Hamiltonian energy field integrating hydrological dynamics and geomorphological structure in the Bogotá river basin

Understanding the spatial organization of hydrological dynamics in complex mountainous basins remains challenging when indicators analyze topography or surface moisture independently. In heterogeneous and heavily modified basins such as the Bogotá River basin, integrated metrics are required to capture the coupling between geomorphological structure and surface hydrological variability. The objective of this study is to characterize the hydro-topographic complexity of the Bogotá River basin using a Hamiltonian indicator that integrates potential energy derived from the Digital Elevation Model (DEM) and kinetic energy associated with the temporal variability of surface moisture represented by the index. The methodology is based on the use of a Shuttle Radar Topography Mission (SRTM) DEM with 30 m spatial resolution and multitemporal series obtained from Sentinel-2 imagery for the period 2018–2025. All datasets were spatially aligned, normalized, and strictly clipped to the basin domain. The Hamiltonian field was formulated as the sum of the normalized energy components, and its spatial gradients were computed to assess hydro-topographic instability. Multitemporal Hamiltonian maps, contour lines, critical points, and stability classifications were generated to analyze the spatial persistence and temporal variability of the system. The results reveal a high spatial persistence of Hamiltonian patterns throughout the analyzed period, indicating a stable energetic organization of the hydro-topographic system despite temporal variations in surface moisture. Areas with high Hamiltonian values correspond to sectors where more complex topography coincides with greater hydrological variability, whereas low values are associated with more homogeneous and stable zones.