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Vol. 53 (2001) No. 6 P 509-531



Since temporal changes in the spatial distribution of population are closely connected to many other aspects of society, an exact understanding of these changes is essential not only for progress in scientific research but also for applications to public policy, planning and business. It is especially critical that population changes in metropolitan areas be explored carefully, since it is here that such changes generally emerge. Furthermore, it is very important to investigate the changes observed in a given metropolitan area, compared to those found in other areas, because, by doing so, we can distinguish conditions common to many metropolitan areas from those peculiar to individual ones.
Based on this perspective, I refer to the problems arising from the use of a dichotomy of dividing a particular metropolitan area into a central city and surrounding suburbs, which is the common method found in previous literature associated with population redistributions in metropolitan areas. Problems arise when such a dichotomy is used; specifically, the location of the central city boundary affects the rate of residents in the central city within an entire metropolitan area, and the aggregation of residents in local municipalities into the suburb as a whole obscures the differences among municipalities. To resolve these issues, this paper uses an urban population-density function model.
Although this model is assumed to explain the spatial variation of the density continuously in terms of distance from the city center, it does not have to aggregate the density values of observations (or local municipalities) as building blocks. However, there is a limitation in that the density function assumes a concentric-circle distribution of population, implying that points with the same distance from the city center have exactly the same density. Consequently, the expansion method, developed by E. Casetti, is employed to overcome this drawback.
The expansion method enables us to incorporate the contextual effect of the spatial system under consideration. By expanding the distance parameter of the density function by direction from the city center, we can redefine the function so that the distance-decay of the population density varies directionally. As a result, the extent of directional bias of the intra-metropolitan population distribution can be measured quantitatively.
The purpose of this article is to analyze and compare the spatio-temporal changes in population distribution within the three largest metropolitan areas in Japan during 1965-95 by the 'expanded' density function model. The Standard Metropolitan Employment Areas (SMEA) advocated by H. Yamada and K. Tokuoka are used here to delineate metropolitan areas. Analyses are carried out in two stages; first, by the traditional Clark model and then by the expanded Clark model.
First, by calibrating the ordinary density function model (or Clark model), which does not consider directional differences, average relations between the distance from the city center and the population density are identified. The explanatory power of the Clark model itself, generally speaking, indicates a gradual improvement over time. It is also confirmed that, the larger the population size of the SMEA, the higher the density of the city center. In addition, the density gradient in Tokyo is the most gentle and that in Nagoya and Osaka is almost the same. Furthermore, population decentralization occurred first in Tokyo and Osaka and then in Nagoya. The time lag of this sequence is ten years. Additionally, based on this finding, one limitation of using the dichotomy for the central city and suburbs is demonstrated. The spatial pattern of the residual obtained from the Clark model shows, however, that similar values tend to concentrate in particular sectors, especially in the Tokyo SMEA, suggesting a necessity to alleviate such concentration by improving the traditional Clark model.

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