Urban Kaya Relation

The efficient, the intensive, and the productive: insights from the urban Kaya relation

Ramana Gudipudi, Diego Rybski, Matthias K. B. Lüdeke, Bin Zhou, Zhu Liu, Jürgen P. Kropp Potsdam Institute for Climate Impact Research, 14473, Potsdam, Germany John F. Kennedy School of Government, Harvard University, Cambridge, Massachusetts 02138, USA Resnick Sustainability Institute, California Institute of Technology, Pasadena, California 91125, USA Cambridge Centre for Climate Change Mitigation Research, Department of Land Economy, University of Cambridge, 19 Silver Street, Cambridge CB3 9EP, UK Dept. of Geo- and Environmental Sciences, University of Potsdam, 14476, Potsdam, Germany

Considering their current CO2 emissions globally, the role of cities in climate change mitigation is unprecedented. Given the strong global urbanization trend, it is crucial to understand whether large urban areas are more emission efficient in comparison to smaller ones. Recent literature on urban scaling properties of emissions as a function of population size led to contradicting results and more importantly lacked an in-depth investigation of the factors leading to such scaling properties. Therefore, in analogy to the well-established Kaya Identity, we developed an urban Kaya relation to investigate different scaling properties of the indicators within the Kaya Identity for a global dataset of 61 cities. Contrary to traditional urban scaling studies which use ordinary least squares regression, we show that orthogonal regression is necessary when complex relations among scaling exponents are to be investigated. Our results show that large cities in developed countries are typically more emission efficient than smaller ones due to their less than proportional emissions given their energy consumption. In contrast, larger cities in developing countries are typically less emission efficient owing to more than proportional GDP and emissions with respect to population and energy consumption, respectively. From a climate change mitigation point of view, our results indicate that large cities in developed regions should prioritize actions on improving energy efficiency while cities in developing regions should focus on adopting improved technologies to reduce emissions from energy conversion.

1 Introduction

Cities, like biological organisms, thrive on natural resources while releasing pollution and waste as by-products. Harbouring more than 50 % of the global population, contemporary cities generate 80 % of the Gross Domestic Product (GDP) while consuming approximately 70 % of energy supply (??) and releasing approximately three quarters of global CO2 emissions (?). Drawing parallels between the allometric scaling in biological systems to that of cities, recent literature has revealed how certain socioeconomic and environmental indicators in cities scale as function of city size (?). Since a large fraction of the global population is expected to be urbanized by the end of this century (?), contemporary and future cities are acknowledged to play a pivotal role in global sustainability and climate change mitigation. Given this strong global urbanization trend, one of the crucial questions that needs to be addressed is whether large cities are more or less emission efficient compared to smaller cities.

The application of allometric scaling to cities (often referred to as “urban scaling”) has triggered copious research in the contemporary science of cities, see e.g. (???????). Urban scaling relates a city indicator (e.g. total urban energy consumption) with city size (e.g. population). Assuming power-law correlations, the analysis depicts how these indicators scale with population size and whether large cities are more or less efficient. A sub-linear scaling (i.e. slope ) indicates that large cities consume less energy given their size, while a unit slope () depicts proportionality, and a super-linear scaling () indicates that large cities consume more energy given their size.

The state-of-the-art research aiming at identifying whether large cities are more energy and emission efficient led to contradicting results and have been largely limited to the cities in the developed world. For instance, studies on total CO2 emissions for cities in the USA showed not only an almost linear (?) but also a super-linear (?) scaling. A similar study for European cities depicted a super-linear scaling (?). Studies on household electricity consumption in Germany and Spain revealed an almost linear scaling (??). With respect to energy consumed and the subsequent emissions from urban transportation in the USA (?) found a negative correlation between population size and gasoline consumption; while (?) showed a super-linear scaling of emissions with population size. A similar study done on British cities (?) found a linear scaling between transport emissions and population size while finding a super-linear relationship between emissions and the total street length. While all the aforementioned studies followed their own criterion for establishing a city definition and choosing an indicator (whether to consider the total energy consumption and subsequent urban emissions or sectoral emissions from buildings and transport separately), little is known regarding the intrinsic factors that lead to such different urban scaling with respect to energy consumption and emissions.

