Analysis of Temporal and Spatial Characteristics of Urban Expansion in Xiaonan District from 1990 to 2020 Using Time Series Landsat Imagery

: With the rapid development in the global economy and technology, urbanization has accelerated. It is important to characterize the urban expansion and determine its driving force. In this study, we used the Xiaonan District in Hubei Province, China, as an example to map and quantify the spatiotemporal dynamics of urban expansion from the two perspectives of built-up area and urban land in 1990–2020 by using remote sensing images. The location of rivers was found to be a primary limiting factor for spatial patterns and expansion of the built-up area. The transfer of the city center and the main direction of expansion generally corresponded well to the topography, policies, and development strategies. The built-up area expanded faster than the urban population in 1995–2020, which caused a waste in land resources. The results showed that the urban expansion ﬁrst decreased and then increased during the research period. The increase in the proportion of the secondary industry was the main driving force of the urban expansion. Based on the characteristics of urban expansion in the past three decades, we conclude that the urban land of Xiaonan District will expand quickly in the future and will occupy vast agricultural land. The government must deploy control measures to balance the beneﬁts and costs of urban expansion.


Introduction
Since the reform and opening up to the international market, China has encountered unprecedented economic growth, resulting in rapid urbanization. From 1949-2020, China's urbanization rate has increased from 10.6% to more than 60% [1,2]. Urbanization, by definition, is the course of progressive change from a customary provincial society that is overwhelmed by agribusiness to an advanced metropolitan culture dominated by nonhorticultural enterprises, which is characterized by metropolitan land development [3]. It poses both opportunities and challenges for the long-term development between human requirements and the global environment [4,5]. On the one hand, the innovation and wealth brought about by urbanization are surprising to the development of cities. Cities have a significant agglomeration effect and a scale benefit, the optimal allocation of economic factors, and the reasonable layout of regional internal industries can be realized in the process of expansion to promote the rapid development of the regional economy [6,7]. On the other hand, with the continuous shift from natural vegetation or cropland to urban land, a series of worrisome problems have gradually arisen, which have been reflected in many dimensions, including waste of land resources [8,9], loss of wildlife habitats and biodiversity [10][11][12], degradation of the ecological environment such as by air and water analyzing the spatial characteristics of expansion. Ning et al. (2020) utilized an assortment of spatial investigation strategies and indicators to analyze the intensity, direction, and pattern of urban expansion in Harbin using remote sensing image data from 2001,2008,2013, and 2017 [28]. Wang (2017) applied the average annual expansion index, spatial and temporal change land division model, urban land use spatial transfer model, and distance decay density model to analyze the spatial and temporal attributes and types of the urban spatial expansion of Changchun [29]. Wang (2014) used the expansion rate, expansion intensity, compaction index, urban center of gravity, and radiation index to characterize the spatial and temporal dynamics of the expansion of the main urban area of Xi'an and analyzed the difference in expansion in terms of spatial orientation [30]. Weng (2002) explored land use change dynamics of the Zhujiang Delta by the joint utilization of satellite remote sensing, GIS, and stochastic modeling technologies [31]. The results demonstrated that there was an outstanding and lopsided metropolitan growth and a gigantic loss in cropland between 1989-1997, and the land use change process has shown no indication of becoming steady. In addition, the relevant concept of landscape ecology has been gradually introduced into research on urban expansion in recent years [32,33]. Xi et al. (2019) selected a series of landscape metrics to analyze the extension interaction and land use changes in the main urban area of Xi'an [34]. Bian et al. (2021) took the Yangtze River Economic Belt as the research object; studied the landscape urbanization from the perspective of multi-scale spatial and temporal pattern, diversity, and sustainability influence; and used landscape index and binary regression method to discuss the connection between landscape urbanization, national development planning, and regional sustainability [35]. Sapena and Ruiz (2015) used a series of multi-temporal fragmentation metrics, including the landscape metrics, to make a dynamic quantification of urban spatial patterns and urban sprawl by using land-use/land-cover (LULC) data obtained from the European Urban Atlas dataset. The results showed that urban expansion monitoring with multi-temporal data using these techniques highlights urbanization trends, having a great potential to quantify and model the geographic development of metropolitan areas [36].
In addition, the research on the quantitative analysis of urban expansion drivers has gradually become a hot spot in recent years. For example, Verburg (2004) used the logistic model to analyze the urban expansion of the Netherlands and proposed that the driving factors for the increase of urban construction land for residential, industrial, commercial, and entertainment facilities are the urban traffic accessibility, relevant government land policies, and interaction of adjacent areas [37]. Ademola et al. (2006) quantified spatial indicators such as topographic variables, accessibility, neighborhood index, and distance from water; analyzed them with a binary logistic regression model of urban land change in Lagos; drew the same conclusion as Verburg; further observed the differences between significant variables of residential and commercial land change models; and proposed that the land use change model should distinguish residential land and commercial land to identify drivers [38]. Peng and Chen (2019) obtained 12 correlation drivers from the population, economy, social, and traffic four dimensions through relevant analysis; used principal component analysis; and proposed that the road area, fiscal expenditure, the proportion of secondary, and the proportion of tertiary industry are the core driver of urban construction land expansion in Hunan province in 2005-2017 [39]. Chen (2020) selected the relevant factors and used the grey relation analysis to conclude that the main driving force for the urban land expansion in the study area was the increase in the population [40]. Zhang (2019) chose geographically weighted regression (GWR) to explore the driving forces of urban land expansion in Shandong Province and used ArcGIS software to visualize the results, which directly reflected the spatial change of each driver [41].
However, research on the urban expansion of cities surrounding large cities is lacking. These cities are usually in a period of rapid development, which is partially driven by large cities [42,43]. If we can identify the existing problems in the process of their urban expansion process, it will be of extraordinary importance to change metropolitan advancement strategies timely for sustainable development. To characterize the urban expansion  the areas around large cities, we quantified the spatiotemporal transformation patterns  of built-up area and urban land expansion in Xiaonan District utilizing multi-temporal  Landsat TM and OLI images from 1990,1995,2000,2005,2010,2015, and 2020 combined with the compaction index, fractional exponent, landscape metrics, sector analysis, and urban growth type. The main content of this paper is as follows: (1) mapping the spatial pattern of built-up area and urban land cover dynamically, (2) characterizing the spatiotemporal features of built-up area and urban land expansion, (3) dissecting the temporal coevolution of the urban population and area, and (4) investigating the driving force of urban expansion.  [44]. Since Xiaogan City was established in 1993, this region has encountered fast urbanization in the past three decades because of its superior geographical conditions [45]. A wide range of development strategies have been taken on in the past three decades, and countless various extensions have happened during this period. Among the seven districts (Xiannan, Dawu, Xiaochang, Hanchuan, Yunmeng, Yingcheng, and Anlu), Xiannan District covers an area of 1018.32 km 2 with a population of 0.98 million in 2020, is located in the east of Xiaogan City, and is regarded as the urban core of Xiaogan City, while the other six regions are characterized mostly by rural areas. To demonstrate the detailed urban expansion of Xiaogan City, our study focused on Xiaonan District (Figure 1), which we selected for the following reasons. First, Xiaonan District is the administrative and industrial center of Xiaogan City. Its urban expansion can represent the development of the entire Xiaogan City. Second, Xiaonan District borders Wuhan, only 60 km from the center of Wuhan, facilitating resource sharing between regions. Xiaonan District exhibits great development potential because of its excellent geographical conditions. It is important to characterize urban expansion and attempt to solve identified problems in the expansion process.

