• Active seismic studies in valley glacier settings: strategies and limitations

      Zechmann, Jenna M.; Booth, Adam D.; Truffer, Martin; Gusmeroli, Alessio; Amundson, Jason M.; Larsen, Christopher S. (International Glaciological Society, 2018-09-20)
      Subglacial tills play an important role in glacier dynamics but are difficult to characterize in situ. Amplitude Variation with Angle (AVA) analysis of seismic reflection data can distinguish between stiff tills and deformable tills. However, AVA analysis in mountain glacier environments can be problem- atic: reflections can be obscured by Rayleigh wave energy scattered from crevasses, and complex basal topography can impede the location of reflection points in 2-D acquisitions. We use a forward model to produce challenging synthetic seismic records in order to test the efficacy of AVA in crevassed and geo- metrically complex environments. We find that we can distinguish subglacial till types in moderately cre- vassed environments, where ‘moderate’ depends on crevasse spacing and orientation. The forward model serves as a planning tool, as it can predict AVA success or failure based on characteristics of the study glacier. Applying lessons from the forward model, we perform AVA on a seismic dataset col- lected from Taku Glacier in Southeast Alaska in March 2016. Taku Glacier is a valley glacier thought to overlay thick sediment deposits. A near-offset polarity reversal confirms that the tills are deformable.
    • Analysis of low-frequency seismic signals generated during a multiple-iceberg calving event at Jakobshavn Isbræ, Greenland

      Walter, Fabian; Amundson, Jason M.; O'Neel, Shad; Truffer, Martin; Fahnestock, Mark; Fricker, Helen A. (American Geophysical Union, 2012-03-27)
      We investigated seismic signals generated during a large-scale, multiple iceberg calving event that occurred at Jakobshavn Isbræ, Greenland, on 21 August 2009. The event was recorded by a high-rate time-lapse camera and five broadband seismic stations located within a few hundred kilometers of the terminus. During the event two full-glacier-thickness icebergs calved from the grounded (or nearly grounded) terminus and immediately capsized; the second iceberg to calve was two to three times smaller than the first. The individual calving and capsize events were well-correlated with the radiation of low-frequency seismic signals (<0.1 Hz) dominated by Love and Rayleigh waves. In agreement with regional records from previously published ‘glacial earthquakes’, these low-frequency seismic signals had maximum power and/or signal-to-noise ratios in the 0.05–0.1 Hz band. Similarly, full waveform inversions indicate that these signals were also generated by horizontal single forces acting at the glacier terminus. The signals therefore appear to be local manifestations of glacial earthquakes, although the magnitudes of the signals (twice-time integrated force histories) were considerably smaller than previously reported glacial earthquakes. We thus speculate that such earthquakes may be a common, if not pervasive, feature of all full-glacier-thickness calving events from grounded termini. Finally, a key result from our study is that waveform inversions performed on low-frequency, calving-generated seismic signals may have only limited ability to quantitatively estimate mass losses from calving. In particular, the choice of source time function has little impact on the inversion but dramatically changes the earthquake magnitude. Accordingly, in our analysis, it is unclear whether the smaller or larger of the two calving icebergs generated a larger seismic signal.
    • Blocking a wave: frequency band gaps in ice shelves with periodic crevasses

      Freed-Brown, Julian; Amundson, Jason M.; MacAyeal, Douglas R.; Zhang, Wendy W. (International Glaciological Society, 2012)
      We assess how the propagation of high-frequency elastic-flexural waves through an ice shelf is modified by the presence of spatially periodic crevasses. Analysis of the normal modes supported by the ice shelf with and without crevasses reveals that a periodic crevasse distribution qualitatively changes the mechanical response. The normal modes of an ice shelf free of crevasses are evenly distributed as a function of frequency. In contrast, the normal modes of a crevasse-ridden ice shelf are distributed unevenly. There are ‘band gaps’, frequency ranges over which no eigenmodes exist. A model ice shelf that is 50 km in lateral extent and 300 m thick with crevasses spaced 500 m apart has a band gap from 0.2 to 0.38 Hz. This is a frequency range relevant for ocean-wave/ice-shelf interactions. When the outermost edge of the crevassed ice shelf is oscillated at a frequency within the band gap, the ice shelf responds very differently from a crevasse-free ice shelf. The flexural motion of the crevassed ice shelf is confined to a small region near the outermost edge of the ice shelf and effectively ‘blocked’ from reaching the interior.
    • Direct observations of submarine melt and subsurface geometry at a tidewater glacier

