Does China's Urban Development Satisfy Zipf's Law? A ...

Currently, whether the urban development in China satisfies Zipf’s law across different scales is still unclear. Thus, this study attempted to explore whether China’s urban development satisfies Zipf’s law across different scales from the National Polar-Orbiting Partnership’s Visible Infrared Imaging Radiometer Suite (NPP-VIIRS) nighttime light data. First, the NPP-VIIRS data were corrected. Then, based on the Zipf law model, the corrected NPP-VIIRS data were used to evaluate China’s urban development at multiple scales. The results showed that the corrected NPP-VIIRS data could effectively reflect the state of urban development in China. Additionally, the Zipf index (q) values, which could express the degree of urban development, decreased from 2012 to 2018 overall in all provinces, prefectures, and counties. Since the value of q was relatively close to 1 with an R 2 value > 0.70, the development of the provinces and prefectures was close to the ideal Zipf’s law state. In all counties, q > 1 with an R 2 value > 0.70, which showed that the primate county had a relatively stronger monopoly capacity. When the value of q < 1 with a continuous declination in the top 2000 counties, the top 250 prefectures, and the top 20 provinces in equilibrium, there was little difference in the scale of development at the multiscale level with an R 2 > 0.90. The results enriched our understanding of urban development in terms of Zipf’s law and had valuable implications for relevant decision-makers and stakeholders.

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1. Introduction

Global cities have entered a stage of rapid development. The growth of an urban area is reflected in its significant changes, such as gross domestic product (GDP) growth, population increases, urban built-up area expansion, and environmental pollution [1,2]. As one of the largest developing countries in the world, China has experienced the largest and fastest urban development in the history of the world [3]. For instance, by 2017, the urban and rural settlement areas as a whole covered 209,950 km2, nearly 13.6 times the 15,364 km2 mapped in 1978 [4]. The magnificent speed of urban development of the kind seen in China is rare and world-leading [5,6,7]. Therefore, an in-depth analysis of China’s urban development is conducive to the implementation of a global sustainable development strategy. According to the “National New Urbanization Planning (2014–2020)” released by the state council in 2014, the urbanization rate of permanent residents should reach about 60% by 2020, which is important information from the perspective of urban strategy in China [8]. If the urbanization rate exceeds 60%, the population will accelerate the migration to metropolitan areas, especially to central cities directly under the control of the central government, provincial capitals, and cities under separate state planning [9]. At present, China’s urbanization has entered a stage in which central cities drive urban agglomeration and thus regional economic development. This stage will be maintained for quite a long time in the future. Reasonable adjustment of the urban development process and urban development layout will be conducive to China’s future sustainable development. However, there are different opinions about the arrangement of the urban development layout during this period of rapid urban development in China. Hence, an in-depth analysis of China’s urban development is conducive to understanding the pattern of urban development and formulating accurate policy guidance in China to guide rational urban development for sustainable development.

Urban development involves the changing and growing process of the status, function, attraction, and radiation forces of an urban area, which are mutually reinforcing. It is a complex changing process of complex systems, including the population, society, economy, ecology, land, culture, and other subsystems [10,11,12]. Horizontal expansion and vertical improvements are deployed in urban development ( ). A horizontal expansion is represented by an increase in the number and scale of cities and the expansion of the urban built-up area, i.e., improvements in the urbanization level and urban size [13,14,15,16]. A vertical improvement represents an increase in the population and GDP growth, i.e., the socio-economic and environmental development of cities [17,18,19,20].

