Spatiotemporal Dynamic Evolution Characteristics of Net Carbon Sinks in County-Level Farmland Ecosystems in Hunan Province, China

Abstract

A quantitative study on the spatial structure and spatiotemporal variation characteristics of net carbon sinks in regional farmland ecosystems is of significant importance for uncovering the multifunctional roles of farmland ecosystems and formulating region-specific agricultural policies and management strategies. Based on the measurement of net carbon sinks in county-level farmland ecosystems across Hunan Province from 2005 to 2020, this research employs methodologies, including the standard deviational ellipse (SDE), spatial autocorrelation, and exploratory spatiotemporal data analysis (ESTDA) to investigate the spatiotemporal evolution characteristics of net carbon sinks in Hunan’s county-level farmland ecosystems. The results show that the net carbon sinks of county-level farmland ecosystems in Hunan Province exhibits a “northeast–southwest” spatial distribution pattern, with a trend toward spatial agglomeration during contraction, and the center of gravity of net carbon sinks has generally shifted northwestward over time. A significant positive spatial correlation exists globally in the net carbon sinks of Hunan’s county-level farmland ecosystems, and the degree of spatial agglomeration has gradually intensified amid fluctuations. The dynamic evolution of local spatial patterns of net carbon sinks in county-level farmland ecosystems in Hunan Province varied significantly, showing strong stability in both local spatial structure and spatial dependence direction. In contrast, eastern and central Hunan exhibited more dynamic local spatial structures compared to southern and northern regions. The local spatial association patterns of the net carbon sinks in county-level farmland ecosystems remained relatively stable, with weak spatial synergy and a pronounced path-dependent locking effect in spatial agglomeration.

1. Introduction

Since the Industrial Revolution, carbon emissions from fossil energy utilization and land use changes have been recognized as the primary drivers of global warming [1]. Due to their intrinsic linkages with human survival and socio-economic development, carbon emissions have garnered worldwide attention, positioning carbon cycle research at the forefront of global change studies [2]. As human activities, industrialization and transportation construction intensify, carbon emissions also increase [3]. Farmland ecosystems, as semi-natural and semi-artificial systems, serve critical production functions by intensively supplying agricultural products [4]. Agricultural production contributes to 10–12% of global anthropogenic carbon emissions [5,6], while farmland ecosystems store over 10% of global terrestrial carbon [7], functioning as both significant carbon sources and sinks in the atmosphere [8]. As vital components of terrestrial ecosystems, farmland ecosystems provide essential ecological services, including climate regulation, soil-water conservation, water resource retention, and biodiversity preservation [9]. Under China’s dual imperatives of agricultural modernization and low-carbon transition, a systematic quantitative analysis of the structural characteristics and spatiotemporal dynamics of carbon sources and sinks within farmland ecosystems serves as a fundamental prerequisite for elucidating regional carbon cycling mechanisms [10]. Furthermore, such research provides critical insights for designing localized agricultural emission-reduction policies, optimizing the multifunctional synergies (e.g., production capacity and ecological services) inherent to farmland ecosystems, and ultimately advancing sustainable agroecological development. At present, research in the field of carbon cycle in farmland ecosystems has achieved fruitful results. The research content covers the measurement and spatiotemporal comparison of carbon sources and carbon sinks in farmland ecosystems [11,12], carbon footprint accounting in farmland ecosystems [13,14], driving mechanism analysis [15,16], carbon emission fairness [17,18], emission reduction paths and policy responses [19], etc. The research focuses on the establishment of a carbon source and carbon sink measurement system for farmland ecosystems and the analysis of driving factors. In recent years, analyzing the stage characteristics and regional differences of carbon sources and sinks in farmland ecosystems from temporal and spatial perspectives has gradually attracted attention [20,21]. However, most of the existing results measure and analyze the carbon sources and sinks of farmland ecosystems separately, and there are fewer studies on net carbon sinks, which play an important role in the development of agricultural production, emission reduction and sink enhancement, and low-carbonization of agriculture [20]. In terms of research scale, the study mainly focuses on national, regional, inter-provincial, prefecture-level city and other large spatial scales, and not many studies have been conducted on county-level units that directly undertake the task of energy conservation and emission reduction in farmland; in terms of research content, more attention has been paid to the characteristics of the temporal changes of carbon sources and sinks in farmland ecosystems, and there is a relative lack of research on spatial linkages of net carbon sinks in farmland ecosystems within the regions, as well as on the dynamics of the evolution of farmland ecosystems. Additionally, various methodologies have been employed in estimating carbon sequestration and emissions within agricultural ecosystems. For instance, statistical models and coefficient-based approaches are widely used to calculate crop carbon uptake and straw coefficients; life cycle analysis and coefficient-based emission inventories provide a unified framework for assessing carbon emissions from agricultural inputs and straw burning. Additionally, spatial statistical techniques (such as standard deviation ellipses and spatial autocorrelation methods) have been employed to analyze the spatiotemporal evolution of carbon fluxes; while studies integrating soil respiration models with field measurements have deepened understanding of emission processes across different agricultural systems. Building upon these established methodologies, this paper integrates and applies them at the county scale to construct a systematic assessment framework for net carbon sequestration in Hunan Province’s agricultural ecosystems.

