Tikalon Blog by Dev Gualtieri

Heat Islands

June 11, 2018

Model railroading was once a popular pastime. Young Sheldon has a large model railroad setting in his parents' garage, and it's been said that early computer clubs evolved from model railroad clubs, such as the MIT Tech Model Railroad Club, since these involved tinkering with electrical circuits, relay logic, and crude automation. As children, my brothers and I were gifted with a Lionel train set, the powerful variable voltage transformer of which I was happy to have for subsequent science experiments. As an indicator of the decline of model railroading as a hobby, Lionel petitioned for Chapter 11 bankruptcy protection in 2004, to recover by 2008.

A model railroad will necessarily have a circular track to allow continuous operation. The circular track will traverse bridges and tunnels in modeled rural areas, but a city setting will often be incorporated in its interior. Although the tracks are circular, the streets of the cityscape are invariably arranged as a rectangular grid. This grid layout is the street pattern of nearly every city.

The street plan of the United States Capital is generally a grid, although its designer, French military engineer, Pierre Charles L'Enfant (1754-1825), mixed things up a bit with some diagonal avenues that intersected some grid points at circles and plazas (see figure).

L'Enfant's plan for the area of the US Capitol

L'Enfant's plan for the area near the US Capitol building. A March, 1792, engraving on paper from the US Library of Congress, via Wikimedia Commons

It's commonly known that cities are warmer than their suburbs, an effect known as urban heat island. This effect can be quite dramatic, amounting to a differential temperature between rural and urban areas up to 5°C (9°F) during night hours. The principal cause of this effect is the structures built on the once natural landscape, although waste heat from the energy used by the city population is another factor. Anyone who's traversed an asphalt parking lot in a city knows that such dark expanses are very efficient in storing the Sun's infrared energy, absorbing more than 75% of solar radiation.

As I wrote in a previous article (White Roofs, March 19, 2012), One way to mitigate heat island effects is by using building materials with a high albedo, the technical term for the ratio of reflected to received irradiance. Fresh snow has an albedo that's generally above 0.8, while fresh asphalt has an albedo of about 0.05. The roof of my house is white, which should keep me cooler in the summer. You can see a portion of my roof in an earlier article (Partial Solar Eclipse at New Jersey, August 24, 2017)

While I don't have supporting data for the white roof principle for my own house, NASA and various New York City organizations tested this idea in 2012. They examined the differences between roofs covered with white and dark roofing materials and found that an inexpensive white roof covering can mitigate the urban heat island effect. Their data for side-by-side roof patches on the Museum of Modern Art showed that a white painted roof surface was 42 °F (23 °C) cooler than an unpainted black roof.[3]

A comparison of white (white) and black (black) roof temperatures atop the Museum of Modern Art in New York City during a roof surfacing materials test, June-August 2011. The white surface was produced using an acrylic paint coating promoted by the New York City CoolRoofs program.(NASA image/Stuart Gaffin, et al.)[2]

Radiation energy loss is most effective at very high temperatures, since it follows the Stefan-Boltzmann law that states that the radiated power from a black body is directly proportional to the fourth power of temperature; viz,

where j is the black-body emissive power, T is the absolute temperature, and σ, called the Stefan-Boltzmann constant, 5.67037 x 10⁻⁸ watt meter⁻² kelvin⁻⁴, can be expressed as a combination of some fundamental constants,

in which k is the Boltzmann constant, h is Planck's constant, and c is the speed of light. In the real world, nothing exists in isolation. At the same time an object is radiating energy, it's absorbing the radiant energy from nearby objects. Water exposed to a clear night sky on a cold night might freeze, since it's radiating a lot more energy than it's absorbing, but that same water in a bowl on your front porch would stay liquid, since its thermal environment is warmer.

A team of engineers from the Massachusetts Institute of Technology (Cambridge, Massachusetts), the Universite Paris-Saclay (Orsay, France), the University of California - Irvine (Irvine, California), and Aix-Marseille Université (Marseille, France), has examined how the texture of a city, as measured by the distribution of buildings and their sky exposure, affects the nocturnal urban heat island effect.[4-6] They examined city layouts and the temperature differences between urban and rural environments over the course of several years for more than fifty cities worldwide using a heat radiation scaling model to demonstrate a strong correlation between the overnight heat storage and city texture.[4-6]

To underscore the idea that mitigating the heat island effect an important problem, a 1995 Chicago heatwave of 100+ degrees (F) killed an estimated 739 people.[6] In response, cities have looked at reflective construction materials, as noted above, planting trees, and painting road surfaces white.[6] Roland J.-M. Pellenq, a Senior Research Scientist at MIT and an author of this study, realized that the relative positioning of buildings might offer insight into the effect, just as the arrangement of atoms on a surface can determine physical properties.[6]

The research team looked at nighttime data, only, since night offered a simplified environment in which heat was just being lost and not also stored. They used a dataset of hourly temperature readings from several years of measurements from 22 weather stations of the National Oceanic Atmospheric Administration in 14 US cities to calculate the differential temperature with respect to representative rural areas.[5-6]

They used Google Maps to analyze how buildings were organized within a three-mile radius of the stations and used a radial distribution function, the probability distribution of finding an object at a given distance from another object, to determine the "crystallinity" of the building arrangement.[5-6] A grid pattern had a crystallinity of 1, while a completely disordered, liquid-like, pattern had a crystallinity of 0. The crystallinity of most cities ranged from 0.5-0.9, with Chicago having the highest, and Los Angeles having the lowest (see figure).[5-6]

Street layouts of Los Angeles and Chicago

Street layouts of Los Angeles (left) and Chicago (right). The texture of Los Angeles resembles a liquid, while that of Chicago is relatively crystalline. Chicago shows a greater urban heat island effect than Los Angeles. (Images from OpenStreetMap.org. Click for larger image.)

While this simple model did not include building height or volume, a strong correlation was demonstrated with enhanced nighttime temperature.[5] A more advanced model that incorporated the areal density of buildings and their height, and thereby their view of the sky, also showed that city "texture" will influence the urban heat island effect.[5] It's conjectured that this texture effect arises from a combination of radiant heat trapping, and by decreased airflow in multiple directions in grid-like layouts.[6] As Pellenq and his colleagues admit, there are opportunities to improve their model by adding other factors.[5-6] All this may yield a city planning tool for urban heat island mitigation.

Heat Islands

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