Study on Production–Living–Ecological Function Accounting and Management in China

: The current insufﬁcient quantiﬁcation and evaluation of major functions fundamentally affected regional sustainable management and policy implementation. This study focused on the problem that no effective quantitative accounting relationship has been established between development activities and resource utilization. In order to establish the relationship between major function accounting and natural resource accounting, we analyzed the relevant studies on the evaluation of major functions, natural resource accounting, environmental accounting, ecosystem services, and assets accounting. The efﬁciency comparison of different functions was completed using the equivalent factor method for ecosystem service value measurement and the input–output method for water footprint measurement. We found that the accounting of major functions and resources can guide regional sustainable management by using function positioning and resource comparative advantages. In addition, administrative units were linked to functional units, providing the possibility of cross-regional comparison of total functional


Introduction
In order to cope with the tightening of resource constraints, serious environmental pollution, and ecosystem degradation, China proposed the Major function zoning, which is considered a major theoretical innovation in China's regional development theory and spatial planning. China's resource and environmental carrying capacity can hardly support high-speed industrialization and urbanization [1]. Major function zoning is a sustainable planning and management system in China designed to guide the spatial division of production, living, and ecological functions, and to coordinate sustainable goals through national resources and red line control [2,3]. Regional coordination and policy evaluation are more complex due to the increase in development activities across management units. Various regional strategies, plans, and policies have multifaceted and multilayered impacts, while indicators and methodological differences add to the complexity of monitoring and evaluation [4]. The differentiation of financial, regional, and industrial development policies inevitably leads to unequal interests between four types of functional zones. Therefore, there is an urgent need to realize unified quantification and comparison across regional scales for major functions [5].
Quantifying the imbalance between production, living demand and ecological supply is a prerequisite for spatial governance, and the quantification of major functions must take into account spatial heterogeneity, functional diversity, and complexity. The basic evaluation of major functions and spatial zoning is "double evaluation" (i.e., resource and environmental carrying capacity evaluation and territorial development suitability evaluation) [6,7]. The indicator system and method of "double evaluation" are closely related to the major function types, but there is no unified evaluation of production, living, Land 2023, 12, 1163 3 of 23 driven the development of carrying capacity research. The concept of carrying capacity was first applied to ecological carrying capacity [18]. With the resource and environmental problems caused by population growth and economic development, resource carrying capacity focuses more on the relationship between population, food and resources (land, water, etc.). To further measure human impact on the ecological environment, the concept of ecological footprint was proposed as a complement and refinement to resource carrying capacity. Subsequently, a series of footprint indicators [19] such as water footprint [20], carbon footprint [21], phosphorus footprint [22], and nitrogen footprint [23] has been developed.
In order to discuss the quantification and comparison of major function zoning, we applied the ecosystem service and footprint accounting to major function accounting, and discussed the regional sustainable evaluation and management in China. By establishing the accounting relationship between resources and major functions (Figure 1), we analyzed the distribution and efficiency of production-living-ecological functions and functional resources in different functional and administrative units. sustainability has also driven the development of carrying capacity research. The concept of carrying capacity was first applied to ecological carrying capacity [18]. With the resource and environmental problems caused by population growth and economic development, resource carrying capacity focuses more on the relationship between population, food and resources (land, water, etc.). To further measure human impact on the ecological environment, the concept of ecological footprint was proposed as a complement and refinement to resource carrying capacity. Subsequently, a series of footprint indicators [19] such as water footprint [20], carbon footprint [21], phosphorus footprint [22], and nitrogen footprint [23] has been developed.
In order to discuss the quantification and comparison of major function zoning, we applied the ecosystem service and footprint accounting to major function accounting, and discussed the regional sustainable evaluation and management in China. By establishing the accounting relationship between resources and major functions (Figure 1), we analyzed the distribution and efficiency of production-living-ecological functions and functional resources in different functional and administrative units.

Study Area: Major Function Zoning in China
The major function zoning divided China's territorial space into different major functional zones according to the development methods and development contents (Table 1). Functional units and administrative units overlapped but did not correspond exactly. In order to establish the linkage between functional units and administrative units, we collected the major functions of 2852 county-level units according to the national and provincial major function planning, and used them as the basic units to account for the

