Spatial Heterogeneity of the Carbon Emission E ﬀ ect Resulting from Urban Expansion among Three Coastal Agglomerations in China

: Land-use change, particularly urban expansion, can greatly a ﬀ ect the carbon balance, both from the aspects of terrestrial ecosystems and anthropogenic carbon emissions. Coastal China is a typical region of rapid urban expansion, and obvious spatial heterogeneity exists from the north to south. However, the di ﬀ erent urban change characteristics and the e ﬀ ect on carbon balance remain undetermined. By unifying the spatial-temporal resolution of carbon source and sink data, we e ﬀ ectively compared the carbon budgets of three coastal urban agglomerations in China. The results show that all of the three urban agglomerations have undergone an obvious urban expansion process, with the built-up area increasing from 1.03 × 10 4 km 2 in 2000 to 3.06 × 10 4 km 2 in 2013. For Beijing–Tianjin–Hebei (BTH), the built-up area gradually expanded. The built-up area in the Yangtze River Delta (YRD) gradually changed before 2007 but rapidly grew thereafter. The built-up expansion of the Pearl River Delta (PRD) passed through three growing stages and showed the largest mean patch size. Carbon emission spatial patterns in the three urban agglomerations are consistent with their economic development, from which the net ecosystem production (NEP) spatial patterns are very di ﬀ erent. Compared to carbon emissions, NEP has a carbon sink e ﬀ ect and can absorb some carbon emissions, but the amounts were all much lower than the carbon emissions in the three urban agglomerations. The carbon sink e ﬀ ect in the Yangtze River Delta is the most obvious, with the Pearl River Delta following, and the lowest e ﬀ ect is in Beijing–Tianjin–Hebei. Finally, a scientiﬁc basis for policy-making is provided for viable CO 2 emission mitigation policies.


