Spatial Pattern of a Comprehensive f E Index for Provincial Carbon Emissions in China

: China has committed to ambitious targets to reduce its carbon emissions in the next decades, in order to combat climate change and improve the environment. The realization of the targets depends on the fair and e ﬀ ective mitigation plans of all provinces. However, with varying ecological and environmental conditions and social-economic development, it is a critical issue to quantify the provinces’ e ﬀ orts equally. This paper proposed a comprehensive f E index in coordinating ecology, equity and economy, by accounting for carbon emissions and sinks to characterize provincial carbon emission status in China, from 2000 to 2017, which shows a spatial pattern of “boundary high, central low”. The provinces with higher f E value ( > 1.5) in boundary areas can be seen as “relative equality” provinces with good ecology circulation, equity and economic e ﬃ ciency. The provinces with lower f E value ( < 0.7) in central areas around Bohai Bay are regarded as “severe inequality” provinces, and are identiﬁed as the hot-spot provinces, which have emitted more CO 2 than their equity share by occupying the carbon emission space of other provinces in recent decades. These results could provide a reference for a provincial guide for carbon reduction and sustainable development of the low-carbon economy.


Introduction
Anthropogenic carbon emission since the industrial revolution has led to severe consequences for the environment and society [1]. Many scientists and policymakers have recognized that the essential environmental issues result from burning fossil fuels, leading to not only climate change, but also environmental issues, like land and water pollution, ecosystem problems, etc. [2,3]. Carbon emission has caught global attention, and thus it is essential to reduce it to acceptable levels in order to eliminate the harmful effects on the environment [4]. In 2015, the Paris agreement was reached, which was committed to "holding the increase in the global average temperature to well below 2 • C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5 • C above pre-industrial levels." It set out to improve and replace the Tokyo Protocol by abandoning the "top-down" international distributions, and encouraged the formulation of a "bottom-up" system through formulating the Nationally Determined Contributions (NDCs) [5].
China, as the largest carbon emitter in the world [6,7], has also committed a series of stringent carbon mitigation policies aiming "to reduce carbon emissions intensity by 40-45% by 2020 from the 2005 Net CO 2 emissions, which present the balance of carbon budget in a region [40], are calculated as CO 2 emissions (including CO 2 emission from energy consumption and industrial processes) minus CO 2 sinks (ecosystem carbon sinks and CCS technology sinks): where Y denotes net CO 2 emissions and is quoted in thousand tons. The net CO 2 emissions were used to calculate the f E index for 30 provinces. Notably, zero net CO 2 emission represents carbon neutrality.

Construction for the f E Index
As discussed in the introduction of this paper, it is not fair to study the spatial pattern of provincial carbon emissions only from the perspective of economy or demography. There are different environmental bearing capacities in different regions due to the influence of resource endowment, population distribution and economic development levels. Supposing that a region has higher carbon emissions, but it also has much greater carbon sink capacity, either ecological carbon sink or CCS sink, which would reduce carbon dioxide from the atmosphere. It is therefore difficult to say that regions with high carbon emissions are unequal. If one region's carbon emissions can develop in harmony with the environment, we can say that its carbon emission is within its ecological carrying capacity, and this is a so-called a good ecosystem cycle. To that end, we attempt to construct a comprehensive index that can include regional ecology, equity and economy. For example, the regional ecological carrying capacity can be represented by the ecological carrying index, which is defined as the ratio of its carbon sink capacity to its carbon emission. Meanwhile, the economic contribution index (ECI) is defined as the ratio of its economic contribution rate to its carbon emission, and the formula of ESI and ECI are as follows: where A i and A are the regional and national carbon sink values respectively, in MtCO 2 ; Y i and Y are the regional and national net CO 2 emissions, respectively, in MtCO 2 . G i and G are the regional and national GDP, respectively; CNY 10 8 . Therefore, inspired by the ecological support index (ESI) and economic contribution index (ECI) proposed in the evaluation matrix, the equitable distribution index (EDI) was proposed by taking the impact of a population and regional area on carbon emissions into account as where P i and P are the regional and national populations, respectively, in millions; S i and S are the regional and national areas, respectively, in km 2 ; and Y i and Y are the regional and national net CO 2 emissions, respectively, in MtCO 2 . Then, combining all three indexes of ESI, ECI, and EDI, a comprehensive indicator was constructed as shown in Equation (7).
where f E is a comprehensive index, which represents regional ecology (ESI), equity (EDI), and economy (ECI); ω 1 , ω 2 and ω 3 are the weighting factors and ω 1 + ω 2 + ω 3 = 1. The Delphi method was employed in this paper, based on the relative importance of two of the three indicators. In accordance with the principle of the analytic hierarchy process, the synergistic weight factors to ecology, equity, and economy are assigned as 0.4, 0.2, and 0.4, respectively.

