A groundwater seepage face exists where the water table intersects the land surface, partitioning groundwater discharge to a waterbody between subaerial groundwater discharge (SGWD) and submerged subsurface discharge. We conducted numerical experiments to assess the effects of surface water level and other parameters on seepage face formation and groundwater discharge partitioning for two-dimensional catchment cross-section domain with two slopes - a bank slope near the waterbody and an upland slope. We performed local and global sensitivity tests for the onset of SGWD, the seepage length fraction and the seepage flow fraction for diverse topographic and hydrogeologic conditions. The results show that the ratio of recharge to hydraulic conductivity required for the onset of SGWD for both slopes varies up to three orders of magnitude with the changing water level. We also find that changing water levels has opposing effects on the metrics of the seepage faces of the two slopes.