How Does Urban Scale Influence Carbon Emissions?

Abstract

Low-carbon cities aim to minimize greenhouse gas emissions in the context of climate change in the process of urbanization. Maintaining these cities at an appropriate physical scale has been proven to contribute to carbon reduction. Therefore, this study extended the definition of the city scale to an integrated framework with three dimensions: the construction land area, population, and economy. The urban construction land of 258 cities in China during 2012 to 2019 was divided into commercial, industrial, residential, and traffic sectors, and carbon emissions were calculated for each. The regression relationship between carbon emissions and the urban scale revealed by panel data analysis showed the following conclusions: (1) carbon emissions were concentrated in north China, provincial capital cities, and municipalities directly under the central government during the research period, and the industrial sector was the main emission resource, accounting for more than 85% of the total emissions. (2) Carbon emissions per unit of land decreased with the increasing land scale, regardless of the land-use type. The growth rate of carbon emissions was slower than that of the population, and cities also became more efficient as their economic scale expanded. (3) Compared with small cities, the large ones benefited more from increasing commercial and traffic land areas, whereas industrial emissions for production needs exhibited significant agglomeration characteristics. Overall, low-carbon planning should focus on the driving role of provincial capital cities as large cities tend to be more efficient, and develop the emission reduction potential of major industrial cities as well.

1. Introduction

The United Nations’ Sustainable Development Goals call for climate actions to address global warming, and China has focused on how to develop cities more sustainably to promote the development of new-type urbanization nationwide. Occupying 2% of the world’s area, cities account for 75% of energy consumption [1]. While they require plenty of materials and commodities [2], cities also discharge waste into the environment during the process of urban metabolism. Thus, building low-carbon cities and improving carbon emission efficiency have become important objectives. However, which cities should we prioritize in urbanization? On what scale are cities most energy-saving? Economies of scale indicate that a larger scale means higher efficiency under certain conditions, but is this law still valid for the relationship between the city scale and carbon emissions? This study attempted to identify whether urbanization and urban growth is beneficial for carbon reduction.

Urbanization inevitably leads to changes in human energy-consuming activities, accompanied by the consumption of traditional fossil energy sources and the emitting of greenhouse gases such as carbon dioxide. From the perspective of efficiency, urban growth and technological innovation can increase carbon efficiency, but there may also be a rebound effect [3]. From the perspective of total emissions, the variability of carbon efficiency is reflected in the non-linear growth of carbon emissions in the process of urban development. Some scholars have corroborated the applicability of the Environmental Kuznets Curve (EKC) in the field of carbon emissions. Empirical studies have shown that the relationship between urbanization and CO₂ emissions is U-shaped, i.e., urbanization initially reduces CO₂ emissions, but after reaching a threshold level, it increases the CO₂ emissions [4,5]. Carbon dioxide emissions have increased significantly due to urbanization, but in the long run, factors such as renewable energy, cleaner technologies, the industrial structure, government intervention, regional differences, and income inequality may lead to an inverted U-shaped curve in carbon dioxide emissions [6,7,8,9,10]. In addition, N and inverted-N trajectories have also been observed [11,12]. The inconsistent conclusions expose the limitations of the EKC, and the intersection of economics and the environmental field is no longer able to well explain the laws of modern urban development. Against this background, scholars have tried to compare the city to a metabolizing organism and to interpret the growth pattern of the city from a more complex biological perspective.

Biological laws have been applied in environmental and urban studies and have shown good applicability and versatility in recent years, for it could explain complex urban metabolic mechanisms. The urban allometric scaling law, derived from the power law and allometry theories [13], reveals the development and agglomeration of a city system, which indicates that variables may not satisfy linear relationships, but rather exponential relationships. The term “size affects rates” indicates the allometric scaling laws in biology, that is, the biological variable depends on body mass [14]. More narrowly, the variable is determined by both the scaling exponent and the characteristic of the kind of organism. Fortunately, the availability of city data has made it possible to exhibit scaling [15], and urban ecosystems have also adhered to this biological law over the last several decades. Some urban indicators, such as income [16], firm sizes [17], patents [18], and number of educational and research institutions, have been found to asymptotically follow power law distributions with population sizes [19].

Compared with the EKC method, the allometric growth relationship between carbon emissions and the urban scale is easier to verify in different cities owing to its concise mathematical model, and this universal law has been widely confirmed as the process of urban metabolism is similar to the metabolism of organisms. Meanwhile, the urban scale is the strongest predictor for carbon neutrality [20]. Carbon emissions have been proven to be related to the urban scale, which is characterized by population, GDP, and land area, respectively [21,22]. For instance, excess carbon emissions, an indicator of traffic congestion, exhibit a superlinear relationship with population size, but this disadvantage does not apply in large cities with populations of more than 3 million people [15,23]. However, existing studies mainly use population as an indicator of urban characteristics, which cannot be adapted to the urbanization process characterized from multiple perspectives including economy, population, land, industry, environment, and society [24,25,26,27]. Therefore, this study attempts to characterize the process of urbanization in terms of multiple dimensions of a city scale and to define the rate of urban carbon metabolism in terms of urban carbon emissions in order to explore the influence of a city scale on carbon emissions under an allometric growth relationship.