Remote Sensing Images and Other Materials
Since 1972, a series of Landsat satellites have been launched and have provided many high-quality remote sensing images for detecting the earth's resources and environment. Seven sequential series of remote sensing images (1990,1995,2000,2005,2010, 2015, and 2020) were chosen to obtain land cover information of the past three decades in the study area. Cloud-free TM images before 2015 and OLI images obtained after 2015 were acquired from the United States Geological Survey (USGS) website (http://www.usgs. gov/, accessed on 18 October 2021). In addition, the remote sensing images from July-September were selected to ensure that the vegetation and crops in the study area are luxuriant as far as possible on the basis of cloud-free images, which can help to improve classification accuracy. The path-row numbers, procurement dates, and resolution of the images used in this study are recorded in Table 1, and we used ENVI version 5.3 and ArcGIS version 10.2 to accomplish the data processing, including radiometric calibration, image mosaic, reprojection, clip, atmospheric correction, classification, and classification accuracy assessment.
In addition to basic remote sensing images, the free land use data of Hubei Province (1 km resolution), which we used to evaluate the reliability of the urban land area we extracted, were downloaded from the website of the Resources and Environmental Sciences and Data Center (https://www.resdc.cn/, accessed on 18 October 2021). The province boundaries inside China, the city boundaries inside the Hubei Provinces, and the district boundaries inside the Xiaonan District in vector format were obtained from the National Catalogue Service For Geographic Information website (https://www.webmap.cn/, accessed on 18 October 2021). Additionally, the socioeconomic data, demographic data, and other statistical data were collected from Xiaonan District Chronicles, Xiaonan Yearbook, Hubei Provincial Statistical Yearbook, and Xiaonan District National Economic and Social Development Statistical Bulletin of 1990-2020 [46][47][48].

Remote Sensing Images and Other Materials
Since 1972, a series of Landsat satellites have been launched and have provided many high-quality remote sensing images for detecting the earth's resources and environment. Seven sequential series of remote sensing images (1990,1995,2000,2005,2010,2015, and 2020) were chosen to obtain land cover information of the past three decades in the study area. Cloud-free TM images before 2015 and OLI images obtained after 2015 were acquired from the United States Geological Survey (USGS) website (http://www.usgs.gov/, accessed on 25 October 2021). In addition, the remote sensing images from July-September were selected to ensure that the vegetation and crops in the study area are luxuriant as far as possible on the basis of cloud-free images, which can help to improve classification accuracy. The path-row numbers, procurement dates, and resolution of the images used in this study are recorded in Table 1, and we used ENVI version 5.3 and ArcGIS version 10.2 to accomplish the data processing, including radiometric calibration, image mosaic, reprojection, clip, atmospheric correction, classification, and classification accuracy assessment.

Methods
As shown in Figure 2, the framework of this research mainly comprised three steps:

Methods
As shown in Figure 2, the framework of this research mainly comprised three steps: (1) extracting the built-up area and urban land, (2) characterizing the expansion process of built-up area and urban land, and (3) exploring the temporal coevolution of built-up area with urban populations and the main driving force of urban land expansion, respectively.