      Sutherland, D. A.; Jackson, R. H.; Kienholtz, C.; Amundson, J. M.; Dryer, W. P.; Duncan, D.; Eidam, E. F.; Motyka, R. J.; Nash, J. D. (American Association for the Advancement of Science, 2019-07-26)
      Ice loss from the world’s glaciers and ice sheets contributes to sea level rise, influences ocean circulation, and affects ecosystem productivity. Ongoing changes in glaciers and ice sheets are driven by submarine melting and iceberg calving from tidewater glacier margins. However, predictions of glacier change largely rest on unconstrained theory for submarine melting. Here, we use repeat multibeam sonar surveys to image a subsurface tidewater glacier face and document a time-variable, three-dimensional geometry linked to melting and calving patterns. Submarine melt rates are high across the entire ice face over both seasons surveyed and increase from spring to summer. The observed melt rates are up to two orders of magnitude greater than predicted by theory, challenging current simulations of ice loss from tidewater glaciers.
    • Dynamic jamming of iceberg-choked fjords

      Peters, Ivo R.; Amundson, Jason M.; Cassotto, Ryan; Fahnestock, Mark; Darnell, Kristopher N.; Truffer, Martin; Zhang, Wendy W. (American Geophysical Union, 2015-02-02)
      We investigate the dynamics of ice mélange by analyzing rapid motion recorded by a time-lapse camera and terrestrial radar during several calving events that occurred at Jakobshavn Isbræ, Greenland. During calving events (1) the kinetic energy of the ice mélange is 2 orders of magnitude smaller than the total energy released during the events, (2) a jamming front propagates through the ice mélange at a rate that is an order of magnitude faster than the motion of individual icebergs, (3) the ice mélange undergoes initial compaction followed by slow relaxation and extension, and (4) motion of the ice mélange gradually decays before coming to an abrupt halt. These observations indicate that the ice mélange experiences widespread jamming during calving events and is always close to being in a jammed state during periods of terminus quiescence. We therefore suspect that local jamming influences longer timescale ice mélange dynamics and stress transmission.
    • Effect of topography on subglacial discharge and submarine melting during tidewater glacier retreat.

      Amundson, J.M.; Carroll, D. (American Geophysical Union, 2017-12-07)
      To first order, subglacial discharge depends on climate, which determines precipitation fluxes and glacier mass balance, and the rate of glacier volume change. For tidewater glaciers, large and rapid changes in glacier volume can occur independent of climate change due to strong glacier dynamic feedbacks. Using an idealized tidewater glacier model, we show that these feedbacks produce secular variations in subglacial discharge that are influenced by subglacial topography. Retreat along retrograde bed slopes (into deep water) results in rapid surface lowering and coincident increases in subglacial discharge. Consequently, submarine melting of glacier termini, which depends on subglacial discharge and ocean thermal forcing, also increases during retreat into deep water. Both subglacial discharge and submarine melting subsequently decrease as glacier termini retreat out of deep water and approach new steady state equilibria. In our simulations, subglacial discharge reached peaks that were 6–17% higher than preretreat values, with the highest values occurring during retreat from narrow sills, and submarine melting increased by 14% for unstratified fjords and 51% for highly stratified fjords. Our results therefore indicate that submarine melting acts in concert with iceberg calving to cause tidewater glacier termini to be unstable on retrograde beds. The full impact of submarine melting on tidewater glacier stability remains uncertain, however, due to poor understanding of the coupling between submarine melting and iceberg calving.
    • Glacier, fjord, and seismic response to recent large calving events, Jakobshavn Isbræ, Greenland

      Amundson, J. M.; Truffer, M.; Luthi, M. P.; Fahnestock, M.; West, M.; Motyka, R. J. (American Geophysical Union, 2008-11-18)
      The recent loss of Jakobshavn Isbræ’s extensive floating ice tongue has been accompanied by a change in near terminus behavior. Calving currently occurs primarily in summer from a grounded terminus, involves the detachment and overturning of several icebergs within 30 – 60 min, and produces long-lasting and far-reaching ocean waves and seismic signals, including ‘‘glacial earthquakes’’. Calving also increases near-terminus glacier velocities by 3% but does not cause episodic rapid glacier slip, thereby contradicting the originally proposed glacial earthquake mechanism. We propose that the earthquakes are instead caused by icebergs scraping the fjord bottom during calving.
    • Ice me ́lange dynamics and implications for terminus stability, Jakobshavn Isbræ, Greenland

