scholarly journals A Bayesian ice thickness estimation model for large-scale applications

2019 ◽  
Vol 66 (255) ◽  
pp. 137-152
Author(s):  
Mauro A. Werder ◽  
Matthias Huss ◽  
Frank Paul ◽  
Amaury Dehecq ◽  
Daniel Farinotti
Keyword(s):  
Large Scale ◽  
Flow Line ◽  
Forward Model ◽  
Ice Thickness ◽  
Estimation Model ◽  
Mountain Glacier ◽  
Ice Flow ◽  
Thickness Estimation ◽  
Surface Ice ◽  
Thickness Measurements

AbstractAccurate estimations of ice thickness and volume are indispensable for ice flow modelling, hydrological forecasts and sea-level rise projections. We present a new ice thickness estimation model based on a mass-conserving forward model and a Bayesian inversion scheme. The forward model calculates flux in an elevation-band flow-line model, and translates this into ice thickness and surface ice speed using a shallow ice formulation. Both ice thickness and speed are then extrapolated to the map plane. The model assimilates observations of ice thickness and speed using a Bayesian scheme implemented with a Markov chain Monte Carlo method, which calculates estimates of ice thickness and their error. We illustrate the model's capabilities by applying it to a mountain glacier, validate the model using 733 glaciers from four regions with ice thickness measurements, and demonstrate that the model can be used for large-scale studies by fitting it to over 30 000 glaciers from five regions. The results show that the model performs best when a few thickness observations are available; that the proposed scheme by which parameter-knowledge from a set of glaciers is transferred to others works but has room for improvements; and that the inferred regional ice volumes are consistent with recent estimates.

BITE, the Bayesian Ice Thickness Estimation model

2020 ◽  
Author(s):  
Mauro Werder ◽  
Matthias Huss ◽  
Frank Paul ◽  
Amaury Dehecq ◽  
Daniel Farinotti
Keyword(s):  
Large Scale ◽  
Flow Line ◽  
Forward Model ◽  
Ice Thickness ◽  
Estimation Model ◽  
Mountain Glacier ◽  
Ice Flow ◽  
Thickness Estimation ◽  
Surface Ice ◽  
Thickness Measurements

<p>Accurate estimations of ice thickness and volume are indispensable for ice flow modelling, hydrological forecasts and sea-level rise projections. We present BITE, a new ice thickness estimation model based on a mass-conserving forward model and a Bayesian inversion scheme. The forward model calculates flux in an elevation-band flow-line model, and translates this into ice thickness and surface ice speed using a shallow ice formulation. Both ice thickness and speed are then extrapolated to the map plane. The model assimilates observations of ice thickness and speed using a Bayesian scheme implemented with a Markov chain Monte Carlo method, which calculates estimates of ice thickness and their error. We illustrate the model's capabilities by applying it to a mountain glacier, validate the model using 733 glaciers from four regions with ice thickness measurements, and demonstrate that the model can be used for large-scale studies by fitting it to over 30 000 glaciers from five regions. The results show that the model performs best when a few thickness observations are available; that the proposed scheme by which parameter-knowledge from a set of glaciers is transferred to others works but has room for improvements; and that the inferred regional ice volumes are consistent with recent estimates.</p>

scholarly journals Ice Flow Along AN Iagp Flow Line, Wilkes Land, Antarctica (Abstract only)

1982 ◽  
Vol 3 ◽  
pp. 346 ◽  
Author(s):  
N.W. Young ◽  
D. SheehY ◽  
T. Hamley
Keyword(s):  
Strain Rate ◽  
Large Scale ◽  
Flow Line ◽  
Accumulation Rate ◽  
Surface Profile ◽  
Ice Thickness ◽  
Shear Strain Rate ◽  
Surface Slope ◽  
Ice Flow ◽  
Wilkes Land

Trilateration and single line surveys have been made to about 900 km inland of Casey, Wilkes Land, to measure surface elevation, ice thickness, horizontal velocity, and other parameters. On the large scale the velocity U increases smoothly from 8 m a−1, 800 km inland, to 280 m a−1 inland of the fast outlet streams. This increase in velocity is associated with a corresponding increase in the large-scale smoothed (over about 30 ice thicknesses) basal shear stress τb from 0.4 to 1.5 bar. The mean shear strain-rate through the ice sheet U/Z = kτb4 , where Z is the ice thickness (range 4 500 to 1 700 m). At scales of one to several ice thicknesses large variations occur in surface slope and ice thickness without proportionally large velocity variations, because of the effect of the longitudinal stress. Detailed measurements made over a 30 km section indicated that the surface longitudinal strain-rate gradient varied from -1.7 to +1.3×l0−6 a−1 m−1 along with variations in surface slope of from -3.5 to +1.5%. A multilayer model, based on the solution of the biharmonic equation for the stream function, was used in a study of the ice flow associated with these surface undulations. Given the bedrock topography and large-scale flow parameters, the model closely predicted the measured surface profile when the variation of the surface accumulation rate over an undulation was also considered.