Study Area: Major Function Zoning in China
The major function zoning divided China's territorial space into different major functional zones according to the development methods and development contents (Table 1). Functional units and administrative units overlapped but did not correspond exactly. In order to establish the linkage between functional units and administrative units, we collected the major functions of 2852 county-level units according to the national and provincial major function planning, and used them as the basic units to account for the products realized by the functions. There were also some prohibited development zones scattered in other functional areas, such as national parks and historical sites, which are not considered separately. In the paper, production, living, and ecological functions were directly used as the accounting objects, and the results based on the raster data realized the functional accounting and integration of different administrative and functional units. In order to quantify the relationship of resource use between regions, the city scale was chosen as the accounting unit to examine the input-output relationship of water resource function. The city scale defined in this paper included densely populated and industrialized urbanized areas as well as subordinate administrative units-districts and counties, which was a multifunctional spatial unit of production, living, and ecological functions. The accounting results covered the functions of 309 cities nationwide, and analyzed the differences in the amount of production, living, and ecological functions and function structures of the country and different types of development zones. The water accounting data source uses the city-scale multi-regional input-output table of the China Carbon Accounting Database (CEADs) for water footprint measurement. The table covers 313 administrative units in China, including 309 cities (prefecture-level administrative units and municipalities directly under the central government) and 4 provinces (Hainan, Yunan, Xizhang, Qinghai), covering more than 95% of the country's population and more than 97% of its GDP. Territorial space has basic natural geographical characteristics as well as economic and political characteristics. Spatial function referred to the division of responsibilities undertaken by spatial units in the ecological, economic, and social system at a certain stage of development, relying on its own development foundation and potential. Spatial function is manifested as land use at the microscopic scale and more as dominant function at the macroscopic scale. Typically, each space is multifunctional and different factors combine in different ways to reflect different functional characteristics, and function and space are complex many-to-many relationships [24].
The functions provided by the national space are mainly the three major functions of production, living, and ecological, as well as other national strategic support functions. They correspond to production space, living space, ecological space, and other functional spaces, respectively. Other spaces include land space for transportation facilities, water conservancy facilities, national defense, and religion, etc. The major functional products provided by different spaces vary, and the same space has multiple functions [25]. For example, urbanized space is a high degree of superposition and overlap between living space and production space, and its major function is to provide industrial goods and service products, as well as to provide the living function carried by the urban population and the ecological function of the urban green space system. The spatial overlap makes the constraints and support relationships between functions more complex. Ecological functions provide material conditions for living and production functions, but at the same time resource and environmental thresholds limit development. The same function may provide several products and services simultaneously, and there is no one-to-one correspondence. For example, the agricultural products of farmland ecosystems are part of the product provisioning services of ecological functions and are also part of agricultural production functions. The relationship between functions is not a simple either/or relationship, so it is necessary to sort out the relationship between each function and product service.

Functional Resources: Land and Water
Based on the resource input and function output relationship, the required resources increase with the increase in regional functions. Natural resources, which play a fundamental supporting role for the major functions, are also the key limiting factors for regional development. Water and land resources are the most important resource indicators and constraints in the initial division and subsequent evaluation of major functional zones. Territorial spatial development at the micro level can be seen as land use and structure, and land use types and functions are closely related. As a basic natural resource and irreplaceable factor, water resources are characterized by limited total amount, difficulty of spatial transfer, and multifunctionality, which are crucial to the division and realization of major functions. The constraint target of resource overconsumption assessment refers to the excessive consumption of various natural resources in the accounting period due to the development needs of the region, including two types of natural overconsumption, where the resource utilization exceeds its renewal capacity, and policy overconsumption, where the resource utilization exceeds the red line of various policies.

Major Function Accounting
Major function accounting is explained as the total accounting of products and services (Y) produced by the use of natural resources and non-natural resources in the economicsocial-ecological system in a specific spatial unit within a certain period of time [26,27].
where Y P is the industrial and service products provided by the production function; Y L is the amount of products and services required by residents' living provided by the living function; and Y E is the value of ecological services provided by the ecological function. The three functions are defined as output results and quantified objects of territorial spatial development activities, which can cover almost all types of products and services produced by human production, living activities, and ecological impacts, thus establishing the inputoutput relationship with resource utilization. The three major functions are accounted for based on the definition of accounting. The production and living functions are accounted for using the input-output method. The living function is first reflected by the population carrying quantity. Second, the final consumption products can also characterize the quantitative and structural differences of regional living functions. Ecological function accounting used the ecosystem service value calculation method. In order to make comparisons at different spatial scales, the accounting method refers to Xie's value equivalent factor method and constructs a table of ecosystem service values per unit area [30]. The regional ecological function values at the city and county levels were calculated by adjusting [31] according to the biomass factor of each province and using the 30 m annual China Land Cover Dataset. The specific calculation equation is as follows: where E a is the value of food production services per unit area of cropland ecosystem in area a (yuan/hm 2 ); n is the main food crop species (rice, wheat, corn) in the study area; m i is the sown area of crop i (hm 2 ); p i is the total yield of crop i (kg); q i is the average price of crop i (yuan/kg); S is the total sown area of food crops (hm 2 ); 1/7 means that the economic value provided by natural ecosystems without human inputs is 1/7 of the economic value of food production services of existing farmland ecosystems per unit area. Statistics on production, prices, and area of crop are taken from the National Compilation of Cost and Benefit Information on Agricultural Products and the China Statistical Yearbook. The equivalent factors for each province in the country are shown in Appendix A Table A1.
where ESV is the ecosystem service value (yuan); A j is the area of the land type j (hm 2 ); E ij is the value of the ecological service i of the land type j (yuan/hm 2 ). Calculate the value of ecosystem services based on the Ecosystem service equivalent value per unit area.

