h_2+0.301h_3+0.173h_4$$

(15)

$$S=0.178s_1+0.275s_2+0.296s_3+0.149s_4+0.101s_5$$

(16)

$$V=0.114v_1+0.567v_2+0.319v_3$$

(17)

For Xiushan County, the RAGA-PP model assigned weights of 0.375 (H), 0.415 (S), and 0.210 (V) (Table 3). These weights were applied to overlay the three components through:

$$R=0.375H+0.415S+0.210V$$

(18)

where H, S, V represent normalized indices for each grid cell, and R denotes the integrated risk level. This methodology ensures systematic integration of multi-dimensional risk components into a unified assessment framework.

4.3. Urban Waterlogging Risk Assessment Results

4.3.1. Disaster-Causing Factor Hazard Analysis

Figure 4 illustrates spatial distribution of disaster-causing factor hazards in the study area, revealing distinct clustering patterns. The high and moderately high hazard zones primarily concentrate along Yuxiu Avenue, Huadeng Square, and adjacent residential complexes. This distribution is predominantly driven by two critical parameters: waterlogging depth and recession time. The urban core along Yuxiu Avenue, characterized by intensive commercial-residential development, demonstrates elevated hazard levels due to extensive impervious surfaces from paved roads and plazas. Such artificial surfaces significantly reduce infiltration capacity while accelerating surface runoff accumulation, creating critical drainage challenges [52]. Similarly, Pingjian Road and Xiubei Avenue exhibit complex hazard profiles. Despite surrounding vegetation coverage, the dense building footprints and impermeable road networks counteract natural retention mechanisms, forming flood-vulnerable hotspots [25].

In contrast, areas south of Fenghuang Avenue and east of Pingjian Road show lower hazard intensities, largely attributable to effective vegetation buffers. Vegetation root systems, particularly those of shrubs and deep-rooted species, enhance soil porosity and hydraulic conductivity, promoting vertical infiltration [53]. Simultaneously, vegetation canopy interception and surface litter layers attenuate runoff velocities while infiltration volumes [54]. The regulatory function of urban rivers further differentiates hazard levels. These natural corridors effectively convey excess stormwater, maintaining hydraulic connectivity and mitigating accumulation risks [55]. By facilitating natural hydrological cycles, these waterways sustain regional water balance, demonstrating their critical role in urban flood mitigation [56]. The interplay between anthropogenic developments and natural hydrological processes thus determines the spatial variability of disaster-causing factor hazards in the study area.

4.3.2. Disaster-Pregnant Environment Sensitivity Analysis

Figure 5 demonstrates the spatial distribution of disaster-pregnant environmental sensitivity across the study area, revealing a pronounced west–east gradient with elevated sensitivity concentrations in the central-eastern zone. This pattern emerges primarily from the dominant influence of slope gradient and terrain ruggedness index in the sensitivity assessment framework. The central-eastern region’s low-lying topography with gentle slopes creates natural depressional areas that act as hydraulic sinks. During rainfall events, surrounding elevated terrains funnel runoff into these depressions, impeding natural drainage and amplifying waterlogging risks [57]. Anthropogenic modifications further exacerbate this vulnerability. Urban development activities, including sports parks, educational institutions, residential communities, and high-rise constructions, have significantly altered local microtopography. These human interventions flatten natural terrain variations, particularly in low-lying areas, which disrupts historical drainage pathways. Such transformations convert previously stable landscapes into flood-prone zones by reducing topographic gradients essential for effective water conveyance [58]. Low-sensitivity areas exhibit fragmented distributions, primarily in central and western sectors, interspersed with high-sensitivity zones. This irregular pattern reflects the study area’s complex mountainous geography, where hydrological responses vary spatially [59]. The absence of clear geographic regularity suggests that waterlogging risks may emerge unpredictably across the region, necessitating comprehensive risk management strategies that account for both natural and anthropogenic factors influencing environmental sensitivity.

