A Physical Model of Moulin Formation and Evolution

Nearly all proglacial water discharge from the present-day Greenland Ice Sheet is routed englacially via moulins. Identification of these moulins in high-resolution imagery is a frequent topic of study, but the processes controlling how and where moulins form, including on past ice sheets for which remote-sensing data are not available, remain poorly understood. Because moulins may reasonably compose approximately 10-15% of the englacial-subglacial hydrologic system, the evolution and shape of moulins can alter the timing of meltwater inputs to the bed. This evolution can impact both the form of the subglacial hydrologic system and the structure of associated geomorphological structures. Here, we develop a physical model of moulin formation and evolution to constrain the role of englacial processes in controlling the form and structure of the subglacial hydrologic system. Ice deformation within and around a moulin is both viscous and elastic, with the rate of turbulent and heat dissipation from water circulation in the moulin controlling both moulin wall melting and warming of the surrounding ice. We find moulin geometry is responsive to changes in these parameters over hours to days, indicating that diurnal and multi-day variations in surface melt can substantially alter the geometry of a moulin and the pressure-discharge relationship at the bed of the ice sheet. These results should be considered carefully when determining surface water inputs for subglacial hydrologic models. In the future, a parameter space study of these results will be combined with an analytic model to create a predictive, stochastic model of moulin and crevasse locations. This future model will be applicable to constraining the potential for surface-to-bed connections in regions where the exact ice-sheet surface morphology is not known, including ice sheets under future warming atmospheric conditions, and paleo ice sheets, where moulins created modern landforms

Physically Based and Stochastic Models for Greenland Moulin Formation, Longevity, and Spatial Distribution

Nearly all proglacial water discharge from the Greenland Ice Sheet is routed englacially, from the surface to the bed, via moulins. Identification of moulins in high-resolution imagery is a frequent topic of study, but the processes controlling how and where moulins form remain poorly understood. We seek to leverage information gained from the development of a physical model of moulin formation, remotely sensed ice-sheet data products, and an analytic model of ice-flow perturbations to develop a predictive stochastic model of moulin distribution across Greenland. Here we present initial results from the physical model of moulin formation and characterize the sensitivity of moulin geometry to a range of model parameters. This parameterization of moulin formation is the first step in developing a stochastic model that will be a predictive, computationally efficient representation of the englacial hydrologic system

A Physical Model of Moulin Evolution on the Greenland Ice Sheet

Nearly all proglacial water discharge from the Greenland Ice Sheet is routed englacially via moulins. Identification of these moulins in high-resolution imagery is a frequent topic of study, but the processes controlling how and where moulins form remain poorly understood. Because moulins may reasonably compose approximately 10-15% of the englacial-subglacial hydrologic system, the evolution and shape of moulins can alter both the timing and variability of meltwater inputs to the bed. This evolution can impact both the form of the subglacial hydrologic system and associated response of ice motion. Here, we develop a physical model of moulin formation and evolution to constrain the role of englacial processes in shaping the form and structure of the subglacial hydrologic system. Within this model, moulin geometry is controlled by a balance of viscous and elastic deformation and is dependent on that deformation, refreezing, and the dissipation of turbulent and sensible heat energy. All of which are dependent on the characteristics of the available supraglacial meltwater and the surrounding ice. We find moulin geometry is responsive to changes in these parameters over the course of hours to days, indicating that diurnal and multi-day variations in melt can substantially alter the geometry of a moulin and, consequently, the pressure-discharge relationship at the bed of the ice sheet. Therefore, there is no single moulin shape that can appropriately represent englacial storage across the Greenland Ice Sheet

The Effect of Firn-Aquifer Drainage on the Greenland Subglacial System or Subglacial Efficiency and Storage Modified by the Temporal Pattern of High-Elevation Meltwater Input

Ice flow in marginal region of the Greenland Ice Sheet dynamically responds to summer melting as surface meltwater is routed through the supraglacial hydrologic system to the bed of the ice sheet via crevasses and moulins. Given the expected increases in surface melt production and extent, and the potential for high elevation surface-to-bed connections, it is imperative to understand how meltwater delivered to the bed from different high-elevation supraglacial storage features affects the evolution of the subglacial hydrologic system and associated ice dynamics. Here, we use the two-dimensional subglacial hydrologic model, GLaDS, which includes distributed and channelized water flow, to test how the subglacial system of an idealized outlet glacier responds to cases of high-elevation firn-aquifer-type and supraglacial-lake-type englacial drainage over the course of 5 years. Model outputs driven by these high elevation drainage types are compared to steady-state model results, where the subglacial system only receives the 1980- 2016 mean MERRA-2 runoff via low-elevation moulins. Across all experiments, the subglacial hydrologic system displays inter-annual memory, resulting in multiyear declines in subglacial pressure during the onset of seasonal melting and growth of subglacial channels. The gradual addition of water in firn-aquifer-type drainage scenarios resulted in small increases in subglacial water storage but limited changes in subglacial efficiency and channelization. Rapid, supraglacial- lake-type drainage resulted in short-term local increases in subglacial water pressure and storage, which gave way to spatially extensive decreases in subglacial pressure and downstream channelization. These preliminary results suggest that the character of high-elevation englacial drainage can have a strong, and possibly outsized, control on subglacial efficiency throughout the ablation zone. Therefore, understanding both how high elevation meltwater is stored supraglacially and the probability of crevassing at high elevations will play an important role in how the subglacial system, proglacial discharge and ice motion will respond to future increases in surface melt production and runoff

