Comprehensive Evaluation of Urban Storm Flooding Resilience by Integrating AHP–Entropy Weight Method and Cloud Model

Abstract

To address urban flooding challenges exacerbated by climate change and urbanization, this study develops an integrated assessment framework combining the analytic hierarchy process (AHP), entropy weight method, and cloud model to quantify urban flood resilience. Resilience is deconstructed into resistance, adaptability, and recovery and evaluated through 24 indicators spanning water resources, socio-economic systems, and ecological systems. Subjective (AHP) and objective (entropy) weights are optimized via minimum information entropy, with the cloud model enabling qualitative–quantitative resilience mapping. Analyzing 2014–2024 data from 27 Chinese sponge city pilots, the results show resilience improved from “poor to average” to “good to average”, with a 2.89% annual growth rate. Megacities like Beijing and Shanghai excel in resistance and recovery due to infrastructure and economic strengths, while cities like Sanya enhance resilience via ecological restoration. Key drivers include water allocation (27.38%), economic system (18.41%), and social system (17.94%), with critical indicators being population density, secondary industry GDP ratio, and sewage treatment rate. Recommendations emphasize upgrading rainwater storage, intelligent monitoring networks, and resilience-oriented planning. The model offers a scientific foundation for urban disaster risk management, supporting sustainable development. This approach enables systematic improvements in adaptive capacity and recovery potential, providing actionable insights for global flood-resilient urban planning.

1. Introduction

Flooding is the most frequent natural disaster in the world and causes very high loss of life and property every year [1]. With the acceleration of global climate change and urbanization, the frequency and impact of urban floods have been expanding, bringing unprecedented challenges to urban flood risk management [2]. All countries are actively seeking methods and strategies to mitigate the impact of urban flooding. For example, the United States successively proposed Best Management Practices (BMPs) and Low Impact Development (LID) in the 1980s [3]; Australia proposed Water Sensitive Urban Design (WSUD) in 1994 [4]; and the United Kingdom proposed Sustainable Drainage System (SUDS) in 1997 [5]. Based on the U.S. LID and the Australian WSUD, New Zealand started the Low Impact Urban Design and Development (LIUDD) program in 2003 [6] and so on [7,8]. Based on this, the concept of “sponge city” was proposed and put into practice in China in 2012 [9], aiming at adapting to environmental changes and improving the resilience of cities against natural disasters caused by rainfall-induced climate change. Meanwhile, the Sendai Framework for Disaster Risk Reduction (2015–2030) [10] issued by the United Nations emphasizes the importance of resilience in disaster prevention and mitigation. The Recommendations of the Central Committee of the Communist Party of China on the Formulation of the Fourteenth Five-Year Plan for National Economic and Social Development and Vision 2035 emphasized enhancement of the resilience of urban systems in order to prevent and resolve major risks. It can be seen that increasing resilience has now become a focus of international attention and is one of the main concerns of flood-prone cities and countries.

Many experts and scholars have emphasized the concept of urban flood disaster resilience, and many research methods and research results have been proposed.

From an overall perspective, Rathnasiri et al. [11] conducted a scientometric analysis using CiteSpace software. They found that China and the United States are the main contributors to research in this field. The analysis identified high-frequency keywords such as “modeling”, “big data”, “prediction”, and “artificial neural network”, reflecting the research hotspots and development trends. It is also argued that data-driven approaches, such as machine learning, artificial intelligence, and building information modeling, can identify and learn patterns and trends in large datasets to improve flood prediction, monitoring, and damage assessment. Among the models currently in use, machine learning models (such as ANN and LSTM) analyze the nonlinear relationships between historical flood data and multi-source environmental variables (such as rainfall and topography), significantly improving prediction accuracy by 15–30% compared to traditional methods, thereby enabling short-term flood risk warnings, while artificial intelligence optimization algorithms (such as PSO-ELM) enhance model generalization capabilities through feature selection and parameter adaptive adjustment, achieving an AUC score exceeding 0.92 in flash flood sensitivity mapping, thereby supporting precise identification of high-risk areas. Wang et al. [12] used bibliometric analysis to investigate the trend of flood management strategies over time and proposed that future flood management strategies reintegrate sustainability, resilience, and adaptation. Gao et al. [13] used social network analysis and hierarchical cluster analysis using VOS Viewer software to present the changes in urban flood research quantitatively and dynamically, noting that urban flood resilience, as an important indicator of urban planning and management, has seen rapid growth in research in the water sector since 2016. Meanwhile, research has focused on climate change adaptation, disaster resilience, urban planning and management, and urban risk tolerance.

The term “resilience” involves concepts that cover a wide range of directions, and this paper focuses on the resilience of cities when they are exposed to heavy rainfall and flooding disasters. Based on a literature review, Martin-Breen and Anderies [14] provide a universal and detailed categorization of flood resilience, which defines resilience into three main categories: engineering resilience, system resilience, and complex adaptive systems.

Many attempts to introduce the concept of resilience into flood management have been limited to improving the stability of drainage systems. This paper argues that the resilience to urban storm flooding disasters involves not only the ability to “bounce back” after a disaster but also the ability to continuously update and upgrade the system after resisting the impact of the disaster, which is a resilient system of complex adaptive systems.

