Identiﬁcation and Optimization of County-Level Ecological Spaces under the Dual-Carbon Target: A Case Study of Shaanxi Province, China

: County-level ecological space, as a crucial level in optimizing the land spatial system, plays a pivotal role in “undertaking superior planning and guiding subordinate implementation”. From a spatial optimization perspective, effectively implementing the dual-carbon goal by increasing carbon sinks in speciﬁc ecological space units is essential. This study focused on 107 districts and counties in Shaanxi Province, China, aiming to construct a comprehensive multivariate identiﬁcation system for ecological space under the dual-carbon target based on an analysis of the spatiotemporal distribution characteristics and driving factors of county-level carbon sinks. Furthermore, by analyzing the ecological spatial distribution pattern, carbon sink land structure, and county clustering characteristics, the study explored differential optimization strategies for ecological spaces of different county types to enhance carbon sinks in the ecosystem. The results demonstrated that: (1) From 2000 to 2020, the total carbon sink in Shaanxi Province exhibited an initial increase followed by a decrease, with a decline from 864.39 × 10 4 t to 863.21 × 10 4 t. The county-level distribution of total carbon sink displayed signiﬁcant spatial heterogeneity, with an overall pattern of south > north > central. (2) The interaction among factors enhanced the explanatory power for spatial differentiation of county-level carbon sinks compared to individual factors, exerting an important impact on the spatial distribution pattern of carbon sinks. (3) The distribution of ecological space in Shaanxi Province was highly uneven, with the core ecological space primarily concentrated in the southern and north-central regions. The proportions of low carbon sink (Type I), medium carbon sink (Type II), and high carbon sink (Type III) counties were 35.51%, 18.69%, and 45.80%, respectively. For different types of county-level ecological spaces, this study proposed a differentiated optimization strategy aimed at reducing carbon emissions and enhancing carbon sink. The results will provide theoretical and technical support for regional ecological construction and land spatial optimization, holding signiﬁcant practical implications for achieving the dual-carbon goal and addressing climate change.


Introduction
Global warming has become an indisputable reality, which is mainly attributed to the increase in the concentration of greenhouse gases such as CO 2 caused by human activities [1]. Over the past two decades (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020), the global surface temperature has risen by 1.09 • C compared to the baseline period (1850-1900) [2]. Global warming has posed serious threats to both natural ecosystems and human well-being, including rising of carbon sinks across different regions. Consequently, optimizing ecological space with the aim of increasing carbon sinks remains a challenge. From the perspective of spatial optimization, further exploration is needed to determine how to effectively implement the goal of increasing carbon sinks in specific ecological space units and how to make increasing carbon sinks become the guiding principle of the development of ecological space.
This study focused on 107 districts and counties in Shaanxi Province, considering factors such as ecological diversity, regional representativeness, and data availability. Its primary objective was to construct a comprehensive and multidimensional identification system for ecological space under the dual-carbon target by analyzing the spatiotemporal changes and driving factors of regional carbon sinks. The study aimed to explore the distribution characteristics and underlying mechanisms of ecological space and propose ecological space optimization strategies for different county types. The findings of this study will fill the research gap in the identification and optimization of county-level ecological space under the dual-carbon target, providing technical support for regional ecological development and land space optimization. Moreover, it holds significant practical implications for achieving the dual-carbon goal and addressing climate change.

Study Area
Shaanxi Province is situated in central China (Figure 1), in the middle reaches of the Yellow River, and possesses a significant geographical position and remarkable ecological functions [35]. The terrain exhibits high elevations in the north and south, and lower elevations in the central region. The province is primarily categorized into three main regions: the Loess Plateau of northern Shaanxi, the Weihe plain of Guanzhong, and the Qinba Mountains of southern Shaanxi. These variations in topography, geomorphology, climatic zones, and natural resources result in evident disparities in the economic structure across Shaanxi Province. Northern Shaanxi boasts abundant energy resources, with the energy industry playing a dominant role in its economy. The Guanzhong area possesses the largest economy and showcases a diversified industrial structure, encompassing agriculture, manufacturing, the modern service industry, and the high-tech sector. Southern Shaanxi, on the other hand, is endowed with plentiful natural resources, primarily focusing on mineral resources and eco-tourism. Shaanxi is a major energy province in China, ranking third in coal production and first in oil and gas equivalents. It is worth mentioning that approximately 93% of China's carbon emissions stem from fossil fuel usage.

