Ecological network analysis of the carbon metabolism system in mountainous cities based on the land–carbon nexus: a case study of the main urban area of Chongqing, China

The analysis of urban carbon metabolism will help to mitigate global warming and achieve China’s “Dual Carbon” targets. Taking the main urban area of Chongqing (MUAC) as an example, this study accounted for the carbon release and carbon absorption in MUAC, constructed an urban carbon flow model based on the land–carbon nexus, and evaluated the urban carbon metabolic system from 2000 to 2020 by using the ecological network analysis method. The results show that MUAC is dominated by a “carbon source” effect, and the net carbon flow is always negative. The negative carbon flow mainly comes from the conversion of cultivated land to construction land, and the positive carbon flow mainly comes from the conversion of construction land to cultivated land and woodland. The ecological relationship of carbon metabolism in MUAC is dominated by exploitation and control relationships, which mainly exist in the ecological relationship between construction land and cultivated land, and the spatial distribution is concentrated in the central and western areas of MUAC. Our research results can provide a reference for Chongqing’s green and low-carbon sustainable development as a means toward the realization of the “Dual Carbon” targets and provide a reference for other similar mountainous cities in western China.


Introduction
The issue of global warming caused by massive CO 2 emissions has become the focus of worldwide attention and poses a great challenge to the sustainable development of nature and human society (Hartley et al. 2021). As the densest and most active areas for human activities, cities account for about 75% of global carbon emissions (Grimm et al. 2008), and they are the main body of focus in reducing such emissions (Mi et al. 2016). Land use/ cover change (LUCC) under rapid urbanization is one of the main sources of urban carbon emissions, accounting for about one-third of urban carbon emissions (IPCC 2014). Under the combined influence of natural conditions and human activities, LUCC can significantly affect the pattern of urban carbon release and carbon absorption, thus changing the urban carbon balance and affecting the urban carbon metabolism process (Chang et al. 2022). In September 2020, at the General Debate of the UN General Assembly, General Secretary Xi Jinping proposed the "Dual Carbon" targets, with the intention for China to  (Tang et al. 2022). Then, in March 2021, the Chinese government officially incorporated the "Dual Carbon" targets into the 14th Five-Year Plan. Therefore, it is important to carry out urban carbon metabolism research in this context to mitigate global warming and balance the regional carbon budget. At present, the analysis and simulation of urban carbon metabolism from the perspective of systems ecology have gradually become the mainstream of research . Ecological network analysis (ENA) is a modeling method for quantitatively analyzing the flow of material and energy in an ecosystem, which consists of compartments and pathways. A compartment is a functional unit in an ecosystem, and a pathway is the means by which material and energy are transferred between compartments (Guan et al. 2019). The ENA method analyzes the flow of matter and energy in ecosystems (Hannon 1973). Patten et al. (1976) published the first study applying the ENA method. The method gradually matured and developed into a complete system of methods, including flow analysis, structure analysis, utility analysis, and function analysis (Borrett et al. 2018). In the current research on urban carbon metabolism, most scholars combine input-output analysis (IOA) and ENA to explore the carbon metabolism system among different social sectors or industries in cities. For example, Li et al. (2012) studied the behavior of carbon metabolism among different industries such as agriculture, mining, and construction in Beijing, and they analyzed the ecological relationships among industries by employing an ecological network utility analysis. Lu et al. (2017) constructed a carbon metabolism network model at the community scale in Beijing and found that the energy and household sectors are the main contributors to the stability of the carbon metabolism system. Han et al. (2018) conducted a comparative analysis of the carbon