*3.1. 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 colors of the various arrows indicate different energy types and different departments, as shown in the legend on the right of the diagram. The thickness of each arrow represents the scale of energy flow, with numbers on it giving the values. The whole energy flow obeys the energy conservation law. Energy losses are not shown in the map but remain included in the energy flow to illustrate the energy allocation through all stages. The energy values are shown in EJ (10<sup>18</sup> J).

Based on the Figure 2 and a previous energy flow diagram of China in 2005 [6], by introducing carbon emission factors, we further mapped China's energy-related carbon flow Sankey diagrams in 2005 and 2015, as shown in Figures 3 and 4.

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 (107 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:

