Analysis and prediction of carbon balance in production-living-ecological space of Henan Province, China

As the carrier of human economic activities, the change of territorial space affects the level of regional carbon balance. Therefore, with regional carbon balance as the goal, this paper proposed a framework from the perspective of production-living-ecological space and took Henan Province of China as a study area for empirical research. First, the study area established an accounting inventory that considers nature, society, and economic activities to calculate carbon sequestration/emission. Then, the spatiotemporal pattern of carbon balance was analyzed by ArcGIS from 1995 to 2015. Later, the CA-MCE-Markov model was used to simulate the production-living-ecological space pattern in 2035, and carbon balance in three future scenarios was predicted. The study showed that from 1995 to 2015, the living space gradually expanded, and the aggregation rose while the production space decreased. Carbon sequestration (CS) was less than carbon emission (CE) and presented an unbalanced state of negative income in 1995, while CS exceeded CE and showed a positive income imbalance in 2015. In 2035, living space has the highest carbon emission capacity under natural change scenario (NC), while ecological space has the highest carbon sequestration capacity under ecological protection scenario (EP), and production space has the highest carbon sequestration capacity under food security scenario (FS). The results are crucial for understanding the carbon balance changes in territorial space and supporting regional carbon balance goals in the future.


Introduction
The latest Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) demonstrated that total net anthropogenic GHG emissions have continued to rise from 2010 to 2019 (IPCC 2022a). Human-induced climate change events, such as extreme heat, heavy precipitation, drought, and fire, are becoming more frequent and intense and have caused widespread adverse impacts and related losses and damages to nature and people, beyond natural climate variability (IPCC 2022b). Hence, it has increasingly become the world consensus to mitigate climate change and promote sustainable development (Xia and Yang 2022). At the 75th Session of the General Assembly of the United Nations in 2020, China made a solemn commitment to peak its carbon dioxide (CO 2 ) emissions by 2030 and achieve carbon neutrality by 2060 .
The impact of carbon on climate change depends not only on carbon emissions but also on carbon sequestration (Sahle et al. 2018). Terrestrial ecosystems are potentially major carbon stocks that offset anthropogenic carbon emissions (Lai et al. 2016) and could absorb about 30% of anthropogenic CO 2 emissions (Keenan et al. 2016). Quantifying ecosystems' carbon balance is necessary to assess the magnitude of carbon sinks and reduce CO 2 emissions (Piao et al. 2009). With the increasing scientific and political interest in terrestrial carbon dynamics (McGuire et al. 2001), there is a solid impetus to better understand the carbon balance (Houghton 2007). It is significant to analyze the carbon balance for China to achieve carbon neutrality, promote sustainable development goals (SDGs), and explore management policies and strategies in territorial spatial planning under climate change and land use change (Huang et al. 2021;Wang et al. 2021;Li et al. 2021).
Research scales of terrestrial ecosystem carbon balance range from global (Cramer et al. 2001), continental (Piao et al. 2011), national (Li et al. 2021) to regional (Zhao et al. 2012), and local scales (Cao and Yuan 2019). Based on the widely accepted methodology of IPCC national greenhouse gas inventory guidelines, some researchers established the carbon budget accounting framework to calculate and analyze carbon sources and sinks (Han et al. 2017). Process-based terrestrial ecosystem models have also been appointed as valuable tools for understanding the terrestrial carbon cycle and predicting ecosystem net primary productivity (NPP) and net ecosystem productivity (NEP) (Piao et al. 2011). Therefore, some studies analyzed the regional carbon balance according to the comparison between the change in carbon storage and the difference between carbon input and output (NEP) (Zhao et al. 2012;Li et al. 2021). Other studies used emission coefficients to estimate carbon sequestration and emissions of different land use types and used net carbon sequestration/emissions to reflect carbon balance Ghosh et al. 2022).
