LMDI Decomposition of Energy-Related CO 2 Emissions Based on Energy and CO 2 Allocation Sankey Diagrams: The Method and an Application to China

: This manuscript develops a logarithmic mean Divisia index I (LMDI) decomposition method based on energy and CO 2 allocation Sankey diagrams to analyze the contributions of various inﬂuencing factors to the growth of energy-related CO 2 emissions on a national level. Compared with previous methods, we can further consider the inﬂuences of energy supply efﬁciency. Two key parameters, the primary energy quantity converted factor ( K PEQ ) and the primary carbon dioxide emission factor ( K C ), were introduced to calculate the equilibrium data for the whole process of energy unitization and related CO 2 emissions. The data were used to map energy and CO 2 allocation Sankey diagrams. Based on these parameters, we built an LMDI method with a higher technical resolution and applied it to decompose the growth of energy-related CO 2 emissions in China from 2004 to 2014. The results indicate that GDP growth per capita is the main factor driving the growth of CO 2 emissions while the reduction of energy intensity, the improvement of energy supply efﬁciency, and the introduction of non-fossil fuels in heat and electricity generation slowed the growth of CO 2 emissions.


Introduction
Facing the challenge of global climate change, most countries have come to a consensus that it is urgent to control anthropogenic GHG (greenhouse gas) emissions, especially energy-related carbon dioxide (CO 2 ) emissions [1]. Therefore, it is essential for policy makers in various countries to understand the main factors influencing the growth of energy-related CO 2 emissions and quantitatively evaluate their contributions [2]. In previous studies, the logarithmic mean Divisia index I (LMDI) decomposition method has been widely applied to analyzing the influencing factors of CO 2 emissions growth in many countries (see the literature review in the following section and Appendix B Table A7). Through the LMDI decomposition method, researchers can identify the contribution of each influencing factor to reducing or increasing CO 2 emissions quantitatively. For example, the increasing proportion planned targets between 2016 and 2020 that were decomposed from the above 2030 targets to promote the implementation [14]. Therefore, the case study on China not only ensures the data source for the method development, but may also examine the applicability of the method by comparing the results with current policies.
In this study, we attempt to develop an LMDI method suitable for analyzing the CO 2 emissions growth of countries with complex energy systems and to apply the method to analyze the influencing factors of CO 2 emissions growth in China. First, by mapping energy allocation Sankey diagrams and CO 2 allocation Sankey diagrams, we studied the physical processes of energy use and CO 2 emissions from the primary energy supply to the end-uses. We derived extra influencing factors to include in the decomposition. Then, using these extra influencing factors, we developed an improved LMDI method suitable for analyzing complex energy systems and applied it to analyze the CO 2 emissions growth in China from 2004 to 2014.
The main contribution of this work is that the extra influencing factors which we derived can contribute to a more elaborate LMDI decomposition method for CO 2 emissions growth. Additionally, the Sankey diagrams and results of LMDI decomposition together can help us to comprehensively understand China's energy-related CO 2 emissions and driving forces behind the growth. The rest of this paper includes a literature review in Section 2, methodology and data input in Section 3, results and discussion in Section 4, and conclusions in Section 5.

Energy and CO 2 Emissions Sankey Diagram
Sankey diagrams are popular tools in energy system analysis. In an energy Sankey diagram, energy flow appears as arrows from one side to another with the color indicating energy types and width indicating energy quantities. There are no losses reflected in the energy allocation Sankey diagrams, which means we can trace the primary energy along the flows, while the energy efficiency Sankey diagrams show energy losses for efficiency analysis. Based on those diagrams, we can depict comprehensive pictures of complex energy system in various countries or regions with high technical resolution. For example, Cullen and Allwood [15,16] presented global energy flows and energy efficiency, Ma et al. [17] presented China's energy flows and compared it with the global energy flow, and Chong et al. [7,18] presented the coal flows in China. The main challenge of mapping those diagrams is how to treat a huge number of primary data points from the energy balance table especially through manual methods. To solve it, Chong et al. [18] presented a programmed data-processing method for mapping energy allocation Sankey diagram and introduced primary energy quantity converted factor (K PEQ ) to connect end-use energy consumption and primary energy consumption. After that, Chong et al. [19] further introduced an input-output approach to acquire K PEQ and generate the data for mapping an energy allocation Sankey diagram. Based on those works and others, Soundararajan et al. [20] provided a review of energy allocation Sankey diagrams and suggested a framework to use it for national level analysis.
Based on energy balance and emission factors, it is also possible to present the flows of CO 2 (as well as greenhouse gases) emissions through Sankey diagrams based on the equilibrium of the carbon element. There are two types of CO 2 Sankey diagrams, according to the treatment method of emission flows of heat and electricity. In the first type, the emission flows start with primary energy sources, energy conversion, and end-use sectors. For example, Mu and Li [3,4] presented the carbon dioxide emissions allocation Sankey diagrams of China, which depict in detail the energy sources and energy conversion sectors. However, it is difficult to clearly observe the emission allocation in end-use sectors. The research determines that energy losses in energy conversion are responsible for the emissions and so end-use sectors are only responsible for a part of total emissions. In the second type, the emission flows start with main sectors of emission sources, such as transport, electricity and heat generation, industry, and agriculture, and then go to detailed sub-sectors. For example, WRI (World Resources Institute) presented the flows of global [5] and U.S. [6] GHG emissions (carbon dioxide, methane, and nitrogen oxide) by using the Sankey diagram in this way.
Through the literature review, we conclude that there are few published works on CO 2 emissions Sankey diagrams based on the energy allocation Sankey diagram, which may present that CO 2 emissions are responsible for main sectors in each stage of the energy system including energy sources, energy conversion, and end-use sectors. Based on our previous works on energy allocation Sankey diagrams [7,18,19], we can acquire the K PEQ of each secondary energy to establish the connection between end-use energy consumption and primary energy consumption. Additionally, we can further derive corresponding parameters by emission factors to establish the connection between end-use energy consumption and CO 2 emissions. Therefore, we are able to develop a methodology for mapping CO 2 allocation Sankey diagrams, which can determine the full responsibility of CO 2 emissions of various sectors in each stage of the energy system and use it as a foundation to improve the LMDI decomposition method of CO 2 emissions growth.

