Complexity

Volume 2018, Article ID 8561675, 18 pages

https://doi.org/10.1155/2018/8561675

## Impact of Rapid Urbanization on Vulnerability of Land System from Complex Networks View: A Methodological Approach

^{1}School of Public Administration, China University of Geosciences, Wuhan 430074, China^{2}School of Economics, Environment and Resources, Hubei University of Economics, Wuhan 430205, China^{3}School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China

Correspondence should be addressed to Xiangmei Li; moc.nuyila@tsuhilmx and Renbin Xiao; nc.ude.tsuh@oaixbr

Received 26 October 2017; Revised 7 February 2018; Accepted 13 March 2018; Published 2 May 2018

Academic Editor: Ilaria Giannoccaro

Copyright © 2018 Ying Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Rapid urbanization is responsible for the increased vulnerability of land systems and the loss of many crucial ecosystem services. Land systems are typical complex systems comprised of different land use types which interact with each other and respond to external environment processes (such as urbanization), resulting in dynamics in land systems. This work develops a methodology approach by integrating complex networks and disruptive scenarios and applies it to a case study area (Wuhan City in China) to explore the effects of urbanization on land system structural vulnerability. The land system network topologies of Wuhan City during five time periods from 1990 to 2015 are extracted. Our results reveal that the urban land expands at a higher speed than the urban population in Wuhan City; the period of 2005–2010 has witnessed more land area conversions from ecological lands to urban land than other periods; the land system is more vulnerable to intentional attacks on nodes with higher integrated node centrality and larger land area, such as paddy, dryland, and lake; and the network efficiency of the land system would decline sharply if the area shrinkage of paddy, dryland, and lake is larger than 30%, 50%, and 20%, respectively. The results provide some insights into building a resilient urban land system, such as increasing the efficiency of existing urban land and controlling the shrinkage rate of important land use types. This study contributes to existing literature on complex networks by expanding its application in land systems, which highlight the potential of complex networks to capture the complexity, dynamics, heterogeneity, and emergent phenomena in land systems.

#### 1. Introduction

In recent decades, rapid urbanization has led to frequent conversions among different land uses and covers, especially from forests or wetlands to artificial uses. Such conversions certainly meet short-term human needs but come at the loss of biodiversity and reductions in many ecosystem services [1], resulting in increased vulnerability of land systems [2]. For example, the Millennium Ecosystem Assessment reported that over 60% of the global ecosystems were degraded or used unsustainably from the 1950s to 2005 [3]. Urbanization is a key contributor. As the largest developing country, China has undergone rapid urbanization since the adoption of the Reform and Opening-up Policy in 1978 and is currently in the middle of the exponential stage of urbanization [4]. The overall rate of urban population climbed from 18% to 57% by 2016 [5]. Meanwhile, the urban land expanded by 5.5 million hectares from the late 1980s to 2010 [6], which encroached ecological lands with crucial ecological values (e.g., farmlands, forests, and wetlands). The shrinkage in ecological lands imposes accumulative pressure on natural ecosystems and threatens regional ecological security [3, 7]. Therefore, knowledge of the relationships between urbanization, land use and cover change (LUCC), and land system vulnerability is imperative for sustainable land management to reduce vulnerability and may contribute to preserving the crucial ecosystem services.

Although the term of “land system” was initially defined by Christian and Stewart in 1947 [8], the study on land systems has received limited attention until 2005 when the Global Land Project (GLP) focusing on land systems was launched by global research agendas. The definition of land systems was also expanded from the initial biophysical systems (consist of topography, soils, and vegetation) [8] to coupled human-natural systems (i.e., mosaics of land use and cover) [9]. Integrating experiences from the Global Change and Terrestrial Ecosystem [10] and Land Use Land Cover Change programs [11], the GLP moved towards studying land systems as complex interactions between natural, social, and coupled processes at various temporal and spatial scales [12]. Yet the research focus of GLP is primarily on the type, amount, distribution, and pattern of land uses and covers [13]. Regarding land system vulnerability, a growing attention is attracted in the past few years when the Future Earth plan (2014–2023) was initiated by the International Council of Scientific Unions (ICSU) in 2014 [14]. The new program aims to develop the knowledge for responding effectively to the risks and challenges of global environmental changes. Thus, the focus of scientific programs is shifted from the observation of changes to more integrative vulnerability and resilience analyses of land systems [15].