Introduction
The carbon cycle is a main driver of global change [1]. The expanding mass-energy exchange on the land surface has accelerated the asymmetry of the carbon cycle. More carbon emissions and less carbon absorption has resulted in increasingly negative impacts on the global climate and environment [2][3][4]. In addition to natural factors, global warming is closely related to CO 2 (carbon dioxide) emissions produced by human socio-economic activities [5,6]. According to the IPCC (Intergovernmental Panel on Climate Change) 5th Assessment Report, approximately 816 ± 124 Gt CO 2 of anthropogenic CO 2 emissions have not been absorbed and remain in the atmosphere, probably resulting in the observed warming since the mid-20th century. Improving the carbon sequestration of terrestrial ecosystems and reducing greenhouse gas emissions are internationally recognized as two of the crucial ways to mitigate climate change [7,8]. As centres of economic activities, population migration, and energy consumption, urban areas play a significant role in addressing CO 2 emissions and global climate change [9], particularly in rapidly developing countries [10,11]. It has been reported that 2% of the global land in urban areas includes more than 50% of the world's population and approximately 75% of the global carbon emissions [12,13]. Thus, examination of the carbon budget in rapidly expanding urban regions is necessary.
Under the government's reform and opening-up policies since 1978, China is undergoing rapid urbanization, industrial processes and land-use/-cover change. Built-up land, where highly populated, has dramatically expanded and occupied large areas of ecological land, especially in coastal regions [14][15][16]. The process has threatened China's sustainable development and the long-term stability of the global climate, which has raised global concerns [17]. As the expansion rate is still rapidly accelerating and has increasingly high carbon emissions intensity, China is encountering intense pressure to reduce its CO 2 emissions [18]. Yangtze River Delta (YRD), Pearl River Delta (PRD) and Beijing-Tianjin-Hebei (BTH) are three of the coastal urban agglomerations in China. As population growth and economic development are concentrated, these regions contribute most to CO 2 release with significant land-use and land-cover change [19][20][21]. Zha et al. found that CO 2 release is higher in urban land than in rural land [22]. CO 2 concentration would increase when forestry lands convert to agriculture [23]. Meanwhile, the three urban agglomerations are distinguished by different natural conditions and socio-economic development. For natural conditions, YRD locates by China's greatest river with mild climate; climate is dry in BTH with worse vegetation growth; while vegetation carbon fixation is the best in PRD with synchronous rain and heat. For socio-economic development, the urbanization process is rapid, and urban development is quite even in YRD; BTH shows lower urban industrial land-use efficiency; and city clusters are most obvious in PRD [24][25][26]. It is significant and feasible to discuss how the natural and man-made factors affect the carbon sources and sinks for possible low carbon development strategies in the three urban agglomerations. There is an impressive and growing literature regarding carbon sources and sinks in these three urban agglomerations [19][20][21][27][28][29]. However, currently, there seem to be no comparable studies that present the same methodology and same data source.
Different data sources have been collected to examine carbon sources and sinks, including field measurements, government statistics and optical remote sensing data. Morton and Andreas attempted to improve the field measurement of the net ecosystem exchange CO 2 flux to identify peatlands acting as either a net CO 2 uptake or release [30]. Using field measurements, many studies have focused on carbon flux calculation to explore carbon sources and sinks in different single ecosystems of a specific type, but these studies are limited in data size and field scale and fail to be directly compared [31,32]. Rahman and Kashem provided the possibility to examine the relationships between carbon emissions, energy consumption and industrial growth in Bangladesh using economic data from the Word Development Indicator and the Central Bank of Bangladesh [33]. Socio-economic statistics published by governments has enabled the use of a top-down method to estimate carbon emissions, but the lack of spatial distribution and the inconsistency of the statistics quality lead to lower data mining accessibility and comparability [34].
Distinctly advantageous for detecting spatial-temporal variation and capturing data at a large scale, data from remote sensing aids research on carbon source and sink more objectively and effectively. It is remote-sensing capabilities that a large number of researchers have previously focused on in studying carbon sources and sinks. Chuai et al. examined the net ecosystem production (NEP) trend, an indicator of whether an ecosystem can fix or release carbon from or into the atmosphere using Moderate Resolution Imaging Spectroradiometer data, meteorological data, and soil organic carbon data [35]. Abdalla and Fadul assessed the relationship between green cover and carbon emissions from cars using remote-sensing data from Landsat and Quick Bird satellites [36]. Meng et al. used nighttime light imagery and statistical energy data to estimate CO 2 emissions [37]. All of these studies either targeted the entirety of China or separately investigated only one of the regions for NEP or carbon emissions. It is still missing that a comprehensive analysis of carbon budgets examination for both socially and physically derived carbon in spatial dimension.
Our overall objective was the presentation of an analytical framework to study the spatial and temporal pattern of regional carbon budgets in the three urban agglomerations. By unifying the spatial-temporal resolution of carbon source and sink data, attempts are made to compare carbon budgets in different urban agglomerations to enhance the understanding of the natural-human dual structure of carbon effects. Then, a scientific basis for policy-making is provided for viable CO 2 emission mitigation policies. The next section addresses the study areas and data sources. The third section introduces the study methods, including urban information extraction, NEP calculation, carbon emission calculation, carbon budgets calculation and spatial statistics. Then we come to the results on the urban expansion characteristics, carbon budgets statistics and spatial patterns of the three urban agglomerations. Finally, we discuss and draw conclusions.

