Analyzing the spatiotemporal carbon change mechanism: a land-based carbon flow network (CFN) for cities

High carbon emissions played a significant role in global climate change, which made cities with rapid urbanization responsible for local carbon mitigation. In this study, a land-based CFN framework was established by taking 15 land use types as different network nodes. The framework was intended to be a dynamic structure containing the carbon emissions/sequestration tracking, land-based carbon network and utility analysis, and carbon change mechanism identification. By taking Guangzhou city as an empirical study, the carbon metabolism patterns were shown as increasing emission expansion and spatial differentiation. The high-level emission patches extended from the city center to the suburb with 1/2 to 1/3 the original size from 2000 to 2020, which featured as land use transition toward T in the north and to C2 in the south. All the changing carbon processes among land nodes were detected to conduct CFN utility analysis for mechanism investigation. Exploitation was found significantly contributed to the carbon emissions in 2000–2005 and fell over time. In the built-up area, the dominant carbon relationship has changed from exploitation to mutualism with enlarged carbon emissions in 2000–2005, 2005–2010, and 2010–2015, and the exploitation became dominant in 2015–2020 with increasing carbon sequestration. Under the increasing competitive relationship, carbon emissions of the related land nodes decreased more than 90% from 2000 to 2020 with favorable mutual restriction between pairwise nodes. It provided valuable insight for the carbon mitigation options at a city level through local urban planning.