In this paper we tackle the problem from a different perspective and transfer the idea of the well-established Kaya Identity to urban CO2 emissions using a homogeneous dataset of 61 global cities. Originally, the Kaya Identity has been proposed to attribute global emissions to demographic, economic, and technological drivers (??). In the case of cities, we make use of urban scaling which leads to an Urban Kaya Relation. Then the scaling of CO2 emissions with city size can be attributed to the scaling between population, GDP, energy, and emissions. To the best of our knowledge, such an attempt to obtain a deeper insight into the scaling of emissions with population using indicators in the Urban Kaya Relation is unprecedented. Recent literature has identified that the energy consumption and the subsequent emissions depend on the city type (i.e affluent and mature cities in developed countries versus cities in transition countries with emerging and nascent infrastructure (??). Therefore, we apply the Urban Kaya Relation to these cities separately.

2 Urban Kaya Relation

The Kaya Identity has been proposed to separate global CO2 emissions into contributions from global population, GDP per capita, energy intensity, and carbon intensity (????). It relates CO2 emissions (), population (), GDP (), and energy () according to


While the GDP per capita () is a common quantity, the energy intensity () can be understood as the energy necessary to generate GDP, and the carbon intensity () as the efficiency in energy production and consumption (technological). Equation (1) is an identity since it cancels down to .

As outlined above, here we are interested in how the urban CO2 emissions scale with urban population size, i.e.


The value of tells us if large or small cities are more efficient in terms of CO2 emissions. Without loss of generality, we propose that the other quantities also exhibit scaling, i.e.


E.g., it has been reported that GDP scales super-linearly () with population (?). In a sense, the exponents take the role of GDP per capita, energy intensity, and carbon intensity in the original Kaya Identity, Eq. (1).

Combining Eq. (2)-(5) leads to


Thus, in analogy to the original Kaya Identity, Eq.(6) provides an Urban Kaya Relation according to which the exponent relating emissions and population is simply given by the product of the other involved exponents. This permits us, to attribute non-linear scaling of emissions with city size, Eq. (2), to potential urban scaling of GDP with population, energy with GDP, or emissions with energy. For the sake of completeness in A we also provide another two complementary forms of Kaya Identities and corresponding Urban Kaya Relations.

However, the exponent is usually obtained from the data and a linear regression , where is another fitting parameter. Equations (2)-(5) represent idealizations and in practice correlations are studied which can come with more or less spread around the regression. Ordinary Least Squares (OrdiLS) might make sense, when dependent and independent variables are clearly defined, e.g. in the case of GDP vs. population it might be preferable to minimize residuals of GDP. Here we found that applying Ordinary Least Squares to and generally leads to (??) so that also Eq. (6) would not be valid. In our context, however, dependent and independent variables need to be exchangeable and we obtained more robust results () by applying Orthogonal Least Squares (OrthLS). Therefore, we apply OrthLS throughout the paper. In OrthLS the distance between the regression manifold and the points to be approximated is measured perpendicular to both the axis in contrast to approximation along the axis of dependent variable in OrdiLS. Technically, we use the prcomp-function in R (version 3.2.3). In order to quantify the uncertainty of the estimated exponents, we explore bootstrapping, i.e. 20,000 replications.

3 Data

A major pre-requisite while investigating the scaling effects of urban energy consumption and emissions is a consistent definition and demarcation of cities from their hinterlands. However, it is often very challenging to find this data at such detailed spatial resolutions. Therefore, the analysis conducted in this paper is limited to 61 global cities, i.e. the union of cities for which the 4 quantities are available, i.e. (i) total final energy consumption, (ii) CO2 emissions, (iii) GDP, and (iv) population.

The population, GDP, and total final energy consumption data used in this study is taken from the Chapter 18 “Urban Energy Systems” of the Global Energy Assessment (?). This database includes the per capita total final energy consumption of 223 global cities, their respective population and GDP for the year 2005. The data on emissions is compiled from various sources including city specific reports (compiled by organizations such as ICLEI, CDP and C40 cities) and data which is published in peer reviewed journal publications (?).

