Supraglacial rivers on the Greenland Ice Sheet (GrIS) transport large volumes of surface meltwater toward the ocean, yet have received relatively little direct research. This study presents field observations of channel width, depth, velocity, and water surface slope for nine supraglacial channels on the south-western GrIS collected between July 23 and August 20, 2012. Field sites are located up to 74km inland and span 494-1485m elevation, and contain measured discharges larger than any previous in situ study: from 0.006 to 23.12m(3)/s in channels 0.20 to 20.62m wide. All channels were deeply incised with near vertical banks, and hydraulic geometry results indicate that supraglacial channels primarily accommodate greater discharges by increasing velocity. Smaller streams had steeper water surface slopes (0.74-8.83%) than typical in terrestrial settings, yielding correspondingly high velocities (0.40-2.60m/s) and Froude numbers (0.45-3.11) with supercritical flow observed in 54% of measurements. Derived Manning's n values were larger and more variable than anticipated from channels of uniform substrate, ranging from 0.009 to 0.154 with a mean value of 0.035 +/- 0.027 despite the absence of sediment, debris, or other roughness elements. Ubiquitous micro-depressions in shallow sections of the channel bed may explain some of these roughness values. However, we find that other, unobserved sources of flow resistance likely contributed to these elevated Manning's n values: future work should explicitly consider additional sources of flow resistance beyond bed roughness in supraglacial channels. We conclude that hydraulic modeling for these channels must allow for both subcritical and supercritical flow, and most importantly must refrain from assuming that all ice-substrate channels exhibit similar hydraulic behavior, especially for Froude numbers and Manning's n. Finally, this study highlights that further theoretical and empirical work on supraglacial channel hydraulics is necessary before broad scale understanding of ice sheet hydrology can be achieved. Copyright (c) 2016 John Wiley & Sons, Ltd.