The estimation of carbon imbalance and driving factors in China's urban residential building sector

Understanding the imbalance of carbon emissions in the urban residential building (URB) sector is beneficial for equitable and effective emission reduction policies. However, carbon imbalance in URB and its major driving factors remain unclear. Therefore, according to the Kaya identity and Zenga index, this study aims to analyze the imbalance in carbon emissions and carbon emission unit area of URB from 2005 to 2019. The results represent the following: 1) Although the overall carbon emission unit area reached its peak value (36.17 kgCO 2 /m 2 ) in 2011, the overall carbon emission of URB did not reach the peak value, arriving at 0.86 BtCO 2 in 2019; 2) the obvious imbalance of carbon emission and carbon emission unit area was led by the population and energy consumption unit area, respectively; 3) Compared to the difference in economy, the difference in climate had a larger impact on inter-group imbalance of carbon emission unit area without heating. In summary, these results and provided policies facilitate future formulation of fair and effective provincial decarbonization responsibility and emission mitigation implementation policies.


Introduction
To mitigate global climate change, China has declared its climate targets: carbon peak by 2030 and carbon neutrality by 2060 (You et al., 2023a). Chinese building sector was regarded as a key point in achieving the Chinese dual carbon target (Wang et al., 2022) since it was responsible for nearly one-quarter of Chinese energy-related CO 2 emissions. And urban residential buildings (URB) accounted for the largest share (47.6% in 2018) (CABEE, 2021). However, the per capita residential energy consumption still be in a low level, only was 72% of Japan, 21% of the US, and 23% of the UK (IEA, 2021). Along with the increasing residents' income, the residents' energy demand will face a rigid growth trend (Ma et al., 2020), which severely hinders the achievement of the Chinese dual carbon Abbreviations: URB, Urban residential buildings; C, Carbon emission; E, Energy consumption; A, Building floor area; P, Population; CI, Carbon emission unit area; EI, Energy consumption unit area; EF, Energy-related emission factor; AS, Per capita floor area; D, Heating period days; INT, Interaction term; NP, North province; TP, Transitional province; SP, South province; HP, High-income provinces; MP, Mid-income province; LP, Low-income province; overall, Carbon emission or energy consumption of Overall part; no-heating, Carbon emission or energy consumption except central heating; heating, Carbon emission or energy consumption of Central heating part; adj-heating, Adjusted carbon emission or energy consumption of Central heating part.

target.
At the national level, Action Plan of Carbon Peak in China's Urban and Rural construction (MOHURD, 2022a) and Building energy conservation and green building development Plan in the 14th Five-Year (MOHURD, 2022b) have been formulated to accelerate the decarbonization process of Chinese URB (Ma et al., 2022). However, there is an obvious difference in the energy utilization and energy structure of URB in different provinces (Li et al., 2021). The "One-size-fits-all" emission mitigation approach may cause huge press on the provinces with severe climate and economic conditions, which have grid energy needs and demand growth (Li et al., 2023b;Yan et al., 2022). For example, the heating demand in China's severe cold and cold area made their mean carbon emission unit area (CI) (50.01 kgCO 2 /m 2 ) approximately four times of other provinces (10.86 kgCO 2 /m 2 ) (CABEE, 2021). And the developed economic provinces (i.e. 49.59kgCO 2 /m 2 in Hebei) have lower end-user energy demand than developed provinces (i.e. 59.27kgCO 2 /m 2 in Beijing). Therefore, understanding the imbalance and driving factor of provincial URB carbon emission is a prerequisite for formulating effective and equitable decarbonization responsibility and strategies at the provincial level (Wang et al., 2020;Yan et al., 2022). Thus, this study mainly addresses the following questions: • What represents the total imbalance of carbon emissions of Chinese URB over the last few years?
• What are the main driving factors for the imbalance of carbon emissions of Chinese URB?
To answer these questions, this study assesses the imbalance of carbon emission (C) and emission unit area (CI) in Chinese URB from 2005 to 2019. By combining the Zenga index and Kaya identity (Wang et al., 2020), this study measured the imbalance of C and CI of URB, and it decomposed the imbalance into the contribution of several multiplied driving factors. Additionally, considering the obvious impact of economy and climate on CI of URB, we divided all provinces into three economy groups and three climate groups and explored the inter-group and intra-group imbalance of CI.
The significant contributions of this paper are:1) Analyze the imbalance of C and CI in URB, which concludes the parts of overall emissions (C overall ), heating emissions (C heating ), and emissions without heating (C no_heating ). Exited studies have evaluated the imbalance of carbon emissions in industrial sectors, and few focus on the imbalance of carbon emission in URB (Cheng et al., 2021;Li et al., 2021;Wang and Feng, 2021). Wang and Feng (2021) adopted the Theil index to analyze the imbalance of carbon emission on URB, they focused on the per-capita carbon emission rather than the carbon emission unit area, and ignored carbon emissions of central heating.
2) Assesses the impact of climate on the imbalance of C and CI of URB. The climatic condition has an obvious impact on the energy consumption of URB and has been integrated into formulating building energy efficiency standards and policies (You et al., 2023b). However, exited studies have not evaluated the impact of climate conditions on emission imbalances, and mainly focused on socialeconomic parameters causing the imbalance of carbon emission (Cheng et al., 2021;Li et al., 2021;Wang and Feng, 2021). By adopting heating periods to amend C heating and CI heating , this study developed an extended Kaya identity of the emission on central heating to explore the imbalance between C heating and CI heating . This study also explored the inter-group and intra-group imbalance of CI no_heating between climate zone groups.
The structure of this paper is as follows: Section 2 reviewed relevant literature. Section 3 introduces the data and research methods, including the computing processes of the Kaya identity and Zenga index. Thereafter, the data sources were introduced. Sections 4 present the results and discussion at the national and group levels, and put some policy implications. The main conclusions and future research directions are presented in Section 5.

