Urban built environments expand through three processes: lateral spreading, infilling, and vertical growth, all contributing to increased building volume. The three-dimensional (3D) urban structure significantly impacts greenhouse gas emissions, material demand, and urban climate. However, there's a lack of scientific understanding and consistent empirical evidence regarding the evolution of the vertical dimension of global urban areas over decades. This study aims to address this knowledge gap by analyzing multi-decadal data to understand changes in urban growth rates. Previous urban remote sensing often characterized urbanization as lateral growth, focusing on land built fraction (BF), neglecting the 3D aspect due to limited data availability. While BF time series capture lateral and infill growth, they cannot directly measure building heights or vertical growth. Although population densities were used for 3D urban representations, the application of remote sensing to measure urban verticality is relatively recent. Existing global remote sensing studies on vertical growth are often limited in temporal or spatial scope. This study leverages global urban microwave backscatter data (PR) from three space-borne scatterometer datasets (ERS, QSCAT, and ASCAT), combined with multi-decadal World Settlement Footprint evolution (WSF-evo) BF data, to characterize changes in the rates and patterns of global 3D urban growth from the 1990s through the 2010s for over 1,550 cities. PR and BF, independent space-borne measures of urban growth, offer a more comprehensive understanding of upward and outward urban growth dynamics, categorized into slow growth, outward growth, upward growth, and up-and-out growth.

Existing research on urban growth often focuses on two-dimensional (2D) outward expansion, utilizing built fraction (BF) data derived from remote sensing. However, BF data alone cannot capture the vertical dimension of urban growth, a critical aspect impacting environmental and societal factors. While population density has been used as a proxy for 3D urban structure, the application of remote sensing techniques to directly measure building height and vertical growth is a relatively recent development. Previous studies using high-resolution Synthetic Aperture Radar (SAR) data have provided valuable insights into 3D urban change but are usually limited to short time spans (3-4 years) and specific metropolises. Global high-resolution 3D studies frequently focus on single time snapshots rather than long-term trends, limiting their ability to reveal decadal patterns of change. Some efforts have attempted to combine building height data with backcasting from Landsat, but these are still constrained by limitations in data availability and accuracy. Active microwave backscatter has shown promise in capturing building structure, correlating with building height and volume, but it cannot disaggregate different growth types. This study builds upon earlier global studies that utilized backscatter data from a single scatterometer and a BF dataset but did not quantify changes in growth rates over time. By using a multi-decadal time series and incorporating data from multiple sensors, it improves the understanding of the dynamics of 3D urban expansion.

The study employed a modified methodology from previous research, incorporating a longer time series of data from three scatterometers (ERS, QSCAT, and ASCAT) to understand the dynamics of 3D urban growth across three decades (1990s-2010s). The spatial analysis covered global urban land on a 0.05° lat/lon grid, with temporal analysis at annual time steps from 1993 to 2021. The study used global Morphological Urban Areas (MUAs) to define urban extents and included 1,567 urban areas across 151 countries. Five MUAs were excluded due to missing data. The study leveraged World Settlement Footprint evolution (WSF-evo) data for built fraction (BF) analysis, providing annual rates of increase in BF for each decade. Urban microwave backscatter (PR) data, extracted from the three scatterometers, were intercalibrated across sensors to account for variations in sensor sensitivity and wavelength differences (C-band and Ku-band). To mitigate the impact of short-term variability not related to urban development, decadal trends in backscatter were calculated separately for each sensor and decade. This approach used a moving average method for smoothing and interpolation of data from multiple sensors. Spatial distribution maps of bivariate decadal trends in PR and BF were created, categorizing grid cells into four building growth patterns: slow growth, outward growth, upward growth, and up-and-out growth. Accelerations and decelerations in growth rates were quantified at regional and individual MUA levels. A k-means clustering analysis grouped MUA grid cells into unique clusters across the three decades to identify urban growth typologies. The analysis included 'initial state' (BF and PR) and growth rates (annual increase in BF and PR trend) to characterise these clusters. The relationship between urban microwave PR, urban BF, and building floor area was tested. The IEA global annual total floor area data (2000-2020) and national building area data from China (1985-2021) along with municipality-level data from Beijing (1990-2020) and Shanghai (1978-2019) were used for this comparison. The study used Python and R for data processing and analysis.