In this study, an urban scale was creatively defined as a three-dimensional concept based on the process of urbanization, including an urban construction land area, population, and economy, to explore the power law relationships under different situations, given the expansion of the meaning of urbanization. In terms of the physical space, a land scale represents how much space a city occupies, and human activities and carbon emissions all come down to specific parcels of land. The expansion of urban physical space can be visually demonstrated by the increase in the urban construction land area. Moreover, population is commonly used when defining the city scale, especially when exploring the influencing factors of carbon emissions, as cities are places where large numbers of people live. In addition, cities are more prosperous than rural areas owing to their differences in production and lifestyles, so wealth is also an important standard for evaluating the urban scale. Considering all the above factors, the area of urban construction land was used as the main measurement of the urban scale. The population and economy scale were introduced as supplementary variables in the relationship between the urban land scale and carbon emissions. Finally, carbon emissions were further divided into four categories according to human activities: commercial, industrial, residential, and traffic emissions, for an individual is not a simple summation of different parts, but contains comprehensive interactions.

This paper is organized as follows: the theoretical framework is provided in the next section, following the description of the data and methods. We describe how we verified whether cities’ carbon emissions and urban scale follow the power law, namely, whether urban carbon emissions have scale benefits, and then detail how a panel data model was applied to 258 cities in China from 2012 to 2019. The temporal and spatial patterns of carbon emissions in different land-use types are visualized. Then, the article follows the power law relationship between the urban scale and carbon emissions, containing the dimensions of urban construction land, population, and economy. In detail, urban land was divided into commercial, industrial, residential, and traffic land for analysis. The spatial distribution of the multiplier effect in different cities is also examined. The results and policy implications are provided in the discussion and conclusions sections.

2. Theoretical Framework

Cities are the largest contributors to carbon emissions, have the greatest potential to reduce emissions, and are at the heart of low-carbon development strategies. Different disciplines have their own definitions of urbanization. From the geographical perspective, urbanization is reflected in changes in the human activity space and geographical landscape, including the transition from dispersed rural areas to clustered cities, and the diffusion of urban landscapes to rural areas [28]. From the demographic perspective, urbanization is the process of transforming a rural population into an urban population, with the population concentrated in urban areas [29]. And from the economic perspective, urbanization is accompanied by industrial structure transformation, with labor shifting from primary industry to secondary and tertiary industries and the growth of the total economic output [29]. During urbanization, size is the major determinant of most characteristics [30], and it influences urban carbon emission processes through socio-economic activities in the three dimensions of land, population, and economy.

Firstly, the change in the urban land scale is mainly manifested by the expansion of the urban landscape. Land finance and land urbanization have significantly affected carbon emissions in the period of rapid urbanization in China [31] because urbanization has dramatically changed the land cover and land use intensity [32]. Greenhouse gas emissions are closely tied to agriculture and forestry for the agricultural activities, forest plantations, and deforestation, with the burgeoning intensification and commoditization of agriculture which contributes to rural–urban migration, that ultimately fuels the haphazard expansion of urban areas [33]. Urban expansion and sprawl have greatly increased the loss of vegetation cover and accelerated carbon emissions [34,35], although urban greening can partially compensate for these releases of carbon dioxide into the atmosphere [36]. Secondly, from the perspective of the urban population scale, carbon emissions have been proven to be proportional to the population size [37,38]. The gathering of people in cities leads to a range of needs such as infrastructure investment, the construction of housing, commuting, household energy consumption, heating, etc., [39,40,41,42,43,44,45]. Meanwhile, rising living standards have a tendency to increase consumption-related carbon emissions as well [46]. As a result, cities with large populations need more energy to keep them running. Last but not least, technological progress and innovation act as a brake on the total carbon emissions through changes in energy efficiency [47,48], but its rebound effect may weaken this effect [49,50]. Industrial agglomeration promotes economies of scale, with varying degrees of carbon reduction for local and neighboring cities [51,52,53]. At the same time, however, the regional specialization of production activities has increased reliance on transportation, and the transport of food as well as of industrial products has in turn led to a higher energy consumption and carbon emissions [54,55]. Overall, agriculture is a low-emission, low-economic-output industry [56]. The economic output of the secondary industry increases significantly compared to agriculture, but is accompanied by a high carbon intensity, especially in heavy industry [57]. In contrast, the tertiary industry, which is dominated by service-oriented industries such as finance and tourism, can achieve high economic output while maintaining low carbon emissions. Therefore, industrial structure transformation and upgrading tends to increase carbon emissions at first and then stabilize or even decrease [58,59]. As a result, the urbanization of the industrial structure is accompanied by a change in the share of industry in the region, with agricultural production moving to the periphery of the city and industry and services gradually taking over, generating large-scale economic output.

Therefore, a theoretical framework was constructed to reveal the impact of an urban scale on carbon emissions based on the perspective of urbanization, as shown in Figure 1. Urban construction land, population, and economy are used as indicators of a city scale, which directly or indirectly affect carbon intensity, carbon sequestration, and carbon emissions through human behaviors and activities, and form the carbon metabolism mechanism in the process of urbanization jointly.

3. Data and Methods

3.1. Study Area

China is located in the eastern part of Asia, on the west coast of the Pacific Ocean, and has a land area of approximately 9.6 million square kilometers, as shown in Figure 2. At the end of 2022, the total population of China was 1411.75 million, of which the urban population accounted for 65.22%. The gross domestic product for the whole year of 2022 was CNY 121,020.7 billion, and the added values of the primary industry, secondary industry, and tertiary industry were CNY 8834.5 billion, CNY 48,316.4 billion, and CNY 63,869.8 billion, respectively. From the perspective of administrative divisions, the country is generally divided into four levels of administrative regions: provincial-level regions, prefecture-level regions, county-level regions, and township-level regions. Among them, a total of 333 prefecture-level administrative regions are the second-level administrative regions, including 293 prefecture-level cities, 7 regions, 30 autonomous prefectures, and 3 alliances. The establishment of prefecture-level administrative regions breaks down administrative barriers and urban–rural divisions between cities and counties, which is conducive to leveraging the role of central cities. This research uses cities at or above the prefecture level as the basic analysis unit to better explore the characteristics of urban carbon emissions.