Object-Oriented and SVM Classification
In this study, we extracted the built-up area and urban land in Xiaonan District and analyzed the urban expansion in Xiaonan District from these two aspects. The "built-up area" is the area with intense human activity. This area includes the concentrated part of

Object-Oriented and SVM Classification
In this study, we extracted the built-up area and urban land in Xiaonan District and analyzed the urban expansion in Xiaonan District from these two aspects. The "built-up area" is the area with intense human activity. This area includes the concentrated part of the urban area and the urban construction land scattered in the suburbs, which are closely correlated with the city and have municipal public facilities [49]. The built-up area is usually an integrated spatial range, and small patches of vegetation and water area should be included. While "urban land" is a concept developed from the perspective of land use. It refers to the non-agricultural areas dominated by artificial surfaces, including industrial and commercial land, scientific and educational land, residential land, roads, and other traffic land, excluding the vegetation and water area inside the city.
For urban built-up area, we applied object-oriented classification combined with visual interpretation to map. The visual interpretation process mainly included the following content: (1) incorporating small green spaces, water spaces, and unused land between construction land into the built-up area to ensure the spatial continuity of the built-up area; (2) removing two large water bodies, the Gunzi River and Xian River, passing through the city; and (3) excluding other land-use types with an obvious distinction between urban boundaries.
Many researchers have studied the influence of different supervised classification methods on the accuracy of classification, proving that the support vector machine (SVM) has a relatively high classification accuracy on the land use information [50][51][52]. For urban land, we first obtained the land cover information by applying SVM classification, including four categories: urban land, grassland and areable land, water, and naked land. Then, we integrated them into two categories: urban and non-urban land. The kappa coefficients and overall accuracy were used to assess the performance of the obtained products [53][54][55].
At the same time, to ensure the reliability of the results we extracted, we compared the area of built-up area with the corresponding data from the China Urban Construction Statistical Yearbook and the area of urban land with the free land use data of Hubei Province (1 km resolution), which we downloaded from the website of the Resources and Environmental Sciences and Data Center (https://www.resdc.cn/, accessed on 18 October 2021). The difference was determined by calculating the absolute and relative errors. The results demonstrate that the areas of built-up areas and urban land were slightly biased from the data in the statistical yearbook and website with small errors.

Compaction Index and Fractional Exponent
A city with a compact pattern is more convenient for centralizing various facilities and improving the utilization efficiency. It can also decrease the waste of resources and environmental pollution caused by urban expansion [56]. In 1961, Richardson proposed a compaction index to intuitively and fully reflect the outer spatial morphology of a city. The index was calculated as follows: where C represents the compaction index, the range of which is 0-1. A is the area of the urban land patch, and L is the perimeter of the external boundary of the urban land patch. The fractional exponent was first proposed by Mandelbrot, B. B. [57]; the term "fractal" represents a pattern in which the smaller components reflect the whole in some form. Fractals are characterized by self-similarity and complexity. Some scholars have proposed that the spatial pattern of a city is usually complex and exhibits similarity over a given period, which can be regarded as exhibiting fractal development over time [58,59]. Therefore, they introduced the theory of fractals into the study of urban expansion. The fractional exponent is an important indicator for describing fractals that measures the regular degree and internal structure complexity of the external shape of urban land patches by its values. In this study, the index was calculated as follows: (2) where D represents the fractional exponent, P is the perimeter of the external boundary of the urban land patch, and A is its area. The larger the fractional exponent, the more complex and irregular the shape of the urban patch.

Sector Analysis
We further examined detailed changes in different directions. Sector analysis is a kind of descriptive GIS spatial analysis method based on stacking statistics and analysis of sector units. It has been widely used in the field of urban expansion research, but there is no standard on how to divide the object into several equal sectors in its application. Peng and Tang (2020) have searched and counted the relevant 171 articles, and found that for the number of sectors, eight sectors were relatively preferred (104/171), for sector orientation, the azimuth sector (there are always 4 sectors facing 4 basic geographical orientations: north, east, south, west) appears relatively more (110/171) [60]. Based on the general applicability of the "eight sectors" model and the feature of the expansion of the built-up area (the expansion of built-up area from 2005-2010 was mainly in the southeast direction), we chose the "eight sectors" model which generated by embedding four middle directions (northeast, northwest, southwest, southeast) in four basic directions (north, east, south, west) derived from a geographic perspective. The specific sector analysis steps are as follows: first, four transects across the city center of 1990 were generated to divide the built-up area into eight sectors (Figure 3), and the expanded area every five years of each sector was calculated. By analyzing the change of construction land in each sector, we identified the difference in expansion in different directions. by embedding four middle directions (northeast, northwest, southwest, southeast) in four basic directions (north, east, south, west) derived from a geographic perspective. The specific sector analysis steps are as follows: first, four transects across the city center of 1990 were generated to divide the built-up area into eight sectors (Figure 3), and the expanded area every five years of each sector was calculated. By analyzing the change of construction land in each sector, we identified the difference in expansion in different directions.

Expansion Velocity and Intensity
We calculated two indexes of urban land expansion: expansion velocity (V) and expansion intensity (R). The two indexes can compare the speed of urban expansion. The definitions of V and R are as follows: where A start and A end are the urban land area at the beginning and end, respectively. d is the time span of the study period.

