The Size Distribution, Scaling Properties and Spatial Organization of Urban Clusters: A Global and Regional Percolation Perspective

Abstract

Abstract:Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms, and urban growth is one of the most eminent transformative processes. We analyze global land cover data and extract cities as defined by maximally connected urban clusters. The analysis of the city size distribution for all cities on the globe confirms Zipf's law. Moreover, by investigating the percolation properties of the clustering of urban areas we assess the closeness to criticality for various countries. At the critical thresholds, the urban land cover of the countries undergoes a transition from separated clusters to a gigantic component on the country scale. We study the Zipf-exponents as a function of the closeness to percolation and find a systematic dependence, which could be the reason for deviating exponents reported in the literature. Moreover, we investigate the average size of the clusters as a function of the proximity to percolation and find country specific behavior. By relating the standard deviation and the average of cluster sizes-analogous to Taylor's law-we suggest an alternative way to identify the percolation transition. We calculate spatial correlations of the urban land cover and find long-range correlations. Finally, by relating the areas of cities with population figures we address the global aspect of the allometry of cities, finding an exponent δ ≈ 0.85, i.e., large cities have lower densities.

The role of city size and urban form in the surface urban heat island

“…Therefore, we need to measure the three quantities for all considered city clusters.

The city size S C is simply given by the number of cells constituting the city clusters multiplied by the area of each cell, 6.25 × 10 −2 km 2 . Due to Zipf’s law for cities 22–26 there are many small cities and few large ones so that we use the logarithm of city size, ln S C , in order to reduce the skewness.

We compute the fractal dimension using the box counting method, assuming , where n is the number of (square) boxes of side length r necessary to cover the structure, see Methods Section. In Fig.…”

Territorial Distribution of the Population in the Russian Federation

“…В последние годы опубликовано значитель-ное количество работ [8][9][10][11][12][13][14][15][16][17][18][19][20][21], в которых иссле-дован вопрос обоснованности применения за-конов Гибрата и Ципфа при анализе законо-мерностей территориального распределения населения и трудовых ресурсов, а также разви-тия фирм. Так, в работе [8] проанализирована литература (более 50 наименований), относя-щаяся к применению закона Гибрата и подраз-деленная на следующие категории:…”

“…Следует отметить также работы, посвящен-ные исследованию пространственной органи-зации городских кластеров [18], взаимосвязи между численностью фирмы и ее ростом (на примере Чехии) [19]. В работе [20] проанализи-рован вопрос справедливости (несправедливо-сти) закона Гибрата для шведских фирм в об-ласти энергетики.…”

“…При этом в разных странах различные фак-торы оказывают влияние на выполнение зако-нов Ципфа и Гибрата. В одних случаях важным фактором является развитие рынка, в других -уровень развития промышленности, сель-ского хозяйства и т. п. В некоторых случаях ре-шающим является комбинация из нескольких факторов.Следует отметить также работы, посвящен-ные исследованию пространственной органи-зации городских кластеров [18], взаимосвязи между численностью фирмы и ее ростом (на примере Чехии) [19]. В работе [20] проанализи-рован вопрос справедливости (несправедливо-сти) закона Гибрата для шведских фирм в об-ласти энергетики.…”

Modeling Spatial Social Complex Networks for Dynamical Processes

“…This "baseline model" was designed with modest goals in mind: (a) The population density resembles the light density observed in satellite pictures of earth at night, (b) the population of "cities" (defined by percolation clusters [27]) and their rankings follow Zipf 's law [28][29][30], (c) the social network of contacts exhibits a scale-free distribution, and (d) highly connected nodes tend to be located in denser and larger population areas. In addition to meeting these basic goals the SSCN baseline model also yielded good qualitative agreement with census data for the population density as a function of city size, and for the weak super-linear dependence of the cumulative degree of nodes in a city on its total population, as suggested from cell-phone data [12].…”