Carbon peak and its mitigation implications for China in the post-pandemic era

China’s carbon peak greatly impacts global climate targets. Limited studies have comprehensively analyzed the influence of the COVID-19 pandemic, changing emission network, and recent carbon intensity (CI) reduction on the carbon peak and the corresponding mitigation implications. Using a unique dataset at different levels, we project China’s CO2 emission by 2035 and analyze the time, volume, driver patterns, complex emission network, and policy implications of China’s carbon peak in the post- pandemic era. We develop an ensemble time-series model with machine learning approaches as the projection benchmark, and show that China’s carbon peak will be achieved by 2021–2026 with > 80% probability. Most Chinese cities and counties have not achieved carbon peaks response to the priority-peak policy and the current implementation of CI reduction should thus be strengthened. While there is a "trade off" between the application of carbon emission reduction technology and economic recovery in the post-pandemic era, a close cooperation of interprovincial CO2 emission is also warranted.


Results and discussion
Decomposition for provinces and city groups. The distributions of the five drivers in 1997-2019 were similar to those in 1997-2012. In addition, the driver patterns of CO 2 emission changed in the post-Kyoto era especially the role of reducing CI. The changes in ranks in terms of CO 2 emissions among Chinese provinces were smaller in the post-Kyoto era than in the Kyoto era, especially in China's central and eastern regions shown in Fig. 1b,c. The relative ranks in the west still changed in the post-Kyoto era, except the Inner Mongolia and Qinghai, which were mainly due to the abundant coal resources and low economic development 27 . In general, the relative ranks changed dramatically for most provinces in the Kyoto era (Fig. 1a,b). For example, Shandong became the greatest emitter among 30 Chinese provinces after the Kyoto era. These results implied that the realization China's climate targets would rely on the CO 2 emission performance of the western region. A tradeoff between CO 2 emission performance and economic development must be considered as the west is the least economically developed among the three regions.
The GDP per capita (PY) and CI were inversely correlated to CO 2 emission from 1997 to 2012 (Fig. 1d) and the whole study period (Fig. 1f) in provinces at varying levels. Following the environmental Kuznets curve 28 www.nature.com/scientificreports/ www.nature.com/scientificreports/ the results were unsurprising since the PY in China increased since the opening-up policy, and the Chinese government's pledge in 2009 to reduce the CI by 40-45% in 2020 30 earned significant results, including those since the post-Kyoto era (Fig. 1e). Conversely, the GDP (Y), population (P), and CO 2 emission per capita (PC) in provinces were positively correlated to CO 2 emissions in 1997-2012, in which Y and PC were the main drivers and generally consistent with Zhang et al. 22 . The Y became the dominant driver increasing the CO 2 emission in the post-Kyoto era while the P had relatively minimal contribution due to the slow population growth. The inflow and outflow of population played a limited role in declining CO 2 emission due to its mobility 31 . According to the World Bank 32 , China's PC in 2011 was 7.242 metric tons per capita, which overtook that of the European Union (7.081 metric tons per capita) for the first time. With the rapid industrialization and urbanization, Y was growing at a high speed of 9.8% (NBSC), thus resulting in high CO 2 emissions from coal that dominated China's energy consumption structure 4 .
Among the six city groups, large cities and very large cities were the two greatest CO 2 emitters, occupying 68.8% of the national population in 2015. These two city groups were followed by midsize cities-I and megacities. As shown in Fig. 2a-f, Y, PC, and P were the three greatest positive drivers of CO 2 emissions from 1997 to 2012 in all city groups except in small cities, which were the same throughout the period except in megacities which may be caused by the slow population growth. Figure 2g-i showed that compared to highly commercial and mixed-economy cities, highly industrial cities' CI contributed a decrease of CO 2 emission from 11.6 to 17.3% in the post-Kyoto era.