metabolism characteristics of four megacities (Shanghai, London, Tokyo, and Paris) based on the different socio-industrial divisions of the cities, such as primary, secondary, and tertiary industries. Duan et al. (2018) used multi-regional IOA and ENA to identify the key regions and sectors of carbon flows in China and propose targeted carbon reduction measures. Wang et al. (2018) constructed an ecological network of implied emissions for 30 provinces in China and explored the ecological network relationships among different provinces through flow-based analysis and utility analysis. Wang et al. (2019) used input-output models and an ENA of implied carbon emissions to study the ecological relationships between four municipalities (Beijing, Tianjin, Shanghai, and Chongqing) and other provinces. Chen et al. (2020) combined IOA and ENA to analyze carbon metabolism in Dongguan, clarifying the key contributors to urban carbon emissions and their pathways of action, and found that total direct and implied carbon flows were mainly concentrated in the manufacturing industry.
As can be seen from the above studies, most scholars combine ENA and IOA to focus on the influence of socioeconomic activities on the urban carbon metabolism process, and few consider the influence of natural environmental elements on urban carbon metabolism, ignoring the differences of different natural attribute subjects within the environment. At present, there is a lack of research on the incorporation of natural subjects into the carbon metabolism process; especially, research on the influence of LUCC on urban carbon metabolism in the urbanization process is still relatively uncertain, resulting in a lack of spatial analysis of the urban carbon metabolism process. In addition, the study area is mainly focused on international metropolises and coastal cities in eastern China, and little research has been reported on carbon metabolism in typical mountainous cities in China. Since the start of the twenty-first century, the implementation of the major national strategy of Western Development and the major project of the Three Gorges Reservoir has promoted the rapid economic development of the western region and the rapid growth of urban carbon emissions. Chongqing is located in inland China and is a typical mountainous city in the western region. It is an important economic center in the upper reaches of the Yangtze River, an important strategic fulcrum for the development of the western region, and an important link between The Belt and Road Initiative and the Yangtze River Economic Belt. In the past 20 years, the city's increase in population has accelerated, energy consumption has grown rapidly, and the scale of the city has continued to expand. In particular, the energy consumption and carbon emission intensity of the main urban area of Chongqing (MUAC) are relatively high, and the land-use changes are very drastic, resulting in serious imbalances in urban carbon metabolism. As land represents one of the important natural elements, this study comprehensively researches carbon metabolism in mountainous cities based on the land-carbon nexus. The research results can be implemented into urban spatial planning and provide scientific support for low-carbon development and carbon emission reduction in mountainous cities.
The remainder of this paper is structured as follows. First, we account for the carbon release and carbon absorption for different land types based on the land-carbon nexus. Second, we established a 5-year land-use transition matrix using remote sensing monitoring data of land use in MUAC from 2000 to 2020. The matrices representing LUCC carbon flows are combined with empirical coefficients to construct urban carbon flow models for the four different periods based on the carbon transitions that have resulted from LUCC. Finally, we use the ENA method to evaluate the carbon metabolism system in MUAC between 2000 and 2020 from the aspects of flow analysis, structure analysis, utility analysis, and function analysis. As it is important to understand the process of carbon metabolism in western mountainous cities before formulating an implementation plan of "Dual Carbon" targets, this paper focuses on a case study to provide a reference for other similar mountainous cities in western China and for the green and low-carbon development of a city and its formulation of differentiated emission reduction policies.