Territorial space is the home for human survival and development (Huang et al. 2017). The change of its utilization is one of the main ways for humans to change the biomass production of the terrestrial ecosystem and affect the carbon cycle process between terrestrial ecosystems and the atmosphere (IPCC 2000;Lai et al. 2016). Carbon sequestration and emission under different land-use types and their changes are the mainstream research contents (Pan et al. 2004;Van Minnen et al. 2009;Hutyra et al. 2011;Guttikunda and Calori 2013;Cui et al. 2020). In the context of ecological civilization, a new classification of productionliving-ecological space appears in territorial space classification according to the National Land Planning Outline (2016)(2017)(2018)(2019)(2020)(2021)(2022)(2023)(2024)(2025)(2026)(2027)(2028)(2029)(2030) in China (Huang et al. 2017). Competition for production, ecological, and living space exists in the process of regional development . However, the optimal allocation and coordinated development of production-living-ecological space can realize the sustainable utilization of land resources ) and help achieve the carbon peak and carbon neutrality (Chen et al. 2021). It is necessary to analyze the regional carbon balance from the perspective of production-living-ecological space, enhance the understanding of carbon sequestration and carbon emission under the planning and utilization of different scales of territorial space, and help realize the carbon commitment of China.
Future carbon simulation is another focus of carbon sequestration and emission research, which can reflect possible regional carbon dynamics (Cui et al. 2020), and is crucial for the effective formulation of low-carbon development policies (Madlener and Sunak 2011;Xu et al. 2015). Current carbon projections mainly concentrate on future carbon sequestration or carbon emissions (Liang et al. 2021), lacking carbon balance simulation that comprehensive carbon sequestration and carbon emission. In addition, due to the limitations of data availability and estimation methods, these studies usually use regression analysis to predict future carbon quantity rather than spatial simulation (Du et al. 2013). And other studies simulate carbon emissions using network models supported by high aggregation data, so they provide a region-level carbon emission without specific analysis of location or people activities He et al. 2020a, b). Since scenarios could be combined with particular future goals and provided useful directional information for decision-makers (Sandhu et al. 2018), some papers set scenarios to simulate carbon emissions and sequestration based on future development Liu et al. 2019). Therefore, based on the comprehensive calculation of carbon sequestration and carbon emissions, the future carbon balance analysis using the scenario simulation method can satisfy the prediction of future carbon balance from the perspective of spatial layout. This is an effective complement to the current research gap.
In conclusion, from the perspective of production-livingecological space, this study analyzed and predicted the state of regional carbon balance and put forward directional suggestions for the territorial space optimization aiming at carbon balance, which has reference significance for the realization of the carbon peak and carbon neutrality goal and the optimal layout of territorial space in the future. Specifically, Henan Province, one of the major grain-producing areas in China, was taken as the research area. First, a comprehensive carbon sequestration and emission accounting inventory for production-living-ecological space was constructed. Second, the changes in carbon balance during 1995-2015 were analyzed from the perspective of quantitative and spatial. Then, the carbon balance of production-life-ecological space in 2035 was predicted under three different scenarios. In addition, the carbon accounting results were verified and the driving factors of carbon balance were detected. This paper could expand the boundary of carbon balance research and point out the direction of national space development.

Study area
Henan province is located in the middle and lower reaches of the Yellow River in the south of the North China Plain, between 31° 23′-36° 22′ N and 110° 21′-116° 39′ E. It has jurisdiction over 17 prefecture-level cities and one provincial county-level administrative unit Jiyuan (Fig. 1). Henan is one of the largest agricultural provinces and the most extensive grain conversion and processing province in China (Wei 2019). Henan Province also has a large population with abundant labor resources and a huge consumer market. In 2020, the permanent resident population was 9,365,519, with males accounting for 50.15% and females for 49.85%. Among them, 55.43% live in cities and towns. Henan enjoys rapid economic development. Its economic aggregate ranks fifth in China and first in central and western provinces, with a GDP of 5,499.707 billion yuan in 2020.
The terrain of Henan is high in the west and low in the east, with Taihang, Funiu, Tongbai, and Dabie Mountains distribution along the provincial boundary. Besides, the Huang-Huai-Hai alluvial plain is in the east, and Nanyang Basin is in the southwest. In the recent ten years, the average annual temperature has been 12.9-16.5 °C, and the average annual precipitation is 464.2-1193.2 mm. The province's total shallow groundwater resources are 20.53 billion m 3 , of which freshwater accounts for 97% and salty water for 3%. Under the influence of the warm temperate zone and north subtropical monsoon climate, zonal brown soil and yellow-brown soil are formed, and the soil types are mainly tidal soil, brown soil, and yellow-brown soil.

