Spatio-Temporal Coupling of Carbon Efficiency, Carbon Sink, and High-Quality Development in the Greater Chang-Zhu-Tan Urban Agglomeration: Patterns and Influences

Abstract

Under the framework of the “dual carbon” goals, promoting the coordinated development of carbon emission efficiency, carbon sink capacity, and high-quality growth has become a critical issue for regional sustainability. Using panel data from 2006 to 2021, this study systematically investigates the three-dimensional coupling coordination among carbon emission efficiency, carbon sink capacity, and high-quality development in the Greater Chang-Zhu-Tan urban agglomeration. The spatiotemporal evolution, spatial correlation characteristics, and influencing factors of the coupling coordination were also explored. The results indicate that the coupling coordination system exhibits an evolutionary trend of overall stability with localized differentiation. The overall coupling degree remains in the “running-in” stage, while the coordination level is still in a marginally coordinated state. Spatially, the pattern has shifted from “northern leadership” to “multi-polar support,” with Yueyang achieving intermediate coordination, four cities including Changde reaching primary coordination, and three cities including Loudi remaining imbalanced. Spatial correlation has weakened from significant to insignificant, with Xiangtan showing a “low–low” cluster and Hengyang displaying a “high–low” cluster. The evolution of hot and cold spots has moved from marked differentiation to a more balanced distribution, as reflected by the disappearance of cold spots. The empirical analysis confirms a three-dimensional coupling mechanism: ecologically rich regions attain high coordination through carbon sink synergies; economically advanced areas achieve decoupling through innovation-driven development; while traditional industrial cities, despite facing the “green paradox,” demonstrate potential for leapfrog progress through transformation. Among the influencing factors, industrial structure upgrading emerged as the primary driver of spatial differentiation, though with a negative impact. Government support also exhibited a negative effect, whereas the interaction between environmental regulation and both government support and economic development was found to be significant.

1. Introduction

As China’s economic development has entered the new normal, high-quality development has become the main theme of economic and social development, emphasizing greater attention to the quality, efficiency, and sustainability of development while maintaining economic growth. Meanwhile, under the guidance of the “dual carbon” goals, promoting comprehensive green transformation of economic and social development has become an imperative of our times. Achieving the strategic objectives of carbon peaking and carbon neutrality requires not only improving carbon emission efficiency through technological innovation and industrial upgrading, but also enhancing carbon sink capacity through ecological construction and environmental protection, thereby establishing a green development system that combines “emission reduction and carbon sequestration enhancement”. However, in practice, carbon reduction often entails economic costs [1], while carbon sequestration requires land and resource inputs [2,3]. Moreover, high-quality development itself demands balancing economic, social, and environmental dimensions [4]. These dynamics impose multiple constraints and coordination challenges on regional sustainable development. In-depth exploration of the coordination mechanisms among carbon emission efficiency, carbon sink capacity, and high-quality development is not only an inherent requirement for achieving the “dual carbon” goals, but also key to promoting regional sustainable development, holding significant theoretical value and practical significance for guiding green transformation practices in developing countries.

Existing research has achieved rich results in carbon emission efficiency measurement, carbon sink capacity assessment, and high-quality development evaluation. From the perspective of carbon emission efficiency research, scholars have experienced methodological evolution from single indicators to total factor evaluation [5,6], but have paid less attention to the interactive relationship with regional development quality. In terms of carbon sink research, existing literature has formed two main methods: direct measurement and calculation based on carbon absorption coefficients [7,8], but exploration of the synergistic mechanism between carbon sink capacity and regional economic development remains insufficient. Regarding high-quality development research, scholars have constructed multi-dimensional evaluation systems based on new development concepts [9,10], but exploration of development paths under environmental constraints and ecological services still needs deepening. Although some studies have begun to examine the interconnections among different factors [11,12], they remain largely confined to two-dimensional analyses, such as carbon emission efficiency and economic development [13], carbon emissions and carbon sinks [14], or carbon sinks and economic development [15]. Systematic investigations into the synergistic relationship among carbon emission efficiency, carbon sink capacity, and high-quality development are still relatively scarce. This fragmented research approach overlooks the intrinsic interconnections among “source-sink-development” elements, failing to comprehensively reflect the systemic characteristics of regional sustainable development. Combining carbon emission efficiency, carbon sink capacity, and high-quality development in integrated analysis can more accurately characterize the complexity and holistic nature of regional economic development, providing new perspectives for constructing comprehensive coordinated development evaluation systems.

Based on this, this paper selects the Greater Chang-Zhu-Tan urban agglomeration as the research object, systematically examining the three-dimensional coupling coordination relationship among carbon emission efficiency, carbon sink capacity, and high-quality development in this region from 2006 to 2021. The selection of this urban agglomeration is highly representative for several reasons. On one hand, as a significant urban agglomeration in central China, it bears the dual burden of shouldering regional development responsibilities while facing emission reduction pressures from concentrated traditional heavy and chemical industries, epitomizing the development dilemma faced by Chinese urban agglomerations under “dual carbon” goal constraints. On the other hand, this region possesses abundant ecological resources including the Dongting Lake wetland system and the Xiangjiang River basin, providing substantial carbon sink potential, while maintaining a relatively complete industrial system that offers ideal research conditions for exploring three-dimensional system coordination mechanisms. Furthermore, the Greater Chang-Zhu-Tan urban agglomeration encompasses cities with diverse development models, including ecologically advantaged cities, economic centers, and traditional industrial cities, enabling the observation of coordinated development pathways under multiple constraints within a unified regional framework.

The main contributions of this research are reflected in four aspects: First, it constructs a coupling mechanism analysis framework for the three-dimensional system of carbon emissions, carbon sinks, and high-quality development, transcending the limitations of traditional research that analyzes these three elements independently or considers only pairwise relationships, and theoretically elucidates the interaction mechanisms among the three subsystems, providing new perspectives for deepening regional sustainable development theory; Second, based on long-term series data, it systematically characterizes the dynamic evolution patterns and spatial differentiation characteristics of the three-dimensional system coupling coordination, changing the limitation of fragmented analysis of carbon emission efficiency, carbon sink capacity, and high-quality development, and combining theoretical mechanisms to deeply explain the internal driving factors of spatiotemporal evolution; Third, it employs spatial autocorrelation analysis methods to identify the spatial agglomeration characteristics and evolution trajectories of three-dimensional coupling coordination, revealing the complete process of transformation from unbalanced development to relatively balanced coordination, providing new analytical perspectives for understanding the spatial mechanisms of regional coordinated development; Fourth, through Tobit regression models and geographical detectors, it conducts in-depth analysis of influencing factors and their interactions, revealing the complex impact mechanisms of factors such as industrial structure upgrading, government support, and economic development level on three-dimensional coupling coordination, providing scientific basis for policy formulation. These research findings not only enrich the theoretical connotations of regional sustainable development but also provide important empirical support and practical guidance for the Greater Chang-Zhu-Tan urban agglomeration and other similar urban agglomerations in formulating green low-carbon transformation and high-quality development policies.

2. Related Research and Theoretical Foundation

2.1. Related Research

With the introduction of the “dual carbon” goals (see Appendix A) and the deepening promotion of high-quality development concepts, the coupling coordination relationship between carbon emissions and high-quality development has gradually become a hotspot in academic circles. Existing research mainly analyzes from the dimensions of spatiotemporal evolution characteristics, spatial correlation, and regional differences, accumulating rich research results.

In terms of spatiotemporal evolution characteristics, scholars generally find significant spatial heterogeneity between carbon emission efficiency and high-quality development [16,17]. Research indicates that the coupling coordination between the two often presents a development pattern radiating from core cities to surrounding areas, while some underdeveloped regions may fall into the spatial lock-in phenomenon of “the weak remain weak” [11]. From the temporal dimension, although the coupling coordination degree generally shows an upward trend, regional gaps often experience dynamic changes of “first narrowing then widening” [12]. Some studies also note that China’s three-dimensional coordination level of carbon reduction, pollution reduction, and economic growth has continuously improved and entered a moderate coordination stage, though regional differences remain pronounced, with eastern regions serving as high-coordination concentration areas [18]. Examining specific regions reveals significant differentiated characteristics. Yang et al. [19] analyzed 21 prefecture-level cities in Guangdong Province, showing that the coupling coordination degree between high-quality urban development and carbon emission intensity shifted from moderate incoordination to moderate coordination, with spatial distribution displaying a pattern of “high in the southeast, low in other areas”. In contrast, Qing et al. [13] studied 30 cities in the Yellow River Basin and found that the coupling coordination degree between agricultural carbon emission efficiency and economic growth exhibited a “high in the west, low in the east” distribution pattern, with fluctuating downward trends during the observation period. Similarly, Wei et al. [20] examined the three-dimensional coordination relationship among ecological environment, economic development, and carbon emissions in the Yellow River Basin, finding that coordinated development areas expanded from downstream to middle and upper reaches, with most regions transitioning from dysfunctional decline to coordinated development. Additionally, Zhang et al. [21] studied 48 cities in the Pearl River Basin, discovering that the coupling coordination degree between carbon emissions and economic development exhibited spatial heterogeneity, with the highest values in the Pearl River Delta region and the lowest in the middle reaches. Meanwhile, Gao et al. [22] research on Inner Mongolia revealed that although the coupling coordination degree between land use carbon emissions and high-quality economic development was generally low, western regions were significantly higher than central and eastern regions.

