Multi-order Landscape Expansion Index: Characterizing urban expansion dynamics

Landscape and Urban Planning 137 (2015) 30–39

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Research Paper

Multi-order Landscape Expansion Index: Characterizing urban expansion dynamics Limin Jiao a,b,∗ , Lifan Mao a,b , Yaolin Liu a,b a b

School of Resource and Environment Science, Wuhan University, 129 Luoyu Road, Wuhan 430079, PR China Key Laboratory of Geographic Information System, Ministry of Education, Wuhan University, Wuhan, PR China

h i g h l i g h t s • • • •

An improved spatial metric is proposed to characterize new urban patches. The metric measures the expansion degree of patches using time series data. The metric can be used to detect expansive areas and outlying urban clusters. The metric helps to characterize the spatial structure of urban expansion dynamics.

a r t i c l e

i n f o

Article history: Received 24 October 2013 Received in revised form 16 October 2014 Accepted 16 October 2014 Keywords: Multi-order Landscape Expansion Index Landscape metrics Urban sprawl Multi-temporal remote sensing images Urban clusters

a b s t r a c t Most of the landscape metrics used in urban expansion studies are capable of reflecting the spatial characteristics for individual time points, but are not efficient to capture the integrated information from time series data. A few spatial metrics, for example, Landscape Expansion Index (LEI), are calculated based on two-time-point data. These metrics are insufficient for the analysis of urban expansion dynamics based on multi-temporal data. In this study, we propose an improved spatial metric, Multi-order Landscape Expansion Index (MLEI), to measure the expansion degree of newly grown urban patches by considering their relationships with old patches and their spatial context in the process of urban expansion. A case study is conducted in Wuhan, a fast-growing metropolis in central China, based on remote sensing images from three time points (2000, 2005 and 2010). The MLEI map in 2010 clearly shows the areas that have experienced expansive growth. The greatest difference between MLEI and LEI occurs where outlying clusters are formed gradually through time. Some spatial analysis methods are applied on the MLEI map in 2010 to delineate outlying urban clusters in urban expansion. The map of urban clusters clearly shows the spatial heterogenicity of urban expansion and the most expansive areas in Wuhan. This study suggests that MLEI is capable to capture multi-temporal information, and can be used to characterize the spatial structure of urban expansion dynamics. © 2015 Elsevier B.V. All rights reserved.

1. Introduction 1.1. Characterizing urban expansion using spatial metrics Since the beginning of the 21st century, half of the global population resided in urban areas (United Nations, 2006). The urbanization rate in China exceeded 50% for the first time in 2012. Urbanization

∗ Corresponding author at: School of Resource and Environment Science, Wuhan University, 129 Luoyu Road, Wuhan 430079, PR China. Tel.: +86 27 8765 2613/13407112066; fax: +86 27 68778893. E-mail addresses: [email protected] (L. Jiao), [email protected] (L. Mao), [email protected] (Y. Liu). http://dx.doi.org/10.1016/j.landurbplan.2014.10.023 0169-2046/© 2015 Elsevier B.V. All rights reserved.

is not only a change in society and economy but also an important geospatial process. Quantitatively characterizing the process is essential for understanding the evolution of cities and prediction of urban growth. Conventional landscape metrics provide fundamental support for characterization and understanding of the spatial pattern of urban expansion. However, these metrics were mainly computed at single-time-point maps and characterize spatial patterns separately in a time series. Until now, there have been few metrics that integrate the information from multi-temporal maps and directly reflect the properties of landscape dynamics. In recent years, researchers have developed numerous landscape metrics with the help of remote sensing and geographic information system (GIS) techniques, which made it possible to quantify the landscape