Functional Resource Accounting
Natural resources are the material basis for the realization of ecological, production, and living functions. The sustainability of regional development means that it depends on the regeneration and replacement of natural resources and the support and improvement of ecosystem services [32]. When the relationship between human and nature shifted from passive adaptation to active utilization, the concept of resource carrying capacity based on the relationship between population and resources was proposed, and its prominent representatives are the carrying capacity of land resources and water resources. We integrated the carrying capacity and footprint to discuss the relationship between key natural resources and functions.
The amount of functional resource input can quantify the difference in the structure of resource utilization in the region, which is manifested by the different amount of resources inputted in different functions and resources. By decomposing and accounting the input resources of the region by functional types, the amount of input resources corresponding to the realization of the function can be obtained, which can characterize the regional resource input situation and the functional resource utilization structure. Usually, the resource utilization structure is closely related to the industrial structure and functional positioning of the spatial scale.
The amount of resource input per unit of function can quantify the amount of resources required to realize one unit of function in a regional unit, i.e., the ratio of the amount of resource input to the amount of function, which can be used to characterize the efficiency of resource utilization in the region and make cross-regional comparison. For example, the corresponding accounting relationships for the amount of water (W) and land (LD) resources required as inputs for the realization of production functions are established as follows.
The amount of water resources to be input to achieve a unit of production function in region i can be calculated as The amount of output per unit of resource can be used to characterize the efficiency of resource use in the region. If the functional efficiency of water resources in region i is higher than in region j, region i has more output per unit of water resources than region j, i.e., w j P > w i P , y i wP > y j wP . The total amount of natural resources that can be used in region i is set, and usually sustainable management goals set thresholds for resource use. For example, the resource boundaries for land and water use are set in the planetary boundaries [33], and the upper line of water use is set in the spatial planning and regional management of China. In which, the total water resource use constraint of region i can be expressed as: That is, the input of water resources in the process of realizing the production, living, and ecological functions of region i should not exceed the upper line of water resource use and the total amount of resources in the region. Region i is usually not a closed space, and resources are imported or exported in the region to support the realization of functions within the region through direct water transfer or indirect virtual water trade exchange. Thus, when discussing water constraints, the flow of imported water (W i I M ) and exported water (W i EX ) through the region i should be considered.
The data used in this paper are all publicly available information and datasets, as detailed in Table 2. Considering the availability of data, 2015 data were used to compare the positioning of major functions and the amount and efficiency of the major functions at the city level. The division of functional land follows the priorities of the major functions and the disturbance level of the ecosystem and is divided into three categories ( Table 3).
The key intermediate results obtained during the collation and calculation of the data are in the Appendix A (Tables A1 and A2). The raster data were calculated using ArcGIS and the input-output analysis of the water footprint was implemented using Matlab. The result maps were based on the standard map provided by the China's Ministry of Natural Resources (mnr.gov.cn). Table 3. Classification of functional land.

Functional Land Corresponding Land Classification
Ecological functional land (LD E ) forest shrub grassland wetland water snow and ice barren Production-ecological functional land (LD P-E ) cropland Production-living functional land (LD P-L ) impervious Functional water was water footprint based on input-output analysis, and the types were divided into three categories: production functional water, living functional water, and ecological water. The quantification of inter-regional water resources and the inputs and outputs realized by different functions is measured on the basis of a multi-regional input-output table [34], which is applicable to water resources accounting at the provincial and district to local and municipal levels, and can consider the regional allocation of water resources from a comprehensive perspective, and verify that the regional functional positioning matches the actual water use structure including virtual water, and that the regional resource endowment constraints match the direct water use structure. The 42 sectors of the table are combined into 8 sectors, as shown in Table A3. In addition, considering the difficulty of deploying physical water between different regions than the difficulty of exchanging product virtual water through trade, and the difference of regional scarcity of water resources, the regional value of water resources can also be reflected by the amount of functional water resources input.

