Research on Urban Flood Risk Assessment Based on Improved Structural Equation Modeling (ISEM) and the Extensible Matter-Element Analysis Method (EMAM)

Abstract

With the rapid development of the global economy, urban flood events are occurring more frequently. Scientific risk assessment methods are of great significance in reducing the loss of life and property. This study is devoted to developing an integrated urban flood risk assessment approach based on improved structural equation modeling and the extensible matter-element analysis method. Firstly, a flood risk assessment index system containing four dimensions (hazard, exposure, vulnerability, and regional shelter capability) is established according to a hydrological–hydrodynamic model and a literature survey. Subsequently, improved structural equation modeling (ISEM) coupled with Pearson’s correlation coefficient is introduced to determine indicator weights while eliminating correlations among indicator variables, thereby enhancing the accuracy of the weight calculation. Finally, the extensible matter-element evaluation analysis method (EMAM) is employed to conduct the urban flood risk assessment, providing a more scientific evaluation of urban flood risks through the calculation results of the correlation degree between index factors and risk levels. The integrated flood risk assessment approach was applied in the Liwan District in Guangzhou City, China, and the results demonstrated that the novel approach effectively enhances the accuracy of urban flood risk assessment by 23.69%. In conclusion, this research offers a novel and high-precision methodology for risk assessment, contributing to decision-making in disaster prevention and control.

1. Introduction

With the rapid development of global economic globalization, cities, as an important component of human civilization, are facing natural disaster threats while promoting social and economic development. Among them, high-intensity flood disasters are the most prominent [1,2,3,4]. In recent years, extreme rainstorms have occurred in many regions of China, triggering extremely severe urban floods, such as the “5·22” flood disaster in Guangzhou in 2020, the “7·20” rainstorm flood in Zhengzhou in 2021, and the rainstorm flood in the Beijing–Tianjin–Hebei region in 2023 [5,6]. These rainstorm events have caused great impacts on people’s production and life, as well as on property safety [7]. Risk assessment constitutes a pivotal non-engineering intervention within the realm of disaster prevention and mitigation, capable of significantly diminishing societal losses.

In recent years, researchers have developed various approaches for assessing urban flood risks, like indicator system methods [8], scenario analysis methods [9], integrated machine learning methods [10], and geographical analysis methods [11,12], which have achieved remarkable results in disaster prevention and mitigation. The indicator system method is one of the most widely used risk assessment approaches, establishing a scientific indicator system to address the challenge of comprehensively calculating the weights of complex and diverse indicators with specific numerical values. Sun et al. established a disaster risk index system encompassing hazard, exposure, vulnerability, and resilience, and they proposed a subjective and objective combined weight assignment method to calculate a comprehensive risk assessment [13]. Liu et al. introduced a comprehensive indicator system encompassing hazard, vulnerability, and sensitivity, and they utilized the cloud model method to assess urban flood risk [8]. Wang et al. evaluated flood risk in the Beijing–Tianjin–Hebei region by applying the fuzzy comprehensive evaluation method [14].

However, these research methodologies exhibit certain limitations. For example, the approaches are centered on statistical indicators and lack consideration of the physical processes of flood disasters [15]. Furthermore, the comprehensiveness of the indicator systems needs to be enhanced [16], especially for the indicators related to regional shelter capability, which were less emphasized in previous research results. To address these limitations, this study proposes an index system for assessing urban flooding, based on the connotations of disaster system and risk system, comprehensively considering various factors, such as the hazard degree of triggering factors (max inundation depth, max inundation velocity), the exposure of the environment conducive to disaster occurrence (elevation, slope, permeability), the vulnerability of disaster-bearing bodies (GDP density, population density, POI distance), and the actual regional refuge capabilities (disaster prevention and mitigation capability, flood control and drainage capacity), from both physical and statistical mechanisms, comprehensively revealing the sources of flooding risk.

The determination of index weights is a crucial part of flood risk assessment [17]. In previous research results, the common calculation methods of index weights mainly focused on subjective or objective methods, like entropy weight and the analytic hierarchy process [18]. Gradually, some scholars have adopted the combined subjective and objective weight calculation method, achieving more accurate results [19]. In fact, the above-mentioned methods of calculating weights all ignore the possibility that there might be some kind of correlation among the indicators in the index system, which leads to inaccurate risk calculation [20,21]. In order to eliminate the correlations among the index variables and determine the final weights of each index factor, an improved structural equation modeling method coupled with Pearson’s correlation coefficient is proposed to modify the index weights.