Land use data
Land use maps of Henan Province with the 1 km resolution in 1995, 2005, and 2015 were obtained from the Resources and Environmental Science and Data Center of the Chinese Academy of Sciences (RESDC) (https:// www. resdc. cn/). Among them, are six land use types: arable land, forest, grassland, water, built-up land, and unused land. The complete accuracy of the RESDC data is more than 90% (Ning et al. 2018), making it one of the most reliable land use data sources in China.

Carbon emission data
The carbon emission factor data for each land category were obtained from relevant literature, Provincial guidelines for GHG, and IPCC Guidelines for national greenhouse gas Inventories. In addition, the economic output of crops, chemical fertilizer, pesticides, agricultural film, diesel use, and irrigation area, the consumption of various energy sources, the output of industrial goods, and the number of people and livestock in 1995 and 2015 were from the Statistical Yearbook of Henan Province (http:// tjj. henan. gov. cn/ tjfw/ tjcbw/ tjnj/) (see Appendix).

Driver data
Driving factors affecting land-use change and carbon balance were selected and classified into five categories: topographic factor, soil factor, climate factor, location factor, and socio-economic factor. Among them, topographic factors include elevation and slope. The elevation data was obtained from the geospatial data cloud (GDC) (http:// www. gsclo ud. cn), and the slope was obtained based on the elevation data using the ArcGIS 10.2 surface slope tool. Soil data came from China's second soil census, Henan Province 1:200,000 soil map. Climate factors of average annual precipitation and average annual temperature were obtained from the RESDC. Location factors include the distance to major roads, railways, and rivers, which were calculated by ArcGIS 10.2 European Distance Tool. The vector distribution data of major roads, railways, and rivers in Henan Province are obtained from China National Geographic Information Center (NGCC) (http:// www. ngcc. cn/ ngcc/). Socio-economic factors of GDP and population density were obtained from the RESDC. In ArcGIS 10.2, a unified spatial resolution in this study was 1 km × 1 km, and the coordinate system was Krasovsky_1940_Albers.

Evaluation of carbon sequestration/emission
The exchanges of carbon between terrestrial ecosystems and the atmosphere are largely caused by biological processes of photosynthesis and respiration (Houghton 2007). Therefore, in this paper, carbon balance was calculated in productionliving-ecological spaces from both photosynthesis and respiration. Specifically, referring to the relationship between carbon sequestration/emission and land use , this paper established an accounting list of carbon that clarifies the relationship between carbon sequestration/emission, land use, and production-living-ecological space Li et al. 2018) (Fig. 2) and used the IPCC carbon emission coefficient method to calculate them (Table 1).
The accounting inventory is a natural, social, and economical integrated system. The carbon sequestration of plant photosynthesis includes crop carbon sequestration in arable land, forest and grassland vegetation, water carbon sequestration, and dry and wet sediment. The carbon emissions from respiration include soil, anthropogenic input emissions from arable land; energy, industry, human, and animal respiration emissions from built-up land; soil respiration carbon emissions from forest and grassland; and volatile carbon emissions from water bodies. It should be noted that, due to data limitations, carbon sequestration and emissions in this paper consider CO 2 instead of all greenhouse gas (GHG). All results were represented by carbon, and the specific process of calculation and data in 1995 and 2015 can be seen in Appendix.