Study Areas and Data Sources
YRD, PRD and BTH are three of the coastal urban agglomerations in China (Figure 1), which contribute most to CO 2 emissions with significant land-use and land-cover change. Occupying a very important strategic position in China's modernization and opening up, the YRD is composed of 26 cities, including the Shanghai city and another 25 cities of the Jiangsu, Zhejiang, and Anhui provinces. The PRD is formed mainly by 14 cities of the Guangdong Province in Southern China, characterized by economic vitality and technological innovation. BTH, in Northern China, is the political and cultural centre of the nation, including the cities of Beijing and Tianjin and the whole of Hebei Province. Our overall objective was the presentation of an analytical framework to study the spatial and temporal pattern of regional carbon budgets in the three urban agglomerations. By unifying the spatial-temporal resolution of carbon source and sink data, attempts are made to compare carbon budgets in different urban agglomerations to enhance the understanding of the natural-human dual structure of carbon effects. Then, a scientific basis for policy-making is provided for viable CO2 emission mitigation policies. The next section addresses the study areas and data sources. The third section introduces the study methods, including urban information extraction, NEP calculation, carbon emission calculation, carbon budgets calculation and spatial statistics. Then we come to the results on the urban expansion characteristics, carbon budgets statistics and spatial patterns of the three urban agglomerations. Finally, we discuss and draw conclusions.  The annual Moderate Resolution Imaging Spectroradiometer(MODIS) net primary productivity (NPP) data from 2000 to 2013 used in this study were downloaded from the Numerical Terradynamic Simulation Group (NTSG) at the University of Montana (http://www.ntsg.umt.edu/). The dataset is in a TIF format and has a resolution of 30-arcsec (approximately 1-km). A detailed description of the NPP model calculation process can be obtained from Zhang et al. [38]. The accuracy of the product has been validated as being consistent with field-observed NPP data [39].  The annual Moderate Resolution Imaging Spectroradiometer(MODIS) net primary productivity (NPP) data from 2000 to 2013 used in this study were downloaded from the Numerical Terradynamic Simulation Group (NTSG) at the University of Montana (http://www.ntsg.umt.edu/). The dataset is in a TIF format and has a resolution of 30-arcsec (approximately 1-km). A detailed description of the NPP model calculation process can be obtained from Zhang et al. [38]. The accuracy of the product has been validated as being consistent with field-observed NPP data [39]. We extracted the global map with the overlay of the study areas. Meteorological data (precipitation and temperature) observed These images were downloaded from the National Geophysical Data Center (NGDC) affiliated with the American National Oceanic and Atmospheric Administration (NOAA) (https://www.ngdc.noaa.gov/). The product contains cloud-free average radiance values that have undergone an outlier removal process to remove fires and other ephemeral lights; grey values range from 1-63, and the resolution is 30 arcsec (approximately 1 km). As nighttime light data slightly vary from different sensors, we adopted the pre-processing approach from Cao to conduct data fusion, image segmentation, irradiance calibration and coordinate translation [40]. The annual energy consumption data of 30 provinces in China from 2000 to 2013 were collected from the China Energy Statistical Yearbook. Maps in the article were all made by using ArcGIS [9.3], (http://www.esri.com/software/arcgis).

Urban Information Extraction
The nighttime light data originated from OLS is sound source data to monitor human activities and has been used to study carbon emissions in a considerable amount of research, as human activity is the main source of carbon emissions. Many studies indicate that DMSP/OLS nighttime light data correlate with carbon emissions. Moreover, nighttime light data can be applied to urban area extraction. We used the thresholding technique along with ancillary data to extract the urban information of the three urban agglomerations [41]. Liu et al. divided China into eight economic regions, extracting a single threshold for each [41]. The YRD is in Eastern Coastal China, the PRD is in Southern Coastal China and BTH is in Northern Coastal China.

Net Ecosystem Production (NEP) Calculation
The net ecosystem production (NEP) indicates the carbon fixation capacity of the terrestrial ecosystem over the short term. The NEP depends strongly on climate and vegetation, reflecting the impacts of nature more than man-made impacts [42]. The NEP can be calculated by subtracting the soil heterotrophic respiration (Rh) from the net primary production (NPP) as follows: where NEP is the annual net ecosystem productivity (gC·m −2 .year −1 ), NPP is the annual net primary productivity (gC·m −2 ·year −1 ) directly provided by the MODIS products, and Rh is the annual soil heterotrophic respiration (gC·m −2 ·year −1 ) [35]. In this study, Rh was calculated from the relationship between Rs and Rh [35]. We collected Rs and Rh data from up to 101 groups, with the observed years from 1994 to 2013. The data included most ecosystems, with a wide distribution across China. According to the collected data, a linear equation presented the best fitting according to the following formula: where Rh is the annual soil heterotrophic respiration (gC·m −2 ·year −1 ) and Rs is the annual soil respiration (gC·m −2 ·year −1 ). were not used in the model parametrization. The GMSR presented a better simulation in China; thus, we used this mode on an annual scale as follows: where T is the annual mean air temperature ( • C), P is the mean monthly precipitation (cm), and SOC is the topsoil (0-20 cm) organic carbon storage density (kg C·m −2 ). An interpolation method was used to generate precipitation and temperature maps, and the inverse distance method was used to finish the interpolation process and set them as 1 km grid layers. The topsoil (0-20 cm) property data sets were obtained from the 2nd national Soil Survey. The grid SOC density data at a depth of 20 cm were obtained based on interpolation from the 1:4,000,000 SOC density vector data.