Urban Growth Type
Scholars have proposed different standards for the definition of urban growth type, leading to a variety of model divisions of urban land. Leorey and Nariida (1999) divided the types of urban land expansion into compact, edge, corridor, and business-as-usual [61]. Emily et al. (2003) also summarized five types: infill, expansion, isolated, linear branch, and clustered branch [62]. The division system of the urban growth type is complex, and the results are highly subjective and dependent on the judgment of researchers. Therefore, to determine the urban land growth type conveniently, accurately, and quickly, Xu et al. (2007) proposed a method of quantitatively dividing urban growth types into infilling, edge-expansion, and leapfrogging categories [63]. Infilling is defined as new urban patches formed by filling gaps in the existing urban patches. Edge-expansion is the newly de-veloped urban patches extending outward along the edge of the existing urban patches. Leapfrogging growth represents new urban patches developed independently and without overlapping with any existing urban patches. The metric S is used to distinguish the three urban growth types: where L C is the length of the boundary between the new urban patch and the old one, and P is the boundary length of the new urban patch. If S = 0, it indicates that the new urban patch has no public border between the old urban patch, indicating that the type of growth is leapfrogging. The type is edge-expansion when 0 < S ≤ 0.5 and infilling when 0.5 < S ≤ 1.

Landscape Metrics
Landscape patterns refer to the spatial structure characteristics of land use [64]. FRAGSTAS is a landscape metric calculation software that can calculate 59 landscape metrics at three different levels. In this study, we selected four landscape metrics: patch density (PD), landscape shape index (LSI), aggregation index (AI), and cohesion index (COHESION) to analyze the landscape pattern characteristics of urban land in Xiaonan District from 1990-2020. The landscape metric values were calculated by using FRAGSTATS version 3.0 with the eight-neighbor rule. The specific information of the four landscape metrics is as follows: (1) Patch density (PD): where n i represents the total area of landscape class i, A represents the total area of all landscape classes, and the value of PD represents the number of patches per unit area.
(2) Landscape shape index (LSI): The value of LSI indicates patch shape complexity by calculating the degree of deviation between a patch and a square or circle with an equal area of the patch. In FRAGSTATS, the calculation of this index is standard by the equal-area square, and the specific formula is as follows: where 0.25 is the square shape parameter, E represents the total boundary length of all patches of a landscape type, and A is the total area of patches for this type. LSI ≥ 1, when LSI = 1 means the patch has the most regular shape, the larger the value of LSI, the more deviated from the square and the more irregular the shape of the patch.
(3) Aggregation index (AI): where g ii represents the number of adjoining patches of landscape class i. If the value of AI get higher with the area of urban land increasing, it indicates the distance between the patches of urban land becomes smaller, and the degree of concentrated land utilization has increased.
(4) Patch cohesion index (COHESION): where p ij represents the boundary length between patches of landscape class i and patches of landscape class j; a ij is the proportion of patch j to class i; and A is the sum area of all patches.

Urban Area-Population Elastic Coefficient and Allometry Model
The urban area-population elastic coefficient is an important index applied for measuring the adaptability of urban population growth and built-up area growth. It describes the quantitative relationship between the growth rate of the built-up area and the urban population, which can reflect the rationality of urban expansion and be calculated as follows: where S i and Pop i are the average growth rates of built-up area and urban population in period i, respectively. The urban area-population elastic coefficient was first proposed by Gehl (2002). He also proposed that urban expansion is reasonable when the value of the urban areapopulation elastic coefficient is 1.12. When the value is lower or higher than 1.12, the urban expansion is less reasonable and will probably affect sustainable urban development in the future, as recognized by many scholars in China [65][66][67].
In general, there is not a simple linear relationship between built-up area expansion and urban population growth, and simply determining the rationality of urban expansion using only the urban area-population elasticity coefficient mentioned above is not sufficiently comprehensive. In the 1950s, some scholars introduced the allometry model in the field of biology into the study of urban expansion to explore the relationship between urban population and urban land [68]. The allometry model is as follows: where A and N represent the areas of the built-up region and urban population, respectively, and a and b are coefficients. The values of a and b can be obtained by examining the built-up area sequence and the urban population sequence of the corresponding year. According to the research of relevant scholars [69][70][71], for Chinese cities, when b = 0.85, the growth rate of built-up areas and growth rate of urban populations are similar, the process of urban expansion in the study period is appropriate. When b < 0.85, urban expansion is regarded as negative growth, and the urban population grows faster than the built-up area, which may cause environmental pollution and a decline in quality of life. When b > 0.85, it is regarded as positive growth, and the growth rate of the urban population is lower than that of the built-up area, which may result in the waste of construction land.