Data
This study required nine types of data: elevation, population, nighttime light image, road, surface temperature, vegetation index, land use, geological disaster, and administrative boundary. A comprehensive overview of all data is provided in Table 1. The SRTM DEM data has a resolution of 30 m, which was utilized for calculating elevation, slope, relief degree, and aspect indicators. To determine nighttime light intensity, population density, traffic network density, land surface temperature, normalized difference vegetation index (NDVI), and geological disaster point density, the following data sources were employed: NPP-VIIRS-like NTL data [36], WorldPop [37], OpenStreetMap [38], 1-km monthly mean temperature dataset for China [39], MOD13Q1, and geological disaster point data, respectively. The GlobeLand30 data [40], also with a resolution of 30 m, was employed to assess land use intensity and habitat quality index.

Data
This study required nine types of data: elevation, population, nighttime light image, road, surface temperature, vegetation index, land use, geological disaster, and administrative boundary. A comprehensive overview of all data is provided in Table 1. The SRTM DEM data has a resolution of 30 m, which was utilized for calculating elevation, slope, relief degree, and aspect indicators. To determine nighttime light intensity, population density, traffic network density, land surface temperature, normalized difference vegetation index (NDVI), and geological disaster point density, the following data sources were employed: NPP-VIIRS-like NTL data [36], WorldPop [37], OpenStreetMap [38], 1-km monthly mean temperature dataset for China [39], MOD13Q1, and geological disaster point data, respectively. The GlobeLand30 data [40], also with a resolution of 30 m, was employed to assess land use intensity and habitat quality index.

Methodologies
The technical process of this study was divided into three steps ( Figure 2). The first step involved data processing, including county-level carbon sink assessment and the calculation of ecological space indicators. The county-level carbon sink assessment primarily relied on the carbon sink coefficient method to calculate the total carbon sink at the county level in Shaanxi Province from 2000 to 2020. Meanwhile, the calculation of ecological space indicators was mainly based on the methods outlined in Section 3.2 to evaluate different types of indicators. This study examined the inherent functions of ecological patches and Remote Sens. 2023, 15, 4009 5 of 21 considered their relationship with the landscape environment. Existing research foundations [10,12,41] were referenced to determine ecological spatial identification indicators from three perspectives: natural ecosystem attributes, artificial ecosystem attributes, and natural-artificial interaction ecosystem attributes. The characteristic indicators of natural ecosystems included elevation, slope, relief degree, and aspect. Elevation, as a fundamental natural attribute, exerts an influence on climatic conditions, species distribution, and ecological processes. Areas at higher elevations are more likely to undertake ecological functions such as water conservation and providing animal habitat. Slope and relief degree are positively correlated with ecological space, and areas with larger slopes and relief degree are more likely to be part of the ecological space. Additionally, the aspect determines the orientation of solar radiation, which affects the microclimatic conditions of the local ecological spatial distribution. For artificial ecosystems, the characteristic indicators encompassed population density, nighttime light intensity, traffic network density, and surface temperature. Population density represents the distribution and concentration of the population, directly influencing land use patterns and habitat fragmentation. The nighttime lighting data provide better insights into the level of urbanization, economic status, energy consumption, and other human activity factors, reflecting the intensity and scope of human activities. Moreover, traffic network density indicates the intensity of urban traffic infrastructure construction and influences landscape connectivity. Surface temperature can reflect the intensity of the urban heat island effect, affecting the local climate and ecological conditions of the region. As for natural-artificial interaction ecosystems, the characteristic indicators consisted of NDVI, land use intensity, geological disaster point density, and habitat quality. NDVI effectively reflects the health and density of vegetation, where higher values suggest a higher likelihood of becoming an ecological space. Meanwhile, land use intensity refers to the degree and intensity of human utilization of existing land, and it can reflect potential ecological disturbance areas. Geological disasters are influenced by both natural geological factors and human activities and are prone to potential destruction of ecological processes. Lastly, habitat quality indicates the relationship between patches and their surrounding environment, reflecting the degree of disturbance they experience. Areas with better habitat quality often hold higher ecological value and have greater significance for protection. The second step involved constructing a county-level ecological spatial identification system under the dual-carbon target. Based on the analysis of the spatiotemporal changes in carbon sinks in Shaanxi Province, the geographical detector (Geodetector) was used to explore the driving factors of carbon sink spatial differentiation at the county level. The second step involved constructing a county-level ecological spatial identification system under the dual-carbon target. Based on the analysis of the spatiotemporal changes in carbon sinks in Shaanxi Province, the geographical detector (Geodetector) was used to explore the driving factors of carbon sink spatial differentiation at the county level. Subsequently, ecological space identification indicators under the dual-carbon target were selected, and a geographical weighted overlay operation was performed after assigning index weights using the analytic hierarchy process (AHP) method.
The third step focused on studying the classification and optimization strategies of county-level ecological space. Initially, the ecological space was classified into different levels using the natural breaks classification (NBC) method, allowing for an analysis of their distribution characteristics and land use structure across various types. Subsequently, the K-means method was employed to conduct cluster analysis on the county's ecological space. Finally, tailored optimization strategies were proposed, taking into account the unique characteristics exhibited by different types of county-level ecological spaces.