Analysis of the temporal and spatial changes in the carbon balance
Based on the calculation of carbon sequestration and carbon emission, the net carbon sequestration/emission (CM) and the ratio of total carbon sequestration to carbon emissions (CMI) were calculated as the quantity of regional carbon balance, and the equations are as follows: where CS represents the amount of carbon sequestration (t); CE represents the amount of carbon emission (t); CM represents net carbon sequestration or emission (t); when CM > 0, carbon sequestration is considered to be greater than carbon emissions, and the larger the absolute value is, the stronger the carbon sequestration capacity is. When CM < 0, the result is the opposite. CMI is Carbon sequestration/ emission inventory in production-living-ecological space. Note: Production space refers to land used for agricultural activities to obtain products and provide supply functions. Living space refers to the land used to carry and guarantee human settlements. Ecological space is mainly used to regulate, maintain, and ensure ecological safety the carbon balance index, the ratio of carbon sequestration to carbon emission. When CMI = 1, carbon sequestration is considered equal to carbon emissions, and carbon balance reaches. When CMI < 1, carbon sequestration is considered less than carbon emission and presents an unbalanced state of negative income. When CMI > 1, carbon sequestration is considered greater than carbon emissions and shows an imbalance of positive income. The greater the difference between 1, the more serious the imbalance.
To further understand whether there is a phenomenon of highvalue and low-value agglomeration in the spatial distribution of carbon balance, this study adopted the statistics tool Hot Spot Analysis (Getis-ord Gi*) in ArcGIS for the carbon balance analysis of Henan Province in 1995 and 2015. The Hot Spot Analysis tool calculates the Getis-Ord Gi* statistic (Getis and Ord 1992) for each feature in a dataset to quantify the degree of spatial dependence in the pronounced scale distance. A statistically significant hot spot is a feature that has a high value and is surrounded by others with high values. The calculation formula is below: The G * i statistic is a z-score. For statistically significant positive z-scores, the larger the z-score is, the more intense the clustering of high values (hot spot). On the contrary, for statistically significant negative z-scores, the smaller the z-score is, the more intense the clustering of low values (cold spot). Carbon sequestration in hot spots areas is higher than carbon emissions, and carbon sequestration capacity is relatively strong. The carbon sequestration of cold spot areas is lower than the carbon emissions, and the carbon emission capacity is strong. The non-significant region indicates that there is not an apparent high or lowvalue agglomeration phenomenon.

Prediction of production-living-ecological space change under different scenarios in 2035
In this study, the CA-Markov combined with the MCE module was used in IDRISI to simulate the territorial space of 2035. In particular, the land use map of 2015 was predicted and tested according to the land use transfer matrix and suitability distribution atlas from 1995 to 2005. Compared with the actual land use map of 2015, the kappa value is 0.9166, and the overall accuracy is 93.4015%. Based on accuracy verification, land-use change in 2035 under different scenarios is predicted according to the land use transfer matrix from 1995 to 2015.
Soil respiration: CE soil−arable = EF soil−arable × Area arable Agricultural material inputs (fertilizers, pesticides, and agricultural films), agricultural machinery uses energy (agricultural diesel), and irrigation energy consumption: Built-up land ----Energy consumption, industrial production, and human and livestock respiratory carbons: Photosynthetic NPP of vegetation: Carbon sequestration and sedimentation, photosynthesis: CS water = C unit−water × Area water + C sub × Area water Water carbon volatilization: CE water = EF water × Area water --Unused land ------

CA-Markov
CA-Markov model integrates the cellular automaton (CA) model and Markov chain model and uses a transition probability matrix to simulate land use/land cover change, which can realize quantitative and spatial simulation and predict land-use change. CA model is a dynamic system that is discrete both in time and space . Markov chain uses the random time series mathematical model to perform matrix analysis and estimates future possibilities according to the current state and change trend .

MCE suitability atlas
In this paper, the multi-criteria evaluation (MCE) module in IDRISI17.0 software was used to produce the suitability map, and the weighted linear combination method (WLC) was used to generate the suitability map by combining factors set and constraints based on specific weights (Zhao et al. 2019). Finally, the Collection Editor tool was used to combine each suitability map into a suitability atlas of land use transfer.