Scholars have applied different methods and models to study and evaluate the concept of “resilience”. Hussain et al. [15] proposed a “Capability-based Flood Resilience Model” (CapFlooR-M), which combines machine learning (ML), geographic information system (GIS), remote sensing (RS), and analytic hierarchy process (AHP) to assess community resilience to flood hazards. The model is divided into four components: flood hazard susceptibility, coping capacity, adaptive capacity, and transformational capacity. Riyadh et al. [16] constructed two models: DROP and SERV. The DROP model implementation selects indicators through Pearson’s correlation coefficient analysis and the Cronbach’s alpha reliability test and calculates the overall resilience score. The SERV model expresses flood resilience as a function of adaptive capacity, flood exposure, and susceptibility and uses principal component analysis (PCA) to screen the indicators and equal-weight combinations to obtain the resilience score. Meng et al. [17] took Xi’an City as an example, constructed an assessment system containing 21 specific indicators from three significant attributes (resistance, adaptability, and resilience) and four dimensions (economy, society, ecology, and infrastructure), determined the weights of the indicators based on the analytic hierarchy process (AHP) and the CRITIC method, and finally used the TOPSIS assessment method to assess the level of urban resilience by calculating the fit of the assessed object to the positive ideal solution. The level of urban resilience is assessed by calculating the fit of the assessment object to the positive ideal solution. Zhu et al. [18] developed an assessment framework using a semi-quantitative method by combining statistical data and expert opinions. The framework includes indicators of resilience, coping, recovery, and adaptive capacity, and it combines VIKOR and gray correlation analysis (GRA) methods for assessing urban flood resilience. Wang et al. [19] used zero-mean normalization and principal component analysis (PCA) to determine the weights of the indicators and the Mann–Kendall trend test and wavelet analysis to determine trends in urban flood resilience and subsystem resilience and constructed a structural equation model (SEM) to analyze the impact of urban systems on urban flood resilience. However, most of the approaches rely on either purely subjective weighting or objective statistical methods, which may introduce bias when used independently. To overcome this limitation, this study adopts an integrated AHP–entropy weight method. The AHP effectively incorporates expert knowledge to capture the hierarchical structure of resilience dimensions, while the entropy weight method quantifies information utility from empirical data to reflect indicator variability. Their combination through minimum information entropy optimization balances subjective expertise with objective data characteristics, minimizing arbitrariness in weight assignment. Based on previous research in flood risk [20], this hybrid approach has demonstrated enhanced robustness in complex system evaluations, such as urban safety assessments and water resource management.

Furthermore, urban flood resilience involves inherent uncertainties from both qualitative perceptions and quantitative measurements. Traditional methods struggle with these ambiguities. The cloud model, founded on probability and fuzzy set theory, addresses this gap by characterizing qualitative concepts through three digital parameters—expectation (Ex), entropy (En), and hyper-entropy (He). It enables bidirectional transformation between linguistic resilience levels and numerical data via probabilistic membership functions, effectively capturing randomness and fuzziness in resilience assessment. This capability is critical for mapping multidimensional indicators to holistic resilience grades.

Therefore, this study constructs a scientific urban flooding disaster resilience evaluation system by integrating AHP–entropy weighting with the cloud model. This framework quantitatively assesses resilience levels while addressing both structural hierarchy and data uncertainty, enabling accurate identification of urban risk-resistant capacities under climate change and natural disasters.

2. Model Construction

2.1. Methods Used in Model Construction

This study analyzes subjective and objective indicator weights using the analytic hierarchy process (AHP) and the entropy weight method, respectively, and the indicator data are comprehensively evaluated using the cloud model. The model framework is shown in Figure 1.

2.1.1. Analytic Hierarchy Process

The AHP is one of the most typical multi-criteria decision-making (MCDM) tools, which was first proposed by Thomas Saaty [21,22]. It is a systematic analysis and decision-making process that decomposes the problem that needs to be decided into multiple levels, including the objective, criterion, and indicator levels, and decomposes the complex problem into manageable parts. The relative importance of the indicators is determined using expert judgment and scoring by decomposing the various indicators affecting the resilience of the city’s flooding disaster management into multiple levels and then through pairwise comparisons. Then, the weights of the indicators are calculated to provide a quantitative basis for decision-making.

Urban storm flooding disaster resilience is a complex adaptive system. According to previous studies [23,24,25], using the AHP, the concept of resilience can be deconstructed into three assessment indicators (resistance, adaptability, and resilience), and then the assessment indicator system can be further refined according to the principles of scientific objectivity, representativeness, independence, and operability to comprehensively assess the level of resilience to urban storm flooding disaster.

2.1.2. Entropy Weight Method

The entropy weight method, as an objective assignment method, can determine the weight of each indicator in the total evaluation while avoiding the interference of human factors. This method is based on the concept of entropy in information theory and reflects the degree of dispersion by calculating the entropy value of each indicator. The larger the entropy value, the greater the variability of the indicator and the less information it provides, so it should be given a smaller weight; on the contrary, the smaller the entropy value, the smaller the variability of the indicator, and the greater the information, so it should be given a more considerable weight.

2.1.3. Cloud Model and Calculation

The cloud model was proposed by Li Deyi [26] in 1995. It is constructed based on probability theory and fuzzy mathematics and realizes the quantitative transformation of qualitative concepts in natural language by integrating randomness and fuzziness through digital feature entropy. Its core regular cloud model relies on three parameters (expectation, entropy, and super entropy), breaks through the traditional usual distribution limitations, and expands the exact affiliation function into the probability distribution expectation function, significantly improving the efficiency of qualitative–quantitative conversion. This study uses the model to construct a resilience evaluation system for urban flooding disasters, realizing the cross-dimensional mapping between the index data and the concept of resilience level.

2.2. Construction of Toughness Assessment Index System

The resilience to urban storm flooding disasters includes three secondary indicators: resistance, adaptability, and resilience. According to the principles of scientificity, objectivity, representativeness, independence, and operability, a total of 24 tertiary indicators are identified in six groups—water resources, society, infrastructure, ecology, economy, and management—as shown in Figure 2 and further details can be found in Appendix A.

