“Matthew Effect” in Global Major Cities Over Decades: In the context of the spatiotemporal 3D urban expansion

“Matthew Effect” in Global Major Cities Over Decades: In the context of the spatiotemporal 3D urban expansion | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article “Matthew Effect” in Global Major Cities Over Decades: In the context of the spatiotemporal 3D urban expansion Wu Xiao, He Tingting, Kechao Wang, Yihua Hu, Runjia Yang, Maoxin Zhang, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4653734/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Urbanization has surged over the past decades. Global major cities’ land urbanization and population urbanization have intensifying pressures on urban climate, public health, and energy consumption. A favorable vision for assessing urban habitats’ living conditions necessitates recognizing the evolution and current status of major global cities’ three-dimensional structure and spatiotemporal trajectories. However, a lack of high-resolution, long-term data hinders obtaining metrics reflecting living conditions. This study addresses this gap by generating a 30-meter resolution spatiotemporal three-dimensional urban expansion dataset for 2071 global major cities (1990–2020). Integrated with socioeconomic data, it reveals adherence to Zipf's Law, reflecting pronounced unequal development and a global-scale Matthew effect. Most cities fell within the 0–1 km³ volume range, with 12 cities and 41 cities’ volume > 9 km³ in 1990 and 2020, respectively. About two-thirds of major cities experienced building expansion rates exceeding population growth rates between 2000 and 2020. Per capita building volume correlates with the GDP. Africa is the only continent to witness a decline in per capita building volume over the past 20 years, indicating a further decline in the living conditions of urban residents. Focusing on internal building structures, an inequality index characterizes height diversity within cities. Asian cities exhibit the highest global inequality index, marked by supertall building additions. This study not only compares major cities' overall size and growth patterns in three dimensions but also analyzes the distribution of building heights within each city in detail. The findings contribute to identifying and addressing urbanization challenges, supporting habitat environmental assessments, and measuring progress toward sustainable goals. Scientific community and society/Social sciences Scientific community and society/Developing world Earth and environmental sciences/Environmental social sciences/Sustainability Earth and environmental sciences/Environmental social sciences Urban 3D expansion Matthew Effect Building height Inequality Spatiotemporal Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction Over the past century, global urbanization processes have thrived. Despite urban areas accounting for merely 3% of the Earth's land, they accommodate over half of the world's population (Nations, 2018 ). By 2030, nearly 60% of the global population is expected to reside in urban regions. Rapid urbanization has exerted significant pressure on urban climate (Lin et al., 2018 ), public health (Miles et al., 2012 ), energy consumption (Stewart & Oke, 2012 ) and other natural and social conditions, directly or indirectly influencing more than half of the targets outlined in the United Nations Sustainable Development Goals (Zhou et al., 2022 ). Therefore, various sectors, including society, government, and academia, have shown a keen interest in the current state of urbanization, the expansion process, and the per capita infrastructure in cities. Urban expansion encompasses both horizontal sprawl and vertical growth. With three-dimensional urban expansion, cities have become increasingly intricate, manifesting complexity in horizontal and vertical configurations (Li et al., 2020 ). Therefore, comprehending the current state of urbanization, especially finely depicting the temporal development of cities in three-dimensional space, is crucial for formulating more effective urban planning and management strategies. Existing global-scale studies predominantly describe urban expansion processes from a two-dimensional perspective (Gong et al., 2020 ; Leyk et al., 2019 ; Li, Verburg et al., 2022 ; Sun et al., 2020 ; Zhao et al., 2022 ). Few three-dimensional studies are often confined to specific time points using building height data (Esch et al., 2022 ; Li, Wang et al., 2022 ; Zhou et al., 2022 ). Due to challenges in obtaining high-resolution urban building height data, global-scale three-dimensional urban studies typically resort to coarse resolutions like 1 km (Li, Wang et al., 2022 ) or 500 m (Zhou et al., 2022 ), introducing inevitable errors during resampling. This hampers the precise data analysis, such as per capita building volume, crucial for accurately depicting residents' living standards. To better depict urbanization stages and capture challenges in different regions worldwide, this study derived a spatiotemporal three-dimensional urban expansion dataset for 2071 major cities (built-up areas exceeding 50 km 2 ) globally, with a resolution of 30-meter, spanning from 1990 to 2020, utilizing open-source remote sensing data on Google Earth Engine (GEE) platform. Moreover, by integrating socioeconomic data such as population and GDP, we discovered that the scale of major global cities adheres to Zipf's Law (Sun et al., 2020 ), experiencing significant unequal development over the past few decades and exhibiting a pronounced Matthew effect on a global scale. This study not only macroscopically compares the three-dimensional scale and developmental trajectories of cities in different stages of global urbanization, but also microscopically analyzes the uneven distribution of building heights within each city. It provides a foundation for identifying and addressing urbanization issues, supporting habitat environmental assessments, and measuring progress towards sustainable goals. 2. Results 2.1 Urban volume distribution and temporal expansion from 1990 to 2020 Between 1990 and 2020, 2,071 urban areas with a built-up area exceeding 50 km² were identified globally. The distribution of the scale of major global cities aligns with Zipf's law, which is characterized by a concentration of large cities alongside numerous smaller ones. The correlation between the built-up area and volume of these major cities in 1990 and 2020 and their spatial distribution is illustrated in Figs. 1 (a) and 1(b). At both time points, cities were categorized into four volume intervals (0–1, 1–2, 2–9, > 9 km³). The majority of cities fell within the 0–1 km³ volume range. In 1990, 1,849 cities (89.3% of the total 2,071) had volumes in this range, decreasing to 1,548 cities (74.7%) in 2020. Correspondingly, cities with volumes in the 1–2 km³, 2–9 km³, and > 9 km³ ranges increased from 118, 92, and 12 in 1990 to 240, 206, and 41 in 2020, respectively. As the scale increases, the number of cities rapidly decreases, with cities > 9 km³ accounting for only 0.58% and 1.98% in 1990 and 2020, respectively. In 1990, the ten cities with the largest volumes were Los Angeles (38.53 km³), Tokyo (21.39 km³), Chicago (14.98 km³), Guangdong (14.97 km³), San Francisco (11.74 km³), Beijing (11.37 km³), Osaka (11.35 km³), São Paulo (10.56 km³), New York City (10.55 km³), and Dallas (10.49 km³). Among them, five were in the United States, two in Japan, two in China, and one in Brazil. In 2020, the cities with volumes ranking in the top ten in 1990 increased to 35, with Guangdong (70.03 km³), Los Angeles (47.48 km³), Jiangsu (39.58 km³), Tokyo (37.21 km³), Beijing (30.12 km³), Shanghai (27.20 km³), Chicago (24.88 km³), Osaka (17.64 km³), Dallas (17.32 km³), and Atlanta (16.87 km³) leading the rankings. Four of the top ten cities were in China, with Jiangsu and Shanghai added compared to 1990. Notably, Guangdong's volume surged from 14.97 km³ to 70.03 km³, moving from the fourth to the first position globally, representing the most aggressive volume growth in the world. From a continental perspective, Asia exhibited the largest building volumes, followed by North America and Europe. South America and Africa demonstrated comparable building volumes over the 30 years, while Oceania had the smallest building volumes (Fig. 1 (c)). Asia experienced the fastest growth, from 440.1 km³ in 1990 to 1,246.4 km³ in 2020, a 2.83-fold increase over three decades, witnessing the burst of the developing economics during the period, such as China and India. By 2020, Asia's building volume accounted for approximately 50% of the global total (Fig. 1 (d)). North America, with the second-largest building volume, observed a nearly 10-percentage-point