A Method for Analyzing Energy-Related Carbon Emissions and the Structural Changes: A Case Study of China from 2005 to 2015

: To systematically analyze energy-related carbon emissions from the perspective of comprehensive energy ﬂow and allocate emissions responsibility, we introduce energy allocation analysis to carbon ﬂow process based on Sankey diagrams. Then, to quantitatively compare di ﬀ erent diagrams and evaluate the structural changes of carbon ﬂow, we deﬁne changes from three dimensions including total amount change, relative growth rate and occupation ratio change (TRO), propose TRO index. The method is applied to China’s case study from 2005 to 2015. We map China’s energy-related carbon ﬂow Sankey diagrams with high technical resolution from energy sources, intermediate conversion, end-use devices, passive systems to ﬁnal services, and conduct TRO index decomposition by stages. The results indicate that in energy sources, the emission share of coal has declined due to energy transition although coal is still the largest contributor to China’s energy-related carbon emissions. In passive systems, the factory passive systems are the largest contributors, among them, emission reduction should focus on the steel, non-ferrous and chemical industries; the building passive systems should pay attention to household appliances; the vehicle passive systems should focus on cars. In ﬁnal services, the demand for structural materials is the strongest driving force for carbon emissions growth.


Introduction
Controlling energy-related carbon emissions and realizing a low-carbon transition in the energy system are important ways to globally address climate change and achieve sustainable development [1]. Considering that energy-related carbon emissions are closely related to complex energy flows in the energy system, it is necessary for policymakers to understand carbon emissions from the perspective of overall energy systems so as to formulate more targeted emission reduction policies [2]. As climate change becomes more severe, recent researches are stimulated to analyze energy-related carbon emissions and emission responsibility underlying the entire process of energy flow, and to discern the changing trend.
In the area of energy system analysis, Sankey diagrams are popular and useful tools for visualizing processes [3], which use arrows to show the flow of a certain object (e.g., energy, exergy, resources, etc.) with width representing the quantity and the colors indicating the types. Some recent examples of Sankey diagrams applied to energy system analysis are shown in Table 1. The literature shows In this field, Cullen and Allwood [4] were early scholars who proposed a systematic energy allocation analysis method based on Sankey diagrams. The method suggested that energy losses in energy conversion sectors should be calculated into and compensated for in the end-use energy consumption but not be presented separately, so as to evaluate the primary energy consumption responsibility of end use sectors and final energy services. This method was then followed by many other scholars, for example, Ma et al. [6] applied the method to national level mapping China's energy flow diagram, Chong et al. [7] introduced it to Malaysia showing the allocation of primary energy consumption responsibility in the energy system. Furthermore, the method was applied to regional energy flow such as China's provinces [8] and Canada's territories [9]. Recent researches also used the method to map CO 2 flow diagrams [12], however, through our literature review, we found some limitations in three main aspects: • Although the application of Sankey diagrams in the analysis of complex energy flow process was popular including comprehensive stages, the application in the analysis of energy-related carbon emissions flow was relatively limited. In the published work about carbon flow diagrams, the division of energy stages was somewhat simple with only supply and end use sides [11].
The resolution of the carbon flow diagram needs to be increased.

•
Research gap also existed in some other diagrams [10] in which a large amount of carbon emissions caused by energy loss in the conversion sector were calculated as a loss, which made it difficult to observe the carbon emission responsibility allocation of the end-use sectors well. It is needed to Energies 2020, 13,2076 3 of 24 apply the idea of energy allocation analysis to carbon allocation analysis to show the emission responsibility comprehensively.