Resilience represents a city system’s inherent ability to withstand rainfall impacts, with a focus on defensive capabilities prior to a disaster occurring. The water resource group (C) indicators directly reflect the hydrological pressures faced by a city and the sustainability of resource utilization; the higher the water consumption, the weaker the system’s buffering capacity against extreme precipitation. Meanwhile, the management group (D) indicators measure proactive prevention and control capabilities. Together, these form the “first line of defense” against disasters. For example, annual precipitation (X9) directly reflects hydrological pressure; the higher the precipitation, the stronger the initial impact on the system. Water consumption of CNY 10,000 GDP (X11) indicates resource utilization efficiency; the higher the water consumption, the stronger the economy’s dependence on water resources, and the more likely a mismatch in water resources caused by heavy rain will lead to systemic collapse. Flood control fiscal expenditure (X13) measures engineering defense investments, with funding directly determining the hardware protection levels of embankments, pump stations, and other infrastructure. Adaptability describes the system’s dynamic regulatory capacity during disasters. The social group (A) indicators reflect the sensitivity of social structures to disasters, while the infrastructure group (B) indicators determine rainwater drainage efficiency, with the two collectively supporting the system’s ability to maintain core functions during disasters. For example, the proportion of the population with a university degree (X1) reflects the knowledge reserves for disaster response; the higher the education level, the stronger the public’s self-rescue and mutual aid capabilities. Regarding the indicator for permanent resident density (X2), it represents the density of the average permanent resident population for that year. Drainage pipeline density (X5) determines rainwater drainage efficiency; the higher the pipeline density, the lower the risk of surface water accumulation during heavy rainfall. The number of warning messages issued (X14) reflects the speed of emergency response, with the frequency of warnings indicating the sensitivity of the monitoring system, thereby securing a critical time window for evacuation. Resilience characterizes the system’s ability to recover and upgrade after a disaster. The economic group (E) indicators provide reconstruction resource guarantees, while the ecological group (F) indicators reduce long-term vulnerability through environmental restoration, with the two groups synergistically promoting system iteration and evolution. For example, per capita GDP (X17) provides resource guarantees for reconstruction, as economic strength determines the ability to allocate funds and materials for post-disaster restoration; urban forest coverage (X21) enhances environmental resilience, as forest roots stabilize soil to reduce landslides and tree canopies intercept rainfall to alleviate flooding; and sewage treatment rate (X22) controls secondary disasters, preventing public health crises caused by sewage overflow due to heavy rainfall.

2.3. Determination of Joint Weights of the AHP and Entropy Weight Method

2.3.1. Determination of Weights by the AHP Method

(1)

Construction of the judgment matrix

Based on the sponge city resilience evaluation index system, expert questionnaires are designed (See Appendix B for details). Using Saaty’s 1~9 scale method, experts are invited to compare the importance of each evaluation index two by two and construct judgment matrices for each level. The specific relationship expression of the judgment matrix is shown in Formula (1):

$$A={\left[a_{ij}\right]}_{n\times n}=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \dots & a_{1n}\\ a_{21}& a_{22}& \dots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{n1}& a_{n2}& \dots & a_{nn}\end{array}\right]$$

(1)

(2)

Hierarchical single sorting

For the judgment matrix, it is necessary to carry out hierarchical single sorting, i.e., to sort the importance of each indicator at this level relative to an indicator at the previous level. First of all, each column of the judgment matrix is normalized, then the normalized matrix is summed up by rows, and finally the resulting vector is normalized again. The calculation steps are shown in Equations (2)–(4):

$$\overline{a_{ij}}={\displaystyle \frac{a_{ij}}{\sum _{i=1}^n{a}_{ij}}}$$

(2)

$$\overline{w_i}=\sum _{i=1}^n\overline{a_{ij}}$$

(3)

$$w_i={\displaystyle \frac{\overline{w_i}}{\sum _{i=1}^n\overline{w_i}}}$$

(4)

Finally, the eigenvectors of the judgment matrix W = [W₁, W₂, W₃, …, W_n]^T are obtained:

$${\lambda }_{max}=\sum _{i=1}^n{\displaystyle \frac{{\left(AW\right)}_i}{n{W}_i}}$$

(5)

$$CI={\displaystyle \frac{{\lambda }_{max}-n}{n-1}}$$

(6)

$$CR={\displaystyle \frac{CI}{RI}}$$

(7)

(3)

Consistency test

The consistency test is carried out on the judgment matrix, i.e., the maximum eigenvalue of the judgment matrix ${\lambda }_{max}$, the consistency index of the judgment matrix CI, and the consistency ratio CR are calculated. When CR ≤ 0.1, the judgment matrix passes the consistency test; if CR > 0.1, it is necessary to adjust the values in the judgment matrix A and re-conduct the consistency test. The correlation calculation is shown in Equations (5)–(7).

The value of the weight of the second-level indicators is multiplied with the value of the weight of the third-level indicators to obtain the subjective weight $W_j^{\alpha }$ of each indicator:

$$W_j^{\alpha }=w_j^A\times w_j^B$$

(8)

In the formula, $W_j^{\alpha }$ is the total hierarchical ordering weight value of the third-level indicator layer for the target layer, $w_j^A$ is the hierarchical single-ordering weight value of the second-level indicator layer for the target layer, and $w_j^B$ is the hierarchical single-ordering weight value of the third-level indicator layer for the corresponding second-level indicator layer.

2.3.2. Determination of Weights by the Entropy Weight Method

(1)

Construction of the original data matrix

The original data matrix is constructed as [$x_{ij}$](i = 1, 2, …, m; j = 1, 2, …, n), where $x_{ij}$ is the value of the jth indicator in the ith year of the study city, m is the number of years, and n is the number of evaluation indicators. The evaluation matrix of the urban storm flooding disaster resilience system obtained is

$$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}& x_{m2}& \dots & x_{mn}\end{array}\right]$$

(9)

(2)

Indicator data standardization

In the evaluation index system, due to the differences in the content and outline of the indicators, it is not possible to calculate the weights directly based on the original data. Therefore, it is necessary to standardize the indicators and transform them into a unified measurement standard. Specifically, after normalizing the matrix $X={\left(x_{ij}\right)}_{mn}$, the standardized indicators $r_{ij}$∈ [0, 1], $R={\left(r_{ij}\right)}_{mn}$ are obtained. Then, the data normalization process is performed to calculate $p_{ij}$, the weight of the jth indicator in year i.

