Scaling laws of CO2 emissions during global urban expansion

Introduction

Cities serve as the primary hubs of human activities and anthropogenic CO₂ emissions. Therefore, there is an urgent need to understand the dynamics and laws governing urbanisation and global CO₂ emissions. Cities are complex systems that can be likened to living organisms¹. They exhibit nonlinear relationships among their main indicators during their growth. This observation has led to the introduction of an urban scaling law, proposing that cities are quantitatively predictable owing to agglomeration effects². The universal nature of scaling has been supported by several studies, which demonstrated the applicability of scaling to various urban indicators, including economic outputs, innovation, crime rates, road length, gasoline stations, job opportunities, and drinking water availability³. Furthermore, exploring whether a scaling relationship exists between CO₂ emissions and urban sizes has gained considerable attention. However, previous studies on this topic primarily focused on country-level analyses or specific city groups^4,5. Given the ongoing global urbanisation trend and the pressing challenge of climate change, it is imperative to understand the laws and dynamics governing urban CO₂ emissions on a global scale.

In urban systems, two approaches have been adopted to address the scaling property of CO₂ emissions. The first approach considers urban CO₂ emissions (C) as a power-law function of population size (P), defining (C sim {P}^{beta }), where (beta) represents the scaling exponent. This analysis describes the scale of CO₂ emissions with respect to population size. When (beta > 1), a superlinear relationship exists, indicating that larger cities emit higher amounts of CO₂ relative to their size. Conversely, a sublinear relationship ((beta < 1)) suggests that larger cities emit lower amounts of CO₂ relative to their size, whereas a linear relationship ((beta approx 1)) denotes constant returns to scale for CO₂ emissions and population size. The second approach explores CO₂ emissions per capita, which are influenced by population density, and can be expressed as (C/P sim {(P/A)}^{beta }), where A represents the urban area. However, a consensus on the results of urban scaling of CO₂ emissions has not been reached. For the (C sim {P}^{beta }) relationship, previous studies have reported nearly linear scaling ((beta =0.933))⁶, sublinear scaling ((beta =0.77))⁷, and even superlinear scaling ((beta =1.46)) for US cities⁸. These discrepancies can be attributed to the different sources and categories of data used in these studies. Some have collected statistical data based on the definition of metropolitan areas⁶, whereas others have used the definition of connected urban areas⁸.

Previous studies examining CO₂ emissions were limited to a few countries or regions, which hampers our understanding of the global urban system and its impact on CO₂ emissions. Studies have also examined the scaling effect of population size ((C sim {P}^{beta })) on CO₂ emissions for European cities ((beta =1.12))² and Chinese cities ((beta =0.6477))⁹. Emissions per capita for US cities ((beta =-0.78 sim -0.82))¹⁰ and Chinese cities (which vary significantly across regions) have also been examined⁹. Although the scaling law has garnered interest in other countries, such as Brazil¹¹, its application to CO₂ emissions has not been explored. Attempts have been made to measure city emissions globally, such as a study by ref. ¹², which included a group of 256 cities worldwide, which suggested superlinear scaling for cities in developing countries and sublinear scaling for developed ones based on population size, and that by ref. ⁵, which calculated the scaling relationship of per capita CO₂ emissions for 20 cities across different continents. However, these studies have limitations, as the limited number of cities included cannot capture the complexity of global urban systems. Additionally, the data used in these studies are highly selective and represent a segment of city growth or part of the entire global urban system, potentially leading to misleading or biased results. Despite the significant urbanisation trends in this century, our knowledge of urban scaling of CO₂ emissions for populous and rapidly urbanising countries or regions, such as India and the African continent, is limited except for China.

