Classification and Planning Strategies of Multidimensional Resilience Units for Urban Waterlogging: A Case Study of the Old City District in Shijiazhuang, China

By inergency On Mar 26, 2024

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1. Introduction

Urban waterlogging is a common disaster triggered by high-intensity, short-duration torrential rains caused by extreme climate changes, overwhelming the capacity of urban drainage systems and leading to extensive water accumulation [1]. With global warming, the frequency of extreme rainfall events is on the rise, exacerbating urban waterlogging issues and posing significant threats to urban environments and public safety [2]. For instance, in the summer of 2021, Zhengzhou city in China faced extraordinary torrential rains, resulting in waterlogging disasters that caused traffic paralysis, direct economic losses of 88.534 billion yuan, and 302 casualties [3]. In August 2022, the capital region of South Korea suffered historic extreme rainfall, with daily precipitation exceeding 380 mm, leading to severe waterlogging and forcing over 7000 people to evacuate [4]. In 2023, Typhoon Dujuan affected 14 provinces and cities in China, causing extreme rainfall and urban waterlogging, with direct economic losses of 14.755 billion yuan in Fujian Province, affecting 8.142 million people. These cases highlight the severe threat of torrential rain and waterlogging disasters to urban development. Therefore, analyzing urban rainwater characteristics and enhancing urban resilience have become key strategies for addressing waterlogging issues.

The term “resilience”, originating from the Latin “resilio”, meaning ‘to bounce back’, refers to the capacity of a system to return to its original state after external shocks [5]. In 1973, Canadian ecologist Holling first introduced the concept of “resilience” to the field of ecology, interpreting it as the capacity of ecosystems to adapt, maintain, resist, and recover balance after disasters or other short-term impacts [6]. In the early 21st century, urban resilience, as a comprehensive and practical approach to climate disasters, gained widespread attention, gradually becoming a core principle guiding urban scientific and policy discussions [7]. In recent years, the application of the resilience concept in urban flood research has been growing. In 2007, Delft University of Technology in the Netherlands first proposed the concept of “rain flood resilience” [8], referring to the city’s capacity to withstand the impacts of flooding despite infrastructure damage and economic losses and to rapidly reorganize its resources and return to its original state after the flood [9]. In 2012, Chinese scholar Liao G first proposed “flood-bearing resilience“, focusing on the city’s capacity to endure flood disasters, after which many domestic scholars began integrating resilience theory into urban planning and flood prevention research [10]. Unlike traditional urban flood risk studies, urban rain flood resilience and flood-bearing resilience place greater emphasis on the recovery capability of urban systems during waterlogging disasters, highlighting the dynamic nature of this process [11].

In studying urban and regional pluvial flooding issues, scholars have established resilience assessment systems to measure and categorize the study area, subsequently proposing optimization strategies [12,13]. In terms of indicator system selection, researchers have constructed an urban resilience assessment indicator system based on resistance, recovery, and adaptability dimensions, evaluating the urban resilience of Wuhan city from 2009 to 2015 [14]. Grounded in the “4R” resilience theory, which encompasses the robustness, rapid recovery, resourcefulness, and redundancy of cities facing flood disasters, the approach has offered new perspectives for urban planning [11]. Coupling urban rainfall models and utilizing the 4R theory to quantify flood elasticity values has enabled the quantification of the spatial distribution of flood resilience in the Xishan District of Kunming City [15]. Other research teams have embarked on assessments of urban flood resilience across natural, economic, social, and infrastructure dimensions, analyzing the resilience and its spatiotemporal changes in Zhejiang Province from 2011 to 2020 [16]. Moreover, the influence–pressure–state–response (PSR) model proposed by Xiao S and collaborators has been recognized as an effective tool for assessing urban pluvial flood resilience [17]. In the realm of research areas for urban flood and pluvial flood resilience assessments, Zhao R and others conducted a city-level resilience evaluation in the Yangtze River Delta region of Jiangsu Province using the socio-ecological system framework [18]. Zhang J et al. studied three communities suffering from waterlogging problems in Jingdezhen City, China, using a community-scale flood resistance assessment method [19]. Cui, P et al. identified indicators of community-level flood resilience involving social, natural, and economic aspects in Nanjing [20]. Conversely, other scholars have focused on urban resilience studies at various scales, including community, metropolitan, urban agglomeration, and regional levels [21].

