2.3.1 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 the main urban area of Chongqing. 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 CO2 and other greenhouse gases, consistent with a “carbon source” effect. On the other hand, crops can absorb a certain amount of CO2 through photosynthesis during their reproductive periods (Wu et al., 2022), which is a “carbon sink” effect. According to the study of Cai et al. (2005), the crop carbon emission coefficient was 0.429 t·hm− 2, and the study of He (2006) showed that the crop carbon uptake coefficient was 0.007 t·hm− 2, which shows that 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):
$$Ci=Si \cdot \theta i$$
1
where Ci is the carbon release or absorption of land-use type i (t); Si is the area of land-use type i (hm2); θi is the carbon source or sink coefficient of land-use type i (t·hm− 2).
(2) Accounting for carbon absorption on woodland
The main urban area of Chongqing 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 was 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 in this study. Finally, this study uses Eq. (1) to calculate the carbon absorption of woodland.
(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 Li et al. (2019) 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.
(4) Accounting for carbon absorption on water
Usually, water is considered to have a “carbon sink” effect. According to the studies of Li et al. (2019), Lai et al. (2010), and Sun et al. (2015), the carbon sink coefficients of waters are 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.
(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 the data of the literature (IPCC, 2006; NBS, 2021) (see Table 1 and Table 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):
$${C_{cons}}=Ce+Cp=\sum\limits_{{i=1}}^{n} {{m_i}} \cdot {n_i} \cdot {\alpha _i}+p \cdot \beta$$
2
where Ccons is the total carbon release of construction land (t); Ce is the carbon release of energy consumption (t); Cp is the carbon release of human respiration (t); mi is the terminal consumption of energy source i (t); ni is the standard coal conversion factor of energy source i (t·t− 1); αi is the carbon emission factor of energy source i (t·t− 1); p is the total resident population (p); β is the carbon release coefficient of human respiration (t·p− 1·a− 1).
Table 1
Standard coal conversion factor and carbon emission factor for various energy sources
Energy type | Raw coal | Cleaned coal | Other washed coal | Coke | Coke oven gas | Blast furnace gas | Other gas | Other coking products | Crude oil |
Standard coal conversion factor | 0.7143 kgce/kg | 0.9000 kgce/kg | 0.2857 kgce/kg | 0.9714 kgce/kg | 0.5714 kgce/m3 | 0.1286 kgce/m3 | 0.1786 kgce/m3 | 1.1000 kgce/kg | 1.4286 kgce/kg |
Carbon emission factor (t C/t) | 0.7559 | 0.7559 | 0.7559 | 0.855 | 0.3548 | 0.4602 | 0.3548 | 0.6449 | 0.5857 |
Table 2
Standard coal conversion factor and carbon emission factor for various energy sources
Energy type | Gasoline | Kerosene | Diesel oil | Fuel oil | Liquefied petroleum gas | Other petroleum products | Natural gas | Heat | Electricity |
Standard coal conversion factor | 1.4714 kgce/kg | 1.4714 kgce/kg | 1.4571 kgce/kg | 1.4286 kgce/kg | 1.7143 kgce/kg | 1.4286 kgce/kg | 1.2143 kgce/m3 | 0.0341 kgce/MJ | 0.1229 kgce/kWh |
Carbon emission factor (t C/t) | 0.5538 | 0.5714 | 0.5921 | 0.6185 | 0.5042 | 0.586 | 0.4483 | 0.26 | 2.5255 |
(4) Accounting for carbon absorption on unused land
The area of unused land in the main urban area of Chongqing is relatively small and is mainly marshland and bare rock gravel. Referring to the studies of Wei et al. (2021), Lai (2010), and Fan et al. (2018) and taking the average of their above 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.
2.3.3 Ecological network analysis method
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 path is the means by which material and energy are transferred between compartments. The ENA method analyzes the flow of matter and energy in ecosystems (Hannon et al., 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, which are widely used by scholars to study the urban nitrogen metabolic system (Zhang et al., 2016a), water metabolic system (Zhang et al., 2019), energy metabolic system (Zhu et al., 2019), and carbon metabolic system (Zhang et al., 2016b).
