scholarly journals On the temperature gradient in the upper part of cold ice sheets

1974 ◽  
Vol 13 (67) ◽  
pp. 148-151
Author(s):  
K. Philberth ◽  
B. Fédérer
Keyword(s):  
Temperature Gradient ◽  
Temperature Profile ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Horizontal Velocity ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Surface Slope ◽  
Geothermal Heat

The influence of the surface slope on the temperature profile in the upper part of a cold ice sheet can be described by a function which is independent of the geothermal heat and the heat of friction. This function is calculated for the two-dimensional and the axisymmetric cases. In the two-dimensional case its simplest form is proportional to the horizontal velocity and to the height above bedrock reduced by a constant; another form of this function is approximately proportional to the square of velocity and height.

scholarly journals On the temperature gradient in the upper part of cold ice sheets

1974 ◽  
Vol 13 (67) ◽  
pp. 148-151
Author(s):  
K. Philberth ◽  
B. Fédérer
Keyword(s):  
Temperature Gradient ◽  
Temperature Profile ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Horizontal Velocity ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Surface Slope ◽  
Geothermal Heat

The influence of the surface slope on the temperature profile in the upper part of a cold ice sheet can be described by a function which is independent of the geothermal heat and the heat of friction. This function is calculated for the two-dimensional and the axisymmetric cases. In the two-dimensional case its simplest form is proportional to the horizontal velocity and to the height above bedrock reduced by a constant; another form of this function is approximately proportional to the square of velocity and height.

scholarly journals A Numerical Study of Plane Ice-Sheet Flow

1986 ◽  
Vol 32 (111) ◽  
pp. 139-160 ◽  
Author(s):  
K. Hutter ◽  
S. Yakowitz ◽  
F. Szidarovszky
Keyword(s):  
Surface Temperature ◽  
Thermal State ◽  
Numerical Study ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Tangential Velocity ◽  
Rigid Base ◽  
Geothermal Heat ◽  
Functional Relations ◽  
External Forcings

AbstractThe plane steady flow of a grounded ice sheet is numerically analysed using the approximate model of Morland or Hutter. In this, the ice behaves as a non-linear viscous fluid with a strongly temperature-dependent rate factor, and ice sheets are assumed to be long and shallow. The climate is assumed to be prescribed via the accumulation/ablation distribution and the surface temperature, both of which are functions of position and unknown height. The rigid base exerts external forcings via the normal heat flow, the geothermal heat, and a given basal sliding condition connecting the tangential velocity, tangential traction, and normal traction. The functional relations are those of Morland (1984) or motivated by his work. We use equations in his notation.The governing equations and boundary conditions in dimensionless form are briefly stated and dimensionless variables are related to their physical counterparts. The thermo-mechanical parabolic boundary-value problem, found to depend on physical scales, constitutive properties, and external forcing functions, has been numerically solved. For reasons of stability, the numerical integration must proceed from the ice divide towards the margin, which requires a special analysis of the ice divide. We present this analysis and then describe the versatility and limitations of the constructed computer code.Results of extensive computations are shown. In particular, we prove that the Morland–Hutter model for ice sheets is only applicable when sliding is sufficiently large (satisfying inequality (30)). In the range of the validity of this inequality, it is then demonstrated that of all physical scaling parameters only a single π-product influences the geometry and the flow within the ice sheet. We analyse the role played by advection, diffusion, and dissipation in the temperature distribution, and discuss the significance of the rheological non-linearities. Variations of the external forcings, such as accumulation/ablation conditions, free surface temperature, and geothermal heat, demonstrate the sensitivity of the ice-sheet geometry to accumulation conditions and the robustness of the flow to variations in the thermal state. We end with a summary of results and a critical review of the model.

scholarly journals A Two-Dimensional Coupled Atmosphere-Ice-Sheet-Continent Model Designed for Paleoclimatic Simulations

1990 ◽  
Vol 14 ◽  
pp. 55-57 ◽  
Author(s):  
M.B. Esch ◽  
K. Herterich
Keyword(s):  
Climate Model ◽  
Hydrological Cycle ◽  
Vertical Plane ◽  
Ice Sheet ◽  
Ice Age ◽  
Balance Model ◽  
Two Dimensional ◽  
Geothermal Heat ◽  
The North ◽  
Slow Evolution

