Multidimensional measures of sprawl

Around the beginning of this century, increased attention was being devoted to urban sprawl and its measurement. Numbers of those efforts conceived of sprawl as being a complex, multidimensional phenomenon and sought to develop sprawl indices combining multiple measures. The two most-cited studies doing this were by Galster and his colleagues, “Wrestling Sprawl to the Ground” (Housing Policy Debate, 2001) and by Ewing, Pendall, and Chen, Measuring Sprawl and Its Impact (from Smart Growth America).

As I am going to be making some criticisms of this approach to sprawl measurement, let me begin by making full disclosure: I was involved in research on multidimensional measurement of sprawl at this time. So the criticisms apply to me as well as others. Mea culpa.

The inspiration for using multiple measures for different dimensions of sprawl comes from at least two sources. First, the literature on sprawl provides widely varying definitions. So it is may not be unreasonable to conclude that sprawl might be a complex phenomenon that has multiple dimensions. And second, sprawl is one type of urban pattern. Urban patterns are obviously complex and vary over many different dimensions. The conclusion is that therefore sprawl has multiple dimensions.

Neither of these arguments is logically very tight. The existence of multiple definitions of sprawl does not imply that the various definitions are even consistent, much less that they represent aspects of a more general concept of urban sprawl. To say that urban patterns are complex and multidimensional and that sprawl is an aspect of the urban pattern does not necessarily imply that urban sprawl (whatever it means) is complex and multidimensional. It could be, but needn’t be.

The multidimensional sprawl efforts did not address these issues. Rather, they begin by asserting that sprawl is a phenomenon to be measured along multiple dimensions. Then comes the identification of the dimensions of sprawl. At least for some of the measures, the approach appeared to be identifying measures of the general urban pattern and adopting these as measures of sprawl. The overall population or housing unit density of the urban area is a measure of the urban pattern, so this can then be considered a measure of sprawl. (Given generally accepted ideas about sprawl, most would not argue with that.) Some other measures of the urban pattern identified were the extent of the variation in density across the urban area and the degree of centralization of the population or housing units within the urban area. So these could be considered to be measures of sprawl as well.

When you identify other measures, it becomes necessary to specify which direction is associated with greater amounts of sprawl and which with less sprawl. This was not explicitly addressed. Instead, the direction was simply asserted, apparently as being obvious. Less variation in density was associated with more sprawl and lower levels of centralization were associated with more sprawl. I believe that these “obvious” choices arose from looking at the characteristics of urban areas thought to be more or less sprawling. The areas seen to be more sprawling had less variation in density and less centralization than areas seen to have less sprawl.

Multiple problems exist with this process. First, there is no logical or empirical connection established between the various measures and any fundamental conception of sprawl. This is, of course, difficult without a clear conception of what sprawl is. And an empirical relationship cannot be established without measures of sprawl, which these projects are attempting to provide. The logical problems go away, however, if the authors are simply asserting that they are providing a definition of sprawl with these measures. They can certainly proceed in this manner. But their work can then be judged on the basis of whether their definition is consistent with other notions of sprawl.

Establishing the direction associated with more sprawl for the various measures is likewise problemmatic. First, to the extent that it is based on the direction of the variation between more-sprawling and less-sprawling urban areas, it is grounded in the subjective judgement about degrees of sprawl in those areas. And second, the judgement is based on differences among urban areas in the United States in the early twenty-first century. Conditions in other eras or in other parts of the world may present a different relationships between sprawl and the directions of variation in different dimensions of the urban pattern.

Consider just the simple measure of the variation in density. Less variation is associated with more sprawl because urban areas exist in the United States with overall low densities (and hence high levels of sprawl) that have very limited variation in density. But what about an urban area with uniformly high densities? I don’t think you would want to consider that area as having high levels of sprawl, higher than an area with some high densities and some low densities. Some will argue that this is not a realistic possibility. But it is a logical possibility, so where should one come down on this?

But let’s ignore this. I think most would agree to two closely related criteria for judging whether a measure can be considered to be a reasonable measure of urban sprawl. If you have two urban areas and most observers would agree (on whatever basis they are using), that one area has more sprawl than the other, the measure should indicate more sprawl for that area. And if a change is made in an urban area that results in what most observers would agree creates less sprawl, then the measure should indicate less sprawl.

The next post will provide a simple example demonstrating how the measures of variation in density and centralization fail to meet these criteria.


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