scholarly journals Of the gradient accuracy in Full-Stokes ice flow model: basal slipperiness inference

2013 ◽  
Vol 7 (4) ◽  
pp. 3853-3897 ◽  
Author(s):  
N. Martin ◽  
J. Monnier
Keyword(s):  
Parameter Identification ◽  
Adjoint Method ◽  
Adjoint Problem ◽  
The Self ◽  
Ice Thickness ◽  
Adjoint Model ◽  
Ice Flow ◽  
Algorithmic Differentiation ◽  
Numerical Assessment ◽  
Linear Friction

Abstract. This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. We quantify the ability to identify the basal slipperiness for such methods with a non-linear friction law. The complete adjoint problem is solved and a comparison with the so called "self-adjoint" method, neglecting the viscosity dependency to the velocity, common in glaciology, is carried out. A lower bound of identifiable wavelengths of 10 ice thickness in the friction coefficient is established, when using the full adjoint method, while the "self-adjoint" method is limited to a maximum of 20 ice thickness wavelengths. In addition, the full adjoint method demonstrates a better robustness and reliability for the parameter identification process. The derivation of the adjoint model using algorithmic differentiation leads to formulate a generalization of the "self-adjoint" approximation towards an incomplete adjoint method, adjustable in precision and computational burden.

scholarly journals Adjoint accuracy for the full Stokes ice flow model: limits to the transmission of basal friction variability to the surface

2014 ◽  
Vol 8 (2) ◽  
pp. 721-741 ◽  
Author(s):  
N. Martin ◽  
J. Monnier
Keyword(s):  
Friction Coefficient ◽  
Parameter Identification ◽  
Adjoint Method ◽  
Synthetic Data ◽  
Adjoint Problem ◽  
Second Order ◽  
The Self ◽  
Algorithmic Differentiation ◽  
Numerical Assessment ◽  
Linear Friction

Abstract. This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability to identify the friction coefficient for such methods with a non-linear friction law. The exact adjoint problem is solved, based on second-order numerical schemes, and a comparison with the so-called "self-adjoint" approximation, neglecting the viscosity dependence on the velocity (leading to an incorrect gradient), common in glaciology, is carried out. For data with a noise of 1%, a lower bound of identifiable wavelengths of 10 ice thicknesses in the friction coefficient is established, when using the exact adjoint method, while the "self-adjoint" method is limited, even for lower noise, to a minimum of 20 ice thickness wavelengths. The second-order exact gradient method therefore provides robustness and reliability for the parameter identification process. In another respect, the derivation of the adjoint model using algorithmic differentiation leads to the formulation of a generalization of the "self-adjoint" approximation towards an incomplete adjoint method, adjustable in precision and computational burden.

scholarly journals Ice thickness estimates of Lemon Creek Glacier, Alaska, from active-source seismic imaging

2021 ◽  
pp. 1-9
Author(s):  
Stephen A. Veitch ◽  
Marianne Karplus ◽  
Galen Kaip ◽  
Lucia F. Gonzalez ◽  
Jason M. Amundson ◽  
...  
Keyword(s):  
Ice Thickness ◽  
Equilibrium Line Altitude ◽  
Seismic Line ◽  
Ice Flow ◽  
Southeast Alaska ◽  
Velocity Modeling ◽  
Active Source ◽  
Valley Glacier ◽  
Subglacial Topography ◽  
The Impact

Abstract Lemon Creek Glacier, a temperate valley glacier in the Juneau Icefield of Southeast Alaska, is the site of long running (>60 years) glaciological studies. However, the most recent published estimates of its thickness and subglacial topography come from two ~50 years old sources that are not in agreement and do not account for the effects of years of negative mass balance. We collected a 1-km long active-source seismic line on the upper section of the glacier parallel and near to the centerline of the glacier, roughly straddling the equilibrium-line altitude. We used these data to perform joint reflection-refraction velocity modeling and reflection imaging of the glacier bed. We find that this upper section of Lemon Creek Glacier is as much as 150 m (~65%) thicker than previously suggested with a large overdeepening in an area previously believed to have a uniform thickness. Our results lead us to reinterpret the impact of basal motion on ice flow and have a significant impact on expectations of subglacial hydrology. We suggest that further efforts to develop a whole-glacier model of subglacial topography are necessary to support studies that require accurate models of ice thickness and subglacial topography.

On the relation between ice thickness changes and glacier speed-up, with application to Pine Island Glacier in West Antarctica 

2021 ◽  
Author(s):  
Jan De Rydt ◽  
Ronja Reese ◽  
Fernando Paolo ◽  
G Hilmar Gudmundsson
Keyword(s):  
Numerical Solutions ◽  
Numerical Models ◽  
Flow Speed ◽  
Ice Thickness ◽  
West Antarctica ◽  
Ice Shelf ◽  
Ice Flow ◽  
Spatially Distributed ◽  
Speed Up ◽  
Induced Changes

<p>Pine Island Glacier in West Antarctica is among the fastest changing glaciers worldwide. Much of its fast-flowing central trunk is thinning and accelerating, a process thought to have been triggered by ocean-induced changes in ice-shelf buttressing. The measured acceleration in response to perturbations in ice thickness is a non-trivial manifestation of several poorly-understood physical processes, including the transmission of stresses between the ice and underlying bed. To enable robust projections of future ice flow, it is imperative that numerical models include an accurate representation of these processes. Here we combine the latest data with analytical and numerical solutions of SSA ice flow to show that the recent increase in flow speed of Pine Island Glacier is only compatible with observed patterns of thinning if a spatially distributed, predominantly plastic bed underlies large parts of the central glacier and its upstream tributaries.</p>

