Spatial and Temporal Changes of Urban Built-Up Area in the Yellow River Basin from Nighttime Light Data

: Nighttime light (NTL) images obtained by the Visible Infrared Imaging Radiometer (VIIRS) mounted on the National Polar-orbiting Partnership (NPP) could objectively represent human activities and instantly identify urban shapes on a temporal and spatial scale. From 2013 to 2020, the built-up areas of eight provincial capital cities were extracted using NPP/VIIRS NTL data to examine the dynamic changes in city expansion and socioeconomic development in the Yellow River Basin during the urbanization process. The spatial characteristics of urban built-up area expansion were generated using the eight-quadrant analysis method and combined with the statistical data of population and (gross domestic product) GDP to analyze the correlations between the light intensity of built-up areas, population and GDP; this enables an understanding of the changes in population and economy in the development of urban built-up area expansion. The ﬁndings show that: (1) unbalanced city development existed in the Yellow River Basin’s upper, middle, and lower reaches, and the expansion and light intensity of cities in the upper reaches were slower than those in the middle and lower reaches; (2) the spatial differentiation of urban expansion was signiﬁcant between each of the reaches in the Yellow River Basin, and greatly inﬂuenced by natural geographical elements; and (3) positive correlation exists between light intensity, population, and GDP in the built-up areas of the middle and lower reaches, while the correlations in the upper reaches were not stable. In conclusion, light data indirectly reﬂects urban development and could be used as a substitute variable for socioeconomic development indicators under certain conditions.


Introduction
China's rapid growth and the regular flow of domestic socioeconomic and population factors have accelerated the urbanization process in the Yellow River Basin in recent years [1,2]. However, it has also brought increasing pressure and challenges to the protection of the ecological environment [2]. The natural ecological land around cities and towns has been encroached upon by humans as a result of the continual expansion of urban land exacerbating the land shortage. This situation will cause the degradation of the ecological environment, resource shortages, the pollution of soil, air, and water, and other problems [3][4][5]. In 2019, "ecological protection and high-quality development in the Yellow River Basin" was incorporated into the national strategy by the government for regional coordination [6]. This national strategy was designed to reduce the ecological conflict between urbanization and natural space; also to explore the ecological priority and green development to promote green urbanization and ecological protection in the Yellow River Basin [4]. Therefore, clarifying the relationship between the characteristics of spatial and temporal changes throughout the urban expansion and socioeconomic, demographic, and physical geographical environment is thus critical for the future qualitative development of cities of Yellow River Basin [1,7].
The emergence of Remote Sensing information technology has made it possible to monitor the built-up area change accurately and rapidly for estimating the urbanization process. Remote sensing data in the form of nighttime light (NTL) provide a consistent and independent measurement of urban built-up areas [8]. The NTL images are formed by detected light radiation induced by human activities on the earth's surface, and they can directly reflect artificial surface regions and locations with significant human activity [9,10]. The most often utilized long-term NTL data sources in recent years have been Defense Meteorological Satellite Program/Operational Linescan System (DMSP/OLS) data and Visible Infrared Imaging Radiometer Suite with National Polar-orbiting Partnership (VIIRS/NPP) data. Since the DMSP/OLS nighttime light images were no longer updated after 2013, NPP/VIIRS images with higher spatial resolution have been the most extensively used [11], and many researchers have demonstrated that NPP/VIIRS data have higher spatial accuracies than DMSP/OLS data for extracting built-up urban areas [12]. The study areas and application fields of remotely sensed NTL data, which are extremely objective and convenient, have substantially increased with the increasing number of data products [13][14][15]. NTL data have been found to have a widespread application in sectors such as urban expansion [9,16,17], social economy, and demographic data modeling and spatialization [18,19].
NTL data are targeted and may be utilized for rapid identification of urban forms and extraction of urban boundaries at spatial and temporal scales, as well as a complete analysis of urban spatial forms and expansion in urban development [20][21][22]. The extraction results of urban built-up regions have become more accurate as the application of NTL data in urban expansion and spatial structure analysis has matured [23]. At present, the threshold approach [23], mutation detection method [24], and spatial comparison method based on auxiliary information [15] are the most commonly used methods for extracting urban spatial patterns. For example, Milesi et al. [13] employed land use classification data to estimate DN thresholds of NTL images, from which urban boundary areas in the southeastern United States were extracted. Su et al. [15] have also demonstrated the applicability of NTL data for extracting the built-up regions in the Pearl River Delta with four periods of DMSP/OLS data between 1996 and 2005. Zheng et al. [9] have incorporated temporal information from the VIIRS time series and produced monthly maps of built-up areas of 30 global megacities to disentangle urban land changes into five categories.
Furthermore, except for the boundary change detection of urban expansion, NTL data has also been utilized to monitor the socioeconomic and human activities as a result of urban expansion [25]. Valuable studies have shown that NTL data have a positive relationship with socioeconomic development indicators such as population, gross national product (GNP), and gross domestic product (GDP) [26,27]. With the help of that good correlation, traditional population and GDP statistics data based on administrative districts can be spatialized to more intuitively depict the scale and distribution characteristics of both, which is useful for fine management and information-based city construction, as well as a better study of regional sustainable development [28,29]. However, some researchers have demonstrated that the use of light intensity in urban expansion and socioeconomic development should be implemented with limited or specific conditions, because of the unstable relationship between light intensity and socioeconomic development factors in different regions [30]. Therefore, this relationship should be reanalyzed in the upper, middle, and lower reaches of the Yellow River Basin that have a regional disparity in economic development.
Due to the sufficient satellite imagery data of long-time series NTL data and a lack of computing resources, the urban expansion detection methods and algorithms have not been applied in practice at a large scale. The Google Earth Engine (GEE) cloud platform is an integrated platform for remote sensing and geographic information data processing [31]; it centralizes cloud computing services for data analysis and consists of petabytes of geospatial data, including full NTL archive data and algorithms for image processing with a JavaScript, Python-based API [32,33]. In this paper, we transferred the annual NPP-VIIRS NTL satellite images from the GEE platform with JavaScript as the data source to analyze the evolution of urban expansion of provincial capitals in the Yellow River Basin. The range of built-up areas of provincial capitals from 2013 to 2020 was obtained by using the OTSU algorithm from NTL images. The quadrant analysis method was used to examine the geographical and temporal change characteristics of provincial capital urban expansion. The aspects of socio-economic development in the urban expansion were addressed, taking into account indices such as population and GDP.

