Spatiotemporal Continuity and Spatially Heterogeneous Drivers in the Historical Evolution of County-Scale Carbon Emissions from Territorial Function Utilisation in China: Evidence from Qionglai City

Abstract

County-level administrative areas serve as fundamental components in China’s territorial spatial governance, and the precision and consistency of their carbon emission reduction policies are directly linked to the efficacy of the “dual-carbon” strategy’s execution. However, the spatiotemporal evolution characteristics, future trends, and driving factors of carbon emissions from territorial spatial function (TSF) utilisation at the county level remain unclear, posing a fundamental theoretical issue that local governments urgently need to address when formulating carbon reduction policies. This study developed a framework to simulate the spatial distribution of carbon emissions resulting from land use at the county level. It simulated the carbon emissions in Qionglai City from 2009 to 2023, analysed the spatial-temporal evolution characteristics and future trends using global Moran’s I, the Getis-Ord $G_i^{*}$ index, and the Hurst index, and employed the Geographically and Temporally Weighted Regression (GTWR) model for analysis. The findings indicated the following: (1) From 2009 to 2023, the city’s total carbon emissions increased from 852,300 tonnes to 1,422,500 tonnes, showing a significant phased trend. Among these, rural production spaces (RPSs) were the primary carbon sources, accounting for over 70% of annual carbon emissions each year. (2) County carbon emissions exhibit a pronounced positive geographical correlation and aggregation distribution, characterised by notable regional heterogeneity. (3) From 2009 to 2023, the city’s regional carbon emissions rose dramatically by 65.69%, while 29.66% of the areas experienced negligible increases; 99% of the regions are projected to maintain the historical growth trend, but this continuity exhibits spatial and temporal variations. (4) Economic growth, industrial structure, and development intensity are the core driving factors of carbon emissions at the county level, with spatial variations in their impact. The research findings not only provide a basis for Qionglai City, China, to formulate precise and sustainable carbon reduction policies (such as developing differentiated carbon emission control measures based on the spatiotemporal heterogeneity of carbon emissions and their driving factors), but also offer insights for similar regions worldwide in controlling carbon emissions and addressing global climate change (for example, by optimizing land spatial function utilisation, reducing carbon sources, and maximizing carbon sink capacity).

1. Introduction

Global climate change, exacerbated by increasing greenhouse gas emissions, poses a significant challenge to sustainable human development [1]. Since industrial development, greenhouse gas concentrations have driven a global average temperature rise of over 1 °C above pre-industrial levels [2]. This warming has intensified extreme weather events, impacting sea levels, ecosystems, and biodiversity [3,4]. Carbon dioxide (CO₂), accounting for approximately 65% of cumulative climate change drivers, is the primary greenhouse gas of concern [5]. Consequently, managing CO₂ emissions is central to global climate governance. China, currently the world’s largest CO₂ emitter [6], has adopted “dual carbon” goals aiming to peak emissions by 2030 and achieve carbon balance by 2060 [7]. Territorial space serves as the foundation and location for human production and existence, encompassing a broader meaning than merely “land” [8]. International scholars predominantly employ “land functions” as a specialised term [9,10], whereas the utilisation of “territorial spatial functions (TSFs)” is infrequent, with only a limited number of Chinese academics utilising the phrases “territorial space functions” or “territorial spatial functional areas” in their publications [11,12]. From both ecological and economic perspectives, the connotation of territorial space and land is often identical. China’s territorial spatial planning system categorises territorial space into three distinct types: production, living, and ecological spaces [8]. Each category is designated according on its dominant function, effectively encapsulating the nine land functions delineated by the SENSOR system [13]. Simultaneously, certain researchers have preliminarily categorised land functions into three distinct categories: production, living, and ecological functions [14,15]. Consequently, from the viewpoints of ecology and economics, the implication of territorial spatial function (TSF) can be synonymous with land function.

Utilisation of TSFs impacts the development and transformation of carbon source-sink patterns by affecting land use and cover changes [16]. Research indicates that carbon emissions resulting from land use alterations constitute approximately one-third of total anthropogenic carbon emissions [17]. In particular, during rapid urbanisation, urban spatial expansion resulting in biomass decline and soil carbon store depletion has emerged as a significant contributor to regional carbon imbalance [18]. Consequently, elucidating the evolutionary traits of carbon emissions resulting from TSFs and their driving mechanisms is a crucial theoretical foundation for attaining carbon emission regulation. Moreover, within China’s national governance framework, county-level administrative districts serve as the principal execution units of the “dual-carbon” objective, as well as the spatial nodes where local development conflicts (e.g., the expansion of construction land versus the preservation of arable land, and the carbon emissions from traditional industries versus the promotion of new energy sectors) converge [19,20]. County governments can more directly influence the TSF allocation through land planning, industrial regulation, and other mechanisms, compared to provincial, municipal, township, and village levels, thereby impacting the distribution of carbon sources and sinks [21,22]. Consequently, elucidating the spatial and temporal evolution characteristics and driving mechanisms of carbon emissions resulting from the TSF utilisation at the county level is crucial for local governments to develop precise and sustainable carbon emission reduction policies and to improve the implementation efficacy of dual-carbon strategy.

Despite significant advancements in carbon emission accounting [23], the characterisation of spatial and temporal evolution [24], and identification of driving factors, notable deficiencies persist in three areas [25]. Primarily, the majority of pertinent studies concentrate on national or provincial and municipal levels, resulting in a relative deficiency of analyses that systematically examine the county level, thereby complicating the elucidation of spatial variability in county carbon emissions during the utilisation of TSFs [26]. Secondly, while numerous studies examine the historical progression of carbon emissions, there is a paucity of simulations regarding the spatial distribution of carbon emissions and projections of future scenarios that utilise the TSFs, leading to an inadequate comprehension of the complete carbon emissions cycle cross-referenced from the existing literature [27]. Third, the operational processes and spatiotemporal dynamics of driving factors are often overlooked, and the spatial heterogeneity of their impacts on carbon emissions from TSF utilisation is not fully revealed. This omission may, to some extent, reduce the accuracy and foresight of carbon-reduction policies [28]. These deficiencies may result in excessive dependence on historical extrapolation in policy formulation, complicating the management of intricate non-linear transformations associated with the carbon neutrality objective, hence diminishing the actual efficacy of carbon emission reduction programs. Consequently, a systematic examination of the spatial and temporal dynamics of carbon emissions resulting from TSF utilisation at the county level, the trajectory of full-cycle evolution, and its underlying mechanisms has emerged as a critical theoretical issue that local governments must urgently address to develop precise and sustainable carbon emission reduction and control policies.

To address the above question, this study calculates county-scale carbon emissions from the utilisation of TSFs and simulates their spatiotemporal evolution and trends across the entire lifecycle. It also identifies the driving factors influencing carbon emission changes, addressing gaps in future emission predictions and the spatial heterogeneity of the driving forces. First, a county-level carbon emission accounting framework integrating LUCE coefficients with the IPCC inventory method was developed to quantify and model the spatial distribution of carbon emissions from TSF utilisation. This fills a critical gap in county-level spatial simulation research on carbon emissions. Second, spatial clustering and historical trends of carbon emissions were analysed using global Moran’s I and Getis-Ord $G_i^{*}$ indices, combined with Mann–Kendall and Hurst indices to forecast future trajectories. Third, the Geographically and Temporally Weighted Regression (GTWR) model examined the spatial heterogeneity of driving factors, identifying key determinants and their varying regional impacts. The study offers a framework for adjusting TSF utilisation to promote low-carbon development in Qionglai City, China, providing a theoretical basis for county-level governments to formulate targeted, sustainable carbon reduction policies. Additionally, it contributes valuable insights for other developing countries aiming to manage carbon emissions and address global environmental change.

Following the introduction, the article is organised as follows: Section 2 consolidates the advancements and challenges in carbon emissions research; Section 3 delineates the research methodology, encompassing specific techniques for simulating the distribution of carbon emissions related to TSFs, analysing the characteristics of spatiotemporal evolution of carbon emissions and forecasting trends, as well as identifying driving factors of carbon emissions; Section 4 elucidates the study’s results, emphasising the analysis of the temporal characteristics of TSFs of carbon emissions, the patterns of spatiotemporal evolution, and their influencing factors; Section 5 articulates the principal research conclusions and suggests relevant policy implications; Section 6 encapsulates the key findings and their significance.

2. Literature Review

2.1. Carbon Emission Accounting Methodologies

Current carbon emission accounting methods primarily include direct measurement, factor decomposition, and the emission factor approach recommended by the IPCC [23,29,30]. The IPCC emission factor method is the dominant framework for quantifying carbon emissions, integrating key variables such as land use and energy consumption [31]. Its strengths lie in a comprehensive methodology and standardized parameters, which facilitate global and regional comparability. However, it requires high-quality data, involves complex calculations, and faces limitations in regional applicability [6]. For instance, Tian et al. [26] and Xu et al. [32] applied the IPCC inventory method to quantify carbon emissions globally and in China, respectively. By contrast, the land use carbon emission (LUCE) coefficient method suits smaller-scale or data-constrained contexts due to its simpler data demands and its ease in representing spatial distribution [31]. Nonetheless, it relies on fixed emission coefficients and does not account for spatiotemporal variation or ecosystem interactions [33]. For example, Yuan et al. [34] applied the LUCE method to assess land use-related carbon emissions in the Beijing-Tianjin-Hebei region from 2000 to 2020, identifying construction land as the primary emission source. Most carbon accounting occurs at provincial, municipal, and county levels, adequately reflecting general emission patterns but inadequately capturing spatial heterogeneity [35]. Grid-based (pixel) units offer finer spatial resolution, effectively addressing the imprecision of regional-scale accounting by accurately representing carbon emission distribution [33]. However, grid-based simulation methods tailored to carbon emissions from the utilisation of TSFs are still underdeveloped. Therefore, by integrating the strengths of the IPCC inventory approach with the land use coefficient method, the development of a grid-based spatial unit carbon emission distribution simulation method is anticipated to overcome the spatial constraints inherent in traditional carbon emission accounting techniques. This approach demonstrates substantial potential for application in simulating the spatial distribution of carbon emissions resulting from the utilisation of TSFs.

2.2. Characteristics of the Spatiotemporal Evolution of Carbon Emissions

Research on the spatiotemporal evolution characteristics of carbon emissions remains limited at finer scales like the county level compared to national, provincial, or urban agglomeration scales [26]. Most existing studies focus on analysing historical carbon emission patterns [36]. For example, Zhou et al. [6] examined carbon emission data across Chinese prefecture-level cities from 1997 to 2017 to explore spatial heterogeneity and its driving mechanisms. However, forecasting future evolution trends is underexplored, which may hinder the maintenance of carbon reduction policies and reduce foresight in planning [27]. Common methods to analyse the spatiotemporal evolution of carbon emissions include the global Moran’s I index, Getis-Ord $G_i^{*}$ statistic, and standard deviation ellipse analysis [24,37,38]. The global Moran’s I effectively measures global spatial autocorrelation, revealing aggregation patterns [39], while Getis-Ord $G_i^{*}$ identifies hotspot and coldspot regions, aiding targeted emission reduction [40]. Nonetheless, these methods have limited capacity to simulate dynamic temporal trends. For predicting spatiotemporal evolution, methods such as the Mann–Kendall trend test, linear regression, Theil–Sen median trend analysis, and the Hurst index are widely used [41]. The Mann–Kendall test is valued for its robustness against outliers [42], making it suitable for retrospective trend classification, as demonstrated by Wang et al. [43] in categorizing emission changes across 30 Chinese provinces. The Hurst index, an emerging tool, captures long-memory properties of time series data, enabling insights into future trends and sustainability of carbon emissions. It has been applied extensively in ecological and financial forecasting [44]. Tang et al. [45] used the Hurst index to predict ecological environment trends in China’s border cities, identifying potential risk areas of degradation. Thus, the Hurst index offers significant value in carbon emissions research related to TSFs, providing quantitative foresight to support proactive carbon reduction policy development.