3.2. Data

This study calculated city-level carbon emissions using Carbon Emission Accounts and Datasets (CEADs, https://www.ceads.net.cn/ (accessed on 14 July 2024)), the China Urban Construction Statistical Yearbook, and Statistical Yearbooks of each province. The CEADs provides data of carbon emissions in 47 socioeconomic sectors at the provincial level [60], and are calculated by the following equation:

$${\mathrm{CE}}_{\mathrm{m}\mathrm{j}}={\mathrm{AD}}_{\mathrm{m}\mathrm{j}}·{\mathrm{NCV}}_{\mathrm{m}}·{\mathrm{CC}}_{\mathrm{m}}·{\mathrm{O}}_{\mathrm{m}\mathrm{j}}$$

(1)

where CE_mj represents carbon emissions from fossil fuel m burned in sector j; AD_mj refers to the fossil fuel consumption by the corresponding fossil fuel types and sectors; NCV_m is the net caloric value, that is, the heat value produced per physical unit of fossil fuel combustion; CC_m (carbon content) refers to the carbon emissions per net caloric value produced by fossil fuel m; and O_mj, the oxygenation efficiency, refers to the oxidation ratio during fossil fuel combustion. This study summed up the emissions from all fossil fuel types as the total emissions from 2012 to 2019, forming an 8-year time series of data. The total carbon emissions of each province were divided into four subsystems (i.e., commercial emissions, industrial emissions, residential emissions, and traffic emissions) by sectoral emission accounting. This study focused on urban land and its emissions, so the relationship between agricultural emissions and agricultural land was not contained. Instead of land areas within the administrative boundaries, the area of urban land for construction purposes was used to define the city scale, as allometric studies based on administrative areas may be prone to endogeneity bias [61]. According to the definition from the China Urban Construction Statistical Yearbook, promulgated by the Ministry of Housing and Urban Rural Development of the People’s Republic of China, the area of urban land for construction purposes includes land for residential development, public facilities, industrial use, storage use, transportation use, roads and squares, utilities facilities, green land, and land for special purposes, excluding the water area and land for other purposes. This article only focuses on commercial land, industrial land, residential land, and traffic land. In detail, the land for commercial use includes wholesale and retail land, accommodation and catering land, commercial and financial land, and other land for commercial use; the industrial land is the land for industrial and mining storage; the residential land is used to meet residential needs; and the traffic land includes railway land, highway land, street land, and airport land. Carbon emissions on the four types of land in each city were calculated as follows:

$${\mathrm{CLE}}_{\mathrm{i},\mathrm{t}}={\mathrm{CLE}}_{\mathrm{province},\mathrm{t}}·{\displaystyle \frac{{\mathrm{Retail}}_{\mathrm{i},\mathrm{t}}}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{Retail}}_{\mathrm{i},\mathrm{t}}}}$$

(2)

$${\mathrm{ILE}}_{\mathrm{i},\mathrm{t}}={\mathrm{ILE}}_{\mathrm{province},\mathrm{t}}·{\displaystyle \frac{{\mathrm{Industry}}_{\mathrm{i},\mathrm{t}}}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{Industry}}_{\mathrm{i},\mathrm{t}}}}$$

(3)

$${\mathrm{RLE}}_{\mathrm{i},\mathrm{t}}={\mathrm{RLE}}_{\mathrm{province},\mathrm{t}}·{\displaystyle \frac{{\mathrm{Buildings}}_{\mathrm{i},\mathrm{t}}}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{Buildings}}_{\mathrm{i},\mathrm{t}}}}$$

(4)

$${\mathrm{TLE}}_{\mathrm{i},\mathrm{t}}={\mathrm{TLE}}_{\mathrm{province},\mathrm{t}}·{\displaystyle \frac{{\mathrm{Vehicles}}_{\mathrm{i},\mathrm{t}}}{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{Vehicles}}_{\mathrm{i},\mathrm{t}}}}$$

(5)

$${\mathrm{TE}}_{\mathrm{i},\mathrm{t}}={\mathrm{CLE}}_{\mathrm{i},\mathrm{t}}+{\mathrm{ILE}}_{\mathrm{i},\mathrm{t}}+{\mathrm{RLE}}_{\mathrm{i},\mathrm{t}}+{\mathrm{TLE}}_{\mathrm{i},\mathrm{t}}$$

(6)

where CLE_i,t, ILE_i,t, RLE_i,t, and TLE_i,t represent the commercial, industrial, residential, and traffic carbon emissions generated on the corresponding land of each city in the year, respectively. CLE_province,t, ILE_province,t, RLE_province,t and TLE_province,t are the total emissions in the whole province on the four land types. These data are publicly available from the CEADs. The emissions were allocated into each city based on the socioeconomic conditions. The carbon emissions of commercial, industrial, residential, and traffic land were considered to be proportional to the total retail sales of consumer goods, the GDP of the secondary industry, residential buildings, and civil motor vehicles, and Retail_i,t, Industry_i,t, Buildings_i,t, and Vehicles_i,t represent the values of all cities within the same province, respectively. The emissions were calculated according to the proportion of socioeconomic data in the whole province. TE_i,t (total emissions) represents the sum of the four types of emissions.

