Perspective Chapter: Spatio-Temporal Analysis of Urban Expansion

Abstract

Understanding the effects of urbanization and formulating sustainable planning strategies begins with an analysis of the dynamics of urban growth at various spatial and temporal scales. Several quantitative methods for analyzing urban expansion and the spatial pattern of urbanized areas have been developed and their applications have been widespread. The choice of an appropriate method for a particular situation depends on different factors, making it difficult for users to make an informed decision and increasing the requirement for knowledge about the various approaches. This chapter gives an overview of the prevailing approaches for spatio-temporal analysis of urban expansion. Given the importance of analyzing the spatio-temporal growth of built-up areas for sustainable urbanization, this chapter provides a good insight into the main features of existing methods. Accordingly, it would help researchers and potential users to undertake effective analysis, balancing between their needs and resource requirements.

1. Introduction

Contemporary urbanization is characterized by the rapid growth of urban populations and the rapid spatial growth of urban areas. Unless properly managed, it can result in serious negative environmental and socioeconomic consequences, such as urban heat islands, reductions in green spaces, insufficient infrastructure and services, and inefficient utilization of resources [1, 2, 3]. Analyzing the spatio-temporal dynamics of the built-up area of a particular urban landscape is the primary step in understanding the impacts of urbanization [4]. Knowledge about the spatial pattern and intensity of urban land changes is critical for a variety of issues, ranging from human-environmental interactions and the provision of urban environmental services to land-use policy development for landscape and urban planning toward sustainable urbanization [5].

The focus on urban change detection has recently switched from detection to quantification of change, pattern measurement, and pattern and process analysis of urban expansion [1, 6, 7]. To describe spatial patterns effectively, comprehend how they develop over time, compare one component to others, or statistically explain variations in these patterns, quantitative measures that summarize one or more of their attributes are necessary [8, 9]. Several quantitative methods have also been developed and applied to determine measures of spatial patterns and dynamics of urban landscapes.

The choice of methodologies for spatio-temporal analysis of built-up area expansion is influenced by a number of factors, making it difficult for users to make an informed decision and increasing the requirement for information about the various approaches. This chapter gives an overview of the available approaches for spatio-temporal analysis of urban expansion.

2. Methods of urban expansion analysis

2.1 Urban spatial expansion index

The urban spatial expansion index (USEI) is an indicator proposed to analyze the growth of urban areas in terms of spatial increase in urban land-use classes. It quantifies the magnitude of urban expansion per unit of time over the study period using a linear change model (Figure 1). USEI for a particular urban area is computed using Eq. (1). When the unit of time is set to a year, it provides the annual change in built-up areas.

Figure 1.

Linear change model (increments of growth remain constant over time).

$$\mathit{\text{USEI}}=\frac{A_{t1}-A_{t0}}{∆t}$$E1

where $A_{t0}$ and $A_{t1}$ denote areas of built-up land at a time $t0$ and $t1,$respectively, and $∆t$ is the length of time from the time $t0$ to $t1$. When $∆t$ is in a unit of the year, then $\mathit{\text{USEI}}$ is the annual average expansion of built-up area over the study period.

This approach provides data on the mean annual quantitative increase in built-up area between the starting and ending years of the study period and/or selected time intervals. It gives constant expansion per unit of time during the study period due to its assumption of linear development. Several studies used the urban spatial expansion index to assess the speed of urban growth in the same study area over different times as well as between different countries. For instance, Dutta et al. [10] used this index to estimate yearly built-up change in the peri-urban areas around Delhi from 1977 to 2014 by dividing the whole study period into two: 1977−2003 and 2003−2014. The authors then used the results to determine the relationship between built-up change and density. The study conducted by Liu et al. [11] can also be mentioned as a case example of USEI application. In this case, the index was used to gauge the velocity of urban expansion in the Xiaonan District in Hubei Province, China, over a period of every five consecutive years between 1990 and 2020. In relation to the assessment of the infrastructure development contributions to urban expansion, Li et al. [1] used USEI as one of the key indicators of the spatial and temporal changes of urban expansion due to the influence of Guangzhou–Foshan Inter-City Rail Transit in South China. Moreover, it has been used for assessing the environmental consequences of urbanization. Dissanayake et al. [12] assessed the change in LULC in Addis Abeba City, Ethiopia during a 15-year period (1986–2016) and compared and contrasted it with changes in land surface temperature in the study area.

