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Julian Marshall

Julian Marshall found patterns in city growth that had lain hidden for decades.

A new look at urban sprawl

Recent arrivals to a city tend to take up twice as much land as established residents

By Charles Plain and Deane Morrison

September 21, 2007

University researcher Julian Marshall has found underlying patterns in urban sprawl and how sprawl relates to population growth, including the observation that newcomers to cities take up twice as much land as the average for established residents. His findings offer a new numerical tool for measuring urban expansion. The work of Marshall, an assistant professor of civil engineering, is featured in the September 2007 issue of Urban Studies. Determining how cities change and grow in response to population increases is a timely question. "This year, for the first time in history, a majority of people will live in urban areas. In future decades, urban population growth will greatly exceed rural population growth," Marshall says. The desire new residents have for bigger homes and yards leads to even greater implications for social, health, and environmental concerns associated with urban sprawl, he explains. Marshall analyzed U.S. census data on urban land-use and population from 1950 to 2000. The patterns he noted emerged from data on the growth of all cities over time; not all individual cities followed them. "I initially found the patterns by accident, just by playing with the data," Marshall says. He realized that in comparing each decade to the preceding decade, newcomers steadily stretched city borders by occupying double the average amount of land occupied by existing residents. More new residents settling in the outer areas, where lots are bigger, made the difference. Marshall made the discovery while developing a new way to predict how urban areas grow over time in response to population increases. Making this prediction for a single city can be difficult, and it depends on land availability and other specifics of the city. Another pattern is that the average number of people in a meter-wide strip of land across cities remains much the same over time. This number is called the linear population density, or LPD.

"The strength of the mathematical associations and the length of time the patterns have held--50 years--is surprising," Marshall says. "I could hardly believe what I found."

"For example, from 1950 to 2000, the average population, land area, and population density changed by more than a factor of two, but the average LPD changed less than 10 percent," Marshall says. "Few, if any, other attributes of urban form have remained so constant during this half-century time-period." This second pattern is possible, he says, because low-density urban growth at the edge of cities is canceled out by new high-density housing in the urban core. A third pattern builds on relationships known as "rank-size rules." The idea is that when cities are ranked from largest to smallest, the size of each city follows a predictable proportion. For example, the population of the second-largest city is equal to one-half that of the largest city, and the population of the third-largest city is one-third that of the largest city, and so on. Marshall discovered that similar rank-size rules hold true for other attributes of cities, such as population density and land area. Marshall's findings provide mathematical descriptions of these observations and offer predictions about city sizes in future decades. But while these results predict how the system as a whole behaves--that is, distributions of values for all cities--they cannot predict what will happen in any one city. "The strength of the mathematical associations and the length of time the patterns have held--50 years--is surprising," Marshall says. "I could hardly believe what I found."