Coupling and decoupling of humans and the built environment under disaster disturbances

Abstract

This study, based on the context of rainstorm and flood disasters, explored the coupling, coordination, and decoupling between humans and the built environment. Combining the coupling coordination model with the Tapio decoupling model, the coupling situation in 16 prefecture-level cities in Anhui province from 2009 to 2020 was analyzed. A random forest method combined with recursive feature elimination was used to identify key driving factors. Constraint line extraction and elasticity analysis were used to determine the response and threshold of the coupling coordination to these driving factors. The results showed an overall upward trend in the coupling coordination of the 16 prefecture-level cities, and in most years, the decoupling between humans and the built environment exhibited varying degrees of coupling intensity. Using the decoupling index (DI) of 0.8 and 1.2 as classification thresholds, the vast majority of the sample exhibited a developmental decoupling pattern, with only a few cities exhibiting a decline-type decoupling pattern in a few years, which is generally consistent with the changing trend of the coupling coordination. GDP, urbanization rate, number of people with college or higher education per 100,000 people, economic losses from flooding, population affected by floods, length of drainage pipes, registered urban unemployment rate, and number of medical institutions are important drivers of changes in the coupling coordination degree. This study provides important insights into the relationship between people and the built environment in the context of heavy rain and flooding, and offers valuable reference and guidance for research and practice in related fields.

Introduction

Natural disasters are a major obstacle to the development of human society. Their destructive capacity to the economy, society, and environment is becoming increasingly serious with the intensification of global climate change and economic activities¹. Among them, rainstorms and floods are becoming more and more threatening to human society, and the losses caused by rainstorms and floods are increasing worldwide^2–5.

The built environment serves as a crucial barrier against natural disasters. Its coupling with human activities directly impacts humanity’s ability to respond and recover from disasters. Therefore, studying the coupling and decoupling relationships between humans and the built environment is of great theoretical and practical significance. Natural disasters such as rainstorms and floods not only directly impact the physical structure of the built environment but also alter the existing coordination between the two by influencing human systems such as population distribution, economic activities, and social organizations. Furthermore, rainstorms and floods offer the most direct reflection of the interactive relationship between humans and the built environment. Heavy rainfall tests the engineering resilience of the built environment, such as drainage infrastructure, while simultaneously examining the resilience of social systems through indicators such as the number of people affected and economic losses. These disasters provide an ideal window for studying the coupled “nature-society” system. Decoupling analysis can reveal whether the human and built environment systems evolve synchronously under disaster perturbations. A strong coupling indicates a coordinated evolution between the two, effectively enhancing overall resilience; a decoupled state, however, reflects an imbalance in development between the systems, potentially exacerbating vulnerability to disasters. By quantifying the degree of coupling, coordination, and decoupling between the two, this study aims to provide a scientific basis for optimizing disaster prevention resource allocation and formulating differentiated resilience enhancement strategies. This dynamic relationship analysis is crucial for sustainable urban development, especially at a time when climate change is exacerbating disaster risks.