•
Most of existing work using Sankey diagrams focused on the situation of a certain year. Although some research presented carbon flow diagrams in different years [12], it still lacked systematical comparison of diagrams in different years. While comparing these diagrams might reveal in-depth structural changes and trends of energy transition. Considering this, a new method for comparing Sankey diagrams and evaluating structural changes is needed.
Recognizing the above limitations, this paper aims to develop a method for analyzing energy-related carbon flow from the perspective of comprehensive energy flow, quantitatively comparing different Sankey diagrams and evaluating the structural changes and trends with energy transition. Firstly, we introduced energy allocation analysis to carbon flow analysis, fully considering the carbon emission responsibility allocation in the whole energy flow process from energy sources, intermediate conversion, end-use conversion devices, passive systems to final services. Secondly, we mapped the energy flow and the energy-related carbon flow Sankey diagrams. Thirdly, we defined the structural changes of Sankey diagrams from three dimensions, proposed index including total amount change (T), relative growth rate (R) and occupation ratio change (O), i.e., TRO index, compared different Sankey diagrams and discussed the political and practical reasons behind these changes.
To apply the method to actual objects, we chose China as a case for its tremendous and dynamic energy consumption and energy-related carbon emissions (see Appendix A, Figure A1). China accounted for 23.6% of global energy consumption and 27.8% of global energy-related CO 2 emissions as the largest energy consumer and CO 2 emission source in 2018 [13]. We chose the decade of 2005-2015 as the research period, because in this decade China's energy development experienced a tough transition. In this period, to achieve energy transition, China issued a package of energy plans ( [14][15][16][17][18][19] as listed in Appendix B, Table A1). These policies resulted in great influences on the energy system and energy-related carbon emissions. Choosing this period can help us understand the notable changes of carbon emissions brought by the transition of the energy system and compare the results with relevant policies to verify this method.
The contribution of this work is to provide a method for analyzing national energy-related carbon emissions and evaluating structural changes based on Sankey diagrams and apply this method to China's case study from 2005 to 2015. Although some parts of methodology referred closely to previous work of energy allocation analysis of China [6], we further introduced the method to carbon allocation analysis of China, mapped its energy-related carbon flow Sankey diagrams in 2005 and 2015 (as well as a newly updated energy flow Sankey diagram in 2015). Additionally, the TRO index was proposed to compare the Sankey diagrams. This method can help us comprehensively understand national energy-related carbon emissions and the structural changes behind energy transition.
The rest of this paper is organized as follows: Section 2 introduces the method for depicting carbon flow process, evaluating structural changes, and data input; Section 3 discusses the carbon flow Sankey diagram results, TRO index decomposition, and the uncertainty; finally, Section 4 presents the conclusions.

Methodology and Data Input
The procedure of the methodology applied in this study is divided into three steps: In the first step, we conducted energy allocation analysis to fully understand the features of China's energy system and mapped China's energy flow Sankey diagram in 2015. In the second step, based on the energy flow Sankey diagram in 2015 and a previous one in 2005 [6], we calculated carbon emissions of each section in the energy system by introducing relevant emission factors. Then we plotted China's energy-related carbon flow diagrams in 2005 and 2015 showing carbon emissions underlying the whole process of energy flow. In the last step, in order to analyze the main trend of carbon flow and determine the key structural changes quantitatively, we applied TRO index decomposition method on these two carbon flow diagrams and analyzed the results of several main sectors.

The Framework for Energy Allocation Analysis Based on Sankey Diagrams
This study divided the energy flow process into five sub-sections: energy sources, intermediate conversion, end-use conversion devices, passive system and final services. In order to keep in line with previous work for later comparison, the concept and scope of each section refer to Ma et al. [6], which is detailed described in Appendix C, Table A2.
We used the Sankey diagram tool to present the energy flow process. The diagrams were plotted on the software called "e!Sankey" [20]. The framework of the energy flow Sankey diagram is shown as Figure 1. In the diagram, the energy flows from left to right with the allocation in different departments. The vertical lines show different stages of energy flow. In the specific Sankey diagrams, the width of the arrow shows the values of energy and the colors show different energy types or uses. and determine the key structural changes quantitatively, we applied TRO index decomposition method on these two carbon flow diagrams and analyzed the results of several main sectors.

The Framework for Energy Allocation Analysis Based on Sankey Diagrams
This study divided the energy flow process into five sub-sections: energy sources, intermediate conversion, end-use conversion devices, passive system and final services. In order to keep in line with previous work for later comparison, the concept and scope of each section refer to Ma et al. [6], which is detailed described in Appendix C, Table A2.
We used the Sankey diagram tool to present the energy flow process. The diagrams were plotted on the software called "e!Sankey" [20]. The framework of the energy flow Sankey diagram is shown as Figure 1. In the diagram, the energy flows from left to right with the allocation in different departments. The vertical lines show different stages of energy flow. In the specific Sankey diagrams, the width of the arrow shows the values of energy and the colors show different energy types or uses. The core of energy allocation analysis is to allocate the energy loss in intermediate conversion stage into the energy consumption responsibility of the end-use stages. Therefore, the energy loss is not shown in energy flow process, and there are only energy allocation among different uses in the whole process from supply to service. How should we look at the energy allocation diagram? Except the clear demonstration of the energy flow process distinguished in different categories, different departments and different links, one of the advantages of the map is an effective combination of three levels of supply-conversion-demand: looking from the left side, it's the distribution of supplies (such as energy sources), from the right side, it's the allocation of demands (such as final services), while in the middle is the condition of specific technical departments (such as end-use conversion devices and passive systems). These will also be the key links to be discussed in the following text.