Study Area
The Yellow River rises in the central Qinghai Province and flows through nine provinces (Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shaanxi, Shanxi, Henan, and Shandong) before joining the Bohai Sea near Kenli County and Dongying City ( Figure 1). The mainstream of the Yellow River stretches over 5734 km, with a 4480 m elevation reduction between west and east. The Yellow River Basin is approximately 1900 km long from west to east and around 1100 km wide from north to south, with a watershed area of 795,000 km 2 . The huge Yellow River Basin is high in the west and low in the east, with large height disparities along the west-east direction, noticeable climate change, and significant regional seasonal differences within the watershed. Annual precipitation in the basin decreases from southeast to northwest and is distributed relatively irregularly throughout the year. The Yellow River Basin stretches across three major economic zones in eastern, central, and western China, and the 69 cities within it differ substantially in terms of economic growth. The provincial capitals in the Yellow River Basin are regional political and economic centers, and their economic and social development is highly indicative of, and has a radiating influence on, the provinces' regional economic and social development. As a result, this study considered eight provincial capitals (except Chengdu) in the basin for analysis (Table 1) and used the NPP/VIIRS night-light photos from 2013 to 2020 to analyze the pattern changes in the built-up areas of each province's capital city.
Land 2022, 11, x FOR PEER REVIEW 3 of 15 been applied in practice at a large scale. The Google Earth Engine (GEE) cloud platform is an integrated platform for remote sensing and geographic information data processing [31]; it centralizes cloud computing services for data analysis and consists of petabytes of geospatial data, including full NTL archive data and algorithms for image processing with a JavaScript, Python-based API [32,33]. In this paper, we transferred the annual NPP-VIIRS NTL satellite images from the GEE platform with JavaScript as the data source to analyze the evolution of urban expansion of provincial capitals in the Yellow River Basin. The range of built-up areas of provincial capitals from 2013 to 2020 was obtained by using the OTSU algorithm from NTL images. The quadrant analysis method was used to examine the geographical and temporal change characteristics of provincial capital urban expansion. The aspects of socio-economic development in the urban expansion were addressed, taking into account indices such as population and GDP.