The CO 2 emissions linked to PY and CI were declining in all city groups, similar to provinces in 1997-2012. The strengthened implementation of CI reduction in the country made this possible. However, we found that the contributions of CI and PY increased with city types, i.e., from small cities to megacities. Therefore, assuming that the population and urbanization continue to expand, the CO 2 emissions may increase (e.g., changing from midsize cities-II cities to midsize cities I). Hence, the role of CI reduction measures among cities becomes essential as the level of urbanization increases 33 . Figure 3 depicted the relationship between PC and PY of provinces and cities. We applied a GKC (Eq. 11) to fit PY and PC for Chinese provinces and cities and then calculated the mean value together of py peak with the confidence intervals 70%, 80%, and 90%, respectively, as described in methodology section. Therefore, we can calculate the national py peak with different confidence intervals since we assumed that the national PC and PY would be constant for most provinces and cities, as also applied by Wang et al. 12 . We found that peak PCs were 8.3-9.3 ton/person. Based on the projections of China's population and economic growth, we projected that China would achieve carbon peak between 2021 and 2026 with > 80% probability, close to the results of Wang et al. 12 and Yu et al. 21 but earlier than that of Fang et al. 7 and Chen et al. 8 . The estimated peak CO 2 emission would be 11.7-13.1 Gt, lesser than that of Wang et al. 12 , and larger than that of Mi et al. 18 and Yu et al. 21 . Figure 4 depicted the carbon emission levels in Chinese provinces, cities, and counties. The results showed that only Beijing and Tianjin cities achieved carbon peaks. A total of 21 cities had unstable carbon peaks while 239 cities did not achieve carbon peaks. Jilin, Shanghai, Henan, Hubei, Sichuan, and Yunnan provinces had unstable carbon peaks in 2019, and more than two-thirds of the provinces have not reached their carbon peaks. At the county level 22 counties achieved carbon peaks, 184 counties showed unstable carbon peaks, and 1526 counties did not achieve their carbon peaks. Policymakers can monitor and update the CO 2 emission levels shown in Fig. 4 to guide in implementing priority-peak policies at local levels. Figure  We further showed that if China would follow the advanced scenario, 2020 could be the year of the county's carbon peak. However, if China would implement the moderate scenario, it could achieve the carbon peak by 2030, depending on the implementation of CI reduction and economic growth. The future implementation of CI reduction in the past decade (2011-2020) may also contribute to a carbon peak in the country. If the rate of CI reduction from 13th FYP period is continued, China will not achieve carbon peak by 2030. In fact, compared with the CI reduction during 12th FYP period, China recently slowed its CI reduction efforts at provincial levels, according to a report by the government 34 . Therefore, strengthening the implementation of CI reduction in the future especially for the 14th FYP (2021-2025) is key for achieving national carbon peak.

Scenario analysis.
Gaps of China's CO 2 emission under three scenarios could be 8.4 Gt in 2030 and 13.4 Gt in 2035. However, due to uncertain CI reduction and economic growth, the future trajectory of CO 2 emission is likely to deviate from the assumed scenarios. Combined with the results of nonlinear estimation using GKC, the scenario analysis indicates that the uncertainty in the achievement of carbon peak by 2030 is primarily due to the pandemic and slowdown in CI reduction. However, we are optimistic that China will achieve its carbon peak target if the implementation of CI reduction is strengthened.

Social network analysis.
To illustrate the changes of regional carbon emission spatial correlation network in China at the sub-national scale (provincial scale in the study) under different emission reduction technology scenarios in the post-pandemic era, we used three representative scenarios to conduct the social network analysis (SNA, the supplementary material S1).  www.nature.com/scientificreports/ emission reduction technology scenarios, the interprovincial carbon emission spatial correlation network presents a complex network structure. Due to the different scenarios of economic recovery in the post-pandemic era and emission reduction technology, the corresponding network characteristics show great differences.
