Global Mapping of Three-Dimensional Urban Structures Reveals Escalating Utilization in the Vertical Dimension and Pronounced Building Space Inequality

Xiaoping Liu; Xinxin Wu; Xuecao Li; Xiaocong Xu; Weilin Liao; Limin Jiao; Zhenzhong Zeng; Guangzhao Chen; Xia Li

doi:10.1016/j.eng.2024.01.025

Engineering ›› 2025, Vol. 47 ›› Issue (4) :93 -107. DOI: 10.1016/j.eng.2024.01.025

Research Precise Positioning and Geoinformation Science—Article

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Global Mapping of Three-Dimensional Urban Structures Reveals Escalating Utilization in the Vertical Dimension and Pronounced Building Space Inequality

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^aGuangdong Key Laboratory for Urbanization and Geo-simulation, School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China

^bCollege of Land Science and Technology, China Agricultural University, Beijing 100091, China

^cSchool of Resource and Environment Science, Wuhan University, Wuhan 430072, China

^dSchool of Environmental Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

^eDivision of Landscape Architecture, Department of Architecture, Faculty of Architecture, The University of Hong Kong, Hong Kong 999077, China

^fKey Lab of Geographic Information Science (Ministry of Education), School of Geographic Sciences, East China Normal University, Shanghai 200062, China

E⁃mail address: xuxiaocong@mail.sysu.edu.cn (X. Xu).

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Abstract

Three-dimensional (3D) urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development. Regrettably, there exists a significant gap in detailed and consistent data on 3D building space structures with global coverage due to the challenges inherent in the data collection and model calibration processes. In this study, we constructed a global urban structure (GUS-3D) dataset, including building volume, height, and footprint information, at a 500 m spatial resolution using extensive satellite observation products and numerous reference building samples. Our analysis indicated that the total volume of buildings worldwide in 2015 exceeded 1 × 10¹² m³. Over the 1985 to 2015 period, we observed a slight increase in the magnitude of 3D building volume growth (i.e., it increased from 166.02 km³ during the 1985–2000 period to 175.08 km³ during the 2000–2015 period), while the expansion magnitudes of the two-dimensional (2D) building footprint (22.51 × 10³ vs 13.29 × 10³ km²) and urban extent (157 × 10³ vs 133.8 × 10³ km²) notably decreased. This trend highlights the significant increase in intensive vertical utilization of urban land. Furthermore, we identified significant heterogeneity in building space provision and inequality across cities worldwide. This inequality is particularly pronounced in many populous Asian cities, which has been overlooked in previous studies on economic inequality. The GUS-3D dataset shows great potential to deepen our understanding of the urban environment and creates new horizons for numerous 3D urban studies.

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Keywords

Three-dimensional / Global mapping / Building volume / Building height / Building space inequality

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Xiaoping Liu, Xinxin Wu, Xuecao Li, Xiaocong Xu, Weilin Liao, Limin Jiao, Zhenzhong Zeng, Guangzhao Chen, Xia Li. Global Mapping of Three-Dimensional Urban Structures Reveals Escalating Utilization in the Vertical Dimension and Pronounced Building Space Inequality. Engineering, 2025, 47(4): 93-107 DOI:10.1016/j.eng.2024.01.025

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1. Introduction

Urban areas have long been the leading centers for accommodating populations and supporting various socioeconomic activities [1], even though they cover less than 1% of the world’s land surface [2]. Promoted by the unprecedented urbanization over the past two centuries, artificial buildings in urban areas have gradually generated various urban morphological structures in both horizontal and vertical aspects [3], [4], for example, from central-compact cities in Tokyo Bay to decentralized-sprawl patterns in the western United States. Currently, the perception and understanding of urban morphological structures are mainly based on the horizontal dimension, that is, the urban extent and built-up area [5], [6], whereas the vertical aspect of urban buildings is usually ignored because of the lack of data. Many studies have suggested that the three-dimensional (3D) urban structure, especially the variations in the building height and density, is a key component related to the local urban climate [7], energy consumption [1], greenhouse gas emissions [8], pollutant dispersion [9], and risk of exposure to extreme weather hazards such as flooding and heatwaves [10], [11].

The accelerated urbanization and population growth in recent decades have exerted significant stress on the built environment, particularly regarding inadequate space and notable inequality in building provision [12], [13]. Profound insights into these issues are pivotal for the realization of Sustainable Development Goals (SDGs), considering that the building sector has demonstrated its direct and indirect impacts on achieving 13 goals and 25 targets of the 2030 SDG Agenda [14], [15]. Notably, the United Nations Human Settlements Programme (UH-Habitat) underscores the crucial role of addressing inadequate building provision space conditions in SDG 11, specifically target 11.1 relating to estimating the indicator of the proportion of the urban population living in slums, informal settlements, or inadequate housing [16]. Furthermore, comprehension of the building space inequality can directly contribute to the achievement of SDG 11 and indirectly contribute to reducing social inequality (in line with SDG 10) [13], [17]. Detailed and consistent 3D building structure data can provide valuable and abundant insights into the built environment, which is a key factor in investigating the provision and inequality of the building space. Unfortunately, the absence of such data results in significant gaps in our knowledge regarding the provision and inequality of the building space across different regions and globally.

On a global scale, persistent efforts have been devoted to mapping urban expansion from a horizontal perspective [5], [6], providing indispensable data sources that contribute to enhancing our understanding of the factors and impacts of urban development [18], [19]. Nevertheless, until now, attempts to capture 3D urban structures with global coverage have remained challenging and limited, whereas detailed and consistent 3D urban structure data are crucial for various academic research and urban planning applications [1], [20], [21]. Remote sensing techniques have notable potential for mapping large-scale building heights through satellite observations such as synthetic aperture radar [4], [22], scatterometer [23], airborne light detection and ranging system [24], [25], and high-resolution optical stereo image [26].