Carbon Emission Calculation
For carbon emission, energy consumption is a main man-made factor [44,45]. Again, the nighttime light data originated from OLS is used to study energy consumption. We investigated the relationships between nighttime light data and energy consumption at the provincial level by regression analysis. The research data covered 30 provinces in China from 2000 to 2013, which offered adequate data size to verify the effectiveness of regression analysis. Consistent with previous studies [46][47][48], we found that the correlation coefficient is highest with a linear fit (R 2 = 0.625). And we assumed that the correlation can be transformed from the provincial level to the 1 km 2 level. Thus, we produced the annual energy consumption grid maps by allocating the provincial energy consumption in proportion to the nighttime light value of the 1-km 2 grid. The formula is as follows: where EC is the annual energy consumption of a province (tC·km −2 ·year −1 ), and NL is the nighttime light values ranging from 1~63.

Carbon Budgets Calculation
By calculating the carbon absorption and emission at the same spatial resolution, we tried to subtract them from one another for comparison. The formula is as follows: where CB is the carbon budget comparing the carbon absorption and emission (gC·m −2 ·year −1 ).

Spatial Statistics
To investigate the distribution pattern of the grid data, spatial statistical tools in the ArcGIS software were adopted, such as mean patch size, shape index, spatial autocorrelation (Moran's I), directional distribution (standard deviational ellipse) and cluster and outlier analysis (Anselin Local Moran's I) [49]. Mean patch size (km 2 ) is defined as the total area of urban patches divided by patch numbers, representing the integrity of the built-up area. The shape index, which is the perimeter to area ratio, can be used to measure the complexity of the patch. Spatial autocorrelation measures spatial autocorrelation based on feature locations and attribute values using the Global Moran's I statistic. Directional distribution creates standard deviational ellipses to summarize the spatial characteristics of geographic features, such as central tendency, dispersion, and directional trends. Cluster and outlier analysis, given a set of weighted features, statistically identifies significant hot spots and cold spots, which depict high and low value collection areas, respectively, using the Anselin Local Moran's I statistic. Some papers can be consulted for more information regarding the tools [50][51][52].

Urban Expansion Characteristics of the Three Urban Agglomerations
We presented the built-up area to describe urban expansion. All of the three urban agglomerations underwent an urban expansion process between 2000 and 2013, with the built-up area increasing from 1.03 × 10 4 km 2 to 3.06 × 10 4 km 2 on the whole. As shown in Figure 2   The shape index can be used to measure the complexity of the patch. From the line chart shown in Figure 4, we found that the shape index decreased in all three urban agglomerations. The shape index is highest in BTH (403.09), followed by the YRD (359.96) and PRD (302.55).   The shape index can be used to measure the complexity of the patch. From the line chart shown in Figure 4, we found that the shape index decreased in all three urban agglomerations. The shape index is highest in BTH (403.09), followed by the YRD (359.96) and PRD (302.55). The shape index can be used to measure the complexity of the patch. From the line chart shown in Figure 4, we found that the shape index decreased in all three urban agglomerations. The shape index is highest in BTH (403.09), followed by the YRD (359.96) and PRD (302.55). Let us come to the information presented in the urban expansion map ( Figure 5). This shows the different urban expansion processes of the three urban agglomerations between 2000 and 2013. We assigned the contiguous built-up areas larger than 500 km 2 as the urban core zones. In BTH, the urban core zone is mainly in the Beijing and Tianjin downtown areas, which increasingly developed and combined with the surrounding clusters, such as the Tanggu and Fangshan districts, during the 14-year period. In the YRD, the urban core zone only includes downtown Shanghai. During the 14 years, downtown Shanghai combined with Suzhou, Wuxi and Changzhou; In addition, Nanjing, Hefei and Hangzhou developed as new urban core zones. In the PRD, the urban core zone is mainly in the Shenzhen and Guangzhou downtown areas, which combined with Dongguan, Foshan and Zhongshan to form a much larger urban core zone.  Let us come to the information presented in the urban expansion map ( Figure 5). This shows the different urban expansion processes of the three urban agglomerations between 2000 and 2013. We assigned the contiguous built-up areas larger than 500 km 2 as the urban core zones. In BTH, the urban core zone is mainly in the Beijing and Tianjin downtown areas, which increasingly developed and combined with the surrounding clusters, such as the Tanggu and Fangshan districts, during the 14-year period. In the YRD, the urban core zone only includes downtown Shanghai. During the 14 years, downtown Shanghai combined with Suzhou, Wuxi and Changzhou; In addition, Nanjing, Hefei and Hangzhou developed as new urban core zones. In the PRD, the urban core zone is mainly in the Shenzhen and Guangzhou downtown areas, which combined with Dongguan, Foshan and Zhongshan to form a much larger urban core zone. Let us come to the information presented in the urban expansion map ( Figure 5). This shows the different urban expansion processes of the three urban agglomerations between 2000 and 2013. We assigned the contiguous built-up areas larger than 500 km 2 as the urban core zones. In BTH, the urban core zone is mainly in the Beijing and Tianjin downtown areas, which increasingly developed and combined with the surrounding clusters, such as the Tanggu and Fangshan districts, during the 14-year period. In the YRD, the urban core zone only includes downtown Shanghai. During the 14 years, downtown Shanghai combined with Suzhou, Wuxi and Changzhou; In addition, Nanjing, Hefei and Hangzhou developed as new urban core zones. In the PRD, the urban core zone is mainly in the Shenzhen and Guangzhou downtown areas, which combined with Dongguan, Foshan and Zhongshan to form a much larger urban core zone.