Regarding spatial correlation research, an increasing number of scholars have employed spatial econometric methods to reveal the spatial clustering characteristics of coupling coordination degrees. Xu and Ci [23] investigated the coupling coordination relationship between digital economy and low-carbon development in the Yellow River Basin, finding that coupling coordination degrees exhibit significant positive spatial correlation with a spatial pattern of “downstream > midstream > upstream”. Li & Ci [24] analyzed 30 provinces in China and discovered that the coupling coordination degree among digital economy, carbon emission efficiency, and high-quality economic development evolved from “mild disorder” to “barely coordinated”. Nie et al. [25] employed Moran’s I index analysis and found that the coupling coordination degree between pollution carbon reduction and high-quality development in the Yangtze River Economic Belt exhibits significant positive spatial autocorrelation characteristics, with spatial distribution primarily manifesting as “high-high” and “low-low” clustering patterns. Zhang et al. [26] further confirmed these findings, with results showing that the Moran’s I index of coupling coordination degree between new quality productive forces and manufacturing carbon emission efficiency demonstrates a sustained upward trend, indicating gradually strengthening spatial spillover effects. From a convergence perspective, some studies have identified β-convergence characteristics in coupling coordination degrees, with convergence rates displaying pronounced regional gradient differences [25]. Furthermore, Guo et al. [27] analyzed the coupling coordination relationship between high-quality economic development and carbon emission intensity across Chinese provinces, finding that inter-provincial network connectivity has significantly strengthened, network density has continuously increased, and the inter-provincial relationship pattern has evolved from “strong east, weak west” toward a more balanced configuration, with central and western regions playing increasingly prominent roles in promoting regional cooperation.

As research deepens, the influencing factors of coupling coordination relationships among regional development elements have gradually become a focus of academic attention. Scholars have explored from both macro and micro levels. Macro-level research indicates that economic foundation, government intervention, urbanization rate, and industrial structure have promoting effects on coupling coordination, while carbon emission intensity shows negative constraining effects [28,29]. Some studies also find that although individual driving factors may have weak separate impacts, they can produce significant synergistic effects through interaction [11]. Micro-level research focuses on enterprise behavior, finding that management improvement and technological innovation are key paths to achieving carbon reduction and quality improvement, but their relative contributions vary with enterprise characteristics [30].

Overall, existing research has formed a relatively rich understanding of the spatiotemporal evolution patterns and influencing factors of coupling coordination between carbon emission efficiency and high-quality development. However, in terms of research objects, studies mainly focus on provincial or large-scale urban agglomerations, with relatively insufficient attention to medium-scale urban agglomerations, particularly important urban agglomerations in central China; in terms of time span, most are medium and short-term analyses, lacking in-depth examination of long-term series evolution patterns; in terms of research content, emphasis is placed on current situation description and characteristic analysis, with discussions on the formation mechanisms of inter-regional differences and evolution driving forces still needing deepening.

2.2. Coupling Mechanism Analysis of Carbon Emissions, Carbon Sinks, and High-Quality Development

2.2.1. Components and Characteristics of the Three Subsystems

Based on systems theory, carbon emissions, carbon sinks, and high-quality development constitute three interconnected complex subsystems, each defined by specific elements, functions, and operational mechanisms.

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Carbon Emission Subsystem

This subsystem encompasses greenhouse gas emissions and their management from regional socio-economic activities. Core elements include: emission sources, emission processes, and regulatory mechanisms. Emission sources encompass energy consumption, industrial production, transportation, building use, and land use changes; emission processes are manifested in specific links such as fossil fuel combustion, industrial production processes, and biomass burning; regulatory mechanisms include technological emission reduction, policy regulation, and market mechanisms.

This subsystem has the following characteristics: First, scale dependency, where total carbon emissions are closely related to economic scale and population scale; second, structural sensitivity, where industrial structure and energy structure have decisive impacts on carbon emission intensity; third, technology-driven nature, where the application of low-carbon technologies can significantly improve carbon emission efficiency; fourth, policy orientation, where environmental regulations and carbon pricing policies have strong constraining effects on emission behavior.

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Carbon Sink Subsystem

This subsystem represents the functional capacity of regional natural and artificial ecosystems to absorb and sequester atmospheric CO₂. Core elements include: carbon sink carriers, carbon sink processes, and carbon sink management. Carbon sink carriers encompass ecosystems such as forests, grasslands, wetlands, farmlands, and oceans; carbon sink processes are manifested in biogeochemical processes such as plant photosynthesis, soil organic carbon accumulation, and oceanic carbon cycling; carbon sink management includes human intervention measures such as ecological protection, vegetation restoration, and land use optimization.

This subsystem has the following characteristics: First, spatial heterogeneity, where carbon sink capacities vary significantly across different geographical locations and ecological types; second, temporal accumulation, where the formation and functioning of carbon sink capacity requires extended time periods; third, environmental sensitivity, where climate change and human activities have important impacts on carbon sink functions; fourth, ecosystem integrity, where carbon sink functions are closely related to biodiversity and ecosystem services.

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High-Quality Development Subsystem

This subsystem embodies a comprehensive framework for coordinated economic, social, and environmental progress guided by new development paradigms. Core elements include: development drivers, development modes, and development objectives. Development drivers encompass endogenous factors such as innovation-driven development, reform and opening-up, and human capital; development modes are manifested in industrial transformation paths of greening, digitalization, and servitization; development objectives include a diversified goal system of economic efficiency, social equity, and environmental friendliness.

This subsystem has the following characteristics: First, multi-dimensionality, encompassing development requirements across economic, social, and environmental dimensions; second, coordination, emphasizing balance and coordinated development among various dimensions; third, innovation, with technological innovation and institutional innovation as core driving forces; fourth, sustainability, focusing on coordination between current and future development.

2.2.2. Three-Dimensional System Coupling Mechanisms

Based on coupling theory and synergetics principles, the three subsystems of carbon emissions, carbon sinks, and high-quality development form complex nonlinear coupling relationships through the exchange of material flows, energy flows, information flows, and value flows. This coupling relationship manifests both as bidirectional interactive two-way coupling and as multi-element collaborative three-dimensional coupling, as specifically shown in Figure 1.

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Bidirectional Coupling Mechanism between Carbon Emissions and High-Quality Development

Carbon emissions and high-quality development exhibit a characteristic inverted U-shaped dynamic coupling relationship, consistent with the Environmental Kuznets Curve (EKC) effect. During initial development stages, economic growth primarily relies on resource input and scale expansion, resulting in a strong positive correlation between carbon emissions and economic activity. As development progresses, industrial restructuring and technological advancement gradually decelerate carbon emission growth. In the high-quality development stage, innovation-driven strategies and green transformation dominate, leading to the decoupling of carbon emissions from economic growth, potentially achieving absolute decoupling.

The impact of high-quality development on carbon emissions operates through three primary channels: First, upgrading towards service and high-tech industries reduces carbon emission intensity.; second, adoption of clean and energy-efficient technologies enhances carbon emission efficiency; third, robust environmental governance systems strengthen carbon emission constraints. Conversely, carbon emissions influence high-quality development through feedback mechanisms: Moderate carbon constraints can stimulate green innovation and facilitate industrial transformation. However, excessive constraints may impede economic growth, potentially inducing a “green paradox”.

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Synergistic Coupling Mechanism between Carbon Sinks and High-Quality Development

Carbon sinks and high-quality development primarily manifest a synergistic positive coupling relationship. High-quality development, emphasizing ecological civilization (see Appendix A) and green growth, provides policy support, financial investment, and technological advancement for enhancing carbon sink capacity. Conversely, increased carbon sink capacity improves regional environmental quality, establishing a robust ecological foundation for sustainable high-quality development.