Introduction
As one of the largest producers of carbon emissions, cities play an important role in global climate change. There has been considerable increase in scientific evidence concerning the carbon emissions from human settlements, which are highly dependent on the economic environment of the cities. Although local governments and institutions often attempt to enact local carbon mitigation mandates, these efforts were often hampered by the fact that they only apply to certain economic sectors, rather than the entire community (Chen et al. 2018). Increasing urbanization with resulting land use changes and population growth reinforced the carbon emissions, which made the carbon reduction a challenge in urban areas. Some researches explored the carbon production, carbon emission, and carbon sequestration that occur in urban environment experiencing land use changes (Kennedy et al. 2010;Kellett et al. 2013;Zhang et al. 2014), which showed that the characteristics of urban carbon change varied across urbanization trajectories, making the effectiveness of carbon mitigation options different across individual cities. Therefore, in order to understand the carbon mitigation potential of a given city from land use perspective, a framework is needed to assess the land-based carbon emission patterns and quantify the carbon change mechanism under multiple land use transitions.
For several decades, studies on carbon assessments have been mainly focused on the carbon emissions. Guidelines established by the IPCC (International Panel on Climate Change) have provided empirical methods for determining the carbon emissions based on the energy usage of a given area (IPCC 2006). Widely studied in different urban areas, carbon emissions from human settlements were found to be very diverse, which referred to different energy end-use activities and varied carbon accounting methods. (Department of Energy & Climate Change 2013). Since most of the carbon emissions were assessed by analyzing related energy consumption for different industries, social economic sectors, or even buildings (Bhan et al. 2021), the carbon emissions in certain land territories, independent of their geographic location and spatial transformation, limited the understanding of the total carbon dynamics. However, carbon emission refers to only the result of current activities but also represent recovery from past disturbances (i.e., the carbon emission increases that would occur in the absence of vegetation land cover) (Searchinger et al. 2018). This implies opportunity to detect these changing emissions. Different from emissions, carbon sequestration was mainly attributed to the land cover types present in each environment (Xu et al. 2016). Carbon storage density, which reflected the sequestration capacity of different land cover types, was often taken as a constant coefficient for quite a long time (Li et al. 2020). Therefore, carbon emissions/sequestration have typically been studies of two aspects: (1) sequestration changes due to land cover changes and (2) emission changes caused by variations in the energy consumption of a socioeconomic system. Although attempts have been made in the understanding of how human activities affect carbon emissions/ sequestration dynamics, there was still much work to be done and more detailed information concerning the carbon metabolism under multiple land use transitions was required. By integrating the carbon emissions/sequestration flows in an urban area or surrounding areas resulting from LUCC (land use/cover change), carbon metabolism provided a good analytical framework for examining the temporal and spatial dynamics of carbon processes to support sustainable urban planning (Xia et al. 2016).
In order to understand the changing mechanism of carbon metabolism in urban systems, the relationship between carbon patterns and urbanization was further investigated by scholars with relate to complex LUCC. For example, the carbon storage losses caused by land use transitions from vegetation cover to new build-up areas in the pan-tropics were found representing ~ 5% of the total system carbon change (Seto et al. 2012). Other studies, which concerned the influence of the changing land use structure on the carbon changes within a certain city, argued that most of the increased carbon emissions have been attributed to the energy use on the enlarged urban land area (Zhang et al. 2014;Edelenbosch et al. 2020). Furtherly, the carbon emission change in different land spaces (agriculture, production and living, and transportation) in China was analyzed, which showed that increasing the extent of land dedicated to different land-uses has increased carbon emissions in many areas, but this finding was not universal for all provinces and spaces (Wu et al. 2012). The land use carbon emissions have also been studied in the Beijing-Tianjin-Hebei urban agglomeration in China, which concluded that the relationship between urbanization and land use carbon emissions can be summarized into three modes: "high urbanizationlow emissions," "middle urbanization-high emissions," and "low urbanization-low emissions" (Zhou et al. 2021). The city of Eindhoven (230,000 inhabitants), Netherlands, was used as a case study to investigate the relation between carbon emission and different land use categories. Based on the land use function and land cover composition, 14 valid land use categories were classified including agriculture, transport, retail trade, green space (with 3 sub-categories), residential (with 7 sub-categories), and others. The outcomes showed that the retail trade and residential land use categories contributed a large proportion of carbon emissions; terrace houses produce more carbon emission than other residential building categories . These knowledge of the relation of land use and carbon emission supported a new sight for urban planning that carbon mitigation should be one of the development targets when those in authority make decisions about land use.
For carbon mitigation potential, it depended on the ability to both remove carbon emissions from the atmosphere and reduce emissions caused by human activities and policy regulation (Cui et al. 2019). Carbon mitigation policies have been studied by scholars to reveal their effectiveness on carbon reduction, which concluded that the quantitative method and refined policy design were very important to reduce consumption-based emissions (Li et al. 2021). An empirical study in Brazil, which uses a new method that combines both energy and land use simulation to explore the complex relationship between agriculture, deforestation, and the energy-related carbon emission, showed that Brazil has the potential to liberate around 24.4 Mha of agricultural land by mid-century, and the large-scale reforestation could have the capacity to sequester around 5.6 GtCO2 (Kerdan et al. 2019). Although these current studies have highlighted varied options for carbon mitigation, related stakeholders may have different views on what land use type was needed in a certain area (UNEP 2009;WBGU 2009). The complex relationships within and between different social sectors make further consensus on carbon reduction difficult (Wang et al. 2018). Accompanied with continuous urbanization, the carbon tradeoffs between different socio-economic sectors were expected to continue, where a node refers to an economic sector of the urban economy, and the flow refers to an observed transfer of carbon emission (Chum et al. 2011;Coelho et al. 2012).
Since ecological network analysis (ENA) provides a group of indicators that reflect the dynamic structure and pattern of ecological systems, it was applied to analyze the carbon metabolic changes in an industrial park in Beijing (Lu et al. 2015). There are even some attempts of using the network approach to evaluate the carbon emissions/sequestration associated with human activities (Zhang et al. 2014), which revealed that the more carbon emissions/sequestration through a sector, the more influence it would exert upon the whole system. From the land use perspective, the ENA was also applied to explore the carbon relationships with relate to land use changes, which explored the distribution of the relationship between land nodes (Xia et al. 2016). But there has not yet been clear how the system-based method derived from ENA can be interpreted for the mechanism of carbon metabolism change. The understanding of carbon change mechanisms under various land use transitions is helpful in monitoring the carbon dynamics and to clarify how this can impel a more systemic strategy of carbon mitigation against global warming.
In this study, we aim at (1) tracking the land-based carbon emissions/sequestration on their space dimension as flow locations over time, (2) assessing structural and functional carbon network evolution under land use transitions with urban development, and (3) providing possible land-use related carbon mitigation options at a city level to support effective local planning policies. The proposed land-based carbon flow network (CFN) framework was established based on the method of Xia et al. (2016), which extended the carbon relationship assessment to the carbon change mechanism exploration. By developing a CFN guidelines for a city level analysis, this framework can be an important supplement to the pure carbon accounting method that treats urban carbon emissions as the problem of individual city sectors. This framework is also useful in facilitating tradeoffs among different land use types under multiple land use transitions in that it captures mechanistic aspects of the of CFN.

Methods
In this section, the land-based CFN framework was established by defining the network nodes, quantifying the carbon emissions/sequestration between pairwise nodes, and investigating the network utilities.

Land-based network nodes and carbon assessment
To ensure a city-level land-based carbon assessment, the system boundary was defined as the territorial boundary, with the scope including the administrative urban and rural areas of a city. Within this physical area, the land use/cover types were classified as 7 major types and 15 sub-categories regarding different natural land covers and anthropogenic land uses. Different land use functions of the land-based network nodes were defined for the carbon emissions/sequestration quantification as shown in Table 1.
Carbon sequestration (denoted as C S ) was largely dictated by the vegetation cover (i.e., nodes G, F, W, and C), while carbon emissions C T , C U , C R , and C C consisted of emissions from nodes T, U, R, and C, respectively. The carbon assessment for each land node was based on the different land use functions listed for each land use type in Table 1. The carbon sequestration coefficients were shown in Supplemental Material 1. The carbon emission calculation and related coefficients were shown in Supplemental Material 2. More detailed information about this assessment method was listed in our previous work (Cui et al. 2019). The carbon emission/sequestration was defined in units of kgC yr −1 (carbon emissions/sequestration amount per year).