Basal channels drive active surface hydrology and transverse ice shelf fracture

Ice shelves control sea-level rise through frictional resistance, which slows the seaward flow of grounded glacial ice. Evidence from around Antarctica indicates that ice shelves are thinning and weakening, primarily driven by warm ocean water entering into the shelf cavities. We have identified a mechanism for ice shelf destabilization where basal channels underneath the shelves cause ice thinning that drives fracture perpendicular to flow. These channels also result in ice surface deformation, which diverts supraglacial rivers into the transverse fractures. We report direct evidence that a major 2016 calving event at Nansen Ice Shelf in the Ross Sea was the result of fracture driven by such channelized thinning and demonstrate that similar basal channel–driven transverse fractures occur elsewhere in Greenland and Antarctica. In the event of increased basal and surface melt resulting from rising ocean and air temperatures, ice shelves will become increasingly vulnerable to these tandem effects of basal channel destabilization

The influence of meltwater on the thermal structure and flow of the Greenland Ice Sheet

Thesis (Ph.D.)--University of Washington, 2015-12As the climate has warmed over the past decades, the amount of melt on the Greenland Ice Sheet has increased, and areas higher on the ice sheet have begun to melt regularly. This increase in melt has been hypothesized to enhance ice flow in myriad ways, including through basal lubrication and englacial refreezing. By developing and interpreting thermal ice-sheet models and analyzing remote sensing data, I evaluate the effect of these processes on ice flow and sea-level rise from the Greenland Ice Sheet. I first develop a thermal ice sheet model that is applicable to western Greenland. Key components of this model are its treatment of multiple phases (solid ice and liquid water) and its viscosity-dependent velocity field. I apply the model to Jakobshavn Isbræ, a fast-flowing outlet glacier. This is an important benchmark for my model, which I next apply to the topics outlined above. I use the thermal model to calculate the effect of englacial latent-heat transfer (meltwater refreezing within englacial features such as firn and crevasses) on ice dynamics in western Greenland. I find that in slow-moving areas, this can significantly warm the ice, but that englacial latent heat transfer has only a minimal effect on ice motion (60%) of the ice flux into the ocean, evidence of deep englacial warming is virtually absent. Thus, the effects of englacial latent heat transfer on ice motion are likely limited to slow-moving regions, which limits its importance to ice-sheet mass balance. Next, I couple a model for ice fracture to a modified version of my thermal model to calculate the depth and shape evolution of water-filled crevasses that form in crevasse fields. At most elevations and for typical water input volumes, crevasses penetrate to the top ~200–300 meters depth, warm the ice there by ~10°C, and may persist englacially, in a liquid state, for multiple decades. The surface hydrological network limits the amount of water that can reach most crevasses. We find that the depth and longevity of such crevasses is relatively robust to realistic increases in melt volumes over the coming century, so that we should not expect large changes in the englacial hydrological system under near-future climate regimes. These inferences put important constraints on the timescales of the Greenland supraglacial-to-subglacial water cycle. Finally, I assess the likelihood that higher-elevation surface melt could deliver water to regions where the bed is currently frozen. This hypothetical process is important because it could potentially greatly accelerate the seaward motion of the ice sheet. By analyzing surface strain rates and comparing them to my modeled basal temperature field, I find that this scenario is unlikely to occur: the conditions necessary to form surface-to-bed conduits are rarely found at higher elevations (~1600 meters) that may overlie frozen beds

Datasets in support of "Limits to future expansion of surface-melt-enhanced ice flow into the interior of western Greenland"