LMDI Decomposition
The index decomposition analysis (IDA) method has been widely applied for analyzing the influencing factors of the growth of CO 2 emissions including those based on the Laspeyres index and the Divisia index. Ang et al. [21][22][23][24][25] presented a review of the development and applications of IDA methods and recommended the logarithmic mean Divisia index I (LMDI) method because it is robust and convenient for many applications. Many studies have utilized the LMDI method to decompose the total CO 2 growth of various sectors and regions. We present a summary of these studies in Table A7. In Table A7, we categorize the previous studies into five groups (A-E) according to the sector they analyzed, as follows.
In these studies, the commonly considered influencing factors are population growth, GDP (or gross output), economic structure (measured by value added or output of the sectors), energy intensity, end-use energy structure, and CO 2 emission factors. There are two major ways to allocate the responsibility of CO 2 emissions of electricity and heat generation: (1) considered as direct emissions of the generation; and (2) considered as indirect emissions of end-use sector. The emission factors of electricity and heat are calculated by the fuel structure of the generation. The latest way is more meaningful as it can show the contribution of the changes of electricity proportion in end-use sectors to the total CO 2 emissions. However, except those only focused on the power sector, most of the studies do not consider the influences of energy efficiency of heat and electricity generation.
Using the literature review, we conclude that in previous studies on a national level, neither the influence of the efficiency of electricity and heat generation nor the influence of efficiency of energy transportation and distribution can be decomposed. Based on K PEQ and other parameters derived from mapping the energy allocation Sankey diagram and CO 2 emission allocation Sankey diagram, we can develop an LMDI method that can analyze the influence of technical energy efficiency to improve the accuracy of the method. Since the energy losses in energy transportation and distribution are normally small and also lack statistical accounting, the technical energy efficiency is mainly decided by the efficiency of electricity and heat generation in this study.

Methodology and Data Input
In this section, we first introduce the primary energy quantity conversion factor (K PEQ ) in Section 3.1 and the primary carbon dioxide emission factor (K C ) in Section 3.2. Then these key parameters are used to map the energy allocation Sankey diagram and the CO 2 allocation Sankey diagram of energy consumption, which is introduced in Section 3.3. Next, the data obtained by the mapping is used in Section 3.4 to develop an LMDI method suitable for analyzing all influencing factors including both normal and extra factors. In the end, we briefly introduce the data input in Section 3.5.

Primary Energy Converted Factor
K PEQ , the primary energy quantity conversion factor, which was suggested by authors in previous studies [7,18,19,26], is a key parameter for establishing the connection between energy consumption of end-use sectors and primary energy consumption. K PEQ is defined as the total number of units of primary energy that are consumed to produce one unit of secondary energy. In previous studies [7,18], the authors presented a method that can generate K PEQ based on a series of standardized steps and rigid equations that can be programmed. In this method, we can express end-use energy consumption in standard quantity (SQ) form or in primary energy quantity (PEQ) form. The SQ form denotes the heat value of secondary energy consumed by end-use sectors while the PEQ form denotes the total primary energy consumed to produce secondary energy by compensating all energy losses upstream. However, the compensating process for the energy losses upstream is complex and involves many interacting conversion sub-sectors. Thus, the authors further introduced an input-output method to acquire the K PEQ of each energy type in a prior study [19].
The input-output method has been widely applied to reveal internal relationships among the economic sectors. The establishment of an input-output table can reflect the balance of material or capital flows among all sectors while the Leontief inverse matrix of the table can establish the connection between the end-use consumption and the total consumption (which includes intermediate and end-use consumption) of the flows. Therefore, using the input-output method, we can construct the energy input-output table of the energy sectors to establish the connection between end-use energy consumption and primary energy consumption by using the Leontief inverse matrix.
3.1.1. Establishment of the Energy Input-Output Table   The energy balance table of China [27,28] has provided detailed data on energy supply, energy conversion, and end-use consumption. Hence, we can modify the energy balance table into an energy input-output table according to the energy balance. However, the 30 energy types in an energy balance table should be combined into 11 energy types according to the sectoral classification in the energy balance table. This is due to the limitation of the input-output method where each intermediate sector can only have one kind of output. The classification of the intermedia sectors and their outputs are listed in Table A1.
Based on the classification, we establish the energy input-output table by using the energy balance  table as shown in Table A2. Q ij is the quantity of energy i consumed to produced energy j, Y i is the final demand of energy i (including net exports and end-use consumption of energy i), and Q i is the total output of energy i. All data in the table are expressed in SQ form.

Leontief Inverse Matrix of Energy Input-Output Table
The mathematical relationship among the elements in Table A2 is expressed in Equation (1) which means the total output of energy i (Q i ) equals the sum of intermedia consumption of energy i for energy conversion ∑ j Q ij and the final demand of energy i for end-use consumption (Y i ). Equation (1) can be further expressed in matrix form, which is shown in Equation (2).
After that, we define direct consumption efficiency a ij as the energy i. This should be consumed to produce one unit of energy j, which is shown in Equation (3).
Equation (5) can be further rewritten as Equation (6). Q is the total output of energy, Y is the final demand of energy, and (I − A) −1 is the Leontief inverse matrix, which is denoted with symbol L as shown in Equation (7).
In the Leontief inverse matrix, L ij indicates the total unit of energy i that should be produced in the energy sector in order to provide one unit of energy j for end-use. Thus, we can further calculate the total unit of fossil fuel that should be consumed in the conversion sector to provide one unit of energy j, K PEQ,j , by using Equation (8).
K PEQ,j Primary energy quantity conversion factor of energy j L 1,j Raw coal to be consumed to provide one unit of end-use energy j in the conversion sector L 2,j Crude oil to be consumed to provide one unit of end-use energy j in the conversion sector L 3,j Natural gas to be consumed to provide one unit of end-use energy j in the conversion sector L 4,j Other fossil fuels to be consumed to provide one unit of end-use energy j in the conversion sector Considering that electricity and heat are generated not only from fossil fuels but also from non-fossil fuels, Equation (8) was revised as below.
where L 5,j = K PEQ,j · E SQ,j,non− f ossil E SQ,j, f ossil + E SQ,j,non− f ossil (10) while L 1,j , L 2,j , L 3,j and L 4,j were revised using Equation (11), in which m included raw coal, crude oil, natural gas, and other fossil fuels.
L m,j = L m,j · E SQ,j, f ossil E SQ,j, f ossil + E SQ,j,non− f ossil (11) K PEQ,j Primary energy quantity conversion factor of energy j L m,j Primary energy to be consumed to provide one unit of end-use energy j in the conversion sector, including raw coal, natural gas, crude oil, and other fossil fuels L m,j Primary energy to be consumed to provide one unit of end-use energy j including raw coal, natural gas, crude oil, other fossil fuels, and non-fossil fuel E SQ,j,fossil Total energy type j which is converted from fossil fuels expressed in SQ form E SQ,j,non-fossil Total energy type j which is converted from non-fossil fuels expressed in SQ form