L. Jiao et al. / Landscape and Urban Planning 137 (2015) 30–39

structures and analyze its dynamics (Forman & Godron, 1986). The landscape metrics are mainly based on size, shape, and arrangement of landscape patches (Matsushita, Xu, & Fukushima, 2006; Riitters et al., 1995; Turner & Gardner, 1991; Turner, O’Neill, Gardner, & Milne, 1989). Landscape metrics have been widely used in various environments; they are also known as spatial metrics (Herold, Couclelis, & Clarke, 2005). These metrics were variously derived from statistical theory, information theory, fractal geometry (Krummel, Gardner, Sugihara, O’neill, & Coleman, 1987; Pielou, 1977; Plotnick, Gardner, & O’Neill, 1993; Turner et al., 1989), and percolation theory (Gardner, O’Neill, & Turner, 1993; Li, Loehle, & Malon, 1996). Landscape metrics have been widely used in characterizing and analyzing various spatial patterns (Bailey & Gatrell, 1995; Csillag & Kabos, 2002; Imbernon & Branthomme, 2001; Liu et al., 2010; Zhang, Zhang, Li, & Cropp, 2006) such as plant communities, animal habitat, soil erosion, land-use and landcover change (LUCC), urban landscape, and urban sprawl (Angel, Parent, Civco, Blei, & Potere, 2011; Fragkias & Seto, 2009; Herold, Goldstein, & Clarke, 2003). Although these indices can be used in time series analysis with multi-time-point landscape metric values, new indices must be developed to capture the information from multi-temporal data and directly characterize the dynamics of landscape patterns. Urban sprawl is a dynamic process, and characterization of the dynamics of the process is important to gain a better understanding of urban growth. Many spatial metrics have been used to quantify the patterns of urban expansion. Researchers have also analyzed spatial dynamics using various spatial variables computed on multi-temporal maps (Luck & Wu, 2002). Tsai (2005) divided spatial variables in urban sprawl into three categories: density, diversity, and spatialstructure pattern. Galster et al. (2001) defined several concepts of urban land use patterns, e.g., density, continuity, concentration, clustering, centrality, and proximity. Many studies focus on establishing indices to analyze urban spatial patterns and urban sprawl based on spatial analyses and spatial metrics (Alberti & Waddell, 2000; Batisani & Yarnal, 2009; Feranec, Jaffrain, Soukup, & Hazeu, 2010; Geoghegan, Wainger, & Bockstael, 1997; Hasse, 2004; Herold et al., 2003; Parker, Evans, & Meretsky, 2001; Torrens, 2008). Some researchers developed entropy-based indices to characterize urban sprawl (Batty, 1976; Bhatta, 2009; Bhatta, Saraswati, & Bandyopadhyay, 2010; Li & Yeh, 2004; Sudhira, Ramachandra, & Jagadish, 2004; Yeh & Li, 2001). Jaeger and Schwick (2014) proposed a multidimensional metric to estimate the degree of urban sprawl. Luck and Wu (2002) studied the gradient analysis method for urban land use. Based on quantitative analysis of the spatial patterns, many researchers discussed the types of urban expansion, including infilling, edge-expansion, and outlying or leapfrog (Herold et al., 2003; Wilson, Hurd, Civco, Prisloe, & Arnold, 2003). Many researchers analyzed the dynamics and trends of urban sprawl by comparing landscape metrics from different time periods (Deng, Wang, Hong, & Qi, 2009; Herold et al., 2003). Some new theories on urban growth dynamics were proposed and investigated in case studies, such as the “rank-size rule” (Batty, Bourke, Cormode, & Anderson-Nicholls, 1974; Batty & Shiode, 2003; Nolè, Lasaponara, & Murgante, 2013; Tang, Wang, & Yao, 2006; Zipf, 1949) and oscillatory theory (Dietzel, Herold, Hemphill, & Clarke, 2005; Dietzel, Oguz, Hemphill, Clarke, & Gazulis, 2005; Martellozzo & Clarke, 2011).

define urban growth types. In their study, the common boundary is captured between a new grown patch and its adjoining existing patches. By their definition, the ratio S is an indicator of patch growth types. An infilling expansion type is assigned when the ratio S is larger than 0.5, otherwise an edge-expansion growth is detected. Sun, Wu, Lv, Yao, and Wei (2013) defined an index R based on the same principle and identified three classes of urban growth types: infilling growth, edge-expansion growth, and outlying growth. The Landscape Expansion Index (LEI) is an analogous spatial metric that is used by Liu et al. (2010) to characterize landscape expansion patterns. They used a buffer around a target patch instead of a one-dimensional boundary in the calculation of the index, which is the primary difference between the S and R indices. The LEI for a newly grown patch is calculated by: LEI =