Our study makes several contributions to the understanding of global urban CO₂ emissions. First, we derived a dataset of global urban CO₂ emissions for multiple periods, which can be regularly updated to provide consistent monitoring of urban CO₂ emissions with the advance of global urbanisation and support the assessment and management of Sustainable Development Goal (SDG) 13 (climate action) and SDG 4 (sustainable cities). The two issues listed here are correlated and require a refined approach to establish a dataset with consistently defined units of analysis that measures the urban scaling of CO₂ emissions at the global level to clarify the extent to which CO₂ emissions are associated with urban characteristics. To establish this dataset, we adopted advanced remote sensing and geoinformation science technology. We derived geo-coded global urban CO₂ data at a (1times 1) ({rm{km}}) grid size resolution by combining data sources such as ESACCI (land use), Landscan Global (population), GADM (geoboundary and administration), and ODIAC (anthropogenic CO₂) (Methods). To the best of our knowledge, this dataset represents the most accurate measurement of urban CO₂ emissions. Given the diverse and incompatible definitions of urban areas and cities worldwide, we defined urban areas as connected built-up areas covering at least 1 km² with a total population of at least 5000 (Methods). We compared the geographical and administrative boundaries of these areas and excluded small scattered areas from our analysis.

Second, our study facilitates temporal comparisons of global urban systems. It is important to note that urban systems are path-dependent, evolving based on their historical context¹³. Our analysis covers five years: 2000, 2005, 2010, 2015, and 2020. We investigated sub-systems in key countries and regions, which allows a comparison of urban CO₂ emissions using the same data and standards. Specifically, we focused on European nations (excluding Russia), which possess some of the oldest extant urban systems in the world², the US, which is known for its well-developed urban system in the last century, China, which has experienced the fastest urbanisation in recent decades, as well as India and Africa, which will be the major areas of urbanisation in the coming decades. We also included Russia and Australia in our analysis. Additionally, we considered different latitude regions because natural conditions can influence energy usage, human behaviour, and city development. This approach enabled us to assess regional and national variations within distinct socioeconomic and natural contexts.

Lastly, with respect to urban characteristics, we expanded beyond population and population density as primary indicators by including the analysis of urban areas and area emission intensity. Although population size is commonly used to gauge the role of (de)urbanisation in climate mitigation¹⁴ and indicates the relative importance of a city within the urban system, it has certain limitations as it is often strongly correlated with other socio-economic indicators¹⁵. Urban sprawl, for example, can negatively impact social welfare, increase commuting times, and raise energy consumption. Area is an important indicator of city size. Larger cities often exhibit complex urban forms and a greater diversity of human activities. Recent studies have attempted to summarise urban CO₂ emissions as a function of the interaction between population and area ((Ptimes A))¹⁶. However, this approach overlooks the strong correlation between these two aspects of urban development¹⁷ and fails to consider the impact of population density and urban form.

Population density reflects how people live within a settlement. For example, Asian cities typically have higher population densities compared to those in the US. Although some studies considered population density as an indicator of urban form⁶, it primarily reflects human behaviours related to aspects such as transportation, lifestyle, and consumption rather than land-related issues. Population density is directly linked to urban functions such as housing, transportation, and recreational and institutional facilities¹⁰, which can vary between low-density and high-density cities of different sizes. For instance, in the US, “doubling residential density across a metropolitan area might lower household VMT (vehicle miles travelled) by approximately 5–12%, and perhaps by as much as 25%, if coupled with higher employment concentrations, significant public transit improvements, mixed uses, and other supportive demand management measures”¹⁸. In cities like Paris, London, Berlin, and Istanbul, neighbourhoods with tall buildings demonstrate higher heat-energy efficiency compared to those with detached housing¹⁹. Therefore, the relationship (C/P sim {(P/A)}^{beta }) reflects CO₂ emissions in connection with human behaviours, as people residing in different cities may contribute to varying levels of CO₂ emissions, which are strongly influenced by population density.