K PEQ of Each Energy Type in China
According to the results of above calculations and data input from the energy balance table [27,28], the K PEQ of each energy type in China is presented in Table 1. K PEQ is further adopted to derive the primary carbon dioxide emission factor in Section 3.2, to obtain the data for mapping the energy allocation Sankey diagram of China in Section 3.3, and to develop the LMDI method to decompose the growth of energy-related CO 2 emissions in China in Section 3.4.

Primary Carbon Dioxide Emission Factor
After introducing the acquirement of K PEQ of each energy type for mapping the energy allocation Sankey diagram, we further introduce the acquirement of the primary carbon dioxide emission factor (K C ) in this section, which is a key parameter for establishing the connection between energy consumption expressed in PEQ form and CO 2 emissions. K C is defined as the total number of units of CO 2 emissions when one unit of end-use energy expressed in PEQ form is consumed, which can be calculated using Equation (12). The CO 2 emissions factors of each primary energy are given in Table 2 [29]. Equation (12) can be further modified as Equation (13), in which K C,SQ,j is defined as the total number of units of CO 2 emissions when one unit of end-use energy expressed in SQ form is consumed.
Primary carbon dioxide emission factor of end-use energy j, which establishes the relationship between energy consumption expressed in PEQ form and CO 2 emissions K C,SQ"j Primary carbon dioxide emission factor of end-use energy j, which establishes the relationship between energy consumption expressed in SQ form and CO 2 emissions K C,m CO 2 emission factor of primary energy m L m,j Primary energy m to be consumed to provide one unit of end-use energy j K PEQ,j Primary energy quantity converted factor of energy j Subscription j Energy type j Subscription m Primary energy type m, including (1) raw coal; (2) crude oil; (3) natural gas; (4) other fossil fuels; and (5) non-fossil fuels. The K C of each energy type in China is presented in Table 3. K C is further adopted to derive the data for mapping the CO 2 (energy-related) allocation Sankey diagram in China in Section 3.3 and to develop the LMDI decomposition method of total CO 2 emissions growth in China in Section 3.4.

Diagram Structure
In this study, the energy allocation Sankey diagrams and the CO 2 allocation Sankey diagrams in China are divided into three stages, including primary energy supply, energy conversion, and end-use sector, as specified by previous studies [7,18,26]. The word "allocation" means there are no energy or mass losses reflected in these Sankey diagrams. By compensating all losses during energy conversion and transport, we can express the consumption of secondary energy in PEQ form to indicate the amount of primary energy consumption required to produce it, and express the CO 2 emissions in mass form. This will indicate the responsibility of each sector in various stages for total CO 2 emissions.
The 13 energy types in the mapping are defined in Table A3 and described in previous studies [7,18,19]. To illustrate the structure of the final energy consumption and CO 2 emissions of each subsector in the diagram, we re-categorized the subsectors as shown in Table A4.

Original Data and Data Processing
The energy balance table and the table of final energy consumption by the industrial sector in the China Energy Statistical Yearbook [27,28] are used as original data sources for mapping the energy allocation Sankey diagram and the CO 2 allocation Sankey diagram of energy consumption.
However, in addition to the oil consumption data in the transport, storage, and post subsector classifications, the actual oil consumption of various vehicles is partly separated into statistical energy consumption in other subsectors due to the current method of constructing the energy balance tables.
To determine this portion of energy consumption, we include in the transportation sector from the original statistical data [30], all gasoline consumption and 95% of diesel consumption in the primary industrial and residential sector, 95% of gasoline consumption and 35% of diesel consumption in the secondary and tertiary industries, all kerosene consumption in other sectors, and 100% of gasoline, diesel, kerosene, fuel oil, LPG (liquefied petroleum gas), natural gas, LNG (liquefied natural gas), and 40% of electricity in the original transport, storage, and post subsector classifications noted in the energy balance table. As such, the energy consumption in the transportation sector only includes the oil consumption for driving various vehicles such as cars, planes, and trucks while the rest of the energy consumption in the transport, storage, and post subsectors is separated into energy consumption for buildings.

Final Data for Diagram Mapping
As demonstrated in previous studies [7,18,19,26], we can use Equation (14) to obtain the data for constructing the energy allocation Sankey diagram, in which K PEQ,j is used to amplify secondary energy to the primary energy, which is required to produce the secondary energy by compensating the energy losses in the conversion sector. The acquisition of K PEQ,j is described in Section 3.1.
E PEQ"j Energy j consumption expressed in PEQ form, which is used for mapping the energy allocation Sankey diagram E SQ,j Energy j consumption expressed in SQ form, which is given in the energy balance table K PEQ,j Primary energy conversion factor of energy j Equation (14) can be further modified with K c,j as seen in Equation (15) to express the data for constructing the CO 2 allocation Sankey diagram of energy consumption, in which K c,j is used to calculate the CO 2 emissions of each type of end-use energy. The acquisition of K c,j is described in Section 3.2. Cj = ESQ, j·KPEQ, j·KC, j C ,j CO 2 emissions, which is used for mapping the carbon dioxide allocation Sankey diagram of energy consumption E SQ Energy j consumption expressed in SQ form, which is given in the energy balance table K PEQ,j Primary energy conversion factor of energy j K C,j Primary carbon dioxide emission factor of end-use energy j, which establishes the relationship between energy consumption expressed in PEQ form and CO 2 emissions.

