Spatiotemporal Analysis of Urban Expansion in Beijing, China

Abstract

Using Landsat TM/OLI remote sensing images and social statistical data from 1995, 2000, 2005, 2010, 2015, and 2020, construction land information in Beijing’s main urban area was extracted with ArcGIS 10.4.1 and other software. Based on calculations of the expansion speed, expansion intensity, fractal dimension, and elasticity coefficient, the spatiotemporal expansion characteristics of the urban area of Beijing were analyzed to reveal the laws and driving forces of urban expansion in Beijing. The results showed that the urban construction land area in Beijing expanded by a factor of 0.53 from 1995 to 2020, and its expansion speed and intensity gradually slowed. The overall expansion trend is that the central urban area remains basically unchanged, while the peripheral areas are rapidly expanding, showing a trend of rapid growth first and then stable growth, and the urban layout is basically stable. The urban expansion of Beijing has led to increasingly complex, tortuous, and unstable boundaries. Overall, the center of gravity of Beijing is moving toward the northeast, and the elasticity coefficient of urban expansion is 1.67 times that of a reasonable coefficient. The intensity and direction of urban expansion in Beijing are most significantly related to population mobility. Research on the expansion of Beijing lies the foundation for the integration and coordinated planning of resources in the various districts of Beijing and provides a basis for its sustainable development.

1. Introduction

Urban expansion is an important balance indicator of the urbanization level, a direct manifestation of urbanization in geographic space [1,2], and a fundamental feature of urbanization. The outward promotion and expansion of regional space in the process of urban development are influenced by human factors such as the economy, politics, and culture of the city center, as well as natural factors such as land use and geological landforms [3,4]. Urban expansion affects the improvement of people’s living standards and the development of the social economy. At present, many scholars mainly analyze urban expansion in three dimensions: population, space, and economy, and explore the influencing factors and mechanisms of urban spatial distribution patterns [5]. Most studies have found that the main factors affecting urban expansion include natural conditions, resource conditions, economic foundation, transportation and location conditions, administrative and institutional factors, market potential, economic globalization, informatization, etc. [6]. The increase in urban population is an important aspect of urban expansion. Research has found that industrial structure has a significant negative impact on urban population density, meaning that the larger the proportion of secondary and tertiary industries to the total regional output value, the lower the population density within the region [7]. The supply of natural resources has a significant negative impact on population size, but the negative impact of urban resources on urban population density is weakening [8]. Urban location has a positive impact on urban population density. Meanwhile, urban spatial expansion is an important dimension of comprehensive urban expansion [9]. The industrial structure has a negative impact on urban spatial expansion, while the supply of natural resources has a positive impact on urban spatial expansion. The level of urban public finance expenditure has a positive promoting effect on urban spatial expansion [10]. On the other hand, urban economic growth has a significant positive impact on factors such as industrial structure, resource supply, and public financial expenditure.

Since the 1990s, China’s urbanization has accelerated, the phenomenon of urbanization has gradually emerged, and the urban system has gradually improved. At the beginning of the 21st century, as we entered a period of accelerated development, we began to expand on a large scale, with an increasing amount of urban construction land and a decreasing amount of available land. Moreover, with the acceleration of urbanization and the continuous expansion of urban scale, problems such as shortages of arable land resources, declines in per capita ecological space, traffic congestion, environmental degradation, and urban heat island effects are becoming increasingly prominent, gradually affecting the living conditions of residents and the urban environment.

With the continuous process of opening up to the outside world, the increasing number of foreign exchanges in Beijing, and the acceleration of modernization, it is proposed that Beijing be built into an international metropolis. Beijing, as China’s political and cultural center, international communication center, and financial management center, is an important gateway for China’s development. Since the 1990s, the urban scale of Beijing has rapidly expanded, with the built-up area continuously expanding and the population skyrocketing. It is also concentrated in the main urban area, where the number of motor vehicles has doubled. This has brought enormous pressure to urban resources, the environment, transportation, and daily operations. If this area is not controlled and continues to expand in a simple and disorderly manner, this will be detrimental to the sustainable development of Beijing. Hence, an urgent task is to take necessary steps to alleviate urban functions and enhance the sustainable development of Beijing.