decrease in its share over the 30 years, reflecting a relatively modest three-dimensional expansion in the global urbanization process for developed economics. We investigated the relationship between the volume increment of 2,071 global cities from 2000 to 2020 and their volume stock in 2000. Our findings reveal the manifestation of the Matthew Effect in the physical expansion of urban space. The Matthew Effect refers to the phenomenon of "the rich get richer, and the poor get poorer," wherein entities or individuals with advantages are more likely to acquire additional resources and opportunities in competition, thereby becoming more powerful. Conversely, relatively disadvantaged entities or individuals find it challenging to catch up due to a lack of these advantages, further declining their strength and stature. This study found that cities with larger volumes in 2000 experienced more substantial increments. This positive correlation aligns with the Matthew Effect principles and reflects Zipf's law regarding patch growth, with larger urban patches growing faster (Sun et al., 2020 ). Figure 2 (a) shows that among the 2,071 major cities, only five witnessed a volume expansion exceeding 10 km³ during 2000–2020. Notably, China's supercities – Guangdong (expanding by 32.3 km³), Jiangsu (30.0 km³), Shanghai (16.1 km³), and Beijing (13.9 km³) – dominated the top ranks. These cities also held the largest volume stocks in 2000, as indicated by the count "5" in the upper right corner of Fig. 2 (d), affirming Matthew Effect dynamics. Figure 2 (d) depicts a heatmap illustrating the positive relationship between stock and increment for the 2,071 cities globally, with the majority clustering near the diagonal. Approximately one-third of cities had a volume below 1 km³ in 2010, with an increment below 0.1 km³. This reflects an uneven development pattern in urban growth under the cumulative effects, making urban expansion more challenging for relatively small cities. 2.2 Building expansion surpasses population urbanization in two-thirds of global major cities Urban building volume growth and urban population growth are two characteristics of urbanization. Both dynamic changes follow the Matthew Effect, where cities with larger volumes can undergo larger-scale urban expansion and, due to their stronger economic and social attractiveness, experience faster population growth. However, these two processes are not entirely synchronized. We compared the volume expansion and population growth of global major cities (Fig. 3 (a)), calculated the ratio of urban two-dimensional and three-dimensional expansion rates to population growth rates (Fig. 3 (b)(c)(d)), and horizontally compared the changes in per capita building volume and area among major cities on six continents (Fig. 3 (e) (f)). From both a two-dimensional and three-dimensional view, about two-thirds of major cities experienced building expansion rates exceeding population growth rates between 2000 and 2020 (R ep ≥1) (Fig. 3 (c)(d)), emphasizing the significance of building urbanization and overpopulation urbanization. Infrastructure development preceded population growth (Li, Verburg, et al., 2022). The categorization of the three-dimensional expansion to population growth ratio (R ep ) into three classes (< 0, 0–1, ≥ 1) revealed spatial patterns. Cities in the eastern United States, western Europe, eastern China, eastern South America, and Australia (red dots in Fig. 3 (b)) demonstrated a predominant three-dimensional expansion, aligning with the largest building volumes globally (Fig. 2 (a)). Conversely, areas like the central-western United States, northern and western Africa, and the Arabian Peninsula had a three-dimensional expansion rate smaller than population growth. Regions with negative population growth were found in eastern Europe, the Middle East, and eastern China. The observed trend indicates that larger cities prioritize building volume expansion over population growth, emphasizing Zipf’s law for physical space over economic and social space represented by population (Li, Verburg et al., 2022 ). As two-thirds of major cities had a building volume expansion rate greater than the population growth rate, most cities experienced increased per capita building volume from 2000–2020 (Fig. 3 (e)). North America has the largest per capita building volume globally, ranking second in Oceania, and Asia rose from the fourth position in 2000 to the third in 2020, surpassing Europe. South America and Africa have the smallest per capita building volumes globally, with little difference between them. Africa is the only continent to experience a decline in per capita building volume over 20 years, indicating that despite significant population growth, infrastructure development in large cities has not kept pace with the process of population urbanization, leading to a further decline in living conditions in these cities. The relative relationship between per capita building area and per capita building volume in two-dimensional and three-dimensional perspectives reflects different levels of building height across continents (Fig. 3 (f)). The situation in Asia and Europe is better in terms of per capita building volume than per capita building area. The latter is very close to South America and Africa, indicating that major cities in Asia and Europe are high-rise cities with higher building heights. At the same time, other continents have low-rise cities, which is also confirmed in Fig. 5 (a). 2.3 Differentiation and variation in per capita building volume Relative to per capita building area, per capita building volume, which considers floor height, more accurately reflects the average infrastructure quantity possessed by residents in a city, thereby providing a more precise indication of the living conditions of urban residents. There is a significant disparity in per capita building volume among the 2,071 major cities globally, with South Asia, Southeast Asia, Africa, and Latin America having the smallest per capita building volumes. In contrast, cities in the eastern United States and Europe in the 50°N-60°N region have the largest per capita building volumes (Fig. 4 (a)). The regions with the greatest per capita building volume growth over the 20 years are eastern and central China and cities in Europe in the 50°N-60°N region (Fig. 4 (b)). Notably, some cities experienced a decrease in per capita building volume over the 20 years, mainly distributed in Africa, the Arabian Peninsula, the central-western United States, Colombia, and Venezuela (Fig. 4 (b)). Combining Fig. 4 (a)(b), cities with larger per capita building volumes also exhibited greater growth over the 20 years, indicating the presence of the Matthew Effect in per capita building volume – the rich become richer, while the weak not only experience minimal growth but may even experience a decline. The per capita GDP of the country in which a city is located can, to some extent, characterize the economic development level of that city. Based on the per capita GDP at the national level in 2019 and using the World Bank classification standards, we categorized global countries into four groups: high-income, upper-middle-income, lower-middle-income, and low-income. On average, major cities in high-income countries have the largest per capita building volume, reaching approximately 2800 km³ per capita, followed by upper-middle-income countries (Fig. 4 (c)). Due to the low number of major cities in low-income countries (only 38, accounting for only 1.8% of the total 2071), the percentiles in Fig. 4 (c) are not the smallest and are slightly larger than those of lower-middle-income countries. On average, major cities in upper-middle-income countries have the largest increment in per capita building volume, reaching around 600 km³ per capita, followed by high-income countries (Fig. 4 (d)). Major cities in upper-middle-income countries are converging towards the level of high-income countries in terms of per capita building volume. Regression analysis further reveals a positive correlation between per capita building volume and per capita GDP (Fig. 4 (e)). Similarly, the increment in per capita building volume positively correlates with the increment in per capita GDP (Fig. 4 (f)). 