Urban development wave: Understanding physical spatial processes of urban expansion from density gradient of new urban land
Introduction
The physical spatial processes of urban expansion have profoundly impacted the coupled human-nature ecosystem at multiple scales, although urban land accounts for <2% of the Earth's surface (Bren d'Amour et al., 2017; Chakraborty, Maity, Dadashpoor, Novotnẏ, & Banerji, 2022; Gao & O'Neill, 2020; Moehl, Rose, & Bright, 2016; van Vliet, Eitelberg, & Verburg, 2017). Therefore, an improved understanding on the underlying physical spatial processes of urban growth is critical for urban planners and policymakers to develop sustainable strategies for future urban planning and development (Bren d'Amour et al., 2017; Güneralp, Reba, Hales, Wentz, & Seto, 2020; Müller & Munroe, 2014).
A plethora of approaches has been applied to analyze urban expansion in terms of the spatial form at an instant of time and its corresponding dynamics over time (Altieri, Cocchi, & Roli, 2019; Coimbra & Beloto, 2019; Liu et al., 2021). Early theories describing urban form include, for example, the concentric zone model (Burgess, 1935) for explanation of urban social structures, the sector model for arrangement of urban land use activities (Hoyt, 1972), and the multicenter model for description of urban structures (Harris & Ullman, 1945). These models usually assume uniform or constant spatial processes during urban growth, and are thus quite qualitative and descriptive, since spatiotemporal details on urban dynamics, especially urban land-use changes, were not available for observation other than at the aggregate level (Dietzel, Herold, Hemphill, & Clarke, 2005). With advances in remote sensing and geographic information science, quantitative approaches have become the focus of research on form and process of urban expansion, both theoretically and empirically (Portugali, 2000). The most intuitive and widely adopted methods for urban expansion quantification are those defined based on ratio or magnitude of urban growth in terms of urban population or built-up land (Cheng, Yang, & Cai, 2021; Güneralp et al., 2020). However, these approaches are too aggregated to reflect the underpinning physical spatial processes (rather than socioeconomic) of urban expansion.
Landscape metrics can provide a snapshot of the spatial form of urban expansion at a given time instant by aggregating the quantitative composition and spatial configuration information of urban land at distinctive levels (Lin, Li, Li, & Wen, 2020; Schneider & Woodcock, 2008), thus were commonly used for spatially-explicit characterization of urban expansion (Chakraborti, Das, Mondal, Shafizadeh-Moghadam, & Feng, 2018; Lin et al., 2020). Sequential snapshots of urban form at multiple time instants often illustrate the dynamics of urban form and have been used as clues to infer the underlying processes of urban expansion over a certain period (Rossi-Hansberg & Wright, 2007). The limitation of landscape metrics in urban expansion characterization tends to be that the underlying physical spatial processes of urban expansion can only be implicitly inferred via the form-related information (Dietzel et al., 2005; Dietzel, Oguz, Hemphill, Clarke, & Gazulis, 2016). The need for more information on the underlying urban expansion processes has facilitated the introduction of approaches to directly describe these physical processes. For example, the landscape expansion index (LEI) (Liu et al., 2010), and many other analogous index (Jiao et al., 2018; Jiao, Mao, & Liu, 2015; Liu, Jiao, et al., 2021; Xu et al., 2007), were proposed to categorize the physical spatial processes of urban expansion as infilling, edge-expansion, outlying, etc. These LEI-like index were mainly created to describe the spatial relation of new urban parcels generated between successive time instances to existing ones. They do not explain how urbanized areas are generated by the underlying physical spatial processes over time.
Gradient analysis is a prevalent tool often coupled with the rate- or landscape-based (landscape metrics and LEI-like indices) methods to investigate the structure and form of urban expansion (Chakraborty et al., 2022; Liu et al., 2021). The gradient can be expressed in a variety of manners, such as grids, moving windows, and concentric rings or buffers (McDonnell & Hahs, 2008). Proxies employed to quantify urban expansion properties along each gradient were oftentimes socioeconomic variables, physical variables, or spatial metrics (Hahs & McDonnell, 2006), among which the density-related variables have been demonstrated as intuitive and effective for urban expansion quantification (Bhatta, Saraswati, & Bandyopadhyay, 2010). Typically, the urban-rural gradient of urban population density has been frequently investigated (Chen, 2010; Newling, 1969). In particular, more than a dozen mathematical functions have been applied to model the outward wave-shaped diffusion of urban population in metropolitan areas, thus to profile urban growth pattern and process (Blumenfeld, 1954; Koreclli, 2010; Morrill, 2010; Xu et al., 2007). For example, Newling (1969) empirically developed a quadratic exponential model to reflect the out-moving of urban population and further formulated a density-profile classification of urban expansion stages. Parr (2007) applied a lognormal model to reflect the density crater phenomenon occurring in city centers during urban growth.