A0 × 100% A0 + Av

(1)

where A0 is the area of the intersection between the buffer zone of the new patch and the existing patches (occupied category) and Av is the area of the intersection between the buffer and the vacant category. An infilling growth patch is defined by an LEI larger than 50 and an edge-expansion growth patch was defined by an LEI smaller than 50 but not equal to zero. The patches with zero LEI were classified as outlying growth. The buffer distance used in computation has an impact on LEI. Liu et al. (2010) argued that the LEI value would be more stable by using a smaller buffer distance, and set the buffer distance equal to 1 m. The buffer distance will be more meaningful if it is set to a value that corresponds to the average size of a type of geographical entity usually used to divide urban blocks such as urban roads. Although LEI captures the information in two-time-point data to quantify the dynamic change of urban expansion, it cannot capture the information from multi-temporal landscape maps to characterize the dynamics and the structure of continuous urban expansion (Fig. 1). Fig. 1 illustrates an example of urban expansion. Patch c grew in 2005 and, according to LEI, is outlying growth. The newly grown patches d, e, and f surrounding patches c, e and f are defined as edgeexpansion growth, whereas d is an infilling patch. However, patches d, e and f show expansive properties to a large degree because they grew around an outlying patch, compared with the patches that grew around the main built-up area, such as patch h. LEI cannot distinguish d, e, and f from h. Thus, LEI cannot effectively quantify the properties of continuously grown patches in more than three

1.2. The indices based on boundary-sharing rate in characterizing the process of urban expansion A set of new spatial metrics to measure the expansion degree of newly grown urban patches was proposed, computed based on the percent of boundary sharing with old patches. Xu et al. (2007) used the ratio between common boundary and patch parameter to

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Fig. 1. An example of urban expansion.

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time points. These four patches, c, d, e, and f, can be regarded as an outlying urban cluster in the structural analysis of urban expansion. We define an outlying cluster as a set of aggregated patches that grow around one or more outlying patches in the previous period and that are isolated from the main urban area. Patches within a cluster connect with each other and are affected by the existing patches in the center of the cluster. An outlying cluster exhibits a self-growing property to some extent. A large outlying cluster could be a potential secondary urban core that may imply a fast growing trend in the future. Identification of these outlying clusters is important in analyzing urban growth structure, predicting urban growth trends, and characterizing urban sprawl patterns. The LEI is not capable of capturing special structures such as outlying clusters. We develop an improved spatial metric in this study, the Multi-order Landscape Expansion Index (MLEI), which captures information from multi-temporal data rather than only the twotime-point data. MLEI characterizes the newly grown patches in the spatial context of continuous urban expansion, and helps to recognize urban structure. This study discusses the definition of MLEI and how to use it to characterize urban sprawl patterns and facilitate analysis of their structure, through a case study in Wuhan, a fast growing metropolis in China. The methods are described in Section 2, and the data and results are presented in Section 3. Section 4 presents some discussion and potential applications of MLEI. Conclusions and future work are summarized in Section 5.

2. Methods 2.1. Multi-order Landscape Expansion Index (MLEI) MLEI is computed based on two or more time point landscape data and is defined by the following equations:

j=1 (t) MLEIi

m

=

(t−1)

(MLEIj

× aij )

(2)

Ai

MLEI0i = 100

(3)

(t)

where MLEIi is the MLEI value of ith newly grown patch at time point t, m is the number of the old patches at time point t − 1 that (t−1) intersect patch i, MLEIj is the MLEI value of the jth patch that intersects patch i at time point t − 1, aij is the area of the intersection between patch i and patch j, and Ai is the area of the buffer (0) zone of the patch i. MLEIi is the MLEI value of the patches at the starting time point that are set to 100. The MLEI of the first time point is the same as LEI, but MLEIs of the subsequent time points are different from LEIs. The difference between MLEI and LEI is that MLEI inherits values from old patches at previous time points as weights in computation. The computation of MLEI in our study was implemented with a Python script in ArcGIS. Fig. 2 shows an example of an MLEI calculation. Patch a, surrounded by four patches (patches b, c, d and e), is the target object whose MLEI is to be calculated. Patch e is a patch at the starting time point with an MLEI of 100. MLEI values of patches b, c, and d are 0, 10, and 0, respectively. S1 , S2 , S3 , and S4 are four intersections with areas of 553 m2 , 355 m2 , 66 m2 , and 355 m2 , respectively. The total area of the buffer zone is 2646 m2 . The MLEI for patch a is computed by: (1)