The promotion of carbon sinks by high-quality development occurs via: First, direct funding for ecological construction and environmental governance boosts carbon sinks; second, application of ecological restoration and carbon sink enhancement technologies scales up sink capacity; third, scientific ecological management and land use planning optimize spatial allocation of carbon sinks. Carbon sinks support high-quality development through: First, enhanced ecological quality improves regional attractiveness and competitiveness; second, enhanced ecological quality improves regional attractiveness and competitiveness; third, economic valorization of carbon sinks expands developmental opportunities.

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Complementary Coupling Mechanism between Carbon Emissions and Carbon Sinks

As the “source” and “sink” components of regional carbon cycles, carbon emissions and sinks are pivotal for carbon balance, characterized by complementarity and substitutability. Complementarity arises as sinks partially offset emissions, mitigating atmospheric greenhouse gas concentrations. Substitutability allows increased sink capacity to substitute for certain emission reduction requirements under specific conditions, thereby lowering abatement costs.

From a spatial perspective, carbon emissions are predominantly concentrated in economically developed, urbanized regions, whereas carbon sinks are primarily located in rural and mountainous areas with favorable ecosystems, creating a spatial pattern characterized by “urban emissions and rural absorption”. In terms of temporal dynamics, carbon emissions exhibit immediate effects, whereas carbon sinks accumulate over time; the temporal disparity between the two necessitates coordination via the establishment of carbon sink reserves and intertemporal optimization. From a management standpoint, carbon emission management emphasizes source control and process emission reduction, while carbon sink management concentrates on ecological protection and enhancing sink capacity; both require coordinated planning and collaborative efforts for advancement.

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Synergistic Coupling Mechanism of the Three-Dimensional System

The integrated system comprising carbon emissions, carbon sinks, and high-quality development exhibits synergistic coupling at a higher systemic level. Synergy is evidenced by: Convergent evolutionary trajectories towards low emissions, high sinks, and high-quality development. Enhanced functional complementarity among subsystems, collectively underpinning sustainable development. Progressively refined inter-subsystem coordination mechanisms, forming a systematic governance framework.

This tripartite synergistic coupling follows distinct patterns: First, coupling intensity and coordination levels vary across developmental stages; second, interactions may induce mutation and transition phenomena; third, coupling relationships evolve with internal and external environmental shifts; fourth, coupling mechanisms differ across micro-, meso-, and macro-levels.

To achieve synergistic coupling within the three-dimensional system, it is essential to construct effective coordination mechanisms: at the objective level, establish dual goals of “carbon neutrality” and “high-quality development”.; at the path level, promote coordinated “emission reduction & sink enhancement” and “transformation & upgrading”; at the policy level, develop integrated “environment-economy-society” policy frameworks; at the technology level, strengthen integrated innovation in “emission reduction, sink enhancement, and green technologies”; and at the institutional level, implement multi-actor (“government-market-society”) governance models.

Overall, the coupling within this three-dimensional system is a complex, dynamic process. Its coordination level directly determines the efficacy of regional sustainable development. A profound understanding of these coupling mechanisms provides crucial theoretical and practical insights for formulating scientific development strategies and policies.

3. Research Methods and Data Sources

3.1. Study Area

This study selects the Greater Chang-Zhu-Tan urban agglomeration as the research object (Figure 2). The urban agglomeration is located in the central and eastern part of Hunan Province and is an important component of the middle Yangtze River urban agglomeration (See Appendix A), including three core cities—Changsha, Zhuzhou, and Xiangtan—and five surrounding cities—Hengyang, Changde, Loudi, Yiyang, and Yueyang. The region covers a total area of 9.68 × 10⁴ km², accounting for 45.7% of Hunan Province’s land area. The region has well-developed water systems, with the Xiangjiang, Zishui, Yuanjiang, and Lishui rivers flowing through it. The terrain is mainly characterized by plains, mountains, and hills, with typical subtropical monsoon climate characteristics.

In 2022, the Greater Chang-Zhu-Tan urban agglomeration had a permanent population of 41.3693 million, accounting for 62.99% of the province’s total; the regional GDP reached 3739.283 billion yuan, accounting for 76.83% of the province’s total. The industrial structure within the region shows distinct spatial differentiation: core cities represented by Changsha and Zhuzhou mainly develop advanced manufacturing and modern service industries, with Changsha, as the provincial capital, leading in economic aggregate, urbanization level, and innovation capacity; resource-based cities such as Loudi are still dominated by traditional heavy industries; Changde, Yiyang, and other areas possess relatively abundant ecological resources, forming distinctive development patterns. In recent years, this urban agglomeration has faced development trends of substantial increases in total carbon emissions and slight decreases in total carbon sinks, which not only brings severe challenges to achieving regional “dual carbon” goals but also highlights the importance of studying the coordination relationship among regional carbon emission efficiency, carbon sink capacity, and high-quality development.

3.2. Data Sources

This study employs city-level data from 2006 to 2021, where socioeconomic data are primarily sourced from the China Urban Statistical Yearbook, China Construction Statistical Yearbook, municipal statistical yearbooks, and national economic and social development bulletins of respective cities. Energy statistical data for each city are obtained from successive editions of the China Energy Statistical Yearbook. Land use data are derived from the annual land cover dataset of China at 30 m resolution spanning 1985–2023, published by Wuhan University [31].

3.3. Methodological Framework

This study constructs a comprehensive methodological framework encompassing efficiency measurement, index construction, coupling coordination analysis, spatial correlation analysis, and influencing factor identification. First, the super-efficiency CCR model, carbon absorption coefficient method, and entropy method are, respectively, employed to measure carbon emission efficiency, carbon sink capacity, and high-quality development levels of cities in the Greater Chang-Zhu-Tan urban agglomeration, providing foundational data support for subsequent analysis. Based on this, a three-dimensional coupling coordination degree model is constructed to quantitatively measure the coordination relationships among the three subsystems, followed by time series analysis, spatial distribution analysis, and spatial autocorrelation analysis to reveal spatiotemporal evolution characteristics, and finally the Tobit regression model and geographical detector are used for in-depth analysis of influencing factors.

3.3.1. Indicator System Construction

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Measurement of Carbon Emission Efficiency

Carbon emission efficiency measurement primarily encompasses two categories: parametric methods (such as Stochastic Frontier Analysis, SFA) and non-parametric methods (such as Data Envelopment Analysis, DEA). Parametric methods require pre-specification of production function forms, posing risks of functional specification bias when handling complex systems with multiple inputs and outputs. DEA methods require no prior assumptions about production function forms and can simultaneously handle multiple input-output problems, making them particularly suitable for this study involving multiple input factors such as labor, capital, and energy, along with both desirable and undesirable outputs. Compared to traditional DEA models, the super-efficiency CCR model can further distinguish decision-making units with efficiency values equal to 1, enhancing the precision of efficiency evaluation. However, DEA methods also have certain limitations, such as sensitivity to outliers and failure to account for random errors, though they remain the mainstream approach in regional comparative studies. Therefore, this study adopts the super-efficiency CCR model for carbon emission efficiency measurement, following the research methodology of Tone [32]. This model not only overcomes measurement biases arising from radial and angular choices but also enables further evaluation of decision-making units with efficiency values greater than 1, thereby obtaining more precise efficiency assessment results.

In terms of indicator system construction, this study refers to the research methods of Guo and Liang [33] and Färe et al. [34], constructing a carbon emission efficiency evaluation indicator system that includes input indicators, expected outputs, and undesired outputs. Specifically, input indicators include energy consumption, year-end employment, and capital stock; expected output is regional GDP; undesired output is urban CO₂ emissions. The detailed indicator settings are shown in

Table 1. Carbon Emission Efficiency Indicators.

Primary Indicator	Secondary Indicator	Indicator Description
Input Indicators	Labor Capital	Number of employed persons in each prefecture-level city over the years
	Capital Stock	Calculated using the perpetual inventory method with a depreciation rate of 9.6%, using 2006 as the base year [35]
	Energy Consumption	Urban energy consumption mainly includes natural gas, liquefied petroleum gas, and electricity consumption. Due to inconsistent units, energy consumption is converted to standard coal. According to the General Rules for Calculation of Comprehensive Energy Consumption (GBT 2589-2020) [36], the conversion coefficients are 1.3300 kgce/m3, 1.7143 kgce/kg, and 0.1229 kgce/(kW·h), respectively
Expected Output	GDP	Regional GDP calculated at constant 2006 prices
Undesired Output	CO2 Emissions	Following the method of Wu and Guo [37], direct carbon emissions from coal gas and liquefied petroleum gas are calculated based on conversion factors provided by IPCC; carbon emissions from electricity are calculated based on the baseline emission factor of the East China regional power grid and electricity consumption of each city. The sum of both constitutes the total carbon emissions of the city

.