The Carbon Flow Sankey Diagram
As carbon allocation analysis is based on energy allocation analysis, the structure of carbon flow Sankey diagram is similar to that of energy flow Sankey diagram (see Figure 1). However, it should be noted that the real carbon emissions occur in the intermediate conversion stage where the energy is burned as direct fuel, electricity generation, heating and energy system own-use. At this stage, the carbon which cannot be oxidized in the fuel will be left, thus leading to a 'non-oxidation' flow in the diagram. In the previous stage of conversion, emissions have not occurred, so the flow shows the total carbon embodied in relevant energy. While in the subsequent stage of conversion, emissions have occurred, this part of diagram shows the carbon emission responsibility of each department because we allocate the energy loss into the end-use energy consumption responsibility, the carbon emission loss is the same. The core of energy allocation analysis is to allocate the energy loss in intermediate conversion stage into the energy consumption responsibility of the end-use stages. Therefore, the energy loss is not shown in energy flow process, and there are only energy allocation among different uses in the whole process from supply to service. How should we look at the energy allocation diagram? Except the clear demonstration of the energy flow process distinguished in different categories, different departments and different links, one of the advantages of the map is an effective combination of three levels of supply-conversion-demand: looking from the left side, it's the distribution of supplies (such as energy sources), from the right side, it's the allocation of demands (such as final services), while in the middle is the condition of specific technical departments (such as end-use conversion devices and passive systems). These will also be the key links to be discussed in the following text.

The Carbon Flow Sankey Diagram
As carbon allocation analysis is based on energy allocation analysis, the structure of carbon flow Sankey diagram is similar to that of energy flow Sankey diagram (see Figure 1). However, it should be noted that the real carbon emissions occur in the intermediate conversion stage where the energy is burned as direct fuel, electricity generation, heating and energy system own-use. At this stage, the carbon which cannot be oxidized in the fuel will be left, thus leading to a 'non-oxidation' flow in the diagram. In the previous stage of conversion, emissions have not occurred, so the flow shows the total carbon embodied in relevant energy. While in the subsequent stage of conversion, emissions have occurred, this part of diagram shows the carbon emission responsibility of each department because we allocate the energy loss into the end-use energy consumption responsibility, the carbon emission loss is the same.

Carbon Emissions Calculation
Because this study only focuses on energy-related carbon emissions, the calculation of emissions is based on the fossil fuel consumption. There are mainly three broad categories and 18 types of fossil fuel (see Table 2) considered in this paper. Equation (1) is used to calculate fuel-related carbon emissions: In this equation, the subscripts i and j denote the i-th sector and the j-th fuel, respectively, C i is the total carbon emissions of different sectors, E ij represents the different energy consumption in different sectors, NCV j refers to the net calorific value of different energy types, CCV j is the carbon content per calorific value of different fuels, O j is the carbon oxidation rate of the fuel. Due to the possible error between the actual carbon emission factors of China's coal and that recommended by Intergovernmental Panel on Climate Change (IPCC) [21], the data of NCV j , CCV j and O j used in this paper are mainly taken from China's official statistics including General Principles for Calculation of the Comprehensive Energy Consumption [22] and Guidelines for GHG Inventories [23], a few of the data not published are from the default value recommended by IPCC [24], all of them are shown in Table 2.

The Method for Evaluating Structural Changes of Sankey Diagrams-TRO index
Through our literature review, we found that the method for evaluating structural changes of the Sankey diagram itself was still limited. It is difficult to systematically and quantitatively compare two Sankey diagrams and to discern the structural changes, because there are too many complex departments with detailed data in the diagram and the changes are reflected in many aspects. In order Energies 2020, 13, 2076 6 of 24 to solve this problem, we proposed TRO index to evaluate the structural changes, defining the structural change from three dimensions: total amount change, relative growth rate and occupation ratio change. In this study, specifically, the method was applied to compare carbon flow Sankey diagrams.
The meaning of TRO index is to help us quickly identify structural changes in complex carbon flow Sankey diagrams, including both obvious total amount changes and relative growth rate that is not easy to visualize. TRO is not only a mathematical indicator, but also has actual physical meaning, e.g., the total amount change reveals change in the industrial production capacity, the relative growth rate reveals potential development trends, and the occupation ratio change reflects the results of structural transition. These three indicators are complementary to each other for comprehensively revealing the structural changes. The meaning and calculation method of each index is explained in detail in the following text.