3.3. Methods

Using city-level carbon emissions by sector and socio-economic data, this research explored the power law relationship between carbon emissions and a three-dimensional city scale, and the technical roadmap of this research is shown in Figure 3.

The panel data, also called pooled time-series and cross-sectional data, combine the two dimensions of time and the section, which is the repeated observation data of individuals in a section at different time-points. Therefore, they are better in identifying and measuring the influencing factors that cannot be found by pure time-series or cross-sectional data. Additionally, they can construct and test more complex behavioral models.

As several variables are related allometrically to the body size, allometric scaling must be considered first to investigate differences between different-sized individuals in most cases. The most well-known allometric scaling function, Kleiber’s Law, states that metabolic costs increase with body size to three-fourths the power [62]. The dependence of biological variables (Y) on body mass (M) is typically characterized by the following form:

Y = Y₀M^b

(7)

where b and Y₀ represent the scaling exponent and constant related to the organism, respectively. Applied in our research, the city scale was compared to the body size, while carbon emissions were regarded as a metabolic variable of the urban system. Therefore, this study derived the basic estimation as follows:

E_i,t = α·A_i,t^β

(8)

where E_i,t represents the carbon emissions of the city in the year; A_i,t refers to the urban land area; α and β are the coefficients to be estimated; α is the multiplier effect, which scales the model; and β is the power relationship between carbon emissions and the urban land area. Previous research on the allometric scaling law in urban systems has discovered three main relationships corresponding to the β value [63]. A linear relationship, in which case, the scaling exponent β is roughly equal to 1, is applicable to human needs that scale with the city or population size, for example, water, houses, and jobs. When the β value is less than 1 in a sublinear relationship, the quantity of interest grows at a slower rate than the variable, which mainly exists between the city scale and materials or infrastructure. A superlinear relationship occurs when the social activity pattern influences the urban indicator with β greater than 1, such as GDP, income, wages, bank deposits, and other socioeconomic aspects [64]. A superlinear relationship usually implies that larger cities generate proportionally more economic activity and human productivity. In our research, if β > 1, the carbon emissions per unit of land will increase with the expansion of the land area, that is, carbon emissions would grow faster than urban construction land, which follows a superlinear relationship. If β ≈ 1, carbon emissions will increase linearly with respect to construction land, and the carbon emission intensity per unit of land area will remain unchanged. A sublinear relationship appears when 0 < β < 1, with the carbon emissions of marginal land decreasing, which indicates that the land scale has scaling effects. β = 0 means that the quantity of carbon emissions is a constant and is independent of the urban construction land area, and β < 0 implies that with the expansion of the urban construction land area, the total carbon emissions decrease.

The models for commercial, industrial, residential, traffic, and total carbon emissions can be converted into linear forms by a logarithmic transformation. The equations are as follows:

lnTE_i,t = ln + β·lnTA_i,t

(9)

lnCLE_i,t = lnα + β·lnCLA_i,t

(10)

lnILE_i,t = lnα + β·lnILA_i,t

(11)

lnRLE_i,t = lnα + β·lnRLA_i,t

(12)

lnTLE_i,t = lnα + β·lnTLA_i,t

(13)

Equations (9)–(13) indicate the relationships between commercial, industrial, residential, traffic, and total carbon emissions and their corresponding urban land areas, namely CLA_i,t, ILA_i,t, RLA_i,t, TLA_i,t, and TA_i,t. Besides the land scale, the population scale and economy scale are also important dimensions measuring the urban scale. This study improved the model by adding demographic and economic dimensions to the original one, and the corresponding revised theoretical equation is shown in Equation (14). For the four land-use types, Equations (15)–(19) are the specific regression equations, where POP is the urban population, and ECON is the GDP of the city:

E_i,t = α·A_i,t^β1·POP_i,t^β2·ECON_i,t^β3

(14)

lnTE_i,t = lnα + β₁·lnTA_i,t + β₂·lnPOP_i,t + β₃·lnECON_i,t

(15)

lnCLE_i,t = lnα + β₁·lnCLA_i,t + β₂·lnPOP_i,t + β₃·lnECON_i,t

(16)

lnILE_i,t = lnα + β₁·lnILA_i,t + β₂·lnPOP_i,t + β₃·lnECON_i,t

(17)

lnRLE_i,t = lnα + β₁·lnRLA_i,t + β₂·lnPOP_i,t + β₃·lnECON_i,t

(18)

lnTLE_i,t = lnα + β₁·lnTLA_i,t + β₂·lnPOP_i,t + β₃·lnECON_i,t

(19)

4. Results

4.1. Spatial–Temporal Pattern of Carbon Emissions

As shown in Figure 4, the total carbon emissions of different cities exhibited great heterogeneity. The cities with the largest carbon emissions were mainly distributed in north and northeastern China, including Beijing city, Tianjin city, the Hebei Province, Shanxi Province, the Inner Mongolia Autonomous Region, Liaoning Province, Jilin Province, and Heilongjiang Province, which were the main regions of the country’s heavy industrial manufacturing industry. Although the cities in the eastern coastal areas occupied a small land area, they had high carbon emissions. The Yangtze River Delta region was another area where carbon emissions were concentrated. In other regions, the peak points of carbon emissions were mostly provincial capital cities. During the research period, the total carbon emissions showed a slightly decreasing trend, but remained at a high level.

