Global increases in built-up volume indicate more divergent and less dispersed urban expansion patterns

Domain: chemistry
Published: 2026-02-21
Editorial outcome: minor_revision

Abstract
Viewing urban spatial structure from a three-dimensional (3D) perspective provides important insights for environmental sustainability. While existing studies mainly examine 3D built-up volume, the spatial distribution of vertical growth remains insufficiently understood. This study investigates centrality and intensity of vertical expansion in newly urbanized areas. Using multi-source remote sensing data, we develop a Centrality Index (CI) and an Intensity Index (II) to characterize 3D urban expansion and compare it with conventional two-dimensional (2D) measures. Results show that: (1) 3D expansion is generally more centralized than 2D expansion. (2) Vertical growth is stronger in the Global South; however, Global South cities outside China, especially in Africa, often demonstrate low 3D centrality. (3) 3D expansion patterns are closely associated with natural and socioeconomic conditions and display strong path dependency. As urbanization shifts toward Africa and South Asia, prevalent low-centrality patterns may improve land-use efficiency but increase commuting-related carbon emissions.

Introduction
Urban expansion can be analyzed from two perspectives: two-dimensional (2D) and three-dimensional (3D). The 2D perspective emphasizes the increase in built-up surface area, while the 3D perspective encompasses the built-up volume. Over the past three decades, urban land area has expanded at a rate exceeding population growth1, leading to dispersed, sprawling, and low-density urban patterns. This trend of horizontal expansion presents significant environmental challenges, including biodiversity loss2, reduced agricultural productivity3, diminished terrestrial carbon sinks4, and increased carbon emissions5. In response, policymakers and planners worldwide have pursued denser, vertical urban growth, often through development controls and ‘compact city’ initiatives. Although analyses taking a 2D perspective have substantively enhanced our understanding of the extent and morphological complexity of urban sprawl and transforamtion6,7, fostering sustainable urbanization globally necessitates improved measurement and deeper insights into 3D urban expansion.

The exploration of 3D urban expansion has long been constrained by the availability of data on urban built-up volume. However, recent advancements in remote sensing and radar technologies have significantly improved our capacity to characterize urban built-up volume. While earlier studies primarily focused on 3D urban expansion within individual cities8,9, more recent research has leveraged high-resolution data to highlight global trends in urban vertical growth10–13. Concurrently, numerous studies have underscored the impact of 3D urban spatial structures on environmental sustainability, encompassing aspects, such as building energy consumption14,15, urban heat island effects16,17, air quality18, and carbon emissions19,20. For instance, research indicates that a higher concentration of high-rise buildings may obstruct natural lighting and ventilation, potentially increasing operational energy consumption20,21 and carbon emissions22. Despite these insights, existing studies on global-scale 3D urban expansion have predominantly concentrated on volume changes associated with vertical growth, often neglecting the spatial distribution of these changes within cities. Considering these geographies would nonetheless be valuable for comprehensively assessing 3D urban expansion and its implications for sustainable urbanization.

Much of the existing research on urban form emphasizes the spatial organization of land and facilities from a 2D perspective, often framed through the concepts of compactness and sprawl. For example, indicators such as the landscape expansion index primarily assess the continuity-fragmentation of urban expansion concerning existing built-up areas23–27, while metrics derived from concentric partitioning and functional fitting analyze the centrality-dispersion dynamics of urban growth relative to city centers28–31. However, these approaches may not fully encapsulate the complexity of urban expansion, particularly as many cities have increasingly transitioned from horizontal to vertical growth over the past three decades11,13. This evolving nature of urban development—where 3D expansion is becoming an increasingly significant phenomenon alongside traditional 2D sprawl—creates a need for analytical frameworks that can capture this compounded, three-dimensional reality. This is particularly relevant for accurately measuring urban concentration, which can diverge significantly between 2D and 3D perspectives and is closely linked to the spatial distribution of increased built-up volume.

Against this background, this study is motivated by a dual imperative: (1) the increasing availability of high-resolution 3D urban data, which now makes possible a comprehensive global analysis that was previously limited in scope; and (2) the need to better understand the complex and evolving patterns of global urban expansion, which are increasingly defined by vertical growth and densification. Together, these imperatives point to knowledge gaps in our current understanding of 3D urban expansion, particularly in terms of its spatial distribution and broader implications. To address these knowledge gaps, we aim to: (1) characterize the centralization trends in global urban expansion from both 2D and 3D perspectives and analyze the differences therein; (2) identify patterns of 3D urban expansion through the frameworks of spatial centralization and verticality; and (3) assess key socioeconomic and environmental correlates of these 3D urban expansion patterns. The levels of centralization in 2D and 3D urban expansion reflect how increased built-up surface area and built-up volume are distributed around urban (sub)centers, respectively. Utilizing gridded data from the global human settlement layer (GHSL) dataset, we investigate 3D urban expansion trends for over 1800 cities worldwide between 2000 and 2018. Our results show that 3D urban expansion is generally less dispersed than 2D measurements. The vertical extent of expansion is greater in the Global South than in the Global North, particularly in the United States. However, cities in the Global South outside China, especially in Africa, often demonstrate low levels of centrality in their 3D expansion. This North–South centrality gap would likely widen further if vertical redevelopment within existing built-up areas is considered. Moreover, 3D expansion patterns are closely linked to natural and socioeconomic conditions and display strong path dependency.

Results
Urban expansion tends to be less dispersed in 3D terms
We observe strong correlations in the Centrality Index (CI) of urban expansion over the past two decades when comparing 2D and 3D measurements (Fig. 1). The CI scores derived from both measurement methods show a statistically significant correlation coefficient of 0.916 at the 0.1% level. This suggests that cities showing more dispersed 3D expansion typically also display more dispersed 2D expansion, and vice versa. Among the top 50 cities with the highest 3D CI scores, 35 are also ranked in the top 50 for 2D-based CI scores (Supplementary Table 1). In addition to the overall correlation between 2D and 3D measurements, further diagnostic tests (see Supplementary Note 1) indicate the vertical concentration represents a distinct though related dimension of urban spatial structure. Notably, the majority of cities show higher CI scores as measured in 3D. Only 51 cities—less than 3% of the global total—exhibit slightly higher CI scores in the 2D measurement. Moreover, the mean 3D-based CI score (52.0) is significantly higher than the mean 2D-based CI score (49.7) at the 0.1% significance level (Fig. 1a). This difference is consistent across continents and countries with varying income levels (Supplementary Fig. 1). These findings imply that, globally, increased built-up volume is more concentrated around urban (sub)centers compared to built-up surface area.

The differences between 3D- and 2D-based CI scores of individual cities vary across global regions (Fig. 1b–d). Cities with larger differences in CI scores (indicated by orange points in Fig. 1b) are predominantly situated in the Global North, whereas cities in the Global South, with the exception of China, typically display smaller CI score differences (i.e., purple and yellow points in Fig. 1b). Furthermore, the average CI score difference in the Global North is higher than that in the Global South (Fig. 1c). At the continental level, cities in Asia and Oceania, Europe, and North America tend to show higher CI score differences, with smaller differences observed in Africa and Latin America and the Caribbean (Fig. 1d).

These patterns of CI score differences remain consistent across different combinations of increased built-up volume and urban center data (Supplementary Fig. 2). In Asia and Oceania, China is particularly notable, with 144 cities exhibiting the highest levels of CI score differences (calculated using the Jenks Natural Breaks method), accounting for 39.1% of the global total (orange points in Fig. 1b). Specifically, Shanwei in Guangdong province registers the highest CI score difference of 9.731. In contrast, Indian cities primarily demonstrated medium and low levels of CI score differences (blue and purple points in Fig. 1b). In Europe, the average CI score difference for cities is the highest, followed by cities in North America, and then those in Asia and Oceania (Fig. 1d). Within North America, there are significant variations: cities along the east coast generally show higher CI score differences, while those on the west coast tend to exhibit lower differences. On average, cities in Africa and Latin America and the Caribbean display lower CI score differences, with African cities showing the lowest mean value at 0.95. Statistically, these regional variations in CI score differences can be attributed to the more heterogeneous distribution of CI scores in 3D compared to 2D measurements; the standard deviation of 3D CI scores (3.1) is significantly greater than that of 2D scores (2.2) at the 0.1% significance level.

As an essential factor influencing urban expansion patterns24,32, urban population is found to be negatively correlated with CI score differences, indicating that cities with larger populations tend to exhibit lower differences in their CI scores (Fig. 1e). Specifically, cities with populations exceeding 5 million (M) have the lowest mean CI score differences, followed by those with populations between 1M and 5M. This trend is expected, given that 41.8% of cities in Africa have populations greater than 1 million (Supplementary Table 2). Conversely, cities with populations below 0.1M demonstrate the highest mean CI score differences, followed by those with populations between 0.1M and 0.5M. This pattern aligns with the observation that 67.2% of European cities, 78.2% of North American cities, and 54.6% of cities in Asia and Oceania have populations fewer than 0.5M (Supplementary Table 2).

Four patterns of 3D urban expansion
While the 3D-based centrality index (CI) measures the extent to which a city’s increased built-up volume is concentrated around its urban (sub)centers, it does not account for the intensity of vertical growth. To address this limitation, we calculate the intensity index (II) of 3D urban expansion, using the average height of the increased built-up surface area as a proxy (Supplementary Fig. 5). All else being equal, higher values of both II and CI point to more centralized and intensive 3D urban expansion, suggesting that newly constructed buildings are generally taller and more concentrated around urban (sub)centers (Fig. 2b). In spite of being calculated based on the same built-up volume dataset, the weak correlation between CI and II measurements indicate that the two indicators capture distinct aspects of vertical urban structure (see Supplementary Note 2). By integrating these two indicators, we can identify four distinct patterns of 3D urban expansion, based on the mean CI and II scores for each city. Findings from this categorization remain consistent when alternative classification methods, including median-based and clustering-based schemes, are used (see Supplementary Note 3, Supplementary Tables 5 and 6, and Supplementary Figs. 20–23).

Globally, 314 or 17.3% of the cities fall into the HC-HI pattern (Fig. 2a), characterized by high CI and II scores. These cities are predominantly located in Asia and Europe (Fig. 2c), including examples such as Shanghai and Berlin (Fig. 3). In contrast, 476 or 26.2% of the cities exhibit the LC-HI pattern (Fig. 2a), defined by low CI and high II scores. This pattern is mainly found in East Asia, Europe, Africa, and South America (Fig. 2c). Additionally, 483 or 26.5% of the cities belong to the HC-LI pattern (Fig. 2a), characterized by high CI and low II scores. These cities are primarily located in North America (Fig. 2c), with examples including Boston, Toronto, and Calgary (Fig. 3). Lastly, 547 or 30.1% of all cities display lower CI and II scores, categorized under the LC-LI pattern (Fig. 2a). These cities are mainly distributed across Africa, Latin America and the Caribbean, as well as North America (Fig. 2c).