Total Amount Change (T)
Total amount change T refers to the change of the total carbon emissions in a relevant section in the Sankey diagrams between different years. To a certain degree, total amount change reflects the change in the size of the industry's production capacity. The sectors with larger total amount change should be paid more attention for emission reduction, because improving the same energy efficiency or reducing the same carbon intensity in these sectors may lead to more emission reduction. The formula of the total amount change of sector i is as Equation (2): where C ti is the total carbon emissions of sector i in the base year t, C Ti is the total carbon emissions of sector i in the observed year T.

Relative Growth Rate (R)
Relative growth rate R refers to the ratio of the carbon emission change of a relevant section in the Sankey diagrams during the observed period to the carbon emission in base year. It can make up for the shortcomings when T index is used for the industry that used to be small and unconcerned but has rapid development in recent years thus leading to high emission growth rate. R index also reflects the orientation of relevant policies and changes of market demand to some extent. These parts are also the ones that should be paid special attention to, because they are likely to become the main driving force for the growth of carbon emissions in the future. Identifying this indicator can help policy makers adjust the energy structure of relevant industries at an early stage, so as to control carbon emissions more effectively. The formula for calculating the relative growth rate of carbon emissions of sector i is as shown in Equation (3):

Occupation Ratio Change (O)
Occupation ratio change O refers to the change of the proportion of a relevant sector in the corresponding stage of the Sankey diagrams during observed period. It reflects the actual changes of carbon flow structure that influenced by energy structure transition. The formula for calculating the occupation ratio change of sector i is seen in Equation (4): In this equation, P ti is the ratio of carbon emissions of sector i to the total emissions in the corresponding link in the base year t, P Ti is that in the observed year T.

Data Input
China's energy data for 2015 are obtained and calculated from China's official statistics sources such as China Energy Statistical Yearbook 2016 [25], The 11th Five-Year Plan for Energy Development [14], The 12th Five-Year Plan for Energy Development [18], and a series of reports such as Energy Data of China 2016 [26], and Survey Analysis of Lighting Power Consumption in China [27]. The China's energy data in 2005 are from Ma et al. [6]. The carbon emission factors are calculated from General Principles for Calculation of the Comprehensive Energy Consumption [22], China Guidelines [23] and IPCC Guidelines [24]. Some other data are from authors' calculation. Detailed data sources and processing are shown in Appendix D, and some key data in the processing are listed in Tables A3-A9.

China's Energy Flow and Energy-Related Carbon Flow Sankey Diagrams
Based on energy allocation analysis method, we first plotted a Sankey diagram of China's energy flow in 2015, as shown in Figure 2, which is a latest Sankey diagram that reflects energy flow process in China's energy system. In the diagram, the energy flow is traced from left to right, and allocated to five stages: energy sources, intermediate conversion, end-use conversion devices, passive systems and final services. The detailed description of each stage can be seen in Table A2 The framework of carbon flow Sankey diagrams is consistent with that of the energy flow Sankey diagrams. The only difference is that the energy-related carbon flow diagram shows the flow of carbon but not energy. In this work, we assumed that energy-related carbon emissions only come from three broad categories and eighteen types as listed in Table 2. Therefore, in the stage of energy sources and intermediate conversion, there are only oil, coal and gas in the diagram. The colors of the various arrows indicate carbon emissions coming from different energy types and consumed by different departments, as shown in the legend on the right of the diagram. The thickness of each arrow represents the scale of carbon flow, with numbers giving the values. The whole carbon flow obeys the law of carbon conservation. The carbon values are reported in 10 Million tons (10 7 tons).
The main advantage of the carbon flow Sankey diagram is that it shows the carbon emission responsibility of each sector in each stage of the energy system because energy losses are allocated into consumption sectors but not presented separately. The arrows in energy sources stage show the total amount of carbon entering the system. The arrows in energy conversion stage show actual carbon emissions. In the conversion stage, the carbon in fuels is oxidized and released, while the non-oxidized parts flow to 'non-oxidation'. The arrows in passive systems and final services reflect the carbon emissions embodied in users' consumption and demand. According to Figures 2-4, the general situation of China's energy system and energy-related carbon emissions can be seen as follows: (