The number of interprovincial carbon emission spatial correlation networks decreased, with different reasons as those under A4 and A21 scenarios. A4 shows that although the carbon emission reduction technology maintains the status quo, the rapid economic growth could widen the original economic gap among provinces and slightly impact carbon emission spatial network ties. Compared with other emission reduction technology scenarios, the use of advanced carbon emission reduction technology could increase the socioeconomic costs and impact the carbon emission spatial network ties. A16 scenario shows that moderate improvement of carbon emission reduction technology will improve the spatial correlation network of carbon emission, implying that there is a "trade off " between application of carbon emission reduction technology and socioeconomic cost of economic recovery.
The other characteristics of overall network also reflect the above patterns. For example, Fig. 6I shows that the overall network efficiency increases under A4 and A21 scenarios but decreases under A16 scenarios. This indicates that moderate carbon emission reduction technology is conducive to improving the connection number of interprovincial carbon emission spatial correlation network and enhancing the network stability. The higher the network density is, the closer the interprovincial carbon emission spatial correlation network is. The changing trend of network density under different scenarios is similar to that of Fig. 6g, which also reflects "trade off. " The results of network hierarchy analysis are slightly different. Figure 6h shows that the network hierarchy of A16 and A21 scenarios has declined except for the A4 scenario, indicating that maintaining the existing carbon emission reduction technology is not conducive to breaking the strict spatial correlation structure of carbon emissions. In contrast, by improving technological progress in carbon emission reduction, the strict spatial correlation structure of interprovincial other emissions can be further broken, whereas the interprovincial network interaction can be enhanced.
In terms of characteristics of individual network, the results of in degree and out degree show that the in degree of Tianjin, Hebei, Shanghai, Zhejiang, Fujian, Shandong, Henan, Guangdong and other provinces is not only higher than the national average in degree, but also higher than their own out degree under the three scenarios ( Fig. 6n-o). Most of them are located in the central and eastern regions with developed economy and high carbon emissions, and they are highly dependent on the energy supply from other provinces, which may lead to carbon emission spillover from other provinces. The analysis on degree centrality is similar to those in degree and out degree results (Fig. 6k). In all scenarios, Tianjin, Shanxi, Inner Mongolia, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong and other provinces with higher degree centrality than the national average are located in coastal areas except Inner Mongolia, suggesting that coastal areas have a strong impact on the spatial correlation network and spatial spillover effect of carbon emissions under different scenarios. www.nature.com/scientificreports/ The results of betweenness centrality analysis show that Tianjin, Shanghai, Zhejiang, Fujian, Shandong, Guangdong and other provinces have a strong ability to influence the carbon emissions interaction among other provinces in the network (Fig. 6m). The closeness centrality of the above major provinces is also higher than the average value of the national closeness centrality (Fig. 6l), suggesting that these provinces can connect with other provinces faster in the carbon emission spatial network, that is, they play a central role in the network.
Although the above analysis highlights the common mode of interprovincial carbon emission spatial correlation network under different scenarios, future relevant policies should consider provinces with different performance including the strength of connections in terms of carbon emission network under different scenarios ( Fig. 6a-f). Regional carbon emission reduction policies should fully consider Shandong, Guangdong, Tianjin, Zhejiang and other provinces with relative strong connections of spatial emission networks, and can be also

Concluding remarks
For Chinese government's goal of achieving carbon neutrality, achieving carbon peak before 2030 is imperative. The pandemic and slowdown in declining CI cannot be ignored. Based on the new and a large-scale dataset of China's CO 2 emissions at provincial, city, and county levels, we developed several methods to analyze the time, volume, driver pattern, emission network, and policy implications of China's carbon peak. For the first time, this study identified peak areas up to the county levels, providing an important reference in formulating prioritypeak policies. The study emphasized the importance of interprovincial closely cooperation of CO 2 emission in complex networks toward the national carbon peak and carbon neutrality targets. This study showed that China would achieve its carbon peak without any exogenous shocks in 2021-2026 at 11.7-13.1 Gt with a high probability of > 80%. However, due to the COVID-19 pandemic and slowing rate of CI reduction, the achievement of the carbon peak by 2030 remains uncertain. Under scenarios between the BAU and the advanced emission reduction technology, gaps in China's CO 2 emissions could be 8.4 Gt in 2030 and 13.4 Gt in 2035. Further, the generalized Divisia index analysis indicated that CI reduction is more important for reducing CO 2 emission in Chinese provinces and cities categorized by population size and economic structure in the post-Kyoto era. Therefore, the current implementation of CI reduction should be strengthened through emission reduction technology innovation to assist in the achievement of the carbon peak by 2030 and leading emissions into a stable downward path for achieving the carbon neutrality target by 2060. Since most provinces, cities and counties in China have not achieved their carbon peaks by 2019, a necessary condition for achieving the national targets above is to formulate close cooperation in terms of interprovincial CO 2 emissions. However, the SNA showed that there is a "trade off " between application of carbon emission reduction technology and economic recovery in the post-pandemic era.
