1. Introduction
As a result of urbanization or the continuous influx of people into cities, the number of worldwide urbanites is predicted to be 6.9 billion by 2050, accounting for 68% of the world’s population [
1]. The urbanization in China has been unprecedentedly rapid as well in the past few decades [
2], reaching 60.6% nationally in 2019 [
3]. Consequently, the grasp of city form and function—that is, how cities look and work—has become the key to our sustainable development. Given the circumstances, city-related research has attracted scientists from a variety of subjects and has, inevitably, become cross-disciplinary, including geography, economics, computer science, and physics, etc. To converge these disciplines, scholars have called for a new science of cities in the past few decades, in which they view cities as an organized complexity [
4], for studying cities’ fractal shapes, complex structures, and nonlinear dynamics (e.g., [
5,
6,
7,
8,
9,
10,
11]).
One major aspect of urban complexity is its underlying scaling properties. The scaling pattern of urban entities can be categorized into two perspectives: The power law distribution of a single quantity, such as city sizes (Zipf’s law [
12]), building heights [
13], street lengths [
14], and leisure venue densities [
15], and the power relationship between two quantities, such as populations versus innovations ([
16,
17]) or gross domestic product (GDP) versus street fractality ([
18,
19]). This study uses the terms scaling and power law interchangeably. Urban scaling is, to a great extent, a ubiquitous pattern across different measures. Moreover, the theory developed by Bettencourt et al. [
16], which is behind the power relationship between urban populations and other socio-economic measures, has been formulated as fundamental laws about cities: Universal scaling law. However, recent studies have shown that the universal scaling law may not work as expected, as the scaling exponent is sensitive to different city boundaries or ineffective urban areas [
20,
21]. This controversy is likely to be bound with the top-down methods of defining geographic units by governments and authorities, such as administrative city boundaries, census tracts, and some equally partitioned cells, which are essentially for management purposes and hardly consider the scaling pattern of urban morphological and functional entities.
The arrival of geospatial big data has triggered a new paradigm for urban analysis since geospatial big data, such as remote sensing (RS) images and location-based social media data, has the capacity to offer fine-grained, massive-scale geographic information [
22]. For instance, nighttime lights (NTL) data, also referred to as RS of human beings and their activities [
23], are globally downloadable and can manifest the development of urban and regional areas. OpenStreetMap (OSM), a pioneering volunteered geospatial information platform, provides street data across the globe for probably the first time in human history [
24]. Both NTL and OSM data help researchers construct alternative modeling units for spatial analyses at both intercity and intracity levels, and remove the barriers of inter-regional incomparability. The most recent relevant studies are so-called natural cities, referring to the objectively defined cities based on different types of urban elements from the open data, such as building footprints, street nodes, and points of interest (e.g., [
25,
26,
27,
28,
29]). However, most of these studies take the derived cities as a whole to understand the scaling structure over a region or country, but seldom calibrate a “local” understanding of such spatial configuration at the intracity level.
Thus, the present study attempts to investigate the intra-urban scaling properties through the lens of city hotspots. A city is formed by highly concentrated areas of human settlements or activities within a country extent [
30]. Likewise, if we scale down our scope from a country to one of its cities, such concentrations can be regarded as urban hotspots. With the advance of geographic information system (GIS) technologies, urban hotspots can be delineated more precisely on the support of geospatial big data and bottom-up approaches. The study contributes to the current literature in three aspects. Firstly, we followed the ideas of previous city delineation methods to derive two types of urban hotspots across 20 Chinese cities: Street-based and NTL-based hotspots, from respectively the spatial clustering of individual street nodes and NTL image pixels with the cutoff determined by data’s inherent scaling properties (see details in
Section 2.2). Secondly, we found that Zipf’s law held remarkably well for both street-based and NTL-based hotspot sizes per city, as do the city-size distributions on the national scale. The scaling exponents derived based on NTL-based hotspots were also consistent with the established regimes, implying that NTL-based hotspots can act as better spatial units for urban analysis. Thirdly, we found that the spatial discrepancy between the street-based and NTL-based hotspots can lead us to deep insights on urban planning and development.
The remainder of this paper is organized as follows.
Section 2 introduces the data sets and the designed methods for urban hotspot delineation and related scaling analyses.
Section 3 presents the maps of the detected hotspots across the top 20 cities in China, as well as the power law metrics of hotspot sizes and associated socio-economic attributes.
Section 4 further discusses the intra-urban scaling properties.
Section 5 concludes the study and points to future research directions.
4. Discussion
Cities have long been treated as complex systems. The formation of cities can be described as a dynamic, self-organized, and nonlinear process of human settlements [
5], demonstrating highly-heterogenous patterns in both its spatial and aspatial aspects [
42]. The spatial aspect can refer to the fractal urban form and the aspatial aspect can refer to the long-tailed distribution of city-related metrics. However, such heterogeneities cannot be revealed effectively since conventional urban data, formed normally through top-down approaches, lack sufficient geographic scope and granularity. In the current geospatial big data era, we can easily conquer this constraint by acquiring fine-grained open data regarding the city form and function at countrywide coverage. Big data is not only big, but also possesses significant fractal and nonlinear properties [
43], based on which we can model and analyze a city in a bottom-up manner. That is, delimiting city boundary at the country level or delineating hotspot area at the city scale by agglomeration of individual-based locations.
