Urban ecological assessment method based on dynamic evolution and spatial correlation
By employing methods such as Markov chains, kernel density estimation, and entropy methods, an urban ecological performance index system was established. This system addresses the problem that traditional assessment methods cannot fully reflect urban ecological performance, and enables dynamic assessment of urban ecological performance and coordinated regional development.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING INST OF TECH
- Filing Date
- 2025-09-16
- Publication Date
- 2026-05-19
AI Technical Summary
Traditional ecological assessment methods fail to fully capture the complexity of urban ecological performance, neglect the complex relationships between different components, and fail to reveal the spatial interactions and dynamic evolution processes between cities, resulting in a lack of targetedness and effectiveness in environmental protection policies.
A city ecological performance index system was established using Markov chain and kernel density estimation methods. The entropy method was used to assign weights, and the spatial correlation of city ecological performance was analyzed by global Moran index and Dagonkini coefficient decomposition method. A convergence model was constructed to assess the long-term development trajectory.
It enables the revelation of the spatiotemporal evolution patterns of urban ecological performance from both temporal and spatial dimensions, improves the accuracy and comprehensiveness of assessments, provides a dynamic understanding method, identifies vulnerable links in the ecosystem and formulates targeted policies, and promotes coordinated regional development.
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Figure CN122066271A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of urban ecological performance technology, and specifically relates to an urban ecological assessment method based on dynamic evolution and spatial correlation. Background Technology
[0002] Since the release of the "Opinions on Comprehensive Green Transformation of Economic and Social Development" in 2024, China has made significant progress in sustainable development and ecological civilization. This progress includes clean heating upgrades for approximately 2 million households in northern China, ultra-low emission upgrades for 80% of the steel industry's production capacity, and a reduction in the national annual average PM2.5 concentration to 29.3 micrograms per cubic meter. By 2025, the implementation of policies centered on urban ecological management has significantly promoted technological innovation in environmental governance, carbon emission reduction, and pollution control. These efforts have not only provided strategic direction for environmental protection but also laid a solid foundation for China's long-term sustainable development by encouraging continuous technological progress and improvements in environmental governance. However, in the process of rapid urbanization, problems such as overexploitation of environmental resources, the urban heat island effect, and degradation of ecosystem services are becoming increasingly serious, posing challenges to the monitoring and reliability of urban ecological performance. For example, between 2020 and 2022, the country's urban building land expanded by an average of about 12,000 square kilometers per year, but the green space area increased by less than 5% during the same period; the average summer temperature in megacities is 3-5°C higher than that in suburbs, and Beijing's heat island intensity index exceeds 2.0°C; these problems highlight the necessity of restoring the urban spatial structure.
[0003] Traditional ecological assessment methods have significant shortcomings in urban ecosystem research. Past methods sometimes neglect the complex relationships between different components of an urban ecosystem, focusing only on specific environmental issues such as solid waste management, water quality, or air quality. Furthermore, these assessment models have limitations, failing to comprehensively capture the complexity of urban ecological performance and failing to fully reveal the spatial interactions and dynamic evolution processes between cities. An urban ecosystem is a complex complex in which the use of ecological resources, environmental protection, and carbon emission reduction interact. The limitations of traditional assessment systems pose numerous challenges to cities in formulating ecological protection policies. Due to the inability to accurately grasp the actual state of the ecological environment, urban managers struggle to identify the root causes of current environmental problems and make accurate predictions of ecological environment development trends due to a lack of comprehensive attention. Moreover, the lack of a comprehensive assessment method makes accurate prediction of ecological environment development trends difficult. These challenges may lead to a lack of sufficient focus in environmental protection policies, hindering the effective resolution of practical environmental problems and consequently affecting the effective implementation of policies. Summary of the Invention
[0004] The purpose of this invention is to address the aforementioned problems by providing an urban ecological assessment method based on dynamic evolution and spatial correlation. This aims to improve upon existing ecological assessment methods that tend to overlook the complex relationships between different components of an ecosystem and focus only on specific environmental issues, resulting in incomplete assessments and an inability to reveal the spatial interactions and dynamic evolution processes between cities.
[0005] The technical solution adopted in this invention is as follows: an urban ecological assessment method based on dynamic evolution and spatial correlation, the method comprising the following steps: A city ecological performance index system is established using Markov chains and kernel density estimation methods to dynamically assess the city's ecological performance; weights are assigned to the city ecological performance index system using the entropy method. The spatial correlation of urban ecological performance was analyzed using the global Moran index and Dagongini coefficient decomposition method; combined with convergence and Convergence models assess the long-term development trajectory of urban ecological performance.
