Urban scaling and the geographic concentration of inequalities by city size

2018 ◽  
Vol 46 (9) ◽  
pp. 1627-1644 ◽  
Author(s):  
Somwrita Sarkar
Keyword(s):  
Urban Policy ◽  
Scaling Laws ◽  
City Size ◽  
Urban Systems ◽  
Scaling Analysis ◽  
Middle Income ◽  
Income Distributions ◽  
Spatial Inequalities ◽  
Housing Costs ◽  
Urban Scaling

Urban scaling laws summarise how socio-economic behaviours of urban systems may be predicted from city size. While most scaling analysis rests on using aggregate quantities (total incomes, GDP, etc.), examining distributions of these aggregate quantities (e.g. income distributions) could shed light on how socio-economic inequalities may correlate or be causally linked to city size. In this direction, this paper examines how geographic distributions and spatial inequalities of income and housing costs vary by city size. The paper presents three principal results. First, it brings out qualitative implications of quantitative scaling by relating scaling of the distributions of income and housing costs to their specific geographic concentrations. Second, it shows that some small and medium sized cities are clear outliers, showing behaviour similar to the largest cities and starkly different from the behaviours of the bulk of small and medium sized cities. Third, this above observation explains why heteroscedasticity, or large and heterogeneous fluctuations, are frequently observed in urban indicator data when plotted as a function of city size. Putting together these three results, overall, it is shown that income distributions and housing costs scale and concentrate in cities by size in a predictable way, where the largest cities superlinearly/disproportionately agglomerate the highest income earners and the highest housing costs, and show relatively lower concentrations of low-middle income earners and low-medium housing costs. In contrast, most of the smaller and medium sized cities show a ‘flipped’ opposite trend. A few small and medium sized cities are outliers: they show trends that match those of the largest cities, due to specialisations of economic functions or concentrations of high-paying occupations in these cities. The empirical findings lead to a discussion on the objective and normative relationships between city size and urban inequalities. It is suggested that due to the concentrations of high income and high housing costs, largest cities may have a resulting housing market structure that will push out lower and medium income earners, thereby making affordability, diversity, and socio-spatial justice emerge as important urban policy issues.

scholarly journals Scaling of urban income inequality in the USA

2021 ◽  
Vol 18 (181) ◽  
pp. 20210223
Author(s):  
Elisa Heinrich Mora ◽  
Cate Heine ◽  
Jacob J. Jackson ◽  
Geoffrey B. West ◽  
Vicky Chuqiao Yang ◽  
...  
Keyword(s):  
Income Inequality ◽  
Income Distribution ◽  
City Size ◽  
Housing Cost ◽  
Scaling Analysis ◽  
Total Income ◽  
Income Distributions ◽  
City Population ◽  
Leibler Divergence ◽  
Urban Scaling

Urban scaling analysis, the study of how aggregated urban features vary with the population of an urban area, provides a promising framework for discovering commonalities across cities and uncovering dynamics shared by cities across time and space. Here, we use the urban scaling framework to study an important, but under-explored feature in this community—income inequality. We propose a new method to study the scaling of income distributions by analysing total income scaling in population percentiles. We show that income in the least wealthy decile (10%) scales close to linearly with city population, while income in the most wealthy decile scale with a significantly superlinear exponent. In contrast to the superlinear scaling of total income with city population, this decile scaling illustrates that the benefits of larger cities are increasingly unequally distributed. For the poorest income deciles, cities have no positive effect over the null expectation of a linear increase. We repeat our analysis after adjusting income by housing cost, and find similar results. We then further analyse the shapes of income distributions. First, we find that mean, variance, skewness and kurtosis of income distributions all increase with city size. Second, the Kullback–Leibler divergence between a city’s income distribution and that of the largest city decreases with city population, suggesting the overall shape of income distribution shifts with city population. As most urban scaling theories consider densifying interactions within cities as the fundamental process leading to the superlinear increase of many features, our results suggest this effect is only seen in the upper deciles of the cities. Our finding encourages future work to consider heterogeneous models of interactions to form a more coherent understanding of urban scaling.

