Understanding factors controlling baseflow (or groundwater discharge) is critical for improving streamflow prediction skills in the arid southwest US. We used a version of Noah-MP with newly-advanced hydrology features and the Routing Application for Parallel computation of Discharge (RAPID) to investigate the impacts of uncertainties in representations of hydrological processes, soil hydraulic parameters, and precipitation data on baseflow production and streamflow prediction skill. We conducted model experiments by combining different options of hydrological processes, hydraulic parameters, and precipitation datasets in the southwest US. These experiments were driven by three gridded precipitation products: the NLDAS-2, the IMERG Final, and AORC. RAPID was then used to route Noah-MP modeled surface and subsurface runoff to predict daily streamflow at 390 USGS gauges. We evaluated the modeled ratio of baseflow to total streamflow (or baseflow index, BFI) against those derived from the USGS streamflow. Our results suggest that 1) soil water retention curve model plays a dominant role, with the Van-Genuchten hydraulic scheme reducing the overestimated BFI produced by the Brooks-Corey (also used by the National Water Model, NWM), 2) hydraulic parameters strongly affect streamflow prediction, a machine learning-based dataset captures the USGS BFI, showing a better performance than the optimized NWM by a median KGE of 21%, and 3) the ponding depth threshold that increases infiltration is preferred. Overall, most of our models with the advanced hydrology show a better performance in modeling BFI and thus a better skill in streamflow predictions than the optimized NWM in the dry southwestern river basins.