      Amundson, J. M.; Fahnestock, M.; Truffer, M.; Brown, J.; Luthi, M. P.; Motyka, R. J. (American Geophysical Union, 2010-01-21)
      We used time-lapse imagery, seismic and audio recordings, iceberg and glacier velocities, ocean wave measurements, and simple theoretical considerations to investigate the interactions between Jakobshavn Isbræ and its proglacial ice me ́lange. The me ́lange behaves as a weak, granular ice shelf whose rheology varies seasonally. Sea ice growth in winter stiffens the me ́lange matrix by binding iceberg clasts together, ultimately preventing the calving of full-glacier-thickness icebergs (the dominant style of calving) and enabling a several kilometer terminus advance. Each summer the me ́lange weakens and the terminus retreats. The me ́lange remains strong enough, however, to be largely unaffected by ocean currents (except during calving events) and to influence the timing and sequence of calving events. Furthermore, motion of the me ́lange is highly episodic: between calving events, including the entire winter, it is pushed down fjord by the advancing terminus (at 40 m d1), whereas during calving events it can move in excess of 50 103 m d1 for more than 10 min. By influencing the timing of calving events, the me ́lange contributes to the glacier’s several kilometer seasonal advance and retreat; the associated geometric changes of the terminus area affect glacier flow. Furthermore, a force balance analysis shows that large-scale calving is only possible from a terminus that is near floatation, especially in the presence of a resistive ice me ́lange. The net annual retreat of the glacier is therefore limited by its proximity to floatation, potentially providing a physical mechanism for a previously described near-floatation criterion for calving.
    • Impact of glacier loss and vegetation succession on annual basin runoff

      Carnahan, Evan; Amundson, Jason; Hood, Eran (Published by Copernicus Publications on behalf of the European Geosciences Union., 2019-03-21)
      We 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.
    • Impact of hydrodynamics on seismic signals generated by iceberg collisions

      Amundson, Jason M.; Burton, Justin C.; Correa-Legisos, Sergio (International Glaciological Society, 2012)
      Full-glacier-thickness icebergs are frequently observed to capsize as they calve into the ocean. As they capsize they may collide with the glaciers’ termini; previous studies have hypothesized that such collisions are the source of teleseismic ‘glacial earthquakes’. We use laboratory-scale experiments, force-balance modeling and theoretical arguments to show that (1) the contact forces during these collisions are strongly influenced by hydrodynamic forces and (2) the associated glacial earthquake magnitudes (expressed as twice-integrated force histories) are related to the energy released by the capsizing icebergs plus a hydrodynamic term that is composed of drag forces and hydrodynamic pressure. Our experiments and first-order modeling efforts suggest that, due to hydrodynamic forces, both contact force and glacial earthquake magnitudes may not be directly proportional to the energy released by the capsizing icebergs (as might be expected). Most importantly, however, our results highlight the need to better understand the hydrodynamics of iceberg capsize prior to being able to accurately interpret seismic signals generated by iceberg collisions.
    • The influence of ice melange on fjord seiches

      MacAyeal, Douglas R.; Freed-Brown, Julian; Zhang, Wendy W.; Amundson, Jason M. (International Glaciological Society, 2012)
      We compute the eigenmodes (seiches) of the barotropic and baroclinic hydrodynamic equations for an idealized fjord having length and depth scales similar to those of Ilulissat Icefjord, Greenland, into which Jakobshavn Isbræ (also known as Sermeq Kujalleq) discharges. The purpose of the computation is to determine the fjord’s seiche behavior when forced by iceberg calving, capsize and melange movement. Poorly constrained bathymetry and stratification details are an acknowledged obstacle. We are, nevertheless, able to make general statements about the spectra of external and internal seiches using numerical simulations of ideal one-dimensional channel geometry. Of particular signifi- cance in our computation is the role of weakly coupled ice melange, which we idealize as a simple array of 20 icebergs of uniform dimensions equally spaced within the fjord. We find that the presence of these icebergs acts to (1) slow down the propagation of both external and internal seiches and (2) introduce band gaps where energy propagation (group velocity) vanishes. If energy is introduced into the fjord within the period range covered by a band gap, it will remain trapped as an evanescent oscillatory mode near its source, thus contributing to localized energy dissipation and ice/melange fragmentation.
    • Laboratory investigations of iceberg capsize dynamics, energy dissipation and tsunamigenesis