The patterns of 3D urban expansion exhibit significant variations across countries (Table 1). In many North American and Western European countries, such as the United States, Canada, and France, the HC-LI and LC-LI patterns predominate (Supplementary Figs. 6 and 11). For example, nearly 92.7% of U.S. cities are of the HC-LI (50.4%) and LC-LI (42.3%) patterns. Only 25 cities, including New York and Los Angeles, exhibit HC-HI or LC-HI patterns (Fig. 3 and Supplementary Fig. 6). In contrast, cities in Asia and Oceania, especially in East Asian countries like China, are primarily characterized by the HC-HI and LC-HI patterns. In China, the HC-HI (34.7%), LC-HI (27.0%), and HC-LI (25.6%) patterns are most common, indicating that newly constructed buildings tend to be taller and more concentrated around urban (sub)centers. Only 56 Chinese cities (12.7%) display the LC-LI pattern, primarily located in the North China Plain (Supplementary Fig. 7). In many countries of the Global South, the LC-LI and LC-HI patterns are dominant, with no clear trend regarding 3D expansion intensity. For instance, nearly 70% of Indian cities exhibit either the LC-LI (37.0%) or LC-HI (32.9%) patterns, with only three cities—Kolkata, Pune, and Vasai-Virar—falling under the HC-HI pattern (Supplementary Fig. 8). This trend is even more pronounced in Brazil and Nigeria, where nearly 90% of Brazilian cities belong to either the LC-LI (50.7%) or LC-HI (38.8%) categories (Supplementary Fig. 9), and all Nigerian cities are classified as either LC-HI (76.5%) or LC-LI (23.5%) (Supplementary Fig. 10). Overall, high-intensity 3D expansion is notably prevalent in East Asia, while low-intensity patterns characterize North America, and a mix of low-centrality patterns is dominant in Africa, Latin America and South Asia, with Europe showing a more diversed distribution.

Correlates of the 3D urban expansion patterns
The socioeconomic and environmental correlates of observed patterns of 3D urban expansion are summarized with a multi-class LightGBM model and the SHAP method. The model attains an overall accuracy of 65.1% on a held-out test set, notably higher than the random prediction baseline of 25% (given the four categories). Performance varies across classes, with LC-LI showing the highest recall and HC-HI exhibiting relatively lower precision and F1-score, while the weighted average F1-score (0.646) indicates a generally consistent predictive capability across classes. We therefore characterize the model as demonstrating moderate yet robust predictive performance, effectively capturing the key associations between urban expansion patterns and their underlying drivers (see Supplementary Note 4 and Supplementary Table 7 for detailed evaluation metrics). It is important to note, however, that these results reveal correlational rather than causal relationships, and thus should be interpreted as indicative associations rather than direct causal mechanisms.

As illustrated in Fig. 4a, Maximum Building Height (MBH) and Baseline Urban Centrality (BUC)—both related to urban form—emerge as the two most significant correlates. Following these, baseline population (BPOPU) and increased built-up volume (IBV), which are indicators of city size, are also significantly associated. Furthermore, factors such as motor roadway density (MRD), terrain relief (TR), and baseline per capita GDP (BPGDP) contribute to enhancing the model’s predictive performance. Among the regional dummy variables, the North America dummy (NAD) is noteworthy, while the other four regional dummies exhibit minimal predictive contributions.

Cities characterized by the HC-HI pattern typically exhibit higher values for maximum building height (MBH), baseline population (BPOPU), baseline urban centrality (BUC), and terrain relief (TR) (Fig. 4b). Additionally, lower values of annual mean temperature (AMT), growth rate of population (GPOPU), and growth rate of per capita GDP (GPGDP) are associated with a greater likelihood of this pattern. In contrast, the relationship between the HC-HI pattern and both motor roadway density (MRD) and baseline per capita GDP (BPGDP) is nonlinear; cities with moderate MRD and exceptionally high BPGDP are more likely to exhibit this pattern (Supplementary Fig. 13).

Cities exhibiting the LC-HI pattern generally demonstrate higher values for baseline population (BPOPU), increased built-up volume (IBV), motor roadway density (MRD), terrain relief (TR), and maximum building height (MBH) (Fig. 4c). Conversely, lower values of baseline urban centrality (BUC) and baseline per capita GDP (BPGDP) are also indicative of this pattern. A notable characteristic of the LC-HI pattern is its inverse U-shaped relationship with urban public transit accessibility (UPTA) (Supplementary Fig. 15), suggesting that cities with moderate UTA values are most likely to exhibit this pattern.

Cities exhibiting the HC-LI pattern are more likely to have higher values of baseline urban centrality (BUC), baseline per capita GDP (BPGDP), growth rate of per capita GDP (GPGDP), and number of urban centers (NUC) (Fig. 4d). Conversely, cities with lower levels of increased built-up volume (IBV), baseline population (BPOPU), motor roadway density (MRD), and terrain relief (TR) also tend to exhibit this pattern. The relationship between the HC-LI pattern and urban slum governance (USG) and annual mean temperature (AMT) is complex; cities with exceptionally high USG and relatively low AMT values are more likely to develop this pattern (Supplementary Fig. 17).

Cities characterized by the LC-LI pattern generally exhibit higher values for growth rate of population (GPOPU) and increased built-up volume (IBV) (Fig. 4e). Conversely, lower values of maximum building height (MBH), terrain relief (TR), baseline urban centrality (BUC), and baseline population (BPOPU) are also indicative of this pattern. The relationship between the LC-LI pattern and Annual mean temperature (AMT), motor roadway density (MRD), and baseline per capita GDP (BPGDP) is complex and nonlinear. For example, cities with moderate levels of MRD are more likely to display the LC-LI pattern. Additionally, cities with AMT values around 20°C tend to exhibit this pattern, while those with AMT values exceeding 25°C are less likely to do so (Supplementary Fig. 19).

Methods
Extracting data on increased built-up footprint and volume for sample cities
We delineate urban boundaries and select sample cities using the 2018 Global urban boundaries (GUB) dataset, which is derived from 30-m resolution Global artificial impervious area (GAIA) data42. Following established methodologies in urban expansion research43, we use built-up area as the primary criterion for sample selection, focusing on cities with built-up areas exceeding 50km². Additionally, in accordance with the United Nations’ definition of cities and relevant studies44, we exclude cities with populations below 50,000, based on the 2018 LandScan population dataset. This selection process results in a final sample of 1944 cities, which collectively house nearly 2 billion people, or approximately half of the global urban population in 2018. Consequently, the selected cities provide broad coverage of the global urban landscape. Notably, these sample cities broadly aligns with the concept of natural cities, including urban agglomerations that span administrative boundaries, such as those in China’s Yangtze River Delta and Pearl River Delta regions.

We then extract data on increased built-up footprint and volume for the sample cities between 2000 and 2018, using urban built-up surface data (GHS-BUILT-S)45 and urban built-up height data (GHS-BUILT-H)46, both at a 100-m resolution, from the 2023 Global Human Settlement Layer (GHSL) data package released by the Joint Research Centre (JRC) of the European Commission. These datasets integrate various data sources, including Sentinel-2, Landsat, global digital surface model (DSM) data, and OpenStreetMap (OSM). Specifically, we derive 100-meter resolution gridded data for increased built-up footprint by subtracting the GHS-BUILT-S data from 2000 from that of 2018. To calculate the increased built-up volume from 2000 to 2018, we multiply the increased built-up footprint data by the 2018 urban built-up height data for each grid.

Due to the absence of built-up height data for the baseline year of 2000, the derived data on increased built-up volume captures only the volumetric changes associated with outward urban expansion, excluding those resulting from urban renewal. For instance, urban areas where low-rise buildings have been replaced by high-rise structures may exhibit significant increases in volume without any corresponding change in footprint, a change that our methodology cannot detect. This limitation is common in studies of 3D urban growth11,47, as time-series high-resolution built-up height data at a global scale remains unavailable. Consequently, our study aims to provide a more nuanced 3D perspective on urban outward expansion rather than comprehensively addressing vertical urban growth.

Measuring centrality index of 2D and 3D urban expansion
We employ a two-step approach to measure the centrality index for both 2D and 3D urban expansion. First, we identify urban centers within the sample cities for the year 2018 using the local indicators of spatial association (LISA) methodology48. This analysis relies on the 2018 LandScan population dataset and NPP-VIIRS-like nighttime light (NTL) data. Specifically, we apply the Cluster and Outlier Analysis (Anselin Local Moran’s I) tool in ArcGIS 10.5 to detect high-high (HH) clusters—grids with high values surrounded by similarly high-value neighbors—based on an inverse distance spatial weight matrix. Separate analyses are conducted for population density and nighttime light intensity, effectively identifying high-density and contiguous urban centers while avoiding arbitrary thresholds49–51. Second, we determine the locations of urban centers by extracting the centroids of the spatial intersections between population-based and nighttime light-based HH clusters. This combined approach enhances the robustness of urban center delineation compared to methods based on a single indicator25. Notably, 124 cities are excluded from the sample because population and nighttime light HH clusters do not overlap for these cities (Supplementary Table 3).

We then calculate the centrality index (CI) of urban expansion for each sample city using the following equations:

CI 2D = 1 / (1 + (\sum_{i=1}^{n} s_i d_i) / (\sum_{i=1}^{n} s' d_i)) × 100 (1)

CI 3D = 1 / (1 + (\sum_{i=1}^{n} v_i d_i) / (\sum_{i=1}^{n} v' d_i)) × 100 (2)

where CI and CI represent the centrality indices for 2D and 3D urban expansion, respectively. s_i and v_i denote the increased built-up footprint and volume of grid i, while s' and v' refer to the averages of the total increased built-up footprint and volume across all grids within a city. d_i represents the distance between the centroid of grid i and the nearest urban center, and n is the total number of grids within a city.

Higher values of CI and CI indicate that new developments are more concentrated around urban centers, reflecting a centralized expansion pattern. Conversely, lower values suggest a more dispersed pattern of urban expansion.

The above equations for the centrality index (CI) ensure a size-neutral assessment of urban expansion. Specifically, the numerators \sum_{i=1}^{n} s_i d_i and \sum_{i=1}^{n} v_i d_i capture the actual spatial distribution of new developments, incorporating influences from both size-related factors (e.g., baseline city size and expansion extent) and the spatial structure of the city. In contrast, the denominators \sum_{i=1}^{n} s' d_i and \sum_{i=1}^{n} v' d_i represent a hypothetical equilibrium scenario based solely on size-related factors, without accounting for spatial structure. This distinction ensures the size neutrality of the CI metric, as both numerator and denominator scale proportionally with size-related factors. Thus, CI offers a standardized measure of the spatial centrality of urban expansion, effectively controlling for variations in city size or expansion extent.

This methodology offers two key advantages. Firstly, unlike most studies that calculate centrality indices using the Gini coefficient without explicitly defining the urban core52,53 or relying solely on historical urban centers28–30,54, our approach identifies multiple urban centers (where applicable) within each city. This enables us to capture the emergence of densely developed subcenters, such as new towns or development zones, which aligns closely with the principles of urban compactness33. Secondly, while existing methods typically focus on either dynamic expansion patterns or static urban forms25,55, our approach evaluates both. By substituting increased built-up footprint and volume with stock built-up footprint and volume in the equations, we are able to measure the centrality degree of urban form for the baseline year 2000. This flexibility supports our subsequent analysis of the correlates of 3D urban expansion patterns.

Exploring correlates of 3D urban expansion patterns
In addition to the centrality index (CI), we introduce the Intensity Index (II) to further characterize the diverse patterns of 3D urban expansion, using the following equation:

II 3D = V / S (3)

where II denotes the intensity index of 3D urban expansion, V refers to the total increased built-up volume, and S represents the total increased built-up footprint for each sample city. This metric effectively captures the average height of newly constructed buildings, with higher values indicating more vertically intensive urban growth.

By combining the CI and II metrics, we are able to classify the sample cities into four distinct categories of 3D urban expansion: HC-HI (cities with higher-than-average CI and II), LC-HI (lower-than-average CI and higher-than-average II), HC-LI (higher-than-average CI and lower-than-average II), and LC-LI (lower-than-average CI and II).

