Coupling approximation levels for modeling ice flow on paleo time scales

• Main Author: van Dongen, Eef (author)
• Other Authors: van Gijzen, Martin (mentor), Delft University of Technology (degree granting institution)
• Format: Master Thesis
• Language: English
• Published: 2017
• Subjects: Finite Element Method; Ice sheet modeling; coupling approximations; full stokes; shallow shelf approximation; shallow ice approximation; Ice Sheet; Ice Shelf
• Online Access: http://resolver.tudelft.nl/uuid:caed0f22-278b-4dc3-ac52-775a17706e3c

Ice flow, forced by gravity is governed by the Full Stokes (FS) equations, which are computationally intensive to solve due to their non-linearity. Therefore, it has been unavoidable to approximate the FS equations when modeling growth and collapse of an ice sheet-shelf system, which requires simulating many thousands of years. However, the most popular Shallow Ice Approximation (SIA) and Shallow Shelf Approximation (SSA) are only accurate in certain parts of an ice sheet, both excluding the grounding line where the ice starts floating. Using the Finite Element software Elmer/Ice, SIA and SSA are dynamically coupled to FS aiming to maintain high precision and reduce computation time. An existing coupling of SIA and FS, called ISCAL [Ahlkrona et al., 2013a], is investigated for robustness. It is shown that instabilities in the FS solution limit ISCAL’s robustness. A novel way of iteratively coupling SSA and FS has been implemented into the open source Finite Element software Elmer/Ice and applied to both 2D and 3D conceptual marine ice sheets. The SSA-FS coupling shows to be very accurate, for both diagnostic and prognostic runs (error in velocity respectively below 0.5% and 5%). Grounding line dynamics of the SSA-FS coupling are similar to the FS model under a periodical forcing in a simulation covering 3000 years. The current implementation does not yield speed up in 2D due to inefficient assembly of the matrices to be solved. In 3D, the cpu time is reduced to two thirds of the cpu time of the FS model despite inefficient assembly. The total number of FS iterations in the SSA-FS coupling is comparable to the FS model, showing a large potential of reducing computation time since computation time of the SSA model is up to 3% of the FS model’s computation time when applied to the same ice shelf ramp. In future research, the SSA-FS coupling can be combined with ISCAL, but this requires both efficient implementation of the SSA-FS coupling and improved stabilization methods for FS. Applied Mathematics