Although a growing number of studies have focused on mapping the 3D information of urban buildings (Table S1 in Appendix A), they are still limited either in terms of their incomplete geographical coverage [3], [4], [27], [28], [29], [30], [31] (e.g., specific cities and countries in North America, Europe, and Asia) or comprehensive building structure details (i.e., 3D and two-dimensional (2D) building structure information including volume, height, and footprint) [32]. For instance, continental-scale vertical building structures (i.e., building height, volume, and footprint) were mapped recently at a 1 km resolution using multiple sources of height and footprint remote sensing observations [3]. Other national-scale building height data were generated for countries such as the United States (̃500 m resolution) [4], China (̃10 m resolution) [33], and Germany (̃10 m resolution) [28]. However, these attempts have yet to fully satisfy the criteria for achieving detailed spatial coverage and resolution [34], as well as comprehensiveness in building structure information [35], mainly due to the difficulties in collecting massive reliable reference data and calibrating robust retrieval models for urban clusters globally.

To provide data and bridge the above knowledge gap, we developed a global consistent and spatially detailed 3D global urban structure (GUS-3D) dataset for 2015, with a spatial resolution of 500 m. This is a high-resolution and consistent public dataset characterizing the building structure across global urban clusters (Appendix A), which provides information on the average building height, building volume, building footprint, and derivative indices of the building coverage ratio (BCR) and building volume density (BVD) at a 500 m × 500 m grid resolution. To reduce local uncertainties in the estimated building height and volume, we focused on characterizing the overall building structure within regular square units instead of individual buildings (Fig. S1 in Appendix A). The GUS-3D dataset was developed using locally adaptive ensemble extreme Gradient Boosting (XGBoost) regression models (Section 2.3) customized for specific regions and are separately calibrated against local reference building data (i.e., vector building footprint with height information). Multisource remote sensing observations (Table S2 in Appendix A), including synthetic aperture radar data, optical satellite imagery, digital surface elevation models, and global extent products, were used to support the derivation of vertical information across global urban clusters. The accuracy and uncertainty in the developed GUS-3D dataset were then comprehensively assessed with independent reference data samples across different regions (for details, Section 3.1 and Tables S3 and S4 in Appendix A). With the developed GUS-3D dataset, we first quantified the large difference in the growth rate over the past decades regarding the 3D building volume and traditional 2D urban extent. Then, we identified different prototypes of the 3D urban morphology across global urban clusters. Finally, we calculated the building volume per capita (BVPC) and assessed its inequality at city and national scales, with the purpose of highlighting the provision and inequality in the built environment worldwide. Our analysis could provide comprehensive insights into the global patterns of building space provision and inequality from a 3D building perspective, unveiling their pivotal roles in achieving urban sustainability development.

2. Data and methodology

2.1. Data sources for mapping the urban building volume and height

We mapped the global building volume and height using remote sensing datasets from multiple accessible sources with global coverage (Table S2). Synthetic Aperture Radar (SAR) data from the Sentinel-1 C-band and Advanced Land Observing Satellite (ALOS) L-band [36] and optical surface reflectance data obtained from Landsat eight images [37] were adopted as the main sources for our mapping tasks. In particular, the SAR backscatter intensity captures the microwave radiation scattered by the observed terrain and is highly sensitive to the sensed object structure, making it practical for the retrieval of building structures [4], [38]. We first collected homogeneous Sentinel-1 C-band ground range detected SAR data for 2015 by selecting scenes with dual polarization, that is, vertical transmit/vertical receive (VV) and vertical transmit/horizontal receive (VH) along the ascending orbit. We then calculated the mean backscatter coefficients at VV and VH polarizations after preprocessing including noise removal, radiometric calibration, and terrain calibration. Similar processes were performed to obtain backscatter coefficients for the ALOS L-band SAR data. Additionally, satellite imagery is commonly recommended as a supplemental resource for unveiling the urban built-up environment [3], [28]. Here, we used six spectral bands (i.e., Bands 2, 3, 4, 5, 6, and 7) from calibrated Landsat 8 top-of-atmosphere (TOA) reflectance data [37], [39]. After cloud removal, median aggregation of all available imagery was performed with regard to each band. For regions not fully covered by the 2015 Landsat 8 image scenes, we performed image capture during the 2014–2016 period. To improve the mapping accuracy, we also collected several ancillary datasets for model development, including the Visible and Infrared Imaging Suite (VIIRS) Day/Night Band (DNB) nighttime light data, ALOS World 3D (AW3D30) global digital surface model (DSM) data [40], normalized difference vegetation index (NDVI) data, and data of the proportion of urban land extracted from the Global Annual Urban Dynamics (GAUD) product [6]. All of these data were converted into a spatial resolution of 500 m × 500 m and could facilitate building structure retrieval for robust and reliable data products.

In our study, the urban extent is defined as impervious surfaces, which is consistent with the definition in the GAUD dataset. The GAUD dataset provides detailed information on global impervious surfaces at a fine-scale spatial resolution of 30 m × 30 m, which was used to estimate the urban extent in our mapping process and to calculate the coverage of man-made artificial structures within a 500 m land grid. Notably, impervious surfaces comprise both urban and rural areas. Existing studies that employ impervious surfaces as the study extent commonly use terms such as urban land or urban extent for descriptive purposes [6], [41], [42]. Additionally, we filtered nonurban regions where the proportion of the urban area in each 500 m × 500 m grid was less than 20% based on our preliminary inspection. This preprocessing could maintain favorable spatial consistency with the original GAUD urban extent (Fig. S2 in Appendix A) and help mitigate the effects of scatter noise and higher sensitivity in these areas of a lower urban area proportion in the mapping process.

