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. Paleoclimate proxies are being used in conjunction with ice sheet modelingexperiments to determine how the Greenland ice sheet responded to pastchanges, particularly during the last deglaciation. Although thesecomparisons have been a critical component in our understanding of theGreenland ice sheet sensitivity to past warming, they often rely on modelingexperiments that favor minimizing computational expense over increased modelphysics. Over Paleoclimate timescales, simulating the thermal structure ofthe ice sheet has large implications on the modeled ice viscosity, which canfeedback onto the basal sliding and ice flow. To accurately capture thethermal field, models often require a high number of vertical layers. This isnot the case for the stress balance computation, however, where a highvertical resolution is not necessary. Consequently, since stress balance andthermal equations are generally performed on the same mesh, more time isspent on the stress balance computation than is otherwise necessary. Forthese reasons, running a higher-order ice sheet model (e.g., Blatter-Pattyn)over timescales equivalent to the paleoclimate record has not been possiblewithout incurring a large computational expense. To mitigate this issue, wepropose a method that can be implemented within ice sheet models, whereby thevertical interpolation along the z axis relies on higher-order polynomials,rather than the traditional linear interpolation. This method is testedwithin the Ice Sheet System Model (ISSM) using quadratic and cubic finiteelements for the vertical interpolation on an idealized case and a realisticGreenland configuration. A transient experiment for the ice thicknessevolution of a single-dome ice sheet demonstrates improved accuracy using thehigher-order vertical interpolation compared to models using the linearvertical interpolation, despite having fewer degrees of freedom. This methodis also shown to improve a model's ability to capture sharp thermal gradientsin an ice sheet particularly close to the bed, when compared to models usinga linear vertical interpolation. This is corroborated in a thermalsteady-state simulation of the Greenland ice sheet using a higher-ordermodel. In general, we find that using a higher-order vertical interpolationdecreases the need for a high number of vertical layers, while dramaticallyreducing model runtime for transient simulations. Results indicate that whenusing a higher-order vertical interpolation, runtimes for a transient icesheet relaxation are upwards of 5 to 7 times faster than using a model whichhas a linear vertical interpolation, and this thus requires a higher number ofvertical layers to achieve a similar result in simulated ice volume, basaltemperature, and ice divide thickness. The findings suggest that this methodwill allow higher-order models to be used in studies investigating ice sheetbehavior over paleoclimate timescales at a fraction of the computational costthan would otherwise be needed for a model using a linear verticalinterpolation.

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