At present, research on urban expansion in Beijing mostly focuses on factor analysis and macro data statistics, and there has not been a systematic study on accurately grasping the dominant factors of urban expansion. There has also been insufficient research on the reasonable regulation of the practical problems brought about by urban expansion. In summary, this article takes the spatial dimension as the main line, integrates various factors, analyzes the specific manifestations and impacts of the spatial dimension in the process of urban expansion, and provides a dataset of Beijing’s urban expansion process and urban spatial-growth boundaries, which is conducive to the sustainable development of Beijing. Suggestions and strategies for the sustainable development of livable large cities have also been proposed through research, which is of great value for studying the expansion of first tier large- and medium-sized cities in different countries around the world.

2. Research Area and Research Methods

2.1. Study Areas

Beijing is located in the northern North China Plain in the middle latitudinal zone (115°25′ E–117°30′ E, 39°28′ N–41°05′ N). The terrain is high in the northwest and low in the southeast. The region has a typical warm temperate semi humid continental monsoon climate, with an average annual temperature of 12.3 °C. The zonal vegetation type is warm temperate deciduous broad-leaved forest. Beijing is the political and cultural center of China. Beijing has 11 districts and counties under its jurisdiction, with a total area of approximately 16,400 km². The circular pattern is orderly, and the radial development axis is distinct. The upward expansion of cities has a typical directionality, and a gradient change occurs along the line, changing outward from the north–south central axis centered on the Forbidden City in a radial direction to form its important development axis [11].

From 1995 to 2020, the nonagricultural population of Beijing increased from 6.969 million to 19.166 million, the total population increased from 12.511 million to 21.893 million, the built-up area increased from 477 km² to 1485 km², an increase of 3.11 times, the GDP increased from 0.15 trillion yuan to 3.59 trillion yuan, accounting for approximately 3.54% of the national GDP, and the total investment in fixed assets increased from 5.705 billion yuan to 96.538 billion yuan, indicating that the urbanization process of Beijing has been accelerating.

The urban development of Beijing has always shown circular and pancake-shaped development, with the boundary of the second green isolation area located within 1 km of the city center to the outside of the Sixth Ring Road. Currently, the boundaries of urban planning areas are also within this range. This study takes the area from the center of Beijing to the boundary of the second green isolation zone (1 km outside the Sixth Ring Road) as the research area (Figure 1), which has a concentric circular layer structure.

2.2. Data Sources and Preprocessing

The land use data are based on the land use data produced by the Liu Jiyuan team of the Institute of Geographic Sciences and Resources of the Chinese Academy of Sciences. The data sources used were Landsat TM (Thermal Mapper: TM) remote sensing image data from 2000 to 2010 and Jilin No. 1 remote sensing satellite mosaic image from Beijing in 2020. According to the land use classification standards, land types are divided into five categories: cultivated land, forestland, water bodies, urban construction land, and unused land.

The digital elevation model (DEM) was derived from the Geospatial Data Cloud GDEMV2 30 m dataset accessed on 1 January 2021 (http://www.gscloud.cn/). The slope data of the study area were obtained through the analysis of elevation data using ArcGIS 10.4.1. Road-related data (such as highway, national highway, railway, and subway), river data, population spatial distribution data, and GDP spatial distribution data are all sourced from the Resource and Environment Data Cloud Platform accessed on 1 January 2021 (www.resdc.cn/). The required urban resident population, socioeconomic indicators, transportation condition indicators, and livability indicators are all sourced from the corresponding year’s Beijing Statistical Yearbook.

2.3. Research Methods for Determining the Quantitative Characteristics of Urban Expansion

2.3.1. Urban Expansion Speed Index

The speed of urban expansion represents the annual growth rate of urban built-up areas during a certain period of time and is generally used to measure the speed of built-up area expansion [12]. The formula is as follows:

$${\mathrm{V}}_{\mathrm{u}}={\displaystyle \frac{{\mathrm{S}}_{\mathrm{b}}-{\mathrm{S}}_{\mathrm{a}}}{\mathrm{T}}}$$

(1)

where ${\mathrm{V}}_{\mathrm{u}}$ represents the expansion speed index, $s_a$ represents the area of urban construction land in the early stage of the study, $s_b$ indicates the area of urban construction land at the end of the research period, and T indicates the research interval time period.