To closely examine the relationship between CO₂ emissions and urban form and spatial structure, it is important to have a comprehensive understanding of urban areas. In addition to technological and market methods, urban planning can serve as a vital pathway for emission reduction²⁰. Built-up areas are a key variable used to measure urbanisation in space, and the power-law function (C sim {A}^{beta }) is employed to quantify urban CO₂ emissions of urban areas. Urban CO₂ emission intensity ((C/A)) reflects emissions during land development, as cities with varying urban forms, infrastructure, facilities, and buildings may generate different levels of CO₂, as indicated by the land use metric land area per capita ((A/P)). (A/P) provides insights into land-use efficiency, where lower land area per capita suggests more efficient land utilisation. This concept forms the crux of the theory of compact cities, which posits that geographic efficiency and physical compactness can optimise land-use functionality. However, empirical studies have presented contrasting findings. Some studies demonstrated that compact cities can reduce CO₂ emissions by reducing household heating²¹ and commuting trips²², whereas other studies argued that physical compactness exacerbates the urban heat island effect, leading to increased demand for cooling and higher energy consumption because of the lack of green spaces²³. These studies suggested that urban function and urban form, although closely related, are not always synonymous. Population density and urban land use per capita represent the compactness of urban populations and the urban built environment, respectively²⁴. Urban areas and land area per capita serve as more suitable indicators for assessing urban form and spatial structure.

Therefore, changes in the four metrics population, land area size, population density, and physical compactness are a reflection of human activities that transform the natural environment, and they reflect changes in the natural environment and impact functional spaces within cities and the avenues for humans to engage in natural-social transformations²⁴. Moreover, these metrics are meaningful in implementing urban design and planning concepts to deal with CO₂ emissions²⁵. In this article, we explore the four complementary approaches that provide a comprehensive global perspective on the scaling of urban CO₂ emissions and their implications for urban planning and policy in the context of climate change.

Results

Global overview of urban expansion and CO₂ emissions

The world’s cities have experienced rapid growth in recent decades, with the number of cities increasing from 22,429 in 2000 to 39,321 in 2020, based on the definition of cities as built-up areas with an area of at least 1 km² and a population with a minimum of 5000 people (Fig. 1a). By 2020, approximately 261,000 km² of land had been transformed to urban area since 2000. This trend has continued and generated 1.1 billion new urban dwellers, which is considerable compared to the global population growth of 1.68 billion inhabitants. These figures highlight the significance of cities as the primary areas where people pursue economic prosperity and social welfare, with urbanisation corresponding to population concentration, industrial agglomeration, infrastructure development, and changes in land use. However, these human activities are not uniformly distributed across the planet, thus giving rise to various urban systems. In 2020, the US accounted for 8.7% of the global urban population, Europe accounted for 9.9%, East Asia accounted for 21.9%, and Africa accounted for 13.8%.

Scaling laws of CO2 emissions during global urban expansion — **Fig. 1: Growth of cities and increase in urban CO₂ emissions globally.**

The rapid growth of cities has led to increased CO₂ emissions, which pose a significant challenge to future climate and sustainability. In 2020, these emissions amounted to 2.95 gigatonnes of carbon (GtC) (Fig. 1b), accounting for approximately 32.7% of global emissions for that year. Over the past two decades, emissions have increased by 1.42 times, with a growth of 0.75 times between 2000 and 2010 and 0.38 times between 2010 and 2020. Notably, the distribution of emissions across cities was uneven (Fig. 1c), while the proportion of global emissions remained relatively stable between 2000 and 2020. Super-large cities (cities with an urban population over 1 million) contributed 25.6% ± 3.1% of the global emissions, large cities (with an urban population between 0.5 million and 1 million) contributed 11.7% ± 0.3%, medium-sized cities (with an urban population between 0.1 and 0.5 million) contributed 29.7% ± 1.6%, and small cities (with an urban population between 10,000 and 100,000) contributed 33.0% ± 1.8%. This distribution remained relatively stable despite changes in the number of cities in each category. The per capita CO₂ emissions also remained stable at approximately 1.06 tonnes of carbon (tC) for all cities. When measured based on urban land area, the intensity of emissions displayed a gradient, with super-large cities emitting 8392 tC km^-2, large cities emitting 6420 tC km^-2, medium-sized cities emitting 5779 tC km^-2, and small cities emitting 3947 tC km^-2 (Fig. 1a).