Drawing upon relevant studies10,56–58, we develop a prediction model to explore the socioeconomic and environmental factors that shape 3D urban expansion patterns. A detailed description of these features can be found in Supplementary Table 4. The natural conditions include Terrain Relief (TR) and annual mean temperature (AMT), both of which are considered in the analysis of urban expansion. The socio-economic factors encompass baseline population (BPOPU), baseline per capita GDP (BPGDP), growth rate of population (GPOPU), and growth rate of per capita GDP (GPGDP). These factors can indirectly shape 3D urban expansion patterns; for instance, BPGDP influences a city’s potential for outward expansion and its capacity to support the construction of taller buildings. The urban form and planning regulations feature variables such as maximum building height (MBH), baseline urban centrality (BUC), increased built-up volume (IBV), number of urban centers (NUC), motor roadway density (MRD), urban public transit accessibility (UPTA), and urban slum governance (USG). These variables have a direct impact on 3D urban expansion patterns; for example, MBH sets the upper limit for building heights, thus affecting vertical expansion potential. Finally, the regional dummies include the Asia and Oceania dummy (AOD), Africa dummy (AFD), Europe dummy (EUD), North America dummy (NAD), and Latin America and the Caribbean dummy (LACD), which capture geographical impacts on expansion patterns.

We employ the LightGBM algorithm for our multi-class classification task, utilizing the four patterns of 3D urban expansion as dependent variables and the 18 previously mentioned features as independent variables. As a tree-based algorithm, LightGBM is particularly well-suited for medium-sized datasets and offers strong interpretability, especially through the TreeSHAP tool. Compared to earlier algorithms like XGBoost, LightGBM offers faster training time and improved scalability without compromising accuracy59. To mitigate overfitting, we split the dataset into training (70%) and testing (30%) sets and applied three-fold cross-validation. To identify the best-performing model, we randomly divided the dataset multiple times and trained the model 20 times, using randomized search each time to explore optimal hyperparameter combinations. The model with the highest prediction accuracy was selected for further analysis. We employ a listwise deletion approach, excluding samples with missing values to enhance model accuracy. This decision is supported by exploratory analysis indicating that removing incomplete observations leads to better predictive performance.

Using the LightGBM model, we apply the TreeSHAP (Tree SHapley Additive exPlanation) method to identify key features correlating with 3D urban expansion patterns and to understand their impacts. SHAP is a widely used framework for interpreting machine learning models based on cooperative game theory, with TreeSHAP being a more efficient implementation tailored specifically for tree-based models like LightGBM60. This method assigns each feature an importance value (SHAP value) that reflects its contribution to the model’s predictions for individual instances. More specifically, a feature’s SHAP value is determined by assessing its marginal contribution across all possible feature coalitions, representing the difference in the model’s prediction with and without that feature. The mean absolute SHAP value of each feature indicates its overall importance, while the distribution of SHAP values across samples reveals how variations in that feature correlate with the predicted outcomes.

Robustness test
To enhance the reliability of our findings, we conduct a two-layer robustness test for the measurement of the centrality index (CI), incorporating alternative methods for calculating increased built-up volume and identifying urban centers. In the baseline method for measuring increased built-up volume, we calculate it by multiplying the increased built-up footprint data by the GHS-BUILT-H data, which reflects the average building height of a 100 m-resolution grid. However, this approach can introduce inaccuracies, particularly in grids where pre-existing built-up volume significantly exceeds the newly added volume. For instance, in grids with many tall buildings, the larger average height could lead to an overestimation of the increased built-up volume, even if the actual change is relatively minor. To address this issue, we develop an alternative calculation method that excludes grids where the existing built-up footprint exceeds the newly added footprint. The remaining grid data are then multiplied by the GHS-BUILT-H data to produce a refined estimate of the increased built-up volume.

Regarding the identification of urban (sub)centers, our baseline method identifies centers based on both population and nighttime light clusters. However, this approach excludes 124 cities where the population and nighttime light centers did not spatially coincide, potentially introducing selection bias. To mitigate this issue, we develop two alternative approaches: one that retains only the population center and another that retains only the nighttime light center. Combining these with our two methods for measuring increased built-up volume yield six different combinations of analysis. We recalculate the CI using data from these alternative methods and find that the conclusions drawn from the alternative CI values are consistent with those obtained from the baseline approach (Supplementary Fig. 2).