Study Area
The Yellow River rises in the central Qinghai Province and flows through nine provinces (Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shaanxi, Shanxi, Henan, and Shandong) before joining the Bohai Sea near Kenli County and Dongying City ( Figure 1). The mainstream of the Yellow River stretches over 5734 km, with a 4480 m elevation reduction between west and east. The Yellow River Basin is approximately 1900 km long from west to east and around 1100 km wide from north to south, with a watershed area of 795,000 km 2 . The huge Yellow River Basin is high in the west and low in the east, with large height disparities along the west-east direction, noticeable climate change, and significant regional seasonal differences within the watershed. Annual precipitation in the basin decreases from southeast to northwest and is distributed relatively irregularly throughout the year. The Yellow River Basin stretches across three major economic zones in eastern, central, and western China, and the 69 cities within it differ substantially in terms of economic growth. The provincial capitals in the Yellow River Basin are regional political and economic centers, and their economic and social development is highly indicative of, and has a radiating influence on, the provinces' regional economic and social development. As a result, this study considered eight provincial capitals (except Chengdu) in the basin for analysis (Table 1) and used the NPP/VIIRS night-light photos from 2013 to 2020 to analyze the pattern changes in the built-up areas of each province's capital city.

NPP/VIIRS NTL Remote Sensing Images
The VIIRS is an essential sensor operated by the National Polar-orbiting Partnership satellite (Suomi NPP). The NPP satellite sensor has a 3000 km sweep width, traverses the equator every four hours, and has a spatial resolution of around 500 m in nW-cm −2 -sr −1 . Because the VIIRS Day/Night Band has a powerful nighttime weak light detection capacity and can identify faint surface lights, it is extremely useful for monitoring the earth's surface brightness at night. The brightness values in NPP/VIIRS photos are used to quantify light intensity, and the NTL data obtained comprised annual and monthly composite images, with radiance values less than 0 indicating no light. In this study, we apply the mean composite approach to generate the annual composite NTL image using monthly NPP/VIIRS composite NTL data from 2013 to 2020. The light intensity images of the administrative boundaries of each city were masked by light intensity thresholds and exported to extract the built-up boundaries. Figure 2 shows an example of the light intensity of the built-up area of Zhengzhou from 2013 to 2020.

Basic Data
The validation data for extracting the urban built-up area boundary came from the land use/cover data set's artificial surface and impermeable layer. The land use/cover data for the Yellow River Basin in 2015 and 2017 were obtained from Prof. Gong Peng of Tsing-

The Validation Data of Land Use
The validation data for extracting the urban built-up area boundary came from the land use/cover data set's artificial surface and impermeable layer. The land use/cover data for the Yellow River Basin in 2015 and 2017 were obtained from Prof. Gong Peng of Tsinghua University's GlobeLand30 dataset FROM-GLC (http://data.ess.tsinghua.edu.cn/, accessed on 13 May 2021) [34]. The Yellow River Basin land use classification in 2020 was derived from GlobleLand30 land cover classification data (http://www.globallandcover.com/, accessed on 27 May 2020) [35]. Because the urban built-up area is mostly made up of artificial surfaces like buildings, streets, and impervious layers, the impervious layer data from the 2015 and 2017 FROM-GLC datasets, as well as the artificial surface data from the 2020 GlobleLand30 V2020 surface cover type, were extracted as validation data to validate the built-up area boundary results.

Socioeconomic Statistics
GDP and population of the urban areas of the Yellow River Basin's capital cities were utilized as statistical indicators of socioeconomic development, and data were acquired from each city's statistical yearbooks from 2014 to 2020. Given the data delay in statistical yearbooks, where the data issued in a given year are the statistics from the previous year, the provinces' statistical yearbooks for 2021 have yet to be produced. As a result, statistical data from 2013 to 2019 were used to examine the relationship between socioeconomic development indicators and urban expansion characteristics.