Evidence for the homothetic scaling of urban forms

2018 ◽  
Vol 47 (5) ◽  
pp. 870-888 ◽  
Author(s):  
Rémi Lemoy ◽  
Geoffrey Caruso
Keyword(s):  
Land Use ◽  
Population Density ◽  
Scaling Laws ◽  
Radial Distance ◽  
Three Dimensions ◽  
City Size ◽  
Cube Root ◽  
Radial Profiles ◽  
Population Grid ◽  
Urban Scaling

The size and form of cities influence their social and environmental impacts. Whether cities have the same form irrespective of their size is still an open question. We analyse the profile of artificial land and population density, with respect to the distance to their main centre, for the 300 largest European cities. Our analysis combines the GMES/Copernicus Urban Atlas 2006 land use database at 5 m resolution for 300 larger urban zones with more than 100,000 inhabitants and the Geostat population grid at 1 km resolution. We find a remarkable constancy of radial profiles across city sizes. Artificial land profiles scale in the two horizontal dimensions with the square root of city population, while population density profiles scale in three dimensions with its cube root. In short, cities of different size are homothetic in terms of land use and population density, which challenges the idea that larger cities are more parsimonious in the use of land per capita. While earlier literature documented the scaling of average densities (total surface and population) with city size, we document the scaling of the whole radial distance profile with city size, thus liaising intra-urban radial analysis and systems of cities. Our findings also yield homogenous spatial definitions of cities, from which we can re-question urban scaling laws and Zipf’s law for cities.

Are the absent always wrong? Dealing with zero values in urban scaling

2018 ◽  
Vol 46 (9) ◽  
pp. 1663-1677 ◽  
Author(s):  
Olivier Finance ◽  
Clémentine Cottineau
Keyword(s):  
Foreign Investment ◽  
Scaling Laws ◽  
Empirical Studies ◽  
Urban System ◽  
Ordinary Least Squares ◽  
Urban Systems ◽  
Zero Values ◽  
Urban Scaling ◽  
Definition Of

Both theoretical and empirical studies have shown the ability of scaling laws to reveal processes of emergence in urban systems. Nevertheless, a controversy about the robustness of results obtained with these models on empirical cases remains, regarding for instance the definition of the ‘city’ considered or the way the estimations are performed. Another source of bias is highlighted in this contribution, with respect to the non-ubiquitous character of some urban attributes (i.e. their partial absence from several cities of the system). The problem with the zero count for cities where these attributes are absent is that the technical necessities of usual estimation procedures make the analysis ignore them altogether even when they represent some valid information. This could seriously impact the results. A precise exploration of the effects of this arbitrary filtering is conducted here, and several solutions are proposed to overcome this limitation. In a case study about foreign investment towards French cities, we show that some erroneous conclusions about a hierarchical diffusion could be drawn when adopting the classical ordinary least squares approach. The framework we suggest specifies how it is possible to avoid misinterpretations deriving from the exclusion of zero values by using methods of analysis which deal with zero values specifically. The conclusion of a diffusion of foreign investment in the French urban system is then rejected.

scholarly journals Understanding the mesoscopic scaling patterns within cities

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Lei Dong ◽  
Zhou Huang ◽  
Jiang Zhang ◽  
Yu Liu
Keyword(s):  
Scaling Laws ◽  
Urban Systems ◽  
Active Population ◽  
Scaling Relationship ◽  
Wide Range ◽  
Simple Scaling ◽  
Population Sizes ◽  
Mesoscopic Level ◽  
Urban Scaling ◽  
Simple Interaction

AbstractUnderstanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale systematically with population sizes across cities, also known as urban scaling laws. However, at the mesoscopic level, we lack an understanding of whether the simple scaling relationship holds within cities, which is a fundamental question regarding the spatial origin of scaling in urban systems. Here, by analyzing four extensive datasets covering millions of mobile phone users and urban facilities, we investigate the scaling phenomena within cities. We find that the mesoscopic infrastructure volume and socioeconomic activity scale sub- and super-linearly with the active population, respectively. For a same scaling phenomenon, however, the exponents vary in cities of similar population sizes. To explain these empirical observations, we propose a conceptual framework by considering the heterogeneous distributions of population and facilities, and the spatial interactions between them. Analytical and numerical results suggest that, despite the large number of complexities that influence urban activities, the simple interaction rules can effectively explain the observed regularity and heterogeneity in scaling behaviors within cities.

scholarly journals A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991–2014

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Yanguang Chen ◽  
Jian Feng
Keyword(s):  
Scaling Laws ◽  
City Planning ◽  
Allometric Scaling ◽  
Scaling Law ◽  
Urban Systems ◽  
Long Term Memory ◽  
Scaling Analysis ◽  
Scaling Exponent ◽  
Random Disturbance ◽  
Chinese Cities

The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf’s law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of R/S analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning.