We evaluate the robustness of the mean-based classification of 3D urban expansion patterns using two alternative methods: a median-based approach and a hierarchical clustering approach (see Supplementary Note 3 for details). Cohen’s Kappa statistic indicated excellent agreement between the mean- and median-based schemes, and moderate agreement with the clustering-based method. While the clustering approach reclassify a small number of cities located near category boundaries, the overall regional distribution of patterns remain highly consistent across all three methods. Robustness is further supported by training LightGBM models on the alternative classifications, which produce stable results in both the relative importance and directional effects of key predictors. These consistent outcomes reinforce the reliability of our main findings on the drivers of different 3D expansion patterns.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study makes a timely and valuable contribution to the global urban expansion literature by foregrounding the three-dimensional (3D) aspects of urban growth, an area that remains underexplored compared to its two-dimensional (2D) counterpart. By introducing and operationalizing two novel indices—Centrality Index (CI) and Intensity Index (II)—the authors provide a compelling empirical framework to categorize and analyze patterns of 3D urban expansion in over 1,800 cities worldwide. The analytical rigor and the scale of the dataset are impressive, and the interpretation of results is generally well-aligned with existing knowledge on urban morphology and sustainability.\n\nThe paper introduces a promising analytical framework to capture the centrality and intensity of 3D urban expansion, but the framing in the introduction leaves the reader uncertain about the core motivation driving the study. Specifically, it is unclear whether the impetus for this work stems primarily from (a) recent technological advances and data availability—particularly improvements in remote sensing and building height data—or from (b) a theoretical and empirical recognition that global urban expansion is transitioning from a predominantly 2D (horizontal) phenomenon to a more 3D (vertical) one. This distinction is not trivial.\n\nThese are both compelling and legitimate starting points, but they represent different research orientations. The former is methodological and data-driven, implying that the research is filling a technical gap in our ability to measure and compare urban form in 3D. The latter is conceptual and theory-driven, suggesting that urban development processes themselves have changed in ways that require new analytical lenses.\n\nThe two motivations are not mutually exclusive, and indeed, the study could be strengthened by embracing them in parallel. However, the authors need to articulate this dual framing more explicitly. At present, the introduction blends these motivations in a way that feels implicit and unresolved. A more deliberate framing would not only sharpen the study’s narrative but also better guide the reader in understanding its broader significance—whether as a methodological advance, a conceptual reframing, or both.\n\nAnother area of concern lies in the potential collinearity or redundancy between the 3D and 2D Centrality Index (CI) measures. While the paper highlights a strong correlation between the two, it raises the question of whether the 3D CI truly offers independent and added information about vertical expansion, or whether it primarily reflects spatial trends already captured in the 2D CI. Without stronger statistical tests (e.g., variance inflation factor analysis, partial correlation, or residual-based comparisons), it remains unclear to what extent vertical growth patterns are being uniquely captured. This is especially important since the study’s key conclusions rest on differences between the 2D and 3D indices. The authors could further clarify this relationship by quantifying the net contribution of verticality after controlling for horizontal patterns, or by examining cases where the two indices diverge substantially and explaining why. While this limitation does not preclude publication, it warrants more explicit discussion or analytical validation.\n\nThe reported high correlation between 2D-CI and 3D-CI (r = 0.916) also raises concerns about the added value of the 3D Centrality Index. In many cases, especially where height gradients mirror horizontal expansion, 3D-CI may not provide substantially new insights. Moreover, in cities with centralized high-rise clusters and sprawling low-rise suburbs, 3D-CI may overemphasize central volumetric outliers, potentially misrepresenting vertical structure as horizontal concentration. The paper would benefit from further analysis to isolate the unique contribution of height to centrality and assess whether 3D-CI captures distinct spatial variance beyond 2D-CI.\n\nThe CI and II thresholds used to define expansion types (e.g., HC-HI, LC-LI) rely on mean-based cutoffs, which may oversimplify underlying distributions or obscure regional nuances. A sensitivity analysis using percentile-based thresholds or cluster-based classification might improve robustness. Nonetheless, the methodological choices are overall reasonable and align with the standards of large-scale spatial analysis in this field.\n\nAnother key conceptual issue lies in the potential structural coupling between the 3D Centrality Index (3D-CI) and the Intensity Index (II). Although the two are presented as capturing distinct aspects of urban expansion—spatial concentration versus vertical intensity—they are both directly derived from the same variable: built-up volume. Specifically, 3D-CI is computed as a distance-weighted average of volume, while II represents the city-wide average building height (volume divided by footprint). This shared dependency on volume raises concerns about whether these indicators are truly orthogonal dimensions of urban structure.\n\nIn practice, their relationship may be heavily influenced by urban morphology. For instance, if tall buildings are concentrated near city centers, both 3D-CI and II will be high; conversely, if high-rise developments emerge in peripheral areas, 3D-CI may decline while II remains high. Such patterns imply that the spatial and vertical metrics are interdependent, and any classification based on their combination (e.g., HC-HI, LC-HI) may be influenced more by structural biases than independent mechanisms.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "Review of \"Global Increases in Built-Up Volume Indicate More Divergent and Less Dispersed Urban Expansion Patterns\"\n\nOverall Evaluation\nThis manuscript addresses a timely and important topic in urban studies and sustainable development. It provides a novel 3D perspective on urban expansion by examining not only the increase in built-up volume but also its spatial distribution within cities, an aspect often neglected in global studies. The authors introduce new metrics – a 3D Centrality Index (CI) and Intensity Index (II) – to characterize how vertically and how centrally cities are growing. Using an extensive dataset of 1,944 cities worldwide (covering ~2 billion people), the study uncovers key global patterns: for example, urban expansion in 3D tends to be less dispersed (more centralized) than in 2D, and the Global South shows greater vertical expansion but often with low centrality (e.g. many African cities exhibit tall growth that is not concentrated in city centers). These findings are highly relevant to sustainable urban development, as 3D urban form influences energy use and carbon emissions. Overall, the manuscript is significant and original. It advances the field by bridging the gap between two-dimensional sprawl metrics and three-dimensional urban form, offering insights with clear implications for urban planning and climate policy. The work is generally well executed and, in my assessment, suitable for publication in Nature Communications after addressing some revisions detailed below.\n\nMajor Strengths\nImportance and Novelty: The study tackles a critical question of how cities grow upward vs outward, which has direct implications for land use efficiency and sustainability. Prior global analyses of urban growth have largely focused on horizontal expansion; by incorporating the vertical dimension and spatial centrality, this work fills an important knowledge gap. The concept of analyzing 3D urban expansion patterns (HC-HI, LC-HI, etc.) is innovative and yields new insights that traditional 2D analyses would miss. This level of novelty and global scope is commendable and of high interest to the urban sustainability research community.\n\nData Breadth and Global Coverage: The analysis is built on an impressively broad dataset (Global Human Settlement Layer and other remote sensing sources) covering nearly two thousand cities worldwide. Such global coverage enhances the robustness and general relevance of the findings. The inclusion of diverse cities (across continents, development levels, etc.) allows the authors to draw meaningful comparisons between, for example, patterns in North America vs. Africa. This comprehensive scope strengthens the paper’s contribution to global urban studies.\n\nMethodological Innovation: The authors develop and apply two new indices – a 3D Centrality Index and a 3D Intensity Index – to quantify urban expansion patterns. The Centrality Index measures how concentrated new development is around urban centers, while the Intensity Index captures the average height (vertical intensity) of new constructions. Integrating these two dimensions is a clever approach to classify cities into four expansion typologies. The methodology (e.g. identifying multiple urban centers via LISA, ensuring indices are size-neutral) is sound and rigorously described. Establishing these metrics is a valuable contribution that other researchers can build upon.\n\nAnalysis of Drivers and Implications: Beyond describing patterns, the paper uses a machine learning model (LightGBM with SHAP analysis) to explore socioeconomic and environmental correlates of the 3D expansion patterns. This adds explanatory depth – for instance, highlighting that baseline urban form (e.g. existing centrality, building height) and city size are strong predictors of a city’s expansion pattern. The discussion insightfully connects the findings to broader implications, such as the trade-off between vertical growth improving land-use efficiency but potentially increasing commuting-related carbon emissions in certain patterns. Linking empirical results to sustainability challenges and policy considerations enhances the impact of the work.\n\nMajor Issues and Suggestions for Improvement\nWhile the manuscript is strong, there are several issues that should be addressed to improve its clarity and robustness:\n\nExclusion of Urban Renewal: A key limitation is that the study captures only outward expansion and does not account for urban “renewal” or densification within existing built-up areas. The authors do acknowledge this limitation, noting that their method cannot detect volume increases without footprint change. They argue that vertical redevelopment (common in developed cities) would, if included, likely increase the measured centrality and intensity in Global North cities, widening the contrast with the Global South. This is an important point, and the manuscript should ensure it is communicated very clearly and up-front. I recommend the authors emphasize in the abstract and conclusions that their results pertain to outward expansion only (new urban areas from 2000–2018), and do not capture vertical growth via redevelopment. Additionally, if possible, provide some quantitative sense of how big this effect might be. For example, could the authors cite studies or data on urban renewal impacts, or at least qualitatively discuss where this limitation is most consequential? Strengthening the discussion of this limitation will make the conclusions more rigorous and prevent over-interpretation of the findings.\n\nThreshold Definition for CI and II (Classification Robustness): The four expansion pattern categories (HC-HI, LC-HI, HC-LI, LC-LI) are defined by whether a city’s CI and II are above or below the “average” (mean) values. This binary thresholding is convenient but somewhat arbitrary, and it raises questions about robustness. The authors should clarify how the threshold was determined (it appears to be the global mean of each index; if so, was this done separately for CI and II?). It would strengthen the paper to demonstrate that the patterns identified are not an artifact of the particular threshold choice. For example, did the authors test using median instead of mean, or examine sensitivity if the threshold shifts slightly? Since the resulting category sizes are somewhat imbalanced (e.g., only ~17% of cities are HC-HI, whereas ~30% are LC-LI), one wonders if the “average” values lie in a skewed part of the distribution. A brief analysis or rationale about threshold selection and stability would be valuable. Alternatively, the authors could consider a clustering approach or provide quantitative justification (e.g., bimodality in the index distributions) for the dichotomous split. Ensuring the classification is robust will increase confidence in all subsequent pattern-based analyses.\n\nSupport for Regional Differences (Fig. 3 and Table 1): The manuscript claims significant regional and country-level differences in 3D expansion patterns, citing Figure 3 (city examples) and Table 1 (counts of cities in each category for selected countries). While the data presented do indicate contrasts – for instance, 92.7% of US cities are in the low-intensity categories (HC-LI or LC-LI) whereas a much larger share of Chinese cities are high-intensity (HC-HI or LC-HI) – the presentation could be improved to more convincingly support these comparisons. Table 1 is useful, but it only lists a handful of countries without explanation of why those were chosen. Are they simply illustrative examples, or the top emitters, or largest urban populations? The authors should clarify the selection and perhaps include additional key regions or a summary (e.g. an aggregate for “North America vs Europe vs Asia vs Africa”) to better highlight regional trends. Similarly, while Figure 3 (visualizations of representative cities) is a nice qualitative illustration of each pattern, it does not on its own demonstrate regional prevalence differences. The global map in Fig. 2c already shows geographic distribution by city; perhaps the authors could more directly highlight regional patterns there or in the text. In summary, I encourage the authors to strengthen the analysis of regional differences – for example, by reporting the percentage of cities in each pattern for each continent or income group – to bolster the claims of divergent regional dynamics. As a minor point, ensure that all statements about regional trends are backed by data (statistical or descriptive) in figures/tables or the Supplementary Information, so readers can verify them easily.