Land-based CFN model
Land use transition from one type into another causes the related human activity change, making the carbon emission/ sequestration different. This carbon differences between the pairwise land nodes were recognized as the carbon flow under transitions (Xia et al. 2016). For each land node, it can associate with the other land nodes through carbon emissions/sequestration under multiple land use transitions. Among the carbon associations under multiple land use transitions, four types of transition were put forward to describe the carbon changes and conduct the flow quantification, which was shown in Fig. 1.
The blue arrow lines connecting different land nodes represented carbon emissions/sequestration under land use transitions in Fig. 1(a-d). The red arrow lines indicated that a node has emitted carbon dioxide into the atmosphere, while a green arrow line indicated that carbon dioxide was pulled from the environment and sequestered by the land node. The width of the red and green lines reflected the carbon density of different land nodes that the thicker of the line, the higher of the density. Since the total amount of carbon emission was always larger than that of the sequestration in an urban area, carbon emission increase or sequestration decrease was defined as the value of the carbon emissions/sequestration, while sequestration increase or emission decrease was recognized as the opposite value of the carbon emissions/sequestration. When transition happened in on node type, as shown in Fig. 1(a) that F4 transits into G1, f G1 F4 represents the flow between nodes F4 and G1 that arises due to the different carbon sequestration capacity of F4 and G1 (denoted as S F4 and S G1 ). In the situation of transition between natural and semi-natural nodes, described as Fig. 1(b), the flow happens when W1 transits into C1 and was calculated by the decrease of the carbon sequestration (S W1 and S C1 ) under W1 to C1, combined with the increase 1 3 of emission of C1 (E C1 ). Figure 1(c) shows the transition between natural and artificial nodes, which produce the flow as that under W1 to T demonstrates. It refers to the carbon emission of node T (E T ) and the sequestration of node W1 (S W1 ), which comprise the related flow amount. The transitions between semi-artificial and artificial nodes are described as Fig. 1(d). The flow under transition from C1 to T is calculated by the increase of the net carbon emission (S C1 and S T ) and the loss of sequestration (S C1 ).
Generally, the carbon emissions/sequestration between pairwise land nodes under transition can be estimated by their emission/sequestration changes, which were calculated by the carbon density differences between pairwise land use node and the areas of transition as shown in Eq. (1): (1) where f ij is the carbon emissions/sequestration between nodes i and j for a land use transition from land use type i to type j in area S t ; DS i and DS j are the carbon densities of land use types i and j, respectively; C i and C j represent the carbon emissions or sequestration of land use types i and j, respectively; S i and S j denote the total land area of land use types i and j, respectively. To facilitate the carbon change analysis, increasing carbon emissions or decreasing carbon sequestration values were categorized as negative changes, while increasing sequestration or decreasing emissions were categorized as positive changes in the network.
The CFN was analyzed based on the conservation of mass principle that the inflow into the node equals the outflow from the node (T in = T out ). The calculation of the system inflow and outflow was shown as Eq. (2): where f kj and fi k represent the flows from component j to component k and from component k to component i, respectively, and n equals the number of components (Xia et al. 2016). E k represents the carbon sequestration from the environment of node k. C represents the change in carbon storage of component k of the system, and the state variable (C k ) equals inflows minus outflows for a given component. Therefore, (C k ) -equals the sum of all inflows minus the absolute value of the state variable the state variable, whereas (C k ) + is equal to the sum of all outflows plus the state variable.

Land-based CFN utility assessment
The land-based CFN utility included both direct utility and integral utility. Direct utility assessed the carbon relationship between pairwise land nodes where the land use transition happened. The integral utility reflected the effect of the multistep pathways in the network that pairwise land nodes took part in under multiple land use transitions. Based on the utility calculation, a set of indicators was introduced from ENA and improved with new interpretation to reveal the changing integral utilities and their contribution on growing carbon emissions.

Direct and integral utilities of the CFN
Since ENA was proved effective in examining and identifying the structure and function inherent in ecosystems (Patten 1991), it enabled the quantification of the relationships between nodes within a complex system (Xia et al. 2016). In this study, the mechanism of the carbon change under multiple land use transitions was observed in the topology of the land-based CFN. The topological process in the CFN was evaluated by the direct and integral network utility as follows. Direct CFN utility (D) was calculated based on the carbon emissions/sequestration ( f ij ), which captured the relationship between pairwise nodes under a land use transition as shown in Eqs. (3) and (4): where d ij was the direct carbon utility between nodes i and j, and T i was the total input flows from the other 14 nodes to node i. The resulting 15 × 15 matrix quantified the relationship defined by the carbon emissions/sequestration caused by multiple land use transition between any two nodes. Because the carbon emission/sequestration to/from the atmosphere greatly exceeded the carbon emissions/sequestration between nodes, the atmospheric carbon emission/ sequestration from input T i was excluded in order to focus on the relationships between pairwise land nodes. Integral CFN (U) defined the indirect relationships between nodes by using multistep pathways in the network. To investigate the mutual benefits/costs of the nodes for a certain land use transition, the integral utility of the relationships between nodes in matrix U was expressed by using intermediate nodes. Figure 2 showed the intermediate nodes and the corresponding multistep pathways in the calculation of matrix U. In this example, D 1 refers to the direct utility between nodes F1 and T, nodes F1 and W2, nodes W2 and U, nodes W2 and T, and nodes U and T. D 2 reflects the integral utility for the two-step flow from F1 to T. D 3 is the integral utility that is defined by the three-step flow from F1 to T. The integral CFN utility for different nodes under multiple land use transitions can be obtained by calculating the matrix exponentiation, which is shown in Eq. (5): The superscript of D is the number of nodes in a flow pathway in the network. D 1 represents the direct utility between pairwise nodes, which equals to matrix D. Using three nodes in a two-step pathway, D 2 captures the two-step indirect flow utility. Therefore, D m reflects the utilities with m steps between (m + 1) nodes. I is the identity matrix.

