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

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.