Carbon Sink Coefficient Method
The carbon sink estimation model is constructed based on different land use types and their corresponding carbon sink coefficients [42]. The estimation of carbon sinks in land use primarily involves cultivated land, forest, grassland, shrubland, wetland, water, and bare land. As cultivated land acts as a carbon source [43], it is not investigated in this study. The carbon sink coefficients for different land use types are determined based on existing literature, as shown in Table 2. The carbon sink estimation model can be expressed as follows: where C t represents the total amount of carbon sink, A i is the area of land use type i, and S i represents the carbon sink coefficient of land use type i. Based on the GlobeLand30 data, this study utilized the Zonal Statistics tool in ArcGIS 10.3 software to calculate the area of different land use types (forest, grassland, shrubland, wetland, water, and bare land) in each county. Subsequently, the Field Calculator tool was used to estimate the total carbon sink in each county.  Table 3 presents the calculation methods for ecological space identification indicators. The computation of certain indicators involved the utilization of the Google Earth Engine (GEE) cloud platform [48]. The platform facilitates online visualization, computation, and analysis of extensive global-scale Earth science data, thereby significantly enhancing the efficiency of indicator calculation.

Geodetector
Geodetector is a set of statistical methods for detecting spatial heterogeneity and explaining the underlying driving forces, including the factor detector, the interaction detector, the risk detector, and the ecological detector [49]. Geodetector can assess spatial heterogeneity, detect explanatory factors, and analyze the interactions between variables, and has been widely applied in various fields such as natural and social sciences [50].
The factor detector is used to explore the spatial heterogeneity of variable Y and quantify the extent to which factor X explains the spatial heterogeneity of Y, measured by the q value. The formula for q is as follows: where L represents the stratification of variable Y or factor X, i.e., classification or zoning; h is the number of classifications or partitions of Y or factor X; N h and N are the number of units in class h and the entire region, respectively; σ 2 h and σ 2 are the variances of variable Y in class h and the entire region, respectively; and SSW and SST respectively represent the within sum of squares and the total sum of squares. The q value ranges from 0 to 1, where a higher value indicates a more pronounced spatial heterogeneity of variable Y. If h is generated by factor X, a larger q value indicates a stronger explanatory power of factor X on variable Y, whereas a smaller q value indicates a weaker explanatory power.
The interaction detector is used to assess the interaction effects between factors X i and X j , reflecting whether the explanatory power of variable Y under the joint influence of these two factors is enhanced, weakened, or independent. The interaction detector typically involves calculating the explanatory power measures q(X 1 ) and q(X 2 ) for the two influencing factors X i and X j on attribute Y, and then calculating the value of q(X 1 ∩ X 2 ) for their interaction. By comparing q(X 1 ), q(X 2 ), and q(X 1 ∩ X 2 ), five possible cases can be identified (Table 4). Table 3. Calculation methods of ecological space identification indicators.

Ecosystem Type Indicator Calculation Method
Natural ecosystem The SRTM DEM data (ee.Image('USGS/SRTMGL1_003')) was acquired from the GEE platform, and subsequently, the elevation data for the study area were obtained using the clipping function (ee.Image.clip()).

Slope (I 2 )
Based on the elevation data of the study area, the slope was calculated using the slope function (ee.Terrain.slope()) of the GEE platform.

Relief degree (I 3 )
The formula for relief degree is as follows: where RDLS is the relief degree, ALT represents the average elevation within the region, H max and H min refer to the relative elevation within the designated area, P(A) represents the flat area within the designated area, A is the total area of the designated region, and 500 represents the reference elevation value for Chinese mountains.

Aspect (I 4 )
Based on the elevation data of the study area, the aspect was calculated using the aspect function (ee.Terrain.aspect()) of the GEE platform. Table 3. Cont.

Ecosystem Type Indicator Calculation Method
Artificial ecosystem Population density (II 1 ) The WorldPop data were acquired from the GEE platform (ee.ImageCollection('WorldPop/GP/100m/pop')), and then the population density data of the study area were obtained using the clipping function (ee.Image.clip()).

Nighttime light intensity (II 2 )
Based on NPP-VIIRS-like NTL data, the Extract by Mask tool in ArcGIS 10.3 software was utilized to obtain the nighttime light intensity of the study area.

Traffic network density (II 3 )
Based on the OpenStreetMap data of the study area, the traffic network density was calculated using the Line Density tool in ArcGIS 10.3 software (Esri, Redlands, California, USA).

Surface temperature (II 4 )
Based on the 1-km monthly mean temperature dataset for China in the study area, the annual average temperature was calculated using the Raster Calculator tool in ArcGIS 10.3 software (Esri, Redlands, California, USA).
Natural-artificial interaction ecosystem Based on the MOD13Q1 data (ee.ImageCollection("MODIS/006/MOD13Q1")) of the study area, the annual average temperature was computed using the mean function (ee.Reducer.mean()) of the GEE platform.