In recent years, research on urban flood disasters has attracted much attention. Many scholars have conducted in-depth discussions in this field and achieved corresponding results. Some scholars have proposed a multi-dimensional indicator system by integrating multiple factors such as meteorology, hydrology, and geography^6,7. At the same time, the relationship between flood disasters and factors such as climate change⁸ and landscape pattern⁹ has also been explored accordingly. Previous studies have been rigorous and detailed, but there is still room for improvement. In the fields of social economy, environmental resources, and ecological risks, there are some discussions on the coupling relationship between systems, such as the coupling between ecological barrier functions and farmers’ livelihood space¹⁰ and the coupling relationship between urban-economic-environmental multi-systems¹¹. In the field of urban rainstorm and flood disasters, Chen Xiaoling analyzed the Wuhan flooding and pointed out that the lake filling and land reclamation and the lagging drainage network jointly led to the “rain-flood-pollution” compound disaster, and smart water services reduced losses by dynamically regulating the relationship between the three¹². The study of the “July 20” flood in Zhengzhou revealed that the coupling of extreme rainfall and subway operation decision-making errors amplified casualties, and the lack of redundancy in the built environment was the key decoupling point¹³. Azizi et al. emphasized that community-level rainstorm and flood management needs to coordinate the matching degree of “resident participation-pipeline maintenance-policy incentives”, otherwise it will lead to the decoupling of governance effectiveness¹⁴. Many of the above studies have explored the relationship between disasters, people, and the built environment from various aspects, but most of them focus on single-point risks and lack the tracking of the long-term evolution of the coordination between people and the environment. The role of built environment factors is mostly assumed to be linear, and their nonlinear constraint relationship with the resilience level has not yet been quantified. Therefore, based on the work of predecessors, this paper refers to the urban resilience system and introduces research methods widely used in fields such as socioeconomic research and ecological risk research, attempting to further analyze the coupling relationship between people and the built environment in the context of rainstorm and flood disaster disturbances.

There are many research methods in the academic community for the coupling relationship between variables. For simple coupling situations, correlation analysis or linear regression can be used for judgment and analysis¹⁵. However, for the coupling and decoupling between two or more complex systems, simple methods such as correlation analysis and linear regression are somewhat insufficient.

In summary, this study takes Anhui Province as a typical case area and, based on the socio-economic, disaster loss, and built environment data from 2009 to 2020, constructs a comprehensive evaluation index system covering population defense capabilities, vulnerability, and the adaptability and disaster resistance of the built environment. Compared with previous studies, the innovation of this work is mainly reflected in the following three aspects: First, in terms of theoretical framework, it breaks through the limitations of single factor or static analysis in traditional disaster research, regards people and the built environment as a dynamic coupling system, introduces the coupling coordination degree model (CCDM) to quantitatively evaluate the coordinated development level of the two, and uses the Tapio decoupling model¹⁶ to reveal the dynamic characteristics of their interaction. Second, at the methodological level, it innovatively combines machine learning with constraint line analysis technology, uses the random forest (RF) algorithm and recursive feature elimination (RFE) method to screen key driving factors, and uses the quantile segmentation method and elasticity analysis to determine the threshold of each factor’s influence on the coupling coordination degree, thereby solving the limitations of traditional statistical methods in identifying nonlinear relationships. Finally, in terms of practical application, this study not only reveals the spatiotemporal evolution of the coupling coordination degree of prefecture-level cities in Anhui Province but also clarifies the dominant factors affecting system coordination at different development stages, providing a scientific basis for local governments to formulate differentiated flood risk management strategies.

In summary, this study, through a multidisciplinary approach, systematically analyzed the coupling and coordination mechanisms between humans and the built environment during rainstorms and flooding disasters. This not only expands the theoretical framework for urban resilience research but also provides quantitative tools and decision-making support for disaster adaptation planning. The findings can inform disaster prevention and mitigation policymaking, urban infrastructure optimization, and resilient community development in similar regions. They also lay the foundation for subsequent research exploring more complex multi-system coupling relationships.

The general situation of the study area

Anhui Province is located in East China, in the Yangtze River Delta region of the People’s Republic of China ( 114°54′ E – 119 °37′ E, 29°41′ N – 34 °38′ N) (Fig. 1). The data used in Fig. 1 comes from the Amap Open Platform (https://lbs.amap.com), creating with ArcGIS Pro 3.0.1 software (https://www.esri.com/zh-cn/arcgis/products/arcgis-pro). Anhui Province covers a total area of 140,100 square kilometers. Its terrain descends from southwest to northeast, with distinct and complex topography from north to south. Geographically, the Huai River divides the province into two major parts, north and south. The Huai River runs west to east across northern Anhui, flowing through eight prefecture-level cities, including Fuyang, Lu’an, Huainan, and Bengbu. The river stretches approximately 430 km, accounting for 43% of the Huai River’s total length, and serves as the most important natural geographical dividing line in Anhui Province. This dividing line has formed distinct regional differences: the area north of the Huaihe River belongs to the southern edge of the North China Plain, with flat terrain and a warm temperate semi-humid climate. There is more rainfall in spring and summer, and therefore frequent rainstorms and floods. According to the data from the “China Flood and Drought Disaster Bulletin” published by the Ministry of Water Resources of the People’s Republic of China, it can be calculated that from 2006 to 2023, the average population affected by floods in Anhui Province was as high as about 6.3183 million, and the average annual direct economic loss was as high as about 9.924 billion yuan. Therefore, choosing Anhui Province as the research area in the background of flood disasters is highly typical.