Sign matrix built for carbon relationship distribution
To visualize the carbon relationship distribution among land nodes, integral matrix U was simplified to devise a sign matrix S. The rational numbers in matrix U were transferred to the sign elements S u in the sign matrix S, including positive sign " + ", negative sign " − ", or zero value. " + " represented an increase (decrease) in the net carbon emissions (sequestration) for a given land use transition and " − " represented a decrease (increase) in the net carbon emissions (sequestration) for a given land use transition. Therefore, nine kinds of relationship in sign matrix S were possible including: mutualism (+ +), commensalism (+ 0), commensal host (0 +), exploitation (+ −), control (− +), neutralism (0 0), amensalism (0 −), amensal host (− 0), and competition (− −).
For example, node pair (S uij , S uji ) = (+ −) implied that node i receives carbon emissions from node j during the land-use transition from node j to node I, which means node i is exploiting node j as shown in Fig. 3 (1). If (S uij , S uji ) = (− +); then node j has exploited node i and node i controls node j, which were shown in Fig. 3 (2). The exploitation and control relationships are the negative of one another, which demonstrated that one node benefitted from the land use change, while the other node became worse under the transition. In the scenario of mutualism, where (S uij , S uji ) = (+ +), nodes i and j are both receiving net carbon emissions during the land use change as shown in Fig. 3 (3). Since this mutualistic relationship between pairwise nodes was indicative of an increasing carbon trend caused by land use transitions, it provides information for policy makers to be aware when this scenario occurs. If (S uij , S uji ) = (− −) happens, nodes i and j both contributed carbon emissions to a third node during the land use transition. This relationship was defined as competitive because nodes i and j are exploiting the third node, which were shown in Fig. 3 (4). Based on the 4 main types of CFN relationships illustrated in Fig. 3, other relationships can be interpreted in the same way.

Quantification of the CFN utility change
The ENA indicators, which were studied in the listed literature (Chen et al. 2018), were used and improved in this section in unfolding the utility change among land use nodes under multiple land use transitions. The designed indicators were quantified based on the integral utility assessment, and their formulation, projection, and implications on land use were summarized in Table 2.
These indicators were defined into 3 types as: (1) the activity, which captured the systematic dynamics; (2) the mutualistic effect, the competitive intensity, and the exploitation/control effect, which described the utility features with relate to their carbon emission contribution; and (3) the system robustness, which quantified the possible carbon mitigation potential under land-use change challenges. The applicability and validity of the indicators for assessing carbon change network was tested in the following case study.

Study area
Guangzhou, the third largest megacity in southern China (Fig. 4.), was taken as the empirical area in this study. It is a megacity with an area of 7434 km 2 and a population of nearly 9.3 million people. As the economic, political, and cultural center of Guangdong Province, Guangzhou has experienced rapid industrial development and population growth, which resulted in continuous land use and landcover changes. The increasing anthropogenic activities in these urbanizing lands have posed serious decarbonization challenges, making the understanding of the relationships between land use and carbon changes necessary. Therefore, the established land-based CFN method was applied in Guangzhou, with the goal of low-carbon initiations by analyzing the spatial variations of the carbon dynamics and changing mechanism under multiple land use transitions. It will provide insight into potential carbon mitigation strategies in the face of ongoing urbanization.

Data preparation
The original datasets of the Chinese Academy of Sciences (CAS, http:// www. resdc. cn) with a resolution of 30 m were used in the study of Guangzhou. The land-use data were discriminated through Landsat TM image processing, which reached the expected discrimination accuracy of more than 95% for all the land-use types. According to the standard classification of the remote-sensing monitoring system of China, the land area and spatial distribution of 15 land-use types were calculated in 2000, 2005, 2010, 2015, and 2020 to facilitate the following spatial carbon assessment. Comparing the land-use distribution in 2000, 2005, 2010, 2015, and 2020, the land use transition of each 5-year time span was derived by using ArcGIS.
Data for carbon assessment was collected and processed based on different land use types, and the following data were obtained from the Guangzhou Statistical Yearbook . It included the fertilizer amounts and the farming machine power for the cultivated land, the livestock quantity, and the fuel consumption for the rural land use, the daily energy consumption and populations for the urban land use, and the energy usage for the transportation and industrial land use (see Supplemental Material 3). All the carbon emission coefficients (see Supplemental Material 4) related to energy usage were derived from the IPCC carbon emission factors (IPCC 2006).