Land use intensity (III 2 )
The formula for land use intensity is as follows: where I is land use intensity, L i represents the land use intensity level of land use type i, and P i represents the proportion of land type i in the total area. Based on the existing research results [51], the land use intensity levels are assigned as follows: bare land has a level of 1; forest, grassland, shrubland, wetland, and water have a level of 2; cultivated land has a level of 3; and construction land has a level of 4.
Habitat quality (III 3 ) Based on the land use data of the study area and referring to existing research results [52], the habitat quality was calculated using the InVEST model.

Geological disaster point density (III 4 )
Based on the geological disaster point data of the study area, the geological hazard point density was calculated using the Kernel Density tool in ArcGIS 10.3 software. Table 4. Judgment basis of the interaction detector.

Comparison Interaction
Single factor nonlinear weakening Nonlinear enhancement

K-means Clustering
K-means clustering is both a representative partition based clustering algorithm and an unsupervised learning algorithm [53]. The core idea of the K-means algorithm is as follows: Firstly, randomly select k initial cluster centers C i (i ≤ 1 ≤ k) from the dataset. Then, calculate the Euclidean distance between the remaining data objects and the cluster centers C i , and assign each data object to the cluster center C i that is closest to it. Finally, compute the average value of the data objects in each cluster as the new cluster center and proceed to the next iteration. The algorithm stops when the cluster centers no longer change or when the maximum number of iterations is reached. The Euclidean distance between data objects and cluster centers in the spatial domain is calculated using the following formula: where X represents the data objects, C i is the i-th clustering center, m represents the dimensionality of the data objects, and X j , C ij represent the j-th attribute values of X and C i , respectively. The formula for calculating the sum of squared errors (SSE) for the entire dataset is as follows: where the size of SSE indicates the quality of the clustering results, and k represents the number of clusters.

Spatiotemporal Analysis of the Total Amount of Carbon Sink in Counties of Shaanxi Province
The total carbon sink in each county of Shaanxi Province from 2000 to 2020 was estimated using the carbon sink coefficient method. Figure 3 illustrates the total amount of carbon sink in Shaanxi Province and the proportion of carbon sinks in different land use types from 2000 to 2020. The figure reveals an initial increase followed by a subsequent decrease in total amount of carbon sink, with levels declining from 864.39 × 10 4 t to 863.21 × 10 4 t. Forest carbon sink represented the primary form, accounting for over 90% of the total, followed by grassland, water, shrubland, wetland, and bare land. From 2000 to 2020, the proportionate composition of carbon sink among different land use types remained relatively stable, although exhibiting slight variations in their evolutionary trends. Forest and water exhibited an increasing trend in their carbon sink proportions, whereas shrubland initially increased and then decreased. Conversely, grassland, wetland, and bare land demonstrated a decreasing trend in their respective carbon sink proportions. Due to the limited carbon sink capacity of bare land, the proportion of carbon sink was negligibly small, approaching zero. The spatial distribution pattern of carbon sink in the counties of Shaanxi Provin from 2000 to 2020 (Figure 4a-c) revealed significant spatial heterogeneity in the tot carbon sink. The overall pattern indicated a higher carbon sink in the southern region followed by the northern and central regions, while the temporal changes exhibited le pronounced characteristics. The areas with high carbon sink were primarily concentrate in southern (Ankang City, Hanzhong City, and Shangluo City) and north-central Shaan (Yan'an City). Conversely, the areas with low carbon sink were predominantly located the Guanzhong area (Xianyang City, Weinan City, and northern Xi'an) and souther Yulin. The spatial distribution pattern of carbon sink in the counties of Shaanxi Province from 2000 to 2020 (Figure 4a-c) revealed significant spatial heterogeneity in the total carbon sink. The overall pattern indicated a higher carbon sink in the southern regions followed by the northern and central regions, while the temporal changes exhibited less pronounced characteristics. The areas with high carbon sink were primarily concentrated in southern (Ankang City, Hanzhong City, and Shangluo City) and north-central Shaanxi (Yan'an City). Conversely, the areas with low carbon sink were predominantly located in the Guanzhong area (Xianyang City, Weinan City, and northern Xi'an) and southern Yulin. followed by the northern and central regions, while the temporal changes exhibited less pronounced characteristics. The areas with high carbon sink were primarily concentrated in southern (Ankang City, Hanzhong City, and Shangluo City) and north-central Shaanxi (Yan'an City). Conversely, the areas with low carbon sink were predominantly located in the Guanzhong area (Xianyang City, Weinan City, and northern Xi'an) and southern Yulin.  The spatial distribution of cold and hot spots in total county-level carbon sink in Shaanxi Province from 2000 to 2020 exhibited consistency (Figure 4d), indicating a stable state of spatial aggregation and overall distribution. The hot spots of total carbon sink were concentrated and contiguous in Ankang, Hanzhong, Shangluo, the southern region The spatial distribution of cold and hot spots in total county-level carbon sink in Shaanxi Province from 2000 to 2020 exhibited consistency (Figure 4d), indicating a stable state of spatial aggregation and overall distribution. The hot spots of total carbon sink were concentrated and contiguous in Ankang, Hanzhong, Shangluo, the southern region of Baoji, and the southern region of Yan'an, representing areas of high ecological space density. On the other hand, the cold spots were primarily distributed in the southern region of Weinan, the northern region of Xi'an, and the northern region of Xianyang, with sporadic distribution in the southeastern part of Yulin. These cold spot areas were significantly influenced by urban development and human activities.

