A topological approach to the strain-rate pattern of ice sheets

1993 ◽  
Vol 39 (131) ◽  
pp. 10-14 ◽  
Author(s):  
J. F. Nye
Keyword(s):  
Strain Rate ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Point Of View ◽  
Principal Strain ◽  
Topological Approach ◽  
Contour Maps ◽  
Isotropic Point ◽  
Horizontal Strain

AbstractThe pattern of horizontal strain rate in an ice sheet is discussed from a topological point of view. In a circularly symmetric ice sheet, the isotropic point for strain rate at its centre is degenerate and structurally unstable. On perturbation the degenerate point splits into two elementary isotropic points, each of which has the lemon pattern for the trajectories of principal strain rate. Contour maps of principal strain-rate values are presented which show the details of the splitting.

A topological approach to the strain-rate pattern of ice sheets

1993 ◽  
Vol 39 (131) ◽  
pp. 10-14 ◽  
Author(s):  
J. F. Nye
Keyword(s):  
Strain Rate ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Point Of View ◽  
Principal Strain ◽  
Topological Approach ◽  
Contour Maps ◽  
Isotropic Point ◽  
Horizontal Strain

AbstractThe pattern of horizontal strain rate in an ice sheet is discussed from a topological point of view. In a circularly symmetric ice sheet, the isotropic point for strain rate at its centre is degenerate and structurally unstable. On perturbation the degenerate point splits into two elementary isotropic points, each of which has the lemon pattern for the trajectories of principal strain rate. Contour maps of principal strain-rate values are presented which show the details of the splitting.

scholarly journals The topology of ice-sheet centres

1991 ◽  
Vol 37 (126) ◽  
pp. 220-227 ◽  
Author(s):  
J.F. Nye
Keyword(s):  
Strain Rate ◽  
Ice Sheet ◽  
Vertical Axis ◽  
Horizontal Component ◽  
Surface Strain ◽  
Principal Strain ◽  
Circular Symmetry ◽  
Two Component ◽  
Horizontal Strain ◽  
Structurally Stable

AbstractAn ice sheet will, in general, possess points where the horizontal component of velocity is zero, and some of these will be ice centres, occurring close to summits. The paper examines the possible flow patterns near such points. The corresponding horizontal strain-rate pattern is studied by considering an ice sheet which initially has perfect circular symmetry about a vertical axis. Before perturbation there is an isotropic point for the horizontal surface strain rate at the centre. It may be shown, on purely topological grounds and without any reference to the mechanism of flow, that, when the symmetry is broken, this point, being degenerate and structurally unstable, breaks up into two structurally stable components. The breakup always occurs in essentially the same way. Around the two component points the trajectories of principal strain-rate directions always have the lemon pattern. The contours of equal principal strain rate around them are usually hyperbolic; however, if the unperturbed flow pattern had a very pronounced spiral character, they would be elliptic. This behaviour is in contrast to that of the ice centre itself, which remains unsplit.

scholarly journals The topology of ice-sheet centres

1991 ◽  
Vol 37 (126) ◽  
pp. 220-227 ◽  
Author(s):  
J.F. Nye
Keyword(s):  
Strain Rate ◽  
Ice Sheet ◽  
Vertical Axis ◽  
Horizontal Component ◽  
Surface Strain ◽  
Principal Strain ◽  
Circular Symmetry ◽  
Two Component ◽  
Horizontal Strain ◽  
Structurally Stable

AbstractAn ice sheet will, in general, possess points where the horizontal component of velocity is zero, and some of these will be ice centres, occurring close to summits. The paper examines the possible flow patterns near such points. The corresponding horizontal strain-rate pattern is studied by considering an ice sheet which initially has perfect circular symmetry about a vertical axis. Before perturbation there is an isotropic point for the horizontal surface strain rate at the centre. It may be shown, on purely topological grounds and without any reference to the mechanism of flow, that, when the symmetry is broken, this point, being degenerate and structurally unstable, breaks up into two structurally stable components. The breakup always occurs in essentially the same way. Around the two component points the trajectories of principal strain-rate directions always have the lemon pattern. The contours of equal principal strain rate around them are usually hyperbolic; however, if the unperturbed flow pattern had a very pronounced spiral character, they would be elliptic. This behaviour is in contrast to that of the ice centre itself, which remains unsplit.