The Structural Changes of Carbon Flow Sankey Diagrams
After getting the full picture of carbon emissions allocation, to evaluate the structural changes more comprehensively, we conducted TRO index decomposition of each section in the diagram to compare the situation of energy-related carbon emissions. The results of the TRO index decomposition of several important sections including energy sources, three passive systems (vehicle, building and factory), and final services are shown as Table 3 and Figure 5. In the following text, the results of each section are discussed one by one and are compared with relative policies, other statistics, and other studies to verify the method.         In energy sources (Figure 5a), results show that the most significant structural changes were from coal. During 2005-2015, although the coal was still the largest contributor to energy-related carbon emissions with largest increment (total amount increased by 3076Mt), its proportion conversely decreased a lot (occupation ratio decreased by 1.2%). Compared with China's policy objectives [18], it can be seen that the effect of coal reduction work in China during this period was quite successful. The proportion of coal in China's energy structure decreased by 6.4% in this period. For one reason, it was related to the national efforts to increase the proportion of natural gas and non-fossil energy consumption [15]. For another reason, it was also closely related to the industrial upgrading and technological progress of the coal industry itself [28].
In contrast, natural gas has become an important energy source for replacing coal in the transition of China's energy structure leading to a rapid growth rate of carbon emissions by 205%, which was closely related to China's strong investment in natural gas infrastructure construction and deep international cooperation. Facts show that in 2009, China cooperated with Russia and Central Asian countries to build the first natural gas pipeline for the introduction of long-distance natural gas delivery from Central Asia; in 2013, China-Myanmar natural gas pipeline was established in cooperation with Myanmar, which became the second onshore natural gas pipeline; in the meantime, the liquefied natural gas (LNG) business was also booming, and the countries China imported LNG from had expanded from Australia, Indonesia and Malaysia to Qatar and Brunei [29]. Renewable energy represented by wind and solar power also developed rapidly in China during this period. For example, the wind power became the energy source with fastest relative growth rate (by 55.7 times) in the decade and contributed a lot of increase of the proportion in energy structure (increased by 1.1 %). The rise of natural gas and renewable energy had slowed the growth of energy-related carbon emissions to some degree.

The Vehicle Passive System Level
In the vehicle passive system (Figure 5b), results show that the largest driving force was the passenger car, which not only had the largest increase in total amount change (231Mt CO 2 ) but also remained a high relative growth rate (158%), making its occupation ratio increased by 9.5% in vehicle passive system and exceed trucks as the largest emission source. While trucks and ships represented a significant decline in the occupation ratio of the emissions structure (trucks reduced by 8.1%, ships reduced by 5.2%). Compared with other statistics, the results kept in line with the fact that China's highway infrastructure had been gradually improved in the past decade (in 2015, the total length of China's highways reached 4.57 Million km, the total length of freeways reached 123,500 km, the proportion of towns with roads reached 99.99% [30]), and the number of civilian vehicles increased rapidly (reached 163 million in 2015, which was ten times more than that in 2005 [26]). In this period, new energy vehicles such as electric vehicles had not been promoted, so the increment of private cars were mainly gasoline-powered cars, which significantly increased the carbon emissions of passenger cars. The transition of the economic structure was another proof. In 2015, the proportion of increased GDP in the tertiary industry exceeded 50% for the first time [31]. As in this period, the tertiary industry had less demand for physical goods compared with the primary and secondary industry, the overall freight demand and the growth rate of the road freight industry slowed down in 2015. Thus the energy consumption growth of trucks and ships slowed down, and carbon emissions did not increase significantly.

The Building Passive System Level
In the building passive system (Figure 5c), in terms of the energy consumption, the most significant increase came from hot water systems (relative energy consumption growth rate by 157%, energy consumption proportion increased by 4.9%), but as for carbon emissions, household appliance was Energies 2020, 13, 2076 14 of 24 noteworthy. Although appliances energy consumption growth rate was only 19%, the relative growth rate of carbon emissions was as high as 158%, and its occupation ratio in the emissions structure increased the most by 4.1%. This result shows the role of R index to reveal potential trends. To explain this, we further calculated the carbon emissions per unit energy consumption (CPE) of these two sectors and found the difference. In this period, the CPE of the hot water system decreased by 31.4%, but that of the household appliance increased by 116.8%. This finding was consistent with another statistics [26], which shows that in the process of replacing traditional home appliances, a large part of the original biofuel appliances were replaced (such as electric cookers, gas stoves replaced firewood stoves, biofuel direct use decreased by 29.7% from 2010 to 2015 [26]), which made carbon emissions of appliances increase significantly although the total energy consumption did not change so much, for biomass was assumed to be carbon neutral. As a policy implication, it could be solved by adjusting the power source structure and introducing more non-fossil energy or biomass power.
The heated/cooled space system contributed the largest increase in total amount change (242 Mt CO 2 ), but considering its large emission base, the relative growth rate is just 42%, which is the smallest in the building system, its occupation ratio also decreased by 4.7%. This was mainly due to the gradual improvement of the infrastructure of municipal heat pipe networks. Centralized heat-supply and gas heat-supply replaced traditional heating methods and improved heating efficiency. The changes were also related to the improvement of energy efficiency of household devices such as heaters. Wang et al. [32] also agreed that China's domestic heating reformation could play a crucial role in achieving energy saving and emission reduction goals. At the spiritual level, this trend reflected a significant improvement of the residents' living standards, the constantly increasing demand for life quality.

