## 4 Discussion
### Evaluation of Method for Estimating BCEs  
This study explored the effectiveness of multi-dimensional remote sensing data in estimating emissions from building operations in the BTH and NCRJ. Multi-scale BCEs showed high consistency with existing databases in terms of the scale trend. However, similar trends do not mean fewer differences in specific emission scales. Figure A4 shows the differences between estimation results and statistical results of public and residential BCEs in the BTH and NCRJ. It can be found that the estimation results of the high-emission prefectures are similar to the statistical results, but there is an overestimation of the prefectures with emissions below 10 million tons (Figure A10a-c). However, differences between the estimated residential BCEs and statistical residential BCEs in the NCRJ are significantly smaller (Figure A10d), which is consistent with the small RMSE in Figure A3b. Although there are differences in the emission scale between estimation results and statistical results, the results after correction using statistical results are practicable because of a similar trend between them.  
Although existing studies have confirmed the effectiveness of nighttime light data in estimating greenhouse gas emissions at different scales [64; 72; 73], the MLR model's accuracy was improved by adding other factors. Moreover, factors related to sector activities should be considered when estimating sectors' CO2 emissions based on nighttime light data [26]. However, the effect of vegetation index on BCEs was not significant as expected. On the one hand, the results indicate the effect of EVI on BCEs is different among regions. On the other hand, the limited samples could not explain the appropriate relationship between vegetation and BCEs. For the improvement approaches, existingstudies made regressions by groups which were divided by climate zones, natural conditions, and economic conditions [22; 61]. Moreover, the data of vegetation dynamics could be considered using alternative dataset, such as gross primary production (GPP) and net primary production (NPP). GPP and NPP are defined as the energy captured per unit area per unit time through the process of vegetation photosynthesis and the energy after subtracting plant respiratory costs from GPP, respectively [74]. Both of them are important parameters for carbon cycle since the consideration of the production of biomass or carbon in ecosystem [75; 76; 74] and existing studies have explored the performances of vegetation indices in estimating GPP and NPP [77; 78; 79]. In addition, previous studies also combined the NPP and economic factors to calculate carbon footprint pressure and analyze the driving factors of carbon intensity [80; 81; 82]. From the direct relationship with vegetation cover, GPP and NPP are alternative to be used to analyze the influencing factors of BCEs.  
Given the limitation of seasonal statistical data on the energy consumption of buildings, the estimations of BCEs at a multi-scale in this study are calculated by year. However, emissions from central heating account for a high proportion of prefecture-level BCEs in the BTH, indicating the high demand of energy in summer and winter (Figure 11). In addition, the differences in proportion between prefectures revealed the different patterns of heating supply between areas with large-scale urban populations and areas with large-scale rural populations. Therefore, analysis by seasons and urban-rural regions is essential for collecting finer statistical data and remote sensing data.