Despite some progress in urban waterlogging resilience research, current methods often rely on qualitative analysis and subjective judgment, leading to limitations in data objectivity and scientific rigor. Existing issues include superficial explanations of resilience levels and an inadequate exploration of the resilience response methods and categorizations. Particularly in old urban districts, torrential rain and waterlogging disasters pose even more severe challenges. Old districts typically lag in infrastructure, drainage systems, and urban planning, making them more prone to waterlogging during rainfall. Additionally, due to their unique geographical environment, urban form, land use, building density, and road networks, the characteristics of old districts differ significantly from modern cities. Therefore, directly applying modern urban resilience theories and assessment methods to old districts is often insufficient. Given this, it is necessary to conduct more detailed categorization and in-depth research on the waterlogging resilience of old districts to better address these challenges.

In light of these challenges, exploring new research methods becomes particularly important. In this regard, applying typological methods to the study of urban rainwater resilience offers a novel perspective. Typology, originating from French thinker Michel Foucault’s theory, focuses on exploring the origins and evolutionary processes of objects or phenomena, revealing their uniqueness and specificity. This approach aids in understanding the interactions, developmental trajectories, and formation principles between entities. Through such an in-depth analysis, it accurately identifies complex relationships within a given group or category, grasping its transformative patterns and evolutionary laws. To date, typological research has laid some foundational work in the field of urban and rural planning [22,23,24]. This method, through a deep analysis of different urban areas and units, can uncover regional differences and specific issues, thereby providing precise improvement and management strategies for planners and decision-makers.

Therefore, this study, taking the old city district of Shijiazhuang as the empirical research object, constructs a rainwater resilience clustering factor system for old urban districts based on the four core resilience attributes of robustness, redundancy, resource deployability, and rapidity. Utilizing this system, we have opted for the K-means++ clustering algorithm and phylogenetic typological methods based on their unique advantages and complementarity in handling complex datasets. The K-means++ algorithm is particularly suited for rapidly partitioning large datasets into multiple similar groups, revealing the intrinsic structure and patterns within the data. The phylogenetic typological approach excels at dealing with subtle differences and hierarchical structures within data, enabling a more nuanced understanding of the relationships between data categories. By combining these methods, we can fully mine the potential information within the data, ensuring the breadth, depth, and accuracy of our research, thereby providing a solid foundation and reference for applying this method to other ecosystems in future research. The study incorporates typological theory and employs clustering analysis methods to categorize and generate spectra for rainwater resilience units. By analyzing the average attributes of the resilience factors among different types of units, this research reveals their specific strengths and existing issues in rainwater resilience, further exploring the diversity of these units in this aspect. Based on this, the study delineates planning response areas and proposes corresponding strategies for enhancing resilience. The entire process aims to improve the scientific rigor and comprehensiveness of urban rainwater resilience research, providing valuable references for future resilience practice optimization, especially in the specific urban context of old city districts.

3. Method

We developed a framework to comprehensively analyze the resilience of urban rainfall inundation. Firstly, statistical units for the study area were defined based on relevant criteria, and a factor system for urban rainfall inundation resilience was established according to the 4R attributes of resilience. Subsequently, data statistics for each factor of the factor system were conducted for each unit. The data were normalized using the range normalization method, and the weights of the factors were determined using the equal-weight method. The characteristics’ values for the 4R dimensions were calculated by combining the factor values with their respective weights. Finally, the optimal clustering value (k) for the four characteristic values was determined using K-Means++, the elbow method, and the silhouette coefficient method for cluster analysis, resulting in the classification of the units.

In the end, we utilized lineage analysis to classify the clustering results into ten categories of urban spatial rainfall inundation resilience. By summarizing the lineage types, we were able to analyze the distribution of superior and inferior clustering units, the 4R dimension characteristics of the unit clusters, and the mean values of the factors for each dimension. Combining these aspects allowed us to plan the zoning of rainfall inundation resilience units in the study area and propose corresponding strategies. The flowchart of the modeling framework is shown in Figure 2.