Additive LMDI Decomposition Method
Based on Equation (15), we can extend the conventional CO 2 identity to further consider technical details about structural and efficiency changes through the complex energy system along stages of the energy supply chain. In this study, we classify the CO 2 emissions of China into two groups, according to the energy statistical data of China. We discuss their influencing factors such as the economic sector, which includes the primary, secondary, and tertiary sectors, and the residential sector, which includes urban and rural areas. These constitute all energy-related CO 2 emissions in China.
For the economic sector, most previous studies have adopted Equation (16) to express the CO 2 emissions and to consider influencing factors such as population (P), GDP per capita ( GDP P ), economic structure ( GDPi GDP ), energy intensity ( ESQ,i GDPi ), energy proportional use ( ESQ,ij ESQ,i ), and CO 2 emission factor (K C,j ) where i represents the economic sector and j represents the energy type.
Our literature review shows that neither the influence of electricity efficiency and heat generation has been decomposed in previous studies nor the influence of efficiency of energy transportation and distribution. Therefore, we modified Equation (16) to overcome the challenge mentioned above as shown in Equation (17).
For the residential sector, we consider the influencing factors, including urban residential CO 2 emissions and rural residential CO 2 emissions. The residential CO 2 emissions can be expressed by population (P), urban and rural structure ( Pi P ), residential energy consumption per capita ( ESQ,i Pi ), energy proportional use ( ESQ,ij ESQ,i ), primary energy conversion factor (K PEQ,j ), and primary carbon dioxide emission factor (K C,j ), which is shown in Equation (18).
The symbols used in Equations (17) and (18) are defined in Tables A5 and A6. In this study, we adopt additive LMDI decomposition. The additive LMDI formulae for decomposing energy-related CO 2 emissions growth in the composite economic and residential sectors of China are presented in Tables 4 and 5. Table 4. Additive LMDI formulae for decomposing the CO 2 emissions growth of economic sector in China.

Influencing Factors Symbols Additive LMDI Formulae
Note: The superscripts 0 and T specify the parameter value at time 0 and time T, respectively. Table 5. Additive LMDI formulae for decomposing CO 2 emissions growth of residential sector in China.

Influencing Factors Symbols Additive LMDI Formulae
Urban and rural structure Primary energy quantity converted factor Note: The superscripts 0 and T give the parameter at time 0 and time T, respectively.

Data Input
We obtained energy data from the China Energy Statistical Yearbook [27,28] and economic data from the China Statistical Yearbook [31]. The K PEQ and K C of each fuel for China in 2004 and 2014 are provided in Tables 1 and 3, which can be found in Sections 3.1 and 3.2, respectively.

Energy and CO 2 Allocation Sankey Diagrams in China
The energy allocation Sankey diagrams and CO 2 allocation Sankey diagrams of energy consumption in China for 2004 and 2014 are presented in Figures 1-4. The main advantage of this CO 2 allocation Sankey diagram is that it can show the full responsibility for CO 2 emissions of various sectors at each stage of the energy supply chain. For example, it illustrates that the energy supply stage determines the amounts of carbon which flows into the system and has the responsibility for introducing more low carbon and non-fossil energy. The energy transformation stage determines the carbon amounts required to provide certain amounts and types of secondary energy and has the responsibility for improving energy conversion efficiency and deploying low-carbon energy sources. The end-use sector has the responsibility for improving the energy efficiency of end-use equipment including industrial boilers, electric motors, and household appliances, etc., as well as controlling the direct burning of fossil fuels.
According to these diagrams, the main features and dynamics of China's energy use and energy-related CO 2 emissions are as follows: (1) Energy supply: raw coal supply contributed 78.8% and 77.5% to energy-related CO 2

Additive LMDI Decomposition Results for CO 2 Emissions Growth in Economic Sector
Through additive LMDI decomposition, we determine the increment in energy-related CO 2 emissions of China's entire economic sector including primary, secondary, and tertiary industries. This was caused by each influencing factor between 2004 and 2014, which accounted for 88.7% and 88.5% of the total energy-related CO 2 emissions, respectively. The decomposition results are given in Table 6 and the summarized decomposition results of the economic sector are shown in Figure 5. The growth of GDP per capita is the dominant factor driving CO 2 emissions growth in 2004-2014, while other influences are relatively small. In the following sections, we discuss each of these influencing factors.

Additive LMDI Decomposition Results for CO2 Emissions Growth in Economic Sector
Through additive LMDI decomposition, we determine the increment in energy-related CO2 emissions of China's entire economic sector including primary, secondary, and tertiary industries. This was caused by each influencing factor between 2004 and 2014, which accounted for 88.7% and 88.5% of the total energy-related CO2 emissions, respectively. The decomposition results are given in Table 6 and the summarized decomposition results of the economic sector are shown in Figure 5. The growth of GDP per capita is the dominant factor driving CO2 emissions growth in 2004-2014, while other influences are relatively small. In the following sections, we discuss each of these influencing factors.  Population growth in China contributed to CO2 emissions growth during 2004 to 2014. However, the contribution is rather limited. The reason may be that population growth in China was relatively small, with a total increase of 5.2% in 2014 when compared to 2004, which is shown in Figure 6. This is due to the rigid population restriction policy that has been in place since the 1970s.  Population growth in China contributed to CO 2 emissions growth during 2004 to 2014. However, the contribution is rather limited. The reason may be that population growth in China was relatively small, with a total increase of 5.2% in 2014 when compared to 2004, which is shown in Figure 6. This is due to the rigid population restriction policy that has been in place since the 1970s.