Setting of scenarios
Taking into account the minimum ratios of 39.6%, 7.2%, and 8.5% of the production-living-ecological space in Henan Province's 2035 territorial spatial pattern, as well as the overall positioning of the region as a leading area for high-quality development in central China, a pilot area for agricultural and rural modernization, and a happy and livable home of Henan Provincial Territorial Spatial Plan (2021)(2022)(2023)(2024)(2025)(2026)(2027)(2028)(2029)(2030)(2031)(2032)(2033)(2034)(2035). Combined with the studies on different scenarios in the relevant literature (Cui et al. 2020;He et al. 2020a, b), the conversion rules of various land classes under the three scenarios of natural change, food safety, and ecological protection are set up to predict land use in 2035.
• Natural change scenario (NC). Based on the current situation of land use in 2015 and the land use transfer matrix and suitability distribution atlas from 1995 to 2015, the land-use area under natural development scenarios in 2035 was predicted • Food security scenario (FS). It is forbidden to transfer arable land to built-up land or unused land; the probability of forest and grass water transferring to arable land will increase by 15%, and the probability of built-up land and unused land transferring to arable land will increase by 15%, respectively • Ecological protection scenario (EP). Forbidding the transfer of forest, grass, and water to arable land, builtup land, and unused land, the transfer of built-up land to forest land will increase by 10%. The probability of transferring built-up land to grass will increase by 5%, and the transfer of unused land to forest and grassland will increase by 5%

Results
Dynamic changes of production-living-ecological space from1995 to 2015 The layout of production-living-ecological space in Henan Province in 1995 and 2015 is shown in Fig. 3. The production space of Henan province is relatively large, accounting for more than 60%, and is mainly distributed in the eastern plain. The living space is the smallest and scattered in the east part of the study area, primarily concentrated in the central towns of each municipality. The ecological space area is moderate and focused on Taihang Mountain on the western edge of the study area, Funiu Mountain on the southwest edge of the Nanyang basin, and Tongbo-Dabie Mountain on the south. From 1995 to 2015, the living space in the north and central-eastern of the study area gradually expanded and became more concentrated. On the contrary, the production space is slowly reduced. Among them, Zhengzhou and Luoyang have the most apparent expansion of living space. This is mainly due to economic development that gradually expands built-up land around urban agglomeration, occupying the surrounding arable land. However, there was little change in ecological space in the southwest, because wood and grassland in the mountains changed less. In general, the area of production space decreased by 2212 km 2 , the area of living space increased by 1833 km 2 , and the area of ecological space decreased slightly by 378 km 2 during the 20 years.

Quantity change of carbon balance
The results of carbon sequestration (CS), carbon emission (CE), net carbon sequestration/emission (CM), and carbon balance index (CMI) in different spaces in 1995 and 2015 were calculated and shown in Table 2. In 1995, the CM of production, living, and ecological spaces was all less than 0, meaning the carbon sequestrations were less than carbon emissions. The CMI of production and ecological space was less than 1 and presented an unbalanced state of negative income. However, in 2015, the CM of production space and ecological space in Henan Province was greater than 0, and the CMI was greater than 1. It reflected carbon sequestration exceeded carbon emission and showed a positive income imbalance. There were similar results in previous studies (Zhao et al. 2016), which reflect the large sown area of crops and the constantly increased grain output in Henan Province in recent years have become a vital advantage of carbon sequestration in the Central Plains Economic Zone.

Spatial change of carbon balance
Hot spot analysis of net carbon sequestration/emission (CM) and carbon balance index (CMI) in 1995 and 2015 were visualized (Fig. 4). As can be seen from Fig. 4, the distribution regions of cold hot spots of CM in 1995 and 2015 were the same (99% confidence interval). The hot spots of CM were concentrated in the ecological space of the study area, with forest, grassland, and water area, which indicated that carbon sequestration was higher than carbon emissions in these areas and carbon sequestration capacity was strong. However, the cold spots of CM were mainly distributed in the production and living space of the eastern plain of Henan Province. The regional land-use types were primarily arable land and built-up land, where carbon emissions were higher than carbon sequestrations. From 1995 to 2015, the clustering of hot and cold spots of CM increased, and the tendency spread to the periphery.
In 1995 and 2015, the distribution of CMI in Henan province was similar and linear (99% confidence interval), while the distribution of cold spots was different (90% confidence interval). During the study period, hot spots are mainly distributed in the water area in the northern, forest and grassland in the southwest of the ecological space, and also a small amount in the production space in the south of the study area. These areas have carbon imbalance, and carbon sequestration is greater than carbon emission. In 1995, the cold spots were mainly concentrated in the southwest of the study area. In 2015, the cold spots increased significantly and covered most of the study area, indicating a growing trend of regional carbon imbalance (Fig. 4).

