Quasi-static granular flow of ice mélange

We use Landsat 8 imagery to generate ice mélange velocity fields at Greenland’s three most productive outlet glaciers: Jakobshavn Isbræ, Helheim Glacier, and Kangerdlugssuaq Glacier. Winter velocity fields are generally steady and highly uniform. Summer velocity fields, on the other hand, tend to be much more variable and can be uniform, compressional, or extensional. We rarely observe compressional flow at Jakobshavn Isbræ or extensional flow at Helheim Glacier, while both are observed at Kangerdlugssuaq Glacier. Transverse velocity profiles from all three locations are suggestive of viscoplastic flow, in which deformation occurs primarily in shear zones along the fjord walls. We analyze the transverse profiles in the context of quasi-static flow using continuum rheologies for granular materials and find that the force per unit width that ice mélange exerts on glacier termini increases exponentially with the ice mélange length-to-width ratio and the effective coefficient of friction. Our estimates of ice mélange resistance are consistent with other independent estimates and suggest that ice mélange may be capable of inhibiting iceberg calving events, especially during winter. Moreover, our results provide geophysical-scale support for constitutive relationships for granular materials and suggest a potential avenue for modeling ice mélange dynamics with continuum models.From acknowledgments: Funding for this project was provided by the U.S. National Science Foundation (DMR-1506446 and DMR-1506307). Digital elevation models were provided by the Polar Geospatial Center under the U.S. National Science Foundation (OPP-1043681, OPP-1559691, and OPP-1542736)Ye

Quasi-static granular flow of ice mélange

We use Landsat 8 imagery to generate ice mélange velocity fields at Greenland’s three most productive outlet glaciers: Jakobshavn Isbræ, Helheim Glacier, and Kangerdlugssuaq Glacier. Winter velocity fields are generally steady and highly uniform. Summer velocity fields, on the other hand, tend to be much more variable and can be uniform, compressional, or extensional. We rarely observe compressional flow at Jakobshavn Isbræ or extensional flow at Helheim Glacier, while both are observed at Kangerdlugssuaq Glacier. Transverse velocity profiles from all three locations are suggestive of viscoplastic flow, in which deformation occurs primarily in shear zones along the fjord walls. We analyze the transverse profiles in the context of quasi-static flow using continuum rheologies for granular materials and find that the force per unit width that ice mélange exerts on glacier termini increases exponentially with the ice mélange length-to-width ratio and the effective coefficient of friction. Our estimates of ice mélange resistance are consistent with other independent estimates and suggest that ice mélange may be capable of inhibiting iceberg calving events, especially during winter. Moreover, our results provide geophysical-scale support for constitutive relationships for granular materials and suggest a potential avenue for modeling ice mélange dynamics with continuum models.From acknowledgments: Funding for this project was provided by the U.S. National Science Foundation (DMR-1506446 and DMR-1506307). Digital elevation models were provided by the Polar Geospatial Center under the U.S. National Science Foundation (OPP-1043681, OPP-1559691, and OPP-1542736)Ye

Quantifying flow and stress in ice mélange, the world’s largest granular material.

Tidewater glacier fjords are often filled with a collection of calved icebergs, brash ice, and sea ice. For glaciers with high calving rates, this “m ́elange” of ice can be jam-packed, so that the flow of ice fragments is mostly determined by granular interactions. In the jammed state, ice m ́elange has been hypothesized to influence iceberg calving and capsize, dispersion and attenuation of ocean waves, injection of freshwater into fjords, and fjord circulation. However, detailed measurements of ice m ́elange are lacking due to difficulties in instrumenting remote, ice-choked fjords. Here we characterize the flow and associated stress in icem ́elange, using a combination of terrestrial radar data, laboratory experiments, and numerical simulations. We find that, during periods of terminus quiescence, ice m ́elange experiences laminar flow over timescales of hours to days. The uniform flow fields are bounded by shear margins along fjord walls where force chains between granular icebergs terminate. In addition, the average force per unit width that is transmitted to the glacier terminus, which can exceed 107N/m, increases exponentially with them ́elange length-to-width ratio. These “buttressing” forces are sufficiently high to inhibit the initiation of large-scale calving events, supporting the notion that ice m ́elange can be viewed as a weak granular ice shelf that transmits stresses from fjord walls back to glacier termini.Ye

