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Ocean temperatures have warmed in the fjords surrounding the Greenland Ice Sheet, causing increased melt along their ice fronts and rapid glacier retreat and contributing to rising global sea levels. However, there are many physical mechanisms that can mediate the glacier response to ocean warming and variability. Warm ocean waters can directly cause melt at horizontal and vertical ice interfaces or promote iceberg calving by weakening proglacial melange or undercutting the glacier front. Sermeq Kujalleq (also known as Jakobshavn Isbræ) is the largest and fastest glacier in Greenland and has undergone substantial retreat, which started in the late 1990s. In this study, we use an ensemble modeling approach to disentangle the dominant mechanisms that drive the retreat of Sermeq Kujalleq. Within this ensemble, we vary the sensitivity of three different glaciological parameters to ocean temperature: frontal melt, subshelf melt, and a calving-stress threshold. Comparing results to the observed retreat behavior from 1985 to 2018, we select a best-fitting simulation which reproduces the observed retreat well. In this simulation, the arrival of warm water at the front of Sermeq Kujalleq in the late 1990s led to enhanced rates of subshelf melt, triggering the disintegration of the floating ice tongue over a decade. The recession of the calving front into a substantially deeper bed trough around 2010 accelerated the calving-driven retreat, which continued nearly unabated despite local ocean cooling in 2016. An extended ensemble of simulations with varying calving thresholds shows evidence of hysteresis in the calving rate, which can only be inhibited by a substantial increase in the calving-stress threshold beyond the values suggested for the historical period. Our findings indicate that accurate simulation of rapid calving-driven glacier retreats requires more sophisticated models of iceberg mélange and calving evolution coupled to ice flow models. 

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 timescales 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 exhibit 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-timescale simulations. For parallel-sided fjords, the model exhibits two possible steady-state solutions. When there is no calving of 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 and treated as constants, the ice mélange evolves into 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 buttressing force appears to increase with calving flux (i.e., glacier thickness) more rapidly than the force required to prevent the capsizing 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. 

Using a simplified two-stage ice sheet model, we explore the potential of statistical data assimilation methods to improve predictions of glacier melt, which has significant implications for reducing uncertainty in projections of sea level rise. Through twin experiments utilizing artificial data, we find that the ensemble Kalman filter improves simulations of glacier evolution initialized with incorrect initial conditions and parameters, providing us with better predictions of future glacier melt. We explore the number of observations necessary to produce an accurate model run. We also explore optimal observation assimilation schemes, and determine that deviations from the true glacier response that stem from having few data points in the pre-satellite era can be corrected with modern observation data. Our results show that statistical data assimilation methods have great potential to improve complex glacier models using real-world observations. 

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. 

glaciome1D is a quasi-one-dimensional continuum model for modeling the flow of dense packs of icebergs (ice mélange) found in some fjords. In many respects the model is similar to one-dimensional models of ice streams and ice shelves, except that it uses the nonlocal granular fluidity rheology of Henann and Kamrin (2013). The model was created with the intention of developing coupled glacier-ocean-melange models. This is reflected in the modeling framework, which mimics that used for ice streams and ice shelves (Schoof, 2007). Using the model involves creating an instance of the glaciome class, which contains information on the glacier velocity, viscosity (granular fluidity), and geometry as well as model parameters and various external forcings. The glaciome class includes several basic and easy to use functions, such as: self.diagnostic(), self.prognostic(), self.steadystate(), self.save(). The model physics and numerics are described in detail in Amundson et al. (in press). This data set includes a single python module that includes all of the functions for setting up and running the model, an example script that runs the model, and a conda environment list that contains python modules that the code has been tested on. 

### Access Dataset and extensive metadata can be accessed and downloaded via: [https://arcticdata.io/data/10.18739/A2CZ32678/](https://arcticdata.io/data/10.18739/A2CZ32678/) ### Overview A limited understanding of how glacier-ocean interactions lead to iceberg calving and melting at the ice-ocean boundary contributes to uncertainty in predictions of sea level rise. Dense packs of icebergs and sea ice, known as ice mélange, occur in many fjords in Greenland and Antarctica. Observations suggest that ice mélange may directly affect iceberg calving by pressing against the glacier front and indirectly affect glacier melting by controlling where and when icebergs melt which can impact ocean circulation and ocean heat transport towards glaciers. However, the interactions between ice mélange, ocean circulation, and iceberg calving have not been systematically investigated due to the difficulty of conducting field work in Greenland fjords. In order to investigate the dynamics of ice mélange (and other floating granular materials) and to inform development of ice mélange models, we conducted a series of laboratory experiments using synthetic icebergs (plastic blocks) that were pushed down a tank by a synthetic glacier. This data set consists of force measurements on the glacier terminus and time-lapse photographs of the experiments that were used for visualizing motion. 

Abstract Variability in oceanic conditions directly impacts ice loss from marine outlet glaciers in Greenland, influencing the ice sheet mass balance. Oceanic conditions are available from Atmosphere‐Ocean Global Climate Model (AOGCM) output, but these models require extensive computational resources and lack the fine resolution needed to simulate ocean dynamics on the Greenland continental shelf and close to glacier marine termini. Here, we develop a statistical approach to generate ocean forcing for ice sheet model simulations, which incorporates natural spatiotemporal variability and anthropogenic changes. Starting from raw AOGCM ocean heat content, we apply: (a) a bias‐correction using ocean reanalysis, (b) an extrapolation accounting for on‐shelf ocean dynamics, and (c) stochastic time series models to generate realizations of natural variability. The bias‐correction reduces model errors by ∼25% when compared to independent in‐situ measurements. The bias‐corrected time series are subsequently extrapolated to fjord mouth locations using relations constrained from available high‐resolution regional ocean model results. The stochastic time series models reproduce the spatial correlation, characteristic timescales, and the amplitude of natural variability of bias‐corrected AOGCMs, but at negligible computational expense. We demonstrate the efficiency of this method by generating >6,000 time series of ocean forcing for >200 Greenland marine‐terminating glacier locations until 2100. As our method is computationally efficient and adaptable to any ocean model output and reanalysis product, it provides flexibility in exploring sensitivity to ocean conditions in Greenland ice sheet model simulations. We provide the output and workflow in an open‐source repository, and discuss advantages and future developments for our method. 

Abstract 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.