Category Archives: Density

60 years of exurban growth

In an earlier post I described the tremendous variation in the sizes of exurban areas surrounding large urban areas in 2010, looking at both their land areas and numbers of housing units. In a subsequent post I looked at variation across census regions and factors associated with this. I have extended the analysis, looking at exurban areas from 1950 to 2010. The variation in size among the exurban areas was very large at every census year. For example, in 1950, the smallest area in terms of land area had only 5 square miles; the largest had near 2,000 square miles. The minimum number of housing units was under 700, the maximum was over 400,000.

The exurban areas exploded in size over this period. The mean land area across the 59 areas grew from 233 square miles in 1950 to over 1,700 square miles in 2010. Mean housing units jumped from just under 40,000 to nearly 240,000. The sizes of the exurban areas were closely related to the sizes of their urban areas throughout the period. But the exurban areas grew more rapidly in size than the urban areas.

I then looked at the sizes of the exurban areas relative to their urban areas, the ratios of exurban to urban land areas and housing units. In 1950, the mean ratios were far higher for exurban areas in the Northeast compared with the other three census regions. But by 2010, the relative sizes of exurban areas in the South had grown rapidly and the mean ratios had virtually caught up with the Northeast. The relative size of exurban areas in the West remained very low. Exurban areas in the Midwest ended up in the middle. As I found for 2010, the relative sizes of exurban areas having arid climates were significantly smaller than for other exurban areas throughout the period.

More information on the the growth and evolution of exurban areas from 1950 to 2010 can be found in my paper, “Exurban Areas Around Large Urban Areas in the U.S., 1950–2010,” which can be downloaded here.

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This is not your father’s (or mother’s) suburb

I currently am living in Southern California, about 35 miles east of downtown Los Angeles. I frequently drive further east into the adjoining city of Rancho Cucamonga for shopping or other activities (recently, jury duty!). A normal person would take the freeway or the main east-west commercial artery, the old Route 66. But being interested in urban patterns, I occassionally will drive on other through streets that run mainly through residential areas. I had certainly seen numbers of apartment complexes, but on one of these explorations I was especially struck by the continuous line of apartments. Not exactly stereotypical suburbia.

First, a little background on Rancho Cucamonga. This is a very new city, largely developed since the 1970s. When I lived in Southern California in the mid–1970s, when driving through this area on the freeway, one passed through miles of vineyards. This was the last undeveloped gap between Los Angeles and San Bernardino to be filled in, as you can see on these maps for 1970 and 2010 of census tracts which I classified as urban for my research:

Urban census tracts in the Los Angeles area in 1970 (Rancho Cucamonga outlined in red).

Urban census tracts in the Los Angeles area in 1970 (Rancho Cucamonga outlined in red).

Urban census tracts in the Los Angeles area in 2010 (Rancho Cucamonga outlined in red).

Urban census tracts in the Los Angeles area in 2010 (Rancho Cucamonga outlined in red).

The popuation of the city of Rancho Cucamonga was 55,000 at the 1980 census and 177,000 according to the 2016 census estimate. No earlier populations are reported as the city was only incorporated in 1977!

Suburban residential development is generally associated with large expanses of single-family housing units on medium- to large-size lots. Some suburbs do have some apartments, but the general impression is that single-family housing dominates. In Rancho Cucamonga in 2015, only 62 percent of the housing units are detached single-family houses. So nearly 40 percent of the housing does not fit the suburban stereotype.

The overall population density for the city in 2016 was 4,430 persons per square mile, certainly more than many suburbs. But even this is misleadingly low. The city still has significant amounts of vacant land and has large areas developed with industrial uses, mainly for warehouse and distribution activities. (The broader area has developed as a huge distribution center, handling many of the millions of containers that come through the ports of Los Angeles and Long Beach.)

A better picture of the level of residential densities can be seen by looking at densities in individual census tracts, some of which will naturally be more residential and more completely developed than others. My research (using 2000 tract boundaries) has 9 census tracts within or predominantly within the City of Rancho Cucamonga. For several reasons, I have chosen to focus on housing units and housing unit densities rather than population densities for my research. The two census tracts with the highest housing unit densities in 2010 have densities of 3,330 and 2,835 units per square mile. Since population densities are more commonly used and are thus more familiar, these can be estimated by using the national average of 2.34 persons per housing unit. This gives estimated population densities for these tracts of 7,791 and 6,634 persons per square mile. The denser of the two tracts has a population density far greater than the overall density of the densest Urbanized Area in the U.S., Los Angeles. Both are denser than the New York Urbanized Area.

There is, of course, no standard criterion specifying what are “suburban” densities as opposed to “urban” densities. I believe that for a variety of reasons, no urbanists want to go there, as there would be no consensus. But an interesting article on the FiveThirtyEight website tried to get at this, reporting on work by the real estate website Trulia that surveyed people asking whether where they lived was urban, suburban, or rural. They also asked for ZIP codes and compared the responses to characteristics of the ZIP codes. The study found, perhaps not surprisingly, that the best predictor of how people described where they lived was the population density of the ZIP code. And the dividing line between suburban and urban was 2,213 households per square mile (or by my estimation of population density, 5,178 persons per square mile). Using that criterion, the two densest tracts in Rancho Cucamonga could easily be considered urban as opposed to suburban, and two more, with over 1,900 units per square mile, come close. (I need to acknowledge that their use of ZIP codes could have produced a lower value than if tracts could have been used.)