Fig. 1.

Schematic diagram -of the study area.

Research methods and data sources

Data source and indicator system

Due to the release lag of official data such as statistical yearbooks, and to ensure the continuity and comparability of indicator data for all 16 prefecture-level cities, this study only covers the period (2009–2020) for which complete statistics are available for all cities. Most indicator data for Anhui Province from 2009 to 2020 in this study were obtained directly or through calculations from the Anhui Statistical Yearbook published by the Anhui Provincial Bureau of Statistics of the People’s Republic of China in the corresponding years, as well as the statistical yearbooks or national economic and social development statistical bulletins of each prefecture-level city in Anhui Province. In addition, data on flood and waterlogging impacts were obtained from the China Flood and Drought Disaster Bulletin published by the Ministry of Water Resources of the People’s Republic of China in the corresponding years. Vector data used to create the Anhui Province overview map and present the research results for each city in Anhui Province were obtained from AutoNavi Maps. All of this data is authoritative and highly timely.

and combined with the data characteristics of the above statistical literature^17,18, this study established an indicator system for the dual system of people and the built environment, as shown in the following table (Table 1):

Table 1.

Index system -of people and the built environment in the background of flood disasters.

First-level indicators	Secondary indicators	Level 3 indicators	Selection instructions
People	Crowd defense index	Total population (person)	The total population determines the upper limit of the comprehensive defense of the population in disasters; the urbanization rate determines the degree of exposure of the population to disasters; and the number of people with college education or above per 100,000 people determines the immediate response capability of the population to disaster defense.
		Urbanization rate (%)
		Population with college education or above per 100,000 people (persons)
	Population vulnerability index	Registered urban unemployment rate (%)	The registered urban unemployment rate reflects the proportion of the population that is most affected by disasters; the proportion of the population aged 60 and above and under 15 years old reflects the proportion of the vulnerable population in disasters; and the population affected by floods and waterlogging disasters directly reflects the degree of damage to the population.
		Proportion of population aged 60 and above and under 15 years old (%)
		Population affected by floods and waterlogging disasters (10,000 people)
Built environment	Built environment defense index	GDP (100 million yuan)	GDP reflects the comprehensive development level of a city; the economic losses caused by floods and waterlogging disasters directly reflect the city’s disaster situation; and the road area reflects the level of transportation and other capabilities under disasters.
		Economic losses from flood disasters (100 million yuan)
		Road area ( 10,000 square meters )
	Built environment adaptability index	Length of drainage pipes (km)	The length of drainage pipes reflects a city’s ability to deal with flood disasters, the number of medical structures plays an important role in the post-disaster recovery of affected people, and the green area reflects the city’s water retention and storage capacity in the context of floods.
		Number of medical institutions
		Green area (hectares)

Data standardization and entropy weighting

Before using the coupling coordination model, it is necessary to calculate the weights of each subsystem and each indicator within each subsystem. This study used the extreme value method combined with the entropy weight method to assign weights to the twelve indicators of sixteen prefecture-level cities in Anhui Province from 2009 to 2020.

When applying the entropy weight method, it is usually necessary to first standardize the indicator data. The significance of data standardization is to eliminate the influence of different dimensions between indicators¹⁹ and normalize the indicators to the same scale. This study uses the extreme value method as the data standardization method. Its calculation formula is as follows: for any indicator x:

If x is a positive indicator:

1

If x is a reverse indicator:

2

Among them e_i are the standardized elements and x_i the indicator data elements ( i = 1, 2, 3…n).