Among the four parts of total carbon emissions, industrial carbon emissions accounted for the largest proportion. In most cities, it reached 85% of the total emissions. Similar to the distribution of total carbon emissions, cities with the highest industrial carbon emissions were located in north and northeastern China. Outward from these two regions, carbon emissions decreased gradually. Commercial emissions, residential emissions, and traffic emissions peaked in provincial capital cities and municipalities directly under the central government, but there was little difference in commercial carbon emissions and residential emissions. Generally, industrial carbon emissions decreased from 2012 to 2019, while traffic carbon emissions gradually increased. However, commercial and residential carbon emissions showed little change because their emissions did not account for a large proportion either.

4.2. Relationship between Carbon Emissions and Urban Scale

After removing cities with missing data, 258 samples for 8 years were assembled for regression analysis. The distribution and development of a city scale follow certain laws [65,66,67], but the resource endowment of different cities varies greatly, resulting in the heterogeneity that exists between cities [68]. This study made a simple assumption that the relationship between carbon emissions and the construction land area is consistent in all cities, with the constant term varying among different cities because of their own attributes. This assumption precisely satisfied the varying intercept and constant coefficient model. This is a mixed effects model, where the intercept term is treated as a random effect and the other regression coefficients are treated as fixed effects. The model is able to deal with group effects and individual differences, and better adapts to realistic data situations. Moreover, this model was always considered to be correct for short panel data. The data analysis was conducted using EViews 10. From the perspective of the total carbon emissions, carbon emissions were negatively correlated with urban land expansion (β = −0.043), which meant that the emissions of cities with larger land areas did not increase, as shown in

Table 1. Regression results of total carbon emissions.

	Coefficient
Variable	Original Model	Revised Model
Constant	3.41 ***	0.898
LAND	−0.043 *	−0.179 ***
POP	/	0.311 **
ECON	/	0.174 ***
Adjusted R-squared	0.934	0.950
F-statistic	113.504 ***	113.933 ***

Note: *** significance at the 1% level, ** significance at the 5% level, and * significance at the 10% level.

. As carbon emissions were also affected by other socioeconomic factors, demographic and economic dimensions were introduced into the original model to refine the results. Considering the possible endogeneity of the socio-economic variables, we analyzed the data using the TSLS method with one-period-ahead and one-period-lagged variables as instrumental variables. When enlarging the concept of the urban scale from one single dimension to three, the effect of land expansion was more significant. The coefficient of the total land area was negative, indicating that cities with a larger construction land area had fewer carbon emissions. Carbon emissions increased sublinearly with the population and GDP for the coefficient that was below 1. The improved model revealed that the carbon emissions increased with the expansion of the demographic and economic scale, but the growth rate of the emission scale was slower than that of the demographic and economic scale. However, cities with a larger land area were likely to experience a decreasing trend in emissions rather than an increasing trend.

4.3. Detailed Analysis of Emissions on Four Types of Urban Construction Land

Differentiated human activities on different land types lead to wide differences in carbon efficiency. Therefore, distinguishing land use types helps to make the research more detailed. The main types of urban construction land are commercial, industrial, residential, and traffic land, all of which exhibited increasing trends nationwide, as shown in Figure 5. Among them, commercial land increased slightly. Industrial land and residential land, which accounted for the largest proportion of the total, increased to a certain extent, while transportation land, although not very large in area, significantly increased during the research period. When there was only one independent variable, the scaling exponents for the commercial, industrial, residential, and traffic land area were −0.013, −0.03, 0.091, and 0.075, respectively. All of these land use types exhibited decreasing emissions per unit of construction land area, with a good linear fit, as shown in

Table 2. Original regression results of commercial, industrial, residential, and traffic emissions.

Emissions Type	CLE	ILE	RLE	TLE
Constant	−0.724 ***	3.13 ***	−0.627 ***	0.253 ***
LAND	−0.013	−0.03 *	0.091 ***	0.075 ***
Adjusted R-squared	0.897	0.924	0.914	0.963
F-statistic	70.909 ***	97.889 ***	85.488 ***	210.823 ***

Note: *** significance at the 1% level and * significance at the 10% level.

. Among the four types of construction land, the scale benefits of commercial land were the most obvious. Similar to the analysis of total carbon emissions, we used the lagged one-period urban built-up land area, population, and GDP as instrumental variables in a two-stage least squares regression. The scale benefits of land increased greatly when demographic and economic variables were added, with β₁ being −0.005, −0.024, −0.128, and −0.074, respectively, as shown in

Table 3. Revised regression results of commercial, industrial, residential, and traffic emissions.

Emissions Type	CLE	ILE	RLE	TLE
Constant	−1.928	1.160	−5.086 ***	−3.813 ***
LAND	−0.005	−0.024	−0.128 **	−0.074 ***
POP	0.554 **	0.528 **	0.147	0.033
ECON	−0.280 ***	−0.158 **	0.581 ***	0.571 ***
Adjusted R-squared	0.894	0.907	0.905	0.951
F-statistic	70.782 ***	97.494 ***	87.614 ***	223.785 ***

Note: *** significance at the 1% level, ** significance at the 5% level.

