The Bogotá River Basin is a mountainous Andean catchment characterized by strong topographic heterogeneity, intense anthropogenic modification, and complex spatial organization of surface hydrological dynamics. Understanding how terrain structure interacts with hydrological variability remains a central challenge for basin-scale analysis. This study develops a Hamiltonian-based spatial framework to quantify hydro-topographic complexity in the Bogotá River Basin. The proposed indicator integrates potential energy derived from a 30 m Digital Elevation Model with a kinetic component representing multitemporal surface moisture variability derived from the Normalized Difference Water Index obtained from Sentinel-2 imagery for the period 2018–2025. After spatial alignment, normalization, and strict clipping to the basin domain, the Hamiltonian field was computed and its spatial gradients were analyzed to characterize hydro-topographic variability. Structural coherence tests, nonlinear statistical metrics, and spatial gradient diagnostics were applied to evaluate the consistency of the terrain–energy coupling. The results reveal a persistent spatial organization of the Hamiltonian field across all analyzed intervals. Mutual information between slope and the Hamiltonian indicator remains nearly constant ( ≈ 0.289 – 0.294 ) , entropy values indicate stable spatial complexity ( ≈ 3.15 – 3.24 ) , and clustering analysis consistently identifies six hydro-topographic regimes. These results indicate that the interaction between terrain morphology and hydrological variability forms a statistically structured spatial pattern rather than random fluctuations. The Hamiltonian framework therefore provides a reproducible spatial indicator capable of identifying zones of hydro-topographic stability and spatial contrasts in a highly modified Andean basin. • Proposes a Hamiltonian-based spatial indicator integrating DEM and multitemporal NDWI variability. • Reveals a persistent nonlinear terrain–energy relationship across the Bogotá River Basin. • Identifies six stable hydro-topographic regimes through clustering and information metrics. • Provides a reproducible framework for analyzing hydro-topographic stability and instability in mountainous basins.
Ladino-Moreno et al. (Thu,) studied this question.