Inner dispersion and outer compaction in a concentric ring Shannon entropy analysis of urban sprawl dynamics in Hyderabad, Pakistan from 1990 to 2021

Urban sprawl in developing-country secondary cities is spatially heterogeneous, varying with distance from the urban core and requiring zone-specific planning responses. Although Shannon's Entropy is widely applied as a sprawl metric, studies that disaggregate it by concentric ring zones across multi-decadal periods remain scarce for South Asian secondary cities, a gap that limits the spatial precision of policy. This study quantifies the spatial structure of urban growth in Hyderabad City Taluka, Pakistan’s sixth-largest urban centre, using three decades of Landsat imagery and Relative Shannon’s Entropy across six concentric ring zones. Four cloud-free Landsat scenes (1990, 2001, 2011, 2021) were classified via supervised Maximum Likelihood Classification and reclassified for entropy analysis. Built-up area grew from 44.9% to 59.1% of the study area, primarily through agricultural-land conversion. Citywide entropy exceeded the 0.5 sprawl threshold in every epoch (0.94, 0.92, 0.99 and 0.97), among the highest ranges in the published entropy literature. The ring analysis found two simultaneous processes: high-entropy dispersion in the inner rings (within 2,100 m of the centre), driven by fragmented agricultural conversion and intensified by displacement following Pakistan's catastrophic 2010 Sindh floods; and a gradual shift toward compactness in the outer rings (beyond 2,700 m), associated with north–south infrastructure corridors. The 2011 entropy peak of 0.99, near-maximum dispersion, is interpreted in relation to post-flood resettlement dynamics, an association not previously made in the sprawl literature. Two policy instruments follow: a statutory Urban Growth Boundary for inner rings and compact mixed-use zoning to formalise the outer-corridor densification already underway.