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.

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 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 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 The retreat of a tidewater glacier: observations and model calculations on Hansbreen, Spitsbergen

2002 ◽  
Vol 48 (163) ◽  
pp. 592-600 ◽  
Author(s):  
Andreas Vieli ◽  
Jacek Jania ◽  
Lezek Kolondra
Keyword(s):  
Direct Response ◽  
Critical Height ◽  
Time Step ◽  
Model Calculations ◽  
Tidewater Glaciers ◽  
Water Line ◽  
Glacier Terminus ◽  
Front Position ◽  
Tidewater Glacier ◽  
Calving Rate

AbstractBased on observations and model calculations, the retreat over the last two decades of Hansbreen, a tidewater glacier in southern Spitsbergen, Svalbard, is investigated. The observations of the calving-front position between 1982 and 1998 show an abrupt retreat in 1990, which is suggested to be related to a depression in the glacier bed. The observed seasonal variations of the front position are mainly due to variations of the calving rate. The observations of Hansbreen further indicate that during periods of slow front-position changes, melting at the water-line may play an important role in triggering the process of calving. The evolution of Hansbreen between 1982 and 1998 is simulated with a numerical model for the dynamics of tidewater glaciers. Using a flotation criterion for calving in which for each time-step the part of the glacier terminus which is below a critical height above buoyancy is removed, we are able to reproduce the observed rapid retreat of Hansbreen through the depression in the glacier bed. From the observations and model calculations, we conclude that the rapid retreat is mainly an effect of basal topography in the terminus region and not a direct response to a change in mass balance.

scholarly journals Modelling the mass budget and future evolution of Tunabreen, central Spitsbergen

2021 ◽  
Author(s):  
Johannes Oerlemans ◽  
Jack Kohler ◽  
Adrian Luckman
Keyword(s):  
Response Times ◽  
Equilibrium Line Altitude ◽  
Future Evolution ◽  
State Response ◽  
The Past ◽  
Glacier Length ◽  
Model Geometry ◽  
Calving Rate ◽  
Meteorological Observations

Abstract. Tunabreen is a 26-km long tidewater glacier. It is the most frequently surging glacier in Svalbard, with four documented surges in the past hundred years. We have modelled the evolution of this glacier with a Minimal Glacier Model (MGM), in which ice mechanics, calving and surging are parameterized. The model geometry consists of a flow band to which three tributaries supply mass. The calving rate is set to the mean observed value for the period 2012–2019, and kept constant. For the past 120 years, a smooth Equilibrium Line Altitude (ELA) history is reconstructed by finding the best possible match between observed and simulated glacier length. There is a modest correlation between this ELA history and meteorological observations from Longyearbyen. The simulated glacier retreat is in good agreement with observations. Runs with and without surging show that the effect of surging on the long term glacier evolution is limited. Due to the low surface slope and associated strong height -mass balance feedback, Tunabreen is very sensitive to changes in ELA. For a constant future ELA equal to the reconstructed value for 2020, the glacier front will retreat by 8 km during the coming hundred years. For an increase of the ELA of 2 m per year, the retreat is projected to be 13 km and Tunabreen becomes a land-based glacier around 2100. The calving rate is an important parameter: increasing its value by 50 % has about the same effect as a 50 m increase in the ELA, the corresponding equilibrium glacier length being 18 km (as compared to 25.8 km in the reference state). Response times vary from 150 to 400 years, depending on the forcing and on the state of the glacier (tidewater or land-based).

scholarly journals Modelling the late Holocene and future evolution of Monacobreen, northern Spitsbergen

2018 ◽  
Vol 12 (9) ◽  
pp. 3001-3015 ◽  
Author(s):  
Johannes Oerlemans
Keyword(s):  
Late Holocene ◽  
Meteorological Data ◽  
Ice Age ◽  
Future Climate Change ◽  
Equilibrium Line Altitude ◽  
Climatic Forcing ◽  
Future Evolution ◽  
Front Position ◽  
Tidewater Glacier ◽  
Glacier Length