Structural equation modeling (SEM) is an objective computational method that analyzes the interrelationships among variables based on their covariance matrices [22,23]. It serves as an effective tool for analyzing multivariate data and is widely used in scientific research fields, such as economics and management, overcoming the subjective dependence of traditional mathematical methods [24,25]. The extensible matter-element analysis method (EMAM) addresses incompatible and contradictory issues arising from different levels by breaking conventional norms and adopting creative decision-making techniques in an expansive manner. The goal is to maximize the transformation of incompatible contradictions into compatible relationships, thus achieving the overall optimal decision-making objective [26,27,28]. This study proposes a novel integrated urban flood risk assessment approach based on improved structural equation modeling (ISEM) coupled with Pearson’s correlation coefficient and the extensible matter-element analysis method (EMAM). This approach will comprehensively reveal the sources of urban flooding risks, significantly improve the accuracy of weight calculation, and achieve scientific zoning of flooding risks.

The structure of this article is arranged as follows: Firstly, a flood risk assessment index system containing four dimensions, including hazard, exposure, vulnerability, and regional shelter capability, is established according to a hydrological–hydrodynamic model and a literature survey. Secondly, an improved structural equation modeling (ISEM) method coupled with Pearson’s correlation coefficient is introduced to determine indicator weights, enhancing the precision of weight calculation. Thirdly, the extensible matter-element evaluation analysis method (EMAM) is employed to perform the urban flood risk assessment, providing a more scientific urban flood risk assessment. Finally, the integrated flood risk assessment approach is applied in the Liwan District, Guangzhou City, China. The results demonstrated that the novel approach effectively enhances the accuracy of urban flood risk assessment.

2. Methodology

This study introduces a novel and comprehensive approach to assess urban flood risk, including index system establishment and quantization, index weight calculation, and urban flood risk assessment. First of all, the index system was built by the SWTM-coupled hydrodynamic model and statistical data, comprehensively considering various factors, like the hazard of disaster-causing factors, the exposure of disaster-pregnant environments, the vulnerability of disaster-affected bodies, and the actual regional refuge capacity. Secondly, a weight calculation method, combined with Pearson’s correlation coefficient and a structural equation model, was proposed to correct and calculate the indicators’ weights. Subsequently, the extension matter-element analysis method was utilized to conduct urban flood risk assessments and analyze the scientific zoning of flood risks. Finally, comparative analyses of risk assessment results were discussed, indicating the advantages of the integrated urban flood risk assessment approach. The whole framework is introduced in Figure 1.

2.1. Index System Establishment and Quantization

In this study, the urban flood indicator system was established by three principles: comprehensiveness, quantifiability, and representativeness. In the context of this study, urban flood risk is defined as the result of the interaction among four influencing factors: the hazard of disaster-causing factors, the exposure of disaster-pregnant environments, the vulnerability of disaster-affected bodies, and the regional refuge capacity. The definitions and calculation methods of each indicator are described as follows:

(1)

Hazard factors.

The hazard factors are mainly manifested in the disaster-causing indicators, including maximum inundation depth and maximum inundation velocity. The one-dimensional pipe network SWMM model was coupled with the two-dimensional surface TELEMAC-2D model to form the SWTM hydrodynamic model, enabling the simulation of the entire process of rainfall generation and concentration, pipe network flow, and two-dimensional surface spreading. Based on the SWTM simulation results, raster data for the maximum inundation depth and maximum inundation velocity were obtained.

(2)

Exposure factors.

The exposure factors consist of three indicators: elevation, slope, and impervious surface rate. The elevation values of the study area were calculated using DEM data with a mask extraction tool. The mean slope was obtained using a slope calculation tool. The impervious surface rate refers to the ability of the ground or land surface to prevent water from infiltrating. The impervious surface rate was calculated based on land use types.

(3)

Vulnerability factors.