Hunan Province has a cultivated land area of 4,148,800 hectares, accounting for about 3.1% of the total cultivated land in the country, Hunan Province is an important agricultural province, a large grain province, the first main rice-producing province, and an important position of the national “rice bag”, “vegetable basket” and “oil can”. Researching the green development status of agriculture in Hunan Province is of representative significance for clarifying the progress of low-carbon agricultural development in central China and better achieving the “dual carbon” goals. At the same time, studying the spatial effect of agricultural carbon budget and agricultural carbon compensation potential from the dual perspectives of carbon emission and carbon absorption can make up for the lack of agricultural carbon emission reduction analysis and enrich the agricultural low-carbon development model to a certain extent. Therefore, scientifically estimating the net carbon sinks of farmland ecosystems and conducting research on the spatiotemporal dynamic characteristics and influencing factors on this basis are particularly important for guiding agricultural carbon emission reduction and low-carbon transformation and development. However, despite Hunan being one of the most important agricultural provinces of China and playing a critical role in low-carbon agricultural development and the achievement of the national ‘dual carbon’ goals, systematic studies on the net carbon sinks of farmland ecosystems in this province, especially at the county level, remain scarce. In view of this, based on the calculation of net carbon sinks in farmland ecosystems of 122 county units in Hunan Province from 2005 to 2020, this study used analytical methods such as standard deviation ellipse, spatial autocorrelation, and exploratory spatiotemporal data analysis to quantify the relationships between counties, explore the spatial pattern and evolution characteristics of net carbon sinks in farmland ecosystems in counties of Hunan Province, and comprehensively reveal the spatiotemporal and heterogeneous nature of net carbon sinks, so as to provide a theoretical basis for Hunan Province to formulate regional differentiated agricultural carbon emission reduction policies and achieve low-carbon agricultural goals, and also provide new ideas for improving the research on carbon cycle of farmland ecosystems.

2. Methodology and Data

2.1. Overview of the Study Region

Hunan Province is located in South Central China, between 108°47′ and 114°15′ east longitude and 24°38′ and 30°08′ north latitude. It borders Jiangxi to the east, Chongqing and Guizhou to the west, Guangdong and Guangxi to the south, and Hubei to the north. The total area of the province is about 211,800 square kilometers, and it has 13 prefecture-level cities and 1 autonomous prefecture (122 counties, cities, and districts) under its jurisdiction (Figure 1). Hunan Province has a complex and diverse terrain, with mountains and hills accounting for more than 80% of the province’s total area. The four major water systems of the Xiangjiang River, Zijiang River, Yuanjiang River and Lishui River run through the province, with a dense river network. Located in the subtropical monsoon climate zone, the annual average temperature is 16–18 °C, the precipitation is abundant, the annual average precipitation is 1300–1800 mm, and the farming conditions are good. According to the data of the 3rd National Land Survey, the cultivated land area in Hunan Province is 4.1488 million hectares, accounting for about 3.1% of the total cultivated land area in China. The cultivated land is generally located in the double-cropping system area designated by the state. By the end of 2020, the urbanization rate reached 58.76%. In the context of regional urbanization, the sustainable use and effective management of cultivated land resources have encountered severe tests.

2.2. Data Source and Processing

The data used to calculate carbon emissions and carbon absorption in this study come from the Hunan Rural Statistical Yearbook from 2005 to 2020 [22]. Hunan Province county-level administrative division vector data come from the Basic Geographic Information Center of the National Administration of Surveying and Mapping (http://www.ngcc.cn, accessed on 10 June 2025), taking the county-level administrative divisions of Hunan Province in 2020 as the benchmark, ArcGIS10.8 software was used for merging processing, and the urban districts of each prefecture-level city were taken as a county unit, and other counties and cities under its jurisdiction were taken as separate units, ultimately obtaining 122 counties as research units. Land use data come from the Resources and Environmental Science Data Center of the Chinese Academy of Science (https://www.resdc.cn/, accessed on 10 June 2025). The resolution is 30 m × 30 m, including 6 primary land types such as cultivated land and forest land, and 24 secondary land types such as paddy field and dry land. After reclassification, six major categories are obtained, including cultivated land, forest land, grassland, water area, construction land and unused land, and land use data for 2005, 2010, 2015 and 2020 are obtained.

Land use data were obtained for 2005, 2010, 2015, and 2020. Linear interpolation was applied for intermediate years, which may not capture abrupt land conversions. Moreover, county statistical yearbooks may contain reporting errors, which could affect annual estimates.

2.3. Research Methods

2.3.1. Calculation Method of Carbon Absorption

In this study, nine major crops in Hunan Province were selected for carbon absorption estimation. The carbon absorption of crops during their entire growth period through photosynthesis is C_absorption (t). The calculation method is shown in Equation (1) [23]:

$$C_{absorption}={\sum }_{i=1}^n{C}_d=\sum _{i=1}^n{\displaystyle \frac{\left[Q_i\ast C_i\ast \left(1-W_i\right)\ast \left(1+R_i\right)\right]}{H_i}},$$

(1)

where i is the i-th crop type; C_d is the carbon absorption of the i-th crop during its growth period (t); Q_i is the economic yield of crop i(t); and C_i, W_i, R_i, and H_i are the carbon absorption rate, water content, root-to-shoot ratio, and economic coefficient of crop i, respectively. The carbon absorption correlation coefficient was determined based on the research results of Dafeng Hui [24], Zhaoying Han [25], and Jiachuan Gu [26] (

Table 1. Correlation coefficient of carbon absorption estimation.

