Assessing urban growth dynamics in Cooch Behar city using the Shannon entropy model

Urban land increase is often conflated with spatial redistribution when entropy is interpreted as a direct measure of growth. This study quantifies built-up change in Cooch Behar City, India, from 1990 to 2022 while distinguishing land-cover compositional entropy from built-up spatial entropy. Landsat images from three epochs were classified using supervised maximum-likelihood classification. Urban growth was measured independently through absolute area change, percentage change, and compound annual growth rates. Normalized Shannon entropy was calculated from built-up shares across 20 wards, six 500-m concentric rings, and eight 45° directional sectors. The effective number of zones, Herfindahl–Hirschman Index, Gini coefficient, repeated-measures statistical testing, and ± 5% and ± 10% perturbation analyses provided complementary concentration and uncertainty checks. Built-up area increased from 2.24 to 6.28 km², representing an increase of 180.36% and a compound annual growth rate of 3.27%. Ward-level entropy increased from 0.918 in 1990 to 0.975 in 2006 and remained nearly stable at 0.973 in 2022, while the Gini coefficient declined from 0.380 to 0.217 before marginally increasing to 0.227. These results indicate a more even cross-ward distribution of built-up land rather than increasing compactness. Ring entropy reached 0.958 in 2022, when the two outermost rings contained 32.44% of the ring-domain built-up area. Directional entropy remained approximately 0.99, although the greatest absolute increases occurred toward the south-east, east, and north. Ward-level temporal change was statistically significant (Friedman χ²(2) = 40.0, p < .001), and sensitivity tests preserved the principal spatial pattern. The 2022 classification achieved 92.91% overall accuracy (95% CI: 87.44–96.10; κ = 0.869), although the absence of independent validation for 1990 and 2006 makes historical change estimates provisional. By separating growth magnitude, land-cover composition, and spatial dispersion and triangulating multiple spatial scales with concentration and uncertainty diagnostics, the study provides a reproducible baseline for planning in a river-constrained small city. The findings demonstrate that entropy alone cannot establish urban growth, compactness, or infilling.