Study area
MUAC is located in west Chongqing. It is the political, economic, cultural, transportation, and financial center of the city, comprising the Yuzhong, Yubei, Jiangbei, Shapingba, Nanan, Beibei, Jiulongpo, Dadukou, and Banan districts. The landforms of MUAC are dominated by mountains and hills, with few platforms and dams, forming a pattern of "two rivers and four mountains," consistent with the layout of a typical mountainous city in southwest China (Xiang et al. 2022). MUAC of 5466 km 2 was home to a resident population of 10.34 million in 2020, accounting for 32% of Chongqing, and it had a gross regional product of 982.2 billion yuan, accounting for 39% of Chongqing (Fig. 1).

Data sources
Land-use data were obtained from the Data Center for Resources and Environmental Sciences of the Chinese Academy of Sciences (http:// www. resde. cn), which had a resolution of 30 × 30 m. The land-use data were reclassified into six major categories: cultivated land, woodland, grassland, water, construction land, and unused land. Five landuse raster maps were obtained for 2000, 2005, 2010, 2015, and 2020

Accounting for urban carbon release and carbon absorption
This study needs to account for carbon release and carbon absorption for the six land types in MUAC. Specifically, cultivated land needs to consider both the "carbon source" and "carbon sink" effects, woodland considers its "carbon sink" effect, grassland considers its "carbon sink" effect, water considers its "carbon sink" effect, construction land considers its "carbon source" effect, and unused land considers its "carbon sink" effect.
(1) Accounting for carbon release and carbon absorption on cultivated land Cultivated land has both "carbon source" and "carbon sink" effects. On the one hand, agricultural production and irrigation processes produce a large amount of CO 2 and other greenhouse gases, consistent with a "carbon source" effect. On the other hand, crops can absorb a certain amount of CO 2 through photosynthesis during their reproductive periods , which is a "carbon sink" effect. According to a study by Cai et al. (2005), which showed a crop carbon emission coefficient of 0.429 t·hm −2 , and a study by He (2006), which showed a crop carbon uptake coefficient of 0.007 t·hm −2 , cultivated land generally exhibits a net "carbon source" effect with a coefficient of 0.422 t·hm −2 . This study calculates the carbon release and carbon absorption of cultivated land using Eq. (1) (Xia and Chen 2020): where C i is the carbon release or absorption of landuse type i (t); S i is the area of land-use type i (hm 2 ); θ i is the carbon source or sink coefficient of land-use type i (t·hm −2 ).
(2) Accounting for carbon absorption on woodland MUAC is located in the subtropical zone, and the types of forest land resources are relatively rich. Fang et al. (2007) showed that the carbon sink coefficient of woodland is 0.644 t·hm −2 , and based on the studies of other scholars on Chongqing and its similar surrounding regions (Xiao et al. 2012;Wang et al. 2017), the average of the coefficients in the above studies was taken as 0.623 t·hm −2 (1) in this study. Finally, this study uses Eq. (1) to calculate the carbon absorption of woodland (Xia and Chen 2020).
(3) Accounting for carbon absorption on grassland Fang et al. (2007) showed that the carbon sink coefficient of grassland is 0.022 t·hm −2 , which is consistent with studies of other scholars in similar areas around Chongqing (Xiao et al. 2012;Wang et al. 2017). Peng et al. (2016) and  took the values of 0.0205 t·hm −2 and 0.022 t·hm −2 for Sichuan and Wuhan, respectively, and their range of variation is not large, so the average value is taken as 0.021 t·hm −2 in this study. Finally, this study uses Eq. (1) to calculate the carbon absorption of grassland (Xia and Chen 2020).
(4) Accounting for carbon absorption on water Usually, water is considered to have a "carbon sink" effect. Studies by , Lai (2010), and Sun et al. (2015) reported carbon sink coefficients of waters of 0.298 t·hm −2 , 0.253 t·hm −2 , and 0.252 t·hm −2 , respectively. In taking the average value of the above research results, this study selects the water carbon sink coefficient as 0.268 t·hm −2 . Finally, this study uses Eq. (1) to calculate the carbon absorption of water (Xia and Chen 2020).
(5) Accounting for carbon release on construction land Carbon release from construction land mainly comes from energy consumption and population respiration. On the one hand, this study considers the actual situation of energy use in Chongqing. To reduce the negative impact of statistical errors on the research results, the selection of energy types should be as comprehensive as possible, including the 18 energy types required for production and life processes and various energy standards. The coal conversion coefficient and the corresponding carbon emission coefficient are consistent with data from the literature (IPCC 2006; NBS 2021) (see Tables 1 and 2). On the other hand, the carbon release owing to population respiration is calculated from the resident population and the carbon release coefficient of human respiration. Kuang et al. (2010) showed that the annual respiration carbon release per person is about 0.079 t. The carbon release on construction land is calculated by Eq.
(2) (Quan et al. 2020): where C cons is the total carbon release of construction land (t); C e is the carbon release of energy consumption (t); C p is the carbon release of human respiration (t); m i is the terminal consumption of energy source i (t); n i is the standard coal conversion factor of energy source i (t·t -1 ); α i is the carbon emission factor of energy source i (t·t -1 ); p is the total resident population (p); and β is the carbon release coefficient of human respiration (t·p −1 ·a −1 ).
(6) Accounting for carbon absorption on unused land The area of unused land in MUAC is relatively small and is mainly marshland and bare rock gravel. Referring to the studies of Wei and Chen (2021), Lai (2010), and Fan et al. (2018) and taking the average of their findings, 0.005 t·hm −2 was selected as the carbon sink coefficient for unused land in this study. Finally, this study uses Eq. (1) to calculate the carbon absorption of unused land (Xia and Chen 2020).

Urban carbon flow model
The transfer of different land types and the changes in carbon metabolism within the same land type make one land type transfer its carbon flow to another land type. In this study, we construct an urban carbon flow model ( Fig. 2) based on the net carbon source or carbon sink rate (defined as carbon metabolic density) per unit area of each land-use type and the transfer area between different land-use types using the following formulas: where f ij is the carbon flow rate from compartment j to compartment i, same below; ΔM is the carbon metabolism density difference; ΔS is the area of compartment j transferred to compartment i; M i and M j are the net carbon flow densities of compartments i and j, respectively; V i and V j are the net carbon flow rates of compartments i and j, respectively; and S i and S j are the areas of compartments i and j, respectively. If f ij > 0, there is a positive carbon flow, and the imbalance of urban carbon metabolism is mitigated by either reducing carbon release or increasing carbon absorption; if f ij < 0, there is a negative carbon flow, and the imbalance of urban carbon metabolism is aggravated by either increasing carbon release or reducing carbon absorption.