Reference building samples with height information (vector data) were collected across the globe to customize the models for different regions for calibrating and evaluating the mapping models (Table S5 in Appendix A). These reference building samples were mainly obtained from Light Detection and Ranging (LiDAR) data (e.g., the United States, Australia, and Mexico), stereo imagery (e.g., Europe), high-resolution digital surface and elevation models (e.g., Canada), and a survey-based inventory of digital maps (e.g., China). Specifically, to obtain representative samples for model development, we executed a systematic data processing approach. This procedure comprised the following steps: preprocessing of the raw data to obtain building structure data with valid height information, which involved tasks such as LiDAR data processing, zero-value building height filtering, and converting floors into height values (considering each floor as exhibiting a height of 3 m); visually interpreting fine-scale building data using high-resolution satellite imagery and street view imagery to assess data completeness; and aggregating the fine-scale building data to derive gridded building volume and height data at a 500 m spatial resolution, weighted by the coverage area of buildings (Fig. S1). Given the potential presence of missing data, our sample set excludes instances with a small proportion of buildings within cells, as these are very sensitive to data deficiencies and noise. In total, more than 89 000 original building samples with height information were collected covering more than 300 cities. These cities are located in regions with different development levels and should therefore account for different 3D urban structures worldwide. Most of the above preprocesses were conducted on the Google Earth Engine (GEE) platform [43], a state-of-the-art cloud-based computational environment.

2.2. Definitions of urban 3D structure indicators in the GUS-3D data

We used three indicators, that is, the building volume, average building height, and building footprint, to characterize the 3D urban building structure across the globe. These indicators were derived at the 500 m × 500 m grid scale (Fig. S1(a)) and were aggregated at the regional scale for further analyses (Table S6 in Appendix A). Here, the building volume (unit: m³) is defined as the total volume of all buildings in the grid (

V_{g r i d}

; an area of 0.25 km², Fig. S1(b)), as follows:

(1)

V_{g r i d} = \sum_{i = 0}^{n} A_{i} H_{i}

where

n

is the number of buildings; and

A_{i}

and

H_{i}

are the covering area and height of building i, respectively. The average building height (

{\bar{H}}_{g r i d}

, unit: m) is defined as the area-weighted average height of all buildings in the grid (Fig. S1(c)), as follows:

(2)

{\bar{H}}_{g r i d} = \frac{\sum_{i = 0}^{n} A_{i} H_{i}}{\sum_{i = 0}^{n} A_{i}}

The building volume and average building height were separately derived from the XGBoost models (Section 2.3) calibrated against multisource remote sensing observations and local reference data (building footprint and building height information). With the two above indicators, we could derive the building footprint (

F_{g r i d}

, unit: m³·m⁻¹) as the area of each 0.25 km² grid covered by buildings, which is conceptually equivalent to the ratio of the volume to the average height, as follows:

(3)

F_{g r i d} = \frac{V_{g r i d}}{{\bar{H}}_{g r i d}}

Note that the building footprint aggregated at the regional scale is always smaller than the traditional urban extent in existing products (e.g., GAUD) since it accounts for the ratio of building coverage in each grid. To further characterize the urban structure, we used two other derivative indicators, that is, the BCR (m²·m⁻²) and BVD (m³·m⁻²), to describe the density of buildings from both 2D and 3D perspectives. The BCR denotes the share of a grid occupied by a building. Thus, the BCR value in a grid (

{B C R}_{g r i d}

) equals the building footprint divided by the total area of the grid (A_grid; 0.25 km²):

(4)

{B C R}_{g r i d} = \frac{F_{g r i d}}{A_{g r i d}}

where

A_{g r i d}

denotes the total area of the grid. Similarly, the BVD characterizes the density of buildings accounting for both horizontal and vertical aspects, defined as the ratio of the building volume to the area of the grid (

{B V D}_{g r i d}

). Thus, the

{B V D}_{g r i d}

equals the BCR_grid multiplied by the average building height, which is equivalent to the theoretical height after flattening all the building volumes over the entire grid:

(5)

{B V D}_{g r i d} = \frac{V_{g r i d}}{A_{g r i d}} = {B C R}_{g r i d} {\bar{H}}_{g r i d}

2.3. Mapping the global urban building volume and height

We estimated global urban building volume and height data using a data-fusing methodology and hierarchical strategy. The overall mapping framework is shown in Fig. 1, which mainly includes the following steps: We began by collecting the necessary spatial materials and reference data and preprocessing them for mapping model development. Specifically, the explanatory variables are the mean and standard deviation of the backscatter coefficients from the SAR data (i.e., Sentinel-1 and ALOS), the reflectance values from the Landsat 8 data, the VIIRS DNB nighttime light data, the NDVI, the urban area fraction from the GAUD product, and the DSM from the AW3D30 product within a 500 m × 500 m grid. The dependent variable is the referenced building volume/height aggregated to a resolution of 500 m from the fine-scale raw building structure data. Following data preprocessing, we systematically gathered explanatory and dependent variables to generate a well-representative sample set designed for use in the calibration and validation processes. To achieve this, we employed a stratified sampling methodology. This involved the creation of six distinct strata based on the aggregated mean volume/height. Subsequently, we adopted a random selection approach to choose a specific number of data samples from each stratum (i.e., 100 in this study). This approach was applied to each city for which reference data were available. The primary objective of this stratified sampling strategy was to involve a diverse range of building volume/height samples representing different values, thereby enhancing the robustness of the model development process. The collected samples were divided into two groups, where 70% of the samples were used for calibration and the remaining 30% were used for validation, as shown in Fig. 1.

