Similitude of ice dynamics against scaling  of geometry and physical parameters

Abstract. The concept of similitude is commonly employed in the fields of fluid dynamics and engineering but rarely used in cryospheric research. Here we apply this method to the problem of ice flow to examine the dynamic similitude of isothermal ice sheets in shallow-shelf approximation against the scaling of their geometry and physical parameters. Carrying out a dimensional analysis of the stress balance we obtain dimensionless numbers that characterize the flow. Requiring that these numbers remain the same under scaling we obtain conditions that relate the geometric scaling factors, the parameters for the ice softness, surface mass balance and basal friction as well as the ice-sheet intrinsic response time to each other. We demonstrate that these scaling laws are the same for both the (two-dimensional) flow-line case and the three-dimensional case. The theoretically predicted ice-sheet scaling behavior agrees with results from numerical simulations that we conduct in flow-line and three-dimensional conceptual setups. We further investigate analytically the implications of geometric scaling of ice sheets for their response time. With this study we provide a framework which, under several assumptions, allows for a fundamental comparison of the ice-dynamic behavior across different scales. It proves to be useful in the design of conceptual numerical model setups and could also be helpful for designing laboratory glacier experiments. The concept might also be applied to real-world systems, e.g., to examine the response times of glaciers, ice streams or ice sheets to climatic perturbations.

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Similitude of ice-sheet dynamics against scaling of geometry and physical parameters

10.5194/tc-2015-226 ◽

2016 ◽

Author(s):

J. Feldmann ◽

A. Levermann

Keyword(s):

Fluid Dynamics ◽

Response Time ◽

Scaling Laws ◽

Flow Line ◽

Ice Sheets ◽

Ice Sheet ◽

Physical Parameters ◽

Dimensionless Numbers ◽

Navier Stokes Equation ◽

Geometric Scaling

Abstract. The concept of similitude is commonly employed in the ﬁelds of ﬂuid dynamics and engineering where scaling laws are derived from the governing equation of ﬂow dynamics, e.g., the Navier-Stokes equation. Here we transfer this method to the problem of ice-sheet ﬂow to examine the dynamic similitude of ice sheets against the scaling of their geometry and physical parameters. Carrying out a dimensional analysis of the stress balance for isothermal ice sheets in shallow-shelf approximation we obtain dimensionless numbers that characterize the ﬂow, similar to the Reynolds or Froude numbers in ﬂuid dynamics. Requiring that these numbers remain constant under scaling we obtain conditions that relate the geometric scaling factors, the parameters for the ice softness, surface mass balance and basal friction as well as the ice-sheet intrinsic response time to each other. We demonstrate that these scaling laws are the same for both the (two-dimensional) ﬂow-line case and the threedimensional case and that they are consistent with ﬂow-line boundary-layer theory. The theoretically predicted ice-sheet scaling behavior agrees with results from numerical simulations that we conduct in ﬂow-line and three-dimensional conceptual setups. In a set of experiments the setup geometry is scaled systematically and the physical parameters are prescribed according to the derived scaling laws. We further investigate analytically the implications of geometric scaling of ice sheets for their response time under constant basal conditions ﬁnding that thicker (thinner) ice sheets have a shorter (longer) response time and that the opposite holds for the horizontal ice-sheet extent. With this study we provide a framework which, under several assumptions, allows for a fundamental comparison of the ice-dynamic behavior across different scales. It proofs to be useful in the design of conceptual model setups but might also be applied to real-world systems, e.g., to examine the response times of glaciers, ice streams or ice sheets to climatic perturbations.

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Ice dynamics and sediment movement: last glacial cycle, Clyde basin, Scotland

Journal of Glaciology ◽

10.3189/2012jog11j207 ◽

2012 ◽

Vol 58 (209) ◽

pp. 487-500 ◽

Cited By ~ 14

Author(s):

Andrew G. Finlayson

Keyword(s):

