地球信息科学学报 ›› 2020, Vol. 22 ›› Issue (11): 2140-2151.doi: 10.12082/dqxxkx.2020.190640

• 地球信息科学理论与方法 • 上一篇    下一篇

城市生长与形态双维分形模型改进及应用

李亚桐1,2(), 张丽君3,*(), 叶士琳1,2, 祁新华1,2   

  1. 1.福建师范大学 湿润亚热带山地生态国家重点实验室培育基地, 福州 350007
    2.福建师范大学地理科学学院, 福州350007
    3.河南大学环境与规划学院, 开封 475000
  • 收稿日期:2019-11-07 修回日期:2020-01-14 出版日期:2020-11-25 发布日期:2021-01-25
  • 通讯作者: 张丽君 E-mail:liyatong97csdl@163.com;zlj7happy@163.com
  • 作者简介:李亚桐(1997— ),女,黑龙江黑河人,硕士生,从事城市–区域发展模拟与规划研究。E-mail: liyatong97csdl@163.com
  • 基金资助:
    国家自然科学基金项目(41901138);国家自然科学基金项目(41671536);教育部人文社会科学研究青年基金项目(19YJCZH225)

Improvement and Application of Two-dimensional Fractal Model of Urban Growth and Morphology

LI Yatong1,2(), ZHANG Lijun3,*(), YE Shilin1,2, QI Xinhua1,2   

  1. 1. State Key Laboratory for Subtropical Mountain Ecology of the Ministry of Science and Technology and Fujian Province, Fujian Normal University, Fuzhou 350007, China
    2. College of Geographic Sciences, Fujian Normal University, Fuzhou 350007, China
    3. College of Environment and Planning, Henan University, Kaifeng 475000, China
  • Received:2019-11-07 Revised:2020-01-14 Online:2020-11-25 Published:2021-01-25
  • Contact: ZHANG Lijun E-mail:liyatong97csdl@163.com;zlj7happy@163.com
  • Supported by:
    National Natural Science Foundation of China(41901138);National Natural Science Foundation of China(41671536);Humanities and Social Sciences Research Fund of Ministry of Education in China(19YJCZH225)

摘要:

分形方法是测度城市生长与形态演化的重要方法,然而其标度区范围的自然识别依然存在瓶颈。本文采用二阶导数识别半径法标度区界线,结合经典计盒法模型提出改进的双维分形标度律测算方法,以郑州市为案例区验证模型的精度与效度,综合解析郑州城市空间形态结构的生长演变特征。结果显示:① 利用二阶导数自动识别半径法标度区界线可显著提升分形模型拟合效果,拟合精度R2由0.920提升至0.996以上;② 郑州城市空间结构存有双标度现象,城市生长扩张并非标准环形波状推进,半径法模型仅在“城市中心边缘—建成区内侧”的环状范围拟合有效,城市结构可能存有自仿射生长或随机多分形特征;③ 1982—2020年郑州城市形态演化为明显的中心蔓延模式,职能用地的空间配置整体均匀程度偏高,功能分异程度较低,存有城市景观较紊乱,系统效率不高的隐患。本研究对半径法分形模型中拟合精度难以提升的应用瓶颈作出了突破性尝试,为城市生长模拟与城市空间结构演变分析提供了一种新方法,丰富了城市分形研究。

关键词: 城市生长, 城市空间形态, 标度区识别, 二阶导数方法, 双维分形模型, 径向维数, 网格维数, 郑州市

Abstract:

Rapid urban expansion has brought disorder and low efficiency to the socioeconomic development and the land utilizatopm. However, due to a large number of scale-free phenomena in the urban complex system, it is difficult to measure its morphological characteristics effectively. In essence, fractal is a hierarchical system which is related to the complex network cascade structure. Fractal structure can be used to measure the spatial cycle subdivision of urban geographic system, which plays an important role in the exploration on the law of urban morphology evolution, and provides an effective mathematical tool for the implementation of territorial spatial planning. Based on the urban fractal theory, this paper forms a logical frame for the evolution of urban functional land, through the dual analysis of the radial dimension and the grid dimension representing urban spatial form. By calculating and analyzing the empirical case of Zhengzhou, a typical representative of urban growth and evolution in China, the validity of using the second derivative to automatically identify the scaling range in the radius method is verified. Finally, the paper discusses the structural and functional problems hidden in the urban evolution process, and provides theoretical reference and method enlightenment for the exploration of integrated optimization scheme of the fractal urban system. The results show that: (1) Using the second derivative method to automatically identify the boundary of scaling range in the radius method can significantly improve the feasibility of the fractal model. The fitting accuracy R2 is increased from 0.920 to above 0.996. This method makes a breakthrough attempt on the application bottleneck in the fractal model of radius method, which is difficult to improve the fitting accuracy. This method has obvious advantages in simulating the urban growth, especially the evolution of urban spatial structure, and can judge the expansion speed and mode, so as to evaluate the city's health. (2) The double scale phenomenon exists in the urban spatial structure of Zhengzhou. The radius method model only fits effectively in the circular range of "the edge of urban center-inside the built-up area", which may have the growth characteristics of self-affine or random multi-fractal. (3) From 1982 to 2020, the urban form of Zhengzhou evolves into a central sprawl mode, and the urban center and the periphery present a dualistic trend. The interaction between the systems is insufficient, the system efficiency is lower, and the urban spatial structure can be further refined and upgraded.

Key words: urban growth, urban spatial form, scaling range identification, second derivative method, two-dimensional fractal model, radial dimension, grid dimension, Zhengzhou