The Census Bureau has just issued a fascinating report (warning: 130 MB pdf) on patterns of metropolitan change between 2000 and 2010. It's loaded with all sorts of interesting statistics. But I was particularly interested in the fact that it embraces population-weighted density as a relevant metropolitan-area metric. The Bureau's justification for the measure more or less matches what I've argued for a few years:

Overall densities of CBSAs [core based statistical areas] can be heavily affected by the size of the geographic units for which they are calculated. Metropolitan and micropolitan statistical areas are delimited using counties as their basic building blocks, and counties vary greatly across the country in terms of their geographic size. With this in mind, one way of measuring actual residential density is to examine the ratio of population to land area at the scale of the census tract, which—of all the geographic units for which decennial census data are tabulated—is typically the closest in scale to urban and suburban neighborhoods. To gain perspective on the densities at which people live, in addition to overall density, the population-weighted density for 2010 was computed for the United States, inside and outside CBSAs, and CBSA size categories. Details on how these measures were calculated are presented in the “Population-Weighted Density” text box.

Table 3.1 shows how overall and population weighted density measures varied by the population size of CBSAs in 2010. The densities at which most people reside are revealed as much higher when the population-weighted density measure is used. While the overall U.S. density stood at 87 people per square mile, population-weighted density shows that people actually lived at an average of 5,369 people per square mile. Density was more intense and the difference between the two density measures was even larger when looking inside CBSAs, in metro areas, and in metro areas of 5.0 million or more, where people were living at an average of over 13,000 people per square mile. Like overall density, population-weighted density decreased with decreasing CBSA size but only dropped to an average of 617 people per square mile for micro areas with populations less than 50,000. The population-weighted density approach reveals that the areas with people living at the highest density levels—metro areas with 5,000 or more people per square mile—were clustered mainly in California and along the corridor stretching from Boston to Washington. Other very dense metro areas included Chicago, Honolulu, Laredo, Las Vegas, Miami, Milwaukee, and San Juan. Low-density metro areas, on the other hand—those with fewer than 1,000 people per square mile— were generally clustered in the South (Figure 3.1).

The Bureau also included a neat graph comparing the weighted densities of the New York and Los Angeles metro areas at various distances from NYC and LA city halls, which the Bureau used as the central points of the metropolitan areas. The graph illustrates nicely why standard density can be such a misleading description.

NY-LA comparison
 The standard density of the New York City metro area is only slightly higher than that of the Los Angeles metropolitan area (2,826 ppsm vs. 2,646 ppsm). But, as we see, within 17 miles of City Hall, New York is denser -- in most cases, multiple times denser -- than Los Angeles. At around the 17 miles mark, the weighted population density of Los Angeles creeps past New York's, and generally stays higher (although not a lot higher) throughout the rest of the metropolitan area. 

The standard density statistic obscures the sharp difference between these density profiles.  But weighted density does not: just knowing that the weighted density of the New York City metropolitan area is 31,251 ppsm and the weighted density of the Los Angeles area is 12,113 ppsm allows you to predict density profiles that look something like the above.