When the indicator is a positive indicator, the normalization formula is as follows:

$$r_{ij}={\displaystyle \frac{x_{ij}-\mathit{min}{x}_{ij}}{\mathit{max}{x}_{ij}-\mathit{min}{x}_{ij}}}$$

(10)

When the indicator is a negative indicator, the normalization formula is as follows:

$$r_{ij}={\displaystyle \frac{\mathit{max}{x}_{ij}-x_{ij}}{\mathit{max}{x}_{ij}-\mathit{min}{x}_{ij}}}$$

(11)

where $\mathit{min}{x}_{ij}$ is the minimum data value in the indicator, and $\mathit{max}{x}_{ij}$ is the maximum data value in the indicator.

The weight $p_{ij}$ of indicator j in year i is normalized using standardized data $r_{ij}$, i.e.,

$$p_{ij}={\displaystyle \frac{r_{ij}}{\sum _{i=1}^m{r}_{ij}}}$$

(12)

(3)

Calculation of indicator information entropy

The information entropy of indicators $e_j$ is calculated using Formula (13):

$$e_j=-{\displaystyle \frac{1}{\mathit{ln}\left(m\right)}}\sum _{i=1}^m{p}_{ij}\mathit{ln}\left(p_{ij}\right)$$

(13)

In the formula, in order to ensure that the $e_j$ calculation results have practical significance, it is specifically stipulated that when $p_{ij}$ = 0, the $p_{ij}\mathit{ln}\left(p_{ij}\right)$ value is taken as 0.

(4)

Calculation of indicator weights

The information entropy $e_j$ is used to calculate the size of the weight of each indicator $W_j^{\beta }$:

$$W_j^{\beta }={\displaystyle \frac{1-e_j}{\sum _{j=1}^{n}1-e_j}}$$

(14)

2.3.3. Determination of Joint Weights

The indicator weights determined by the AHP mainly reflect the subjective preferences of decision-makers, while the weights of the entropy weight method focus more on the interrelationships between the data. In order to play the advantages of the two methods and reduce the influence of subjective factors in the AHP, the weights obtained by the two methods can be combined, and based on the principle of minimum information entropy, the optimized Lagrange multiplier method is used to calculate the joint weights $W_j$, which is calculated by the following formula:

$$W_j={\displaystyle \frac{{\left[W_j^{\alpha }\times W_j^{\beta }\right]}^{\rho }}{\sum _{j=1}^n{\left[W_j^a\times W_j^{\beta }\right]}^{\rho }}}$$

(15)

where $\rho$ is the discrimination coefficient; a value of ρ = 0.5 is adopted to balance the contributions of subjective ($W_j^{\alpha }$) and objective ($W_j^{\beta }$) weights, ensuring neither dominates disproportionately. ρ = 0.5 yields the most stable evaluation outcomes across pilot cities. Values of ρ < 0.5 overemphasize subjective preferences, increasing model volatility, while ρ > 0.5 amplifies data noise, particularly in indicators with high dispersion. The moderate ρ = 0.5 optimally supports robustness in resilience assessment [27].

The joint weights $W_j$ are further calculated to obtain the urban flooding disaster resilience level index ${RI}_j$:

$$R{I}_j=\sum _{i=1}^n{r}_{ij}\times W_j$$

(16)

2.4. Resilience Evaluation of Urban Flooding Disaster Based on Cloud Modeling

The key to the cloud model is to construct a cloud generator to realize the mutual conversion between qualitative description and quantitative data so as to effectively deal with the ambiguity and uncertainty problems in the resilience evaluation process. The specific operation steps are as follows.

2.4.1. Establishment of Evaluation Criteria Cloud

First of all, the comment set is defined, and the corresponding grade interval is set for each evaluation. A rubric set is a collection of all possible evaluation results given by the evaluator to the evaluation object, which is used to assist experts in scoring. Based on the rubric set, the standard evaluation cloud is determined. According to the number of urban resilience grade divisions, the indicator evaluation thesis is divided into n sub-intervals, where the ith sub-interval is denoted as $\left[x_i^{min},x_i^{max}\right]$, and the numerical eigenvalue of the normal cloud of this sub-interval (expectation $E{x}_i$, entropy $E{n}_i$, hyper-entropy $H{e}_i$) can be expressed as

$$\left\{\begin{array}{c}E{x}_i={\displaystyle \frac{\left(X_i^{max}+X_i^{min}\right)}{2}}\\ E{n}_i={\displaystyle \frac{\left(X_i^{max}-X_i^{min}\right)}{6}}\\ H_{e_i}=k\end{array}\right.$$

(17)

In this sub-interval, $x_i^{min}$ and $x_i^{max}$ represent the minimum and maximum values; k is an empirical constant, which can be adjusted according to the specific situation, with a value of 0.5 taken in this study.

2.4.2. Construction of Evaluation Index Cloud

According to the processed data of each toughness indicator, the evaluation matrix is obtained, assuming that the indicator data of the evaluated city in years m and n indicators are selected; then, the evaluation matrix is expressed as follows, in which the toughness score of indicator j in year i of the city is expressed as $z_{ij}$:

$$Z=\left[\begin{array}{cccc}{z}_{11}& z_{12}& \dots & z_{1n}\\ z_{21}& z_{22}& \dots & z_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ z_{m1}& z_{m2}& \dots & z_{mn}\end{array}\right]$$

(18)

The mean, variance, and evaluation cloud parameters of each indicator are obtained through the inverse cloud generator. The evaluation cloud for the jth indicator is C_j($E{x}_j$, $E{n}_j$, $H{e}_j$), j = 1, 2, …, n. This study uses the SBCT-1^stM algorithm with the following formula:

$$\left\{\begin{array}{c}E{x}_j={\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m}{x}_{ij}\\ E{n}_j=\sqrt{{\displaystyle \frac{\pi }{2}}}\times {\displaystyle \frac{1}{m}}{\displaystyle \sum _{i=1}^m}\left|x_{ij}-E{x}_j\right|\\ S_j^2={\displaystyle \frac{1}{m-1}}{\displaystyle \sum _{i=1}^m}{\left(x_{ij}-E{x}_j\right)}^2\\ H{e}_j=\sqrt{S_j^2-E{n}_j^2}\end{array}\right.$$

(19)

where m is the number of years of the evaluated city toughness indicator data, n is the number of evaluation indicators, and $S_j^2$ is the variance of the jth evaluation indicator.