[0006] Furthermore, the urban ecological performance index system includes: The Urban Resilience Index (UESI) measures the current state and inherent resilience of urban ecosystems, quantifying urban stability under the combined influence of human activities and natural factors. The Urban Resilience Index (UEPI) is used to reflect the external pressures faced by urban ecosystems. The Response Resilience Index (UEMI) is used to reflect a city's ability to cope with ecological pressures and directly reflects the degree of improvement in a city's ecological performance.
[0007] The urban ecological performance index system enables cities to effectively protect the ecological environment and enhance ecological resilience while developing their economies by identifying vulnerable links in the ecosystem in advance and formulating targeted policies and measures.
[0008] Furthermore, the kernel density estimation method constructs a kernel density function based on the kernel function, calculates the kernel density function value for each data point, and performs a weighted average of the function values to obtain the overall kernel density function estimate. The spatial distribution characteristics of urban ecological performance can be inferred through kernel density estimation. The kernel density function is: ; in, The number of sample data. For the observed values in the sample, The mean of the observed values, is the Gaussian kernel density, used to measure the weight of observations in urban ecological performance. The smoothing bandwidth for kernel density estimation.
[0009] Furthermore, Markov chains are used to analyze the dynamic evolution trend of urban ecological performance inferred by kernel density estimation methods; the calculation formula for Markov chains is: ; in, During the sample period, by Year belongs to Type of area in Year transferred to The sum of the number of cities of each type For all years belonging to The sum of the number of cities of each type.
[0010] Furthermore, the entropy method is used to assign weights to each system of the urban ecological performance index system. Through standardization, calculation of information entropy and weights, a comprehensive score is obtained. Standardize the original values: ; in, For the city index The standardized value, prefecture-level city index The original value, As an indicator The original value; Calculation indicators Information entropy: ; in, As an indicator Information entropy The number of sample data. For the city, For the city index The standardized value; Calculation indicators Weights: ; in, As an indicator The weight, As an indicator Information entropy For the city, The number of indicators; Calculate cities Overall score for economic resilience: ; in, For the city The overall score for economic resilience, As an indicator, As an indicator The weight, For the city index The standardized value, The number of indicators.
[0011] Furthermore, the Dagongini coefficient is decomposed into within-group coefficients using the subgroup decomposition method. Between-group coefficients and supervariable density coefficient Overall Gini coefficient The calculation formula is as follows: ; in, The total number of regions is divided for prefecture-level cities. The total number of prefecture-level cities. and Indicates the divided regions, and Indicates prefecture-level cities, Indicates the division of regions Number of prefecture-level cities in mainland China Indicates the division of regions Number of prefecture-level cities in mainland China These are the weighting coefficients. For division regional prefecture-level cities The city's ecological performance index For division regional prefecture-level cities The city's ecological performance index This represents the average urban ecological performance index nationwide during the sample period. Intragroup Gini coefficient and intergroup Gini coefficient The calculation formula is as follows: ; ; in, and They represent Region and The average ecological performance index of the region. and For division regional prefecture-level cities The city's ecological performance index Indicates the division of regions Number of prefecture-level cities in mainland China; Set the contribution of regional differences as The contribution of net asset value differences between regions is and inter-regional hypervariable density : ; ; in, and Each represents a different region. and The proportion of prefecture-level cities included in the entire sample. and Each represents a different region. and The proportion of urban ecological performance index in the total sample index. The Gini coefficient within the group. The inter-group Gini coefficient. Indicates the region and The relative impact on urban ecological performance between them The calculation formula is as follows: ; ; ; in, Indicates the region and The difference in urban ecological performance between them Indicates the region and The super-variable first moment between them, and Representing regions , The cumulative density distribution function of urban ecological performance.
[0012] Furthermore, the global Moran index is used to measure the spatial autocorrelation between data points, and the Moran index for coupling coordination is calculated using Stata software.
[0013] Furthermore, The convergence model is used to measure the degree of dispersion of urban ecological performance levels in different regions over time, and the coefficient of variation is used to calculate the variation. The calculation converges, if the change If the convergence coefficient shows a decreasing trend over time, then the dispersion of ecological performance among prefecture-level cities in this region is gradually decreasing, meaning that the differences in ecological performance among cities in the region are constantly narrowing and tending towards the mean.