Land use change and land-based carbon change
During the study period, the natural land cover area decreased considerably, with the human settlements (the old city center in central Guangzhou and two smaller aggregates in the northern and southern areas, separately) expanding to the north and south directions. This observations on spatial Fig. 3 Four main types of CFN utilities that occur during a land use transition from node i to node j Table 2 The integral indicators that describe the carbon change mechanism of CFN Indicators System robustness Competition effect/ (mutualistic effect + exploitation/ control effect) The general land-based carbon metabolism system robustness The high value of this index highlights a beneficial direction of the system evolution from the carbon mitigation perspective land use distribution indicated a rapid urbanization with land use transitions in Guangzhou. The detailed data of land use change was listed in the Supplemental Material 5. In 2000, the northern region was featured with forest and grassland cover, while the southern region was characterized by water and cultivated land. In 2020, the central developed region has expanded considerably in both the northern and eastern directions. The area of human settlements in Panyu has grown dramatically and eventually increased to join up with the central high-population region, making the urban area in Guangzhou aggregated and enlarged. This urban expansion in the southern part was largely featured as land use transition from cultivated land to urban land, which was different from the land use change in the northern region that the transportation and industrial area increase was the main observed change during the urbanization.
From 2000 to 2020, the dominant land uses were F1, C1, and U among the total 15 types assessed by areas, as shown in Fig. 5. Both F1 and C1 decreased on area, but the land area of U doubled. Meanwhile, the area of T increased more than tripled, showing the considerable urbanization in this time period. As a result, the overall carbon emissions increased and the sequestration decreased under these land use changes. The emission increase was almost attributed to land use T, which was responsible for nearly 60-70% of the total emissions during the study period. Land use U was the second largest carbon emission contributor, accounting for nearly 30% of the total emissions. In contrast, land use R and C1 exhibited slight decreases in their carbon emissions, which were accompanied by land use transitions to land use types T or U.
From the spatial distribution of the carbon emissions (Supplemental material 6), the mid-central Guangzhou was suffered by the highest carbon emissions, with decreasing levels to the north, east, and south. The high-level emission patches extended from the city center to the suburb with 1/2 to 1/3 the original size from 2000 to 2020. The northern region produced moderate amounts of carbon emission in 2000 and developed more scattered areas with higher levels of carbon emission in 2020, which corresponded to the increasing areas of land T. While the south region further increased their carbon emission levels within certain areas, accompanied with the increased areas of land C2. This highlighted that the understanding on carbon emission increase should be focused on the land use transition toward T (in the north) and C2 (in the south).
The largest contributor to carbon sequestration (~ 80%) in Guangzhou was land use F1, which was in the northern part of Guangzhou (Fig. 7). From 2000 to 2020, the carbon sequestration of F1 decreased significantly (from 172.05 × 10 6 kgC yr −1 to 167.07 × 10 6 kgC yr −1 ). For other natural land covers (F2, F3, F4, G1, W3, C1, and C2), the sequestration declined from 2000 to 2015 and rose in 2020. The changing sequestration share of the natural land covers showed significantly decreased from for F1 and increase for F2, F4, and W1. From spatial distribution, high sequestration Fig. 4 The location and administrative zone of Guangzhou patches increased in the northern suburbs, while the low sequestration patches became more randomly distributed throughout the study area from 2000 to 2005. After 2005, the areas characterized by low carbon sequestration grew until most of the study area experienced a significant decrease in carbon sequestration by 2020. Generally, the total carbon sequestration was too weak to offset the emissions, making carbon mitigation a significant challenge.