Ecological, Production, and Living Functions
In order to describe the situation of the major functions at different scales of the national space, quantitative accounting was conducted using the total amount and efficiency of production, living and ecological functions, and the provincial accounting results are shown in Table 4.
The distribution of ecological function was significantly different from the distribution of production and living function nationwide. In 2019, Guangdong Province still ranked first, with a total function value of 10,626.90 billion yuan of Y P and 1029.19 billion yuan of Y E .
The top ten provinces in total production function were Guangdong, Jiangsu, Shandong, Zhejiang, Henan, Sichuan, Hubei, Fujian, Hunan, and Shanghai, accounting for 62.12% of the national total function. The top ten provinces in total ecological functions were Tibet, Sichuan, Hunan, Inner Mongolia, Jiangxi, Guangdong, Xinjiang, Heilongjiang, Yunnan, and Guangxi, accounting for 62.12% of the national total ecological functions. Accounting for ecological functions with the value of ecosystem services in 2019, the total value of ecosystem services in 2019 nationwide was 22,042.95 billion yuan. There are differences in the ecological functions provided by different ecosystem types (Table 5). From the perspective of the major functions, croplands mainly provided agricultural products, accounting for 7.60% of the total Y E , while forests and grasslands accounting for 51.46% and 21.04% of total Y E , respectively. From the perspective of the types of ecosystem services, the value of ecological regulating services was the largest, at 15,561.08 billion yuan, accounting for 70.55% of the total Y E , while product supply services were 1309.52 billion yuan, accounting for only 5.94% of the total Y E , indicating that the supply of physical products in ecological functions was not the major function, and ecological regulating services such as hydrological regulation and climate regulation were important value-accounting content.
In terms of the total amount of ecological functions, there are clear differences at the regional level (Figure 2). The regions with higher total ecological values were distributed in the southwestern, northeastern, and southeastern provinces. The top five provinces were Tibet, Sichuan, Hunan, Inner Mongolia, and Jiangxi. In terms of the efficiency of ecological functions, the south of China was higher than the north, and the Yangtze River Delta region as well as Hunan and Fujian were among the top regions in the country in terms of ecological value per unit. The addition of ecological function values changed the total amount and structure of functions nationwide, especially in provinces where the scale of economic development was relatively small. The total ecological function of Tibet is 2959.11 billion yuan, accounting for 94.86% of the total functions. And among them, the ecological value mainly came from grassland ecosystem. Grassland covered 73.38% of Tibet's area. It provided an ecological value of 1776.33 billion yuan, accounting for 60.04% of Y E . The hydrological regulation and climate regulation functions accounted for 35.40% and 20.25% of Tibet, respectively. The areas with a high ecological value per unit were concentrated in the forest ecological zone of the southeastern Tibetan Plateau and the desert ecological zone of the northwestern Tibetan Plateau, which was consistent with its positioning as a national key ecological function zone.

Results of Production and Living Function Accounting
The spatial distribution of production and living function shows an obvious southeastern regional concentration (Figures 3 and 4). In 2019, the total national production function was 95,427.83 billion yuan, and the living function was 1399.34 million people. The top five provinces with the highest total production function were Guangdong, Jiangsu, Shandong, Henan, and Sichuan, and the top five provinces with the highest total living function are Guangdong, Shandong, Henan, Sichuan, and Jiangsu. In terms of efficiency, the distribution of production function per unit area and living function per unit area also showed a regional concentration in Southeast China. Developed provinces with

Results of Production and Living Function Accounting
The spatial distribution of production and living function shows an obvious southeastern regional concentration (Figures 3 and 4). In 2019, the total national production function was 95,427.83 billion yuan, and the living function was 1399.34 million people. The top five provinces with the highest total production function were Guangdong, Jiangsu, Shandong, Henan, and Sichuan, and the top five provinces with the highest total living function are Guangdong, Shandong, Henan, Sichuan, and Jiangsu. In terms of efficiency, the distribution of production function per unit area and living function per unit area also showed a regional concentration in Southeast China. Developed provinces with a high degree of urbanization have the major function of providing industrial goods and services, and the production and living functions are much larger than the ecological functions. Among them, Shanghai, Beijing and Tianjin, as mega cities and national optimized development zones, were at the top in terms of scale and efficiency of production and living functions. eastern regional concentration (Figures 3 and 4). In 2019, the total national produc function was 95,427.83 billion yuan, and the living function was 1399.34 million peo The top five provinces with the highest total production function were Guangdo Jiangsu, Shandong, Henan, and Sichuan, and the top five provinces with the highest t living function are Guangdong, Shandong, Henan, Sichuan, and Jiangsu. In terms of ciency, the distribution of production function per unit area and living function per area also showed a regional concentration in Southeast China. Developed provinces w a high degree of urbanization have the major function of providing industrial goods services, and the production and living functions are much larger than the ecological fu tions. Among them, Shanghai, Beijing and Tianjin, as mega cities and national optimi development zones, were at the top in terms of scale and efficiency of production living functions.

