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

Abstract

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 15 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 20 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 25 method that can be implemented within ice sheet models, whereby the vertical interpolation along the zaxis 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 30 vertical interpolation compared to models using the linear vertical interpolation, despite having fewer degrees of freedom. This method is also shown to improve a models 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 35 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 10 to 57 times faster than using a model which has a linear vertical interpolation, and 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 40 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 ...

Long‐term projections of sea‐level rise from ice sheets

“…Despite these apparent problems, considerable progress has been made in numerical modeling of long‐term SLR. The Ice Sheet System Model, for example, has the advantage of an anisotropic mesh in order to better resolve grounding lines, but is nonetheless computationally cheap enough that it can also be used for millennial‐scale simulations (Åkesson, Nisancioglu, Giesen, & Morlighem, ; Cuzzone, Morlighem, Larour, Schlegel, & Seroussi, ). Many models now routinely use parallelized computation to run faster or higher‐resolution simulations (Aschwanden, Fahnestock, & Truffer, ; Bueler & Brown, ; Cuzzone et al, ; Martin et al, ).…”

“…The Ice Sheet System Model, for example, has the advantage of an anisotropic mesh in order to better resolve grounding lines, but is nonetheless computationally cheap enough that it can also be used for millennial‐scale simulations (Åkesson, Nisancioglu, Giesen, & Morlighem, ; Cuzzone, Morlighem, Larour, Schlegel, & Seroussi, ). Many models now routinely use parallelized computation to run faster or higher‐resolution simulations (Aschwanden, Fahnestock, & Truffer, ; Bueler & Brown, ; Cuzzone et al, ; Martin et al, ). Other groups have proposed the inclusion of processes such as ice shelf hydrofracture (Pollard et al, ), or use fully coupled simulations that better capture ice–ocean–atmosphere (Gierz, Lohmann, & Wei, ) or ice‐sheet–sea‐level (Gomez, Latychev, & Pollard, ) feedbacks.…”

Sensitivity of the Northeast Greenland Ice Stream to Geothermal Heat

“…We use linear P1 elements for the stress balance analysis and quadratic P2 elements for the thermal analysis. The P1P2 elements have been tested and validated in ISSM by Cuzzone et al (2018) and allow us to capture sharp thermal gradients, despite having only five layers.…”

A new vertically integrated MOno-Layer Higher-Order (MOLHO) ice flow model

“…However, for long transient runs and/or sensitivity analyses that require running the model for large ensembles, the HO model still demands relatively high computational resources. Recently, numerical schemes were applied to improve the computational efficiency of the HO model without compromising numerical accuracy (e.g., Langdon and Raymond, 1978;Bassis, 2010;Brinkerhoff and Johnson, 2015;Cuzzone et al, 2018;Shapero et al, 2021). These schemes rely on the finite element method (FEM), which allows the employment of polynomial functions of a degree equal to or greater than 2 to model the vertical variation in the horizontal velocities.…”