NEP and Carbon Emission Statistics for the Three Urban Agglomerations
The NEP was evaluated from the aspects of mean value, standard deviation, and Moran's I (Table 1). During 2000-2013, the mean annual NEP shows that the NEP in the YRD and PRD seem to be approximately the same, while in BTH it is much lower and negative for most of the years. Standard deviation analysis during 2000-2013 shows that the NEP in the YRD and BTH gradually changed, and a weak fluctuation trend was found for the PRD. By calculating Moran's I, we found that the spatial aggregation of the NEP in the YRD and BTH is more intense than that in the PRD.
Extracting the NEP mean values in the built-up area (Table 1), we found large changes in all the three urban agglomerations, and the mean values are much lower than those of the whole urban agglomerations. The mean value is the highest in the YRD (31.59 gC·m −2 ·year −1 ), while it is negative in BTH (−48.22 gC·m −2 ·year −1 ) and the PRD (−13.92 gC·m −2 ·year −1 ). By calculating Moran's I, we found that the NEP spatial aggregation in the built-up area is less intense than that in the whole urban agglomeration.

NEP and Carbon Emission Statistics for the Three Urban Agglomerations
The NEP was evaluated from the aspects of mean value, standard deviation, and Moran's I (Table 1). During 2000-2013, the mean annual NEP shows that the NEP in the YRD and PRD seem to be approximately the same, while in BTH it is much lower and negative for most of the years. Standard deviation analysis during 2000-2013 shows that the NEP in the YRD and BTH gradually changed, and a weak fluctuation trend was found for the PRD. By calculating Moran's I, we found that the spatial aggregation of the NEP in the YRD and BTH is more intense than that in the PRD.
Extracting the NEP mean values in the built-up area (Table 1), we found large changes in all the three urban agglomerations, and the mean values are much lower than those of the whole urban agglomerations. The mean value is the highest in the YRD (31.59 gC·m −2 ·year −1 ), while it is negative in BTH (−48.22 gC·m −2 ·year −1 ) and the PRD (−13.92 gC·m −2 ·year −1 ). By calculating Moran's I, we found that the NEP spatial aggregation in the built-up area is less intense than that in the whole urban agglomeration.
Statistics from the 2000-2013 annual carbon emission grid data ( Table 2) suggest notable increasing trends in all three urban agglomerations. The PRD has the lowest carbon emission. Carbon emissions in the YRD and BTH are similar. Meanwhile, variation coefficients of carbon emission decreased during the 14 years, which shows that the carbon emission values increasingly concentrated. Calculation of Moran's I suggests that the spatial aggregation of carbon emission is highest in the YRD, followed by the PRD and BTH. The 2000-2013 carbon budget calculation (Table 3) demonstrates an evident increasing trend as a carbon source, except for the years between 2000 and 2004 in the PRD. Carbon liabilities are the most evident in BTH, followed by the YRD and PRD. Calculation of Moran's I shows high spatial aggregation of the carbon budget in the YRD.