Crop Name	Carbon Absorption Rate	Economic Coefficient	Moisture Content	Root-to-Shoot Ratio
paddy	0.414	0.45	0.120	0.600
corn	0.471	0.400	0.130	0.156
wheat	0.485	0.400	0.120	0.393
soybean	0.450	0.350	0.130	0.129
potatoes	0.423	0.700	0.700	0.175
vegetables	0.450	0.650	0.900	-
peanut	0.450	0.430	0.100	0.720
rapeseed	0.450	0.250	0.100	0.040
cotton	0.450	0.2767	0.115	0.122
tobacco	0.45	0.525	0.15	0.3175

Note: The economic yield of potatoes and peanuts is tubers, so the root-to-shoot ratio of potatoes and peanuts is used; vegetables have complex composition, so the root-to-shoot ratio of vegetables is not considered.

).

2.3.2. Calculation Method of Carbon Emissions

(1)

Carbon Emissions from Farmland Inputs

According to the IPCC (2006) National Greenhouse Gas Emission Inventory [27], the main sources of carbon emissions from farmland ecosystems are pesticides, agricultural irrigation, fertilizers, agricultural films, agricultural diesel, and farmland tillage. In this study, the carbon emissions from the six pathways are mainly considered. The calculation method is shown in Equation (2):

$$E_{input}=\sum E_i=T_i\ast {\delta }_i,$$

(2)

where $E_{input}$ is the total carbon emissions of farmland ecosystems in the study area (t); $T_i$ represents the use of various types of agricultural carbon sources (t); and ${\delta }_{\dot{i}}$ denotes the carbon emission coefficients of various types of carbon sources. According to the research results of related scholars [28,29], the carbon emission coefficients corresponding to various farmland inputs were determined as shown in

Table 2. Carbon emission coefficient for various types of farmland inputs.

Farmland Inputs	Carbon Emission Coefficient	Reference
farmland tillage	3.126 kgCO2/hm2	College of Biology and Technology, China Agricultural University
fertilizer	0.8956 kgCO2/kg	Oak Ridge National Laboratory, USA
agricultural film	5.18 kgCO2/hm2	Institute of Agricultural Resources and Ecological Environment, Nanjing Agricultural University
agricultural diesel	0.5927 kgCO2/kg	IPCC 2006 [27]
pesticide	4.9341 kgCO2/kg	Oak Ridge National Laboratory, USA
agricultural irrigation	25 kgCO2/hm2	Dubey [30]
crop residues	1.247 tCO2/t	Gehua Wang [31]

.

(2)

Carbon emissions from open burning of crop residues are as follows:

$$E_{burning}=Q_i\ast N_i\ast F\ast P\ast a_i,$$

(3)

where E_burning is the total carbon emission from open burning of crop residues (t); Q_i represents the economic yield of crop i(t); denotes the residue-to-product ratio (RPR) of crop i; F is the fraction of crop residues subjected to open burning (%); P indicates the combustion efficiency for open burning of crop residues; and a_i is the carbon emission coefficient for open burning of crop residues. The RPR (N_i) and the carbon emission coefficient of crop residues (a_i) were derived from peer-reviewed regional studies by Jiang Du et al. [32] and Lijing Guo et al. [33], with detailed values provided in

Table 3. Residue-to-Product Ratio and carbon emission coefficient for open burning of crop residues.

Crop Name	Residue-to-Product Ratio	Carbon Emission Coefficient	Combustion Efficiency
paddy	0.98	1.11	0.93
wheat	1.38	1.47	0.92
corn	0.96	1.35	0.92
soybean	1.52	1.58	0.68
potatoes	0.52	1.58	0.68
cotton	3.35	1.35	0.8
rapeseed	2.98	1.58	0.8
peanut	1.26	1.58	0.82
vegetables	1.00	1.58	-

.

(3)

Carbon emissions from food consumption

Hunan Province is a major grain-producing province, and the main grain variety, paddy, has achieved self-sufficiency, and the remaining paddy is stored locally or sold out of the province, which can be regarded as carbon accumulation in the system in the current year. Carbon fixed by crops through photosynthesis is re-emitted to the atmosphere in various forms in the same year as it is consumed as food for humans [6]. Based on the dietary and nutritional pagoda of Chinese residents and the China Food and Nutrition Development Program, the carbon emissions from food consumed annually in each county unit of Hunan Province were estimated based on a per capita food consumption of 400 kg·a⁻¹, and on the carbon emission intensity coefficients of food (1 kg of food = 0.27 kg·CO₂) of Zhihong Cao et al. [34].

(4)

Carbon emissions from farmland soil respiration

Soil respiration in farmland has strong spatial and temporal heterogeneity and is jointly influenced by factors such as soil temperature and humidity, crop physiological conditions, and field management practices. Research by Chompunut Chayawat et al. shows that rainfall plays a crucial role in soil carbon emissions [35]. Therefore, the results of the current research on soil respiration and carbon emission in agricultural fields vary widely [36]. In Hunan Province, where the main crop is paddy, the average annual carbon respiration in farmland was roughly taken as 0.710 t C·hm⁻²·a⁻¹, mainly with reference to the studies of Jufeng Zheng et al. [37], Weizhao Wei et al. [38], and Shuntao Zhang et al. [39].

