A Model of Icebergs and Sea Ice in a Joint Continuum Framework

Abstract

The ice mélange, a mixture of sea ice and icebergs, often present in front of outlet glaciers in Greenland or ice shelves in Antarctica, can have a profound effect on the dynamics of the ice‐ocean system. The current inability to numerically model the ice mélange motivates a new modeling approach proposed here. A continuum sea‐ice model is taken as a starting point and icebergs are represented as thick and compact pieces of sea ice held together by large tensile and shear strength, selectively introduced into the sea‐ice rheology. In order to modify the rheology correctly, an iceberg tracking procedure is implemented within a semi‐Lagrangian time‐stepping scheme, designed to exactly preserve iceberg shape through time. With the proposed treatment, sea ice and icebergs are considered a single fluid with spatially varying rheological properties. Mutual interactions are thus automatically included without the need for further parametrization. An important advantage of the presented framework for an ice mélange model is its potential to be easily included within sea‐ice components of existing climate models.

A continuum model (PSUMEL1) of ice mélange and its role during retreat of the Antarctic Ice Sheet

“…(For simplicity we use the term Jakobshavn throughout and do not use separate names for the glacier and fjord, Jakobshavn Isbrae and Ilulissat Icefjord, respectively.) There are no comprehensive datasets of mélange properties in Jakobshavn or other fjords to our knowledge, but there are many individual studies with relevant observations and modeling (Joughin et al, 2008(Joughin et al, , 2014bAmundson et al, 2008Amundson et al, , 2010Motyka et al, 2011;MacAyeal et al, 2012;Walter et al, 2012;Cook et al, 2014;Sundal et al, 2013;Foga et al, 2014;Foga, 2016;Sutherland et al, 2014;Todd et al, 2014;Cassotto et al, 2015;Krug et al, 2015;Moon et al, 2015;Murray et al, 2015;Enderlin et al, 2016;Burton et al, 2018). The main properties reported in these studies that are pertinent here, with quantities rounded to the nearest order of magnitude for Jakobshavn, are as follows.…”

“…One possible choice for a continuum-mechanical model of mélange is the viscous-plastic (VP) fluid formulation developed for sea ice (Hibler, 1977;Hibler and Tucker, 1979), which has been used and extended in many subsequent studies (e.g., Hunke and Dukowicz, 1997) including a simplified cavitating-fluid (CF) version (Flato and Hibler, 1992). Recently Vankova and Holland (2017) used cavitating-fluid dynamics in a continuum model of mélange. Their model is quite different from ours, explicitly incorporating large icebergs within a matrix of sea ice, and may be suited for smaller scales than considered here.…”

“…The VP-CF approach involves the concept of an internal pressure that resists convergence, which is an empirical function of sea ice thickness and represents ridging of ice slabs. As noted by Vankova and Holland (2017), ridging is not relevant for mélange, but this function can still be used to represent resistance to convergence when large ice pieces in the mélange become closely packed. Instead of using a VP-CF approach, we use shallow-shelf approximation (SSA) equations commonly used for ice shelf dynamics, modified to include (i) strong resistance to convergence beyond a certain "packing density" and (ii) very little resistance to divergence.…”

“…Calving of ice from thick ( ∼ 1 km) glacial termini generates substantial amounts of floating ice debris called mélange, as observed in the fjords of major outlet glaciers of Greenland and in places in Antarctica (Macayeal et al, 1998;Joughin et al, 2008Joughin et al, , 2014bFricker et al, 2009;Khazendar et al, 2009;Amundson et al, 2010;Scambos et al, 2011). In Greenland, mélange occupies some or all of the fjords downstream of the ice terminus (Joughin et al, 2012;Sundal et al, 2013;Sutherland et al, 2014;Moon et al, 2015) and is thought to provide significant back pressure on the ice 5150 D. Pollard et al: PSUMEL1 face, reducing calving and ice velocities especially in winter (Joughin et al, 2008(Joughin et al, , 2014bAmundson et al, 2010;Walter et al, 2012;Todd et al, 2014). The lateral scales of these modern ice faces and fjords are 5 to 10 km.…”

“…Our approach is to use continuum physics, in a model that captures basic dependencies between rate of mélange supply, downstream export, side drag and ocean bottom resistance, which combine to produce back pressure on ice faces. Two other continuum models have been applied to mélange to our knowledge (Seneca Lindsey and Dupont, 2012;Vankova and Holland, 2017), discussed briefly in Sect. 3.…”