4.3.3. Disaster-Affected Body Vulnerability Analysis

The spatial distribution of vulnerability is fundamentally shaped by population density gradients. Figure 6 illustrates that high-vulnerability zones are clustered between Fenghuang Avenue (north) and Dongfeng Road (south), corresponding to Xiushan County’s central urban corridor. This area distinguishes itself through several critical characteristics: (i) intense population concentrations, (ii) advanced economic development metrics, (iii) heavy pedestrian and vehicular traffic volumes, and (iv) dense commercial establishments lining major roadways. These elements collectively create a vibrant yet highly exposed urban environment. During waterlogging events, this configuration produces compound risks. Hydrological stresses disrupt transportation networks while simultaneously endangering commercial assets and residential infrastructure [60]. The concentration of economic activities amplifies potential damages, translating environmental hazards into significant financial losses. Conversely, peripheral areas demonstrate lower vulnerability indices due to three primary factors: reduced building densities, dispersed population settlements, and increased green space allocations. Vegetated areas enhance infiltration capacities while mitigating surface runoff impacts, creating natural buffers against urban flooding [61]. This spatial disparity in vulnerability underscores critical risk management priorities. The central urban zone’s confluence of population, economy, and infrastructure exposes it to disproportionate disaster impacts during extreme rainfall events. Effective mitigation strategies must therefore address both the hydrodynamic challenges and socio-economic exposures inherent to this high-risk area.

4.3.4. Comprehensive Assessment of Urban Waterlogging Risk

The application of the integrated risk model (Equation (18)) was pivotal in synthesizing multi-dimensional risk drivers into an actionable spatial diagnosis. By linearly aggregating the standardized H, S, and V components into a composite index (R), this model enables the mapping of continuous spatial risk distribution (Figure 7) and facilitates the identification of dominant factors underlying observed risk patterns. This application of Equation (18) thus transcends mere calculation to provide a mechanistic understanding of risk, directly informing the targeted mitigation strategies outlined in Section 5. Figure 7 reveals distinct spatial patterns of waterlogging risk under both 100-year and 20-year return periods. High-risk zones consistently cluster around Huadeng Square and Yuxiu Avenue across scenarios. This concentration arises from two primary factors: (i) the region’s low-lying topography that promotes surface water pooling, and (ii) its central location within the county characterized by high impervious surface coverage, population density, and economic development, which collectively elevate its susceptibility to waterlogging. In contrast, areas like Xiubei Avenue (northwest), Fengqi South Road-Baisha Avenue intersection (south), and Huadeng Avenue vicinity exhibit lower comprehensive risk despite containing high-hazard zones (Figure 4). Their reduced sensitivity stems from three mitigating factors: elevated topographic positions, steeper gradients facilitating runoff, and lower population densities. These characteristics minimize societal impacts even when localized flooding occurs. Additionally, riverine systems adjacent to the urban core provide natural hydraulic buffering [62], as seen in reduced risk ratings for left-bank roadways despite observed waterlogging.

Comparative analysis between scenarios reveals significant risk expansion under the 100-year event. Medium-to-high risk areas increase notably compared with the 20-year event, particularly in central urban districts and Pingjian Road regions. This pattern indicates critical deficiencies in stormwater infrastructure resilience during extreme rainfall events. The drainage network’s limited capacity becomes evident as expanding high-risk zones correlate with increasing rainfall intensities [63], underscoring systemic vulnerabilities to climatic extremes.

5. Urban Waterlogging Risk Mitigation Strategies

The study reveals elevated comprehensive waterlogging risk levels in Huadeng Square and the mid-section of Yuxiu Avenue (Figure 7). To address this critical issue, mitigation strategies should prioritize the two highest-weighted risk components: hazard intensity of disaster-causing factors and sensitivity of disaster-pregnant environmental conditions. As shown in Table 3, waterlogging depth and recession time play a dominant role in the disaster-causing risk. In the assessment of sensitivity of the disaster-pregnant environment, slope and topographic roughness carry greater weight. Considering that Huadeng Square and the mid-section of Yuxiu Avenue are located in the central built-up area, where slope and topographic roughness are difficult to modify, the focus should be on addressing waterlogging depth and recession time within disaster-causing risk to mitigate waterlogging risk in these areas.

A multi-pronged approach combining green and gray infrastructure solutions is proposed to effectively reduce waterlogging risks in these urban zones. Urban areas can benefit from integrated sponge city features such as bioretention cells, rain gardens, and permeable pavements. These sustainable solutions enhance rainwater infiltration capacity, shorten drainage cycles, and reduce waterlogging depths [61], thereby decreasing the disaster-causing factor hazard.

While green infrastructure demonstrates proven effectiveness in managing rainwater runoff, optimization challenges persist even with advanced deployment planning [64]. This underscores the need for complementary gray infrastructure solutions. Storage tanks emerge as critical components in urban flood control systems. Existing studies confirm that storage tanks significantly enhance detention capacity, attenuate peak flows, reduce overflow incidents, and lower pollutant loads under both design and extreme storm conditions [65,66]. For instance, a multi-objective optimization study by Duan et al. showed that integrating storage tanks with low-impact development measures under a 20-year return period storm reduced flooding nodes from 14 to 1 in one optimal scenario, while also lowering total cost and decreasing peak discharge at a critical node from over 6.8 m³/s to about 4.9 m³/s [67]. Such empirical evidence supports the classification of storage tanks as best management practices (BMPs) for mitigating urbanization impacts on drainage systems and receiving water bodies [68]. Given their documented effectiveness in reducing surface runoff volumes and alleviating hydraulic stress on downstream networks [69], this study employs the InfoWorks ICM model to evaluate storage tank effectiveness in critical waterlogging zones within our study area. The simulation results are expected to provide actionable insights to guide engineering implementation and optimize urban flood resilience planning.