A mass-flux perspective of the tidewater glacier cycle

I explore the tidewater glacier cycle with a 1-D, depth- and width-integrated flow model that includes a mass-flux calving parameterization. The parameterization is developed from mass continuity arguments and relates the calving rate to the terminus velocity and the terminus balance velocity.I explore the tidewater glacier cycle with a 1-D, depth- and width-integrated flow model that includes a mass-flux calving parameterization. The parameterization is developed from mass continuity arguments and relates the calving rate to the terminus velocity and the terminus balance velocity. The model demonstrates variable sensitivity to climate. From an advanced, stable configuration, a small warming of the climate triggers a rapid retreat that causes large-scale drawdown and is enhanced by positive glacier-dynamic feedbacks. Eventually, the terminus retreats out of deep water and the terminus velocity decreases, resulting in reduced drawdown and the potential for restabilization. Terminus readvance can be initiated by cooling the climate. Terminus advance into deep water is difficult to sustain, however, due to negative feedbacks between glacier dynamics and surface mass balance. Despite uncertainty in the precise form of the parameterization, the model provides a simple explanation of the tidewater glacier cycle and can be used to evaluate the response of tidewater glaciers to climate variability. It also highlights the importance of improving parameterizations of calving rates and of incorporating sediment dynamics into tidewater glacier models.E.M. Enderlin provided model code and assistance during the initial stages of model development. I.M. Howat provided mass-flux data for Greenland outlet glaciers. Funding was provided by the National Oceanic and Atmospheric Association (NA13OAR4310098). This manuscript was greatly benefitted from discussions with M. Truffer and thorough reviews from A. Vieli, an anonymous reviewer and scientific editor H.A. Fricker.Ye

Impact of glacier loss and vegetation succession on annual basin runoff

Evan Carnahan is a UAS B.S. Math graduateWe use a simplified glacier-landscape model to investigate the degree to which basin topography, climate regime, and vegetation succession impact centennial variations in basin runoff during glacier retreat. In all simulations, annual basin runoff initially increases as water is released from glacier storage but ultimately decreases to below preretreat levels due to increases in evapotranspiration and decreases in orographic precipitation. We characterize the long-term ( > 200 years) annual basin runoff curves with four metrics: the magnitude and timing of peak basin runoff, the time to preretreat basin runoff, and the magnitude of end basin runoff. We find that basin slope and climate regime have strong impacts on the magnitude and timing of peak basin runoff. Shallow sloping basins exhibit a later and larger peak basin runoff than steep basins and, similarly, continental glaciers produce later and larger peak basin runoff compared to maritime glaciers. Vegetation succession following glacier loss has little impact on the peak basin runoff but becomes increasingly important as time progresses, with more rapid and extensive vegetation leading to shorter times to preretreat basin runoff and lower levels of end basin runoff. We suggest that differences in the magnitude and timing of peak basin runoff in our simulations can largely be attributed to glacier dynamics: glaciers with long response times (i.e., those that respond slowly to climate change) are pushed farther out of equilibrium for a given climate forcing and produce larger variations in basin runoff than glaciers with short response times. Overall, our results demonstrate that glacier dynamics and vegetation succession should receive roughly equal attention when assessing the impacts of glacier mass loss on water resources.Ye

Seismic Tremor Reveals Spatial Organization and Temporal Changes of Subglacial Water System