2.3. Analysis of Factors Affecting Carbon Emissions

Current research indicates that the primary drivers of changes in carbon emissions encompass energy consumption structure, industrial structure, development intensity, the utilisation structure of TSFs, economic growth, and population density [25,46,47]. The structure of energy consumption directly influences carbon emission levels by dictating the proportion of fossil fuel utilisation [48]. Regions characterised by a predominance of the secondary industry, particularly traditional sectors, typically exhibit elevated levels of carbon emissions [49]. Increased development intensity results in a greater concentration of construction activities and carbon emission-intensive processes, thereby amplifying carbon emissions [50]. The structure of TSF utilisation has an indirect effect on carbon emission intensity. For example, the effectiveness of carbon reduction in agricultural spaces depends on the implementation of scale and low-carbon technologies. Conversely, economic concentration in production and residential spaces, coupled with the densification of transportation networks, increases emissions [51]. The correlation between economic growth and carbon emissions is well-established, with population density playing a significant role in increasing energy consumption, thereby elevating carbon emissions [52]. Common approaches to examining the determinants of carbon emissions include the LMDI decomposition method, geographic detector, and GTWR [53,54,55]. Although the LMDI method is commonly used to decompose carbon emission drivers—focusing on emission intensity, industrial structure, and economic growth—it does not address the spatiotemporal heterogeneity of these factors or their dynamic variability with respect to time and space [56]. To overcome this limitation, Geographically Weighted Regression (GWR), GTWR, and Multi-scale Geographically Weighted Regression (MGWR) models, as well as geographic detectors, have been employed to analyse the spatial variability of carbon emission driving forces, with the GTWR model being particularly notable [57]. The GTWR model accurately represents spatial heterogeneity and integrates temporal variations, allowing detailed analysis of how driving factors affect regions and timeframes, making it suitable for examining intricate dynamic mechanisms of carbon emissions [55]. The GTWR model has been widely employed in examining the factors influencing LUCE [58]. For instance, Shi et al. [59] utilised the GTWR model to study the spatiotemporal effects of urban form on CO₂ emissions, revealing notable spatial and temporal heterogeneity. Despite the GTWR model’s advantages in addressing spatiotemporal heterogeneity and serving as a valuable tool for analysing carbon emission changes over time and space, many studies fail to conduct sensitivity tests on model parameters or assess the robustness of spatial weight functions, which may compromise the reliability of their conclusions. This issue warrants further investigation in future research.

Existing research provides foundational support for exploring the spatiotemporal evolution characteristics and full-cycle evolution trends of carbon emissions from the utilisation of TSFs at the county level in China, as well as their driving factors, but there remain three aspects of deficiency. First, carbon emission assessments often focus on national, provincial, or municipal administrative units, overlooking county-level characteristics, which are essential for localized policy implementation. For example, carbon emissions in Shaanxi counties show distinct spatial variation, with higher emissions in northern areas and lower in the south [60]. Second, most studies simulate LUCE spatial distribution at regional or administrative levels, while grid-scale spatial simulations remain limited. Research on the spatial distribution of carbon emissions from the perspective of TSF utilisation is especially scarce; many studies analyse historical evolution between 2000 and 2020 [61] but rarely explore future scenario simulations. Third, investigations of carbon emission driving mechanisms commonly assume geographic uniformity, neglecting the dynamic variability of factor effects [28]. Therefore, there are three specific issues that need to be addressed in order to carry out this research: (1) How can carbon emissions from the utilisation of TSFs be accurately accounted for at the county level in China? (2) What are the spatiotemporal evolution characteristics and trends of these emissions, and how do past and future patterns differ? (3) What are the primary drivers contributing to variations in carbon emissions from TSF utilisation at this scale? Addressing these questions will provide empirical evidence to support policy development aimed at China’s carbon neutrality goals.

3. Materials and Methods

3.1. Study Area and Data

3.1.1. Overview of the Study Area

Qionglai City is located in western China, in the transitional zone between the Chengdu Plain and the Longmen Mountains, between 30°12′ N and 30°33′ N, and 103°04′ E and 103°45′ E, as shown in Figure 1. The topography gently slopes from northwest to southeast, with elevations ranging from 451 to 1991 m, and includes plains, mountainous areas, and hills. The region is endowed with abundant water resources and experiences a subtropical humid monsoon climate, characterized by an average annual temperature of 16.3 °C and mean precipitation of 1117.3 mm. Predominant soil types include water-affected and purple soils, while the vegetation is largely composed of subtropical evergreen broadleaf forests.

This study selects Qionglai City as a representative case to investigate the spatiotemporal evolution and driving mechanisms of territorial spatial functional carbon emissions at the county scale. Firstly, the city exhibits a diverse array of TSFs, encompassing urban production and living and rural production and living alongside ecological supply, regulation, and support services. Secondly, the city is located in the core region of the Qionglai Mountain biodiversity conservation red line, an essential area for food production and agricultural reserves in the west, as well as within the Chengdu-Chongqing urban agglomeration development zone. It confronts the encroachment of urban expansion on ecological spaces, with economic growth leading to increased carbon emissions, exemplifying typical county-level contradictions [62]. Notably, its trajectories of urbanization, economic development, and carbon emissions closely mirror patterns observed across China and several developing countries, many of which have committed to carbon neutrality targets to mitigate global climate change [63]. Consequently, insights derived from Qionglai provide not only context-specific implications but also offer valuable references for analogous regions confronting similar environmental and developmental challenges.

Figure 1. Geographical location of the research area [64] (Reprinted with permission from Ref. [64]. 2021, Ou, D.; Zhang, Q.; Qin, J.; Gong, S.; Wu, Y.; Zheng, Z.; Xia, J.; Bian, J.; Gao, X. More details about “Copyright and Licensing” are available via the following link: https://doi.org/10.11975/j.issn.1002-6819.2021.24.032 (accessed on 27 September 2025)).

Figure 1. Geographical location of the research area [64] (Reprinted with permission from Ref. [64]. 2021, Ou, D.; Zhang, Q.; Qin, J.; Gong, S.; Wu, Y.; Zheng, Z.; Xia, J.; Bian, J.; Gao, X. More details about “Copyright and Licensing” are available via the following link: https://doi.org/10.11975/j.issn.1002-6819.2021.24.032 (accessed on 27 September 2025)).

3.1.2. Data Sources and Processing

The data employed in this study mainly comprise raster data, vector data, and panel data (

Table 1. Data types and sources.

Data Type	Data Name	Time-Series (Year)	Resolution	Data Source
Raster Data	DEM	2020	12.5 m	91 Visitor Assistant (https://www.91weitu.com/) (accessed on 19 January 2025)
	Remote sensing image	2020	10 m	Earth engine data catalog (https://developers.google.com/earth-engine/datasets) (accessed on 19 January 2025)
	Functional map of territorial space	2009–2023	50 m	Previous research datasets [64]
Vector Data	Administrative boundary	2020	1:5000	Land survey results (Key laboratory of investigation, monitoring, protection and utilization of cropland resources, MNR, PRC)
	Land use status data	2009–2023	1:5000	Land survey results (Key laboratory of investigation, monitoring, protection and utilization of cropland resources, MNR, PRC)
Panel Data	Number of pigs, Cows, and sheep, Agricultural management data	2009–2023	County level	Qionglai Statistical Yearbook
	Urban and rural population, Gross domestic product (GDP)		Township level
	Comprehensive energy consumption of industrial enterprises above designated size in terms of GDP per 10,000 yuan of total industrial output value, per capita consumption of electricity, natural and liquefied gas	2009–2023	City level	Chengdu Statistical Yearbook
	Chemical oxygen demand in wastewater	2009–2023	Provincial level	China Energy Statistical Yearbook

). To ensure consistency, geographic coordinates were standardized to WGS-1984, projected coordinates to UTM, and raster resolution unified at 100 m × 100 m. The 100-m resolution of the spatial data was chosen based on insights from the prior study’s scale selection, considering the potential loss of essential spatial information from excessively low resolution, the data redundancy from excessively high resolution, and the significant increase in computational demands [65,66]. The basic data preparation involved mapping panel data accordingly. The panel data cover two main categories: national economic and social development indicators, and energy statistics. Economic and social development data, using municipal and town units, follow methodologies from the existing literature [64] and were spatialized into a 100 m × 100 m vector grid. Energy consumption parameters were derived from IPCC guidelines [30,67] and the China Energy Statistical Yearbook.

Due to the lack of localized data on energy consumption and chemical oxygen demand (COD) in industrial wastewater for Qionglai City, proxy data from Chengdu and Sichuan Province were used for estimation. Urban energy consumption was estimated by multiplying Chengdu’s comprehensive energy consumption per 10,000 yuan of industrial output by the total industrial output of the study area. Urban residential energy consumption was calculated by multiplying per capita electricity, natural gas, and liquefied gas consumption in Chengdu by the urban population within the study area. Rural residential energy consumption was computed similarly, based on rural population figures. COD in industrial wastewater was estimated by applying the average COD in Sichuan Province scaled by the ratio of total industrial output in the study area to that of the province [68]. This integrated data processing framework supports the refined analysis of the spatiotemporal dynamics and driving mechanisms of territorial spatial functional carbon emissions [69,70,71,72].

3.2. Methodology

3.2.1. A Method-Based Framework for Modeling the Spatial Distribution of Carbon Emissions Resulting from the Utilisation of TSFs

At present, limited simulation methods exist that specifically address the spatial distribution of carbon emissions resulting from the utilisation of TSFs. This research presents a simulation framework for analysing the spatial distribution of carbon emissions resulting from the utilisation of TSFs organised by spatial units. This framework’s construction process comprises the following steps: Initially, we developed a county-level carbon emission accounting inventory for TSFs, classifying both carbon emissions and absorption under the term carbon emissions, where positive values represent carbon sources and negative values denote carbon sinks. Then, the total carbon emissions for each TSF were calculated, and the carbon emission coefficients for each function were established. Finally, the study area was segmented into multiple spatial units, and net carbon emissions for each unit were computed, yielding a spatial distribution map of carbon emissions from the utilisation of TSFs in the area (Figure 2).