Optimized development zones and prioritized development zones
According to major function zoning, optimized development areas refer to urbanized areas with more developed economy, more dense population, higher development intensity, more prominent resources, and environmental problems, and thus should be optimized for industrialized urbanization and development. Optimized development areas at the national level mainly include the Bohai Sea region, Yangtze River Delta, and Pearl River Delta regions. They are related to regional development strategies for the Beijing-Tianjin-Hebei region, the Yangtze River Delta region, and the Guangdong-Hong Kong-Macao Greater Bay Area, which form the strategic pattern of China's regional development.
According to the accounting results in Table 6, the optimized development zones accounted for only 2.41% of the national land area, but carried 30.47% of the production function and 17.66% of the living function. Prioritized development zones are urbanized areas that have a certain economic foundation, strong resource and environmental carrying capacity, higher development potential, and better conditions for population and economic, and thus should focus on industrialized urbanization and development. The prioritized development zones accounted for 15.83% of the national land area, and carry 40.30% of the production function and 38.41% of the living function. Prioritized development zones are functionally positioned as important growth poles for national economic growth and dense areas for population and economy. The optimized development zones and prioritized development zones are both urbanized areas with the same development content in general, but different development intensity and development methods. In terms of functional efficiency, the production function per unit area in the optimized development zone was 127.5 million yuan/km 2 , much higher than that in the key development area, which was 25.7 million yuan/km 2 .

2.
Main agricultural production zones and key ecological function zones The main agricultural production zones with better agricultural production conditions at the national level, with the main function of providing agricultural products and other functions of providing ecological products, service products and industrial products, need to be restricted from large-scale and high-intensity industrialized urbanized development in order to maintain the agricultural production capacity.
The key ecological function zones with restricted development at the national level are areas where the ecosystem is very important and related to the ecological security of the whole country or a larger area, and where the ecosystem is currently degraded, and need to be restricted from large-scale and high-intensity industrialized urbanized development in order to maintain and improve the ecological supply capacity.
From the perspective of functional land, the main agricultural production zones accounted for 23.99% of the national land area, of which the proportion of cropland accounted for 43.38% of the country, in line with its main functional positioning of providing mainly agricultural products. Key ecological function zones accounted for 68.94% of the country's ecological function land, carrying 111.833 billion yuan of ecological functions, accounting for 49.92% of the country's ecological function ratio. The highest proportion of ecological land was occupied by grassland, forest land, and barren land, accounting for 36.62%, 25.07%, and 26.89% of the functional areas, respectively. The main ecosystem services provided by different types of land use differ. Cropland has a stronger capacity for agricultural product supply services and a weaker capacity for regulating, cultural, and support services; forest has a stronger capacity for regulating and support services and a weaker capacity for product supply services. Therefore, the efficiency represented by the major function shows a differential distribution.