Research on quantifying the carbon emission of URB
Accurate data foundation is a prerequisite for estimating the imbalance of carbon emission in provincial URB. There are two methods of accounting data: bottom-up and up-bottom methods (You et al., 2023b). The bottom-up method collects the energy intensity of representative buildings and multiplies it by building floor area to obtain national building energy consumption (Swan and Ugursal, 2009). Surveys and engineering simulations are the main methods for collecting building energy intensity (Huo et al., 2018). A residential energy consumption survey requires to collect nationally representative samples. The USA. (EIA, 2020), European Union (Eurostat, 2022) and other developing countries have established residential energy consumption surveys covering energy characteristics in the housing unit, usage patterns, and household demographics. Engineering simulation relies on input data (i.e. climate, dwelling characteristics, appliance and system characteristics, and occupant behavior) (Swan and Ugursal, 2009), and adopted equations describing the physical behavior of systems to calculate the building energy intensity (ASHRAE, 2009). The bottom-up method facilitates to obtain energy consumption in end-user services and analyze the difference in carbon emissions and energy consumption of different regions (Huo et al., 2018;Swan and Ugursal, 2009). But it usually needs some hypothesis and large-scale survey. There is little authoritative open data for reference in China (Wang et al., 2023). By contrast, up-bottom methods mainly adopt splitting energy balance sheets to establish time series of URB energy consumption and carbon emission (Huo et al., 2018), which is official and authoritative, such as the International Energy Agency (IEA, 2021), Energy Information Agency (EIA, 2020), China's Yearbook (NBS, 2020), andEurostat (Eurostat, 2022). In China, Wang and Feng (2021) established the time series of URB during the period of 2005-2017, but not deduct other household energy consumption such as household transportation. Li et al. (2021) solved this problem by deducting part of the oil consumption from the energy balance sheet but ignored the central heating consumption since central heating consumption belongs to the heating sector, not the residential sector. You et al. (2021) combined data derived from the Chinese Urban Yearbook with the regional energy balance sheet to calculate the carbon emissions of central heating.
In summary, based on existing studies, this study established an energy consumption and carbon emission database of URB including overall URB emissions (C overall ), heating emissions (C heating ), and emissions without heating (C no_heating ).