Combining the cloud parameters and joint weights of each indicator, and considering the interconnection between the indicators, the evaluation indicators are transformed into a more comprehensive generalized cloud model through the comprehensive cloud algorithm in the virtual cloud theory, and the resilience comprehensive cloud parameters (Ex, En, and He) are finally summarized:

$$\left\{\begin{array}{c}Ex={\displaystyle \sum _{j=1}^n}\left(E{x}_j\times {\omega }_j\right)\\ En=\sqrt{{\displaystyle \sum _{j=1}^n}\left(E{n}_j^2\times {\omega }_j^2\right)}\\ He=\sqrt{{\displaystyle \sum _{j=1}^n}\left(H{e}_j^2\times {\omega }_j^2\right)}\end{array}\right.$$

(20)

where n is the number of indicators, ${\omega }_j$ is the joint weight of the jth indicator, and (Ex_j, En_j, He_j) is the cloud parameter of the indicator.

2.4.3. Model Calculation and Comprehensive Evaluation

MATLAB software (Ver R2023b) is used to draw the standard cloud diagram, and the forward cloud generator is used to generate the comprehensive cloud diagram for toughness evaluation and compare it with the evaluation standard cloud diagram to determine the toughness grade intuitively and preliminarily. At the same time, the CFSM algorithm [28] is used to calculate the similarity between the evaluation comprehensive cloud and the standard cloud model, and the toughness level is objectively determined according to the principle of maximum similarity. The resilience assessment results of urban storm flooding disasters are divided into five resilience levels, which are “excellent”, “good”, “average”, “fair”, and “poor”.

The similarity is calculated by the following formula:

$$\left\{\begin{array}{c}\alpha ={\displaystyle \frac{\left|E{x}_1-E{x}_2\right|}{\sqrt{E{n}_1+H{e}_1}+\sqrt{E{n}_2+H{e}_2}}}\\ {\phi }_{\left(\alpha \right)}=\underset{-\infty }{\overset{\alpha }{\int }}{\displaystyle \frac{1}{\sqrt{2\pi }}}{e}^{-{\displaystyle \frac{x^2}{2}}}dx\\ C\left(N_1,N_2\right)={\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2{\phi }_{\left(a\right)}}}-{\phi }_{\left(\alpha \right)}\end{array}\right.$$

(21)

where $C\left(N_1,N_2\right)$ denotes the similarity between two sets of normal cloud models: N₁ and N₂.

3. Case Study and Results

3.1. Case Overview

Based on the proposed concept of sponge city, the State Council of China issued the Guiding Opinions of the General Office of the State Council on Promoting the Construction of Sponge Cities in 2015, which clearly defines the definition and objectives of sponge cities and proposes that 70% of rainfall be absorbed and utilized on-site through the measures of “seepage, lagging, storage, purification, use and drainage”. Based on this document, China’s Ministry of Finance, Ministry of Housing and Urban-Rural Development, and Ministry of Water Resources released 30 national-level sponge city construction pilots supported by the central government in two batches in 2015 and 2016. In order to ensure the comparability of the study area and the uniformity of the data, this paper excludes the areas of county-level cities and prefectural-level cities, such as Qian’an City, Xixian New Area, and Gui’an New Area. Finally, it retains 27 prefectural-level city pilots as the study unit. The basic information about the city is shown in

Table 1. Basic information on the 27 pilot cities.

City	Population/Million People	Area/km2	City Size
Baicheng	1.553	25,683	Mid-sized city
Beijing	21.843	16,410	Megacity
Changde	5.253	18,189	Mid-sized city
Chizhou	1.331	8399	Mid-sized city
Dalian	7.512	13,630	Metropolis
Fuzhou	8.448	11,968	Metropolis
Guyuan	1.142	10,541	Mid-sized city
Hebi	1.572	2182	Mid-sized city
Jinan	9.336	10,244	Metropolis
Jiaxing	5.551	4015	Large city
Nanning	8.892	22,112	Metropolis
Ningbo	9.618	9816	Metropolis
Pingxiang	1.805	3823	Mid-sized city
Qingdao	10.342	11,293	Metropolis
Qingyang	2.159	27,119	Mid-sized city
Sanya	1.066	1921	Mid-sized city
Xiamen	5.308	1700	Large city
Shanghai	24.759	6341	Megacity
Shenzhen	17.682	1997	Megacity
Suining	2.782	5326	Mid-sized city
Tianjin	13.63	11,946	Metropolis
Wuhan	13.739	8569	Megacity
Xining	2.476	7660	Large city
Yuxi	2.25	14,941	Mid-sized city
Zhenjiang	3.217	3840	Large city
Chongqing	32.133	82,400	Megacity
Zhuhai	2.477	1736	Large city

.

Meanwhile, China’s rapid urbanization process has led to the continuous expansion of towns and cities; significant changes in land use; and increasing problems of urban flooding, water resource shortage, and water environment pollution. In recent years, China has experienced several extreme heavy precipitation events, which have caused serious problems for economic and social development. Therefore, this study takes the 27 pilot cities as an example, focusing on the study of their heavy rainfall and flooding problems, and tries to assess their resilience level to inland flooding disasters and evaluate the construction of sponge cities to provide a reference for urban flood prevention and mitigation and water resource safety.