      Burton, J. C.; Amundson, J. M.; Abbot, D. S.; Boghosian, A.; Cathles, L. M.; Correa-Legisos, S.; Darnell, N.; Guttenberg, N.; Holland, D. M.; MacAyeal, D. R (American Geophysical Union, 2012-01-20)
      We present laboratory experiments designed to quantify the stability and energy budget of buoyancy-driven iceberg capsize. Box-shaped icebergs were constructed out of low-density plastic, hydrostatically placed in an acrylic water tank containing freshwater of uniform density, and allowed (or forced, if necessary) to capsize. The maximum kinetic energy (translational plus rotational) of the icebergs was 15% of the total energy released during capsize, and radiated surface wave energy was 1% of the total energy released. The remaining energy was directly transferred into the water via hydrodynamic coupling, viscous drag, and turbulence. The dependence of iceberg capsize instability on iceberg aspect ratio implied by the tank experiments was found to closely agree with analytical predictions based on a simple, hydrostatic treatment of iceberg capsize. This analytical treatment, along with the high Reynolds numbers for the experiments (and considerably higher values for capsizing icebergs in nature), indicates that turbulence is an important mechanism of energy dissipation during iceberg capsize and can contribute a potentially important source of mixing in the stratified ocean proximal to marine ice margins.
    • A mass-flux perspective of the tidewater glacier cycle

      Amundson, Jason M. (International Glaciological Society, 2016-04-06)
      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.
    • Meltwater Intrusions Reveal Mechanisms for Rapid Submarine Melt at a Tidewater Glacier

      Kienholtz, C.; Sutherland, D. A.; Jackson, R. H.; Nash, J. D.; Amundson, J. M.; Motyka, R. J.; Winters, D.; Skyllingstad, E.; Pettit, E. C. (American Geophysical Union, 2019-11-25)
      Submarine melting has been implicated as a driver of glacier retreat and sea level rise, but to date melting has been difficult to observe and quantify. As a result, melt rates have been estimated from parameterizations that are largely unconstrained by observations, particularly at the near-vertical termini of tidewater glaciers. With standard coefficients, these melt parameterizations predict that ambient melting (the melt away from subglacial discharge outlets) is negligible compared to discharge-driven melting for typical tidewater glaciers. Here, we present new data from LeConte Glacier, Alaska, that challenges this paradigm. Using autonomous kayaks, we observe ambient meltwater intrusions that are ubiquitous within 400 m of the terminus, and we provide the first characterization of their properties, structure, and distribution. Our results suggest that ambient melt rates are substantially higher (×100) than standard theory predicts and that ambient melting is a significant part of the total submarine melt flux. We explore modifications to the prevalent melt parameterization to provide a path forward for improved modeling of ocean-glacier interactions.
    • The morphology of supraglacial lake ogives

      Darnell, K.N.; Amundson, J.M.; Cathles, L.M.; MacAyeal, D.R. (International Glaciological Society, 2013-02-12)
      Supraglacial lakes on grounded regions of the Greenland and Antarctic ice sheets sometimes produce ‘lake ogives’ or banded structures that sweep downstream from the lakes. Using a variety of remote-sensing data, we demonstrate that lake ogives originate from supraglacial lakes that form each year in the same bedrock-fixed location near the equilibrium-line altitude. As the ice flows underneath one of these lakes, an ‘image’ of the lake is imprinted on the ice surface both by summer- season ablation and by superimposed ice (lake ice) formation. Ogives associated with a lake are sequenced in time, with the downstream ogives being the oldest, and with spatial separation equal to the local annual ice displacement. In addition, lake ogives can have decimeter- to meter-scale topographic relief, much like wave ogives that form below icefalls on alpine glaciers. Our observations highlight the fact that lake ogives, and other related surface features, are a consequence of hydrological processes in a bedrock-fixed reference frame. These features should arise naturally from physically based thermodynamic models of supraglacial water transport, and thus they may serve as fiducial features that help to test the performance of such models.
    • Non-linear glacier response to calving events, Jakobshavn Isbræ, Greenland