The Influence of GDP per Capita
Along with rapid industrialization, urbanization, and motorization, the GDP per capita of China increased 11.1% annually from 2004 to 2014 and had a significant influence on CO2 emissions in China. Referring to Reference [7], gross capital formation, which is accompanied by a rapid expansion of energy-intensive industries such as steel, cement, and chemicals, is a main driving force of economic growth in China. This further accelerated the growth of CO2 emissions. Moreover, with a large capacity of energy-intensive products domestically, the net exports depend more on the export of these products. The rapid economic growth in China is guided by the political goals of the Communist Party in China since China is a collectivist society with a strong central government ruled by the Party [32]. Referring to these political goals, we can summarize that rapid economic growth was always a prioritized political goal in the 2004 to 2014 period, while ecological and environmental protection was more and more emphasized to optimize the economic structure and control the speed of growth.

The Influence of Economic Structure and Energy Intensity
Although changes in economic structure and energy intensity both decreased CO2 emissions from 2004 to 2014, the influence of energy intensity was more significant. The proportion of primary industry, secondary industry, and tertiary industry adjusted from 12.9%, 45.9%, and 41.2% in 2004 to 9.1%, 43.1%, and 47.8% in 2014. The energy intensities of China are illustrated in Table 7.
Although China experienced a rapid expansion of energy-intensive secondary industries, especially iron and steel, cement, and chemicals, the government of China devoted much more effort than before to restricting the extensive development and energy consumption of these industries. The major goal was setting energy intensity as a constraint in the 11th Five Year Plan, including setting reduction targets for each economic subsector [33]. These efforts led to a great reduction of CO2 emissions from 2004 to 2014.

The Influence of GDP per Capita
Along with rapid industrialization, urbanization, and motorization, the GDP per capita of China increased 11.1% annually from 2004 to 2014 and had a significant influence on CO 2 emissions in China. Referring to Reference [7], gross capital formation, which is accompanied by a rapid expansion of energy-intensive industries such as steel, cement, and chemicals, is a main driving force of economic growth in China. This further accelerated the growth of CO 2 emissions. Moreover, with a large capacity of energy-intensive products domestically, the net exports depend more on the export of these products. The rapid economic growth in China is guided by the political goals of the Communist Party in China since China is a collectivist society with a strong central government ruled by the Party [32]. The transition of political goals can be summarized in three stages as follows: (1) Table 7.
Although China experienced a rapid expansion of energy-intensive secondary industries, especially iron and steel, cement, and chemicals, the government of China devoted much more effort than before to restricting the extensive development and energy consumption of these industries. The major goal was setting energy intensity as a constraint in the 11th Five Year Plan, including setting reduction targets for each economic subsector [33]. These efforts led to a great reduction of CO 2 emissions from 2004 to 2014. The energy value type is expressed in SQ form, and the price is based on the 2014 constant price.

The Influence of Energy Structure in End-Use
The progression of the end-use energy structure in the end-use sector in China with increased CO 2 emissions and the influence of each energy type are shown in Figure 7.  The energy value type is expressed in SQ form, and the price is based on the 2014 constant price.

The Influence of Energy Structure in End-Use
The progression of the end-use energy structure in the end-use sector in China with increased CO2 emissions and the influence of each energy type are shown in Figure 7. The increased proportion of electricity, gas, and natural gas in end-use energy consumption in the economic sector in China significantly increased CO2 emissions, while the decreased proportion of oil products reduced those CO2 emissions. The increased proportion of electricity has been a major contributor to CO2 emissions growth. For example, when 1 tce of electricity is consumed, 2.54 tce of primary energy will be consumed and 4.67 tons of CO2 will be emitted.

The Influence of Primary Energy Conversion Factors
The increase in energy conversion efficiency, represented by KPEQ,j and shown in Figure 8, is primarily due to improved electricity supply efficiency. This is the main factor that reduced CO2 emissions growth in China from 2004 to 2014. In the last decade, the government of China has shut down power plants with low efficiency and promoted advanced power plants with high efficiency and large capacity [34]. In addition, the introduction of natural gas combined with cycle power plants that have higher energy conversion efficiency also helped to gradually improve the primary energy consumption per unit of supplied electricity.  The increased proportion of electricity, gas, and natural gas in end-use energy consumption in the economic sector in China significantly increased CO 2 emissions, while the decreased proportion of oil products reduced those CO 2 emissions. The increased proportion of electricity has been a major contributor to CO 2 emissions growth. For example, when 1 tce of electricity is consumed, 2.54 tce of primary energy will be consumed and 4.67 tons of CO 2 will be emitted.

The Influence of Primary Energy Conversion Factors
The increase in energy conversion efficiency, represented by K PEQ,j and shown in Figure 8, is primarily due to improved electricity supply efficiency. This is the main factor that reduced CO 2 emissions growth in China from 2004 to 2014. In the last decade, the government of China has shut down power plants with low efficiency and promoted advanced power plants with high efficiency and large capacity [34]. In addition, the introduction of natural gas combined with cycle power plants that have higher energy conversion efficiency also helped to gradually improve the primary energy consumption per unit of supplied electricity.

The Influence of the Primary Carbon Emissions Factor
The decrease in the carbon emissions factor, represented by KC,j, is primarily due to the increment in the proportion of non-fossil fuels with low CO2 emissions and in the proportion of natural gas with a smaller carbon emissions factor compared to raw coal in the fuel mix of heat and electricity generation. This is mainly because the government of China struggled to diversify the fuel mix in heat and electricity generation in China and to introduce non-fossil fuels and natural gas. The fuel mix in heat and electricity generation can be seen in Figure 9.

LMDI Additive Decomposition Results for Emissions Growth in the Residential Sector
Through LMDI additive decomposition, we acquired the incremental energy-related CO2 emissions for China in its residential sector driven by each influencing factor between 2004 and 2014,

The Influence of the Primary Carbon Emissions Factor
The decrease in the carbon emissions factor, represented by K C,j , is primarily due to the increment in the proportion of non-fossil fuels with low CO 2 emissions and in the proportion of natural gas with a smaller carbon emissions factor compared to raw coal in the fuel mix of heat and electricity generation. This is mainly because the government of China struggled to diversify the fuel mix in heat and electricity generation in China and to introduce non-fossil fuels and natural gas. The fuel mix in heat and electricity generation can be seen in Figure 9.