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Measurement of Carbon Sink Capacity

Carbon sink capacity measurement primarily encompasses two methods: direct measurement and coefficient estimation. While direct measurement methods offer high precision, they require extensive field monitoring data, making them costly and difficult to implement for long-term time series analysis at the urban agglomeration scale. Coefficient estimation methods, based on standard carbon absorption capacities of different land use types combined with high-precision land use data, enable large-scale, long-term carbon sink assessment and represent the mainstream approach in current regional carbon sink research. Therefore, this study measures the carbon sink capacity of the Greater Chang-Zhu-Tan urban agglomeration based on carbon absorption coefficients from existing research and land cover data, as specified in Equation (1):

$${\mathrm{C}}_{\mathrm{s}} = {\mathrm{S}}_{\mathrm{s}} \times \mathrm{C}{\mathrm{S}}_{\mathrm{s}}$$

(1)

where C_s represents various types of carbon sinks, Ss represents various types of land areas, and CS_s represents carbon absorption coefficients for various types of land. To accurately obtain land area data, this study extracts land use data for the study area based on vector data of administrative divisions of the Greater Chang-Zhu-Tan urban agglomeration, obtaining land use raster data, and uses raster reclassification tools to divide it into five major categories: forestland, grassland, cropland, water bodies, and unused land.

Regarding the determination of carbon absorption coefficients, this study comprehensively refers to multiple existing research results: According to Fang’s [38] research, the carbon absorption coefficient for forestland is 0.581 kg(C)/(m²·a), and for grassland is 0.09482 kg(C)/(m²·a); According to He’s [39] research, the carbon absorption coefficient for cropland is 0.0692 kg(C)/(m²·a); According to Duan et al.’s [7] research, the carbon emission coefficient for water bodies is 0.0253 kg(C)/(m²·a); According to Lai’s [40] research, the carbon absorption coefficient for unused land is 0.0005 kg(C)/(m²·a). The specific classification of land types and their corresponding carbon absorption coefficients are shown in

Table 2. Carbon Absorption Coefficients by Land Use Type.

Primary Category	Secondary Category	Carbon Absorption Coefficient
Cropland	Mountain paddy fields	0.0692 (kg(C)/(m2·a))
	Hilly paddy fields
	Plain paddy fields
	Mountain dry land
	Hilly dry land
	Plain dry land
Forestland	Forested land	0.581 (kg(C)/(m2·a))
	Shrubland
	Sparse woodland
	Other forestland
Grassland	High-coverage grassland	0.09482 (kg(C)/(m2·a))
	Medium-coverage grassland
Water Bodies	Rivers and channels	0.0253 (kg(C)/(m2·a))
	Lakes
	Reservoirs and ponds
	Beaches
Unused Land	Marshland	0.0005 (kg(C)/(m2·a))

Data source: Carbon sink coefficients are derived from calculations by Fang [38], He [39], Duan et al. [7], Lai [40], and others.

.

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Measurement of High-Quality Development Index

Weight determination methods for high-quality development indices primarily include subjective weighting methods (such as Analytic Hierarchy Process, AHP, and expert scoring methods) and objective weighting methods (such as entropy weighting method and Principal Component Analysis, PCA). Subjective weighting methods rely on expert subjective judgment and may suffer from subjective preferences and cognitive limitations; while PCA is objective, it can alter the original economic meanings of indicators and may generate negative weights. The entropy weighting method objectively determines weights based on the degree of dispersion in indicator data, where indicators with smaller information entropy receive greater weights, effectively utilizing the inherent information characteristics of the data while avoiding interference from subjective factors, making it particularly suitable for this study’s multidimensional, multi-indicator comprehensive evaluation. This study employs the entropy weighting method to measure urban high-quality development levels. Using the entropy weighting method to measure regional high-quality development indices is not only relatively objective but also effectively overcomes information overlap between different indicators, making the calculated results more valid and scientific. The specific methodology for determining indicator weights using the entropy weighting method is as follows:

First, the data matrix is standardized using the extreme value method, with the calculation formulas as follows:

$$\mathrm{For} \mathrm{positive} \mathrm{indicators}: {\mathrm{y}}_{\mathrm{ij}} = {\displaystyle \frac{{\mathrm{x}}_{\mathrm{j}} - {\mathrm{x}}_{\min }}{{\mathrm{x}}_{\max } - {\mathrm{x}}_{\min }}} , \left(\mathrm{i} = 1,2\dots \dots \mathrm{j}; \mathrm{j} = 1,2\dots \dots \mathrm{n}\right)$$

(2)

$$\mathrm{For} \mathrm{negative} \mathrm{indicators}: {\mathrm{y}}_{\mathrm{ij}}={\displaystyle \frac{{\mathrm{x}}_{\max }-{\mathrm{x}}_{\mathrm{j}}}{{\mathrm{x}}_{\max }-{\mathrm{x}}_{\min }}} , \left(\mathrm{i}=1,2\dots \dots \mathrm{j}; \mathrm{j}=1,2\dots \dots \mathrm{n}\right)$$

(3)

where y_ij is the standardized value of the jth indicator for city i; x_max and x_min are the maximum and minimum values of the jth indicator, respectively. Second, calculate the information entropy E_j of indicator j, with the specific calculation method as follows:

$${\mathrm{E}}_{\mathrm{j}} = -\left({\displaystyle \frac{1}{\mathrm{lnZ}}}\right){\sum }_1^{\mathrm{Z}}{\mathrm{p}}_{\mathrm{ij}}\ln \left({\mathrm{p}}_{\mathrm{ij}}\right)$$

(4)

$${\mathrm{p}}_{\mathrm{ij}}={\displaystyle \frac{{\mathrm{y}}_{\mathrm{ij}}}{{\sum }_{\mathrm{i}=1}^{\mathrm{z}}{\mathrm{y}}_{\mathrm{ij}}}}$$

(5)

where E_j is the information entropy; z is the number of cities; p_ij is the proportion of city i under indicator j relative to that indicator. Third, determine the weight W_j of indicator j. With the information entropy of each indicator being E_j, the weight W_j is:

$${\mathrm{W}}_{\mathrm{j}} = {\displaystyle \frac{1 - {\mathrm{E}}_{\mathrm{j}}}{{\sum }_{\mathrm{i}=1}^{\mathrm{z}}\left(1 - {\mathrm{E}}_{\mathrm{j}}\right)}}$$

(6)

Therefore, the high-quality development level G is:

$$\mathrm{G} = {\sum }_{\mathrm{i}=1}^{\mathrm{z}}{\mathrm{y}}_{\mathrm{ij}}{\mathrm{w}}_{\mathrm{j}}$$

(7)

In terms of parameter selection, this study constructs an evaluation system including five dimensions: industrial structure, inclusive TFP, technological innovation, residents’ living standards, and ecological environment, based on the method of Zhao et al. [41] and considering the availability of city-level data. As shown in

Table 3. High-Quality Development Indicators.

Primary Indicator	Secondary Indicator	Indicator Description	Direction
Industrial Structure	Structural Advancement	Tertiary Industry/Secondary Industry	+
	Structural Rationalization	Theil index measuring the ratio of employment and output among the three industries	−
	Proportion of Productive Service Industries	Proportion of productive service industry employees to total urban employees	+
Inclusive Total Factor Productivity	Capital Input	Capital factor input estimated using the perpetual inventory method [35]	+
	Labor Input	Number of employed persons	+
	Real GDP	Real GDP obtained by deflating with 2006 as the base period	+
	Urban-Rural Income Ratio	Ratio of urban residents’ disposable income to rural residents’ disposable income	−
Technological Innovation	Technological Innovation Index	Uses the China City and Industry Innovation Index jointly released by the Research Institute of Innovation and Digital Economy (RIDE) and the Center for Industrial Development Research (FIND) at Fudan University	+
Ecological Environment	Sulfur Dioxide Removal Rate	Sulfur dioxide removal amount/(sulfur dioxide emissions + sulfur dioxide removal amount)	+
	PM2.5 Concentration	Annual average concentration of fine particulate matter	−
	Industrial Solid Waste Comprehensive Utilization Rate	Industrial solid waste comprehensive utilization rate	+
Residents’ Living Standards	Per Capita GDP	GDP/total regional population	+
	Per Capita Education Expenditure	Education expenditure/total regional population	+
	Hospital Beds per 10,000 People	Number of hospital beds/total regional population	+

, the industrial structure dimension is measured through structural advancement, structural rationalization, and the proportion of productive service industries; the inclusive TFP dimension includes capital input, labor input, expected output, and undesired output; the technological innovation dimension uses the urban innovation index; the ecological environment dimension covers sulfur dioxide removal rate, PM2.5 values, and industrial solid waste comprehensive utilization rate; the residents’ living standards dimension includes per capita GDP, per capita education expenditure, and per capita hospital beds.

