Austin Contrarian

The distribution of Texas population by density

For stats geeks only.

Urban Texas

I didn't believe it, so I checked my calculations three times:  Texas has a weighted density of 3,042 people per square mile.  1,704 of its 4,388 census tracts, or 39%, are denser than this (hundreds are much, much denser).  The median census tract has a density of 2,000 ppsm.  In 2000, roughly 8.8 million Texans lived at a density of over 3,000 ppsm; roughly 11 million lived at over 2,000 ppsm.

As a benchmark, the Census Bureau uses 1,000 ppsm as the threshold density for urbanized areas.  Atlanta's urbanized area has a weighted density of 2,362 ppsm, which means the average Texan -- East Texas farmers and West Texas ranchers included -- lives at a higher density than the average resident of Atlanta's urbanized area.

I guess Texas's standard density of 78 ppsm doesn't quite convey how the average Texan lives.

All data from the 2000 Census.

(My eyes were a little blurry when I wrote this last night.  Maybe I'll check my numbers once again.)

Radical Cartography on density

A very nice chart depicting the distribution of U.S. census tracts by density.  Just eyeballing it, it looks like most Americans live at a density of 2,500+ ppsm. (The area under the curve represents total U.S. population.)

Another feature of weighted density

Another in an occasional series on weighted density.

Below the jump I discuss a rather odd feature of weighted density:  It can fall even as a city's standard density rises.  This is truly a feature and not a bug, though, because it allows weighted density to yield some interesting information about how a city is growing.

More on weighted density for the crackpot blogging stats geeks

I've hit on this in the comments to other posts, but one of the nice features of weighted density is that it permits us to compare apples to apples (even though the comparison may be royal gala to red delicious).  Standard density is extremely sensitive to geographic boundaries.  This is why most debates over density quickly turn into squabbles over the proper geographic unit.  CMSA?  MSA?  Urbanized area?  Central city?  And then it's just a matter of time before someone brings up City  X's moutains or parks or other uninhabitable land that drag down its density. 

Because weighted density is determined by the density at which most people live, adding or subtracting land at the margin -- even a lot of land -- does not matter much unless the land contains a large chunk of the population.  Weighted density does not depend on precisely how the geographic area is defined.

Example:  In 2000, Houston's urbanized area had a population of 3,822,000 and a standard density of 2,951/square mile.  Houston's Primary Metropolitan Statistical Area* had nearly four times the land area but only about 355,000 (10%) more people.  (The PMSA has a lot of cows.)  As a result, Houston's PMSA had a measley 706 persons per square mile, just a little over one person/acre.

The PMSA's weighted density, however, was a more respectable 4,296.  That's only 5% off the urbanized area's weighted density of 4,514.  Adding a bunch of cow pastures does not change the fact that the vast majority of the PMSA population was bunched at a much higher density.

The same holds for Portland.  In 2000, its PMSA had a standard density of just 381/square mile.  But the PMSA's weighted density was 3,943/square mile, down just 10% or so from the urbanized area's weighted density of 4,383. 

Note that a lot of the vacant land around Houston is vacant simply because no one has gotten around to developing it yet.  A lot of the land around Portland is vacant because of policies designed to preserve open space and slow sprawl.  This difference is often a flash point for disagreements over geographic boundaries. Weighted density allows us to sidestep these arguments by focusing on the density at which the average person lives.

*A PMSA consists of one or more counties within an MSA that have substantial commuting interchange.

Density calculations for U.S. urbanized areas, weighted by census tract

I recently calculated the weighted densities for a number of cities using the Census Bureau's "central place/non-central place" classification.  As I explained in that post and the comments, this is actually a coarse measure of weighted density because central places themselves are usually large cities with pockets of wildly varying density.

I have now calculated the weighted density of 34 large urbanized areas using census tracts.  (See my last post for an explanation of weighted (or "perceived") density.)

I took the 32 largest U.S. urbanized areas and added Austin and Honolulu for good measure.  I pulled the Census data on each census tract partially or completely contained within each of these urbanized areas.  I calculated the standard density (i.e., total population/total land area) for each census tract.  I also calculated each census tract's share of the total population of the urbanized area.  I then assigned each tract's density a "weight" equal to its share of the total population.  I summed the weights to get the weighted density for the urbanized area. 

I'm preparing a permanent page with more information on the methodology and limits of this approach.  (It's a very good method, though, in my opinion.)

But that technical stuff can wait a few days.  Here are the weighted densities, ranked from most dense to least dense:

         

(Chart on Scribd)

This approach obviously does a much better job of reflecting our perceptions of a city's density.  LA's urbanized area is denser than NY's when using the standard density metric; NY's urbanized area is almost three times denser using weighted density.  (LA is still quite dense, though.) 