Ecological network analysis method
Flow analysis Flow analysis is the basis of ENA, which is used to analyze the distribution of ecological network flows and to identify direct and indirect effects. The flow analysis needs to be based on the carbon flux T of each compartment, so the carbon flux T i of compartment i is defined in this study as equal to all carbon flows into or out of compartment i minus or plus the state variable x i . If x i < 0, T i is equal to all carbon flows into i minus x i ; if x i > 0, T i is equal to all carbon flows out of i plus x i . The calculation of T i is given as follows (Xia et al. 2019a, b): where T i is the carbon flux of compartment i, same as below; f ji is the carbon flow from compartment i to compartment j, same as below; and x i is the state variable, which refers to the difference between the inflow carbon and the outflow carbon in compartment i.
In this study, we first calculate the dimensionless direct flow intensity matrix G based on the direct flow between each compartment f ij and the carbon flux T j of each compartment, and then calculate the dimensionless total flow matrix N based on this matrix G, and define the ratio of indirect flow to direct flow as the H-index as follows (Xia et al. 2019a, b): where T j is the carbon flux of compartment j; G is the dimensionless direct flow intensity matrix, same as below; g ij is an element in matrix G; N is the dimensionless total flow matrix; I is the unit matrix, same as below; N-I-G is the dimensionless indirect flow matrix; H is the ratio of indirect flow to direct flow; G 0 is the self-feedback matrix, which represents the self-feedback effect of the carbon flow flowing through each compartment; G 1 is the direct flow intensity matrix, which represents the direct carbon flow transferred between each compartment and is expressed by the higher power of the direct flow intensity matrix G indirect flow intensity with different path lengths; and G m (m ≥ (d represents the indirect flow intensity with a path length of m between compartments. Structure analysis Structure analysis is used to calculate the weight of each compartment within the urban carbon metabolic system, which reflects the importance of the carbon flow input and output related to that compartment in the carbon metabolic process of the entire urban system; this calculation encompasses the carbon flow contribution of that compartment in the urban carbon metabolic system and facilitates the identification of critical compartments. In this study, the structure analysis W-index in ENA is used to characterize the weight of different compartments. The specific formulas are given as follows (Xia et al. 2019a, b): where W is the structure analysis index; N′ is the quantified overall flow matrix; and n′ ij is an element in matrix N′.
Utility analysis Utility analysis is used to explore the utility relationship between each compartment in the urban carbon metabolic system, clarify the roles and functions of each compartment in the urban carbon metabolic system, and reveal the inherent mutualism, exploitation, control, and competition of ecological relationships between each compartment. To characterize the effective direct utility between each compartment, the direct utility matrix D and the dimensionless total utility matrix U are defined in this study. The specific formulas are given as follows (Xia et al. 2019a, b): where D is the direct utility matrix; d ij is an element in matrix D; U is the dimensionless integral utility matrix and represents the overall relationship between any two nodes in the network; u ij is an element in matrix U; matrix D 0 is the self-feeding of traffic in each compartment; matrix D 1 represents the direct traffic utility between two nodes in the network system; and matrix D k (k ≥ 2) is the non-direct traffic utility between two nodes in the network system after k steps.
In this study, the positivity and negativity of element u ij in the dimensionless integral utility matrix U are defined as the matrix Sgn (U), where the element is denoted as Su ij , which represents the interactive relationship between two compartments, including nine ecological relationships (Table 3). The utility symbols between compartments 1 and 2 are denoted as Su 12 and Su 21 , where Su 12 represents the utility flow from compartment 2 to compartment 1, and Su 21 represents the utility flow from compartment 1 to compartment 2. If (Su 21 , Su 12 ) = (+ , −), it means that compartment 2 preys on compartment 1; if (Su 21 , Su 12 ) = (− , +), it means that compartment 2 is controlled by compartment 1; if (Su 21 , Su 12 ) = (− , −), it means that there is a competitive relationship between compartments 1 and 2, with negative effects on both sides; if (Su 21 , Su 12 ) = (+ , +), it means that there is a mutualism relationship between compartments 1 and 2, with positive effects on both sides; if (Su 21 , Su 12 ) = (0, 0), it means that there is a neutralism relationship between compartments 1 and 2, with no effects on either sides.
Among the nine ecological relationships mentioned above, five (commensalism, commensalism host, neutralism, amensalism, and amensal host) are not involved because the case of Su ij = 0 usually does not occur in the ecological network of the urban carbon metabolism system. Therefore, the ecological relationship is composed of only four common relationships: mutualism, exploitation, control, and competition. Based on the dimensionless integral utility matrix U, this study defines the symbiosis K-index as an objective function of the symbiosis network of the urban carbon metabolic system, which is used to determine the overall symbiosis status of the urban carbon metabolic system. When K > 1, the positive utility in this system is greater than the negative utility, indicating that the overall positive symbiosis of the system is greater than the negative competition and that land-use change has a positive effect on the balance of urban carbon metabolism; the larger the K-index, the more obvious the positive effect. When K < 1, the negative utility in this system is greater than the positive utility, indicating that the negative competitiveness of the system is greater than the positive symbiosis, and the land-use change has a negative effect on the urban carbon metabolism balance; the smaller the K-index, the more obvious the negative effect. The K-index is calculated as follows (Xia et al. 2019a, b): where S + (U) is the number of positive utilities in the utility matrix U; S − (U) is the number of negative utilities in the utility matrix U.