3.2. Combined Weight Determination Based on the AHP and Entropy Weight Method

According to the requirements of the indicators, the indicator data of 27 pilot cities in the past 11 years, from 2014 to 2024, are selected, and the moving average and trend interpolation methods supplement the missing data. For the assessment of indicator values, all indicator data is obtained by querying or purchasing directly from official government websites, official statistical yearbooks of each city, and certified databases, resulting in a data matrix for all indicators from 2014 to 2024, which is then calculated by formulas. First, the hierarchical indicator system is constructed through expert decision-making using the AHP. The indicators are compared two by two using the 1–9 scale method to form a judgment matrix. The subjective weights of the indicators at each level are determined through normalization and consistency tests. Then, the entropy weight method is applied to calculate the entropy value of each indicator through normalization of the original data matrix to calculate the objective weights of each indicator. Finally, based on the Lagrange multiplier method, the weights determined by the AHP and the entropy weight method are substituted into Equation (15) to calculate each indicator’s joint weight, as shown in Figure 3.

3.3. Determination of Resilience Level of Heavy Rainfall and Flooding Disaster Based on Cloud Modeling

3.3.1. Evaluation Criteria Cloud

The resilience evaluation standard cloud measures the city’s ability to resist flooding disasters. This study synthesizes fuzzy linguistic features and expert recommendations to construct an urban flooding resilience evaluation system containing five levels: extremely poor, poor, general, good, and excellent resilience. Through the theoretical derivation of the cloud model, the cloud model parameters corresponding to each level are determined based on Equation (17), which serves as the evaluation standard of toughness and is used to subsequently define the level of evaluation. The specific values are detailed in

Table 2. Classification of urban flooding disaster toughness and standard evaluation cloud parameters.

Evaluation Grade	Grade Interval	Ex	En	He
Poor	[0.0, 20.0)	10.0	3.3333	0.5
Fair	[20.0, 40.0)	30.0	3.3333	0.5
Average	[40.0, 60.0)	50.0	3.3333	0.5
Good	[60.0, 80.0)	70.0	3.3333	0.5
Excellent	[80.0, 100.0]	90.0	3.3333	0.5

(the diffusion coefficient is set to s = 0.5). The parameter k corresponds to the hyper-entropy (H_ei) in the cloud model. Sensitivity analyses confirm that Hei = 0.5 maintains a balanced trade-off between fuzziness (ambiguity in resilience grades) and randomness (data volatility), avoiding over-dispersion (H_ei > 1.0) or over-precision (H_ei < 0.2).

Then, using the forward cloud generator to generate 2000 groups of normal digital features, 2000 cloud drops are calculated to determine the degree of affiliation, and the standard cloud map of five resilience classes is obtained, as shown in Figure 4, which serves as a comparison map of the class standards for subsequent evaluation. Each cloud’s vertical dispersion reflects the uncertainty in resilience classification; the cloud peak marks the most probable resilience level, while hyper-entropy controls the cloud’s dispersion degree. A larger He widens the cloud band (increasing ambiguity), while a smaller He narrows it (reducing classification flexibility).

3.3.2. Evaluation Index Cloud

In accordance with the urban flood hazard resilience evaluation index system, basic data are collected, and a multi-temporal resilience evolution analysis model is constructed to systematically assess the development trajectory of the comprehensive resilience level of urban flood hazards in 27 pilot cities between 2014 and 2024. The inverse cloud algorithm is used to realize the conversion of indicator data to cloud model, and the cloud parameter set of each sub-indicator is derived according to Equation (19), which is shown in

Table 3. Cloud parameters of each sub-indicator.

Indicator	Expectation Ex	Entropy En	Hyper-Entropy He
Percentage of population who graduated from university, X1	57.4067	8.0926	2.2979
Density of resident population, X2	49.8697	3.6863	1.4488
Urbanization rate of resident population, X3	81.8763	0.4686	0.1159
Average wage, X4	59.034	7.563	2.298
Drainage density, X5	78.1328	1.5413	0.6612
Density of water supply pipes, X6	66.1334	1.3611	0.501
Urban road area per capita, X7	82.3809	5.1967	3.0464
Average age of drainage pipes, X8	79.0909	4.6972	0.0696
Annual precipitation, X9	59.9238	13.4055	2.4251
Flood season precipitation, X10	69.7045	14.1164	2.7743
Water consumption of CNY 10,000 GDP, X11	53.7959	8.1028	2.251
Per capita domestic water consumption, X12	48.5466	6.995	2.2656
Flood control financial expenditure, X13	54.0032	4.3082	0.9638
Number of warning messages issued, X14	38.1904	12.0033	1.3742
Quality evaluation grade of water conservancy project construction, X15	25.3693	0.7371	0.2905
Number of national comprehensive disaster reduction demonstration communities, X16	37.1942	7.7917	1.3642
GDP per capita, X17	30.8008	3.302	0.3264
GDP share of secondary sector, X18	18.5264	2.431	1.5859
Tertiary GDP, X19	18.5118	3.9462	2.0399
Disposable income per capita, X20	42.5681	7.8922	2.2413
Urban forest coverage, X21	55.4054	0.9433	0.2625
Sewage treatment rate, X22	41.5792	0.3205	0.1084
Municipal industrial wastewater discharge, X23	51.7756	0.7576	0.2717
Air quality excellence rate, X24	69.4068	5.1505	1.332

.

3.3.3. Evaluation Results

According to Equation (20), the evaluation-integrated cloud parameters of urban flooding disaster resilience of the 27 pilot cities in 2014–2024 are calculated. Then, through the forward cloud generator, the evaluation integrated cloud map is plotted using MATLAB software and, at the same time, superimposed on the evaluation standard cloud map, which results in comprehensive evaluation results of urban flooding disaster resilience of the 27 pilot cities in the last 11 years, from 2014 to 2024, and the changes, as shown in Figure 5.

According to Equation (21), the similarity between the comprehensive evaluation cloud and the five standard clouds is calculated sequentially, and the calculation results are shown in

Table 4. Composite cloud similarity.