The vulnerability factors include GDP, population density, and POI distance. GDP refers to the value created per square kilometer of land. Population density refers to the number of people per unit of land area. POI distance refers to the distance from each grid point to the nearest POI (such as industrial, commercial, transportation, and educational facilities). The smaller the distance, the safer the grid point is. This is because that point can evacuate to the POI quickly, indicating that the risk of the grid point is relatively low. The raster resampling tool was used to convert 1 km raster data to a resolution of 5 m × 5 m. Formulas (1)–(4) were then used to calculate the GDP values for each house. Finally, the nearest neighbor analysis tool was employed to calculate the distance from each grid point in the study area’s POI shp layer to the nearest POI. The POP quantization method is the same as that of GDP.

$${\overline{GDP}}_i={\displaystyle \frac{GD{P}_i}{S_i}}$$

(1)

$$GD{P}_{ij}=\overline{GD{P}_i}\times S_j$$

(2)

$$\overline{GD{P}_{jn}}={\displaystyle \frac{GD{P}_{ij}}{{\displaystyle \sum _{n=1}^N{S}_n}}}$$

(3)

$$GD{P}_{jn}=\overline{GD{P}_{jn}}\times S_n$$

(4)

where GDP_i represents the economic output of the i-th independent region; S_i represents the area of the i-th independent region; GDP_ij represents the economic output of the i-th independent region within the j-th clipped research area; and GDP_jn represents the economic output of the j-th clipped research area within the n-th grid of the research area.

(4)

Regional refuge capacity factors.

Regional refuge capacity factors were divided into two aspects: disaster prevention and mitigation capabilities and flood control and drainage capabilities. Disaster prevention and mitigation capabilities refer to the ability of individuals or communities to take measures to reduce the risk of urban floods. Flood control and drainage capabilities refer to the ability of a certain area to effectively prevent flooding and drain accumulated water during extreme precipitation events. In this study, various schools, squares, parks, stadiums, hospitals, and other facilities within the study area were identified as emergency shelters. Point density analysis was conducted on the number of shelters within the study area to obtain the disaster prevention and mitigation capabilities. The flood control and drainage capabilities were obtained by calculating the pipe network density index value within each grid according to Formula (5).

$${\rho }_i={\displaystyle \frac{L_i}{S_i}}$$

(5)

where ρ_i represents the pipe network density of the i-th grid cell; S_i represents the area of the i-th grid cell; and L_i represents the length of the pipe segment in the i-th grid cell.

2.2. Index Weight Calculation

Structural equation modeling (SEM) is an objective computational method that analyzes the interrelationships among variables based on their covariance matrices [22,23]. It serves as an effective tool for analyzing multivariate data and is widely used in scientific research fields, overcoming the subjective dependence of traditional mathematical methods [24]. Here, an improved structural equation modeling (ISEM) method coupled with Pearson’s correlation coefficient is introduced to determine indicator weights, which eliminates the existing correlation among the indicator variables, enhancing the precision of weight calculation. The specific steps are as follows:

Step 1: Standardize indicator variables. Based on the literature research and selection principles, this study selected appropriate internal flooding risk indicators and proposed hypotheses regarding the relationships among variables. The standardized formulas are as follows:

$$x^{\prime }={\displaystyle \frac{x-x_{\min }}{x_{\max }-x_{\min }}}(Positive Orientation Index)$$

(6)

$$x^{\prime }={\displaystyle \frac{x_{\max }-x}{x_{\max }-x_{\min }}}(Negative Orientation Index)$$

(7)

where x represents the original value of each indicator; x_min represents the minimum value of each indicator; x_max represents the maximum value of each indicator; and x′ represents the normalized value of each indicator, ranging within the range of [0,1].

Step 2: Variable validation analysis. Based on the risk assessment index system determined, this study evaluates the extent to which different risk influencing factors affect the urban flooding risk. We selected grid cells as the risk assessment units, which describe the characteristics of the study area more accurately and provide more spatial resolution. The risk assessment index system of urban waterlogging in the research area includes multiple factors, such as natural geography and social economy. By using the natural discontinuity point method in Arcgis (Version 10.3 ) software, the risk levels of various assessment indicators were divided into five grades: low, relatively low, medium, relatively high, and high. And by using the reclassification tool in Arcgis technology, the five divided risk levels were assigned values ranging from 1 to 5. The organized indicator data was imported into SPSS 19.0 (Statistical Product and Service Solutions, Version 19.0) software for reliability and validity testing, descriptive analysis, and the examination of data credibility to determine the suitability for factor analysis. The reliability test coefficient, i.e., Cronbach’s alpha, ranges from 0 to 1, with values closer to 1 indicating higher data reliability. The validity exploratory test coefficient, i.e., the KMO test, also ranges from 0 to 1, with values closer to 1 indicating stronger correlations among indicator variables. The formulas are as follows:

$$\mathrm{Cronbach}\prime \alpha =\left({\displaystyle \frac{n}{n-1}}\right)\left(1-\frac{{\displaystyle \sum {S_i}^2}}{S^2}\right)$$

