Geomorphic controls on flood response using the Width Function Instantaneous Unit Hydrograph framework

The hydrological response of a basin is fundamentally controlled by geomorphic processes, structures, and physiographic characteristics. Horton’s geomorphological laws, basin topology, and kinematic properties have long been employed to derive flood response in ungauged basins through various Geomorphological Instantaneous Unit Hydrograph (GIUH) frameworks. This study investigates ten ungauged tributary sub-basins of the Shilabati River in eastern India to analyse how basin morphometry and topology regulate travel-time distribution of water particles and flash-flood potential. The Width Function Instantaneous Unit Hydrograph (WFIUH), a GIUH variant, is applied to derive the geomorphological control on peak flow and time to peak, while the morphometric analysis is performed to investigate the effect of basin characteristics on these hydrologic response parameters. The WFIUH is obtained using the flow length extracted from the SRTM DEM, together with spatially variable and fixed hillslope velocities estimated from land use-land cover and slope using the Soil Conservation Services (SCS), uniform-flow, and Manning’s velocity formulae. Due to the absence of observed streamflow, WFIUH results are evaluated against the Geomorpho-climatic Instantaneous Unit Hydrograph (GcIUH) derived from climate-dependent channel velocity and drainage network topology, as well as observed flood events. 
Results show that all variable-velocity WFIUHs have longer time bases and a lower peak flow than fixed-velocity WFIUHs, because the highest velocity cells are associated with the smallest drainage contributing areas. The SCS-based variable velocity WFIUH aligns with the GcIUH, reproducing both the peak flow and time to peak of the IUH more accurately compared to the other methods. Small, circular, and comparatively steeper sub-basins exhibit shorter times to peak (8.5-10.5 hours), indicating a high flash-flood potential, mainly in sub-basins 3-6. On the contrary, elongated and well-bifurcated sub-basins reveal slightly delayed peaks (10.5-15.5 h) but remain capable of producing moderate-to-high floods due to their larger drainage areas, as confirmed by the flash flood event in 2025 in sub-basins 1, 8-10. Correlation analysis reveals that circularity ratio, relief ratio, and hypsometric integral are positively associated with peak flow, suggesting enhanced flow synchronization in compact and steep sub-basins. In contrast, time to peak shows moderate to strong negative correlations with these parameters and positive correlations with stream length and bifurcation ratios, indicating delayed response in elongated and highly branched drainage networks due to dispersed flow paths.
Therefore, basin morphometry and drainage network topology effectively govern hydrologic responses of the sub-basins. The spatially variable SCS velocity-based WFIUH provides a more realistic depiction of hydrologic response in ungauged sub-basins. Hence, this method is well-suited for event-based lumped hydrological modelling as well as for sub-basin prioritization in flash flood risk assessment.