(2)

MLEI1 =

Fig. 2. An example of an MLEI calculation. Table 1 MLEI and LEI values of the patches in clusters in Fig.3. LEI in Fig. 3 Patch b Patch c Patch d

Fig. 3b (MLEIa = 20)

Fig. 3c (MLEIa = 0)

12 48 6

8 16 2

0 0 0

2.2. Properties of MLEI Possible MLEI values vary between 0 and 100. Lower MLEI values indicate that the corresponding patches are more expansive. As for time series landscape maps, the MLEI of any patch is the same as LEI for the second time point, whereas MLEI is equal or smaller than LEI for the subsequent time points. The largest differences between MLEI and LEI are among the outlying clusters of newly grown patches. Fig. 3 shows a comparison between MLEI and LEI in three different cases. The clusters in Fig. 3(a–c) have the same structure but different locations relative to the original urban area. Suppose the LEI values of patches b, c, and d are 20, 80, and 10, respectively. Patch a is classified as infilling in Fig. 3(a), edge-expansion in Fig. 3(b) and outlying in Fig. 3(c). The MLEI values of patches b, c, and d are presented in Table 1. Although the positions of patches b, c, and d relative to the main built-up area are quite different, their LEI values are consistent in Fig. 3(a–c). However, MLEI presents differentiable values for these cases as a supplement to LEI. The LEI values of newly grown patches are determined by their spatial relationships to the nearest old patches, but their MLEI values depend on both their spatial relationships to the nearest old patches and the relationships to the older patches; thus, MLEI reflects the process of continuous growth. MLEI values of the patches with the same LEI values within the same “local” expansion structure may vary according to the spatial relationships between the “local” cluster and the main urban area. We can use MLEI to characterize continuous urban growth and capture expansion clusters. Therefore, MLEI is an improvement and complement to LEI in the recognition of spatial structure of urban expansion. 3. Data and results 3.1. Data Our case study was conducted in Wuhan City, Hubei Province, China (Fig. 4). The total area of the study area is 3113.4 km2 . Wuhan

(1)

MLEI1 × a11 + MLEI2 × a12 + MLEI3 (1) × a13 + MLEI4 (1) × a14 A1

20 80 10

Fig. 3a (MLEIa = 60)

=

100 × 355 + 0 × 553 + 10 × 355 + 0 × 66 = 14.8 2646

(4)

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Fig. 3. Comparison between MLEI and LEI in different cases.

is the largest city in central China, located in northeastern Jianghan Plain, with the Yangtze and Hanjiang Rivers converging in the center of the city. Wuhan has experienced rapid urban expansion coupled with fast economic growth since the 1990s. Three cloud-free satellite images covering the study area were used as source data: a Thematic Mapper (TM) image from November 7, 2000, an Enhanced Thematic Mapper (ETM+) image from September 11, 2005, and an ETM+ image from September 17, 2010. Preprocessing of the images included geometric correction, radiometric calibration, and resampling to 30-m resolution using ENVI 5.0. The land use maps in 1999 and 2009, produced in a government land use investigation, were used to extract boundary information and help to select samples. Online Google maps were also used as references to acquire ancillary information. Although only urban land was focused in the study, to build a database for subsequent studies, we defined four classes were in image classification: urban land, vegetation, water, and others. It should be noted that “urban” is used here to be synonymous with “built-up”. Each image was classified by the Maximum Likelihood method in ENVI 5.0, using more than 200 samples in total and at least 50 samples for each class. The training samples for the images of 2000 and 2010 were selected by visual interpretation referring the land use maps from