(8)

$$KMO={\displaystyle \frac{{\displaystyle \sum {\displaystyle {\sum }_{i\ne j}{r_{ij}}^2}}}{{\displaystyle \sum {\displaystyle {\sum }_{i\ne j}{r_{ij}}^2}}+{\displaystyle \sum {\displaystyle {\sum }_{i\ne j}{p_{ij}}^2}}}}$$

(9)

where α represents Cronbach’s alpha coefficient; n represents the total number of measurable variable items; S_i² represents the variance of each indicator; S_i represents the total variance of all indicators; KMO represents the Kaiser–Meyer–Olkin measure, used to assess the suitability of data for factor analysis by comparing simple correlations and partial correlations between variables; r_ij represents the simple correlation coefficient for each pair of original variables; and p_ij represents the partial correlation coefficient for each pair of original variables.

Step 3: Construct an indicator model. Based on the proposed hypotheses regarding variable relationships, we established influencing paths and constructed a model of the urban flooding risk assessment indicator system. The indicator data was imported into AMOS (Analysis of Moment Structure, Version 23.0) software, and the risk assessment indicator system model was modified to determine the load coefficient weights of each indicator variable in the final model.

Step 4: Revise indicator weights. To eliminate the correlation between indicators, this study used Pearson’s correlation coefficient to revise the indicator weights, reflecting the closeness of the correlation between variables [25]. The larger the absolute value of the correlation coefficient ∣r∣, the stronger the correlation; the smaller the absolute value of r, the weaker the correlation. This study introduced the correlation coefficient r to subtract the correlation coefficient value from other indicator variables. The formulas are as follows:

$$r={\displaystyle \frac{{\displaystyle \sum _{i=1}^n\left(x_i-\overline{x}\right)\left(y_i-\overline{y}\right)}}{\sqrt{{\displaystyle \sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}}}}$$

(10)

$$W_i={\displaystyle \frac{{\omega }_i\times \left(1-{\displaystyle \sum _{\mathrm{j}=\mathrm{i}+1}^n{r}_{ji}}\right)}{{\displaystyle \sum _{i=1}^n{\omega }_i\times \left(1-{\displaystyle \sum _{\mathrm{j}=\mathrm{i}+1}^n{r}_{ji}}\right)}}}$$

(11)

where x_i represents the value of the i-th indicator; y_i represents the value of the i-th indicator; $\overline{x}$ represents the mean value of x_i; $\overline{y}$ represents the mean value of y_i; r_ij represents the correlation coefficient value for each pair of original variables; ω_i represents the weight for the i-th risk indicator; and W_i represents the correction weight for the i-th risk indicator.

2.3. Urban Flood Risk Assessment

The extensible matter-element analysis method (EMAM) addresses incompatible and contradictory issues arising from different levels by breaking conventional norms and adopting creative decision-making techniques in an expansive manner. The goal is to maximize the transformation of incompatible contradictions into compatible relationships, thus achieving the overall optimal decision-making objective [26,27,28]. This method can effectively handle a large number of uncertainties and fuzzy issues, improving the efficiency and accuracy of data analysis. In this study, EMAM was introduced to perform the urban flood risk assessment. The specific process is as follows:

Step 5: Construct the matter-element matrix. Matter-element analysis typically uses three fundamental units—N, C, and V—to represent entities. The mathematical expression for this is:

$$R=\left[\begin{array}{c}{R}_1\\ R_2\\ \cdot \\ R_n\end{array}\right]=\left[N\begin{array}{c}{c}_1\\ c_2\\ \cdot \\ c_n\end{array}\begin{array}{c}{v}_1\\ v_2\\ \cdot \\ v_n\end{array}\right]$$

(12)

where C represents the n features of the matter-element to be evaluated, where C = (c₁,c₂,…,c_n); V represents the measured values of the n features, where V = (v₁,v₂,…,v_n); and N represents the entity to be evaluated.