(1)

Accounting List of Carbon Emissions from the Utilisation of TSFs

This study utilises the county-level land spatial classification system developed in prior research and integrates the benefits of the LUCE coefficient method with the IPCC inventory method to create a project inventory of carbon emissions resulting from the utilisation of TSFs. Specifically, the territorial space of Qionglai City is classified into seven primary categories: urban production space (UPS), urban living space (ULS), rural production space (RPS), rural living space (RLS), ecological provisioning services space (EPSS), ecological regulation services space (ERSS), and ecological support services space (ESSS) [64]. Furthermore, according to the “IPCC 2006 Guidelines for National Greenhouse Gas Inventories” (2019 Revision), carbon emission projects in Qionglai City are classified into five primary categories: terrestrial ecosystems, energy consumption, waste, population and animals, and others. Finally, by integrating the relationship between territorial spatial types and land use types, along with the correspondence between land use and carbon emission projects, a list of carbon emission projects corresponding to various territorial spatial frameworks has been established (

Table 2. Carbon emissions associated with the utilisation of TSFs.

Type of Territorial Space	Terrestrial Ecosystem	Energy Consumption	Waste	Population and Animals	Other
Urban production space		Industrial energy consumption, service sector energy consumption	Industrial waste water	Urban population breathing	Transportation land
Urban living space		Energy consumption in urban life	Industrial waste water	Urban population breathing	Transportation land
Rural production space	Cultivated land, garden land			Animal respiration, intestinal fermentation in animals, and feces.	Transportation land
Rural living space		Rural energy consumption	Industrial waste water	Rural population breathing
Ecological supply services space	Woodland, water bodies, grassland
Ecological regulation services space	Woodland, water bodies, grassland
Ecological support services space	Woodland, water bodies, grassland

).

(2)

Total Carbon Emissions Accounting and Coefficient Calculation for the Utilisation of TSFs

• Step 1: Total carbon emission accounting

The previously constructed checklist for carbon emissions from the utilisation of TSFs employed an indirect accounting method utilising LUCE coefficients to calculate the carbon emissions associated with terrestrial ecosystems and other relevant factors. The coefficients and accounting methods are derived from analogous studies (Table 3). Conversely, carbon emissions resulting from energy consumption, waste, population, and animal respiration are assessed through direct measurement of petrol carbon emissions (Table 4). This study clarifies that regional carbon emissions encompass both the emissions directly generated by local production and consumption activities and those indirectly produced by these activities.

To prevent the indefinite expansion of the accounting scope for indirect emissions, which may result in ambiguous accounting boundaries and substantially elevate accounting costs and complexities, we limited our consideration to emissions from secondary energy sources, such as electricity, heating, cooling, or steam imported from outside the city, when calculating indirect carbon emissions. Other indirect emissions, including greenhouse gas emissions from the procurement of raw materials and goods such as building materials, equipment, food, water, and clothing sourced externally, were excluded. In addition, because other gases (such as nitrogen oxides and fluorinated gases) have relatively low carbon content, this study refers to relevant research [73,74] and limits the gases to be calculated to carbon dioxide (CO₂) and methane (CH₄). This choice enhances the precision of focus on primary greenhouse gases and streamlines the accounting process.

Table 3. Method for accounting for carbon emissions from land use.

Land Type	Formula	Variable Meaning	Parameter Explanation
Arable land	$C_a=C_{sou}-C_{sin}$ $C_{sou}={\mu }_e{S}_a$ $C_{sin}={\mu }_a{S}_a$	$C_a$ indicates the net carbon benefit of arable land; $C_{sou}$ indicates the carbon emissions from arable land; $C_{sin}$ indicates the carbon sequestration from arable land; $S_a$ indicates the area of arable land; ${{\mu }_e,\mu }_a$ indicates the carbon source and carbon sink coefficients of arable land.	Referring to the calculation method of Shi et al. [75], the net carbon emission coefficient for arable land is determined by the difference between the carbon emission coefficient of crops, which is 0.0504 kg/(m2·a) [76], and the carbon absorption coefficient of crops, which is 0.0007 kg/(m2·a) [77]. Thus, the net carbon emission coefficient for arable land is 0.497 t/(hm2·a).
Forest land, Garden land, Grass land, Water bodies, Transportation land	$C_i=\sum {\mu }_i{S}_i$	$C_i$ denotes the net carbon emissions of land category $i$;${ S}_i$denotes the area of the land category; ${\mu }_i$ denotes the net carbon emission coefficient for each land category.	The national average net carbon emission level of 0.644 t/(hm2·a) obtained by Fang et al. [78] using the continuous function method of conversion factors was used as the net carbon emission coefficient of forest land. Referring to the research results of Zhao et al. [79], the net carbon emission coefficient of garden land was determined as 0.73 t/(hm2·a). Referring to the national average carbon sink level of pastureland obtained from Fang et al. [78], the net carbon emission coefficient of grassland was determined as −0.021 t/(hm2·a). For water bodies, the carbon sequestration coefficient is derived by averaging values reported by Duan et al. [80] (0.0248 kg/m2·a) and Lai et al. [81] (0.0257 kg/m2·a)., the net carbon emission coefficient of the waters was determined to be the average value of the two, i.e., −0.0253 t/(hm2·a). Referring to the research results of Zhao et al. [79], the net carbon emission coefficient of transport land was determined as 96.9 t/(hm2·a).

Table 3. Method for accounting for carbon emissions from land use.

Land Type	Formula	Variable Meaning	Parameter Explanation
Arable land	$C_a=C_{sou}-C_{sin}$ $C_{sou}={\mu }_e{S}_a$ $C_{sin}={\mu }_a{S}_a$	$C_a$ indicates the net carbon benefit of arable land; $C_{sou}$ indicates the carbon emissions from arable land; $C_{sin}$ indicates the carbon sequestration from arable land; $S_a$ indicates the area of arable land; ${{\mu }_e,\mu }_a$ indicates the carbon source and carbon sink coefficients of arable land.	Referring to the calculation method of Shi et al. [75], the net carbon emission coefficient for arable land is determined by the difference between the carbon emission coefficient of crops, which is 0.0504 kg/(m2·a) [76], and the carbon absorption coefficient of crops, which is 0.0007 kg/(m2·a) [77]. Thus, the net carbon emission coefficient for arable land is 0.497 t/(hm2·a).
Forest land, Garden land, Grass land, Water bodies, Transportation land	$C_i=\sum {\mu }_i{S}_i$	$C_i$ denotes the net carbon emissions of land category $i$;${ S}_i$denotes the area of the land category; ${\mu }_i$ denotes the net carbon emission coefficient for each land category.	The national average net carbon emission level of 0.644 t/(hm2·a) obtained by Fang et al. [78] using the continuous function method of conversion factors was used as the net carbon emission coefficient of forest land. Referring to the research results of Zhao et al. [79], the net carbon emission coefficient of garden land was determined as 0.73 t/(hm2·a). Referring to the national average carbon sink level of pastureland obtained from Fang et al. [78], the net carbon emission coefficient of grassland was determined as −0.021 t/(hm2·a). For water bodies, the carbon sequestration coefficient is derived by averaging values reported by Duan et al. [80] (0.0248 kg/m2·a) and Lai et al. [81] (0.0257 kg/m2·a)., the net carbon emission coefficient of the waters was determined to be the average value of the two, i.e., −0.0253 t/(hm2·a). Referring to the research results of Zhao et al. [79], the net carbon emission coefficient of transport land was determined as 96.9 t/(hm2·a).

Table 4. Approaches for quantifying energy consumption, wastewater, respiration, animal enteric fermentation, and manure carbon emissions.

Items	Formula	Variable Meaning	Parameter Explanation
Energy consumption	$C_e=\sum {\left(Q_e\right)}_i{\left(K_e\right)}_i\left[{\left(V_{C{O}_2}\right)}_i+{\left(V_{C{H}_4}\right)}_i\right]$	${\left(Q_e\right)}_i$ indicates the consumption of class $i$ energy; ${\left(K_e\right)}_i$ indicates the unit net calorific value of class $i$ energy; ${\left(V_{C{O}_2}\right)}_i$ and ${\left(V_{C{H}_4}\right)}_i$ respectively indicate the carbon emission factors of class $i$ energy.	Net heat value $K_e$ was obtained by querying the China Energy Statistics Yearbook; $C{O}_2$carbon emission factor and $C{H}_4$ carbon emission factor, obtained by querying the IPCC [30,67].
Industrial waste water	$C_p={\displaystyle \frac{12}{16}}\times Q_{COD}{P}_{C{H}_4}$	$Q_{COD}$ is the weight of Chemical Oxygen Demand (COD) in the wastewater;${ P}_{C{H}_4}$ is the maximum $C{H}_4$ production capacity.	Chemical Oxygen Demand (COD) in wastewater $Q_{COD}$ from China Energy Statistical Yearbook, $C{H}_4$ maximum production capacity of 0.25 [82].
Domestic wastewater	$C_l=365\times {\displaystyle \frac{12}{16}}\times N_i{\rho }_{BOD}{\gamma }_{BOD}{V}_{BOD}{F}_{BOD}$	$N_i$ indicates the population of a $i$ spatial area (in people); ${\rho }_{BOD}$ refers to the organic content of biochemical oxygen demand (BOD) per capita; ${\gamma }_{BOD}$ is the proportion of BOD that is readily deposited; $V_{BOD}$ indicates the emission factor of BOD; $F_{BOD}$ refers to the proportion of anaerobic degradation of BOD in wastewater.	The organic matter content of BOD per capita is 60 g BOD/person/day; the proportion of BOD that is readily deposited is 0.5; the emission factor for BOD is 0.6 g CH4/g; and the proportion of anaerobically degraded BOD in the wastewater is 0.8 [83].
Population, animal respiration	$C_b=\sum N_i{V}_i$	$N_i$ indicates the number of animals; $V_i$ indicates the carbon emission coefficients of animals	The respiratory carbon emission coefficients for humans, pigs, cattle and sheep were 0.079, 0.082, 0.796, 0.041 t/a [84,85].
Animal enteric fermentation and faeces	$C_f=\sum N_i\left[{\left({\upsilon }_{C{O}_2}\right)}_i+{\left({\upsilon }_{C{H}_4}\right)}_i\right]$	$N_i$ indicates the number of animals; ${\left({\upsilon }_{C{O}_2}\right)}_i$ and ${\left({\upsilon }_{C{H}_4}\right)}_i$ represent the carbon emission coefficients of CO2 and CH4 production from enteric fermentation and faecal species of the ith animal, respectively.	By querying the IPCC [30,67], the carbon emission coefficients of CO2 production from enteric fermentation and faeces in pigs, cattle and sheep were obtained as 3.89, 59.33 and 45 kg/a, and the carbon emission coefficients of CH4 production were 5.18, 79.11 and 9.93 kg/a.

Table 4. Approaches for quantifying energy consumption, wastewater, respiration, animal enteric fermentation, and manure carbon emissions.