3.1. Construction of Urban Waterlogging Resilience Factor System

Based on a comprehensive review and comparative analysis of the relevant urban resilience assessment literature, this study constructed a framework for urban spatial rainwater resilience clustering factors, utilizing the ‘4R attributes’ theory of urban resilience [26]. The four attributes, namely robustness, redundancy, resource allocability, and rapidity, were employed as the target layer. A factor system for urban spatial rainwater resilience clustering was developed by selecting resilience clustering factors through the analysis of existing research. Indicators such as municipal drainage [27], disaster mitigation facilities, topography [28], public spaces, storage capacity, and safety capacity were included in the first-level indicator layer. Specific factors contained within various urban spatial elements constituted the second-level indicator layer. In total, the system consisted of 30 factors under four categories in the target layer (Table 2).

(1): Robustness refers to the ability of urban systems and infrastructure to resist, absorb, and mitigate disasters and stress events, with a focus on maintaining core services and functions to minimize losses, protect lives and property, and sustain the stability of urban economies and social activities. This attribute mainly comes into play before heavy rain events, emphasizing the effectiveness of existing terrain conditions and municipal engineering measures. It was assessed using seven factors, including the terrain elevations within resilience units, rainfall slope, drainage system, rainfall pipe density, rainfall pipe diameter, and the density of rainwater storage facilities [29,30,31,32,33].
(2): Redundancy focuses on the degree of backup of internal elements within the urban system, ensuring resilience by guaranteeing the continuity of critical services when some system components fail. It increases the flexibility and fault tolerance of urban responses to rainwater-related disasters, shortening recovery times. This attribute is more oriented towards the rainwater carrying capacity and subsurface conditions within urban spaces. It was assessed using ten factors, including the green space ratio, the proportion of public space area, impermeability rate, surface water storage capacity, and green infrastructure coverage [34,35,36,37,38,39,40].
(3): Resource allocability refers to how efficiently a system can mobilize material and human resources to solve problems after a disaster occurs. It represents the city’s ability to use existing resources effectively, formulate response strategies quickly, and efficiently organize their implementation. This ensures that sufficient resources can reach disaster points in a timely manner, expediting emergency responses and recovery processes. It emphasizes preparedness, safety, and adaptability and is assessed using seven factors, including emergency shelter density, regional medical facility density, road space GSI rate, and waterlogging evacuation capacity [41,42,43].
(4): Rapidity is the ability to complete tasks in a timely manner according to priorities to ensure the normal operation of the system. It is characterized by a swift urban system response, fast recovery, and the ability to promptly repair damaged infrastructure to mitigate disaster impacts and restore normal operation. A swift response is crucial for protecting lives, reducing property losses, and quickly restoring social operations. This attribute places greater emphasis on the completeness of disaster mitigation facilities and rescue capabilities. It was assessed using six factors, including regional road density, external traffic connectivity, urban maintenance and construction capacity, distance to emergency shelters, and distance to medical facilities [44,45,46].

3.2. Urban Waterlogging Resilience Clustering Method

3.2.1. Clustering Factor Standardization Processing

Given the availability of data, 22 quantifiable indicators were further selected from a system of 34 urban-built environment clustering factors aimed at addressing urban waterlogging. These indicators served as clustering factors for resilience typology. The indicator data comprised five metrics under the target layer for robustness (B), including ground elevation (a), rainfall slope (b), and stormwater network density (c). Eight metrics under the redundancy (D) layer, such as the proportion of public space area (f), green space rate (g), and impervious surface rate (h), among others, were also included. Five metrics tied to the resource mobilization (S) layer, including the emergency shelter space density (n) and regional medical facility density (o), were accounted for, along with four metrics under the rapidity (P) layer, like regional road density (s) and external traffic connectivity (t), as depicted in Figure 3.

By standardizing the data through range normalization, we ensured that all indicators’ values fell between 0 and 1. This approach not only maintained the positivity of the data, making subsequent clustering computations more straightforward and preventing the generation of negative values in the data processing phase, but it also made the comparison of the 4R attributes in unit clustering more intuitive. Especially in strategy formulation and resilience assessment, this method clearly displayed each unit’s strengths and weaknesses, thereby simplifying the decision-making process and data interpretation and better guiding practical operations and decision-making.