Distribution of the land-based carbon emissions/ sequestration
By using the natural breaks method to categorize the carbon emissions/sequestration size, six grades of the carbon emission and sequestration flows were defined separately. The spatial distribution of the carbon emissions/sequestration was visualized by using ArcGIS in the regions of net carbon emissions (red) and net carbon sequestration (green) in Guangzhou for the time intervals 2000-2005, 2005-2010, 2010-2015, and 2015-2020 (Fig. 6). From 2000 to 2015, the intensity of the emission flows has greatly exceed the intensity of the sequestration flows (nearly by an order of magnitude during [2000][2001][2002][2003][2004][2005]. The carbon emissions/ sequestration during 2015 to 2020 was featured as more carbon sequestration flows in the southern part of Guangzhou, which can be seen as the positive process. Since most of the sequestration patches were shown as low grade and small size for the periods of 2000-2005, 2005-2010, and 2010-2015, they were emphasized by the magnified circles in Fig. 6, while the sequestration patches were easy to identify without extra circle mark.
The largest carbon emission flows were in middle and southern Guangzhou with the magnitude of the flows decreasing during 2000-2005, 2005-2010, and 2010-2015. While both the beneficial and harmful process were strengthened in 2015-2020. The size and grade of both the carbon emission and sequestration flows in the southern region increase over these 5 years, indicating that the carbon change in Panyu and Nansha districts should be concentrated on for policy makers.
The temporal change of the carbon emissions/sequestration was shown by the network with different lines (Fig. 7). The artificial land nodes were largely responsible for the increase in emission flows as the red bold lines demonstrated. From 2000 to 2005, the largest carbon emission flows were directly related to the transitions from F1 to T, C1 to T, C1 to U, and C2 to T (Fig. 7a). The large sequestration flows occurred in the transition from T to U. From 2005 to 2010, the flows from T to W2 and F4 implied that the magnitude of the sequestration flows have significantly increased (green bold lines in Fig. 7b).
In 2010-2015, both the carbon emissions and sequestration flows have weakened (thin lines in Fig. 7c). Despite this overall diminishing size, the carbon emissions still easily surpassed the carbon sequestration in the study area at this time. Like the previous time intervals, the primary emission flows occurred from C1, C2, and F to node T. These continuous emission flows have greatly underlined the areas that should be paid special attention during the ongoing urbani- Highlighted by the land-based CFN, areas that are responsible for growing carbon emissions can be identified: (1) specific locations, for example, the central area of Guangzhou (Yuexiu, Haizhu, and Tianhe district), where further efforts on vegetation coverage increase were needed (e.g., a green circle of vegetation around could both increase the green space and offset the carbon emissions); and (2) different implications for the northern and southern Guangzhou, which provided by the differentiated spatial carbon patterns. The land use planning for industrial and transportation land use should be the priority in the northern region, while the mixed land uses, including job-housing balance, should be more addressed in the southern area. The Guangzhou case study has proved that different land use transitions can worsen or alleviate the growing carbon emissions, which provided useful information to cities that want to grow strategically without carbon emission increase.

Direct relationship between land nodes
The land use transition and related carbon emissions/sequestration happened between 105 pairwise land nodes during the study period, making the network complex to understand the relationships between land nodes from a systematic way. By examining the direct utility between pairwise nodes, the direct carbon change under a certain land use transition was revealed. Taking the direct utility between nodes F1 and U from 2000 to 2005 as an example, which was shown as (D F1,U , D U, F1 ) = (0.073, 149.92), 0.073 implied that the transition from F1 to U was not a significant contributor to the total carbon change of land node U. In contrast, 149.92 indicated that the transition from U to F1 contributed to the total carbon change of land node F1 significantly. With a direct utility of (D R, U , D U, R ) = (0.27, -4.13) from 2000 to 2005, the transition from land node R to U had little impact on the total carbon change of land node U, while the total carbon change of R was reduced by the transition from U to R. The positive value demonstrated that the carbon emissions/sequestration during the transition between land nodes R and U contributed to the total carbon change of R, while the negative utility showed that the carbon emissions/sequestration has limited the total carbon change of U. The direct utility considered the interaction between two land nodes, which could help to identify the direct effect of land use transitions on the carbon emission change from a network perspective.
Among all the land use transitions during the study period, transitions from C (both C1 and C2) to U were the main carbon emission increase of land U, and transitions Fig. 6 Spatial variations in the carbon emissions/sequestration due to land use transitions in 2000-2005, 2005-2010, 2010-2015, and 2015-2020 from F1 and C1 to T were recognized as the main contributor of the carbon emission increase of land T. Combined with the spatial analysis in Sections 4.1 and 4.2, the former transitions were mostly found in the south Guangzhou, and the later transitions have mainly occurred in the north Guangzhou, which could further support the land use planning for the target of carbon emission control. These findings can therefore enhance the understanding of the carbon changes under land use transitions for effective policy making.