Input-Output Analysis of Water Resources and Major Functions
As a key factor of sustainable development, water resources must be fully considered to support and constrain the realization of the major functions of the region. In this section, the relationship between the use of water resources and the realization of the major function has been portrayed through the quantitative accounting of the major function and water resources, identifying and sorting out the use patterns of water resources in the realization of different major functions at different scales in regions, provinces, and cities, and accounting for the amount of the major function and the amount of water resources required for the realization of the function in each region.
According to the water footprint accounting results, the 313 selected regions used 568.65 billion m 3 of direct water in 2015, including 393.23 billion m 3 of direct water for agriculture, 128.09 billion m 3 of direct water for industry, 63.55 billion m 3 of water for residential use, and 12.24 billion m 3 of water for ecological functions ( Figure 5). According to the water footprint accounting results (Results for only 309 cities in Table A4), the total water footprint of the production function was 565.44 billion m 3 , including 140.65 billion m 3 for the agricultural sector, 265.90 billion m 3 for the industrial sector, and 89.81 billion m 3 for the service sector.
Functional water use, by flowing through the economic and social ecosystem, simultaneously provides support for production, living and ecological functions, reflecting the multi-functionality of water resources. According to provincial administrative regions, three provinces with water consumption more than 40 billion m 3 are Xinjiang, Jiangsu, and Guangdong, while five provinces with water consumption less than 5 billion m 3 are Tianjin, Qinghai, Tibet, Beijing, and Hainan. Agricultural water consumption accounted for more than 75% of the total water consumption in Xinjiang, Tibet, Ningxia, Heilongjiang, Gansu, Qinghai, and Inner Mongolia; industrial water consumption accounted for more than 35% of the total water consumption in Shanghai, Jiangsu, Chongqing, and Fujian; domestic water consumption accounted for more than 20% of the total water consumption in Beijing, Chongqing, Zhejiang, Shanghai, and Guangdong.
In terms of direct water use, the largest share of water was used for industrial and agricultural production in 2015. Water for production supports different types of industries by flowing through production activities, while combined with intermediate products containing virtual water from other sectors, supporting the production function of the whole region. Part of the final product corresponding to the production function was used for local consumption, supporting the living function; agricultural production supported by produced water also provided the ecological function. There was a gap between direct water inputs and the accounting results of water inputs for functional use. More water flows through the input-output system through virtual water than through direct water use. Cities in developed regions consumed more functional water through products with large water footprints, such as food and other intermediate products imported from other regions. The top provinces in terms of total water footprint for living functions are Xinjiang, Guangdong, Jiangsu, Sichuan, and Heilongjiang. Water for domestic consumption was the main source of water demand (Figure 5c), and in Xinjiang and Heilongjiang, water for domestic consumption accounted for 71.75% and 66.58% of the total water footprint, respectively. Export water footprint was also a major source in Guangdong, Zhejiang, Shanghai, Jiangsu, and Shandong, accounting for 38.06%, 38.96%, 38.61%, 25.22%, and 24.55% of the total, respectively.
The structure of major functional resources (land and water) was consistent with its main functional structure, and there were regional distribution differences in efficiency. According to the water per unit function of the accounting results (Table A4), the optimized development zone has the lowest water consumption per unit of production and living function, 3.40 m 3 /thousand yuan and 6.30 m 3 / thousand yuan, respectively. The proportion of industrial and service water consumption was much higher than that of agricultural water consumption. This was related to the dense economic population in the optimized development zone and the high efficiency of water use for production and living functions. At the same time, the water input for ecological functions in the optimized development zones was 3.137 billion m 3 , accounting for 30.52% of the national ecological The top provinces in terms of total water footprint of the production function were mainly concentrated in the southeast (Figure 5b), with the largest total water footprint being Guangdong with 58,558 billion m 3 , followed by Jiangsu, Xinjiang, Zhejiang and Hubei. The sectoral structure of Xinjiang's water footprint was much higher than that of other provinces in terms of agricultural water use, accounting for 62.61%, while the other top provinces mainly used water in the industrial sector. In the megacities of Beijing and Shanghai, the service sector accounted for 49.83% and 33.76% of water use, respectively. The bottom five provinces in terms of total amount were Qinghai, Tibet, Hainan, Ningxia, and Tianjin, with production water footprints of 25.68, 29.893, 35.81, 5.658, and 6.261 billion m 3 , respectively, of which, except for Tianjin, where the water use sector is concentrated in light industry and construction, all other provinces are small-scale and have the highest proportion of water use in agriculture.
The top provinces in terms of total water footprint for living functions are Xinjiang, Guangdong, Jiangsu, Sichuan, and Heilongjiang. Water for domestic consumption was the main source of water demand (Figure 5c), and in Xinjiang and Heilongjiang, water for domestic consumption accounted for 71.75% and 66.58% of the total water footprint, respectively. Export water footprint was also a major source in Guangdong, Zhejiang, Shanghai, Jiangsu, and Shandong, accounting for 38.06%, 38.96%, 38.61%, 25.22%, and 24.55% of the total, respectively. The structure of major functional resources (land and water) was consistent with its main functional structure, and there were regional distribution differences in efficiency. According to the water per unit function of the accounting results (Table A4), the optimized development zone has the lowest water consumption per unit of production and living function, 4.00 m 3 /thousand yuan and 6.30 m 3 / thousand yuan, respectively. The proportion of industrial and service water consumption was much higher than that of agricultural water consumption. This was related to the dense economic population in the optimized development zone and the high efficiency of water use for production and living functions. At the same time, the water input for ecological functions in the optimized development zones was 3.137 billion m 3 , accounting for 30.52% of the national ecological water consumption, while the water consumption per unit of ecological function (1.86 m 3 /thousand yuan) was much higher than that of other regions. In contrast, the water input of key ecological functions for ecological functions was relatively small, but provided a large amount of ecological functions, and the water consumption per unit of ecological function was only 0.205 m 3 /thousand yuan, indicating that the demand for human allocation of water resources in the process of ecosystem function output in ecological function areas was weak, and from the perspective of providing ecological functions, key ecological function zones have resource advantages among all kinds of function zones. Such areas should ensure and maintain the good operation of ecosystem functions, rather than excessive allocation of water resources.