2.4 Inequality in the internal building heights of global major cities In addition to the disparities in volume among cities and the unequal development of expansion dynamics, our research results also reflect variations in the internal architectural structure of different cities, with a resolution of 30m. We computed an inequality index measuring the degree of spatial inequality in urban built infrastructure proposed by Brelsford et al. (Brelsford et al., 2017 ) and Pandey et al. (Pandey et al., 2022 ). We mapped the spatial distribution of the average building height and the inequality index of building height (Hereinafter referred to as “inequality”) for 2,071 major global cities in 2020 (Fig. 5 (a)). The inequality in China mostly exceeds 0.29, with the average height mostly exceeding 19m, indicating high average building height and significant diversity (large red and orange dots). In contrast, the southern part of Russia is characterized by the highest number of major cities with high and less diverse average building heights (large blue dots). The majority of the United States has moderate building height and moderate diversity (medium-sized yellow dots). The relationship between the change in the inequality of building height within cities from 2000 to 2020 for major global cities is described by the fitted function y = 0.938x + 0.0166 (Fig. 5 (b)). The seven countries with the highest building inequality globally (ranked by median) are China, Kazakhstan, Romania, Ukraine, Germany, Brazil, and Russia. The first four are Asian and Eastern European countries, with substantial gaps and differences in inequality compared to the fifth (Fig. 5 (c)). Among the six continents globally, Asia has the highest inequality, while Oceania has the lowest. According to Fig. 5 (d), in 2000, the median inequality in Asia and Europe was higher than the global median; from 2000 to 2020, Asia's inequality gradually increased, while Europe's decreased. By 2020, only Asia's median was higher than the global median, indicating a growing disparity between Asia and the other five continents in the inequality, with Asia taking the lead. 3. Discussion As hubs for the majority of the population and key economic activities, cities significantly impact more than half of the United Nations Sustainable Development Goals (Thacker et al., 2019 ). The developmental paths and future trajectories of major cities across the globe play a vital role in addressing issues of fairness among nations and cities. The Matthew Effect is evident in the static and dynamic patterns of global major cities, the distribution and growth of population size, and the dynamic development patterns of per capita building volume. This reflects the cumulative effects of stronger entities becoming even more formidable in urban physical and socioeconomic spaces. The scale and living environment of major global cities exhibit extreme imbalance. Over the past two decades, a positive correlation between the expansion of building volume and its existing stock has emerged. This is partly due to larger building volume stocks signifying stronger economic vitality and larger populations, leading to greater synergetic effects and accelerating further expansion. This has resulted in the current distribution where a few large cities coexist with numerous smaller ones. Whether viewed from a two-dimensional or three-dimensional perspective, two-thirds of global major cities’ building volume growth rates have surpassed the population growth rates. This contradicts sustainable development goal 11.3 (Li, Verburg, et al., 2022), which stipulates that the growth rate of construction land should not exceed the population growth rate, posing a significant challenge to sustainable development. From a three-dimensional perspective, we assess the per capita building volume and its dynamic changes in global major cities. This objectively evaluates the spatial occupancy of per capita building resources in major cities, closely linked to habitat environment, resident well-being, and urban sustainability. The per capita building volume is positively correlated with the per capita GDP of the corresponding country. Africa is the only continent to witness a decline in per capita building volume over the past 20 years, indicating that despite significant population growth, infrastructure development in cities has not kept pace with population urbanization, resulting in a further decline in the living conditions of urban residents. Additionally, shifting the focus to the internal building structures of each city, we employ an inequality index to characterize the diversity of building heights within each city. Asian major cities have the highest inequality index globally, with a continuing upward trend, marked by the addition of numerous supertall buildings. This trend is common in countries that have undergone significant urbanization in recent decades (Zhou et al., 2022 ). The inequality in urban building height represents the degree of diversity in building height within the city, unrelated to urbanization and economic development. Developed regions, such as North America, also exhibit an increasing trend in the inequality index. Inequality and inequity are two distinct concepts. Inequality is relatively objective, representing differences in quantity, degree, conditions, and other aspects of an object. On the other hand, inequity is more subjective, emphasizing unfairness or injustice, often focusing on the unethical or unfair distribution of treatment or resources. This study reveals a global pattern of Matthew effect and inequality in large cities' distribution and dynamic development. Influenced by factors such as the accumulation effects, industrial and economic concentration effects, and social network effects, the pattern tends to reinforce the strong and weaken the weak. This phenomenon contradicts the SDG10 goal of “reducing inequality within and among countries.” However, some scholars argue that economic development alone cannot address spatial inequities in infrastructure, as inequality is a characteristic of urbanization (Pandey et al., 2022 ; Zhou et al., 2022 ). In other words, economic development and urbanization inevitably lead to differentiated patterns in the global landscape. Although this inequality is rooted in unfair resource distribution, it is deemed unavoidable. This suggests that advancing global equity requires implementing economic and social intervention measures to redirect resources toward smaller cities. This may entail sacrificing potential economic growth and urbanization rates, necessitating a trade-off between economic growth and promoting fairness (Dong et al., 2023 ). This study investigates the expansion of physical urban space and the corresponding socioeconomic growth indicated by population changes. It addresses the dual aspects of land development and population growth within the context of urbanization, revealing Matthew effects in both forms of urbanization. Notably, two-thirds of major cities, particularly those with substantial volumes, located in the eastern United States, Western Europe, and eastern China, exhibit a building expansion rate that surpasses the population growth rate. This indicates that land urbanization is outpacing population urbanization, possibly due to the marginal cost of physical space expansion being lower for globally prominent cities than the marginal cost of attracting population concentration. In the case of China, the urbanization process in recent decades has witnessed a phenomenon where cities expand horizontally or compete vertically for supremacy. Moreover, national land spatial planning remains dominated by incremental planning. Facing the prospect of peaking and declining population, there is a potential risk of significant urban contraction and the emergence of numerous “ghost cities” (Liu et al., 2023 ; Ruan, Lou, et al., 2022 ). The government should streamline redevelopment efforts by identifying and addressing inefficient land use, shifting from incremental to stock planning (S. Liu et al., 2020 ; Ruan, He et al., 2022 ). This study analyzes results based on our constructed urban three-dimensional expansion dataset, covering major cities globally over a long period (1990–2020). The dataset boasts high precision (as validated in the supplementary materials) and fine granularity (30m resolution within a 10m grid). It is the first globally comprehensive three-dimensional structural dataset with concurrent high resolution, accuracy, and temporal information. The proposed methodology in this study enables efficient, rapid, and real-time prediction of building heights on a global scale for construction land. The well-trained Random Forest (RF) model is applicable worldwide, utilizing open-source and freely accessible data as input. In the future, we aim to extend this method to cover global construction land, including small settlements and rural areas. This approacSh facilitates systematic monitoring of urbanization processes in low-income countries and regions with scarce population and data resources. Such tracking is crucial for achieving United Nations Sustainable Development Goals 8 and 9 (Sun et al., 2020 )。