Simulation of production-living-ecological space in 2035
It is expected that the pattern of production, living, and ecological space in 2035 will generally be the same as before (Fig. 5), that is, production space will be the largest, distributed in the eastern plain area of the study area, living space will be scattered between production space, and ecological space will be concentrated in the western and northern mountainous areas of the study area. However, some changes have occurred in each space's areaspecific gravity. Under the NC scenario, the proportions of production space, living space, and ecological space in Henan province are 58.01%, 16.33%, and 25.67%, respectively. Under the EP scenario, the proportion of ecological space in Henan province increased more than that in NC, and the proportion of production space, living space, and ecological space were 56.99%, 13.98%, and 29.03%, respectively. Under the FS scenario, the production space in Henan province increased more than that in NC, and the production space, living space, and ecological space accounted for 68%, 10.2%, and 21.79%, respectively.

Future carbon balance under different scenarios
Based on the calculation results of carbon sequestration and emission during the study period above, the table of carbon effect coefficients in different spaces was established ( Table 3). The parameters for 2035 are the result of trend extrapolation based on coefficients of different land-use patterns over the years. Since carbon sequestration intensity is mainly reflected in soil and vegetation, which has not changed much over the years, the carbon sequestration coefficient of 2035 is still the value of 2015. The carbon emission data involves changes in human activities, and the parameters have increased over the years. Based on the research methods of relevant literature (Zhao et al. 2013), the carbon emission coefficient in 2035 was predicted according to the growth rate from 1995 to 2015.
The hot spots of carbon balance distribution under different scenarios in 2035 are shown in Fig. 6. For CM, the spatial aggregation of high and low values was obvious (99% confidence interval). In three scenarios, hot spots were concentrated in the ecological space in the southwest and south of the study area. In contrast, cold spots were distributed in the eastern plain of the study area with obvious changes under different scenarios. In the NC scenario, hot spots with strong carbon sequestration ability were focused on the west and south areas that were consistent with the ecological spaces. Meanwhile, cold spots, which store more carbon, were concentrated in living spaces. In the FS scenario, hot spots with high carbon absorption capacity were reduced compared with NC, and the cold spots with strong carbon emission capacity were also more dispersed. In the EP scenario, hot spots with strong carbon sequestration capacity and cold spots with strong carbon emission capacity decreased compared with the NC scenario.
For CMI, the hot spot agglomeration was obvious (99% confidence interval), and their distributions were similar under different scenarios. That is, the hot spots of CMI were concentrated in the ecological space of water, forest, grassland, and a small amount of production space such as arable land in the study area. These areas were in a positive carbon imbalance state where carbon sequestration was greater than carbon emission. However, the cold spot regions with negative carbon imbalance, where carbon emission was greater than carbon sequestration, had similar spatial agglomeration distribution and various spatial significance. In the NC scenario, the significance of most cold spots was in the 95% confidence interval. While, in the EP scenario, the significance of cold spots in the production space located in the eastern plain of the study area was the 99% confidence interval. Besides, in the FS scenario, the significance of the cold spot region decreased (90% confidence interval).

Comparison and verification of carbon accounting results
The accuracy of carbon sequestration and carbon emission accounting affects the assessment result of carbon balance and plays an essential role in realizing the "double carbon" goal. To verify the accuracy of the evaluation results in this paper, the emission inventories for 30 provinces in the carbon emission accounts and datasets for emerging economies accounting database list of provincial emissions (CEADs) (https:// www. ceads. net. cn/) were regarded as standard data of carbon emission. The inventory includes inventories of energy and carbon dioxide emissions from 31 provinces in China from 1997 to 2019, covering 47 socio-economic sectors, 17 fossil fuel combustion, and cement production-related processes. The IPCC sectoral emission accounting method (45 production and two residential sectors) was used to regularly publish China's latest CO 2 emission data and its 30 provinces and cities (Shan et al. 2018). This dataset used updated emission factors, which were lower than the IPCC default values and considered more accurate . Moreover, the carbon sequestration standard data were from the county-level carbon sequestration values of terrestrial vegetation in China (2000-2017) (Chen et al. 2020a, b). Given that all carbon accounting exists errors, the CEADs database above should only be used as a reference standard. After unit unification and comparative analysis of carbon sequestration and emission, it is found that the carbon sequestration and emissions in this paper were of the same magnitude as the values given by the CEADs database, indicating that the carbon accounting in this study is generally reasonable. However, the carbon sequestration of this study was greater than the data in the database, because the CEADs do not cover the water area carbon sequestration. However, the carbon emission in this study was slightly less than the data in the database, which may be due to the incomplete consideration of industrial departments in carbon emission accounting. In general, the carbon accounting of this study was based on actual statistical data and relevant research (refer to Appendix), which is relatively reasonable.