Construction of County-Level Ecological Space Identification System under the Dual-Carbon Target
To elucidate the driving mechanism behind the spatial differentiation of total carbon sink in counties within Shaanxi Province and identify key factors associated with natural, artificial, and natural-artificial interactive ecosystems, we conducted an analysis using the factor detector and the interaction detector of Geodetector. The factor detector results provide insights into the explanatory power of each factor in the spatial differentiation of total carbon sink in the counties, with q-values representing the explanatory power and p-values indicating significance. By analyzing the factor detector results (Figure 5a), we observed the following order of explanatory power for each factor in relation to the spatial differentiation of total carbon sink in Shaanxi Province: land use intensity (III 2 ) > habitat quality (III 3 ) > NDVI (III 1 ) > slope (I 2 ) > nighttime light intensity (II 2 ) > traffic network density (II 3 ) > population density (II 1 ) > relief degree (I 3 ) > elevation (I 1 ) > surface temperature (II 4 ) > density of geological disaster points (III 4 ) > aspect (I 4 ). The q-values of four factors, namely land use intensity, habitat quality, NDVI, and slope, exceeded 0.6, indicating their significant impact on the spatial distribution pattern of total carbon sink in the counties. On the other hand, the q-values of density of geological disaster points and aspect were below 0.15, with p-values exceeding 0.05 (geological disaster point density p-value: 0.056, aspect p-value: 0.209, and p-values of other factors: 0). Therefore, these two factors had a limited influence on the spatial differentiation of total carbon sink and were excluded from the construction of the county-level comprehensive identification system for ecological spaces under the dual-carbon target. The interaction detector enables the exploration of the combined effects of differe types of factors, facilitating further investigation into the driving mechanisms of spat differentiation in county-level total carbon sink. Analyzing the interactive detecti results (Figure 5b), it was observed that all factor interactions exhibited either biline The interaction detector enables the exploration of the combined effects of different types of factors, facilitating further investigation into the driving mechanisms of spatial differentiation in county-level total carbon sink. Analyzing the interactive detection results (Figure 5b), it was observed that all factor interactions exhibited either bilinear enhancement or nonlinear enhancement, with no instances of mutual independence or weakening. The q-values for interactions between different types of factors were significantly higher than those for single factors. The q-values of the majority of interactions between factors were greater than 0.6, accounting for over 80%. Particularly, the interaction of land use intensity, habitat quality, and NDVI with other factors demonstrated a significant explanatory power for the spatial differentiation of total carbon sink in counties, with an average q-value surpassing 0.8. The results indicate that the interaction among different factors affects the spatial distribution of total carbon sink in counties.
In conclusion, in the construction of the county-level ecological space multivariate comprehensive identification system under the dual-carbon target, the factors of aspect and geological disaster point density, which had low influence on the spatial differentiation of total carbon sink, were excluded. Additionally, the land use intensity with low spatial attribute in ecological space identification was eliminated. To incorporate the elements of carbon sink into the ecological space identification, the carbon sink intensity index was introduced. The index represents the carbon sink capacity per unit land area [54]. Referring to existing studies on index weight allocation [55,56], the AHP method was employed to assign weights to each index. To comprehensively summarize the influence of various factors on ecological space identification under the dual-carbon target, the method of gradient hierarchical assignment was adopted for each single factor. The final indicators were divided into 10 grades based on the direction and degree of influence using the NBC method. Geographically weighted superposition was then performed based on the weight of each index to obtain the recognition results. Higher values in each grid indicate greater importance of the ecological space under the dual-carbon target. Table 5 presents the indicators and weights of the county-level ecological space identification system under the dual-carbon target. It should be noted that, during the process of ecological space identification, the indicators for artificial ecosystem, natural-artificial interaction ecosystem, and carbon sink element need to utilize data from the same year.

