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Urban areas play an unprecedented role in potentially mitigating climate change and supporting sustainable development. In light of the rapid urbanisation in many parts on the globe, it is crucial to understand the relationship between settlement size and CO 2 emission efficiency of cities. Recent literature on urban scaling properties of emissions as a function of population size have led to contradictory results and more importantly, lacked an in-depth investigation of the essential factors and causes explaining such scaling properties. Therefore, in analogy to the well-established Kaya Identity, we develop a relation combining the involved exponents. We demonstrate that application of this Urban Kaya Relation will enable a comprehensive understanding about the intrinsic factors determining emission efficiencies in large cities by applying it to a global dataset of 61 cities. Contrary to traditional urban scaling studies which use Ordinary Least Squares (OLS) regression, we show that the Reduced Major Axis (RMA) is necessary when complex relations among scaling exponents are to be investigated. RMA is given by the geometric mean of the two OLS slopes obtained by interchanging the dependent and independent variable. We discuss the potential of the Urban Kaya Relation in main-streaming local actions for climate change mitigation.

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Much of human progress today can be attributed to the conglomeration of skilled people to a certain space at a given time. Modern day cities stand tall as epitomes of human innovative power and co-creation capacity. However, similar to the "Yin and Yang" depicted in the ancient Chinese philosophy, cities as dynamic systems do exhibit their "Yin" side. Urbanization, increasing prosperity, and (physical, social) infrastructure systems lead to an unprecedented increase in global energy and resource consumption. Much of anthropogenic transformation of Earth's environment in terms of environmental pollution at local level to planetary scale in the form of climate change is currently taking place in cities. Therefore, the ultimate fate of humanity predominantly lies in the hands of technological innovation, urbanites' attitudes towards energy and resource consumption and development pathways undertaken by current and future cities.The complex nature of cities lead to the quest for identifying appropriate theories and models which capture urban dynamics more appropriately. Drawing inspiration from the advances in the complexity sciences, a new science of cities evolved in the recent years which acknowledged cities as a result of various bottom-up evolutionary processes (Batty, 2012). Amongst others, urban scaling (Bettencourt et al., 2007) has been identified as a crucial part in understanding urban dynamics. Urban scaling depicts that certain urban indicators (I) such as GDP, crime rates, infrastructure, and innovation can be described through a power-law relationship as a function of urban population (P) as follows