Construction of Evaluation Matrix
In order to compare the f E index and analyze the spatial pattern of carbon emission, the evaluation matrix was constructed using the ESI and the ECI based on Lu's method [36]. China's provinces can be divided into four groups according to the conditions of the evaluation matrix in Table 1.

Data Sources
In order to calculate the index in China's 30 provinces between 2000 and 2017, three types of data were collected to represent provincial carbon emissions, carbon sink, and socio-economics.
Concerning carbon emissions, there are no official statistics accessible on provincial carbon emissions in China. Therefore, carbon emissions were calculated from fossil energy consumption of the 30 provinces from the China Energy Statistics Yearbooks [41]. To improve data accuracy, eight types of final energy consumption (ton) were used (such as raw coal, coke, crude oil, gasoline, kerosene, diesel oil, fuel oil, and natural gas). Carbon emission factors (tons CO 2 /ton of fuel) were obtained from the 2006 IPCC Guidelines for National Greenhouse Gas Inventories, which listed emission factors for each energy (IPCC, 2006). The data of cement output (ton) in each province were obtained from the China Cement Yearbooks [42].
In terms of carbon sink data, land use and CCS data for each province were collected. The land usage data, including forest land, grassland, and cropland, were from the China Statistical Yearbooks [43], while the carbon absorption factor was from the Food and Agriculture Organization (FAO), with its unit as ton CO 2 /ha [44]. The capture capacity of CCS in each project in China from 2000 to 2017 was obtained from the Global Status of CCS, with units in million tons per year [45]. Since the Global Status of CCS report mainly presented large-scale global integration projects in different countries, the data of small-scale CCS projects were obtained from China's Carbon Capture and Storage technology reports [46,47].
Besides the carbon emissions data, some socioeconomic data were collected as well. The annual population and the gross domestic product (GDP) data of 30 provinces (excluding Tibet, Hong Kong, Macao and Taiwan for lack of data) were derived from the China Statistical Yearbook [40]. To eliminate the impacts of inflation, the GDP was converted into the 2010 fixed price.
In addition, to interpolate the f E index with the Gini coefficient on a national scale, the national Gini coefficients, annual population, GDP and other socioeconomic data from 2000 to 2017 were derived from the World Bank [48]. Again, the GDP was converted into 2010 fixed price. Ecosystem carbon sink data in different countries, including forest land, grassland and cropland, were derived from the world FAO [44]. The annual CCS data was obtained from the global carbon capture institute [45].

Carbon Emissions and Sinks
The total carbon emissions and carbon sink capacity of each province, from 2000 to 2017, were calculated based on Equations (1) to (4), and results are listed in Table A1, and plotted in Figures 1  and 2, respectively. The carbon sink capacities remained basically unchanged during the last decades, except for Heilongjiang, Shaanxi, Shandong, Jilin, Hubei, and Hebei provinces (see Figure 2a and 2b). The carbon sink capacity increase observed in Heilongjiang and Jilin is mainly attributed to the six major afforestation projects launched by the Chinese government in the past 20 years, while the increase observed in Shaanxi, Shandong, Hubei, and Hebei provinces is largely due to the development of CCS projects. The growth of carbon emissions in China's provinces far exceeds that of carbon sinks, and significant spatial inconsistency is observed between carbon emissions and sink regions. It suggests adopting differentiated mitigation policies according to the different emission and sink conditions of each province.

