  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.