Research on the imbalance of carbon emission
Existing studies have adopted different methods to estimate the imbalance of regional carbon emission and analyze its driving factors (Ahn and Uejio, 2022;You et al., 2023b). The three common method categories include spatial econometric analysis, convergence analysis, and imbalance index (Wang et al., 2020). Spatial econometric analysis adopted Moran' I Index to investigate interrelationships of regional carbon emissions. According to Moran' I Index, Yu et al. (2022) investigated the spatial agglomeration of Chinese urban carbon intensity and pointed out its spatial agglomeration increased in the past years. However, spatial econometric analysis mainly focuses on spatial autocorrelation characteristics of carbon emission (spatial agglomeration level) and doesn't comprehensively discuss the regional difference.
By contrast, convergence analysis is usually adopted to estimate the imbalance of regional carbon emissions. δ convergence analysis and β convergence analysis are the most common convergence analysis methods (Dogah and Awaworyi Churchill, 2022;Ivanovski and Awaworyi Churchill, 2020). The former means the reduction of horizontal differences between regions, while the latter means that countries with a relatively low level tend to rise relatively quickly, thus realizing the catch-up hypothesis (Zheng and Yuan, 2023). Han et al. (2018) analyzed the energy efficiency convergence of countries along the "One Belt And One Road" from 2000 to 2014. They found that the energy efficiency differences among countries showed a convergence trend before 2010, and then showed a trend of divergence. Song et al. (2021) found that carbon emissions in different parts of China are converging in the form of a convergence club (countries of the same type show a tendency to converge), and the high-emission club converges fastest.
The imbalance index is most common for estimating the imbalance of regional carbon emission since it can descript the imbalance of carbon emission at the global level and be decomposed into the contributions of multiple driving factors or regions (Wang et al., 2020). Common imbalance indices include coefficient of variation (You et al., 2021), Gini index (Ahn and Uejio, 2022), Theil index (Li et al., 2021) and Zenga index (Wang et al., 2020). Gini index and Theil index have been widely adopted to evaluate the imbalance of carbon emission and its driving factors in regions (Ahn and Uejio, 2022), transportation (Liu et al., 2021), industry sector (Zhang and Dong, 2022) and other sectors. The imbalance of URB carbon emission has been few focused. It is noticed that, although Li et al. (2021) and Wang and Feng (2021) adopted the imbalance index to analyze the imbalance of carbon emission on URB, they focused on the per capita carbon emission rather than the carbon emission unit area and ignored carbon emissions of central heating. Besides, decomposing Gini index and Theil index usually exist residual (Li et al., 2021). This study adopted Zenga index, which can be completely decomposed without residuals and can measure the imbalance in the each location in distribution and reveal the contribution to the total imbalance (Wang et al., 2020).

Research workflow diagram
The research workflow diagram is shown in Fig. 1, and mainly included three steps: 1) referring to the method of Huo et al. (2018) and You et al. (2021), this study calculated carbon emission without heating (C no_heating ) and heating emission (C heating ) in provincial URB; 2) calculated the Zenga index to estimate the imbalance of carbon emission of provincial URB, and combined the Zenga index with Kaya identity to quantify the contribution of driving factors on the imbalance (Wang et al., 2020).3) considering the obvious impact of economic and climate conditions on the energy consumption of URB, the study divided 30 provinces into three climate zone groups and three economy groups, respectively. and decomposed the imbalance into inter-group and intra-group imbalance. ZK index is employed to analyze the polarization which reflects the relationship between groups and groups' cohesion (Zenga and Radaelli, 2012).

Study area and data source
Due to the lack of energy balance sheet in Tibet, this study selected other 30 provinces in China mainland as the study area. Referring to the method of Huo et al. (2018) and You et al. (2021), this study employed splitting energy balance sheet method to quantify the carbon emission and energy consumption of provincial URB during the period 2005-2019. The carbon emission and energy consumption include heating and no-heating parts. The provincial urban residential building area from the Chinese building energy and emission database (CABEE, 2021), which is calculated by building stock turnover model. Population and per capita disposable income are derived from the National and Provincial Statistical Yearbook (NBS, 2020). The heating period used to adjust heating energy consumption is derived from the Chinese Building Energy Efficiency Standard (MOHURD, 1995).
Besides, in order to quantify the contribution of inter-group and intra-group imbalance on overall imbalance, this study divided 30 provinces into three climate zone groups and three economy groups, respectively (Table.A1). The principle of climate zone groups refers Chinese Building Energy Efficiency Standard (MOHURD, 1995), which divided China into five climate zones based on heating degree days (HDD) and cooling degree days (CDD): Sever cold area (HDD ≥ 3800), Cold area (3800 ≥ HDD ≥ 2000), Hot summer and cold winter area (1200 ≥ HDD ≥ 700), Hot summer and warm winter area (700 ≥ HDD, CDD ≥ 10), and Moderate area (HDD ≤ 700, CDD ≤ 10). According to the heating behavior, we merged Sever cold area and Cold area into the North area (adopt central heating), merged the Hot summer and warm winter area and Moderate area into the South area (no heating), and called the Hot summer and cold winter area as Transition area (adopt individual heating) (Li et al., 2023a) (See Fig. 2). The principle of the economic group is based on per capita disposable urban residents' income and all provinces are divided equally into three groups. Take 2019 as an example, per capita disposable urban residents' income of high, mid, and low-income provinces is 73, 782,40,016, and 36,016-32,299 yuan, respectively.