Interpretation of the fE Index
Before analyzing the spatial pattern of carbon emissions, the fE index needs to be interpreted. This paper here considers the relationship between the fE index and the Gini coefficients, in order to provide probable equality interpretations of the fE index. In a statistical method, the curve of the Gini coefficient (adopted from the World Bank) versus the fE index at the national level was plotted (the  The carbon sink capacities remained basically unchanged during the last decades, except for Heilongjiang, Shaanxi, Shandong, Jilin, Hubei, and Hebei provinces (see Figure 2a and 2b). The carbon sink capacity increase observed in Heilongjiang and Jilin is mainly attributed to the six major afforestation projects launched by the Chinese government in the past 20 years, while the increase observed in Shaanxi, Shandong, Hubei, and Hebei provinces is largely due to the development of CCS projects. The growth of carbon emissions in China's provinces far exceeds that of carbon sinks, and significant spatial inconsistency is observed between carbon emissions and sink regions. It suggests adopting differentiated mitigation policies according to the different emission and sink conditions of each province.

Interpretation of the fE Index
Before analyzing the spatial pattern of carbon emissions, the fE index needs to be interpreted. This paper here considers the relationship between the fE index and the Gini coefficients, in order to provide probable equality interpretations of the fE index. In a statistical method, the curve of the Gini coefficient (adopted from the World Bank) versus the fE index at the national level was plotted (the The carbon emissions have gradually increased, and nearly two thirds of provinces had emitted more than 200 Mt from 2000 to 2010, and 2011 to 2017(see Figure 1a,b). These high emitter provinces are mainly located in the eastern and central regions, which is the main area of China's industrial development.
The carbon sink capacities remained basically unchanged during the last decades, except for Heilongjiang, Shaanxi, Shandong, Jilin, Hubei, and Hebei provinces (see Figure 2a,b). The carbon sink capacity increase observed in Heilongjiang and Jilin is mainly attributed to the six major afforestation projects launched by the Chinese government in the past 20 years, while the increase observed in Shaanxi, Shandong, Hubei, and Hebei provinces is largely due to the development of CCS projects.
The growth of carbon emissions in China's provinces far exceeds that of carbon sinks, and significant spatial inconsistency is observed between carbon emissions and sink regions. It suggests adopting differentiated mitigation policies according to the different emission and sink conditions of each province.

Interpretation of the f E Index
Before analyzing the spatial pattern of carbon emissions, the f E index needs to be interpreted. This paper here considers the relationship between the f E index and the Gini coefficients, in order to provide probable equality interpretations of the f E index. In a statistical method, the curve of the Gini coefficient (adopted from the World Bank) versus the f E index at the national level was plotted (the related data are shown in Appendix A Table A2). As shown in Figure 3, a negative nonlinear correlation was observed between the Gini coefficient and f E index, which is similar to the result of Hailemariam et al. (2019) [49], where the carbon emissions were shown to be negatively related to the income Gini coefficients. The higher f E index values correspond to the lower Gini coefficients, showing higher equality. Besides, it was found that the f E values of developed countries were higher and relatively concentrated (more than 1.0), with their Gini coefficients less than 0.4, while they were more scattered for developing countries. As a widely-used inequality indicator, a Gini coefficient equaling 0.3-0.4 is considered as the criteria of inequality. When the Gini coefficient is less than 0.3, it is considered as relative equality (>0.2) or absolute equality (<0.2); otherwise, it is relative inequality (0.4-0.5) or severe inequality (>0.5). By fitting the nonlinear regression of the f E index on the Gini coefficients, corresponding equity interpretations of different f E indexes are derived and listed in Table 2.
Energies 2020, 13, x FOR PEER REVIEW 7 of 16 related data are shown in appendix Table S2). As shown in Figure 3, a negative nonlinear correlation was observed between the Gini coefficient and fE index, which is similar to the result of Hailemariam et al. (2019) [49], where the carbon emissions were shown to be negatively related to the income Gini coefficients. The higher fE index values correspond to the lower Gini coefficients, showing higher equality. Besides, it was found that the fE values of developed countries were higher and relatively concentrated (more than 1.0), with their Gini coefficients less than 0.4, while they were more scattered for developing countries. As a widely-used inequality indicator, a Gini coefficient equaling 0.3-0.4 is considered as the criteria of inequality. When the Gini coefficient is less than 0.3, it is considered as relative equality (>0.2) or absolute equality (<0.2); otherwise, it is relative inequality (0.4-0.5) or severe inequality (>0.5). By fitting the nonlinear regression of the fE index on the Gini coefficients, corresponding equity interpretations of different fE indexes are derived and listed in Table 2.