Accounting for carbon release and carbon absorption in MUAC
As can be seen from Table 4, in terms of carbon release, the overall carbon release in MUAC has increased in the last 20 years, which is due to the rapid economic development and the significant increase in social consumption level in MUAC in the past 20 years. Industries such as real estate and automobiles have led to the rapid expansion of high-carbon manufacturing industries such as extractive, petroleum and metal processing, and building materials industries, resulting

Carbon flow transfer in MUAC
The carbon flow transfer in MUAC during the study period is calculated based on the carbon flow model (Table 5).
The results show that the total carbon flow in MUAC has shown increased volatility in the past 20 years, and the total carbon flow from 2015 to 2020 was 3.02 times that of 2000 to 2005. During the study periods, the positive carbon flow was 0.034 times, 0.030 times, 0.031 times, and 0.115 times that of the negative carbon flow, respectively, resulting in a negative net carbon flow in MUAC and an imbalance of the urban carbon metabolism. From 2000 to 2020, most of the negative carbon flow in MUAC came from the conversion of cultivated land to construction land (Cu → Co), and a small part came from the conversion of woodland to construction land (Wo → Co), accounting for 93.51% and 5.14% of the total negative carbon flow, respectively. This result is because the rapid development of urbanization and industrialization in Chongqing, a modern industrial base of national importance, has led to a dramatic increase in the demand for construction land, resulting in the conversion of construction land from cultivated land and woodland. The positive carbon flow in MUAC mainly came from the conversion of construction land to cultivated land (Co→Cu) and construction land to woodland (Co→Wo), accounting for 69.79% and 13.75% of the total positive carbon flow, respectively. This phenomenon occurred because of two reasons. First, the State Council of China strictly investigated the illegal occupation of cultivated land for construction land in 2009, and second, the construction of the protection project in the upper reaches of the Yangtze River has increased the local carbon sink in MUAC and brought some positive carbon flow. Increased attention has been paid to woodland protection, which could significantly improve urban carbon metabolism as an important urban carbon sink.

Flow analysis
It can be seen from  the pathways of the carbon metabolism system in MUAC decreased during this period, and the direct and indirect pathways tended to be simplified, which was not conducive to the stability of the urban carbon metabolism. The H-index rebounded significantly from 2015 to 2020, and the results indicated that compared with the past, the pathways of urban carbon metabolism increased during this period, and the direct and indirect pathways tended to be more complicated, promoting a more stable connectivity between different compartments. In this way, the stability of the carbon metabolism process in MUAC has been restored. Figure 4 shows that the influence and contribution levels of different compartments on the urban carbon metabolic system are quite different. During the whole study period, the carbon flow contribution level of each compartment remained basically stable when ranked from largest to smallest: cultivated land > construction land > woodland > water > grassland > unused land. This result indicates that the cultivated land compartment exerts a significant influence on maintaining the carbon metabolic system in MUAC, with a contribution between 34.50 and 37.66%. This is because cultivated land is the most widely distributed compartment within MUAC, accounting for 58.15% of the total. Not only is cultivated land one of the main sources of carbon emissions, it is also an important component of carbon sequestration and plays an important role in maintaining the regional carbon cycle. The construction land compartment is the second largest contributor to the carbon metabolism system in MUAC, with a contribution between 24.19 and 30.20%. This is because the scale of construction land in MUAC has expanded rapidly in the past 20 years, which has accelerated the rate of urban carbon metabolism, reflecting the inherent laws of urbanization. In addition, the weight of the unused land compartment and the grassland compartment within the whole system is not high, with contributions ranging from 7.35 to 10.05% and 7.39 to 10.11%, respectively, indicating that the role and influence of these two compartments on the carbon metabolic process in MUAC are limited. This is because the area of unused land and grassland in MUAC is extremely small, accounting for about 1% in total, with a weak carbon sink capacity and a low degree of impact on the carbon metabolism system.

Utility analysis
From Fig. 5, the symbiosis K-index of the carbon metabolic system in MUAC from 2000 to 2020 was 1.40, 0.80, 0.57, and 1.40 respectively, showing a "U-shaped" trend, indicating that the symbiosis level of the carbon metabolic system in MUAC in the last 20 years first decreased before increasing. In addition, the symbiosis K-index was less than one in 2005 ~ 2015, indicating that the negative utility between the compartments in the system was greater than the positive utility during this period. It follows that the urban carbon metabolism system was developing in a negative and disorderly direction, and LUCC had a negative effect on the urban carbon metabolic process. The symbiosis K-index was greater than one in 2000 ~ 2005 and 2015 ~ 2020, indicating that the positive utility between the compartments in the system was greater than the negative utility during these two periods. At this time, the urban carbon metabolism system showed sustainability and developed in a positive and orderly direction, and LUCC had a certain degree of positive effect on the urban carbon metabolic process.