Grey Relation Analysis
The grey system theory was first proposed by Tan and Deng based on system control theory in the field of systems engineering [72]. It is a method for analyzing and determining the degree of influence or contribution to the main behavior between a series of relevant factors. Based on the grey system theory, we can obtain the correlation between the factors through data processing with incomplete information and then identify the main influencing factor by comparing the value of the coefficient. The steps for the grey relation analysis in our study are as follows: (1) The sequences to analysis were determined. In this paper, the area of urban land was used as the reference sequence (x) and the relevant index sequence group (y i ) as the comparison sequence.
Previous research shows the expansion of urban land is the result of internal factors (e.g., terrain and natural environment) and external factors (e.g., population, economy, transportation, and policy) [73][74][75]. Internal factors restrict the direction of urban expansion and the spatial shape of cities, while external factors promote the expansion of urban land. The population is the most dynamic driving factor of urban expansion [76]. The rapid development of the city makes many people transfer to the city, which will inevitably increase the demand for residential buildings, roads, hospitals, parks, shopping malls, and other related living facilities, resulting in an increase in urban land. Economic factors are the most direct and fundamental factor for urban expansion. The high-level economic development will attract many high-quality enterprises to settle in the region, bringing the expansion of industrial land and transportation land. The gross domestic product (GDP) can be used to reflect the economic level of a region directly. The government invests most public revenue into urban land development, so government revenue can also promote an increase in urban land. Investment in fixed assets can stimulate the rapid development of the local economy, increase the proportion of the secondary and tertiary industries, and consistently upgrade the industrial structure, which will also lead to an increase in industrial land, commercial land, road transportation land, public facilities, and other urban land. Based on the qualitative analysis above and the availability of the corresponding statistical data, the factors including total population, GDP, proportion of secondary industry, proportion of tertiary industry, government revenue, and investment in fixed assets of the whole society were selected to study the main driving force of the urban land expansion in Xiaonan District as the comparison sequence (y i ).
(2) Dimensionless processing. The multiple indicators we selected have different dimensions and different units. In order to avoid errors caused by different dimensions, data need to be dimensionless. In this study, each value of sequence was divided by the first value of this sequence (initial value).
(3) The absolute value of the difference between comparison sequence group (y i ) and reference sequence (x) was calculated to find the maximum z(k) max and minimum z(k) min .
(4) Correlation coefficients were calculated as follows: where ρ is the resolution coefficient that increases the difference significance between the correlation coefficients, and the value of the ρ is in the range of 0-1, usually taking a value of 0.5. (5) Correlation indexes were calculated on the correlation coefficients.

Spatiotemporal Dynamics of Built-Up Area Expansion
The spatial patterns and expansions of the built-up area are shown in Figure 4.  In order to make a more detailed analysis of the expansion dynamics of the Xiaonan District's built-up area, we overlapped the Xiaonan District built-up area every five years ( Figure 5). The radar charts that demonstrate the expansion area of each sector and each period were drawn separately ( Figure 6). The urban expansion was concentrated to the east of the old built-up area from 1990-1995. The reason was that, in June 1990, the government established the Xiaogan New Industry Development and Opening Pilot Zone in the eastern part of the built-up area. Taking advantage of the opportunity for enterprise relocation, a number of enterprises have been introduced. The Decision of Xiaogan Mu-    Figure 7 illustrates the values of the compaction index and fractional exponent. Because of the special geographical location of the study area, the Xian and Gunzi rivers restrict the boundaries of the built-up area (Figures 5 and 6); thus, the value of the compaction index in every period was not high. The value of the compaction index declined between 1990-2020, and the value was relatively high between 1990-2005. This occurred because the built-up area was limited to the river bend between the Xian and Gunzi rivers, and the scale of the built-up area was small and did not reach the highest saturation during this period. The highest compaction index value (0.51) in 1995, which represents the spatial pattern of built-up area in this period was the most compact. After 2005, large urban patches appeared opposite to the Xian and Gunzi rivers, resulting in the pattern of the entire built-up area becoming narrow and complex, and the compaction index of the built-up area was greatly reduced.  Figure 7 illustrates the values of the compaction index and fractional exponent. Because of the special geographical location of the study area, the Xian and Gunzi rivers restrict the boundaries of the built-up area (Figures 5 and 6); thus, the value of the compaction index in every period was not high. The value of the compaction index declined between 1990-2020, and the value was relatively high between 1990-2005. This occurred because the built-up area was limited to the river bend between the Xian and Gunzi rivers, and the scale of the built-up area was small and did not reach the highest saturation during this period. The highest compaction index value (0.51) in 1995, which represents the spatial pattern of built-up area in this period was the most compact. After 2005, large urban patches appeared opposite to the Xian and Gunzi rivers, resulting in the pattern of the entire built-up area becoming narrow and complex, and the compaction index of the built-up area was greatly reduced.
The fractional exponent increased from 1990-2020, showing that the internal structure of the built-up area became increasingly complex and irregular during the study period. The lowest fractional exponent of the built-up area occurred in 1995, with a value of 1.41. Throughout the entire study period, the value of the fractional exponent varied greatly from the standard value of 1, indicating that the internal spatial structure of the built-up area was very complex and that the land resources had not been completely utilized.
Our investigation revealed that the change in fractional exponent was closely related to the government's land planning. For example, the Xiaonan District government created a new plan for development between 1990-2005, which was called "One city, two ring, and three lines" plan. This plan required that urban scale, spatial layout, zoning function, and supporting facilities must be scientifically planned, and the new construction land should be neatly divided according to the traffic road. Thus, the fractional exponent during this period was not large, and urban expansion did not make the internal structure more complex. Between 2005-2010, the fractional exponent increased greatly because the expansion of the built-up area ushered in a new wave during this period under the government's planning. However, the new construction land had not been connected, leading to an increase in the fractional exponent. Between 2010-2020, the government focused more on the rationality of urban expansion, so the value of the fractional exponent was almost unchanged during this period.