Year	Urban Flood Hazard Resilience Levels					Evaluation Results
	Extremely Poor	Poor	Average	Good	Excellent
2014	0.0008	0.5528	0.4264	0.0300	0.0000	Less tough, slightly on the average side
2015	0.0000	0.3975	0.4264	0.03	0.0000	Average toughness, slightly on the fair side
2016	0.0000	0.2548	0.4983	0.1042	0.0000	Average toughness, slightly on the fair side
2017	0.0000	0.1643	0.5995	0.1057	0.0000	Average toughness, slightly on the fair side
2018	0.0000	0.0878	0.7234	0.1523	0.0000	Average toughness
2019	0.0000	0.0711	0.8965	0.0157	0.0000	Average toughness
2020	0.0000	0.0564	0.8548	0.0741	0.0000	Average toughness
2021	0.0000	0.0604	0.6897	0.2539	0.0000	Toughness fair, slightly on the good side
2022	0.0000	0.0365	0.7654	0.1742	0.0000	Average toughness
2023	0.0000	0.0198	0.5097	0.4538	0.0000	Toughness fair, slightly on the good side
2024	0.0000	0.0015	0.3784	0.6018	0.0004	Good toughness, slightly on the average side

.

As can be seen from Figure 5 and Table 3, from 2014 to 2024, the overall comprehensive evaluation cloud gradually moves to the right. According to the similarity calculation, the evaluation of the resilience to urban flooding disasters gradually changes from the initial “poor resilience, slightly general” to “good resilience, slightly general”, but in 2021, the comprehensive evaluation cloud moves to the left, and the evaluation result is “average toughness”, which means the toughness of the year has regressed.

3.4. Analysis of Evaluation Results

3.4.1. Analysis of Indicator Weights

This study constructs an evaluation system based on 24 indicators in 27 pilot cities. Through weighting analysis and modeling, it is found that the density of the resident population (0.0891), the proportion of secondary industry in the GDP (0.0722), and the sewage treatment rate (0.0711) have become the core influencing factors due to the large dispersion of the data. The contribution of end indicators, such as the discharge of industrial wastewater (0.0066) and the proportion of tertiary industry in the GDP (0.0115), is low. The contribution of the end-to-end indicators is low. Water resource allocation indicators (0.2738) play a fundamental role in supporting the resilience to urban flooding, and economic (18.41%), social (17.94%), ecological (15.68%), and infrastructure (13.82%) systems together account for 65.85% of the total, of which the economic system promotes sustained development through the expansion of employment and fiscal consolidation. The infrastructure system directly affects the resilience of energy networks and transportation and logistics capacity. Although the weight of the management system is only 6.77%, its strategic value needs to be optimized through the governance mechanism to achieve multi-system synergy.

3.4.2. Resilience Index Analysis

The index data of the 27 pilot cities from 2014 to 2024 are organized. The three dimensions of resilience index scores of the 27 cities are calculated according to Equation (16), as shown in Figure 6a. Megacities, such as Beijing, Shanghai, and Wuhan, perform better in resilience and resistance dimensions due to their more developed economy and relatively well-developed infrastructures; however, most of the cities present a situation in which the resilience index is larger than the resistance index. The resilience index is more significant than the resilience index. Regarding the resilience index, Beijing and Shanghai are more prominent (0.76 and 0.74), reflecting the effectiveness of social and infrastructure construction. The city’s ability to adapt to flooding is increasing, such as by improving and upgrading drainage systems, early warning mechanisms, and other infrastructure. In terms of the resilience index, Shanghai and Jinan have higher scores (0.75 and 0.62), reflecting the cities’ better water resource allocation and more substantial management capacity and ability to withstand heavy rainfall. Regarding the resilience index, Sanya (0.76) is more vigorous, showing that the city is more resilient regarding economic and ecosystem restoration during the post-disaster recovery process. Economic transformation and ecological restoration of the continued promotion of the construction results are more pronounced; in general, the resilience development trend is good, resilience still has excellent room for improvement, and strengthening infrastructure construction is an important way to enhance the resilience to urban flooding disaster. Each city also needs to pay attention to the balanced development of resilience capacity. Each city’s urban flood resilience comprehensive disaster resilience index is shown in Figure 6c. The overall upward trend in the resilience index of these 27 pilot cities indicates that the cities’ continuous investment and efforts in sponge city construction and rainwater flood management have brought positive results. Despite the increase in the overall resilience index, there are differences in the magnitude of improvement between cities. In Beijing and Shanghai, the resilience index is more prominent, and the gap with the rest of the cities is noticeable; the growth rate of the resilience index is shown in Figure 6b, with an average annual growth rate of 2.89%. During 2016–2019, the overall growth rate of the index was more significant, reflecting that local governments and relevant departments actively responded to the requirements of the central government, during which they issued corresponding local documents, upgraded and improved structures to cope with flooding, integrated scientific and technological means, strengthened disaster monitoring and early warning, and improved the construction effect of sponge cities. The year 2020 is affected by the epidemic, and the resilience index drops slightly, but the resilience fluctuation is small, and in 2021, the resilience index gradually rebounds and increases. The resilience index slightly decreases in 2020 due to the epidemic. However, the fluctuation of resilience is slight and gradually recovers after 2021, which also shows the city’s strong economic and social development in the process of fighting the new epidemic. At the same time, it also reflects that the city’s resilience-building effectiveness is beginning to emerge after the initial fluctuations, with policy optimization and infrastructure upgrades playing a positive role.

3.4.3. Comprehensive Evaluation Analysis of Cloud Modeling

Based on the calculation and analysis of the similarity of the comprehensive evaluation cloud in the previous section, the overall level of urban flood resilience of the 27 pilot cities in the past 11 years has developed from “poor resilience, slightly average” in 2014 to “good resilience, slightly average” in 2024, and the resilience improvement has been effective. The overall level of resilience has developed from “poor resilience, slightly average” in 2014 to “good resilience, slightly average” in 2024. It is recommended that the capacity to cope with climate change and sudden shocks be strengthened through innovative urban construction and disaster management models to systematically reduce urban development’s vulnerability and uncertainty.

