Urbanization is a significant global trend, with over half the world's population now residing in cities. Understanding urban spatial structures and the dynamics of urban expansion is crucial for sustainable development. Cities exhibit a center-periphery structure due to the spatial agglomeration of urban elements. Central Place Theory explains the hierarchical organization of cities, with city centers serving as core areas with concentrated functions. This leads to a population density gradient that decreases with distance from the city center. Concentric zone theory further describes concentric zones with unique social and economic characteristics. However, the differences in spatial gradients between socioeconomic and physical elements remain unclear. Previous studies mainly focused on population and urban land, using linear models or inverse-S functions. Nighttime light (NLI) from satellite imagery provides a useful proxy for measuring the intensity of socioeconomic activities and complements traditional land-use data. This study aims to compare the spatial gradients of NLI and ULD in 30 global megacities to quantify the patterns and dynamics of urban expansion and offer policy implications for sustainable development. The choice of 30 cities (21 megacities with populations exceeding 10 million and 9 regional central cities) ensures a global representation, considering factors beyond population size to encompass diverse urban contexts.

Existing research on urban spatial patterns has primarily focused on population and urban land, utilizing methods such as linear models and inverse-S functions to describe the spatial distribution of urban land. The inverse-S function, in particular, has been successfully applied to various urban elements. However, these studies often neglect the dynamics of socioeconomic activities. Nighttime light imagery has emerged as a valuable tool for monitoring socioeconomic dynamics and urban growth. It's been used to estimate energy consumption and assess urban development in terms of spatial and socioeconomic status. Studies have analyzed spatial distributions of urban elements, highlighting the spatial agglomeration of different elements and the significance of understanding their distributions. However, the comparison of physical expansion (represented by land use data) and social expansion (represented by nighttime light) in a comprehensive global context is still lacking.

This study uses a concentric ring analysis to investigate the spatial gradients of urban land density (ULD) and nighttime light intensity (NLI) in 30 global megacities. Data for 2020 include ESRI 10m Global Land Cover products for land use and NPP-VIIRS nighttime light imagery. Land use data was reclassified into built-up areas, water bodies, and open space. Nighttime light intensity was standardized to a scale of [0,1]. Concentric rings were created around the city center (identified using high-resolution imagery), and ULD was calculated as the ratio of built-up area to the total land area (excluding water). NLI was calculated as the average digital number value within each ring. The inverse-S function, f(r) = 1/(1+e^-a(r-c))+c, was used to fit the spatial gradients of both ULD and NLI, where 'r' is the radius, and 'a', 'c', and 'D' are parameters representing urban form and extent. Parameter 'D' represents the city radius, 'a' represents compactness, and 'c' represents background density. A concentration degree index (CDI) was calculated as the ratio of parameter 'D' for NLI and ULD to compare the spatial agglomeration of socioeconomic and physical elements. The study also analyzed poly-centric cities by adjusting buffer partitioning based on the spatial distribution of nighttime light.

Both ULD and NLI exhibited an inverse-S shaped spatial distribution in all 30 megacities. The inverse-S function provided a good fit (R² > 0.85) for both ULD and NLI spatial gradients. NLI decreased more rapidly than ULD, resulting in smaller radii ('D' parameter) for NLI than ULD in most cities. This indicates that socioeconomic activities are more concentrated near city centers than urban land expansion. The concentration degree index (CDI), which represents the ratio of the radii of NLI and ULD, varied between 0.098 and 0.904 (average 0.474). Cities with larger CDI values have a more balanced spatial distribution between social and physical space. In poly-centric cities (e.g., Ho Chi Minh City, Seoul), the inverse-S function still applies well after adjusting buffer partitioning to account for multiple sub-centers. Parameters 'a' for ULD were generally larger than those for NLI, indicating more compact physical forms than social forms. The significant differences in the radii (parameter D) for NLI and ULD highlight the imbalance between physical and social space expansion in many megacities.

The findings demonstrate that the inverse-S function effectively models the spatial gradients of both ULD and NLI in megacities, providing a quantitative way to compare the spatial distribution of physical and socioeconomic elements. The consistently smaller radius for NLI compared to ULD across most cities suggests a significant mismatch between the physical extent of urban areas and the spatial concentration of socioeconomic activities. This mismatch indicates potential issues with urban sprawl, inefficient resource allocation, and unbalanced development. The CDI offers a useful metric for evaluating the balance between physical and social space in urban development. The study's findings support the importance of planning interventions for a more coordinated and sustainable urban development, balancing urban sprawl with effective utilization of existing infrastructure and resources.

This study demonstrates that both urban land density and nighttime light intensity follow inverse-S spatial gradients in 30 global megacities. However, nighttime light intensity decreases faster than urban land density, reflecting a more compact spatial distribution of socioeconomic activity. The inverse-S function and CDI provide useful tools for assessing urban spatial patterns and identifying imbalances between physical and social development. This research underscores the need for strategies promoting balanced urban expansion to foster sustainable megacity development. Further research could investigate the application of these methods across diverse urban contexts and over time, incorporating other urban elements for a more comprehensive understanding of urban spatial dynamics.

While this study employs a comprehensive dataset of 30 global megacities, its reliance on 2020 data limits the assessment of temporal trends. The use of nighttime light as a proxy for socioeconomic activity is subject to limitations related to its sensitivity to factors beyond economic activity (e.g., weather, light pollution). The three-dimensional nature of urban development isn’t fully captured by the two-dimensional analysis of land use. Future research could incorporate multi-source data including population density and three-dimensional building information for a more robust analysis. Also, the definition of city centers could influence the results. Variations in data resolution and quality across cities could affect the model's accuracy.