Abstract. Monacobreen is a 40 km long surge-type tidewater glacier in northern Spitsbergen. During 1991–1997 Monacobreen surged and advanced by about 2 km, but the front did not reach the maximum Little Ice Age (LIA) stand. Since 1997 the glacier front is retreating at a fast rate (∼125 m a−1). The questions addressed in this study are as follows: (1) Can the late Holocene behaviour of Monacobreen be understood in terms of climatic forcing?, and (2) What will be the likely evolution of this glacier for different scenarios of future climate change? Monacobreen is modelled with a minimal glacier model, including a parameterization of the calving process as well as the effect of surges. The model is driven by an equilibrium-line altitude (ELA) history derived from lake sediments of a nearby glacier catchment in combination with meteorological data from 1899 onwards. The simulated glacier length is in good agreement with the observations: the maximum LIA stand, the front position at the end of the surge, and the 2.5 km retreat after the surge (1997–2016) are well reproduced (the mean difference between observed and simulated glacier length being 6 % when scaled with the total retreat during 1900–2016). The effect of surging is limited. Directly after a surge the initiated mass balance perturbation due to a lower mean surface elevation is about -0.13mw.e.a-1, which only has a small effect on the long-term evolution of the glacier. The simulation suggests that the major growth of Monacobreen after the Holocene climatic optimum started around 1500 BCE. Monacobreen became a tidewater glacier around 500 BCE and reached a size comparable to the present state around 500 CE. For the mid-B2 scenario (IPCC, 2013), which corresponds to a ∼2ma-1 rise of the ELA, the model predicts a volume loss of 20 % to 30 % by the year 2100 (relative to the 2017 volume). For a ∼4ma-1 rise in the ELA this is 30 % to 40 %. However, much of the response to 21st century warming will still come after 2100.

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 Application of a minimal glacier model to Hansbreen, Spitsbergen

2010 ◽  
Vol 4 (3) ◽  
pp. 949-979
Author(s):  
J. Oerlemans ◽  
J. Jania ◽  
L. Kolondra
Keyword(s):  
Ice Age ◽  
Change Scenario ◽  
Main Stream ◽  
Global Dynamics ◽  
Equilibrium Line Altitude ◽  
Climate History ◽  
Glacier Terminus ◽  
Holocene Climatic Optimum ◽  
Wide Range ◽  
Climatic Optimum

Abstract. Hansbreen is a well studied tidewater glacier in the southwestern part of Spitsbergen, currently about 16 km long. Since the end of the 19th century it has been retreating over a distance of 2.7 km. In this paper the global dynamics of Hansbreen are studied with a minimal glacier model, in which the ice mechanics are strongly parameterised and a simple law for iceberg calving is used. The model is calibrated by reconstructing a climate history in such a way that observed and simulated glacier length match. In addition, the calving law is tuned to reproduce the observed mean calving flux for the period 2000–2008. Equilibrium states are studied for a wide range of values of the equilibrium line altitude. The dynamics of the glacier are strongly nonlinear. The height-mass balance feedback and the water depth – calving flux feedback give rise to cusp catastrophes in the system. For the present climatic conditions Hansbreen cannot survive. Depending on the imposed climate change scenario, in AD 2100 Hansbreen is predicted to have a length between 10 and 12 km. The corresponding decrease in ice volume (relative to the volume in AD 2000) is 45 to 65%. Finally the late-Holocene history of Hansbreen is considered. We quote evidence from dated peat samples that Hansbreen did not exist during the Holocene Climatic Optimum. We speculate that at the end of the mid-Holocene Climatic Optimum Hansbreen could advance because the glacier bed was at least 50 m higher than today, and because the tributary glaciers on the western side may have supplied a significant amount of mass to the main stream. The excavation of the overdeepening and the formation of the shoal at the glacier terminus probably took place during the Little Ice Age.

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