In this regard, we recommend the following policies. First, implementing green economy recovery after the coronavirus pandemic, increasing the scale of green investment, and balancing economic growth and emission reduction targets. Although China has the second-largest green investment scale in the world 35 , the current policies may be insufficient to achieve China's carbon peak and other climate goals. The investment in hydrogen energy, carbon capture and storage (CCS), energy storage, electric transport, electric heat, and renewable energy should be further increased in the future. Additionally, given that green finance is an important investment, the government should also standardize its green bond issuance as soon as possible, and the relevant standard system should be in line with the international standards, similar to those in Europe. In line with this, China can strengthen cooperation with the European Union and other regions to improve the scale and quality of green bonds and the contribution of China's green proposal to the global climate target below 1.5-2 °C.
Second, the Chinese government can establish a rapid response system of regional carbon peaks to implement a guideline for prioritizing various areas. Real-time monitoring is difficult when an area reaches the carbon peak. Therefore, increasing the timeliness of updating CO 2 emission data with a unified carbon inventory accounting system based on the top-down and bottom-up methods is essential. Additionally, given the drivers important role in changing CO 2 emissions, policy makers can also consider using different methods (e.g., generalized Divisia index method, GDIM) to track and project the trend of the regional CO 2 emissions and carbon peak. Furthermore, when formulating regional peak strategies, policymakers should fully consider carbon sequestration based on vegetation and the differences of vertical management structure of regional carbon peak plans. For example, policymakers can formulate the relevant carbon peak policies from the differences of key industries and urbanization process in provinces, cities and counties.
Third, the government should manage the regional CI targets through dynamic optimization especially in the 14th FYP, a key period for achieving its carbon goals in the long term. The local governments, in particular, www.nature.com/scientificreports/ should ensure timely update of the CI reduction for dynamic management of the targets. If we maintain the CI's decline rate as that during the 13th FYP (2016-2020), CO 2 emissions may spike in the future. It is, therefore, necessary for the government to focus on CI reduction; however, considering the urgency of economic recovery, this may be difficult. Policymakers should also formulate more detailed regional emission reduction cooperation plans at city and county levels to balance the overall economic growth and the local emission reduction targets. The study is not free from limitations. First, although the study set many scenarios to depict the trend of future carbon emission, as a result of the smooth setting of parameters, the scenario model may not be able to effectively capture the rebound effect of carbon emissions during a certain period, which is likely to occur with the increase of energy consumption during the economic recovery after COVID-19 pandemic. Actually, the increase in energy consumption caused by strong economic recovery in the post epidemic era may delay the time to achieve carbon peak to a certain extent. However, due to the large space for carbon peak, we are optimistic that China will finally achieve carbon peak by 2030. Second, due to the lack of city-and county-level sectoral carbon emission data, the study used the total carbon emission data of provinces, cities and counties and thus we did not analyze the carbon peak from the perspective of carbon emission structure. It is expected to make a breakthrough in developing city-and county-level sectoral carbon emission inventories in future, so as to better support carbon peak and carbon neutral policymaking. Third, although the study covered most provinces, cities and counties, there are still some cities and counties outside the carbon peak analysis due to the lack of data, leading to the weakened support for the full implementation of the regional priority carbon peak policy at the city and county level. Those deficiencies should be addressed in future studies.