2.3.3. Estimation of Net Carbon Sinks

$$C_{net}=C_{absorption}-E_{input}-E_{burning}-E_{consumption}-E_{respiration},$$

(4)

where C_net is the net carbon sinks of regional farmland ecosystems (t); E_consumption represents the carbon emission from food consumption (t); and E_respiration denotes the carbon emission from farmland soil respiration (t).

This study defines net carbon sink as the difference between absorption and emissions, encompassing both natural and anthropogenic processes. This definition renders it more suitable as an indicator of ecological balance rather than a direct measure of emission reduction potential. The primary purpose of employing this metric is to conduct comparative analysis of spatiotemporal evolution characteristics at the county level in Hunan Province. Furthermore, future research will validate these results using independent carbon flux observation data (such as eddy covariance monitoring and soil sampling).

2.3.4. Standard Deviation Ellipse

In this study, the weighted standard deviation ellipse was used to reveal the spatial distribution of the convergent and dominant directions of the net carbon sinks of farmland ecosystems in counties of Hunan Province, using the indicators of net carbon sinks of farmland ecosystems as weights. The standard deviation number 1 (default value) was chosen as the expressible range, which covers about 68% of the gravity center of net carbon sinks in farmland ecosystems. The principle and detailed calculation procedure are described in the literature [40].

2.3.5. Spatial Correlation

The global Moran’s I index and local Moran’s I index were used to quantitatively study the spatial correlation characteristics of net carbon sinks in county-level farmland ecosystems across Hunan province. The global Moran’s I index is used to measure the overall spatial agglomeration characteristics of the net carbon sinks, while the local Moran’s I index is used to measure the degree of spatial agglomeration of the net carbon sinks, and analyze whether there is high-value agglomeration or low-value agglomeration. The fundamental concepts and specific calculations of these two indices draw upon Yang Qiang’s research [41].

2.3.6. Exploratory Spatiotemporal Data Analysis Methods

Rey et al. [42] added the temporal dimension to the original exploratory spatial data analysis (ESDA) focusing on the spatial dimension and proposed exploratory spatiotemporal data analysis (ESTDA), which realizes the spatiotemporal interactive fusion of regional geographic elements. This study used the LISA time path in the ESTDA framework to analyze the spatiotemporal dynamics of net carbon sinks in farmland ecosystems in counties of Hunan Province. The spatiotemporal transition situations are divided into four types: I, II, III and IV, which, respectively, indicate that over time, neither this county nor neighboring counties have transitioned; only this county has transitioned; only neighboring counties have transitioned; both this county and neighboring counties have transitioned.

3. Results and Discussion

3.1. Temporal Characteristics of Net Carbon Sinks

Based on the land use and energy consumption data of Hunan Province in 2005–2020, the total net carbon sinks of farmland ecosystems in each city in 2005~2020 were obtained (Figure 2 and the calculation results of net carbon sinks of each city in Hunan Province from 2005 to 2020 is listed in Supplementary Materials). From 2005 to 2010, the total net carbon sinks of farmland ecosystems in Hunan Province increased steadily, from 712.36 Mt in 2005 to 762.01 Mt in 2010. However, with the urbanization process and the evolution of industrial structure, the net carbon sinks of farmland ecosystems in Hunan Province continued to decline from 2010 to 2020, first from 762.01 Mt in 2010 to 549.18 Mt in 2015, and then to 512.21 Mt in 2020. This is mainly because the rapid urbanization in Hunan Province during this period led to a large amount of farmland being converted into construction or industrial land, and the reduction in cultivated land area directly weakened the carbon sequestration capacity of farmland ecosystems, while soil degradation and mechanization of energy consumption led to an increase in carbon emissions, which contributed to the decline of the net carbon sinks of farmland to a large extent. According to the net carbon sinks on farmland in each county over the years, it is known that the net carbon sinks on farmland in the region show significant differences due to the differences in the urbanization process, cultivated land area, planting structure, and farming methods in each county.

3.2. Spatial Characteristics of Net Carbon Sinks

The standard deviational ellipse (SDE) method was applied to characterize the spatial distribution patterns of net carbon sinks in county-level farmland ecosystems across Hunan Province. From 2005 to 2020, the center of gravity of net carbon sinks in county-level farmland ecosystems in Hunan Province did not change much, mainly located in the three neighboring counties of Xiangxiang City, Louxing District and Shuangfeng County. The path of the center of gravity movement has experienced the changes in “northwest (2005–2006)–southwest (2006–2007)–northwest (2007–2012)–northeast (2012–2016)-southwest (2016–2017)–northwest (2017–2019)–southwest (2019–2020)”, and generally shows an oscillating trend of moving toward the northwest (Figure 3).