Description of this collection of datasets: Moulins are important conduits for surface meltwater to reach the bed of the Greenland Ice Sheet. It has been proposed that in a warming climate, newly formed moulins associated with the inland migration of supraglacial lakes could introduce surface melt to new regions of the bed, introducing or enhancing sliding there. By examining surface strain rates, we found that the upper limit to where crevasses, and therefore moulins, are likely to form is ~1600 m. This is also roughly the elevation above which lakes do not drain completely. Thus, meltwater above this elevation will largely flow tens of kilometers through surface streams into existing moulins downstream. Furthermore, results from a thermal ice-sheet model indicate that the ~1600-m crevassing limit is below the wet–frozen basal transition (~2000 m). Together, these datasets suggest that new supraglacial lakes will have a limited effect on the inland expansion of melt-induced seasonal acceleration.Description of the files: FrozenOver2000.dbf, FrozenOver2000.shp, FrozenOver2000.shx: Creator(s) of the data: Kristin Poinar --- Title of data: Lakes with floating ice cover in the summer of 2000. --- Date created: May 2014 --- Abstract: Supraglacial lakes with floating ice covers on the western Greenland Ice Sheet were identified using Landsat and Radarsat imagery. These shape files give the locations and approximate boundaries of all such lakes (570) in the year 2000. Description of the files: FrozenOver2010.dbf, FrozenOver2010.shp, FrozenOver2010.shx: Creator(s) of the data: Kristin Poinar --- Title of data: Lakes with floating ice cover in the summer of 2010. --- Date created: May 2014 --- Abstract: Supraglacial lakes with floating ice covers on the western Greenland Ice Sheet were identified using Landsat and Radarsat imagery. These shape files give the locations and approximate boundaries of all such lakes (387) in the year 2010. Description of the files: FrozenOver2013.dbf, FrozenOver2013.shp, FrozenOver2013.shx: Creator(s) of the data: Kristin Poinar --- Title of data: Lakes with floating ice cover in the summer of 2013. --- Date created: May 2014 --- Abstract: Supraglacial lakes with floating ice covers on the western Greenland Ice Sheet were identified using Landsat and Radarsat imagery. These shape files give the locations and approximate boundaries of all such lakes (183) in the year 2013. Description of the file: Streams2004_2014.dbf, Streams2004_2014.qix, Streams2004_2014.shp, Streams2004_2014.shx: Creator(s) of the data: Kristin Poinar --- Title of data: Surface streams in western Greenland in the summer of 2004. --- Date created: May 2014 --- Abstract: Surface streams occurring on the western Greenland Ice Sheet in the summer of 2004 were identified using Landsat and Radarsat imagery. These shape files give the locations and paths of the 247 approximately largest surface streams in the area in 2004. Description of the file RacmoSurfaceMelt_mmyr.csv: Creator(s) of the data: Kristin Poinar, Jan T. M. Lenaerts, Michiel R. van den Broeke --- Title of data: Surface melt from RACMOv2.3. --- Date created: December 2014 --- Abstract: Output from RACMO regional climate model, version 2.3, for the total melt (ice melt plus snow melt) on the ice-sheet surface within the study area in western Greenland. Data are averaged into elevation bands, e.g., 0-200 meters elevation, which are given in the first two columns for each row. The data are also averaged in time to one year resolution (1958-2013); these data appear in the following columns. Surface melt is given in mm/yr, water equivalent. Description of the file StudyArea.csv: Creator(s) of the data: Kristin Poinar --- Title of data: Outline of the study area in western Greenland --- Date created: July 2014 --- Abstract: The analyses presented in this paper were performed on the areas of the ice sheet inside this polygon. Description of the file WetBed_FoxMaule.csv: Creator(s) of the data: Kristin Poinar --- Title of data: Modeled basal temperate area in western Greenland using Fox Maule et al. (2005) geothermal flux. --- Date created: July 2014 --- Abstract: Results of the thermal model runs in western Greenland using geothermal flux from Fox Maule et al. (2005) as a boundary condition. The (x,y) points in this file outline the wet-bedded region: the model predicts that points inside the polygon have a wet (temperate) bed. Description of the file WetBed_ShapiroRitzwoller.csv: Creator(s) of the data: Kristin Poinar --- Title of data: Modeled basal temperate area in western Greenland using Shapiro and Ritzwoller (2004) geothermal flux. --- Date created: July 2014 --- Abstract: Results of the thermal model runs in western Greenland using geothermal flux from Shapiro and Ritzwoller (2004) as a boundary condition. The (x,y) points in this file outline the wet-bedded region: the model predicts that points inside the polygon have a wet (temperate) bed

Englacial latent-heat transfer has limited influence on seaward ice flux in western Greenland

Surface meltwater can refreeze within firn layers and crevasses to warm ice through latent-heat transfer on decadal to millennial timescales. Earlier work posited that the consequent softening of the ice might accelerate ice flow, potentially increasing ice-sheet mass loss. Here, we calculate the effect of meltwater refreezing on ice temperature and softness in the Pâkitsoq (near Swiss Camp) and Jakobshavn Isbræ regions of western Greenland using a numeric model and existing borehole measurements. We show that in the Jakobshavn catchment, meltwater percolation within the firn warms the ice at depth by 3-5°C. By contrast, meltwater refreezing in crevasses (cryo-hydrologic warming) at depths of ~300 m warms the ice in Pâkitsoq by up to 10°C, but this causes minimal increase in ice motion (<10 m a-1). Pâkitsoq is representative of western Greenland's land-terminating ice, where the slow movement of ice through a wide ablation zone provides ideal conditions for cryo-hydrologic warming to occur. We find that only ~37% of the western Greenland ice flux, however, travels through such areas. Overall, our findings suggest that cryo-hydrologic warming will likely have only a limited effect on the dynamic evolution of the Greenland ice sheet