Since vulnerability and resilience describe the capacity of a system to cope with external perturbations, a system-level understanding of the dynamics in land systems is crucial. However, most previous research on land systems has focused on land use or land cover, while the integrality and systematicness of land systems are often neglected [16]. Thus, there is a growing need for modeling tools that can unpack the complexity of land systems and dissect the conversion relationships and processes among land system components under perturbations or stressors, which may contribute to revealing the mechanism of land system vulnerability.

The last decade has witnessed a rapidly growing interest in adopting complex networks to analyze systems that are large, complex, and dynamic [17]. Its successful applications in many real-world networks, such as social networks, brain networks, and infrastructure networks, have revealed that the complex network analysis is capable of uncovering the organizing principles that govern the formation and evolution of such complex systems [18]. In particular, the network analysis converts complex systems into networks with nodes and links, which facilitate analyzing important properties of complex systems at system-level from the perspective of network topology [19]. By integrating disruptive scenarios, the complex network analysis can be further extended to predict system vulnerability under a set of scenarios that represent varying extents of disturbance. For example, Ouyang et al. [20] introduced the complex network method in evaluating structural and functional vulnerabilities of interdependent infrastructures. Li and Xiao [21] extracted the topological structure of eco-industrial parks based on complex network methods and analyzed the resilience of the parks under different attack strategies. Regarding the applications of complex network analysis in land systems, existing studies are still in an early phase of extracting network topology [22], identifying key land use types or dominant land use conversions [16, 23]. To our knowledge, no study to date has used the complex network methods to analyze the resilience or vulnerability of land systems. Thus, we attempt to bridge the gap by integrating theories and approaches of complex network analysis to enhance the understanding of land system vulnerability, which could be potentially very relevant for building a more resilient land system.

To illustrate how complex network analysis works, we conduct a case study in Wuhan City— a megalopolis in central China that is experiencing rapid urbanization. In particular, this paper has three specific objectives to obtain: to describe the topological characteristics of the case study area from 1990 to 2015 based on commonly used measures of complex network approaches; to identify the important land use types and land use conversions in the land system; and to explore the response of land system structural vulnerability to different urbanization scenarios.

#### 2. Complexity Analysis of Land Systems

Complex systems consist of interconnected components that interact in a network or a geographic space following simple rules and lead to all kinds of interesting dynamics [24, 25]. By definition, the complexity of complex systems originates from three key sources: heterogeneous components, dynamic interactions, and emergent system functions. Land systems have most of the key sources of complexity described above and thus are widely deemed as typical complex systems [12, 26].

First, land systems are huge systems that consist of hierarchical and heterogeneous components. From a macroscopic perspective, a land system is composed of cropland, water, forest, grassland, and urban subsystems. Each of the subsystems is constituted by subsystems of the lower level; for example, the terrestrial water system is made up of river, lake, wetland, reservoir, and aquifer subsystems. From a microscopic point of view, a land system is an assembly of land units (e.g., a site or satellite image pixel) which are geographically related [26]. In the paper, we are mainly concerned about different land types, focusing on the ecological lands (cropland, grassland, forest, water, and so on) to analyze the roles of different land types in LUCC processes.

Second, different land types that interact with each other across both spatial and temporal scales form complex conversions between different land types. The subsystems exchange fluxes and flows, such as nutrients, energy, carbon, and information [26]. These interactions occur at different spatial locations and take place within the internal environment of land systems. In addition, as land systems are human-influenced, the interactions among subsystems also drive and respond to external environment changes, such as climate, urbanization, and macroeconomy [9]. In this paper, we extract the conversion relationships between different land types incurred by rapid urbanization area as edges. It is noted that the conversions in land systems have directed and weight features.

Last, land systems generate emergent phenomena and nonlinear behaviors due to the dynamic interactions among the heterogeneous components. Emergent phenomena are described as the aggregate outcomes that cannot be predicted by inspecting the components of the system in isolation [27]. An example of emergent phenomena includes the famous spatial segregation model by Schelling. The model specifies that a spatial setup comprises households from different races that form racially mixed neighborhoods. The households prefer residing with households of similar race and can relocate until the ratio of neighborhoods of similar race is above a satisfactory threshold [28]. The model finally exhibits high levels of segregation, illustrating how local interactions can lead to surprising aggregate spatial patterns. Another example is the aggregate distribution of commercial and residential areas, which can be identified as emergent properties of land markets. To conclude, land systems can be denoted as directed weighted complex systems composed of different land types (nodes) and conversions between different land types (edges), which is interconnected in LUCC processes. Complex network theory provides a powerful tool to gauge the structural vulnerability within land systems and contributes to preserving the stable ecological functions in order to build resilient cities in rapid urbanization area.

