Spatial gradients of urban land density and nighttime light intensity in 30 global megacities

The study addresses how urban physical elements (urban land) and socioeconomic activity (nighttime lights) vary with distance from city centers and whether their spatial gradients differ. In the context of accelerating global urbanization and the importance of monitoring urban expansion, the authors note that cities exhibit spatial agglomeration with core-periphery structures. Prior work often measured physical expansion (impervious surfaces) but less so the social dynamics. Nighttime light imagery serves as a proxy for socioeconomic intensity. The research aims to quantify and compare the spatial gradients of urban land density (ULD) and nighttime light intensity (NLI) across 30 globally significant megacities, testing whether both follow an inverse-S decay from city centers and what their fitted parameters imply about urban form and extent. Understanding these differences is important for assessing balance between physical expansion and socioeconomic development, with implications for sustainable urban planning.

Prior studies have characterized urban expansion and spatial organization using population and land-based measures, including linear two-stage models, the inverse-S function, and Geographic Micro-Process (GMP) models to describe urban land density patterns. Remote sensing of impervious surfaces captures physical development but misses socioeconomic dynamics. Nighttime light (NTL) imagery has been widely used to monitor socioeconomic activity, urban growth, and energy consumption due to its sensitivity and coverage (e.g., VIIRS NPP). Studies have shown urban elements generally agglomerate and can follow similar spatial patterns; the inverse-S land density function has been extended to other elements such as population density, road density, and land surface temperature. Literature also highlights mismatches between land expansion and socioeconomic growth caused by sprawl, increasing land-take per capita, and uneven growth across city sizes, with megacities becoming key sites of expansion. This work builds on that foundation by jointly evaluating ULD and NLI gradients and their parameterized differences across many global megacities.

Study area: 30 globally distributed cities were selected, including 21 megacities (>10 million population) and 9 regional central cities (e.g., Berlin, Rome, Madrid) to ensure geographic and functional representativeness beyond population size alone. Data sources and preprocessing: - ESRI 10 m Global Land Cover (2020) derived from Sentinel-2 was reclassified into three classes: built-up areas, water bodies, and open space (all non-water, non-built classes with potential for conversion). - Annual NPP-VIIRS nighttime lights (2020) were used to represent socioeconomic activity intensity. - Administrative boundaries were used to clip data to study areas. Concentric ring analysis: - City center definition: Using Google high-resolution imagery, each city’s center was identified as the CBD or the city’s birthplace. - Equidistant concentric buffer rings (e.g., 1 km intervals) were generated outward from the center, covering the main urban extent. - Urban Land Density (ULD) per ring: ULD = (built-up area) / (total land area − water area). - Nighttime Light Intensity (NLI) per ring: computed as mean VIIRS digital number per ring and then min–max normalized to [0,1] across rings for each city. Inverse-S function fitting: - The inverse-S function f(r) was fitted to ring-based ULD and NLI profiles as a function of distance r from the center. Parameters: a (controls slope; indicates compactness), c (background density/intensity in the hinterland), and D (city radius/extent of main aggregation). Goodness of fit (R^2) was computed. Concentration Degree Index (CDI): - CDI = D_NLI / D_ULD quantifies the relative aggregation radius in social vs physical space. A larger CDI means social-space extent approaches physical-space extent. Polycentric adjustment (for selected cases): - For cities showing multiple centers (e.g., Ho Chi Minh City, Seoul), sub-centers were identified from NLI clustering and corroborated by fluctuations in the fitted profiles. Boundaries between centers were set at rings with local minima in density/intensity between peaks. Customized polycentric buffers were constructed and the inverse-S function was re-fitted within these partitions to reduce profile fluctuations. Note: cross-city comparisons are made using single-center concentric buffers to ensure consistency.