Light Threshold Extraction Using OTSU Thresholding Technique
To classify the NTL data, the threshold segmentation technique was employed for urban built-up area boundary extraction. NTL pixels that are greater than the given light threshold are classified as built-up areas, whereas NTL pixels that are lower than the light threshold are classified as unbuilt-up areas. The OTSU algorithm was utilized for threshold segmentation, which can be easily updated and employed in GEE to obtain light thresholds for urban boundary extraction.
The OTSU algorithm is used to calculate the following: if an image comprises N pixels, the grayscale value range is [0, L − 1], the number of grayscale pixels i is n i , and the probability of occurrence of each grayscale pixel is P i , then: P i = n i /N, so that t takes values in the interval [0, L − 1] and the t corresponding to maximum δ 2 t is the optimal threshold to separate the two classes of pixels [36].

Quadrant Analysis
The quadrant analysis method was used to analyze the spatial differentiation of cities in the Yellow River Basin, starting with the geometric center of the extracted urban built-up area and dividing the built-up area into 8 quadrants (N, EN, E, ES, S, WS, W, and WN) for statistics of light intensity, slop, and urban expansion area, etc. in each quadrant, and then the spatial expansion differences between cities in different periods, different directions and different elements were compared and analyzed to reflect the dominant direction and driving factors of the spatial and temporal changes of urban expansion.

Analysis of Urban Spatial Expansion
Urban spatial expansion is characterized by urban land expansion, the rate of expansion and the intensity of expansion are the characteristics of urban spatial expansion.
The expansion rate is the average yearly growth rate of an urban area during a given period, reflecting the absolute difference in the urban area's expansion speed per unit time. The calculating formula is: where V is the expansion rate; ∆U is the urban expansion area; ∆t is the time span. The expansion intensity N is the annual expansion ratio of the built-up area in a certain period relative to the built-up area in the baseline year, which represents the relative difference in the built-up area's expansion speed throughout that time horizon.
where N is the intensity of urban expansion and M is the built-up area in the baseline year.

Evaluation of the Accuracy of Urban Built-Up Area Extraction
The mean value approach was utilized in GEE to generate annual composite NTL images from 2013 to 2020, and the OTSU algorithm was used to compute light thresholds for built-up regions in cities in the Yellow River Basin in different years. Because of the Yellow River Basin's large spatial span, the light characteristics of different regions in different years are affected differently by climate and human activity images, so the light thresholds of urban built-up areas were calculated by region and year to extract the urban built-up area boundaries. The NTL results of the built-up region of each provincial capital city derived using the OTSU technique were validated using impervious layer and man-made surface data (LUCC) from ground cover categorization data from 2015, 2017, and 2020 ( Figure 3). The NTL extraction results correlate well with the LUCC data, with R values larger than 0.8. The results show that the built-up areas retrieved in the GEE using the OTSU algorithm are highly accurate and may be used to study the expansion pattern of urban built-up regions.

Temporal Characteristics of Urban Built-Up Area Expansion in the Yellow River Basin
The built-up areas of cities from 2014 to 2020 were superimposed onto the built-up areas in 2013, and the quadrant analysis method was used to divide the built-up areas of provincial capitals into equal sectors to objectively reflect the dynamic change characteristics of urban built-up area expansion in the Yellow River Basin (Figure 4). From 2013 to 2020, the built-up areas of cities in the upper, middle, and lower parts of the Yellow River

Temporal Characteristics of Urban Built-Up Area Expansion in the Yellow River Basin
The built-up areas of cities from 2014 to 2020 were superimposed onto the built-up areas in 2013, and the quadrant analysis method was used to divide the built-up areas of provincial capitals into equal sectors to objectively reflect the dynamic change characteristics of urban built-up area expansion in the Yellow River Basin (Figure 4). From 2013 to 2020, the built-up areas of cities in the upper, middle, and lower parts of the Yellow River Basin increased yearly and expanded outward surrounding each city's historic urban centers, resulting in varied spatial form features of built-up areas ( Table 2). The built-up area, AREA, and expansion rate V of cities in the upper Yellow River Basin (Lanzhou, Hohhot, Xining, and Yinchuan) are significantly smaller than those of cities in the middle and lower Yellow River Basins (Xi'an, Zhengzhou, Taiyuan, and Jinan), but among the upper river basin cities as Yinchuan and Xining outperform the middle river cities as Zhengzhou and Xi'an. Lanzhou, an important central city in Gansu Province, has a decreasing rate of urban built-up area increase. Jinan, the final major city downstream of the Yellow River Basin, has the highest expansion rate V and expansion intensity N of any city, at 28.95% and 9.31%, respectively.