Our fine-grained data at a 30-m spatial resolution, combined with other geographical and socioeconomic data, has extensive potential applications in various domains, including urban climate (Lin et al., 2018 ), urban carbon emissions (Zhang et al., 2022 ), urban transportation and energy consumption (Stewart & Oke, 2012 ; Zhou et al., 2022 ), and public health (Miles et al., 2012 ). 4. Methods This study employed machine learning techniques to construct a global three-dimensional expansion dataset for major cities from 1990 to 2020, and conducted further analysis by integrating socioeconomic data, including population and GDP. In obtaining building heights, we used two datasets as labels for model training, including a global building height dataset from 1990 to 2010 (He et al., 2023 ) and GEDI height data (Potapov et al., 2021 ). We adopted an innovative three-step sampling method, which involves “CCDC detection,” “pixel selection,” and “stratified sampling” to ensures the scientific rigor and reliability of the machine learning model. Various temporally and spatially aggregated remote sensing data sources served as input variables. A Random Forest model was developed to estimate additional building heights for major global cities from 2010 to 2020, resulting in a comprehensive urban three-dimensional expansion dataset covering three decades. 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Sustainable Cities and Society, 78 , 103633. https://doi.org/10.1016/j.scs.2021.103633 Zhao, M., Cheng, C., Zhou, Y., Li, X., Shen, S., & Song, C. (2022). A global dataset of annual urban extents (1992–2020) from harmonized nighttime lights. Earth System Science Data, 14 (2), 517–534. https://doi.org/10.5194/essd-14-517-2022 Zhou, Y., Li, X., Chen, W., Meng, L., Wu, Q., Gong, P., & Seto, K. C. (2022). Satellite mapping of urban built-up heights reveals extreme infrastructure gaps and inequalities in the Global South. Proceedings of the National Academy of Sciences , 119 (46), e2214813119. 2023-11-16. https://doi.org/10.1073/pnas.2214813119 Additional Declarations There is NO Competing Interest. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4653734","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":331303775,"identity":"594b6c3f-44ed-48a7-91d1-3c09cc6fc8b9","order_by":0,"name":"Wu Xiao","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxUlEQVRIiWNgGAWjYDACZjBpw8DYAKR4SNCSRooWCDgMoYjSYnCc+eFj3rbz9swzEhgfvG1jkDcnpEWymc3YmLftNjPjjARmw7ltDIY7Gwho4WdmMJPObbvNBtTCJs3bxpBgcICAFjZm9m9ALed4gFrYfxOlhZ+ZB2TLAQmQLcxEaZFs5ik2/nMu2YCx52Gz5JxzEoYbCGkxOH9848MZZXb2hu3JBz+8KbORJ2gLHBg2gCNTglj1QCBPgtpRMApGwSgYYQAAPIU2hVaaBg4AAAAASUVORK5CYII=","orcid":"","institution":"Zhejiang University","correspondingAuthor":true,"prefix":"","firstName":"Wu","middleName":"","lastName":"Xiao","suffix":""},{"id":331303776,"identity":"9e7505f3-e17f-4f87-8a29-bbb28a2f9570","order_by":1,"name":"He Tingting","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"He","middleName":"","lastName":"Tingting","suffix":""},{"id":331303777,"identity":"95afa512-c13d-46ca-af66-24663d8868bd","order_by":2,"name":"Kechao Wang","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Kechao","middleName":"","lastName":"Wang","suffix":""},{"id":331303778,"identity":"9ad635f9-abe9-4808-a679-7db3a45546e8","order_by":3,"name":"Yihua Hu","email":"","orcid":"","institution":"State key laboratory of pulsed power laser technology","correspondingAuthor":false,"prefix":"","firstName":"Yihua","middleName":"","lastName":"Hu","suffix":""},{"id":331303779,"identity":"a9ef9d74-fbe8-4609-8738-086b569e0dca","order_by":4,"name":"Runjia Yang","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Runjia","middleName":"","lastName":"Yang","suffix":""},{"id":331303780,"identity":"f378171a-bfe8-4da3-8637-62d1cfb1fe0f","order_by":5,"name":"Maoxin Zhang","email":"","orcid":"","institution":"College of Public Administration \u0026 Law, Fujian Agricultural and Forestry University","correspondingAuthor":false,"prefix":"","firstName":"Maoxin","middleName":"","lastName":"Zhang","suffix":""},{"id":331303781,"identity":"ac1972b6-0934-4c05-83f0-16d3ceaee0ba","order_by":6,"name":"Yuwei Chen","email":"","orcid":"","institution":"Advanced Laser Technology Laboratory of Anhui Province","correspondingAuthor":false,"prefix":"","firstName":"Yuwei","middleName":"","lastName":"Chen","suffix":""}],"badges":[],"createdAt":"2024-06-28 09:41:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4653734/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4653734/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":61267844,"identity":"c4749e7f-efb9-40b7-b5b4-1c436a09972f","added_by":"auto","created_at":"2024-07-29 01:00:32","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":6633773,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution and Temporal Expansion of Building Volumes in Global Major Cities from 1990 to 2020. (a)(b) depict the relationships between building area and volume for major cities in 1990 and 2020, respectively, with pie charts illustrating the proportions of cities in different volume ranges. (c) represents the changes in building volumes over the past 30 years for major cities across six continents, and (d) illustrates the percentage changes in building volumes over the past 30 years for major cities across six continents.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-4653734/v1/cd445091c14a4f8a6ccbafb4.png"},{"id":61267845,"identity":"81e70d94-6beb-4fab-a014-709cac310eaf","added_by":"auto","created_at":"2024-07-29 01:00:32","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":4723036,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between Building Volume Stock and Increment in Global Major Cities. (a) Spatial distribution of the relationship between building volume stock in 2000 and volume expansion from 2000 to 2020 for major cities with built-up areas exceeding 50 km² globally. (b) Relationship between building volume stock and increment in major cities in the United States. (c) Relationship between building volume stock and increment in major cities in the eastern region of China. (d) Heatmap illustrating the relationship between building volume in the year 2000 and volume expansion from 2000 to 2020 for global major cities.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-4653734/v1/69c153f33016863651630745.png"},{"id":61268241,"identity":"ab47b7eb-75e7-43b7-b356-b3e88966781f","added_by":"auto","created_at":"2024-07-29 01:08:32","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":12171924,"visible":true,"origin":"","legend":"\u003cp\u003eRelationships between Three-dimensional Expansion and Urban Population Growth in Global Major Cities from 2000 to 2020. (a) Spatial distribution of the coupling relationship between volume growth and population growth in major global cities with built-up areas exceeding 50 km² from 2000 to 2020. (b) The ratio of three-dimensional expansion rate to population growth rate in major global cities over the 20 years. (c) (d) Pie charts depicting the distribution of ratios of two-dimensional expansion rate to population growth rate and three-dimensional expansion rate to population growth rate in major global cities over 20 years, categorized into three intervals. (e) Box plots illustrating per capita building volume across six continents in 2000 and 2020. (f) Box plots showing per capita building area and per capita building volume across six continents in 2020.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-4653734/v1/8418fbead462856873dc7c29.png"},{"id":61267847,"identity":"5662b4b9-7ce3-4b7f-a048-65cfc299f676","added_by":"auto","created_at":"2024-07-29 01:00:32","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":12532273,"visible":true,"origin":"","legend":"\u003cp\u003eGlobal Distribution, Changes, and Relationship between Per Capita Building Volume and Income Levels in Major Cities. (a) Spatial distribution of per capita building volume in major cities with built-up areas exceeding 50 km² in 2020. (b) Spatial distribution of changes in per capita building volume in major cities with built-up areas exceeding 50 km² from 2000 to 2020. (c) Per capita building volume in major cities of countries with different income levels. (d), (e), (f) Heatmaps illustrate the relationship between global per capita building volume in major cities in 2000 and 2020.