2.3.2. Urban Expansion Intensity Index

The urban expansion intensity index represents the growth rate of urban construction land area within a certain period of time and is generally used to measure the strength of expansion [13,14]. The formula is as follows:

$$R_u={\displaystyle \frac{S_b-S_a}{S_a\times T}}\times 100\%$$

(2)

where $R_u$ expresses expansion intensity index.

2.4. Research Methods on the Spatial Characteristics of Urban Expansion

2.4.1. Fractal Dimension of Urban Space

The fractal dimension represents the logarithmic ratio of the perimeter to the area of urban construction land boundary lines and is generally used to measure the complexity of the spatial form of urban construction land [15,16]. The fractal dimension is calculated as follows:

$$D_t=2\times {\displaystyle \frac{{\ln (C}_t\times 0.25)}{\ln S_t}}$$

(3)

In the formula, $D_t$ represents the fractal dimension of the city in year t (1 ≤$D_t$ ≤ 2), $C_t$ indicates the perimeter of the urban edge in year t, and $s_t$ represents the urban area in year t. The theoretical value of the fractal dimension is 1–2, and the larger the dimension is, the more complex the boundary of urban construction land becomes.

2.4.2. Transfer of the Urban Spatial Center of Gravity

The transfer of the urban spatial center of gravity can reflect the direction and magnitude of urban expansion and can clearly reflect the trajectory of changes in the urban center of gravity in time and space [17]. Generally, this approach is used to analyze urban evolution and changes in land use types [18], and the formula is as follows:

$$D_{ab}=\sqrt{{({\mathrm{x}}_{\mathrm{b}}-{\mathrm{x}}_{\mathrm{a}})}^2+{({\mathrm{y}}_{\mathrm{b}}-{\mathrm{y}}_{\mathrm{a}})}^2}$$

(4)

In the formula, $D_{ab}$ indicates the distance of the urban spatial center of gravity transfer from year a to year b, and x and y are the horizontal and vertical coordinates, respectively, that represent the center of gravity of a geographical unit during a certain period.

2.4.3. Elastic Coefficient of Urban Expansion

The elasticity coefficient of urban expansion represents the coordinated relationship between the speed of urban expansion and population growth and is generally used to evaluate the rationality of urban expansion [19]. The formula is as follows:

$${\mathrm{R}}_{\mathrm{t}}={\displaystyle \frac{A_t}{P_t}}$$

(5)

In the formula, ${\mathrm{R}}_{\mathrm{t}}$ is the elasticity coefficient of urban expansion in the t-th period, $A_t$ is the average growth rate of the urban area at time t, and $P_t$ is the average growth rate of the total urban population at time t.

2.5. Establish the Urban Expansion Technology System

Urban expansion technology system (

Table 1. Urban expansion technology system.

Classified	Index
Research methods for determining the quantitative characteristics of urban expansion	Urban expansion speed index
	Urban expansion intensity index
Research methods on the spatial characteristics of urban expansion	Fractal dimension of urban space
	Transfer of the urban spatial center of gravity
	Elastic coefficient of urban expansion

) refers to a series of technologies, methods, means and tools involved in the process of supporting and promoting urban expansion. It is a comprehensive concept, which is of great significance for promoting urban expansion and promoting urban sustainable development.

