The preceding post described problems with the efforts to develop multidimensional measures of sprawl. I concluded by posing the criteria that anything offered as a measure of a dimension of sprawl meet these simple tests: If observers generally agree that one area has a greater level of sprawl than another area, then the measure should indicate more sprawl. If a change is made in one area that most observers agree results in less sprawl, then the measure should indicate less sprawl.
This post will address these criteria with respect to two measures used in the multidimensional measurement of sprawl: Variation in population or housing unit density and the degree of centralization of population or housing units within urban areas. Both the Galster, et al. and the Ewing, Pendall, and Chen sprawl indices included such measures.
For the example, consider an older large urban area in the Northeast or Midwest with a high density core and density decreasing to very low levels in the sprawling suburbs. Variation in density would be fairly high, as would be the degree of centralization. (This would be in comparison to all large urban areas in the United States.)
Now let’s imagine that reducing sprawl and promoting smart growth catches on in this urban area. In response, a major new development is built near the periphery of the urban area that embodies smart growth principles and has moderately high-density housing, far greater than the density in the surrounding area. Perhaps it is a transit-oriented development around a transit stop.
I believe that virtually everyone would agree that this development is the antithesis of urban sprawl and that building this development has resulted in the reduction of the level of urban sprawl in the area. Certainly there is less sprawl than if the area had been developed as very low-density single-family housing.
Now look at the two measures of sprawl, first variation in density. The density of the new development is much higher than the low densities in other areas at the periphery. But it is very doubtful that even what would be considered a reasonably high-density development in that setting would have a density as high as that near the center of the urban area. Instead, it would fall somewhere in the middle, closer to the mean density of the urban area. Result: The variation in density for the urban area would be reduced. But variation in density when used as a measure of sprawl says that a reduction in variation implies more sprawl. So variation in density fails as a measure of sprawl.
Now for centralization. The new development adds significant numbers of people and housing units at a location that is very distant from the center. Any measure of centralization, whether based on the estimated parameters of the negative exponential model or some other measure based on distances to the center will show a decline in centralization. And again, when used as a measure of sprawl, less centralization means more sprawl. So centralization likewise fails as a measure of sprawl.