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-4653734/v1/315cabf9f5fcb056cf542531.png"},{"id":61267843,"identity":"2e9e732e-b993-4d0d-bb96-d0e4257e2d42","added_by":"auto","created_at":"2024-07-29 01:00:32","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":4260994,"visible":true,"origin":"","legend":"\u003cp\u003eInequality in the internal building heights of global major cities. (a) Spatial distribution of the relationship between internal building height inequality and average building height in major cities worldwide with a built-up area exceeding 50 km2 in 2020. (b) Inequality in internal building heights of major cities worldwide in 2000 and 2020. (c) Box plots of the top 7 countries with the highest inequality in building height in 2020. (d) Box plots of building height inequality in major cities across six continents and globally in 2000 and 2020.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-4653734/v1/b9914bfd59f27bc206d5848d.png"},{"id":64209439,"identity":"f454a159-770c-4529-9e42-b18a8d0c47d2","added_by":"auto","created_at":"2024-09-10 06:44:46","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":52767696,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4653734/v1/cd0a65b4-acc0-49fb-bb29-911522342df1.pdf"},{"id":61267848,"identity":"39ff63ac-76e1-4555-ab54-f287796900e9","added_by":"auto","created_at":"2024-07-29 01:00:32","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":1256849,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-4653734/v1/bd7bc44158b65e00c08a58d7.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"“Matthew Effect” in Global Major Cities Over Decades: In the context of the spatiotemporal 3D urban expansion","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eOver the past century, global urbanization processes have thrived. Despite urban areas accounting for merely 3% of the Earth's land, they accommodate over half of the world's population (Nations, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). By 2030, nearly 60% of the global population is expected to reside in urban regions. Rapid urbanization has exerted significant pressure on urban climate (Lin et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), public health (Miles et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), energy consumption (Stewart \u0026amp; Oke, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) and other natural and social conditions, directly or indirectly influencing more than half of the targets outlined in the United Nations Sustainable Development Goals (Zhou et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Therefore, various sectors, including society, government, and academia, have shown a keen interest in the current state of urbanization, the expansion process, and the per capita infrastructure in cities. Urban expansion encompasses both horizontal sprawl and vertical growth. With three-dimensional urban expansion, cities have become increasingly intricate, manifesting complexity in horizontal and vertical configurations (Li et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Therefore, comprehending the current state of urbanization, especially finely depicting the temporal development of cities in three-dimensional space, is crucial for formulating more effective urban planning and management strategies.\u003c/p\u003e \u003cp\u003eExisting global-scale studies predominantly describe urban expansion processes from a two-dimensional perspective (Gong et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Leyk et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Li, Verburg et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Sun et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Zhao et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Few three-dimensional studies are often confined to specific time points using building height data (Esch et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li, Wang et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhou et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Due to challenges in obtaining high-resolution urban building height data, global-scale three-dimensional urban studies typically resort to coarse resolutions like 1 km (Li, Wang et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) or 500 m (Zhou et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), introducing inevitable errors during resampling. This hampers the precise data analysis, such as per capita building volume, crucial for accurately depicting residents' living standards. To better depict urbanization stages and capture challenges in different regions worldwide, this study derived a spatiotemporal three-dimensional urban expansion dataset for 2071 major cities (built-up areas exceeding 50 km\u003csup\u003e2\u003c/sup\u003e) globally, with a resolution of 30-meter, spanning from 1990 to 2020, utilizing open-source remote sensing data on Google Earth Engine (GEE) platform.\u003c/p\u003e \u003cp\u003eMoreover, by integrating socioeconomic data such as population and GDP, we discovered that the scale of major global cities adheres to Zipf's Law (Sun et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), experiencing significant unequal development over the past few decades and exhibiting a pronounced Matthew effect on a global scale. This study not only macroscopically compares the three-dimensional scale and developmental trajectories of cities in different stages of global urbanization, but also microscopically analyzes the uneven distribution of building heights within each city. It provides a foundation for identifying and addressing urbanization issues, supporting habitat environmental assessments, and measuring progress towards sustainable goals.\u003c/p\u003e"},{"header":"2. Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Urban volume distribution and temporal expansion from 1990 to 2020\u003c/h2\u003e \u003cp\u003eBetween 1990 and 2020, 2,071 urban areas with a built-up area exceeding 50 km\u0026sup2; were identified globally. The distribution of the scale of major global cities aligns with Zipf's law, which is characterized by a concentration of large cities alongside numerous smaller ones. The correlation between the built-up area and volume of these major cities in 1990 and 2020 and their spatial distribution is illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a) and 1(b). At both time points, cities were categorized into four volume intervals (0\u0026ndash;1, 1\u0026ndash;2, 2\u0026ndash;9, \u0026gt;\u0026thinsp;9 km\u0026sup3;). The majority of cities fell within the 0\u0026ndash;1 km\u0026sup3; volume range. In 1990, 1,849 cities (89.3% of the total 2,071) had volumes in this range, decreasing to 1,548 cities (74.7%) in 2020. Correspondingly, cities with volumes in the 1\u0026ndash;2 km\u0026sup3;, 2\u0026ndash;9 km\u0026sup3;, and \u0026gt;\u0026thinsp;9 km\u0026sup3; ranges increased from 118, 92, and 12 in 1990 to 240, 206, and 41 in 2020, respectively. As the scale increases, the number of cities rapidly decreases, with cities\u0026thinsp;\u0026gt;\u0026thinsp;9 km\u0026sup3; accounting for only 0.58% and 1.98% in 1990 and 2020, respectively.\u003c/p\u003e \u003cp\u003eIn 1990, the ten cities with the largest volumes were Los Angeles (38.53 km\u0026sup3;), Tokyo (21.39 km\u0026sup3;), Chicago (14.98 km\u0026sup3;), Guangdong (14.97 km\u0026sup3;), San Francisco (11.74 km\u0026sup3;), Beijing (11.37 km\u0026sup3;), Osaka (11.35 km\u0026sup3;), S\u0026atilde;o Paulo (10.56 km\u0026sup3;), New York City (10.55 km\u0026sup3;), and Dallas (10.49 km\u0026sup3;). Among them, five were in the United States, two in Japan, two in China, and one in Brazil. In 2020, the cities with volumes ranking in the top ten in 1990 increased to 35, with Guangdong (70.03 km\u0026sup3;), Los Angeles (47.48 km\u0026sup3;), Jiangsu (39.58 km\u0026sup3;), Tokyo (37.21 km\u0026sup3;), Beijing (30.12 km\u0026sup3;), Shanghai (27.20 km\u0026sup3;), Chicago (24.88 km\u0026sup3;), Osaka (17.64 km\u0026sup3;), Dallas (17.32 km\u0026sup3;), and Atlanta (16.87 km\u0026sup3;) leading the rankings. Four of the top ten cities were in China, with Jiangsu and Shanghai added compared to 1990. Notably, Guangdong's volume surged from 14.97 km\u0026sup3; to 70.03 km\u0026sup3;, moving from the fourth to the first position globally, representing the most aggressive volume growth in the world.\u003c/p\u003e \u003cp\u003eFrom a continental perspective, Asia exhibited the largest building volumes, followed by North America and Europe. South America and Africa demonstrated comparable building volumes over the 30 years, while Oceania had the smallest building volumes (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(c)). Asia experienced the fastest growth, from 440.1 km\u0026sup3; in 1990 to 1,246.4 km\u0026sup3; in 2020, a 2.83-fold increase over three decades, witnessing the burst of the developing economics during the period, such as China and India. By 2020, Asia's building volume accounted for approximately 50% of the global total (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(d)). North America, with the second-largest building volume, observed a nearly 10-percentage-point decrease in its share over the 30 years, reflecting a relatively modest three-dimensional expansion in the global urbanization process for developed economics.