Extended Kaya identity of URB
Kaya identity has been used to represent the coupling relationship between carbon emissions and related driving factors (Kaya, 1989). The original Kaya identity measured carbon emissions using four parameters, population, per capita GDP, energy intensity, and emission factor (O'Mahony, 2013). Previous studies have developed the Kaya identity of each sector, such as industry (Zhang and  Dong, 2022) and regions (O'Mahony, 2013). Notably, associated with the characteristics of building energy consumption, some scholars have developed the Kaya identity of carbon emission on residential building sector (Liang et al., 2019;Wang and Feng, 2021). Based on above studies (See Table 1), this study selected four driving factors (emission factor, energy consumption unit area, per capita floor area, population) and establish the Kaya identity of C and CI in URB. In addition, this study doesn't integrate economic parameter into kaya identity since the residents' incomes are considered as a basis for grouping to calculate the inter-group imbalance of different economic groups.
The formulas are as follows: where E, P, and A indicate energy consumption, urban population, and floor area of urban residential building, respectively, and EF, EI, and AS indicate the emission factor, energy consumption unit area, and per capita floor area of URB, respectively. Additionally, this study divides the overall carbon emission (CI overall ) of URB into two parts, carbon emissions excluding central heating (CI no-heating ) and carbon emissions from central heating (CI heating ). Because climatic condition can lead an underestimate or overestimate on the real central heating techniques conditions, which doesn't have the interference of climate condition and reflects the real central heating techniques (e.g building envelope, heating-produce-related techniques). Refer the method of You et al. (2021), we selected the heating period days (D) to amend CI heating to conduct a fairly assess. D considers the combined action of regional temperature and actual heating period days. For example, Shenyang and Taiyuan have the same actual heating period days (150 days); however, D of Shenyang (152 days) is longer than that of Taiyuan (135 days) (MOHURD, 1995). D of each province is weighted mean of D in prefecture-level cities weighted by the population. The Kaya identity of amended carbon emission unit area (CI adj-heating ) is as follows: where EF heating , EI heating represents the energy-related emission factor and amended energy consumption unit area, respectively.

Zenga index in the imbalance of C and CI on URB
Zenga index uses the relative gap between average upper carbon emissions and average lower carbon emissions to estimate the imbalance in carbon emissions (Pasquazzi and Zenga, 2018;Shao et al., 2020). The Zenga index of C overall , C heating , C no_heating , and C adj_heating were calculated using the same method. To save space, C and CI were used to explain the method. To measure the imbalance of C, we first ranked Chinese provinces in ascending order of C and used province t (t = 1, 2, …,30) to represent the province with the t h lowest C. Mathematically, the Zenga index is based on the weighted ratio of the upper and lower averages (Zenga and Radaelli, 2012).
The contribution of the interaction term (Z int t (C)) was calculated using the following formula: The overall imbalance of C in URB was calculated using Eq. (11). The calculations of the contribution of EF, EI, AS, and P and the interaction term were similar.
Similarly, according to a previous method (Greselin et al., 2013) and Eq.
(2), we measured the imbalance of CI and decomposed it into three driving factors, Z EF t (CI), Z EI t (CI), and Z int t (CI). The formulas are as follows: where M + t (CI), M + t (EF), and M + t (EI) are the means of CI, EF, and EI in provinces with a higher CI than CI t , respectively, and M − t (CI), M − t (EF), and M − t (EI) are the means of CI, EF, and EI in provinces with lower CI than CI t , respectively. The contribution of province t to the imbalance of CI can be calculated, and the contribution of province t can be decomposed into three multiplied driving factors, Z EF t (CI), Z EI t (CI), and Z int t (CI).

Measuring the inter-group and intra-group imbalance of CI no_heating
There are the significant influence of climatic and economic condition on provincial CI no_heating of URB . We think the provinces group with same climatic or economic condition may achieve emission mitigation more easily by a mutual technology spillover or reference. In order to explore this possible, this study further explored the imbalance of different types of regional groups. We first ranked the provinces in ascending order of CI no_heating , and divided the 30 provinces into three climate zone groups and three economy groups, respectively. The Zenga index can be decomposed into intra-group (Z a (CI)) and inter-group imbalance (Z b (CI)), and it does not have a residual term (Shao et al., 2020;Wang et al., 2020). The formulas are as follows: where A t represents the building floor area of province t, A total represents the floor area of national urban residential building, and Z + gt (CI) and Z − gt (CI) represent the mean of CI no_heating of provinces of group g with higher and lower CI no_heating than province t. Z + ht (CI) represents the mean of CI no_heating of provinces of group h than province t. b(g|t), u(g|t), and u(h|t) were calculated using the following formulas: where A − gt and A + gt represent the sum of A of provinces with lower and higher CI no_heating than province t, respectively, and A − t and A + t represent the sum of A of provinces with lower or equal and higher CI no_heating than province t, respectively. Additionally, according to Eqs. (12), (13), (14), the intra-group and inter-group imbalances of CI no_heating can be divided into the contributions of three driving factors. Polarization reflects the relationship between groups and groups' cohesion (Duclos et al., 2004). In other words, as CI no_heating within the group diminishes, that is, as the groups become more homogeneous internally, differences across groups are, relatively speaking, magnified, and the polarization is higher. The ZK index usually explains the polarization effect (Wang and Tsui, 2000) since it is calculated based on the intra-group and inter-group imbalances as follows:

The imbalance in carbon emissions of URB
The total imbalance of C overall in URB is shown in Fig. 3. Overall, there were significant imbalances in the C overall of URB between the 30 provinces, all of which were higher than 0.75 in overall study period. C overall from the urban residential building sector in each province were still unevenly distributed. Although, the imbalance in the C overall of URB was continuously decreased, the decreased trend was inconspicuous. Meanwhile, the C overall of URB represented an increasing trend. It increased from 0.57 BtCO 2 in 2005 to 0.86 BtCO 2 in 2019, and it still not reached the peak value, which is consistent with the results of Ma et al. (2020). On contrary, CI of Chinese URB achieved a peak value in 2011, reaching 36.17 kgCO 2 /m 2 . Fig. 3a also shows that population and energy consumption unit area were the major contributors to the imbalance of C overall , and they accounted for >90% of the total imbalance, emphasizing that provinces with higher carbon emissions in URB are characterized by more population and energy consumption unit area. On contrary, although, the contribution of emission factor was much lesser, accounting for <2%, it had changed impacts on the imbalance of Chinese URB in different periods. For example, after 2014, the imbalance of emission factor exchange from mitigating to exacerbating, and resulted in 0.71% of the imbalance of C overall in Chinese URB.
Heating carbon emissions usually account for a larger proportion of C overall and E overall in URB (Lin and Lin, 2017). The data indicated that the urban residential building sector produced 0.41 BtCO 2 from heating in 2019, accounting for 47.57% of carbon emissions of the URB sector (CABEE, 2021;Du et al., 2018). Therefore, this study suggests that central heating may be an important factor leading to an imbalance in carbon emissions in URB. Fig. 3b shows the imbalances of URB carbon emissions without central heating. Compared to Fig. 1a, the Zenga Index was significantly smaller (<0.7 in the overall study period, consistent with the above assumption). Fig. 3c and d show the imbalance of C heating and C adj_heating , respectively. The Zenga Index of C heating showed a slightly decreasing trend from 0.72 in 2005 to 0.66 in 2019. Emission factor and energy consumption unit area had the most positive and negative impacts on the imbalance of C heating , respectively, indicating that provinces with higher C heating usually have a lower energy consumption unit area and higher emission factor. Therefore, provinces with higher C heating and those with lower C heating can achieve emission reductions in reducing emission factor and energy consumption unit area, respectively, through mutual technology spillover and reference between them. Additionally, we found that the Zenga index of C adj-heating was obviously larger than that of C heating during the study period, indicating that climatic differences magnified the imbalance of C heating . This was because the climate parameter reduced the imbalance of energy consumption unit area, the absolute contribution of energy consumption unit area reduced by >6% of the overall imbalance after adjusting in overall study periods.

The imbalance in CI of URB
As shown in Fig. 4a, before 2011, the decreased speed of CI heating (1.04 kg/m 2 /year) exceeded the increased speed CI no-heating (0.42 kg/m 2 /year), the CI overall exhibited continuous decreased trend is study period.
The CI overall represented an obvious imbalance, and the Zenga index was >0.7 in the overall study period. The contribution of emission factor exchanged from negative to positive after 2013. That results may be related to the more clean energy structure in southern provinces. Specifically, coal's share of the total final energy consumption in southern and north provinces arrived at 6.48% and 21.56% in 2019. At the same time, at the major energy type, electricity generation owned a lower emission factor in south provinces (3.01 kgCO 2 /kgce) compared with north provinces (5.63kgCO 2 /kgce) (CABEE, 2021). Additionally, the imbalance of energy consumption unit area was the major contributor to the imbalance of CI overall , accounting for >80% of the total study period.
Similar to Section 4.1, this study also showed an imbalance of CI no_heating , CI heating , and CI adj_heating in Fig. 4b, c, and d, respectively. Compared with Fig. 4a, we found that the imbalance of CI no_heating was significantly less than the imbalance of CI overall , which indicates that central heating was one of the major reasons leading to the high imbalance of CI overall .
As for CI heating and CI adj_heating , the Fig. 4c and d represent that CI heating (32.61 kgCO 2 /m 2 in 2019) was obviously higher than CI overall (25.16 kgCO 2 /m 2 in 2019), although CI heating and EI heating continuously decreased in the overall study period. By comparing the Zenga index of CI heating and CI no_heating , we found that climatic differences significantly magnified the imbalance of CI heating . Therefore, to accurately assess the real provincial heating technology and make rational emission mitigation share targets and policies, policymaking departments should fully consider the magnifying effect on CI heating nergy consumption unit area. (Note: Fig. 3a, b, c, and d represent imbalances in C overall , C no_heating , C heating , and C adj_heating , respectively. EF, EI, AS, P and INT represent emission factor, energy consumption unit area, per capita floor area, population and interaction term, respectively.) Fig. 5a represents the spatial distribution of carbon emission unit area excluding heating part (CI no_heating ) in 2019, and it indicates that there is a significant difference in CI no_heating at the provincial level. In specifically, the largest CI no_heating (Inner Mongolia, 48.80kgCO 2 /m 2 ) was nearly 8 times of the smallest (Yunnan, 6.49kgCO 2 /m 2 ).

