Graphical abstract A) Some cities, like Valledupar, Colombia, have more compact urban footprints than other cities: Their shape is closer to that of a circle, the most compact of shapes. In 2014, 84% of the urban footprint of Valledupar was within its Equal Area Circle (red) centered at its centroid. In contrast, Cabimas, Venezuela (right) had only 19% of its urban extent within its Equal Area Circle in that year. Valledupar was the most compact and Cabimas the least compact in a global sample of 200 cities. The shape compactness of urban footprints matters, just like urban density matters. Other things being equal, both metrics determine the average travel distances in cities, and hence affect their energy consumption and their greenhouse gas emissions. They also affect the length of infrastructure lines and the length of commutes. But while urban population density has featured in a large body of literature on the compact city as the key compactness attribute of cities, the shape compactness of urban footprints has hardly deserved a mention. This essay seeks to correct that. B) The urban footprints of some cities, like Caracas, Venezuela, are not compact in the sense of their shape being close to that of its Equal Area Circle (red). Only 63% of its footprint was within its Equal Area Circle in 2014. But Caracas was as compact as can be when considering its Buildable Land Circle, a circle centered at the centroid of its urban footprint that contained a dry land area with a slope of 15% or less equal to the area of its urban footprint (orange). In comparison, Modesto, USA, situated on a flat, dry plane, had the same level of compactness when considering its Buildable Land Circle: Only 59% of its urban footprint was both within its Equal Area Circle and within its Buildable Land Circle. Display Omitted

Highlights • Both urban density and the shape compactness of urban footprints determine travel distances in cities, and hence their greenhouse gas emissions. • We explore and illustrate the strong forces that push urban footprints to become more or less compact—i.e. more or less circular in shape—over time. • Maps of urban footprints of a global sample of 200 cities circa 1990, 2000 and 2014 are used to measure, compare, and track their shape compactness. • We find that the shape compactness of cities is independent of city size, area, density, and income and that it is strongly affected by topography. • We also find that the shape compactness of urban footprints has declined between 1990 and 2014 and explain some of the sources of this decline.

Abstract Urban population density has featured in a large body of literature on the Compact City paradigm as the key compactness attribute of cities, yet the shape compactness of urban footprints has hardly deserved a mention. This essay seeks to correct that. We review the literature on the Compact City Paradigm with a special focus on the relationship between urban form and climate change, and focus on twelve physical attributes of cities that make them more or less compact. Other things being equal, both population density and shape compactness help determine the average travel distances in cities, and hence affect their energy consumption and their greenhouse gas emissions. They also affect the length of infrastructure lines and the length of commutes. In principle, therefore, increasing either the shape compactness or the population density of cities can contribute—in different yet similar measure—to mitigating climate change. There are strong forces that push urban footprints to become more compact—that is, circular or near circular in shape—and these forces have evolved over time. There are also powerful forces that have pushed urban footprints to become less compact over time. We introduce these forces and illustrate their effects on particular cities. We then focus on a small set of metrics for measuring the shape compactness of cities. We use them to measure urban footprints obtained from satellite imagery in a stratified global sample of 200 cities in three time periods: 1990, 2000, and 2014. We find that the shape compactness of urban footprints the world over is independent of city size, area, density, and income and that, not surprisingly, it is strongly affected by topography. We also find that it has declined overall between 1990 and 2014 and explain some of the sources of this decline. We conclude the paper by assessing the ways in which the shape compactness of cities can be increased to make them better able to mitigate climate change in decades to come.