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe investigated the relationship between the volume increment of 2,071 global cities from 2000 to 2020 and their volume stock in 2000. Our findings reveal the manifestation of the Matthew Effect in the physical expansion of urban space. The Matthew Effect refers to the phenomenon of \"the rich get richer, and the poor get poorer,\" wherein entities or individuals with advantages are more likely to acquire additional resources and opportunities in competition, thereby becoming more powerful. Conversely, relatively disadvantaged entities or individuals find it challenging to catch up due to a lack of these advantages, further declining their strength and stature. This study found that cities with larger volumes in 2000 experienced more substantial increments. This positive correlation aligns with the Matthew Effect principles and reflects Zipf's law regarding patch growth, with larger urban patches growing faster (Sun et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a) shows that among the 2,071 major cities, only five witnessed a volume expansion exceeding 10 km\u0026sup3; during 2000\u0026ndash;2020. Notably, China's supercities \u0026ndash; Guangdong (expanding by 32.3 km\u0026sup3;), Jiangsu (30.0 km\u0026sup3;), Shanghai (16.1 km\u0026sup3;), and Beijing (13.9 km\u0026sup3;) \u0026ndash; dominated the top ranks. These cities also held the largest volume stocks in 2000, as indicated by the count \"5\" in the upper right corner of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(d), affirming Matthew Effect dynamics. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(d) depicts a heatmap illustrating the positive relationship between stock and increment for the 2,071 cities globally, with the majority clustering near the diagonal. Approximately one-third of cities had a volume below 1 km\u0026sup3; in 2010, with an increment below 0.1 km\u0026sup3;. This reflects an uneven development pattern in urban growth under the cumulative effects, making urban expansion more challenging for relatively small cities.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Building expansion surpasses population urbanization in two-thirds of global major cities\u003c/h2\u003e \u003cp\u003eUrban building volume growth and urban population growth are two characteristics of urbanization. Both dynamic changes follow the Matthew Effect, where cities with larger volumes can undergo larger-scale urban expansion and, due to their stronger economic and social attractiveness, experience faster population growth. However, these two processes are not entirely synchronized. We compared the volume expansion and population growth of global major cities (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a)), calculated the ratio of urban two-dimensional and three-dimensional expansion rates to population growth rates (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b)(c)(d)), and horizontally compared the changes in per capita building volume and area among major cities on six continents (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(e) (f)). From both a two-dimensional and three-dimensional view, about two-thirds of major cities experienced building expansion rates exceeding population growth rates between 2000 and 2020 (R\u003csub\u003eep\u003c/sub\u003e\u0026ge;1) (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(c)(d)), emphasizing the significance of building urbanization and overpopulation urbanization. Infrastructure development preceded population growth (Li, Verburg, et al., 2022). The categorization of the three-dimensional expansion to population growth ratio (R\u003csub\u003eep\u003c/sub\u003e) into three classes (\u0026lt;\u0026thinsp;0, 0\u0026ndash;1, \u0026ge;\u0026thinsp;1) revealed spatial patterns. Cities in the eastern United States, western Europe, eastern China, eastern South America, and Australia (red dots in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b)) demonstrated a predominant three-dimensional expansion, aligning with the largest building volumes globally (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a)). Conversely, areas like the central-western United States, northern and western Africa, and the Arabian Peninsula had a three-dimensional expansion rate smaller than population growth. Regions with negative population growth were found in eastern Europe, the Middle East, and eastern China. The observed trend indicates that larger cities prioritize building volume expansion over population growth, emphasizing Zipf\u0026rsquo;s law for physical space over economic and social space represented by population (Li, Verburg et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAs two-thirds of major cities had a building volume expansion rate greater than the population growth rate, most cities experienced increased per capita building volume from 2000\u0026ndash;2020 (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(e)). North America has the largest per capita building volume globally, ranking second in Oceania, and Asia rose from the fourth position in 2000 to the third in 2020, surpassing Europe. South America and Africa have the smallest per capita building volumes globally, with little difference between them. Africa is the only continent to experience a decline in per capita building volume over 20 years, indicating that despite significant population growth, infrastructure development in large cities has not kept pace with the process of population urbanization, leading to a further decline in living conditions in these cities. The relative relationship between per capita building area and per capita building volume in two-dimensional and three-dimensional perspectives reflects different levels of building height across continents (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(f)). The situation in Asia and Europe is better in terms of per capita building volume than per capita building area. The latter is very close to South America and Africa, indicating that major cities in Asia and Europe are high-rise cities with higher building heights. At the same time, other continents have low-rise cities, which is also confirmed in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Differentiation and variation in per capita building volume\u003c/h2\u003e \u003cp\u003eRelative to per capita building area, per capita building volume, which considers floor height, more accurately reflects the average infrastructure quantity possessed by residents in a city, thereby providing a more precise indication of the living conditions of urban residents. There is a significant disparity in per capita building volume among the 2,071 major cities globally, with South Asia, Southeast Asia, Africa, and Latin America having the smallest per capita building volumes. In contrast, cities in the eastern United States and Europe in the 50\u0026deg;N-60\u0026deg;N region have the largest per capita building volumes (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a)). The regions with the greatest per capita building volume growth over the 20 years are eastern and central China and cities in Europe in the 50\u0026deg;N-60\u0026deg;N region (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b)). Notably, some cities experienced a decrease in per capita building volume over the 20 years, mainly distributed in Africa, the Arabian Peninsula, the central-western United States, Colombia, and Venezuela (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b)). Combining Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a)(b), cities with larger per capita building volumes also exhibited greater growth over the 20 years, indicating the presence of the Matthew Effect in per capita building volume \u0026ndash; the rich become richer, while the weak not only experience minimal growth but may even experience a decline.