(4) 

Measurement of Coupling Coordination Degree

The Coupling Coordination Degree Model originates from the coupling concept in physics and is used to measure the degree of coordination in interactions among multiple systems. This model is based on the following assumptions: interactions and influences exist among subsystems; coordinated system development requires simultaneous consideration of both the development levels of individual subsystems and their mutual coordination degree; and coordinated development is a dynamic process. The coupling degree reflects the intensity of interactions among systems, while the coordination degree comprehensively considers both system development levels and coupling degrees. This methodology has been widely applied in multi-system coordination analysis across fields such as regional development and environmental economics. In economics, coupling refers to the phenomenon where different economic subsystems or industrial systems mutually influence each other through certain mechanisms and generate synergistic effects. Higher coupling coefficients indicate stronger coordination among systems, which is more conducive to synergistic development among systems and generates a “1 + 1 > 2” coupling effect. Based on this theoretical foundation, this study constructs a three-dimensional coupling coordination degree model for carbon emission efficiency, carbon sink capacity, and high-quality development to measure and analyze the coupling coordination state of these three systems.

$$\mathrm{C}=\mathrm{n}\ast {\left[{\displaystyle \frac{{\mathrm{U}}_1\ast \dots \ast {\mathrm{U}}_{\mathrm{n}}}{{\left({\mathrm{U}}_1+\dots +{\mathrm{U}}_{\mathrm{n}}\right)}^{\mathrm{n}}}}\right]}^{{\displaystyle \frac{1}{\mathrm{n}}}}$$

(8)

where n is the number of system dimensions, and in this section, Ui represents the comprehensive evaluation index of each system; C represents the coupling degree of the system, with C ∈ [0, 1]. The larger the C value, the higher the coupling coordination degree of the system, indicating better coupling between the two systems and greater ability to promote the system toward a new ordered structure, and vice versa. However, when two systems are at relatively low development levels, the calculation results may conversely yield high coordination between systems, which contradicts the research intention. Therefore, to objectively reflect the research results, a coupling coordination degree model for carbon emission efficiency and high-quality development is constructed on the above basis:

$$\mathrm{T} = \mathsf{\alpha }{\mathrm{U}}_1 + \mathsf{\beta }{\mathrm{U}}_{2 }+ \mathsf{\delta }{\mathrm{U}}_3$$

(9)

$$\mathrm{D}=\sqrt{\mathrm{C} \times \mathrm{T}}$$

(10)

where D is the coupling coordination degree; T is the comprehensive coordination index; α, β, and δ are coefficients to be determined. Since carbon emission efficiency, carbon sinks, and high-quality development are equally important in the coordinated development process, they are all set to 1/3.

To relatively accurately determine the coupling degree and coupling coordination development stages of the three dimensions of carbon emission efficiency, carbon sinks, and high-quality development, this study refers to existing research results [42] and divides the coupling coordination degree levels into 10 categories according to the size of the D value, as shown in

Table 4. Classification of Coupling Degree and Coupling Coordination Degree Levels.

Coordination Degree	Coupling Relationship	Coupling Coordination Degree	Coordination Relationship
[0.0, 0.6]	Disordered development	[0.0, 0.1]	Extreme imbalance
		(0.1, 0.2]	Severe imbalance
(0.6, 0.7]	Low coupling period	(0.2, 0.3]	Moderate imbalance
		(0.3, 0.4]	Slight imbalance
(0.7, 0.8]	Antagonistic period	(0.4, 0.5]	On the verge of imbalance
		(0.5, 0.6]	Barely coordinated
(0.8, 0.9]	Running-in period	(0.6, 0.7]	Primary coordination
		(0.7, 0.8]	Intermediate coordination
(0.9, 1.0]	High coupling period	(0.8, 0.9]	Good coordination
		(0.9, 1.0]	Superior coordination

.

In terms of spatiotemporal evolution characteristic analysis, this study employs time series analysis methods to identify the temporal evolution patterns of three-dimensional coupling coordination degrees, revealing overall evolutionary characteristics and local differentiation phenomena by calculating annual averages and city-specific change trends. Meanwhile, spatial distribution analysis methods are used to select typical years for drawing spatial distribution maps, identifying spatial pattern evolution characteristics and differentiation patterns, and combining theoretical mechanisms to analyze the formation causes and evolution trends of spatial differentiation.

3.3.2. Spatial Autocorrelation Analysis Method

To identify the spatial correlation characteristics and clustering patterns of three-dimensional coupling coordination degrees, this study employs global and local Moran’s I indices for spatial autocorrelation analysis. The global Moran’s I index is used to measure the degree of spatial autocorrelation across the entire study region and determine whether spatial clustering phenomena exist; the local Moran’s I index is used to identify local correlation patterns of specific spatial units, capable of identifying different spatial clustering types such as “high-high” clusters, “high-low” clusters, “low-high” clusters, and “low-low” clusters.

3.3.3. Tobit Regression Model

The coupling coordination degree takes values in the range of 0–1, representing a bounded interval dependent variable. Ordinary Least Squares (OLS) fails to fully consider the truncated characteristics of the dependent variable, potentially leading to biased regression results. Therefore, this study adopts a random effects panel Tobit regression model, using Maximum Likelihood Estimation (MLE) to estimate model parameters. The Tobit regression model is constructed as follows:

$${\mathrm{Y}}_{\mathrm{it}} = {\mathsf{\alpha }}_0 + {\mathsf{\alpha }}_1{\mathrm{gr}}_{\mathrm{it} }+ {\mathsf{\alpha }}_2{\mathrm{ecod}}_{\mathrm{it} }+ {\mathsf{\alpha }}_3{\mathrm{urb}}_{\mathrm{it}} + {\mathsf{\alpha }}_4{\mathrm{ind}}_{\mathrm{it} }+ {\mathsf{\alpha }}_5{\mathrm{rul}}_{\mathrm{it}} + {\mathsf{\alpha }}_6{\mathrm{infor}}_{\mathrm{it}} + {\mathsf{\alpha }}_7{\mathrm{techs}}_{\mathrm{it}} + {\mathsf{\mu }}_{\mathrm{i}} + {\mathsf{\lambda }}_{\mathrm{i}} + \sum {\mathsf{\alpha }}_{\mathrm{i}}\mathrm{Year} + {\mathsf{\epsilon }}_{\mathrm{it}}$$

(11)

where Y represents the three-dimensional system coupling coordination degree, and other variables are: industrial structure upgrading (Ind_Struct), government support (Gov_Sup), urbanization rate (Urban), technological support intensity (Tech_Sup), economic development level (Econ_Dev), environmental regulation intensity (Env_Reg), and informatization level (Info). μ_i and λ_t represent spatial effects and time effects, respectively, and ε_it is the random error term.

3.3.4. Geographical Detector and Grid Point Method

This study employs geographical detectors to measure the spatial differentiation characteristics of coupling coordination, utilizing factor detectors and interaction detectors to diagnose the effects of dominant factors and their interactions on spatial differentiation.

(1) 

Differentiation and Factor Detection. This detects the explanatory degree of each influencing factor on the spatial differentiation of coupling coordination, measured by the q-value:

$$\mathrm{q}=1 -{\displaystyle \frac{\mathrm{WSS}}{\mathrm{TSS}}}$$

(12)

$$\mathrm{WSS}={\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{N}}_{\mathrm{i}}{\mathsf{\delta }}_{\mathrm{i}}^2$$

(13)

$$\mathrm{TSS}=\mathrm{N}{\mathsf{\delta }}^2$$

(14)

where i = 1, 2, …, n represents the stratification of coupling coordination degree (D) or influencing factors (X), and Ni and N represent the number of units in stratum i and the entire region, respectively. δ_i² and δ² represent the variances of coupling coordination degree (D) in stratum i and the entire region, respectively. WSS and TSS represent the sum of within-stratum variances and the total variance of the entire region, respectively. The value range of q is [0, 1]. The larger the q value, the more obvious the spatial differentiation of coupling coordination degree (D); if the stratification is caused by an influencing factor (X), then the larger the q value, the stronger the explanatory degree of the influencing factor (X) on coupling coordination degree (D), and vice versa.