Analysis and Simulation of Altimeter Performance for the Production of Ice Sheet Topographic Maps

1986 ◽  
Vol 8 ◽  
pp. 141-145 ◽  
Author(s):  
K.C. Partington ◽  
C.G. Rapley
Keyword(s):  
High Precision ◽  
Systems Analysis ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Data Interpretation ◽  
Topographic Maps ◽  
Error Signal ◽  
Tracking Systems ◽  
Tracking Mode ◽  
Non Linear

Satellite-borne, radar altimeters have already demonstrated an ability to produce high-precision, topographic maps of the ice sheets. Seasat operated in a tracking mode, designed for use over oceans, but successfully tracked much of the flatter regions of the ice sheet to ± 72° latitude. ERS-1 will extend coverage to ± 82° latitude and will be equipped with an ocean mode similar to that of Seasat and an ice mode designed to permit tracking of the steeper, peripheral regions. The ocean mode will be used over the flatter regions, because of its greater precision.Altimeter performance over the ice sheets has been investigated through a study of Seasat tracking behaviour and the use of an altimeter performance simulator, with a view to assessing the likely performance of ERS-1 and the design of improved tracking systems. Analysis of Seasat data shows that lock was frequently lost, as a result of possessing a non-linear height error signal over the width of the range window. Having lost lock, the tracker frequently failed to transfer rapidly and effectively to track mode. Use of the altimeter performance simulator confirms many of the findings from Seasat data and it is being used to facilitate data interpretation and mapping, through the modelling of waveform sequence.

scholarly journals Comparison of Quantitative Morphology of Layered and Arbitrary Patterns: Contrary to Visual Perception, Binary Arbitrary Patterns Are Layered from a Structural Point of View

2021 ◽  
Vol 11 (14) ◽  
pp. 6300
Author(s):  
Igor Smolyar ◽  
Daniel Smolyar
Keyword(s):  
Boolean Function ◽  
Layer Structure ◽  
Central Element ◽  
Morphological Characteristics ◽  
Building Blocks ◽  
Point Of View ◽  
Living Systems ◽  
Seismic Profiles ◽  
Contour Maps ◽  
Anisotropic Layers

Patterns found among both living systems, such as fish scales, bones, and tree rings, and non-living systems, such as terrestrial and extraterrestrial dunes, microstructures of alloys, and geological seismic profiles, are comprised of anisotropic layers of different thicknesses and lengths. These layered patterns form a record of internal and external factors that regulate pattern formation in their various systems, making it potentially possible to recognize events in the formation history of these systems. In our previous work, we developed an empirical model (EM) of anisotropic layered patterns using an N-partite graph, denoted as G(N), and a Boolean function to formalize the layer structure. The concept of isotropic and anisotropic layers was presented and described in terms of the G(N) and Boolean function. The central element of the present work is the justification that arbitrary binary patterns are made up of such layers. It has been shown that within the frame of the proposed model, it is the isotropic and anisotropic layers themselves that are the building blocks of binary layered and arbitrary patterns; pixels play no role. This is why the EM can be used to describe the morphological characteristics of such patterns. We present the parameters disorder of layer structure, disorder of layer size, and pattern complexity to describe the degree of deviation of the structure and size of an arbitrary anisotropic pattern being studied from the structure and size of a layered isotropic analog. Experiments with arbitrary patterns, such as regular geometric figures, convex and concave polygons, contour maps, the shape of island coastlines, river meanders, historic texts, and artistic drawings are presented to illustrate the spectrum of problems that it may be possible to solve by applying the EM. The differences and similarities between the proposed and existing morphological characteristics of patterns has been discussed, as well as the pros and cons of the suggested method.

scholarly journals Attention Multi-Scale Network for Automatic Layer Extraction of Ice Radar Topological Sequences

2021 ◽  
Vol 13 (12) ◽  
pp. 2425
Author(s):  
Yiheng Cai ◽  
Dan Liu ◽  
Jin Xie ◽  
Jingxian Yang ◽  
Xiangbin Cui ◽  
...  
Keyword(s):  
Deep Learning ◽  
Global Climate ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Sheet Thickness ◽  
Learning Methods ◽  
Convolutional Network ◽  
Multi Scale ◽  
Ice Surface ◽  
Layer Extraction