The entropy weight method is a commonly used multi-indicator comprehensive evaluation method, which is usually used to determine the weights of multiple indicators. Based on the information entropy theory, it assigns weights to indicators by calculating the degree of indicator variation. Its core idea is: the greater the degree of indicator variation, the more information the indicator provides, and therefore the higher its weight.

The entropy weight method is as follows:

For the information entropy of indicator x , the calculation formula is:

3

4

Where m is the number of indicators and n is the total number of data elements in indicator x.

weight calculation formula for indicator x is:

5

Coupling coordination model

The coupling coordination model is a quantitative analysis method for evaluating the degree of coordinated development between two or more systems. It is widely used in various fields, including natural sciences and social sciences. The coupling coordination model measures the degree of interaction and coordination between subsystems by calculating their coupling and coordination.

The calculation formula is as follows:

6

Where D is the coupling coordination degree, C is the coupling degree, and T is the coordination degree. The calculation formulas for coupling degree and coordination degree are as follows:

7

8

Where is the comprehensive value of the ith subsystem, is the weight corresponding to the ith subsystem.

Finally, the coupling coordination level type of the city in that year is determined by the value of the coupling coordination degree. This study refers to previous research on coupling coordination degree²⁰ and uses the following intervals to divide the coupling coordination type (Table 2):

Table 2.

Coupling coordination types.

Coupling coordination level interval	Coupling coordination type
[0,0.2)	Severe disorders
[0.2,0.4)	Mild disorders
[0.4,0.6)	Endangered Disorders
[0.6,0.8)	Basic coordination class
[0.8,1.0]	High-quality coordination

Decoupling model

The Tapio decoupling model analyzes the decoupling relationship between two variables. It is widely used in fields such as environmental economics and sustainable development to assess the decoupling relationship between economic activity and environmental impact. By comparing the growth rates of two variables, the model categorizes decoupling states into different types, revealing the dynamic relationship between them.

This study refers to the research methods of previous studies²¹ and constructs the Human Resilience Index (PRI) and the Built Environment Resilience Index (BRI) according to certain rules based on various indicators of people and the built environment.

Population resilience index

Taking into account the six indicators related to people, they are grouped into the Population Vulnerability Index and the Population Defense Index. The construction method is as follows:

9

10

11

Among them, is the population vulnerability index, which is composed of “affected population”, “proportion of population aged 60 and above but under 15 years old” and “registered urban unemployment rate”; is the population defense index, which is composed of “total population”, “population with college education or above per 100,000 people” and “urbanization rate”; and is the standardized value of the j-th indicator in the i -th year, and is the weight of the corresponding indicator.

Built environment resilience index

Taking into account the six indicators related to the built environment, they are grouped into the built environment defense index and the built environment adaptation index. The construction method is as follows:

12

13

14

Among them, is the built environment defense index, which is composed of “economic losses”, “GDP”, and “urban road area”;  is the built environment adaptation index, which is composed of “number of medical institutions”, “green area” and “length of drainage pipes”; and is the standardized value of the j-th indicator in the i- th year, and is the weight of the corresponding indicator.

Decoupling index and decoupling type

Referring to Tapio’s decoupling model, the calculation formula for the decoupling index DI is as follows:

15

Where t is a certain year, t-1 is the previous year, ΔBRI is the coefficient of change of the built environment resilience index from t-1 to t, and similarly, ΔPRI is the coefficient of change of the human resilience index from t-1 to t. The decoupling index DI is the ratio of the two.

Tapio’s decoupling model divides decoupling into eight types, using a decoupling index of 0.8 and a decoupling index of 1.2 as the demarcation line. For example, the X-axis represents value A (meaningless) and the Y-axis represents value B (meaningless). The decoupling model is divided into eight types (Table 3):

Table 3.