Items	Formula	Variable Meaning	Parameter Explanation
Energy consumption	$C_e=\sum {\left(Q_e\right)}_i{\left(K_e\right)}_i\left[{\left(V_{C{O}_2}\right)}_i+{\left(V_{C{H}_4}\right)}_i\right]$	${\left(Q_e\right)}_i$ indicates the consumption of class $i$ energy; ${\left(K_e\right)}_i$ indicates the unit net calorific value of class $i$ energy; ${\left(V_{C{O}_2}\right)}_i$ and ${\left(V_{C{H}_4}\right)}_i$ respectively indicate the carbon emission factors of class $i$ energy.	Net heat value $K_e$ was obtained by querying the China Energy Statistics Yearbook; $C{O}_2$carbon emission factor and $C{H}_4$ carbon emission factor, obtained by querying the IPCC [30,67].
Industrial waste water	$C_p={\displaystyle \frac{12}{16}}\times Q_{COD}{P}_{C{H}_4}$	$Q_{COD}$ is the weight of Chemical Oxygen Demand (COD) in the wastewater;${ P}_{C{H}_4}$ is the maximum $C{H}_4$ production capacity.	Chemical Oxygen Demand (COD) in wastewater $Q_{COD}$ from China Energy Statistical Yearbook, $C{H}_4$ maximum production capacity of 0.25 [82].
Domestic wastewater	$C_l=365\times {\displaystyle \frac{12}{16}}\times N_i{\rho }_{BOD}{\gamma }_{BOD}{V}_{BOD}{F}_{BOD}$	$N_i$ indicates the population of a $i$ spatial area (in people); ${\rho }_{BOD}$ refers to the organic content of biochemical oxygen demand (BOD) per capita; ${\gamma }_{BOD}$ is the proportion of BOD that is readily deposited; $V_{BOD}$ indicates the emission factor of BOD; $F_{BOD}$ refers to the proportion of anaerobic degradation of BOD in wastewater.	The organic matter content of BOD per capita is 60 g BOD/person/day; the proportion of BOD that is readily deposited is 0.5; the emission factor for BOD is 0.6 g CH4/g; and the proportion of anaerobically degraded BOD in the wastewater is 0.8 [83].
Population, animal respiration	$C_b=\sum N_i{V}_i$	$N_i$ indicates the number of animals; $V_i$ indicates the carbon emission coefficients of animals	The respiratory carbon emission coefficients for humans, pigs, cattle and sheep were 0.079, 0.082, 0.796, 0.041 t/a [84,85].
Animal enteric fermentation and faeces	$C_f=\sum N_i\left[{\left({\upsilon }_{C{O}_2}\right)}_i+{\left({\upsilon }_{C{H}_4}\right)}_i\right]$	$N_i$ indicates the number of animals; ${\left({\upsilon }_{C{O}_2}\right)}_i$ and ${\left({\upsilon }_{C{H}_4}\right)}_i$ represent the carbon emission coefficients of CO2 and CH4 production from enteric fermentation and faecal species of the ith animal, respectively.	By querying the IPCC [30,67], the carbon emission coefficients of CO2 production from enteric fermentation and faeces in pigs, cattle and sheep were obtained as 3.89, 59.33 and 45 kg/a, and the carbon emission coefficients of CH4 production were 5.18, 79.11 and 9.93 kg/a.

• Step 2: Carbon emission coefficient calculation

The net carbon emission coefficients for seven types of territorial space—UPS, ULS, RPS, RLS, EPSS, ERSS, and ESSS—are determined by dividing the total net carbon emissions within each spatial scope by the respective total area of that space. The calculation formula is as follows:

$${\psi }_k={\displaystyle \frac{{\sum }_{j=1}^5{\left(C_{net}\right)}_{kj}}{A_k}}$$

(1)

where ${\psi }_k$ represents the net carbon emission coefficient for the $k$-th type from the utilisation of TSFs (detailed calculation results are provided in Table S1 of Supplementary Materials); ${\left(C_{net}\right)}_{kj}$ denotes the net carbon emission amount for the $j$-th carbon emission project of the $k$-th type of TSF; $A_k$ indicates the area of the $k$-th type of TSF; and $j,k$represents the project and type codes for carbon emissions from the utilisation of TSFs, $k=\mathrm{1,2},3,\cdots ,N$.

(3)

Calculation of Carbon Emissions in Territorial Spatial Units

This study utilised the Create Fishnet tool in Esri ArcGIS 10.8 software (Environmental Systems Research Institute (ESRI), Redlands, CA, USA) to delineate territorial spatial units within the vector boundary of Qionglai City. In determining the size of spatial units, we carefully considered the influence of spatial unit size on research outcomes. Spatial units that are excessively small may forfeit macro-variability characteristics and heighten data redundancy, whereas those that are overly large may neglect local variations, thereby diminishing the precision of the results. Therefore, this article cites pertinent research findings [86,87] and establishes the dimensions of territorial spatial units in Qionglai City as a 100 m × 100 m grid, resulting in a total of 139,736 spatial units. These spatial units effectively encapsulate the macro characteristics of territorial space while maintaining sufficient detail for accurate analysis. Based on this, we employed the Tabulate Intersection tool to determine the area of various TSFs within specific spatial units, subsequently multiplying these areas by the net carbon emission coefficients associated with TSF utilisation for each year. This enabled the acquisition of the carbon emissions distribution map resulting from the utilisation of TSFs from 2009 to 2023. The formula for calculating the carbon emissions of a single territorial space unit is as follows:

$${\left(C_{total}\right)}_i=\sum _{k=1}^N{\psi }_k{A}_{ik}$$

(2)

where ${\left(C_{total}\right)}_i$ represents the net carbon emissions of the $i$-th territorial spatial unit; $A_{ik}$ denotes the area of the $k$-th TSF type in the $i$-th territorial spatial unit, where $i=\mathrm{1,2},\cdots ,\mathrm{139,736}$; and ${\psi }_k, k$ has the same meaning as indicated in Formula (1).

3.2.2. Analysis of the Evolution Characteristics of Carbon Emissions from the Utilisation of TSFs and Simulation Methods for Their Change Trends

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Analysis Method for the Evolution Characteristics of Carbon Emissions from the Utilisation of TSFs

Spatial association analysis serves as a valuable method for uncovering the interrelations and interactions among regions in the examination of spatial distribution patterns of geographical elements [88]. The spatial heterogeneity and spatial auto-correlation of carbon emissions from the utilisation of TSFs are examined in this study using the global Moran’s I index and the Getis-Ord $G_i^{*}$ statistic. It elucidates the spatial distribution characteristics of carbon emissions resulting from the utilisation of TSFs in Qionglai City, thereby offering a foundation for the development of county-level carbon reduction policies.

The global Moran’s I index is a statistical measure utilised to assess the clustering characteristics of spatial data, focusing on the identification of significant clustering patterns within such data [89]. This index illustrates the spatial distribution pattern of carbon emissions resulting from the utilisation of TSFs by analysing the similarity between the carbon emissions of each spatial unit in the study area and those of adjacent units, thereby offering a foundation for comprehending the spatial heterogeneity of carbon emissions. The global Moran’s I index has a value range of −1 to 1. A positive value signifies the existence of positive spatial auto-correlation, indicating that carbon emissions resulting from the utilisation of TSFs tend to display spatial clustering; a negative value signifies negative spatial auto-correlation, indicating that carbon emissions from the utilisation of TSFs are likely to be spatially dispersed. A value near 0 indicates a random spatial distribution, suggesting the absence of significant clustering or dispersion trends in carbon emissions associated with the utilisation of TSFs. A value near 1 signifies a distinct trend of clustering in carbon emissions associated with the utilisation of TSFs, indicating that regions with high carbon emissions are likely to be located near other high emission regions, whereas areas with low carbon emissions are similarly clustered with other low emission areas. The formula [90] for calculating the global Moran’s I index is as follows:

$$I={\displaystyle \frac{n{\sum }_{i=1}^n{\sum }_{j=1}^n{\omega }_{ij}\left(c_i-\overline{c}\right)\left(c_j-\overline{c}\right)}{{\sum }_{i=1}^n{\left(c_i-\overline{c}\right)}^2{\sum }_{i=1}^n{\sum }_{j=1}^n{\omega }_{ij}}}$$

(3)

where $I$ is the Moran’s I index; ${\omega }_{ij}$ is the spatial weight function; ${ y}_i$ and $y_j$ are the carbon emissions of spatial units $i$ and $j$, respectively; $\overline{y}$ is the average carbon emissions of the spatial units; and $n$ is the number of spatial units in the study area.

The Getis Ord $G_i^{*}$ statistic identifies anomalous patterns in spatial data, which is crucial for analysing the spatial distribution characteristics of carbon emissions and developing targeted emission reduction strategies [34]. This study employs the Getis Ord $G_i^{*}$ statistic to identify areas of high-value clustering (hot spots) and low-value clustering (cold spots) of carbon emissions resulting from the utilisation of TSFs. This statistic evaluates whether these regions significantly differ from the overall average distribution by analysing the joint distribution of carbon emissions within each region and its neighbouring regions. If the Getis Ord $G_i^{*}$ statistic is statistically significant for a region, it indicates the presence of a hot spot, suggesting that carbon emissions in this area are above average and demonstrate a clustering of high values relative to adjacent regions. Conversely, if the results are statistically significant, the area is classified as a cold spot, indicating that carbon emissions in this region are below average, characterised by low-value clustering. The calculation formula for the Getis Ord $G_i^{*}$ statistic is as follows [91]:

$$G_i^{*}={\displaystyle \frac{{\sum }_{j=1}^n{\omega }_{ij}{c}_j-\overline{c}{\sum }_{j=1}^n{\omega }_{ij}}{\sqrt{{\sum }_{j=1}^n{j}_2^c/n-{\left(\overline{c}\right)}^2}\sqrt{\left[n{\sum }_{j=1}^n{ij}_2^{\omega }-{\left({\sum }_{j=1}^n{\omega }_{ij}\right)}^2\right]/\left(n-1\right)}}}$$

(4)

where $G_i^{*}$ tatistic is the $z$-score. When the $z$-score is greater than 0, the high values of the target object’s attributes become more concentrated, forming a hotspot; if the $z$-score is less than 0, the lower the value, the more concentrated the low values of the target object’s attributes become, forming a cold spot. $c_j$represents the carbon emissions of the $j$-th territorial spatial unit; ${\omega }_{ij}$ represents the spatial weight between the $i$-th and $j$-th territorial spatial units; $n$ represents the number of territorial spatial units; and $\overline{c}$ is the average carbon emissions of the territorial spatial units.