The wave-shaped movement of urban population usually induces physical diffusion of urban land, as has been empirically verified in previous studies (Vizzari & Sigura, 2015; Xu et al., 2007). Increases in urban population often requires growth in settlements to sustain the population (Schneider & Woodcock, 2008). However, the diffusion processes of urban land should differ from that of urban population since a parcel, once physically urbanized, does not move nor becomes deurbanized (Dietzel et al., 2016). The compelling question here is that is there a universal law, similar with that of urban population diffusion, for describing the physical expansion processes of urban land based on specific density-related proxies?
Early studies on densify of urban land were straightforward, mainly enumerating and comparing the density signatures of urban land among different subregions, such as gird, rings, buffers, or administrative unit (Angel, Parent, & Civco, 2007; Tsai, 2005; Wu, Sumari, Dong, Xu, & Liu, 2021; Xu et al., 2007). Until recently, Jiao (2015) identified a universal and spatially explicit rule for the density gradient of urban land, and proposed an inverse S-shaped model to mathematically describe the distance-decayed rule of urban land density (Dong, Jiao, Xu, Yang, & Liu, 2019; Xu et al., 2019; Xu et al., 2019). In Jiao's subsequent study, a geographic micro-process (GMP) model was empirically proposed by obtaining snapshots of the observed density gradient of urban land. The GMP model assumes that the increases of urban land density in a process of urban expansion follows a power law (Jiao et al., 2021), and theoretically explains how the distance-decayed pattern of urban land density emerges from sequential spatial processes (hypothesized rather than empirically observed).
Commonalities among the abovementioned methods, either gradient-based or not, for understanding urban expansion and the underlying spatial processes tend to be that they were mainly proposed from a form-oriented perspective to characterize urban expansion at a single instant or urban expansion dynamics over time, rather than from a process-oriented perspective to directly address the observed physical spatial processes of urban expansion over a certain period of time. Notably, these form-oriented approaches adopted a “process-from-form” paradigm (the observed macroscale form was analyzed, after which the underlying spatial processes were inferred) instead of a “form-form-process” paradigm (direct investigation of the observed spatial processes and subsequent macroscale form profiling) to understand urban expansion.
Physical spatial processes of urban expansion and their space-time dynamics are important aspects of urban growth, since their complex interaction and overlap over time create the manifested urban form. However, a deeper understanding of the physical spatial processes of land urbanization remains lacking due to the fact that form of urban expansion observed in an instant of time often obscures the subtle spatial and temporal processes generating the observed form (Dietzel et al., 2005; Dietzel et al., 2016; Lu & Guldmann, 2012). Furthermore, none of these form-oriented methods empirically explain how sequential physical spatial processes of urban expansion create the urbanized areas. Therefore, to advance the understanding of urban expansion, researchers need to disentangle the observed form into independent spatial processes to permit direct investigation of the physical spatial processes, which allows straightforward link between the spatial processes and urban growth properties, as well as the underlying biophysical and socioeconomic factors. The imperative questions here is that what knowledges can these disentangled physical spatial processes convey about themselves and the long-term trends of urban expansion.
In this case, we proposed a Gaussian-based model to directly describe the physical spatial processes of urban expansion. Specifically, the physical spatial processes of urban expansion, in this study, refer to empirically observed urban development events (i.e., new transformation from non-urban land to urban land) occurring within a short period (e.g., one year in this study), and the macroscale form of urban expansion as a snapshot of the distribution of urban land at an instant of time (Volaire, Gleason, & Delzon, 2020). This model borrows the idea of employing a wave analog to describe urban population diffusion (Blumenfeld, 1954; Morrill, 2010; Newling, 1969). The spatiotemporal diffusion process of urban expansion at a time instant and over a period were empirically detected, mathematically simulated, and systematically characterized with the proposed model in terms of density gradient of new urban land. The major objective of this study is to answer the following questions: 1) whether the physical spatial processes of urban expansion exhibit an outgoing wave-shaped regularity, and can be simulated with the proposed model in terms of density gradient of new urban land; 2) what knowledge the proposed model can convey regarding the properties of the urban expansion process itself, and the long-term urban expansion trends from a process-oriented perspective.