Spatial Patterns of the fE Index
According to Equation (9), the fE indexes of 30 provinces from 2000 to 2017 were calculated and plotted in Figure 4. In general, the fE index showed a spatial pattern of "boundary high and central low ". The boundary provinces, such as Heilongjiang in the northeast, Inner Mongolia in the North, Xinjiang and Qinghai in the West, and Yunnan and Guangxi in the South, had a higher fE value (>1.5), which could be considered as "relative equality". It indicates that the carbon emissions in these provinces are in the state of a good ecosystem cycle, fair carbon emissions, and high economic efficiency. The fE values of Gansu, Fujian, and Hainan were between 1.0 and 1.5, and those of Anhui, Hubei, Chongqing, and Guizhou were between 0.7 and 1.0, which are relatively low fE values and rank between "proper equality" and "relative inequality", respectively. If these provinces do not take positive measures, they will inevitably occupy the emission space of other provinces in the future. Meanwhile, the provinces around the Bohai Bay (such as Shanxi, Liaoning, Hebei, Henan, Tianjin, Shandong and Ningxia) had lower fE values (<0.7). This is generally because almost all these

Spatial Patterns of the f E Index
According to Equation (9), the f E indexes of 30 provinces from 2000 to 2017 were calculated and plotted in Figure 4. In general, the f E index showed a spatial pattern of "boundary high and central low ". The boundary provinces, such as Heilongjiang in the northeast, Inner Mongolia in the North, Xinjiang and Qinghai in the West, and Yunnan and Guangxi in the South, had a higher f E value (>1.5), which could be considered as "relative equality". It indicates that the carbon emissions in these provinces are in the state of a good ecosystem cycle, fair carbon emissions, and high economic efficiency. The f E values of Gansu, Fujian, and Hainan were between 1.0 and 1.5, and those of Anhui, Hubei, Chongqing, and Guizhou were between 0.7 and 1.0, which are relatively low f E values and rank between "proper equality" and "relative inequality", respectively. If these provinces do not take positive measures, they will inevitably occupy the emission space of other provinces in the future. Meanwhile, the provinces around the Bohai Bay (such as Shanxi, Liaoning, Hebei, Henan, Tianjin, Energies 2020, 13, 2604 8 of 18 Shandong and Ningxia) had lower f E values (<0.7). This is generally because almost all these province's economy increases are extensive (excessive resource consumption, severe environment destruction and higher carbon emissions), resulting in "severe inequality". Thus, they are regarded as hot-spot provinces of carbon emissions in China. For their economic development in the future, stricter policies and measures should be taken to "limit and mitigate" the carbon emissions induced by these regions' rapid economic development. Otherwise, because of the limitation and irreplaceability of carbon emissions space, there will gradually develop a bottleneck of further development in these regions.
Energies 2020, 13, x FOR PEER REVIEW 8 of 16 as hot-spot provinces of carbon emissions in China. For their economic development in the future, stricter policies and measures should be taken to "limit and mitigate" the carbon emissions induced by these regions' rapid economic development. Otherwise, because of the limitation and irreplaceability of carbon emissions space, there will gradually develop a bottleneck of further development in these regions.  On the other hand, the fE values of Gansu, Hunan, Fujian, Hainan, and Jiangxi gradually decreased. This is mainly because these provinces still use traditional economic development models (i.e., economic increment from scale effect, excessive resource consumption, etc.), accompanied by a On the other hand, the f E values of Gansu, Hunan, Fujian, Hainan, and Jiangxi gradually decreased. This is mainly because these provinces still use traditional economic development models (i.e., economic increment from scale effect, excessive resource consumption, etc.), accompanied by a slow adjustment of industrial structures and insufficient technical innovation. Although these provinces are under "proper equality", if following the current decreasing trend, the f E values of these provinces will reduce below 1.0, and even into a state of "relative inequality". This will inevitably infringe on the interests of other regions in the near future, and bring negative effects upon economic development and the ecological environment.
The category, it is reasonable to believe that, with the support of CCS, these provinces will be on track for rapid low-carbon economic developments, bringing about a state of "relative equality" in the future.