\n\nModel Accuracy and Interpretation: The use of a multi-class LightGBM model to identify correlates of expansion patterns is an excellent approach. The model’s accuracy is reported as 65.1%, significantly above a 25% random guess baseline (for four classes). This indeed suggests the features chosen have predictive power, but I urge caution in how this result is interpreted. At 65% accuracy, the model is only moderately successful, meaning it still misclassifies roughly one in three cities. The authors describe this as a “strong predictive capacity”, which might be an overstatement. I recommend the authors temper this language and provide a bit more detail on model evaluation. For instance, was the 65.1% accuracy obtained via cross-validation or on a held-out test set? Providing this detail will assure readers the result is not overfit. It would also help to report class-specific performance (confusion matrix, precision/recall for each pattern) because a high overall accuracy could still mean certain categories (perhaps the smaller HC-HI class) are predicted poorly. If one class dominates the accuracy, that would affect how we interpret the SHAP importance of features. Including these additional metrics, perhaps in a supplement, would improve confidence that the model’s insights (e.g. the top predictors like MBH, BUC, etc.) are reliable. Finally, the authors should clarify that the model reveals associations, not causation – it identifies correlates of where different patterns occur, but this should not be over-interpreted as a causal mechanism without further evidence.\n\nGeneralization of Concepts and Policy Implications: The manuscript draws broad conclusions using its new terminology and makes some policy-relevant statements. Generally, this is fine, but the authors should be careful about over-generalization. For example, the title refers to “more divergent and less dispersed” patterns, which is somewhat abstract phrasing. It might help to more explicitly define what “divergent” means in this context (divergent across regions? diverging from historical norms?). In the Discussion, the authors mention that as urbanization shifts to Africa and South Asia (with predominantly LC-HI and LC-LI patterns), these patterns may increase land-use efficiency but also heighten commuting carbon emissions. While this insight is important, it should be communicated with nuance – real outcomes will depend on local transportation infrastructure, planning policies, etc. I suggest the authors moderate the policy implications to acknowledge context: e.g., vertical expansion in peripheral areas could lead to more driving emissions if transit options remain poor. In general, ensure that newly introduced concepts (like the four-pattern typology names or “path dependency” of expansion) are clearly explained and that any recommendations are proportionate to the evidence. This will prevent readers or policymakers from misapplying the findings beyond their scope.\n\nClarity of Presentation (Figures and Language)\nThe manuscript is well written in a clear and scholarly style. The logic flows well from introducing the problem to presenting results and discussion. I noted no major grammatical errors. Technical terms and acronyms (CI, II, HC-HI, etc.) are mostly defined and used consistently. One suggestion is to provide an acronym glossary or ensure all acronyms (especially in figures) are explained upon first use, given the large number of variables and indices introduced (MBH, BPOPU, IBV, etc.). The overall organization (with a combined analysis of 2D vs 3D, then pattern identification, then drivers) is effective. The figures are generally of high quality and informative:\n\nFigure 1 and Figure 2 nicely illustrate the core quantitative findings. In Fig. 2a, plotting the four categories in CI–II space is helpful; the use of 0.5th–99.5th percentile limits to handle outliers is reasonable. Just ensure the axes are clearly labeled with units or index definitions (e.g., CI and II are dimensionless indices – perhaps indicate “Centrality Index (unitless)” or similar). The conceptual diagrams in Fig. 2b and the map in Fig. 2c add clarity. One minor thought: if any cities were excluded (124 cities where centers didn’t overlap, per methods), perhaps note on the map or figure caption that the map shows 1,820 cities (if I recall correctly) to avoid confusion.\n\nFigure 3 provides compelling visual examples of each expansion pattern using representative cities. The visuals (with grids normalized by area, etc.) are useful for readers to intuitively grasp what HC-HI vs LC-LI patterns look like on the ground. The figure is clear. To enhance it, consider labeling each city and its pattern in the subpanels, and maybe include the city name in the caption (currently it says “including examples like Shanghai and Berlin…” but perhaps explicitly label them in the panels). This will help readers who may not recognize the skylines or layouts.\n\nFigure 4 and associated Supplementary Figures: The SHAP value plots are appropriate for explaining the model results. Ensure the color scheme and labels are accessible (color-blind friendly) and that each feature’s acronym is expanded in the figure or caption for clarity (e.g., TR = Terrain Relief, etc.). The ranking of feature importance (Fig. 4a) is good; perhaps also report the overall model R² or pseudo-R² if available, to give a sense of variance explained. The supplement figures (S6–S11, S13, S15, S17, S19, etc., as referenced) seem to contain additional supportive analysis; it’s good that these are provided for thoroughness.\n\nIn terms of language, my only suggestions are minor: avoid subjective terms like “strong predictive capacity” as noted, and consider simplifying a few long sentences for readability. Otherwise, the tone and clarity meet the standards of Nature Communications. The abstract effectively summarizes the findings, and the introduction contextualizes the work with recent literature. I also appreciate that the authors cite very recent studies (through 2024) which shows the manuscript is up-to-date.\n\nRecommendation\nIn conclusion, I am positive about this manuscript and its contributions. The study is ambitious in scope and offers valuable insights into urban expansion patterns that are highly relevant for sustainable urban development scholarship and practice. The evidence presented generally supports the conclusions, and the work is within the scope of Nature Communications in terms of broad interest and scientific rigour. However, before acceptance, the authors should address the above issues to strengthen the paper. Most of the concerns (urban renewal limitation, threshold robustness, clarity of figures, etc.) can be resolved with additional explanation, minor analyses, or revisions to the text and do not require new data collection. I believe these revisions will considerably improve the clarity and impact of the work. Recommendation: Accept with minor revisions.\nOnce the authors have incorporated the suggested clarifications and improvements, I am confident that the paper will be suitable for publication in Nature Communications."}, "author_response": "Response Letter NCOMMS-24-83684\nResponse to Reviewer #1\nWe greatly appreciate your positive and constructive comments and suggestions. We\nare very pleased that you recognize our study’s timely and valuable contribution to\nurban expansion literature, especially by foregrounding the crucial 3D aspects of urban\ngrowth. We appreciate your commendation of our novel Centrality and Intensity Indices,\nthe impressive analytical rigor, and the extensive dataset, noting how our interpretations\nalign with existing urban morphology and sustainability knowledge.\n\nWe have carefully revised the paper based on these comments and would like to\nhighlight the major changes in the structure of the paper in the following aspects:\n We rewrote the Introduction section to clearly articulate the dual motivation of this\nwork: the conceptual objective of capturing the three-dimensional nature of urban\nexpansion, and the methodological advance enabled by recent improvements in\nremote sensing and building height data.\n Second, we added a comparative analysis of 2D and 3D centrality indices,\nconfirming that they are correlated but reflecting distinct dimensions of urban\nspatial structure. To provide a detailed explanation of this issue, we have added\nSupplementary Note 1.\n Third, we further examined the relationship between 3D centrality and intensity,\nshowing that these two indices capture different aspects of city form and jointly\nexplain the diversity of 3D expansion trajectories. To provide a detailed\nexplanation of this issue, we have added Supplementary Note 2.\n Fourth, we performed robustness checks of city classification, demonstrating that\nboth the typological patterns and the predictive performance of LightGBM models\nremain consistent under alternative classification approaches. To provide a detailed\nexplanation of this issue, we have added Supplementary Note 3.\nBelow, we provide point-by-point responses to your comments.\n\nComment 1:\nThe paper introduces a promising analytical framework to capture the centrality and\nintensity of 3D urban expansion, but the framing in the introduction leaves the reader\nuncertain about the core motivation driving the study. Specifically, it is unclear whether\nthe impetus for this work stems primarily from (a) recent technological advances and\ndata availability—particularly improvements in remote sensing and building height\ndata—or from (b) a theoretical and empirical recognition that global urban expansion\nis transitioning from a predominantly 2D (horizontal) phenomenon to a more 3D\n(vertical) one. This distinction is not trivial.\nresearch orientations. The former is methodological and data-driven, implying that the\nresearch is filling a technical gap in our ability to measure and compare urban form in\n3D. The latter is conceptual and theory-driven, suggesting that urban development\nprocesses themselves have changed in ways that require new analytical lenses.\nThe two motivations are not mutually exclusive, and indeed, the study could be\nstrengthened by embracing them in parallel. However, the authors need to articulate\nthis dual framing more explicitly. At present, the introduction blends these motivations\nin a way that feels implicit and unresolved. A more deliberate framing would not only\nsharpen the study’s narrative but also better guide the reader in understanding its\nbroader significance—whether as a methodological advance, a conceptual reframing,\nor both.\n\nResponse:\nWe appreciate your comment regarding the core motivation of our study and agree that\narticulating a clearer dual framing will significantly strengthen the narrative. You\ncorrectly identified that our impetus stems from both (a) recent technological advances\nand data availability and (b) a theoretical and empirical recognition of the increasingly\nimportant 3D (vertical) dimension of urban expansion.\nWe have revised the introduction to address this point by more explicitly articulating\nthis dual framing.\n We have strengthened the conceptual and theory-driven motivation by clearly\nstating that the “evolving nature of urban development”, from predominantly 2D\nsprawl to increasingly 3D densification, necessitates new analytical lenses and\nframeworks to capture this compounded, three-dimensional reality:\nThis evolving nature of urban development—where 3D expansion is becoming an\nincreasingly significant phenomenon alongside traditional 2D sprawl—creates a\npressing need for analytical frameworks that can capture this compounded, three-\ndimensional reality. (page 2).\n We have introduced a concluding sentence that explicitly states our study is\n“motivated by a dual imperative”, clearly listing both the data availability and the\ncritical need to understand changing urban development patterns:\nAgainst this background, this study is motivated by a dual imperative: (1) the\nunprecedented availability of high-resolution 3D urban data, which now makes\npossible a comprehensive global analysis that was previously out of reach; and (2)\nan urgent need to better understand the complex and evolving patterns of global\nurban expansion, which are increasingly defined by vertical growth and\ndensification. Together, these imperatives point to critical knowledge gaps in our\ncurrent understanding of 3D urban expansion, particularly in terms of its spatial\ndistribution and broader implications. (page 2)\nAnother area of concern lies in the potential collinearity or redundancy between the 3D\nand 2D Centrality Index (CI) measures. While the paper highlights a strong correlation\nbetween the two, it raises the question of whether the 3D CI truly offers independent\nand added information about vertical expansion, or whether it primarily reflects spatial\ntrends already captured in the 2D CI. Without stronger statistical tests (e.g., variance\ninflation factor analysis, partial correlation, or residual-based comparisons), it remains\nunclear to what extent vertical growth patterns are being uniquely captured. This is\nespecially important since the study’s key conclusions rest on differences between the\n2D and 3D indices. The authors could further clarify this relationship by quantifying\nthe net contribution of verticality after controlling for horizontal patterns, or by\nexamining cases where the two indices diverge substantially and explaining why. While\nthis limitation does not preclude publication, it warrants more explicit discussion or\nanalytical validation.\nThe reported high correlation between 2D-CI and 3D-CI (r = 0.916) also raises concerns\nabout the added value of the 3D Centrality Index. In many cases, especially where\nheight gradients mirror horizontal expansion, 3D-CI may not provide substantially new\ninsights. Moreover, in cities with centralized high-rise clusters and sprawling low-rise\nsuburbs, 3D-CI may overemphasize central volumetric outliers, potentially\nmisrepresenting vertical structure as horizontal concentration. The paper would benefit\nfrom further analysis to isolate the unique contribution of height to centrality and assess\nwhether 3D-CI captures distinct spatial variance beyond 2D-CI.\n\nResponse:\nThank you and we agree that it is important to verify whether 3D-based CI offers\nindependent information on vertical expansion beyond what is already captured by 2D-\nbased CI. To address this concern, we performed two diagnostic analyses: (1) a\ncondition index test based on the eigenvalues of the correlation matrix, and (2) a\nresidual-based analysis.\nThe Pearson correlation coefficient between 3D-based CI and 2D-based CI is 0.916 (p\n< 0.001), confirming a strong linear relationship. However, the condition index equals\n22.85, which is below the common multicollinearity threshold (30), indicating that the\ntwo indices are correlated but not redundant.\nIn the residual analysis, we regressed 3D-based CI on 2D-based CI and examined the\nunexplained component. The residual variance (1.6) relative to the total variance of 3D-\nbased CI (9.8) suggests that about 16% of 3D-CI’s variance cannot be explained by 2D-\nCI. This independent portion reflects meaningful divergence from purely horizontal\npatterns, particularly in cities where high-rise clusters emerge unevenly within the built-\nup area. Details of the condition index and residual analyses have been provided in\nSupplementary Note 1.\nAs visually illustrated in Fig. 1a, although the 2D-based CI and 3D-based CI generally\n3\nfollow a similar trend, there are substantial variations between them. Each horizontal\nslice of the scatter plot corresponds to multiple cities sharing the same 2D-based CI\nvalue but exhibiting a wide range of 3D-based CI values. For instance, when the 2D-\nbased CI is 50, the corresponding 3D-based CI values range from approximately 49 to\n55 across cities.\nFig. 1a Statistical distribution of 2D- and 3D-based CI scores.\nThis divergence can be conceptually understood by considering two hypothetical urban\nexpansion scenarios. In both scenarios, cities exhibit identical horizontal expansion\npatterns and the same total amount of vertical growth—meaning they share identical\n2D-based CI and II values. However, in the first scenario, high-rise buildings are\nconcentrated near the city center, whereas in the second, they are dispersed toward the\nurban periphery. This directly addresses the reviewer’s insightful point: in a city with a\n“centralized high-rise cluster and sprawling low-rise suburbs,” the 3D-based CI would\nindeed be high, correctly identifying the intense volumetric concentration in the center.