Step 6: Determine the classical domain matrix and the interval domain matrix. The classical domain is determined based on the specific characteristics of the evaluated matter-element and the corresponding range of values. This study performed dimensionless standard processing on the risk assessment indicator data. The EMAM was applied to calculate the risk level. The section domain was determined based on the value ranges of various evaluation indicators. Assuming the evaluation levels are divided into m levels, the classical domain matter-element matrix R_j and the interval domain matter-element matrix R_p can be represented as:

$$\begin{gathered} R_j=\left[N_j\begin{array}{c}{c}_1\\ c_2\\ \cdot \\ c_n\end{array}\begin{array}{c}{v}_{j1}\\ v_{j2}\\ \cdot \\ v_{jn}\end{array}\right]=\left[N_j\begin{array}{c}{c}_1\\ c_2\\ \cdot \\ c_n\end{array}\begin{array}{c}\left(a_{j1},b_{j1}\right)\\ \left(a_{j2},b_{j2}\right)\\ \cdot \\ \left(a_{jn},b_{jn}\right)\end{array}\right] \\ {R}_p=\left[N_p\begin{array}{c}{c}_1\\ c_2\\ \cdot \\ c_n\end{array}\begin{array}{c}{v}_{p1}\\ v_{p2}\\ \cdot \\ v_{pn}\end{array}\right]=\left[N_p\begin{array}{c}{c}_1\\ c_2\\ \cdot \\ c_n\end{array}\begin{array}{c}\left(a_{p1},b_{p1}\right)\\ \left(a_{p2},b_{p2}\right)\\ \cdot \\ \left(a_{pn},b_{pn}\right)\end{array}\right] \end{gathered}$$

(13)

where N_j represents the j-th evaluation level; c_i represents the i-th evaluation criterion; v_ij represents the value range of the i-th evaluation criterion under level j, where v_ij = (a_ji,b_ji); v_pi represents the value range of the interval domain matter-element for the feature ci, where v_pi = (a_pi,b_pi); and (a_pi,b_pi) represents the union of all ranges (a_ji,b_ji) for the i-th criterion.

Step 7: Determine the matter-element matrix. In this study, the factors influencing the risk level of urban flooding were represented as matter-elements:

$$R_{\mathrm{x}}=\left[P_{\mathrm{x}}\begin{array}{c}{c}_1\\ c_2\\ \cdot \\ c_n\end{array}\begin{array}{c}{v}_1\\ v_2\\ \cdot \\ v_n\end{array}\right]$$

(14)

where R_x represents the matter-element to be evaluated; P_x represents the evaluation level of the indicators for urban flooding risk; and v_i represents the measured value for the i-th evaluation criterion c_i under the evaluation level P, indicating the actual value of the indicator for the urban flooding risk evaluation level.

Step 8: Determine the relevance degree. The relevance degree refers to the magnitude of the correlation between matter-elements. According to the definition in the theory of matter-element analysis, the larger the relevance degree, the better the conformity with its level set. The expressions for the relevance functions are as follows:

$$k_j\left(v_i\right)=\left\{\begin{array}{c}{\displaystyle \frac{-{\rho }_{ji}\left(v_i,v_{ji}\right)}{\left|v_{ji}\right|}}\left(v_i\in v_{ji}\right)\\ {\displaystyle \frac{{\rho }_{ji}\left(v_i,v_{ji}\right)}{{\rho }_{ji}\left(v_i,v_{pi}\right)-{\rho }_{ji}\left(v_i,v_{ji}\right)}}\left(v_i\notin v_{ji}\right)\end{array}\right.$$

(15)

$$\rho \left(v_i,v_{ji}\right)=\left|v_i-{\displaystyle \frac{1}{2}}\left(a_{ji}+b_{ji}\right)\right|-{\displaystyle \frac{1}{2}}\left(b_{ji}-a_{ji}\right)$$

(16)

$$\rho \left(v_i,v_{pi}\right)=\left|v_i-{\displaystyle \frac{1}{2}}\left(a_{pi}+b_{pi}\right)\right|-{\displaystyle \frac{1}{2}}\left(b_{pi}-a_{pi}\right)$$

(17)

where k_j(v_i) represents the relevance degree for the j-th level of the matter-element to be evaluated, specifically for the i-th criterion; ∣v_ji∣ is the modulus of the defined interval; ρ_ji(v_i,v_ji) represents the distance between the i-th measured value v_i and the finite interval of the corresponding classical domain value range v_ji; and ρ_ji(v_i,v_pi) represents the distance between the i-th measured value v_i and the finite interval of the corresponding interval domain value range v_pi.