The proposed model is a significant complement to current researches on urban growth profiling based on urbanization gradient analysis. This approach provides new insights into urban geography with a deeper understanding of the physical spatial processes associated with land urbanization. Moreover, this study contributes to answer the question of how the spatial form of an urbanized area emerges from the underlying physical spatial processes over time, which has long been an imperative question regarding urban theory (Dietzel et al., 2016). Case studies were obtained from 27 large cities in China to verify the proposed model. The spatiotemporal variation in density of new urban land within concentric rings in these cities was annually investigated from 1990 to 2017 with the proposed Gaussian-based model.
Section snippets
Selection of the sample cities
The following criteria were considered to select the sample cities. First, the sample cities should be big in size and should have witnessed conspicuous urban expansion during the past decades. This criterion quickly draws our attention to the provincial capitals or municipalities in mainland China. Also, it would be nice to be able to compare our results with previous studies, thus to further verify its feasibility. Jiao (2015) has analyzed how the density of total urban land decays from the
Empirical observations of urban expansion processes
Investigation of the shape and spatiotemporal variations in density of new urban land in a typical city (e.g., Hefei) where the wave-shaped diffusion process of urban development was completely manifested during 1990 and 2017 (please refer to Fig. 3) informs us the general features of the physical spatial processes of urban expansion and outline the basic requirements of the model in representing the processes. First, if a city is in its early stage of expansion, the density gradient of new
Concentric partitioning of cities based an urban expansion process
Concentric partitioning of cities based on urban population density and other spatial metrics has commonly been applied by urban geographers to analyze the urban form and quantify urban sprawl and compactness (Felt et al., 2018; Irwin & Bockstael, 2007; Taubenböck, Wegmann, Roth, Mehl, & Dech, 2009). Particularly, Jiao (2015) proposed a concentric partitioning scheme of the main urban areas based on the density of the total urban land contained in concentric rings. Similarly, in this study, we
Inferring urban form from spatial processes of urban expansion
In this section, we present how the model helps answer the question regarding the manner in which the macroscale urban development form, as represented by the distance-decayed density gradient of the total urban land area, was generated via sequential spatial processes of urban expansion over time. Intuitively, city growth entails a continuous urban development process extending outward from urban centers to the periphery (Miao & Phelps, 2021). Thus, the macroscale spatiotemporal pattern of
Discussion
The density gradient of new urban land in the 27 sample cities emphasized that the physical spatial processes of urban expansion all exhibited an ongoing wave-shaped regularity and could be represented well by the proposed Gaussian-based model. This Gaussian-based model advances our understanding of the physical spatial processes and long-term trends of urban development from a process-focused perspective, including concentric partitioning schemes for cities, and methods to quantify the
Conclusion
Elucidation, understanding and well-planning of future urbanization pathways require a thorough understanding of the physical spatial processes of urban expansion. This study verified the regularity whereby the physical spatial processes of urban expansion over a certain period present a wave-shaped diffusion fashion from the urban centers outward to the periphery, and can be well fitted with a spatiotemporal Gaussian-based model. The Gaussian-based model provide critical information on urban
Funding
This study was supported by the National Natural Science Foundation of China (Nos. 42101275, 42071254, and 41871172); and the Fundamental Research Funds for the Central Universities, China University of Geosciences (GUGL170408 and CUGGG-2021).
CRediT authorship contribution statement
Jianxin Yang: Conceptualization, Methodology, Software, Writing – original draft. Jingjing Li: Conceptualization, Methodology, Writing – review & editing, Formal analysis, Writing – review & editing. Feng Xu: Conceptualization, Writing – original draft, Supervision. Shuaicheng Li: Software, Visualization. Minrui Zheng: Formal analysis, Writing – review & editing. Jian Gong: Resources, Data curation, Funding acquisition.
Declaration of Competing Interest
No potential conflicts of interest are reported by the authors.
Acknowledgments
The authors thank Yingjian Ren, Yingge Wang, and Lin Zhou for their assistance.
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