scholarly journals Ice Flow Leading to the Deep Core Hole at Dye 3, Greenland

1984 ◽  
Vol 5 ◽  
pp. 185-190 ◽  
Author(s):  
I. M. Whillans ◽  
K. C. Jezek ◽  
A. R. Drew ◽  
N. Gundestrup
Keyword(s):  
Flow Line ◽  
Surface Velocity ◽  
Surface Pattern ◽  
Ice Thickness ◽  
Surface Slope ◽  
Core Hole ◽  
Lateral Velocity ◽  
Ice Flow ◽  
The Core ◽  
Surface Ice

Detailed studies of the last 20 km of the flow-line leading to the core hole at Dye 3 Greenland, provide a description of ice flow over and around basal hills. The surface pattern is very simple. Velocity vectors are nearly parallel to one another and the largest variations in velocity are speed changes along the direction of flow. The surface elevation is stepped and the speed is faster than average where the surface slope is steepest. These positions correspond to basal highs, and the surface velocity increases as expected, based on the decrease in ice thickness, which indicates that most of the ice thickness must vary in velocity as does surface ice. Further support for this comes from the form of an internal radio-reflecting layer, which, in general, has the same shape as the bed but with much reduced relief. The damping of the relief is the same both along and across the flowline, suggesting that lateral velocity fluctuations are not important and that flow around and between obstacles is not well developed at the surface or at depth. At two sites, however, the internal layer does not match the bed and at one of these there must be important third-dimensional flow at depth.

scholarly journals Ice Flow Leading to the Deep Core Hole at Dye 3, Greenland

1984 ◽  
Vol 5 ◽  
pp. 185-190 ◽  
Author(s):  
I. M. Whillans ◽  
K. C. Jezek ◽  
A. R. Drew ◽  
N. Gundestrup
Keyword(s):  
Flow Line ◽  
Surface Velocity ◽  
Surface Pattern ◽  
Ice Thickness ◽  
Surface Slope ◽  
Core Hole ◽  
Lateral Velocity ◽  
Ice Flow ◽  
The Core ◽  
Surface Ice

Detailed studies of the last 20 km of the flow-line leading to the core hole at Dye 3 Greenland, provide a description of ice flow over and around basal hills. The surface pattern is very simple. Velocity vectors are nearly parallel to one another and the largest variations in velocity are speed changes along the direction of flow. The surface elevation is stepped and the speed is faster than average where the surface slope is steepest. These positions correspond to basal highs, and the surface velocity increases as expected, based on the decrease in ice thickness, which indicates that most of the ice thickness must vary in velocity as does surface ice. Further support for this comes from the form of an internal radio-reflecting layer, which, in general, has the same shape as the bed but with much reduced relief. The damping of the relief is the same both along and across the flowline, suggesting that lateral velocity fluctuations are not important and that flow around and between obstacles is not well developed at the surface or at depth. At two sites, however, the internal layer does not match the bed and at one of these there must be important third-dimensional flow at depth.

scholarly journals Ice Flow Along AN Iagp Flow Line, Wilkes Land, Antarctica (Abstract only)

1982 ◽  
Vol 3 ◽  
pp. 346-346
Author(s):  
N.W. Young ◽  
D. SheehY ◽  
T. Hamley
Keyword(s):  
Strain Rate ◽  
Large Scale ◽  
Flow Line ◽  
Accumulation Rate ◽  
Surface Profile ◽  
Ice Thickness ◽  
Shear Strain Rate ◽  
Surface Slope ◽  
Ice Flow ◽  
Wilkes Land