With the collected samples, we experimented with three machine learning regression methods in estimating the building volume and height, including the XGBoost model [44], a back propagation neural network [45], and a random forest algorithm [46]. After the initial assessment of the overall samples, it was determined that the XGBoost regression model outperformed the other two methods (Fig. S3 in Appendix A). Ultimately, we chose the XGBoost regression method for mapping our global dataset. Furthermore, we adopted a hierarchical strategy to develop worldwide volume/height models and applied it to global building structure data mapping. This strategy aimed to construct local models for different regions on a global scale based on the collected sample sets (Tables S3 and S4) to ensure accurate data mapping. We initially constructed the local models for different countries based on their collected samples. These models are subsequently applied to map the building structure data to each country and their corresponding continental regions (Table S7 in Appendix A). In particular, the national boundary is acquired from the Database of Global Administrative Areas (GADM) and the continental regions boundary is obtained from the Large Scale International Boundary (LSIB) dataset (Table S6). However, on a global scale, some areas lack either effective samples sets or with limited samples available for data mapping. Within this context, we utilized neighboring models or incorporated samples from neighboring areas to construct models for our mapping purposes. That is, for example, there lack of representative sample set for model development in Central Asia and Southwest Asia. We therefore employed a well-trained European model to map the building structure in these areas by considering the geographical proximity of the Central and Southwest Asian regions to Europe. In addition, the available samples of North Asia, represented by the Russian sample set, are limited. Therefore, we developed a robust estimation model for the North Asia region by adding available samples from neighboring regions (i.e., a sample set of Europe) to the original Russian sample set. This strategy is expected to yield robust models and ensure the quality of the mapping data. In summary, we constructed a total of 11 region-specific models to map the diverse geographical areas across the globe (Fig. 1 and Table S7). The ultimate GUS-3D product was derived from the combination of the outputs of these regional models.

2.4. Assessment of the derived building volume and height

We adopted three accuracy indicators to assess the performance of the calibrated models and the reliability of the derived dataset for each region, namely, the correlation coefficient (R), mean absolute error (MAE), and root mean square error (RMSE):

(6)

R = \frac{C o v (x, y)}{σ_{x} σ_{y}}

(7)

M A E = \frac{|x_{j} - y_{j}|}{m}

(8)

R M S E = \sqrt{\frac{\sum_{j = 1}^{m} {(x_{j} - y_{j})}^{2}}{m}}

where

x

and

y

are the estimated and reference building height data, respectively;

C o v (x, y)

is the covariance of variables

x

and

y

;

σ_{x}

and

σ_{y}

are their standard deviations; and

m

is the number of observations and j represents the jth observation. These three assessment indicators were calculated for each mapping region with independent building volume and height reference data samples (Fig. 2, Fig. 3, respectively). In addition, we compared our GUS-3D dataset with existing regional 3D urban structure maps for Europe, USA, and China through visual interpretation and kernel density evaluations (Fig. S4 in Appendix A). We further assessed the stability of each adaptive local estimation model by repeatedly calibrating the model 100 times with different model initializations and data samples. Then, the coefficient of variation (CV) was calculated to measure the stability of the models:

(9)

C V = \frac{σ}{μ}

where

σ

and

μ

are the standard deviation and mean value, respectively, of a corresponding cell for these 100 runs. The assessment results are shown in Fig. S5 in Appendix A.

2.5. Calculation of the growth rate of building volume and urban extent

We overlapped the derived GUS-3D dataset with the global annual urban GAUD dataset [6] (providing annual urban expansion information from 1985 to 2015, with a spatial resolution of 30 m) to indirectly derive the urban building structure in 1985 and subsequently estimate the growth rate of the building volume from 1985 to 2015. Note that the derived urban building structure for 1985 does not consider the changes in the building volume during this period due to urban renewal, which may cause uncertainty in the estimated growth rate. The urban extent data from the GAUD dataset were aggregated at a resolution of 500 m to maintain consistency with the derived GUS-3D dataset. Similar to the processing of the GAUD urban extent data for 2015, we excluded nonurban regions if the proportion of the urban area in each 500 m × 500 m grid was less than 20%. The growth rates of the building volume and urban extent from 1985 to 2015 were calculated as follows:

(10)

R_{v o l} = \frac{{V o l}_{2015} - {V o l}_{1985}}{{V o l}_{1985}}

(11)

R_{e x t} = \frac{{E x t}_{2015} - {E x t}_{1985}}{{E x t}_{1985}}

where

R_{v o l}

and

R_{e x t}

denote the growth rates of the building volume and urban extent, respectively, from 1985 to 2015 relative to the base year of 1985;

{V o l}_{2015}

and

{V o l}_{1985}

are the building volumes in 2015 and 1985, respectively; and

{E x t}_{2015}

and

{E x t}_{1985}

denote the urban extents in 2015 and 1985, respectively.

2.6. Quantification of building space provision and inequality

The building volume information retrieved from the GUS-3D dataset and population information from the LandScan product were integrated to calculate the BVPC in each 500 m × 500 m grid and quantify the inequality worldwide at the city and country scales. The LandScan product provides gridded populations at a 1 km spatial resolution. We aggregated the building volume into the same 1 km grids and calculated the BVPC as follows:

(12)

B V P C = \frac{V_{g r i d}}{P_{g r i d}}

where

P_{g r i d}

denote the population within the 1 km grid. We then adopted the Gini coefficient of the BVPC to quantify building space inequality on a global scale at both the city and national levels. The Gini coefficient offers a quantitative assessment of the inequality in the distribution of two variables, using the Lorenz curve as its foundation. Its applicability extends to diverse scientific disciplines [35], [47], [48], [49] and conforms with the methodology utilized by the World Bank for computing income Gini coefficients and gauging economic inequality. We first constructed a Lorenz curve of the BVPC that represents a ranked distribution depicting the cumulative percentage of the population on the horizontal axis relative to the cumulative percentage of the building volume on the vertical axis (Fig. S6(a) in Appendix A). Then, the Gini coefficient was derived as the ratio of the area between the equality line and the Lorenz curve to the area under the perfect equality line, which can be defined as follows:

(13)

G i n i = \frac{A_{L C}}{A_{P E}}

where

A_{L C}

is the area between the Lorenz curve and the perfect equality line (the area marked as A in Fig. S6(a)), and

A_{P E}

is the area under the perfect equality line (the area combining A and B in Fig. S6(a)). Thus, the Gini coefficient of the BVPC offers a means to assess the degree of inequality within a specified geographic region (Fig. S6(b) in Appendix A). In our investigation, we identified the urban extent by examining impervious surfaces using the GAUD dataset. This approach resulted in the calculation of Gini coefficients that cover both urban and rural areas within the specified total area. We also confirmed that there were enough samples (i.e., grid cells) of cities for calculating the Gini coefficient (Fig. S7 in Appendix A). In our analysis, we used the Gini coefficient as a measure to quantify the inequality in the building space. This enabled us to assess how much the actual distribution of the building space deviates from the ideal state of an equal distribution. The Gini coefficient ranges from 0 to 1, where 0 denotes a state of perfect equality, and 1 denotes the presence of complete building space inequality (Fig. S6(b)).