Spatial Patterns Using Other Indicators
The spatial pattern of CEIs, calculated by the amount of CO 2 emissions per unit of GDP produced in 2000, 2010 and 2017, are shown in Figure 6a-c, respectively. In general, a significant decreasing trend of CEI in each province from 2000 to 2017 was observed. This, however, differs from the trend of the f E index. Spatially, the CEI gradually increased from southeast to the northwest. The CEIs in provinces of Fujian, Guangdong, Guangxi, Hainan, Shanghai and Zhejiang Provinces were lower, while those of Shanxi, Guizhou, Qinghai, Ningxia, Hebei, Shannxi, Gansu, Xinjiang and Inner Mongolia Provinces were higher in 2010. However, this is just a comparative description of the spatial pattern of absolute quantity, as the CEI only considers the relationship between CO 2 emissions and GDP in each province. If the rate of GDP grows faster than carbon emissions, CEI will fall. While this keeps with the current situation of China's economic development, it ignores the effect of other factors (e.g., carbon sinks) on the differences of carbon emissions. Thus, it is difficult to provide detailed insights into specific mitigation policies apart from the economic perspective.
Energies 2020, 13, x FOR PEER REVIEW 9 of 16 slow adjustment of industrial structures and insufficient technical innovation. Although these provinces are under "proper equality", if following the current decreasing trend, the fE values of these provinces will reduce below 1.0, and even into a state of "relative inequality". This will inevitably infringe on the interests of other regions in the near future, and bring negative effects upon economic development and the ecological environment.
The fE values of Hubei, Shandong, Jiangsu, Inner Mongolia, and Chongqing decreased from 2000 to 2010, and gradually increased from 2010 to 2017. The reasons for the increase in fE index may be both progressive emission reduction policies and the development of green and low-carbon technologies. Especially, CCS projects carried out in these provinces have greatly improved their carbon sinks (see Figure 2b). For example, the carbon sink capacity of Shandong increased from 59.9 Kt (fE = 0.44) in 2010 to 119.9 Kt (fE = 0.59) in 2017, and that of Jiangsu also increased from 5.78 Kt (fE = 0.53) in 2010 to 13.7 Kt (fE = 0.69) in 2017. Although their current carbon emissions still fall into the "severe inequality" category, it is reasonable to believe that, with the support of CCS, these provinces will be on track for rapid low-carbon economic developments, bringing about a state of "relative equality" in the future.