Discussion
In the process of achieving regional sustainable development strategic goals, different regions have different dominant or advantageous functions, and the dominant or advantageous functions may change dynamically with the adjustment of development strategic goals, the depletion of advantageous resources, or the emergence of certain types of emerging resources. The major function zoning is inseparable from the control of some key resource related to the development of land space. This study focused on the problem that no effective accounting relationship has been established between development activities and resource utilization. The value of ecosystem services has been linked with resource accounting and economic accounting to establish a relational framework that meets the needs of economic and social development and management.
Therefore, this paper attempts to solve the quantification and comparison of heterogeneous functions at different spatial scales, taking the key resources of water and land as examples. The cross-regional ecological function evaluation and conversion have become the practical and theoretical problems in the promotion of major function zoning. Land use change and human activities can directly or indirectly affect the trade-offs and synergistic issues of ecosystem services [35]. In order to establish the relationship between major function accounting and natural resource accounting, we synthesized the relevant studies on the evaluation of major functions, natural resource accounting, environmental accounting, ecosystem services, and assets accounting [36]. Chinese scholars systematically studied ecosystem service functions [37], introduced the "ecosystem service valuation" proposed by Costanza et al. [38] and established a unit area value table for terrestrial ecosystem services in China [39]. This method has been widely used to assess ecosystem service at regional scales in China by determining standard equivalence factors and establishing equivalence factor tables for different ecosystem services [40,41]. Based on this method, we also conducted a quantitative and comparative analysis of functions in the nationalprovincial-municipal-county administrative units and four types of functional zones.
The results showed that the accounting of production, living, and ecological functions were basically consistent with the major function positioning. The production and living functions were generally consistent in terms of spatial distribution, and the production functions were more concentrated than the living functions. The cities in the optimized development zones accounted for 4.03% of the national land area, and their production and living functions accounted for 35.14% and 36.63% of the value of production and living functions, respectively, while the population carrying accounted for 21.02% of the country, while the ecological function was 7.41%, which is in line with the main function positioning of the optimized development zones as the provision of industrial goods and service products. Key ecological function zones provide 10.63% of production function, 9.68% of population carrying and 54.00% of ecological service value with 63.85% of the national land area.
There were differences between the country as a whole and the regions in terms of total size and efficiency across functions. At the national level, the Yangtze River Delta, Pearl River Delta, Beijing-Tianjin-Hebei, and other city agglomerations are national optimization development zones with high overall economic level and dense population [42,43]. However, within the optimization development zones, each region performs different major functions, and there are differences in both scale and structure. Among them, within Beijing-Tianjin-Hebei, according to the accounting results, Beijing and Tianjin were highly dense in production and living functions, accounting for 50% of the production and living functions in Beijing-Tianjin-Hebei with 13.1% of region area. Meanwhile, Hebei Province provided the most important ecological functions in the Beijing-Tianjin-Hebei region, and its functional value reached 446.468 billion yuan, 84.44% of the total ecological functions in the Beijing-Tianjin-Hebei region, which was related to the forests, grasslands, and farmlands in northern Hebei. Therefore, there are differences in the comparative advantages and relative function efficiency within and outside the major functions of the region.
Based on the accounting relationship of major function and resources in Figure 1, this paper considered land and water as natural resources that play a fundamental supporting role for major functions, and are also key constraints for regional development. Due to the limited total water resources and redlines, the accounting of major functions and the efficiency of functional resource input are carried out, and the comparative advantages of different functions in terms of structure and resource efficiency are coordinated to support the maximum allocation of resources with regional functions. We found that the accounting of major functions and resources can guide regional sustainable management by using function positioning and resource comparative advantages. The results showed that the targets set for major functions were basically consistent with the current structure of resource use. There were differences in comparative advantages and relative function realization efficiency of regional major functions. By analyzing the water consumption of 42 sectors in 309 cities using the multi-regional input-output table, we compared the total amount and water efficiency of major functions among regions. In addition, based on grid cells and county-level accounting, administrative units were linked to functional units, providing the possibility of cross-regional comparison of total functional resources, efficiency, and structure of major functions.
In the analysis of water and major functions, it was found that there were regional and functional heterogeneity differences in the supporting and constraining effects of resources on functions [44,45]. Water consumption for ecological functions requires further consideration of the comparative advantages of local ecosystems and resources, as the efficiency of water supporting the realization of ecological functions largely depends on the efficiency of local ecosystems, rather than the input-output efficiency of traditional economic water use. Therefore, regional resource allocation must fully take into account the efficiency of relative function realization of resources [46]. In the quantitative relationship between resources and functions, the resource allocation goal of maximizing functions is achieved [47].