During the study period, the azimuth angle θ gradually increased during the fluctuation process from 7.04° in 2005 to 18.90° in 2020, indicating that the net carbon sinks in the farmland ecosystems in Hunan Province have shown a spatial distribution pattern of “northeast–southwest” in the past 16a. In addition, the lengths of the long axis and minor axis of the standard deviation ellipse expanded during the fluctuations, increasing by 15,100.69 m and 13,556.66 m, respectively, during the 16 years. It indicates that the net carbon sinks of county-level farmland ecosystems in Hunan Province showed different degrees of expansion in the northeast–southwest direction (long-axis direction) and northwest-southeast direction (minor-axis direction) during the period from 2005 to 2020, and the expansion trend in the long-axis direction was more significant. Under the combined effect of the long axis and the minor axis, the area of the standard deviation ellipse in 2020 increased by 17.92% compared with 2005. The above characteristics comprehensively reflect that the spatial pattern of net carbon sinks in farmland ecosystems in counties of Hunan Province tends to be concentrated while expanding during the study period (

Table 4. Ellipse parameters of net carbon sinks standard deviation in county-level farmland ecosystems of Hunan Province during 2005–2020.

Year	Long Axis/km	Minor Axis/km	Azimuth Angle/◦	Coordinates of Gravity Center		Shift of Gravity Center
				Longitude	Latitude	Direction	Distance/km
2005	186.26	149.32	7.04	112°14′11″	27°40′1″	-	-
2006	185.12	145.9	6.83	112°13′13″	27°46′1″	Northwest	4.57
2007	187.92	153.2	6.96	112°13′38″	27°46′52″	Southwest	1.08
2008	185.47	151.73	11.92	112°8′5″	27°48′29″	Northwest	8.66
2009	186.83	152.44	3.09	112°4′25″	27°50′41″	Northwest	6.83
2010	191.59	153.21	7.20	112°4′31″	27°50′38″	Southwest	1.66
2011	188.71	149.46	6.42	112°3′48″	27°51′49″	Northwest	1.58
2012	190.69	148.71	6.54	112°1′12″	27°51′33″	Southwest	2.97
2013	189.62	148.09	5.45	112°1′17″	27°51′10″	Northeast	0.46
2014	190.25	148.10	4.55	112°3′39″	27°51′12″	Northeast	2.55
2015	190.71	147.00	3.69	112°4′50″	27°52′6″	Northeast	2.28
2016	187.70	146.88	4.17	112°4′16″	27°52′25″	Northeast	0.81
2017	191.09	157.01	6.34	112°0.2′13″	27°49′44″	Southwest	7.92
2018	195.27	156.96	8.41	111°58′15″	27°50′15″	Northwest	3.79
2019	197.78	156.08	11.57	111°59′41″	27°54′31″	Northeast	2.4
2020	201.36	162.87	18.90	111°58′34″	27°52′5″	Southwest	2.29

).

3.3. Local Spatial Association Patterns

The Global Moran’s I values of net carbon sinks in farmland ecosystems in Hunan Province from 2005 to 2020, calculated by GeoDa 1.20 software, were all positive and passed the significance test (p < 0.05), it indicates that the spatiotemporal distribution between net carbon sinks of county-level farmland ecosystems in Hunan province is not a completely random state, but shows a significant positive spatial correlation. From 2005 to 2020, Global Moran’s I value fluctuated and increased from 0.149 in 2005 to 0.259 in 2020, indicating that the spatial clustering of similar areas of net carbon sinks in farmland ecosystems gradually increased, which is consistent with the results obtained from the standard deviation ellipse analysis mentioned above.

In order to further reveal the local spatial correlation types of net carbon sinks in county-level farmland ecosystems of Hunan Province, 2005, 2010, 2015 and 2020 were selected as research sections, and based on the scatter distribution of Local Moran’s I values, ArcGIS 10.8 was used to draw the LISA cluster map of net carbon sinks in county-level farmland ecosystems in Hunan Province (Figure 4), and the spatial concentration types of 122 counties were categorized into four classes: (1) HH clusters, the net carbon sinks of farmland ecosystems in this county and neighboring counties are above average. (2) HL clusters, the net carbon sinks of farmland ecosystems in the county itself are higher than the average, but that of its neighboring counties are lower than the average. (3) LH clusters, the net carbon sinks of farmland ecosystems in the county itself are lower than the average value, but the neighboring counties are higher than the average value. (4) LL clusters, net carbon sinks in farmland ecosystems in and around the county are below average.

On the whole, the net carbon sinks in county-level farmland ecosystems in Hunan Province showed a significant spatial clustering characteristic of “high in the east and low in the west”, dominated by the LL clusters, which accounted for more than 50% of the total number of the four types of clusters (Figure 5). HH clusters are mainly maintained in some counties in eastern Hunan, LL clusters tend to be located in some counties in western and eastern Hunan, and HL and LH clusters are mainly located in some counties in eastern and central Hunan, and the local spatial correlation pattern is relatively stable. In terms of the evolution of local spatial patterns, the share of HH clusters decreases from 3.3% in 2005 to 0 in 2020. As far as LL clusters are concerned, the number from 2005 to 2020 has increased by only one, but the distribution has become more centralized and concentrated to the east, with increased spatial agglomeration, mainly in counties such as Wangcheng District, Kaifu District, Changsha County, Tianxin District and Yuhua District in eastern Hunan, and in Suxian District in southern Hunan. This disparity primarily stems from the contrasting agroecological conditions between eastern and western Hunan. The fertile soils and flat terrain in eastern Hunan provide optimal conditions for crop cultivation, enhancing carbon sequestration through high biomass productivity and soil organic matter accumulation. In contrast, the mountainous topography and less fertile soils in western Hunan limit agricultural intensification, resulting in reduced carbon sequestration potential due to lower vegetation cover and accelerated soil erosion. However, with the acceleration of urbanization, a large number of over-cultivation and farmland degradation phenomena occurred, and the LL clusters moved from western Hunan to eastern Hunan. The number of HL and LH clusters has decreased by one each. By 2020, the HL clusters are distributed in Xiangtan County and Liling City, which are adjacent to the LL cluster, while the LH clusters are scattered in two counties, Wuling District and You County.