Function analysis
The carbon metabolism system in MUAC contains six compartments and thirty pairs of ecological relationships (Fig. 6). As the exploitation relationships and control relationships are essentially the same in the urban carbon metabolic system, and they refer to one compartment obtaining carbon utility from another compartment, this study combines them into one relationship for function analysis. The mutualism relationships mean that both compartments benefit from the relationship, exhibit interdependence, and promote the mutual development of each other. The competition relationships mean that both compartments suffer carbon damage under the relationship, resulting in an increased urban carbon imbalance.  Fig. 6 The distribution of the ecological relationship of carbon metabolism in MUAC. Note: The red area represents the exploitation relationships; the blue area represents the control relationships; the yellow area represents the competition relationships; and the green area represents the mutualism relationships negative carbon metabolic compartment and intense carbon storage plundering behavior compared to other compartments, seriously affecting the balance of the urban metabolic system. The second area is the competition relationship, accounting for 35% of all ecological relationships. These are mainly concentrated in the cultivated land compartment, which indicates that the cultivated land compartment functions as a negative carbon metabolic compartment and competes more intensely with other compartments for carbon storage. It follows that the cultivated land compartment has a degree of negative impact on maintaining the balance of the urban carbon metabolic system. Finally, the mutualism relationships accounted for 13.33% of all ecological relationships, which indicated that ecological conflicts were obvious in the process of land-use change in MUAC in the past 20 years, and there was an intense competition for carbon storage among compartments. From the spatial distribution of ecological relationships (Fig. 7), the white area indicates that no land-use transfer has occurred. The land transfer area in MUAC increased from 104.90 to 643.70 km 2 from 2000 to 2020, respectively, indicating that LUCC was more intense under the guidance of urbanization, resulting in a subsequent increase in carbon flow caused by LUCC and prompting the spatial expansion of the distribution of ecological relationships.

Fig. 5 Changes of the symbiosis K-index in MUAC
From 2000 to 2005, the distribution of ecological relationships in MUAC was relatively small because this period coincided with the early stage of development of Chongqing when urbanization was in its initial stage, and the process of land-use change was relatively gradual. The distribution of the exploitation and control relationships was patchy and spatially concentrated in Jiangbei, Nanan, and the southwestern part of Yubei, mainly from the transfer of cultivated land to construction land, leading to the carbon cycle proceeding in a negative direction. The competition relationships were scattered throughout the whole area of MUAC, mainly between cultivated land and woodland.
From 2005  since 2005, causing the trend of land-use changes to become increasingly obvious. This is mainly the result of the spatial conversion of cultivated land and woodland to construction land and is mainly distributed in Shapingba, Nanan, and the southwest of Yubei, with a patchy distribution. The distribution area of competition relationships is small, primarily concentrated in Jiangbei and Banan, and the distribution is scattered, mainly between cultivated land and woodland. From 2010 to 2015, the proportion of exploitation and control relationships in MUAC continued to increase. These relationships were widely distributed in all urban areas, especially in Beibei, Yubei, and Jiangbei, mainly due to large amounts of cultivated land being replaced by construction land. The competition relationships were also distributed at scattered points within the entire study area, mainly between the cultivated land and the woodland. There were no mutualism relationships during the study period.
From 2015 to 2020, the proportion of exploitation and control relationships in MUAC decreased, mainly between cultivated land and construction land, and they were mainly distributed in the central part of MUAC, including Yubei, Jiangbei, and Shapingba. The competition relationships were scattered in MUAC, primarily concentrated in Shapingba and Jiulongpo, mainly between cultivated land and woodland.
In terms of the area and proportion of ecological relationships (Table 7), the proportion of exploitation and control relationships is the largest (66.53 ~ 87.75%), followed by competition relationships (12.25 ~ 31.69%), and the proportion of mutualism relationships is the smallest (0 ~ 1.78%). In general, the exploitation and control relationships mainly exist in the ecological relationship between construction land and cultivated land, indicating that the occupation of cultivated land by construction land expansion plays an important role in the urban carbon metabolism process. The competition relationships mainly exist in the ecological relationship between cultivated land and woodland due to the large degree of land transfer between these two compartments. The mutualism relationships mainly exist in the ecological relationship between unused land and grassland, with a very small distribution area.

Innovation and significance of the study
China faces the huge challenge of realizing the "Dual Carbon" targets. To this end, it is urgent and realistic to research urban carbon metabolism, which can provide an effective framework for tracking urban carbon flow ). Most previous studies used different socio-economic sectors or industries as compartments to explore the impact of socio-economic factors on the urban carbon metabolism process Xu et al. 2021;. However, the impact of natural factors with different attributes on urban carbon metabolism was often ignored, resulting in a lack of spatial analysis of urban carbon metabolism, which makes it difficult to implement the research results into the spatial planning adjustment of urban low-carbon development. Therefore, this study complements this research gap by exploring the impact of LUCC on urban carbon metabolism based on the land-carbon nexus using the ENA method, which is helpful for low-carbon urban development and carbon emission reduction. In addition, previous study areas on urban carbon metabolism have mainly focused on Beijing (Xia et al. 2017(Xia et al. , 2018Xia et al. 2019a, b) and eastern coastal cities Xia and Chen 2020;Guan et al. 2021). Studies on carbon metabolism in western mountainous cities have not yet been conducted. Due to the variability of carbon metabolism characteristics in different types of cities , it is difficult for existing studies to provide a reference for western mountainous cities. This paper provides a case study of a typical mountainous city with Chongqing as the research object, which helps to fill the abovementioned knowledge gap of mountainous cities. Our research results can provide scientifically based support strategies to help realize the "Dual Carbon" targets for the same type of mountainous cities in China.

