Ralf Greve

Dynamics of ice sheets and glaciers

Ice in the Climate System.- Vectors, Tensors and Their Representation.- Elements of Continuum Mechanics.- Constitutive Equations for Polycrystalline Ice.- Large-Scale Dynamics of Ice Sheets.- Large-Scale Dynamics of Ice Shelves.- Dynamics of Glacier Flow.- Glacial Isostasy.- Advanced Topics.- Conclusions, Summary and Outlook.- Erratum.

Application of a Polythermal Three-Dimensional Ice Sheet Model to the Greenland Ice Sheet: Response to Steady-State and Transient Climate Scenarios

Abstract Steady-state and transient climate-change computations are performed with the author’s three-dimensional polythermal ice sheet model Simulation Code for Polythermal Ice Sheets for the Greenland Ice Sheet. The distinctive feature of this model is the detailed consideration of the basal temperate ice layer, in which the water content and its impact on the ice viscosity are computed; its transition surface to the cold ice region is accounted for by continuum-mechanical jump conditions on this interface. The simulations presented include steady states subject to a range of physical parameters and two different climates (present and glacial conditions), as well as three types of transient scenarios, namely (i) sinusoidal Milankovic-period forcing, (ii) paleoclimatic forcing from the Greenland Ice Core Project core reconstruction, and (iii) future greenhouse warming forcing.

Results from the EISMINT model intercomparison: the effects of thermomechanical coupling

This paper discusses results from the second phase of the European Ice sheet Modelling Initiative (EISMINT). It reports the intercompartison of ten operational ice-sheet models and uses a series of experiments to examine the implications of thermomechanical coupling for model behaviour. A schematic, circular ice sheet is used in the work which investigates both steady states and the response to stepped changes in climate. The major finding is that radial symmetry implied in the experimental design can, under certain circumstances, break down with the formation of distinct, regularly spaced spokes of cold ice which extended from the interior of the ice sheet outward to the surrounding zone of basal melt. These features also manifest themselves in the thickness and velocity distributions predicted by the models. They appear to be a common feature to all of the models which took part in the intercomparison, and may stem from interactions between ice temperature, flow and surface form. The exact nature of these features varies between models, and their existence appears to be controlled by the overall thermal regimne of the ice sheet. A second result is that there is considerable agreement between the models in their predictions of global-scale response to imposed climate change.

Relation of measured basal temperatures and the spatial distribution of the geothermal heat flux for the Greenland ice sheet

Abstract The thermomechanical, three-dimensional ice-sheet model SICOPOLIS is applied to the Greenland ice sheet. Simulations over two glacial–interglacial cycles are carried out, driven by a climatic forcing interpolated between present conditions and Last Glacial Maximum anomalies. Based on the global heat-flow representation by Pollack and others (1993), we attempt to constrain the spatial pattern of the geothermal heat flux by comparing simulation results to direct measurements of basal temperatures at the GRIP, NorthGRIP, Camp Century and Dye 3 ice-core locations. The obtained heat-flux map shows an increasing trend from west to east, a high-heat-flux anomaly around NorthGRIP with values up to 135 mWm–2 and a low-heat-flux anomaly around Dye 3 with values down to 20 mW m–2. Validation is provided by the generally good fit between observed and measured ice thicknesses. Residual discrepancies are most likely due to deficiencies of the input precipitation rate and further variability of the geothermal heat flux not captured here.

Large-scale instabilities of the Laurentide ice sheet simulated in a fully coupled climate-system model

[1] Heinrich events, related to large-scale surges of the Laurentide ice sheet, represent one of the most dramatic types of abrupt climate change occurring during the last glacial. Here, using a coupled atmosphere-ocean-biosphereice sheet model, we simulate quasi-periodic large-scale surges from the Laurentide ice sheet. The average time between simulated events is about 7,000 yrs, while the surging phase of each event lasts only several hundred years, with a total ice volume discharge corresponding to 5–10 m of sea level rise. In our model the simulated ice surges represent internal oscillations of the ice sheet. At the same time, our results suggest the possibility of a synchronization between instabilities of different ice sheets, as indicated in paleoclimate records. INDEX TERMS: 1827 Hydrology: Glaciology (1863); 1620 Global Change: Climate dynamics (3309); 3344 Meteorology and Atmospheric Dynamics: Paleoclimatology; 5416 Planetology: Solid Surface Planets: Glaciation. Citation: Calov, R., A. Ganopolski, V. Petoukhov, M. Claussen, and R. Greve, Largescale instabilities of the Laurentide ice sheet simulated in a fully coupled climate-system model, Geophys. Res. Lett., 29(24), 2216, doi:10.1029/2002GL016078, 2002.