Conclusions
This paper established an accounting relationship between two kinds of key functional resources-land and water, and the three major functions of production, living, and ecology. Based on this, it further discussed the way to apply to the sustainable management of major functions, which is a regional and divisional sustainable management system. The ecosystem service value approach provides a basic quantitative basis for major function accounting. If it is to be applied to regional management, it must be linked to administrative and functional units.
Aiming to achieve the sustainable use of natural resources, this paper has established an accounting relationship framework and indicators for the value of major functions and the input of functional resources, aiming at the quantitative relationship between resources and major functions. This approach basically realizes the computability, decomposability, and comparability of the functional structure and efficiency among the three major functions in different spatial units.
In this paper, the major function accounting process combined the economic and ecosystem service accounting methods to reflect the functional output and the footprint analysis of resource use. It established an analysis of resource input and functional value, which is complementary for the unclear two-way relationship between resources and regional development goals, and is helpful for further discussion of the relationship between regional functional management and resource use optimization in future research.
Based on the major function accounting to guide the allocation and optimization of resources, this paper analyzed the use of water resources in 42 sectors of 309 cities in the multi-regional input-output table, the relationship between the major function and the efficiency of functional resources was calculated from the perspective of limited constraints on water resources. Water and land as natural resources that have a fundamental supporting role for the major functions is also a key constraint factor for regional development. Finally, it provides a quantitative basis for cross-regional comparison of the total amount, efficiency, and structure of resources and major functions between different regions.
The limitations of this research are as follows: (1) In order to reflect the structure and flows of water use among regions, the study selected the city-level multi-regional input-output method to measure the water footprint. The advantage of this method was that it can compare the resource consumption of different sectors and the final demand at the city level, but this method relied more on the availability of data and is very restrictive for continuous year analysis. In addition, there was a partial lack of statistical data on water resources at both the city and industry levels. (2) Many cross-system accounting methods did not fully consider the reality of resource needs in the process of achieving goals such as economic development and strategic security. The application of the major function classification in the management of national sustainable development goals requires the coordination of various existing accounting methods. At the same time, the trade-off between development and protection in different administrative units and functional units should also be reflected in the evaluation benchmarks when downscaling the results of the major function zoning from the national level to the provincial, municipal, and county levels. (3) Only the land area has been considered in this study, and the functions of the sea area should be included in the future. China's economically developed regions are also adjacent to the sea, the high-quality growth of the developed regions must be adjusted to the protection of the marine ecological environment. for Young Talents in Ideological and Cultural Publicity (Publicity Department of the CPC Central Committee), the Computational Social Science Research and Cultivation Project (Harbin Institute of Technology) and the Young Scholars Development Grant Program (Harbin Institute of Technology). We would like to thank the reviewers and editors for their useful comments and feedback, which helped us to improve the paper.

Conflicts of Interest:
The authors declare no conflict of interest.  Table A2. Different ecosystem service functions at the provincial level Correspondence of multi-regional input-output tables. Table A3. Correspondence of multi-regional input-output tables.

Industry
Mining industry (Mi) 2 "Mining and washing of coal" 3 "Extraction of petroleum and natural gas" 4 "Mining and processing of metal ores" 5 "Mining and processing of nonmetal and other ores" Light industry (Li) 6 "Food and tobacco processing" 7 "Textile industry" 8 "Manufacture of leather, fur, feather, and related products" 9 "Processing of timber and furniture" 10 "Manufacture of paper, printing and articles for culture, education and sport activity" Heavy industry (He)

11
"Processing of petroleum, coking, processing of nuclear fuel" 12 "Manufacture of chemical products" 13 "Manuf. of non-metallic mineral products" 14 "Smelting and processing of metals" 15 "Manufacture of metal products" 16 "Manufacture of general purpose machinery" 17 "Manufacture of special purpose machinery" 18 "Manufacture of transport equipment" 19 "Manufacture of electrical machinery and equipment" 20 "Manufacture of communication equipment, computers and other electronic equipment" 21 "Manufacture of measuring instruments" 22 "Other manufacturing" 23 "Comprehensive use of waste resources" 24 "Repair of metal products, machinery and equipment" Electricity, gas and water production and supply (EGW) 25 "Production and distribution of electric power and heat power" 26 "Production and distribution of gas" 27 "Production and distribution of tap water" Construction (Con) 28 "Construction" Service Transportation (Tran)  30 "Transport, storage, and postal services" Service industry (Serv) 29 "Wholesale and retail trades" 31 "Accommodation and catering" 32 "Information transfer, software, and information technology services" 33 "Finance" 34 "Real estate" 35 "Leasing and commercial services" 36 "Scientific research and polytechnic services" 37 "Administration of water, environment, and public facilities" 38 "Resident, repair, and other services" 39 "Education" 40 "Health care and social work" 41 "Culture, sports, and entertainment" 42 "Public administration, social insurance, and social organizations"