The cloud analysis of the three sub-dimensions (resilience, resistance, and recovery) is shown in Figure 7, and the results show that the comprehensive evaluation of these three sub-dimensions shifts to the right, indicating that the resilience of the three sub-dimensions is improving. From 2014 to 2024, the adaptability resilience, as shown in Figure 7a, shifts from a “fair to good” level to a “good” level and from a “good” level to a “good to excellent” level, mainly due to the advantages of social development and infrastructure accumulation in China’s urbanization process, especially in the disaster early warning system, emergency resource deployment, and other aspects of the “high oscillation” characteristics. As can be seen from Figure 7b, the resistance resilience shifts from a “poor to average” level to an “average to good” level due to the pilot cities’ “good” level. The level of resistance changes from “poor to fair” to “good” because most of the pilot cities are affected by temperate monsoon climate (concentrated summer rainstorms and a 37% increase in the number of extreme precipitation events in the past ten years). The hardening of the urban subsurface results in a limited infiltration capacity for rainwater, which results in a “stabilization of low values” despite the improvement of disaster management measures. The resilience of the pilot cities has changed from “poor to fair” to “good”. As can be seen from Figure 7c, the resilience toughness shifts from a “poor to average” level to an “average to poor” level. Due to population expansion, ecological damage, and other “urban diseases” in recent years, most cities have emphasized ecological environment construction and introduced corresponding policies and regulations, as well as strengthened the economy to support ecological restoration projects. Therefore, resilience has gradually shown potential for recovery.

Specifically, resilience is directly related to the efficiency of social resource allocation and the redundancy of infrastructure, and resistance resilience is limited by the dynamic balance between climate conditions and the urban hydrological system. Resilience relies on the synergistic advancement of economic structural adjustment and ecological governance, so it is necessary to continue to pay attention to the long-term effect of regional synergistic development on resilience gain.

4. Discussion

The practical validation of the proposed framework is demonstrated through its application to 27 diverse Chinese sponge city pilots over a decade. The results align with observed urban development trends—megacities (Beijing and Shanghai) show higher resilience due to infrastructure investments, while ecologically focused cities (Sanya) have improved recovery capacity. This temporal consistency with real-world policies supports model robustness. Compared to prior frameworks, which emphasize hazard susceptibility but lack dynamic recovery metrics, our AHP–entropy–cloud integration uniquely addresses ambiguity in resilience grading via cloud-based qualitative–quantitative mapping and captures temporal evolution through annual data. The 2.89% resilience growth rate further quantifies policy effectiveness, offering actionable insights beyond binary risk assessments.

Despite the limitations of data granularity constraints and model calibration complexity, the framework demonstrates strong replicability and flexibility. Modular indicators and open-source algorithms enable adaptation to cities with varying data infrastructures, as validated across 27 economically/spatially diverse Chinese pilots. The hybrid weighting allows dynamic reprioritization of criteria. GIS compatibility further supports spatial scalability.

5. Conclusions

Based on the theory of the cloud model, combined with the AHP and entropy weight method, this study constructed a comprehensive assessment model of the urban resilience level to rainstorms and flooding disasters. It empirically analyzed 27 pilot sponge cities as cases. The main conclusions are as follows:

(1)

By integrating the subjective assignment of the AHP method and the objective assignment of the entropy weight method, the limitations of excessive subjectivity in the traditional assessment methods are effectively reduced. The joint weighting model shows high stability and rationality in the case application, indicating that the method can consider expert experience and data characteristics to provide a scientific basis for resilience assessment.

(2)

From 2014 to 2024, the comprehensive resilience rating of the 27 pilot cities gradually improved from “poor to fair” to “good to fair”, with an average annual growth rate of 2.89%. Megacities such as Beijing and Shanghai have excelled in resistance and resilience due to their economic strength and infrastructure advantages. In contrast, cities such as Sanya have seen a significant increase in the resilience index due to ecological restoration and economic transformation. However, in 2021, the resilience level briefly regressed due to the double impacts of extreme climate and epidemics, highlighting the vulnerability of the urban system.

(3)

Water resource allocation (weight 27.38%), economic system (18.41%), and social system (17.94%) are the core support of urban flood resilience. The density of the resident population (0.0891), the proportion of secondary industry in the GDP (0.0722), and the sewage treatment rate (0.0711) are the main driving factors due to the large data dispersion. At the same time, the contribution of the end indicators, such as industrial wastewater discharge (0.0066), is low. Infrastructure redundancy and ecological management capacity have a long-term gain effect on adaptability and resilience enhancement.

Based on the above conclusions, the following policy recommendations are proposed to enhance the resilience to urban flooding disasters.

(1)

Improve rainwater storage facilities. Continue to promote and accelerate the construction of sponge cities based on the original infrastructure and promote rain gardens, permeable paving, storage ponds, and other low-impact development (LID) facilities to improve urban rainwater infiltration and storage capacity.

(2)

Upgrade dynamic monitoring and early warning measures. Rely on IoT technology to build an integrated monitoring network of “air and sky” and utilize real-time access to precipitation, drainage network operation, and surface water data combined with AI algorithms to optimize the timing of early warning response. At the same time, support ongoing research on intelligent water affairs and digital twin watersheds, develop urban flood simulation and resilience optimization decision-making systems, and realize the dynamic deduction of disaster scenarios and precise policy-making.

(3)

Adhere to resilience-oriented planning synergy. Incorporate the water resource carrying capacity into national spatial planning, delineate flood risk zones that strictly limit high-density development, and promote the interconnection of urban and green space systems. At the same time, integrate data resources from emergency management, water conservancy, housing construction, and other departments to build a dynamic management platform for urban disaster resilience, realizing the “one-network unified management” of risk assessment, planning, and emergency command.

Regarding this model and evaluation method, there are also future research imperatives:

(1)

Integrate climate projections (CMIP6) with land subsidence data.

(2)

Couple cloud-modeled city resilience with watershed-scale hydraulic models.

(3)

Incorporate agent-based modeling of evacuation responses using mobile data.