Spatial Expansion Characteristics of Urban Built-Up Areas
From 2013 to 2020, the built-up area in eight directions was evaluated to show the expansion direction of different cities' built-up areas ( Figure 5). During the period 2013-2020, the urban area of Xining expanded primarily westwards and southwestwards around the east-west axis; the urban area of Lanzhou did not expand significantly during this period; the urban area of Yinchuan expanded northwards and westwards around the "southeastnorthwest" axis; the urban area of Hohhot expanded noticeably in the northeast direction; the urban area of Taiyuan expanded significantly southwards and southwestwards mainly around the "east-west" axis, with a slight change in the built-up area in the northern area; Xi'an expanded on both sides of the "northwest-southeast" axis, with the largest expansion in the northeast and west directions; the built-up area of Jinan expanded mainly in the east and northeast regions, with a slow expansion in the southwest; the built-up area of Zhengzhou expanded outwards in a "pancake" pattern, with a larger area growth in the northwest and southeast directions.

Light Intensity Changes in Urban Built-Up Area Expansion
The capital cities of the Yellow River Basin are located along the upper, middle, and lower reaches of the river, with the built-up area steadily increasing from the upper to the lower reaches. Average nighttime light intensity (ANTL) and total nighttime light intensity (TNTL) data from urban built-up areas were divided into quadrants by upstream, middle, and downstream; they were studied to determine their correlation with urban

Light Intensity Changes in Urban Built-Up Area Expansion
The capital cities of the Yellow River Basin are located along the upper, middle, and lower reaches of the river, with the built-up area steadily increasing from the upper to the lower reaches. Average nighttime light intensity (ANTL) and total nighttime light intensity (TNTL) data from urban built-up areas were divided into quadrants by upstream, middle, and downstream; they were studied to determine their correlation with urban built-up areas. The TNTL and the built-up area (AREA) had a significant positive correlation, with a correlation coefficient R = 0.902 ( Figure 6). The ANTL was also positively correlated with AREA, but the correlation was weaker, with a correlation coefficient R of only 0.185. built-up areas. The TNTL and the built-up area (AREA) had a significant positive correlation, with a correlation coefficient R = 0.902 ( Figure 6). The ANTL was also positively correlated with AREA, but the correlation was weaker, with a correlation coefficient R of only 0.185. The majority of built-up areas in the Yellow River Basin are in the middle and lower reaches, which likewise have higher overall light intensity; the places with the lowest total light intensity are generally found upstream. The built-up areas of cities in the upper, medium, and lower reaches revealed a lesser variation in terms of average light intensity. The greater the city's built-up area, the greater its ability to accommodate the population, and with the increase in population, the corresponding total light intensity is relatively high overall; however, due to the spatial distribution characteristics of the population and urban lights, the average light intensity per unit area of the built-up area is not closely correlated to the actual size of the built-up area.

Correlation between Urban Light Intensity and Human Activities
Urban expansion is represented not only in an increase in an urban area but also in an increase in the intensity of human activity in the cities. Changes in the intensity of human activity can be seen indirectly in socioeconomic parameters such as population and GDP. As a result, the correlation between urban light intensity (TNTL and ANTL) and socioeconomic indicators closely related to human activities, such as population and GDP in the Yellow River Basin, was examined to reflect the intensity of human activity and socioeconomic variations in each city's built-up areas during urban expansion.
From 2013 to 2019, the TNTL in built-up areas of cities in the Yellow River Basin showed a significant positive correlation with both GDP and population (Table 3), with the correlation between TNTL and population (R = 0.8586) being higher than the correlation between TNTL and GDP (R = 0.7338). The average light intensity ANTL was not connected with GDP or population in general (R < 0.001), but the ANTL of built-up regions of cities in various geographical areas was considerably and positively correlated with GDP and population, particularly in cities in the middle and lower reaches. The light intensity had a correlation coefficient of around 0.9 with both GDP and population in Jinan's built-up area, whereas in Hohhot, the correlation coefficient R between light intensity and GDP was less than 0.2, but the correlation coefficient R between light intensity and the population was close to 0.9. The light intensity in the built-up region of Lanzhou is nega- The majority of built-up areas in the Yellow River Basin are in the middle and lower reaches, which likewise have higher overall light intensity; the places with the lowest total light intensity are generally found upstream. The built-up areas of cities in the upper, medium, and lower reaches revealed a lesser variation in terms of average light intensity. The greater the city's built-up area, the greater its ability to accommodate the population, and with the increase in population, the corresponding total light intensity is relatively high overall; however, due to the spatial distribution characteristics of the population and urban lights, the average light intensity per unit area of the built-up area is not closely correlated to the actual size of the built-up area.

