Understanding the melting of Greenland's largest glacial ice tongue with high-resolution modelling and adaptive coordinates
Authors: Reinert Markus , Lorenz Marvin , Klingbeil Knut , Burchard Hans 
Published: March 2022

&lt;p&gt;&lt;span&gt;Melting of the Greenland ice sheet has a big influence on the climate system. Therefore, it is important to &lt;/span&gt;&lt;span&gt;understand&lt;/span&gt; &lt;span&gt;how &lt;/span&gt;&lt;span&gt;the ice&lt;/span&gt;&lt;span&gt; melts. Since direct measurements at the underside of floating ice tongues are sparse, high-resolution models for the interaction of ocean and &lt;/span&gt;&lt;span&gt;glacial &lt;/span&gt;&lt;span&gt;ice are needed to determine sub-glacial melt rates and to &lt;/span&gt;&lt;span&gt;understand&lt;/span&gt; &lt;span&gt;melt &lt;/span&gt;&lt;span&gt;processes. A common problem is that model resolution is &lt;/span&gt;&lt;span&gt;often &lt;/span&gt;&lt;span&gt;too low, so that the meltwater plume is &lt;/span&gt;&lt;span&gt;only &lt;/span&gt;&lt;span&gt;represented by &lt;/span&gt;&lt;span&gt;one or two layers, and thus &lt;/span&gt;&lt;span&gt;the entrainment of warmer water into the plume is &lt;/span&gt;&lt;span&gt;not well &lt;/span&gt;&lt;span&gt;captured&lt;/span&gt;&lt;span&gt;. &lt;/span&gt;&lt;span&gt;However, this heat transport towards the ice is crucial for the sub-glacial melt &lt;/span&gt;&lt;span&gt;rate&lt;/span&gt;&lt;span&gt;.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;In this talk, we &lt;/span&gt;&lt;span&gt;show&lt;/span&gt;&lt;span&gt; how w&lt;/span&gt;&lt;span&gt;e solve&lt;/span&gt; &lt;span&gt;this problem &lt;/span&gt;&lt;span&gt;with the General Estuarine Transport Model (&lt;/span&gt;&lt;span&gt;GETM&lt;/span&gt;&lt;span&gt;)&lt;/span&gt;&lt;span&gt;. &lt;/span&gt;&lt;span&gt;GETM features &lt;/span&gt;&lt;span&gt;adaptive vertical coordinates &lt;/span&gt;&lt;span&gt;that &lt;/span&gt;&lt;span&gt;zoom automatically to areas of interest, &lt;/span&gt;&lt;span&gt;in particular strong density gradients. A high density contrast exists &lt;/span&gt;&lt;span&gt;in the entrainment layer &lt;/span&gt;&lt;span&gt;between the relatively fresh and cold meltwater of the plume, and the ambient ocean water.&lt;/span&gt; &lt;span&gt;By zooming towards this interface, &lt;/span&gt;&lt;span&gt;our &lt;/span&gt;&lt;span&gt;adaptive vertical coordinates&lt;/span&gt; &lt;span&gt;resolve the &lt;/span&gt;&lt;span&gt;meltwater &lt;/span&gt;&lt;span&gt;plume with several layers, &lt;/span&gt;&lt;span&gt;while keeping the total number of model layers at a modest level to ensure a feasible computation time&lt;/span&gt;&lt;span&gt;. &lt;/span&gt;&lt;span&gt;In addition, t&lt;/span&gt;&lt;span&gt;he &lt;/span&gt;&lt;span&gt;coordinate levels align to the moving isopycnals &lt;/span&gt;&lt;span&gt;&amp;#8211; they &amp;#8220;&lt;/span&gt;&lt;span&gt;follow&amp;#8221; the plume&lt;/span&gt;&lt;span&gt; &amp;#8211;&lt;/span&gt;&lt;span&gt;, which strongly reduces numerical mixing and pressure gradient errors.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;We &lt;/span&gt;&lt;span&gt;p&lt;/span&gt;&lt;span&gt;resent&lt;/span&gt;&lt;span&gt; this&lt;/span&gt; &lt;span&gt;for the&lt;/span&gt; &lt;span&gt;fjord of&lt;/span&gt; &lt;span&gt;the 79&amp;#176;N-Glacier &lt;/span&gt;&lt;span&gt;(79NG)&lt;/span&gt;&lt;span&gt;, &lt;/span&gt;&lt;span&gt;which has the &lt;/span&gt;&lt;span&gt;largest floating ice tongue &lt;/span&gt;&lt;span&gt;in &lt;/span&gt;&lt;span&gt;Greenland. &lt;/span&gt;&lt;span&gt;In our&lt;/span&gt; &lt;span&gt;idealized 2D-&lt;/span&gt;&lt;span&gt;s&lt;/span&gt;&lt;span&gt;etup, &lt;/span&gt;&lt;span&gt;we obtain &lt;/span&gt;&lt;span&gt;layers&lt;/span&gt; &lt;span&gt;as thin as &lt;/span&gt;&lt;span&gt;0.2 &lt;/span&gt;&lt;span&gt;m to 1 &lt;/span&gt;&lt;span&gt;m in the meltwater plume, for only 100 levels over a water column of several 100 m depth. &lt;/span&gt;&lt;span&gt;Thanks to&lt;/span&gt;&lt;span&gt; this high resolution of plume &lt;/span&gt;&lt;span&gt;and entrainment layer&lt;/span&gt;&lt;span&gt;, our &lt;/span&gt;&lt;span&gt;model &lt;/span&gt;&lt;span&gt;reproduces &lt;/span&gt;&lt;span&gt;the overturning circulation in the glacier cavity &lt;/span&gt;&lt;span&gt;correctly&lt;/span&gt;&lt;span&gt;; in particular, it &lt;/span&gt;&lt;span&gt;shows&lt;/span&gt;&lt;span&gt; that the salinity stratification &lt;/span&gt;&lt;span&gt;of&lt;/span&gt;&lt;span&gt; the adjacent ocean determines the level at which the meltwater plume detaches from the ice tongue. &lt;/span&gt;&lt;span&gt;Almost all sub-glacial melting occurs &lt;/span&gt;&lt;span&gt;before this detachment, &lt;/span&gt;&lt;span&gt;&lt;em&gt;i.e.,&lt;/em&gt;&lt;/span&gt; &lt;span&gt;where the plume is directly at the ice&amp;#8211;ocean interface. &lt;/span&gt;&lt;span&gt;Furthermore, &lt;/span&gt;&lt;span&gt;we can confirm that &lt;/span&gt;&lt;span&gt;the highest melt rates exist near the grounding line of the glacier. &lt;/span&gt;&lt;span&gt;Finally, our simulated melt rates are &lt;/span&gt;&lt;span&gt;consistent&lt;/span&gt; &lt;span&gt;with observations at 79NG&lt;/span&gt;&lt;span&gt;.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;O&lt;/span&gt;&lt;span&gt;ur &lt;/span&gt;&lt;span&gt;model, developed in&lt;/span&gt;&lt;span&gt; the GROCE (Greenland ice sheet&amp;#8211;ocean interaction) project, will form the basis of a realistic 3D-model of the 79NG-&lt;/span&gt;&lt;span&gt;fjord &lt;/span&gt;&lt;span&gt;in the &lt;/span&gt;&lt;span&gt;future&lt;/span&gt;&lt;span&gt;.&lt;/span&gt;&lt;/p&gt;