3.4. Dynamic Evolution of Local Spatial Correlation Patterns

LISA time path analysis can further reflect the dynamics of the local spatial structure of the net carbon sink of farmland ecosystems in Hunan province counties and the volatility of the spatially dependent direction. The relative lengths of the LISA time paths were calculated and then visualized using ArcGIS 10.8 software with the natural breakpoint method and manual classification (Figure 4).

There are 73 counties with a relative length of LISA time path less than 1, accounting for 59.84% of the total, indicating that the local spatial structure of net carbon sinks in county-level farmland ecosystems of Hunan Province is relatively stable as a whole. The relative length is the longest in the eastern part of Hunan, followed by the central part of Hunan, and the shortest in the southern and northern parts of Hunan, it shows that the eastern and central Hunan regions, represented by Liuyang City and Xiangxiang City, have a strong dynamic spatial structure, while the northern Hunan regions, represented by Sangzhi County and Yongshun County, and the southern Hunan regions, represented by Linwu District and Guiyang County, have a more stable spatial structure. Among them, Ningxiang City (3.13) is the county with the longest relative length of LISA time path, while Changsha County (2.80), Taoyuan County (2.75), Chengbu Miao Autonomous County (2.58), Dongkou County (2.56), Liuyang City (2.22), Wangcheng District (2.14), and Anxiang County (2.08). The relative lengths of LISA time paths in these seven counties are all greater than 2, and they are counties with longer relative moving lengths. Beita District (0.39), Lanshan County (0.39), Zhuhui District (0.39), Sangzhi County (0.38), Wulingyuan District (0.35), Shuangpai County (0.34), Jiahe County (0.28), and Yanfeng District (0.27) are the eight counties with the shortest relative lengths, and their relative lengths are all less than 0.40. Similarly, ArcGIS 10.8 software was used to express the curvature of LISA time paths in a hierarchical manner using the natural breakpoint method. The curvature of time path for net carbon sinks in county-level farmland ecosystems across Hunan Province exhibits a laterally decreasing gradient from the central region toward the eastern and western peripheries, with curvature values consistently exceeding 1. This pattern indicates strong spatial dependence in the dynamics of net carbon sinks in county-level farmland ecosystems processes in Hunan Province. The three counties with the largest curvature were Leiyang City (11.37), Jiahe County (8.43), and Shigu District (6.11), and it indicating that these counties had the largest fluctuation in the direction of spatial dependence, and the net carbon sinks of the farmland ecosystems showed a more dynamic spatial variation process. Meanwhile, the counties with the smallest curvature were Chaling County (1.00), Longshan County (1.00) and Ningxiang City (1.00). This indicates that the spatial dependence direction of these counties has the greatest stability, and the net carbon sinks level of farmland ecosystems in these counties also remains relatively stable.

3.5. Analysis of Spatiotemporal Transfer of Local Spatial Correlation Patterns

The spatiotemporal transition method proposed by Rey et al. [42] was used to reveal the transfer characteristics of local spatial association types of net carbon sinks in county-level farmland ecosystems in Hunan Province (

Table 5. Spatiotemporal transition matrices of net carbon sinks in county-level farmland ecosystems of Hunan Province.

t/t + 1	HH	LH	LL	HL	Type	Percent	n
HH	I (0.87)	II (0.09)	IV (0.02)	III (0.02)	I	0.83	302
LH	II (0.16)	I (0.74)	III (0.10)	IV (0.00)	II	0.09	33
LL	IV (0.03)	III (0.06)	I (0.88)	II (0.04)	III	0.07	25
HL	III (0.26)	IV (0.00)	II (0.13)	I (0.61)	IV	0.02	6

Note: Type I, II, III, IV represent four distinct scenarios of spacetime transition, which, respectively, indicate that over time, neither this county nor neighboring counties have transitioned; only this county has transitioned; only neighboring counties have transitioned; both this county and neighboring counties have transitioned.