The Factory Passive System Level
In the factory passive system (Figure 5d), the steel mining industry was still the sector with the largest carbon emissions and increment (CO 2 emissions increased by 851 Mt). This was related to the over-capacity inertia of the steel industry in China, and it was difficult to achieve de-capacity in short term which was also pointed out by Zhou and Yang [33]. Results also show that the non-ferrous metal mining industry and chemical industry had become new driving forces of carbon emission growth (the relative growth rate of non-ferrous metal industry reached 171%, accounting for an increase of 2.9% in the emission structure, and the chemical industry's emission growth rate reached 1.01, accounting for an increase of 2.0% in the emission structure). The improvement of macroeconomics, industrialization and urbanization had brought huge demand for non-ferrous metal materials and chemical raw materials, and also provided a good economic environment for relevant manufacturing. The significant profit growth of chemical industry (in 2015, its profit increased by 7.7%, which is the largest increase in all industrial sectors of China [34]) brought great opportunities for the development of chemical-related enterprises.
Compared with previous work in this field, Li et al. [11] conclude that in 2013 the 'electricity and heating' emitted the most in the secondary industry (factory), following by 'metals' (including ferrous and non-ferrous), while chemical industry just accounted for nearly 3.1%. This differs from our results, as the division of stages of carbon flow diagram in their work only included energy sources and end use sectors, and the 'electricity and heating' was regarded in a parallel relation with other industrial sectors. But in fact, most of electricity and heating served as secondary energy supply and were consumed by steel, non-ferrous metal and chemical industries. When we discuss carbon emissions responsibility, it is inappropriate to allocate all of these emissions to the electricity generation sector. Concerning this, in another work, Li et al. [35] allocated the emission responsibility of electricity generation to end use sectors and kept in line with our result that the ferrous (steel) industry took the largest CO 2 emissions responsibility, but the main difference was that the non-ferrous metal industry only accounted for 3% of end use sectors responsibility in their study. This was because in their carbon flow Sankey diagram, a large amount of emissions caused by energy loss in the conversion stage such as electricity and heat generation were regarded as conversion loss and not allocated to end use responsibility. However, the Energies 2020, 13, 2076 15 of 24 fact is that the non-ferrous industry consumed a lot more electricity and heat but less direct fuels than other industries [25]. Since the emissions responsibility of electricity generation had been allocated to end use sectors, the loss of this stage should also be considered. This just illustrates the importance of energy allocation analysis method in carbon emissions analysis.
We also found that the industry whose growth of carbon emissions slowed significantly was the non-metallic mineral mining manufacturing industry. Although it had large emissions (517 Mt CO 2 in 2005), the relative growth rate was only 60%, and the occupation ratio of emissions shrunk by 2.0%. This partly differs from previous work [11] concluding that the non-metallic mineral would continue to increase rapidly. Actually, during the "12th Five-Year Plan" period when China had strengthened the management and rectification of non-metallic mineral mines, standardized the mining order, and shut down nearly 10,000 nonstandard enterprises [36]. The result illustrates the effectiveness of comprehensively considering TRO index to analyze the changing trend.

The Final Services Level
In final services (which is also the demand side, as shown in Figure 5e), results show the strongest driving force of carbon emissions was the demand for structural materials (CO 2 emissions increased by 2218Mt, the occupation ratio of emissions increased by 3.9%) and passenger service (the relative growth rate was as high as 166%, the occupation ratio increased by 2.1%). The increase of demand for structural materials was closely related to the rapid urbanization process and the rapid development of the infrastructure construction industry in China in the past decade. Compared with national economic statistics [37], during 2006-2011, the total output value of the construction industry maintained a super-high-speed growth of more than 20% for six consecutive years as the pillar industry of economic growth, which caused large demand for structural materials.
In contrast, the occupation ratio of thermal comfort and sustenance demands in emission responsibility significantly reduced (thermal comfort reduced by 2.3% and sustenance reduced by 2.2%). The slowdown in emissions growth of thermal comfort was mainly related to the improvement of energy efficiency of heated/cooled system in building passive systems, which had been explained in Section 3.2.3. The slowdown in emissions growth of sustenance was related to the reduction of proportion of the primary industry such as agriculture [26]. This also reflected the rising of people's life pursuit from sustenance to high-quality life.