[0014] Furthermore, Convergence models include absolute Convergence and conditions Convergence, absolute Convergence is used to gradually converge the value of regional ecological products to the same level over time, while keeping other factors constant; conditions Convergence takes into account the heterogeneity of various factors in different regions, and incorporates the value of ecological products in each region.
[0015] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. This invention uses methods such as Markov chains, kernel density estimation, and entropy method to reveal the spatiotemporal evolution patterns and spatial correlation characteristics of urban ecological performance from the perspectives of time and space. This allows for the connection between the dynamic changes of cities and between different cities, comprehensively reflecting the overall performance of cities in terms of ecological resource utilization, environmental protection, and carbon emission control. This improves the shortcomings of the existing assessment system and enhances the accuracy, comprehensiveness, and scientific nature of the assessment.
[0016] 2. This invention introduces a dynamic evolution perspective, using kernel density estimation and Markov chain analysis to examine the temporal dynamics and regional differences in urban ecological performance, revealing the evolution of ecological performance and identifying key inflection points, thereby providing a dynamic understanding method for urban ecological performance.
[0017] 3. This invention analyzes the regional distribution patterns and agglomeration effects of urban ecological performance using the global Moran index and Dagonkini coefficient decomposition method, connecting various cities and promoting coordinated regional development through spatial analysis.
[0018] 4. This invention establishes a multi-dimensional urban ecological performance index system based on ecological economics and sustainable development, covering key dimensions such as resource intensification, environmental carrying capacity, and energy decarbonization, ensuring the comparability and scientific nature of the assessment, and establishing a solid framework for assessing urban ecological performance. Attached Figure Description
[0019] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a table showing the indicator system for urban ecological performance in this invention; Figure 3 This invention presents a table showing the dynamic evolution characteristics of urban ecological performance across the country and in three major regions. Figure 4 This is the urban ecological performance kernel density map of the present invention; Figure 5 This is the spatial Markov chain probability matrix table of the present invention; Figure 6 This is a decomposition diagram of the Dagongini coefficient of the present invention; Figure 7 This is a table showing the global Moran index changes in urban ecological performance according to the present invention. Figure 8 For the urban ecological performance of this invention Convergence index line chart; Figure 9 The absolute urban ecological performance of this invention from 2000 to 2021 Convergence results table; Figure 10 The urban ecological performance conditions for 2000-2021 as described in this invention Convergence results table. Detailed Implementation
[0020] The present invention will now be described in detail with reference to the accompanying drawings.
[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0022] like Figure 1 As shown, this invention constructs a framework to dynamically assess urban ecological performance from three dimensions: economic intensification, environmental carrying capacity, and energy decarbonization, through an indicator system; it also quantitatively calculates and analyzes the weighted values of the indicators; based on Markov chains and kernel density estimation methods, it reveals the polarization characteristics, evolution trends, and path dependence of urban ecological performance distribution at the dynamic evolution analysis level; based on the global Moran index and Dagonkini coefficient decomposition method, it analyzes the spatial autocorrelation and differences across the country and the three major regions of East, Central, and West at the spatial analysis level; finally, it constructs a convergence model to evaluate the dynamics of regional convergence.
[0023] This framework combines convergence models with spatial measurement methods, considering the dynamic evolution of urban ecological performance from a temporal perspective and revealing the correlation of urban ecological performance from a spatial perspective, thus breaking through the limitations of a single spatiotemporal perspective.
[0024] A city ecological assessment method based on dynamic evolution and spatial correlation includes the following steps: A city ecological performance index system is established using Markov chains and kernel density estimation methods to dynamically assess the city's ecological performance; weights are assigned to the city ecological performance index system. The kernel density estimation method constructs a kernel density function based on the kernel function, calculates the kernel density function value for each data point, and performs a weighted average of the function values to obtain the overall kernel density function estimate. The spatial distribution characteristics of urban ecological performance can be inferred through kernel density estimation. The kernel density function is: ; in, The number of sample data. For the observed values in the sample, The mean of the observed values, is the Gaussian kernel density, used to measure the weight of observations in urban ecological performance. The smoothing bandwidth for kernel density estimation.
[0025] Markov chains are further used to analyze the dynamic evolution trend of urban ecological performance inferred by kernel density estimation methods; the calculation formula for Markov chains is as follows: ; in, During the sample period, by Year belongs to Type of area in Year transferred to The sum of the number of cities of each type For all years belonging to The sum of the number of cities of each type.