The spatial distribution of CI no_heating
Furthermore, CI no_heating represents obvious difference in climate and economy group. First, because of the difference in climate condition, Chinese provinces are usually divided into three geographical climate groups, north provinces (NPs), transitional provinces (TPs) and south provinces (SPs) (You et al., 2023a). As shown in Fig. 5a, CI no_heating (17.49 kgCO 2 /m 2 ) of north provinces was higher than that of south provinces (10.16 kgCO 2 /m 2 ) and transitional provinces (11.04 kgCO 2 /m 2 ) since the higher energy consumption unit area and emission factor of NPs. In specifically, because of the heating utilization, that energy consumption unit area of SPs (3.89 kgce/ m 2 ) and TPs (4.13 kgce/m 2 ) were obviously lower than that of NPs (5.42 kgce/m 2 ). Meanwhile, Fig. 5b indicates emission factor of SPs (2.61 kgce/m 2 ) and TPs (2.68 kgce/m 2 ) were lower than that of NPs (3.22 kgce/m 2 ), that may be caused by a high proportion of coal in the energy structure. In 2019, coal accounted for 21.84% of the total energy consumption of URB of NPs. However, in SPs and TPs, coal has been replaced by natural gas, which has a lower carbon emission unit area, and only accounted for 3.29% and 4.99% of the total energy consumption of the URB of SPs and TPs, respectively (CABEE, 2021). As a major energy in the energy consumption of URB, electricity usually owns a higher emission factor in NPs due to a high proportion of thermal plants in the energy structure of generation. The electricity emission factor of NPs (5.63 kgCO 2 /kgce) was >1.5 times that of TPs (3.60 kgCO 2 /kgce) and SPs (3.01 kgCO 2 /kgce). Considering the high cost of natural gas and high emission factor of electricity, emission reduction by optimizing the building energy structure is not easy to achieve and it is more of a long-term objective (Zenga and Radaelli, 2012).
Secondly, Fig. 5d shows that the differences of CI no_heating on URB may be a result of differences in economic condition to a large extent. For example, although Beijing and Henan are located in the same climate zone. As an economic developed province, Beijing owned CI no_heating of 26.23 kgce/m 2 , far exceeding the Henan (9.64 kgce/m 2 ). That is caused by the high end user service demand of high-income families (Li et al., 2021). Similar condition can be seen in global wide, the China's per capital building energy intensity only was 21% of the US, 72% of Japan and 23% of the UK (IEA, 2021). In summary, considering the differences in economy and climate, adopting convergence emission reduction policies on all provinces to reduce CI no_heating rather than formulating pointed Fig. 4. The Imbalance in CI of URB. (Note: Fig. 4a, b, c, and d represent imbalances in CI overall , CI no_heating , CI heating , and CI adj_heating , respectively. EF, EI, and INT represent emission factor, energy consumption unit area, and interaction term, respectively.) emission reduction targets based on the regional imbalance within different provinces groups is bound to have a negative impact on emission reduction and harm social equity and residents' welfare. According to IPCC, formulating emission reduction policies should follow the principle of "common but differentiated" (Harris, 1999). Particularly, provinces with the same economic and climate conditions can easily achieve decreases in CI no_heating through intra-group technology spillover and local technology improvements. Therefore, further analysis of the causes of emission inequality at the group level using Eqs. (15)-(20) is helpful to put forward pertinent suggestions and set reasonable carbon emission reduction targets. In this study, based on the climate zone and per capita income, we divided 30 provinces into three climate zone groups (north, transitional, south provinces) and three economic groups (provinces with high residents' income (HPs), provinces with middle residents' income (MPs) and provinces with low residents' income (LPs)). The group divisions are listed in Table A1 (Appendix A).