2.2 Urban expansion intensity index

The urban expansion intensity index (UEII) is the ratio of the change in urban land area in a unit of time to the total land area in a spatial unit. In other words, it quantifies the change in a built-up area between different given points in time as a proportion of the total area of the landscape. UEII is computed using Eq. (2), and the higher value implies fast urban expansion [13].

$$\mathit{\text{UEII}}=\left(\frac{∆A_{∆t}}{A_L}\right)\ast \frac{1}{∆t}$$E2

where $\mathit{\text{UEII}}$ is the changing intensity for a given time interval (e.g., t0–t1); $∆A_{∆t}$ is the area of land change from non-built-up to built-up during the given time interval; $A_L$ is the area of the entire landscape; and $∆t$ is the time span of the given time interval.

UEII normalizes the mean annual expansion based on the total land area of the landscape and makes the results comparable in temporal sets [6, 14, 15]. Additionally, UEII could be employed to recognize the preferences of urban growth and to compare the speed or intensity of land use changes in a particular urban setting in a certain period.

The annual urban expansion intensity of a spatial unit can be used to compare the quantitative characteristics of urban expansion over different study periods [16]. UEII was among the key indicators used to examine urban expansion from the perspective of nonurban to urban conversion, detailing the spatiotemporal variations and impact factors of urban expansion in Qingdao [6]. It has also been applied in the identification and analysis of urban sprawl of the Tripoli metropolitan area, conducted by Al-sharif et al. [17].

2.3 Urban spatial expansion rate

The urban spatial expansion rate (USER) is an indicator based on the concept of the pace of urban development and the dynamic change in the spatial structure of a given urban region as varying in time. The rate of land-use change is critical for determining the conversion process associated with urban development and expansion [10]. USER assumes that urban growth is an exponential process (Figure 2) that is theoretically equivalent to the yearly rate of compound interest [14]. The formula in Eq. (3) is used to calculate the USGR.

Figure 2.

Geometric change model (increments of growth increase over time, at a constant rate of increase).

$$\mathit{\text{USER}}={\left(\frac{A_{t1}}{A_{t0}}\right)}^{\frac{1}{∆t}}-1$$E3

where $A_{t0}$ and $A_{t1}$ denote areas of built-up land at a time $t0\left(\mathit{\text{initial}}\right)$ and $t1\left(\mathit{\text{final}}\right),$ respectively, and $∆t$ is the length of time from the time $t0$ to $t1$. When $∆t$ is in a unit of a year, then $\mathit{\text{USER}}$ is the annual rate of change in the spatial extent of built-up land.

By avoiding the size effect, USER converts urban expansion into a standard metric, which makes it more suitable for intercomparison of urban growth in different spatial zones and different years, as well as among different cities. Accordingly, it has been widely applied in various studies to compare the spatio-temporal dynamics of urban growth in several cities [9, 15, 16, 18, 19]. For instance, Terfa et al. [9] employed USER in order to compare the patterns of yearly urban growth in three Ethiopian cities: Adama, Hawassa, and Addis Abeba. Furthermore, Forget et al. [19] utilized this index to study the urban expansion of 45 Urban Areas in sub-Saharan Africa, whereas Zhao et al. [15] used USGR to assess the pace of urban expansion of 32 major Chinese cities over three decades.

2.4 Urban expansion type (UET)

The urban expansion type (UET) is a quantitative method for distinguishing between urban development typologies. The spatial link between existing urban regions and newly built components determines how urban development types are classified [7, 18]. The expansion types of newly developed urban land are classified as leapfrogging, edge expansion, and infilling (Figure 3). Infilling development denotes nonurban land that is surrounded by urban land that has experienced a change to built-up; edge-expansion or urban fringe development refers to newly developed urban areas that spread out from the edges of pre-growth built-up areas; leapfrogging refers to the development of a new urban patch that has no spatial connection to existing urban land. Infilling is associated with a more compact urban form, whereas edge expansion and leapfrogging lead to a more distributed urban form.

Figure 3.

Typology of urban growth.

The UET is calculated using Eq. (4) and the value can range from 0 to 1. Xu et al. [20] proposed that the type of the observed growth be determined as infilling $\left(\mathit{UET}>0.5\right)$, edge-expansion (0 < $\mathit{UET}$ ≤ 0.5), and leapfrogging ($\mathit{UET}$ = 0), which shows no shared boundary.

$$\mathit{UET}=\frac{L_{\mathit{com}}}{P_{\mathit{new}}}$$E4

where $L_{\mathit{com}}$ denotes the length of the common edge between the newly developed and the pre-growth urban patches; $P_{\mathit{new}}$ represents the perimeter of the new urban patches.

