A NEW MODEL OF POPULATION DENSITY DISTRIBUTION FOR THE TWIN CITIES AND ITS APPLICATION

The applicability of the models for isolated cities (e, g., the Clark model) has been identified in studies of urban population density. As for the application of the model for multi-centered cities presented by Griffith (1981), however, two problems exist. First, parameters of the model do not directly indicate the morphological features of population density distribution. Second, the model does not make a satisfactory prediction of population density, especially for regions where density profiles overlap. The purpose of this paper is to improve the Griffith model in the above aspects and to examine the population density distribution and its changes in multi-centered cities. This study limits the subject to twin cities as the simplest forms of multi-centered cities. If it is assumed that a density crater does not appear in the centers, the Griffith equation is written as<br> d (s, t)=d_Aexp (-as)+d_Bexp (-bt), <br> where d (s, t) is the population density at distance s from the center A and distance t from the center B; d_A, a, d_B, and b are parameters.<br> The following new indices of the morphological features of density profiles are defined by combining parameters which cannot stand alone: i, e., outside density gradient, inside density gradient, connectivity of population density, and equilibrium point of population density.<br> We developed a new model by adopting the concept ‘bias’ to show spatial distortion of population density. By substituting biased distance for physical distance in the Griffith equation, the new model's equation becomes<br>_??_<br> where s* and t* are biased distance written as<br>_??_<br> d (s*, t*) is the population density at the location P, namely at distance s from the center A and distance t from the center B; d_A, a, d_B, and b are parameters; λ is ∠PAB; μ is ∠PBA; β is the degree of bias, and the attributes of β are as follows: (1) The range of its value is between -1 and 1. (2) The absolute value shows the strength of bias. (3) The sign shows the direction of bias. (4) If β is zero, the new model is equivalent to the Griffith model.<br> In this study, the Clark, the Griffith, and the new model are applied to three districts : the Numazu-Mishima, Shizuoka-Shimizu, and Maebashi-Takasaki districts. The results of the applica-tions of the new model are summarized as follows: (1) The applicability of the new model is higher than that of the other two models. (2) In Numazu-Mishima and Shizuoka-Shimizu, the outside density gradient is more relaxed than the inside gradient. This indicates that in these districts the urbanized area has grown outward rather than inward (3) The connectivity of population density increases gradually in three districts. This indicates that each of the pairs of urbanized areas are becoming spatially connected. (4) The degree of bias is positive in Maebashi-Takasaki, where the connectivity is relatively low, while in the other two districts, the degree is negative. The degree of bias tends to decrease in all three districts. (5) A negative correlation between the connectivity and the degree of bias is identified from (3) and (4).