1999 and 2009, respectively. Google maps were also used as a reference in the classification of images of 2010 due to the proximity in time. The training samples in the classification of the image of 1990 were mainly selected by careful visual interpretation. We further evaluated these training samples by computing their separability using transformed divergence (TD) in ENVI 5.0 to test whether these samples clearly represent pre-defined classes. Training samples were edited to ensure good separability (TD values are larger than 1.8). After supervised classification, hand-editing was used to correct misclassified pixels, which can be detected by comparing the classified images with original images and our reference data. The stratified random sampling strategy was employed to select 150 samples to assess the accuracy of the classified images. These test samples were determined using land use maps and visual interpretation. The overall accuracies were 88.4%, 85.3%, and 89.7%, respectively. The results show that the total area of urban land in the study area increased from 403.6 km2 in 2000 to 588.8 km2 in 2005 and 824.7 km2 in 2010. We then converted the classified images to vector maps and extracted urban areas for focus of urban growth for analysis in ArcGIS 10.1. The urban areas of Wuhan in 2000, 2005, and 2010 are shown in Fig. 5. The buffer distance employed in the calculation of MLEI will affect the results, as is the case for LEI calculation. Liu et al. (2010) argued that smaller buffer distance would lead to more stable results in LEI computation; a buffer distance of 1 m is used in their study. Xu et al. (2007) and Sun et al. (2013) employed the common boundary between patches in the computation of similar metrics.

Fig. 4. Study area.

Fig. 5. Urban areas of Wuhan in 2000, 2005, and 2010.

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Fig. 6. Histogram of MLEI/LEI value (2005).

Their methods are special cases of LEI when the buffer distance is set to zero. According to Liu et al. (2010), the LEI was robust when the buffer distance was small (1–5 m), but the LEI changed significantly when the buffer distance was increased to 30 m. Their finding regarding the sensitivity of LEI is influenced by the resolution of the data in their study being 30 m. In our case study, we found that MLEI and LEI were sensitive to the buffer distance when it changed due to data resolution. The very small or zero buffer distance in LEI computation in previous studies may lead to the overestimation of outlying patches because patches that are very close to but not adjoining old patches are still classified as outlying patches according to the methods detailed above. It is not necessary in terms of geographical reasoning to set such a strict rule to define outlying patches. The classification of newly grown patches that are in accordance with geospatial analysis of urban growth can be obtained when the buffer distance is set in geographic context. It is also difficult and controversial to determine a reasonable buffer distance with clear geographic meaning. Fortunately, MLEI and LEI are still meaningful when comparing the expansion degrees of new patches at a given buffer distance. For convenience, we classify a patch isolated from old patches for more than the average width of urban roads as outlying because urban roads are common separators of urban blocks. According to “The Master Plan of Wuhan 2010–2020”, the widths of urban expressways, main urban roads, and secondary urban roads are 40–65 m, 40–70 m, and 25–40 m, respectively. In our case study,

the buffer distance in the MLEI computation is set to 50 m, which approximates the average width of urban roads in Wuhan (Wuhan Land Resources and Planning Bureau, 2014).

3.2. Results The MLEI and LEI values of patches grown in 2000–2005 and 2005–2010 were computed by using our Python script in ArcGIS 10.0, as described in Section 2. Histograms of LEI and MLEI values for the two periods are shown in Figs. 6–8. The MLEI and LEI values for the former period are the same according to Eqs. (1) and (2) because they have the same initial time point data. In Figs. 6 and 7, the largest number of patches has MLEI and LEI values in the range of [0,5]; values between [45,50] and [95,100] are two local maxima. These three peaks are typical characteristics of LEI (Liu et al., 2010). There are 21,991 newly grown patches in the former five years (2000–2005). The MLEI values of the patches grown during this period have an average of 34.96 with a standard deviation of 32.9. 23.4% of these patches have an MLEI value of 0. In the latter five years (2005–2010), 65,162 patches grew, with an average MLEI value of 16.09 and a standard deviation of 23.6. 37.6% of these patches were outlying (MLEI = 0). The frequency dropped significantly within the range of [0,25]. Afterwards, it changed slightly, with a downward trend until a gentle increase in [95,100].