Analysis of County-Level Ecological Space Distribution Characteristics under the Dual-Carbon Target
The ecological space of Shaanxi Province in 2020 was identified using the ecological space identification system under the dual-carbon target as outlined in Table 5. Based on the existing research findings on ecological regionalization delineation [57,58], the ecological space of Shaanxi Province was classified into four categories using the NBC method [59,60]: non-ecological space, baseline ecological space, auxiliary ecological space, and core ecological space (Figure 6a and Table 6).
The ecological space of Shaanxi Province in 2020 was identified using the ecologi space identification system under the dual-carbon target as outlined in Table 5. Based the existing research findings on ecological regionalization delineation [57,58], t ecological space of Shaanxi Province was classified into four categories using the NB method [59,60]: non-ecological space, baseline ecological space, auxiliary ecological spa and core ecological space (Figure 6a and Table 6).    The core ecological space encompassed high-intensity patches (8.14-9.91), covering an area of approximately 846.88 km 2 , accounting for 41.48% of Shaanxi Province's total area and 58.40% of its total ecological space area. This ecological space was predominantly characterized by forest, primarily distributed in the Qinba Mountains in southern Shaanxi and the Loess Plateau in the north-central region (including Ziwuling Mountain and Huanglong Mountain in the southern part of Yan'an City). Among the three types of ecological space, the core ecological space held paramount importance as it exhibited extensive distribution and possessed a robust carbon sink capacity. It served as a critical area for ecological protection. The Qinba Mountain area, with its well-developed water system, abundant runoff resources, and high forest coverage, plays a pivotal role as an ecological barrier in China. It fulfills significant functions such as biodiversity conservation and water resource preservation. Ziwuling Mountain and Huanglong Mountain exhibit similar land use patterns to the Qinba Mountain area, with higher vegetation coverage and noticeably stronger carbon sink capacity compared to northern Shaanxi and Guanzhong. However, the continuous encroachment of human activities has resulted in the gradual reduction of this space, and artificial planting practices have led to excessive regularization within certain areas, diminishing its ability to radiate to surrounding regions.
The auxiliary ecological space comprised patches of medium intensity (5.97-8.14), covering an area of approximately 132.66 km 2 , which accounted for 6.50% of the total area of Shaanxi Province and 9.15% of the total ecological space area. This type of ecological space included land types such as grassland, water, wetland, forest, and others. It was primarily distributed surrounding the core ecological space and served as a buffer zone between the core ecological space and the baseline ecological space. Among the three types of ecological space, the auxiliary ecological space had the smallest distribution area, and its ecological function and carbon sink capacity were moderate. However, due to a lack of connectivity, the auxiliary ecological space was characterized by a fragmented and isolated distribution pattern.
The baseline ecological space comprised patches of low intensity (4.10-5.97), covering an area of approximately 470.64 km 2 . It accounted for 23.05% of the total area of Shaanxi Province and 32.45% of the total ecological space area. Grassland was the predominant land use type in this ecological space, distributed extensively across Shaanxi Province, with the highest density observed in the Loess Plateau of northern Shaanxi. The Loess Plateau holds strategic significance for soil and water conservation, playing a vital role in the ecological protection, high-quality development, and ecological security of the Yellow River basin. However, the Loess Plateau falls within the continental monsoon climate region, characterized by arid conditions and limited rainfall, primarily consisting of mountains, hills, and ravines, with undulating topography and severe soil erosion, rendering the ecological environment fragile. This category of space represented a moderate distribution area among the three types of ecological spaces, providing residents with various functions, including leisure, entertainment, tourism, and sightseeing. The ecological functionality and carbon sink capacity of the baseline ecological space were weakened due to the influences of county-level economic development, urban expansion, and its own land use structure.
The non-ecological space (1.39-4.10) covered an area of approximately 591.61 km 2 , accounting for 28.98% of the total area of Shaanxi Province. The primary land use types in non-ecological space were construction land and cultivated land, which were distributed throughout Shaanxi Province, with a particular concentration in the Guanzhong urban agglomeration.