Three Dimensional ◽

Ice Sheets ◽

Ice Sheet ◽

High Standard ◽

Glacial Cycle ◽

Ice Dynamics ◽

Sediment Distribution ◽

Alternative Approach ◽

Borehole Logs ◽

Sediment Mobilization

AbstractThe nature and behaviour of sediment beneath glaciers influences how they flow and respond to changing environmental conditions. The difficulty of accessing the bed of current glaciers is a key constraint to studying the processes involved. This paper explores an alternative approach by relating sediments under the beds of former mid-latitude ice sheets to changing ice behaviour during a glacial cycle. The paper focuses on the partly marine-based Pleistocene British-Irish ice sheet in the Clyde basin, Scotland. A three-dimensional computation of subsurface glacial sediment distribution is derived from 1260 borehole logs. Sediment distribution is linked to an empirically based reconstruction of ice-sheet evolution, permitting identification of distinctive phases of sedimentation. Maximum sediment mobilization and till deposition (~0.04ma_1) occurred during ice advance into the basin from adjacent uplands. Transport distances were generally short. Subglacial processes were influenced locally by the relative stiffness of pre-existing sediments, the permeability of the sub-till lithology, and topography; the resulting mean till thickness is 7.7 m with a high standard deviation of 7.0 m. In places, focused till deposition sealed pre-existing permeable substrates, promoting lower effective pressures. Sediment remobilization by meltwater was a key process as ice margins retreated through the, basin.

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The response of large ice sheets to climatic change

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.1992.0143 ◽

1992 ◽

Vol 338 (1285) ◽

pp. 235-242 ◽

Cited By ~ 23

Keyword(s):

Mass Balance ◽

Sea Level ◽

Ice Sheets ◽

Ice Sheet ◽

Sea Level Change ◽

Mixing Ratio ◽

Ice Dynamics ◽

Environmental Models ◽

Level Change ◽

The Antarctic

The prediction of short-term (100 year) changes in the mass balance of ice sheets and longer-term (1000 years) variations in their ice volumes is important for a range of climatic and environmental models. The Antarctic ice sheet contains between 24 M km 3 and 29 M km 3 of ice, equivalent to a eustatic sea level change of between 60m and 72m. The annual surface accumulation is estimated to be of the order of 2200 Gtonnes, equivalent to a sea level change of 6 mm a -1 . Analysis of the present-day accumulation regime of Antarctica indicates that about 25% ( ca. 500 Gt a -1 ) of snowfall occurs in the Antarctic Peninsula region with an area of only 6.8% of the continent. To date most models have focused upon solving predictive algorithms for the climate-sensitivity of the ice sheet, and assume: (i) surface mass balance is equivalent to accumulation (i.e. no melting, evaporation or deflation); (ii) percentage change in accumulation is proportional to change in saturation mixing ratio above the surface inversion layer; and (iii) there is a linear relation between mean annual surface air tem perature and saturation mixing ratio. For the A ntarctic Peninsula with mountainous terrain containing ice caps, outlet glaciers, valley glaciers and ice shelves, where there can be significant ablation at low levels and distinct climatic regimes, models of the climate response must be more complex. In addition, owing to the high accumulation and flow rates, even short- to medium -term predictions must take account of ice dynamics. Relationships are derived for the mass balance sensitivity and, using a model developed by Hindmarsh, the transient effects of ice dynamics are estimated. It is suggested that for a 2°C rise in mean annual surface tem perature over 40 years, ablation in the A ntarctic Peninsula region would contribute at least 1.0 mm to sea level rise, offsetting the fall of 0.5 mm contributed by increased accum ulation.

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Marine Ice Sheet Instability and Ice Shelf Buttressing Influenced Deglaciation of the Minch Ice Stream, Northwest Scotland

10.5194/tc-2018-116 ◽

2018 ◽

Cited By ~ 1

Author(s):

Niall Gandy ◽

Lauren J. Gregoire ◽

Jeremy C. Ely ◽

Christopher D. Clark ◽

David M. Hodgson ◽

...

Keyword(s):