\u003c/p\u003e \u003cp\u003eThe per capita GDP of the country in which a city is located can, to some extent, characterize the economic development level of that city. Based on the per capita GDP at the national level in 2019 and using the World Bank classification standards, we categorized global countries into four groups: high-income, upper-middle-income, lower-middle-income, and low-income. On average, major cities in high-income countries have the largest per capita building volume, reaching approximately 2800 km\u0026sup3; per capita, followed by upper-middle-income countries (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(c)). Due to the low number of major cities in low-income countries (only 38, accounting for only 1.8% of the total 2071), the percentiles in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(c) are not the smallest and are slightly larger than those of lower-middle-income countries. On average, major cities in upper-middle-income countries have the largest increment in per capita building volume, reaching around 600 km\u0026sup3; per capita, followed by high-income countries (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(d)). Major cities in upper-middle-income countries are converging towards the level of high-income countries in terms of per capita building volume. Regression analysis further reveals a positive correlation between per capita building volume and per capita GDP (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(e)). Similarly, the increment in per capita building volume positively correlates with the increment in per capita GDP (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(f)).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Inequality in the internal building heights of global major cities\u003c/h2\u003e \u003cp\u003eIn addition to the disparities in volume among cities and the unequal development of expansion dynamics, our research results also reflect variations in the internal architectural structure of different cities, with a resolution of 30m. We computed an inequality index measuring the degree of spatial inequality in urban built infrastructure proposed by Brelsford et al. (Brelsford et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) and Pandey et al. (Pandey et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). We mapped the spatial distribution of the average building height and the inequality index of building height (Hereinafter referred to as \u0026ldquo;inequality\u0026rdquo;) for 2,071 major global cities in 2020 (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(a)). The inequality in China mostly exceeds 0.29, with the average height mostly exceeding 19m, indicating high average building height and significant diversity (large red and orange dots). In contrast, the southern part of Russia is characterized by the highest number of major cities with high and less diverse average building heights (large blue dots). The majority of the United States has moderate building height and moderate diversity (medium-sized yellow dots). The relationship between the change in the inequality of building height within cities from 2000 to 2020 for major global cities is described by the fitted function y\u0026thinsp;=\u0026thinsp;0.938x\u0026thinsp;+\u0026thinsp;0.0166 (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b)). The seven countries with the highest building inequality globally (ranked by median) are China, Kazakhstan, Romania, Ukraine, Germany, Brazil, and Russia. The first four are Asian and Eastern European countries, with substantial gaps and differences in inequality compared to the fifth (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(c)). Among the six continents globally, Asia has the highest inequality, while Oceania has the lowest. According to Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(d), in 2000, the median inequality in Asia and Europe was higher than the global median; from 2000 to 2020, Asia's inequality gradually increased, while Europe's decreased. By 2020, only Asia's median was higher than the global median, indicating a growing disparity between Asia and the other five continents in the inequality, with Asia taking the lead.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Discussion","content":"\u003cp\u003eAs hubs for the majority of the population and key economic activities, cities significantly impact more than half of the United Nations Sustainable Development Goals (Thacker et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The developmental paths and future trajectories of major cities across the globe play a vital role in addressing issues of fairness among nations and cities. The Matthew Effect is evident in the static and dynamic patterns of global major cities, the distribution and growth of population size, and the dynamic development patterns of per capita building volume. This reflects the cumulative effects of stronger entities becoming even more formidable in urban physical and socioeconomic spaces. The scale and living environment of major global cities exhibit extreme imbalance. Over the past two decades, a positive correlation between the expansion of building volume and its existing stock has emerged. This is partly due to larger building volume stocks signifying stronger economic vitality and larger populations, leading to greater synergetic effects and accelerating further expansion. This has resulted in the current distribution where a few large cities coexist with numerous smaller ones. Whether viewed from a two-dimensional or three-dimensional perspective, two-thirds of global major cities\u0026rsquo; building volume growth rates have surpassed the population growth rates. This contradicts sustainable development goal 11.3 (Li, Verburg, et al., 2022), which stipulates that the growth rate of construction land should not exceed the population growth rate, posing a significant challenge to sustainable development. From a three-dimensional perspective, we assess the per capita building volume and its dynamic changes in global major cities. This objectively evaluates the spatial occupancy of per capita building resources in major cities, closely linked to habitat environment, resident well-being, and urban sustainability. The per capita building volume is positively correlated with the per capita GDP of the corresponding country. Africa is the only continent to witness a decline in per capita building volume over the past 20 years, indicating that despite significant population growth, infrastructure development in cities has not kept pace with population urbanization, resulting in a further decline in the living conditions of urban residents.\u003c/p\u003e \u003cp\u003eAdditionally, shifting the focus to the internal building structures of each city, we employ an inequality index to characterize the diversity of building heights within each city. Asian major cities have the highest inequality index globally, with a continuing upward trend, marked by the addition of numerous supertall buildings. This trend is common in countries that have undergone significant urbanization in recent decades (Zhou et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The inequality in urban building height represents the degree of diversity in building height within the city, unrelated to urbanization and economic development. Developed regions, such as North America, also exhibit an increasing trend in the inequality index.\u003c/p\u003e \u003cp\u003eInequality and inequity are two distinct concepts. Inequality is relatively objective, representing differences in quantity, degree, conditions, and other aspects of an object. On the other hand, inequity is more subjective, emphasizing unfairness or injustice, often focusing on the unethical or unfair distribution of treatment or resources. This study reveals a global pattern of Matthew effect and inequality in large cities' distribution and dynamic development. Influenced by factors such as the accumulation effects, industrial and economic concentration effects, and social network effects, the pattern tends to reinforce the strong and weaken the weak. This phenomenon contradicts the SDG10 goal of \u0026ldquo;reducing inequality within and among countries.\u0026rdquo; However, some scholars argue that economic development alone cannot address spatial inequities in infrastructure, as inequality is a characteristic of urbanization (Pandey et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Zhou et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). In other words, economic development and urbanization inevitably lead to differentiated patterns in the global landscape. Although this inequality is rooted in unfair resource distribution, it is deemed unavoidable. This suggests that advancing global equity requires implementing economic and social intervention measures to redirect resources toward smaller cities. This may entail sacrificing potential economic growth and urbanization rates, necessitating a trade-off between economic growth and promoting fairness (Dong et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis study investigates the expansion of physical urban space and the corresponding socioeconomic growth indicated by population changes. It addresses the dual aspects of land development and population growth within the context of urbanization, revealing Matthew effects in both forms of urbanization. Notably, two-thirds of major cities, particularly those with substantial volumes, located in the eastern United States, Western Europe, and eastern China, exhibit a building expansion rate that surpasses the population growth rate. This indicates that land urbanization is outpacing population urbanization, possibly due to the marginal cost of physical space expansion being lower for globally prominent cities than the marginal cost of attracting population concentration. In the case of China, the urbanization process in recent decades has witnessed a phenomenon where cities expand horizontally or compete vertically for supremacy.