Driving forces of carbon balance
Geodetector is a novel tool to investigate Spatial stratified heterogeneity (SSH) and reveal its driving factors (Wang and Xu 2017). It has unique advantages in dealing with categorical variables (Wu et al. 2016) and has been gradually applied to land use, landscape pattern, rural residential areas, and other fields in recent years (Chen et al. 2020a, b). In this paper, ten natural and socioeconomic influence factors of soil organic carbon (SOC), slope, road distance, water distance, rail distance, DEM, temperature, population density, precipitation, and GDP collected above (Fig. 7) were analyzed by the factor detector and interaction detector of geodetector, respectively. The operations rely on geodetector (http:// www. geode tector. cn/) and Rstudio.
Factor detection results of the geographic detector (Fig. 8) showed that the top five factors with large q-statistic in 1995 and 2015 are population density, GDP, DEM, slope, and temperature for CM, indicating that social and economic factors of population density and GDP have a significant influence on CM, while DEM, slope, and temperature also have some effects on CM. Except for water distance, the q-statistic of all factors in 2015 was greater than their corresponding values in 1995, mainly because the economic development and urbanization of Henan Province in the past 20 years have accelerated, and the effects of all socioeconomic factors on CM have increased. In addition, water distance, temperature, and population density highly impact the CMI, while rail distance, road distance, and slope have little impact on the CMI. As socioeconomic development has reached a relatively stable stage, the influence of population and GDP on CMI has gradually diminished.
According to the interaction between explanatory variables table, the q value of every single factor and the q value after the superposition of two factors are compared, respectively, to determine whether there is an interaction between the two factors, as well as the strength, direction, linear, or non-linear of interaction (Wang and Xu 2017). The results in Fig. 8 showed that CM was primarily influenced by the interaction between the socioeconomic factor of population density and other factors, while CMI was strongly affected by the interaction between the natural condition of water distance and other factors, and the interaction enhanced the explanatory power of CM and CMI, respectively. For CM, except for the independent relationships between road distance and temperature in 1995 and slope and precipitation in 2015, all variables existed in interaction relationships. In addition, the mutual effect of factors demonstrated the twofactor enhancement and non-linear enhancement. For CMI, there were interactions among all variables, which manifested as two-factor enhancement and non-linear enhancement, which was the pairing impact that could enhance the explanatory power of CMI.