Methods
Ensemble time-series forecasting model. The prediction based on TS encounters various uncertainties in the future. The prediction method based on ML can capture the nonlinear relationship of data changes at a high accuracy. Its explanatory power, however, is weak due to the "black box" in the operation process. In contrast, the traditional TS prediction method (i.e., non-ML method) usually has high explanatory power but unsatisfactory prediction accuracy relative to ML-based prediction methods. In this regard, integrating the two prediction methods is necessary to enhance the generalization ability and accuracy of TS forecasting.
The ensemble TS forecasting model developed in the study consists of the following 12 methods (Fig. 7). The ML methods include the (1)  Generalized Divisia decomposition approach. The GDIM proposed by Vaninsky 36 was utilized to decompose the changes in aggregate CO2 emission in Chinese cities. In addition to GDIM approach, logarithmic mean Divisia index (LMDI) 37 is another widely used decomposition approach. However, LMDI quantitatively describes the economic and population indicators while the intensity indicators (e.g., GDP per capita and www.nature.com/scientificreports/ per capita CO 2 emission) are hardly analyzed in a single decomposition framework. In addition, the LMDI has different factorial decompositions due to varied factor models. On the contrast, The GDIM overcomes the disadvantages of LMDI above and has been used in energy or emission studies (e.g., 22,38 ). Following the framework in Vaninsky 36 , we decompose the changes in China's overall CO 2 emission in 1997-2019 as follows: where i represents a city ( i = 1, 2, . . . , 262 ); C the CO 2 emission, Y the GDP, P the population, CI the carbon intensity, and PC the CO 2 emission per capita. Then, this equation is derived from Eq. (1): To analyze the five factors, i.e., CI , Y , PC , P , and PY , in a single decomposition framework, we followed Vaninsky 36 , rewriting Eqs. (1) and (2) as follows: , the gradient of the function C i (X) and Jacobian matrix X are listed in Eqs. (6) and (7).
Due to the interconnections of different factors, decomposing changes in CO 2 emission can be rewritten as the following: where, in Eq. (8), Period denotes the time span, I the identity matrix, and "+" the generalized inverse matrix. When the columns of the matrix X satisfy the condition of linear independence, + X = T X X −1 T X . Finally, changes in CO 2 emission for city i can be decomposed into the following drivers: where m denotes the corresponding drivers ( m = 1, 2, . . . , 5 ). The change in CO 2 emission for a specific city group can be decomposed as where g ( g = g 1 , g 2 , · · · , g n ) denotes different city groups. Equations (9) and (10) consider five drivers, i.e., economic scale ( C Y ), carbon intensity ( C CI ), population ( C P ), CO 2 emission per capita ( C PC ) and GDP per capita ( C PY ).

Gaussian Kuznets curve.
According to the EKC theory 28,29 , pollution such as CO 2 emission should increase with economic development and then decline after reaching a peak. Based on such assumption, we used this curve to link the CO 2 emission and GDP in China.
The Gaussian Kuznets curve can be expressed as where pc denotes the CO 2 emission per capita, py the GDP per capita; parameters a , b , and c reflect the peak CO 2 emission per capita (maximum height of the function), the GDP per capita at vertex a (position of the function along the horizontal axis), and the shape of the function, respectively.