(2) 

Interaction Detection. Interaction detection can be used to identify the interactions between different influencing factors, detecting whether the explanatory degree of coupling coordination degree (D) is enhanced or reduced when influencing factors X1 and X2 act together, or whether these factors’ effects on coupling coordination degree (D) are mutually independent [43]. According to relevant research, the interaction detection process mainly includes: First, separately calculate the $q$ values of influencing factors X1 and X2 on habitat quality (D), namely q(X1) and q(X2); Second, calculate the q value when influencing factors X1 and X2 interact, namely q(X1∩X2); Finally, conduct comparative analysis of q(X1), q(X2), and q(X1∩X2) to obtain interaction detection results, which mainly include five situations: nonlinear weakening, single-factor nonlinear weakening, bi-factor enhancement, mutual independence, and nonlinear enhancement. This study adopts 5000 m × 5000 m grid units to divide the study area into 3879 sample points, and uses geographical detector to detect dominant factors and interactions by calculating the coupling coordination degree and influencing factors of each grid unit.

4. Result

4.1. Spatiotemporal Evolution of Three-Dimensional Coupling Coordination

4.1.1. Temporal Evolution Characteristics

Figure 3 shows the average change trends of three-dimensional coupling degree and coupling coordination degree of carbon emission efficiency, carbon sink capacity, and high-quality development in the Greater Chang-Zhu-Tan urban agglomeration from 2006 to 2021. From the overall evolution characteristics, the three-dimensional coupling degree in this region fluctuates within the range of [0.802, 0.850], with a mean value of 0.824, remaining in the running-in stage overall and showing relatively stable characteristics. Among these, 2018 reached the highest value of 0.850, while 2007 saw the lowest value of 0.802, with relatively small fluctuation amplitude. The coupling coordination degree shows an overall fluctuating upward trend, rising from 0.507 in 2006 to 0.593 in 2021, an increase of 17.0%, consistently maintaining the barely coordinated stage. Notably, a significant decline to the lowest point of 0.502 occurred in 2018, primarily associated with the policy shock of supply-side structural reforms proposed by the Chinese government, where capacity reduction and inventory reduction policies led to short-term adjustments in traditional manufacturing industries, while Sino-US trade frictions and intensified environmental supervision exerted negative impacts on the regional economy, creating a “gap period” for the conversion between old and new development drivers. Subsequently, the coupling coordination degree rebounded rapidly, with significant improvements in 2020–2021 for two consecutive years, reaching 0.588 and 0.593, respectively, achieving new highs during the study period. This trend reflects the positive adjustments made by various cities in policy responses and coordinated development following the introduction of the “dual carbon” goals.

Overall, the three-dimensional system of the Greater Chang-Zhu-Tan urban agglomeration has maintained a relatively stable coordination state, with good interactions among subsystems, but there remains considerable room for improvement in coordination quality. The fluctuation characteristics of coupling coordination degree indicate that the three-dimensional system is relatively sensitive to external policy shocks, while also reflecting the adaptive adjustments made by the region in exploring coordinated pathways among carbon emission efficiency, carbon sink capacity, and high-quality development.

Analysis of temporal evolution by individual cities reveals significant differentiated development characteristics in three-dimensional coupling coordination (Figure 4 and Figure 5). From the temporal evolution of coupling degree (Figure 4), cities show distinct tiered development patterns. The first tier, represented by Changde and Yueyang, maintains high coupling levels above 0.9 for extended periods, with further improvements to peak values of 0.958–0.982 in 2020–2021, demonstrating the natural advantages of ecologically rich cities in three-dimensional system coordination. The second tier includes Yiyang, Hengyang, and Changsha, with coupling degrees mostly in the 0.8–0.9 range of the running-in period, where Yiyang and Changsha achieved leaps in 2020–2021, reaching 0.983 and 0.982, respectively, while Hengyang even broke through to a historical high of 0.998. The third tier of Zhuzhou, Xiangtan, and Loudi shows divergent trends: Zhuzhou declined from around 0.8 in earlier periods to around 0.70 in 2020–2021; Xiangtan has long lingered in the 0.6–0.7 low coupling range, further declining to 0.537 in 2021; Loudi dropped from the 0.65–0.75 range to 0.531 in 2020 before a slight recovery.

From the temporal evolution of coupling coordination degree (Figure 5), cities show significantly different coordination level improvement pathways. Yueyang City performs most prominently, steadily improving from 0.554 in 2006 to 0.740 in 2021, becoming the only city to break through the intermediate coordination threshold (above 0.7), and reaching a historical high of 0.716 in 2020. Changde City’s coordination degree has long remained in the 0.55–0.65 range, jumping to 0.708 in 2020 before falling back to 0.681, overall in the transition stage from primary to intermediate coordination. Yiyang, Hengyang, and Changsha show similar patterns of “early fluctuation, later improvement,” all breaking through 0.6 to enter the primary coordination stage in 2020–2021, with Yiyang reaching 0.695, Hengyang reaching 0.660, and Changsha reaching 0.652.

In contrast, the coordination degree evolution trajectories of Zhuzhou, Xiangtan, and Loudi are more tortuous. Zhuzhou City declined from the 0.50–0.55 range in earlier periods to around 0.46 in 2020–2021, falling back to the on-the-verge-of-imbalance state; Xiangtan City has long fluctuated in the 0.43–0.48 on-the-verge-of-imbalance range, once dropping to the lowest point of 0.414 in 2020; Loudi City’s coordination degree has continuously declined, from 0.427 in 2006 to 0.376 in 2021, becoming the only city to fall into slight imbalance (0.3–0.4).

This differentiated development pattern reflects the significant differences in response capacity and adaptability among cities after the introduction of the “dual carbon” goals. Cities with abundant ecological resources and relatively clean industrial structures (such as Yueyang and Changde) demonstrate stronger resilience in coordinated development; cities with good economic foundations and strong innovation capabilities (such as Changsha and Hengyang) achieved leaps in coordination levels through policy adjustments; while traditional industrial cities (such as Loudi, Xiangtan, Zhuzhou) experienced varying degrees of coordination decline under transformation pressure, reflecting the nonlinear characteristics of three-dimensional system coupling and the “green paradox” effect.

4.1.2. Spatial Pattern Characteristics

Figure 6 shows the spatial distribution evolution characteristics of three-dimensional coupling degree and coupling coordination degree in the Greater Chang-Zhu-Tan urban agglomeration for 2006, 2011, 2016, and 2021. From the overall spatial evolution perspective, the three-dimensional coupling coordination degree presents a clear spatial restructuring process of “high in the north, low in the south, core diffusion”.

From the spatial evolution of three-dimensional coupling degree (Figure 6a), the overall coupling level of the Greater Chang-Zhu-Tan urban agglomeration shows an upward trend while maintaining high levels, presenting distinct “periphery-core” spatial pattern evolution characteristics. In 2006, the northern and southern regions performed prominently, with Yueyang (0.976) and Changde (0.946) forming a northeast-northwest high coupling axis, while Zhuzhou (0.847) and Hengyang (0.900) constituted the second-tier high coupling area. By 2011, the spatial pattern evolved from north–south high coupling areas to a gradient distribution decreasing from north to southwest. At this time, Xiangtan was in the low coupling period, Loudi and Hengyang were in the antagonistic period, while the other five cities were in the running-in and high coupling periods, forming a distinct north–south differentiation pattern. In 2016, high coupling areas were mainly concentrated in Changde and Yueyang, while central-south cities including Loudi, Xiangtan, and Zhuzhou were in the antagonistic and low coupling periods. In 2021, significant spatial restructuring occurred with substantial expansion of high coupling areas: Hengyang in the south leaped to the highest position, Changsha in the center and Yueyang in the northeast ranked second jointly, while Changde in the northwest and Yiyang in the central-west also maintained high positions, forming a high coupling network covering most areas of the north, center, and south. Only Zhuzhou in the southeast, Loudi in the southwest, and Xiangtan in the central-south remained at relatively low positions.