\nConversely, in the second scenario, a similarly high 2D-based CI would be paired with\na lower 3D-based CI, accurately reflecting the dispersal of vertical mass. Thus, rather\nthan misrepresenting structure, the 3D-based CI is precisely capturing the difference\nbetween these two distinct urban forms that the 2D-based CI alone would conflate.\nThese distinct spatial configurations of vertical development would lead to\ndifferentiated outcomes in terms of population distribution, commuting patterns,\neconomic agglomeration, and microclimate effects. Critically, the 3D-based CI is able\nto capture this difference, while the 2D-based CI cannot (even when combined with the\nII indicator).\nrelated—which is expected, as building volume derives from both footprint and\nheight—the 3D-based CI retains statistically significant independent information. It\ncaptures the volumetric dimension of spatial concentration, which modifies or amplifies\nhorizontal centrality in a meaningful way.\nAccordingly, we have revised the Result section in our main text to clarify this point,\npresented below for your easy reference:\nIn addition to the overall correlation between 2D and 3D measurements, further\ndiagnostic tests (see Supplementary Note 1) indicate the vertical concentration\nrepresents a distinct though related dimension of urban spatial structure. (page 3)\n\nComment 3:\nThe CI and II thresholds used to define expansion types (e.g., HC-HI, LC-LI) rely on\nmean-based cutoffs, which may oversimplify underlying distributions or obscure\nregional nuances. A sensitivity analysis using percentile-based thresholds or cluster-\nbased classification might improve robustness. Nonetheless, the methodological\nchoices are overall reasonable and align with the standards of large-scale spatial\nanalysis in this field.\n\nResponse:\nIn response, we performed comprehensive sensitivity tests, comparing the baseline\nmean-based classification with (a) a median-based scheme and (b) a hierarchical\nclustering solution; full details and results are reported in Supplementary Note 3.\nBelow we summarize three lines of evidence that support the robustness of our results.\nFirst, we quantified concordance between the mean-based and alternative schemes\nusing Cohen’s Kappa. The median-based scheme shows high agreement with the mean-\nbased classification (κ = 0.83), while the clustering-based scheme yields a moderate\nagreement (κ = 0.54). These statistics indicate that the median threshold produces near-\nidentical assignments, and that the clustering approach—while more data-driven and\nsomewhat more polarized—does not produce wholly different typologies.\nSecond, the continental and regional distributions of the four patterns remain effectively\nunchanged across classification methods. The principal spatial hierarchies reported in\nResults (Section 2- Four patterns of 3D urban expansion)—for example, the relative\nprevalence of HC–HI in Asia & Oceania and Europe, HC–LI dominance in North\nAmerica, and the concentration of LC–HI and LC–LI in rapidly expanding regions—\nare preserved under both median and clustering schemes (see Supplementary Table S6).\nThis demonstrates that our substantive geographic conclusions are not an artifact of the\nmean-based cutoffs.\nThird, to assess whether downstream inferences are sensitive to the choice of\nclassification, we re-trained the LightGBM classifier using the median- and clustering-\nderived labels and conducted SHAP-based interpretation for each model. We evaluated\n5\nthe full set of predictors rather than any single indicator. The results are highly\nconsistent: (1) the overall ranking pattern of variable importance is preserved across\nmodels (the same set of top predictors appears repeatedly, although exact rank order\nvaries slightly), and (2) the direction and qualitative shape of the relationships between\nindividual predictors and each expansion pattern remain stable.\nTo make these robustness checks transparent to readers, we have added two brief\npointers in the Results section and the Materials and Methods section, respectively:\nFindings from this categorization remain consistent when alternative classification\nmethods, including median-based and clustering-based schemes, are used (see\nSupplementary Note 3). (pages 5-6)\nWe evaluate the robustness of the mean-based classification of 3D urban expansion\npatterns using two alternative methods: a median-based approach and a\nhierarchical clustering approach (see Supplementary Note 3 for details). Cohen’s\nKappa statistic indicated excellent agreement between the mean- and median-\nbased schemes, and moderate agreement with the clustering-based method. While\nthe clustering approach reclassify a small number of cities located near category\nboundaries, the overall regional distribution of patterns remain highly consistent\nacross all three methods. Robustness is further supported by training LightGBM\nmodels on the alternative classifications, which produce stable results in both the\nrelative importance and directional effects of key predictors. These consistent\noutcomes reinforce the reliability of our main findings on the drivers of different\n3D expansion patterns. (page 18)\nFull tables, Kappa statistics, regional breakdowns, variable-importance comparisons,\nand illustrative SHAP plots for each alternative model are provided in Supplementary\nNote 3. Together, these analyses demonstrate that the typology and all subsequent\nresults are robust to alternative thresholding strategies, and that the mean-based scheme\nprovides a consistent and interpretable basis for large-scale cross-city comparison.\n\nComment 4:\nAnother key conceptual issue lies in the potential structural coupling between the 3D\nCentrality Index (3D-CI) and the Intensity Index (II). Although the two are presented\nas capturing distinct aspects of urban expansion—spatial concentration versus vertical\nintensity—they are both directly derived from the same variable: built-up volume.\nSpecifically, 3D-CI is computed as a distance-weighted average of volume, while II\nrepresents the city-wide average building height (volume divided by footprint). This\nshared dependency on volume raises concerns about whether these indicators are truly\northogonal dimensions of urban structure.\nIn practice, their relationship may be heavily influenced by urban morphology. For\ninstance, if tall buildings are concentrated near city centers, both 3D-CI and II will be\nhigh; conversely, if high-rise developments emerge in peripheral areas, 3D-CI may\n6\ndecline while II remains high. Such patterns imply that the spatial and vertical metrics\nare interdependent, and any classification based on their combination (e.g., HC-HI, LC-\nHI) may be influenced more by structural biases than independent mechanisms.\n\nResponse:\nWe agree that, in principle, both metrics are derived from the same underlying\nvariable—built-up volume—and thus their independence warrants empirical validation.\nIn response, we have conducted additional statistical analyses to examine their\nrelationship, and the results are included in the revised manuscript and detailed in\nSupplementary Note 2.\nAlthough both indices originate from volumetric information, their empirical\nassociation is weak. The Pearson correlation coefficient between 3D-based CI and II is\n−0.203 (p < 0.001), indicating that cities with highly centralized 3D structures do not\nnecessarily exhibit high average vertical intensity. This result remains consistent even\nafter controlling for confounding factors such as population size and GDP per capita\n(partial correlation r = −0.195, p < 0.001), confirming that the limited correlation is not\nsimply driven by scale effects. Furthermore, a residual-based regression analysis shows\nthat 96% of the total variance in 3D-based CI cannot be explained by 3D-based II.\nThese results collectively indicate that the two indices are not structurally redundant\nbut instead describe complementary dimensions of urban volumetric form—3D-based\nCI captures the spatial concentration of built-up volume, while II reflects its average\nvertical intensity across the urban fabric (see more in Supplementary Note 2).\nWe have accordingly added the following statement in the main text:\nIn spite of being calculated based on the same built-up volume dataset, the weak\ncorrelation between CI and II measurements indicate that the two indicators\ncapture distinct aspects of vertical urban structure (see Supplementary Note 2).\n(page 5)\nWe also acknowledge the reviewer’s point that both indices may be influenced by\nunderlying urban morphology—for instance, whether tall buildings cluster in central or\nperipheral areas. However, we argue that this morphological influence is not a\nmethodological flaw but a substantive feature of our typology. The spatial arrangement\nof vertical elements is precisely what differentiates distinct growth configurations. In\nthis sense, the combined use of CI and II allows us to distinguish meaningful volumetric\npatterns, such as HC–HI versus LC–HI forms, which reflect fundamentally different\nmodes of urban development. Recognizing where and how vertical intensity manifests\nacross urban space is crucial for understanding sustainability and planning implications,\nand this dual-metric framework provides a conceptually and empirically justified way\nto capture that complexity.\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\n\nResponse:\nWe appreciate that you are participating in Nature Communications’ initiative to\nsupport Early Career Researchers in peer review, and we value the insightful comments\nyou have provided.\nWe sincerely appreciate your comprehensive and encouraging review. In response, we\nhave made a series of substantial revisions to strengthen the analytical rigor and\nconceptual clarity of the paper.\n We incorporated an explicit discussion and assessment of the potential influence of\nurban renewal, clarifying how renewal activities may affect the interpretation of\nour findings. To provide a detailed explanation of this issue, we have added\nSupplementary Note 5.\n We performed a comprehensive robustness test of the city classification,\nconfirming that the identified typologies and related main conclusion remain\nconsistent under alternative clustering and thresholding methods. To provide a detailed\nexplanation, we have added Supplementary Note 3.\n We presented regional variations across expansion modes more clearly.\n We conducted a more comprehensive evaluation of the LightGBM model. To\nprovide a detailed explanation, we have added Supplementary Note 4.\n We expanded the discussion on the generalization of concepts and policy\nimplications, situating our findings within broader urban development and\nplanning frameworks.\n We refined the language and visual presentation throughout the manuscript to\nenhance clarity and readability.\nBelow, we provide point-by-point responses to your comments.\n\nComment 1:\nExclusion of Urban Renewal: A key limitation is that the study captures only outward\nexpansion and does not account for urban “renewal” or densification within existing\nbuilt-up areas. The authors do acknowledge this limitation, noting that their method\ncannot detect volume increases without footprint change. They argue that vertical\nredevelopment (common in developed cities) would, if included, likely increase the\nmeasured centrality and intensity in Global North cities, widening the contrast with the\nGlobal South. This is an important point, and the manuscript should ensure it is\ncommunicated very clearly and up-front. I recommend the authors emphasize in the\nabstract and conclusions that their results pertain to outward expansion only (new urban\nareas from 2000–2018), and do not capture vertical growth via redevelopment.\nAdditionally, if possible, provide some quantitative sense of how big this effect might\nbe. For example, could the authors cite studies or data on urban renewal impacts, or at\nleast qualitatively discuss where this limitation is most consequential? Strengthening\nthe discussion of this limitation will make the conclusions more rigorous and prevent\nover-interpretation of the findings.\nThank you for highlighting this limitation. To address this concern, we have performed\na targeted assessment, reported in Supplementary Note 5, and revised the manuscript\naccordingly.\nWe first clarified the conceptual scope of “urban renewal” in this study, defining it as\nredevelopment or reconstruction that increases built-up volume without expanding the\nbuilding footprint. This definition distinguishes it from routine renovation and from\ninfill development on previously vacant urban plots, the latter of which is captured by\nour method. Because comprehensive, regionally comparable data are limited, we\nassembled and synthesized available quantitative evidence for the study period,\nfocusing on the best-documented cases (United States and China) and on cross-regional\nindicators that allow informed inference for other regions. Key findings are:\nUnited States: The U.S. Environmental Protection Agency (EPA) data for 209\nmetropolitan areas (2000–2009) indicate that ~21% of new housing was built as infill\nwithin previously developed areas1. Because infill includes both redevelopment and\nnew construction on vacant urban parcels, the share attributable to pure redevelopment\n(i.e., renewal without footprint change) is plausibly lower—likely < 20% for that\ndecade.\nChina: Official reconstruction statistics for 2023 report the initiation of approximately\n1.59 million rebuilt housing units2. When scaled by average unit area, this corresponds\nto roughly 15% of the recent new residential floor area3,4. However, as large-scale\nrenewal programs in China intensified after 20095, the share during 2000–2018 was\nplausibly somewhat lower.\nCross-regional inference: Multi-temporal remote-sensing analyses that map upward-\ndominant versus outward-dominant growth indicate that upward-dominant patterns are\nmore prevalent in advanced economies (notably Europe and East Asia) and less\nprevalent in Latin America, India and Africa6. While upward dominance is not identical\nto renewal, it correlates with a greater prevalence of redevelopment-oriented vertical\ngrowth.\nSynthesis: Taken together, available evidence indicates that genuine redevelopment—\ndefined as renewal that increases built volume without expanding the urban footprint—\ntypically accounts for several tens of percent of new construction in developed and East\nAsian contexts, but remains far less prevalent across much of the Global South during\nthe study period. On a conservative global average for 2000–2018, redevelopment\nlikely represents no more than ~15% of total new urban construction, with higher shares\nin Europe and East Asia, and substantially lower contributions in Latin America, South\nAsia, and Africa.\nBecause renewal tends to occur in central urban areas7,8, including such processes\nwould increase measured 3D centrality in places where renewal is concentrated—\nprimarily in the Global North and parts of East Asia. Therefore, incorporating renewal\n10\nwould strengthen the main geographic contrast reported in the manuscript (i.e., Global\nNorth cities would show even higher 3D-based centrality relative to Global South\ncities), rather than undermine it.\nTo make these points clear to readers, we have clarified this limitation upfront in both\nthe Abstract and Discussion. In the revised Abstract, we now explicitly state:\nThe North-South centrality gap would further widen if vertical redevelopment\nwithin existing built-up footprints is considered.