3. Results

3.1. Quantitative Characteristics of Urban Expansion in Beijing

According to Figure 2, the urban construction land area in the urban area of Beijing (the red areas in the study area) expanded by 0.53 times from 1995 to 2020 (Figure 3, Appendix A). Among these areas, the construction land area decreased by a factor of 0.02 from 1995 to 2000, expanded by a factor of 0.08 from 2000 to 2005, expanded by a factor of 0.29 from 2005 to 2010, expanded by a factor of 0.08 from 2010 to 2015, and expanded by a factor of 0.03 from 2015 to 2020. The urban expansion of Beijing from 1995 to 2020 showed the characteristic of “contraction slow medium slow” (Figure 4). According to the study by Li et al. [20], the expansion intensity in Beijing was slow from 2000 to 2005, moderate from 2005 to 2010, and slow from 2010 to the present. The expansion speed and intensity in Beijing are gradually slowing, and urban construction land is showing a stable trend.

As shown in Figure 5, there are differences in the expansion of different urban areas. Xicheng District, Dongcheng District, and Shijingshan District did not expand between 1995 and 2020, and the urban construction land area remained basically unchanged. The area and expansion speed of urban construction land in other districts are as follows: Daxing > Shunyi > Fangshan > Tongzhou > Changping > Chaoyang > Haidian > Mentougou > Fengtai > Shijingshan > Xicheng > Dongcheng. Compared with the urban construction land area in 1995, Daxing, Shunyi, Fangshan, Tongzhou, Changping, Chaoyang, Haidian, Mentougou, and Fengtai had expanded by factors of 1.22, 0.74, 0.61, 0.65, 0.6, 0.37, 0.22, 0.35, and 0.2, respectively. The expansion intensity was as follows: Mentougou > Daxing > Shunyi > Tongzhou > Fangshan > Changping > Chaoyang > Haidian > Fengtai > Shijingshan > Xicheng > Dongcheng. Construction land resources in the central urban area of Beijing are scarce, and the land utilization rate is high. The land resources in peripheral urban areas are abundant, and the expansion cost is lower, increasing the suitability for expansion. The results also reveal that the expansion area, expansion speed, and expansion intensity of peripheral urban areas are greater than those of central urban areas. Overall, the expansion type of Beijing is the extensional type.

According to Table 1, from 1995 to 2000, except for Shijingshan, Xicheng, and Dongcheng, the urban construction land area in other districts showed a decreasing trend. During the three periods of 2000–2005, 2005–2010, and 2015–2020, the expansion speed of Daxing District was the fastest, and the expansion intensity of Mentougou was the highest. From 2010 to 2015, Fangshan District had the fastest expansion, and Tongzhou had the highest expansion intensity. From 1995 to 2020, the expansion speed and intensity of Mentougou in Daxing District were particularly prominent. The overall expansion of Beijing is characterized by the central urban area remaining basically unchanged, while the peripheral areas are rapidly expanding, showing a phenomenon of rapid growth first and then stabilizing, and the urban layout is basically stable.

3.2. Characteristics of Urban Expansion Space in Beijing

The fractal dimension can reflect the complexity and tortuosity of urban edges [21]. A fractal dimension value between 1 and 1.5 indicates a simple and well-planned urban boundary, while a fractal dimension value between 1.5 and 2 indicates a trend toward complex and unstable urban boundaries. The dimensions of urban spatial classification in Beijing in 1995, 2000, 2005, 2010, 2015, and 2020 were 1.52, 1.56, 1.58, 1.59, 1.60, and 1.59, respectively, showing a trend of increasing and then decreasing within the theoretical range, indicating that the boundaries of Beijing are gradually becoming more complex, tortuous and unstable.

As shown in Figure 6, the perimeter of the study area in 1995 was 701.46 km, exhibiting complex boundaries and scattered land use. In 2000, the perimeter of the research area was 922.75 km, an increase of 221.29 km compared to that in 1995. The urban boundary is complex and has no significant change overall. In 2005, the perimeter of the research area was 1193.68 km, which represents an increase of 270.93 km compared to that in 2000, and the urban boundaries were more complex. In 2010, the perimeter of the research area was 1278.4 km, an increase of 84.72 km compared to that in 2005. In 2015, the perimeter of the research area was 1430.96 km, an increase of 152.56 km compared to that in 2010. In 2020, the perimeter of the research area was 1430 km, which is basically the same as that in 2015. Moreover, the center point coordinates of the study area patches were obtained for each time period, the horizontal and vertical coordinates of the center of gravity of the study area were calculated, as was the transfer distance. The center of gravity of the research area moved 0.84 km to the northwest between 1995 and 2000 and 0.94 km to the northeast between 2000 and 2005; it basically remained unchanged from 2005 to 2010; it moved 0.62 km to the northeast between 2010 and 2015 and 0.65 km to the northeast between 2015 and 2020. Overall, the center of gravity of the study area has shifted 2.25 km to the northeast.