Ice Sheets ◽

Ice Sheet ◽

Last Deglaciation ◽

Ice Shelf ◽

Dynamical Processes ◽

Ice Dynamics ◽

Surface Mass ◽

Ice Shelves ◽

Ice Stream ◽

The Last Deglaciation

Abstract. Uncertainties in future sea level projections are dominated by our limited understanding of the dynamical processes that control instabilities of marine ice sheets. A valuable case to examine these processes is the last deglaciation of the British-Irish Ice Sheet. The Minch Ice Stream, which drained a large proportion of ice from the northwest sector of the British-Irish Ice Sheet during the last deglaciation, is well constrained, with abundant empirical data which could be used to inform, validate and analyse numerical ice sheet simulations. We use BISICLES, a higher-order ice sheet model, to examine the dynamical processes that controlled the retreat of the Minch Ice Stream. We simulate retreat from the shelf edge under constant "warm" surface mass balance and subshelf melt, to isolate the role of internal ice dynamics from external forcings. The model simulates a slowdown of retreat as the ice stream becomes laterally confined at a "pinning-point" between mainland Scotland and the Isle of Lewis. At this stage, the presence of ice shelves became a major control on deglaciation, providing buttressing to upstream ice. Subsequently, the presence of a reverse slope inside the Minch Strait produces an acceleration in retreat, leading to a "collapsed" state, even when the climate returns to the initial "cold" conditions. Our simulations demonstrate the importance of the Marine Ice Sheet Instability and ice shelf buttressing during the deglaciation of parts of the British-Irish Ice Sheet. Thus, geological data could be used to constrain these processes in ice sheet models used for projecting the future of our contemporary ice sheets.

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Self-consistency of the regolith hypothesis for the mid-Pleistocene Transition

10.5194/egusphere-egu21-13787 ◽

2021 ◽

Author(s):

Matthew Drew ◽

Lev Tarasov

Keyword(s):

Sediment Transport ◽

State Of The Art ◽

Flow Line ◽

Ice Sheets ◽

Balance Model ◽

Clear Understanding ◽

Ice Dynamics ◽

Ice Volume ◽

Systems Model ◽

Fully Coupled

Is the regolith hypothesis consistent with the physics of glacial removal of mechanically weak surface material?&#160;&#160;The&#160; mid-Pleistocene transition (MPT) from small 40 kyr glacial cycles to large, abruptly terminating 100 kyr ones represents a major climate system reorganization for which a clear understanding is lacking. A leading mechanism for this transition is a stabilization of ice sheets due to a shift to higher friction substrate. The Pleistocene saw the removal of deformable regolith -- laying bare hard higher-friction bedrock that would help preserve regional ice during warm interstadials. This is the regolith hypothesis.&#160;&#160;The removal of regolith by Pleistocene ice sheets remains poorly constrained. To date, only models with a forced change in area of regolith cover or 1D flow line models with simplistic sediment transport have been used to probe the role of regolith in the MPT. It is therefore unclear if the appropriate amount of regolith removal can occur within the time-frame of the MPT.&#160;To properly test the hypothesis, at least three components are required: capable model, observational constraint, and a probe of uncertainties. A capable model must explicitly represent relevant processes in a fully coupled self-consistent manner. We have therefore configured a state of the art 3D glacial systems model (GSM). The GSM incorporates a state-of-the-art fully coupled sediment production/transport model, subglacial hydrology, visco-elastic glacial isostatic adjustment, 3D thermomechanically coupled hybrid shallow ice/shallow shelf ice dynamics, and internal climate solution from an energy balance model. The model generates sediment by quarrying and abrasion, and both subglacial and englacial sediment transport. The subglacial hydrology model employs a linked-cavity system with a flux based switch to tunnel drainage, giving dynamic effective pressure needed for realistic sediment and sliding processes. The coupled model is driven only by prescribed atmospheric CO2 and orbitally derived insolation.&#160;The required observational constraints include present-day regolith distribution and inferred Pleistocene ice volume from proxy records.&#160;The final component is&#160; a large ensemble of full Pleistocene simulations that probe both initial regolith distribution uncertainties and model parametric uncertainties. We present the results of such an ensemble, examining both rates of computed regolith removal and changes in ice volume cycling across the MPT interval.

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8. Glaciers of the past

Glaciation: A Very Short Introduction ◽

10.1093/actrade/9780198745853.003.0008 ◽

2018 ◽

pp. 146-152

Author(s):

David J. A. Evans

Keyword(s):

Numerical Models ◽

Ice Core ◽

Three Dimensional ◽

Ice Sheets ◽

Ice Sheet ◽

Aerial Imagery ◽

The Past ◽

Glacial Landforms

To reconstruct the former extent and dynamics of ice sheets and glaciers requires a knowledge of process-form relationships that goes beyond individual landform types. Instead, glacial geomorphologists need to analyse large areas of glaciated terrain in a more holistic way, combining the whole range of glacial landforms and sediments to reconstruct glacier systems of the past, a subject now known as palaeoglaciology. ‘Glaciers of the past’ explains how the combination of aerial imagery and landform analysis is used in palaeoglaciological reconstruction. Increasingly powerful computers are making it possible to compile sophisticated numerical models that use our knowledge of glaciological processes and ice-core-derived palaeoclimate data to create three-dimensional glacier and ice sheet reconstructions.