Optimization Strategies for Ecological Space in Different Types of Counties
As a crucial component of optimizing the national ecological space system, county ecological space assumes a significant role, not only accommodating the planning patterns from higher authorities but also guiding the practical implementation at the subordinate level [10]. One of the fundamental keys to achieving the dual-carbon goal lies in the comprehensive improvement and optimization of ecological space, thus facilitating the establishment of ecological civilization and sustainable development [61]. The enhancement of ecosystem carbon sink capacity is an effective approach to achieving the dual-carbon target [62]. Existing ecological space optimization strategies primarily focus on multidimensional analyses of natural entities, ecosystem services, ecological security patterns, and ecological functions, while neglecting carbon sink elements and lacking research at the county level [15,[28][29][30]. Shaanxi Province exhibits notable spatial discrepancies in terms of geographical characteristics, economic structure, and ecological patterns [63]. To achieve the dual-carbon target in different county-level regions, a comprehensive analysis of the ecological spatial structure, carbon sink land use types, and spatiotemporal variations in carbon sink across various county types is essential. Targeted and scientifically rational strategies for emission reduction and carbon sink enhancement should be explored from the perspectives of urban development boundary control, ecological space transformation, land use structure optimization, carbon sink compensation mechanisms, and industrial structure adjustment.
Based on the ecological space zoning results of Shaanxi Province under the dualcarbon target, the data were normalized using the range normalization method, and the K-means clustering method was employed for county classification. The K-means clustering method ensured the closest proportion of ecological space types among different counties, exhibiting the highest level of similarity [64]. According to the clustering results, the counties in Shaanxi Province can be classified into three types: low carbon sink (Type I), medium carbon sink (Type II), and high carbon sink (Type III) (Figures 6b and 7 and Table 7). and scientifically rational strategies for emission reduction and carbon sink enhancem should be explored from the perspectives of urban development boundary cont ecological space transformation, land use structure optimization, carbon s compensation mechanisms, and industrial structure adjustment.
Based on the ecological space zoning results of Shaanxi Province under the du carbon target, the data were normalized using the range normalization method, and K-means clustering method was employed for county classification. The K-mea clustering method ensured the closest proportion of ecological space types amo different counties, exhibiting the highest level of similarity [64]. According to clustering results, the counties in Shaanxi Province can be classified into three types: l carbon sink (Type I), medium carbon sink (Type II), and high carbon sink (Type (Figures 6b and 7 and Table 7).    Type I counties were characterized by a dominant presence of non-ecological space and baseline ecological space, with a minimal amount of auxiliary and core ecological space. The proportions of different ecological space types in terms of area followed the order of non-ecological space (73.65%) > baseline ecological space (18.69%) > core ecological space (6.03%) > auxiliary ecological space (1.63%). These counties were numerous and concentrated, especially in the Guanzhong urban agglomeration with dense population and developed economy. The unregulated expansion of construction land has a substantial negative impact on county-level carbon sink [65]. However, they exhibited the smallest total ecological space under the dual-carbon target, with non-ecological space occupying the highest proportion. In southern Shaanxi, only Hantai District belonged to the category of type I counties. The carbon sink land within type I counties primarily comprised grassland, bare land, and other types with limited carbon sink capacity. During the transition to the industrialization stage of economic development, the leading factors driving land use change are the market dynamics of land products or services and the comparative benefits of different land uses. Consequently, land is redirected towards secondary and tertiary industries that offer higher efficiency. This process has resulted in a rapid decline in ecological land, bare land, and agricultural land, leading to varying degrees of carbon sink reduction. To improve the quantity and quality of ecological space in Type I counties, it is necessary to focus on urban development boundary control, ecological space transformation, and the establishment of mechanisms for ecological carbon sink compensation (Table 8). Table 8. Optimization strategies for ecological space in different types of counties.

County Type Optimization Strategies
Low carbon sink (Type I) Adhere to urban development boundaries and establish priority areas for enhancing the quality and efficiency of carbon sink. Promote the transformation of non-ecological space and baseline ecological space into auxiliary and core ecological space. Improve the compensation and trading mechanisms for ecological carbon sink and enhance public participation awareness.

Medium carbon sink (Type II)
Establish ecological corridors to enhance ecological space connectivity. Optimize land use structure to promote land conservation and intensive utilization. Guide industrial layout in a rational manner to promote green and low-carbon development.
High carbon sink (Type III) Implement strict land use regulations to prevent the conversion of core ecological space into non-ecological space.
Optimize land management mechanisms to maintain and strengthen the carbon sink capacity of existing carbon sink land types. Make rational use of carbon sink resources and encourage and support the development of carbon sink industries.
In comparison to the other two types of counties, type II counties exhibited a more balanced distribution of ecological and non-ecological spaces. The proportions of different space types in terms of area followed the order of baseline ecological space (52.33%) > non-ecological space (33.19%) > core ecological space (7.44%) > auxiliary ecological space (7.04%). The number of counties falling under this category was the smallest, accounting for 18.69% of the total, and they were mainly distributed in the energy-rich Loess Plateau region of northern Shaanxi. However, these counties faced challenges such as landscape fragmentation and limited ecological connectivity. In recent years, the quantity and quality of carbon sink land in these counties have been declining due to factors like economic development, urban expansion, and energy exploitation. Therefore, it is essential to optimize the ecological space of type II counties under the dual-carbon target through initiatives such as ecological corridor construction, land use structure optimization, and industrial layout adjustment (Table 8).
Type III counties exhibited the characteristics of a large quantity and concentrated distribution, with the core ecological space accounting for 69.79% of the total area. The order of the proportion of different space types in terms of area was as follows: core ecological space (69.79%) > baseline ecological space (11.55%) > non-ecological space (10.61%) > auxiliary ecological space (8.05%). These counties were primarily located in the Qinba Mountains in southern Shaanxi and the Loess Plateau in the north-central part of Shaanxi Province. Type III counties had a larger original area of carbon sink land, mainly comprising forest, wetland, and other types with a high carbon sink coefficient. However, due to factors such as county economic development and urban expansion, most counties experienced a continuous decrease in total carbon sink from 2000 to 2020, particularly in Taibai County, Linyou County, and Zhenba County. To enhance the regional carbon sink capacity in such counties, attention should be given to three aspects: the implementation of land use regulations, the optimization of land management mechanisms, and the utilization of carbon sink resources (Table 8).

