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.

中文翻译：

---

城市足迹的形状紧凑性

摘要 城市人口密度在大量关于紧凑城市范式的文献中被描述为城市的关键紧凑性属性，但城市足迹的形状紧凑性几乎不值得一提。本文试图纠正这一点。我们回顾了关于紧凑城市范式的文献，特别关注城市形态与气候变化之间的关系，并关注城市的十二个物理属性，这些属性使它们或多或少地紧凑。在其他条件相同的情况下，人口密度和形状紧凑度都有助于确定城市的平均出行距离，从而影响其能源消耗和温室气体排放。它们还会影响基础设施线路的长度和通勤时间。因此，原则上，增加城市的形状紧凑性或人口密度可以以不同但相似的措施为缓解气候变化做出贡献。有强大的力量推动城市足迹变得更加紧凑——即圆形或接近圆形的形状——这些力量随着时间的推移而演变。随着时间的推移，还有强大的力量推动城市足迹变得不那么紧凑。我们介绍这些力量并说明它们对特定城市的影响。然后，我们将重点放在一小组用于衡量城市形状紧凑性的指标上。我们使用它们来测量从三个时间段的 200 个城市的分层全球样本中从卫星图像中获得的城市足迹：1990、2000 和 2014 年。我们发现世界各地城市足迹的形状紧凑性与城市规模、面积无关， 密度，和收入，毫不奇怪，它受到地形的强烈影响。我们还发现它在 1990 年至 2014 年间总体下降，并解释了这种下降的一些来源。我们通过评估增加城市形状紧凑性的方式来结束本文，以使其能够在未来几十年更好地缓解气候变化。