(1) www.nature.com/scientificreports/ We used the minpack.lm R package to obtain the abovementioned parameters for each province and city (see Figs. S3-1 and S3-2). Given that py peak in provinces and cities followed a normal distribution and logarithmic normal distribution in the study, we then obtained the overall peak by calculating the mean value from all provinces and cities at 70%, 80%, and 90% confidence intervals. We utilized the CO 2 emission per capita in Eq. (11) as an exogenous variable to project China's national CO 2 emission peak at different confidence intervals.
Wang et al. 12 also applied the same method to estimate China's carbon peak based on 50 cities from 2000 to 2016. However, there remains uncertainty for estimating China's carbon peak; hence, a large-scale study covering most cities and counties remains warranted. Moreover, due to recent changes in CO 2 emission of China, a new and comprehensive analysis is required. The Chinese government conducted the priority-peak policy for China's carbon peak while there remains no study quantifying the status quo of carbon peaks at local levels. The identification of carbon peaks at different levels, especially at city and county levels, is of great importance for formulating carbon peak strategies in the country and future carbon neutrality target by 2060.
For robust results, we estimated China's overall carbon peak at provincial and city levels based on the updated datasets in 2019. Further, we classified the provinces, cities, and counties according to their position in the curve (Fig. 4d).
Scenario analysis. The scenario analysis was conducted to consider the impacts of COVID-19 outbreak and the slump in CI decline. The scenarios were based on the changes in economic growth rates and CI, the greatest positive and negative drivers, respectively, contributing to the increase in CO 2 emission based on the decomposition analysis.
To project the trajectories of CO 2 emission, we made the following assumptions (supplemental method S1). We set three scenarios, namely the BAU, moderate, and advanced, to describe China's economy in the next 15 years. In the BAU scenario, no significant changes in the emission reduction policies and technical progress will occur 39 . In the moderate scenario, the overall growth rate of the Chinese economy will be higher than that in the BAU scenario by implementing the double circulation strategy and increasing the investments in technological innovation. In the advanced scenario, a growth rate higher than that in the moderate scenario will occur by implementing an in-depth economic structural optimization and releasing high-tech benefits. We then calculated the economic AAGRs during the 13th FYP for the BAU scenario, both 12th and 13th FYP (2011-2020) for the moderate scenario and the 12th FYP for the advanced scenario. In the moderate scenario, we excluded the impact of the pandemic on the economy. Notably, using the latest 2020 economic growth data of China's economy improved the accuracy of scenarios and provided a new benchmark for carbon peak analysis. (Tables S2-1, S2-3, and S2-5).
We assumed three corresponding AAGRs to reduce the CI in 2021-2035 based on the three scenarios. In the BAU scenario, the AAGRs would be similar to the 13th FYP period, and the impact of the coronavirus on CI reduction would be short-term. In the moderate scenario, the AAGRs would be similar to those in the last decade (2011-2020), and the CI reduction would be less affected by the pandemic. In addition, low-carbon, energysaving technologies, and new power generation factories would be established. In the advanced scenario, the AAGRs would be similar to those in the 12th FYP period, and strengthened CI reduction would be implemented as most provinces would exceed the targets during that period. The advanced scenario requires technological breakthroughs such as CCS and advanced nuclear energy technologies (Tables S2-2, S2-4 and S2-6).
Social network analysis. SNA is an interdisciplinary analysis method for "relation data." SNA can be used for determining spatial pattern of many topics such as economic growth, energy consumption and carbon emission. In this study, we used SNA to capture the spatial pattern of interprovincial CO 2 emission network in the post-pandemic era under the carbon peak background for China. According to Scott 40 and Furht 41 , the network is defined as a group of nodes connected by links, in which "nodes" in the network indicate "participants". "Nodes" in the study refer to "provinces" and thus "connection" represents the relationship between provinces.