Weighted densities straighten out a lot of other counterintuitive "facts."  Austin and Tampa are not really denser than Boston (as the standard density figures suggest), and the sprawling suburbs of Riverside County are not actually denser than Chicago. 

Note that Portland's urbanized area is less dense than Houston's.  The urbanized area most like Portland's, viewed strictly by their density profiles, is Riverside-San Bernardino.

New York is an outlier at the upper end, while Atlanta is an outlier at the lower end.

The "density gradient index" is a term I made up to dignify what is a pretty simple calculation:  weighted density divided by standard density.  The index would be an even 1 if a city's population were uniformly distributed across the landscape.  The larger the index, the more uneven the distribution.  I'll go into this in more detail on the permanent page, but you can get a rough idea of a city's urban form just by looking at the weighted density, standard density and density gradient index.

(There really is something called the "density gradient," but it is a curve rather than a number, and there is no "index" for it, as far as I know.)

Related posts:

1. Perceived density (March 16, 2008).
2. More on weighted density for the crackpot blogging stats geeks (March 27, 2008).
3. Another feature of weighted density (May 20, 2008).

Perceived density

Every once in a while -- invariably in a debate over sprawl -- someone will toss out the "fact" that the Los Angeles metropolitan area is denser than the New York metropolitan area. 

It's true.  At least, it's true if one uses the standard definition of density as gross population divided by gross land area.  According to 2000 U.S. census data, the Los Angeles "urbanized area" has a density of 7,068 persons per square mile.  The New York urbanized area has 5,309 persons per square mile.  Ergo, Los Angeles is denser than New York.

But common sense tells us that this coarse statistic is misleading.  Ryan Avent puts it well:

Los Angeles is hemmed in by its geography, so it can’t just keep spreading at ever lower densities out into the wilderness. As such, its density profile is like a plateau–not all that tall at anyone point, but with a respectable average height, because the long tails are excised. New York, by contrast, is like a mountain. It has an enormous peak containing most of the mass, but the flattening sides of the mountain continue on for miles.

In other words, the fact that the last million or so people in the New York metro area occupy an incredibly large area while the last million or so Angelenos are in moderate density suburbs packed against the very edge of the basin, skews the relative density figures, making them pretty uninformative.

A more meaningful metric is "weighted" density or "average perceived density."  Carve the metropolitan area into distinct regions (census tracts, for example), compute the density of each, and then assign each a weight based on its percentage of the total population.  This discounts large, sparsely populated census tracts, and gives extra weight to densely populated tracts.

An extreme but simple example:  Suppose Metropolis consists of a central core of 100,000 residents on 10 square miles, and a suburb of 10,000 on 100 square miles.  Its standard density is 1,000 persons per square mile. 

But this is a meaningless number.  Most of the residents of Metropolis live in a very dense environment.   The roughly 90% who live in the core are packed in at 10,000 per square mile, while just 10% live at the rural density of 100 per square mile.  By giving the core's density a weight of 90%, we get an adjusted density of 9,100 persons per square mile, a much better description of the density perceived by the average resident. 

I show the weighted densities for some U.S. cities below the jump. 

A Rorschach test for density

Take a look at this photo of Budapest from The Overhead Wire (republished with permission):

What's your gut reaction to it?

Do you see a place that is visually interesting, energizing, and socially, culturally and intellectually stimulating?

Or do you see congestion, overcrowding, noise, crime, and lack of privacy?

My guess is that you could accurately predict a person's stand on most land-use issues by his gut reaction to this picture.

This might also explain the dynamics of single-family neighborhood opposition to new density nearby.  Most single-family homeowners are highly risk-averse, which makes them anxious about dense development.  Some of these homeowners have a visceral distaste for density.  Others have an equally visceral, positive reaction to it.  You end up with one group that is anxious about home values and that dislikes density, and another group that is anxious about home values but likes density.  The first group intensely opposes the development, while the second (probably smaller) group is more ambivalent, even if it supports it on balance.  Presto!  Neighborhood opposition.

OK, nothing profound here.  I really just liked the picture.

"High density" is a relative term

From The Spatial Organization of Cities: Deliberate Outcome or Unforeseen Consequences? by Alain Bertaud:

Comparing some city densities

Here are maps of a few cities, color coded by density.  All of the maps can be generated at the Census Bureau website.

I see density figures quoted all the time (and quote them myself).  Think of this as the gestalt method for comparing densities.

All maps are based on 2000 data, the most recent available.  All maps are coded by "block group," with seven standardized data classes.  I used the 20-mile resolution for all of them, but cropped the maps of some of the small cities (small geographically).

Bright green represents 8,000+ per square mile; dark green, 10,000+ per square mile.  Click to enlarge.