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Simulation Methods for the Evolution Trends of Carbon Emissions from the Utilisation of TSFs

Firstly, this study uses the Mann–Kendall mutation test and linear regression model to analyse historical trends in carbon emissions resulting from the utilisation of TSFs. Among them, the Mann–Kendall mutation test, a non-parametric statistical method, does not depend on a specific distribution of sample data and demonstrates high robustness against outliers, rendering it appropriate for analysing carbon emission time series [92]. Linear regression modelling is appropriate for evaluating the relationship between variables over time and has emerged as a widely utilised method for analysing trends in carbon emissions and other long time series [93]. This study employed the Mann–Kendall test to identify time-varying trends in carbon emissions resulting from the utilisation of TSFs and to evaluate the statistical significance of these trends. The Mann–Kendall test statistic $S$ is defined as

$$S=\sum _{i=1}^{n-1}\sum _{j=i+1}^{n}S\left(i,j\right)$$

(5)

where $S\left(i,j\right)$ is a sign function, for any two points $i$ and $j$(where $i<j$), there are the following: when $x_j>x_i$, $S\left(i,j\right)=1$; when $x_j=x_i$, $S\left(i,j\right)=0$; and when $x_j<x_i$, $S\left(i,j\right)=-1$. $S$ denotes the net number of positive and negative variances; if $S>0$, it means that the sequence has an upward tendency, if $S<0$, the sequence has a downward trend, and if $S=0$, there is no significant trend. In order to ensure the statistical significance of the test results, $S$ needs to be standardized and the standardized test statistic $Z$ is as follows:

$$Z=\left\{\begin{array}{r}{\displaystyle \frac{S-1}{\sqrt{Var\left(S\right)}}},S>0\\ 0,S=0\\ {\displaystyle \frac{S+1}{\sqrt{Var\left(S\right)}}},S<0\end{array}\right.$$

(6)

where $Var\left(S\right)$is the variance, $Var\left(S\right)=n\left(n-1\right)\left(2n+5\right)-{\sum }_{p=1}^q{t}_p\left(t_p-1\right)\left(2t_p+5\right)$; $S$ is the approximation obeys the normal distribution, $q$ is the number of groups with the same data, and $t_p$ is the number of data identical to that of the $p$ group. In the trend test, the original hypothesis $H_0$ indicates that the data set samples are independently and identically distributed and no trend exists. Given the significance level, if $|Z|\ge Z_{1-{\displaystyle \frac{\alpha }{2}}}$, then the original hypothesis will not be true, indicating that the series has a significant trend; if $Z>0$, it means that the series has a significant upward trend, and if $Z<0$, it means that the series has a significant downward trend. Instead, the original hypothesis $H_0$ is accepted.

After confirming the significance of the carbon emission trend through the Mann–Kendall test, this study further employs a univariate linear regression model to analyse the changing trends of carbon emissions in various territorial spatial units. The mathematical model is as follows:

$${\beta }_k={\displaystyle \frac{n{\sum }_{i=1}^n\left(t_i{c}_i\right)-{\sum }_{i=1}^n{t}_i{\sum }_{i=1}^n{c}_i}{n{\sum }_{i=1}^n{t_i}^2-{\left({\sum }_{i=1}^n{t}_i\right)}^2}}$$

(7)

where ${\beta }_k$ epresents the slope of the regression equation; $n$ is the time sequence number; $c_i$ is the carbon emission of territorial spatial unit in the $t_i$ year. If ${\beta }_k>0$, it means that the carbon emissions of the territorial spatial unit show an increasing trend over time; if ${\beta }_k<0$, it means that the carbon emissions show a decreasing trend over time. The larger the absolute value of $\left|{\beta }_k\right|$, the more obvious the trend of change, and vice versa, the less obvious the trend of change. To ensure the validity of the analysis results, the $F$-test method was applied to conduct a significance test on the linear regression results of carbon emissions [94]. The mathematical expression of the $F$ statistic is

$$F={\displaystyle \frac{{\left[n{\sum }_{i=1}^n\left(t_i{c}_i\right)-{\sum }_{i=1}^n{t}_i{\sum }_{i=1}^n{c}_i\right]}^2\left(n-2\right)}{\left(n{\sum }_{i=1}^n{t_i}^2-{\left({\sum }_{i=1}^n{t}_i\right)}^2\right)\left(n{\sum }_{i=1}^n{c_i}^2-{\left({\sum }_{i=1}^n{c}_i\right)}^2\right)-{\left[n{\sum }_{i=1}^n\left(t_i{c}_i\right)-{\sum }_{i=1}^n{t}_i{\sum }_{i=1}^n{c}_i\right]}^2}}$$

(8)

where when $F>F_{\alpha }\left(1,n-2\right)$, it indicates that the trend of linear change of carbon emission over time in the territorial spatial unit reaches the significant level of $\alpha$.

Secondly, we apply the Hurst index to analyze the future evolution trend of carbon emissions. Auto-correlation and long-range dependence are prevalent characteristics in the analysis of natural phenomena. The Hurst index demonstrates long-range dependence in time series, serving as a crucial foundation for forecasting the dynamic behaviour of complex systems. As a result, it has found extensive application in climatology and environmental science [95,96]. Currently, methods for estimating the Hurst index include the absolute value method, periodogram method, residual analysis method, wavelet analysis method, and re-scaled range analysis method [97]. Research indicates that the re-scaled range analysis method is more reliable for estimating the Hurst index [98]. Therefore, this study utilises this method to evaluate the time series characteristics of carbon emissions resulting from the utilisation of TSFs and to predict future trends. The main steps are

Step 1: Divide the time series of carbon emissions from territorial spatial units $C_i\left(i=\mathrm{1,2},\cdots ,N\right)$ into $M$ groups of continuous sub-intervals $c_{ij} \left(i=\mathrm{1,2},3,\cdots ,M;j=\mathrm{1,2},3,\cdots ,n\right)$ with a length of $n$;

Step 2: Calculate the average values of $M$ groups of sub-intervals for different sub-intervals of length $n$: ${\overline{c}}_i={\displaystyle \frac{1}{n}}{\sum }_{j=1}^n{c}_{ij}$;

Step 3: For each sub-interval of length $n$, calculate its cumulative deviation: $z_{ij}={\sum }_{k=1}^j\left(c_{ik}-{\overline{c}}_i\right)$;

Step 4: Calculate the range of a single sub-interval: $R_i=max\left(z_{ij}\right)-min\left(z_{ij}\right)$ and standard deviation: $S_i=\sqrt{{\displaystyle \frac{1}{n-1}}{\sum }_{j=1}^n{\left(c_{ij}-{\overline{c}}_i\right)}^2}$;

Step 5: Calculate the re-scaled extreme deviation value on each sub-interval: ${RS}_i=R_i/S_i$, since there is a scaling relationship between the average re-scaled extreme deviation value and the sample length, i.e.,: ${RS}_n=\kappa \times n^H$. Therefore, repeat the above process for different time scales (i.e., different dividing lengths of $n$), and then perform a double-logarithmic regression of the average re-scaled extreme deviation value ${\overline{RS}}_i$ on $n$, and then the corresponding Hurst index can be obtained; the mathematical expression is as follows:

$$\mathit{log}\left({\overline{RS}}_n\right)=\mathit{log}\left(\kappa \right)+H\mathit{log}\left(n\right)$$

(9)

where $H$ is Hurst index, which can be obtained by least squares fitting. The value of $H$ is between 0–1. If $H=0.5$, it means that the time series is a random series, i.e., there is no correlation between past and future changes in carbon emissions from the utilisation of TSFs; if $H<0.5$, it means that the past and future changes of the time series are negatively correlated, indicating that the future changes of spatial carbon emissions in the country have an anticontinuity, and the closer $H$ is to 0, the stronger the anticontinuity is; if $H>0.5$, it means that the time series has a positive correlation between past and future changes, i.e., the future changes in carbon emissions from the utilisation of TSFs have positive persistence, and the closer $H$ is to 1, the stronger the positive persistence is [99].

3.2.3. Analysis Method for the Spatiotemporal Evolution Factors of Carbon Emissions from the Utilisation of TSFs

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Analysis of the Influencing Factors of Carbon Emission Spatiotemporal Evolution Based on the GTWR Model

The spatiotemporal evolution of carbon emissions from the utilisation of TSFs is influenced by several factors, including energy consumption structure, industrial structure, development intensity, TSF utilisation structure, economic growth, and population density, as identified in six main aspects [25,46,47]. This research identified key indicators for assessing the influence of these factors on the spatiotemporal dynamics of carbon emissions (

Table 5. Factors influencing the spatiotemporal evolution of carbon emissions from TSF utilisation.

Indicator Name	Hidden Meaning	Unit
Energy consumption structure	Net carbon emissions per unit of territorial space area	Ton/Hectare
Industrial structure	Tertiary sector value added as a percentage of GDP	%
Development intensity	Proportion of construction land in territorial spatial units	%
The utilisation structure of TSFs	Conversion area between different types of TSFs	Hectares
Economic growth	Total GDP of territorial spatial units	Ten thousand yuan
Population density	Population per unit of national space area	Persons/km2

). Due to the considerable heterogeneity of these influencing factors across time and space, we selected the GTWR model for their analysis. The GTWR model integrates the benefits of GWR and Time Weighted Regression (TWR), highlighting the spatiotemporal variations in the factors affecting carbon emissions across various regions. This facilitates the identification of critical factors influencing carbon emissions across different regions and time frames, offering a scientific foundation for the development of targeted emission reduction strategies [100]. The mathematical expression of the GTWR model is as follows:

$$y_i={\beta }_0\left({\mu }_i,{\nu }_i,t_i\right)+\sum _k{\beta }_k\left({\mu }_i,{\nu }_i,t_i\right)X_{ik}+{\epsilon }_i$$

(10)

where $y_i$ represents the net carbon emissions of the $i$-th spatial unit; ${\beta }_0$ represents the intercept; ${\mu }_i$, ${\nu }_i$ and $t_i$ represent the latitude, longitude, and time of the center point of the $i$-th spatial unit; ${\beta }_k$ represents the fitting coefficient of the $k$-th influencing factor for the $i$-th spatial unit; $X_{ik}$ represents the value of the $k$-th influencing factor for the $i$-th spatial unit; and ${\epsilon }_i$ represents the random error.

(2)

Model Sensitivity Analysis Based on Parameter Variation Analysis Method

The GTWR model depends on intricate spatiotemporal data and conducts weighted regression over both spatial and temporal dimensions. Consequently, its results may be influenced by factors like parameter selection and bandwidth function configurations, resulting in possible uncertainty in the model outcomes. To ensure the robustness of the GTWR model analysis, this study utilises a one-at-a-time (OAT) sensitivity analysis to evaluate the GTWR model’s sensitivity to various parameter configurations, thereby confirming the robustness and reliability of the model’s results. The specific steps are as follows:

Step 1: Select the bandwidth methods (Akaike Information Criterion corrected value (AICc) and Cross-Validation (CV)) that have a significant impact on the GTWR model analysis results and the kernel types (fixed bandwidth (fixed) and adaptive bandwidth (adaptive)) as key parameters for sensitivity analysis.

Step 2: Select different bandwidth methods and kernel types to form various parameter combinations and explore their impact on model output.

Step 3: Record the regression coefficients, R² values, and other metrics of the GTWR model under different combinations, and analyse which parameter variations lead to significant fluctuations in the regression results.

Step 4: Evaluate the sensitivity of each parameter to the model results. If a parameter’s variation leads to significantly different regression outcomes, it indicates that the model is highly sensitive to that parameter.