- Both ULD and NLI decline with distance from city centers in a characteristic inverse-S pattern: slow decay near the core, rapid decline in inner to suburban zones, and slow decay toward the periphery/background. - Model fit: The inverse-S function provided strong fits for both elements in all cities (R^2 values generally > 0.85; see Table 1). - Parameter differences: ULD typically exhibits larger a and D than NLI, indicating that physical urban entities are more extensive and often more compact than the spatial footprint of socioeconomic activity. - a (compactness): - ULD a ranged 1.54–5.92 (mean ≈ 3.49). - NLI a ranged 0.68–3.73 (mean ≈ 2.04). - Exceptions where a(NLI) > a(ULD): Dhaka, Ho Chi Minh City, Kolkata (more compact social-space form). - c (hinterland background): generally < 0.3; can be higher where built-up density remains large at the outskirts (e.g., Shanghai, New York, Kolkata). - D (radius/extent): D_ULD > D_NLI in most cases, confirming smaller social-space aggregation radii than physical extents. - CDI (D_NLI / D_ULD): ranged 0.098–0.904 (mean ≈ 0.474). Toronto had the lowest CDI; large cities like Tokyo, Shanghai, Toronto, and New York exhibit very large physical extents with much smaller NLI radii, reflecting concentrated socioeconomic cores and sprawling physical footprints. Madrid showed relatively similar ULD and NLI curves and close D values. - Polycentric cities: Adjusting buffer partitioning around identified sub-centers reduced fluctuations and improved fits: - Ho Chi Minh City (polycentric): ULD α=2.98, c=0.17, D=41.69, R^2=0.986; NLI α=2.27, c=0.06, D=18.20, R^2=0.974. - Seoul (polycentric): ULD α=2.25, c=0.25, D=38.39, R^2=0.954; NLI α=1.15, c=0.02, D=20.93, R^2=0.957. - Interpretation: NLI declines faster than ULD, indicating stronger agglomeration of socioeconomic activity. Many megacities show physical expansion outpacing social/economic intensity at edges, suggesting potential inefficiency and sprawl.

The findings confirm that urban elements exhibit spatial agglomeration with an inverse-S gradient from city centers. However, socioeconomic activity (NLI) is more tightly clustered and declines faster than physical urban land (ULD), resulting in smaller social-space radii relative to physical extents. This mismatch implies that many megacities have expanded physically beyond the effective reach of socioeconomic activity, leading to low-intensity peripheries and potentially inefficient, sprawling growth. The parameterization via the inverse-S function provides interpretable indicators of compactness (a), background intensity (c), and spatial extent (D) for both physical and social spaces, enabling cross-city comparisons and diagnosing imbalance. Policy-wise, enhancing infrastructure and services in suburban/new urban areas could redistribute activity and populations, reduce pressure on cores, and improve coordination between physical expansion and socioeconomic development. The approach generalizes to polycentric cities with customized buffers and can be extended to other urban elements to build a more complete picture of urban structure.

This study demonstrates that the inverse-S function, originally proposed for urban land density, also effectively models nighttime light intensity gradients. Across 30 global megacities, both ULD and NLI share inverse-S spatial patterns, but NLI declines faster and has smaller aggregation radii, indicating stronger clustering of socioeconomic activity relative to physical urban extents. The parameterized differences (a, c, D) reveal urban compactness and extent in physical versus social space, offering a tool to assess coordination of urban development. Many megacities show larger physical footprints than social-space coverage, highlighting risks of inefficient sprawl. The framework can inform policies promoting balanced, sustainable urban growth. Future work should integrate multi-source data (e.g., population density, road density, 3D building information) and conduct time-series analyses to track evolving relationships among urban elements and test the inverse-S applicability more broadly.

- Proxy limitations: Nighttime light captures nocturnal activity and may not reflect daytime socioeconomic vitality or sectors with low lighting. Urban land density is a 2D measure and omits vertical development (3D built volume and available living space). - Normalization effects: Min–max normalization of NLI per city drives edge values toward zero, potentially accentuating gaps with ULD at the periphery. - Temporal scope: Analyses are based on 2020 datasets; dynamics over time are not captured here. - Center definition and ring design: City center identification (CBD/birthplace) and ring width may influence gradients; cross-city comparability is maintained with single-center rings but may not fully capture polycentric structures without customized buffers. - Data classification: Reclassification of land cover into built-up, water, and open space simplifies heterogeneous land uses and may introduce classification errors.