The cities with available data are located in 12 countries. The GDP per capita of these countries shows two groups. One ranging from 740 USD to 4,700 USD and the other from 26,000 USD to 44,000 USD (year 2005). These two groups can be considered developing and developed countries and represent the Non-Annex 1 and Annex 1 countries as reported by the United Nations Framework Convention on Climate Change (UNFCCC), respectively.

Amongst the 61 cities used in this analysis 22 cities are from the Annex I countries and 39 cities from Non-Annex I countries. The database consists of cities of varying population sizes across 6 continents including 7 megacities (with a reported population above 10 million). Within countries in Annex 1 regions, 7 cities in the USA, 4 cities from the UK, 2 cities from Germany, Spain, Australia, Italy, France respectively, and 1 city from Japan are considered in this study. With respect to cities in Non-Annex 1 countries 33 cities from China, 2 cities from India, South Africa, and Brazil were included.

Apparently, on the country scale, CO2 emissions per capita strongly depend on the development of the considered country, see e.g. (?) and references therein. Here we pool together cities from many different countries, including from developing countries; as a consequence, the data needs to be normalized prior to the analysis in order to account for such baseline emissions. Therefore, we employ the method proposed by (?) and normalize the data for each country by the average logarithmic city size () and indicator value (e.g. ) within our sample.

4 Results

We begin by looking at the scaling of emissions with population size for all the 61 cities considered in this study. The slope of this logarithmic orthogonal regression (see Fig. 1) is almost equal to one (), however, the pattern of residuals is diverse as also reported in some earlier studies (?). This clearly depicts the diversity in urban energy metabolism leading to varying emissions (?). This result shows that typically large cities are not more emission efficient compared to smaller cities. However, as it can be observed in Fig. 1, cities from the developed world (Annex 1 cities showed in green color) seem to fit much better than cities from the developing world (all Non-Annex 1 cities). Therefore, as a next step, we analyzed the scaling properties of emissions with size independently for these cities depending on the economic geography (i.e. Annex 1 cities vs. Non-Annex 1) of the country in which these cities are located.

Figure 1: Scaling of CO2 emissions with population size for 61 global cities. The data has been normalized by substracting average logarithmic values, see Sec. 3. The solid line is the regression obtained from Orthogonal Least Squares (Sec. 2) and the slope is , see Tab. 1 for details.

In Fig. 2 we see that the scaling of emissions with the population size indeed has a dependence on the economic geography of the country. We found a sub-linear scaling for cities in Annex 1 regions () and a super-linear scaling for cities in the Non-Annex 1 regions (), see Tab. 1. The fit appears to be good for cities in Annex 1 regions which are broadly characterized as service sector oriented economies. However, in industry dominated Non-Annex 1 cities with widely varying personal and energy intensity of production the goodness of fit appears to be relatively poor. This result shows either that the emissions data from Non-Annex 1 cities is not as accurate, or that population is a good proxy to estimate emissions for cities in Annex 1 regions while there seems to be other factors that influence emissions for cities in Non-Annex 1 cities.

Figure 2: Scaling of CO2 emissions with population for cities in Annex 1 countries (panel A) and in Non-Annex 1 countries (panel B). Each bubble reflects the emission intensity and GDP per capita for a given city in Annex 1 (panel A) and Non-Annex 1 countries (panel B), respectively. While the slope of the Orthogonal Least Squares for Annex 1 countries is found to be sub-linear (), it is super-linear () with respect to cities in Non-Annex 1 countries. As in Fig. 1 the data of both axis has been normalized subtracting average logarithmic values, see Sec. 3. The grey line indicates a slope of 1 and is included for comparison.
Equation: Eq. (2) Eq. (3) Eq. (4) Eq. (5) Eq. (6)
Scaling of: Emissions with population GDP with population Energy with GDP Emissions with Energy
All Cities 1.02 [0.84,1.23] 1.16 [1.04,1.30] 0.89 [0.69,1.09] 0.96 [0.75,1.22] 0.03
Annex 1 0.87 [0.76,0.97] 1.04 [1.00,1.07] 0.99 [0.67,1.45] 0.79 [0.54,1.15] 0.06
Non-Annex 1 1.31 [0.81,1.76] 1.40 [1.07,1.87] 0.78 [0.54,1.00] 1.16 [0.90,1.48] 0.04
All Cities (OrdiLS) 0.80 0.98 0.64 0.67 0.38
Table 1: Scaling exponents and Urban Kaya Relation. The Table lists the various estimated exponents and the last column shows how well the Urban Kaya Relation performs. The exponents are listed for all cities, cities in Annex 1 countries, and cities in Non-Annex 1 countries (see Sec. 3). All exponents have been obtained from Orthogonal Least Squares (see Sec. 2) except for the last row, where Ordinary Least Squares have been applied for comparison. The square brackets give 95 % confidence intervals from bootstrapping (20,000 replications). Inspired by the notation used in (?) we put the following symbols. , at least 66.6 % of the replications lead to exponents larger than ; , 33.3 % to 66.6 % of the estimates are larger than , and , less than 33.3 % are larger than . While Eq. (6) works reasonably well for Orthogonal Least Squares, for Ordinary Least Squares the estimated exponents are incompatible (last row).