Comparison of carbon metabolism between MUAC and other cities
The results of the accounting of carbon release and carbon absorption show that carbon emissions in MUAC have demonstrated an increasing trend whereas carbon absorption has shown a decreasing trend over the past 20 years, and the magnitude of the former is much larger than that of the latter. Similar results were obtained in the studies of Guangdong, China (Pei et al. 2018), and the Bangkok metropolitan area, Thailand (Ali et al. 2018). Pei et al. (2018) found that total carbon emissions in Guangdong increased sharply from 76.11 to 140.19 Tg between 2005 and2013, and the carbon absorption decreased from 54.52 to 53.20 Tg. Ali et al. (2018) also found that between 1987 and 2015, carbon emissions in the Bangkok metropolitan area, Thailand, increased by nearly four times, whereas carbon absorption fell to half of its original level. Carbon flow transfer analysis shows that the negative carbon transfer in MUAC was mainly caused by the conversion of cultivated land to construction land, which is similar to Beijing (Zhang et al. 2014), Nanjing (Zhao et al. 2014), and Zhejiang (Xia and Chen 2020), as the expansion of construction land due to urbanization and industrialization was mainly due to encroachment upon the cultivated land. The positive carbon flow mainly came from the conversion of construction land to cultivated land, which was due to the efforts of the Ministry of Natural Resources in strictly investigating and dealing with all kinds of illegal occupation of cultivated land or the change in cultivated land use in recent years, curbing the "non-agriculturalization" of cultivated land and restoring construction land occupied by cultivated land back to cultivated land. The negative carbon flow in MUAC in 2000 ~ 2020 was 9.1 ~ 33.3 times that of the positive carbon flow, resulting in a negative net carbon flow in MUAC. Similar results were reflected in the study by Xia and Chen (2020), who found that the negative carbon flow was 3.6 ~ 12.5 times that of the positive carbon flow in Zhejiang from 1995 to 2010.
The results of utility analysis show that the symbiosis K-index of MUAC was greater than one from 2000 ~ 2005, which is inconsistent with the results from Xia and Chen (2020) on Zhejiang from 2000 to 2005. This discrepancy is likely due to the fact that urban development affects the characteristics of urban carbon metabolism to some extent. Chongqing is located in the inland west, and its development conditions are limited; furthermore, its development start time is later than that of the developed cities along the eastern coast. At the beginning of the twenty-first century, when the "Western Development" strategy was first implemented, land-use development was low, and the contradiction between humans and land was not yet prominent. This is in contrast to Zhejiang, which was already in the stage of rapid development; consequently, the contradiction between land use intensified, resulting in the symbiosis K-index of Zhejiang being less than one from 2000 to 2005. Compared with 2000 ~ 2015, the symbiotic level of the carbon metabolism system in MUAC demonstrated improvement from 2015 to 2020, mainly due to the scientific delineation of urban development boundaries in Chongqing in the 13th Five-Year Plan. This had the net effect of revitalizing the stock space and promoting intensive and compact orientation. On the other hand, there has been a continuous adjustment of the industrial structure. The high-tech manufacturing industry has been vigorously developed, energy utilization efficiency has been improved, and urban carbon emissions have decreased. The same change trend is reflected in Shanghai (Xia et al. 2019a, b). In addition, the symbiosis K-index in MUAC fluctuates between 0.57 and 1.40, which is inconsistent with the typical wetland cities (Guan et al. 2019), and the symbiosis K-index in Dongying is more stable (between 1.2 and 1.3), which may be due to the more mature development status and more stable ecosystem relationships between compartments compared to MUAC.
The results of the function analysis show that the ecological relationship of carbon metabolism in MUAC is dominated by exploitation and control relationships that mainly exist in the ecological relationship between cultivated land and construction land as a result of rapid urban expansion, which is consistent with the study results of Xia et al. (2017) on Beijing and Guan et al. (2019) on Dongying. Symbiotic relationships, which guarantee the balanced development of urban carbon metabolism, mainly exist between compartments with lower carbon metabolism density and are not easily formed between compartments with higher carbon metabolism. Similar conclusions are reflected in the study of Xia et al. (2017). There is competition between cultivated land and woodland, exacerbating local carbon imbalances. The strict protective system of cultivated land has led to the occupation of land such as woodland and grassland as the same exploited object by cultivated land. As the carbon storage of woodland is higher than that of cultivated land, the conversion of woodland to cultivated land causes carbon emissions (Tong et al. 2020). Therefore, it is necessary to avoid maintaining the balance of cultivated land at the expense of woodland loss during the rapid urban expansion process.