Integral contribution on carbon change
From 2000 to 2005, exploitation/control relationships contributed ~ 72% of the total carbon emissions under land use transitions, which followed by the mutualistic relationship as the second largest contributor generating 21% of the carbon emissions. From 2005 to 2010, the exploitation and control relationships maintained the main contributor of the total carbon emissions, and after 2010, the carbon emissions were mainly attributed to the mutualism relationships. Especially for the time span 2015-2020, mutualistic relationship was the largest emission contributor, and the exploitation/control relationships transferred as a carbon sequestration contributor.
The changing integral utility features in time period 2000-2020 were visualized by the integral indicators as shown in Fig. 8. The activity showed an increasing trend during study period, which demonstrated a slightly decrease in 2015-2020. It indicated that the interconnections among nodes were enhanced by the carbon emissions/sequestration under multiple land use transitions, and this increasing complexity of the system interactions among nodes made carbon mitigation a great challenge.
The mutualism effect showed a large increase during the 2010-2015 and 2015-2020 intervals, which suggested that the nodes with mutualistic relationships have enlarged their contribution on growing carbon emissions under multiple land use transitions. The exploitation/ control effect decreased sharply from 0.72 in 2000-2005 and 0.78 in 2005-2010 to 0.18 in 2010-2015, a trend that reflected a major utility shift away from exploitation/ control to mutualistic relationships. In 2015-2020, the exploitation/control effect showed a negative effect on carbon emissions, indicating the exploitation/control relationship among land nodes has begun to working toward a carbon sequestration direction. Fig. 7 The land-based CFN in Guangzhou in 2000-2005, 2005-2010, and 2010-2015 Under the increasing competitive relationship, carbon emissions of the related land nodes decreased more than 90% from 2000 to 2020.The competitive effect increased from 0.07 to 0.32 (2005-2010 to 2010-2015) and decreased to 0.0045 in 2015-2020. Since competitive relationship reflected the inhibited carbon emissions/sequestration between pairwise nodes, the changing effect showed strong carbon reduction from the land transition of competition relationship during 2000 to 2015 and weak influence in 2015-2020. Gained from the competitive relationship, system robustness increased from 0.08 in 2005-2010 to 0.47 in 2010-2015, which implied that the carbon emissions/ sequestration and the related utility relationships generated by multiple land use transitions were evolving in a positive direction under the competitive effect increase. The increasing system robustness has sharply decreased in 2015-2020, indicating that the system has disturbed by external force, for example, the land use change Panyu and Nansha district.

Changing distribution of the integral relationships
The distribution of the integral relationships was demonstrated in Fig. 9 to reveal how the carbon emission increase happened under multiple land use transitions. Exploitation and competition relationships dominated the integral utilities under transitions from natural land nodes to semi-artificial and artificial land nodes (e.g., the transitions from F to U, R, and T). As exploiters, the semi-artificial and artificial land obtained positive carbon increase from the corresponding natural land, which enables the trace on related emission increase source through the emission relationship to further improve the land use structure for the emission goal. This was the urbanization influence on the carbon changes of Guangzhou in the early stage. Competition relationship led to carbon reduction impacts for both land nodes. There were 23 pairs of competitive relationship in the integral utility matrix 2000-2005 ( Fig. 9), such as nodes F1 and C1, indicating that these two land nodes were competitors of the carbon emission flows. The transition between nodes F1 and C1 was conducive to emission reduction because of the mutual restriction effects. It highlighted that the land use transition of urbanization could also conduct positively in carbon mitigation under competition relationship.
For the artificial and semi-artificial land nodes (U, T, R, C1, and C2), which referred to the anthropogenic areas, mutualism was the dominant relationship between pairwise land nodes under land use transitions. It was an unfavorable relationship that the two land nodes were mutually reinforcing the emission of carbon dioxide and the status quo should be changed, which provided potential opportunity to reduce the carbon emissions. The time period of 2000-2005 was then recognized as the initial stage of the urbanization (rapid urbanization and artificial land use sprawl) with the exploitation and control relationships as the primary utilities and related carbon increase from the carbon metabolism perspective.
From 2005 to 2010, the distribution of the integral relationships showed different from that during 2000-2005 (Fig. 9). The quantity of the exploitation relationship decreased in the transitions within the 9 natural land nodes and aggregated in the transitions between U, T, R, C1, and C2 (artificial/ semi-artificial land nodes), driving the carbon emission increase. The transition from natural land to artificial/ semi-artificial land demonstrated a diminishing trend, and the later kind of land nodes began to transit to the former types, which was accompanied with increasing quantity of the mutualistic relationships in this stage. Although the mutualistic relationships contributed to carbon emissions for both pairwise nodes, the amount of the carbon emission increase was not as large as that in the time period of 2000-2005. This implied that the land use transitions among different natural lands or from artificial/semi-artificial land to natural land were positive on carbon emission control. Another feature was that the development of the bare land has increased, which transited to both natural land and artificial/semi-artificial land and brought carbon emission increase. This time period can be recognized as the exploring stage with significant integral utility changes and carbon emission increase under multiple land use transitions.
In 2010-2015, the mutualism relationships have aggregated in the transitions from natural lands to artificial/ semi-artificial lands and the transitions within different natural lands. Accompanied with the increasing land use transitions from natural types to the artificial/semi-artificial types, the quantity of the mutualism relationships increased, which was detected as the feature of the urbanization from 2010 to 2015 (Fig. 9). The quantity of the competition relationships was also found increased with related carbon emission increase compared with the time period of 2005-2010. These increased competition relationships implied that the integral utility has become more complex because these mutual restrictions on carbon emission were obtained by influencing the carbon emission of the other land nodes.
In 2015-2020, the transitions featured as exploitation relationship were found increased, indicating the carbon relationship changes during the land use adjustment in the built-up area. It highlighted that changing urban expansion mode for urban connotative development was of great significance to influence the urban carbon metabolism. The carbon emission mitigation of the artificial/semi-artificial land nodes can be controlled by urban land use adjustment and regulation. Meanwhile, the development of the bare land decreased in the third stage, which mainly transited to the artificial/semi-artificial land uses. These change utilities showed that the urbanization was at a deepening stage accompanied with the mutualism as a primary utility with enlarged carbon emission amount, and exploitation diminished with declined carbon emission under multiple land use transitions in the study area.

