scholarly journals ‘Calving laws’, ‘sliding laws’ and the stability of tidewater glaciers

2007 ◽  
Vol 46 ◽  
pp. 123-130 ◽  
Author(s):  
Douglas I. Benn ◽  
Nicholas R.J. Hulton ◽  
Ruth H. Mottram
Keyword(s):  
Water Depth ◽  
Ice Thickness ◽  
Strain Rates ◽  
Effective Pressure ◽  
Ice Shelves ◽  
Tidewater Glaciers ◽  
Surface Gradient ◽  
Ice Velocity ◽  
Calving Rate ◽  
The Stability

AbstractA new calving criterion is introduced, which predicts calving where the depth of surface crevasses equals ice height above sea level. Crevasse depth is calculated from strain rates, and terminus position and calving rate are therefore functions of ice velocity, strain rate, ice thickness and water depth. We couple the calving criterion with three ‘sliding laws’, in which velocity is controlled by (1) basal drag, (2) lateral drag and (3) a combination of the two. In model 1, velocities and strain rates are dependent on effective pressure, and hence ice thickness relative to water depth. Imposed thinning can lead to acceleration and terminus retreat, and ice shelves cannot form. In model 2, ice velocity is independent of changes in ice thickness unless accompanied by changes in surface gradient. Velocities are strongly dependent on channel width, and calving margins tend to stabilize at flow-unit widenings. Model 3 exhibits the combined characteristics of the other two models, and suggests that calving glaciers are sensitive to imposed thickness changes if basal drag provides most resistance to flow, but stable if most resistance is from lateral drag. Ice shelves can form if reduction of basal drag occurs over a sufficiently long spatial scale. In combination, the new calving criterion and the basal–lateral drag sliding function (model 3) can be used to simulate much of the observed spectrum of behaviour of calving glaciers, and present new opportunities to model ice-sheet response to climate change.

scholarly journals Relationship between tidewater glacier calving velocity and water depth at the calving front

1991 ◽  
Vol 15 ◽  
pp. 115-118 ◽  
Author(s):  
Mauri S. Pelto ◽  
Charles R. Warren
Keyword(s):  
Water Depth ◽  
Reasonable Accuracy ◽  
Ice Streams ◽  
Ice Shelves ◽  
Tidewater Glaciers ◽  
Tidewater Glacier ◽  
Iceberg Calving ◽  
Calving Rate ◽  
The Relationship ◽  
Water Depths

An analysis of the relationship between iceberg calving rates and water depth has been completed for 22 tidewater glaciers. A linear relationship provides reasonable accuracy, with a correlation coefficient of 0.85, for all tidewater glaciers examined, whether they be polar or temperate. The polar glaciers have a slightly lower calving rate for a given water depth. This relationship indicates a lower calving rate for water depths over 50 m than determined by Brown and others (1982). It is based only on glaciers or ice streams and cannot be applied to ice shelves.

scholarly journals Relationship between tidewater glacier calving velocity and water depth at the calving front

1991 ◽  
Vol 15 ◽  
pp. 115-118 ◽  
Author(s):  
Mauri S. Pelto ◽  
Charles R. Warren
Keyword(s):  
Water Depth ◽  
Reasonable Accuracy ◽  
Ice Streams ◽  
Ice Shelves ◽  
Tidewater Glaciers ◽  
Tidewater Glacier ◽  
Iceberg Calving ◽  
Calving Rate ◽  
The Relationship ◽  
Water Depths

An analysis of the relationship between iceberg calving rates and water depth has been completed for 22 tidewater glaciers. A linear relationship provides reasonable accuracy, with a correlation coefficient of 0.85, for all tidewater glaciers examined, whether they be polar or temperate. The polar glaciers have a slightly lower calving rate for a given water depth. This relationship indicates a lower calving rate for water depths over 50 m than determined by Brown and others (1982). It is based only on glaciers or ice streams and cannot be applied to ice shelves.

scholarly journals Upper and lower limits on the stability of calving glaciers from the yield strength envelope of ice

2011 ◽  
Vol 468 (2140) ◽  
pp. 913-931 ◽  
Author(s):  
J. N. Bassis ◽  
C. C. Walker
Keyword(s):  
Yield Strength ◽  
Water Depth ◽  
Shear Failure ◽  
Ice Sheets ◽  
Direct Consequence ◽  
Ice Thickness ◽  
Tightly Coupled ◽  
The Stability ◽  
Induced Changes ◽  
Lower Limits