Trilateration and single line surveys have been made to about 900 km inland of Casey, Wilkes Land, to measure surface elevation, ice thickness, horizontal velocity, and other parameters. On the large scale the velocity U increases smoothly from 8 m a−1, 800 km inland, to 280 m a−1 inland of the fast outlet streams. This increase in velocity is associated with a corresponding increase in the large-scale smoothed (over about 30 ice thicknesses) basal shear stress τb from 0.4 to 1.5 bar. The mean shear strain-rate through the ice sheet U/Z = kτb4, where Z is the ice thickness (range 4 500 to 1 700 m).At scales of one to several ice thicknesses large variations occur in surface slope and ice thickness without proportionally large velocity variations, because of the effect of the longitudinal stress. Detailed measurements made over a 30 km section indicated that the surface longitudinal strain-rate gradient varied from -1.7 to +1.3×l0−6 a−1 m−1 along with variations in surface slope of from -3.5 to +1.5%.A multilayer model, based on the solution of the biharmonic equation for the stream function, was used in a study of the ice flow associated with these surface undulations. Given the bedrock topography and large-scale flow parameters, the model closely predicted the measured surface profile when the variation of the surface accumulation rate over an undulation was also considered.

scholarly journals Implementing an empirical scalar constitutive relation for ice with flow-induced polycrystalline anisotropy in large-scale ice sheet models

2018 ◽  
Vol 12 (3) ◽  
pp. 1047-1067 ◽  
Author(s):  
Felicity S. Graham ◽  
Mathieu Morlighem ◽  
Roland C. Warner ◽  
Adam Treverrow
Keyword(s):  
Constitutive Relation ◽  
Enhancement Factor ◽  
Large Scale ◽  
Flow Line ◽  
Ice Sheet ◽  
Computationally Efficient ◽  
Ice Shelf ◽  
Stress Regime ◽  
Ice Flow ◽  
Polycrystalline Ice

Abstract. The microstructure of polycrystalline ice evolves under prolonged deformation, leading to anisotropic patterns of crystal orientations. The response of this material to applied stresses is not adequately described by the ice flow relation most commonly used in large-scale ice sheet models – the Glen flow relation. We present a preliminary assessment of the implementation in the Ice Sheet System Model (ISSM) of a computationally efficient, empirical, scalar, constitutive relation which addresses the influence of the dynamically steady-state flow-compatible induced anisotropic crystal orientation patterns that develop when ice is subjected to the same stress regime for a prolonged period – sometimes termed tertiary flow. We call this the ESTAR flow relation. The effect on ice flow dynamics is investigated by comparing idealised simulations using ESTAR and Glen flow relations, where we include in the latter an overall flow enhancement factor. For an idealised embayed ice shelf, the Glen flow relation overestimates velocities by up to 17 % when using an enhancement factor equivalent to the maximum value prescribed in the ESTAR relation. Importantly, no single Glen enhancement factor can accurately capture the spatial variations in flow across the ice shelf generated by the ESTAR flow relation. For flow line studies of idealised grounded flow over varying topography or variable basal friction – both scenarios dominated at depth by bed-parallel shear – the differences between simulated velocities using ESTAR and Glen flow relations depend on the value of the enhancement factor used to calibrate the Glen flow relation. These results demonstrate the importance of describing the deformation of anisotropic ice in a physically realistic manner, and have implications for simulations of ice sheet evolution used to reconstruct paleo-ice sheet extent and predict future ice sheet contributions to sea level.

scholarly journals The stability of a viscous till sheet coupled with ice flow, considered at wavelengths less than the ice thickness

1998 ◽  
Vol 44 (147) ◽  
pp. 285-292 ◽  
Author(s):  
Richard C. A. Hindmarsh
Keyword(s):  
Large Scale ◽  
Flow Instability ◽  
Ice Thickness ◽  
Ice Flow ◽  
Perturbation Amplitude ◽  
Sediment Flow ◽  
Viscous Models ◽  
The Stability ◽  
Parameter Ranges ◽  
Ice Sheet Modelling

AbstractA perturbation method is used to analyse the stability of a thin till layer overlain by a deep ice layer. Ice is modelled as a linearly viscous fluid, while the till viscosity has power-law dependence on stress and effective pressure. A linearized set of equations yields descriptions of the coupling of the ice flow with the sediment flow and reveals parameter ranges where the till-perturbation amplitude can grow. This sheet-flow instability is an essential part of any theory of drumlin formation and shows that viscous models of till have the ability to explain typical deforming-bed features. This is of great significance for large-scale ice-sheet modelling.

scholarly journals The stability of a viscous till sheet coupled with ice flow, considered at wavelengths less than the ice thickness

1998 ◽  
Vol 44 (147) ◽  
pp. 285-292 ◽  
Author(s):  
Richard C. A. Hindmarsh
Keyword(s):  
Large Scale ◽  
Flow Instability ◽  
Ice Thickness ◽  
Ice Flow ◽  
Perturbation Amplitude ◽  
Sediment Flow ◽  
Viscous Models ◽  
The Stability ◽  
Parameter Ranges ◽  
Ice Sheet Modelling

