Abstract
Abstract. Poor convergence with resolution of ice sheet models when simulating grounding line migration has been known about for over a decade. However, some of the associated numerical artefacts remain absent from the published literature. In the current study we apply a Stokes-flow finite-element marine ice sheet model to idealised grounding line evolution experiments. We show that with insufficiently fine model resolution, a region containing multiple steady-state grounding line positions exists, with one steady state per node of the model mesh. This has important implications for the design of perturbation experiments used to test convergence of grounding line behaviour with resolution. Specifically, the design of perturbation experiments can be under-constrained, potentially leading to a “false positive” result. In this context a false positive is an experiment that appears to achieve convergence when in fact the model configuration is not close to its converged state. We demonstrate a false positive: an apparently successful perturbation experiment (i.e. reversibility is shown) for a model configuration that is not close to a converged solution. If perturbation experiments are to be used in the future, experiment design should be modified to provide additional constraints to the initialisation and spin-up requirements. This region of multiple locally stable steady-state grounding line positions has previously been mistakenly described as neutral equilibrium. This distinction has important implications for understanding the impacts of discretising a forcing feedback involving grounding line position and basal friction. This forcing feedback cannot, in general, exist in a region of neutral equilibrium and could be the main cause of poor convergence in grounding line modelling.
Highlights
Resolution-dependent behaviour when implementing grounding line movement in a marine ice sheet model was identified by Vieli and Payne (2005) and was further characterised as a convergence problem by subsequent studies (Durand et al, 2009; Goldberg et al, 2009; Gladstone et al, 2010a, b, 2012)
We argue that ice dynamic model (IDM) exhibit, as a numerical artefact, a region containing multiple locally stable equilibria and not a region of neutral equilibrium
The established poor convergence of many marine ice sheet models regarding grounding line movement is characterised by a region of multiple locally stable states
Summary
Resolution-dependent behaviour when implementing grounding line movement (sometimes referred to as grounding line migration) in a marine ice sheet model was identified by Vieli and Payne (2005) and was further characterised as a convergence problem by subsequent studies (Durand et al, 2009; Goldberg et al, 2009; Gladstone et al, 2010a, b, 2012). Various forms of mesh refinement help to address the problem, though very high resolution is still needed (Goldberg et al, 2009; Cornford et al, 2013), and special treatments of the grid cell or element containing the grounding line can improve convergence (Pollard and DeConto, 2009; Gladstone et al, 2010b; Gagliardini et al, 2016; Seroussi et al, 2014; Feldmann et al, 2014) This problem has been described as neutral equilibrium (Durand et al, 2009; Pattyn et al, 2006) in modelling studies. This leads to a discussion on discretisation of a forcing feedback involving basal friction and model state (Sect. 5)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