). Statistics were conducted every five years, and the number of spatiotemporal transition types of net carbon sinks in county-level farmland ecosystems in Hunan Province were calculated using 2005–2010, 2010–2015 and 2015–2020 as research sections. As shown in Table 5, there was little migration between spatiotemporal categories of net carbon sinks in farmland ecosystems in Hunan province from 2005 to 2020. Among them, LH→HH and HL→HH are the two types with the lagest migration probabilities, which are 0.16 and 0.26, respectively, and the number of migrations is only 20 times, while the transfer probabilities between other types are relatively low. Especially between HH and LL, LH and HL, and HL and LH, there is basically no transfer, which indicates that it is impossible to happen that the net carbon sinks of farmland ecosystems in counties and neighboring counties change at the same time, and that the factors of counties themselves play a decisive role in the change in the types of net carbon sinks of farmland ecosystems. According to the four types of spatial transitions divided by Rey et al. [42], the probability of type I spatiotemporal transition of net carbon sinks in county-level farmland ecosystems of Hunan Province from 2005 to 2020 is 82.51%, that is, the types without spatiotemporal transition account for the majority. This finding indicates that most counties and their adjacent areas maintained consistent spatial association patterns throughout the study period. This may reflect low cross-regional linkage, demonstrate path dependency in local agricultural management, or be influenced by the spatial weighting parameters selected.

4. Conclusions

Based on the measurement of net carbon sinks in farmland ecosystems, the spatial pattern of net carbon sinks in farmland ecosystems and their spatiotemporal dynamics in counties of Hunan Province were studied using standard deviation ellipse, spatial correlation, and exploratory spatiotemporal data analysis, and the results showed that the following:

(1)

During the period 2005–2020, the center of gravity for net carbon sinks in county-level farmland ecosystems of Hunan Province was predominantly located within Xiangxiang City, following a dynamic trajectory of “northwest–southwest–northwest–northeast–southwest–northwest.” This path reflects a general northwestward migration of the center of gravity, indicating that western and northern counties exhibited higher growth rates in net carbon sequestration compared to other regions. Analysis of the Standard Deviational Ellipse (SDE) further reveals a “northeast–southwest” spatial distribution pattern of net carbon sinks in county-level farmland ecosystems of Hunan Province, which demonstrates a contracting trend with increasing spatial agglomeration over the study period.

(2)

From 2005 to 2020, the net carbon sinks of county-level farmland ecosystems in Hunan Province showed a significant spatial positive correlation, and the degree of aggregation gradually increased amid fluctuations. From a local perspective, the clusters of net carbon sinks of county-level farmland ecosystems in Hunan Province show a significant spatial agglomeration characteristic of “high in the east and low in the west”. The HH clusters were mainly distributed in some counties in eastern Hunan represented by Xiangtan County, and the LL clusters were mainly distributed in some counties in eastern Hunan represented by Yuelu District and Yuhua District. Over time, the LL clusters moved from western Hunan to eastern Hunan. The spatial scale and number of counties in different clusters types fluctuated slightly over time.

(3)

From 2005 to 2020, the dynamic evolution of the local spatial correlation pattern of net carbon sinks in county-level farmland ecosystems in Hunan Province showed obvious differences. The areas with larger LISA time path moving lengths are mainly distributed in some counties in eastern and central Hunan, and the overall trend is eastern Hunan > central Hunan > northern and southern Hunan. This shows that eastern and central Hunan have more dynamic local spatial structures, while southern and northern Hunan have relatively stable local spatial structures. The curvature of the LISA time path shows a trend of decreasing horizontally from the center to the east and west. Leiyang City, Jiahe County and Shigu District have the greatest volatility in the spatial dependence direction, while the spatial dependence direction of Chaling County, Longshan County and Ningxiang City is the most stable.

(4)

From 2005 to 2020, the LISA spatiotemporal transition analysis showed that the probability of type I spatiotemporal transition of net carbon sinks in county-level farmland ecosystems of Hunan Province is 82.51%, that is, the types without spatiotemporal transition account for the majority. This indicates that the local spatial correlation pattern of net carbon sinks in county-level farmland ecosystems of Hunan Province is relatively stable, and the local spatial linkage in most counties is weak. And there is a lack of motivation to jointly move to the HH clusters, and the spatial agglomeration shows a high path locking feature. The factors of counties themselves play a decisive role in the change in the types of net carbon sinks of farmland ecosystems.

However, there are still some limitations in this study. The reference value of carbon emission coefficient in this study comes from the existing research literature. Selecting the research results of Hunan Province and its surrounding similar areas, in order to reduce the negative impact of single error in the research results, the average value method is adopted, which has been reflected in other scholars’ research [43,44] and has certain rationality, but it is not as accurate as field sampling and survey [45,46]. In addition, the results of this study should be interpreted as a partial carbon budget, primarily covering crop- and input-related fluxes that can be reliably measured through statistical yearbooks. It is important to note that, given the study’s focus on relative spatiotemporal evolution characteristics (such as SDE, Moran’s I, and LISA clustering), the omission of these fluxes may lead to an overestimation of the absolute value of net carbon sequestration. However, this omission does not compromise the robustness of conclusions regarding spatial patterns. It should be emphasized that this study’s consolidation of urban districts into county-level units may introduce certain statistical biases. Administrative boundary adjustments or urban expansion over the 16-year period could alter spatial relationships, but their impact is highly limited. Jelinski and Wu (1996) found that scale effects and partitioning effects influence statistical values, yet spatial autocorrelation patterns (such as hotspots) remain identifiable across multiple scales [47]. Tuson (2019) proposed evaluating autocorrelation stability across scales through Bayesian spatial modeling, demonstrating that robust spatial relationships persist even when regional boundaries are adjusted [48]. Collectively, these studies indicate that while MAUP may alter the absolute values of Moran’s I or LISA clustering, the observed trends of enhanced spatial aggregation and stable regional disparities between eastern and western regions at the county level remain credible.

