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Description of a hybrid ice sheet-shelf model, and application to Antarctica
D. Pollard,R. M. DeConto
Geoscientific Model Development (GMD) & Discussions (GMDD) , 2012, DOI: 10.5194/gmd-5-1273-2012
Abstract: The formulation of a 3-D ice sheet-shelf model is described. The model is designed for long-term continental-scale applications, and has been used mostly in paleoclimatic studies. It uses a hybrid combination of the scaled shallow ice and shallow shelf approximations for ice flow. Floating ice shelves and grounding-line migration are included, with parameterized ice fluxes at grounding lines that allows relatively coarse resolutions to be used. All significant components and parameterizations of the model are described in some detail. Basic results for modern Antarctica are compared with observations, and simulations over the last 5 million years are compared with previously published results. The sensitivity of ice volumes during the last deglaciation to basal sliding coefficients is discussed.
Description of a hybrid ice sheet-shelf model, and application to Antarctica  [PDF]
D. Pollard,R. M. DeConto
Geoscientific Model Development Discussions , 2012, DOI: 10.5194/gmdd-5-1077-2012
Abstract: The formulation of a 3-D ice sheet-shelf model is described. The model is designed for long-term continental-scale applications, and has been used mostly in paleoclimatic studies. It uses a hybrid combination of the scaled Shallow Ice and Shallow Shelf Approximations for ice flow. Floating ice shelves and grounding-line migration are included, with parameterized ice fluxes at grounding lines that allows relatively coarse resolutions to be used. All significant components and parameterizations of the model are described in some detail. Basic results for modern Antarctica are compared with observations, and simulations over the last 5 million yr are shown to be similar to previously published results using an earlier model version. The sensitivity of ice retreat during the last deglaciation to basal sliding coefficients is discussed.
The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 1: Model description  [PDF]
R. Winkelmann,M. A. Martin,M. Haseloff,T. Albrecht
The Cryosphere , 2011, DOI: 10.5194/tc-5-715-2011
Abstract: We present the Potsdam Parallel Ice Sheet Model (PISM-PIK), developed at the Potsdam Institute for Climate Impact Research to be used for simulations of large-scale ice sheet-shelf systems. It is derived from the Parallel Ice Sheet Model (Bueler and Brown, 2009). Velocities are calculated by superposition of two shallow stress balance approximations within the entire ice covered region: the shallow ice approximation (SIA) is dominant in grounded regions and accounts for shear deformation parallel to the geoid. The plug-flow type shallow shelf approximation (SSA) dominates the velocity field in ice shelf regions and serves as a basal sliding velocity in grounded regions. Ice streams can be identified diagnostically as regions with a significant contribution of membrane stresses to the local momentum balance. All lateral boundaries in PISM-PIK are free to evolve, including the grounding line and ice fronts. Ice shelf margins in particular are modeled using Neumann boundary conditions for the SSA equations, reflecting a hydrostatic stress imbalance along the vertical calving face. The ice front position is modeled using a subgrid-scale representation of calving front motion (Albrecht et al., 2011) and a physically-motivated calving law based on horizontal spreading rates. The model is tested in experiments from the Marine Ice Sheet Model Intercomparison Project (MISMIP). A dynamic equilibrium simulation of Antarctica under present-day conditions is presented in Martin et al. (2011).
The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 1: Model description  [PDF]
R. Winkelmann,M. A. Martin,M. Haseloff,T. Albrecht
The Cryosphere Discussions , 2010, DOI: 10.5194/tcd-4-1277-2010
Abstract: We present the Potsdam Parallel Ice Sheet Model (PISM-PIK), developed at the Potsdam Institute for Climate Impact Research to be used for simulations of large-scale ice sheet-shelf systems. It is derived from the Parallel Ice Sheet Model (Bueler and Brown, 2009). Velocities are calculated by superposition of two shallow stress balance approximations within the entire ice covered region: the shallow ice approximation (SIA) is dominant in grounded regions and accounts for shear deformation parallel to the geoid. The plug-flow type shallow shelf approximation (SSA) dominates the velocity field in ice shelf regions and serves as a basal sliding velocity in grounded regions. Ice streams naturally emerge through this approach and can be identified diagnostically as regions with a significant contribution of membrane stresses to the local momentum balance. All lateral boundaries in PISM-PIK are free to evolve, including the grounding line and ice fronts. Ice shelf margins in particular are modeled using Neumann boundary conditions for the SSA equations, reflecting a hydrostatic stress imbalance along the vertical calving face. The ice front position is modeled using a subgrid scale representation of calving front motion (Albrecht et al., 2010) and a physically motivated dynamic calving law based on horizontal spreading rates. The model is validated within the Marine Ice Sheet Model Intercomparison Project (MISMIP) and is used for a dynamic equilibrium simulation of Antarctica under present-day conditions in the second part of this paper (Martin et al., 2010).
Grounding line transient response in marine ice sheet models  [PDF]
A. S. Drouet,D. Docquier,G. Durand,R. Hindmarsh
The Cryosphere Discussions , 2012, DOI: 10.5194/tcd-6-3903-2012
Abstract: Marine ice sheet stability is mostly controlled by the dynamics of the grounding line, i.e., the junction between the grounded ice sheet and the floating ice shelf. Grounding line migration has been investigated in the framework of MISMIP (Marine Ice Sheet Model Intercomparison Project), which mainly aimed at investigating steady state solutions. Here we focus on transient behaviour, executing short-term simulations (200 yr) of a steady ice sheet perturbed by the release of the buttressing restraint exerted by the ice shelf on the grounded ice upstream. The transient grounding line behaviour of four different flowline ice sheet models has been compared. The models differ in the physics implemented (full-Stokes and Shallow Shelf Approximation), the numerical approach, as well as the grounding line treatment. Their overall response to the loss of buttressing is found to be consistent in terms of grounding line position, rate of surface elevation change and surface velocity. However, large discrepancies (>100%) are observed in terms of ice sheet contribution to sea level. Despite the recent important improvements of marine ice sheet models in their ability to compute steady-state configurations, our results question models' capacity to compute reliable sea-level rise projections.