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Dynamic influence of pinning points on marine ice-sheet stability: a numerical study in Dronning Maud Land, East Antarctica

The Cryosphere ◽

10.5194/tc-10-2623-2016 ◽

2016 ◽

Vol 10 (6) ◽

pp. 2623-2635 ◽

Cited By ~ 28

Author(s):

Lionel Favier ◽

Frank Pattyn ◽

Sophie Berger ◽

Reinhard Drews

Keyword(s):

Data Assimilation ◽

Sea Level ◽

Ice Sheets ◽

Ice Sheet ◽

East Antarctica ◽

Ice Shelf ◽

Ice Dynamics ◽

Outlet Glacier ◽

Ice Shelves ◽

Dronning Maud Land

Abstract. The East Antarctic ice sheet is likely more stable than its West Antarctic counterpart because its bed is largely lying above sea level. However, the ice sheet in Dronning Maud Land, East Antarctica, contains marine sectors that are in contact with the ocean through overdeepened marine basins interspersed by grounded ice promontories and ice rises, pinning and stabilising the ice shelves. In this paper, we use the ice-sheet model BISICLES to investigate the effect of sub-ice-shelf melting, using a series of scenarios compliant with current values, on the ice-dynamic stability of the outlet glaciers between the Lazarev and Roi Baudouin ice shelves over the next millennium. Overall, the sub-ice-shelf melting substantially impacts the sea-level contribution. Locally, we predict a short-term rapid grounding-line retreat of the overdeepened outlet glacier Hansenbreen, which further induces the transition of the bordering ice promontories into ice rises. Furthermore, our analysis demonstrated that the onset of the marine ice-sheet retreat and subsequent promontory transition into ice rise is controlled by small pinning points, mostly uncharted in pan-Antarctic datasets. Pinning points have a twofold impact on marine ice sheets. They decrease the ice discharge by buttressing effect, and they play a crucial role in initialising marine ice sheets through data assimilation, leading to errors in ice-shelf rheology when omitted. Our results show that unpinning increases the sea-level rise by 10 %, while omitting the same pinning point in data assimilation decreases it by 10 %, but the more striking effect is in the promontory transition time, advanced by two centuries for unpinning and delayed by almost half a millennium when the pinning point is missing in data assimilation. Pinning points exert a subtle influence on ice dynamics at the kilometre scale, which calls for a better knowledge of the Antarctic margins.

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A three-dimensional calving model: numerical experiments on Johnsons Glacier, Livingston Island, Antarctica

Journal of Glaciology ◽

10.3189/002214310791968539 ◽

2010 ◽

Vol 56 (196) ◽

pp. 200-214 ◽

Cited By ~ 43

Author(s):

Jaime Otero ◽

Francisco J. Navarro ◽

Carlos Martin ◽

Maria L. Cuadrado ◽

Maria I. Corcuera

Keyword(s):

Three Dimensional ◽

Ice Sheets ◽

Prognostic Models ◽

Current Position ◽

Polar Ice ◽

Ice Dynamics ◽

Ice Shelves ◽

Tidewater Glaciers ◽

Livingston Island ◽

Polar Ice Sheets

AbstractCalving from tidewater glaciers and ice shelves accounts for around half the mass loss from both polar ice sheets, yet the process is not well represented in prognostic models of ice dynamics. Benn and others proposed a calving criterion appropriate for both grounded and floating glacier tongues or ice shelves, based on the penetration depth of transverse crevasses near the calving front, computed using Nye’s formula. The criterion is readily incorporated into glacier and ice-sheet models, but has not been fully validated with observations. We apply a three-dimensional extension of Benn and others’ criterion, incorporated into a full-Stokes model of glacier dynamics, to estimate the current position of the calving front of Johnsons Glacier, Antarctica. We find that two improvements to the original model are necessary to accurately reproduce the observed calving front: (1) computation of the tensile deviatoric stress opening the crevasse using the full-stress solution and (2) consideration of such a tensile stress as a function of depth. Our modelling results also suggest that Johnsons Glacier has a polythermal structure, rather than the temperate structure suggested by earlier studies.