Step 9: Determine the risk level. The comprehensive relevance degree of the matter-element with respect to the risk level is denoted by K:

$$k_j\left(N\right)={\displaystyle \sum _{i=1}^n{W}_i{k}_j\left(v_i\right)}$$

(18)

$$C(P)={\displaystyle \sum _{j=1}^n{W}_I{k}_j\left(N\right)}$$

(19)

where W_I represents the first-level risk indicator correction weight and C(P) represents the final risk assessment level.

3. Case Study

3.1. Study Area

This study focuses on the central urban area of the Liwan District in Guangzhou City, China. Its boundary extends from Renmin South Road in the east to Penglai Road in the west, and from Liuer San Road along the Inner Ring Road in the south to Enning Road in the north, covering a total area of 1 square kilometer. The geographical location of the study area is illustrated in Figure 2. The Liwan District is characterized by its warm and rainy climate, abundant sunshine, and an average annual temperature ranging from 21.4 °C to 21.8 °C. The daily average temperature remains above 0 °C. The region experiences ample rainfall throughout the year, averaging 1650.33 mm, with an uneven distribution throughout the year. Heavy rains occur primarily during the flood seasons, which span from May to September, contributing approximately 80% of the annual rainfall. Such climatic conditions make the Liwan District vulnerable to frequent flood disasters. Therefore, it is essential to assess flood risk here for better urban management.

3.2. Data Sources

This study employs the SWTM hydrodynamic model, which couples the SWMM and TELEMAC-2D models, to obtain hazard factors. The SWMM model is primarily used for simulating rainfall runoff and pipe network hydraulics, and the TELEMAC-2D model is applied to perform the two-dimensional hydrodynamic simulations [29,30,31,32]. The DEM data required for model construction was obtained from satellite imagery, while the land use type data was acquired from geospatial data clouds. The data on pipe networks, inspection wells, measured well fluid levels, and water accumulation points were collected through on-site measurements. The data on exposure factors, vulnerability factors, and regional refuge capacity factors were mainly obtained through the statistical analysis of the original data.

The sources of flood risk index data are summarized in

Table 1. Data sources of flood risk assessment indicators.

Class	Factor	Short Title	Data Sources
Hazard factors	Max inundation depth	MaxD	Model simulation results
	Max inundation velocity	MaxV	Model simulation results
Exposure factors	Elevation	DEM	National Geomatics Center of China
	Slope	Slope	GIS technology extraction
	Imperv	Imperv	GIS technology extraction
Vulnerability factors	GDP density	GDP	Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences
	Population density	POP	Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences
	POI distance	POI DIST	Gaode Map
Regional refuge capacity factors	Disaster prevention and mitigation capability	FCDC	<Guangzhou Statistical Yearbook>
	Flood control and drainage capacity	DPMC	GIS calculation for pipeline network density

.

3.3. Urban Flood Risk Assessment Results

3.3.1. Results of Index Factor Analysis

Hazard Factors

The hazard factors include max inundation depth and max inundation velocity, which were calculated by the SWTM model. Based on the generalized study area, a one-dimensional pipe network SWMM model was constructed, as shown in Figure 3.

In the TELEMAC-2D model, the entire study area was divided into unstructured triangular grids, amounting to a total of 175,304 grids and 97,107 point sources, as shown in Figure 4a. Geometric files of elevation for the model and the bottom friction of Manning’s coefficient were established, as shown in Figure 4b,c.

The water level in the gully pot and the surface inundation were used to calibrate and validate the one-dimensional pipe network model and the two-dimensional surface inundation model in the SWTM, respectively. This study selected two rainfall events recorded in the on-site actual measurement data on 25 July and 19 August 2021 for calibration and verification. The infiltration model adopted the Horton model in the SWTM. The Horton model has three main parameters: minimum infiltration rate, maximum infiltration rate, and attenuation factor. The maximum infiltration rate represents the initial infiltration rate, and the minimum infiltration rate represents the stable infiltration rate. The Horton model simulates the trend of the infiltration rate decreasing over time through the attenuation factor value until a stable permeation state. Therefore, the model will dynamically calculate the water accumulation and infiltration processes for each sub-watershed based on the three parameters of the Horton model. The SWTM model’s physical parameters are adjusted through trial calculation, and the main parameters of the adjusted model are shown in

Table 2. Calibration values of SWTM model parameters in the study area.