4. Results and Analysis

4.1. Temporal Characteristics of Carbon Emissions from the Utilisation of TSFs

4.1.1. Overall Characteristics of Carbon Emission Changes

From 2009 to 2023, carbon emissions in Qionglai City rose from 852,300 tonnes to 1,422,500 tonnes, reflecting an average annual increase of 40,700 tonnes (Figure 3). The variation displays clear phased characteristics, characterised by a gradual increase from 2009 to 2018, with an average annual growth of 19,900 tonnes. From 2018 to 2023, the growth rate accelerated significantly, reaching an average annual increase of 78,100 tonnes. The observed trend is likely associated with the rapid industrialisation and urbanisation occurring in Qionglai City, which has achieved an average annual urbanisation rate of 49.93%. The carbon source space of Qionglai City encompasses various spatial types, including urban and rural production. Notably, the RPS exhibits the highest carbon emissions, rising from 710,800 tonnes in 2009 to 1,032,800 tonnes in 2023. The compound average growth rates of carbon emissions across different territorial categories, listed in descending order, are as follows: UPS (10.24%) > ULS (6.21%) > RLS (2.98%) > RPS (2.7%). The most significant increase was observed in UPS, attributed to the acceleration of industrialisation and urbanisation, resulting in the gradual concentration of energy-intensive industries and a rapid rise in output value. This has resulted in a higher carbon emission growth rate compared to other spaces. Meanwhile, RPS encompasses a significantly larger area than UPS and has historically utilised a considerable amount of energy; consequently, its carbon emissions have consistently been elevated. The carbon sink space in Qionglai City includes ecological supply services, ecological regulation services, and ecological support services. The ecological regulation services sector exhibits the highest carbon sink capacity, with an average carbon sink volume of 27,600 tonnes.

4.1.2. Characteristics of Phased Changes in Carbon Emissions

From 2009 to 2023, the carbon emissions in Qionglai City exhibited distinct phased characteristics. From 2009 to 2018, emissions grew slowly throughout the first phase, rising from 852,300 tonnes to 1,031,600 tonnes of carbon emissions overall. Urban production spaces (UPSs) see an average yearly increase in carbon emissions of about 8000 tonnes, whereas rural production spaces (RPSs) see an average annual increase of 5700 tonnes. This is because urban growth and the loss of arable land in rural spaces have combined to increase carbon emissions from urban production and dwelling areas. Urban growth and the loss of rural arable land are the two main causes of this increase in carbon emissions from urban production and dwelling areas. Urban growth and rural industrial development have first advanced inside the territorial area, with UPSs’ carbon emissions reaching their highest point in 2018 (Figure 4). However, there have been few swings in carbon emissions in ecological spaces, suggesting that there has not been significant damage to these areas. The second phase, which lasted from 2018 to 2023, had a sharp increase in carbon emissions, which went from 1.0316 million tonnes to 1.4225 million tonnes. UPSs saw an increase in annual carbon emissions of 11,700 tonnes, while RPSs saw an accelerating growth rate of 54,000 tonnes. The increased urbanisation and industrialisation process in Qionglai City is largely responsible for the sharp increase in carbon emissions from both urban and rural living spaces (RLSs). Population concentration and infrastructure expansion significantly increased energy consumption. However, the carbon sinks in ecological spaces exhibited relative stability with minor fluctuations, suggesting that Qionglai City has consistently enacted ecological restoration and vegetation protection measures to uphold the structural and functional integrity of ecosystems, including forests and grasslands.

4.1.3. Characteristics of Structural Changes in Carbon Emissions

The carbon emissions from RPSs consistently account for more than 70% of the total carbon emissions across the territorial space, constituting a significant component of the city’s overall carbon emissions (Figure 5). This is attributed to Qionglai City’s well developed primary industry, relatively low urbanization rate, and its continuous emphasis on strengthening the primary and tertiary industries. The proportion of carbon emissions from UPSs within the total territorial carbon emissions has steadily increased year by year, rising from 5.28% in 2009 to 12.4% in 2023. This trend is closely related to Qionglai City’s urbanization rate, which grew from 32% in 2009 to 56% in 2023. Furthermore, ecological spaces in Qionglai City function as the principal carbon sinks, exhibiting stable annual carbon sequestration. This stability is primarily attributed to the city’s extensive forest resources, significant vegetation coverage, and effective ecological management practices.

4.2. Spatiotemporal Characteristics of Carbon Emissions from the Utilisation of TSFs

4.2.1. Spatial Distribution and Evolution Characteristics of Carbon Emissions

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Fundamental Evolutionary Characteristics of the Spatial Distribution of Carbon Emissions

From 2009 to 2023, carbon emissions resulting from the utilisation of TSFs in Qionglai City displayed a spatial differentiation pattern characterised by higher levels in the east and lower levels in the west (Figure 6). In 2009, Qionglai City displayed predominantly low to medium carbon emissions, with localised high carbon emission areas situated in urban production zones adjacent to the Nanhe and Xiejiang Rivers. In 2014, certain urban living spaces (ULSs) in the central and eastern regions of Qionglai City exhibited a transition from medium to elevated carbon emissions. From 2014 to 2018, the geographical extent of high carbon emissions increased, but the rate of carbon emissions growth decelerated in most regions. This may relate to government-enforced environmental protection policies, the promotion of renewable energy sources, and initiatives aimed at enhancing energy efficiency. By 2023, carbon emissions have risen markedly, with urban regions in the central and eastern sectors of Qionglai City escalating from relatively high to high levels of carbon emissions. Overall, ULSs have undergone a transition from medium carbon emissions to relatively high and then high carbon emissions, while the RPSs in the central and eastern regions have gradually shifted from low to medium carbon emissions due to agricultural modernization, adjustments in crop planting structures, and economic development.

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Evolutionary Characteristics of the Spatial Correlation of Carbon Emissions

From 2009 to 2023, the Moran’s I index values of carbon emissions in the study area consistently remained around 0.6, indicating positive values. This indicates a notable positive spatial correlation in carbon emissions, suggesting that emissions from the utilisation of TSFs in Qionglai City display spatial clustering, reflecting a concentrated distribution pattern (

Table 6. Moran’s I value of carbon emissions in Qionglai City from 2009–2023.

Year	2009	2010	2011	2012	2013	2014	2015	2016
Global Moran’s I index	0.6920 ***	0.6805 ***	0.6711 ***	0.6680 ***	0.6846 ***	0.6263 ***	0.6221 ***	0.6158 ***
Z	364.7341	358.6914	353.715	352.07	360.8221	330.1621	328.0139	324.6805
Year	2017	2018	2019	2020	2021	2022	2023
Global Moran’s I index	0.6265 ***	0.6212 ***	0.6451 ***	0.6331 ***	0.6360 ***	0.6384 ***	0.6353 ***
Z	330.2885	327.4854	340.0697	333.7729	335.2974	336.5106	334.8876

Note: *** indicates significance at the 1% level, with the global Moran’s I analysis yielding p-values all below 0.001.

). On the other hand, the Moran’s I index of carbon emissions in the study area exhibited a general decline, falling from 0.692 in 2009 to 0.6353 in 2023. This indicates a weakening spatial correlation of carbon emissions within the study area, with the spatial distribution becoming increasingly uniform. This trend may be associated with the economic structural transformation and enhanced energy utilisation efficiency in Qionglai City. However, in 2019, the Moran’s I index values of carbon emissions in Qionglai City increased from 0.6212 in 2018 to 0.6451 in 2019. This suggests a slight recovery in the spatial clustering of carbon emissions in Qionglai City, potentially linked to heightened agricultural activities in RPSs, intensified localised economic activities, and a temporary growth in traditional high-energy-consuming industries.

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Evolutionary Characteristics of the Spatial Heterogeneity of Carbon Emissions

Between 2009 and 2023, carbon emissions in Qionglai City displayed a spatial distribution pattern, with notable hot spots in the eastern region and cold spots in the western region (Figure 7a). The highly significant hot spots are primarily concentrated around the southern river, both sides of the Jingkun Line, and the banks of the Xiejiang River, while the significant and moderately significant hot spots are distributed across the central urban area, the eastern industrial zone, and the ancient town of Pingle, forming a pattern of “multi-centred hot spots clustering”. Conversely, areas with low carbon emissions are located in the western Tiantai Mountain region, Nanbao Mountain region, and Huaqiu Mountain region, demonstrating a pattern of “clustered cold spots.” Further analysis indicates that cold spots are primarily located in the western ecological zones, while sub-cold spots are distributed along the fringes of the western natural ecological spaces, the two river basins, and the easternmost hilly regions (Figure 7b). Most of the central and eastern regions are secondary hotspot areas, while hotspot areas are mainly concentrated in industrial parks and urban areas along the Pingle Ancient Town, Nanhe River, and Xiejing River, primarily representing the distribution characteristics of UPSs.

4.2.2. Spatial Evolutionary Trends and Characteristics of Carbon Emissions

(1)

Spatial and Historical Evolution Characteristics of Carbon Emissions

From 2009 to 2023, the maximum absolute value recorded in the Qionglai City region was 5.15, while the average value was 2.89. A total of 65.69% of regions demonstrate a statistically significant upward trend at the 99% confidence level (greater than 2.58) (Figure 8). Carbon emissions from RPSs in the central and eastern regions of Qionglai City demonstrate a notable increase, primarily due to the continuous progress of rural industrialisation, heightened agricultural production intensification, expansion of cultivated land, and changes in the energy consumption structure. The western ecological space and the eastern river regions show no significant trend characteristics in carbon emissions ($Z$ = 0), accounting for 29.66% of the area. This is mainly due to continuing industrialisation in the region’s countryside (the average annual decline in the rural labour force is 0.27%), expansion of cultivated land area (average annual growth rate 2.68%), increased intensification of agricultural production, and a change in energy-consumption patterns (average annual growth rate of total agricultural-machinery power 3.71%). Furthermore, within the stringent limitations imposed by the ecological redline protection policy, there has been no notable alteration in the types of TSFs in this region, and the land use structure has exhibited relative stability. The functional types within the grid and their carbon emission coefficients have remained largely unchanged, resulting in carbon emissions that do not exhibit a distinct upward or downward trend. Therefore, the carbon emission dynamics in this region demonstrate stable characteristics.

(2)

Future Evolution Characteristics of Carbon Emissions

The calculation results of the Hurst index show that the index values range from 0.2187 to 0.9391, with an average value of 0.6825 (Figure 9a). Among these, 99.1% of the study area exhibits a Hurst index greater than 0.5, indicating strong positive persistence in carbon emissions from the utilisation of TSFs in Qionglai City. The vast majority of its territorial spaces will continue the carbon emission trends observed from 2009 to 2023, maintaining a state of sustained growth. This is likely closely related to the accelerated industrialization process in Qionglai City, rising energy demand, the concentration of high energy-consuming industries, a fossil fuel-dependent energy structure, and rapid urbanization.

