基于分形理论的北京城市形态结构遥感分析

 城市形态结构分析对北京市的长远规划具有重要意义,运用分形思想规划城市对人居环境的改良和人地关系的协调也有着重要意义。本研究基于分形理论，运用GIS空间分析等方法，对北京城市形态结构和变化进行了定量的分析与评价，预测了北京市未来城市发展范围。利用TM遥感影像监督分类，提取1992、1999和2006年北京市建筑用地面积，以城市中心为圆心，取几十个半径递增的同心圆进行剪裁，得出各个同心圆内的城市建筑用地面积。通过反复试验确定双标度区并得到城市建筑用地面积折线图，并对面积进行基于乘幂关系的函数拟合，拟合优度R2≥0.995。并得到分维数D以及北京市范围及其变化。在得到这些数据后，进行了深入的分析以解释这些现象，同时对北京市与其他大城市的城市形态进行对比。最后，对北京市的城市建筑用地的未来发展以及可能出现的情况做出预测。

Remote Sensing Analyses of the Urban Morphology of Beijing Based on Fractal Theory

Analyses of the urban morphology are important for Beijing's long-term planning. Based on fractal theory, this paper qualitatively analyzes the morphology and changes of Beijing from 1992 to 2006, and then predicts the future evolution of the city. Firstly, the city construction area data were extracted from Beijing TM images in 1992, 1999 and 2006 by using supervised classifications, then with the city center as the center of circles, dozens of concentric circles with increasing radius were used to delimit the construction area. Secondly, the critical points of two scale zones were determined through repeated computations, together with the area of construction. Thirdly, on different scales, the power relationships between the construction area and the scale zone number were fitted with the goodness of fit R2>0.995 to obtain the fractal dimension and the change scope of Beijing. Based on these experimental data, with further analyses and comparison of the form of Beijing with that of other major cities, the future development of Beijing urban construction land and other possible circumstances are predicted. Fractal theory was first proposed by American mathematician Mandelbrot in 1967. Self-similar principle and iterative generative principle are the main principle of it, which means that fractal has the characteristics of invariance under the usual geometric transformation, namely, scaling invariance. Its basic parameter is the fractal dimension. Batty studied the fractal city morphology in 1985, and also the city boundaries and urban land-use with Longley. Based on the data of TM image, this paper obtained the fractal dimension through ERDAS IMAGINE and ArcGIS. It is shown that the city of Beijing has clear fractal characteristics. From 1992 to 2006, the radius of the Beijing city boundaries is increased from 7.5km to 10km. It is predicted that the radius will increase to 14km in 2020 and the fractal dimension will be dropped down to 1.9.