We present a two-dimensional climate model to be used for basic dynamic studies on ice-age time scales (103 to 106 years). The model contains an ice sheet, where flow and temperature are calculated in a vertical plane, oriented in the north-south direction. The model ice sheet is forced by a zonally-averaged atmospheric energy-balance model, including a seasonal cycle and a simplified hydrological cycle, which specifies ice temperature and the mass balance at the ice-sheet surface. At the bottom of the ice sheet, the geothermal heat flux is prescribed. In addition, delayed bedrock sinking (or bedrock rising) is assumed.A stationary state is achieved after 200 000 model years. This long time scale is introduced by the slow evolution of the temperature field within the ice sheet. Using reasonable parameter values and presently observed precipitation patterns, modified by ice-sheet orography, the observed thickness to length ratio (4 km/3300 km) of the Laurentide ice sheet can be simulated within a realistic build-up time (40 000 years). Near the ice bottom, temperate regions developed. They may have had an important effect on ice-sheet build-up and ice-sheet decay.

scholarly journals Modes of Operation of Thermo-Mechanically Coupled Ice Sheets

1989 ◽  
Vol 12 ◽  
pp. 57-69 ◽  
Author(s):  
Richard C.A. Hindmarsh ◽  
Geoffrey S. Boulton ◽  
Kolumban Hutter
Keyword(s):  
Temperature Field ◽  
Time Scale ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Thermal Inertia ◽  
Coupled System ◽  
Thermal Processes ◽  
Temperature Dependent ◽  
Geothermal Heat ◽  
Diffusive Time

A dimensionless model of thermo-mechanically coupled ice sheets is used to analyse the operation of the system. Three thermal processes are identified: (i) dissipation, having a maximum time-scale of thousands of years; (ii) advection, having a time-scale of tens of thousands of years; and (iii) conduction, having a time-scale of 100000 years. Kinematical processes occur on two time-scales: (i) a marginal advective time-scale of thousands of years; and (ii) a diffusive time-scale of tens of thousands of years dominant in the divide area.The coupling with the temperature field in the bed produces fluctuations to the depth of a few kilometres, which means that horizontal conduction in the bed can be ignored except perhaps in the marginal area. The thermal inertia of the bed could produce significant fluctuations in the geothermal heat gradient.The operation of the thermo-mechanically coupled system is explored with a time-dependent thermo-mechanically coupled numerical algorithm. Dependence of the basal friction on temperature is introduced heuristically, and an enthalpy method is used to represent the effect of latent heat. The marginal area is shown to be dissipation-driven, and always reaches melting point. The divide area can show two modes of behaviour: a warm-based mode where the ice sheet is thin, and a cold-based mode where the ice sheet is thick. Which mode operates depends upon the applied temperature field and the amount of heat conducted from the bed.Calculations where sliding is limited were not found to be possible owing to problems with the reduced model which resulted in a violation of the approximation conditions at the margin. Cases which did work required a substantial sliding component; as a result, a significant coupling between geometry and temperature can only be demonstrated when sliding is made temperature-dependent.

scholarly journals The Effect of Longitudinal Stress on the Shear Stress at the Base of an Ice Sheet

1969 ◽  
Vol 8 (53) ◽  
pp. 207-213 ◽  
Author(s):  
J. F. Nye
Keyword(s):  
Shear Stress ◽  
Theoretical Basis ◽  
Ice Sheets ◽  
Ice Sheet ◽  
High Accuracy ◽  
Longitudinal Stress ◽  
Surface Slope ◽  
Two Dimensional Flow ◽  
Basal Shear ◽  
Longitudinal Strain Rate

Robin (1967) and Budd (1968, unpublished) have succeeded in connecting the variations in surface slope of an ice sheet with variations in the gradient of the longitudinal strain-rate. This paper tries to improve the theoretical basis of their work. By choice of a suitable coordinate system and suitable redefinition of the variables, Budd’s formula for the basal shear stress is derived with a minimum of restrictive assumptions. The resulting formula, containing the gradient of a longitudinal stress, is thought to be of high accuracy for the two-dimensional flow of cold ice sheets, and is valid for slopes of any magnitude.

scholarly journals Stochastic marine ice sheet variability

2018 ◽  
Vol 843 ◽  
pp. 748-777 ◽  
Author(s):  
T. E. Mulder ◽  
S. Baars ◽  
F. W. Wubs ◽  
H. A. Dijkstra
Keyword(s):  
Transition Probabilities ◽  
Accumulation Rate ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Field Measurements ◽  
Multiple Equilibrium ◽  
Short Time Scale ◽  
Two Dimensional ◽  
Grounding Line ◽  
Short Time