The combined analysis of simple linear regression and the Hurst index reveals that carbon emissions in Qionglai City exhibit significant spatiotemporal differentiation (Figure 9b). This phenomenon is attributed to the uneven economic development and resource distribution in Qionglai City, which results in variations in the processes of industrialization and urbanization across different regions, as well as divergent choices in industrial structure. Among these, RPSs in central and eastern regions exhibit a weakly sustained growth trend, making them key areas for future carbon emission reduction efforts. The western mountainous areas and the eastern river regions exhibit a weak but consistent declining trend, accounting for 24.79% of the total area. These should be designated as core zones for carbon sink enhancement and prioritized for protection. Additionally, the areas with increasing carbon emissions (0.37%) are primarily distributed in Huilong Town, Baolin Town, Shuikou Town, and Kongming Township, while the areas with decreasing emissions (0.53%) are concentrated in the hilly regions of Huilong Town and along both banks of the Nanhe River. Urban spaces (such as Pingle Town, Sangyuan Town, Yang’an Town, and Ranyi Town) exhibit moderate to strong sustained growth trends. Meanwhile, there are areas with moderate and strong continuous decline in ecological space, accounting for 2.06% and 1.65% of the total area, respectively.

4.3. Analysis of the Spatiotemporal Evolution and Influencing Factors of Carbon Emissions from the Utilisation of TSFs

4.3.1. Analysis of Influencing Factors in the Spatiotemporal Evolution of Carbon Emissions

The factors influencing carbon emissions are ranked in descending order of their impact as follows: economic growth > industrial structure > development intensity > population density > the utilisation structure of TSFs (

Table 7. Regression coefficients for the GTWR model driving factors.

Analysis Parameters	Variables	Upper Quartile	Minimum	Lower Quartile	Maximum	Mean
AICc+Fixed/ CV+Fixed	C1_ZF1	0.0335	−0.0841	−0.0733	0.0906	−0.0318
	C2_ZF2	0.5360	0.5469	0.0175	0.7565	0.2973
	C3_ZF3	1.1821	−0.0989	0.7376	10.0671	1.2210
	C4_ZF4	0.0113	−0.0602	−0.0366	0.2011	−0.0026
	C5_ZF5	0.0402	−0.4160	0.0095	0.1188	0.0269
	R2	0.7526 20,364
	AICc/CV
AICc+Adaptive/ CV+Adaptive	C1_ZF1	0.0280	−1.7576	−0.1381	1.3363	−0.0529
	C2_ZF2	0.5254	−0.1137	0.0300	1.0495	0.3045
	C3_ZF3	2.5472	0.3379	0.7596	26.4596	2.5198
	C4_ZF4	0.0124	−0.1166	−0.0421	0.5998	0.0013
	C5_ZF5	0.0363	−0.1111	−0.0079	0.1787	0.0156
	R2	0.7593
	AICc/CV		20,016.3

Note: C1_ZF1, C2_ZF2, C3_ZF3, C4_ZF4, and C5_ZF5 respectively represent the regression coefficients of five driving factors: development intensity, industrial structure, economic growth, the utilisation structure of TSFs, and population density.

). The regression coefficients for economic growth vary from −0.0989 to 10.0671, with a mean of 1.2210. For industrial structure, the coefficients range from 0.5469 to 0.7565, averaging 0.2973. The coefficients for development intensity span from −0.0841 to 0.0906, with a mean of −0.0318. Population density coefficients range between −0.4160 and 0.1188, averaging 0.0269. Lastly, the coefficients for the utilisation structure of TSFs range from −0.0602 to 0.2011, with an average of −0.0026. Economic growth, industrial structure, and development intensity are the main factors driving carbon emissions in Qionglai City.

Further analysis reveals significant spatiotemporal heterogeneity in the explanatory power of key carbon emission drivers in Qionglai City (see Figure S1, Supplementary Materials). The regression coefficient for development intensity decreases from east to west, whereas those for industrial structure and economic growth increase along the same gradient. Economic growth strongly influences carbon emissions, positively correlating with urbanization, residents’ lifestyles, and industrial activity. Changes in industrial structure directly affect energy consumption intensity and carbon emission scale, with greater tertiary industry shares typically linked to lower emissions. Development intensity indirectly impacts carbon emissions through resource allocation and land use efficiency; areas with higher construction land proportions exhibit increased energy demand and emissions. The effect of TSFs utilisation structure is comparatively minor, likely due to stable land use types and functional zoning in Qionglai City.

4.3.2. Model Sensitivity Analysis Based on Parameter Variation Method

This study identified four key analytical parameters for the model, organising them into four comparison groups: the first group includes AICc and Fixed; the second group consists of CV and Fixed; the third group features AICc and Adaptive; and the fourth group combines CV and Adaptive. The findings demonstrate that carbon emissions in Qionglai City are predominantly influenced by three factors: industrial structure, development intensity, and economic growth (Table 7). The R² value for the initial two groups was 0.7526, and the AICc/CV value was 20,364. The findings from the third and fourth groups demonstrate that carbon emissions in Qionglai City are predominantly affected by the same three driving factors, exhibiting an R² value of 0.7526 for both groups, along with an AICc/CV value of 20,364. This suggests that the driving factors identified by the GTWR model demonstrate a level of stability across various analytical parameters.

However, the explanatory power of each driving factor differs. The utilisation of the Adaptive setting results in higher regression coefficients for various driving factors, suggesting increased sensitivity of the model to the configuration of bandwidth parameters. The dynamic adjustment capability of Adaptive enhances the model’s ability to accurately capture local features and variations, thus improving prediction accuracy. The Fixed model lacks the ability to adapt to the varying data characteristics across different regions, potentially leading to biased parameter estimates. In practical applications, the selection of an appropriate bandwidth setting is essential for ensuring the model’s reliability and effectiveness.

5. Discussion

5.1. Spatiotemporal Heterogeneity and Evolution Trends of Carbon Emissions from the Utilisation of TSFs

This study extensively explores the spatiotemporal development of carbon emissions from TSF use in Qionglai City, showing a considerable increase over the past 15 years with significant variation. The spatiotemporal evolution characteristics of carbon emissions identified by other scholars at different administrative sizes [101,102] support the commonality of territorial spatial carbon emission dynamics across several levels.

First, the time-series analysis indicates that RPS significantly contributes to carbon emissions, accounting for over 70% of the functional structure of territorial space in the study area. This is attributed to extensive agricultural production and dependence on fossil energy sources, challenging traditional perceptions. The highest rate of carbon emissions growth occurs in UPSs, supporting the established conclusion that urbanisation and industrialisation contribute to increased carbon emissions [103]. Further analysis indicates that variations in carbon emissions exhibit distinct phases. From 2009 to 2018, the rapid increase in emissions was driven mainly by accelerated industrialisation and urbanisation in western China. From 2018 to 2023, the growth rate of carbon emissions slowed, a deceleration attributable to the implementation of the ecological civilisation strategy and the “dual-carbon” initiative. This slowdown is also closely associated with industrial restructuring, the enforcement of ecological protection regulations, and measures to phase out high-emission activities.

Second, the spatial distribution shows significant variation: the eastern region is marked by urban production and living, as well as rural production, which includes concentrated industries and high energy consumption, leading to carbon emissions that are much higher than those in the western region. Conversely, the west primarily serves as an ecological functional space, demonstrating a robust carbon sink capacity and low emission intensity. The spatial heterogeneity of regional carbon emissions is supported by Schwanitz et al.’s study of the European Union. Their findings indicate that economic core regions, such as Germany’s Ruhr area and France’s Paris Basin, exhibit markedly higher carbon emission intensities than the agricultural regions of Eastern Europe, thereby underscoring substantial spatial disparities [104].

Third, model projections indicate that, before 2030, carbon emissions in the study area will continue the growth trend observed from 2009 to 2023, but they will exhibit significant spatial heterogeneity. In the eastern region, emissions are expected to rise steadily owing to accelerated urbanisation and industrialisation. This outcome is compatible with the relatively slower economic development of western China, the transitional period required for industrial structural upgrading, and the actual relocation of industries from east to west, and it is consistent with findings at national and provincial scales [105,106,107]. By contrast, carbon emission growth in western ecological protection zones is markedly constrained by ecological red-line protection requirements, a pattern that closely corresponds to their designation as ecological core areas. Overall, this spatial pattern of emission growth reflects the rational distribution of regional economic and ecological functions and echoes Pata and Caglar’s finding of a significant inverted-U relationship between economic growth and carbon emissions in G7 countries [108].

5.2. Spatiotemporal Heterogeneity of Driving Factors and Their Explanatory Power for Carbon Emissions from the Utilisation of TSFs

In analysing the differentiation mechanisms of the driving factors of carbon emissions related to county TSFs, it is essential to systematically select the driving factors and methodologies. Prior research indicates that the determinants of carbon emissions primarily encompass industrial structure, development intensity, spatial utilisation structure, economic growth, and population size [25,46,47]. Given data availability and the extent of spatial analysis, we selected the ratio of tertiary industry value added to GDP, the proportion of construction land within each territorial-spatial unit, the transformed area among various territorial-spatial function types, the total GDP of each territorial-spatial unit, and population density to characterise these influencing factors individually. Among these indicators, the ratio of tertiary-industry value added to GDP is widely regarded as significantly related to carbon emissions. This relationship has been demonstrated in numerous studies, and the ratio serves as an effective indicator of the impact of industrial structure on carbon emissions [109]. The proportion of construction land reflects the intensity of urban development. An increase in this proportion may lead to the expansion of carbon-intensive land uses and thus represents the intensity of territorial-space development. The area converted between different territorial-space function types (for example, the conversion of agricultural land to urban land) directly indicates the indirect effect of changes in spatial-use structure on carbon emissions. In addition, total GDP and population density capture the effects of economic scale and population distribution on emissions through energy and resource consumption.

We used the GTWR model for driver mechanism resolution since carbon emission drivers are sensitive to both time and place. By including a spatiotemporal weighting matrix, the GTWR model combines the benefits of geographically and temporally weighted regression with the GWR model. This allows for a more thorough characterisation of the driving mechanisms of the factors and reveals the temporal and spatial differences of regional carbon emission driver [55,110]. Indicating that the model has excellent explanatory power, the GTWR model’s goodness of fit, or R², achieved 0.75, which is comparable to studies conducted in the Yangtze River Delta, Beijing-Tianjin-Hebei, and other parts of the county research results are comparable [111,112]. Moreover, parameter-sensitivity tests based on cross-combinations of AICc, CV, Fixed, and Adaptive configurations indicate that, across different parameter settings, the explanatory power of each factor remains consistent, with average variation within 30%. The model fit (R²) exceeds 0.75 in all cases. These results confirm the robustness and reliability of GTWR for analysing the driving mechanisms of territorial-space carbon emissions.

This study demonstrates that economic growth, industrial structure, and development intensity are the primary factors influencing carbon emissions from the spatial functions of the national territory, aligning with findings from related research [113]. In addition, we found that the explanatory power of these factors for carbon emissions from territorial-space functions exhibits significant spatial heterogeneity. The explanatory power of economic growth and development intensity for emissions in urban and rural spaces is higher in the east and lower in the west. By contrast, industrial structure shows the opposite pattern, with greater explanatory power in the west and lower explanatory power in the east. This contrast is closely related to the spatial agglomeration of economic activities within the study area. The concentration of industrial enterprises above designated size in the eastern region produces substantially higher carbon emissions than in the west, which accords with observed regional economic development and industrial distribution. The western portion of the study area is designated as an ecological red-line protection zone, where human economic activity is restricted and development intensity is low. Consequently, the carbon-sequestration capacity of territorial space in the west is markedly greater than in the east. This gradient—higher sequestration in the west and higher emissions in the east—results in an increase in net carbon emissions from west to east and produces a west-high, east-low distribution of the explanatory power of the driving factors (see Supplementary Materials Figure S2).