Spatiotemporal Dynamics of Urban Land Expansion
According to our experimental results, the urban land area increased from 51.74-138.89 km 2 in 1990-2020. Spatial distributions of the urban extent and urban expansion for Xiaonan District from1990-2020 can be seen in Figure 8. In 2010-2020, the existing urban groups became more compact, and a large number of small urban land patches were generated among the patches which have a long distance from each other. Figure 9 shows the expansion velocity (V) and expansion intensity (R) of the urban land. The result shows that urban land expanded rapidly during 2015-2020. Throughout the study period, the expansion velocity and intensity both exhibited trends of first decreasing and then increasing gradually. In 1990-1995, the city underwent important changes, including the determination of development goals, the establishment of an economic development zone, and opening and attracting numerous enterprises. As a result, rural construction accelerated at the same time, leading to the rapid expansion of construction land. The main reason for the low expansion velocity between 1995-2000 was that the expansion was limited by the rivers, and there was sufficient space to expand the built-up area.  Xiaohua train line, Beijing-Hong Kong-Macao expressway, Hanshi expressway, and other interurban roads boosted the urban development of surrounding towns. From 2010-2020, the government of Xiaonan District was integrated into the construction of "The Belt and Road" and the Yangtze River Economic Belt. Relying on Wuhan, Xiaonan District developed a large area of urban land near Minji Town, which is the nearest municipality to Wuhan. The economic and social development of Xiaonan District ushered in a boom, and the expansion velocity and intensity were greatly improved.    Between 2010-2015, the urban land expansion in Xiaonan District was mainly based on the edge-expansion of the old patches, followed by leapfrogging, and the proportion of infilling patches increased. Between 2015-2020, the urban patches underwent continuous filling expansion, the patterns were almost complete, and there was hardly any non-urban land inside. Therefore, the proportion of infilling patches in this period was very small, and the expansion was dominated by edge-expansion and leapfrogging. Figure 11 shows the trends in the urban landscape changes. Because urban expansion was dominated by edge expansion during the research period, the PD gradually decreased between 1990-2020. It is worth mentioning that the value of PD suddenly rose in 2010, but obvious urban land growth was not observed because the main type of urban growth was leapfrogging in 2005-2010. The continuous decline of the PD also indicated that there is a continuous reduction in the degree of fragmentation of urban land. From the perspective of LSI, the overall value is relatively high, which deviates much from the standard value of 1, indicating that the shape of urban land is complex and irregular during the research period. It had the lowest value of LSI in 2015 when the urban land had the most regular shape and the highest centralized use of the land. The AI and COHESION constantly increased during the research period, and the upward trend of AI was not as obvious as COHESION, indicating that the aggregation degree between the urban land types had increased, the distance between the urban patches had constantly decreased, and the urban land had been constantly concentrated and distributed. Simultaneously, the connectivity between the urban patches improved, and the urban land was gradually connected into pieces. Overall, the centralized utilization degree of the land exhibited an increasing trend. main rivers. The center of urban development moved to the east side of the Gunzi River, and a large amount of new urban land was observed. Between 2005-2010, leapfrogging patches surpassed edge-expansion patches and became the main expansion type during this period. Between 2010-2015, the urban land expansion in Xiaonan District was mainly based on the edge-expansion of the old patches, followed by leapfrogging, and the proportion of infilling patches increased. Between 2015-2020, the urban patches underwent continuous filling expansion, the patterns were almost complete, and there was hardly any non-urban land inside. Therefore, the proportion of infilling patches in this period was very small, and the expansion was dominated by edge-expansion and leapfrogging. Figure 10. Composition of three urban growth types of urban land from 1990-2020. Figure 11 shows the trends in the urban landscape changes. Because urban expansion was dominated by edge expansion during the research period, the PD gradually decreased between 1990-2020. It is worth mentioning that the value of PD suddenly rose in 2010, but obvious urban land growth was not observed because the main type of urban growth was leapfrogging in 2005-2010. The continuous decline of the PD also indicated that there is a continuous reduction in the degree of fragmentation of urban land. From the perspective of LSI, the overall value is relatively high, which deviates much from the standard value of 1, indicating that the shape of urban land is complex and irregular during the research period. It had the lowest value of LSI in 2015 when the urban land had the most regular shape and the highest centralized use of the land. The AI and COHESION constantly increased during the research period, and the upward trend of AI was not as obvious as COHESION, indicating that the aggregation degree between the urban land types had increased, the distance between the urban patches had constantly decreased, and the urban land had been constantly concentrated and distributed. Sim- ultaneously, the connectivity between the urban patches improved, and the urban land was gradually connected into pieces. Overall, the centralized utilization degree of the land exhibited an increasing trend. Figure 11. Landscape changes of urban land in Xiaonan District from 1990-2020.