Decoupling type.

DI	A	B	Decoupling type
0 < DI < 0.8	A > 0	B > 0	Weak decoupling
0.8 < DI < 1.2	A > 0	B > 0	Expansion Coupling
1.2 < DI	A > 0	B > 0	Expansive negative decoupling
DI < 0	A < 0	B > 0	Strong negative decoupling
DI < 0	A > 0	B < 0	Strong decoupling
0 < DI < 0.8	A < 0	B < 0	Weak negative decoupling
0.8 < DI < 1.2	A < 0	B < 0	Decay-type coupling
1.2 < DI	A < 0	B < 0	Decay-type decoupling

The classification of the Tapio decoupling model is based on the assumption that the dual system is a forward system and a reverse system. Since both systems established in this study are forward systems, the classification of the decoupling types has been modified accordingly. The classification of the decoupling types in this study is as follows (Fig. 2):

Fig. 2.

Classification of decoupling advantages and disadvantages.

Driving factor extraction and threshold analysis

There are many ways to analyze driving factors. Considering the number of indicator data and data characteristics, this study ultimately used a random forest model combined with a recursive feature elimination method. This method used random forests to comprehensively evaluate the importance of the features of 12 indicators, eliminated indicators with lower importance, and then repeated the above process for the remaining indicators. Ultimately, eight indicators with a significant impact on the level of coupling and coordination between humans and the built environment under the background of heavy rain and flooding were identified. The selection process is shown in the following table (Table 4):

Table 4.

Driving factor extraction results.

Feature to be selected	Feature selection
Total population (person)	FALSE
Urbanization rate (%)	TRUE
Population with college education or above per 100,000 people (persons)	TRUE
Registered urban unemployment rate (%)	TRUE
Proportion of population aged 60 and above and under 15 years old (%)	FALSE
Population affected by floods and waterlogging disasters (10,000 people)	TRUE
GDP (100 million yuan)	TRUE
Economic losses from flood disasters (100 million yuan)	TRUE
Road area ( 10,000 square meters )	FALSE
Length of drainage pipes (km)	TRUE
Number of medical institutions	TRUE
Green area (hectares)	FALSE

In studies of ecological risks, disasters, and social economy, the variables often do not exhibit obvious linear or nonlinear characteristics. In this case, the response relationship between the variables is more representative. By fitting the upper boundary curve of the scatter cloud between the two variables, the constraint relationship between the limiting variable and the response variable can be obtained²², which represents the maximum response of the response variable to the limiting variable.

Elasticity analysis²³ is a method used to determine the sensitivity of the response variable to the constraint variable. For the constraint variable and the response variable , the elasticity curve is calculated as follows:

16

The inflection point of the elasticity curve is the impact threshold of .

This study used the quantile segmentation method to fit the constraint relationship between eight important characteristics and coupling coordination, obtained the constraint line, and used elasticity analysis to determine the influence threshold between some important characteristics and coupling coordination.

Result

Coupling coordination degree of prefecture-level cities in Anhui province

As shown in Fig. 3.

Fig. 3.

Coupling coordination degree trend from 2009 to 2020.

Between 2009 and 2020, the lowest level of coupling coordination among all cities studied was 0.3363, indicating mild disharmony, and the highest was 0.9701, indicating excellent coordination. Taking 2017 as the dividing line, the coupling coordination levels of all cities studied between 2009 and 2017 were on the verge of disharmony or worse. Between 2017 and 2020, the coupling coordination levels of all cities studied gradually entered and largely maintained excellent coordination.

From 2009 to 2020, the coupling coordination level of the sixteen prefecture-level cities in Anhui Province showed an overall fluctuating upward trend.

The coupling coordination level of most cities reached its lowest point in 2009, gradually increased between 2010 and 2015, fluctuated between 2015 and 2017, reached its highest value in 2019, and then declined in 2020. The coupling coordination level of a few cities showed an upward trend between 2019 and 2020.