The imbalance of CI no_heating at climate zone group level
The Fig. 6 represents imbalance of CI no_heating in the inter-and intra-climate zone groups. The results showed that inter-group imbalance was the major contributor to the overall imbalance of CI no_heating , accounting for >70%. Meanwhile, there was a severe polarization in CI no_heating of URB, and the ZK index was more than three, indicating that the inter-group imbalance was more than three times the intra-group imbalance. Polarization was largely caused due to imbalances between NPs and other groups, accounting for >65% of the overall imbalance of CI no_heating . On the contrary, the imbalance between SPs and NPs was smaller, reaching only 9.30% in 2019. (Note: Fig. 5a, b, and c represent the spatial distribution in CI no_heating , EI no_heating , and EF no_heating , respectively. CI, EF, and EI represent carbon emission unit area, emission factor and energy consumption unit area, respectively. NPs, TPs and SPs represents north, transitional and south provinces, respectively.) The intra-group imbalance was smaller; however, it still amounted to approximately 22% of the overall imbalance of CI no_heating , and it represented an increasing trend from 17.44% in 2005 to 22.12% in 2019, which suggests that reducing the intra-climate zone group imbalance of CI no_heating can significantly mitigate carbon emissions. The largest intra-group imbalance of CI no_heating was NPs, with >10% of the overall imbalance of CI no_heating , indicating that NPs can easily achieve carbon emission reduction through intra-group technology spillover. The imbalance of energy consumption unit area was the major cause of intra-group imbalance in CI no_heating . Fig. 7 represents the imbalance of CI no_heating in the inter-and intra-economy groups. Compared to the impact of climate zone, the economy had a lesser impact on the imbalance of CI no_heating because the ZK index of economy groups was <3.0 in the overall study period. The contribution of the imbalance of energy consumption unit area on the inter-group imbalance of CI no_heating decreased in the past five years, suggesting that the provincial gap of energy consumption unit area converged. This may be attributed to two reasons, 1) the near saturation demand for household energy in developed provinces and 2) the rapidly increasing demand for household energy in less developed provinces. Taking Guizhou as an example, in 2019, the number of air conditioners per 100 households (37.23) doubled as compared to that in 2013(18.70) (NBS, 2020). This suggests that less-developed provinces should pursue a mix of policies to improve building energy efficiency to offset the negative impact of rising energy demand on China's emission targets (Wang and Feng, 2021).

Imbalance of CI no_heating at the economy group level
For the intra-group imbalance, high-income provinces represented the largest contribution, accounting for >14%, and the imbalance in energy consumption unit area contributed the most to the overall imbalance (>80%) of High-income provinces CI no_heating . Therefore, high-income provinces should exploit the possibility of emission reduction by improving their building energy efficiency. Considering the higher income of residents of high-income provinces, the option is easier to achieve by adopting more efficient household appliances and promoting energy renovation of buildings (Lekavičius et al., 2020). In contrast, low-income provinces had the smallest impact on the imbalance of CI no_heating , and the contribution of the imbalance of low-income provinces' energy consumption unit area on the imbalance of low-income provinces' CI no_heating decreased, indicating that the gap between energy consumption unit area of low-income provinces' gradually narrowed.

Impact of EI on the emission mitigation of URB
For both CI no_heating and CI heating , energy consumption unit area (EI) has always been the major contributor leading to imbalance, which indicates the importance of improving the energy efficiency of URB. The future change in EI is affected by two factors, the residents' demand for end-user services(e.g., heating, cooling, lighting, cooking, hot water, and other household appliances) and techniques for building energy efficiency (Zhou et al., 2018). The former is largely based on residents' income (Yang et al., 2017), and the residents of high-income provinces usually tend to have frequent household energy utilization behaviors (Li et al., 2021). Income can influence residents' behaviors (Jin et al., 2022) and caused household energy consumption imbalance. The results of this study showed that the gap in EI between the three economic groups gradually narrowed, indicating that mid-income provinces and lowincome provinces will face a faster rigid growth in end-user service demand for a long time in the future. This is undoubtedly a significant challenge to the emission reduction of URB (Ma et al., 2020). To offset this energy demand growth and to further promote the reduction of EI and CI, the national and provincial governments should promote higher mandatory building energy efficiency design standards for new URB and energy renovation for existing URB to improve the performance of lighting systems, building thermal insulation, and heating and air conditioning systems (You et al., 2023a). Meanwhile, the government also promotes the utilization of highly efficient household appliances (LBNL, 2016). Additionally, occupant behavior is thought to be one of the major reasons for the difference in EI (Jiang, 2015;Li et al., 2021). Especially for high-income provinces whose energy demand is higher, the local government actively guides residents' awareness of green life by formulating relevant policies and completing market mechanisms, such as implementing charges by heating metering, reasonable electricity ladder prices (Sun, 2015), and green lifestyle propaganda (You et al., 2023a) to form a low-carbon and environmentally friendly sustainable development system for URB.

