Urban scaling and Zipf's law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about the connection between these two laws using population and GDP data from almost five thousand consistently-defined cities in 96 countries. We empirically demonstrate that both laws are tied to each other and derive an expression relating the urban scaling and Zipf exponents. This expression captures the average tendency of the empirical relation between both exponents, and simulations yield very similar results to the real data after accounting for random variations. We find that while the vast majority of countries exhibit increasing returns to scale of urban GDP, this effect is less pronounced in countries with fewer small cities and more metropolises (small Zipf exponent) than in countries with a more uneven number of small and large cities (large Zipf exponent). Our research puts forward the idea that urban scaling does not solely emerge from intra-city processes, as population distribution and scaling of urban GDP are correlated to each other.
Urban scaling theory explains the increasing returns to scale of urban wealth indicators by the per capita increase of human interactions within cities. This explanation implicitly assumes urban areas as isolated entities and ignores their interactions. Here we investigate the effects of commuting networks on the gross domestic product (GDP) of urban areas in the US and Brazil. We describe the urban GDP as the output of a production process where population, incoming commuters, and interactions between these quantities are the input variables. This approach significantly refines the descriptio…
Urban green space has been regarded as contributing to citizen happiness by promoting physical and mental health. However, how urban green space and happiness are related across many countries of different socioeconomic conditions has not been explained well. By measuring urban green space score (UGS) from high-resolution Sentinel-2 satellite imagery of 90 global cities that in total cover 179,168 km$^2$ and include 230 million people in 60 developed countries, we reveal that the amount of urban green space and the GDP can explain the happiness level of the country. More precisely, urban green…
We undertake an exploration of the economic income (Gross Domestic Product, GDP) of Indian districts and cities based on scaling analyses of the dependence of these quantities on associated population size. Scaling analysis provides a straightforward method for the identification of network effects in socioeconomic organization, which are the tell-tale of cities and urbanization. For districts, a sub-state regional administrative division in India, we find almost linear scaling of GDP with population, a result quite different from urban functional units in other national contexts. Using deviat…
We propose hypotheses describing the empirical finding of an association between the exponents of urban GDP scaling and Zipf's law for cities. These hypotheses represent various combinations of directional or reciprocal causal links between the two phenomena and include inter- and intra-city processes. Future theories and models can be motivated with and categorized according to these hypotheses. This paper intends to stimulate the discussion around the processes behind these phenomena and pave the way to a Unified Urban Theory.
The urban transition, the increased ratio of urban to rural population globally and within countries, is a hallmark of the 21st century. Our analysis of publicly available data from the World Bank spanning several decades for ~195 countries show that across and within nations over time, per capita Gross Domestic Product (GDP), energy use, and CO2 emissions are lowest in predominantly rural countries (rural > urban pop.), increase rapidly across urbanizing countries (rural urban pop.) and are highest in the most urban countries (rural < urban pop.). These trends coincide with changes in employm…
In this article, we introduce the method of urban association rules and its uses for extracting frequently appearing combinations of stores that are visited together to characterize shoppers' behaviors. The Apriori algorithm is used to extract the association rules (i.e., if -> result) from customer transaction datasets in a market-basket analysis. An application to our large-scale and anonymized bank card transaction dataset enables us to output linked trips for shopping all over the city: the method enables us to predict the other shops most likely to be visited by a customer given a particu…
Understanding cities is central to addressing major global challenges from climate and health to economic resilience. Although increasingly perceived as fundamental socio-economic units, the detailed fabric of urban economic activities is only now accessible to comprehensive analyses with the availability of large datasets. Here, we study abundances of business categories across U.S. metropolitan statistical areas to investigate how diversity of economic activities depends on city size. A universal structure common to all cities is revealed, manifesting self-similarity in internal economic str…
As huge complex systems consisting of geographic regions, natural resources, people and economic entities, countries follow the allometric scaling law which is ubiquitous in ecological, urban systems. We systematically investigated the allometric scaling relationships between a large number of macroscopic properties and geographic (area), demographic (population) and economic (GDP, gross domestic production) sizes of countries respectively. We found that most of the economic, trade, energy consumption, communication related properties have significant super-linear (the exponent is larger than …
Quantifying the topological similarities of different parts of urban road networks (URNs) enables us to understand the urban growth patterns. While conventional statistics provide useful information about characteristics of either a single node's direct neighbors or the entire network, such metrics fail to measure the similarities of subnetworks considering local indirect neighborhood relationships. In this study, we propose a graph-based machine-learning method to quantify the spatial homogeneity of subnetworks. We apply the method to 11,790 urban road networks across 30 cities worldwide to m…
