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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. 

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. 

### 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. 

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.