Adaptive mesh, finite volume modeling of marine ice sheets Stephen L. Cornford a , Daniel F. Martin b , Daniel T. Graves b , Douglas F. Ranken c , Anne M. Le Brocq d , Rupert M. Gladstone a , Antony J. Payne a , Esmond G. Ng b , William H. Lipscomb c a School of Geographical Sciences, University of Bristol, UK b Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, Berkeley, California c Los Alamos National Laboratory, New Mexico d Geography, College of Life and Environmental Sciences, University of Exeter, UK Abstract Continental scale marine ice sheets such as the present day West Antarctic Ice Sheet are strongly affected by highly localized features, presenting a challenge to numerical models. Perhaps the best known phenomenon of this kind is the migration of the grounding line — the division between ice in contact with bedrock and floating ice shelves — which needs to be treated at sub-kilometer resolution. We implement a block- structured finite volume method with adaptive mesh refinement (AMR) for three dimensional ice sheets, which allows us to discretize a narrow region around the grounding line at high resolution and the remainder of the ice sheet at low resolution. We demonstrate AMR simulations that are in agreement with uniform mesh simulations, but are computationally far cheaper, appropriately and efficiently evolving the mesh as the grounding line moves over significant distances. As an example application, we model rapid deglaciation of Pine Island Glacier in West Antarctica caused by melting beneath its ice shelf. 1. Introduction The West Antarctic Ice Sheet (WAIS) is the world’s major present-day continent-sized marine ice sheet [1]. In general, a marine ice sheet consists of an expanse of grounded ice in contact with a bed that is largely below sea level, joined at some (or all) of its edge to floating ice shelves across a contour known as the grounding line. In their turn, the ice shelves end at calving fronts [2], which then form part or all of the ice sheet’s horizontal boundary. Ice flowing across the grounding line into the ice shelves is ultimately lost to the ocean, either through melting, departing across the calving front as icebergs, or even through large-scale disintegration of an ice shelf [3]. In 1979, Mercer proposed that the ice shelves surrounding WAIS may be vulnerable to additional melting due to anthropogenic global warming, which may in turn make the ice sheet unstable [4], a proposal that is still considered credible [5]. Theoretical and numerical studies have shown that marine ice sheets can be unstable, and so might undergo rapid change, if they lie on beds that slope upward toward the sea. The ice shelves which surround WAIS are all fed by narrow, fast flowing ice streams, whose velocity is dominated by sliding at the base. Schoof proved that for an idealized ice stream flowing in the xz−plane that does not vary in y the flux of ice across the grounding line increases with its thickness there and hence the bedrock depth [6, 7]. Thus, the grounding line cannot come to stable equilibrium anywhere that the bedrock slopes up toward the sea, something also seen in numerical studies which permit both sliding and vertical shear [8]. Now, the flow of marine ice sheets which vary in y is buttressed, that is, stabilized by additional stresses arising from the motion of ice shelf within a bay [9] or across obstructions [10]. Provided that the regions of up-sloping bed are wide enough at the grounding line, removal (or reduction) of the ice shelves can lead to an unstable marine ice sheet [11]. Email addresses: s.l.cornford@bristol.ac.uk (Stephen L. Cornford), dfmartin@lbl.gov (Daniel F. Martin) Preprint submitted to Elsevier August 29, 2012