## 2 Materials and Methods
### Estimation of Multi-Scale Emissions from Building Operations
#### 2.3.1 Calculation of BCEs at the Prefecture Level  
In the operation stage, carbon emissions from energy consumption are mainly caused by living, commercial, and office activities. In this paper, we used the IPCC method to calculate building operation emissions at the provincial and prefecture levels using the BTH's provincial energy consumption statistical data and the NCRJ's prefecture-level energy consumption data.  
\[CE=\sum_{i=1}EC_{i}\times NCV_{i}\times CC_{i}\times COF_{i}\times 44/12 \tag{1}\]  
where \(CE\) refers to CO\({}_{2}\) emissions caused by energy consumption; and \(EC_{i}\), \(NCV_{i}\), \(CC_{i}\), and \(COF_{i}\) are the energy consumption, net calorific value, carbon content, and carbon oxide  
Figure 1: Location and administrative division of the Beijing–Tianjin–Hebei urban agglomeration and the National Capital Region of Japan.  
rate of \(i\) type of energy. The energy consumption at the provincial level and the factors above of the BTH referred to China's Energy Statistical Yearbook ([[https://data.cnki.net/](https://data.cnki.net/)]([https://data.cnki.net/](https://data.cnki.net/))) (accessed on 12 November 2022) We referenced the Agency for Natural Resources and Energy ([[https://www.enecho.meti.go.jp/](https://www.enecho.meti.go.jp/)]([https://www.enecho.meti.go.jp/](https://www.enecho.meti.go.jp/))) (accessed on 12 November 2022) and Ministry of the Environment ([[https://www.env.go.jp/en/](https://www.env.go.jp/en/)]([https://www.env.go.jp/en/](https://www.env.go.jp/en/))) (accessed on 12 November 2022) for the NCRJ's energy consumption at the provincial level and the factors shown above.  
Considering the available data and estimation scales, the calculation of building operation emissions (BCEs) in this study relied on dividing building operations' energy consumption from different sectors.  
\[BCE_{1}=BCE_{c}+BCE_{r}+BCE_{o}+BCE_{t} \tag{2}\]  
\(BCE_{1}\) is one part of BCEs, including emissions from the commercial and retail sector (\(BCE_{c}\)), residential sector (\(BCE_{r}\)), other sectors (\(BCE_{o}\)), and transport sector (\(BCE_{t}\)). Because energy balance sheets in the BTH and NCRJ record various levels of energy consumption by activity sectors, the energy consumption in commercial, residential, and other sectors also includes energy related to transport; the energy related to transport in the above sectors is removed to a certain extent. The specific proportion was referred to in previous studies [21; 41]. For instance, 95% of gasoline consumption and 35% of diesel consumption in the commercial and retail sectors were removed, 95% of gasoline consumption and 35% of diesel consumption in other sectors were removed, and 95% of gasoline consumption and all diesel consumption in the residential sector were removed from the calculation. Since the transport stations and storage are public buildings and need energy to maintain operations, coal and 40% of electricity consumption were used to calculate the BCEs in transport stations, storage, and post-sector.  
\[BCE_{2}=BCE_{cheating}-\left(BCE_{c}^{heating}+BCE_{r}^{heating}+BCE_{o}^{heating}\right) \tag{3}\]  
Figure 2: The research framework for this study.  
\(BCE_{2}\) are the emissions caused by heating. To avoid double counting, the heat used by sectors in the energy balance sheet was removed, and heating emissions were calculated based on central heating supply statistics (\(BCE_{heating}\)). Since the central heating supply is concentrated in Northern China, Equation (3) applies to the BTH calculation. The emissions from heating in the NCRJ were calculated by the consumption levels of sectors using Equation (2).  
\[BCE=BCE_{1}+BCE_{2} \tag{4}\]  
\(BCE\) represents the total emissions from building operations of the region.  
The prefecture-level statistics of sectors' energy consumption in Hebei Province are limited. Therefore, the top-down decomposition method was adopted to obtain BCEs at the prefecture level in Hebei Province. The corresponding decomposition indicators are shown in Table A1 Appendix A.