Numerous urban indicators scale with population in a power law across cities, but whether the cross-sectional scaling law is applicable to the temporal growth of individual cities is unclear. Here we first find two paradoxical scaling relationships that urban built-up area sub-linearly scales with population across cities, but super-linearly scales with population over time in most individual cities because urban land expands faster than population grows. Different cities have diverse temporal scaling exponents and one city even has opposite temporal scaling regimes during two periods, strongl…
We present in this work some results from analysing the spread of Covid-19 in different countries and regions around the world and the potential relations with climate, geographical location, and GDP. While the situation remains dynamic, we believe this analysis has the potential to uncover certain underlying trends. We primarily intend the results to drive further, more detailed analysis of the relevant data by other researchers that would help us gather a better understanding of the situation, aiding our preparedness. Our observations show that countries in high latitudes, with temperate and…
The production of waste as a consequence of human activities is one of the most fundamental challenges facing our society and global ecological systems. Waste generation is rapidly increasing, with corresponding shifts in the structure of our societies where almost all nations are moving from rural agrarian societies to urban and technological ones. However, the connections between these radical societal shifts and waste generation have not yet been described. Here we apply scaling theory to establish a new understanding of waste in urban systems. We identify universal scaling laws of waste ge…
Given that a group of cities follows a scaling law connecting urban population with socio-economic or infrastructural metrics (transversal scaling), should we expect that each city would follow the same behavior over time (longitudinal scaling)? This assumption has important policy implications, although rigorous empirical tests have been so far hindered by the lack of suitable data. Here, we advance the debate by looking into the temporal evolution of the scaling laws for 5507 municipalities in Brazil. We focus on the relationship between population size and two urban variables, GDP and water…
The area-perimeter allometric scaling is a basic and important approach for researching fractal cities and has been studied for a long time. However, the boundary dimension of a city is always numerically overestimated by the traditional formula. An adjusting formula has been derived to revise the overestimated boundary dimension and estimate the form dimension, but the association between the global and local fractal parameters is not clear. This paper is devoted to describing the urban evolution by using the improved fractal parameters based on the area-perimeter measure relation. A system o…
There are different functional regions in cities such as tourist attractions, shopping centers, workplaces and residential places. The human mobility patterns for different functional regions are different, e.g., people usually go to work during daytime on weekdays, and visit shopping centers after work. In this paper, we analyse urban human mobility patterns and infer the functions of the regions in three cities. The analysis is based on three large taxi GPS datasets in Rome, San Francisco and Beijing containing 21 million, 11 million and 17 million GPS points respectively. We categorized the…
Global sustainability relies on our capacity of understanding and guiding urban systems, and their metabolism, in an adequate way. It has been proposed that bigger and denser cities are more resource-efficient than smaller ones because they tend to demand less infrastructure, consume less fuel for transportation and less energy for cooling or heating in per capita terms. This hypothesis is also called Brand's Law. But as cities get bigger, denser and more resource-efficient they also get richer. And richer inhabitants buy more, increasing its resource demand and associated environmental impact…
Using U.S. nationwide travel surveys for 1995, 2001, 2009 and 2017, this study compares Millennials with their previous generation (Gen Xers) in terms of their automobile travel across different neighborhood patterns. At the age of 16 to 28 years old, Millennials have lower daily personal vehicle miles traveled and car trips than Gen Xers in urban (higher-density) and suburban (lower-density) neighborhoods. Such differences remain unchanged after adjusting for the socio-economic, vehicle ownership, life cycle, year-specific and regional-specific factors. In addition, the associations between r…
Previous works have shown the universality of allometric scalings under density and total value at city level, but our understanding about the size effects of regions on them is still poor. Here, we revisit the scaling relations between gross domestic production (GDP) and population (POP) under total and density value. We first reveal that the superlinear scaling is a general feature under density value crossing different regions. The scaling exponent $β$ under density value falls into the range $(1.0, 2.0]$, which unexpectedly goes beyond the range observed by Pan et al. (Nat. Commun. vol. 4,…
A global framework to estimate urban spatial cycling patterns based on crowdsourced data
Digital Geography Lab, Department of Geosciences and Geography, University of Helsinki（赫尔辛基大学地球科学与地理系数字地理实验室）；Built Environment Solutions Unit, Finnish Environment Institute（芬兰环境研究所建成环境解决方案单元）
In an impending urban age where the majority of the world's population will live in cities, it is critical that we improve our understanding of the strengths and limitations of existing city designs to ensure they are safe, clean, can deliver health co-benefits and importantly, are sustainable into the future. To enable this, a systematic and efficient means of performing inter- and intra-city comparisons based on urban form is required. Until now, methods for comparing cities have been limited by scalability, often reliant upon non-standardised local input data that can be costly and difficul…
The rank-size plots of a large number of different physical and socio-economic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a dynamical approach is crucial: during their evolution, some systems are attracted towards Zipf's law, while others presents Zipf's law only temporarily and, therefore, spuriously. A truly Zipfian dynamics is characterized by a dynamical constraint, or coherence, among the parameters of the generating PDF, and the number of elements in the system. A clear-cut…