Observations indicate that substantial changes in the dynamics of marine-terminating ice sheets and glaciers are tightly coupled to calving-induced changes in the terminus position. However, the calving process itself remains poorly understood and is not well parametrized in current numerical ice sheet models. In this study, we address this uncertainty by deriving plausible upper and lower limits for the maximum stable ice thickness at the calving face of marine-terminating glaciers, using two complementary models. The first model assumes that a combination of tensile and shear failure can render the ice cliff near the terminus unstable and/or enable pre-existing crevasses to intersect. A direct consequence of this model is that thick glaciers must terminate in deep water to stabilize the calving front, yielding a predicted maximum ice cliff height that increases with increasing water depth, consistent with observations culled from glaciers in West Greenland, Antarctica, Svalbard and Alaska. The second model considers an analogous lower limit derived by assuming that the ice is already fractured and fractures are lubricated by pore pressure. In this model, a floating ice tongue can only form when the ice entering the terminus region is relatively intact with few pre-existing, deeply penetrating crevasses.

scholarly journals A minimal model of a tidewater glacier

2005 ◽  
Vol 42 ◽  
pp. 1-6 ◽  
Author(s):  
J. Oerlemans ◽  
F.M. Nick
Keyword(s):  
Velocity Field ◽  
Water Depth ◽  
Ice Thickness ◽  
Global Dynamics ◽  
Equilibrium Line Altitude ◽  
Glacier Terminus ◽  
Tidewater Glacier ◽  
Glacier Length ◽  
Parameterized Model ◽  
Calving Rate

AbstractWe propose a simple, highly parameterized model of a tidewater glacier. The mean ice thickness and the ice thickness at the glacier front are parameterized in terms of glacier length and, when the glacier is calving, water depth. We use a linear relation between calving rate and water depth. The change in glacier length is determined by the total change in the mass budget (surface balance and calving flux), but not by the details of the glacier profile and the related velocity field. We show that this may still yield relatively rapid rates of retreat for an idealized bed geometry with a smooth overdeepening. The model is able to simulate the full cycle of ice-free conditions, glacier terminus on land, tidewater glaciers terminus, and backwards. We study two cases: (i) a glacier with a specific balance (accumulation) that is spatially uniform, and (ii) a glacier in a warmer climate with the specific balance being a linear function of altitude. Equilibrium states exhibit a double branching with respect to the climatic forcing (equilibrium-line altitude). One bifurcation is related to the dependence of the calving process on the bed profile; the other bifurcation is due to the height–mass-balance feedback. We discuss the structure of the solution diagram for different values of the calving-rate parameter. The model results are similar to those of Vieli and others (2001), who combined a fairly sophisticated two-dimensional (vertical plane) numerical ice-flow model with the modified flotation criterion suggested by Van der Veen (1996). With regard to the global dynamics of a tidewater glacier, we conclude that the details of the glacier profile or velocity field are less significant than the bed profile and the relation between the water depth and the calving rate.

scholarly journals Interferometric radar observations of Glaciar San Rafael, Chile

1996 ◽  
Vol 42 (141) ◽  
pp. 279-291 ◽  
Author(s):  
Eric Rignot ◽  
Richard Forster ◽  
Bryan Isacks
Keyword(s):  
Flow Direction ◽  
Strain Rates ◽  
Equilibrium Line Altitude ◽  
Band Frequency ◽  
Radar Observations ◽  
Tidewater Glaciers ◽  
Lateral Shearing ◽  
Ice Velocity ◽  
The One ◽  
San Rafael