[0026] like Figure 2 As shown, the urban ecological performance index system includes: The Urban Resilience Index (UESI) measures the current state and inherent resilience of urban ecosystems, quantifying urban stability under the combined effects of human activities and natural factors; it can effectively assess the baseline conditions and resource endowments of the urban ecological environment. The Urban Resilience Index (UEPI) is used to reflect the external pressures faced by urban ecosystems, such as industrial wastewater discharge and PM2.5 concentration. The Response Resilience Index (UEMI) is used to reflect a city's ability to cope with ecological pressures and directly reflects the degree of improvement in a city's ecological performance, including measures such as pollution control and resource recycling.
[0027] The entropy method is used to assign weights to each system of the urban ecological performance index system. Through standardization, calculation of information entropy and weights, a comprehensive score is obtained. Standardize the original values: ; in, For the city index The standardized value, prefecture-level city index The original value, As an indicator The original value; Calculation indicators Information entropy: ; in, As an indicator Information entropy The number of sample data. For the city, For the city index The standardized value; Calculation indicators Weights: ; in, As an indicator The weight, As an indicator Information entropy For the city, The number of indicators; Calculate cities Overall score for economic resilience: ; in, For the city The overall score for economic resilience, As an indicator, As an indicator The weight, For the city index The standardized value, The number of indicators.
[0028] The spatial correlation of urban ecological performance was analyzed using the global Moran index and Dagongini coefficient decomposition method; combined with convergence and Convergence models assess the long-term development trajectory of urban ecological performance.
[0029] This invention divides 283 prefecture-level cities into three regions: eastern, central, and western. By using the Dagonkini coefficient and its decomposition method, it further analyzes the spatial differentiation components and their sources of urban ecological performance, which can solve the problem of the source of spatial differentiation and the problem of cross-over between subsamples.
[0030] The Dagongini coefficient is decomposed into within-group coefficients using the subgroup decomposition method. Between-group coefficients and supervariable density coefficient Overall Gini coefficient The calculation formula is as follows: ; in, The total number of regions is divided for prefecture-level cities. The total number of prefecture-level cities. and Indicates the divided regions, and Indicates prefecture-level cities, Indicates the division of regions Number of prefecture-level cities in mainland China Indicates the division of regions Number of prefecture-level cities in mainland China These are the weighting coefficients. For division regional prefecture-level cities The city's ecological performance index For division regional prefecture-level cities The city's ecological performance index This represents the average urban ecological performance index nationwide during the sample period. Intragroup Gini coefficient and intergroup Gini coefficient The calculation formula is as follows: ; ; in, and They represent Region and The average ecological performance index of the region. and For division regional prefecture-level cities , The city's ecological performance index Indicates the division of regions Number of prefecture-level cities in mainland China; Set the contribution of regional differences as The contribution of net asset value differences between regions is and inter-regional hypervariable density : ; ; in, and Each represents a different region. and The proportion of prefecture-level cities included in the entire sample. and Each represents a different region. and The proportion of urban ecological performance index in the total sample index. The Gini coefficient within the group. Indicates the region and The relative impact on urban ecological performance between them The calculation formula is as follows: ; ; ; in, Indicates the region and The difference in urban ecological performance between them Indicates the region and The super-variable first moment between them, and Representing regions , The cumulative density distribution function of urban ecological performance.
[0031] The Global Moran's I index measures the spatial autocorrelation and clustering of data points, with a value ranging from -1.1. It is calculated using Stata software to determine the degree of coupling and coordination. The specific calculation formula is as follows: ; in, Indicates the number of prefecture-level cities. , They represent the first 1 prefecture-level city and the first Urban ecological performance of each prefecture-level city This represents the average value of urban ecological performance. Represents variance. This represents the spatial weight matrix.
[0032] Among them, the global Moran index This indicates a positive spatial correlation, with a clear clustering of elements within the region. Indicates spatial negative correlation. This indicates that the space is uncorrelated.
[0033] The convergence model is used to measure the degree of dispersion of urban ecological performance levels in different regions over time, and the coefficient of variation is used to calculate the variation. The calculation converges, if the change If the convergence coefficient shows a decreasing trend over time, then the dispersion of ecological performance among prefecture-level cities in this region is gradually decreasing, meaning that the differences in ecological performance among cities in the region are constantly narrowing and tending towards the mean.
