QUANTITATIVE GEOGRAPHY

Abstract

It is in the present decade that quanntitative-geographical studies began to undergo a marked development based on a new viewpoint in geography. In geography, too, mathematical and statistical techniques have been utilized since a long while ago as well as in other sciences. Those techniques of late are however characterized by the quantitative-geographical viewpoint as to the ‘nomothetic’ subjects in pursuit of some general law concerning the spatial regularities of various phenomena on the earth. In this respect, it should be clearly distinct from the ‘ideographic’ viewpoint in regional geography, which is interested in unique items to put emphasis on the intensive studies of individual cases, if the mathematical and statistical techniques are employed as a mere means for description of regions.The studies from quantitative-geographical viewpoint pay further attention to spatial aspects of the phenomena on the earth, make models derived from some hypothesis, put them to practical tests, and formulate the theories on which the hypothesis is based. The models used there range from deterministic to probabilistic, and static to dynamic models.The quantitative geography is assumed to contain the following seven branches of research: (1) Point Pattern Analysis, (2) Network Analysis, (3) Trend-Surface Analysis, (4) Regionalization Analysis, (5) Spatial Interaction Analysis, (6) Spatial Diffusion Analysis, and (7) Spatial Behavior Analysis. A large number of studies have added to the literatures of quantitative geography. Among the abovelisted seven branches of quantitative geography, the spatial diffusion analysis seems to show more sufficient development in connection with a theoretical formulation.The spatial diffusion analysis has been studied in a considerable number of geographical papers, since a Swedish geographer Torsten Hägerstrand understood the diffusion of information and innovation as a spatial process. The significance of Hagerstrand's studies seem to be briefly summarized in two sentences as follows: (1) the spatial process of diffusion in a geographic space was approached through his analysis of the diffusion of information and innovation, and (2) the Monte Carlo simulation technique was first employed for the analysis of geographic space. His diffusion theory of information and innovation might be regarded as comparable to the Christaller's central-place theory.The present writer attempted an analysis of the intra-urban migration in the pursuit of a theoretical formulation of geographic space, assuming the geographic space as a system of purely spatial components. And the geographic space is assumed to organize a ‘geographic field’ as probability surface given in form of ‘Mean Migration Field’ for the intra-urdan migration. Thus the MMF as a geographic field organized rationally for a given geographic space may probabilistically control the intra-urban migration as a spatial and geographic phenomenon. An example was drawn from an analysis of intra-urban migation on the built-up area, defined as a Densely Inhabited District by the national population census, of Fukaya city (approximately 60, 000 population), Saitama prefecture. The following four stochastic models were formulated to test the hypotheses concerning geographic space considered for the intra-urban migration by means of the Hägerstrand type of Monte Carlo simulation: (1) MODEL I to simulate the migration under a complete random process on a hypothesis of the completely uniform geographic space, ‘Isotropic Plain’, (2) MODEL II for a simulation of the migration pattern within a geographic space assuming the friction effect of distance involved, (3) MODEL III by which simulation is attempted for the intra-urban migration within a geographic space characterized by the uneven distribution of population or the densities effect