Urban scaling in rapidly urbanising China

Urban Studies ◽  
2021 ◽  
pp. 004209802110178
Author(s):  
Weiqian Lei ◽  
Limin Jiao ◽  
Gang Xu ◽  
Zhengzi Zhou
Keyword(s):  
Urban Population ◽  
Economies Of Scale ◽  
Scaling Laws ◽  
Temporal Evolution ◽  
Urban System ◽  
Scaling Analysis ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Economic Output ◽  
Urban Scaling

Understanding the scaling characteristics in China is critical for perceiving the development process of rapidly urbanising countries. This paper conducts a comprehensive scaling analysis with quantitative assessment of a large number of diverse urban indicators of 275 Chinese cities. Our findings confirm that urban scaling laws can also be applied to rapidly urbanising China but demonstrate some unique features echoing its distinct urbanisation. Chinese urban population agglomeration results in more effective economic production but the economies of scale for infrastructure are less obvious. Some urban indicators associated with infrastructure and living facilities surprisingly scale super-linearly with urban population size, contrary to expected sublinear scaling behaviours. In developing countries, different-sized cities have diverse agglomeration, industrial and resource allocation advantages, which can be reflected by scaling exponents. We characterise these unique features in detail, exploring the spatial disparities and temporal evolution of scaling exponents ( β). Strong regional variations and differences are particularly pronounced in Northeast China and the Beijing-Tianjin-Hebei Urban Agglomeration. Scaling exponent variations over time reflect the temporal evolution of the urban system and measure the coordination and balance of urbanisation. Economic output was most efficient in 2009 and β of GDP was slightly greater than 1.15 in recent years. Urban land expansion has been accelerating since 2000 with β remaining around 0.85–0.90. The study of urban scaling in China is enlightening in elaborating the uniqueness and coordination of urban development in rapidly urbanising countries and provides support in formulating differentiated urban planning for different-sized cities to promote coordinated development.

scholarly journals Constructing cities, deconstructing scaling laws

2015 ◽  
Vol 12 (102) ◽  
pp. 20140745 ◽  
Author(s):  
Elsa Arcaute ◽  
Erez Hatna ◽  
Peter Ferguson ◽  
Hyejin Youn ◽  
Anders Johansson ◽  
...  
Keyword(s):  
Population Density ◽  
Population Size ◽  
Scaling Laws ◽  
City Size ◽  
Scaling Analysis ◽  
Large Set ◽  
England And Wales ◽  
Universal Scaling ◽  
Definition Of ◽  
Nonlinear Correlations

Cities can be characterized and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al . have proposed that many of these urban measures can be predicted through universal scaling laws. We develop a framework to consistently define cities, using commuting to work and population density thresholds, and construct thousands of realizations of systems of cities with different boundaries for England and Wales. These serve as a laboratory for the scaling analysis of a large set of urban indicators. The analysis shows that population size alone does not provide us enough information to describe or predict the state of a city as previously proposed, indicating that the expected scaling laws are not corroborated. We found that most urban indicators scale linearly with city size, regardless of the definition of the urban boundaries. However, when nonlinear correlations are present, the exponent fluctuates considerably.

scholarly journals The effect of dragon-kings on the estimation of scaling law parameters

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Carmen Cabrera-Arnau ◽  
Steven R. Bishop
Keyword(s):  
Traffic Accidents ◽  
Scaling Laws ◽  
Road Traffic ◽  
House Prices ◽  
Scaling Law ◽  
Large Population ◽  
Estimation Procedure ◽  
Urban Systems ◽  
Scaling Analysis ◽  
Scaling Parameters