From the spatial evolution of three-dimensional coupling coordination degree (Figure 6b), the overall pattern shows an evolution trajectory from “northern leadership” to “north-south coordination” and then to “multi-polar support”. In 2006, the coordination degree presented a relatively balanced distribution pattern, with Changde in the northwest ranking first, followed closely by Yiyang in the central-west and Yueyang in the northeast. Changsha in the center and Zhuzhou in the southeast were at the barely coordinated level, while Hengyang in the south, Xiangtan in the central-south, and Loudi in the southwest were in the on-the-verge-of-imbalance state. In 2011, the northern axis advantage was further highlighted, with Changde firmly maintaining the first position and Yueyang following closely. Hengyang in the south achieved a breakthrough to enter the barely coordinated stage, while Yiyang in the central-west and Zhuzhou in the southeast remained stable. However, Loudi in the southwest and Xiangtan in the central-south still remained at low coordination levels. In 2016, the coordination pattern was relatively stable, with Yueyang in the northeast surpassing Changde to leap to first place. Yiyang in the central-west and Zhuzhou in the southeast maintained moderate coordination levels. Notably, Changsha in the center experienced a decline, reflecting the coordination pressure faced by the provincial capital during rapid development. In 2021, significant improvement occurred with fundamental changes in spatial pattern: Yueyang in the northeast was the first to break through the intermediate coordination threshold, followed closely by Yiyang in the central-west, while Changde in the northwest, Hengyang in the south, and Changsha in the center all entered the primary coordination stage, forming a high coordination network covering major cities in the north, center, and south. Conversely, although Zhuzhou in the southeast and Xiangtan in the central-south showed some recovery, they remained in the on-the-verge-of-imbalance state, while Loudi in the southwest fell into slight imbalance, becoming the only low coordination area.

This spatial evolution pattern reflects three important theoretical mechanisms: First, the northern region (Yueyang, Changde) achieved high coordinated development through the pathway of “ecological resources → carbon sink capacity → ecological industries → high-quality development” by leveraging abundant lake and wetland resources and an excellent ecological environment; Second, the economic core area (Changsha) and important southern node cities (Hengyang) successfully constructed decoupling mechanisms between carbon emissions and economic growth through innovation-driven development and industrial upgrading; Third, traditional industrial concentration areas (Xiangtan, Zhuzhou) showed obvious differentiation during transformation, with some areas facing “green paradox” challenges and still experiencing considerable coordinated development pressure. Overall, the three-dimensional coupling coordination degree of the Greater Chang-Zhu-Tan urban agglomeration presents spatial differentiation characteristics of “northern leadership, core driving, southern differentiation,” and the spatial structure of regional coordinated development is being reshaped.

4.1.3. Hot–Cold Spot Evolution Characteristics Analysis

To further reveal the spatial clustering characteristics of three-dimensional coupling coordinated development, this study conducts hot–cold spot analysis on the coupling coordination degree of carbon emission efficiency, carbon sink capacity, and high-quality development in the Greater Chang-Zhu-Tan urban agglomeration, identifying typical high-value clustering areas (hot spots) and low-value clustering areas (cold spots), and analyzing their evolution mechanisms, as specifically shown in Figure 7.

In 2006, the Greater Chang-Zhu-Tan urban agglomeration presented a significant hot–cold differentiation pattern. Changde, as a major agricultural city, had a relatively low proportion of secondary industry, especially heavy industry, resulting in relatively small carbon emission intensity. Its vast farmlands, water bodies, and forests provided strong carbon sink capacity. Additionally, with a low economic development base but reasonable growth rate and small environmental pressure, it achieved good three-dimensional coordination and became a coordination hot spot area. In contrast, Xiangtan, as an old industrial base, had an extremely high proportion of heavy chemical industries such as steel and chemicals, resulting in massive carbon emission totals and intensity. The dense built-up areas led to scarce carbon sink space, and the high resource consumption and heavy pollution resulted in costly economic growth, leading to extremely poor coordination and forming a cold spot area.

By 2011 and 2016, the region’s overall industrialization and urbanization accelerated, with manufacturing and infrastructure construction expansion driving rapid growth in carbon emissions across the board. Urban spatial expansion encroached on carbon sink space, and the resource-environmental costs of development became prominent. The relative advantages of cities like Changde were weakened, and the high total volumes of core cities like Changsha masked coordination issues. No cities within the region significantly outperformed their neighbors, causing hot spot areas to disappear. Xiangtan persisted as a cold spot area due to lagging industrial structure transformation, large inertia in heavy industry development, and heavy high-carbon emission burdens. Urban spatial constraints limited carbon sink enhancement, and coordination degree remained significantly below the regional average, highlighting the difficulties of old industrial base transformation.

In 2021, important changes occurred in the pattern: the Xiangtan cold spot disappeared. Through industrial transformation and upgrading (closing high-pollution enterprises, developing advanced manufacturing, promoting energy-saving technologies, and ecological restoration), its carbon emission intensity significantly decreased, carbon sink capacity slightly improved, and economic growth quality enhanced, with coordination degree approaching the regional average level. Simultaneously, driven by the “dual carbon” goals and the integrated policies of the Chang-Zhu-Tan Two-Oriented Society/Metropolitan Area, cities universally promoted green low-carbon transformation (Changsha strengthened green innovation, Zhuzhou upgraded technology, and cities around Dongting Lake enhanced ecological protection), significantly reducing internal regional coordination degree differences.

This evolution trajectory clearly reflects the Greater Chang-Zhu-Tan region’s journey from unbalanced and uncoordinated development (coexistence of high emissions and low quality), through transformation difficulties (widespread intensified environmental pressure and difficult transformation of old industrial bases), to finally moving toward relatively balanced and coordinated green low-carbon high-quality development. The disappearance of hot–cold spot areas in 2021 marks the region’s entry into a new stage requiring continued deepening of transformation and pursuit of higher-level coordination, rather than the endpoint of perfect coordination. This provides important insights for other urban agglomerations facing similar challenges: traditional industrial cities can completely achieve leapfrog improvement in three-dimensional coordinated development through systematic industrial transformation, ecological restoration, and development model innovation.

4.2. Spatial Correlation of Three-Dimensional Coupling Coordination Degree

4.2.1. Global Moran’s I Index Analysis

To further explore the spatial correlation of three-dimensional coupling coordination degree among carbon emission efficiency, carbon sink capacity, and high-quality development in the Greater Chang-Zhu-Tan urban agglomeration, this study calculated the global Moran’s I indices for four time points: 2006, 2011, 2016, and 2021. The results shown in

Table 5. Global Moran’s I Coefficients.

Year	Moran’s I Index	Z-Value	p-Value
2006	0.394	2.349	0.019
2011	0.139	1.233	0.217
2016	0.2	1.487	0.137
2021	0.075	0.948	0.343

indicate that the Moran’s I indices for all years are greater than 0, showing positive spatial correlation in three-dimensional coupling coordination degree, but the correlation strength shows a fluctuating downward trend. Among these, the Moran’s I index for 2006 was 0.394 with a p-value of 0.019, passing the 5% significance level test, indicating that cities had relatively significant spatial correlation relationships in the early study period. However, as time progressed, spatial correlation gradually weakened, with the Moran’s I indices for 2011, 2016, and 2021 all failing to pass significance tests.

This evolution trend reflects profound changes occurring in the spatial correlation characteristics of three-dimensional coupling coordinated development in the Greater Chang-Zhu-Tan urban agglomeration. In the early period, cities had relatively similar development levels, with small coordination degree differences between adjacent cities, showing strong spatial clustering effects. With the introduction of the “dual carbon” goals and the implementation of differentiated development strategies by various cities, intercity coordinated development pathways began to diverge, spatial spillover effects gradually weakened, and cities increasingly formed unique coordinated development models based on their own resource endowments and development foundations.

4.2.2. Local Spatial Moran’s I Index Analysis

Although the global Moran’s I index shows that overall spatial correlation has weakened, local spatial autocorrelation analysis reveals more complex spatial clustering patterns. As shown in Figure 8, the three-dimensional coupling coordination degree of the Greater Chang-Zhu-Tan urban agglomeration presents stable local spatial clustering characteristics, mainly manifested as two typical spatial correlation patterns.

Xiangtan City continuously formed a “Low-Low” clustering pattern throughout the study period, meaning it has low coordination degree itself and is surrounded by cities with similarly low coordination degrees. As a traditional old industrial base, Xiangtan City achieved relatively high economic development levels supported by heavy chemical industries such as steel and chemicals, but faced prominent problems of high carbon emissions, low carbon sinks, and poor development quality, resulting in long-term low levels of three-dimensional coupling coordination degree. Meanwhile, surrounding cities such as Loudi, Changsha, and Zhuzhou also face coordination challenges between carbon emissions and high-quality development during industrialization, forming regional low-coordination clustering effects. The formation of this spatial pattern reflects both historical development path dependence factors and the common difficulties faced by traditional industrial areas during green transformation.

In contrast, Hengyang City formed a stable “High-Low” clustering pattern, meaning it has relatively high coordination degree but is surrounded by cities with relatively low coordination degrees. As an important node city in southern Hunan, Hengyang has improved production processes and workflows through traditional manufacturing upgrading and transformation in recent years, enhancing production efficiency and reducing energy consumption and operating costs. Simultaneously, the widespread application of green technologies has increased the proportion of new clean energy and renewable energy, enabling good coordination among carbon emissions, carbon sinks, and high-quality development. However, surrounding cities such as Zhuzhou, Xiangtan, and Loudi still face issues of unclear decoupling effects between carbon emissions and economic growth during industrial transformation, with relatively lagging coordinated development levels, forming a spatial pattern of Hengyang “standing out alone”.