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Deep and extensive meltwater system beneath the former Eurasian Ice Sheet in the Kara Sea

Geology ◽

10.1130/g46968.1 ◽

2019 ◽

Vol 48 (2) ◽

pp. 179-183 ◽

Cited By ~ 1

Author(s):

Aleksandr Montelli ◽

Julian A. Dowdeswell ◽

Anastasiya Pirogova ◽

Yana Terekhina ◽

Mikhail Tokarev ◽

...

Keyword(s):

Ocean Circulation ◽

Late Quaternary ◽

Thermal Structure ◽

Three Dimensional ◽

Ice Sheet ◽

Kara Sea ◽

Yamal Peninsula ◽

Arctic Seas ◽

Ice Dynamics ◽

Eastern Margin

Abstract The Eurasian ice sheet extended across the Barents and Kara Seas during the late Quaternary, yet evidence on past ice dynamics and thermal structure across its huge eastern periphery remains largely unknown. Here we use three-dimensional seismic data sets covering ∼4500 km2 of the Kara Sea west of Yamal Peninsula, Siberia (71°–73°N), to identify, for the first time in the Russian Arctic seas, several buried generations of vast subglacial tunnel valley networks. Individual valleys are up to 50 km long and are incised as much as 400 m deep; among the largest tunnel valleys ever reported. This discovery represents the first documentation of an extensively warm-based eastern margin of the Eurasian ice sheet during the Quaternary glaciations. The presence of major subglacial channel networks on the shallow shelf, with no evidence of ice streaming, suggests that significant meltwater discharge and subsequent freshwater forcing of ocean circulation may be long-lived rather than catastrophic, occurring during the latest stages of deglaciation in areas where the ice sheet flows slowly and is grounded largely above sea level. Furthermore, the first account of an extensive hydrological network across large areas of the Kara Sea provides important empirical evidence for active subglacial hydrological processes that should be considered in future numerical modeling of the eastern margin of the Quaternary Eurasian ice sheet.

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Hydrodynamic Model Of Glaciers and Ice Sheets Interacted With Ocean

Annals of Glaciology ◽

10.3189/s0260305500009150 ◽

1990 ◽

Vol 14 ◽

pp. 347-347

Author(s):

V.L. Mazo

Keyword(s):

Shear Stress ◽

Hydrodynamic Model ◽

Evolution Equations ◽

Three Dimensional ◽

Ice Sheets ◽

Ice Sheet ◽

Longitudinal Stress ◽

First Order ◽

Longwave Approximation ◽

Different Parts

Tidewater glaciers and large ice sheets, e.g. the Antarctic ice sheet and a late-Würm Arctic ice sheet, are complex but single dynamic systems composed of terrestrial, marine and floating parts. Morphology and dynamics of the different parts are different. The terrestrial parts are convex and their dynamics are controlled by shear stress only (the longitudinal stress is zero); the floating parts are concave and their dynamics are controlled by longitudinal stress only (the shear stress is zero). To connect the different parts we should consider transitional zones where shear and longitudinal stresses are comparable.To describe glacier and ice-sheet dynamics, longwave approximation of the first order is used. In this approximation it is impossible to connect terrestrial and floating parts dynamically, only morphologically and kinematically. It means that the first-order longwave approximation is not sufficient.If the transitional zone between the terrestrial and floating parts is long in comparison to ice thickness (in hydrodynamics the term “weak” is used) we can do the next step in the longwave approximation to describe the single dynamical system consisting of the terrestrial and floating parts and the weak transitional zones (ice streams). It is a purely hydrodynamical approach to the problem without ad hoc hypothesis.The presented model is a non-stationary three-dimensional hydrodynamic model of glaciers and ice sheets interacted with ocean, involving the conditions of ice continuity and dynamic equilibrium, ice rheology, and boundary conditions on the free surface (dynamic and kinematic) and on the bed (ice freezing or sliding). Longwave approximation is used to reduce the three-dimensional model to a two-dimensional one. The latter consists of (1) evolution equations for grounded and floating parts and weak transitional zones; (2) boundary conditions on the fronts (e.g. the conditions of calving); (3) equations governing the junctions of the parts (the most important junction is the grounded line) with the conditions connecting the evolution equations.

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