As a next step we looked at scaling of each of the indicators in the Urban Kaya Relation namely: the scaling of GDP with population () Eq. (3), scaling of energy intensity () Eq. (4), and carbon intensity () Eq. (5), in these cities. Table 1 lists the exponents of each of these indicators. From a global perspective, our results suggest that the almost linear scaling of emissions with population size could be attributed to the almost linear scaling of carbon intensity and the trade-off between scaling of GDP with population and the scaling of energy intensity (i.e. they compensate each other).

In the case of cities in Annex 1 countries, our results show that the large cities typically have lower emissions per capita compared to smaller cities because of the sub-linear scaling of the carbon intensity. This can be attributed to the carbon intensity of the electricity generation supply mix, vehicle fuel economy and the quality of public transit in these cities (?). We found a linear scaling of GDP with population. Our result shows that doubling the GDP in these cities will lead to an almost similar increase in energy consumption. Such a linear scaling can be largely attributed to the consumption patterns and infrastructure lock-in behavior in largely service based economies (??).

We further checked if the sub-linear scaling of emissions with population for cities in Annex 1 countries could be attributed to a possible sub-linear scaling with respect to their total final energy consumption Eq. (A). Even in a completely decarbonized world, the question of energy efficiency will persist. Our results show that large cities in Annex 1 countries are not energy efficient (with respect to their population) () compared to smaller cities. This result indicates that although the per capita energy consumption in large cities is similar to that of smaller cities, it is the better technologies employed in larger cities that makes their per capita emissions lower than smaller cities.

With respect to cities in Non-Annex 1 countries, our results show that the super-linear scaling of emissions with population is due to two factors: (1) super-linear scaling of GDP with population and (2) super-linear scaling of carbon intensity. However, we found that doubling the GDP in these cities will lead to a less than double increase in energy consumption. This can be attributed to the prevalence of energy poverty in these cities (?). Large cities in Non-Annex 1 countries benefit economically (more GDP) from the urban poor who consume less energy and have limited access to electricity. Therefore, large cities in this region are more energy efficient compared to smaller ones.

5 Discussion & Conclusions

Urban areas are often identified as the focal spatial units for improving energy efficiency and climate change mitigation (??). Given the strong global urbanization trend, the debate whether large cities are more energy and emission efficient compared to smaller cities is extremely relevant as this dictates much of the policy level interventions at regional and national scale.

The predominant factors that determine the energy consumption in cities include: urban form, local climate defining the amount of building heating/cooling energy requirement, the age and type of public infrastructure, the choices of personal (and freight) transport within the city, the degree of industrialization and the price of the fuels finally determining the electricity and energy consumption behavior of the urbanites (?). Apart from the aforementioned factors, total emissions at urban scale depend profoundly on the definition of the city (i.e. the city boundaries), the accounting approach (consumption or production based), the energy intensity of the economy, the emission intensity of the electricity production, the fuel mix and the efficiency of the technologies employed at local level to consume the energy (???). Therefore, it is often difficult to find a consistent dataset at a global scale covering all these aspects. Since the number of cities considered in this analysis is constrained by the data scarcity, the broader conclusions drawn in this paper should be treated cautiously. For cities where energy consumption and emission data are available, we propose in this paper how the indicators in the Kaya Identity can be used to further disentangle the scaling relationship between emissions and population.

