Effect of higher-order stress gradients on the centennial mass evolution of the Greenland ice sheet

Abstract

Abstract. We use a three-dimensional thermo-mechanically coupled model of the Greenland ice sheet to assess the effects of marginal perturbations on volume changes on centennial timescales. The model is designed to allow for five ice dynamic formulations using different approximations to the force balance. The standard model is based on the shallow ice approximation for both ice deformation and basal sliding. A second model version relies on a higher-order Blatter/Pattyn type of core that resolves effects from gradients in longitudinal stresses and transverse horizontal shearing, i.e. membrane-like stresses. Together with three intermediate model versions, these five versions allow for gradually more dynamic feedbacks from membrane stresses. Idealised experiments are conducted on various resolutions to compare the time-dependent response to imposed accelerations at the marine ice front. If such marginal accelerations are to have an appreciable effect on total mass loss on a century timescale, a fast mechanism to transmit such perturbations inland is required. While the forcing is independent of the model version, inclusion of direct horizontal coupling allows the initial speed-up to reach several tens of kilometres inland. Within one century, effects from gradients in membrane stress alter the inland signal propagation and transmit additional dynamic thinning to the ice sheet interior. But the centennial overall volume loss differs only by some percents from the standard model, as the dominant response is a diffusive inland propagation of geometric changes. For the experiments considered, this volume response is even attenuated by direct horizontal coupling. The reason is a faster adjustment of the sliding regime by instant stress transmission in models that account for the effect of membrane stresses. Ultimately, horizontal coupling decreases the reaction time to perturbations at the ice sheet margin. These findings suggest that for modelling the mass evolution of a large-scale ice sheet, effects from diffusive geometric adjustments dominate effects from successively more complete dynamic approaches.

Last Interglacial climate and sea-level evolution from a coupled ice sheet–climate model

“…Given the large remaining uncertainties in the climate forcing during the LIG and a limited impact of an improved physical approximation for ice flow applied to future projections (Fürst et al, 2013), we consider improving the representation of ice sheet dynamics to be of secondary importance. However, fully physical treatment of the surface mass balance solution in a coupled climate-ice sheet model framework, as currently targeted by several groups (e.g.…”

Application of a two-step approach for mapping ice thickness to various glacier types on Svalbard

“…These stress gradients are comparable to membrane stresses in thin body mechanics (Hindmarsh, 2006). Membrane stresses can instantly transmit perturbations upglacier but this transmission was shown to be a secondary factor in terms of centennial ice-sheet volume evolution (Fürst et al, 2013). The associated scaling length is usually expressed as a multiple l of the ice thickness H .…”

Effect of uncertainty in surface mass balance–elevation feedback on projections of the future sea level contribution of the Greenland ice sheet

“…The unstructured mesh allows a variable grid resolution to focus computational resources at the ice sheet margin; here we use a minimum horizontal grid size of less than 1 km. GISM-SIA is a thermomechanical ISM (Huybrechts and de Wolde, 1999) that has been modified and extended for projections on centennial timescales using a new higher-order approximation of the force balance (GISM-HO: Fürst et al, 2011Fürst et al, , 2013. The MPAS-Land Ice model is based on the MPAS (Model for Prediction Across Scales) climate modelling framework of Ringler et al (2008); here we use a regular 5 km resolution hexagonal mesh.…”