Advantages and Limitations of Research Methods
Ecological space identification is a prerequisite and foundation for optimization and control research, with significant practical implications for rational urban spatial planning, achieving sustainable development, and safeguarding the ecological environment [10,22,23]. The traditional approach of directly using imagery to identify ecological spaces suffers from issues of inconsistent standards and reliance on subjective judgments [24,25]. The conventional comprehensive multi-factor grading method primarily considers the functional attributes of ecological patches themselves when selecting ecological spatial indicators, neglecting the spatial structural significance of ecological patches within the entire landscape and their relationship with the surrounding environment [12,28]. In this study, a multivariate identification method for ecological space under the dual-carbon target was proposed, which started with the intrinsic functions of ecological patches, considered the patch-landscape environment relationship, and determined ecological space identification indicators from three perspectives: natural ecosystem attributes, artificial ecosystem attributes, and natural-artificial interaction ecosystem attributes. Furthermore, the impact of carbon sink factors on ecological space was taken into account, and carbon sink intensity was incorporated into the ecological space identification system. This research method comprehensively and objectively reflected the distribution characteristics of ecological spaces in the study area under the dual-carbon target, thereby establishing the groundwork for subsequent differentiated policy development for different county types. Compared to the "double evaluation" approach in national spatial planning [66,67], which primarily focused on a comprehensive assessment of land resources and environmental carrying capacity, the methodology employed in this research delved deeply into the underlying mechanisms of spatial differentiation in carbon sinks. It underscored the carbon sink attribute of ecological space identification indicators. Additionally, targeted optimization strategies were proposed for diverse county-level ecological spaces, offering valuable insights for achieving regional dual-carbon goals. However, the research methods still have certain limitations, such as the need to consider additional indicators (e.g., forest, water) in the ecological space identification system that reflect the spatial structure importance of ecological patches within the landscape and their relationship with the surrounding environment. Future research should focus on further improving the identification methods of ecological spaces under the dual-carbon target.

Conclusions
Based on the carbon sink coefficient method and Geodetector, this study analyzed the spatiotemporal distribution characteristics and driving factors of county-level carbon sinks in Shaanxi Province from 2000 to 2020. Ecological space identification indexes were selected based on three aspects: natural ecosystem attributes, artificial ecosystem attributes, and natural-artificial interaction ecosystem attributes, thereby proposing a multidimensional identification method for county-level ecological space under the dual-carbon target. By analyzing the distribution characteristics, land use structure, and county clustering characteristics of core, auxiliary, baseline, and non-ecological spaces, differentiated ecological space optimization strategies were explored for different types of counties. The results showed that: (1) From 2000 to 2020, the total carbon sink in Shaanxi Province exhibited an initial increase followed by a decrease, with carbon sink decreasing from 864.39 × 10 4 t to 863.21 × 10 4 t. Furthermore, there was significant spatial heterogeneity in the total carbon sink across the counties, displaying an overall pattern of south > north > middle. (2) The factor detector identified that land use intensity, habitat quality, NDVI, and slope all had q-values exceeding 0.6, indicating their substantial influence on the spatial distribution pattern of total carbon sink at the county level. The interaction between these factors enhanced the explanatory power for the spatial differentiation of total carbon sink in the counties to varying degrees compared to the individual factors. (3) The distribution of ecological space in Shaanxi Province was extremely uneven, and the core ecological space was mainly distributed in the Qinba Mountains in the south, and Ziwuling and Huang-long Mountains in the north-central region. The proportion of counties classified as low carbon sink (Type I), medium carbon sink (Type II), and high carbon sink (Type III) was 35.51%, 18.69%, and 45.80%, respectively. Based on the characteristics of ecological space in different county types, this study proposed tailored optimization strategies to enhance carbon sinks in the ecosystem. The results will provide valuable insights and strategies for optimizing county-level ecological space under the dual-carbon target, with important practical implications for regional land space optimization, carbon emissions reduction, and carbon sink enhancement.   Table 1 presents the download links for all publicly available datasets utilized in this study.