AbstractScaling laws are used to model how different quantifiable properties of cities, such as the number of road traffic accidents or average house prices, vary as a function of city population size, with parameters estimated from data. Arcaute et al. raised the issue of whether specific cities with extremely large population sizes, known as dragon-kings, should be considered separately from other smaller cities when estimating the scaling law parameters since the two types of cities tend to display different behaviour. Through the analysis of randomly generated samples, we find that the inclusion of dragon-kings in the scaling analysis does not affect the estimated values for the parameters but only provided that all the data points satisfy the same scaling law. We also analyse randomly generated samples where data corresponding to a particular city deviates from the scaling law followed by the rest of the cities. We then show that deviations corresponding to dragon-king cities have the most significant effect on the estimated values of the scaling parameters. The extent of this effect also depends on which estimation procedure is used. Our results have important implications on the suitability of scaling laws as a model for urban systems.

scholarly journals Experimental investigation to characterize simple versus multi scaling analysis of hydraulic conductivity at a mesoscale

2021 ◽  
Author(s):  
Guglielmo Federico Antonio Brunetti ◽  
Samuele De Bartolo ◽  
Carmine Fallico ◽  
Ferdinando Frega ◽  
Maria Fernanda Rivera Velásquez ◽  
...  
Keyword(s):  
Hydraulic Conductivity ◽  
Spatial Variability ◽  
Hydraulic Properties ◽  
Scaling Laws ◽  
Scaling Analysis ◽  
Field Scale ◽  
Porous Formation ◽  
Proper Design ◽  
First Time

AbstractThe spatial variability of the aquifers' hydraulic properties can be satisfactorily described by means of scaling laws. The latter enable one to relate the small (typically laboratory) scale to the larger (typically formation/regional) ones, therefore leading de facto to an upscaling procedure. In the present study, we are concerned with the spatial variability of the hydraulic conductivity K into a strongly heterogeneous porous formation. A strategy, allowing one to identify correctly the single/multiple scaling of K, is applied for the first time to a large caisson, where the medium was packed. In particular, we show how to identify the various scaling ranges with special emphasis on the determination of the related cut-off limits. Finally, we illustrate how the heterogeneity enhances with the increasing scale of observation, by identifying the proper law accounting for the transition from the laboratory to the field scale. Results of the present study are of paramount utility for the proper design of pumping tests in formations where the degree of spatial variability of the hydraulic conductivity does not allow regarding them as “weakly heterogeneous”, as well as for the study of dispersion mechanisms.

scholarly journals Empowering Urban Governance through Urban Science: Multi-Scale Dynamics of Urban Systems Worldwide

2020 ◽  
Vol 12 (15) ◽  
pp. 5954
Author(s):  
Juste Raimbault ◽  
Eric Denis ◽  
Denise Pumain
Keyword(s):  
Urban Growth ◽  
Path Dependence ◽  
Dynamic Models ◽  
Network Flows ◽  
City Size ◽  
Urban Systems ◽  
Scale Model ◽  
Multi Scale ◽  
The World ◽  
Urban Science

Cities are facing many sustainability issues in the context of the current global interdependency characterized by an economic uncertainty coupled to climate changes, which challenge their local policies aiming to better conciliate reasonable growth with livable urban environment. The urban dynamic models developed by the so-called “urban science” can provide a useful foundation for more sustainable urban policies. It implies that their proposals have been validated by correct observations of the diversity of situations in the world. However, international comparisons of the evolution of cities often produce unclear results because national territorial frameworks are not always in strict correspondence with the dynamics of urban systems. We propose to provide various compositions of systems of cities in order to better take into account the dynamic networking of cities that go beyond regional and national territorial boundaries. Different models conceived for explaining city size and urban growth distributions enable the establishing of a correspondence between urban trajectories when observed at the level of cities and systems of cities. We test the validity and representativeness of several dynamic models of complex urban systems and their variations across regions of the world, at the macroscopic scale of systems of cities. The originality of the approach resides in the way it considers spatial interaction and evolutionary path dependence as major features in the general behavior of urban entities. The models studied include diverse and complementary processes, such as economic exchanges, diffusion of innovations, and physical network flows. Complex systems dynamics is in principle unpredictable, but contextualizing it regarding demographic, income, and resource components may help in minimizing the forecasting errors. We use, among others, a new unique source correlating population and built-up footprint at world scale: the Global Human Settlement built-up areas (GHS-BU). Following the methodology and results already obtained in the European GeoDiverCity project, including USA, Europe, and BRICS countries, we complete them with this new dataset at world scale and different models. This research helps in further empirical testing of the hypotheses of the evolutionary theory of urban systems and partially revising them. We also suggest research directions towards the coupling of these models into a multi-scale model of urban growth.

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