Spatial Patterns Using Other Indicators
The spatial pattern of CEIs, calculated by the amount of CO2 emissions per unit of GDP produced in 2000, 2010 and 2017, are shown in Figure 6a, 6b and 6c, respectively. In general, a significant decreasing trend of CEI in each province from 2000 to 2017 was observed. This, however, differs from the trend of the fE index. Spatially, the CEI gradually increased from southeast to the northwest. The CEIs in provinces of Fujian, Guangdong, Guangxi, Hainan, Shanghai and Zhejiang Provinces were lower, while those of Shanxi, Guizhou, Qinghai, Ningxia, Hebei, Shannxi, Gansu, Xinjiang and Inner Mongolia Provinces were higher in 2010. However, this is just a comparative description of the spatial pattern of absolute quantity, as the CEI only considers the relationship between CO2 emissions and GDP in each province. If the rate of GDP grows faster than carbon emissions, CEI will fall. While this keeps with the current situation of China's economic development, it ignores the effect of other factors (e.g., carbon sinks) on the differences of carbon emissions. Thus, it is difficult to provide detailed insights into specific mitigation policies apart from the economic perspective. When we turn to the matrix method, the spatial patterns of carbon emissions are described via their economy and ecology. The spatial pattern of matrices in 2000, 2010 and 2017 are shown in Figure  7a, 7b and 7c, respectively. It can be seen that the spatial distribution of matrices overall also shows imbalances between the provinces of the Southeast and the Northwest. Unlike the fE index, the evaluation matrix only divides China's 30 provinces into four groups by ESI and ECI. For instance, the provinces of Guangxi, Hainan, Jiangxi, Shaanxi and Shanghai are in Group 1, with higher economic development and higher carbon sink capacity. Although these provinces all rank in "equality" using the fE index, the equality conditions are different. The provinces of Guangxi and Shaanxi rank "relative equality", and the remaining provinces are recognized as "proper equality". When we turn to the matrix method, the spatial patterns of carbon emissions are described via their economy and ecology. The spatial pattern of matrices in 2000, 2010 and 2017 are shown in Figure 7a-c, respectively. It can be seen that the spatial distribution of matrices overall also shows imbalances between the provinces of the Southeast and the Northwest. Unlike the f E index, the evaluation matrix only divides China's 30 provinces into four groups by ESI and ECI. For instance, the provinces of Guangxi, Hainan, Jiangxi, Shaanxi and Shanghai are in Group 1, with higher economic development and higher carbon sink capacity. Although these provinces all rank in "equality" using the f E index, the equality conditions are different. The provinces of Guangxi and Shaanxi rank "relative equality", and the remaining provinces are recognized as "proper equality". In this respect, the f E index could help to analyze the spatial pattern of carbon emissions in more detail. Besides, when referring to the equity of carbon emissions, the matrix method also exposes its limitations, in that it evaluates the spatial pattern of carbon emissions only from the perspective of economy and ecology. As a result, it fails to provide an equity assessment, which is important for assigning the task of carbon reduction between regions.
Energies 2020, 13, x FOR PEER REVIEW 10 of 16 detail. Besides, when referring to the equity of carbon emissions, the matrix method also exposes its limitations, in that it evaluates the spatial pattern of carbon emissions only from the perspective of economy and ecology. As a result, it fails to provide an equity assessment, which is important for assigning the task of carbon reduction between regions.

Discussion
As mentioned in previous sections, the provinces can be divided into five levels based on the fE index: "absolute equality", "relative equality", "proper equality", "relative inequality" and "severe inequality". Without any region satisfying "absolute equality", China's 30 provinces fell into the remaining four levels. The averaged GDP and CEI of different years were shown in Figure 8a and Figure 8b, to discover the further insights of the fE index.
For the provinces of "relative equality", like Heilongjiang, Inner Mongolia, Xinjiang, Qinghai, Yunnan and Guangxi (fE > 1.5), their having high CEI and being located in the third group of the evaluation matrix required them to limit their carbon emissions immediately from the perspective of economic development. However, their GDP is lower than the average (Figure 8a), and their CEI is far above average (Figure 8b). Limiting carbon emissions only from economic development would certainly exacerbate the differences (i.e., income gap and CEI gap) among provinces, which is inconsistent with China's current development goal of "developing economy and eliminating poverty" [21]. By the fE index, though, these provinces are evaluated as displaying "relative equality", and will be able to relax emissions reduction policies appropriately to realize sustainable economic and social development.