An analysis based on Zipf’s law revealed that the trend of CO₂ emissions became more serious (Fig. 1d). For example, cities with the same ranking emit increasing amounts of CO₂ over time. In 2000, there were 144 super-large cities, accounting for 0.6% of the total number of cities worldwide and emitting 20.3% of global urban CO₂ emissions. In 2020, 317 super-large cities (0.8% of the total number of cities globally) contributed to 28.5% of global CO₂ emissions. When combined with large cities, these two categories accounted for approximately 40% of urban CO₂ emissions after 2015 despite representing only 2% of cities globally.

Urban scaling relationships of CO₂ emissions

Population size is a key indicator that is often strongly correlated with other socio-economic indicators¹⁵ and provides insights into the general trend of urbanisation’s impact on climate change, particularly in terms of anthropogenic emissions. This indicator is crucial for policymakers and planners as they strive to balance promoting urban population growth and implementing measures and regulations to mitigate its associated effects. From 2000 through 2020, the scaling component ((beta)) for urban populations increased from 0.91 to 1.10, implying that CO₂ emissions have been growing at a faster rate than population growth in urban areas. This finding highlights that regulating the growth of large cities is a major global concern. Large cities face enormous social pressures due to their sheer size and complexity²⁶, and the agglomeration of population continues to increase carbon emissions with industrial and transportation growth²⁷.

Variations among countries were observed for this metric. For European and Japanese cities, the scaling component remained relatively stable at approximately 1 between 2000 and 2020, suggesting a more or less proportional increase in CO₂ emissions with population growth. In contrast, a significant increase was observed for Africa (from 0.65 to 1.04) and Australia (from 0.99 to 1.31), indicating the immense pressure faced by these regions in controlling CO₂ emissions with increasing urbanisation. Africa’s energy intensity remains the highest in the world, increasing from 2.6 times in 1990 to 2.7 times in 2013 more than the global average, and continues to rise^28,29. Australia is also experiencing a steady increase in carbon emissions, making it difficult to achieve the 2030 emissions reduction agenda³⁰. The scaling component for the US, China, Canada, and Russia was quite similar at approximately 1.2. This is due to the fact that these developed economies, have generally developed a “decoupled” industrial structure and show increasing concern for environmental protection, active energy conservation, emission reductions, and vigorous green technology development. China is also approaching the transition from its fast-growth stage under the carbon neutral goal, as its economic growth rate is slowing down³¹.

Geolocation may be another important factor when examining emissions because daily behaviours, construction materials, and energy use for production and consumption can vary based on climate and temperature. Our analysis revealed that the scaling component rapidly increased from 0.94 to 1.16 for cities in the temperate zone, and from 0.96 to 1.14 for the continental zone from 2000 to 2020, which may have been due to the rapid urban development of these zones. Rapid urbanisation is accompanied by a steady increase in residential consumption patterns and energy consumption, especially for fossil-fuel-dependent heating and cooling and electricity supply systems in cities in temperate regions^32,33. In contrast, the scaling component increased slowly and even dropped after 2010 for cities in the arid zone and 2015 for cities in the tropical zone, which was possibly because these zones, such as the African continent, are still at a relatively low development stage. Africa currently accounts for only 3% of the world’s carbon emissions³⁴, and after nearly 30 years of rapid industrialisation and the introduction of foreign direct investment, the CO₂ emissions from these cities have only begun to rise steadily³⁵ (Fig. 2).