Among several recent studies that applied UET, Terfa et al. [9] used this index to categorize and contrast the growth types of different Ethiopian cities. Zhao et al. [15] also applied UET to determine the urban growth process of China’s major cities. Moreover, this index was used in the research of Anees et al. [7], which examined the various types of growth that occurred in Srinagar city and its environs between 1999 and 2017.

2.5 Landscape metrics

The landscape metrics are quantitative indices developed to characterize and assess the landscape patterns of a specific geographic area. They are also known as spatial metrics, spatial indices, or landscape indices. Although the term “landscape metrics” has traditionally been used to describe metrics for quantifying patterns in categorical maps [21], the use of these indices has opened up a new way of describing the spatial heterogeneity of urbanized land and urban morphological characteristics in recent decades. As a result, these indices are becoming increasingly used for studying land use patterns and urban growth processes [22, 23].

Landscape indices are computed using patches as a basic building block. A patch is a spatially homogenous region with similar thematic features that are distinct from the surrounding environment. Figure 4 depicts several patches with eight distinct land use and land cover classes. Built-up areas are commonly employed as a thematic class of interest in urban spatial pattern research [1, 24].

Figure 4.

Patches of different urban land use and land cover classes.

Landscape indices quantify the two most important aspects of landscape pattern: composition and configuration. Composition refers to the number, amount, and area of each patch type without taking into account the individual patches’ spatial characteristics, placement, or location in the landscape [25]. The proportion or area of each class, as well as the number of various classes present in a landscape, are examples of composition. On the other hand, configuration denotes the spatial arrangement and distribution of the various land cover classes. Individual patch shapes (e.g., compact or sinuous) and their distribution throughout the landscape, such as whether they are aggregated or scattered, are examples of configuration.

A number of urban studies have used landscape metrics: for instance, the analysis of spatio-temporal urban dynamics in 11 smart cities in Uttar Pradesh, India [23]; a study of the growth patterns and status of urban sprawl in Chennai city’s administrative boundary and areas within a 10 km buffer; and an assessment of landscape changes based on a multiple-scenario modeling approach in the Munich region [26]. Despite the fact that a number of spatial metrics have been developed and their applications are widespread, among the commonly applied indices in the quantification of urban expansion patterns in urban studies are explained below by categorizing the indices based on the potential of metric computations at three conceptual levels of analysis: patch-level, class-level, and landscape-level.

2.5.1 Patch-level indices

Patch level indices describe the spatial nature and context of individual patches and are defined for each one. Although the calculated values of each individual patch may have minimal interpretative significance in most cases, these indices are typically used as the computational basis for numerous landscape metrics, such as average patch characteristics over all patches in a class or landscape. Patch area (PA) and perimeter (PERIM) are the most useful characteristics of a particular patch. The area of each patch that makes up a landscape mosaic is perhaps the most essential and valuable piece of information contained in the landscape, as it is the basis of the patch, class, and landscape indices [21]. The range of PA is limited by the size of the landscape; in some cases, PA may be further constrained by the specification of minimum patch size. A perimeter is another fundamental piece of information available about a landscape. The perimeter of a patch is specifically regarded as an edge, and the intensity and distribution of edges are key features of landscape design. Furthermore, most indices are based on the relationship between PERIM and PA.

2.5.2 Class level-indices

The class-level indices integrate all the built-up patches. The unique configuration of patches throughout the terrain results in new aggregate attributes at the class level. The class level indices separately measure the amount and spatial arrangement of urbanized patches, allowing for a quantitative assessment of the extent and fragmentation of built-up land in the landscape. In urban studies, the most commonly used class level indices are the number of patches, mean patch size, largest path index, landscape shape index, area weighted mean patch fractal dimension, and patch cohesion index.

The number of patches (NP) represents the degree of fragmentation in built-up land; it is used to calculate the degree of disintegration of the urbanized area. Having a higher NP value indicates a dispersed distribution of patches, whereas a lower value of NP indicates a compact distribution of patches. For instance, the number of patches of the built-up area is high; it shows highly scattered settlement; segregated settlement areas with other land use and land cover classes existed in between, resulting in a higher amount of dispersed distribution of built-up patches and resulting in heterogonous distribution of the built-up area [23].