Physical Parameters Land Use Type	Roadway	Building	Hardening of the Pavement	Vegetation	Bare Soil	Else
Manning coefficients	0.02	0.02	0.025	0.15	0.04	0.02
Maximumfill volume (mm)	2	2	2	6	5	2
Impermeable percentage	0.92	0.92	0.92	0.15	0.3	0.3
Initial infiltration rate (mm·h−1)	58.45	58.45	58.45	76	35.82	34.72
Stable infiltration rate (mm·h−1)	0	0	0	20	6	6.6
Attenuation factor	20	20	20	2.28	3.3	3.3

.

The degree of conformity between the simulated and observed values of the inundation depth is usually used to determine whether the model parameters are reasonable. The Nash–Sutcliffe efficiency coefficient (Formula (20)) is utilized to verify and analyze the accuracy of the SWTM. A Nash efficiency coefficient (E) value closer to 1 suggests that the simulation result is close to the observed value.

$$E=1-{\displaystyle \frac{{\displaystyle \sum _{t=1}^T{\left(Q_0^{t}t-Q_m^t\right)}^2}}{{\displaystyle \sum _{t=1}^T{\left(Q_0^{t}t-\overline{Q_0}\right)}^2}}}$$

(20)

where $Q_0^{t}t$ represents the observed value at time t; $Q_m^t$ represents the simulated value at time t; and $\overline{Q_0}$ represents the mean of observations.

Using the one-dimensional pipe network model, Figure 5 shows the calibration and verification water level results of gully pots (No.000088, No.000077). Figure 6 shows the calibration and verification inundation depth results of inundation points (No.0060110041, No.0060110004). The results show that both the Nash Efficiency Coefficients are more than 0.7, indicating that the SWTM model has a high simulation accuracy.

Then, the SWTM was applied to perform the simulation of urban flooding under the circumstance of rainfall of 20a. The study area’s storm intensity formula in this paper refers to the “Storm Intensity Formula and Calculation Charts for the Central Urban Area of Guangzhou” (June 2011 edition). The Chicago rainfall model, because of its high degree of parameterization and ease of operation, has become one of the preferred models for urban drainage design in China. Consequently, the Chicago storm pattern [33] was employed to estimate the 2h rainfall process under a return period of p = 20a. The formula is as follows:

$$q={\displaystyle \frac{3618.427\left(1+0.438LgP\right)}{{\left(t+11.259\right)}^{0.750}}}$$

(21)

where q represents the designed storm intensity, in (L/s)/hm²; t represents the rainfall duration, in min; and P represents the design return period, in years.

Then, based on the SWTM simulation results, the maximum water depth and maximum velocity grid maps were calculated and retrieved, as shown in Figure 7. It can be observed that areas with deep water accumulation and high flow velocities are mainly concentrated in the southern part of the study area.

Exposure Factors

The results of the exposure factors, including elevation, slope, and impervious area percentage raster values for the research area, are shown in Figure 8. It can be observed that the eastern part of the study area has a higher terrain, and the overall slope is relatively gentle. Additionally, the impervious area percentage is relatively low in the southeastern and southwestern regions of the study area.

Vulnerability Factors

Based on Formulas (1)–(4), the GDP, POP, and POI distance raster results for the study area were obtained, as shown in Figure 9. It can be observed that the areas with the highest GDP values and population density are primarily located in the eastern region. Additionally, the POI distance distribution in the study area is relatively uniform.

Regional Shelter Capability

The results of the regional shelter capabilities, including disaster prevention and mitigation capabilities, as well as flood control and drainage capabilities within the study area, are shown in Figure 10. This figure clearly shows that the disaster prevention points are densely distributed in the central region of the study area, while the pipe network density is moderate and relatively concentrated.

3.3.2. Index Weight Results

Based on the ISEM model constructed in Steps 1 to 4, the results of the reliability and validity analysis, as well as the goodness-of-fit parameters, are presented in

Table 3. Risk assessment indicator reliability and validity analysis results.

	Criterial-Layer Index	Cronbach’s Alpha		Variable	KMO	Bartlett’s Test of Sphericity
						Approximate Chi-Square	Degrees of Freedom	Significance
Reliability Analysis	Hazard risk of causative factors	0.886	Validity Analysis	F1	0.600	117.926	1	<0.001
	Exposedness of disaster environment	0.813		F2	0.668	134.949	3	<0.001
	Vulnerability of the affected system	0.830		F3	0.663	171.134	3	<0.001
	Regional shelter capability	0.729		F4	0.600	89.656	3	<0.001
	Total	0.936		Total	0.903	898.884	45	<0.001

and

Table 4. ISEM model fit index verification.