Decoupling types and overall trends of prefectural-Level cities in Anhui province

Between 2010 and 2020, the decoupling types of the sixteen prefecture-level cities in Anhui Province varied greatly, but still showed certain regularities, As shown in (Fig. 4). The data used in Fig. 4 comes from the Amap Open Platform (https://lbs.amap.com), creating with ArcGIS Pro 3.0.1 software (https://www.esri.com/zh-cn/arcgis/products/arcgis-pro).

Fig. 4.

Decoupling types from 2010 to 2020.

Overall, the development situation is the main part of the decoupling results, the secondary development situation is the secondary part of the decoupling results, and the decline situation only accounts for a small part of the decoupling results. In most results, the coefficient of change of the built environment resilience index (ΔBRI) and the coefficient of change of the human resilience index (ΔPRI) basically meet the requirement that at least one of them is positive, that is, at least one system between the human resilience index and the built environment resilience index is in a development state, As shown in (Fig. 5).

Fig. 5.

Decoupling type frequency.

Between 2010 and 2020, overall, the ΔBRI was more stable among the sixteen study cities. Except for a very small number of cities, most cities basically showed a similar pattern. It first increased and then decreased between 2010 and 2012, and then fluctuated slightly within the range of [-0.2, 0.5]. The ΔPRI varied more than the ΔBRI. Between 2010 and 2012, the ΔPRI value also basically showed a pattern of first increasing and then decreasing, and then fluctuating within the range of [-0.5, 1.5]. Its fluctuation was higher than that of the ΔBRI. However, between 2016 and 2020, the volatility of the ΔPRI of each city decreased and basically maintained a similar pattern, As shown in (Fig. 6).

Fig. 6.

Trends in ΔPRI and ΔBRI from 2010 to 2020.

Driving factors and their impact thresholds

Through random forest and recursive feature elimination methods, 8 important features were identified from the original 12 indicators. The constraint curves between the 8 important features and the coupling coordination degree were fitted using different polynomials using the quantile splitting method. The threshold of the influence of each important feature on the coupling coordination degree was determined through elastic analysis.

As shown in Fig. 7, Among them, the coupling coordination degree of the four positive indicators, namely “urbanization rate”, “population with college education or above per 100,000 people”, “length of urban drainage pipelines”, and “number of urban medical institutions”, basically increases with the increase of indicator values. In the range above the indicator influence threshold (“urbanization rate”>63.56%, “population with college education or above per 100,000 people”>24,927 people, “length of urban drainage pipelines”>4,928.87 km, “number of urban medical institutions”>1,883), the upward trend of coupling coordination degree is more obvious.

Fig. 7.

Fitting of constraint lines of various driving factors.

The two inverse indicators, “disaster-affected population” and “unemployment rate”, are opposite to the above indicators. The coupling coordination level basically decreases as the indicator data increases. In the range above the indicator impact threshold (“disaster-affected population”>963,200 people, “unemployment rate”>5.58%), the downward trend of the coupling coordination level is also more obvious.

The constraint line between " GDP " and the coupling coordination level is a cubic polynomial. After many attempts, a linear polynomial was finally used to fit the relationship between the two. The accuracy is poorer than the relationship between the above indicators and the coupling coordination level, but to a certain extent, it can reflect the response relationship between the coupling coordination level and “GDP”.

“ economic loss " indicator, and the coupling coordination level is more difficult to extract. After many attempts at different fitting functions, this study finally found that the commonly used fitting functions had a relatively poor fitting effect on the constraint line between the two. However, through the scatter cloud composed of the “economic loss” indicator and the coupling coordination level data, it can be seen that, except for occasional exceptions, the vast majority of data points are basically negatively correlated. The closer the “economic loss” is to 0, the higher the level of coupling coordination.

Conclusion and discussion

Conclusion

Based on coupling coordination theory and decoupling analysis method, this study systematically explored the interaction between people and the built environment under the background of heavy rain and flood disasters in Anhui Province from 2009 to 2020.