3.3. Rationality of Urban Expansion in Beijing

The elasticity coefficient of urban expansion, which describes the relationship between the rate of urban expansion and the rate of population growth, was used to measure the rationality of urban expansion. The China Urban Planning and Design Research Institute has analyzed the urbanization process over the years and concluded that a coefficient of elasticity for urban expansion of 1.12 was more reasonable [22]. According to

Table 2. Population elasticity coefficient of Beijing from 1995 to 2020.

	Average Growth Rate of Area	Average Population Growth Rate	Elastic Coefficient
1995–2000	0.169	0.090	1.875
2000–2005	0.262	0.128	2.053
2005–2010	0.071	0.276	0.257
2010–2015	0.119	0.107	1.120
2015–2020	−0.001	−0.008	0.084

, the elasticity coefficient of urban expansion in the study area from 1995 to 2000 was 1.67 times the reasonable coefficient. The elasticity coefficient of urban expansion in the research area from 2000 to 2005 was 1.83 times the reasonable coefficient. The elasticity coefficient of urban expansion in the research area from 2005 to 2010 was 0.22 times the reasonable coefficient. The elasticity coefficient of urban expansion in the study area from 2010 to 2015 was a reasonable value. The elasticity coefficient of urban expansion in the research area from 2015 to 2020 was 0.08 times the reasonable coefficient. From 1995 to 2005, the urban expansion rate in the research area was much greater than the population growth rate, and a large amount of land resources were converted to urban construction land, while the population had not yet begun to flow in. From 2005 to 2010, the urban expansion rate of the research area was lower than the population growth rate, which provided a large number of spatial resources for the development of the research area in the early stage. The population began to gradually flow in to accelerate the development of Beijing. The population growth rate from 2010 to 2015 matched the urban expansion rate, and the city was in a coordinated development stage. The urban expansion rate from 2015 to 2020 was much lower than the population growth rate, and a large volume of talent continued to flow into Beijing. However, the urban construction land area did not respond in a timely manner.

3.4. The Driving Force of Urban Expansion in Beijing

The factors that affect urban expansion are complex and diverse. The main indicators were selected for correlation analysis. The results of the analysis were shown in

Table 3. Pearson correlation analysis between urban expansion and influencing factors.

	Number of Permanent Residents	Socioeconomic Indicators (Gross Domestic Product)	Traffic Condition Indicators (Number of Public Transport Operations)	Livability Index(Green Area)
Construction land area	0.985 **	0.972 **	0.737	0.968 **

** indicates a significant correlation at the 0.01 level.

. Beijing’s urban expansion was significantly positively correlated with the resident population, socioeconomic indicators, and livability indicators, with the closest relationship with the number of permanent residents, followed by socioeconomic indicators and livability indicators. There was a positive correlation with transportation conditions. The permanent population of Beijing increased from 12.51 million in 1995 to 21.893 million in 2020, indicating a large influx of foreign people into Beijing, which has played a strong driving role in urban expansion. The rapid increase in population has driven rapid socioeconomic development, increasing the GDP from 150.77 billion yuan in 1995 to 3610.26 billion yuan in 2020, which has had a large driving effect on the urban expansion of Beijing.

