C43A-01 INVITED
A first calving law for ice shelves: spreading-rate control of calving rate
The rate of iceberg production from floating, cold ice shelves increases with the along-flow spreading rate near the ice-shelf front, based on a curve-fit to preliminary data from several ice shelves. Although calving almost certainly depends on many forcings, ice-shelf properties, and pre-existing flaws, we suggest that the spreading rate of the ice is the most important control (that is, the rate at which ice shelves fall apart is controlled primarily by their tendency to fall apart). We obtain calving rate from near-frontal velocity assuming steady state, and strain rate from the velocity gradient, focusing on central flowlines of ice shelves. A best-fit relation explains a significant and important fraction of the variance in the data set, motivating further investigation. Implementing this calving relation in models will typically produce instability in the absence of buttressing, consistent with many observations on ice shelves.
C43A-02
How Do We Actually Solve the Equations for Ice Shelves and Streams?
The standard shallow approximation of the balance of momentum in ice shelves and ice streams is a pair of equations which determine the horizontal velocity of the ice. They are supposed to determine the velocity given the ice thickness, bed topography, the temperature within the ice, and boundary conditions (where the fast-flowing ice meets ice ridges and at the calving front, for instance). How is one supposed to solve these equations efficiently and at the high resolution necessary to model narrow ice streams and the parts of ice shelves with complex geometry? How does one know that the solution method is accurate? Can one use modern numerical tools to solve these equations? This talk will address, and even attempt an answer to, these questions. We recognize that the ice shelf/stream equations are a lower-dimensional model for the full three-dimensional Stokes problem for ice flow, and conclusions about the shelf/stream case may have broader consequences.
C43A-03
Ice sheet/shelf dynamics at grounding lines
We present a novel experimental and theoretical analysis of the conditions under which an ice sheet loses contact with its basal bed rock to form a floating ice shelf. The experiments consist of modelling the ice sheet by a Newtonian viscous fluid, either glycerine or golden syrup. The `ocean' is represented by a relatively dense solution of aqueous potassium carbonate, made up to be more dense than the viscous fluid of the `ice' shelf. The viscous fluid is input just above the `ocean' surface at a constant flux to propagate in a two-dimensional fashion down an inclined ramp into the `ocean'. The grounding line, at which the viscous fluid leaves the ramp and flows over the aqueous ocean, was observed to approach a steady position dependent on the values of the flux, the bed slope, the kinematic viscosity of the viscous fluid and its density difference from the underlying `ocean'. A simple but powerful, complementary theory was developed, based on balancing horizontal forces at the grounding line, where the differing flow regimes of the ice sheet and ice shelf must match. The theoretical results for the downslope position of the grounding line are in good agreement with our experimental observations. Video sequences of the experiments will be presented.
C43A-04
Inferring the surface shape of the ice sheet-ice shelf transition zone using a full-Stokes model.
Grounding line migration plays an important role in the stability of marine ice-sheets such as the West Antarctica ice sheet. For modelling purpose, it is generally assumed that the grounding line position, as well as its stability, is determined by the floating condition constrained by the sea water level. With such approach, the vertical position of the sea-ice interface depends only on the ice thickness at this place, so that the non-hydrostatic part of the stress within the ice does not play any role. In this presentation, the floating condition is compared with the solution for which the sea water action is modelled by the buoyancy pressure. In the proposed method, the sea- ice interface is treated as a free surface submitted to the buoyancy sea pressure. The starting point of this surface, i.e. the grounding line, is determined by solving a contact problem. The full-Stokes equations, the air/ice free surface as well as the sea/ice free surface equations are solved in a coupled way with the finite element code Elmer. The resulting free surface is compared to measured surfaces. As observed, the modelled ice thickness at the grounding line is found to be greater than that of the floating ice in hydrostatic equilibrium. Moreover, the particular depression of the air/ice surface downstream the grounding line is also well reproduced by our model, which is in full agreement with topographic observations.
C43A-05
How Sensitive is a Greenland Ice Sheet Model?
No model is better than its physical ingredients, approximations, parameterizations, boundary and initial conditions. This is particularly true for models of the Greenland Ice Sheet (GrIS). There is an urgent need to determine the predictability of models for the response of GrIS to rising temperatures and the amount of freshwater flux that can be expected into the ocean. We explore the sensitivity of a GrIS model to various model components; the resolution, the modeled climate (surface boundary condition), geothermal heat flux beneath the ice sheet and a few warming scenarios. Simulations are done with the polythermal ice sheet model SICOPOLIS. Model time for all simulations is from 250 kyr BP until today. Initial conditions are provided by spin-up simulations from 422 kyr BP until 250 kyr BP. Climate forcing is based on the GRIP temperature history from the δ18O record. Surface melting is parameterized by a degree-day method. First experiments indicate strong dependency on how the present climate and the geothermal heat flux are defined. Generally the periphery is controlled by the surface boundary condition and the central ice thickness by the geothermal heat flux.