Analytical analysis of small-amplitude perturbations in the shallow ice stream approximation
G. H. Gudmundsson
The Cryosphere Discussions , 2008,
Abstract: New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow ice stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow ice sheet approximation, and with solutions of the full Stokes equations. The shallow ice stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow ice sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow ice stream approximation overestimates the effects of bedrock perturbations on surface topography for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow ice stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow ice stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow ice sheet approximation. In contrast to the shallow ice sheet approximation, the shallow ice stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed. In accordance with the full system solutions, the shallow ice sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses.
The Potsdam Parallel Ice Sheet Model (PISM-PIK) – Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet  [PDF]
M. A. Martin,R. Winkelmann,M. Haseloff,T. Albrecht
The Cryosphere , 2011, DOI: 10.5194/tc-5-727-2011
Abstract: We present a dynamic equilibrium simulation of the ice sheet-shelf system on Antarctica with the Potsdam Parallel Ice Sheet Model (PISM-PIK). The simulation is initialized with present-day conditions for bed topography and ice thickness and then run to steady state with constant present-day surface mass balance. Surface temperature and sub-shelf basal melt distribution are parameterized. Grounding lines and calving fronts are free to evolve, and their modeled equilibrium state is compared to observational data. A physically-motivated calving law based on horizontal spreading rates allows for realistic calving fronts for various types of shelves. Steady-state dynamics including surface velocity and ice flux are analyzed for whole Antarctica and the Ronne-Filchner and Ross ice shelf areas in particular. The results show that the different flow regimes in sheet and shelves, and the transition zone between them, are captured reasonably well, supporting the approach of superposition of SIA and SSA for the representation of fast motion of grounded ice. This approach also leads to a natural emergence of sliding-dominated flow in stream-like features in this new 3-D marine ice sheet model.
Analytical solutions for the surface response to small amplitude perturbations in boundary data in the shallow-ice-stream approximation  [PDF]
G. H. Gudmundsson
The Cryosphere , 2008,
Abstract: New analytical solutions describing the effects of small-amplitude perturbations in boundary data on flow in the shallow-ice-stream approximation are presented. These solutions are valid for a non-linear Weertman-type sliding law and for Newtonian ice rheology. Comparison is made with corresponding solutions of the shallow-ice-sheet approximation, and with solutions of the full Stokes equations. The shallow-ice-stream approximation is commonly used to describe large-scale ice stream flow over a weak bed, while the shallow-ice-sheet approximation forms the basis of most current large-scale ice sheet models. It is found that the shallow-ice-stream approximation overestimates the effects of bed topography perturbations on surface profile for wavelengths less than about 5 to 10 ice thicknesses, the exact number depending on values of surface slope and slip ratio. For high slip ratios, the shallow-ice-stream approximation gives a very simple description of the relationship between bed and surface topography, with the corresponding transfer amplitudes being close to unity for any given wavelength. The shallow-ice-stream estimates for the timescales that govern the transient response of ice streams to external perturbations are considerably more accurate than those based on the shallow-ice-sheet approximation. In particular, in contrast to the shallow-ice-sheet approximation, the shallow-ice-stream approximation correctly reproduces the short-wavelength limit of the kinematic phase speed given by solving a linearised version of the full Stokes system. In accordance with the full Stokes solutions, the shallow-ice-sheet approximation predicts surface fields to react weakly to spatial variations in basal slipperiness with wavelengths less than about 10 to 20 ice thicknesses.
Resonance Type Instabilities in the Gaseous Disks of the Flat Galaxies I. The Acoustical Resonance Type Instability and the Absence of Vortex Sheet Stabilization on Shallow Water  [PDF]
J. V. Mustsevaya,V. V. Mustsevoy
Physics , 1998,
Abstract: Linear analysis of vortex sheet stability in the rotating gaseous disk or shallow water layer shows that presence of a central reflecting surface changes system stability significantly. An effect of absence of vortex sheet stabilization has been found as compressibility exceeds Landau criterion. The properties of multimode short-scale instability of acoustical resonance type are investigated and probability of its influence upon experiments on the rotating shallow water is discussed.
Derivation of a numerical solution of the 3D coupled velocity field for an ice sheet – ice shelf system, incorporating both full and approximate stress solutions  [PDF]
T. J. Reerink,R. S. W. van de Wal,P.-P. Borsboom
Geoscientific Model Development Discussions , 2009,
Abstract: To overcome the mechanical coupling of an ice sheet with an ice shelf, one single set of velocity equations is presented covering both the sheet and the shelf. This set is obtained by applying shared sheet-shelf approximations. The hydrostatic approximation and a constant density are the only approximations that are applied to the full-Stokes momentum equations. The remaining stress terms from the momentum equations and the stress terms from the usual ice-flow law are multiplied by coefficients which can be put to zero or one, facilitating several stress approximations per domain within one model. In addition we derived a matrix format for the discretized set of the fully coupled velocity equations on a three-dimensional vertically scaled grid, in which all linear derivative terms are treated implicitly. The compact vector format of this sparse matrix equation is developed, including the boundary conditions.
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