Density: Of population - and between the ears
Certain loyal and disloyal opponents expend significant time and effort comparing gross population densities of various urban areas - without reference to land areas, the factors which determine administrative boundaries, and so forth.
Some countries and sub-national jurisdictions facilitate the growth of cities through annexation of adjacent others. Others restrict or prevent this, in some cases on a "city-specific" basis. One very good example, described previously, is Paris.
The share of land within municipal boundaries that is not "built up" varies greatly among cities. This is true even with reference to cities located within the same country. An interesting "compare and contrast" exercise includes the cities of Ōsaka and Sapporo, Japan.
 
2010 Statistics
Population
Land Area
Population Density
Sapporo
1,896,000
1,121.12 km2 (430 sq mi)
1,691 / km2 (4,400 / sq mi)
Ōsaka
2,668,000
222.30 km2 (85.5 sq mi)
12,002 / km2 (31,223 / sq mi)
Index
0.7
5.0
0.1
 
Ōsaka is the third-largest city in Japan by population, after Tōkyō (the 23 "special wards") and Yokohama. Nagoya ranks fourth, and Sapporo ranks fifth.
As shown in the table above, the population of is about 70 percent of that of Ōsaka. However, the Sapporo municipal boundary encloses five times the land area as the Ōsaka municipal boundary. Therefore, according to a line of reasoning that we'll call "Coxlogic," Sapporo has but one-tenth the population density of Ōsaka. The fact that this, as a practical matter, is untrue quickly becomes apparent when examining aerial images (preceding links; scale is about 20 mm = 2 km, or 1:100,000).
Most of the land within the Ōsaka municipal boundary is built up, except for parks and waterways. By contrast, more than half of the area enclosed by the Sapporo municipal boundary is a rugged mountain area that is virtually uninhabited - and uninhabitable. The "gross population density" statistic for the city is deceptively low, in a manner which is not true of Ōsaka.
Sapporo's "mountain zone" lies due west, southwest and south of the city center. Much of it is included within the boundary of Minami Ward, but not all. The boundaries of Chūō, Nishi, Toyohira, Teine and Kiyota wards also include significant areas of the "mountain zone." Therefore, "gross population density" statistics for these wards are also deceptively low.
The "mountain zone" of Sapporo is not uninhabited. It has scattered ski areas, temples and so forth. It also has relatively small areas of level land (valleys) that are intensively urbanized. However, it seems safe to say that the mountainous parts of this area will "never" be subdivided, simply because the slopes are too steep.
The "gross population density" statistics for most of the "other" wards of Sapporo are also deceptively low, because a significant amount of land within the municipal boundary is used for agriculture.
Ōsaka was Japan's most important economic center for centuries, and so has long been a "big" city. The modern municipal government was created in 1889, at which time the city had an area of 15 km2 and 470,000 residents. By 1925, following two annexations of adjacent land, Ōsaka grew to 182 km2 and 2.11 million residents. It was the largest city in Japan by population and by land area.
A third annexation, in 1955, brought the land area to 202 km2. The city has grown since then to 222.30 km2, but this was accomplished by reclamation of land from Ōsaka Bay.
Sapporo was built from 1871 on land long inhabited by the indigenous Ainu people. In that year, the town, built as the administrative center of Hokkaidō, had 5.5 km2 and 624 residents. By 1886, the town had a land area of 14.6 km2, about the same as Ōsaka but with a much smaller population (nearly 15,000). Sapporo grew very rapidly and continued to annex land through 1967. Thereafter, the population increased by nearly one million people and continues to grow.
We estimate that the gross population density of Sapporo, deducting the mountainous and agricultural land, is about 8,000 / km2 (about 20,000 / sq mi). That is roughly five times higher than implied by the crude "population density" statistic above.
Barter, Kenworthy and Laube (2003) state that the residential density of Sapporo is 72 persons per hectare (about 180 / acre); this works out to 7,200 / km2. The equivalent figure for Ōsaka is nearly 100 persons / hectare (nearly 250 / acre), which works out to nearly 7,200 / km2.
The residential density of Ōsaka is therefore about 28 percent greater than that of Sapporo.
By any measure, Sapporo is by no means a "high-density" city as are Tōkyō, Yokohama and Ōsaka. As one might expect, private autos are the dominant mode of urban transport in Sapporo, with a 50.3-percent modal share (at 2005). Buses, bicycles and taxis carried 36 percent. Rail services carried 13 percent.
Within the Sapporo municipal boundary, the Hokkaidō Railway Company (JR-Hokkaidō) carried about 190,000 passengers per (calendar) day during the 2005 fiscal year. That, in accordance with Japanese practice, implies about 70 million annual boardings. The total system length of JR-Hokkaidō lines within Sapporo is 50.6 km.
The municipal metro system, which has three lines and a total system length of 48.0 km, carried about 570,000 passengers per (calendar) day at FY 2005. That implies about 208 million annual boardings.
We think that the population dynamics of urbanized areas - that is, short- and long-term changes in factors such as location, size and age composition - is important for transportation analysis and planning. However, gross "population density" as a single indicator makes a poor surrogate for the various factors which determine various aspects of urban transportation traffic.
 
Reference:
Barter, Paul, Jeff Kenworthy and Felix Laube. 2003. Lessons from Asia on Sustainable Urban Transport. In: Low, N.P. and B. J. Gleeson (eds.). Making Urban Transport Sustainable. Basingstoke UK: Palgrave-Macmillan.