Computation of a combined spherical-elastic and viscous-half-space earth model for ice sheet simulation

TL;DR

This paper develops a fast spectral collocation method to simulate earth deformation under ice sheets, comparing different earth models and demonstrating the importance of model validation for accurate ice sheet simulations.

Contribution

It introduces a spectral collocation numerical strategy based on FFT for earth deformation modeling in ice sheet simulations, improving computational efficiency.

Findings

The new method is significantly faster than previous approaches.

Numerical errors are smaller than differences between various earth models.

Validating earth models is crucial for accurate ice sheet simulation results.

Abstract

This report starts by describing the continuum model used by Lingle & Clark (1985) to approximate the deformation of the earth under changing ice sheet and ocean loads. That source considers a single ice stream, but we apply their underlying model to continent-scale ice sheet simulation. Their model combines Farrell's (1972) elastic spherical earth with a viscous half-space overlain by an elastic plate lithosphere. The latter half-space model is derivable from calculations by Cathles (1975). For the elastic spherical earth we use Farrell's tabulated Green's function, as do Lingle & Clark. For the half-space model, however, we propose and implement a significantly faster numerical strategy, a spectral collocation method (Trefethen 2000) based directly on the Fast Fourier Transform. To verify this method we compare to an integral formula for a disc load. To compare earth models we build an accumulation history from a growing similarity solution from (Bueler, et al.~2005) and and simulate the coupled (ice flow)-(earth deformation) system. In the case of simple isostasy the exact solution to this system is known. We demonstrate that the magnitudes of numerical errors made in approximating the ice-earth system are significantly smaller than pairwise differences between several earth models, namely, simple isostasy, the current standard model used in ice sheet simulation (Greve 2001, Hagdorn 2003, Zweck & Huybrechts 2005), and the Lingle & Clark model. Therefore further efforts to validate different earth models used in ice sheet simulations are, not surprisingly, worthwhile.