The formation of these local spatial correlation characteristics reflects both the differentiated impacts of various cities’ resource endowments, industrial foundations, and development strategies, and deep-seated issues such as internal regional development imbalance and imperfect coordination mechanisms. The existence of “Low-Low” clustering areas indicates collective transformation difficulties among traditional industrial city groups, requiring strengthened policy coordination and regional cooperation. The “High-Low” clustering pattern shows that the demonstration and driving effects of advanced cities have not been fully realized, and regional collaborative development mechanisms need further improvement.

4.3. Influencing Factors of Three-Dimensional Coupling Coordination Degree

To deeply understand the driving mechanisms of three-dimensional coupling coordination degree in the Greater Chang-Zhu-Tan urban agglomeration, this study employs Tobit regression models and geographical detector methods to systematically analyze the effects and interactions of factors including industrial structure upgrading, government support, economic development level, urbanization rate, technological support intensity, environmental regulation intensity, and informatization level on three-dimensional coupling coordination degree.

The Tobit regression results shown in

Table 6. Regression results.

Variable	Three-Dimensional System Coupling Coordination Degree
Government Support	−0.0578 **
	(−2.0086)
Economic Development	0.0336 *
	−1.783
Urbanization	0.0032
	−0.0236
Industrial Structure	−0.0830 ***
	(−3.2365)
Environmental Regulation	−0.0098
	(−0.3756)
Informatization	−0.026
	(−1.3716)
Technological Support	0.0015
	−0.0499
Constant	0.2467
	−1.5763
N	128

Note: ***, **, * represent significance at 1%, 5%, and 10% levels, respectively.

indicate that industrial structure upgrading exhibits a negative correlation with three-dimensional coupling coordination degree (coefficient = −0.0830), primarily because industrial structure upgrading requires high-quality human capital and substantial capital investment, while the Greater Chang-Zhu-Tan urban agglomeration faces supply shortages in the short term, leading to temporary negative shocks during the transformation period. Government support also demonstrates a significant negative correlation (coefficient = −0.0578), reflecting that mandatory governance models may reduce factor allocation efficiency by replacing market mechanisms through selective industrial policies, while excessive intervention damages research and innovation vitality. In contrast, economic development level shows a significant positive correlation with three-dimensional coupling coordination degree (coefficient = 0.0336), consistent with Environmental Kuznets Curve logic, as enhanced economic strength provides strong guarantees for environmental governance, technological innovation, and development quality improvement.

Geographical detector analysis shows (Figure 9) that industrial structure upgrading is the most important factor influencing spatial differentiation of three-dimensional coupling coordination degree (q = 0.471), followed by economic development level (q = 0.398) and environmental regulation (q = 0.329). Compared to two-dimensional systems, the influence of technological support intensity is significantly reduced in the three-dimensional system (q = 0.096), reflecting the relative prominence of natural ecosystem effects after introducing the carbon sink dimension.

Interaction detection results show (

Table 7. Factor Interaction Effects.

Variable	Gov_Sup	Econ_Dev	Urban	Ind_Struct	Env_Reg	Info	Tech_Sup
Gov_Sup	0.248
Econ_Dev	0.698	0.398
Urban	0.716	0.615	0.181
Ind_Struct	0.789	0.648	0.597	0.471
Env_Reg	0.921	0.906	0.65	0.89	0.329
Info	0.674	0.77	0.529	0.842	0.715	0.268
Tech_Sup	0.678	0.569	0.274	0.633	0.543	0.56

) that the interaction between environmental regulation and government support is most significant (q = 0.921), and the interaction effect between environmental regulation and economic development level (q = 0.906) is also prominent, reflecting that environmental policy implementation requires government support and economic foundation guarantees. Comprehensive analysis indicates that improving three-dimensional coupling coordination degree requires coordinated optimization of industrial structure, transformation of government governance, and enhancement of economic development quality, particularly fully leveraging the synergistic effects between environmental regulation and government support, and between environmental regulation and economic development level.

5. Conclusions and Policy Implications

Using panel data from the Greater Chang-Zhu-Tan urban agglomeration (2006–2021), this study systematically examined the three-dimensional coupling coordination among carbon emission efficiency, carbon sink capacity, and high-quality development. The results show that the region’s coupling coordination generally exhibits “overall stability with partial differentiation”. Temporally, the system remains in a transitional stage, evolving through three phases—initial coupling, adaptive stabilization, and differentiation adjustment—with the coordination level fluctuating around a barely coordinated state. Spatially, the region has shifted from a “northern-led” pattern to a “multi-polar” structure: Yueyang achieved intermediate coordination; Changde and three other cities reached primary coordination; while Loudi and two others remained imbalanced. Hotspot evolution indicates a transition from marked divergence to relative equilibrium, with cold spots disappearing—signaling a move toward more balanced regional development.

Spatial correlation analysis reveals a gradual weakening of spatial dependence, as differentiated local strategies have reduced spillover effects. Local spatial patterns exhibit a persistent “low–low” cluster in Xiangtan and a stable “high–low” cluster in Hengyang, reflecting persistent regional disparities. Empirical evidence supports the theoretical mechanism of tri-dimensional coupling: resource-endowed areas enhance coordination through carbon sink–development synergies; economically advanced regions decouple growth from emissions via innovation-driven paths; and traditional industrial cities, despite “green paradox” constraints, can achieve transformative improvements through systemic upgrading.

Among influencing factors, industrial structure upgrading emerges as the dominant driver of spatial differentiation, though its transitional impact remains negative due to limited human and capital resources. Government support also exerts negative effects, highlighting inefficiencies in top-down administrative control. The positive effect of economic development aligns with the Environmental Kuznets Curve hypothesis. Moreover, interaction analysis identifies the synergistic effects of environmental regulation with government support and economic development as the most significant, suggesting that effective coordination requires multi-dimensional policy integration.

Based on these findings, three key policy directions are proposed:

(1)

Establish differentiated coordination guidance mechanisms. Cities should adopt tailored strategies according to their coordination levels. Highly coordinated cities should develop eco-industrial demonstration zones, improve ecological value realization mechanisms, and lead regional green transitions. Less coordinated cities should advance industrial restructuring, promote the green transformation of traditional heavy industries, and establish green transition funds coupled with flexible evaluation mechanisms. Transitional buffer mechanisms and phased policy pathways are needed to mitigate short-term adjustment costs.

(2)

Develop regionally coordinated spatial optimization mechanisms. For “low–low” clusters, collaborative transformation mechanisms among traditional industrial cities should be established; for “high–low” clusters, spillover and demonstration functions should be strengthened. Cooperation between ecologically advantaged and innovation-led cities should be promoted and supported by a regional coordination development fund. A cross-regional carbon sink trading system should also be developed to optimize spatial resource allocation.

(3)

Optimize policy integration and innovation support. Given the strong interactive effects among environmental regulation, government support, and economic development, an integrated environment–economy–society evaluation framework should be established. Market-oriented instruments such as carbon trading, ecological compensation, and green finance should be refined, while excessive administrative intervention should be reduced. Simultaneously, innovation support should be enhanced through integrated platforms for emission reduction, carbon sinks, and green technologies, promoting collaborative innovation among industry, academia, and research sectors.

Despite its contributions, this study has certain limitations. Data sources may suffer from inconsistent statistical standards and time lags; fixed coefficients for carbon absorption fail to reflect ecological heterogeneity; and limited micro-scale data restrict deeper mechanism analysis. Methodologically, the super-efficiency CCR model assumes linearity, constraining its capacity to capture nonlinear dynamics; equal weighting in the coupling model overlooks changing dimensional importance; and the geographic detector inadequately represents complex nonlinear interactions.

Future research should advance in several directions. At the scale level, analyses can be extended to counties or enterprises to explore finer coordination mechanisms and behavioral heterogeneity during green transitions, while cross-regional and international comparisons can enhance generalizability and external validity. In methodology, integrating AI and machine learning with coupling coordination analysis can improve dynamic precision and model adaptability, leveraging big data, remote sensing, and IoT technologies. In policy evaluation, examining the synergistic effects and optimal configurations of policy instruments can support the development of evaluation systems aligned with tri-dimensional coordination goals, providing stronger evidence for policy optimization and targeted governance. These efforts will further enrich the theoretical framework of regional sustainable development and offer robust scientific guidance for achieving low-carbon, high-quality growth in urban agglomerations worldwide.