*3.3. 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 Due to the outdated statistical data of the electric motors and light devices, we extrapolated relevant historical energy consumption data.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 CO2 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.

## **4. 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.

**Author Contributions:** H.Y. coordinated the main theme of this paper and wrote this manuscript. L.M. provided methodological guidance. L.M. and Z.L. discussed the research results and reviewed the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** This work was supported by Tsinghua-BP Clean Energy Research and Education Centre. The authors also gratefully acknowledge support from Institute of Climate Change and Sustainable Development as well as Tsinghua-Rio Tinto Joint Research Centre for Resources, Energy and Sustainable Development. Finally, Honghua Yang wants to thank, in particular, the invaluable support from Yiwei Dai over the years.

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