Discussion
As mentioned in previous sections, the provinces can be divided into five levels based on the f E index: "absolute equality", "relative equality", "proper equality", "relative inequality" and "severe inequality". Without any region satisfying "absolute equality", China's 30 provinces fell into the remaining four levels. The averaged GDP and CEI of different years were shown in Figure 8a,b, to discover the further insights of the f E index.
Energies 2020, 13, x FOR PEER REVIEW 10 of 16 detail. Besides, when referring to the equity of carbon emissions, the matrix method also exposes its limitations, in that it evaluates the spatial pattern of carbon emissions only from the perspective of economy and ecology. As a result, it fails to provide an equity assessment, which is important for assigning the task of carbon reduction between regions.

Discussion
As mentioned in previous sections, the provinces can be divided into five levels based on the fE index: "absolute equality", "relative equality", "proper equality", "relative inequality" and "severe inequality". Without any region satisfying "absolute equality", China's 30 provinces fell into the remaining four levels. The averaged GDP and CEI of different years were shown in Figure 8a and Figure 8b, to discover the further insights of the fE index.
For the provinces of "relative equality", like Heilongjiang, Inner Mongolia, Xinjiang, Qinghai, Yunnan and Guangxi (fE > 1.5), their having high CEI and being located in the third group of the evaluation matrix required them to limit their carbon emissions immediately from the perspective of economic development. However, their GDP is lower than the average (Figure 8a), and their CEI is far above average (Figure 8b). Limiting carbon emissions only from economic development would certainly exacerbate the differences (i.e., income gap and CEI gap) among provinces, which is inconsistent with China's current development goal of "developing economy and eliminating poverty" [21]. By the fE index, though, these provinces are evaluated as displaying "relative equality", and will be able to relax emissions reduction policies appropriately to realize sustainable economic and social development. Those provinces of "proper equality" (e.g., Beijing, Fujian, Gansu, Guangdong, Hainan, Hunan, Jilin, Shanghai and Sichuan) and "relative equality" (e.g., Anhui, Chongqing, Guizhou, Zhejiang and Hubei) have a medium GDP but lower CEI (see Figure 8a and Figure 8b). Although these provinces are currently in proper low-carbon economic development, the fE index remains between equity and inequity due to higher population density and low ecological carbon sink capacity. In the future, For the provinces of "relative equality", like Heilongjiang, Inner Mongolia, Xinjiang, Qinghai, Yunnan and Guangxi (f E > 1.5), their having high CEI and being located in the third group of the evaluation matrix required them to limit their carbon emissions immediately from the perspective of economic development. However, their GDP is lower than the average (Figure 8a), and their CEI is far above average (Figure 8b). Limiting carbon emissions only from economic development would certainly exacerbate the differences (i.e., income gap and CEI gap) among provinces, which is inconsistent with China's current development goal of "developing economy and eliminating poverty" [21]. By the f E index, though, these provinces are evaluated as displaying "relative equality", and will be able to relax emissions reduction policies appropriately to realize sustainable economic and social development.
Those provinces of "proper equality" (e.g., Beijing, Fujian, Gansu, Guangdong, Hainan, Hunan, Jilin, Shanghai and Sichuan) and "relative equality" (e.g., Anhui, Chongqing, Guizhou, Zhejiang and Hubei) have a medium GDP but lower CEI (see Figure 8a,b). Although these provinces are currently in proper low-carbon economic development, the f E index remains between equity and inequity due to higher population density and low ecological carbon sink capacity. In the future, more attention should be given to harmony between humans and the environment. This should include steps such as improving people's awareness of environment protection, guiding the public's consumption choices and lifestyle, as well as encouraging people to adopt lifestyles that are geared towards low carbon.
Finally, the hot-spot provinces around Bohai Bay, like Shandong, Shanxi, Henan and Hebei, display a higher GDP (see Figure 8a) and have nearly the national average CEI (see Figure 8b). These are traditional industry-and energy-intense regions. In terms of emission reduction, these provinces should pay more attention to industrial transformation and upgrading, optimizing production technology, and improving energy efficiency. In addition, replacing fossil energy with clean energy is also an effective measure to reduce carbon emissions. Meanwhile, wind and nuclear energy have achieved good application results in coastal provinces [50]. Of course, industrial transformation and energy replacement will be a long and arduous process, which needs to be planned by the sources of policy formulating.
Compared with the influence of emissions reduction on economic development, improving carbon sink capacity had less impact. China's forest fraction coverage increased from 16.55% in 2000 to 21.93% in 2017 [51], but the ecological carbon sink capacities in these hot-spot provinces were far below average (see Figure 2). Fortunately, CCS technology is regarded as a very promising reduction technology in coordinating economic development with environmental protection. Some scholars predict that China has great CO 2 storage potential, which is estimated to be over 1841 Gt in theory, and CO 2 capture capacity was 0.623-0.753 Mtpa up to 2017 [52]. With the joint efforts and support of policy and finance, CCS will make a great contribution to the development of a low-carbon economy for China and the world in the future.
As mentioned above, the f E index describes the spatial pattern of carbon emissions with more aspects, and thus will provide a reference for the government to formulate targeted emission reduction strategies in different provinces. For example, differentiated measures and actions should be taken in different provinces according to their f E index. The lower the f E value, the stronger these measures and actions are expected to be. It is urgent for hot-spot provinces to proceed with compulsory industrial transformation, and even increase carbon taxes to urge improvement in energy efficiency and eliminate backward output capacity. Furthermore, for the "relative equality" provinces, it is necessary to guide them to improve production equipment, expand production scale and stimulate economic development. Thus, with the help of the f E index, China's carbon reduction will be guided in an ecological, equitable and efficient direction.