Future research should conduct sensitivity and uncertainty analyses to further validate the robustness of SDE and Moran’s I results, thereby enhancing the precision of the study. Due to the limitation of data, this paper only studies the changes in urban total carbon emissions in Hunan province from 2005 to 2020. The sample data need to be further enriched in the future. To further enhance the accuracy of research findings, subsequent studies should conduct in-depth analyses of carbon emission factors based on the actual conditions of each city and county in Hunan Province, while accounting for the impact of interannual variations. This approach will enable the derivation of more suitable carbon emission factors for each city in Hunan Province.

5. Policy Recommendations

The advent of the low-carbon era presents systemic challenges to agricultural modernization. Hunan Province must implement sustainable development principles to facilitate the transition from conventional to low-carbon agricultural paradigms. Combined with the analysis of the spatiotemporal evolution characteristics of net carbon sinks in county-level farmland ecosystems in Hunan Province, the following policy recommendations are put forward for the development of low-carbon agriculture in Hunan Province:

• In response to the pattern of “the center of gravity shifting westward and the divergence between eastern and western regions,” implement targeted regional adjustments by optimizing land use structures. The net carbon sink center of Hunan Province’s farmland ecosystems has shifted northwestward, exhibiting a “northeast–southwest” spatial distribution with increasing concentration. The LL aggregation zone has migrated from western to eastern Hunan. Consequently, eastern Hunan should implement a “construction land reduction and efficiency enhancement with farmland resilience improvement” plan. Strictly delineate urban development boundaries and permanent basic farmland: Immediately halt the encroachment of disorderly urban expansion on surrounding high-quality farmland. Stabilize the carbon sink baseline through rigid constraints in the master land use plan. This is the most direct prerequisite for curbing the degradation of carbon sink functions in the region. Simultaneously, implement the “urban–rural integrated complex” model, encouraging the consolidation of fragmented farmland within and on the periphery of urban clusters into multifunctional spaces combining ecological landscapes, recreational education, and efficient production. Require new development projects to incorporate high-standard green infrastructure (e.g., ecological ditches, buffer zones) to reduce non-point source pollution and lower soil respiration carbon emissions caused by environmental stress. Implement rice straw shredding and deep plowing for return to fields: Immediately shift from traditional burning or removal practices through agricultural machinery subsidy policies.
• Overcoming the “spatial lock-in” effect by stimulating county-level transformation through altered field management practices. Spatiotemporal analysis of net carbon sinks in Hunan’s county-level farmland ecosystems reveals low transition probabilities, with county-specific factors playing a decisive role and a lack of shared motivation for transitioning to HH zones. Therefore, counties should enhance their carbon sequestration capacity by launching a “farmland management measures carbon sink certification and subsidy” program. Direct subsidies to measurable land use practices. Farmers adopting no-till/reduced-till farming, straw incorporation, and ecological ditch restoration receive direct subsidies based on applied area. These measures immediately reduce soil disturbance and improve aeration, directly lowering emissions from the critical source of “agricultural soil respiration.” Simultaneously, promote “smart drip irrigation” technology, particularly in the hilly regions of central and southern Hunan. By subsidizing drip irrigation equipment, directly change irrigation methods to reduce the anaerobic conditions necessary for methane production, thereby lowering methane emissions from paddy fields.
• Leveraging the sensitivity of “dynamically unstable zones,” prioritize land use change as the core of policy experimentation. Local spatial structures in eastern and central Hunan exhibit dynamic instability and heightened sensitivity to change. Special zones for monitoring land use change responses could be established in these areas. Priority should be given to rapidly advancing farmland “mechanization-friendly” transformation (e.g., consolidating small plots into larger ones, converting slopes into terraces) while simultaneously deploying IoT sensors to monitor real-time changes in soil carbon stocks, moisture levels, and respiration rates post-land consolidation. This approach would yield immediate first-hand data on the net carbon sink impacts of different engineering measures, providing evidence for province-wide implementation. Pilot the “farmland fertility enhancement and carbon sink gain” project. In suburban areas near cities, encourage the immediate conversion of degraded or polluted farmland to plant seedlings with strong carbon sequestration capabilities, energy crops, or wetland systems for ecological restoration. By altering land use types, achieve rapid conversion and enhancement of carbon sink functions.
• Strengthening Scientific and Technological Support: building an intelligent monitoring and decision-making platform coupled with land use.

With the advancement of agricultural modernization, Hunan Province can establish a “smart farmland digital twin platform” that integrates high-resolution remote sensing, drone aerial photography, and ground sensor data. This platform will focus on monitoring directly observable land use variables such as “crop type changes,” “straw burning hotspots,” “soil moisture,” and “expansion of construction land.” The platform’s core functionality lies in scenario simulation: modeling the impacts of policies like “promoting 100,000 mu of rapeseed rotation in Leiyang City” or “reducing fertilizer use by 5000 mu in Changsha County” on the spatial distribution of net carbon sinks at both county and provincial levels. This enables policymakers to anticipate immediate effects of policies on land use and carbon sinks, achieving unprecedented precision in regulatory adjustments.