The clustering factor data for the old resilient units of Shijiazhuang were standardized by statistical processing and normalization of the aforementioned data indicators. This entailed a conversion of negatively correlated factors to positive expressions and an adjustment of all factor values to fall within a range of 0 to 1, eliminating the discrepancies resulting from the units and scales.

$x_{i^{*}} = \frac{x_{i} - x_{m i n}}{x_{m a x} - x_{m i n}}$

(1)

The normalized index value $x_{i^{*}}$ represents the normalized indicator value, $x_{i}$ is the indicator’s original value, and $x_{m i n}$ and $x_{m a x}$ are the minimum and maximum values observed for the indicator, respectively. This process coincided with the numbering of the 40 resilience units in the old town of Shijiazhuang, designated as 1–40.

3.2.2. Index Factor System Weight

Currently, two common methods to determine the index weights include non-equal weighting and equal weighting. The former relies on expert scoring and analytic hierarchy process techniques, while the latter assigns equal importance to each indicator [47]. Lacking standardized variables for calculating waterlogging resilience, the current trend is to assign equal weight to all indicators [29]. Studies have shown that equal weighting is more objective and less influenced by subjectivity compared to non-equal weighting methods. Consequently, in this study, each indicator was normalized and conferred equal importance through equal weighting to calculate the urban waterlogging resilience.

3.2.3. Principle of K-Means Clustering Algorithm

As a typical unsupervised learning method, clustering algorithms play a crucial role in multiple research domains, facilitating the segmentation of datasets into cohesive clusters based on similarity. Among various clustering techniques, hierarchical clustering, K-means, as well as the EM algorithm [48] and DBSCAN algorithm [49] each has distinct advantages and is tailored for specific scenarios. Owing to the numerical nature of the chosen clustering factors and the effectiveness of K-means in managing large numeric datasets—its quick computation and ease of implementation for convex clusters [50]—this study primarily employed the K-means algorithm.

The advantage of utilizing the K-means++ clustering analysis in the field of urban block unit rainwater resilience or disaster resilience lies in its efficient sample grouping capability—it can divide the city into several groups with similar properties based on the different 4R characteristics of the urban block units. The key advantage of this method was that it minimized the variability within clusters while maximizing the differences between clusters, providing precise data support for urban rainwater resilience planning. With the K-means++ algorithm, it was possible to accurately identify the areas in the city that were most sensitive to rainwater events and in greatest need of intervention. Furthermore, K-means++, as an improved version of the K-means algorithm, reduced sensitivity to the selection of initial clustering centers, improving the stability and accuracy of the clustering results. Therefore, applying K-means++ clustering analysis in our research not only enhanced the efficiency and precision of the study but also improved urban rainstorm waterlogging resilience, reducing the negative impact of rainwater disasters.

The choice of K-means++ as our clustering method was primarily based on its optimization of the initial cluster center selection. In each iteration, the algorithm assigned data points to the nearest cluster center and recalculated the center of each cluster. This process iterated until the convergence criteria were met, such as minimal changes in cluster centers or reaching a predetermined number of iterations. This significantly enhanced the adaptability and accuracy of the clustering process for heterogeneous datasets. Subsequently, by showcasing the clustering results, this method effectively revealed the intrinsic connections between samples within the relevant clusters.

This method presumes clusters to be spherical, leading to comparatively low variance within each cluster—a natural fit with the inherent variance definitions of numerical data. Despite the requirement to define the number of clusters (k) a priori, this is usually informed by domain knowledge or heuristic analysis [51], from which an optimal number can be inferred to enhance the algorithm’s performance for the respective issue.

In the employed K-means clustering process, clusters were differentiated based on spatial proximity—with closer data points in the coordinate system exhibiting higher similarity [52]. The clustering commenced with the random selection of candidate center points and iteratively computed them to optimize these initial points, minimizing intra-cluster variance, thus ensuring the optimal clustering of all data points. The objective function stands as follows:

$J = \sum_{j = 1}^{k} \sum_{x_{i} \in w_{i}}^{k} {||x i - c j||}^{2}$

(2)

$C j = \frac{1}{n} \sum_{x i}^{n} (\binom{n}{k}) x^{k} a^{n - k}$

(3)

Here, $J$ represents the K-means objective function, $w_{i}$ is the sample dataset, $x_{i}$ refers to the $i$ th data sample in the dataset, and $C j$ denotes the center point of the jth cluster.