3. Results and discussion

3.1. Performance of the GUS-3D dataset

We collected more than 89 000 building footprint and height data samples worldwide from various data providers (Table S5 for details). These data samples were processed and aggregated into building volume/height estimates within 500 m × 500 m grids (Section 2.2), of which 70% were used to calibrate the models and the remaining 30% were used to validate the derived GUS-3D dataset. Models were developed for 11 regions with the XGBoost algorithm (Fig. 1).

The accuracy assessment results demonstrated that the GUS-3D dataset agrees well with the reference data samples regarding the building volume (Fig. 2(a) and Table S3) and height (Fig. 3(a) and Table S4)) and is robust across the different regions (Figs. 2(b) and 3(b)). The correlation coefficient (R) values for the building volume and height are 0.91 and 0.87, respectively, with RMSE values of 2.43 × 10⁵ m³ and 3.70 m, respectively, as assessed with more than 78 000 reference samples across a range of representative urban regions worldwide. Geographically, higher building volume accuracies were achieved in cities in the United States (R = 0.96, RMSE = 2.01 × 10⁵ m³), Canada (R = 0.93, RMSE = 1.51 × 10⁵ m³), European countries (R = 0.93, RMSE = 1.85 × 10⁵ m³), and China (R = 0.84, RMSE = 2.78 × 10⁵ m³). These satisfactory accuracies could be mainly attributed to the use of locally adaptive estimation models separately calibrated with sufficient data samples for these regions. Lower accuracies were found in cities in Russia (R = 0.72, RMSE =1.34 × 10⁵ m³), Africa (R = 0.55, RMSE = 0.62 × 10⁵ m³), and countries in South America (R = 0.52, RMSE = 1.41 × 10⁵ m³), mainly due to the limited reference data for model calibration in these regions (Table S3).

The assessment results for the building height estimates showed a similar geographical pattern to that of the building volume. Higher accuracies of the building height estimates were found in cities in the United States (R = 0.90, RMSE = 3.11 m), European countries (R = 0.83, RMSE = 2.96 m) and China (R = 0.81, RMSE = 5.63 m). Acceptable performance levels were obtained in cities in Canada, Mexico, Australia, and other urban regions with available reference data samples, with R values ranging from 0.39 to 0.67 and RMSE values ranging from 1.12 to 8.68 m (Table S4). We also compared our GUS-3D dataset with existing regional 3D urban structure maps [3] in representative cities in Europe, the United States, and China. The comparison results clearly showed that our building height estimates not only provide many more spatial details but also visually agree with the reference building data to a higher degree (Fig. S4). Additionally, quantitative comparison demonstrated substantially a higher accuracy of our building height estimates (lower bias, higher R, and lower RMSE values) than the existing ones across most cities (Table S8 in Appendix A). Moreover, we found that the importance of the explanatory variables varies in the different regions. The feature importance analysis results revealed that the SAR and DSM data and elevation features are the most valuable for estimating the building height, while the urban spatial features, such as the urban area ratio and nighttime light data, are crucial for estimating the building volume (Fig. S8 in Appendix A).

However, there are still limitations of our GUS-3D dataset. The acquisition of reference data from regions in the global south poses notable challenges, resulting in a deficiency of samples of the global south in model development. This may lead to uncertainty in our dataset in these regions. To partially overcome this challenge, we strategically utilized representative samples in close proximity to these regions for model development and mapping, with the primary objective of enhancing the robustness of our model for ensuring accurate mapping. Additionally, our 500 m resolution data could not be employed for certain microclimatic urban analyses, which may require building-level 3D structure information for deriving precise urban morphology parameters [50], such as the ground-level sky-view factor (SVF) and height-width ratio of urban canyons [51], [52]. Despite the lack of spatial detail, our GUS-3D data with building height, footprint, and volume information can support urban studies, as they provide global coverage and a transferable data size with abundant building structure information. Since our methodology mainly entailed the use of open-source data, we believe that subsequent studies can apply the same approach in building-level 3D structure estimation and mapping. Our global 3D urban building structure maps (GUS-3D dataset) are freely available online with a consistent framework (Appendix A).

3.2. Global layout of the 3D urban building structure

According to the derived GUS-3D dataset, the estimated global urban building volume in 2015 reached 1.06 × 10¹² m³ (Fig. 4). If summing all the buildings, theoretically, we could even construct an Earth–Moon bridge, with a cross-sectional area of 50 m × 50 m. Geographically, the spatial distribution of the global building volume revealed distinctive variations in the vertical building height across global urban regions (Fig. 4(a)). A high proportion of the building volume was distributed in mid-low latitude regions of the Northern Hemisphere, for example, metropolitan areas and city clusters in North America, East Asia, and Europe (peaks of the longitudinal and latitudinal profiles are shown in Fig. 4(a)). China (237.37 × 10⁹ m³, 22.35%), the United States (170.88 × 10⁹ m³, 16.13%), Japan (62.69 × 10⁹ m³, 5.91%), Russia (54.80 × 10⁹ m³, 5.17%), and Germany (50.47 × 10⁹ m³, 4.76%) are the top five countries that account for more than half of the global building volume (Table S9 in Appendix A). The massive building volume observed in cities in the United States and European countries mainly occurs because of the large horizontal urban extents, although the building height in these cities rapidly declines from the urban center to rural areas (e.g., New York City and London in Fig. 4(b) and the corresponding fitted S-shaped curve [53] shown in Fig. S9 in Appendix A). The situation is slightly different in cities in Eastern Asia. China accounts for more than 22% of the global building volume, mainly attributed to both the rapid urban expansion in recent decades and high-rise buildings in and around urban areas (e.g., Shanghai in Fig. 4(b)). Although the urban extent is similar between Japan and India, that is, approximately 3.5% of the global urban extent, the building volume in Japan is more than double that in India (62.69 × 10⁹ m³ vs 24.48 × 10⁹ m³), as Japan features a much greater average building height (16.973 m).