Correlation between Urban Light Intensity and Human Activities
Urban expansion is represented not only in an increase in an urban area but also in an increase in the intensity of human activity in the cities. Changes in the intensity of human activity can be seen indirectly in socioeconomic parameters such as population and GDP. As a result, the correlation between urban light intensity (TNTL and ANTL) and socioeconomic indicators closely related to human activities, such as population and GDP in the Yellow River Basin, was examined to reflect the intensity of human activity and socioeconomic variations in each city's built-up areas during urban expansion.
From 2013 to 2019, the TNTL in built-up areas of cities in the Yellow River Basin showed a significant positive correlation with both GDP and population (Table 3), with the correlation between TNTL and population (R = 0.8586) being higher than the correlation between TNTL and GDP (R = 0.7338). The average light intensity ANTL was not connected with GDP or population in general (R < 0.001), but the ANTL of built-up regions of cities in various geographical areas was considerably and positively correlated with GDP and population, particularly in cities in the middle and lower reaches. The light intensity had a correlation coefficient of around 0.9 with both GDP and population in Jinan's built-up area, whereas in Hohhot, the correlation coefficient R between light intensity and GDP was less than 0.2, but the correlation coefficient R between light intensity and the population was close to 0.9. The light intensity in the built-up region of Lanzhou is negatively correlated with GDP and population among the major cities in the entire Yellow River Basin. This demonstrates that the correlations between light intensity (TNTL and ANTL) and GDP and population in various Yellow River Basin cities are not consistent.

Correlation between NTL and Human Activities in Urban Expansion
Many studies have found significant correlations between light intensity values influenced by NTL and social and economic indicators, and the use of NTL data allows spatialization of socioeconomic factors such as urban population and GDP to investigate the characteristics of uneven socioeconomic development at the regional scale [27,[37][38][39]. The correlation analysis of light intensity and GDP and population of cities in the Yellow River Basin from 2013 to 2019 revealed that the correlation between NTL data and socioeconomic activity indicators differs by area, which is consistent with the previous study [40]. The more economically developed intermediate and downstream cities have greater commercial economic vitality and mature commercial spatial structures in built-up areas, demonstrating a stronger association between light intensity and human activities and social economy. Because the distribution of commercial spatial structure and service capacity within the metropolitan area of Jinan is the best among Yellow River Basin capital cities [41], the light intensity has a high and significant correlation with human activities and social economy in Jinan. In upstream, less economically developed cities, the correlation coefficients between light intensity and GDP and population are lower than that in middle and downstream cities.
Lanzhou, one of the upstream cities in the Yellow River Basin, had a negative relationship between light intensity and GDP, and population. Lanzhou's GDP and population increased from 2013 to 2019, yet the light intensity of the built-up region fell during the same period (Figure 7). Lanzhou's total light intensity has significantly fallen since 2014, and the maximum light intensity (MAXTL) in the built-up region has similarly shown a decreasing trend since 2013. According to an investigation, the train station is the geographic location with the highest light intensity in the built-up area. Lanzhou statistics from 2013 to 2019 demonstrate that the city's social economy was transitioning from conventional energy-consuming industries to high-tech businesses. In Lanzhou, the added value of high energy-consuming businesses such as thermal power generation, petroleum industry, and petrochemical industry was gradually dropping, while investment in fields such as the electronics industry was gradually expanding. As a result, the nighttime light intensity in Lanzhou gradually decreased over five years. Thus, despite deviations from national statistical results, estimation results of socioeconomic indicators using NTL data can still be used as an observed variable to analyze socioeconomic progress under particular conditions [42][43][44].
value of high energy-consuming businesses such as thermal power generation, petroleum industry, and petrochemical industry was gradually dropping, while investment in fields such as the electronics industry was gradually expanding. As a result, the nighttime light intensity in Lanzhou gradually decreased over five years. Thus, despite deviations from national statistical results, estimation results of socioeconomic indicators using NTL data can still be used as an observed variable to analyze socioeconomic progress under particular conditions [42][43][44].