Temporal Coevolution of Built-Up Area with Urban Population
To obtain further understanding of the urbanization in Xiaonan District, we examined the temporal coevolution of the built-up area with population. It should be noted

Temporal Coevolution of Built-Up Area with Urban Population
To obtain further understanding of the urbanization in Xiaonan District, we examined the temporal coevolution of the built-up area with population. It should be noted that because Xiaonan District was established in 1993, the population data had been counted since 1995.
With the urban area-population elastic coefficient and allometry model, which are used to scale the adaptability of urban population growth and built-up area growth in the process of urban expansion, we found that the elastic coefficient generally deviated from the standard value (Table 2). This pattern was disrupted in 2010-2015, during which the coefficient was close to the critical value of 1.12. The value was far less than 1.12 in 2005-2010, showing that the built-up area increased but the urban population declined during this period, and the urban expansion was very unreasonable in that it did not correlate well with the population level. In 1995-2000, the elastic coefficient was less than 1.12, showing that the built-up area expanded more slowly than the urban population. In 2000-2005 and 2015-2020, the elastic coefficient was greater than 1.12, indicating that the built-up area expanded faster than the urban population. According to the built-up area sequence and urban population sequence of Xiaonan District from 1995-2020, the fitting equation for the allometry model is shown in Figure 12.
The results indicate that the fitting accuracy is high, and the allometry coefficient of the allometry model is 1.33, which is greater than the standard value of 0.85, showing that the expansion speed of built-up area was faster than the growth rate of the built-up area population during 1995-2020.
If Xiaonan District does not take some corresponding control measures in the future, it will cause vacant construction land and land resource waste and affect sustainable development in the long term.

Driving Force of Urban Expansion in Xiaonan District
The correlation between the driving force indexes and urban expansion was calculated according to grey relation analysis (Table 3). These data were also counted starting in 1995. The results reveal the following order of driving factors: proportion of secondary industry > total population > proportion of tertiary industry > GDP > government revenue > investment in fixed assets of the whole society. Thus, the proportion of secondary industry was identified as the main driving factor. The primary, secondary, and tertiary industries of Xiaonan District accounted for 45.8, 23.2, and 31%, respectively, in 1995, and 11.2, 31.5, and 57.3% in 2020, respectively. In 1995-2020, the proportion of secondary and tertiary industries continued to increase (Figure 13). High-tech industrial agglomeration areas have been developed and gradually formed a new model that promotes the secondary and tertiary industry development to drive urbanization. Population growth also had a direct driving effect on the expansion. In 1995-2020, the total population increased by 22.3%, the urban population increased by 218.4%, and the proportion of urban population increased from 25.4-66.2% (Figure 14). With the increased inflow of migrants, a lot of people are constantly gathering in urban areas, promoting an increase in urban residential land, public facilities land, and other urban land. In recent years, the natural population growth rate of Xiaonan District has increased, and the migration rate is high. It can be expected that in the next few years, the population of Xiaonan District will grow, and the demand for new urban land will continue to be maintained at a certain level and constantly drive the expansion of urban land. The primary, secondary, and tertiary industries of Xiaonan District accounted for 45.8, 23.2, and 31%, respectively, in 1995, and 11.2, 31.5, and 57.3% in 2020, respectively. In 1995-2020, the proportion of secondary and tertiary industries continued to increase ( Figure 13). High-tech industrial agglomeration areas have been developed and gradually formed a new model that promotes the secondary and tertiary industry development to drive urbanization. Population growth also had a direct driving effect on the expansion. In 1995-2020, the total population increased by 22.3%, the urban population increased by 218.4%, and the proportion of urban population increased from 25.4-66.2% ( Figure 14). With the increased inflow of migrants, a lot of people are constantly gathering in urban areas, promoting an increase in urban residential land, public facilities land, and other urban land. In recent years, the natural population growth rate of Xiaonan District has increased, and the migration rate is high. It can be expected that in the next few years, the population of Xiaonan District will grow, and the demand for new urban land will continue to be maintained at a certain level and constantly drive the expansion of urban land.

Characteristics and Drivers of Urban Expansion
The main objective of this study is to obtain the characterization of urban expansion in Xiaonan District from 1990-2020; form the two aspects, built-up area and urban land; and explore the temporal coevolution of built-up area with urban populations and main driving factor by using time series Landsat imagery.
Previous studies focused mainly on the spatial pattern of urban land in megacities, large cities, and urban agglomeration by using DMSP/OLS night light data of the U.S. Department of Defense and its follow-on platform, Landsat data of USGS Earth Resources Observation and Science (EROS) Center, or other data sources [77][78][79]. They paid more attention to the growth of the urban land area and boundary, using simulation models of cellular automaton (CA) to simulate the future urban land distribution [80], and concentric circle and sector analysis to compare expansion rates at different distances and in different directions [81,82]. In recent studies, researchers began to care about the dynamics of spatial structure and growth types in the process of urban land expansion, usually using a series of indexes and methods to evaluate them.
The expansion of urban land is indeed the most significant feature of urbanization, but the built-up area is the main urban area with the most densely urban residents, and the reasonable expansion of the built-up area is an important factor affecting the life quality of residents. However, there are few studies considering the expansion of built-up area and whether the expansion corresponds to the urban population when studying urban expansion. Research on the urban expansion of cities surrounding large cities which are usually in a period of rapid development is lacking.
In contrast, this study provides new ideas for studying small-scale urban expansion. We studied the expansion of the Xiaonan District from the two perspectives, the built-up area and overall urban land, and we chose two different methods (object-oriented and SVM classification, respectively) to extract the corresponding information according to the definitions and characterizations of them, which made the results more reasonable. We selected compaction index and fractional exponent to analyze the spatial morphology change and divided Xiaonan District into eight directions to analyze the difference in the expansion direction of the built-up area. Additionally, we also applied the urban area-population elastic coefficient and allometry model to discuss the rationality of the