Overlapping the GUS-3D dataset with the state-of-the-art global annual urban expansion dataset (GAUD) [6] (Section 2.5), we found that the net growth in the global building volume from 1985 to 2015 was 341.10 × 10⁹ m³, equivalent to 47.44% of the total volume constructed before 1985. As a comparison, the global urban extent increased by 80.11% during the same period [6], which is almost two times higher than the growth rate of the building volume (Table S10 in Appendix A). When examining the growth rate of the building volume over the earlier period from 1985 to 2000, the 3D building volume growth rate is lower than the corresponding 2D building footprint growth rate (23.09% vs 27.95%). Conversely, during the subsequent period from 2000 to 2015, the 3D building volume growth rate surpasses the 2D growth rate (19.77% vs 12.62%; Table S10 in details). This recent trend agrees with the findings of previous studies [29], [54], [55]. Although the 3D building volume growth rate declined from 23.09% during the 1985–2000 period to 19.77% during the 2000–2015 period, the magnitude of the observed 3D building volume growth slightly increased in the last 15 years (166.02 km³ from 1985 to 2000 vs 175.08 km³ from 2000 to 2015). We further found that these trends hold particular significance in Asia (Table S10). However, in terms of the growth rate of the urban extent, it consistently surpassed the growth rates of both the 3D building volume and 2D footprint, indicating growth rates of 43.25% from 1985 to 2000 and 25.58% from 2000 to 2015.

Even though slightly more vertical space was used for building construction (an average building height of 9.53 m from 1985 to 2015 vs 8.93 m before 1985, Table S10), the BCR in urban areas considerably decreased from 22.18% before 1985 to only 12.31% from 1985 to 2015. Many of the newly developed urban lands were not used for building construction but emerged as large open spaces and wide roads between buildings. This unbalanced growth between the urban extent and building volume was more pronounced in developed European countries such as Germany, Italy, and the United Kingdom. During the same period, statistical data from the United Nations [56] show a population increase of 53%, which suggests no significant changes in the building space per capita considering the similar growth rate of the building volume (47.44%). Nevertheless, the built environment has improved given that there are many more open spaces among the newly developed urban areas.

Note that in the face of the consequent saturation of the available land for construction, some cities are undergoing varying degrees of urban renewal, which contributes to the change in the surface morphology in urban areas [57]. Detecting the urban renewal process is highly complex, and the current utilization of remote sensing technology for global-scale identification of this phenomenon continues to pose a persistent resource-intensive challenge [58], [59]. We simplified the building space change process by only considering the urban expansion detected by the time-series GAUD data, which do not incorporate the influence of urban renewal on building space growth rate calculation. Further exploration and analysis are necessary to identify the impact of urban renewal on building space dynamics.

Traditionally, we perceive our urban planet from a horizontal perspective, covering the land surface and quantifying the size of cities with the urban extent. Indeed, it is more intuitive and appropriate to observe the city size and urban morphology through the full 3D structure since it accounts for both the horizontal size and vertical space. The availability of information on the urban building volume and height in the derived GUS-3D dataset provides new insights into the city size and urban morphology from the additional vertical dimension occupied for living accommodations and socioeconomic activities. To investigate the city size difference between these two perceptions, we calculated the shares and ranked the global urban clusters from the two perspectives of the horizontal urban extent and 3D building volume (Fig. 5, Figs. S10 and S11 in Appendix A). We found that although cities in the United States account for the highest share of the urban extent by covering an area of 1.40 × 10¹¹ m² (21.13%) according to the GAUD dataset [6], they only account for 16.12% (170.9 × 10⁹ m³, ranking second) of the global building volume (Fig. 5 and Fig. S10(a)). This could be explained by the combination of both a lower average building height (7.12 m, ranking 15th) and relatively low BVD (Section 2.2, 1.22 m³·m⁻², ranking 18th). Hotspots of a similar mismatch between a larger urban extent and smaller building volume, that is, ratio of the volume share to the extent share < 1 (warmer color in Fig. S10(b)), were also found in cities in India, Australia, and most countries in Africa and South America, such as Sudan, Congo, and Brazil. Moreover, the results of a lower BVD together with a lower BCR (Section 2.2) for these countries (Fig. 5; Table S9) suggest low utilization of both horizontal and vertical spaces for building construction.

In contrast, China was estimated as containing the highest share of the building volume (237.4 × 10⁹ m³, 22.39%), despite its smaller urban extent (1.34 × 10¹¹ m², 20.23%) relative to the Unites States. This result contradicts the traditional perception and highlights a larger number of cities in China from a 3D perspective. Similarly, much larger city sizes quantified by the 3D building volume (than those quantified by the 2D urban extent) were commonly observed in cities in East Asia, Middle East Asia, and European countries (colder color in Fig. S10(b)). Among them, Japan and Republic of Korea feature notably greater average building heights (16.97 and 27.53 m, respectively, as shown in Fig. 5), suggesting a much higher vertical space utilization leading to a higher BVD building volume density. In contrast, higher BCR values ranging from 0.25 to 0.31 are the main contributors to the reasonable building volume in European countries such as Russia, Spain, Germany, and the United Kingdom (Fig. 5; Table S9), revealing a denser and flatter building pattern with a relatively low city skyline in these countries.

