ISMIP-HEINO experiment revisited: effect of higher-order approximation and sensitivity study

Abstract

We revisit the results of the ISMIP-HEINO benchmark by first analyzing the differences in various model outputs using a wavelet-based spectral technique. Second, the ISMIP-HEINO benchmark experiments are recomputed with a novel numerical ice-sheet model based on the SIA-I algorithm that enables both the shallow-ice and a higher-order approximation of the ice-flow equations to be performed. To assess the significance of the higher-order approximation in the ISMIP-HEINO experiment, a numerical sensitivity study for the shallow-ice approximation (SIA) simulations is also carried out. A high sensitivity of the SIA model response to surface temperature perturbations is found. We conclude that the variations in ISMIP-HEINO results are due to the differences in (1) simulated basal temperatures and (2) numerical treatment of the basal sliding condition.

A 3 Ga old polythermal ice sheet in Isidis Planitia, Mars: Dynamics and thermal regime inferred from numerical modeling

“…While it is possible in the model to improve the SIA solution by an iterative algorithm, described in Souček and Martinec (2008) and successfully tested in Pattyn et al (2008), only the first step of the algorithm, corresponding to the SIA solution, is used in the presented simulation. The model is numerically implemented by a finite difference technique (Souček, 2010;Souček and Martinec, 2011). The modeling domain is a spherical rectan-…”

Numerical issues in modeling ice sheet instabilities such as binge-purge type cyclic ice stream surging

“…Meaningful modeling of binge-purge type HEs and surges in general is challenging. Sensitivity in model response to different numerical choices are evident (Calov et al, 2010;Roberts et al, 2016;Ziemen et al, 2019) and small perturbations of the system can significantly vary the form, amplitude, and period of binge-purge oscillations (Souček and Martinec, 2011;Mantelli et al, 2016). The exact cause of the numerical sensitivities is often unclear.…”

“…To date, uncertainties associated with the numerical aspects of a model have received limited attention in studies examining ice sheet surging (e.g., Payne, 1995;Marshall and Clarke, 1997;Calov et al, 2002;Papa et al, 2006;Steen-Larsen and Dahl-Jensen, 2008;Calov et al, 2010;Robel et al, 2013;Feldmann and Levermann, 2017). Souček and Martinec (2011) thus rightfully conclude that "... the implementation of surgetype physics in large-scale ice-sheet models is rather problematic since the information about the physical instability may be lost in the numerics". Furthermore, the theory underpinning the understanding of the instability mechanisms is not fully developed, especially in the context of a spatially extended 3D system, thus precluding systematic benchmarking of numerical models.…”

Impact of arithmetic asymmetries on simulated thermodynamic ice-sheet evolution

“…In addition, Hindmarsh (2011) pointed out a fourth possibility, which may be termed the small amplitude instability of thermoviscous flow. Soucek and Martinec (2011) discussed a fifth possibility, that the extreme sensitivity of basal sliding activation to temperature variations causes random behavior in the results, which breaks symmetry in the long-term model behavior, due to rounding errors of the order of machine precision in such a chaotic dynamical system. None of these studies have discussed in detail how such breaking of symmetry influences the simulation.…”