[0034] The calculation method is as follows: ; in, Indicates the first Within the group area The ecological performance of each sample city Indicates the first Within the group area The average urban ecological performance of each sample Indicates the first Number of samples within a group region Let be the coefficient of variation; if If the coefficient shows a downward trend over time, it indicates that the dispersion of ecological performance among prefecture-level cities in the region is gradually decreasing, that is, the difference in ecological performance between cities in the region is constantly narrowing and tending towards the mean.
[0035] Convergence models include absolute Convergence and conditions Convergence, absolute Convergence is used to gradually converge the value of regional ecological products to the same level over time, while keeping other factors constant; when When the value is less than 0 and passes the significance test, there exists an absolute... Convergence, or conversely, no absolute convergence. Convergence; because urban ecological performance may exhibit spatial correlation, a spatial Durbin model is introduced to address the conventional... The convergence model is modified by using the spatial lag model and the general form of the spatial error model of the spatial Durbin model, resulting in a better spatial correlation of urban ecological performance. The modified absolute value is... The convergent model is constructed as follows: ; condition Convergence takes into account the heterogeneity of various factors in different regions, and converges the value of ecological products in each region; conditions The convergent model is constructed as follows: in, represent Urban ecological performance level The growth rate of the period; It is the convergence coefficient. A value less than 0 indicates that the city's ecological performance exhibits convergence characteristics. A value greater than or equal to 0 indicates that the city's ecological performance exhibits divergent characteristics. The sum of spatial autoregressive coefficients, It is a spatial weight matrix, which describes the spatial relationships through a spatial adjacency matrix. For a series of control variables, For the estimated coefficients of the control variables, This is the space overflow coefficient. For spatial effects, For time effect, For random disturbance terms; Convergence speed Depend on The convergence coefficient is calculated to reflect the catching-up speed of regions with lower ecological product value to regions with higher ecological product value. The formula is as follows: ; in, For time.
[0036] Example 1 This embodiment demonstrates, through a spatiotemporal analysis of the ecological performance of 283 prefecture-level cities in China from 2006 to 2021, that their evolution exhibits significant temporal trends and geographical differentiation characteristics.
[0037] Comparing 2006 and 2021, from a time perspective, the overall ecological performance of cities nationwide showed an upward trend. This indicates that during the experimental period, cities significantly improved their efficiency in ecological resource utilization, environmental governance effectiveness, and carbon emission constraints, demonstrating a steady improvement in ecological governance capacity and sustainable development levels. However, regional differences still exist: the ecological performance of the eastern region is generally better than that of the central and western regions, which is closely related to the eastern region's strong economic foundation, well-developed industrial structure, and policy support. Although the ecological performance of the central and western regions has improved, the eastern region still maintains its leading position, highlighting the uneven development of the region.
[0038] From a spatial perspective, the distribution of urban ecological performance exhibits a clear clustering characteristic. High-performing cities are mainly concentrated in the eastern coastal areas and some central provinces, while low-performing areas are concentrated in the western and central regions. This uneven spatial pattern is closely related to regional economic development levels, industrial structures, and natural environmental conditions. The eastern region has benefited from technological progress, infrastructure resilience, and rapid economic growth, strengthening its ecological governance capabilities and resource utilization efficiency; while the central and western regions face significant challenges in improving ecological performance due to lagging economic development, a heavy industrial structure, and a surge in environmental protection demands.
[0039] Example 2 like Figures 3-4 As shown, another embodiment of the present invention uses kernel density estimation to visualize the dynamic changes in regional differences in urban ecological performance across the country and in the three major regions. Kernel density estimation results show that the overall ecological performance of 283 prefecture-level cities in China showed an upward trend from 2006 to 2021. Specifically, the kernel density curve shifted to the right, indicating an overall improvement in performance. At the national scale, the peak value of the kernel density curve first rose and then fell, while the dispersion first contracted and then expanded, exhibiting fluctuating characteristics. The "right tail" phenomenon indicates that the gap between extreme values and the mean continued to widen, with both single-peak and double-peak polarization trends coexisting. At the regional level: the kernel density curve in the eastern region shifted significantly to the right, with increased dispersion, exhibiting single-peak or double-peak characteristics; the curve in the central region shifted to the right synchronously, showing a double-peak or multi-peak pattern, reflecting increased polarization of ecological performance; the kernel density curve in the western region showed a significant rightward shift, mainly driven by some high-performance cities. These cities have a significant impact on the overall ecological performance level of the region, and the dispersion and polarization phenomena in this region are particularly prominent.