Characteristics and Drivers of Urban Expansion
The main objective of this study is to obtain the characterization of urban expansion in Xiaonan District from 1990-2020; form the two aspects, built-up area and urban land; and explore the temporal coevolution of built-up area with urban populations and main driving factor by using time series Landsat imagery.
Previous studies focused mainly on the spatial pattern of urban land in megacities, large cities, and urban agglomeration by using DMSP/OLS night light data of the U.S. Department of Defense and its follow-on platform, Landsat data of USGS Earth Resources Observation and Science (EROS) Center, or other data sources [77][78][79]. They paid more attention to the growth of the urban land area and boundary, using simulation models of cellular automaton (CA) to simulate the future urban land distribution [80], and concentric circle and sector analysis to compare expansion rates at different distances and in different directions [81,82]. In recent studies, researchers began to care about the dynamics of spatial structure and growth types in the process of urban land expansion, usually using a series of indexes and methods to evaluate them.
The expansion of urban land is indeed the most significant feature of urbanization, but the built-up area is the main urban area with the most densely urban residents, and the reasonable expansion of the built-up area is an important factor affecting the life quality of residents. However, there are few studies considering the expansion of built-up area and whether the expansion corresponds to the urban population when studying urban expansion. Research on the urban expansion of cities surrounding large cities which are usually in a period of rapid development is lacking.
In contrast, this study provides new ideas for studying small-scale urban expansion. We studied the expansion of the Xiaonan District from the two perspectives, the built-up area and overall urban land, and we chose two different methods (object-oriented and SVM classification, respectively) to extract the corresponding information according to the definitions and characterizations of them, which made the results more reasonable. We selected compaction index and fractional exponent to analyze the spatial morphology change and divided Xiaonan District into eight directions to analyze the difference in the expansion direction of the built-up area. Additionally, we also applied the urban area-population elastic coefficient and allometry model to discuss the rationality of the built-up area expansion in Xiaonan District from the perspective of whether the built-up area growth and population growth were suitable, which is helpful for the sustainable and healthy development of the city.
Regression analysis, variance analysis, principal component analysis, and logistic models are usually used to explore which factor has the greatest effect among many influencing factors [83][84][85][86]. Therefore, some researchers introduce them to study the drivers of urban expansion. However, these methods have some common shortcomings: for example, these methods need a lot of supporting data. If there are only a few data, the results will be meaningless. Sometimes these methods also require data to obey a special distribution. However, grey relation analysis is based on developmental trends among factors, and no large size and standard distribution rules of the sample data are required [87,88], which makes it more reasonable to explore the drivers of urban land expansion in areas with inadequate data like Xiaonan District. According to the results of grey relation analysis, the driving forces of urban land expansion of Xiaonan District in 1995-2020 are mainly the increase of proportion of the secondary industry, followed by the population growth, proportion of the tertiary industry, and GDP growth. This is consistent with the view of many previous studies that urban expansion is the result of many comprehensive factors, including society, economy, policy, population, traffic, and natural conditions. The results are also consistent with results of other researchers obtained in the Xiaonan District [89].

Study Limitations
It should be noted that our study has several limitations. Due to time, space, and funding constraints, we selected medium-resolution remote sensing images as our original data. The area of Xiaonan District is not large, and we can improve the accuracy by using higher resolution images in the future. Moreover, there is a dispute over the scope of the built-up area, and the built-up area was mapped based on object-oriented classification and artificial visual interpretation in our study, which requires further study. The driving force of urban land expansion in Xiaonan District should be further discussed. Although we have analyzed the driving forces of urban expansion qualitatively and quantitatively, the factor system is not comprehensive, and relevant data such as real estate development data are lacking. The selected indicators are universal, but it is difficult to reflect the regional characteristics of Xiaonan District.

Conclusions
In the past decades, China's rapid urbanization and rapid economic growth have aroused worldwide attention. However, studies on the internal rates, forms, and driving forces of cities around the big city are still lacking. In this study, we have a comprehensive understanding of the urban expansion, the temporal evolution of the built-up area and urban population, and main driving factor of the expansion in Xiaonan District.
The expansion rate of the built-up area first decreased and then increased from 1990-2020. It expanded fastest in 2005-2010. The location of rivers was the main factor limiting the expansion of built-up area. The transfer of the city center and main direction of expansion generally corresponded well to the topography, policies, and city development strategies. The degree of land concentration in the built-up area was not high, and the spatial form of the built-up area was complex and irregular. In 1995-2020, the expansion of built-up area was not suitable for urban population growth. The expansion was unreasonable as there is still unused land in the study period.
The magnitude of urban land expansion is ranked as follows: 2015-2020 > 2010- 2015 > 1990-1995 > 2000-2005 > 2005-2010 > 1995-2000. The results of landscape metrics show that although the overall shape of urban land remained complex and irregular throughout the research period, the connectivity between urban land patches has improved and gradually connected in recent years. The increase in the proportion of secondary industries leads to the driving force of urban expansion in Xiaonan District over the study period.