Spatial Pattern of Carbon Source and Sink
The carbon emission spatial patterns in the three urban agglomerations are consistent with their economic development to a certain extent, with increasing trends and gradual development [53]. In BTH (Figure 6), hot spots concentrate in the downtown of each major city, particularly Beijing and Tianjin. In southern BTH, hotspots are not obvious in 2000, while in 2013, Shijiazhuang, Handan and Anyang appear to be hot regions. In the YRD (Figure 7), hot spots mainly occur in Shanghai and the surrounding areas, southern Jiangsu Province (Suzhou, Wuxi, Changzhou and Nanjing City) and northern Zhejiang Province (Hangzhou City). Downtown Hefei city is also a hotspot. The YRD hot regions are much larger and more contiguous in 2013 than in 2000. In the PRD (Figure 8), hot spots are concentrated in the core of the Pearl River Estuary in the south, downtown Guangzhou, Shenzhen and Zhuhai and the area among them. Cold spots are spread over the periphery of the north, east and west in 2000, but with some hotspots occurring in 2013. BTH (Figure 6), hot spots concentrate in the downtown of each major city, particularly Beijing and Tianjin. In southern BTH, hotspots are not obvious in 2000, while in 2013, Shijiazhuang, Handan and Anyang appear to be hot regions. In the YRD (Figure 7), hot spots mainly occur in Shanghai and the surrounding areas, southern Jiangsu Province (Suzhou, Wuxi, Changzhou and Nanjing City) and northern Zhejiang Province (Hangzhou City). Downtown Hefei city is also a hotspot. The YRD hot regions are much larger and more contiguous in 2013 than in 2000. In the PRD (Figure 8), hot spots are concentrated in the core of the Pearl River Estuary in the south, downtown Guangzhou, Shenzhen and Zhuhai and the area among them. Cold spots are spread over the periphery of the north, east and west in 2000, but with some hotspots occurring in 2013.    However, the NEP spatial patterns in the three urban agglomerations are very different from the carbon emission patterns. In BTH (Figure 9), the hot spots are mainly in Qinhuangdao counties in the east and the junction of Shijiazhuang, Baoding and Hengshui in the south. Cold spots mainly occur on the outskirts of Beijing and southern Chengde. In the YRD (Figure 10), hot spots occur along the northern coastal areas, such as Yancheng and Nantong in Jiangsu Province, and the southern areas, such as the junction of Taizhou, Ningbo and Shaoxing in Zhejiang Province. Cold spots occur around downtown areas in the western and northern Anhui Province and are dispersed in southern Jiangsu Province and northern Zhejiang Province. In the PRD (Figure 11), hot spots occur at the junction of Huizhou, Heyuan and Shanwei in the east. Cold spots mainly occur in the west, from Qingyuan in the north to Jiangmen in the south. The high NEP value is typically well determined by good vegetation growth status and moderate climatic conditions [54,55]. The aforementioned findings show that the junctions of the cities in the three agglomerations are well vegetated. We are aware that cold spots of carbon sink do not appear in the core urban areas of the three urban agglomerations probably because of the government-managed greening measures.      By carbon budget calculation, we explored the spatial pattern of carbon source and sink in the three urban agglomerations with sources larger than sinks. In BTH (Figure 12), carbon sinks mainly occurred in Qinhuangdao; Zhangjiakou in the north and Baoding, Hengshui, Shijiazhuang in the southwest. From 2000 to 2013, carbon sinks in BTH seem to move from the south to north. In the YRD (Figure 13), the carbon sinks mainly occur in Chuzhou, Chaohu, Anqing, Chizhou, and Xuancheng in the west; the outskirts of Hangzhou, Jinhua, Shaoxing, Taizhou, Ningbo in the south and Yancheng in the north. From 2000 to 2013, the carbon sink in the central and the northern YRD greatly decreased. In the PRD (Figure 14), carbon sinks occur on the periphery, mainly Yunfu, Zhaoqing, Qingyuan, Shaoguan, Hequan, Huizhou and Shanwei. From 2000 to 2013, carbon sinks in the PRD decreased but not significantly. YRD (Figure 13), the carbon sinks mainly occur in Chuzhou, Chaohu, Anqing, Chizhou, and Xuancheng in the west; the outskirts of Hangzhou, Jinhua, Shaoxing, Taizhou, Ningbo in the south and Yancheng in the north. From 2000 to 2013, the carbon sink in the central and the northern YRD greatly decreased. In the PRD (Figure 14), carbon sinks occur on the periphery, mainly Yunfu, Zhaoqing, Qingyuan, Shaoguan, Hequan, Huizhou and Shanwei. From 2000 to 2013, carbon sinks in the PRD decreased but not significantly.   Xuancheng in the west; the outskirts of Hangzhou, Jinhua, Shaoxing, Taizhou, Ningbo in the south and Yancheng in the north. From 2000 to 2013, the carbon sink in the central and the northern YRD greatly decreased. In the PRD (Figure 14), carbon sinks occur on the periphery, mainly Yunfu, Zhaoqing, Qingyuan, Shaoguan, Hequan, Huizhou and Shanwei. From 2000 to 2013, carbon sinks in the PRD decreased but not significantly.