Natural Factor Constraints in the Urban Expansion of the Yellow River Basin
The natural geographical factors around the city not only provide the initial conditions for the formation and development but also play a restricting role in urban expansion. The Yellow River Basin comprises a broad west-east swath and the number of provincial capital cities diminishes from upstream to downstream, with elevation decreasing from 2237 m to 68 m [2]. Diverse spatial differentiation features were shaped throughout urban expansion as a result of the different geographical factors of each metropolis. The basin's urban built-up area is inversely correlated to elevation and slope, with correlation coefficients of −0.5501 and −0.3515, respectively. Although the cities expand outwards in different directions, they all have one thing in common: they all expand gradually outwards along with gently sloping regions. As a result, among the geographical elements, landform is a key factor restricting urban expansion [45,46].
The majority of the cities in the upper parts of the Yellow River Basin are located at higher altitudes (Table 1) and are surrounded by mountains; among them, Lanzhou and Xining have the highest altitudes and are more obviously influenced by topographical factors. The growth of GDP and the increase in urban population would undoubtedly cause the outward expansion of urban built-up regions in the process of socioeconomic development of cities; changing the terrain to allow human habitation will considerably increase the cost of urban expansion. As a result, cities in the Yellow River Basin's upper reaches, which are more constrained by natural geographical elements, are less developed and expanded than those in the middle and lower reaches.

Conclusions
(1) The Yellow River Basin's NTL data can objectively depict the spatial and temporal dynamics of urban expansion in the basin. From 2013 to 2020, the built-up area of each province's capital city in the Yellow River Basin steadily rose from upstream to

Natural Factor Constraints in the Urban Expansion of the Yellow River Basin
The natural geographical factors around the city not only provide the initial conditions for the formation and development but also play a restricting role in urban expansion. The Yellow River Basin comprises a broad west-east swath and the number of provincial capital cities diminishes from upstream to downstream, with elevation decreasing from 2237 m to 68 m [2]. Diverse spatial differentiation features were shaped throughout urban expansion as a result of the different geographical factors of each metropolis. The basin's urban built-up area is inversely correlated to elevation and slope, with correlation coefficients of −0.5501 and −0.3515, respectively. Although the cities expand outwards in different directions, they all have one thing in common: they all expand gradually outwards along with gently sloping regions. As a result, among the geographical elements, landform is a key factor restricting urban expansion [45,46].
The majority of the cities in the upper parts of the Yellow River Basin are located at higher altitudes (Table 1) and are surrounded by mountains; among them, Lanzhou and Xining have the highest altitudes and are more obviously influenced by topographical factors. The growth of GDP and the increase in urban population would undoubtedly cause the outward expansion of urban built-up regions in the process of socioeconomic development of cities; changing the terrain to allow human habitation will considerably increase the cost of urban expansion. As a result, cities in the Yellow River Basin's upper reaches, which are more constrained by natural geographical elements, are less developed and expanded than those in the middle and lower reaches.

Conclusions
(1) The Yellow River Basin's NTL data can objectively depict the spatial and temporal dynamics of urban expansion in the basin. From 2013 to 2020, the built-up area of each province's capital city in the Yellow River Basin steadily rose from upstream to downstream, with an increasing tendency over time. The cities in the upstream, middle, and downstream exhibit imbalanced urban development, with the upstream cities having a smaller urban expansion area, expansion rate, and intensity than the middle and downstream cities. The natural geographical factors surrounding cities have a spatial influence on the urban expansion process, and each city's expansion has distinct spatial differentiation characteristics. (2) During the urbanization process, more developed middle and downstream cities have a significant positive correlation between light intensity, GDP, and population. The relationship between light intensity and GDP and population is weaker in upstream cities. During the development of cities in the Yellow River Basin's middle and lower reaches, their built-up areas shaped a well-developed commercial economic structure and a high degree of coordination with the spatial pattern of human flow distribution, and light data can well demonstrate GDP and population development changes. The cities in the upper Yellow River Basin are constrained by their natural geographical environment; their urban development is slower than that of the cities in the middle and lower reaches, and the commercial structure within the cities must be adjusted to promote urban economic development and to accommodate population growth caused by urban development. Institutional Review Board Statement: Not applicable.