[0040] Example 3 like Figure 5 As shown, this embodiment explores the impact of spatial factors on the ecological performance development level of different prefecture-level cities, with a time lag of 1 year. Figure 5 For experimental results; from Figure 5In this diagram, L represents low level, ML represents low-to-medium level, MH represents medium-to-high level, and H represents high level. The "drag effect" of low-level neighborhoods: when a neighboring region is low-level L, other types of cities are significantly negatively affected. Taking a medium-to-high level MH city as an example, in the traditional matrix, its probability of upward migration is 17.54%, and its probability of downward migration is 8.15%; however, in the spatial matrix, the probability of upward migration drops to 16.05%, while the probability of downward migration rises to 19.75% due to the influence of low-level neighborhoods. This fully demonstrates the "drag effect" of low-level neighborhoods on medium-to-high level regions, hindering their ecological performance improvement and increasing the risk of decline. Changes in the stability of high-level regions: For a high-level H city adjacent to a low-level region L, the probability of maintaining its original level decreases from 94.94% to 69.70%, reflecting the significant impact of neighborhood interaction on the stable development of high-level regions. Radiation effects drive the upgrading of low-level regions: When low-level L regions are adjacent to medium-high MH and high-level H regions, the probability of transferring to medium-low ML levels is 34.32% and 36.67%, respectively, significantly higher than the 23.29% in the traditional matrix, indicating that the radiation effect of high-level neighbors effectively promotes the improvement of performance in low-level regions. The "mutual assistance effect" of high-level regions: The transfer probability between high-level H regions increases to 97.97%, possibly due to their cooperative effect enhancing the stability of ecological performance. Competition-driven development among regions of the same level: When medium-low level ML regions are influenced by neighbors of the same level, the probability of upward transfer increases slightly, possibly due to competition among regions of the same level driving development.
[0041] On the other hand, the probability of upward migration in medium-to-high-level MH regions decreases under the influence of neighboring areas of the same level, reflecting that resource competition among neighboring areas of the same level imposes specific constraints on their development. These results indicate that the improvement of urban ecological performance is influenced by both external conditions and historical development paths. Therefore, urban managers need to recognize that improving ecological performance requires long-term policy support and continuous investment, especially for low-performing cities, where targeted policies need to be developed to break path dependence.
[0042] Example 4 like Figure 6 As shown, during the experiment, the Gini coefficient of urban ecological performance in China rose from 0.137 to a peak of 0.164 in 2021, an increase of 0.027, indicating that the differentiation of urban ecological performance across the country has intensified.
[0043] The trend of the Gini coefficient in the region is as follows Figure 6 (a) At the regional level, the differences are greatest in the western region, followed by the eastern region, and smallest in the central region. The overall trend shows a "decline followed by an increase" characteristic, with more significant fluctuations in the west and relatively milder changes in the east and central regions. This indicates that spatial differentiation in urban ecological performance in China continues, and the differences at both the national and regional levels are widening.
[0044] inter-regional Gini coefficient trends are as follows Figure 6(b) During the experimental period, the average Gini coefficient between the East and West was 0.133, indicating the highest degree of divergence; the coefficient between the Central and Western regions was 0.112, and between the East and Central regions was 0.108. The overall trend showed a "contraction followed by expansion" characteristic, with smaller changes in the East and Central regions and more significant widening of differences in the Central and Western regions. In addition, there were slight fluctuations between the East and Central regions and between the East and West.
[0045] The contribution trend of the Gini coefficient decomposition term is as follows: Figure 6 As shown in (c), the contribution of hypervariable density to the national ecological performance differences is significant: it fluctuated with a pattern of "first rising, then falling, then rising again" from 2006 to 2013, showed stable growth from 2013 to 2019, and then decreased before rising again from 2019 to 2021. The contribution of regional differences fluctuated less, while the contribution of inter-regional differences showed a pattern of "first falling, then rising," but its impact was weak. Therefore, the main driving factor for the differences in urban ecological performance in China is hypervariable density (51.47%), followed by regional differences (32.99%), while inter-regional differences have the smallest impact (15.54%).