4. Discussion

The speed and direction of urban expansion are influenced by various social and urban factors, including economic policies, environmental sustainability, social needs, technological progress, cultural values, and urban planning. The government’s economic development strategy and urban planning policies have a direct impact on urban expansion [23]. For example, the government may encourage the development of specific regions by providing infrastructure construction funds, tax incentives, or other incentives. With increasing attention paid to climate change and environmental issues, the direction of urban expansion may lean towards environmentally friendly development, such as the development of green buildings, public transportation, and urban green spaces. Urban expansion needs to meet the housing, employment, education, and healthcare needs of residents. These changes in demand will affect the speed and direction of urban expansion to accommodate population growth and improved quality of life. The direction of urban expansion is also influenced by local cultural values. Some cities may place greater emphasis on historical preservation and cultural characteristics, and therefore pay attention to protecting traditional neighborhoods and historic buildings during the expansion process [24]. The ideas and goals of urban planners have a decisive impact on the direction of urban expansion. Planners may develop expansion plans based on the specific conditions and long-term goals of the city to achieve a balanced development of the economy, society, and environment. The migration of population from rural areas to urban areas is an important factor driving urban expansion. This type of migration is usually in search of better employment opportunities and living conditions. The construction and improvement of infrastructure such as transportation, energy, and communication can promote urban expansion, especially in areas where infrastructure can enhance regional accessibility and attractiveness.

The expansion models used for urban development differ significantly, and there are also differences in the expansion characteristics and influencing factors of different cities. The urban construction land area in Beijing expanded by a factor of 0.53 from 1995 to 2020, and its expansion speed and intensity gradually slowed. The overall expansion trend is that the central urban area remains basically unchanged, while the peripheral areas are rapidly expanding, showing rapid growth first and then stabilization, and the urban layout is basically stable. This is related to the fact that Beijing, as the capital, has a great ability to attract talent and funds. Beijing’s economic advantages can attract floating populations and accelerate urban expansion [25]. The distribution of construction land in Beijing is closely related to the distribution of transportation arteries [26], especially the distribution of subway lines, which greatly affects the direction and speed of urban expansion. The impact of the relocation of the municipal government and the construction of Daxing International Airport on Beijing’s urban expansion is smaller than that of the subway line. The integrated development of Beijing–Tianjin–Hebei also has an important impact on the urban expansion of Beijing. The phenomenon of rapid development in Beijing is consistent with the view of Professor Zhou Lian that the faster a city develops, the more inclined it is to expand towards the outskirts of the city. Beijing has a large increase in new population and housing demand, but land supply is tightening and new buildings are on the low side, resulting in an increasing supply–demand gap and leading to a contradiction between population and urban development.

With the continuous development of urban expansion, the boundaries of Beijing have become increasingly complex, tortuous, and unstable. Overall, the center of gravity of Beijing is moving toward the northeast, and the elasticity coefficient of urban expansion is 1.67 times that of a reasonable coefficient. The Beijing Urban Master Plan (2016–2035) proposes to “curb the development of urban sprawl” and proposes a spatial layout orientation of “increasing residential land and housing supply in areas outside the central urban area” [27]. In the future, the spatial layout of Beijing’s construction land will shift outward, and the expansion focus will continue to strengthen the trend of spatial expansion in areas outside the central city [28]. To prevent the excessive dispersion of spatial patterns during outward transfer, optimize the spatial structure of urban land use, and curb the trend of land expansion due to “spreading big cakes”, it is necessary to strengthen the guidance and control of residential land supply locations and strengthen the rational planning of public routes.

Therefore, the spatial dimension plays a crucial role in urban expansion, as it not only affects the physical form of the city, but also influences its economic, social, and environmental development. Therefore, urban planning and management need to comprehensively consider these factors to achieve the sustainable development of the city.

5. Conclusions

The urban construction land area in Beijing expanded by a factor of 0.53 between 1995 and 2020, and its expansion speed and intensity gradually slowed. The overall expansion trend is that the central urban area remains basically unchanged, while the peripheral areas are rapidly expanding, showing a trend of first rapid growth and then stable growth, and the urban layout is basically stable. The urban expansion of Beijing has led to increasingly complex, tortuous, and unstable boundaries. Overall, the center of gravity of Beijing is moving toward the northeast, and the elasticity coefficient of urban expansion is 1.67 times that of a reasonable coefficient. The intensity and direction of urban expansion in Beijing are most significantly related to population mobility.