AbstractInterferometric radar observations of Glaciar San Rafael, Chile, were collected in October 1994 by NASA’s Spaceborne Imaging Radar C (SIR-C) at both L- (24 cm) and C-band frequency (5.6 cm), with vertical transmit and receive polarization. The C-band data did not yield good geophysical products, because the temporal coherence of the signal was significantly reduced alter 24 h. The L-band data were, however, successfully employed to map the surface topography of the icefield with a 10 m uncertainty in height, and measure ice velocity with a precision of 4 mm d−1or 1.4 m a−1. The corresponding error in strain rates is 0.05 a−1at a 30 m horizontal spacing. The one-dimensional interferometric velocities were subsequently converted to horizontal displacements by assuming a flow direction and complemented by feature-tracking results near the calving front. The results provide a comprehensive view of the ice-flow dynamics of Glaciar San Rafael. The glacier has a core of rapid flow, 4.5 km in width and 3.5° in average slope, surrounded by slower-moving ice, not by rock. Ice velocity is 2.6 m d−1or 0.95 km a−1near the equilibrium-line altitude (1200 m), increasing rapidly before the glacier enters the narrower terminal valley, to reach 17.5 md−1or 6.4 k ma−1at the calving front. Strain rates are dominated by lateral shearing at the glacier margins (0.4–0.7 a−1), except for the terminal-valley section, where longitudinal strain rates average close to 1 a−1. This spectacular longitudinal increase in ice velocity in the last few kilometers may be a fundamental feature of tidewater glaciers.

Dynamics of tidewater glaciers: comparison of three models

2006 ◽  
Vol 52 (177) ◽  
pp. 183-190 ◽  
Author(s):  
F.M. Nick ◽  
J. Oerlemans
Keyword(s):  
Water Depth ◽  
Mass Conservation ◽  
Equilibrium States ◽  
The Other ◽  
Tidewater Glaciers ◽  
One Dimensional ◽  
Glacier Terminus ◽  
Tidewater Glacier ◽  
Linear Behaviour ◽  
Calving Rate

AbstractA minimal model of a tidewater glacier based solely on mass conservation is compared with two one-dimensional numerical flowline models, one with the calving rate proportional to water depth, and the other with the flotation criterion as a boundary condition at the glacier terminus. The models were run with two simplified bed geometries and two mass-balance formulations. The models simulate the full cycle of length variations and the equilibrium states for a tidewater glacier. This study shows that the branching of the equilibrium states depends significantly on the bed geometry. The similarity between the results of the three models indicates that if there is a submarine undulation at the terminus of a tidewater glacier, any model in which the frontal ice loss is related to the water depth yields qualitatively the same non-linear behaviour. For large glaciers extending into deep water, the flotation model causes unrealistic behaviour.

scholarly journals Tidewater calving

1996 ◽  
Vol 42 (141) ◽  
pp. 375-385 ◽  
Author(s):  
С.J. Van Der Veen
Keyword(s):  
Water Depth ◽  
Fold Increase ◽  
Actual Rate ◽  
Tidewater Glaciers ◽  
Glacier Terminus ◽  
Tidewater Glacier ◽  
Iceberg Calving ◽  
Speed Up ◽  
Calving Rate ◽  
Subglacial Drainage

AbstractData from Columbia Glacier are used to identify processes that control calving from a temperate tidewater glacier and to re-evaluate models that have been proposed to describe iceberg calving. Since 1981, Columbia Glacier has been retreating rapidly, with an almost seven-fold increase in calving rate from the mid-1970s to 1993. At the same time, the speed of the glacier increased almost as much, so that the actual rate of retreat increased more slowly. According to the commonly accepted model, the calving rate is linearly related to the water depth at the terminus, with retreat of the glacier snout into deeper water, leading to larger calving rates and accelerated retreat. The Columbia Glacier data show that the calving rate is not simply linked to observed quantities such as water depth or stretching rate near the terminus. During the retreat, the thickness at the terminus appears to be linearly correlated with the water depth; at the terminus, the thickness in excess of flotation remained at about 50 m. This suggests that retreat may be initiated when the terminal thickness becomes too small, with the rate of retreat controlled by the rate at which the snout is thinning and by the basal slope. The implication is that the rapid retreat of Columbia Glacier (and other comparable tidewater glaciers) is not the result of an increase in calving as the glacier retreated into deeper water. Instead, the retreat was initiated and maintained by thinning of the glacier. For Columbia Glacier, the continued thinning is probably associated with the increase in glacier speed and retreat may be expected to continue as long as these large speeds are maintained. It is not clear what mechanism may be responsible for the speed-up but the most likely candidate is a change in basal conditions or subglacial drainage. Consequently, the behavior of tidewater glaciers may be controlled by processes acting at the glacier bed rather than by what happens at the glacier terminus.

scholarly journals Calving relation for tidewater glaciers based on detailed stress field analysis