Overall Trends
After comprehensively considering above analysis of each section, if we review the carbon flow Sankey diagrams combing demand side and supply side, we can discern the overall trends and interpret the inherent dilemma and of China's energy low-carbon transition during 2005-2015. In this period, China was still in the stage of rapid industrialization and urbanization investing huge amounts of infrastructure construction and fixed assets (China invested CNY 4 trillion in infrastructure construction during 2008-2010 [38]), which kept the demand for structural materials huge and growing. This made the industry represented by steel, chemical and non-ferrous metal maintain booming, some even over-capacity. These energy-intensive industries relied on coal and electricity, which brought difficulty for the energy system to cut coal consumption and to decarbonize. Meanwhile, the structure of energy final services did have changed. An obvious trend was that people's demand for high-quality life kept increasing, for example, the demand for passenger transportation, hygiene and communication services grew rapidly. Accordingly, the energy consumption and carbon emissions underlying the cars, planes, hot water supply and modern appliances increased rapidly, which could be new driving forces for energy-related carbon emissions. Discerning the trends may help policy makers to formulate more effective emission reduction strategies.

Uncertainties
Although authors have tried to make the method and data more accurate, uncertainties still exist in two aspects. One is the uncertainty of energy consumption data. When mapping the energy flow Sankey diagram, due to the lack of local data, the proportion of energy consumption in some sectors of factory passive systems and building passive systems referred to the average level of global-level research (see Appendix D.3.). Due to the outdated statistical data of the electric motors and light devices, we extrapolated relevant historical energy consumption data. Non-commercial energy consumption (although mainly are biomass including straw and wood which adopt carbon neutrality assumptions) related to CO 2 emissions was not audited in this study due to a lack of official statistical data.
The other one is the uncertainty of carbon emission data. Although most of the emission factors used in this paper were from China's local official statistics, there were still some data not provided referring the default values recommended by the IPCC [24], which lacked aboriginality to some extent. Carbon capture and storage technology were not discussed in this study as well.

Conclusions
This study proposed a method for systematically analyzing energy-related carbon emissions and quantitatively evaluating internal structural changes from the perspective of energy system. The method includes visualizing carbon flow process and emission responsibility allocation based on Sankey diagrams and energy allocation analysis and analyzing structural changes of carbon emissions based on TRO index decomposition which was put forward for the first time in our work. Then, this method was applied to China's case. We mapped China's energy-related carbon flow Sankey diagrams in 2005 and 2015 from energy sources, end-use conversion devices, passive systems to final services, then used TRO index decomposition to compare these two diagrams and reveal internal structural changes of carbon emissions caused by energy transition, finally discussed the trend and relevant reasons.
The results indicate that China's huge investment on infrastructure construction during 2005-2015 expanded the demand for structural materials on the consumption side, which made some high energy-intensive industries such as steel, chemical and non-ferrous metal maintain their booming status or even led to over-capacity, thus making it difficult for the energy system to cut coal consumption and decarbonize, while a new trend was that people's demand for high-quality of life kept increasing, and the demand for passenger transportation, hygiene and communication services grew rapidly. Accordingly, the energy consumption and carbon emissions underlying the cars, planes, hot water supply and modern appliances increased rapidly, which needed attention as new driving forces for energy-related carbon emissions. The results also provide a new perspective to analyze structural changes of energy-related carbon emissions from the terminal demand side. Compared with other statistics and studies, the method proved to be effective for analyzing energy-related carbon flow and evaluating structural changes.
However, there is still some uncertainty in processing of the energy data and emission factors. The limitation also lies in that the carbon emissions of energy loss in conversion stage were not considered separately in the analysis. In future work, the accuracy of the relevant data will be further improved, the impact of energy efficiency will be shown separately in carbon flow diagrams, and this method will be applied to more regions. Funding: This research received no external funding.

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

Appendix A
Historical data of China's primary energy consumption and energy-related CO 2 emissions in 1965-2018 from British Petroleum (BP) statistics [13].

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

Appendix A
Historical data of China's primary energy consumption and energy-related CO2 emissions in 1965-2018 from British Petroleum (BP) statistics [13].