\u003c/p\u003e \u003cp\u003eMoreover, national land spatial planning remains dominated by incremental planning. Facing the prospect of peaking and declining population, there is a potential risk of significant urban contraction and the emergence of numerous \u0026ldquo;ghost cities\u0026rdquo; (Liu et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Ruan, Lou, et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The government should streamline redevelopment efforts by identifying and addressing inefficient land use, shifting from incremental to stock planning (S. Liu et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Ruan, He et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis study analyzes results based on our constructed urban three-dimensional expansion dataset, covering major cities globally over a long period (1990\u0026ndash;2020). The dataset boasts high precision (as validated in the supplementary materials) and fine granularity (30m resolution within a 10m grid). It is the first globally comprehensive three-dimensional structural dataset with concurrent high resolution, accuracy, and temporal information. The proposed methodology in this study enables efficient, rapid, and real-time prediction of building heights on a global scale for construction land. The well-trained Random Forest (RF) model is applicable worldwide, utilizing open-source and freely accessible data as input. In the future, we aim to extend this method to cover global construction land, including small settlements and rural areas. This approacSh facilitates systematic monitoring of urbanization processes in low-income countries and regions with scarce population and data resources. Such tracking is crucial for achieving United Nations Sustainable Development Goals 8 and 9 (Sun et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2020\u003c/span\u003e)。Our fine-grained data at a 30-m spatial resolution, combined with other geographical and socioeconomic data, has extensive potential applications in various domains, including urban climate (Lin et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), urban carbon emissions (Zhang et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), urban transportation and energy consumption (Stewart \u0026amp; Oke, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Zhou et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), and public health (Miles et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2012\u003c/span\u003e).\u003c/p\u003e"},{"header":"4. Methods","content":"\u003cp\u003eThis study employed machine learning techniques to construct a global three-dimensional expansion dataset for major cities from 1990 to 2020, and conducted further analysis by integrating socioeconomic data, including population and GDP. In obtaining building heights, we used two datasets as labels for model training, including a global building height dataset from 1990 to 2010 (He et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) and GEDI height data (Potapov et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). We adopted an innovative three-step sampling method, which involves \u0026ldquo;CCDC detection,\u0026rdquo; \u0026ldquo;pixel selection,\u0026rdquo; and \u0026ldquo;stratified sampling\u0026rdquo; to ensures the scientific rigor and reliability of the machine learning model. Various temporally and spatially aggregated remote sensing data sources served as input variables. A Random Forest model was developed to estimate additional building heights for major global cities from 2010 to 2020, resulting in a comprehensive urban three-dimensional expansion dataset covering three decades. We compared the inverted building heights with the official reference heights from various locations for validation purposes. Detailed data, methods, and validation result can be found in the supplementary document.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of Competing Interest\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch3\u003eAcknowledgments\u003c/h3\u003e\u003ch2\u003eData availability\u003c/h2\u003e \u003cp\u003eData will be made available on request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBrelsford, C., Lobo, J., Hand, J., \u0026amp; Bettencourt, L. M. A. (2017). 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Satellite mapping of urban built-up heights reveals extreme infrastructure gaps and inequalities in the Global South. \u003cem\u003eProceedings of the National Academy of Sciences\u003c/em\u003e, \u003cem\u003e119\u003c/em\u003e(46), e2214813119. 2023-11-16. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1073/pnas.2214813119\u003c/span\u003e\u003cspan address=\"10.1073/pnas.2214813119\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Urban 3D expansion, Matthew Effect, Building height, Inequality, Spatiotemporal","lastPublishedDoi":"10.21203/rs.3.rs-4653734/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4653734/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cdiv language=\"En\" class=\"ArticleSubTitle\"\u003eUrbanization has surged over the past decades. Global major cities\u0026rsquo; land urbanization and population urbanization have intensifying pressures on urban climate, public health, and energy consumption. A favorable vision for assessing urban habitats\u0026rsquo; living conditions necessitates recognizing the evolution and current status of major global cities\u0026rsquo; three-dimensional structure and spatiotemporal trajectories. However, a lack of high-resolution, long-term data hinders obtaining metrics reflecting living conditions. This study addresses this gap by generating a 30-meter resolution spatiotemporal three-dimensional urban expansion dataset for 2071 global major cities (1990\u0026ndash;2020). Integrated with socioeconomic data, it reveals adherence to Zipf's Law, reflecting pronounced unequal development and a global-scale Matthew effect. Most cities fell within the 0\u0026ndash;1 km\u0026sup3; volume range, with 12 cities and 41 cities\u0026rsquo; volume\u0026thinsp;\u0026gt;\u0026thinsp;9 km\u0026sup3; in 1990 and 2020, respectively. About two-thirds of major cities experienced building expansion rates exceeding population growth rates between 2000 and 2020. Per capita building volume correlates with the GDP. Africa is the only continent to witness a decline in per capita building volume over the past 20 years, indicating a further decline in the living conditions of urban residents. Focusing on internal building structures, an inequality index characterizes height diversity within cities. Asian cities exhibit the highest global inequality index, marked by supertall building additions. This study not only compares major cities' overall size and growth patterns in three dimensions but also analyzes the distribution of building heights within each city in detail. The findings contribute to identifying and addressing urbanization challenges, supporting habitat environmental assessments, and measuring progress toward sustainable goals.\u003c/div\u003e","manuscriptTitle":"“Matthew Effect” in Global Major Cities Over Decades: In the context of the spatiotemporal 3D urban expansion","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-29 01:00:27","doi":"10.21203/rs.3.rs-4653734/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"aafc9833-636e-4621-91c8-209b62df20c8","owner":[],"postedDate":"July 29th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":35076319,"name":"Scientific community and society/Social sciences"},{"id":35076320,"name":"Scientific community and society/Developing world"},{"id":35076321,"name":"Earth and environmental sciences/Environmental social sciences/Sustainability"},{"id":35076322,"name":"Earth and environmental sciences/Environmental social sciences"}],"tags":[],"updatedAt":"2024-09-10T06:36:06+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-29 01:00:27","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4653734","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4653734","identity":"rs-4653734","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}