**Fig. 2: Scaling laws between urban CO₂ emissions and population size during 2000–2020.**

Although population size is the key indicator of urbanisation, it has limited applicability for understanding the characteristics and behaviours of citizens. For instance, suburban households may have higher energy consumption than urban households¹⁰. The relationship between CO₂ emissions per capita and population density can be associated with the construction and road sectors, with (beta) ≈−0.8 observed in US cities^10,16. Additionally, cities with high population density tend to have lower per capita gasoline consumption compared to cities with low population density³⁶.

Globally, the scaling component for this relationship was −0.748 in 2000, which gradually changed to −0.651 in 2020, indicating that an increase in population density may lead to a reduction in CO₂ emissions per capita. However, the impact has diminished, likely due to increased consumption as the world becomes more affluent.

Clear discrepancies were observed among countries. The negative impact of population density on per capita CO₂ emissions has been increasing in Africa, India, and China over the past 20 years, as these regions have experienced rapid urban population growth. From 2000 to 2020, Africa, India, and China witnessed urban population increases of 105.50%³⁷, 66.36%³⁸, and 97.83%³⁹, respectively. In contrast, the impact of population density on emissions per capita decreased in Japanese, European, Canadian, and Australian urban systems in which many cities witnessed a population decline due to factors such as decreasing fertility rates and an ageing population^40,41,42,43. For US cities, the impact initially increased from 2000 to 2005, but subsequently decreased, reaching a range of approximately −0.44 to −0.6 from 2005 to 2020. This impact is lower than the previously reported values of approximately −0.8^10,16, which could be attributed to differences in the measurement criteria used in this study as we focused on connected urban areas with a minimum population of 5000.

Geolocational analysis revealed significant differences among cities located in different temperature zones in terms of the effects of the scaling factors of population density on emissions. Scaling components for cities in the temperate zone levelled off and slightly dropped, indicating that the emissions measured per capita were stable relative to those measured by population density. In comparison, the scaling components for cities were higher in arid and continental zones, implying less efficient energy and resource use and greater associated emissions. These regions have greater energy consumption and emission problems due to their energy consumption structure, industrial structure, and climatically adapted building and transportation modes. For example, the average CO₂ emissions in Africa increased rapidly from 452,922.6 kilotonnes from 1980 to 1989 to 775,774 kilotonnes from 2010 to 2014, which was driven by crude technology and rapid industrialisation³⁵. The scaling factor increased rapidly from −0.60 to −0.34 for cities in the tropical zone. This was because under a rough energy consumption model, population agglomeration can significantly improve energy efficiency by realising more centralised infrastructure, efficient public transportation systems, and optimal allocation of resources, which can contribute to more rapid and greater carbon emission reductions^5,44 (Fig. 3).

Although urban population is often associated with urban areas, the size of urban areas is an important indicator of urban form and land development. A larger land area allows cities to have more diverse urban functions, including housing, industries, transportation, recreation, and institutional facilities. Therefore, it is crucial to examine the trade-off between the benefits of urban growth and the associated CO₂ emissions. At the global level, the scaling factor has remained at approximately 1.2 over the past two decades, implying that a 1% increase in urban land results in a 1.2% growth in CO₂ emissions. However, this relationship varies greatly. The relationship was linear for Europe (1.05) and superlinear for the US (1.30), Canada (1.36), Russia (1.43), Japan (1.47), Australia (1.53), China (1.58), and India (1.61) in 2020, and it changed from sublinear in 2000 to superlinear after 2005 in Africa. Although the scaling factor was very high in China, it decreased from 2000 to 2020, thus reflecting the emission reduction efforts made by Chinese cities, which represent the largest urban system in the world. Additionally, cities in hotter areas may have lower emissions than those in colder areas, with factors of 1.35 for the tropical zone, 1.36 for the temperate zone, and 1.47 for the frigid zone on average during 2000–2020. The climatic characteristics of tropical cities greatly reduce the amount of energy needed to heat buildings, which can significantly reduce energy consumption and carbon emissions compared to cities in colder regions, which must rely on coal, gas, and electricity to provide centralised or decentralised heating^45,46.