Policy
Issue date The 11th Five-Year Plan for Energy Development [14] 2007 The Mid-Long Term Plan for Renewable Energy Development [15] 2007 The 11th Five-Year Plan for Renewable Energy Development [16] 2011 Renewable Energy Law of the People's Republic of China [17] 2012 The 12th Five-Year Plan for Energy Development [18] 2013 Enhanced Actions on Climate Change: China's Intended Nationally Determined Contributions [19] 2015

Appendix C
In the energy Sankey diagram of this study, the energy sources reflect the sources (including indigenous production, import, export, and stock change) of various primary energy (including oil, coal, gas, biomass, and other) that input into the energy system. The intermediate conversion reflects different forms of utilization of primary energy, e.g. directly used as fuels for engines and burners, used for power generation and heat generation, used by energy industrials themselves, and transformed to other industrial materials. The end-use conversion devices are devices where the primary energy is converted into useful energy such as motion, heat, cooling etc. The passive systems are places where useful energy output by end-use conversion devices is lost as low-grade heat in exchange for final services, such as vehicle, factory and building. The final services are the goods and services provided by useful energy in passive systems, such as transport services, production services and living services. The detailed classification and description of each part in the Sankey diagram is listed in Table A2.

Policy Issue Date
The 11th Five-Year Plan for Energy Development [14] 2007 The Mid-Long Term Plan for Renewable Energy Development [15] 2007 The 11th Five-Year Plan for Renewable Energy Development [16] 2011 Renewable Energy Law of the People's Republic of China [17] 2012 The 12th Five-Year Plan for Energy Development [18] 2013 Enhanced Actions on Climate Change: China's Intended Nationally Determined Contributions [19] 2015

Appendix C
In the energy Sankey diagram of this study, the energy sources reflect the sources (including indigenous production, import, export, and stock change) of various primary energy (including oil, coal, gas, biomass, and other) that input into the energy system. The intermediate conversion reflects different forms of utilization of primary energy, e.g., directly used as fuels for engines and burners, used for power generation and heat generation, used by energy industrials themselves, and transformed to other industrial materials. The end-use conversion devices are devices where the primary energy is converted into useful energy such as motion, heat, cooling etc. The passive systems are places where useful energy output by end-use conversion devices is lost as low-grade heat in exchange for final services, such as vehicle, factory and building. The final services are the goods and services provided by useful energy in passive systems, such as transport services, production services and living services. The detailed classification and description of each part in the Sankey diagram is listed in Table A2.  In passive systems, the energy flows from engines (including diesel engines, gasoline engines, aircraft engines, and other engines) are input into the vehicle passive system. All of electric motors, and most of electric heater and electronic devices are input into the factory passive system. The rest of electric devices are allocated to the building passive system.
The flows of different vehicles are based on previous flows of engines and the proportion are estimated based on the energy consumption data of transportation [26], as shown in Table A3 (e.g., the diesel engines are used not only by trucks, but also by trains, ships, agro-vehicles and motors in factories).  Diesel  -59%  4%  -15%  9%  13%  Gasoline  100%  ------Aircraft  ---100%  ---Other  48%  -52% ---- The proportion of heat flows into the factory and the building [25] is shown in Table A4. Due to lack of indigenous data, after getting the total input data, the fuel directly used in the factory is estimated based on the proportion of fuel used in U.S. industry [39] as shown in Table A5. And the energy allocation of fuel and heat used in the building is estimated by the shares of household energy use on global average [40] as shown in Table A6.

Appendix D.4 Data for Final Services
The energy flows from vehicles to transportation services are estimated from transportation statistics [26]. In this study, road transportation has been allocated (cars for passenger, trucks for freight), but shares of passenger and freight transport in other transportation (e.g., train, ship, plane) are estimated according to their utilization as shown in Table A7. The energy flows from buildings to final services is estimated based on the global average data of household fuel use [40] and the data of electricity consumption by home appliances in China [26], as shown in Table A8. It is difficult to allocate energy flows from the factory passive system into various final services, because there are too many sub-sectors in the system serving for different final services. To simply the calculation, firstly, we divided the industrial sectors in the sheet of 2015 Final Energy Consumption by Industrial Sector (Standard Quantity) [25] into 11 groups as shown in Table A2 (factory). Then, the allocation of energy flows into relevant final services is estimated based on these subdivided departments. For instance, the steel, mineral, non-ferrous metals and construction are allocated into structure. The energy used for producing transport equipment is reckoned to be divided equally between the passenger and the freight. Some items in the machinery and other industrials whose usage can not be easily sorted (e.g., manufacture of general equipment, recycling of the waste) are assumed to be equally allocated among the various final services. Food and agriculture are allocated to sustenance. Textile flows to thermal comfort. Paper is allocated to communication.