The Influence of the Primary Carbon Emissions Factor
The decrease in the carbon emissions factor, represented by KC,j, is primarily due to the increment in the proportion of non-fossil fuels with low CO2 emissions and in the proportion of natural gas with a smaller carbon emissions factor compared to raw coal in the fuel mix of heat and electricity generation. This is mainly because the government of China struggled to diversify the fuel mix in heat and electricity generation in China and to introduce non-fossil fuels and natural gas. The fuel mix in heat and electricity generation can be seen in Figure 9.

LMDI Additive Decomposition Results for Emissions Growth in the Residential Sector
Through LMDI additive decomposition, we acquired the incremental energy-related CO2 emissions for China in its residential sector driven by each influencing factor between 2004 and 2014,

LMDI Additive Decomposition Results for Emissions Growth in the Residential Sector
Through LMDI additive decomposition, we acquired the incremental energy-related CO 2 emissions for China in its residential sector driven by each influencing factor between 2004 and 2014, which accounted for 11.3% and 11.5% of the total energy-related CO 2 emissions, respectively. The LMDI additive decomposition results for the residential sector are illustrated in Table 8. A summary of the decomposition results of the residential energy consumption is shown in Figure 10.
which accounted for 11.3% and 11.5% of the total energy-related CO2 emissions, respectively. The LMDI additive decomposition results for the residential sector are illustrated in Table 8. A summary of the decomposition results of the residential energy consumption is shown in Figure 10.  In 2014, residential-energy-related CO2 emissions accounted for 11.5% of the total energy-related CO2 emissions in China. Population growth, urban and rural structure change, residential energy consumption per capita growth, and end-energy proportional use change are the main contributors to the residential energy-related CO2 emissions growth, while the primary energy conversion factor and primary carbon dioxide emission factor change helped to decrease the residential CO2 emissions in China. From 2004 to 2014, the urbanization rate of China increased from 41.8 to 54.8%, which caused an increase in CO2 emissions since the residential energy consumption per capita of urban areas was higher than rural areas. Along with GDP growth per capita, residential energy consumption growth per capita also increased rapidly between 2004 and 2014 especially in rural areas. From 2004 to 2014, the residential energy consumption per capita in urban and rural areas in China increased from 0.1685 tce/person to 0.2672 tce/person and 0.0801 tce/person to 0.2339 tce/person, respectively.
The changing energy structures in the residential end-use sector contributed to residential CO2 emissions growth in China from 2004 to 2014 due to an increased proportion of electricity, natural gas, and gas. However, the decreased proportion of coal products is the main negative contributor to residential CO2 emissions growth. The influence of the changing residential end-use energy consumption structure is shown in Figure 11. 34   In 2014, residential-energy-related CO 2 emissions accounted for 11.5% of the total energy-related CO 2 emissions in China. Population growth, urban and rural structure change, residential energy consumption per capita growth, and end-energy proportional use change are the main contributors to the residential energy-related CO 2 emissions growth, while the primary energy conversion factor and primary carbon dioxide emission factor change helped to decrease the residential CO 2 emissions in China. From 2004 to 2014, the urbanization rate of China increased from 41.8 to 54.8%, which caused an increase in CO 2 emissions since the residential energy consumption per capita of urban areas was higher than rural areas. Along with GDP growth per capita, residential energy consumption growth per capita also increased rapidly between 2004 and 2014 especially in rural areas. From 2004 to 2014, the residential energy consumption per capita in urban and rural areas in China increased from 0.1685 tce/person to 0.2672 tce/person and 0.0801 tce/person to 0.2339 tce/person, respectively.
The changing energy structures in the residential end-use sector contributed to residential CO 2 emissions growth in China from 2004 to 2014 due to an increased proportion of electricity, natural gas, and gas. However, the decreased proportion of coal products is the main negative contributor to residential CO 2 emissions growth. The influence of the changing residential end-use energy consumption structure is shown in Figure 11. The influence of population growth and the primary energy quantity type conversion factor are also discussed in Sections 4.2.1 and 4.2.6.

Comparison with Current Policies to Reduce CO2 Emissions
Currently, the government of China has made many efforts to fulfill its promise [12,13] to reduce CO2 emissions by 2030, as mentioned in the introduction. One of the most important policies is the 13th Five-Year-Plan [35] enacted in 2016, which announced several targets to control CO2 emissions from 2016 to 2020. They include reducing the energy intensity by 15% when compared to energy intensity in 2015, reducing the CO2 emission intensity by 18% when compared to the emission intensity in 2015, increasing the proportion of non-fossil energy to 15% of total primary energy consumption by 2020, and increasing the proportion of the tertiary industry to 56% in total GDP by 2020.
Compared with our LMDI additive decomposition results, this policy is quite consistent with the research findings that reducing energy intensity was a major contributor to reducing CO2 emissions growth between 2004 and 2014, which is followed by the optimization of the economic structure and the increase of the proportion of low carbon energy supply (reflected by the decreased primary CO2 emission factor).
However, there are still many challenges facing China when fulfilling its promise. The major challenge is the continuously rapid GDP per capita growth of China. In the 13th Five-Year Plan, a limitation of average GDP growth rate of 6.5% is set as the lower limit and no upper limit is set. The GDP per capita of China in 2015 was 8028 USD and still lags behind the world (10,058 USD) and the Asia Pacific region (9398 USD) [36]. As such, there is still a gap for China to increase its GDP per capita. Furthermore, the urbanization and industrialization of Western China are not yet complete. Therefore, fixed-asset investment in Western China will still make a significant contribution to the GDP growth and CO2 emissions growth in the future. Hence, the government in China should carefully control its GDP per growth by constraining unnecessary infrastructure construction to avoid energy waste. The same view is also provided by Zhang et al. [37] in their scenario analysis.
Moreover, the reduction of energy intensity and CO2 emissions intensity should be a goal further distributed to specific sub-sectors to determine the responsibility of each sub-sector for reducing energy consumption and CO2 emissions. The influence of population growth and the primary energy quantity type conversion factor are also discussed in Sections 4.2.1 and 4.2.6.