3.3. Prototypes of the 3D urban morphology

To further enhance our knowledge of the 3D urban morphology from a global perspective, we grouped the global urban clusters into four prototypes according to the combination of the derived BCR (to characterize the building density horizontally) and average building height (to describe the building skyline vertically) at the city scale (Section 2.2). Specifically, the global urban clusters were classified into four prototypes, that is, sparse–low-rise, compact–low-rise, sparse–high-rise, and compact–high-rise, further divided into 16 subcategories (Fig. S12 in Appendix A). Clearly, there were obvious continental differentiations in the 3D urban morphology prototype from a global perspective (Fig. 6). Most cities in East and Southeast Asia are characterized by distinctive compact–high-rise (̃50%) and sparse–high-rise (40%) prototypes, forming hotspots of very high urban skylines, especially in coastal areas such as the Taiheiyo Belt of Japan, Greater Bay Area of China, and Greater Kuala Lumpur of Malaysia (Fig. 6(a) and Table S11 in Appendix A). In particular, the average building height in cities of East Asia reaches 16.88 m (median value, similarly hereinafter), almost twice as high as that in cities in South (8.13 m) and Southwest (8.30 m) Asia (Fig. 6(b); Table S12 in Appendix A). In contrast, Africa and South America are dominated by cities labeled as sparse–low-rise prototypes, with more than 85% of cities featuring both lower skylines (average building height: ̃5 m) and a low building density (BCR: ̃0.05; Fig. 6(c) and Table S12).

Compared with the other continents, divergent 3D urban prototypes were observed in cities in developed countries in Europe and North America. Nearly 90% of European cities showed a pattern of denser footprints (BCR: 0.23) but much lower heights (average building height: 7.11 m). Exceptions are the capital cities of countries and cities in the European part of Russia (west of the Ural Mountains), exhibiting a dense–high-rise building arrangement to accommodate a higher share of the population of Europe [60] (Table S13 in Appendix A). In North America, there was a notable difference and mixture of 3D urban prototypes, ranging from the sparse–low-rise (30.4%) and dense–low-rise (65.2%) building patterns across the entire continent to the sparse–high-rise pattern in the inland west and dense–high-rise prototype in the Great Northeast of the United States.

3.4. Global building space provision and inequality patterns

Rapid urbanization together with profound changes in the urban morphology worldwide have raised issues undermining the sustainable development of current civilization [61], [62]. One of the greatest challenges facing urban sustainability is understanding current building space provision and inequality [12], [13], which needs more attention to advance the SDGs, for example, SDG 10 to reduce inequalities and SDG 11 to develop sustainable cities and communities. Spatially explicit building volume data enable us to thoroughly analyze the building space from a 3D building perspective, considering the two essential dimensions of the building space provision and inequality, which was previously unachievable. These two dimensions address different scientific subjects: one concerns assessing the adequacy of building space provision, while the other pertains to investigating the equitable distribution of the building space, which is quantitatively measured by the BVPC and Gini coefficient of the BVPC (BV-Gini).

By aggregating the BVPC indicator at the city and national scales (Section 2.6), we found that the global average BVPC value is 308.18 m³·person⁻¹ but largely varies from country to country (Fig. 7, Fig. S13 in Appendix A). People in developed countries in Europe and North America possess much a larger building space than the global average, ranging from 500.13 m³·person⁻¹ in Poland to 715.93 m³·person⁻¹ in the United States and even more than 973.78 m³·person⁻¹ in Belgium (Figs. 7(a) and S13). This is mainly attributed to the large size of the single detached dwelling buildings in these sparsely populated countries [63], [64]. Despite the large population and scarce land resources, the BVPC in Japan (632.98 m³·person⁻¹) and Republic of Korea (490.19 m³·person⁻¹) still exceeds the global average because of the high utilization of the vertical space of their cities (Fig. 5, Fig. 7(a), and S13). As the most populous country, China (321.10 m³·person⁻¹) manages to reach the global BVPC average value, mostly because of the higher urban expansion than population growth rate over the past decades. Massive high-rise residential buildings were constructed in and around the urban clusters in many coastal cities in China. In contrast, the residents of India (64.12 m³·person⁻¹), Brazil (56.61 m³·person⁻¹), Indonesia (143.55 m³·person⁻¹), and many less-developed counties in Africa suffer from overcrowding and inadequate building space (Fig. S13), as indicated by BVPC values below the global average. Much more attention is urgently needed considering overcrowded building space conditions as one of the key sources of many social problems and the spread of infectious diseases, such as COVID-19 [65], [66], [67].

We further quantified the inequality of the 3D building space for global urban clusters with the BV-Gini and Lorenz curve commonly used to measure the inequality of income or wealth (Section 2.6). Interestingly, we found a notable difference in inequality between the BVPC and income per capita across the globe, which highlights the building space inequality in many populous regions not revealed previously via economic inequality (Figs. 7(b), Figs. S14 and S15 in Appendix A). Significant inequality in the building space was evident in most cities in East, Southeast, and South Asia (red colors in Fig. 7(b), Table S14 in Appendix A), where over 3.38 billion people (̃54% of the world’s population) reside, although a lower income inequality was reported in these regions according to World Bank statistics [68]. For instance, high values of the BV-Gini were observed in the cities of Hwaseong (0.544, Republic of Korea), Tianjin (0.537, China), Zhuhai (0.625, China), Ho Chi Minh (0.502, Vietnam), Pune (0.609, India), Singapore (0.440, Singapore), and Melaka (0.615, Malaysia) (Fig. 7(b)). These results highlight a pronounced inequality in the building space that does not effectively mirror the inequality level from an economic viewpoint (Fig. S15). Among these countries, India suffers from not only shortages (only 1/5 of the global average, Fig. S13) but also high inequality in its building space, and the situation will worsen in the near future considering the sustained rapid population growth. Elsewhere, profound inequalities in both income and building space were observed in most cities in Mexico and countries in southern Africa (Fig. 7(b), Fig. S14–S16 in Appendix A), for example, Leon (0.630, Mexico), Bloemfontein (0.606, South Africa), and Lusaka (0.571, Zambia). These results call for urgent attention to reduce not only economic inequality but also building space inequality in these regions to advance future SDGs.