. The newly added dimension of population can also alleviate carbon emissions as the β₂ values were 0.554, 0.528, 0.147, and 0.033, all of which were below 1. However, in economic terms, the regression coefficient between commercial and industrial carbon emissions and the economic scale was negative, while residential and traffic carbon emissions all exhibit a sublinear relationship, (β₃ values were −0.280, −0.158, 0.581, and 0.571, respectively). The p-values of the regression coefficients for GDP were all less than 0.05 when analyzing carbon emissions from all the four land-use types, indicating that the findings were statistically significant. However, this result was not sufficiently significant in some of the analyses of the urban construction land area and population. This may be due to the fact that the reliability of the results was affected by the accuracy of the data. However, the expansion of urban construction land did not necessarily bring about large emissions, and there was a sub-linear growth relationship between the carbon emissions and population, with the growth rate of carbon emissions being lower than that of population growth. The revised regression results indicate that when economic output doubles, there is no need to bear the cost of double carbon emissions, reflecting the phenomenon of economies of scale. Additionally, the relationships between commercial and industrial carbon emissions and population factors were closer according to the comparison of coefficients, while residential and traffic carbon emissions were more consistent with the economic scale.

4.4. Distribution of Multiplier α of Carbon Emissions

The model assumes that individuals share the same β, that is, different cities follow one common power law. However, inconsistent constant terms indicate that the multiplier α after the logarithm in Equation (14) varies according to the cities’ intrinsic natural and social conditions. The final lnα of each county or municipal district equals the constant of the model plus the fixed effects of the individual. Figure 6 shows the final α (after obtaining the exponential function) of each city with different land-use types in the revised model, which scales the model. The multiplier α can characterize the increase in carbon emissions under the same degree of urban scale expansion, and the larger the value, the faster the growth. The α values of the total emissions were greater than 1 in most cities, that is, the growth rate of carbon emissions was greater than the power of the urban scale. The fastest growing districts were concentrated in industrial cities and municipalities directly under the central government across the country. Provincial capital cities also had high multiplier effects. A detailed mapping of the multiplier α showed the differences among the four types of urban construction land. The multiplier effect of residential land and traffic land was at a low level, and there was not much divergence between different cities, although provincial capital cities had larger effects, while the multiplier effect of commercial land was clearer compared to them. It is worth noticing that the industrial emissions grew faster than the power of urban expansion, for the multiplier α > 1 in most cities, and this phenomenon was more obvious in the north of China which was dominated by heavy industrial production. The distribution of the multiplier α was very similar to the quantity of carbon emissions, and a higher α value meant that in cities with already high carbon emissions, the increased amount may be larger when the urban scale shares the same degree of urban expansion.

5. Discussion

5.1. Implications for Developing a Low-Carbon Land-Use Layout

Since human activities differ in various land-use types, the carbon emission intensity changes accordingly [69]. The capacity of carbon sequestration and carbon emissions depends on the type of land use [70]. Urban and rural land for residential use, industrial land, and traffic land have net carbon emissions; cultivated land has the ability to emit and absorb carbon dioxide; and water, grassland, and forest are considered carbon sinks because water and the photosynthesis of plants absorb carbon dioxide. Except for the net carbon emissions of the land-use type, the characteristics of growth also follow different laws when the land-use type changes. In view of the heterogeneity of the land-use types, this study analyzed the regular patterns of commercial, industrial, residential, and traffic land emissions separately, as they are the four main sources of energy consumption and carbon emissions in cities.

The area of urban construction land increased from 2012 to 2019, but carbon emissions grew slowly, and even negative growth occurred. A positive correlation exists between the growth of the urban construction land area and carbon emissions [71,72], but in this case, this phenomenon only occurred in the residential and traffic sectors, which may be due to the implementation and promotion of national energy-saving and emission reduction actions in the industrial industry. The discrepancy between their growth rates indicated the differentiated efficiency of urban construction land in energy conservation and emission reduction. Commercial land and traffic land were of a small scale in the initial research period, while both industrial land and residential land exhibited a large initial scale. From the perspective of carbon emissions, commercial land < residential land < traffic land < industrial land, while industrial land emissions were much higher than those of the other three land types. This result was similar to the order of carbon emissions per capita in all sectors [73] and the sectorial shares of global energy consumption [74]. Moreover, four kinds of carbon emissions in China were relatively high in provincial capital cities and municipalities directly under the central government. Human activities on commercial land include wholesale, retail trade and catering services, and other activities that consume less energy. Moreover, the area of commercial land was not very large, causing minor carbon emissions. However, the provincial capital cities and municipalities directly under the central government had relatively high commercial carbon emissions, which served as regional centers of commerce [75]. Carbon emissions mostly arose from industry [76]; thus, industrial land was the largest source of carbon emissions [31], as a massive amount of raw coal is used for the production and supply of electric power, steam, and hot water. Furthermore, industrial emissions were concentrated in north China, and the distribution of key industrial production areas had led to this situation [77]. Residential emissions accounted for most of the energy consumed by residential sectors. Although residential land occupied a large area of land, carbon emissions were not alarming owing to their low energy intensity. Passenger traffic and freight traffic are the main functions of traffic land, resulting in significant carbon emissions because of the tremendous amount of diesel oil consumption, and the concentration of infrastructure such as commercial and medical in the central city increases regional transportation demands from the outlying cities.

Therefore, realizing the construction of low-carbon cities requires the good control of carbon sources such as industrial land, and the land-use layout also plays an important role in emission reduction due to the differentiated carbon emission intensity. Spillover effects in information, technology, and human capital occur with industrial agglomeration, leading to higher energy efficiency. The residential sector has great potential for developing low-carbon cities through the use of new electrical appliances and heating equipment [78]. Regarding the transportation sector, the city scale affects traffic emissions by influencing the average travel distance, and the increasing pattern diverges in cities. Therefore, developing public transportation is necessary in metropolises. In small or medium cities, attention should be paid to emission reduction in the private transportation sector, which produces more carbon emissions [79].

