Impact of arithmetic asymmetries on simulated thermodynamic ice-sheet evolution

Abstract

Numerical ice-sheet model experiments sometimes exhibit asymmetries in the solutions, despite the symmetric conditions imposed. By first identifying arithmetic asymmetry in the models as one of the reasons for symmetry-breaking through loss of trailing digits, this paper presents a numerical procedure to preserve the symmetries by restructuring the order of the floating-point evaluation of the equations in the numerical ice-sheet model. Re-examination of the series of experiments in the HEINO topic of the ISMIP demonstrates that small perturbations triggered by arithmetic asymmetries significantly amplify and cause qualitative differences in the simulated ice-sheet evolutions. This study shows that it is imperative to apply a symmetric scheme to maintain overall symmetries in the simulation of ice-sheet evolution, at least under a highly idealized configuration.