In terms of geolocation, diverse trends were observed, with increases observed for temperate and continental zones and decreases observed for arid and tropical zones. Thus, CO₂ emissions from cities in temperate and continental zones are increasing at a faster rate than those from urban areas, while CO₂ emissions from cities in tropical and arid zones are lagging behind those from urban areas. This finding is consistent with the current rapid growth of cities in tropical regions, including Africa and South Asia, particularly Africa, which is one of the fastest urbanising regions in the world^34,47 (Fig. 4).

Land area per capita is a commonly used parameter for assessing land-use efficiency, and larger values indicate more inefficient use of land. An alternative approach for assessing land-use efficiency is the compact city theory, which emphasises the physical compactness of cities. This theory aims to optimise the functional aspects of urban built environments and promote geographic efficiency¹⁴. In general, a negative sublinear scaling relationship occurs between CO₂ emission intensity and land-use inefficiency, with variations ranging from −0.25 to −0.35 at the global level between 2000 and 2020.

Land use per capita is closely related to planning culture, and the scaling effect varies due to different planning cultures worldwide. For example, the scaling factor ranged from −0.36 to −0.57 for the US, −0.41 to −0.76 for Canada, −0.52 to −0.76 for Europe, −0.54 to −0.85 for Japan, and −0.83 to −0.95 for Russia during the specified period. In particular, the factor considerably changed from −0.6 to −1.1 for Australia. Notably, these countries and regions have relatively modern urban systems with a long history. In comparison, such an effect was relatively low for countries and regions with ‘new’ urban systems, such as Africa (−0.15), China (−0.18), and India (−0.30), in 2020, for which the scaling effect was lower. Thus, greater land use leads to limited reductions in emissions per unit area.

The negative scaling relationships indicate that higher land-use efficiency may be associated with lower emissions per area. Some studies have suggested that the urban heat island effect, often a result of compactness, can lead to higher emissions in certain areas, as reflected in emission intensity. However, this study measured the average status of entire built-up areas, suggesting that discrepancies among studies on emissions in compact cities^24,25,48 arise from differences in measurement approaches.

In comparison, the scaling factor for cities in the temperate zone increased from −0.36 to −0.32, implying that people in this area occupied more land, although emissions were not reduced based on land area. The scaling factor decreased dramatically for the topical zone, which may be related to a more spacious land area available for urban use. For example, due to the relative abundance of land resources and relative lack of industrial development in Africa, urban sprawl is not overly dense; thus, CO₂ emissions have not increased rapidly compared to the rapid increase in per capita land area⁴⁹ (Fig. 5).

Given that city parameters are closely related to city size⁵⁰, such as the higher population density in larger cities, scale-independent ranking (({SAI})) (as a dimensionless measurement) is used to measure and rank cities based on their CO₂ emissions per capita and emission density, independent of city size⁵⁰. Following such analysis, CO₂ emissions per capita and emission density are evidently overestimated in larger cities, whereas those in smaller cities are underestimated. Thus, it would be unwise to overlook emissions in small cities, as they could have higher CO₂ emissions if they were the same size as larger cities.

Irrespective of scale, cities with high CO₂ emissions per capita are concentrated in the US, Western Europe, Russia, China, Japan, and South Korea. These cities form a belt along the latitude range of 26°9′N–70°29′N, where approximately 68.4% of the top 25% ({SAI}) cities are located. Three additional concentration areas include southeast Australia and New Zealand, South Africa, and Argentina. Conversely, cities with low CO₂ emissions per capita are mainly found in Brazil, India, and western Africa (Fig. 6). In terms of CO₂ emissions per unit area, cities with high scores are mainly located in East and South Asia.