To analyze the complex interprovincial carbon emission network, we use provincial CO2 emission data as the network "node", and defined the "line" between two nodes in the network as spatial correlation of carbon emission. Similar to previous studies (e.g., 42 ), we used a modified gravity model to construct the spatial correlation of interprovincial carbon emission in China as follows: where i and j are compared provinces; y ij is the gravitation of carbon emission between province i and province j ; C is carbon emission; P and G denote population scale and GDP; g and D represent GDP per capita and the spherical distance between the provincial capitals; C i C i +C j reflects the gravity coefficient of carbon emission from province i to province j.
Based on Eq. (12), we can construct the gravity matrix of interprovincial carbon emission and obtain the complex interprovincial carbon emission network above. We then further analyzed the network characteristics with emphasis on the overall network characteristics and individual network characteristics. We use network tie, network density, network hierarchy and network efficiency to describe the overall network characteristics, and use degree centrality, betweenness centrality and closeness centrality to analyze the individual networks characteristics (supplemental method S1). www.nature.com/scientificreports/ Data process. The CO 2 emission data ( C ) of the provinces were collected from Shan et al. 43 and Shan et al. 44 while that of the cities and counties were gathered from Chen et al., 45 . Furthermore, we updated the dataset of China's CO 2 emissions in 2018-2019 at all levels using a top-down approach where we found that the annual ratios of CO 2 emissions at all levels to the national CO 2 emission does not change significantly. We, therefore, assumed that the ratios in most areas at all levels would follow their changing trends in 2018 and 2019. We then used Holt-Winters filter method to forecast the CO 2 emission at all levels. We found that the forecasting errors of aggregated CO 2 emissions were 0.01% in 2018 and 2019 in provinces, − 0.10% in 2018 and − 0.08% in 2019 in cities, and 0.12% in 2018 and 0.27% in 2019 in counties (Supplemental data S1). The GDP ( Y ) data of provinces, cities, and counties were obtained from the NBSC, China Premium Database (CEIC) 46 , and China County Statistical Yearbook (1999-2019) 47 , respectively. The population ( P ) data of the provinces were obtained from the NBSC, while that of the cities and counties were collected from the CEIC www.nature.com/scientificreports/ and China Stock Market Accounting Research (CSMAR) 48 , respectively, in which some missing values were completed by spline interpolation as the resident population of a place usually would not change dramatically during a certain period. The future population at provincial level in SNA analysis was collected from Chen et al. 49 .
To minimize the impact of missing data on the analysis, we used the datasets from the provinces in 1997-2019, cities in 2002-2019, and counties in 2003-2018.
To determine the drivers of CO 2 emission changes, we classified the cities into nine groups based on population scale and economic structure. Following the Chinese government's classification scheme in 2014 50 , the cities were grouped into megacities (population of > 10 million), very large cities (population of 5-10 million), large cities (population of 3-5 million), midsize cities-I (population of 1-3 million), midsize cities-II (population of 0.5-1 million), and small cities (population of < 0.5 million). Similar to Ramaswami et al. 51 and Tong et al. 52 , we also divided the cities into three city groups by economic structure: the highly industrial in which the secondary industrial GDP% was higher than the national average plus one standard deviation, highly commercial where the tertiary industrial GDP percentage was higher than the national average plus one standard deviation, and mixed-economy cities that did not fall in the abovementioned two types. We also classified the provinces into three regions, i.e., the eastern, central and western regions according to Chen et al. 53 . Figure 8a,c,e described the relationships between GDP per capita and CO 2 emission per capita across regions in 2019, implying that there may exist a simple relationship between the two variables above despite the skewed spatial distributions. Further, Fig. 8b,d,f depicted the changing trends of CO 2 emission in Chinese provinces, cities and counties over 1997-2019, indicating carbon emissions among regions also presented skewed distributions with increasing trends over time. Therefore, the heterogeneity of carbon emissions at different levels should not be neglected in carbon peak analysis.

Data availability
See the data process section for historical CO 2 emission, GDP, population at all levels in the study and the estimated CO 2 emission in 2018 and 2019 at all levels are available from the corresponding authors upon request. www.nature.com/scientificreports/