The bottom line is that this very recent development in Rancho Cucamonga does not look like the traditional idea of suburbia with single-family homes on spacious lots.

More on the sizes of exurban areas

The post before this one described the tremendous variation in the sizes of exurban areas surrounding large urban areas in the United States. And since exurban area land area and housing units are strongly related to those quantities for the urban area, looking at the ratios of exurban to urban size proved useful for considering the relative sizes of exurban areas.

The relative sizes of the exurban areas as measured by these ratios varied greatly across the census regions. The mean ratios in the Northeast were the largest for both land area and housing units, and exurban areas in the South were nearly as high. Exurban areas in the West were on average the smallest in relative terms, with ratios around one-third of those for the Northeast. The Midwest exurban areas fell in the middle.

This raises the question as to why exurban areas were so much smaller in the West. Ironically, the clue comes from the area having the smallest exurban area in relative terms, Miami-Fort Lauderdale-West Palm Beach. Expansion of the urban and exurban areas is constrained by the Atlantic Ocean to the east and by the Everglades to the west. The urban area has expanded to include most of the available land, drastically limiting the size of the exurban area.

So barriers to urban and exurban expansion can limit the size of exurban areas (note that I am not the first to raise this possibility). Many areas in the West have various barriers to expansion. These include mountains and federal lands not available for development. Also, the arid climates and the dependence on water often brought in from a distance by centralized agencies can mean that water utilities are only expanded at the edge of the existing urban area to serve new urban development.

I subjectively identified those urban and exurban areas for which expansion was significantly constrained by mountains or federal lands. For arid climate, an objective measure could be used, areas that received average annual rainfall of less than 20 inches. Note that the areas facing these barriers were all in the West region with the exception of El Paso. While that area is in Texas, in the South, it is literally as far west in the South region as possible. Comparing the mean exurban size ratios for areas with and without these barriers, the differences were large and highly significant. But the areas with mountains, federal lands, and arid climates overlap to a very high degree, so it is impossible to distinguish their effects.

Looking at the areas with arid climates, the one objective measure, the average ratio of exurban to urban land area for the arid areas was about 40 percent of the ratio for the non-arid areas. For housing units, the arid ratio was about one-third the non-arid ratio. Using simple regression models to predict exurban land areas and housing units yielded these differences: Areas with arid climates had exurban areas that were on average 934 square miles smaller and had 120,000 fewer housing units.

More information on the exurban areas in 2010 can be found in my paper, “Exurban Areas Around Large Urban Areas in the U.S. in 2010,” which can be downloaded here.

Sizes of exurban areas vary tremendously

A post made some time ago describes my definition of exurban areas for the urban patterns research and the previous post refers to a paper in which I address this in greater detail. These are areas of contiguous census tracts with a minimum density of one housing unit per 15 acres around the 59 large urban areas.

After delineating the areas, I began by looking at the sizes of the exurban areas in 2010. The variation of exurban area sizes was amazing. In terms of land area, the exurban areas ranged from 171 square miles to nearly 7,800 square miles. Numbers of housing units went from 19,000 for the smallest exurban area to 1.2 million for the largest. The smallest exurban area was around the Albuquerque urban area and the largest was New York. Of course some of the variation is due to differences in the sizes of the metropolitan areas. But it is noteworthy that San Diego, not a small area, had the third smallest exurban area.

So perhaps it is more reasonable to compare the areas by looking at the ratio of their land areas and housing units to the areas and units in their urban areas. The smallest ratio for exurban land area to urban land area was about one-third, for Miami. Knoxville was the largest exurban area relative to its urban land area, nearly 8 times as large. Miami likewise had the smallest number of housing units relative to its urban area, 3 percent. And Knoxville had 1.4 times as many exurban housing units as urban units.

The contrast can be seen in the maps of the Miami and Knoxville urban and exurban areas. Also included is Portland, which had the median ratio of exurban to urban land area of about 23 percent. (The three maps are at approximately the same scale.)

 

Urban and exurban areas for the areas with the smallest, median, and largest ratios of exurban land area to urban land area

Urban and exurban areas for the areas with the smallest, median, and largest ratios of exurban land area to urban land area

More information on the exurban areas in 2010 can be found in my paper, “Exurban Areas Around Large Urban Areas in the U.S. in 2010,” which can be downloaded here.

Defining exurban areas–an update

About 6 months ago, I wrote a post describing how I went about defining exurban areas for my urban patterns research. As I started to do the analysis and prepare for the writing of research papers on these exurban areas, I realized that the question of how I had defined these areas was sufficiently important that this deserved extended treatment in a paper. In the paper, I consider the literature addressing prior attempts to at defining exurban areas and present the logic underlying my approach in greater detail. The paper also includes a far more detailed and formal analysis of the extent to which the 2010 areas of contiguous exurban density are contained within the 2010 Combined Statistical Areas and Metropolitan Statistical Areas.