Urban development has been found to follow Zipf’s law. It says that if all cities in a certain region are ranked according to the size of their population, the sizes of the cities are inversely proportional to their rank, that is, the product of the rank of any city and its population size is equal to the size of the population of the first city in a certain region. Auerbach and Zipf first proposed that the empirical relationship between the city’s ranking and population size in a real urban system conforms to Zipf’s law [21]. Some existing studies have investigated whether urban development satisfies Zipf’s law from different perspectives, such as GDP, built-up areas, and population [22,23,24]. For example, Deng et al. [25] explored China’s urban built-up area with Zipf’s law to explain that the built-up areas of all cities in China had maintained a growth trend, but the rate of expansion varies greatly from period to period. Census data from the National Institute of Statistics were combined with the population and GDP to estimate the Zipf’s index [26,27,28,29]. Previously, Wen et al. [30] showed that China’s urban scale distribution was relatively balanced, virtually conforming to Zipf’s law by using China’s urban population data from 1990 to 2010 and a double-logarithmic regression model to test China’s urban scale and urban rank through Zipf’s law. However, many problems were still unsolved using traditional data because of the long lag time from generation to analysis, the large cost, the lack of digital form and spatial information, different levels of details on different scales, and the incapability of showing the full picture. There was a long lag time between when the written statistical data were generated and when they were available to the public. For instance, the authoritative data for China’s population statistics were the census, but the data were collected only once every 10 years, which made it difficult to track the population changes of large, medium, and small cities over the years. Additionally, the built-up area data were normally obtained from traditional remote sensing data. High- and medium-spatial-resolution remotely sensed images, such as those captured by the Landsat Thematic Mapper (TM) and the IKONOS satellite, the Sentinel-2 satellite, has been exploited in a variety of studies to characterize urban built-up areas to study urban development and processes [31,32]. However, such studies were cost-intensive given their limited geographic coverage and required a large amount of time and human resources to extract the urban information for a large region. Furthermore, the GDP and population data were written statistical data, which had deficiencies regarding digital analysis. The data also lacked adequate spatial details because statistical yearbook data, such as for GDP and population, used for urban development research were usually collected at the administrative unit scale. Moreover, most statistical yearbook data were openly published at the provincial and municipal levels, while county data were not, leaving the different levels of detail at different spatial scales. Lastly, although the GDP, population, and built-up area could describe the development of the city, they were only a part of the information on urban development, reflecting only one aspect each. Thus, they cannot show the full picture of the urban development of cities in China.

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The nighttime light time-series images provide a new perspective on the spatiotemporal changes for urban development [33,34]. The nighttime light data can detect urban nighttime lights and even low-intensity lights emitted by small-scale residential areas and traffic flows. The nighttime light data can reflect the degree of urban development, such as the population concentration, urbanization, economic activity, and other socio-economic aspects, and then reflect the socio-economic conditions of a country and the actual urban development situation [35,36,37]. Since nighttime light data can reflect the socio-economic and other relative activities of human beings well, and the activities related to various aspects of urban development are closely related to social and economic activities, nighttime light data can be used for more accurate for urban development monitoring, which has been proved by scholars at home and abroad. For example, Amaral et al. [38] analyzed nighttime light imagery as an information source to detect human settlements and to estimate the urban population in the Amazon region, as well as identify the potential ability of nighttime light images for estimating urban population and the technical limitations of using such images as a way to annually monitor urban population dynamics in a region. Shi et al. [39] combined nighttime light images and statistical data to assess spatiotemporal variations in urban CO2 emissions in China. Yu et al. [40] proposed a preprocessing method that applied a logarithmic transformation to the original nighttime light composite data for urban built-up area extraction. Shi et al. [41] applied linear regression to fit the correlation between the total nighttime light (TNL) data and the EPC (electricity power consumption) and GDP at provincial- and prefectural-level divisions. Additionally, many other studies discussed PM2.5 emissions [42,43], population [35,44], EPC [45], and other fields related to urban development. Hence, the nighttime light data provides a comprehensive way to study urban development in the form of a spatiotemporal pattern. Compared with the first-generation nighttime light data, i.e., the Defense Meteorological Satellite Program’s Operational Linescan System (DMSP-OLS) data, the national polar-orbiting partnership’s visible infrared imaging radiometer suite (NPP-VIIRS) nighttime light data’s spatial resolution, temporal resolution, and radiation resolution has been greatly improved, and these data were more suitable for the study of human economic and social activities.