It is well known that deterministic two-dimensional marine ice sheets can only be stable if the grounding line is positioned at a sufficiently steep, downward sloping bedrock. When bedrock conditions favour instabilities, multiple stable ice sheet profiles may occur. Here, we employ continuation techniques to examine the sensitivity of a two-dimensional marine ice sheet to stochastic noise representing short time scale variability, either in the accumulation rate or in the sea level height. We find that in unique regimes, the position of the grounding line is most sensitive to noise in the accumulation rate and can explain excursions observed in field measurements. In the multiple equilibrium regime, there is a strong asymmetry in transition probabilities between the different ice sheet states, with a strong preference to switch to the branch with a steeper bedrock slope.

scholarly journals Flow Of Ice Sheets In The Vicinity Of Subglacial Peaks

1982 ◽  
Vol 3 ◽  
pp. 290-294 ◽  
Author(s):  
G. de Q. Robin ◽  
D. H. M. Millar
Keyword(s):  
Flow Line ◽  
Ice Sheets ◽  
Sharp Peak ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Surface Slope ◽  
Antarctic Ice Sheet ◽  
The Third ◽  
Third Dimension ◽  
The Antarctic

Although changes of surface slope across a subglacial peak can be explained at least semi-quantitatively on a two-dimensional basis in terms of gradients of longitudinal and shear stresses along a flow line, we lack appreciation of flow in the third dimension which may tend to cause lower layers to flow around rather than over a sharp peak. This paper collects and surveys evidence relevant to flow in the third dimension and discusses the processes involved, particularly the evidence from radio-echo layering, and also discusses possible reasons for the lack of radio-echo layers near the base of the Antarctic ice sheet.

scholarly journals Flow Of Ice Sheets In The Vicinity Of Subglacial Peaks

1982 ◽  
Vol 3 ◽  
pp. 290-294 ◽  
Author(s):  
G. de Q. Robin ◽  
D. H. M. Millar
Keyword(s):  
Flow Line ◽  
Ice Sheets ◽  
Sharp Peak ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Surface Slope ◽  
Antarctic Ice Sheet ◽  
The Third ◽  
Third Dimension ◽  
The Antarctic

Although changes of surface slope across a subglacial peak can be explained at least semi-quantitatively on a two-dimensional basis in terms of gradients of longitudinal and shear stresses along a flow line, we lack appreciation of flow in the third dimension which may tend to cause lower layers to flow around rather than over a sharp peak. This paper collects and surveys evidence relevant to flow in the third dimension and discusses the processes involved, particularly the evidence from radio-echo layering, and also discusses possible reasons for the lack of radio-echo layers near the base of the Antarctic ice sheet.

scholarly journals Sensitivity of the frozen/melted basal boundary to perturbations of basal traction and geothermal heat flux: Isunnguata Sermia, western Greenland

2011 ◽  
Vol 52 (59) ◽  
pp. 43-50 ◽  
Author(s):  
Douglas J. Brinkerhoff ◽  
Toby W. Meierbachtol ◽  
Jesse V. Johnson ◽  
Joel T. Harper
Keyword(s):  
Heat Flux ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Thermal Conditions ◽  
Two Dimensional ◽  
Adjoint Model ◽  
The West ◽  
Geothermal Heat ◽  
Coupled Numerical Model ◽  
The Difference

AbstractA full-stress, thermomechanically coupled, numerical model is used to explore the interaction between basal thermal conditions and motion of a terrestrially terminating section of the west Greenland ice sheet. The model domain is a two-dimensional flowline profile extending from the ice divide to the margin. We use data-assimilation techniques based on the adjoint model in order to optimize the basal traction field, minimizing the difference between modeled and observed surface velocities. We monitor the sensitivity of the frozen/melted boundary (FMB) to changes in prescribed geothermal heat flux and sliding speed by applying perturbations to each of these parameters. The FMB shows sensitivity to the prescribed geothermal heat flux below an upper threshold where a maximum portion of the bed is already melted. The position of the FMB is insensitive to perturbations applied to the basal traction field. This insensitivity is due to the short distances over which longitudinal stresses act in an ice sheet.

scholarly journals Position of Ice Divides and Ice Centers on Ice Sheets

1973 ◽  
Vol 12 (66) ◽  
pp. 353-360 ◽  
Author(s):  
J. Weertman
Keyword(s):  
Ice Sheets ◽  
Ice Sheet ◽  
Two Dimensional ◽  
Model Calculations ◽  
Accumulation Pattern ◽  
Rate Of Accumulation

Model calculations are made of the magnitude of the shift of the portion of an ice divide on a two dimensional ice sheet and of the “center” (the position of highest elevation) of a circular ice sheet when the rate of accumulation is different on different sides or in different sectors of an ice sheet. It is concluded that gross changes in the accumulation pattern are required to cause an appreciable shift of the position of ice divides or ice centers if the positions of the edge of the ice sheet are fixed.

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