The mean patch size (MPS) is a function of the number of patches in the class and total class area (Eq. (5)), and it measures the average area of a patch in a particular class. Although MPS is derived from the number of patches, it does not convey any information about how many patches are present. A mean patch size of 5 ha could represent 1 or 100 patches.

$$\mathit{MPS}=\frac{{\sum }_{j=1}^n{a}_{\mathit{ij}}}{n_i}$$E5

where

$$A_{\mathit{min}}<\mathit{MPS}\le A_{\mathit{max}}$$

The largest patch index (LPI) quantifies the percentage of landscape area occupied by the largest patch of a class (Eq. (6)).

$$\mathit{LPI}=\frac{{\mathit{Max}}_{a_{\mathit{ij}}}}{A}$$E6

where

$$0<\mathit{LPI}\le 1$$

LPI can simply be understood as a measure of the dominance of a patch in the overall landscape. Having an LPI value close to zero indicates that the corresponding patch size is becoming small, whereas a larger patch size close to 1 indicates entire landscape is dominated by a particular patch type [24].

The Landscape shape index (LSI) describes the irregularity of the complete landscape (Eq. (7)). The value of LSI indicates patch shape complexity by computing the degree of deviation, a patch has from a square or circle with an equal area [11].

$$\mathit{LSI}=\frac{0.25E^{\ast }}{\sqrt{A}}$$E7

where 0.25 is the square shape parameter, $E^{\ast }$ = total length of the edge of built-up patches; A = total area of built-up land

LSI > 1, with no limit. LSI = 1 indicates that the patch has the most regular form; the higher the LSI value, the further the patch deviates from the square and the more irregular the shape.

Area weighted mean patch fractal dimension (AWMPFD) is a specialized landscape metric for landscape pattern analysis and its minimum and maximum values are 1 and 2, respectively [21]. It determines the overall shape and edge of urbanized land (Eq. (8)). Aggregated shapes better establish connections among various patches.

By weighing patches according to size, AWMPFD averages the fractal dimensions of all urban patches. A perimeter-area comparison is used to describe the patch’s complexity and fragmentation. When a patch has a compact rectangular form with a small perimeter as compared to its area, it has a low value. At similar area sizes, more complex and fractured patches have larger perimeters, resulting in a higher fractal dimension [16].

$$\mathit{\text{AWMPFD}}=\sum _{i=1}^m\sum _{j=1}^n\left[\frac{2ln\left(0.25P_{\mathit{ij}}\right)}{ln{a}_{\mathit{ij}}}\right]\left(\frac{a_{\mathit{ij}}}{A}\right)$$E8

$a_{\mathit{ij}}$ area of patch ij.

$P_{\mathit{ij}}$ perimeter of patch ij.

2.5.3 Landscape-level indices

Landscape-level indices incorporate all patches of all classes of the entire landscape. These, like class metrics, can be combined using simple or weighted averaging, or they can reflect aggregate patch mosaic features. The pattern (i.e., configuration and composition) of the landscape mosaic is of main interest in many urban studies [9, 24, 26]. In urban studies, indices such as percentage of landscape, Patch density (PD), edge density, and mean euclidean distance neighbor are frequently used at the landscape level.

Percentage of landscape (PLAND) quantifies the proportional abundance of each type of patch in the landscape (Eq. (9)); i.e., the relative abundance of each urbanized part of the landscape. Because it is a relative measure, it may be a better measure of landscape composition than a class area for comparing landscapes of different sizes [23].

$$\mathit{\text{PLAND}}=\frac{{\sum }_{j=1}^n{a}_{\mathit{ij}}}{A}\ast 100$$E9

$a_{\mathit{ij}}$ is area of the jth patch of ith class.

A = total landscape area.

Patch density (PD) is the number of patches of a particular class per unit area (Eq. (10)), and indicates urban fragmentation; i.e., as the number of patches increases, patch density increases, representing higher fragmentation (scatter), whereas low PD reflects infilling, implying aggregation.

Patch density is a fundamental aspect of landscape pattern. It has the same basic utility as the number of patches as an index, except that it expresses the number of patches on a per unit area basis that facilitates comparisons among landscapes of varying sizes. If total landscape area is held constant, then patch density and the number of patches convey the same information. Like the number of patches, patch density often has limited interpretive value by itself because it conveys no information about the size and spatial distribution of patches.

$$\mathit{PD}=\frac{\mathit{\text{Number of patches}}}{\mathit{\text{Total area of the landscape}}}$$E10

Edge density (ED) is used to characterize the irregularity and shape complexity of urban patches (Eq. (11)).

$$\mathit{ED}=\frac{{\sum }_{k=1}^m{e}_{\mathit{ik}}}{A}$$E11

$e_{\mathit{ik}}$ = total length of edge in landscape with patch type (class) i, including landscape boundary and patch type i background segments.

