Shallow shelf approximation as a “sliding law” in a thermomechanically coupled ice sheet model

By Ed Bueler, Jed Brown. 2008

556 citations recorded by the source corpus.

[1] The shallow shelf approximation, a balance of membrane stresses for ice flow, is an effective "sliding law" for ice sheet modeling. Our use of it as a sliding law becomes a standard model for ice stream flow when the sliding velocity is large (100 m a -1 and faster). Following Schoof (2006a), we describe the basal resistance as plastic till for which the yield stress is given by a Mohr-Coulomb formula. Pore water pressure is related to basal melt rate. The velocity field used in the mass continuity and conservation of energy equations is an average of velocities from the shallow shelf approximation and the nonsliding shallow ice approximation. Using this scheme, our model has realistic, time-dependent ice streams which exhibit the range of surface velocities seen in actual ice streams. We demonstrate the model at high spatial resolution (5 km grid) over multiple millenia using its implementation in the Parallel Ice Sheet Model. Numerical experiments show that the entire scheme is stable with respect to many parameter changes. Some experiments reveal significant ice stream variability in a hypothetical steady climate, with characteristic cycles on the order of 1000 years. We believe this is the first practical whole ice sheet model with a unified treatment of vertical shear stresses and membrane stresses. It is capable of high-resolution, thermomechanically coupled, multimillenia simulations of ice sheets containing ice streams.

Subfields: Atmospheric Science, Management, Monitoring, Policy and Law

View Paper: https://www.semanticscholar.org/paper/333e1682db9544ef678520004d06e622c916370a

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Citations in the corpus

The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 1: Model description (2010, unknown): “For the discretization of the mass transport, the SSA velocities are transferred onto that same staggered grid by averaging over the SSA velocities from the adjacent grid cells.”
A variationally derived, depth-integrated approximation to a higher-order glaciological flow model (2011, methodology): “which can be seen as a regularized Coulomb-plastic sliding law (Schoof, 2006; Bueler and Brown, 2009), with the yield stress, τc, having the spatial dependence”
Resolution-dependent performance of grounding line motion in a shallow model compared with a full-Stokes model according to the MISMIP3d intercomparison (2014, unknown): “D, finite-difference model (Bueler and Brown, 2009; www.pism-docs.org).”
Safe and just Earth system boundaries (2023, unknown): “We used simulations from the Parallel Ice Sheet Model (Bueler and Brown 2009; Winkelmann et al. 2011; Albrecht et al. 2020a, 2020b) for the Greenland and Antarctic ice sheets, and the Lund-Potsdam-Jena managed Land model LPJmL (Schaphoff et al.”
Kinematic first-order calving law implies potential for abrupt ice-shelf retreat (2011, methodology): “Brief model description of PISM-PIK In this study, we apply a derived version of the open-source Parallel Ice Sheet Model version stable 0.2 (PISM, see user’s manual (PISM-authors) and model description5 paper (Bueler and Brown, 2009)).”
Marine ice-sheet profiles and stability under Coulomb basal conditions (2015, methodology): “…model of Tulaczyk and others (2000b), the theoretical treatment of Schoof (2006), and the numerical glacier models of Truffer and others (2000) and Bueler and Brown (2009), none of these studies specifically address the question of ice sheet profiles near the grounding line or the differences in…”
Dependence of century-scale projections of the Greenland ice sheet on its thermal regime (2013, background): “Most ice-flow models rely on simplified first-order approximations of the momentum balance equations, such as the shallow-ice approximation (SIA; Hutter, 1982), the shelfy-stream approximation (SSA; MacAyeal, 1989; Greve and others, 2011; Aschwanden and others, 2012a) or a combination of SIA and SSA”