A new surface meltwater routing model for use on the Greenland Ice Sheet surface
Authors: Yang Kang , Smith Laurence C. , Karlstrom Leif , Cooper Matthew G. , Tedesco Marco , van As Dirk , Cheng Xiao , Chen Zhuoqi , Li Manchun 
Published: November 2018

Abstract. 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 km2) mid-elevation (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 m s−1) and fast open-channel flow
(∼10-1 m s−1); (2) the slow interfluve velocities are
physically consistent with shallow, unsaturated subsurface porous media flow
(∼10-4–10−5 m s−1) more than overland sheet flow
(∼10-2 m s−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.