2017 ◽  
Author(s):  
Rémy Mercenier ◽  
Martin P. Lüthi ◽  
Andreas Vieli
Keyword(s):  
Stress State ◽  
Water Level ◽  
Water Depth ◽  
Field Analysis ◽  
Ice Thickness ◽  
Dynamical Process ◽  
Tidewater Glaciers ◽  
Damage Initiation ◽  
Relative Water ◽  
Basal Sliding

Abstract. Ocean terminating glaciers in Arctic regions have undergone rapid dynamic changes in recent years, which have been related to a dramatic increase in calving rates. Iceberg calving is a dynamical process strongly influenced by the geometry at the terminus of tidewater glaciers. We investigate the effect of varying water level, calving front slope and basal sliding on the stress state and flow regime for an idealized grounded ocean-terminating glacier and scale these results with ice thickness and velocity. Results show that water depth and calving front slope strongly affect the stress state while the effect from variations in basal sliding is much smaller. An increased relative water level or a reclining calving front slope strongly decrease the stresses and velocities in the vicinity of the terminus and hence have a stabilizing effect on the calving front. We find that surface stress magnitude and distribution are determined by solely the water depth relative to ice thickness for simple geometries. Based on this scaled relationship for the stress peak at the surface, and assuming a critical stress for damage initiation, we propose a simple and new parametrization for calving rates for grounded tidewater glaciers that is in good agreement with observations.

scholarly journals An observationally validated theory of viscous flow dynamics at the ice-shelf calving front

2012 ◽  
Vol 58 (208) ◽  
pp. 375-387 ◽  
Author(s):  
Richard C.A. Hindmarsh
Keyword(s):  
Analytical Theory ◽  
Ice Shelf ◽  
Ice Streams ◽  
Ice Flow ◽  
Grounding Line ◽  
Interior Flow ◽  
Ice Velocity ◽  
Calving Rate ◽  
The Stability ◽  
Low Sensitivity

AbstractAn analytical theory is developed for ice flow velocity in a boundary layer couplet at the calving front. The theory has simple quantitative characteristics that relate ice front velocity to thickness, strain rate and shelf width, matching one set of empirically derived relationships (Alley and others, 2008) and implying that these relationships predict ice velocity rather than calving rate. The two boundary layers are where longitudinal and transverse flow fields change from the interior flow to patterns consistent with the calving-front stress condition. Numerical simulations confirm the analytical theory. The quantitative predictions of the theory have low sensitivity to unmeasured parameters and to shelf plan aspect ratio, while its robustness arises from its dependence on the scale invariance of the governing equations. The theory provides insights into calving, the stability of ice-shelf calving fronts, the stability of the grounding line of laterally resisted ice streams, and also suggests that the calving front is an instructive dynamical analogue to the grounding line.

scholarly journals Calving relation for tidewater glaciers based on detailed stress field analysis

2018 ◽  
Vol 12 (2) ◽  
pp. 721-739 ◽  
Author(s):  
Rémy Mercenier ◽  
Martin P. Lüthi ◽  
Andreas Vieli
Keyword(s):  
Water Level ◽  
Water Depth ◽  
Field Analysis ◽  
Ice Thickness ◽  
Dynamical Process ◽  
Tidewater Glaciers ◽  
Damage Initiation ◽  
Relative Water ◽  
Basal Sliding ◽  
Iceberg Calving

Abstract. Ocean-terminating glaciers in Arctic regions have undergone rapid dynamic changes in recent years, which have been related to a dramatic increase in calving rates. Iceberg calving is a dynamical process strongly influenced by the geometry at the terminus of tidewater glaciers. We investigate the effect of varying water level, calving front slope and basal sliding on the state of stress and flow regime for an idealized grounded ocean-terminating glacier and scale these results with ice thickness and velocity. Results show that water depth and calving front slope strongly affect the stress state while the effect from spatially uniform variations in basal sliding is much smaller. An increased relative water level or a reclining calving front slope strongly decrease the stresses and velocities in the vicinity of the terminus and hence have a stabilizing effect on the calving front. We find that surface stress magnitude and distribution for simple geometries are determined solely by the water depth relative to ice thickness. Based on this scaled relationship for the stress peak at the surface, and assuming a critical stress for damage initiation, we propose a simple and new parametrization for calving rates for grounded tidewater glaciers that is calibrated with observations.

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