©2019. American Geophysical Union. All Rights Reserved.Subglacial water flow impacts glacier dynamics and shapes the subglacial environment. However, due to the challenges of observing glacier beds, the spatial organization of subglacial water systems and the time scales of conduit evolution and migration are largely unknown. To address these questions, we analyze 1.5‐ to 10‐Hz seismic tremor that we associate with subglacial water flow, that is, glaciohydraulic tremor, at Taku Glacier, Alaska, throughout the 2016 melt season. We use frequency‐dependent polarization analysis to estimate glaciohydraulic tremor propagation direction (related to the subglacial conduit location) and a degree day melt model to monitor variations in melt‐water input. We suggest that conduit formation requires sustained water input and that multiconduit flow paths can be distinguished from single‐conduit flow paths. Theoretical analysis supports our seismic interpretations that subglacial discharge likely flows through a single‐conduit in regions of steep hydraulic potential gradients but may be distributed among multiple conduits in regions with shallower potential gradients. Seismic tremor in regions with multiple conduits evolves through abrupt jumps between stable configurations that last 3–7 days, while tremor produced by single‐conduit flow remains more stationary. We also find that polarized glaciohydraulic tremor wave types are potentially linked to the distance from source to station and that multiple peak frequencies propagate from a similar direction. Tremor appears undetectable at distances beyond 2–6 km from the source. This new understanding of the spatial organization and temporal development of subglacial conduits informs our understanding of dynamism within the subglacial hydrologic system.Raw seismic data described in this paper are available through the Incorporated Research Institutions for Seismology Data Management Center (http://ds.iris.edu/mda/ZQ? timewindow=2015‐2016; Amundson et al., 2015). The raw weather data used in this paper can be found through the Arctic Data Center (https://doi.org/ 10.18739/A2H98ZC7V; Bartholomaus & Walter, 2018). Python code developed to carry out the analyses presented here is available at https://github.com/ voremargot/Seismic‐Tremor‐Reveals‐ Spatial‐Organization‐and‐Temporal‐ Changes‐of Subglacial‐Water‐System and https://github.com/ tbartholomaus/med_spec. This study was made possible with support from the University of Texas Institute for Geophysics and the University of Idaho. We thank Ginny Catania for the loan of weather stations. J. P. W.'s and J. M. A.'s contributions to this work were supported by the U.S. National Science Foundation (OPP‐1337548 and OPP‐ 1303895). T. C. B. thanks Dylan Mikesell for an early conversation, which inspired the analysis presented here.Ye

Seismic Tremor Reveals Spatial Organization and Temporal Changes of Subglacial Water System

©2019. American Geophysical Union. All Rights Reserved.Subglacial water flow impacts glacier dynamics and shapes the subglacial environment. However, due to the challenges of observing glacier beds, the spatial organization of subglacial water systems and the time scales of conduit evolution and migration are largely unknown. To address these questions, we analyze 1.5‐ to 10‐Hz seismic tremor that we associate with subglacial water flow, that is, glaciohydraulic tremor, at Taku Glacier, Alaska, throughout the 2016 melt season. We use frequency‐dependent polarization analysis to estimate glaciohydraulic tremor propagation direction (related to the subglacial conduit location) and a degree day melt model to monitor variations in melt‐water input. We suggest that conduit formation requires sustained water input and that multiconduit flow paths can be distinguished from single‐conduit flow paths. Theoretical analysis supports our seismic interpretations that subglacial discharge likely flows through a single‐conduit in regions of steep hydraulic potential gradients but may be distributed among multiple conduits in regions with shallower potential gradients. Seismic tremor in regions with multiple conduits evolves through abrupt jumps between stable configurations that last 3–7 days, while tremor produced by single‐conduit flow remains more stationary. We also find that polarized glaciohydraulic tremor wave types are potentially linked to the distance from source to station and that multiple peak frequencies propagate from a similar direction. Tremor appears undetectable at distances beyond 2–6 km from the source. This new understanding of the spatial organization and temporal development of subglacial conduits informs our understanding of dynamism within the subglacial hydrologic system.Raw seismic data described in this paper are available through the Incorporated Research Institutions for Seismology Data Management Center (http://ds.iris.edu/mda/ZQ? timewindow=2015‐2016; Amundson et al., 2015). The raw weather data used in this paper can be found through the Arctic Data Center (https://doi.org/ 10.18739/A2H98ZC7V; Bartholomaus & Walter, 2018). Python code developed to carry out the analyses presented here is available at https://github.com/ voremargot/Seismic‐Tremor‐Reveals‐ Spatial‐Organization‐and‐Temporal‐ Changes‐of Subglacial‐Water‐System and https://github.com/ tbartholomaus/med_spec. This study was made possible with support from the University of Texas Institute for Geophysics and the University of Idaho. We thank Ginny Catania for the loan of weather stations. J. P. W.'s and J. M. A.'s contributions to this work were supported by the U.S. National Science Foundation (OPP‐1337548 and OPP‐ 1303895). T. C. B. thanks Dylan Mikesell for an early conversation, which inspired the analysis presented here.Ye