(1) 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 Ti 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 xi. If xi < 0, Ti is equal to all carbon flows into i minus xi; if xi > 0, Ti is equal to all carbon flows out of i plus xi. The calculation of Ti is given as follows:
\({T_i}=\sum\limits_{{j=1}}^{n} {{f_{ij}}} - {x_i}\) (xi<0), (5)
\({T_i}=\sum\limits_{{j=1}}^{n} {{f_{ji}}} +{x_i}\) (xi>0), (6)
where Ti is the carbon flux of compartment i, the same below; fji is the carbon flow from compartment i to compartment j, the same below; xi 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 fij and the carbon flux Tj 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:
$$G{\text{=}}\left( {gij} \right){\text{=}}\left( {\frac{{fij}}{{Tj}}} \right)$$
7
,
$$N{\text{=}}\left( {nij} \right){\text{=}}\sum\limits_{{m=0}}^{\infty } {{G^m}} {\text{=}}{G^0}+{G^1}+{G^2}+ \cdots +{G^k}+ \cdots ={(I - G)^{ - 1}}$$
8
,
$$H=\frac{{\sum\limits_{{i=1}}^{{\text{n}}} {\sum\limits_{{j=1}}^{{\text{n}}} {\left( {{n_{ij}} - {i_{ij}} - {g_{ij}}} \right)} } }}{{\sum\limits_{{i=1}}^{{\text{n}}} {\sum\limits_{{j=1}}^{{\text{n}}} {{g_{ij}}} } }}=\frac{{\operatorname{sum} (\operatorname{sum} (N - I - G))}}{{\operatorname{sum} (\operatorname{sum} (G))}}$$
9
,
where Tj is the carbon flux of compartment j; G is the dimensionless direct flow intensity matrix, same below; gij is the element of matrix G; N is the dimensionless total flow matrix; I is the unit matrix, same below; N-I-G is the dimensionless indirect flow matrix; H is the ratio of indirect flow to direct flow. G0 is the self-feedback matrix, which represents the self-feedback effect of the carbon flow flowing through each compartment; G1 is the direct flow intensity matrix, which represents the direct carbon flow transferred between each compartment; it is expressed by the higher power of the direct flow intensity matrix G Indirect flow intensity with different path lengths, Gm (m ≥ 2) represents the indirect flow intensity with a path length of m between compartments.
(2) 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 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:
$$G^{\prime}{\text{=}}\left( {g^{\prime}ij} \right){\text{=}}\left( {\frac{{fij}}{{Ti}}} \right)$$
10
,
$$N^{\prime}{\text{=}}\left( {n^{\prime}ij} \right){\text{=}}\sum\limits_{{m=0}}^{\infty } {{{\left( {G^{\prime}} \right)}^m}} {\text{=}}{\left( {G^{\prime}} \right)^0}+{\left( {G^{\prime}} \right)^1}+{\left( {G^{\prime}} \right)^2}+ \cdots +{\left( {G^{\prime}} \right)^k}+ \cdots ={(I - G^{\prime})^{ - 1}}$$
11
,
$$W=\frac{{\sum\limits_{{i=1}}^{n} {n^{\prime}ij} }}{{\sum\limits_{{i=1}}^{n} {\sum\limits_{{j=1}}^{n} {n^{\prime}ij} } }}$$
12
,
where W is the structure analysis index; Nʹ is the quantified overall flow matrix; nʹij is the element in matrix Nʹ.
(2) 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:
$$D{\text{=}}\left( {dij} \right){\text{=}}\left( {\frac{{{f_{ij}} - {f_{ji}}}}{{{T_i}}}} \right)$$
13
,
$$U=\left( {{u_{ij}}} \right)={D^0}+{D^1}+{D^2}+ \cdots +{D^k}+ \cdots +={(I - D)^{ - 1}}$$
14
,
where D is the direct utility matrix; dij 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; uij is an element in matrix U; Matrix D0 is the self-feeding of traffic in each compartment; matrix D1 represents the direct traffic utility between two nodes in the network system; Matrix Dk (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 uij in the dimensionless integral utility matrix U is defined as the matrix Sgn (U), where the element is denoted as Suij, which represents the interactive relationship between two compartments, including nine ecological relationships (Table 3). The utility symbols between compartments 1 and 2 are denoted by Su12 and Su21, where Su12 represents the utility flow from compartment 2 to compartment 1 and Su21 represents the utility flow from compartment 1 to compartment 2. If (Su21, Su12) = (་, -), it means that compartment 2 preys on compartment 1; if (Su21, Su12) = (།, ་), it means that compartment 2 is controlled by compartment 1; if (Su21, Su12) = (།, །), it means that there is a competition relationship between compartments 1 and 2, with negative effects on both sides; if (Su21, Su12) = (་, ་), it means that there is a mutualism relationship between compartments 1 and 2, with positive effects on both sides; if (Su21, Su12) = (0, 0), it means that there is a neutralism relationship between compartments 1 and 2, with no effects on either sides.
Table 3
Ecological relationships classification
Matrix notation | Positive ་ | Neutral 0 | Negative - |
Positive ་ | (་, ་) Mutualism | (་, 0) Commensalism | (་, -) Exploitation |
Neutral 0 | (0, ་) Commensalism host | (0, 0) Neutralism | (0, -) Amensalism |
Negative - | (-, ་) Control | (-, 0) Amensal host | (-, །) Competition |
Among the nine ecological relationships mentioned above, the five ecological relationships of commensalism, commensalism host, neutralism, amensalism and amensal host are not involved because the case of Suij=0 usually does not occur in the ecological network of the urban carbon metabolism system. 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 the land-use change has a positive effect on the balance of urban carbon metabolism; and 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 negatively affects on the urban carbon metabolism balance; and the smaller the K-index, the more obvious the negative effect. The K-index is calculated as:
$$K=\frac{{{S_+}(U)}}{{{S_ - }(U)}}$$
15
,
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.