Assessment of Urban Expansion and Spatial Redistribution of Built-Up Areas in Varanasi, India

Abstract Rapid urbanization in heritage-rich cities like Varanasi has led to significant land use changes, necessitating high-resolution monitoring of built-up dynamics. This study addresses the research gap in quantifying fine-scale spatiotemporal urban transformations by employing the Normalized Difference Built-up Index (NDBI) from Sentinel-2 imagery over the period of 2019–2025. Statistical analysis reveals the lowest mean NDBI in 2021 −0.0568), indicating a temporary reduction in built-up intensity, followed by a steady increase to −0.0223 in 2025. Spatial autocorrelation assessed via Local Moran’s I shows strong clustering in 2019 (mean I = 0.2755; skewness = 3.53) and persistent hotspots through 2025, reflecting structured urban growth. k -means clustering identified the top five high-density built-up zones per year, with mean intercluster distance peaking in 2021 (0.0867°) and decreasing convex hull area to 0.0020 deg 2 in 2025, suggesting increased decentralization yet confined urban expansion. A novel quantile-mapped gradient analysis detected an average NDBI shift magnitude of 5.76°, highlighting both directional growth and localized development shocks. The correlation analysis shows that absolute NDBI shifts are strongly influenced by both X - and Y -directional movements, with high Pearson correlations ( r > 0.76). In contrast, the weaker correlation between X and Y shifts ( r = 0.27) suggests spatially varied directional growth patterns. These results fill a methodological void by integrating spatial autocorrelation, clustering, and gradient-based shift analysis. The spatial data can guide equitable infrastructure planning and heritage conservation amid urban growth. Future scope includes integrating socioeconomic and policy variables with remote sensing indicators to develop predictive urban growth models supporting sustainable urban planning initiatives.