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

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 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 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 ∼ 10 0 -10 1 m and ∼ 10 3 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-mediaPublished by Copernicus Publications on behalf of the European Geosciences Union. 3792 K. Yang et al.: A new surface meltwater routing model flow occurs even in the bare-ice ablation zone. Together, bothinterfluves and open channels combine to modulate the timing and ...

Inter-comparison of surface meltwater routing models for the Greenland Ice Sheet and influence on subglacial effective pressures

“…In contrast, the generally ad hoc partitioning of slow and fast flow can substantially impact the performance of SRLF and RWF without careful calibration. Moreover, SRLF and RWF rely on surface DEMs to calculate meltwater flow paths (Yang et al, 2018) and SRLF also relies on DEMs to calculate meltwater routing velocities (Arnold et al, 1998). Characteristics such as slope, flow direction, flow length, drainage area, and drainage networks are readily extracted from DEMs but are scale-dependent (Montgomery and Foufoula-Georgiou, 1993), signifying that DEM spatial resolutions influence their computation (Zhang and Montgomery, 1994;Hancock et al, 2006).…”

“…Meltwater transport time (t) for each DEM pixel was then determined as t = L/v. To compare with SUH and RWF, a one-hour UH was calculated by hourly binning the transport time raster (Yang et al, 2018), with the resultant UH termed SRLF-UH.…”

“…In the latter instances, RCM instantaneous runoff is simply summed over a given drainage catchment to estimate supraglacial moulin discharge, to drive models of subglacial hydrologic system evolution and/or ice flow dynamics (Bartholomew et al, 2011;Bartholomew et al, 2012). This simplification may be appropriate for small drainage catchment or for long-term studies; however, surface meltwater routing has been found to substantially modify ice surface runoff (Banwell et al, 2012;Banwell et al, 2013;Arnold et al, 2014), thus altering the magnitude and timing of peak moulin discharge (Smith et al, 2017;Yang et al, 2018). As such, supraglacial routing has strong potential to affect subglacial hydrologic system evolution and hydrodynamics, especially for large catchments and short (i.e., diurnal) time scales.…”

“…Surface meltwater routing may be characterized by meltwater transport velocity (v), flow length (L), and transport time (t). Meltwater transport velocity and flow length can be estimated from ice surface topography (Arnold et al, 1998), with the distribution of transport times representing the hydrologic response of a particular supraglacial catchment to surface melt (Yang et al, 2018). Alternately, empirical unit hydrograph (UH) methods can be used to estimate the hydrologic response based on catchment shape and area alone, enabling derivation of moulin hydrographs through convolution of input RCM surface runoff with remotely-sensed UH parameters (Smith et al, 2017).…”

“…CC BY 4.0 License. Yang et al (2018) utilized Rescaled Width Function (RWF) (D'Odorico and Rigon, 2003) to further partition the bare ice surface into either interfluve (i.e., hillslope) or open-channel zones using high-resolution satellite imagery discern the two. Catchment-averaged meltwater transport velocities for each zone were then calibrated using a fieldmeasured moulin hydrograph (Smith et al, 2017), with slow interfluve flow (~10 -3 -10 -4 m/s) and fast open-channel flow (~10 -1 m/s) combined to simulate the downstream moulin hydrograph.…”