Conclusions
Based on the accounting of fossil energy carbon sources, and ecosystem and CCS carbon sinks, this paper proposes a new-built f E index to describe the spatial pattern of carbon emissions in China's provinces from 2000 to 2017.The conclusions are as follows: (1) The growth of carbon emissions in China's provinces far exceeds that of carbon sinks during 2000 to 2017, which shows a significant spatial inconsistency. High carbon emission can be attributed to rapid industrial development within the province's geographical area. Provinces with high carbon sink capacities are the result of various afforestation and CCS projects. (2) The f E index of China shows a spatial pattern of "boundary high, central low". The boundary provinces present a higher f E index (>1.5) and rank as "relative equality". The f E values in sub-central provinces are between "proper equality" and "relative inequality". The central provinces around the Bohai Bay rank as "severe inequality", with a lower f E index (<0.7), and these are hot-spot provinces of carbon emissions. Stricter policies should be taken to limit their carbon emissions induced by rapid economic development. Specifically, Beijing and Shanghai rank from "severe inequality" to "proper equality", which indicates that the carbon emissions in these areas are moving in a low-carbon, ecologically favorable and highefficiency direction. This is due to China's low-carbon economy policy. (4) The f E index, established under the framework of ecology, equity and economy, is able to characterize the spatial pattern of carbon emission in China from a new perspective and reasonably describe provincial carbon emission trends, which could provide references for the task of allocating carbon emissions in China's regional economic development and the implementation of low-carbon economic policy.
However, there are still some limitations in this study. The spatial patterns of carbon emissions are analyzed from 2000 to 2017, which is a relatively short period and not conducive to the long-term cyclic development of the whole ecosystem. In a future study, we would extend the f E index to more countries and a more prolonged period, to explore the trends of spatial patterns in carbon emissions. In addition, the data sources from cement, rough Word Bank indexes and IPCC 2006 may have certain limitations. Therefore, in the future, more emission sources should be evaluated and the corresponding method upgraded to acquire the emission data accurately.