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 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 A rapidly converging initialisation method to simulate the present-day Greenland ice sheet using the GRISLI ice sheet model (version 1.3)

2019 ◽  
Vol 12 (6) ◽  
pp. 2481-2499 ◽  
Author(s):  
Sébastien Le clec'h ◽  
Aurélien Quiquet ◽  
Sylvie Charbit ◽  
Christophe Dumas ◽  
Masa Kageyama ◽  
...  
Keyword(s):  
Root Mean Square ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Thickness ◽  
Strong Impact ◽  
Good Representation ◽  
Mean Square ◽  
Method Performance ◽  
Ice Flow ◽  
Mean Square Errors

Abstract. Providing reliable projections of the ice sheet contribution to future sea-level rise has become one of the main challenges of the ice sheet modelling community. To increase confidence in future projections, a good knowledge of the present-day state of ice flow dynamics, which is critically dependent on basal conditions, is strongly needed. The main difficulty is tied to the scarcity of observations at the ice–bed interface at the scale of the whole ice sheet, resulting in poorly constrained parameterisations in ice sheet models. To circumvent this drawback, inverse modelling approaches can be developed to infer initial conditions for ice sheet models that best reproduce available data. Most often such approaches allow for a good representation of the mean present-day state of the ice sheet but are accompanied with unphysical trends. Here, we present an initialisation method for the Greenland ice sheet using the thermo-mechanical hybrid GRISLI (GRenoble Ice Shelf and Land Ice) ice sheet model. Our approach is based on the adjustment of the basal drag coefficient that relates the sliding velocities at the ice–bed interface to basal shear stress in unfrozen bed areas. This method relies on an iterative process in which the basal drag is periodically adjusted in such a way that the simulated ice thickness matches the observed one. The quality of the method is assessed by computing the root mean square errors in ice thickness changes. Because the method is based on an adjustment of the sliding velocities only, the results are discussed in terms of varying ice flow enhancement factors that control the deformation rates. We show that this factor has a strong impact on the minimisation of ice thickness errors and has to be chosen as a function of the internal thermal state of the ice sheet (e.g. a low enhancement factor for a warm ice sheet). While the method performance slightly increases with the duration of the minimisation procedure, an ice thickness root mean square error (RMSE) of 50.3 m is obtained in only 1320 model years. This highlights a rapid convergence and demonstrates that the method can be used for computationally expensive ice sheet models.

scholarly journals Numerical simulations of the ice flow dynamics of George VI Ice Shelf, Antarctica

2007 ◽  
Vol 53 (183) ◽  
pp. 659-664 ◽  
Author(s):  
Angelika Humbert
Keyword(s):  
High Spatial Resolution ◽  
Thickness Distribution ◽  
Satellite System ◽  
Flow Dynamics ◽  
Ice Thickness ◽  
Ice Shelf ◽  
Ice Flow ◽  
Ice Shelves ◽  
Flow Geometry ◽  
Grounding Line

A diagnostic, dynamic/thermodynamic ice-shelf model is applied to the George VI Ice Shelf, situated in the Bellinghausen Sea, Antarctica. The George VI Ice Shelf has a peculiar flow geometry which sets it apart from other ice shelves. Inflow occurs along the two longest, and almost parallel, sides, whereas outflow occurs on the two ice fronts that are relatively short and situated at opposite ends of the ice shelf. Two data sources were used to derive the ice thickness distribution: conventional radioecho sounding from the British Antarctic Survey was combined with thickness inferred from surface elevation obtained by the NASA GLAS satellite system assuming hydrostatic equilibrium. We simulate the present ice flow over the ice shelf that results from the ice thickness distribution, the inflow at the grounding line and the flow rate factor. The high spatial resolution of the ice thickness distribution leads to very detailed simulations. The flow field has some extraordinary elements (e.g. the stagnation point characteristics resulting from the unusual ice-shelf geometry).

scholarly journals Tributaries to West Antarctic ice streams: characteristics deduced from numerical modelling of ice flow

2000 ◽  
Vol 31 ◽  
pp. 184-190 ◽  
Author(s):  
Christina L. Hulbe ◽  
Ian R. Joughin ◽  
David L. Morse ◽  
Robert A. Bindschadler
Keyword(s):  
Numerical Modelling ◽  
Stream Flow ◽  
Water Storage ◽  
Consistent Pattern ◽  
Ice Thickness ◽  
Ice Streams ◽  
The West ◽  
Ice Flow ◽  
West Antarctic ◽  
Ice Stream

AbstractA network of relatively fast-flowing tributaries in the catchment basins of the West Antarctic ice streams transport ice from the inland reservoir to the heads of the ice streams. Branches of the network follow valleys in basal topography but not all valleys contain tributaries. We investigate the circumstances favoring tributary flow upstream of Ice Streams D and E, using a combination of observation and numerical modelling. No consistent pattern emerges. The transition from tributary to ice-stream flow occurs smoothly along the main tributary feeding into the onset of Ice Stream D, with ice thickness being relatively more important upstream, and sliding being relatively more important downstream. Elsewhere, the downstream pattern of flow is more complicated, with local increases and decreases in the contribution of sliding to ice speed. Those changes may be due to variations in basal water storage, subglacial geologic properties or a combination of the two.

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