A unifying framework for iceberg-calving models

We propose a general framework for iceberg-calving models that can be applied to any calving margin.We propose a general framework for iceberg-calving models that can be applied to any calving margin. The framework is based on mass continuity, the assumption that calving rate and terminus velocity are not independent and the simple idea that terminus thickness following a calving event is larger than terminus thickness at the event onset. The theoretical, near steady-state analysis used to support and analyze the framework indicates that calving rate is governed, to first order, by ice thickness, thickness gradient, strain rate, mass-balance rate and backwards melting of the terminus; the analysis furthermore provides a physical explanation for a previously derived empirical relationship for ice-shelf calving (Alley and others, 2008). In the calving framework the pre- and post-calving terminus thicknesses are given by two unknown but related functions. The functions can vary independently of changes in glacier flow and geometry, and can therefore account for variations in calving behavior due to external forcings and/or self-sustaining calving processes (positive feedbacks). Although the calving framework does not constitute a complete calving model, any thickness-based calving criterion can easily be incorporated into the framework. The framework should be viewed as a guide for future attempts to parameterize calving.Support for this project was provided by NASA’s Cryospheric Sciences Program (NNG06GB49G), the US National Science Foundation (ARC0531075 and ARC0909552) and an International Polar Year student traineeship funded by the Cooperative Institute for Arctic Research (CIFAR) through cooperative agreement NA17RJ1224 with the US National Oceanic and Atmospheric Administration. The paper was inspired by discussions with E. Bueler, M. Fahnestock, M.P. Lu ̈thi, R.J. Motyka, J. Brown and D. Podrasky. We thank A. Vieli, an anonymous reviewer and the scientific editor, R. Greve, for thorough reviews that helped to focus the manuscript.Ye

Seasonal and interannual variations in ice melange and its impact on terminus stability, Jakobshavn Isbræ, Greenland

We used satellite-derived surface temperatures and time-lapse photography to infer temporal variations in the proglacial ice melange at Jakobshavn Isbræ, a large and rapidly retreating outlet glacier in Greenland.We used satellite-derived surface temperatures and time-lapse photography to infer temporal variations in the proglacial ice melange at Jakobshavn Isbræ, a large and rapidly retreating outlet glacier in Greenland. Freezing of the melange-covered fjord surface during winter is indicated by a decrease in fjord surface temperatures and is associated with (1) a decrease in ice melange mobility and (2) a drastic reduction in iceberg production. Vigorous calving resumes in spring, typically abruptly, following the steady up-fjord retreat of the sea-ice/ice-melange margin. An analysis of pixel displacement from time-lapse imagery demonstrates that melange motion increases prior to calving and subsequently decreases following several events. We find that secular changes in ice melange extent, character and persistence can influence iceberg calving, and therefore glacier dynamics over daily-to-monthly timescales, which, if sustained, will influence the mass balance of an ice sheet.This research was supported by funds from the Gordon and Betty Moore Foundation (GBMF2627), NASA (NNX08AN74G), the US National Science Foundation (ANT0944193 and ANS0909552) and the New Hampshire Space Grant Consortium (NNX10AL97H). We thank CH2M HILL Polar Services and Air Greenland for logistics support, and PASSCAL (Program for the Array Seismic Studies of theContinental Lithosphere) for the use of seismic instrumentation. Ian Joughin derived TerraSAR-X velocities and terminus positions from images provided by the German (DLR) space agency under NASA grant NNX08AL98A. We acknowledgethe use of Rapid Response imagery from the Land Atmosphere Near-real time Capability for EOS (LANCE) system operated by the NASA/GSFC/Earth Science Data and Information System (ESDIS) with funding provided by NASA HQ. Glacier surface elevations were provided by CReSIS, and bed elevations by CReSIS and Mathieu Morlighem. The manuscript was significantly improved by comments from Tim Bartholomaus and an anonymous reviewer.Ye

Tidewater glacier response to individual calving events

Tidewater glaciers have been observed to experience instantaneous, stepwise increases in velocity during iceberg-calving events due to a loss of resistive stresses. These changes in stress can potentially impact tidewater glacier stability by promoting additional calving and affecting the viscous delivery of ice to the terminus. Using flow models and perturbation theory, we demonstrate that calving events and subsequent terminus readvance produce quasi-periodic, sawtooth oscillations in stress that originate at the terminus and propagate upstream. The stress perturbations travel at speeds much greater than the glacier velocities and, for laterally resisted glaciers, rapidly decay within a few ice thickness of the terminus. Consequently, because terminus fluctuations due to individual calving events tend to be much higher frequency than climate variations, individual calving events have little direct impact on the viscous delivery of ice to the terminus. This suggests that the primary mechanism by which calving events can trigger instability is by causing fluctuations in stress that weaken the ice and lead to additional calving and sustained terminus retreat. Our results further demonstrate a stronger response to calving events in simulations that include the full stress tensor, highlighting the importance of accounting for higher order stresses when developing calving parameterizations.© The Author(s), 2022. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.Ye