\nIn the revised Discussion section, we now explicitly state (pages 12-13):\nThis study focuses on outward urban expansion and does not account for urban\nrenewal, i.e. the redevelopment of existing built-up footprints. Unlike simple\nbuilding renovation, urban renewal typically involves replacing low-rise or aging\nstructures with high-rise developments concentrated in urban centers, thus\ncontributing substantially to vertical growth40,41. Although this process is beyond\nthe detection scope of our method (which identifies only built-up footprint\nexpansion), its potential impact warrants consideration. Available evidence\nsuggests that the proportion of urban renewal relative to total urban growth\nremains modest globally—generally below 15% during the study period—with\nsomewhat higher shares in Europe and East Asia and lower shares in regions such\nas Latin America, India, and Africa (see Supplementary Note 5). Given that urban\nrenewal is most common in city centers, the inclusion of urban renewal would likely\namplify the centrality of 3D growth, particularly in Global North and East Asian\ncities. Consequently, incorporating urban renewal would strengthen rather than\nchallenge the observed North–South centrality gap in 3D urban expansion. Future\nresearch should investigate how urban renewal interacts with existing patterns of\n3D expansion and examine its environmental sustainability implications,\nparticularly in the context of ongoing urbanization in the Global South.\nReferences:\n1. Ramsey, K. Residential Construction Trends in America’s Metropolitan Regions:\n2. Statistical Communiqué of the People’s Republic of China on the 2023 National\nEconomic and Social Development. (National Bureau of Statistics of China,\nBeijing, 2023).\n3. China Population Census Yearbook 2020. (National Bureau of Statistics of China,\nBeijing, 2020).\n4. National Real Estate Development and Sales in 2022. (National Bureau of\nStatistics of China, Beijing, 2022).\n5. He, S. & Wu, F. China’s emerging neoliberal urbanism: Perspectives from urban\nredevelopment. Antipode 41, 282-304 (2009).\n6. Frolking, S., Mahtta, R., Milliman, T., Esch, T. & Seto, K. C. Global urban\nstructural growth shows a profound shift from spreading out to building up. Nat.\n7. der Krabben, E. v. & Needham, B. Land readjustment for value capturing: a new\nplanning tool for urban redevelopment. Town Plan. Rev. 79, 651-672 (2008).\n8. Broitman, D. & Koomen, E. The attraction of urban cores: Densification in Dutch\ncity centres. Urban Stud. 57, 1920-1939 (2020).\n\nComment 2:\nThreshold Definition for CI and II (Classification Robustness): The four expansion\npattern categories (HC-HI, LC-HI, HC-LI, LC-LI) are defined by whether a city’s CI\nand II are above or below the “average” (mean) values. This binary thresholding is\nconvenient but somewhat arbitrary, and it raises questions about robustness. The\nauthors should clarify how the threshold was determined (it appears to be the global\nmean of each index; if so, was this done separately for CI and II?). It would strengthen\nthe paper to demonstrate that the patterns identified are not an artifact of the particular\nthreshold choice. For example, did the authors test using median instead of mean, or\nexamine sensitivity if the threshold shifts slightly? Since the resulting category sizes\nare somewhat imbalanced (e.g., only ~17% of cities are HC-HI, whereas ~30% are LC-\nLI), one wonders if the “average” values lie in a skewed part of the distribution. A brief\nanalysis or rationale about threshold selection and stability would be valuable. Alternatively,\nthe authors could consider a clustering approach or provide quantitative\njustification (e.g., bimodality in the index distributions) for the dichotomous split.\nEnsuring the classification is robust will increase confidence in all subsequent pattern-\nbased analyses.\n\nResponse:\nAs this important issue was also raised by the first reviewer, our response here is largely\nconsistent with our reply to Reviewer #1’s Comment 3.\nWe agree that clarifying the thresholding rationale and assessing its robustness are\nessential for ensuring the validity of the four-pattern typology. In our main analysis, the\nthresholds for the Centrality Index (CI) and Intensity Index (II) were independently\ndetermined using their respective global mean values across all cities (mean CI and\nmean II). This approach offers a balanced and intuitive distinction between cities\nexhibiting above- and below-average levels of 3D centrality and intensity. Nevertheless,\nas the reviewer rightly notes, mean-based thresholds may be influenced by\ndistributional skewness, and therefore we further tested the robustness of our\nclassification using alternative thresholding methods.\nTo address this concern, we conducted comprehensive sensitivity analyses comparing\nthe baseline mean-based classification with two alternative schemes: (a) a median-\nbased thresholding and (b) a hierarchical clustering–based classification. The results\nare reported in Supplementary Note 3, and the main outcomes are summarized below.\nFirst, we assessed the classification agreement between the mean-based and alternative\nschemes using Cohen’s Kappa statistic. The median-based scheme shows high\n12\nagreement with the mean-based classification (κ = 0.83) and, as expected, produces a\nslightly more balanced partition of cities above and below each threshold. The\nclustering-based scheme yields a moderate but acceptable agreement (κ = 0.54), reflecting\nits tendency to produce more polarized groupings driven by the intrinsic data\nstructure. These results confirm that while clustering highlights stronger contrasts, it\ndoes not produce fundamentally different typologies.\nSecond, the spatial consistency of the results is strong. The continental and regional\ndistributions of the four expansion patterns remain highly similar under all three\nschemes. The spatial hierarchies highlighted in Results section (Four patterns of 3D\nurban expansion)—for example, the dominance of HC–HI in Asia & Oceania and\nEurope, HC–LI in North America, and LC–HI/LC–LI in rapidly expanding regions—\nare all preserved (see Supplementary Table S5). Hence, the observed global\ndifferentiation of 3D expansion modes is not an artifact of the specific threshold choice.\nThird, we tested model consistency by re-estimating the LightGBM classifier under\neach classification scheme and performing SHAP-based interpretation for all models.\nThe findings are highly consistent across methods:\n The relative ranking of predictor importance remains stable, with the same key\nvariables repeatedly emerging as top contributors; and\n The direction and qualitative form of each variable’s relationship with the four\nexpansion types are nearly identical.\nThese results confirm that neither the explanatory hierarchy nor the mechanism\ninterpretation is dependent on how the thresholds are defined.\nTo make these robustness checks transparent to readers, we have added two brief\npointers in the Results section and the Materials and Methods section, respectively:\nFindings from this categorization remain consistent when alternative classification\nmethods, including median-based and clustering-based schemes, are used (see\nSupplementary Note 3). (pages 5-6)\nWe evaluate the robustness of the mean-based classification of 3D urban expansion\npatterns using two alternative methods: a median-based approach and a\nhierarchical clustering approach (see Supplementary Note 3 for details). Cohen’s\nKappa statistic indicated excellent agreement between the mean- and median-\nbased schemes, and moderate agreement with the clustering-based method. While\nthe clustering approach reclassify a small number of cities located near category\nboundaries, the overall regional distribution of patterns remain highly consistent\nacross all three methods. Robustness is further supported by training LightGBM\nmodels on the alternative classifications, which produce stable results in both the\nrelative importance and directional effects of key predictors. These consistent\noutcomes reinforce the reliability of our main findings on the drivers of different\n3D expansion patterns. (page 18)\nvisualizations for all alternative models are provided in Supplementary Note 3.\nTogether, these analyses demonstrate that the typology and all subsequent results are\nrobust to alternative thresholding strategies, and that the mean-based scheme provides\na consistent and interpretable basis for large-scale cross-city comparison.\n\nComment 3:\nSupport for Regional Differences (Fig. 3 and Table 1): The manuscript claims\nsignificant regional and country-level differences in 3D expansion patterns, citing\nFigure 3 (city examples) and Table 1 (counts of cities in each category for selected\ncountries). While the data presented do indicate contrasts – for instance, 92.7% of US\ncities are in the low-intensity categories (HC-LI or LC-LI) whereas a much larger share\nof Chinese cities are high-intensity (HC-HI or LC-HI) – the presentation could be\nimproved to more convincingly support these comparisons. Table 1 is useful, but it only\nlists a handful of countries without explanation of why those were chosen. Are they\nsimply illustrative examples, or the top emitters, or largest urban populations? The\nauthors should clarify the selection and perhaps include additional key regions or a\nsummary (e.g. an aggregate for “North America vs Europe vs Asia vs Africa”) to better\nhighlight regional trends. Similarly, while Figure 3 (visualizations of representative\ncities) is a nice qualitative illustration of each pattern, it does not on its own demonstrate\nregional prevalence differences. The global map in Fig. 2c already shows geographic\ndistribution by city; perhaps the authors could more directly highlight regional patterns\nthere or in the text. In summary, I encourage the authors to strengthen the analysis of\nregional differences – for example, by reporting the percentage of cities in each pattern\nfor each continent or income group – to bolster the claims of divergent regional\ndynamics. As a minor point, ensure that all statements about regional trends are backed\nby data (statistical or descriptive) in figures/tables or the Supplementary Information,\nso readers can verify them easily.\n\nResponse:\nWe have made the following changes to address this comment concerning the\npresentation of regional differences in 3D urban expansion patterns.\nFirst, we have updated Table 3 to include aggregated statistics for each continent/major\nregion (Africa, Latin America and the Caribbean, Asia and Oceania, North America,\nEurope). This provides a clearer overview of continental-level trends. We have also\nclarified that the specific countries listed within each region in Table 3 were chosen\nbased on having the largest number of sample cities in our dataset for that respective\nregion, thus serving as robust and representative illustrative examples. This is noted in\nthe table caption (page 8).\nSecond, to further strengthen the analysis and avoid redundancy, we have added a\nconcise summary sentence at the end of the second paragraph of the Discussion section\nthat synthesizes the key regional divergences observed. This directly follows the\n14\ndetailed country-level examples:\nOverall, high-intensity 3D expansion is notably prevalent in East Asia, while low-\nintensity patterns characterize North America, and a mix of low-centrality patterns\nis dominant in Africa, Latin America and South Asia, with Europe showing a more\ndiverse distribution. (page 8)\n\nComment 4:\nModel Accuracy and Interpretation: The use of a multi-class LightGBM model to\nidentify correlates of expansion patterns is an excellent approach. The model’s accuracy\nis reported as 65.1%, significantly above a 25% random guess baseline (for four classes).\nThis indeed suggests the features chosen have predictive power, but I urge caution in\nhow this result is interpreted. At 65% accuracy, the model is only moderately successful,\nmeaning it still misclassifies roughly one in three cities. The authors describe this as a\n“strong predictive capacity”, which might be an overstatement. I recommend the\nauthors temper this language and provide a bit more detail on model evaluation. For\ninstance, was the 65.1% accuracy obtained via cross-validation or on a held-out test set?\nProviding this detail will assure readers the result is not overfit. It would also help to\nreport class-specific performance (confusion matrix, precision/recall for each pattern)\nbecause a high overall accuracy could still mean certain categories (perhaps the smaller\nHC-HI class) are predicted poorly. If one class dominates the accuracy, that would\naffect how we interpret the SHAP importance of features. Including these additional\nmetrics, perhaps in a supplement, would improve confidence that the model’s insights\n(e.g. the top predictors like MBH, BUC, etc.) are reliable. Finally, the authors should\nclarify that the model reveals associations, not causation – it identifies correlates of\nwhere different patterns occur, but this should not be over-interpreted as a causal\nmechanism without further evidence.\n\nResponse:\nTo address these concerns, we have substantially expanded the model evaluation and\nclarified the interpretation of its predictive capacity and scope.\nFirst, we now provide a detailed evaluation of the multi-class LightGBM model,\nincluding a transparent explanation of its training, validation, and testing procedures in\nSupplementary Note 4. We explain that the model was trained using 10-fold cross-\nvalidation for hyperparameter tuning, and the reported overall accuracy of 65.1% was\nobtained on a held-out test set that was entirely unseen during training. This approach\noffers an unbiased estimate of model generalization and strengthens the credibility of\nthe reported results.\nSecond, we now include additional performance metrics in Table S7, including\nPrecision, Recall, and F1-score for each of the four expansion categories as well as the\nmacro-averaged and weighted-averaged metrics. The results show that while class-\nspecific performance varies (with HC–HI being relatively less well predicted due to\nsmaller sample size and feature overlap), the model maintains balanced performance\n15\noverall, with a weighted-average F1-score of 0.646 and a macro-averaged F1-score of\n0.611. These metrics confirm that the model’s predictive ability is not dominated by\nany single class and that its insights regarding feature importance are consistent across\ncategories.\nThird, we fully acknowledge the reviewer’s caution regarding the interpretation of our\nresults. In the revised manuscript and Supplementary Information, we have clarified\nthat the model identifies associative patterns rather than causal mechanisms.\nAccordingly, the SHAP-based feature importance results are interpreted as indicators\nof the strength and direction of correlations, not as evidence of causality. The revised\ntext in the manuscript now reads (pages 8-9):\nThe model attains an overall accuracy of 65.1% on a held-out test set, notably\nhigher than the random prediction baseline of 25% (given the four categories).\nPerformance varies across classes, with LC–LI showing the highest recall and\nHC–HI exhibiting relatively lower precision and F1-score, while the weighted\naverage F1-score (0.646) indicates a generally consistent predictive capability\nacross classes. We therefore characterize the model as demonstrating moderate yet\nrobust predictive performance, effectively capturing the key associations between\nurban expansion patterns and their underlying drivers (see Supplementary Note 4\nfor detailed evaluation metrics). It is important to note, however, that these results\nreveal correlational rather than causal relationships, and thus should be\ninterpreted as indicative associations rather than direct causal mechanisms.