Fit Index	Model Computation Results (Standard)	Fit Degree
X2/DF	2.815 (<5)	Fit
RMSEA	0.05 (<0.08)	Fit
GFI	0.851(>0.8)	Fit
AGFI	0.835(>0.8)	Fit
CFI	0.868(>0.8)	Fit
IFI	0.830(>0.8)	Fit

, respectively. The goodness-of-fit parameters of the ISEM model were analyzed and calculated using Partial Least Squares (PLS) analysis. The fitting index X2/DF value and the other fitting metrics all met the evaluation criteria. A comparison of the corrected weights based on the correlation coefficient method is illustrated in Figure 11. This figure clearly shows that the weights of MaxD and MaxV are the highest for the ISEM model. Compared with the SEM results, the ISEM results have a more significant emphasis on the importance of MaxD and MaxV in calculating the weights.

3.3.3. Flood Risk Assessment Results

Based on the integrated urban flood risk assessment approach, the results of the flood risk in the study area are presented in Figure 12. It is evident that the risk of urban flood is closely related to the hazard of disaster-causing factors, the exposure of disaster-pregnant environments, the vulnerability of disaster-bearing bodies, and the regional evacuation capacity. Overall, the proportion of the area for each risk level (from low to high, i.e., from level 1 to level 5) in the study area is as follows: 61.41%, 23.19%, 12.64%, 2.15%, and 0.61%. The southern and central–eastern regions are at a high flood risk, characterized by low ground elevations, underlain by buildings, and low regional shelter capability. Moderate-risk areas are mainly located in the central part of the study area, which has higher pipe network densities, as regions with effective drainage capacity and fast evacuation speeds can reduce the overall potential risk. Additionally, the northern and western regions have a low flood risk level due to the uniform ground elevations and lower impervious surface rates.

4. Discussion

4.1. Advantage Analysis of the Integrated Approach

This study introduces the correlation coefficient to modify weights, aiming to avoid redundant calculations between indicators and enhance the accuracy of assessment results. This approach mitigates the risk of inadvertently eliminating important indicators because of their high correlation coefficients with other indicators. The advantages of the integrated approach are shown by a comparative analysis of weights both before and after modification using the correlation coefficient method.

The flood risk results without weight modification indicate that most of the central areas are vaguely classified as low-risk regions. However, the results obtained using the correlation coefficient method to modify weights demonstrate a more pronounced distinction in risk levels, rendering the risk assessment outcomes more convincing, as illustrated in Figure 13.

To further illustrate the robustness of the new method, this paper calculated the grid matching degree of risk level cloud maps and inundation depth level cloud maps under different recurrence periods of rainfall. The calculation results are shown in Figure 14. The average grid matching degree calculated using the correlation coefficient factor method is 77.51%. In contrast, the grid matching degree of the unmodified weight calculation results is approximately 53.82%. This suggests that the risk assessment results obtained through the correlation coefficient method for weight modification are superior, and the calculation accuracy is enhanced by 23.69%.

4.2. Limitations and Future Work

Urban flood risks are the result of the combined effects of numerous influencing factors. Due to the difficulty in obtaining data for some indicators, like the investment amount in engineering and non-engineering measures for disaster prevention and mitigation, there may be a lack of comprehensiveness in the selection of indicators, which may lead to deviations in research results. Additionally, some actual data values of indicators are quantified through questionnaire surveys, like regional shelter capability, which may affect the accuracy of the assessment results. Therefore, in subsequent studies, a more complete and representative risk indicator system should be constructed to reduce research errors.

5. Conclusions

This study aims to develop an integrated and universal urban flood risk assessment framework to enhance disaster prevention and mitigation strategies. The main findings can be summarized as follows: (1) A novel multi-dimensional indicator system is constructed, comprising four core components, including hazard, exposure, vulnerability, and regional resilience capacity, through hydrological–hydrodynamic modeling combined with a systematic literature review. (2) An enhanced weighting methodology is proposed by integrating improved structural equation modeling (ISEM) coupled with Pearson’s correlation coefficient analysis, significantly improving the accuracy of indicator weight determination by 23.69%. (3) The extensible matter-element analysis method (EMAM) is innovatively applied for risk quantification, providing a robust scientific basis for urban flood risk stratification. (4) Comparative analysis reveals that the integrated methodology outperforms traditional assessment approaches in terms of risk assessment accuracy, demonstrating significant potential for flood risk management applications.