Fig. 7. Histogram of LEI value (2010).

L. Jiao et al. / Landscape and Urban Planning 137 (2015) 30–39

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Fig. 8. Histogram of MLEI value (2010).

By comparing the frequency distribution of MLEI and LEI values for 2010, we found that the number of patches for the first eight intervals of MLEI is smaller than the number of patches for corresponding intervals of LEI, whereas the converse is true for other intervals. Based on the definition of MLEI and LEI, we can infer that the greater the difference between MLEI and LEI values in a dataset, the more outlying clusters exist. In other words, the difference between the two indices for the same data and the degree of urban sprawl manifested by massive outlying patches are positively correlated. The gathering outlying patches will form the hot zones of urban growth and could be the new growth centers among local areas. Figs. 9 and 10 show the spatial distributions of LEI and MLEI for 2010, respectively. We employ graduated colors for visualization of the metrics and to illustrate the expansion degree reflected. Many newly grown patches (2010) surrounding the old urban area (2005) that are classified by LEI as low-expansion-degree in Fig. 9 are classified as high-expansion degree by MLEI in Fig. 10. However, a large part of these patches was developed around existing outlying patch clusters, which makes the outlying clusters grow. LEI did not distinguish these patches from the patches grown inside or adjoining to the main urban area. The former group can be seen as expansive, while the latter group represents the “compact” growth in terms of urban land density (Schneider & Woodcock, 2008; Tsai,

2005). On the contrary, patches that formed outlying clusters were delineated clearly by MLEI, and Fig. 10 presents a more distinct spatial distribution of urban growth pattern. Fig. 11 shows LEI and MLEI values in a local area. In Fig. 11, A, B, and C denote three newly grown areas. The LEI and MLEI values are divided into five levels in the three pictures in Fig. 11 by natural breaks using the Jenks optimization method (Jenks, 1967). The LEI of A and B are 4.0 and 15.2, respectively, and Fig. 11(b) shows that A is much more expansive than B. This result is not reasonable because both A and B are outlying new urban clusters with similar conditions. By examining Fig. 11(a), we find that there are many more new patches in area B compared with area A in 2005, which results in the LEI value of A to be much smaller than the LEI of B. The MLEI of A and B are 2.8 and 5.9, respectively. They are classified as the same level in Fig. 11(c). It can be seen clearly that there is a growing new urban cluster in area C in Fig. 11(c), and it is classified as expansive. This is consistent with the fact that the area experienced expansive and fast urban growth. The cluster is not easily recognized in area C in Fig. 11(b), and only less expansive patches are found there. Urban sprawl is a dynamic spatial process. MLEI provides a tool to characterize the spatial patterns of the process, which will contribute to a quantitative description of urban sprawl structure and a more reasonable prediction of future expansion trends.

Fig. 9. The spatial distribution of LEI values (2010).

Fig. 10. The spatial distribution of MLEI values (2010).

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Fig. 11. MLEI and LEI values in a local area.

4. Discussions

Table 2 Statistics of the patches according to difference value intervals.

4.1. Comparison of MLEI and LEI

Intervals

Percent in count (%)

Percent in area (%)

Intervals

Percent in count (%)

Percent in area (%)

Based on the results of MLEI and LEI computation for 2010, the MLEI value of a newly grown patch is always less than or equal to the LEI value of the patch. To compare the MLEI and LEI results, we derived a difference map by subtracting the MLEI value from the LEI value on a patch-by-patch basis. The difference values were classified into five classes by the natural breaks method (Jenks, 1967); their distribution is shown in Fig. 12. Most patches were classified into the first four classes, i.e., the difference values between LEI and MLEI were falling between 0 and 53.978. Only a small fraction of patches have a difference value larger than 53.978, which is not easily seen in the figure. We summarized the counts and total areas of the patches according to intervals of the difference value with a step of one. The patches with difference values less than one account for 73.1% of the number of patches and 35.4% of the study area. Patches with difference values larger than one but less than two are 2.1% of the number of patches and 4.0% of the total area; this is much smaller than for difference values of less than 1. The percentages of patch number for the subsequent intervals decrease gradually from 1.6% to approximately zero. The percentages of total area for the subsequent intervals generally decrease from 2.7% to approximately zero. The statistics for typical intervals are shown in Table 2. Fig. 13

