A new surface meltwater routing model for use on the Greenland Ice Sheet surface

Large volumes of surface meltwater are routed through supraglacial internally drained catchments (IDCs) on the Greenland Ice Sheet surface each summer. Because surface routing impacts the timing and discharge of meltwater entering the ice sheet through moulins, accurately modeling moulin hydrographs is crucial for correctly coupling surface energy and mass balance models with subglacial hydrology and ice dynamics. Yet surface routing of meltwater on ice sheets remains a poorly understood physical process. We use high-resolution (0.5 m) satellite imagery and a derivative high-resolution (3.0 m) digital elevation model to partition the runoff-contributing area of the Rio Behar catchment, a moderately sized (∼ 63 km ²) midelevation (1207-1381 m) IDC in the southwestern Greenland ablation zone, into open meltwater channels (supraglacial streams and rivers) and interfluves (small upland areas draining to surface channels, also called "hillslopes" in terrestrial geomorphology). A simultaneous in situ moulin discharge hydrograph was previously acquired for this catchment in July 2015. By combining the in situ discharge measurements with remote sensing and classic hydrological theory, we determine mean meltwater routing velocities through open channels and interfluves within the catchment. Two traditional terrestrial hydrology surface routing models, the unit hydrograph and rescaled width function, are applied and also compared with a surface routing and lake-filling model. We conclude that (1) surface meltwater is routed by slow interfluve flow (∼ 10 ^-3-10 ^-4 ms ^-1) and fast open-channel flow (∼ 10 ^-1 ms ^-1); (2) the slow interfluve velocities are physically consistent with shallow, unsaturated subsurface porous media flow (∼ 10 ^-4-10 ^-5 ms ^-1) more than overland sheet flow (∼ 10 ^-2 ms ^-1); (3) the open-channel velocities yield mean Manning's roughness coefficient (n) values of ∼ 0:03-0.05 averaged across the Rio Behar supraglacial stream-river network; (4) interfluve and open-channel flow travel distances have mean length scales of ∼ 100-101 m and ∼ 103 m, respectively; and (5) seasonal evolution of supraglacial drainage density will alter these length scales and the proportion of interfluves vs. open channels and thus the magnitude and timing of meltwater discharge received at the outlet moulin. This phenomenon may explain seasonal subglacial water pressure variations measured in a borehole ∼ 20 km away. In general, we conclude that in addition to fast open-channel transport through supraglacial streams and rivers, slow interfluve processes must also be considered in ice sheet surface meltwater routing models. Interfluves are characterized by slow overland and/or shallow subsurface flow, and it appears that shallow unsaturated porous-media flow occurs even in the bare-ice ablation zone. Together, both interfluves and open channels combine to modulate the timing and discharge of meltwater reaching IDC outlet moulins, prior to further modification by englacial and subglacial processes.