Discussion
Although the spatial carbon change showed that land use transitions can worsen or alleviate the growing carbon emissions, the CNF utility analysis could help to reveal what kind of transition can increase/reduce the total carbon emissions. In the case study of Guangzhou, the competition relationship has shown its effect on carbon reduction, and the mutualism relationship was responsible for the increasing carbon emissions. The spatial differentiation on carbon relationships highlighted that land use transition in built-up areas could benefit carbon changes in urbanization and providing focal information for urban planning. By using ENA, a land-related carbon emission research was also conducted in Xuzhou city, which investigated the spatial distribution of two carbon relationships among 8 land use types (Zou et al. 2022). They found that the mutually relationship of land transition was distributed in subordinate districts and counties, which were mostly natural types land use and suffering from the urbanization. The competition relationship was distributed in central urban areas to drive a further land use transition for carbon balance.
Compared with the Xuzhou case, this study provided more detailed information on the structural and functional carbon network evolution under land use transitions. For the north areas in Guangzhou, where the main land cover was F and G, were detected changing from exploitation to mutualism relationship under land use transitions (usually from F, G to T, U, and R) during the study period. But in the middle and south area, almost the built-up areas, the utility change was different from that in the north region. The main carbon relationship between related land nodes was on the way that changing from mutualism to exploitation and competition over time. These changes implied that (1) the mutualism relationship in the north area should be the focal point on their space dimension as the mechanism of the carbon emission increase, which should be focused in the low-carbon urban planning, and (2) the multiple land use transitions in the urbanization area have become more favorable on carbon emission reduction than before, which has important implications for decision makers to explore effective carbon mitigation options in the coming land use changes.
In contrast, in another carbon metabolic network study in Beijing, mutualism relationship was found not stable when disturbed by urban expansion, and the transportation and industrial land and urban land were found the most important contributors to exploitation and control relationships and may be important indicators of spatial adjustment (Xia et al. 2016). It identified the spatial heterogeneity for different carbon ecological relationships, which was the reference of this study and was extended to explore the carbon change mechanism. There is also other study that investigates the carbon interaction among land use nodes. For example, Zhang and Yang (2009) found that the artificial nodes exploited the natural nodes in the cities of Tianjin, Chongqing, and Guangzhou, whereas the artificial nodes were controlled by the natural nodes in Beijing, Shanghai, and Shenzhen. In this study, the evolution of the carbon relationships was concluded that the carbon relationships among multiple land nodes changed during the different development periods with a spatial differentiation feature and, therefore, elaborately analyzed the changing mechanism with relate to different land transition categories and urbanization stages.
This proposed CFN analysis was found an effective method of assessing the carbon relationships that arise during multiple land use transitions within a growing city and can be considered in policy making for further urban planning.

Conclusion
This study developed a CFN framework for location-specific carbon emissions/sequestration analysis for cities. It engaged in tracking the land-based carbon emissions/sequestration on their space dimension as flow locations, which was followed by the CFN analysis to reveal the complex carbon change mechanism. Its theoretical contribution referred to the comprehensive guidelines for carbon emissions/sequestration pattern identification and indicators for carbon relationships investigation. Practically, it can be used to reveal what kind of land use change can benefit carbon mitigation and support policy design.
Guangzhou case was used to testify the established framework and the results showed that the regions characterized by carbon sequestration were largely confined to the northern part of Guangzhou, and the areas that contributed to high carbon emissions were more ubiquitous with the highest levels occurring in the city center and keep moving south over time. The spatiotemporal distribution of the carbon change provided possible mitigation focus for the central, north, and south area of Guangzhou with locationspecific insights toward carbon neutrality. The CFN utility analysis explored what kind of transition can increase/ reduce the carbon emissions. As an unfavorable relationship, mutualistic relationship dominated the carbon utility of the built-up areas, resulting in increasing carbon emissions. Competition relationship demonstrated an enlarged distribution under multiple land use transitions and presented emission reduction features because of significant mutual restriction effects. Under exploitation relationship, the artificial/semi-artificial land obtained positive carbon increase from related natural land as exploiters, which made the trace tracking of the emission increase possible to improve land use structure for carbon mitigation goal. Especially for the period 2015-2020, increasing exploitation/control has gained much more carbon sequestration than ever before in the south Guangzhou. This highlighted that the multiple land use transitions in Guangzhou were evolving in a positive direction for carbon reduction, and the urbanization could also be conducted positively on carbon mitigation under competition relationships.
This study provided insight for policy makers to promote their urban planning toward multiple targets, taking carbon mitigation as one of their goals. The identified carbon features in this case study can be used as a reference for other case studies (e.g., other developing areas experiencing rapid urbanization). In the future, the land-based CFN method could be applied to more cities and metropolitan areas. The establishment of the land-based carbon profiles and mitigation guidelines in regions much larger than a single city is also expected to be conduct in the following studies.