Without storage tanks, Huadeng Square’s low-lying topography and open space configuration create a natural water convergence point (Figure 8a). The proposed intervention involves installing a 4 m-high rectangular storage tank (2000 m² surface area) downstream of node 5YS1741, connected via diameter-matched piping to ensure hydraulic compatibility. The ICM simulations compared two scenarios, including baseline scenario (i.e., without storage tank) and intervention scenario (i.e., with storage tank), under 20-year return period rainfall event (120 min duration). The implementation of a centralized stormwater storage tank at Huadeng Square produced marked improvements in flood mitigation outcomes across the study area compared to the baseline scenario without such infrastructure, as visualized in Figure 8b,d,f,h.

Simulation results illustrated in Figure 8i demonstrate that without implementing storage tanks, the study area experiences a total overflow volume of 74,684 m³, accompanied by a maximum waterlogging depth reaching 0.74 m. In contrast, implementing the proposed storage tank scheme results in significant hydraulic improvements. Specifically, the overflow volume is reduced by 50.88% to 36,682 m³, and the peak waterlogging depth decreases by 28.38% to 0.53 m. Additionally, the storage tank intervention significantly reduces waterlogging duration, accelerates waterlogging recession, lowers surface flow velocity, and decreases inundation area. These findings demonstrate storage tanks’ effectiveness in reducing drainage system overload, optimizing hydraulic load distribution, and mitigating urban waterlogging risks. The results validate hybrid infrastructure approaches as practical solutions for urban resilience enhancement, offering valuable guidance for future engineering projects.

6. Conclusions

This study investigates urban flood resilience in Xiushan County through the development of an integrated 1D-2D hydrological modeling framework using InfoWorks ICM. The research simulates waterlogging dynamics under varying rainfall return periods, incorporating a multi-criteria risk classification system that evaluates inundation depth, persistence duration, recession time, and flow velocity to generate spatially explicit risk maps. By synergistically analyzing hazard-forming environments and vulnerable elements, we propose a novel RAGA-optimized PP model to derive objective indicator weights. This methodology enables three-dimensional risk assessment—encompassing hazard intensity, environmental sensitivity, and socio-economic vulnerability—producing risk zonation maps for 20-year and 100-year storm events. Key findings reveal critical risk zones spatially clustered around Huadeng Square and Yuxiu Avenue, characterized by topographic depressions, high population densities, and advanced economic development. Notably, while certain areas exhibit elevated hazard indices, overall risk remains moderate due to reduced environmental sensitivity and lower vulnerability of exposed assets. The study validates that strategic implementation of storage infrastructure significantly moderates waterlogging risks, though mitigation effects show spatial variability. Urban renewal strategies should prioritize hybrid gray-green infrastructure solutions in low-lying, densely populated, and economically vital districts. Evidence-based deployment paradigms, informed by high-resolution hydrological modeling, are recommended to enhance flood mitigation efficacy.

To enhance simulation fidelity, future research could focus on several key areas: (i) refining model integration by incorporating riverine systems within the InfoWorks ICM framework to capture backwater effects on urban drainage dynamics; (ii) improving data granularity through LiDAR-derived digital elevation models and parcel-level socioeconomic datasets to refine topographic representations and vulnerability assessments; (iii) innovating risk quantification methods via dynamic weighting algorithms that account for seasonal and inter-annual variations in hazard exposure and socio-spatial vulnerability profiles; and (iv) expanding scenario analysis to explore compound flood events (e.g., concurrent pluvial and fluvial flooding) and project long-term risk trajectories under climate change scenarios. Addressing these gaps would strengthen the precision and transferability of urban flood risk management frameworks, thereby supporting the development of climate-resilient cities through evidence-based adaptation strategies. Furthermore, to validate and generalize the proposed methodology, we intend to extend empirical validation to urban contexts with diverse climatic, topographic, and developmental characteristics, thereby ensuring broader applicability and supporting the development of evidence-based, climate-resilient cities through adaptive and context-sensitive strategies.