Liu Lingbo, Peng Zhenghong, Wu Hao

Keywords： Big Data; Natural Cities; Long Tail Rule; Rank-Size; Head/Tail Breaks; TIN

Abstract：

Scale hierarchy and boundary delimitation play important roles in urban research. Traditional statistic data such as population and economic scale cannot precisely define the real status, alternatively, new data such as light remote sensing, mobile phone signaling, road intersection and location-based social network (LBSN) have been introduced recently by more and more studies, intending to delimit the built up area boundary and measure the size and scale of the city with bottom-to-up approach. However, there are still two problems: lacking dividing standards and representing feature, therefore the H/T breaks point method is provided to classify scale and define boundary for cities. Based on to make a triangular irregular network (TIN) generated by point of interest (POI) data which represents various economic activities, the H/T breaks method is applied classifying the natural city scale in mainland China. The results show that the natural city boundary based on POI reflects the relative scale and density of human settlements, the H/T breaks point classification follows the Zipf’s law in rank-size method, offers a more scientific classifying method for naturally grouping of city scale according to the long tail rule and fractal structure of natural cites. The method has promotional value on urban scale measuring and classifying, with the advantage of precision and real data acquisition.

Funds：

• [1] FRAGKIAS M, SETO K C. Evolving rank-size distributions of intrametropolitan urban clusters in south China[J]. Computers Environment & Urban Systems, 2009, 33(3): 189-199.

  [2] KAUFMANN R K, SETO K C, SCHNEIDER A, et al. Climate response to rapid urban growth: evidence of a human-induced precipitation deficit[J]. Journal of Climate, 2007, 20(10): 2299-2306.

  [3] JA?D?EWSKA I. Spatial and dynamic aspects of the rank-size rule method. Case of an urban settlement in Poland[J]. Computers Environment & Urban Systems, 2017, 62: 199-209.

  [4] 戚伟, 刘盛和. 中国城市流动人口位序规模分布研究[J]. 地理研究, 2015, 34(10): 1981-1993.

  [5] 王法辉. 我国城市规模分布的统计模式研究[J]. 城市问题, 1989 (1): 14-20.

  [6] 余吉祥, 周光霞, 段玉彬. 中国城市规模分布的演进趋势研究——基于全国人口普查数据[J]. 人口与经济, 2013 (2): 44-52.

  [7] SCHWEITZER F, STEINBINK J. Urban cluster growth: analysis and computer simulation of urban aggregations[M] // SCHWEITZER F. Selforganization of complex structures: from individual to collective dynamics. London: Gordon and Breach, 1997: 501-518.

  [8] PUMAIN D. Hierarchy in natural and social sciences[M]. Dordrecht: Springer Netherlands, 2006: 14-19.

  [9] CHEN Y. The mathematical relationship between Zipf’s law and the hierarchical scaling law[J]. Physica A: Statistical Mechanics & Its Applications, 2012, 391(11): 3285-3299.

  [10] CHEN Y. The evolution of Zipf’s law indicative of city development[J]. Physica A: Statistical Mechanics & Its Applications, 2015, 443: 555-567.

  [11] JIANG B, JIA T. Zipf’s law for all the natural cities in the United States: a geospatial perspective[J]. International Journal of Geographical Information Science, 2011, 25(8): 1269-1281.

  [12] JIANG B, MIAO Y. The evolution of natural cities from the perspective of location-based social media[J]. The Professional Geographer, 2015, 67(2): 295-306.

  [13] LONG Y. Redefining Chinese city system with emerging new data[J]. Applied Geography, 2016, 75: 36-48.

  [14] JIANG B. Head/tail breaks: a new classification scheme for data with a heavy-tailed distribution[J]. Professional Geographer, 2013, 65(3): 482-494.

  [15] MASUCCI A P, ARCAUTE E, HATNA E, et al. Logistic growth and ergodic properties of urban forms[EB/OL]. (2015-10-27)[2017-05-18]. arXiv:1504.07380v3.

  [16] 钮心毅, 王垚, 丁亮. 利用手机信令数据测度城镇体系的等级结构[J]. 规划师, 2017, 33(1): 50-56.

  [17] ALEXANDER C. The city is not a tree[J]. Archit Forum, 1965, 122: 58-62, 58-61.

  [18] JIANG B. A city is a complex network[M]. Portland: Sustasis Press, 2015.

  [19] BATTY M. The new science of cities[J]. Building Research & Information, 2013, 38(1): 123-126.

  [20] BATTY M, LONGLEY P. Fractal cities: a geometr y of form and funct ion[EB/OL]. [2017-05-18] . ht tps://www.researchgate.net/publication/30867789_Fractal_Cities_-_A_Geometry_of_Form_and_Function

  [21] BATTY M. Cities and complexity: understanding cities with cellular automata, agent-based models, and fractals[M]. Cambridge MA: MIT Press, 2007: 113-115.

  [22] JIANG B. A complex-network perspective on Alexanders wholeness[J]. Physica A: Statistical Mechanics & Its Applications, 2016, 463: 475-484.

  [23] JIANG B. Wholeness as a hierarchical graph to capture the nature of space[J]. International Journal of Geographical Information Science, 2015, 29(9): 1632-1648.

  [24] JENKS G F. Generalization in statistical mapping[J]. Annals of the Association of American Geographers, 1963, 53(1): 15-26.

  [25] BREWER C A, PICKLE L. Evaluation of methods for classifying epidemiological data on choropleth maps in series[J]. Annals of the Association of American Geographers, 2002, 92(4): 662-681.

  [26] JIANG B, LIU X. Scaling of geographic space as a universal rule for map heneralization[J]. Annals of the Association of American Geographers, 2011, 103(4): 844-855.

  [27] JIANG B, YIN J. Ht-index for quantifying the fractal or scaling structure of Geographic features[J]. Annals of the Association of American Geographers, 2013, 104(3): 530-540.

  [28] GAO P, LIU Z, TIAN K, et al. Characterizing traffic conditions from the perspective of spatial-temporal heterogeneity[J]. ISPRS International Journal of Geo-Information, 2016, 5:34.

  [29] JIANG B. Head/tail breaks for visualization of city structure and dynamics[J]. Cities, 2015, 43(3): 69-77.

  [30] LONG Y, SHEN Y. Mapping parcel-level urban areas for a large geographical area[EB/OL]. [2017-05-18]. https://arxiv.org/abs/1403.5864.

  [31] JIANG B. Axwoman 6.3: an ArcGIS extension for urban morphological analysis. [EB/OL]. [2017-05-18]. http://giscience.hig.se/binjiang/axwoman/.