      Cassoto, Ryan; Fahnestock, Mark; Amundson, Jason M.; Truffer, Martin; Boettcher, Margaret S.; De La Pena, Santiago; Howat, Ian (International Glaciological Society, 2018-11-29)
      Jakobshavn Isbræ, a tidewater glacier that produces some of Greenland’s largest icebergs and highest speeds, reached record-high flow rates in 2012 (Joughin and others, 2014). We use terrestrial radar interferometric observations from August 2012 to characterize the events that led to record-high flow. We find that the highest speeds occurred in response to a small calving retreat, while several larger calving events produced negligible changes in glacier speed. This non-linear response to calving events suggests the terminus was close to flotation and therefore highly sensitive to terminus position. Our observations indicate that a glacier’s response to calving is a consequence of two competing feedbacks: (1) an increase in strain rates that leads to dynamic thinning and faster flow, thereby promoting desta- bilization, and (2) an increase in flow rates that advects thick ice toward the terminus and promotes restabilization. The competition between these feedbacks depends on temporal and spatial variations in the glacier’s proximity to flotation. This study highlights the importance of dynamic thinning and advective processes on tidewater glacier stability, and further suggests the latter may be limiting the current retreat due to the thick ice that occupies Jakobshavn Isbræ’s retrograde bed.
    • Observing calving-generated ocean waves with coastal broadband seismometers, Jakobshavn Isbræ, Greenland

      Amundson, Jason M.; Clinton, John F.; Fahnestock, Mark; Truffer, Martin; Luthi, Martin P.; Motyka, Roman J. (International Glaciological Society, 2012)
      We use time-lapse photography, MODIS satellite imagery, ocean wave measurements and regional broadband seismic data to demonstrate that icebergs that calve from Jakobshavn Isbræ, Greenland, can generate ocean waves that are detectable over 150 km from their source. The waves, which are recorded seismically, have distinct spectral peaks, are not dispersive and persist for several hours. On the basis of these observations, we suggest that calving events at Jakobshavn Isbræ can stimulate seiches, or basin eigenmodes, in both Ilulissat Icefjord and Disko Bay. Our observations furthermore indicate that coastal, land-based seismometers located near calving termini (e.g. as part of the new Greenland Ice Sheet Monitoring Network (GLISN)) can aid investigations into the largely unexplored, oceanographic consequences of iceberg calving.
    • Outlet glacier response to forcing over hourly to interannual timescales, Jakobshavn Isbræ, Greenland

      Podrasky, David; Truffer, Martin; Fahnestock, Mark; Amundson, Jason M.; Cassoto, Ryan; Joughin, Ian (International Glaciological Society, 2012-09-07)
      The loss of the floating ice tongue on Jakobshavn Isbræ, Greenland, in the early 2000s has been concurrent with a pattern of thinning, retreat and acceleration leading to enhanced contribution to global sea level. These changes on decadal timescales have been well documented. Here we identify how the glacier responds to forcings on shorter timescales, such as from variations in surface melt, the drainage of supraglacial lakes and seasonal fluctuations in terminus position. Ice motion and surface melt were monitored intermittently from 2006 to 2008. Dual-frequency GPS were deployed 20–50 km upstream of the terminus along the glacier center line. Gaps in surface melt measurements were filled using a temperature-index model of ablation driven by surface air temperatures recorded during the same time period. Our results corroborate the premise that the primary factors controlling speeds on Jakobshavn Isbræ are terminus position and geometry. We also observe that surface speeds demonstrate a complex relationship with meltwater input: on diurnal timescales, velocities closely match changes in water input; however, on seasonal timescales a longer, more intense melt season was observed to effectively reduce the overall ice flow of the glacier for the whole year.
    • Quantifying flow and stress in ice mélange, the world’s largest granular material.

      Burton, J. C.; Amundson, J. M.; Cassotto, R.; Kuo, C. C.; Dennin, M. (PNAS Proceedings of the National Academy of Sciences, 2018-03-29)
      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.
    • Quasi-static granular flow of ice mélange

      Amundson, J. M.; Burton, J. C. (American Geophysical Union, 2018-09-11)
      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.