Discussion
Studies on the NEP and energy consumption as important indicators to understand the natural-human dual structure of carbon effects are not new [56][57][58]. The NEP and energy consumption calculations in this study have been effectively verified by previous studies [35,[46][47][48]. Compared with previous studies, however, carbon budget estimations in this study have advantages. By unifying the spatial resolution (approximately 1 km), we provided the possibility to generate a carbon budget comparison in a locally regional scale, which is our main contribution different from other research. BTH has the lowest NEP level and a high Moran's I level because of its relatively dry environment that prevents vegetation growth [35,59]. In view of its vulnerable ecology, a favourable policy on ecological protection should be adopted here, particularly in the location where the NEP is low. Carbon emission here is the highest of the three urban agglomerations and highly concentrated in the core zone. Industry should be optimized and upgraded to reduce carbon emission. For example, the iron and steel industry is a main carbon source, and its energy efficiency should be improved [60,61]. In the spatial allocation of urban planning, there is no doubt that Beijing and Tianjin are the core cities, which should be given greater roles in stimulating the development of surrounding areas. By the urban expansion pattern analysis, development could well be southward and seaward. In the north and the west where the carbon sink occurs, ecological conservation should be a priority to expand the regional eco-capacity.
The YRD has a high NEP and Moran's I levels, indicating good vegetation growth status and moderate climatic conditions in the whole region [35]. The YRD has a high urbanization rate and a low level of carbon emission concentration. The YRD plays a leading role in Chinese economic growth, and considerable energy is needed for economic growth and social development [62]. The main industries of the YRD include electronic equipment manufacturing, transportation equipment manufacturing, electricity supply, ferrous metal smelting and processing, chemical materials and products manufacturing, and light industry such as the textile industry [63]. With flourishing tertiary industries and high-tech secondary industries, the ecological and environmental condition is better than that in BTH. However, the urban areas are expanding too rapidly, resulting in the destruction of rural arable land and natural resources [64]; thus, limiting construction land and using land more intensively should be a focus in this region. Shanghai is the core city, whose radiative effects are well exerted throughout the whole region. Nanjing and Hangzhou, sub-centres of the urban agglomeration, can more comprehensively develop to be a powerful force for regional development [65]. For the part in Anhui with a low NEP and unbalanced carbon emission, balanced development, industrial upgrading and ecological protection is required, on the prospect of