In contrast, despite the higher income inequality reported in countries in South America, such as Brazil, we found a relatively equal pattern of the BVPC in most cities in these countries, suggesting a smaller difference in live space between the rich and poor. Similarly, lower BV-Gini values were observed in cities in the United States, even though their income inequality has continued to increase in recent years [69]. Note that cities in the east exhibit higher inequality in infrastructure provision than those in the west, which is consistent with the income inequality pattern in the United States at the city and county levels (Fig. 7(b), Fig. S17 in Appendix A). In northern and western Europe, we found lower infrastructure provision inequality in most populous and developed cities, for example, London (0.127, United Kingdom), Paris (0.171, France), and Madrid (0.229, Spain), combined with spatial differentiation in inequality in cities in Eastern Europe, such as Kiev (0.520, Ukraine) and Moscow City (0.404, Russia). In addition, we found that some typical regions (e.g., India and African countries) exhibit lower inequality (a low Gini coefficient), while they showed significant inadequate building space (low BVPC values below the global average) to accommodate their population. Solving the problem of an inadequate building space is probably the primary concern in these regions.

Notably, our BVPC and corresponding Gini coefficient results cannot be directly compared with economic metrics such as the Gini coefficient of income inequality due to the differences in subject matter and data representation. Specifically, the 3D building space and inequality in this study were primarily derived from our GUS-3D dataset and gridded population data, which are processed at a spatial resolution of 1 km² and then summarized into administrative boundaries. In contrast, many economic metrics are derived based on household units and census tracts. Moreover, our results may exhibit potential bias due to the differences in spatial extent between our data and regional administrative boundaries, as well as data uncertainty originating from the estimates of the 3D urban structure. Future validation and exploration of the application of alternative administrative or other boundary definitions are needed to link our data within specific urban contexts. Moreover, our calculations consider urban and rural areas collectively, providing an aggregated measure that does not account for urban–rural disparities.

Overall, our analysis is fundamentally grounded in the concept of facilitating comparisons of building space provision and inequality using the above two measures among cities worldwide, with particular attention to regions falling below the global average. Our analysis findings primarily serve as an alternative standpoint, which inherently possesses uncertainties. These results may not be suitable for direct comparison with pertinent official standards or benchmarks, as they may focus on separate topics and cover different concerns. Despite these limitations, the methodology of measuring the BVPC and its Gini coefficient provides a cost-effective and efficient way to identify and assess the provision and inequality in the global 3D building space. The findings are particularly useful for those areas experiencing rapid urbanization but lacking urban survey data or with high data acquisition costs. In particular, understanding the inequality in the building space could help evaluate the process of SDG achievement, mainly SDG 11 and actively contributing to reducing inequality (SDG 10). Our findings could offer valuable references and practical applications for policy-makers and city planners to address the provision and inequality issues of the building space in alignment with the SDGs and achieve urban sustainability.

4. Conclusions

The 3D building structure in urban areas serves as a key manifestation of land surface changes dominated by human activities. The current description of the urban building space is still insufficient, primarily due to the absence of detailed and consistent urban building space data covering multiple morphological indicators in both 3D and 2D space. In this study, we introduced a publicly accessible, high-resolution global building structure dataset (GUS-3D), offering consistent building space information on volume, height, and footprint to delineate the urban morphology across global urban clusters. Our unique dataset, with its fine resolution and abundant information, could provide novel insights into urban studies, thereby addressing pivotal questions and alleviating the challenges associated with urban sustainability. With the use of the GUS-3D dataset, we obtained key insights and integrated 3D and 2D perspectives on the building space structure, including quantification of a morphological indicator of the global building space and identification of diverse urban morphology prototypes across global urban clusters. Moreover, with the GUS-3D dataset, we have a comprehensive understanding of building space provision and inequality within a global context, revealing their critical role in the realization of SDGs. In particular, we underscored the significant building space inequality in numerous cities across East, Southeast, and South Asia—regions that are home to over half of the world’s population—an aspect overlooked in previous studies focusing on economic inequality. Looking forward, the provided consistent and detailed morphological information on the building space structure has significant potential to advance research in various aspects, such as modeling and assessment of energy consumption, air pollution, carbon footprint, hazard risk management, and various other urban stainable development studies. These implications can further contribute to addressing the numerous critical urban issues toward achieving the SDGs.

CRediT authorship contribution statement

Xiaoping Liu: Conceptualization, Funding acquisition, Supervision, Writing – review & editing. Xinxin Wu: Formal analysis, Visualization, Validation, Investigation. Xuecao Li: Conceptualization, Investigation. Xiaocong Xu: Conceptualization, Methodology, Formal analysis, Funding acquisition, Writing – original draft, Writing – review & editing. Weilin Liao: Investigation, Writing – review & editing. Limin Jiao: Writing – review & editing. Zhenzhong Zeng: Writing – review & editing. Guangzhao Chen: Visualization, Writing – review & editing. Xia Li: Supervision, Writing – review & editing.

Declaration of competing interest

The 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.

Acknowledgments

This study was supported by the National Science Fund for Distinguished Young Scholars (42225107), the National Natural Science Foundation of China (42001326, 42371414, 42171409, and 42271419), the Natural Science Foundation of Guangdong Province of China (2022A1515012207), the Basic and Applied Basic Research Project of Guangzhou Science and Technology Planning (202201011539).

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2024.01.025.

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1. Introduction

2. Data and methodology

2.1. Data sources for mapping the urban building volume and height

2.2. Definitions of urban 3D structure indicators in the GUS-3D data

2.3. Mapping the global urban building volume and height

2.4. Assessment of the derived building volume and height

2.5. Calculation of the growth rate of building volume and urban extent

2.6. Quantification of building space provision and inequality

3. Results and discussion

3.1. Performance of the GUS-3D dataset

3.2. Global layout of the 3D urban building structure

3.3. Prototypes of the 3D urban morphology

3.4. Global building space provision and inequality patterns

4. Conclusions

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Appendix A. Supplementary data

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