5.2. Impact of Urban Scale on Carbon Emissions

When setting up the panel data model, instead of carbon intensity or carbon emissions per capita [80], this study tested and verified the relationship between the land area and total carbon emissions of cities. The selection of indicators ensured that the research object was the whole city, so the β value could be an index reflecting urban carbon metabolism efficiency. For the total carbon emissions, note that β < 1 when exploring the relationship with the construction land area, which meant that the expansion of the land scale increased the carbon efficiency. Disregarding the land scale, the improved model took the population and economy scale into account. As an indicator of the population scale, the population with a permanent residence can accurately identify the total population living in cities comparatively, and GDP represents the level of economic development. It was found that the correlation between carbon emissions and the population scale was strongest (β = 0.311), but also much less than 1. The exponent of the land scale was negative, which indicated significant scale benefits. However, a negative value does not mean that an increase in the land area reduces the local total carbon emissions, but rather that cities with a large construction land area have more of an emission reduction capacity if other conditions remain unchanged. In other words, a city with a larger land area tends to save more energy than others. The sub-linear relationship between carbon emissions and GDP signaled that economic growth would no longer come at the expense of environmental well-being, and that technological innovations could achieve economic output with lower carbon emissions.

When distinguishing between land types, the four types of land use all followed the power law with exponent β < 1 from the perspective of the land scale, reflecting a common marginal decline in carbon emissions associated with the land area. The impact of the total land area on the total carbon emissions seemed to be stronger than the four detailed types, so the combination and proportion of different land-use types had obvious impacts on the energy efficiency, and mixed-function areas played significant roles in carbon emissions from the perspective of the urban form, considering the land-use structure and the characteristics of different land-use types [81]. Therefore, reducing carbon emissions through land-use structure optimization might be an effective approach [82,83]. The β values of four types of land area were rather small, as technological innovation caused by knowledge spillover and shared infrastructure reduced the waste of energy and resources. Correspondingly, a more significant reduction in carbon emissions was observed as urban areas expanded, reaffirming that the productivity advantages brought by scale benefits are much larger for the non-manufacturing sector than for the manufacturing sector [84]. Moreover, a higher β value of traffic land than that of industrial land shows that the energy-saving ability of transportation was relatively less obvious, as industrialization and urbanization permit economies of scale in production, but also generate more transportation demands [85]. However, industrial development and expansion promote technological innovation and industrial transformation and upgrading, which eliminate low-energy-intensive enterprises and help reduce carbon emissions [86]. Compared to previous research, one contradictory finding is that there was still a β < 1 when analyzing traffic emissions in this work, but traffic congestion led to increasing energy consumption in the preceding one [87]. One probable cause is the distinct process of data collection and the carbon emissions calculation. In addition, this study expanded the study area from a single city to a nationwide study area and used cities as analysis units. A larger sample may make the conclusion more representative. Additionally, the growth pattern of carbon emissions from transportation might be different in cities of different scales [87]. The β component in our research reflects the general pattern of the whole country, with city scales being highly changeable, so the choice of research scale may be the reason why the conclusion could change. In addition, transportation networks at the national level contribute to energy savings, as the transportation organizations are beginning to play an increasingly important role in emission reduction [88].

After introducing the population and economic dimensions, as we did when analyzing the total emissions, the β values decreased. When the β value was less than 1, regardless of whether it was below 0, urban expansion realized economies of scale, and a negative value represented a more obvious effect. The results indicate that the expansion of all the four types of land reduced the carbon emissions per unit of land and the revised model enhanced the scale benefits, giving rise to the negative β value which was significantly less than 1. Similarly, population also plays a conspicuous role in mitigating carbon emissions. From the perspective of economy, large cities were more efficient, regardless of which type of carbon emissions they belonged to, but the scale effects of commercial and industrial emissions were relatively more significant compared to other types. The increase in the urban land, population, and economic scale could also reduce carbon emissions in commercial, industrial, residential, and traffic sectors, that is, large cities are more efficient from the perspective of carbon emissions. However, the limiting factor for the reduction effects of different types of emissions varies. Among them, commercial and industrial carbon emissions tended to decrease as the size of the economy increased because the service sector produced fewer carbon emissions and technological advances could reduce the environmental pollution caused by corporate production. Meanwhile, population is the main limiting factor for carbon emissions in residential and traffic sectors because population gathering is more likely to generate demand for these activities, but the utility of emission reductions in these two sectors is not yet evident.

5.3. Multiplier Effect of Urban Expansion

Geographic variables exhibit uncontrolled variance [89], and influencing factors of core emission areas are distinct from low emission areas. Carbon emissions per capita are characterized by conspicuous regional imbalances in China, decreasing from the eastern coastal region to central areas and then to the west. At different estimation scales, regions where carbon emissions agglomerate also shift [90]. From a dynamic perspective, China’s carbon emission process is always consistent with its economic development [91]. Cities in western, central, and northern China tend to have slowly growing carbon emissions, while large carbon emissions are mainly concentrated in southern and eastern coastal areas. The significance of influencing factors for carbon emissions has also been found to vary between provinces as a result of their respective economic level. As for the scaling law of carbon emissions, the growth patterns have shown great variability among large-, medium-, and small-sized cities [23,92], depending on their population size [61]. Research on the mechanism of carbon emissions has usually analyzed the regular patterns of several cities with a single equation, ignoring individual effects. To compensate for this defect, a panel data model was used in this study, as it constructed equations for each individual. Moreover, visualization was applied to present a concrete display of the spatial–temporal pattern and changing rules of carbon emissions among cities to reveal the spatial heterogeneity in this work.