AbstractA perturbation method is used to analyse the stability of a thin till layer overlain by a deep ice layer. Ice is modelled as a linearly viscous fluid, while the till viscosity has power-law dependence on stress and effective pressure. A linearized set of equations yields descriptions of the coupling of the ice flow with the sediment flow and reveals parameter ranges where the till-perturbation amplitude can grow. This sheet-flow instability is an essential part of any theory of drumlin formation and shows that viscous models of till have the ability to explain typical deforming-bed features. This is of great significance for large-scale ice-sheet modelling.

scholarly journals Implementing an empirical scalar tertiary anisotropic rheology (ESTAR) into large-scale ice sheet models

2017 ◽  
Author(s):  
Felicity S. Graham ◽  
Mathieu Morlighem ◽  
Roland C. Warner ◽  
Adam Treverrow
Keyword(s):  
Enhancement Factor ◽  
Large Scale ◽  
Flow Line ◽  
Ice Sheet ◽  
Computationally Efficient ◽  
Ice Shelf ◽  
Ice Flow ◽  
Maximum Value ◽  
Polycrystalline Ice ◽  
Flow Enhancement

Abstract. The microstructural evolution that occurs in polycrystalline ice during deformation leads to the development of anisotropic rheological properties that are not adequately described by the most common, isotropic, ice flow relation used in large-scale ice sheet models – the Glen flow relation. We present a preliminary assessment of the implementation in the Ice Sheet System Model (ISSM) of a computationally-efficient, empirical, scalar, tertiary, anisotropic rheology (ESTAR). The effect of this anisotropic rheology on ice flow dynamics is investigated by comparing idealised simulations using ESTAR with those using the isotropic Glen flow relation, where the latter includes a flow enhancement factor. For an idealised embayed ice shelf, the Glen flow relation overestimates velocities by up to 17 % when using an enhancement factor equivalent to the maximum value prescribed by ESTAR. Importantly, no single Glen enhancement factor can accurately capture the spatial variations in flow over the ice shelf. For flow-line studies of idealised grounded flow over a bumpy topography or a sticky base – both scenarios dominated at depth by bed-parallel shear – the differences between simulated velocities using ESTAR and the Glen flow relation vary according to the value of the enhancement factor used to calibrate the Glen flow relation. These results demonstrate the importance of describing the anisotropic rheology of ice in a physically realistic manner, and have implications for simulations of ice sheet evolution used to reconstruct paleo-ice sheet extent and predict future ice sheet contributions to sea level.

scholarly journals Ice-thickness Patterns and the Dynamics of the Ross Ice Shelf, Antarctica

1979 ◽  
Vol 24 (90) ◽  
pp. 287-294 ◽  
Author(s):  
Charles R. Bentley ◽  
John W. Glough ◽  
Kenneth C. Jezek ◽  
Sion Shabtaie
Keyword(s):  
Large Scale ◽  
Rapid Change ◽  
Thickness Variation ◽  
Ice Thickness ◽  
Ice Shelf ◽  
Mountain Glacier ◽  
Ross Ice Shelf ◽  
Scale Turbulence ◽  
Thickness Variations ◽  
Ice Water

AbstractAs part of the Ross Ice Shelf Geophysical and Glaciological Survey, a detailed map of ice thickness has been produced from airborne radar measurements closely tied to the network of survey stations on the ice-shelf surface. The map, drawn with a 20 m contour interval, reveals a highly complex pattern of thickness variations reflecting presumably, at least in part, complex ice-shelf dynamics. Many features of the thickness variation pattern appear to be associated with zones of grounded ice, but not all. Features of interest include many ice thickness minima, with closures up to 120m; a narrow, greatly elongated ridge-trough system 450 km or more in length; a few ice thickness maxima; steep regional gradients of 10 m/km in freely floating ice; highly contorted contours suggesting a large-scale “turbulence”; and at least two remarkable step-like changes in ice thickness. The irregularity of many of these features suggests dynamic non-equilibrium, i.e. the existence of transients in the dynamic system, so that the ice shelf as a whole suggests a state of rather rapid change. Flow-bands constructed on the basis of the strengths of the echo from the ice-water interface clearly delineate the outflow from the main East Antarctic outlet glaciers in the grid eastern part of the shelf. A discontinuous flow band originating in a small mountain glacier (Robb Glacier) suggests a variable mesoclimate in the vicinity of the glacier within the last thousand years. Strong reflections near the ice front suggest bottom melting of saline ice previously frozen on to the underside of the ice. Several rifts or incipient rifts in the ice shelf characteristically show two lateral bands of strong reflections with a non-reflecting zone in between.

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