The paper is entitled “Defining Exurban Areas for the Analysis of Urban Patterns Over Time.” It is on the Research page and can also be downloaded here.

Scattered, leapfrog development vs. low-density development

Two residential development patterns are most often associated with urban sprawl. Scattered or leapfrog development refers to the building of new residences, either separately or in a subdivision, at some distance from existing built-up areas. Low-density development refers to the construction of individual houses on larger lots. It is possible, of course, for scattered development to also be done on larger lots, though this is not the distinguishing feature of such leapfrog patterns.

In looking at densities in areas larger than the actual residential lots, scattered development will also be low-density because of the vacant land that has been skipped over. But I think most people would agree that scattered, leapfrog development and low-density development are two distinctive types of residential development and sprawl.

But how different are the two? Here is a thought experiment: Imagine an undeveloped area of land one mile square at the edge of an urban area. Now consider two ways in which this land might be developed. The first will be very low-density development. The area is divided into 64 10-acre lots and a house is built on each, completely developing the area. (For simplicity, we will be ignoring the need for land for roads to provide access.) Let’s assume that the owners only landscape small areas surrounding their residences, leaving the remainder of their lots undisturbed.

Now consider the second alternative of extreme scattered development. Sixty-four houses are constructed on 1-acre lots that are fairly evenly distributed across the mile-square area. In this case, only 10 percent of the land has been developed, but the developed area is 10 times as dense as in the previous case. Now suppose that these 64 houses are exactly the same as the very-low density houses and are located in exactly the same places. There would literally be no way to distinguish the scattered development from the very low-density development based on any physical characteristics of the developments. The only way to tell whether the development is very low-density or scattered is by looking at the land records.

Of course that difference in ownership matters–to a degree. The owners of the homes on the scattered 1-acre lots have no control over the undeveloped 90 percent of the land, which could be developed at any time. In the case of the very low-density development, each owner exercises control over 10 acres surrounding the residence by virtue of ownership. One might assume that these very large lots were acquired because the owners wanted the space and the control. (Though it is possible that land use regulations and/or choices made by the prior owner or developer of the area limited options available to the purchasers of these lots.) It is very likely that you are not going to see the purchasers of these large lots soon subdividing their land for higher-density development.

But the operative word here is “soon.” Over time, as demand increases and conditions change, further subdivision and development in the very low-density area becomes an increasing possibility. I currently live in an area that was developed from that late 1960s through the early 1980s with lots around a half acre. There are several lots in the neighborhood where the owners have built a second, substantial house on the rear portion of the lot (more than just an accessory unit or “granny flat.”)

So the very low-density developed area perhaps is not that completely different from the area with the scattered development.

The negative exponential model and the size of cities

Researchers have long noted the tendency for densities to decline as a negative exponential function of distance from the center. They have looked at declines in the density gradient over time as a measure of decentralization in urban areas. They have noted the relationships of the estimated parameters of the model–the density gradient and the density at the center–to a variety of characteristics of urban areas, including, naturally, the size of the area. The consistent finding has been that the gradients tend to be smaller for larger urban areas, while the central densities tend to be larger.

Consider the relationships among the three–the gradient, the central density, and the size of the urban area. If density declines with distance following the negative exponential model, these three values must necessarily be mathematically related. But what affects what? It seems reasonable to believe that the size of the urban area is primarily affected by factors other than the parameters of the negative exponential model.

But what about the model parameters? Housing is long lasting and once established, the patterns in developed areas can remain remarkably stable for many decades. The density of urban development was much higher before widespread use of the automobile. And it turns out that the central densities are very strongly related to the sizes of urban areas in 1910. So it may not be unreasonable to conclude that, at least to some extent the density gradient is determined by the central density and the size of the urban area.

Solving for the mathematical relationship between the gradient, central density, and size yields a somewhat complex expression. However, a simplified approximation can be used. This approximation has the density gradient being directly proportional to the square root of the central density and inversely proportional to the square root of the size of the urban area.

As described in an earlier post and in a paper, I had used my urban patterns data to estimate the parameters of the negative exponential model for large urban areas in the United States from 1950 to 2010. It was straightforward to test for the conformity with the expected relationships among the density gradient, central density, and the size of the urban area. The gradient was indeed approximately inversely proportional to the size of the area, as expected. And the gradient did increase with the central density, though the proportionality was closer to the density itself rather than the square root. It may be possible that this is the result of the fact that the census tract densities in my data (and used by most other researchers) are measures of gross density including nonresidential uses, streets, and vacant land and are therefore lower than the net residential densities within the residential areas alone.

More information on this analysis, including the mathematical derivation of the relationship among the 3 values, is in the paper “Negative Exponential Model Parameters and the Size of Large Urban Areas in the U.S., 1950–2010,” which can be downloaded here.