In this analysis, the objective function revealed the distances between the dataset points and the cluster centers. The K-means algorithm allocated groups based on the similarity between data points and centers so that points within a cluster are highly similar, with clear distinctions between different clusters. This aligned with our grouping objectives in the research, as it was a quantitative interpretation based on the natural classification features generated by the K-means algorithm [53]. The K-means clustering involved four consecutive stages: initially, the algorithm randomly selected k data points (0 k ≤ n) from n samples as initial cluster cores; then, in each iteration, each of the other data points was assigned to the nearest cluster based on proximity to these centers; subsequently, new cluster centers were determined by calculating and updating the mean of the newly formed cluster members; finally, this iterative process continued until one of two possible termination conditions was met—either convergence of the algorithm’s objective function was achieved or the positions of cluster centers no longer changed.

3.2.4. Determination of the Best Clustering Value K

(1): Elbow Method SSE

The elbow method is a technique used to determine the optimal number of clusters, k, in K-means clustering based on the sum of squared errors (SSE). Graphically, the SSE decreases rapidly as the number of clusters increases, but after reaching a certain point, the decline in the SSE rate slows down, creating a turning point resembling an elbow in the curve. This specific k value represents the best cluster number [54]. The formula for the SSE is as follows:

$S S E = \sum_{i = 1}^{k} \sum_{p \in C_{i}} {| P - m_{i} |}^{2}$

(4)

In this formula, SSE is the sum of squared errors, $C_{i}$ is the ith cluster, $P$ is the sample data point within $C_{i}$ , and $m_{i}$ is the center of the $i$ th cluster.

(2): Silhouette Coefficient Method

The silhouette coefficient method measures the cohesion and separation of clusters resulting from various k values by computing the distance between samples within a cluster [53]. Typically, the k value corresponding to the largest silhouette coefficient score indicates the most suitable number of clusters for that dataset. The silhouette coefficient for the

i

-th data sample point (

X_{i}

) in the dataset is calculated with the following formula:

$S = \frac{b - a}{\max (a, b)}$

(5)

In this formula, (

S

) represents the silhouette coefficient; (

C_{i}

) is the

i

th cluster; (

a

) is the average distance of the sample point (

X_{i}

) to the other sample points within the same cluster, indicating the degree of cohesion within the cluster; (

b

) is the average distance from the sample point (

X_{i}

) to all sample points within the nearest cluster, shedding light on the separation between different clusters [54]. The formula for determining the closest cluster is the following:

$C_{j} = \arg {m i n}_{C_{k}} \frac{1}{n} \sum_{p \in C_{k}} {| P - X_{i} |}^{2}$

(6)

Here, ( $P$ ) is any data sample point within the $K$ th cluster, and the average distance from the sample points within cluster ( $X$ ) to the sample points in other clusters serves as the measure of distance to that cluster, with the smallest average distance indicating the nearest cluster.

In this study, the Python programming language, along with Sklearn.Cluster and Sklearn.Metrics modules were utilized to compute the SSE and silhouette coefficients for the standardized data. We then used Matplotlib.Pyplot for visualization. As depicted in Figure 4a, the SSE initially decreased rapidly with an increase in k but exhibited a noticeable rate change at k = 10, presenting an elbow-shaped inflection point. As depicted in Figure 4b, It was also observed that the silhouette coefficients peaked at k = 5 and k = 6, suggesting better clustering effects at these points. However, when compared to the left graph, the SSE remains high at these values. Nevertheless, considering the combined assessment of the SSE and silhouette coefficients, we discovered a relatively high silhouette score at k = 10, indicating a superior clustering effect. After evaluating the SSE inflection points via the elbow method and the results from the silhouette coefficient approach, the study designated k = 10 as the optimal clustering value. This will aid in better understanding the underlying structure of the dataset and yielding high-quality clustering outcomes consistent with the categorization demands and features of the 4R attributes (robustness, rapidity, reliability, and resilience).

