Implementation of higher-order vertical finite elements in ISSM v4.13 for improved ice sheet flow modeling over paleoclimate timescales
Authors: Cuzzone Joshua K. , Morlighem Mathieu , Larour Eric , Schlegel Nicole , Seroussi Helene 
Published: May 2018

Abstract. Paleoclimate proxies are being used in conjunction with ice sheet modeling
experiments to determine how the Greenland ice sheet responded to past
changes, particularly during the last deglaciation. Although these
comparisons have been a critical component in our understanding of the
Greenland ice sheet sensitivity to past warming, they often rely on modeling
experiments that favor minimizing computational expense over increased model
physics. Over Paleoclimate timescales, simulating the thermal structure of
the ice sheet has large implications on the modeled ice viscosity, which can
feedback onto the basal sliding and ice flow. To accurately capture the
thermal field, models often require a high number of vertical layers. This is
not the case for the stress balance computation, however, where a high
vertical resolution is not necessary. Consequently, since stress balance and
thermal equations are generally performed on the same mesh, more time is
spent on the stress balance computation than is otherwise necessary. For
these reasons, running a higher-order ice sheet model (e.g., Blatter-Pattyn)
over timescales equivalent to the paleoclimate record has not been possible
without incurring a large computational expense. To mitigate this issue, we
propose a method that can be implemented within ice sheet models, whereby the
vertical interpolation along the z axis relies on higher-order polynomials,
rather than the traditional linear interpolation. This method is tested
within the Ice Sheet System Model (ISSM) using quadratic and cubic finite
elements for the vertical interpolation on an idealized case and a realistic
Greenland configuration. A transient experiment for the ice thickness
evolution of a single-dome ice sheet demonstrates improved accuracy using the
higher-order vertical interpolation compared to models using the linear
vertical interpolation, despite having fewer degrees of freedom. This method
is also shown to improve a model's ability to capture sharp thermal gradients
in an ice sheet particularly close to the bed, when compared to models using
a linear vertical interpolation. This is corroborated in a thermal
steady-state simulation of the Greenland ice sheet using a higher-order
model. In general, we find that using a higher-order vertical interpolation
decreases the need for a high number of vertical layers, while dramatically
reducing model runtime for transient simulations. Results indicate that when
using a higher-order vertical interpolation, runtimes for a transient ice
sheet relaxation are upwards of 5 to 7 times faster than using a model which
has a linear vertical interpolation, and this thus requires a higher number of
vertical layers to achieve a similar result in simulated ice volume, basal
temperature, and ice divide thickness. The findings suggest that this method
will allow higher-order models to be used in studies investigating ice sheet
behavior over paleoclimate timescales at a fraction of the computational cost
than would otherwise be needed for a model using a linear vertical
interpolation.