#### 3. Methodology

##### 3.1. An Introduction to Complex Networks

Complex network analysis (both theories and methods), which has its origin in graph theory and statistical physics, is considered as an important tool to study complex evolving systems [29]. It is capable of modeling real-world networks that comprise a large number of components interacting with each other in a complicated manner [30] and dynamically evolves in time [31]. Specifically, the rapidly growing interest in complex networks was triggered by the emergence of the small-world model (1998) [32] and the scale-free networks (1999) [29]. Since then, complex network analysis has been widely applied to the investigation of real-world networks such as, for example, the World Wide Web [33], electric power grids [34], transportation systems [35], ecological networks [21], genetic regulatory networks [36], and brain networks [17].

The fundamental units of a network include a collection of nodes that identify the components of a system and edges that denote relationships between pairs of components. Edges in complex networks can have directions and weights (e.g., the length, thickness, capacity, load, or strength associated with an edge). In general, networks can be divided into four categories according to whether directions and weights are considered, namely, undirected unweighted, directed unweighted, undirected weighted, and directed weighted networks.

Based on complex properties of land systems, we extract the topology structure of land systems and established directed weighted networks for land systems. Therefore, an introduction of basic concepts and important network measures of complex network methods is given focus on weighted complex networks based on several review papers [31, 37, 38] and a book on complex networks [24].

Mathematically, a weighted directed network with nodes is denoted as , where is the set of nodes. is the set of edges, where stands for a link from node to node . For directed networks, . For directed weighted networks, denote the set of weights of the link from node to node . An adjacency matrix is made up by all links between each pair of nodes. For unweighted networks, the adjacency matrix is made up by . For weighted networks, it is formed by . The diagonal of the adjacency matrix contains zeros.

*Node Degree*. The number of edges incident with the node is defined in terms of the adjacency matrix* A* as follows:In directed networks, it is possible to distinguish two different degrees: the in-degree , referred to as the incoming edges linked to node , and the out-degree , referred to as the outgoing edges from node . The total degree and the average total degree of a network are then defined as

*Node Strength*. It is a key metric that measures the importance and the connectivity of a node in a network by taking into account all the weights linked to the node. Similarly, for a directed weighted network, the node strength consists of two parts: out-strength and in-strength. The out-strength (), in-strength (), total node strength (), and average node strength of a network () can be defined as

*Node Betweenness*. Two nonadjacent nodes (e.g., and ) can be linked via a path starting from node , passing through several pairs of nodes and eventually connecting to node . Thus, nodes with more edges passing through to connect other nodes play more important roles in a network to maintain its connectedness. Here, we introduced the node betweenness () to identify key nodes in complex systems:where is the total number of geodesics connecting and in the network and is the number of these geodesics that pass through node* i. *Specifically, .

*Shortest Path Length*. It is an important measure of the efficiency of information and resource transmission. For example, for electricity network and railway network, the shortest path provides an optimal pathway to achieve a fast transfer of loads and passengers. The shortest path length () between node and node is defined as the number of edges along the shortest path connecting and . Accordingly, the average shortest path length () is the average value of for all the possible pairs of nodes in the network:

*Clustering Coefficient*. It measures the extent to which nodes in a network tend to cluster together. The weighted clustering coefficient is the ratio of the number of edges among the neighbors of node to the maximum number of possible edges. measures the centralization degree of a system. Therefore, the formula for is defined aswhere ; is the number of directed triangles actually formed with its weighted counterpart; is the maximum number of possible edges among the neighbors of node . As defined before, is the node degree. Mathematically, node can be possibly linked to a maximum of pairs of edges. Node and each pair of edges can form up to two triangles as the edge between them can be oriented in two ways; thus, the maximum number of possible triangles is . However, the “false” triangles formed by and by a pair of directed edges pointing to the same node are included, for example, and . Therefore, we estimate by subtracting . The average clustering coefficient for the whole network () is then defined as follows:

##### 3.2. A Complex Network Method to Analyze Land System Vulnerability

To investigate system vulnerability that arises from land system structural dynamics, we proposed a hybrid method with three steps. First, we extracted the topology structure of the land system and established a set of networks to represent the land system at different time-steps. Then the topological properties of land system networks were studied based on the important measures of complex network analysis as introduced above. In particular, an integrated node centrality indicator was adopted to identify key land use types and conversions. Finally, we evaluated the structural vulnerability of the land system using a network efficiency indicator by integrating the scenario analysis. The process of how we analyzed land system dynamics and vulnerability is displayed in Figure 1.