The performance of watershed models in simulating stream discharge depends on the adequate representation of important watershed processes. In snow-dominated systems, snow, surface and subsurface hydrologic processes comprise a complex network of nonlinear interactions that influence the magnitude and timing of discharge. This study aims to identify critical processes and interactions that control discharge hydrographs in five major mountainous snow-dominated river basins in Colorado, USA. A comprehensive watershed model (Soil and Water Assessment Tool) and a variance-based global sensitivity analysis technique (Fourier Amplitude Sensitivity Test) were used in conjunction to identify critical models parameters and processes that they represent. Average monthly streamflow and streamflow root mean square error over a period of 20 years were used as two separate objective functions in this analysis. Examination of the sensitivity of monthly streamflow revealed the influence of parameters on flow volume, whereas the sensitivity of streamflow root mean square error also exposed the influence of parameters on the timing of the hydrographs. A stability analysis was performed to investigate the computational requirements for a robust sensitivity analysis. Results show that streamflow volume is mostly influenced by shallow subsurface processes, whereas interactions between groundwater and snow processes were the key in the timing of streamflows. A large majority of important parameters were common among all study watersheds, which underlies the prospect for regionalization of process-based hydrologic modelling in headwater river basins in Colorado.