Comparison with Current Policies to Reduce CO 2 Emissions
Currently, the government of China has made many efforts to fulfill its promise [12,13] to reduce CO 2 emissions by 2030, as mentioned in the introduction. One of the most important policies is the 13th Five-Year-Plan [35] enacted in 2016, which announced several targets to control CO 2 emissions from 2016 to 2020. They include reducing the energy intensity by 15% when compared to energy intensity in 2015, reducing the CO 2 emission intensity by 18% when compared to the emission intensity in 2015, increasing the proportion of non-fossil energy to 15% of total primary energy consumption by 2020, and increasing the proportion of the tertiary industry to 56% in total GDP by 2020.
Compared with our LMDI additive decomposition results, this policy is quite consistent with the research findings that reducing energy intensity was a major contributor to reducing CO 2 emissions growth between 2004 and 2014, which is followed by the optimization of the economic structure and the increase of the proportion of low carbon energy supply (reflected by the decreased primary CO 2 emission factor).
However, there are still many challenges facing China when fulfilling its promise. The major challenge is the continuously rapid GDP per capita growth of China. In the 13th Five-Year Plan, a limitation of average GDP growth rate of 6.5% is set as the lower limit and no upper limit is set. The GDP per capita of China in 2015 was 8028 USD and still lags behind the world (10,058 USD) and the Asia Pacific region (9398 USD) [36]. As such, there is still a gap for China to increase its GDP per capita. Furthermore, the urbanization and industrialization of Western China are not yet complete. Therefore, fixed-asset investment in Western China will still make a significant contribution to the GDP growth and CO 2 emissions growth in the future. Hence, the government in China should carefully control its GDP per growth by constraining unnecessary infrastructure construction to avoid energy waste. The same view is also provided by Zhang et al. [37] in their scenario analysis.
Moreover, the reduction of energy intensity and CO 2 emissions intensity should be a goal further distributed to specific sub-sectors to determine the responsibility of each sub-sector for reducing energy consumption and CO 2 emissions.

Uncertainties
Although the method and data used in this work represent the best attempts of the authors, uncertainties do exist because of the lack of more accurate data. This is explained as follows: 1.
The emissions factor of raw coal and coal products is arguable, as the coal quality-which is mainly denoted by its heat value, volatile component, and ash content-is quite different across China depending on the production mines. The default CO 2 emissions factor of raw coal suggested by the IPCC was adopted in this study.

2.
We assumed that all fossil fuels are combusted completely in all sectors and that the elemental carbon they contain is 100% converted into CO 2 .

3.
Non-commercial energy consumption (mainly biomass including straw and wood) related to CO 2 emissions is not audited in this study due to a lack of official statistical data.

4.
Carbon capture and storage technology is not discussed in this study.

Conclusions
In this study, we first constructed an energy input-output table for China and acquired the K PEQ and K C of each energy type using the Leontief inverse matrix of the energy input-output table. After that, we constructed energy allocation diagrams and CO 2 emissions allocation diagrams of China to present the energy balance and carbon balance from the primary energy supply stage to the end-use energy consumption stage in 2004 and 2014. Based on these, we developed an LMDI method to decompose and analyze the contributions of the main influencing factors, which includes both the normal factors and the extra factors, to the growth of energy-related CO 2 emissions on a national level. Compared with the conventional LMDI method, our method can further consider the impact of the efficiency of energy conversion and transportation, especially electricity efficiency and heat generation. This LMDI method was then applied to analyze the influencing factors of energy-related CO 2 emissions growth in China in both the economic and residential sectors from 2004 to 2014.
We conclude that the main features of energy-related CO 2 emissions in China are that raw coal supply is the major carbon contributor to energy-related CO 2 emissions in China, accounting for 77.5% of total CO 2 emissions in 2014. Additionally, the CO 2 emissions per unit heat and electricity generation decreased from 2004 to 2014 due to the introduction of non-fossil fuels and the improvement of energy conversion efficiency. Lastly, the manufacturing sector is the main CO 2 emitter in China and accounted for 71% of the total CO 2 emissions.
The results of the LMDI additive decomposition regarding the growth of energy-related CO 2 emissions indicate that GDP growth per capita is the main driving force of CO 2 emissions growth in China. In addition, the improvement of energy intensity and electricity supply efficiency helps reduce the CO 2 emissions growth in China. This same effect is seen with the introduction of non-fossil fuels in heat and electricity generation. The residential energy-related CO 2 emissions sector grew 8.9% annually due to the increased residential energy consumption per capita and the increased proportion of electricity in end-use energy.
In this study, although we extended the conventional top-down LMDI decomposition approach by using K PEQ to consider the contributions of improved energy conversion and transportation efficiency to the growth of CO 2 emissions, more detailed technical influencing factors should be further considered in the next step, such as the end-use energy efficiency. Considering its importance to reducing CO 2 emissions, most countries have enacted policies to improve end-use energy efficiency. For example, China's government has forbidden the use of industrial boilers with low efficiency and inferior environmental performance. As such, the energy efficiency of end-use equipment such as furnaces, electric motors, and transport engines should be considered further in future experiments. Moreover, in future experiments, we suggest analyzing the contribution of various influencing factors to energy-related SO 2 and NO x emissions growth due to the damage of air pollution in China and the lack of studies that use similar methods to those seen in this work. Author Contributions: Linwei Ma, Chinhao Chong and Xi Zhang coordinated the main theme of this paper and wrote this manuscript. Linwei Ma proposed the methodology and constructed the analysis framework. Chinhao Chong and Xi Zhang processed the energy and CO 2 emissions data through input-output approach and launched additive LMDI decomposition to analyze the contribution of each influencing factor to the CO 2 emissions growth. Chinhao Chong mapped the Sankey diagrams. Pei Liu and Weiqi Li discussed the research results and commented on the manuscript. Final review was done by Zheng Li and Weidou Ni. All the authors read and approved the final manuscript.

Conflicts of Interest:
The authors declare no conflict of interest.