C43A-06 INVITED
A Three-Dimensional, First-Order Model of ice Flow: Numerical Implementation, Validation, and Initial Application to Iceland and Greenland
We present a new, three-dimensional ice sheet model that accounts for vertical and horizontal stress gradients to first order. The horizontal stress balance equations are caste in terms of velocity gradients (e.g. Blatter [1995], the 'LMLa' scheme of Hindmarsh [2004]) by employing a constitutive relation for ice (Glen's flow law). The resulting coupled, non-linear elliptic equations are solved by the Finite Difference Method, using the iterative technique of Hindmarsh and Payne [1996] and the PETSc linear solver library. An innovative approach is used to incorporate first order surface and basal boundary conditions of Dirichlet, Neumann, and mixed types. We validate the model by comparing output against (1) analytical solutions for end-member geometries and boundary conditions, such as sheet flow, stream flow, and shelf flow, and (2) by comparing output against benchmarking experiments for full-stress and higher-order models (Pattyn and others, 2007). We present and discuss initial velocity and stress solutions for the Langjokull ice cap (Iceland) and the Greenland ice sheet, based on currently available ice sheet geometries and simplified assumptions about the effective viscosity.
C43A-07 INVITED
Dynamic/Thermodynamic Modeling of the Gorshkov Crater Glacier at Ushkovsky Volcano, Kamchatka
Glaciers which develop in volcano craters are unique systems because of their particular morphologies (large thickness-to-width ratio) and thermodynamic conditions (large geothermal heat flux). Here, we investigate the Gorshkov crater glacier, which is situated in the summit caldera of Ushkovsky volcano, Kamchatka, and fills the concave crater bed to a maximum depth of 240~m. The crater diameter is approx.\ 750~m. The glacier surface is gently inclined towards the northern crater rim, where the ice flows out of the crater and down the slope of the volcano. The geothermal heat flux at the crater rim is estimated to be as large as 10\;W m-2 based on direct measurements. Furthermore, large parts of the glacier consist of firn rather than pure ice, which alters its rheological properties. We apply the three-dimensional, thermo-mechanically coupled, full-Stokes flow model "Elmer/Ice" (based on the open-source finite-element tool "Elmer") to the Gorshkov crater glacier. By assuming steady-state conditions and a spatial distribution of the geothermal heat flux obtained by an optimization procedure, the present-day density, velocity, temperature and age fields are simulated. We find that flow velocities are generally small (10's of centimeters per year). Horizontal and vertical velocities are of comparable magnitude, which shows that the shallow-ice approximation is not applicable. Owing to the spatially variable volcanic heat flux, the thermal regime at the ice base is cold in the deeper parts of the glacier and temperate in the shallower parts. The measured temperature and age profiles at the K2 borehole (close to the deepest point of the glacier) are reproduced quite well, and remaining discrepancies may be attributed to transient (non-steady-state) conditions.
C43A-08
Benchmark Experiments for Higher-Order and Full Stokes Ice Sheet Models
The ISMIP-HOM intercomparison exercise, launched in 2006, aims at comparing so-called higher-order ice sheet models to analytical solutions and at setting out a benchmark for such models. Higher-order models are models that incorporate further mechanical effects, principally longitudinal stress gradients, or the full Stokes system. These stresses become increasingly important in transition zones between ice sheets and ice shelves (ice streams), but also at the ice divide and in areas of complex basal topography. The proposed experiments are made accessible for a variety of model types, i.e. flowline models, vertically integrated planform models, as well as full three-dimensional models. The experiments are valid for both finite difference (FD) and finite element (FE) models. Furthermore, the grid type (regular or not) is unimportant. All thermomechanical effects are neglected and an isotherm ice mass is considered. Experiments include ideal geometry tests as well as a real case experiment on Haut Glacier d'Arolla. Most experiments are diagnostic, i.e. time evolution is not considered. This means that for a given geometry of the ice mass, a Glen-type flow law, and given appropriate boundary conditions, the stress and velocity field can be calculated. One experiment considers time-dependent response (the experiment is run until the free surface and velocity field reach a steady state) for a constant viscosity (linear flow law). For this experiment analytical solutions exist that are developed by Gudmundsson (2003). 28 numerical models of varying physical complexity participated in the exercise. The results show a very good convergence of the different models at different resolutions. At higher resolutions – and conform theory – a clear distinction can be made between higher-order models and those that solve the full system of equations (full Stokes models). The model results seem not to be influenced by the used numerical approaches, which is clearly demonstrated by the comparison of the different full Stokes models.