**Fig. 6: Scale-independent ranking and its global distribution based on SAI.**

Discussion

Cities serve as natural and social experiments, embodying both complex systems and heterogeneous characteristics. Utilising a global dataset with uniform and consistent definitions, we examined global urban CO₂ emissions in the 21st century, focusing on four pairs of scaling relationships: total emissions with population size, total emissions with urban land area size, emission per capita with population density, and emission intensity with physical compactness. Our findings revealed that scaling represents an important relationship between population and land area size and emissions, with land area size exerting a stronger influence than population size. Notable, the former remains fairly constant while the latter increases. Therefore, there is a need for more deliberate planning measures.

These systematic scaling relationships highlight how cities, within a broader paradigm, necessitate energy consumption to maintain structure and order. In this regard, cities can be explained using natural laws with flows, nonlinearities, and feedback loops integrating complex interactions among the individuals, households, firms, and these actors and their activities operating in spaces⁶. Furthermore, cities possess distinct social characteristics, as evidenced by scaling relationships, particularly in the context of emissions per capita with population density and emission intensity with physical compactness owing to path dependency, historical factors, and diverse planning cultures and practices across different urban systems¹³. Our research sheds light on the paradoxical view of urbanisation: some perceive cities as natural organisms³, whereas others emphasise their social and human heterogeneity¹³.

Our analysis highlights the inherent challenges posed by urbanisation in addressing climate change, necessitating the forging of synergy among various SDGs, notably SDG 13 (climate action), SDG 11 (sustainable cities), and SDG 8 (economic growth). Such challenges are evidenced by the continuously advancing ranking distribution frontier (Zipf’s law) from 2000 to 2020 and the superlinear scaling relationship between urban population and area size and emissions. Currently, global urban emissions are disproportionally concentrated in large cities in which controlling and reducing emissions become increasingly difficult as city size increases. However, scale-free analysis cautions against underestimating small cities in terms of CO₂ emissions per capita and density. In emerging urbanising regions, such as Africa, CO₂ emissions are increasing at a faster rate than urban population and land area, highlighting the potential benefits of smarter emission strategies for these cities. To achieve this, a ‘learning alliance’ mechanism could be established between ‘mature and young’ cities, facilitating the exchange of ideas, policymaking, planning techniques, and other measures to help young cities minimise their emissions, driven by the underlying principles at play.

Our analysis of the relationship (C/P sim {(P/A)}^{beta }) demonstrates that higher population density may contribute to lower urban CO₂ emissions overall, underscoring the significance of population density as a crucial parameter for urban planning and management in combating climate change. However, it is important to note that high land-use intensity is associated with higher emissions per area. Thus, sophisticated planning and management approaches are necessary to strike a balance between population density and land-use intensity, such as the adoption of a polycentric city structure, which could serve as a key solution towards achieving the aforementioned goals. For example, population density may increase emissions in a particular area but decrease emissions over a wider region. Thus, a tipping point or relationship between these factors should be investigated. Additionally, promoting innovation and the widespread application of eco-friendly technologies to support urbanisation is crucial. Significant efforts are required in this regard, as evidenced by the continued increase in urban emissions, particularly in large cities, which are hubs of innovation.

Our study is based on an ODIAC dataset, which is a production-based accounting approach that is heavily reliant on night-time light data. Although the dataset used here has been improved based on the calibration of power plant emissions, it might be biased in areas where there is a lack of night-time light. More importantly, as cities continuously interact with their hinterlands and exchange energy and materials with areas outside city limits, urban CO₂ emissions are not limited to their built-up area. Therefore, a consumption-based accounting approach is required to consider indirect emissions during urban expansion in future studies.

Methods

Zipf’s law

Following the rank-size rule, Zipf’s law⁵¹ was used to examine the distribution characteristics of city size.

$${rm{InR}}=mathrm{ln}{rm{K}},-,{rm{alpha }}mathrm{ln}{rm{P}}+{rm{varepsilon }},$$

(1)

where R represents the rank of cities, P denotes the population size of cities, α refers to the Pareto index, K is a constant, and ε represents the perturbation term. If the Pareto index α equals 1, it indicates conformity with Zipf’s. A smaller α value signifies a more concentrated distribution of city sizes, resulting in an increased population size gap between cities.