\n\nComment 5:\nGeneralization of Concepts and Policy Implications: The manuscript draws broad\nconclusions using its new terminology and makes some policy-relevant statements.\nGenerally, this is fine, but the authors should be careful about over-generalization.\nFor example, the title refers to “more divergent and less dispersed” patterns, which is\nsomewhat abstract phrasing. It might help to more explicitly define what “divergent”\nmeans in this context (divergent across regions? diverging from historical norms?). In\nthe Discussion, the authors mention that as urbanization shifts to Africa and South Asia\n(with predominantly LC-HI and LC-LI patterns), these patterns may increase land-use\nefficiency but also heighten commuting carbon emissions. While this insight is\nimportant, it should be communicated with nuance – real outcomes will depend on local\ntransportation infrastructure, planning policies, etc. I suggest the authors moderate the\npolicy implications to acknowledge context: e.g., vertical expansion in peripheral areas\ncould lead to more driving emissions if transit options remain poor. In general, ensure\nthat newly introduced concepts (like the four-pattern typology names or “path\ndependency” of expansion) are clearly explained and that any recommendations are\nproportionate to the evidence. This will prevent readers or policymakers from\nmisapplying the findings beyond their scope.\n\nResponse:\ninterpretive nuance in response to this comment.\nFirst, we acknowledge the reviewer’s suggestion to clarify the term “divergent” in the\ntitle. In the revised manuscript, we explicitly explain “divergent” in the Discussion\nsection to reflect two dimensions of meaning:\n Multi-dimensional perspective: Our study diverges from conventional 2D\nassessments by incorporating both the vertical and concentration dimensions of\nurban expansion. This provides a more comprehensive and differentiated\nunderstanding of growth patterns beyond the traditional sprawl–compact\ndichotomy. This clarification has been added in the second paragraph of the\nDiscussion (page 11):\nThe four 3D urban expansion patterns identified based on the Centrality Index (CI)\nand Intensity Index (II) offer deeper insights into 3D urban forms and their\nimplications for environmental sustainability, representing a divergence from\nsimpler 2D classifications by considering both the vertical and agglomeration\ndimensions of urban growth.\n Increased inter-city disparities: Our analysis demonstrates that disparities in\ncentrality among cities are greater when viewed in 3D than in 2D, revealing a more\npronounced North–South contrast. Cities in the Global South (particularly in Africa\nand Latin America, excluding most Chinese cities) show smaller differences\nbetween their 3D- and 2D-based CI scores than those in the Global North, while\ntheir II values indicate taller newly built structures. Together, these results\nunderscore that the North–South divergence is a defining feature of 3D urban\nexpansion. This clarification appears in the first paragraph of the Discussion (page\n11):\nMoreover, the 3D perspective reveals a more divergent contrast between the Global\nSouth and the Global North. On the one hand, cities in the Global South—\nparticularly in Africa and Latin America, with the exception of most Chinese\ncities—generally display smaller differences between 3D- and 2D-based CI scores\nthan those observed in the Global North. This also suggests that the North-South\ncontrast is more pronounced for 3D urban expansion, compared to what 2D\nanalyses reveal (Fig. S3 and S4). On the other hand, our analysis of the Intensity\nIndex (II) for 3D urban expansion reveals that cities in the Global South generally\nfeature taller newly constructed buildings than their counterparts in the Global\nNorth. This aligns with previous findings suggesting that urbanization in the\nGlobal South consumes less per capita land29,34 and that vertical expansion plays\na dominant role in the global urbanization process10.\nSecond, as suggested, we have clarified the meanings of newly introduced concepts\nsuch as the four-pattern typology and path dependency:\n17\n Parenthetical explanations for each of the four 3D expansion patterns are now\nadded upon their first mention in the second paragraph of the Discussion, and again\nin the final paragraph for consistency (page 12). Although these were defined\nearlier in the Results section, this repetition ensures clarity for readers who may\nbegin directly with the Discussion.\n A concise explanation of path dependency has also been added in the third\nparagraph of the Discussion (page 12):\nSpecifically, cities with higher centrality at a base period tend to exhibit higher\ncentrality in their subsequent spatial growth phases.\nThird, we revised the policy implications to better reflect contextual variability, as\nrecommended. The revised final paragraph of the Discussion (page 13) now explicitly\nacknowledges that the sustainability outcomes of different 3D expansion patterns\ndepend on local infrastructure, planning, and socioeconomic contexts. The updated text\nreads as follows:\nFuture expansion will likely be driven by cities in Africa and South Asia, which are\nprimarily characterized by LC-HI (Low Centrality and High Intensity) and LC-LI\n(Low Centrality and Low Intensity) patterns of 3D urban expansion. While these\npatterns may improve land-use efficiency to some extent, they are also likely to\npresent challenges in reducing commuting-related carbon emissions. It is\nimportant to acknowledge that the real outcomes of these patterns will be highly\ndependent on local contexts, including the quality of transportation infrastructure,\nthe effectiveness of land-use planning policies, and socioeconomic factors. For\nexample, vertical expansion in peripheral areas could lead to significantly higher\ndriving emissions if public transit options remain poor or if car-centric\ndevelopment is incentivized. Conversely, with strategic investments in multimodal\ntransit and integrated land-use planning, these patterns could be managed to\nsupport more sustainable urban development. Therefore, policymakers should\nconsider these findings with nuance, developing context-specific strategies that\naddress both land-use efficiency and emissions reduction tailored to their unique\nurban development trajectories and infrastructure capabilities.\n\nComment 6:\nClarity of Presentation (Figures and Language): The manuscript is well written in a\nclear and scholarly style. The logic flows well from introducing the problem to\npresenting results and discussion. I noted no major grammatical errors. Technical terms\nand acronyms (CI, II, HC-HI, etc.) are mostly defined and used consistently. One\nsuggestion is to provide an acronym glossary or ensure all acronyms (especially in\nfigures) are explained upon first use, given the large number of variables and indices\nintroduced (MBH, BPOPU, IBV, etc.). The overall organization (with a combined\nanalysis of 2D vs 3D, then pattern identification, then drivers) is effective. The figures\nare generally of high quality and informative.\nWe have implemented the reviewer’s suggestion to ensure that all acronyms are defined\nupon first use, particularly given the number of variables and indices used in the study.\nBesides, in the revised manuscript, each variable abbreviation is now clearly defined\nwithin the caption of Figure 4, allowing readers to understand the terminology directly\nwhere the variables are introduced.\n\nComment 7:\nFigure 1 and Figure 2 nicely illustrate the core quantitative findings. In Fig. 2a, plotting\nthe four categories in CI–II space is helpful; the use of 0.5th–99.5th percentile limits to\nhandle outliers is reasonable. Just ensure the axes are clearly labeled with units or index\ndefinitions (e.g., CI and II are dimensionless indices – perhaps indicate “Centrality Index (unitless)” or similar). The conceptual diagrams in Fig. 2b and the map in Fig. 2c add clarity. One minor thought: if any cities were excluded (124 cities where centers didn’ centers didn’t overlap, per methods), perhaps note on the map or figure caption that the map\nshows 1,820 cities (if I recall correctly) to avoid confusion.\n\nResponse:\nWe appreciate the reviewer’s suggestions regarding axis labeling and clarification of\nthe number of cities displayed. We have implemented these revisions in the updated\nmanuscript as follows:\n The captions of Figures 1 and 2 have been revised to explicitly state that the\nCentrality Index (CI) and Intensity Index (II) are dimensionless indicators.\n We have added notes to the captions of Figure 1b and Figure 2c indicating that the\nmaps and diagrams represent results “across 1,820 sample cities.” This clarification\nensures transparency regarding the scope of the analysis and eliminates potential\nconfusion.\n\nComment 8:\nFigure 3 provides compelling visual examples of each expansion pattern using\nrepresentative cities. The visuals (with grids normalized by area, etc.) are useful for\nreaders to intuitively grasp what HC-HI vs LC-LI patterns look like on the ground. The\nfigure is clear. To enhance it, consider labeling each city and its pattern in the subpanels,\nand maybe include the city name in the caption (currently it says “including examples\nlike Shanghai and Berlin…” but perhaps explicitly label them in the panels). This will\nhelp readers who may not recognize the skylines or layouts.\n\nResponse:\nThank you for your positive assessment of Figure 3 and for recognizing its effectiveness\nin illustrating urban expansion patterns. In response to your comments, we have revised\nFigure 3 as follows:\n Cities and their corresponding countries are now clearly indicated in the upper-left\n19\ncorner of each subfigure.\n Cities in the same row belong to the same continent/region, providing additional\ngeographical context.\n Cities in the same column correspond to the same expansion pattern, facilitating\ndirect comparison of how the pattern manifests across different cities.\n The figure caption has been updated accordingly to explain these visual\narrangements.\n\nComment 9:\nFigure 4 and associated Supplementary Figures: The SHAP value plots are appropriate\nfor explaining the model results. Ensure the color scheme and labels are accessible\n(color-blind friendly) and that each feature’s acronym is expanded in the figure or\ncaption for clarity (e.g., TR = Terrain Relief, etc.). The ranking of feature importance\n(Fig. 4a) is good; perhaps also report the overall model R² or pseudo-R² if available,\nto give a sense of variance explained. The supplement figures (S6–S11, S13, S15, S17,\nS19, etc., as referenced) seem to contain additional supportive analysis; it’s good that\nthese are provided for thoroughness.\n\nResponse:\nThank you for your valuable feedback on Figure 4 and the associated Supplementary\nFigures. In response:\n We have ensured that all variable abbreviations are defined within the caption of\nFigure 4, and we have adjusted the color schemes to be accessible and color-blind\nfriendly.\n We have included standard performance metrics—accuracy, precision, and F1-\nscore—in the Figure 4 caption, which more appropriately reflect the model’s\npredictive performance.\n\nComment 10:\nIn terms of language, my only suggestions are minor: avoid subjective terms like\n“strong predictive capacity” as noted, and consider simplifying a few long sentences\nfor readability. Otherwise, the tone and clarity meet the standards of Nature\nCommunications. The abstract effectively summarizes the findings, and the\nintroduction contextualizes the work with recent literature. I also appreciate that the\nauthors cite very recent studies (through 2024) which shows the manuscript is up-to-\ndate.\n\nResponse:\nWe have carefully reviewed the manuscript and implemented your minor suggestions.\nSeveral long sentences have been divided for improved readability. In addition,\nsubjective expressions such as “strong predictive capacity” have been replaced with\nmore precise and objective wording to ensure a consistently academic tone throughout\nthe manuscript.\n\nComment 11:\nRecommendation: In conclusion, I am positive about this manuscript and its\ncontributions. The study is ambitious in scope and offers valuable insights into urban\nexpansion patterns that are highly relevant for sustainable urban development\nscholarship and practice. The evidence presented generally supports the conclusions,\nand the work is within the scope of Nature Communications in terms of broad interest\nand scientific rigour. However, before acceptance, the authors should address the above\nissues to strengthen the paper. Most of the concerns (urban renewal limitation, threshold\nrobustness, clarity of figures, etc.) can be resolved with additional explanation, minor\nanalyses, or revisions to the text and do not require new data collection. I believe these\nrevisions will considerably improve the clarity and impact of the work.\nRecommendation: Accept with minor revisions. Once the authors have incorporated\nthe suggested clarifications and improvements, I am confident that the paper will be\nsuitable for publication in Nature Communications.\n\nResponse:\nThank you very much for your comprehensive review and constructive feedback. We\nwould like to assure you that we have carefully considered and addressed all the issues\nraised, including those related to the limitations of urban renewal detection, the\nrobustness of threshold selection, and the clarity of figures, among others.\nResponse to Reviewer #1\nComment:\nThank you for your thorough and thoughtful revisions. I have carefully reviewed the\nrevised manuscript as well as your point-by-point responses to my previous comments.\nOverall, I am pleased to see that the authors have addressed all major concerns raised\nin the first round.\nThe rewritten Introduction now clearly articulates both the conceptual motivations and\nthe methodological innovations behind incorporating 3D urban expansion. This\nsignificantly improves the framing and readability of the study.\nThe newly added comparative analysis and Supplementary Note 1 effectively\ndemonstrate the distinct yet related dimensions of 2D and 3D centrality. This addresses\nmy previous concern about potential conceptual overlap.\nThe extended analysis and Supplementary Note 2 convincingly show how these two\nindices capture different facets of urban form and together shape 3D expansion\ntrajectories. This clarification strengthens the theoretical contribution.\nThe robustness checks (including alternative classification approaches and LightGBM\nperformance verification) presented in Supplementary Note 3 adequately respond to\nmy earlier request. The results appear consistent and reinforce the reliability of your\nfindings.\nOverall, the manuscript has been substantially improved and now presents a clear,\nrigorous, and compelling contribution to the literature on 3D urban expansion and urban\nmorphology.\n\nResponse:\nWe appreciate your positive feedback and are glad to hear that the revised manuscript\nis now considered clear, rigorous, and compelling. Thank you for your valuable\ncontribution to this study.\n\nResponse to Reviewer #2\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\n1\nmanuscripts.\n\nResponse:\nWe appreciate that you are participating in Nature Communications’ initiative to\nsupport Early Career Researchers in peer review, and we value the insightful comments\nyou have provided.\n2"}]

Decision letter