**2. 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.