[0,1) [1,5) [5,10) [10,15) [15,20) [20,25) [25,30) [30,35) [35,40) [40,45) [45,50)

73.1 6.5 5.5 3.2 2.4 2.0 1.4 1.2 1.0 0.9 0.7

35.4 10.4 13.0 8.5 9.5 6.5 3.8 5.7 2.4 2.2 1.3

[50,55) [55,60) [60,65) [65,70) [70,75) [75,80) [80,85) [85,90) [90,95) [95,100]

0.6 0.5 0.3 0.2 0.2 0.1 0.1 0.0 0.0 0.0

0.5 0.3 0.2 0.1 0.1 0.1 0.0 0.0 0.0 0.0

Fig. 12. The difference between MLEI and LEI.

shows the change of count and area for different intervals except [0,1), which has dominated both. It can be seen from Table 2 and Fig. 13 that the area for the interval [50,55) and greater is very small. We reclassified the difference value into three intervals, namely, [0,1), [1,50), and [50,100], and divided the patches into three groups accordingly. The MLEI values of the patches in the first group (difference value less than one) are almost equal to their LEI values, whereas the MLEI values of the patches in the third group (difference value larger than 50) are very different from their LEI values. The patches in the second group (difference value ranges from 1 to 50) account for the majority in area (63.3%) and represent the gradual change of the difference between MLEI and LEI. Fig. 14 shows the overall distribution of the three groups and a local illustration. Most of the patches with difference values less than one (shown in Fig. 14(a and d)) are isolated small patches grown in a leapfrog manner, and some are infilling patches in the original urban areas. In both cases, the MLEI and LEI values are almost the same, which are both about zero and approximately 100, respectively.

Fig. 13. The change of count and area of the patches for different MLEI intervals.

L. Jiao et al. / Landscape and Urban Planning 137 (2015) 30–39

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Fig. 14. Distribution of three groups of new patches in 2010.

The patches grown in 2005, shown in Fig. 14(c and f), are infilling or edge-growing patches, which have small MLEI values but large LEI values. The patches shown in Fig. 14(b and e) represent the majority of the area grown in 2010, and most of the patches grew around the expansive patches grown in 2005.

4.2. Outlying cluster detection by spatial analysis Newly grown outlying urban clusters tend to be new local centers and usually cover fast developing areas. Identification of these outlying clusters is useful in the recognition of urban expansion structure and prediction of the future growth. We employed spatial analysis methods and produced a map of MLEI values (Fig. 10) to detect outlying clusters through three steps: selection of patches, aggregation of the selected patches, and simplification of the cluster polygons. First, we selected large and expansive patches to form clusters. There are many small urban patches in the map derived from satellite images. These small patches denote isolated construction, temporary land use, or bare lands. The minimum area of a patch was set to 1 hectare to exclude the small patches in order to reduce the computation complexity and the influence of random factors. According to the MLEI classification in Fig. 10 and the MLEI definition, the five levels shown in the figure are very expansive, expansive, slightly expansive, not expansive, and compact infilling. Thus the MLEI threshold was set to 51.639 (the first three levels). By applying the area and MLEI thresholds, 5425 patches were selected to form clusters. Secondly, we aggregated the selected patch polygons using the aggregation tool in ArcGIS 10.1. The aggregation distance, the threshold to be satisfied between polygon boundaries, was set to 50 m. The aggregation distance is as the same as the buffer distance employed in

the computation of MLEI. Thirdly, the boundaries of the polygons derived by aggregation were simplified using data generalization tools in ArcGIS 10.1. Finally, we selected the 100 largest polygons as the primary newly grown urban clusters (Fig. 15). Fig. 15 delineates the expansive areas from 2000 to 2010. The outlying urban clusters cover a large area outside the main urban area, and most are scattered in a leap-frog manner. This means that the city has experienced highly expansive urban sprawl and indicates that the trend will likely continue in the coming years.

