Focus: City Structure Influences Nighttime Temperatures

Physics 11, 25
Mathematical analysis of the two-dimensional layout of a city reveals much about its three-dimensional structure and provides useful measures of the urban heat island effect.
Getty Images/kokouu/choness
In the heat of the night. The geometry of Chicago (left) is relatively crystalline, while Los Angeles (right) is more liquid. A city’s “texture” shows a strong correlation with the magnitude of its nighttime heat island effect.

Cities tend to be warmer than surrounding rural areas. The general reasons for this “urban heat island” (UHI) effect are not hard to understand, but a statistical analysis now establishes a connection between the magnitude of the nighttime temperature excess and the geometrical pattern of city streets and buildings. The relationship between heating and what the researchers call the “texture” of a city’s layout may prove helpful in devising energy conservation strategies in downtown neighborhoods and in designing new urban areas.

Some studies have indicated a loose correlation between the size of the UHI effect and population. Others have looked at the geometry of individual streets, in particular the “sky view” factor, which measures the fraction of the sky that is visible from the street and influences how well buildings soak up daytime heat and radiate it away at night. But the connections between such factors and the UHI effect have proven hard to tease out.

Atmospheric processes complicate daytime urban heating, so Roland Pellenq of Aix-Marseille University, France, and the Massachusetts Institute of Technology, Cambridge, and his colleagues chose to focus on the nighttime UHI effect, which arises almost entirely from the release of heat that was absorbed by structures and pavement during the day. They used several years’ worth of hourly temperature measurements from 22 weather stations in mainly residential areas of 14 US cities and compared them with similar data from nearby rural areas. For each urban station they derived a single number that indicated how much warmer the city location was at night than the corresponding rural area.

The next step was to find a metric that would combine both large-scale and street-scale aspects of a city’s layout. Pellenq and his colleagues adapted a tool commonly used in condensed matter physics called the radial distribution function. This function represents the probability of finding an atom at a given distance from another atom; it shows peaks corresponding to favored interatom distances in a crystal lattice but is flatter for an amorphous solid or a liquid.

For each of the 22 stations, the researchers marked every building or group of connected buildings within 3 miles as a point and calculated the radial distribution function. Each function had a characteristic cluster size, measured by the radius at which the radial distribution function fell to its first minimum, which turned out to be 1.5 times the average separation between buildings. Although this scale is a purely two-dimensional measure of a city’s layout, taking no account of building heights or volumes, it showed a strong inverse correlation with the average nighttime UHI effect: the closer packed the buildings, the greater the excess temperature.

To investigate the reason for this correlation, the team delved further into city plans. Using the Mermin order parameter, a statistic that distinguishes between grid-like and more random city layouts, they found that Chicago is the most crystalline of the cities they studied, while Los Angeles is the most liquid. A combination of the Mermin parameter and building density correlated well with the cluster size, suggesting that more orderly neighborhoods are built from smaller clusters of buildings. Thus the cluster size, despite being a two-dimensional average over all orientations, is a good proxy for more complex measures of a city’s geometry, says Pellenq.

The team also constructed a model of the building radiation responsible for the UHI effect in terms of the total surface area of buildings in each cityscape. This model incorporated building heights, so it effectively included the sky view factor. It also reproduced the correlation between cluster size and the UHI effect—further evidence that this two-dimensional measure captures important aspects of the three-dimensional structure, or what the team calls the city “texture.” The researchers note that the weather station neighborhoods have uniform building styles (such as high rise or single story), which may explain why 2D parameters can effectively represent 3D properties.

Pellenq and his colleagues say that understanding the relationship between city texture and the UHI effect could help planners both in warm- and cold-climate cities, because it can either increase demand for air conditioning or lower demand for heating. Scott Krayenhoff, an environmental scientist at the University of Guelph, Ontario, likes the research but points out some shortcomings. For example, identical city layouts can show different UHI effects depending on what building materials are used. Nevertheless, Krayenhoff says that the work is notable, as it applies spatial analysis techniques to urban climatology, and he hopes that it will trigger more collaborative research between the two fields.

This research is published in Physical Review Letters.

–David Lindley

David Lindley is a freelance writer in Alexandria, Virginia, and author of Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science (Doubleday, 2007).


Subject Areas

Energy ResearchStatistical PhysicsInterdisciplinary Physics

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