On the Response of the Greenland Ice Sheet to Greenhouse Climate Change

Numerical computations are performed with the three-dimensional polythermal ice-sheet model SICOPOLIS in order to investigate the possible impact of a greenhouse-gas-induced climate change on the Greenland ice sheet. The assumed increase of the mean annual air temperature above the ice covers a range from ΔT = 1°C to 12°C, and several parameterizations for the snowfall and the surface melting are considered. The simulated shrinking of the ice sheet is a smooth function of the temperature rise, indications for the existence of critical thresholds of the climate input are not found. Within 1000 model years, the ice-volume decrease is limited to 10% of the present volume for ΔT ≤ 3°C, whereas the most extreme scenario, ΔT = 12°C, leads to an almost entire disintegration, which corresponds to a sea-level equivalent of 7 m. The different snowfall and melting parameterizations yield an uncertainty range of up to 20% of the present ice volume after 1000 model years.

A full Stokes-flow thermo-mechanical model for firn and ice applied to the Gorshkov crater glacier, Kamchatka

Abstract The Gorshkov crater glacier at Ushkovsky volcano, Kamchatka, is characterized by a large aspect ratio and special thermodynamic conditions at the bedrock caused by a locally enhanced and spatially varying geothermal heat flux. Furthermore, large parts of this glacier consist of firn rather than pure ice, which alters the rheological properties (such as viscosity and compressibility) of the glacier. We present a newly developed, thermo-mechanically coupled, three-dimensional flow model based on the finite-element (FE) modeling software Elmer, and apply it to the Gorshkov crater glacier. By assuming steady-state conditions, the present-day velocity field, temperature field, basal melting rate and age distribution are simulated. We find that flow velocities are generally small (tens 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 profile and age horizons at the K2 borehole are reproduced quite well, and remaining discrepancies may be attributed to transient (non-steady-state) conditions. Firn compressibility is identified as a crucial element for the modeling approach.

Insights into spatial sensitivities of ice mass response to environmental change from the SeaRISE ice sheet modeling project I: Antarctica

Sophie Nowicki, Robert A. Bindschadler, Ayako Abe-Ouchi, Andy Aschwanden, Ed Bueler, Hyeungu Choi, Jim Fastook, Glen Granzow, Ralf Greve, Gail Gutowski, Ute Herzfeld, Charles Jackson, Jesse Johnson, Constantine Khroulev, Eric Larour, Anders Levermann, William H. Lipscomb, Maria A. Martin, Mathieu Morlighem, Byron R. Parizek, David Pollard, Stephen F. Price, Diandong Ren, Eric Rignot, Fuyuki Saito, Tatsuru Sato, Hakime Seddik, Helene Seroussi, Kunio Takahashi, Ryan Walker, and Wei Li Wang

Motion of a granular avalanche in a convex and concave curved chute : experiments and theoretical predictions

This paper deals with the theoretical-numerical and experimental treatment of two dimensional avalanches of cohesionless granular materials moving down a confined curved chute. Depth-averaged field equations of balance of mass and linear momentum as prescribed by Savage & Hutter (1991) are used. They describe the temporal evolution of the depth averaged streamwise velocity and the distribution of the avalanche depth and involve two phenomenological parameters, the internal angle of friction, ϕ,and the bed friction angle, δ, both as constitutive properties of Coulomb-type behaviour. The equations incorporate weak to moderate curvature effects of the bed. Experiments were carried out with different granular materials in a chute with partly convex and partly concave curved geometry. In these experiments the motion of the granular avalanche is followed from the moment of release to its standstill by using high speed photography, whence recording the geometry of the avalanche as a function of position and time. Two different bed linings, drawing paper and no. 120 SIA sandpaper, were used to vary the bed friction angle, δ. Both, the internal angle of friction, ϕ, and the bed friction angle, δ, were measured, and their values used in the theoretical model. Because of the bump and depending upon the granulate-bed combination an initial single pile of granular avalanche could evolve as a single pile throughout its motion and be deposited above or below the bump in the bed; or it could separate in the course of the motion into two piles which are separately deposited above and below the bump. Comparison of the experimental findings with the computational results proved to lead to good to excellent correspondence between experiment and theory. Even the development of the detailed geometry of the granular avalanche is excellently reproduced by the model equations, if δ < ϕ. Occasional deviations may occur; however, they can in all cases be explained by onsetting instabilities of the numerical scheme or by experimental artefacts that only arise when single particles have shapes prone to rolling.

Unconfined Flow of Granular Avalanches along a Partly Curved Surface. II. Experiments and Numerical Computations

In this paper the agreement between laboratory experiments performed with three-dimensional granular avalanches moving along a partly curved surface and their numerical predictions shall be examined. First, the most important elements of the theory describing the flow of a cohesionless granular material down a rough bed are presented. Based on the depth-averaged model equations, an advanced numerical integration scheme is developped by making use of a Lagrangian representation (i. e., the grid moves with the deforming pile) and a finite difference approximation that handles the numerically two-dimensional problem accurately. Second, experiments are described that were conducted with a finite mass of granular material moving down, respectively, an inclined plane and a surface consisting of an inclined and a horizontal plane connected by a curved transition area; the initial geometry of the avalanche is generated by a spherical cap. Third, for a number of different experiments a comparison is carried out between the experimentally determined positions of the granular avalanche during its motion and the numerical prediction of these positions. It shows that the numerical results fit the experimental data surprisingly well.