The results show that the degree of coupling coordination in 16 prefecture-level cities in Anhui Province has generally shown an upward trend, gradually developing from mild imbalance in the early stages to a high-quality coordination state. 2017 marked a key turning point in the significant improvement in coordination. Analysis using the Tapio decoupling model revealed that most cities exhibited developmental decoupling characteristics during the study period, indicating that the human and built environment systems generally maintained a favorable trend of coordinated development. However, in 2020, due to a sudden increase in flood disaster intensity, coordination levels in most cities declined. The study identified eight key driving factors, including GDP, urbanization rate, education level, disaster losses, and drainage infrastructure, and determined the impact thresholds for each factor, such as an urbanization rate of 63.56% and a drainage pipe length of 4,928.87 km. These findings not only validate the dynamic evolution of the coupled coordination of social-environmental systems in the context of disasters but also provide a quantitative basis for building urban resilience.

This study innovatively combines a coupling coordination model, decoupling analysis, and machine learning methods to provide a new analytical framework for urban flood disaster research. The methodology can be extended to risk assessment and planning management in other disaster-prone areas. Future research could further expand the indicator system, optimize the constraint line extraction method, and conduct comparative studies across different climate zones to enhance the universality and application value of the conclusions.

Interpretation and analysis of coupling coordination results

From the coupling coordination result curve, the coupling coordination degree of all studied cities basically shows a step-by-step upward pattern, and most cities eventually reach the level of high-quality coordination. This process can also be confirmed from the decoupling type results. Among all the decoupling results of the sixteen cities, development and sub-development account for the vast majority of years, and only a few years show a decline. Therefore, the coupling coordination level curves of each city are basically reasonable.

However, from 2019 to 2020, the coupling coordination degree of most cities showed a downward trend. Even though almost all cities reached the level of high-quality coordination in 2020, the maximum coupling coordination degree of most cities was in 2019. The main reason for this result may be the difference in flood losses. The number of people affected by floods in Anhui Province in 2019 and the economic losses caused by floods were far lower than the same indicators in 2020. This led to a sudden increase in the impact of disaster reverse indicators in 2020. Although some indicators also had certain fluctuations, compared with the impact threshold analysis of driving factors on the coupling coordination level, the fluctuations of most indicators did not reach the impact threshold. Therefore, the main reason for the sudden drop in coupling coordination degree from 2019 to 2020 can basically be determined to be the drastic changes in disaster intensity.

The frequency statistics of the decoupling type results show that between 2010 and 2020, most decoupling types were development and sub-development types, but in 2020, almost all cities showed a weak decoupling type, which was a recession type. Only a few cities showed a strong negative decoupling type, which was a sub-development type. According to the decoupling value calculation formula, the decoupling value is jointly determined by the change coefficient of the human resilience index and the change coefficient of the built environment resilience index, both of which are determined by the human resilience index and the built environment resilience index in the study year and the previous year. Therefore, the decoupling type in 2020 describes the changes in the coupling and coordination status between people and the built environment under the background of flood disasters in cities from 2019 to 2020. The changes between 2019 and 2020 are also reflected in the results of the coupling coordination level. The reason for this phenomenon is the same as mentioned above, which is the sharp difference in disaster intensity between 2019 and 2020.

The upward trend of the coupling coordination degree and the distribution of decoupling types found in this study reveal the dynamic coordination mechanism of the human-built environment system in Anhui Province under the disturbance of heavy rain and floods. However, its volatility (such as the sharp drop in the coordination degree in 2020) needs to be further explained in combination with the disaster background and human behavior. The study of the “7.20” flood in Zhengzhou by Tang Junqing et al. showed that the mobility behavior of the crowd under extreme disasters showed a counterintuitive resilience pattern, and the resilience of vulnerable groups was significantly reduced due to the lack of normal travel capacity²⁴. This finding can explain the decline in the coupling coordination degree under heavy rainfall in 2020 in this study: when the disaster intensity exceeded the built environment defense threshold, the sudden change in the crowd behavior pattern exacerbated the system imbalance, highlighting the key role of infrastructure redundancy and behavioral response matching.