In terms of the total carbon emissions, the multiplier α was strongly consistent with the carbon emissions, which means that carbon emissions increase more in large cities when the construction land area expands by the same amount, reflecting a self-reinforcing agglomeration in carbon emissions [88]. The multiplier effect reflects that the growth of carbon emissions is not only related to the β value, but also affected by the initial emission values of the city [45]. The main source of carbon emissions is the industrial sector; thus, the distributions of the multiplier α showed great similarity between these two results, and north China was the concentrated area of a high α value from the perspective of industrial carbon emissions. Therefore, the carbon emission patterns of cities are closely related to the industrial layout.

When considering the type of carbon emissions, cities with a high α value of commercial emissions overlapped with densely populated and bustling cities, and it can be clearly seen that the pattern of commercial carbon emissions had a concentrated distribution characteristic. However, this phenomenon was not significant in the residential and traffic sectors because the differences of the α value between cities were relatively small. On the one hand, it might be due to the fact that the total amount of these two types of emissions was limited. On the other hand, the residential demand is a broad demand that does not have a polarized distribution, while the transportation sector connects different cities, thus exhibiting a certain degree of spatial continuity, which leads to a relatively average distribution of the α value.

6. Conclusions

China surpassed the United States to become the world’s largest emitter of carbon dioxide in 2004, and exploring the patterns of urban carbon emissions can provide the direction for urban development. The change in the city scale is an essential symptom of urbanization, and can be concentrated in the three dimensions of the land scale, population scale, and economic scale. This study analyzed the carbon emissions and urban land area of the commercial, industrial, residential, and traffic sectors from 2012 to 2019, applying the allometric scaling law. The temporal–spatial distribution of carbon emissions was visualized at the city level nationwide. Based on the results of the panel data analysis, we argue that there is a nonlinear relationship between carbon emissions and urban construction land, and the case of Chinese cities suggests that large cities may be more energy efficient in terms of carbon emissions. The main conclusions are as follows.

During the research period, the carbon emissions in north China were the highest, but the total carbon emissions in the study area decreased. This is mainly due to the reduction in industrial carbon emissions, which are the largest carbon source. On the contrary, traffic carbon emissions, which ranked second in emissions, had an increasing trend. Provincial capitals and municipalities directly under the central government were often points of high carbon emissions.

The power law is a common relationship between carbon emissions and their corresponding city scale. The urban scale was defined from three perspectives inspired from the process of urbanization, namely the land area, population, and economic scale, and it was found that urbanization and the expansion of the urban scale contributed to emission reduction. A large population and land area could alleviate the increase in carbon emissions. However, carbon emissions show consistency with the economic scale, although the economies of scale’s effects could still be observed due to the economic agglomeration. We noticed an increase in energy efficiency when combining all types of urban land as a whole for a lower β value, which indicates that the land use structure and the combination of different land use types may affect carbon efficiency. Exponent β for the four types of land use was below 1, demonstrating decreasing emissions on newly expanded urban construction land. When the analysis took another two dimensions into account, the scale benefits of land became more significant. Population also played a non-negligible role in mitigating carbon emissions, and the efficiency of large cities also increased from an economic point of view. The economies of scale of commercial and industrial carbon emissions mainly came from the economic dimension, while residential and traffic carbon emissions mainly came from population gathering.

In addition, carbon emissions displayed great heterogeneity in different cities. The multiplier effect of total carbon emissions was similar to that of industrial emissions. Cities benefited from the increasing scale of residential land for living needs. For production needs, however, industrial emissions were concentrated in regions with good industrial foundations, while commercial and traffic emissions were more likely to occur in large cities, reflecting self-reinforcing aggregation.

For future urban planning, three approaches may help achieving urban carbon emissions’ reduction: First, industrial land is still the main source of carbon emissions and the area with the greatest potential for emission reduction. Its spatial layout depends on the industrial foundation of the city, which is difficult to shift. Improving production technology may be an effective way to reduce emissions in such important industrial zones. Second, provincial capitals and municipalities directly under the central government are often emission hotspots in the region. This study shows that large cities are more efficient, no matter whether from the perspectives of land, population, or economy. Regional planning needs to better leverage the economies of scale of these leading cities. Finally, the carbon effect of the total urban construction land is not a simple superposition of the carbon effects of various types of land. Therefore, it is necessary to adapt to the local conditions in land use planning in order to maximize the comparative advantages of the city’s leading industries, and optimize the whole carbon effect by constructing a more reasonable land use structure.

This article has made two main contributions. Firstly, the carbon emissions on different land use types at the city level were accounted for accurately. Secondly and most importantly, the power law rule was used to explore the relationship between the city size and carbon emissions in three dimensions: land, population, and economy. The results of this study presented the commonalities among cities as well as the multiplier effects that differentiate different cities. It was found that large cities are more efficient from the perspective of carbon emissions, in terms of land expansion, population agglomeration, and industrial upgrading in the economic structure during urbanization, for the β values were all less than 1 in the research period, which indicates that carbon emissions grow more slowly than urban expansion. The carbon reduction effect of commercial, industrial, residential, and traffic land varies according to the emission type, and cities with higher emissions themselves may exhibit a self-reinforcing aggregation. The findings could provide the theoretical support for developing a low-carbon land-use layout and building low-carbon cities. However, the selected study area and study period were limited owing to data availability, and we assumed that energy consumption and social activities are proportional in a province. Future work will include additional cities and will use quantitative methods to classify cities of different types to identify whether all city types follow the same growth pattern, as well as attempting to account for the carbon emissions of each city in terms of real energy consumption.