A novel spatiotemporal melt factor framework for quantifying snow and glacier melt in alpine basins

Global temperature changes affect alpine regions unevenly, shaped by gradients in elevation and land cover. Yet, runoff modelling primarily relies on temperature-index methods with constant degree-day factor, limiting representation of melt variability. This study develops spatiotemporal melt factor formulation that incorporates nonlinear relationships among temperature, snow density, shortwave and longwave radiation. The resulting formulation employs empirical coefficients to represent integrated basin-scale melt sensitivity. The formulation is integrated into the modified Spatial Processes in Hydrology (SPHY) model to simulate runoff dynamics in transboundary Satluj River Basin. The model reproduces daily discharge with high accuracy (R2 values of 0.91–0.93) and improves seasonal runoff representation relative to conventional constant degree-day factor approach by reducing melt overestimation. Projections under CMIP6 scenarios indicate increasing rainfall contributions and gradual shift from melt-driven runoff to rainfall-influenced regimes. The proposed formulation provides a physical approach for improving runoff simulations in alpine regions under changing climate conditions.Graphical abstract