Trend Surface Mapping of Dynamic Process of Urban Expansion and its Implication

Abstract

The expansion of built-up area in western Kobe is quantitatively analysed and mapped through trend surfaces. Two trend surface techniques, 3-variable and 4-variable trend surfaces, are fitted to the distribution of gross floor index calculated by census tract-wise.First, by using 3-variable trend surface analysis, six cross-section surfaces are mapped at five years intervals from 1950 to 1975 (Fig. 2 a-f). Between 1955 and 1960, we find remarkable expansion of the built-up area into the southwestern suburbs, which is more adequately presented through quartic surface. From 1960, therefore, we change the degree of trend from cubic to quartic. Each map of isopleth lines lucidly explains the regional trend of expansion.Secondly, 4-variable trend surface analysis, which unites time and space coordinates, is applied in order to consider the spatial-temporal process of expansion. Time slices over the study periods present almost same results as in case of 3-variable trend surface fitting (Fig. 4 a-f).Regional trends are largely composed of the following three elements; the westward principal expansion from the high density core area which involves maximum in isopleth pattern, the northern mountain parts which shape minimum and work as hindrance to the advance of built-up area, and the recent construction of large-scale public housing estates which are found in southwestern parts and form newly emerged maximum.Residuals found on the 4-variable trend surface are carefully considered from both spatial and temporal series. Various factors affect the functional characteristics of dwelling agglomeration in each census tract. The following factors, which are considered as significant to interpret the deviation from general trend patterns, are pointed out.(1) Relative rapidity and delay in expansion of built-up area with comparison to the neighbouring tracts, which particularly explain residual occurences in temporal series.(2) The differences in land use and residential use. Especially the high ratio of industrial area is a factor for negative residuals, and the presense of commercial area is related to positive residuals. As for residential use, high ratios of row houses and dwelling houses combined with other uses, distribution of which coincides with densely inhabited area, account for positive residuals.(3) Moutains and relief energy as physical barriers against the expansion. This factor, however, gradually loses its hidrance effects through the progress of civil engineering technology.(4) The development of large-scale public housing estates, which brings about the drastic changes in residual values and keep the values high and stable hereafter.Among above factors, factor (2) is considered as most important. The effects of factor (2) on residual distribution are confirmed through principal components regression analysis (Tab. 1. and 2).Two suggestive conclusions are obtained from the present article.(1) We can safely say that the temporal change such as the expansion of built-up area may well be examined in a spatial-temporal system.(2) Spatial autocorrelation problem has been curiously considered to be removed as a noise. However, spatial autocorrelation in residual distribution patterns should be positively incorporated into spatial models, for it seems to have possibility to offer new angle to interpret spatial patterns. It will open the way to overcome the limitation of trend surface analysis as a simple procedure for areal smoothing and to construct the more strict spatial model which would lead to further refining of spatial forecasting.