By adopting the fractal and nonlinear ways of thinking and doing, the cutoff for hotspot boundary derivation was located effectively. Specifically, drawing the border of hotspots is similar to measuring the length of a coastline—a commonality between the two is that, in reality, there is no ground truth for them. The father of fractal geometry, Benoit Mandelbrot [
44], has made it clear that the length of a coastline is immeasurable, while the nonlinearity or scaling property is always measurable. In the present study, we characterized the data’s nonlinearity in its inherent scaling hierarchy (by head/tail breaks) and power-law or Zipf’s law distribution (by the MLE method), by which we obtained the cutoff guiding the spatial clustering. Taking the NTL image as an example, the nested mean values enable us to quickly classify pixels iteratively into a minority of light ones and a majority of dark ones, without exhausting all pixel values by increasing the threshold one at a time. Accordingly, only a few times of experiments on grouping-light-pixel operations for each city led us to generate hotspot polygons whose sizes follow Zipf’s law.
The successfully detected Zipf’s law of street- and NTL-based hotspots across 20 cities further strengthen the fractal structure of geographic space. It is well-known that a part of a fractal is similar geometrically or statistically to the whole, termed as self-similarity. Since there has been a good agreement among scholars that Zipf’s law holds for cities at the country scale [
36,
45], such a repeated statistical regularity for hotspots at the city scale in the present study can be considered evidence of the self-similarity of geographic space. The self-similarity across multiple scales makes us connect the system of geographic space with that of biology, where similar power law statistics appear across multiple layers in a human body from organs, to tissues, and further to cells [
46,
47]. Therefore, we believe that Zipf’s law can hold within even smaller sub-units than city hotspots (such as neighborhoods), and thus more refined urban center areas could be further identified with the proposed methods. This certainly warrants further study as long as the data granularity allows.
The detected hotspots in both types constituted only a small part of the city area, but accounted for a considerable portion of the urban population, wealth, and energy. This imbalanced ratio between hotspot sizes and the associated socio-economic statistics sheds light on the fact that not all city areas for people live or perform activities. This is also known as the potential problem of the administrative city boundary for urban analysis [
21]. Without an accurate capture of human urban activities, the urban scaling estimations may be subjected to unexpected variations. We also examined the power relationship between selected urban measures within the entire administrative boundary among 20 cities, and failed to achieve expected scaling exponents (small R
2 values or in wrong regimes), similar to the case when using the street-based hotspots. By contrast, through the NTL-based hotspots, the derived scaling relationships of area/GDP/CO
2 to population were consistent with the established regimes (e.g., [
17,
48]). The obtained scaling exponents, shown in
Figure 7, indicated that due to a more concentrated settlement and use of infrastructure, the growth of urban economy paced quicker than that of the population (super-linear regime), while the demands of urban areas and the related energy consumption accelerates slower than the population growth (sub-linear regime). The presence of scaling law further implied that the NTL-based hotspots could work as a new, effective instrument for exploring the system of cities.
The hotspots identified by both street and NTL data, by and large, tally with the locations of central urban areas of these 20 cities in China. As noted, street-based hotspots can represent a city’s morphological aspects, whereas NTL-based hotspots can accurately reflect a city’s functional aspects. The comparison between the two can give us a comprehensive image of how people utilized the urban space. It is noteworthy that the disparity occurs in their spatial distributions. Given that NTL-based hotspots illustrate the aggregation of human activities, we refer that the NTL-based hotspots better manifest the actual urban populous areas than the street-based hotspots, in the context that the street network constructed or traffic planning normally show a time lag. This discrepancy normally hints the evolution of urban centers. That is, these regions are preferred by humans, but apt to be neglected by the municipal authorities or urban scholars. Thus, the planning authorities should at least pay attention to these regions and other urban infrastructure should be strengthened in order to keep pace with real human needs, as well.
By computing IoU metrics, we are able to find that two types of hotspots have less overlays in coastal cities than in inland cities, while coastal cities in China normally have better economic status. Meanwhile, it is worth mentioning that the NTL-based hotspots are very dispersed in the four headmost metropolises, indicating that well-developed cities tend to exhibit a balanced distribution of human activities. It is further referred that cities with higher economic status shift to a more decentralized structure upon urban autonomous development. On this basis, the governments need to take more measures to promote urban justice (including the even distribution of urban resources, etc.) on the process of urban development.
5. Conclusions
The ultimate goal of city science is closely related to urban smart growth and sustainable development. In natural and societal phenomena, it has been widely adopted that the scaling pattern and power-law statistics are signs of sustainability [
49]. This paper provides an intra-urban perspective to study the underlying scaling structure of urban space through novel spatial units: Urban hotspots, detected from geospatial big data including OSM street data and VIIRS imagery. In contrast to conventional spatial units that were imposed by local authorities, the present study adopted the objectively delineated concentration areas as hotspots using the spatial clustering approach. This is mainly motivated by the instability of urban scaling exponents affected by different cities and its sub-unit demarcations. In sum, we found (1) that Zipf’s law also holds strikingly at the intra-urban level; and (2) that NTL-based hotspots can be good proxies for city populous areas, by which the urban scaling relationship can be correctly maintained.
The method for hotspot detection acts as a promising tool and could supplement innovative urban planning toolboxes in the big data era. Despite the strengths of urban hotspot in this work, there is still room for improvement in terms of the following. Firstly, whether the intra-urban scaling law exists in other countries remains to be verified from a global view, in addition to these 20 cities in China. Secondly, it is important to add NTL images before 2020 to check whether and how the intra-urban scaling exponents change or evolve. Further, the updated raster data sets of GDP, population, and CO2 emissions after 2010 will be combined once they are available, for eliminating possible biases or inaccuracies that occurred due to the difference in data time acquisition. Thirdly, the multiscale effect of scaling analytics (e.g., detecting a more refined spatial unit and related power law statistics) within one city needs to be further conducted. Fourthly, the underlying mechanism of this scaling law has not been revealed yet, concerning policy, landform or demographic traits, etc. Future work will point to these directions.