The spatial and temporal heterogeneity of the explanatory power of key drivers of carbon emissions in the territorial space is an important reason for the obvious spatial and temporal heterogeneity of carbon emissions in the territorial space, which illustrates the complexity of the role of the drivers. Therefore, in the formulation of carbon emission reduction policies, it is necessary to pay attention to the spatial and temporal heterogeneity of carbon emissions and their driving factors, clarify the explanatory power of different driving factors in a specific spatial and temporal range, and formulate precise carbon emission reduction measures for the spatial categorisation of production, living and ecological functions. In this way, the blindness and lagging problem of the current carbon emission reduction policy can be effectively solved, and carbon emissions in the territorial space can be effectively reduced.

5.3. Policy Implications

Research indicates that carbon emission reduction policies often overlook the spatial and temporal variability of carbon emissions and their determinants, along with future evolution trends, leading to a deficiency in targeted and proactive policy measures. This study identifies the spatial and temporal variability of carbon emissions and the factors influencing TSFs. It also analyses the prospective trends in carbon emissions to inform the development of more effective carbon reduction strategies, which are outlined in three key policy recommendations.

Firstly, the primary challenge of China’s low-carbon transition is the contradiction between economic growth and the reduction of carbon emissions. Research indicates that optimising land use structure, regulating construction land expansion, and safeguarding ecological land can effectively restrict carbon sources and enhance carbon sinks, thereby facilitating the concurrent advancement of economic growth and carbon emission reduction [114]. The simulation and analyses of functional carbon emissions in territorial space indicate that optimising functional structures and adjusting spatial layouts to minimise carbon source areas while enhancing carbon sink areas is a crucial strategy for advancing low-carbon development [115].

Secondly, the notable spatial and temporal variation of carbon emissions across national land necessitates differentiated management strategies. Carbon emissions in the production sectors of towns and villages have increased significantly, rising from 888,600 tonnes in 2009 to 1,458,600 tonnes in 2023, thereby exerting pressure on regional emission reduction efforts. Consequently, in the carbon source domains of urban centres (primary areas of urban production and habitation such as Pingle Town and Sangyuan Town), there is a need to implement strategies for intensive land development, advocate for green building practices, and enhance energy utilisation efficiency. Conversely, in rural carbon-source areas (regions integrating agriculture and rural industries such as Linji Town and Tiantaishan Town), attention should be paid to developing clean energy and increasing green space to limit the growth of carbon emissions. The carbon sink domain, characterised by ecological supply and regulatory and support functions, exhibits unstable spatial and temporal heterogeneity in carbon sink capacity (carbon emissions fluctuating from −36,300 tonnes in 2009 to 36,100 tonnes in 2023). Thus, the active implementation of natural and artificial restoration measures, such as forest closure and tree planting, is essential to augment carbon storage and enhance the carbon sink effect.

Finally, a dynamic response system must be established to address the spatiotemporal heterogeneity of the driving mechanisms behind carbon emissions from the utilisation of TSFs. Carbon emission reduction measures and dynamic decarbonisation targets must be formulated with precision, taking into account the spatiotemporal heterogeneity of factors such as economic growth, industrial structure, development intensity, and population density on carbon emissions. In eastern production and living spaces (Yangan Township, Wenjun Street, Linji Township, Guyi Township, Chujiang Township and other townships), which are marked by substantial economic growth and high population density, it is essential to prioritise the control of development intensity and the optimisation of industrial structure adjustments to mitigate the ongoing rise in carbon emissions. In the western region (Baolin Township, Bifengxia Township, Longmenshan Township, Jieguan Township, Ranyi Township, Huojing Township, Shukou Township and other townships), which emphasises ecological functions, priority must be assigned to the advancement of industrial structure adjustment and the transformation of economic development, thus facilitating the regularisation of development control.

5.4. Innovation, Limitations, and Future Prospects

This study presents an innovative investigation of carbon emissions associated with the utilisation of TSFs at the county scale. First, by integrating the IPCC inventory method and the land-use carbon emission coefficient approach, we develop a simulation framework for the spatial distribution of county-scale territorial space carbon emissions and achieve high-resolution characterisation of small-scale emission heterogeneity. Second, we verify the spatial differentiation of territorial space carbon emissions using complementary analyses based on global Moran’s I and the Getis-Ord $G_i^{\mathrm{*}}$ statistic, and we also employ the Hurst index to reveal future emission trends. Third, we apply the GTWR model to overcome the limitations of traditional regression techniques that assume spatial homogeneity, and to quantify spatial and temporal variations in the driving mechanisms. Collectively, these investigations establish a foundational theoretical framework for devising precise and forward-looking carbon-reduction strategies and provide a scientific basis for implementing refined carbon emission management.

However, this study nevertheless has limitations regarding the comprehensiveness of carbon emission impact factors and the availability of data for land-use carbon emission coefficients. Specifically, owing to the absence of statistics data on energy consumption and chemical oxygen demand in industrial wastewater in Qionglai City, the study employs statistical data from Chengdu City or Sichuan Province to derive indirect estimates. Qionglai City, a county-level administrative region under Chengdu City in Sichuan Province, exhibits significant policy control and economic interconnections; however, existing research has employed data substitution methods for higher-level administrative units to address analogous issues [116,117]. To mitigate the uncertainty arising from absent data, this study refrains from directly substituting the data from the higher administrative unit; instead, it employs this data as a parameter to adjust the measured data of the study area. Urban production energy consumption is calculated by multiplying the comprehensive energy consumption of Chengdu’s industrial enterprises, based on an industrial output value of CNY 10,000, by the total industrial output value of Qionglai. The energy consumption for urban and rural living is calculated by multiplying the per capita utilisation of electricity, natural gas, and liquefied petroleum gas in Chengdu by the respective population in the study area. The chemical oxygen demand in industrial wastewater is adjusted to the average value for Sichuan Province based on the ratio of the total industrial output value of the study area to that of the province. Figure 2 and Table 2 indicate that, during the spatial simulation of carbon emissions distribution, the study compiles the carbon emission inventory associated with the spatial functions of the national territory, computes the carbon emission coefficients for these spatial functions, and subsequently executes the spatial distribution simulation based on a 100 m×100 m vector grid. The simulation results indicate that carbon emissions exhibit significant spatial and temporal heterogeneity characteristics (Figure 6), suggesting that the potential bias of individual data points does not substantially affect the analysis of the spatial and temporal heterogeneity of carbon emissions related to TSFs.

Thus, future studies should focus on the following: (1) developing subregional LUCE coefficients to improve accounting precision; (2) constructing a comprehensive system of national spatial function carbon emission impact indicators that quantitatively represent policy, planning, and technological drivers; and (3) establishing dynamic monitoring mechanisms for carbon emission drivers to model future evolution and support informed low-carbon policy-making.

6. Conclusions

This study uses Qionglai City, China, as a case study and integrates the IPCC inventory method with the LUCE coefficient method to simulate the spatial distribution of carbon emissions from the utilisation of TSFs in the study area. It further combines global Moran’s I, Getis-Ord $G_i^{\mathrm{*}}$ statistic, and the Hurst index to analyze the spatiotemporal evolution characteristics and future trends. In addition, the study examines the driving mechanisms of these changes using the GTWR model. By addressing inadequate county-scale predictions of carbon emission trends and the frequently overlooked spatiotemporal heterogeneity of driving factors, the study offers decision-making support for county governments in formulating precise and proactive carbon-reduction policies. The primary conclusions are as follows:

(1) The simulation framework for spatial distribution of county-level carbon emissions from the utilisation of TSFs has significantly enhanced the accuracy of carbon accounting and the representation of spatial heterogeneity. Between 2009 and 2023, total carbon emissions in Qionglai City increased from 852,300 tonnes to 1,422,500 tonnes, with an average annual increment of 40,700 tonnes, exhibiting distinct phased growth characteristics. Specifically, from 2009 to 2018, the total carbon emissions rose gradually from 852,300 tonnes to 1,031,600 tonnes, followed by a rapid increase to 1,422,500 tonnes between 2018 and 2023. While RPSs, accounting for over 70% of the area, were the largest source of regional carbon emissions, UPSs exhibited the fastest growth rate, consistent with the development trends of industrialization and urbanization in the region.

(2) The distribution of carbon emissions from the utilisation of TSFs at the county-level scale exhibit significant positive spatial autocorrelation (Moran’s I = 0.60–0.69) and clustered distribution characteristics. Specifically, the eastern urban and rural production-living spaces, due to industrial agglomeration and high energy consumption, form high-value hotspots, whereas western ecological functional spaces, owing to strong carbon sink capacity, are low-value cold spots, showing obvious spatial heterogeneity.

(3) The spatiotemporal differentiation of carbon emissions resulting from the utilisation of TSFs at the county-level scale is significant. During the historical period from 2009 to 2023, 65.69% of the city’s regions exhibited a marked upward trend in carbon emissions, whereas only 29.66% showed insignificant growth. Projections indicate that 99.1% of regions will maintain their historical growth trends (Hurst index = 0.6825), although the persistence of these trends will vary spatially. Specifically, carbon emissions in the east will continue to grow due to human production and living activities, while those in the west will show a growth suppression trend due to ecological protection policies.

(4) Economic growth, industrial structure, and development intensity are the primary drivers of the spatiotemporal evolution of county-level carbon emissions, as evidenced by the mean regression coefficients from the GTWR model (1.2210, 0.2973, and −0.0318, respectively). Notably, the effects of these factors exhibit pronounced spatial heterogeneity. Specifically, economic growth has a greater influence on carbon emissions in eastern regions compared to western regions. In contrast, the impact of industrial structure on reducing carbon emissions is significantly stronger in the western region than in the eastern region. Furthermore, the inhibitory effect of development intensity on carbon emissions weakens from east to west.

In summary, the spatiotemporal heterogeneity of carbon emissions arising from the utilisation of TSFs stems from differences in emission magnitude, temporal trends, and the influence of driving factors. Carbon reduction policies should therefore account for these spatiotemporal characteristics and their drivers by implementing dynamic, spatially differentiated regulatory measures for urban, rural, and ecological functional spaces. For example, eastern production and living spaces should prioritise controlling development intensity and optimising industrial structure, whereas western ecological spaces require strengthened protection to enhance carbon-sequestration capacity. Although this study offers theoretical support for county-scale carbon reduction policy formulation, limitations in data availability and the challenges of quantifying policy impacts constrain the characterisation of spatiotemporal heterogeneity in emission distribution modelling. In addition, the suite of driving-factor indicators does not cover all relevant variables, which may reduce the comprehensiveness of the results. Future work should further optimise accounting methods for carbon emissions from TSF utilisation, construct a more systematic indicator framework and deepen dynamic simulation of driving mechanisms to provide more accurate and forward-looking decision support for county-scale carbon reduction policymaking.