[0046] Example 5 like Figure 7 As shown, this embodiment uses the Moran index to determine whether neighboring regions exhibit similar high- and low-value clustering patterns. When both high- and low-value regions show a positive Moran index... When the value is [value missing], geographic clustering exists on the surface. The results of the Moran index for coupled coordination calculated by Stata software are as follows: Figure 7 Moran, 2006-2021 The values are consistently positive and significant at the 1% level, indicating a persistent spatial autocorrelation among prefecture-level cities; furthermore, Moran... The overall value shows a downward trend, the surface spatial agglomeration effect weakens, and the distribution of urban ecological performance scheduling tends to be more balanced and multi-centered. Figure 7 middle, , , These indicate significance at the 1%, 5%, and 10% levels, respectively.
[0047] Example 6 like Figures 8-9 As shown, the dynamic convergence of ecological performance among regions is evaluated using a convergence model. Figure 8 For the urban ecological performance of the whole country and three major regions The convergence index line chart shows that the national coefficient of variation exceeds 0.2 and is on the rise, indicating an increasing dispersion in urban ecological performance. Among the three major regions, the central region has the lowest coefficient of variation, the eastern region has the highest, and the western region is next. After 2014, the coefficient of variation in the eastern region surged from 0.2 to approximately 0.8, mainly due to the rapid upgrading of industrial infrastructure and significant progress in technological innovation. As an economically developed region, the eastern region faces enormous development pressure, leading to uneven growth between cities and enterprises, further widening the gap in ecological performance.
[0048] The central region showed relative stability, with the coefficient of variation remaining around 0.2. In the western region, the coefficient of variation surged from 0.2 to nearly 1.3 in 2007 before falling back to pre-2007 levels. In the following year, western provinces and cities gradually adapted to the new policies, and research found an equilibrium phase before 2014, narrowing the ecological performance gap and stabilizing development conditions. After 2014, the coefficient of variation in the west rose again, and the urban ecological performance gap widened again.
[0049] Figure 9 For absolute Convergence results table, on a national scale, absolute If the convergence coefficient is significantly negative at the 1% significance level, then absolute convergence exists nationwide. The convergence rate of 0.023 indicates a tendency for convergence in urban ecological performance. Regionally, this is observed in the eastern, central, and western areas. All values are negative and pass the significance test. The absolute values in the western region... A higher value and faster convergence speed (0.031) indicate that its absolute value is higher. The convergence is stronger. Lower-performing prefecture-level cities are catching up with higher-performing cities through a "catch-up effect," and this effect is more pronounced in the west than in the central and eastern regions. All three regions show significant positive spatial correlations, indicating strong regional interaction in urban ecological performance.
[0050] Figure 10 As a condition Convergence results table, national level conditions The convergence coefficient remains negative and passes the 1% significance test, further confirming the existence of conditional convergence. Control variables show that industrial structure has a significant negative impact on ecological performance, possibly stemming from industrial relocation: receiving areas face increased environmental pressure, while sending areas face industrial decline. The contradiction in land resource allocation is prominent—industrial upgrading requires large-scale land construction for industrial parks and research facilities, leading to the encroachment on urban green spaces and ecological protection zones, weakening the city's ecological regulation function. Conditional convergence exists in the eastern, central, and western regions. Convergence was observed, with the western region converging significantly faster than the central and eastern regions. Control variables reflecting regional heterogeneity showed that government intervention significantly inhibited improvements in ecological performance in the central region, but failed the significance test in the eastern and western regions.
[0051] Figure 9 and Figure 10 middle, , , The values in parentheses indicate significance at the 1%, 5%, and 10% levels, respectively, with the t-value in parentheses (in Stata regression analysis, the t-value is a statistic used to test the significance of regression coefficients).
[0052] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for urban ecological assessment based on dynamic evolution and spatial correlation, characterized in that, The method includes the following steps: A city ecological performance index system is established using Markov chains and kernel density estimation methods to dynamically assess the city's ecological performance; weights are assigned to the city ecological performance index system using the entropy method. The spatial correlation of urban ecological performance was analyzed using the global Moran index and Dagongini coefficient decomposition method; combined with convergence and Convergence models assess the long-term development trajectory of urban ecological performance.
2. The urban ecological assessment method based on dynamic evolution and spatial correlation according to claim 1, characterized in that, The urban ecological performance index system includes: The Urban Resilience Index (UESI) measures the current state and inherent resilience of urban ecosystems, quantifying urban stability under the combined influence of human activities and natural factors. The Urban Resilience Index (UEPI) is used to reflect the external pressures faced by urban ecosystems. The Response Resilience Index (UEMI) is used to reflect a city's ability to cope with ecological pressures and directly reflects the degree of improvement in a city's ecological performance.