Current studies focusing on Zipf’s law in urban development were from only a single or large scale. For instance, Small et al. [46] compared size–frequency distributions with size–area distributions and illustrated the effect of detection frequency thresholds on the number of contiguous lights and total lighted area to explore urban extent. Li et al. [47] analyzed the spatial and temporal patterns of national urban development for countries along the One Belt And One Road line, and Jiang et al. [20] analyzed whether Zipf’s law describes global natural cities. Huang et al. [48] analyzed city-size evolution at the city level based on nighttime light data at the national level and demonstrated that the nighttime light data and the Zipf’s law method were effective at uncovering urban development dynamics more consistently from both national and city perspectives. Many studies have also explored whether Zipf’s law describes global natural cities using nighttime light data [49]. Other studies have used nighttime light data to investigate Zipf’s law for urban agglomerations or prefectures [25,50]. However, there is a lack of multiscale spatial-temporal research on urban development in China. Zipf’s law on a single scale is not always consistent with that on other scales; therefore, the results of urban development on other scales are unknown. Although there have been extensive studies on urban development from different perspectives, little is known about China’s urban development at different levels. However, the problem is that most previous studies were conducted on a single spatial scale or in a single city with various geographical and political contexts. Analysis of data at different scales yields different results. Different scales have different influence mechanisms. In the field of geography, the influence of the selected area unit on the analysis result was defined as the modifiable areal unit problem (MAUP) [51], which is one of the main reasons for uncertainty in spatial data analysis results. Theoretically, the current basic administrative divisions of the People’s Republic of China are divided into three levels in mainland China: province, prefecture, and county. China has multiple dimensions of geographically administrative divisions. The temporal and spatial variations of urban development reflect the evolution of urban development in time and space. As the administrative area cannot completely describe the city size and the implementation of the urban development strategy policy main body, to achieve the evaluation of urban development, it is necessary to analyze the different administrative scales of urban development in line with the differentiation of urban development characteristics in different regions for the development of policies and measures. Currently, most studies have preferred to focus on the dynamic spatiotemporal variations of an administrative region, and thus multiscale research on urban development is lacking. In particular, the study of the dynamics of the national urban development spatiotemporal pattern has been mostly at the provincial level, while the smaller-scale studies, such as those focusing on the prefecture-level and county-level urban development spatiotemporal patterns, have been ignored. Spatial data had multi-granular and multiscale characteristics, and the relationship between the attribute data often changes with the research granularity and regionalization. When spatial analyses were carried out on the same geographic area with different resolutions or different scales, inconsistencies often occurred, which is called the scale effect [48]. The scale effect has become a central topic in geographical research. The space scale and the developmental trends of the geographical phenomena behind the influencing factors and mechanisms are likely to be different due to different spatial scales. Especially for the administrative regional scale, higher administrative units, more often than low-level administrative units, have more administrative, economic, and financial rights, leading to the urban development at different administrative scales presenting different time and space distribution patterns. The multiscale viewpoint has been demonstrated to be effective in many empirical analyses, such as regional economics, ecosystem management, and metropolitan governance. Specifically, it was worth noting that higher administrative units generally had stronger powers (e.g., financial, fiscal, and cultural powers) than lower administrative units in China, which likely led to differential impacts on both the scope and scale of urban development.

In summary, the following specific research questions remained unsolved: (1) Does Zipf’s law hold in China’s urban development? (2) What were the differences in Zipf’s law for China’s urban development from a multiscale perspective? To address the above questions, we selected 31 Chinese provincial cities, 333 Chinese prefectural cities, and 2845 Chinese county-level cities as study cases and conducted experiments using the NPP-VIIRS data. First, the NPP-VIIRS data was corrected to remove outliers to accurately reflect China’s urban development. Next, in combination with the Zipf’s law model, this study compared the urban development at three different scales, i.e., the province-level, prefecture-level, and county-level scales. The paper offers a scientific and effective way to deepen our understanding of the urban development according to Zipf’s law in Chinese cities at multiple scales and suggests a rational path for the government to improve the quality of urban development through sustainable urban planning.

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