The majority of large cities in Annex 1 regions have mature urban infrastructure with rather well established energy consumption patterns. Therefore, the per capita energy consumption in large cities is typically similar to that of smaller cities. However, our results show that large cities in these regions have lower emissions compared to smaller cities, which clearly depicts the usage of more efficient technologies in electricity generation and by use of more emission efficient modes of public transportation. Since it is projected that cities in these regions will further urbanize (although at a slower rate compared to those in Non-Annex 1 countries)(?), from climate change mitigation point of view, the key challenge in these cities is to further decrease their energy and carbon intensity while ensuring economic stability.

Cities in emerging countries such as China, India and Brazil where the economic geography is (pre)dominated by the secondary sector face a bigger challenge with respect to climate change mitigation. Our results show that larger cities in these regions typically have more per capita emissions compared to smaller cities. From one point of view, it may be good news that large cities in these regions are not emission efficient since much of the urbanization in these regions is going to happen in small and medium size cities (?). However, since it is projected that most of the future megacities are going to be in these regions, the challenges these cities face are twofold: (1) improving the carbon intensity by deploying efficient technologies for the generation of electricity and improvement of public transportation, while (2) ensuring that these cities don’t develop similar energy consumption patters to those of Annex 1 cities (with infrastructure lock-in behavior) and addressing the issue of energy poverty.

It is important to mention two caveats on urban scaling. Firstly, as mentioned in Sec. 3, city definitions can have an influence on urban scaling (???). An illustrative example is the city of Chongqing. Its urban boundary is much bigger than the city of Chongqing itself. Therefore, the urban population of Chongqing exceeds that of Shanghai and Beijing. However, here we had to build our analysis on available data and leave detailed studies based on e.g. the methodology proposed in (?) to follow-up research. Secondly, it has been shown that whether the estimated exponents are statistically different from 1 depends on the assumptions made (?). In this paper, we assumed scaling enabling exponents different from 1. We show the consistency in these scaling parameters in the form of Eq. (6.)

Our results corroborate the results of previous studies which showed the significance of economic geography on the scaling properties of emissions with population (?). Further support comes from a recent study, where a methodology other than urban scaling has been applied and completely different data has been used (?). In this study, we further elaborate on the intrinsic factors leading to such scaling of emissions with population using the indicators in the Kaya Identity. While the question whether large cities are more energy and emission efficient can be addressed more profoundly as reliable and consistent data on energy consumption and emissions at finer resolutions on a global scale is available, the measures to improve energy efficiency and curtailing emissions are already taking place in cities globally. As focal points for climate change mitigation, our results therefore suggest that cities in Annex 1 regions should primarily focus on improving their energy efficiency while cities in the Non-Annex 1 regions should focus on a technological shift towards providing universal access to energy and deploy more efficient technologies.

Last but not least, we need to mention the role of urban population density as an important factor in determining the energy consumption and subsequent emissions. On the one hand, it has been shown that urban CO2 emissions from transport energy per capita decrease with population density (???). On the other hand, there is a theoretical connection between urban indicators, population, and area scalings (??). Combining density with the Urban Kaya Relation introduces further complexity which we leave to be addressed by future research.


We thank M. Barthelemy, H. V. Ribeiro, and L. Costa for useful discussions. This work emerged from ideas discussed at the symposium Cities as Complex Systems (Hanover, July 13th-15th, 2016) which was generously funded by VolkswagenFoundation. The research leading to these results has received funding from the European Community’s Seventh Framework Programme under Grant Agreement No. 308497 (Project RAMSES). Zhu Liu acknowledges support by the Green Talents Program held by the German Federal Ministry of Education and Research (BMBF).

Appendix A Kaya II and III

It needs to be mentioned that there are another two identities complementary to the original Kaya Identity, Eq. (1), namely

or variations. We propose to denote Eqs. (1), (A), and (A), “Kaya I”, “Kaya II”, and “Kaya III’, respectively. The identities Kaya II and III involve two intensities which do not appear in Kaya I, namely and , i.e. energy per capita and carbon per GDP, respectively. In the urban scaling picture these take the form

The relations corresponding to Eqs. (A) and (A) are

Other combinations of , , , or involve only two components each.



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