Grounding-line flux formula applied as a flux condition in numerical simulations fails for buttressed Antarctic ice streams

Abstract

Abstract. Currently, several large-scale ice-flow models impose a condition on ice-flux across grounding lines using an analytically motivated parameterization of grounding-line flux. It has been suggested that employing this analytical expression alleviates the need for highly resolved computational domains around grounding lines of marine ice sheets. While the analytical flux formula is expected to be accurate in an unbuttressed flow-line setting, its validity has hitherto not been assessed for complex and realistic geometries such as those of the Antarctic Ice Sheet. Here the accuracy of this analytical flux formula 5 is tested against an optimized ice flow model that uses a highly-resolved computational mesh around the Antarctic grounding lines. We find that when applied to the Antarctic Ice Sheet the analytical expression provides inaccurate estimates of ice fluxes for almost all grounding lines. Furthermore, in many instances direct application of the analytical formula gives rise to unphysical complexed-valued ice fluxes. We conclude that grounding lines of the Antarctic Ice Sheet are, in general, too highly buttressed for the analytical parameterization to be of practical value for the calculation of grounding-line fluxes.

Millennial‐Scale Vulnerability of the Antarctic Ice Sheet to Regional Ice Shelf Collapse

“…Durand et al, 2009;Pattyn et al, 2013;Reese et al, 2018). Such fine resolution has been demonstrated to be necessary for the correct representation of the stresses at the GL, to the extent that numerical error can otherwise overshadow projections of AIS mass budget and stability (Cornford et al, 2013Durand et al, 2009;Pattyn et al, 2013;Reese et al, 2018). Such fine resolution has been demonstrated to be necessary for the correct representation of the stresses at the GL, to the extent that numerical error can otherwise overshadow projections of AIS mass budget and stability (Cornford et al, 2013Durand et al, 2009;Pattyn et al, 2013;Reese et al, 2018).…”

Improvements in one-dimensional grounding-line parameterizations in an ice-sheet model with lateral variations

“…If the buttressing factor θ falls to zero or below in (6), this corresponds to net zero or compressive horizontal deviatoric stress normal to the grounding line, and zero or compressive (negative) strain in the direction of flow. However, its use in the Schoof formation for grounding-line ice velocity (1) predicts zero velocity for θ = 0, and becomes invalid for θ < 0, as noted by Reese et al (2018). In our application, θ in Eq.…”

The Utrecht Finite Volume Ice-Sheet Model: UFEMISM (version 1.0)

“…Different semianalytical solutions for the ice flux across the grounding line in the absence of buttressing have been proposed (Schoof et al, 2007;Tsai et al, 2015). However, implementing those in numerical models has proven difficult (Pollard and DeConto, 2012;Pattyn et al, 2013), and recent work has demonstrated that these analytical solutions cannot be feasibly altered to account for buttressing, which is the case for the majority of Antarctic grounding lines (Reese et al, 2018). This means that the problem of solving the stress balance near the grounding line in numerical models without resorting to very high (< 100 m) resolutions remains open, and is not solved by this new model configuration.…”

“…The dynamics of the Antarctic ice sheet at present are strongly influenced by the presence of floating ice shelves (Pattyn, 2018). Different studies have investigated the physical processes affecting these ice shelves, including surface melt induced by atmospheric processes (Bevan et al, 2017;Kuipers Munneke et al, 2018), bottom melt induced by intrusion of warm ocean water (Depoorter et al, 2013;Lazeroms et al, 2018, Reese et al, 2018, brittle fracturing of ice cliffs (Pollard et al, 2015), and the response of the grounding line to changes in sea level and bedrock elevation (Gomez et al, 2013;Barletta et al, 2018).…”

“…Different approaches have been proposed where semi-analytical solutions (Schoof, 2007;Tsai et al, 2015) are implemented as boundary conditions in numerical models, to maintain physical accuracy at lower resolutions (Pollard & DeConto, 2012;Pattyn, 2017). However, while these approaches achieve good results in situations without buttressing (Pattyn et al, 2013), their performance in simulating realistic ice shelves, where buttressing is usually a significant factor, is poor (Reese et al, 2018). Ice-sheet model computation time increases rapidly with model resolution, due to the increasing number of grid points, the decreasing time step required for numerical stability, and the increasing number of topographic features that are resolved.…”