Scaling measurement

The urban scaling law demonstrates the quantitative relationship between city indices and population size at the same time point within a city system. The equation takes the form of a power function:

$${rm{Y}}={{rm{Y}}}_{0}{{rm{N}}}^{{rm{beta }}},$$

(2)

where Y represents the city index, such as built-up area or urban CO₂ emission, N denotes the urban population size, Y0 and β are parameters, and β is the scaling component factor. By taking the logarithm of both sides of Eq. (2), we obtain Eq. (3):

$$log {rm{Y}}={rm{beta }}times log {rm{N}}+log {{rm{Y}}}_{0},$$

(3)

The urban scaling law pertains to the dynamics of urban systems. Traditionally, per capita indicators have been used to measure urban performance, such as per capita GDP or per capita patent numbers. However, this approach overlooks the nonlinear scaling relationship between urban indicators and population size. To eliminate the influence of urban population size, ref. ⁵⁰. proposed scale-adjusted metropolitan indicators (SAMI). In this study, we adopted a similar concept, proposing a scale-adjusted indicator as follows:

$${{SAI}}_{i}=log {Y}_{i}-log ({Y}_{0}{N}_{i}^{beta })=log ({Y}_{i}/{Y}_{0}{N}_{i}^{beta }),$$

(4)

where SAI_i is an indicator (such as GDP) of city i that eliminates the impact of size, which is the residual of the fitting equation of population size of the city indicator, representing the degree of deviation from its expected value. Y_i is the true value of an index for city i, Y₀N_i^β represents the estimated value of an indicator for city i, N_i signifies the permanent population size of city i, and Y₀ and β are the fitting parameters.

Robustness analysis

To ensure data reliability, in addition to extracting cities based on connected built-up areas with a minimum 5000 inhabitants for each period, we re-extracted all data using 2010 as the base year to measure place-focused city growth. Patches that had not developed into cities by 2000 and 2005 were considered as cities, whereas some cities in 2015 and 2020 were excluded, that is, thus ensuring a consistent number of cities for each year. Comparing the results of the two derived datasets confirmed the reliability of our analysis (Supplementary Information).

Identification and derivation of cities worldwide

Defining cities is critical; however, the definition used for cities varies worldwide². The Organisation for Economic Cooperation and Development has made significant efforts to define functional cities based on connected built-up areas, which is conceptually meaningful and empirically consistent, facilitating global investigation and comparison⁵². Additionally, many countries utilise population as a key indicator for defining cities, often employing a threshold of 5000 inhabitants^52,53. Accordingly, cities in this study were defined and measured based on connected built-up areas over 1 km² inhabited by at least 5000 individuals.

Built-up area was derived from global land-use data with a spatial grid resolution of 300 m obtained from the European Space Agency Climate Change Initiative dataset. Global population data were obtained from Landscan Global, which is part of ORNL’s Landscan program. Additionally, administrative boundaries of countries and cities worldwide were acquired from the Global Administrative Division Database (GADM) to assist with the analysis. The analytical periods considered in this study were 2000, 2005, 2010, 2015, and 2020.

Calculating CO₂ emissions

To calculate CO₂ emissions, we utilised the urban areas and aggregated monthly emission data for each analysed year. These data were obtained from the ODIAC Fossil Fuel Emission Dataset published by the Global Environmental Research Centre (Nike.go.JP), at a spatial resolution of 1 × 1 km. The records covered the period from 2000 to 2019, and data from 2019 were used as a proxy for 2020.

Introduction

Results

Global overview of urban expansion and CO2 emissions

Urban scaling relationships of CO2 emissions