Furthermore, a study of the Yangtze River Delta urban agglomeration pointed out that the improvement of flood resilience dominated by economic level has a “natural resilience shortcoming”. Although high-GDP cities have a higher degree of coordination in the short term, the lack of ecosystem services (such as water conservation) will weaken long-term stability²⁵. This confirms that GDP, as a strong driving factor in this study, failed to avoid the phenomenon of recession-type decoupling in 2020. Economic investment can quickly improve engineering defense capabilities, but the ecological regulation function, such as insufficient green space, is weakened, making the system ineffective in excessive rainfall. Similarly, empirical evidence from the Manohara River Basin in Nepal shows that urban expansion has led to a decrease in river meandering, and the encroachment of floodplains has decoupled the built environment’s defense capacity from natural hydrological processes. The high-risk area for floods has expanded to 26.4% of the total area²⁶. This is consistent with the threshold effect of “drainage pipe length” in the built environment adaptation index of Anhui Province, forming a cross-regional confirmation, which together shows that human activities must intervene in natural systems based on ecological constraints.

Limitations of this study

From the perspective of the indicator system, due to the differences in statistical indicators in the statistical yearbooks or national economic and social development statistical bulletins of various provinces and cities in China, the indicator system established by this study is difficult to adapt to all provinces and cities. In the end, only the multi-year data of Anhui Province was used for research. Due to the slight shortage of sample size, the universality of the experimental results will be affected to a certain extent.

However, because Anhui Province is often severely affected by torrential rain and flooding, this study still has a certain degree of typicality. Taking into account the influence of factors such as longitude and latitude differences and climate types, this study has certain reference value for provinces and cities in southeastern China and regions with similar geographical environments around the world.

From a research methodological perspective, this study mainly used the coupling coordination model and the Tapio decoupling model to explore the coupling relationship and decoupling between humans and the built environment under the disaster context. After extracting the driving factors, the quantile segmentation method was used to extract the constraint line between the driving factors and the coupling coordination degree. When the data points are not evenly distributed, the quantile segmentation method will extract unreasonable data points in some locations. This method still has room for optimization.

Suggestions for future research directions

This study carefully analyzed the coupling and decoupling relationship between humans and the built environment under disaster disturbances. In order to expand the adaptability of the research, since different regions have different latitude and longitude characteristics and climate characteristics, and urban development levels are also different, an indicator system that is more adapted to local geographical characteristics can be established in different regions; or the research methods can be optimized by combining the more advanced artificial intelligence technology at present to improve the accuracy and reliability of the research results.

Constraint lines, this study found that the commonly used constraint line extraction methods²⁷ all have certain drawbacks. The relatively excellent quantile segmentation method also has the problem of difficulty in accurately selecting boundary points when the data points are unevenly distributed. Therefore, when using this method, there are certain requirements for the amount of data and the uniformity of the data distribution. The more evenly distributed the data is, the more accurate the constraint lines can be extracted. The larger the data volume, the easier it is to reflect the distribution law. On this basis, it may be possible to further screen the extraction positions to improve the accuracy and rationality of the data points used for fitting.

The coupling coordination model originated from physics and is used to calculate the interaction relationship between two or more quantitative systems²⁸. It has since been widely used in the fields of social economy, ecological risk, etc. It can be seen that multidisciplinary cooperation is conducive to the development of new research ideas and methods. Therefore, future research can refer to and learn from advanced research results in other fields, and combine methods or technologies such as big data analysis and machine learning to conduct more detailed research.

Author contributions

Wu. Data collection, model building, data analysis, manuscript writing, Chart preparationChen. Technical guidance, project supervision, manuscript checkingAll authors reviewed the manuscript.

Data availability

No datasets were generated or analysed during the current study.

Declarations

Competing interests

The authors declare no competing interests.