Policy implications
As the negative carbon flow mainly comes from the conversion of cultivated land to construction land, it is suggested that the Chongqing municipal government should, on the one hand, accelerate industrial upgrading, gradually phase out industrial enterprises with high energy consumption and high emission, develop low-carbon industries, improve energy use efficiency, and reduce carbon emissions from construction land. On the other hand, we will strictly approve construction land; strengthen the efficient, economical, and intensive use of construction land; curb the encroachment of cultivated land; and reduce carbon emissions in MUAC by adjusting the optimization of land-use structure. In addition, from the perspective of carbon sink, scientific afforestation can strengthen forest protection and management, enhance forest quality, improve forest ecological functions, optimize the structure of afforestation seedlings, and further increase the carbon sink of forest and grass, which can better promote the realization of Chongqing's "Dual Carbon" targets.
Ecological relationships also provide an effective way to achieve carbon emission reduction. The structure analysis found that cultivated land and construction land are two important compartments that affect the sustainability of the urban carbon metabolic system. The function analysis found that exploitation and control relationships were the most obvious, mainly in the ecological relationship between construction land and cultivated land. Therefore, it is suggested that the Chongqing municipal government should pay attention to the reasonable layout and allocation of cultivated land and construction land in each region in future urban planning, focus on the protection of cultivated land and the reasonable supply of construction land, and emphasize intensive urban development, which is of great significance for improving the carbon metabolism of the city.

Limitations
Regarding the carbon emissions and absorption accounting method, this study adopts the commonly used empirical coefficient method to calculate the carbon emissions and absorption in MUAC, and the reference values of the carbon source/sink coefficient are taken from the existing research literature. If the value of the carbon source coefficient is larger, the results would show that the imbalance of urban carbon metabolism has increased; if the value of the carbon sink coefficient is larger, the results would show that the imbalance of urban carbon metabolism has been alleviated. Therefore, in this study, to reduce the negative impact of a single error on the research results, the research results of Chongqing and its surrounding similar regions were selected, and the coefficients were chosen by calculating the average value used by other scholars (Xia and Chen (2020); Chen et al. 2020), which is reasonable and conducive to reducing errors. To further improve the accuracy of the accounting results, future studies should combine field sampling and modeling methods (Pan et al. 2011), conduct a deep analysis of carbon source/sink coefficients for the actual situation of MUAC, and consider the influence of inter-annual variation to obtain a more suitable carbon sink coefficient for MUAC. Regarding the ENA method, the division of compartments will affect the results of the evaluation of the urban carbon metabolic system (Xia et al. 2018). Due to the difficulty and limitation of data acquisition, this study has made a relatively rough division of the compartments in MUAC, and only six common land types have been classified, so the realistic guiding significance of the results of this study is somewhat limited. Future studies can further divide the compartments within the carbon metabolic system into more detailed divisions to better identify the relationship of the urban carbon metabolic ecological network and provide more detailed scientific support for urban planning.

Conclusions
This study analyzed the carbon flow transfer in MUAC based on the urban carbon flow model and evaluated the urban carbon metabolic system from 2000 to 2020 using the ENA method from the aspects of flow analysis, structure analysis, utility analysis, and function analysis. The main conclusions are as follows: From 2000 to 2020, the carbon emission in MUAC was 31.43 times, 31.53 times, 49.43 times, 51.99 times, and 51.58 times that of carbon absorption, respectively, causing the city to behave as a net carbon source. In the past 20 years, the net carbon flow in MUAC has been negative, with a fluctuating downward trend. The negative carbon flow mainly came from the conversion of cultivated land to construction land, and the positive carbon flow mainly came from the conversion of construction land to cultivated land and woodland.
The flow analysis showed that the H-index of MUAC in the past 20 years was 0.287, 0.189, 0.094, and 0.330, respectively, showing a "V-shaped" trend. The structure analysis showed that the carbon flow contribution levels of each compartment were in the following order: cultivated land > construction land > woodland > water > grassland > unused land. The utility analysis showed that the symbiosis K-index of MUAC from 2000 to 2020 was 1.40, 0.80, 0.57, and 1.40, respectively, showing a "U-shaped" trend. The function analysis showed that the ecological relationship of carbon metabolism in MUAC was dominated by exploitation and control relationships, which mainly existed in the ecological relationship between construction land and cultivated land. Its spatial distribution was concentrated in the central and western areas of MUAC, including Jiangbei, Shapingba, Nanan, and the southwestern part of Yubei.
The Chongqing municipal government should pay attention to the reasonable layout and distribution of cultivated land and construction land in each region in future urban planning, adjust the optimization of urban land-use structure to reduce carbon emissions in the main urban area, and carry out scientific afforestation and greening to further increase