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Abstract. Field and remote sensing studies suggest that ice mélange influences glacier-fjord systems by exerting stresses on glacier termini and releasing large amounts of freshwater into fjords. The broader impacts of ice mélange over long time scales are unknown, in part due to a lack of suitable ice mélange flow models. Previous efforts have included modifying existing viscous ice shelf models, despite the fact that ice mélange is fundamentally a granular material, and running computationally expensive discrete element simulations. Here, we draw on laboratory studies of granular materials, which exhibit viscous flow when stresses greatly exceed the yield point, plug flow when the stresses approach the yield point, and stress transfer via force chains. By implementing the nonlocal granular fluidity rheology into a depth- and width-integrated stress balance equation, we produce a numerical model of ice mélange flow that is consistent with our understanding of well-packed granular materials and that is suitable for long time-scale simulations. For parallel-sided fjords, the model exhibits two possible steady state solutions. When there is no calving of new icebergs or melting of previously calved icebergs, the ice mélange is pushed down fjord by the advancing glacier terminus, the velocity is constant along the length of the fjord, and the thickness profile is exponential. When calving and melting are included, the ice mélange evolves to another steady state in which its location is fixed relative to the fjord walls, the thickness profile is relatively steep, and the flow is extensional. For the latter case, the model predicts that the steady-state ice mélange buttressing force depends on the surface and basal melt rates through an inverse power law relationship, decays roughly exponentially with both fjord width and gradient in fjord width, and increases with the iceberg calving flux. The increase in buttressing force with the calving flux, which depends on glacier thickness, appears to occur more rapidly than the force required to prevent the capsize of full-glacier-thickness icebergs, suggesting that glaciers with high calving fluxes may be more strongly influenced by ice mélange than those with small fluxes.

 

Increasing ice flux from glaciers retreating over deepening (retrograde) bed topography has been implicated in the recent acceleration of mass loss from the Greenland and Antarctic ice sheets. We show in observations that some glaciers have remained at peaks in bed topography without retreating despite enduring significant changes in climate. Observations also indicate that some glaciers which persist at bed peaks undergo sudden retreat years or decades after the onset of local ocean or atmospheric warming. Using model simulations, we show that persistence of a glacier at a bed peak is caused by ice slowing as it flows up a reverse-sloping bed to the peak. Persistence at bed peaks may lead to two very different future behaviors for a glacier: one where it persists at a bed peak indefinitely, and another where it retreats from the bed peak after potentially long delays following climate forcing. However, it is nearly impossible to distinguish which of these two future behaviors will occur from current observations. We conclude that inferring glacier stability from observations of persistence obscures our true commitment to future sea-level rise under climate change. We recommend that further research is needed on seemingly stable glaciers to determine their likely future.

 

Abstract. Many marine-terminating outlet glaciers have retreated rapidly in recent decades, but these changes have not been formally attributed to anthropogenic climate change. A key challenge for such an attribution assessment is that if glacier termini are sufficiently perturbed from bathymetric highs, ice-dynamic feedbacks can cause rapid retreat even without further climate forcing. In the presence of internal climate variability, attribution thus depends on understanding whether (or how frequently) these rapid retreats could be triggered by climatic noise alone. Our simulations with idealized glaciers show that in a noisy climate, rapid retreat is a stochastic phenomenon. We therefore propose a probabilistic approach to attribution and present a framework for analysis that uses ensembles of many simulations with independent realizations of random climate variability. Synthetic experiments show that century-scale climate trends substantially increase the likelihood of rapid glacier retreat. This effect depends on the timescales over which ice dynamics integrate forcing. For a population of synthetic glaciers with different topographies, we find that external trends increase the number of large retreats triggered within the population, offering a metric for regional attribution. Our analyses suggest that formal attribution studies are tractable and should be further pursued to clarify the human role in recent ice-sheet change. We emphasize that early-industrial-era constraints on glacier and climate state are likely to be crucial for such studies. 

Abstract. The dynamics of marine-terminating outlet glaciers are of fundamental interest in glaciology and affect mass loss from ice sheets in a warming climate. In this study, we analyze the response of outlet glaciers to different sources of climate forcing. We find that outlet glaciers have a characteristically different transient response to surface-mass-balance forcing applied over the interior than to oceanic forcing applied at the grounding line. A recently developed reduced model represents outlet-glacier dynamics via two widely separated response timescales: a fast response associated with grounding-zone dynamics and a slow response of interior ice. The reduced model is shown to emulate the behavior of a more complex numerical model of ice flow. Together, these models demonstrate that ocean forcing first engages the fast, local response and then the slow adjustment of interior ice, whereas surface-mass-balance forcing is dominated by the slow interior adjustment. We also demonstrate the importance of the timescales of stochastic forcing for assessing the natural variability in outlet glaciers, highlighting that decadal persistence in ocean variability can affect the behavior of outlet glaciers on centennial and longer timescales. Finally, we show that these transient responses have important implications for attributing observed glacier changes to natural or anthropogenic influences; the future change already committed by past forcing; and the impact of past climate changes on the preindustrial glacier state, against which current and future anthropogenic influences are assessed.