Beyond urban boundaries: Percolation reveals land-consumptive growth in India
Abstract
Cities often extend beyond their administrative boundaries, complicating assessments of urban sustainability. Using Global Human Settlement Layer data for India's 50 largest urban agglomerations (1975--2025), we develop a percolation-based framework for urban delineation. Within district-based regions, we apply unrestricted DBSCAN to spatial coordinates of 100-m cells with positive population and built-up surface. We treat neighborhood distance as the percolation control parameter and the proportion of eligible cells in the largest connected cluster as the empirical order parameter. Sharp increases in this proportion reveal characteristic percolation transitions. Post-transition connection lengths declined (median:650m to 350m), indicating that previously disconnected settlements coalesce at progressively shorter spatial distances alongside increasing urban land consumption. Urban footprint increased from 447.6 to 1,382.7km2, while population densities declined. SDG11.3.1 land-consumption-to-population-growth ratios generally exceeded unity. Zipf and allometric relationships describe cross-sectional urban structure, but land-consumptive growth shows little relationship with city size. Urban delineation thus shapes sustainability assessments.
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BibTeX
@misc{sarkar2026beyond,
title = {{Beyond urban boundaries: Percolation reveals land-consumptive growth in India}},
author = {Somwrita Sarkar and Chirag Deb and Carolina Pantoja Mardones and Anmol Gaur and Arunim Anand and Rashi Shrivastava and Anusha Roy and Arnab Jana and Eswar Rajasekaran and David Levinson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37073},
eprint = {2610.37073},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37073},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Beyond urban boundaries: Percolation reveals land-consumptive growth in India
AU - Somwrita Sarkar
AU - Chirag Deb
AU - Carolina Pantoja Mardones
AU - Anmol Gaur
AU - Arunim Anand
AU - Rashi Shrivastava
AU - Anusha Roy
AU - Arnab Jana
AU - Eswar Rajasekaran
AU - David Levinson
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37073
UR - https://arxiv.org/abs/2610.37073
AB - Cities often extend beyond their administrative boundaries, complicating assessments of urban sustainability. Using Global Human Settlement Layer data for India's 50 largest urban agglomerations (1975--2025), we develop a percolation-based framework for urban delineation. Within district-based regions, we apply unrestricted DBSCAN to spatial coordinates of 100-m cells with positive population and built-up surface. We treat neighborhood distance as the percolation control parameter and the proportion of eligible cells in the largest connected cluster as the empirical order parameter. Sharp increases in this proportion reveal characteristic percolation transitions. Post-transition connection lengths declined (median:650m to 350m), indicating that previously disconnected settlements coalesce at progressively shorter spatial distances alongside increasing urban land consumption. Urban footprint increased from 447.6 to 1,382.7km^2, while population densities declined. SDG11.3.1 land-consumption-to-population-growth ratios generally exceeded unity. Zipf and allometric relationships describe cross-sectional urban structure, but land-consumptive growth shows little relationship with city size. Urban delineation thus shapes sustainability assessments.
ER -