The study revealed a substantial shift in global urban growth patterns from outward expansion to upward development. Mean annual BF and PR increased across all regions and cities, but growth rates exhibited regional and temporal variations. Increases in PR and BF correlated with increases in floor area at various scales. In China, BF increases associated with floor area growth have slowed recently, while PR increases have not. Many large cities showed a transition from rapid BF growth and slow PR growth (outward growth) to rapid PR growth and slow BF growth (upward growth). Some cities experienced rapid growth in both BF and PR (up-and-out growth). The shift from lateral to vertical growth often began in city centers before spreading outwards, with Dhaka being an exception. A similar shift was observed across most global regions, with a significant temporal lag across East Asia, China, Southeast Asia, and India. China had the largest area with rapid growth in one or both metrics. Globally, the area with slow growth rates decreased, while the areas experiencing upward and up-and-out growth increased significantly. Growth rate acceleration and deceleration varied regionally and across cities. China, the Middle East, and East Asia showed greater PR growth acceleration from the 1990s to the 2000s, while Africa had greater acceleration from the 2000s to the 2010s. Most regions showed decelerating BF growth except for China, which experienced a substantial acceleration initially, and then a slight deceleration. Most large cities had accelerating PR and decelerating BF growth. K-means clustering identified seven unique urban growth clusters across the three decades, revealing distinct typologies including ‘budding,’ ‘outward,’ ‘upward,’ ‘slow-up-and-out,’ and ‘fast-up-and-out’. The ‘fast-up-and-out’ typology was prominent in Chinese cities during a period of rapid real estate development.

The findings challenge traditional models of urbanization like von Thünen's and Burgess's, suggesting a distinct city-building process with phases corresponding to economic development. The study demonstrates that this process, while universal, has regionally varying phases and sequences. The combined analysis of BF and PR data reveals four broad patterns of urban growth: slow growth, outward, upward, and up-and-out growth. The shift towards predominantly upward growth in large cities mirrors a potential transition from manufacturing-based economies to service-based economies. The observed temporal lag in the shift from outward to upward growth across regions (East Asia to India) is consistent with regional development patterns. This multivariable analysis offers a more nuanced understanding of urban growth than single-variable studies. The rapid upward growth observed, particularly in China, is attributed to a real estate boom. This study's long-term, large-scale analysis provides insights into global physical capital accumulation (urban buildings). The findings have implications for urban eco-environmental analyses and resource management, particularly in estimating material use. While limited by spatial resolution and sensor inconsistencies, the study's broad geographic coverage provides valuable insights into global urbanization trends.

This study demonstrates a global shift in urban growth patterns from outward expansion to upward development over the past three decades, especially pronounced in larger cities outside advanced economies. This shift is a complex phenomenon influenced by several factors, including economic development and population growth, manifesting in regionally and temporally varying rates of change. The findings highlight the importance of considering the 3D urban structure in urban planning and environmental modeling, calling for further research to integrate high-resolution data with other socioeconomic datasets to more comprehensively understand the dynamics and implications of this global transition. Future research should focus on integrating higher-resolution data and exploring the interplay of social and economic factors with these observed spatial and temporal patterns of growth.

The study's coarse spatial resolution (~5-10km) prevents detailed analysis at the neighborhood scale and limits its applicability to smaller cities. The use of data from multiple sensors with inherent differences in sensitivity and wavelength introduces challenges in constructing a completely continuous time series. Intercalibration methods were used to address these sensor differences but introduce further uncertainty. The inability to disaggregate different types of building volume changes within a single grid cell (new low buildings, new tall buildings, or replacement of low buildings with tall buildings) limits the precision of interpreting backscatter data. Furthermore, the lack of comprehensive reference data (e.g., lidar) across multiple cities and time periods restricts detailed interpretations. The IEA building floor area data is not restricted to urban domains, nor is the China new building floor area data, and the Beijing and Shanghai statistical floor area data are for these municipality provinces, whose spatial extent does not fully align with the Beijing+ and Shanghai+ MUAs.