3. The urban ecological assessment method based on dynamic evolution and spatial correlation according to claim 2, characterized in that, The kernel density estimation method constructs a kernel density function based on the kernel function, calculates the kernel density function value for each data point, and performs a weighted average of the function values to obtain the overall kernel density function estimate. The spatial distribution characteristics of urban ecological performance can be inferred through kernel density estimation. The kernel density function is: ； in, The number of sample data. For the observed values in the sample, The mean of the observed values, is the Gaussian kernel density, used to measure the weight of observations in urban ecological performance. The smoothing bandwidth for kernel density estimation.
4. The urban ecological assessment method based on dynamic evolution and spatial correlation according to claim 3, characterized in that, Markov chains are further used to analyze the dynamic evolution trend of urban ecological performance inferred by kernel density estimation methods; the calculation formula for Markov chains is as follows: ； in, During the sample period, by Year belongs to Type of area in Year transferred to The sum of the number of cities of each type For all years belonging to The sum of the number of cities of each type.
5. The urban ecological assessment method based on dynamic evolution and spatial correlation according to claim 4, characterized in that, The entropy method is used to assign weights to each system of the urban ecological performance index system. Through standardization, calculation of information entropy and weights, a comprehensive score is obtained. Standardize the original values: ； in, For the city index The standardized value, prefecture-level city index The original value, As an indicator The original value; Calculation indicators Information entropy: ； in, As an indicator Information entropy The number of sample data. For the city, For the city index The standardized value; Calculation indicators Weights: ； in, As an indicator The weight, As an indicator Information entropy For the city, The number of indicators; Calculate cities Overall score for economic resilience: ； in, For the city The overall score for economic resilience, As an indicator, As an indicator The weight, For the city index The standardized value, The number of indicators.
6. The urban ecological assessment method based on dynamic evolution and spatial correlation according to claim 5, characterized in that, The Dagongini coefficient is decomposed into within-group coefficients using the subgroup decomposition method. Between-group coefficients and supervariable density coefficient Overall Gini coefficient The calculation formula is as follows: ； in, The total number of regions is divided for prefecture-level cities. The total number of prefecture-level cities. and Indicates the divided regions, and Indicates prefecture-level cities, Indicates the division of regions Number of prefecture-level cities in mainland China Indicates the division of regions Number of prefecture-level cities in mainland China These are the weighting coefficients. For division regional prefecture-level cities The city's ecological performance index For division regional prefecture-level cities The city's ecological performance index This represents the average urban ecological performance index nationwide during the sample period. Intragroup Gini coefficient and intergroup Gini coefficient The calculation formula is as follows: ； ； in, and They represent Region and The average ecological performance index of the region. and For division regional prefecture-level cities The city's ecological performance index Indicates the division of regions Number of prefecture-level cities in mainland China; Set the contribution of regional differences as The contribution of net asset value differences between regions is and inter-regional hypervariable density : ； ； in, and Each represents a different region. and The proportion of prefecture-level cities included in the entire sample. and Representing the divided regions and The proportion of urban ecological performance index in the total sample index. The Gini coefficient within the group. The inter-group Gini coefficient. Indicates the region and The relative impact on urban ecological performance between them The calculation formula is as follows: ； ； ； in, Indicates the region and The difference in urban ecological performance between them Indicates the region and The super-variable first moment between them, and Representing regions , The cumulative density distribution function of urban ecological performance.
7. The urban ecological assessment method based on dynamic evolution and spatial correlation according to claim 6, characterized in that, The global Moran index is used to measure the spatial autocorrelation between data points. The Moran index for coupling coordination is calculated using Stata software.
8. The urban ecological assessment method based on dynamic evolution and spatial correlation according to claim 7, characterized in that, The convergence model is used to measure the degree of dispersion of urban ecological performance levels in different regions over time, and the coefficient of variation is used to calculate the variation. The calculation converges, if the change If the convergence coefficient shows a decreasing trend over time, then the dispersion of ecological performance among prefecture-level cities in this region is gradually decreasing, meaning that the differences in ecological performance among cities in the region are constantly narrowing and tending towards the mean.
9. The urban ecological assessment method based on dynamic evolution and spatial correlation according to claim 8, characterized in that, Convergence models include absolute Convergence and conditions Convergence, absolute Convergence is used to gradually converge the value of regional ecological products to the same level over time, while keeping other factors constant; conditions Convergence takes into account the heterogeneity of various factors in different regions, and incorporates the value of ecological products in each region.