Fig. 15. The primary newly grown urban clusters.

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Six areas, denoted by dashed line circles with Arabic numerals in Fig. 15, were determined as future urban growth centers in The Master Plan of Wuhan City (2005–2020), and continue to be planned as new satellite town centers in a revised version of the plan, The Master Plan of Wuhan City (2010–2020). Fig. 15 shows that the planned new centers of No. 2, No, 4, No. 5, and No, 6 grew remarkably and formed large urban land clusters. These areas experienced very expansive growth from 2000 to 2010. Particularly, area No. 2 contains the Wuhan East Lake High-tech Development Zone, known as a national optoelectronics industry base (the Optics Valley of China, OVC). The OVC area has experienced dramatic development since 2001, especially after 2007, and has formed several outlying clusters. Area No. 4 is known as a car industry center. Area No. 5 is a center of food and light industry. The Wuhan Tianhe International Airport is located near area No. 6, and logistics industry has developed quickly there. We can see some moderate or small urban clusters in areas No. 1 and No. 3. The clusters are scattered and expansive, which possibly will connect with each other through future urban lands. In this type of circumstance, coalitions form. Area No. 1 is a center of ports, steel industry, and chemical industry. Area No. 3 is a center of R&D and logistics industry. Eleven other large urban clusters not described above were also delineated in Fig. 15 and were labeled from A to I. Area A is a newly grown transportation center and the Wuhan high-speed train station is located there. Construction on the station began in 2006 and was open for use in 2009. Meanwhile, auxiliary construction was completed in this area. The Wuhan international expo center is located in area E, on which construction began in 2006. It is the third largest expo center in China. Areas D, I, and J are mainly industrial areas. Areas B, C, F, and G are mainly residential developments. Areas H and K have been developed for multiple uses, including residential, tourism, and education.

5. Conclusions Landscape metrics have been used extensively to characterize the spatial pattern of urban expansion with the help of GIS and remote sensing. They are also used to analyze long-term urban expansion. Most of these metrics can only capture the information for individual time point data and are insufficient in the analysis of urban expansion dynamics. A metric that captures the information from multi-temporal data is needed to characterize the process of urban expansion. LEI used in previous research and MLEI proposed in this study are important supplements to conventional spatial metrics. LEI is computed based on data from two time points and can be used to classify newly grown patches. However, LEI ignores the location of new patches within the overall urban structure through time. The MLEI index proposed in this study is computed on multi-temporal urban expansion maps, and captures information from time series data. We presented the definition of MLEI and discussed its properties. MLEI and LEI are the same for only two time points. However, for multi-temporal data, the greatest difference between MLEI and LEI occurs where outlying clusters are formed gradually from through time. MLEI can be employed to analyze the structure of urban expansion dynamics. We implemented a case study in Wuhan, a metropolis in central China, and verified the MLEI algorithm and its advantages. The case study shows that Wuhan experienced rapid urban sprawl between 2000 and 2010, characterized by massive outlying newly grown patches. In other words, a large part of newly grown patches have low LEI and MLEI values. The MLEI grid maps clearly illustrate the fast growth of outlying clusters in Wuhan urban expansion. The maps of the difference between MLEI and LEI values indicate that MLEI values are substantially different from LEI values for

the majority of the new patches, especially for those new patches that adjoin outlying clusters. Using some simple spatial analysis on MLEI maps, the outlying clusters of urban expansion can be identified. The resultant map produces spatially detailed information about outlying urban clusters, which helps to understand the urban growth dynamics and their spatial distribution. We found six new town centers planned in Wuhan’s city plan clearly exhibit characteristic clustering outlying growth in the past decade. Many other large urban clusters were recognized based on the urban cluster map. These analyses of MLEI reveal the spatial heterogeneity of urban expansion dynamics, and increases understanding of the spatial structure of urban growth. Future research could include further discussion of the parameters in MLEI-based analysis and applications of the combination of different metrics. The development of self-organizing or automated methods to form multi-scale maps of urban expansion structure based on these metrics should also be discussed.

Acknowledgment This research was funded by the National Natural Science Foundation of China (41171312).

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