Discussion
Studies on the NEP and energy consumption as important indicators to understand the natural-human dual structure of carbon effects are not new [56][57][58]. The NEP and energy consumption calculations in this study have been effectively verified by previous studies [35,[46][47][48]. Compared with previous studies, however, carbon budget estimations in this study have advantages. By unifying the spatial resolution (approximately 1 km), we provided the possibility to generate a carbon budget comparison in a locally regional scale, which is our main contribution different from other research. BTH has the lowest NEP level and a high Moran's I level because of its relatively dry environment that prevents vegetation growth [35,59]. In view of its vulnerable ecology, a favourable policy on ecological protection should be adopted here, particularly in the location where the NEP is low. Carbon emission here is the highest of the three urban agglomerations and highly concentrated in the core zone. Industry should be optimized and upgraded to reduce carbon emission. For example, the iron and steel industry is a main carbon source, and its energy efficiency should be improved [60,61]. In the spatial allocation of urban planning, there is no doubt that Beijing and Tianjin are the core cities, which should be given greater roles in stimulating the development of surrounding areas. By the urban expansion pattern analysis, development could well be southward and seaward. In the north and the west where the carbon sink occurs, ecological conservation should be a priority to expand the regional eco-capacity.
The YRD has a high NEP and Moran's I levels, indicating good vegetation growth status and moderate climatic conditions in the whole region [35]. The YRD has a high urbanization rate and a low level of carbon emission concentration. The YRD plays a leading role in Chinese economic growth, and considerable energy is needed for economic growth and social development [62]. The main industries of the YRD include electronic equipment manufacturing, transportation equipment manufacturing, electricity supply, ferrous metal smelting and processing, chemical materials and products manufacturing, and light industry such as the textile industry [63]. With flourishing tertiary industries and high-tech secondary industries, the ecological and environmental condition is better than that in BTH. However, the urban areas are expanding too rapidly, resulting in the destruction of rural arable land and natural resources [64]; thus, limiting construction land and using land more intensively should be a focus in this region. Shanghai is the core city, whose radiative effects are well exerted throughout the whole region. Nanjing and Hangzhou, sub-centres of the urban agglomeration, can more comprehensively develop to be a powerful force for regional development [65]. For the part in Anhui with a low NEP and unbalanced carbon emission, balanced development, industrial upgrading and ecological protection is required, on the prospect of integrating into the Yangtze River Area [66]. In northern coastal areas, such as Yancheng and Nantong, with high NEPs but also high carbon sources, industry improvement should be particularly considered.
The PRD has a high NEP level and low Moran's I level because of the unbalanced vegetation growth status [35]. Urbanization occurred greatly according to policy guidance. For example, the coordinate development program released in 2004 deferred the local urban expansion [67], while the Asian Games in Guangzhou in 2011 greatly promoted urban land use in the surrounding regions [68]. The highest urban patch size suggests construction land clusters, such as new districts and development zones, which occupy too much land and exhibit low-efficiency utilization [69]. At the forefront of China's reform and opening up, the PRD has become the largest global manufacturing base. The PRD has undergone manufacturing relocation because of severe land and labour shortages, as well as rising rent costs in urban core zones, such as Shenzhen and Guangzhou downtown areas [70]. Balanced economic development should be a focus here because the development gap between the south-central areas and other locations is great, with significant characteristics of a regional layer structure [71,72]. Guangzhou, Shenzhen and Zhuhai are the absolute poles in this region, and their radiative effects should be given full priority. Other locations, such as Huizhou, Heyuan and Shanwei, can properly develop tourism with green hills and waters to bridge the economic gap [73,74]. Although the ecological and environmental conditions are fine, a protective policy should be assured, particularly in the west.
As the three urban agglomerations underwent rapid urban expansion between 2000 and 2013, it became urgent to optimize the urban size and structure and bring about positive economic and social impacts. Consistent with the urban planning policy, a balance should be sought between construction land for economic development and other land for ecological protection in the three urban agglomerations. For BTH, a regional synergetic strategy should be implemented, particularly in the promotion of joint industries and cooperative ecological protection. The YRD, which has world-class development prospects, should focus on limiting construction land and optimizing resource allocation. The PRD, the whole region in the same province, should realize integration development with a unified advantage.

Conclusions
BTH, YRD and PRD are three of the coastal urban agglomerations in China. As population growth and economic development have been concentrated in these regions during the past 20 years, these regions are typical developed regions in China. We presented an analytical framework to study the spatial and temporal pattern of regional carbon budgets in the three regions and made a comparison. By unifying the spatial-temporal resolution of carbon source and sink data, we made it possible to compare carbon budgets in different urban agglomerations. The adoption of the carbon effect study in these three regions is representative of other developing countries, which is supposed to be generalized to the other carbon budgets' calculation in a locally regional scale. But some problems remain to be solved. For example, parameters used in NEP calculations should be proved to be reliable or adjustable and can be extended to other regions. So, additional research ought to be conducted to test the practical application of the analytical framework.
In conclusion, as discussed above, urban expansion and carbon source and sink patterns are different among these three regions. The built-up area in BTH gradually expanded and combined with the surrounding clusters. Carbon liabilities are the most evident in BTH, with its ecological vulnerability and carbon-intensive industries. The built-up area in the YRD rapidly grew and generated many new urban core zones. Despite good ecological status, carbon emissions and liabilities in the YRD show high spatial aggregation. There is great polarization in the carbon budget pattern of the PRD between the urban core zone and its periphery. Nevertheless, industrial growth, regional equilibrium and ecological protection are common goals. Therefore, a land-use policy in the whole of the three urban agglomerations should be sought to balance the construction land for economic development and other land for ecological protection.