3.3. Clustering Pedigree-Type Summary Method

The pedigree method is an attribute-based analysis method. The content of genealogy has been introduced in the previous introduction. In view of the urban waterlogging resilience studied in this paper, the clustering data of waterlogging resilience can not only be analyzed. The clustering results can be summarized by using the pedigree classification method, which can reveal the characteristics and attribute arrangement of the clustering distribution, but can also be named for different clusters and reveal the meaning of their resilience attributes. Through an in-depth analysis of the data, this method enables us to fully and accurately understand the characteristics of different clusters and their advantages and disadvantages in terms of resilience. The summary of this method includes the following aspects:

Firstly, we can reveal the distribution characteristics of different clusters by analyzing the polyline trend of clustering data and the arrangement of the index values. For example, by combining different robustness, redundancy, resource allocation, and speed attributes, different types of resilient units are formed. Then, by combining different resilience attributes, each cluster is named to reflect its resilience characteristics. By further analyzing the clustering results, we can obtain the distribution of the toughness unit-type lineage in the region so as to better understand the diversity and complexity of different toughness attributes. For example, high robustness–high redundancy–high resource redeployment–high speed (HB-HD-HS-HP) indicates that the cluster has high robustness, redundancy, resource allocability, and speed attributes. Finally, by visualizing the distribution of different types of ductile units in the region, intuitive information is provided to help better evaluate and improve the resilience of the region. These genealogical types provide key information for decision-makers to better evaluate and improve the resilience and adaptability of the region and provide an important basis for more targeted planning and decision-making for future waterlogging resilience.

5. Conclusions

In this study, we delved into the core components of urban resilience—robustness, redundancy, resourcefulness, and rapidity—and successfully developed a novel clustering factor analysis framework specifically designed to assess and understand the resilience characteristics of urban spaces during waterlogging events. By selecting the old-town district of Shijiazhuang as a case study and employing the K-Means++ algorithm to process the resilience factor data, we meticulously categorized the urban spatial units of the old town into 10 distinct resilience types. Through comprehensive analysis and phylogeny construction, this research delineates the strengths and vulnerabilities of the Shijiazhuang old town in facing waterlogging disasters.

Building upon this, we further refined the cluster types into three major categories—dominant, disadvantaged, and combined types—and delved into the primary issues and characteristics of different types by integrating the average performance of each resilience unit within the categories. The methodologies and findings proposed in our research not only guided the formulation of relevant planning and measures but also provided valuable references for urban managers to tailor their strategies to strengthen the resilience of cities in response to waterlogging disasters.

The outcomes of this research underscore the importance of recognizing the heterogeneity among various urban units when confronted with waterlogging threats, and the extensive analysis of the unit types and their details within the “4R” dimensions of urban resilience significantly enhances our understanding of the weak links. Ultimately, this study not only bolstered the adaptability of individual urban units but also vigorously advanced the construction of an overall more resilient urban space against waterlogging disasters.

The case study of Shijiazhuang’s old urban area illustrates the application of clustering and phylogenetic studies in addressing the multidimensional characteristics and complexity of urban resilience, thereby offering an innovative methodological framework for assessing urban resilience. This research contributes new insights into the robust development of increasingly complex urban environments, which are pertinent to the current studies and practices in urban resilience. Moreover, it encompasses a comprehensive analysis of various dimensions and types of disaster resilience, thereby laying a foundation for further optimization in other urban contexts and providing theoretical and methodological support for urban rainwater resilience research and prevention planning across diverse regions.

Looking forward, future studies are anticipated to continually validate the effectiveness of clustering methods in the domain of urban rainwater resilience research. There is also a pressing need to deepen our understanding of the phylogenetic-type division within urban resilience frameworks, aiming to bolster urban defenses against rainwater disasters and foster healthier, more sustainable urban development. Presently, this research encounters limitations in data sampling, most notably, the restricted scope of unit samples primarily concentrated in old urban districts. Subsequent research endeavors should extend their focus to newer urban areas to achieve a more comprehensive outlook. Furthermore, considering the potential influence of seasonal and temporal variations on urban rainwater resilience, forthcoming studies are encouraged to investigate the direct links and impacts of these factors on regional rainwater resilience. Venturing into these new areas of research will pave the way for a more thorough comprehension and enhancement of urban adaptability and recovery capabilities in the face of rainwater disasters, ultimately contributing to the promotion of healthier and more sustainable urban development.

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