Impact of EF on the emission mitigation of URB
Although emission factor (EF) has a smaller impact on the imbalance between CI no_heating and CI heating , the impact represents a sharply increasing trend, indicating that optimizing the energy structure plays an increasingly important role in the achievement of carbon peak and carbon neutrality of URB (Li et al., 2021;Ma et al., 2020), especially for north provinces. First, the URB sector should actively promote the clean utilization of primary energy by implementing the coal-to-gas project (Tanaka et al., 2019) and adopting the techniques of renewable energy in buildings, such as building integrated photovoltaics and ground-source heat pumps (IEA, 2020a). For secondary energy, the secondary energy of Chinese URB mainly has two forms, central heating and electricity. For central heating, the national and provincial governments should eliminate the outdated and inefficient small-and medium-sized fired boilers as soon as possible and promote efficient large coal-fired boilers and cogeneration boilers to improve fuel conversion efficiency (Du et al., 2018). Meanwhile, associated with provincial resource endowment, fully tap the emission mitigation potential of renewable energy on central heating (IEA, 2020b). For example, Heilongjiang, Liaoning, Jilin, and other heavy industry provinces can increase industrial waste heat recovery, and Inner Mongolia can increase the application of wind energy in central heating. As the major energy forms of URB (CABEE, 2021), there was an obvious difference in the regional emission factor of electricity generation (Fig. 8). Particularly, the electricity emission factor of NPs was significantly higher than that of SPs and TPs, which was approximately 2.5 times of coal and four times of natural gas, respectively. Therefore, the electricity process of north provinces needs to be carefully arranged based on the appliance efficiency and cost. For example, the energy efficiency ratio (EER) of a heating pump was higher than three, and the EER of heating by directly firing coal was less than one, indicating that this "coal-to-electricity" process was environmental friendly. However, due to a similar EER of the electric water heater and coal-fired water heater, the "coal-to-electricity" process should be delayed. Additionally, for provinces with similar natural resource endowments, technology spillovers between provinces will easily achieve the optimization of energy structure (Wang et al., 2020). (Note: Fig. 7a represents the imbalance of inter and intra economic groups; Fig. 7b represent the contribution of each driving factors. The percentage of each sub-figures is the ratio of the contribution of different driving factors to the sum of the absolute value of the contribution of all driving factors. HPs, MPs and LPs represents high, mid, and low income provinces, respectively. INT, EF, and EI represents interaction term, emission factor and energy consumption unit area, respectively.)

Main conclusion
This study adopted an approach based on the Zenga index and an extended Kaya identity to analyze the imbalance of C and CI (overall emissions, emissions excluding central heating, emissions on central heating, and adjusted emission of central heating) on URB for 2005-2019, and it decomposed the Zenga index into several contributors' multiplication. Furthermore, based on the residents' income and climate zone, we decomposed the imbalance of CI no_heating into intra-and inter-groups.
The main conclusions are as follows: 1) The overall C of URB increased from 0.57 BtCO 2 in 2005 to 0.86 BtCO 2 in 2019, and it has kept rising ever since. In contrast, CI overall , CI no_heating , and CI heating achieved a peak in 2011 (36.17kgCO 2 /m 2 ), 2011 (20.39 kgCO 2 /m 2 ), and before 2005 (47.12 kgCO 2 /m 2 ). 2) There was an obvious imbalance in C and CI of URB. The imbalance of population was the major contributor to the imbalance of C overall , which accounted for >60% and showed an increasing trend. The imbalance of energy consumption unit area dominated the imbalance of CI overall . Meanwhile, the central heating exacerbated the imbalance of C overall and CI overall , and the climate parameter (heating period day, D) had a significant impact on the imbalance between C heating and CI heating. 3) Climate and per capita residents' income were major reasons for the provincial gap in CI no_heating . North provinces had a higher CI no_heating due to the high-carbon energy structure of URB. Meanwhile, the high demand for EI no_heating caused by high per capita residents' income renders high-income provinces to have a higher CI no_heating. 4) There was an obvious polarization on CI no_heating . Specifically, the inter-group imbalance of CI no_heating was approximately thrice that of the intra-group imbalance of CI no_heating in 2019. Compared to the impact of the difference in climate, the difference in economy had a lesser impact on the imbalance of CI no_heating .

Future research orientation
Although some meaningful findings were obtained in this study, several gaps can be filled with future endeavors. Firstly, in the perspective of sector, the study focused only on the URB sector. Given the different energy consumption characteristics, the major contributors to the imbalance of CI in different building types, such as URB, rural residential buildings, and commercial buildings, may vary significantly. For example, economic development of the tertiary industry may have a larger impact on the CI of commercial buildings. In the perspective of space, there is only the national and provincial energy balance energy sheet in China. The data of URB at city level is lack. Future study will establish time serials of carbon emission in URB at Urban level and analyze their imbalance, which will benefit to formulate more specific URB decarbonization strategies and exploit the potential of technology spillovers between cities.