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Volume 11, issue 5 | Copyright
Geosci. Model Dev., 11, 1683-1694, 2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Development and technical paper 03 May 2018

Development and technical paper | 03 May 2018

Implementation of higher-order vertical finite elements in ISSM v4.13 for improved ice sheet flow modeling over paleoclimate timescales

Joshua K. Cuzzone1,2, Mathieu Morlighem1, Eric Larour2, Nicole Schlegel2, and Helene Seroussi2 Joshua K. Cuzzone et al.
  • 1University of California, Irvine, Department of Earth System Science, Croul Hall, Irvine, CA 92697-3100, USA
  • 2Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive MS 300-323, Pasadena, CA 91109-8099, USA

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.

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Short summary
This paper details the implementation of higher-order vertical finite elements in the Ice Sheet System Model (ISSM). When using higher-order vertical finite elements, fewer vertical layers are needed to accurately capture the thermal structure in an ice sheet versus a conventional linear vertical interpolation, therefore greatly improving model runtime speeds, particularly in higher-order stress balance ice sheet models. The implications for paleoclimate ice sheet simulations are discussed.
This paper details the implementation of higher-order vertical finite elements in the Ice Sheet...