Implications for territorial space planning
Establishing territorial spatial planning systems and legislation plays a vital role in national space governance (Li et al. 2021). Under the background of carbon neutrality and ecological environment protection, the Chinese government is 1 3 promoting more careful work on territorial spatial planning. By comparing the quantity and spatial distribution of carbon balance under different scenarios and analyzing the factors, decision-makers can achieve the carbon balance goal in the regional territorial space.
In 2035, carbon emission is greater than carbon sequestration and will show an unbalanced state of negative income. The living space shows carbon emission, while both production and ecological space show carbon sequestration. The carbon sequestration capacity of production space is stronger than that of ecological space, which is consistent with the previous studies on carbon sequestration in this area, that is, the main grain-producing areas in the Huang-Huai-Hai Plain have higher carbon sequestration intensity (Zhao et al. 2016). While, in the FS scenario, the absolute value of CM is the smallest in the study area, and the difference between the CMI and 1 is the smallest. It illustrates the carbon emission capacity is relatively weakened and the imbalance of carbon is also reduced. In addition, taking the impact factors in 1995 and 2015 as examples, the factors that had a large impact in both periods will be the persistent impact factors. Assuming that they will still have a large impact in 2035, regional CM could be adjusted by those persistent impact factors. For instance, population density, GDP, DEM, slope, and temperature have a bigger influence on the quantity of CM; and water distance, temperature, and population density greatly affect CMI.
Henan province is a major grain production province, sticking to the Farmland Protection Red Line (FPRL) and the grain production bottom line for bears on regional development and national security (Wei 2019). Taking the relative regional carbon balance as the goal, that is, enhancing regional carbon sequestration capacity and weakening regional carbon emission capacity, the direction of future territorial space planning can be the layout of territorial space under the FS scenario. The spatial layout under the FS development scenario not only matches the regional natural resources but also supports China's food security and contributes to the goal of carbon neutrality in territorial space. Based on natural development, the production space in the central and eastern plains of the study area should be increased, the living space in the concentrated contiguous areas should be reduced, and the ecological space in the mountain edge should be appropriately compressed. In addition, planners could adjust the social and economic factors such as population density and economic development level in territorial space planning, reducing the carbon emissions of living space. They could also adjust the spatial layout according to the natural factors such as elevation, slope, and temperature and increase the suitability and matching degree of the production-living-ecological space to realize the carbon balance.

Limitations and future research direction
This study established a set of methods for analyzing and predicting carbon balance in territorial space and conducted empirical verification in major grain-producing areas in China. The result showed that this method was feasible and could be extended on a regional scale. However, in the current carbon calculation, there are some differences in the calculation results of each authoritative carbon sequestration/  (Piao et al. 2005;Feng et al. 2007), which leads to the difficulty of testing the accuracy of accounting results. Given the vital role of carbon accounting, future research should strengthen the basic research of carbon accounting and the testing of carbon accounting data. The analysis of carbon balance dynamics only used the data from 1995 and 2015, which may not fully reflect the changing trend of the study period.
In addition, this paper uses the CA-MCE-Markov model to select ten driving factors for future simulation. These factors have an excellent fitting effect on various types of land, and the final simulation results have high accuracy. However, the limitations of the model itself are still inevitable, which leads to the difference in the prediction of future results , and the limited help for national spatial planning and carbon neutrality goals. In achieving the regional carbon balance goal, low carbon emission reduction can be achieved by decomposing the number of carbon emissions. Based on this study, down-scale research can be carried out to analyze the carbon balance at the municipal, county, and township scales to serve lower-level planning by combining the system of China's territorial spatial planning.

Conclusions
This study evaluated and predicted carbon balance in major grain-producing areas of China. The results showed that from 1995 to 2015, the living space in the north and middle, and east of the study area gradually expanded and became more concentrated. However, the production space has a gradual reduction. CS was less than CE and presented an unbalanced state of negative income in 1995, while CS exceeded CE and showed a positive income imbalance in 2015. The clustering of hot and cold spots of CM in the study area constantly increases and spreads to the periphery. In 1995 and 2015, the distribution of CMI in Henan province was similar and linear, while the distribution of cold spots was different. In 2035, the carbon emission capacity of living space is the strongest in the NC, the carbon sequestration capacity of ecological space is the strongest in the EP, while the carbon sequestration capacity of production space is the strongest in the FS. Hot spots of CM were concentrated in the ecological space in the southwest and south of the study area in three scenarios, while cold spots were distributed in the eastern plain of the study area with obvious changes under different scenarios. Meanwhile, the hot spots of CMI are concentrated in the ecological space of water, forest, grassland, and a small amount of production space such as arable land in the study area. The cold spot regions with negative carbon imbalance have similar spatial agglomeration distribution and various spatial significance. In addition, population density, GDP, DEM, slope, and temperature have a greater influence on carbon balance. In the future, the territorial spatial layout of Henan Province can be developed to the FS scenario, which can not only support China's food security but contribute to the realization of the carbon neutrality goal of territorial space. These results provide a method for the assessment and prediction of carbon balance in major grain-producing regions, which can effectively support regional spatial planning and optimization for low-carbon development.