A = total landscape area.

Mean Euclidean distance Neighbor (${\mathit{EMN}}_{\mathit{MN}}$) measures the average of the distances between the nearest patches in a class (Eq. (12)). It increases when the distance between the respective patches keeps increasing.

$${\mathit{EMN}}_{\mathit{MN}}=\frac{{\sum }_{j=1}^n{d}_{\mathit{ij}}}{n_i}$$E12

where $d_{\mathit{ij}}$ is the Euclidean distance between patches i and j and $n_i$ is the total number of patches in the landscape. Range > 1 without limit.

3. Factors affecting selection of indices

Different urban expansion analysis methods are discussed in the previous section. Although these techniques have been applied in different studies, selection among the methods requires understanding of features of the techniques that are summarized in Table 1. On the other hand, the selection of an appropriate method of spatio-temporal analysis of urban growth can be influenced by several factors, including the purpose and objectives of the analysis, the detail of the required information, available resources, and the scale of the analysis.

Index	Strength	Limitation
Urban spatial expansion index (USEI)	Relatively, it is simple to calculate and understand.	Provides a constant magnitude of change over the study period/time interval considered, which may not reflect the realistic nature of urban growth. As it can be influenced by the spatial extents of the study areas, it may not provide reliable results in the comparative assessment of the impacts of urbanization on different urban regions. It provides limited information about the urban growth process.
Urban expansion intensity index (UEII)	It normalizes the mean annual expansion based on the total land area of the landscape and makes the results comparable in temporal sets. When used for different land uses in a particular urban area, it enables us to recognize the preferences of urban growth.	In other words, because the spatial extents of the cities differ, comparing them using this index may not yield a reliable result.
Urban spatial expansion rate (USER)	It assumes the dynamic change in the spatial structure of a given urban region varies in time, which reflects the more realistic nature of urban growth. It avoids the size effect and is more suitable for comparative analysis between different spatial zones and different years, as well as among different cities.	It does not provide the magnitude of expansion.
Urban expansion type (UET)	It is a simple quantitative method to distinguish the growth types; thereby useful for identifying the types of urban form. It is suitable to characterize the evolution process of urban expansion, and it provides a deeper understanding of the landscape transformation processes.	It does not provide the magnitude, rate, and patterns of expansion. Obtaining input information for computation could require more time. The range of the values to define the growth type could be subjective, as there is no standard. It focuses on one-dimensional (linear) properties of old and new built-up patches.
Landscape metrics	It is suitable to assess the composition and configuration of landscapes. It allows the analysis at different spatial scales. It enables identification of patch expansion types. It allows capturing the evolution process of urban expansion patterns.	They can only quantitatively reflect the landscape patterns and their distribution for one single time period. It is difficult to extract input information and requires special software packages for data processing Some landscape metrics are limited interpretive value by themselves (e.g., number of patches), because they convey no information about the Area, distribution, and density of patches. Unless the metrics are selected carefully, they could provide the same information as the landscape, as most of them are redundant and correlated.

Table 1.

Summary of features of the urban expansion analysis methods.

A particular analysis could simply aim to determine the magnitude of expansion, or it could require information on how the changes occur. In other cases, there may be a need for information about the patterns or to determine the typologies of urban expansion. The needed accuracy or level of detail in an analysis also plays an important role in selecting the methods of analysis. The requirements of information must be adapted to achieve a good balance between the time, the cost, and the quality aspects of a project.

Landscape indices, on the other hand, are based on the same fundamental measurements (i.e., amount, area, perimeter, adjacency, and distance). Indices that measure or represent the same basic information are considered conceptually redundant since they measure the same item and hence offer the same landscape information. Indices that comprise similar measures for the basic components of configuration and composition are often empirically redundant because they are statistically correlated [26]. Many indices are also scale-dependent, which means that their values vary as the scale of the input data increases (both resolution and extent). As a result, it is the researcher’s responsibility to choose a collection of nonredundant metrics that are suitable for studying the situation at hand.

4. Conclusions

This chapter provided an overview of the prevailing methods of spatio-temporal analysis of built-up expansion. It presented various approaches to quantify the absolute magnitude of expansion, rate, intensity, and growth type. Moreover, landscape indices, which are devoted to determining the composition and configuration of built-up expansion, are also discussed. Each of these methods has benefits and drawbacks for applications, posing a lot of work for users to select an appropriate method for the situation at hand. In this respect, this chapter provides a good insight into the main features of existing methods and would help researchers and potential users undertake effective analysis, balancing between their needs and resource requirements.