Subscript i
Economic sub-sector i involved in the LMDI decomposition of CO 2 emissions growth in the economic sector including primary industry, secondary industry, and tertiary industry/Area i involved in the LMDI decomposition of CO 2 emissions growth in the residential sector including urban areas or rural areas Subscript Energy type j consumption of economic sub-sector i expressed in SQ form during the LMDI decomposition of CO 2 growth in economic sector/Energy type j consumption of area i expressed in SQ form during the LMDI decomposition of CO 2 emissions growth in the residential sector E PEQ,j Energy type j consumption expressed in PEQ form C economic Total CO 2 emissions of economic sector C residential Total CO 2 emissions of residential sector C ,j CO 2 emissions used for mapping the carbon dioxide allocation Sankey diagram of energy consumption Q ij The quantity of energy i consumed to produced energy j in energy input-output table Q i The total output of energy i in energy input-output table Y i The final demand of energy i in energy input-output table

L ij
The element of the Leontief inverse matrix of the energy input-output table, which indicates the quantity of energy i consumed to provide one unit of end-use energy j L m,j Primary energy m to be consumed to provide one unit of end-use energy j in the conversion sector including raw coal, natural gas, crude oil, and other fossil fuels L m,j Primary energy m to be consumed to provide one unit of end-use energy j, including raw coal, natural gas, crude oil, other fossil fuels, and non-fossil fuel E SQ,j,fossil Total energy type j which is converted from fossil fuels expressed in SQ form E SQ,j,non-fossil Total energy type j, which is converted from non-fossil fuels expressed in SQ form K C Primary carbon dioxide emission factor of end-use energy j, which established the relation between energy consumption expressed in PEQ form and CO 2 emissions K C,SQ"j Primary carbon dioxide emission factor of end-use energy j, which established the relation between energy consumption expressed in SQ form and CO 2 emissions K C,m Carbon dioxide emissions factor of primary energy m C 0 Total energy related CO 2 emissions at time 0 C T Total energy related CO 2 emissions at time T P Population GDP Gross domestic production GDP i Value added within economic sub-sector i Q GDP per capita    Crude oil 3.
Natural gas: Natural gas and LNG 4.
Manufacturing of non-metallic mineral and chemical products 7.
Manufacturing of raw chemical materials and chemical products 8.
Manufacturing of food and beverages • Processing of food from agricultural products • Manufacturing of food • Manufacturing of liquor, beverages, and refined tea Rural living 3.

Items Descriptions
Subscript i Primary energy quantity conversion factor of energy type j K C,j Primary carbon dioxide emission factor of energy type j Table A6. Symbols used in Equation (18).

Items Descriptions
Subscription i 1. Urban area 2.

Population P i
Population of area i E SQ,i Energy consumption of area i expressed in SQ form E SQ,ij Fuel j consumption of area i expressed in SQ form K PEQ,j Primary energy quantity conversion factor of energy type j K C,j Primary carbon dioxide emission factor of energy type j Table A7. A summary of LMDI decomposition of energy related CO 2 emissions in recent years.

No
Sector Identity CO 2 Emission of Electricity Author Region

A1
All sector The CO 2 emission factor of electricity is considered to be zero.
The CO 2 emission factor of electricity is considered to be zero.
The CO 2 emission factor of electricity is considered to be zero.
Chen and Yang [53] China The CO 2 emission factor of electricity is calculated according to the fuel mix in electricity generation sectors.
The CO 2 emission factor of electricity is considered to be zero. However, the energy consumption to generate that electricity is counted into each sector according to its electricity consumption and the fuel mix of electricity generation of the region.
Mahony et al. [71,72] Ireland The CO 2 emission factor of electricity is considered to be zero.
Jiang et al. [73] China The CO 2 emission factor of electricity is considered to be zero.
Cansino [74] Spain The CO 2 emission factors of electricity and heat are calculated according to the fuel mix in electricity and heat generation sectors.
The CO 2 emission factor of electricity is considered to be zero.

C8
Kopidou et al. [83] EU The CO 2 emission factor of electricity is calculated according to the fuel mix in electricity generation sectors.
Zhao et al. [84] Shanghai City, China The CO 2 emission factor of electricity is considered to be zero.
Shao et al. [85] Shanghai City, China The CO 2 emission factor of electricity is considered to be zero.

D1
Residential sector The CO 2 emission factor of electricity is considered to be zero.
Zhang et al. [69] Beijing City, China The CO 2 emission factor of electricity is considered to be zero.
Liu et al. [70] China D3 Tan et al. [58,59] Chongqing City, China The CO 2 emission factor of electricity is considered to be zero.
Yeo et al. [88] China and India The CO 2 emission factor of electricity is considered to be zero. However, the energy consumption to generate that electricity was counted into each sector according to its electricity consumption and the fuel mix of electricity generation of the region. The CO 2 emission factor of electricity is calculated according to the fuel mix in electricity generation sectors.

Sun et al. [101] China
Note: Some elements in the identities have been modified with unified abbreviations based on the classification need. The abbreviations can be referred as below. Subscription i: Economic sector i or industrial sector i; Subscription j: Energy j; C all : Total CO 2 emissions of the region; C eco : Total CO 2 emissions of economic sector; C ind : Total CO 2 emissions of industrial sector; C pow : Total CO 2 emissions of power sector; C sec : Total CO 2 emissions of specific sector; P: Population; Q: Level of activity, normally indicated by GDP or gross output; Q i : Value-added or gross output of sector i; E: Total energy consumption; E i : Total energy consumption of sector i; E j : Consumption of energy j; E ij : Consumption of energy j in sector i; FF: Total fossil fuel consumption; FF i : Total fossil fuel consumption of sector i; FF j : Total consumption of fossil fuel j; FF ij : Consumption of fossil fuel j in sector i; C: Total CO 2 emissions; C j : Total CO 2 emissions of sector i; C j : CO 2 emissions of energy j; C ij : CO 2 emissions of energy j in sector i; RE: Total renewable energy consumption; CF: Fossil fuel and biomass consumption; I i : Fixed asset investment of sector i; R i : R&D expenditure of sector i; THN: Total household number; Income: Total disposable income; AHI: Disposable income per household; Ele: Electricity output in power sector; Ele FF : Fossil fuel consumption for power generation; Ele FF,j : Fossil fuel j consumption for power generation; Ele need : Electricity consumption; Ele dom : Domestic electricity production; IS: Employment of the sector.