Analyzing the surface and bedrock locations in radar imagery enables the computation of ice sheet thickness, which is important for the study of ice sheets, their volume and how they may contribute to global climate change. However, the traditional handcrafted methods cannot quickly provide quantitative, objective and reliable extraction of information from radargrams. Most traditional handcrafted methods, designed to detect ice-surface and ice-bed layers from ice sheet radargrams, require complex human involvement and are difficult to apply to large datasets, while deep learning methods can obtain better results in a generalized way. In this study, an end-to-end multi-scale attention network (MsANet) is proposed to realize the estimation and reconstruction of layers in sequences of ice sheet radar tomographic images. First, we use an improved 3D convolutional network, C3D-M, whose first full connection layer is replaced by a convolution unit to better maintain the spatial relativity of ice layer features, as the backbone. Then, an adjustable multi-scale module uses different scale filters to learn scale information to enhance the feature extraction capabilities of the network. Finally, an attention module extended to 3D space removes a redundant bottleneck unit to better fuse and refine ice layer features. Radar sequential images collected by the Center of Remote Sensing of Ice Sheets in 2014 are used as training and testing data. Compared with state-of-the-art deep learning methods, the MsANet shows a 10% reduction (2.14 pixels) on the measurement of average mean absolute column-wise error for detecting the ice-surface and ice-bottom layers, runs faster and uses approximately 12 million fewer parameters.

scholarly journals Measurement of ice-sheet topography using satellite-radar interferometry

1996 ◽  
Vol 42 (140) ◽  
pp. 10-22 ◽  
Author(s):  
Ian Joughin ◽  
Dale Winebrenner ◽  
Mark Fahnestock ◽  
Ron Kwok ◽  
William Krabill
Keyword(s):  
Ice Sheets ◽  
Ice Sheet ◽  
Surface Displacement ◽  
Horizontal Resolution ◽  
Radar Interferometry ◽  
Altimeter Data ◽  
Laser Altimeter ◽  
Digital Elevation ◽  
Satellite Radar ◽  
Ice Sheet Topography

AbstractDetailed digital elevation models (DEMs) do not exist for much of the Greenland and Antartic ice sheets. Radar altimetry is at present the primary, in many cases the only, source of topographic data over the ice sheets, but the horizontal resolution of such data is coarse. Satellite-radar interferometry uses the phase difference between pairs of synthetic aperture radar (SAR) images to measure both ice-sheet topography and surface displacement. We have applied this technique using ERS-1 SAR data to make detailed (i.e. 80 m horizontal resolution) maps of surface topography in a 100 km by 300 km strip in West Greenland, extending northward from just above Jakobshavns Isbræ. Comparison with а 76 km long line of airborne laser-altimeter data shows that We have achieved a relative accuracy of 2.5 m along the profile. These observations provide a detailed view of dynamically Supported topography near the margin of an ice sheet. In the final section We compare our estimate of topography with phase contours due to motion, and confirm our earlier analysis concerning vertical ice-sheet motion and complexity in ERS-1 SAR interferograms.

Topology of fine-scale motions in turbulent channel flow

1996 ◽  
Vol 310 ◽  
pp. 269-292 ◽  
Author(s):  
Hugh M. Blackburn ◽  
Nagi N. Mansour ◽  
Brian J. Cantwell
Keyword(s):  
Strain Rate ◽  
Channel Flow ◽  
Velocity Gradient ◽  
Outer Region ◽  
Turbulent Channel Flow ◽  
Principal Strain ◽  
Wall Region ◽  
Fine Scale ◽  
Stable Focus ◽  
Topological Features

An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.

scholarly journals Dynamical processes involved in the retreat of marine ice sheets

2001 ◽  
Vol 47 (157) ◽  
pp. 271-282 ◽  
Author(s):  
Richard C.A. Hindmarsh ◽  
E. Le Meur
Keyword(s):  
Ice Sheets ◽  
Ice Sheet ◽  
Ice Shelf ◽  
Ice Streams ◽  
Antarctic Ice Sheet ◽  
West Antarctic Ice Sheet ◽  
West Antarctic ◽  
Grounding Line ◽  
Neutral Equilibrium ◽  
Generally True

AbstractMarine ice sheets with mechanics described by the shallow-ice approximation by definition do not couple mechanically with the shelf. Such ice sheets are known to have neutral equilibria. We consider the implications of this for their dynamics and in particular for mechanisms which promote marine ice-sheet retreat. The removal of ice-shelf buttressing leading to enhanced flow in grounded ice is discounted as a significant influence on mechanical grounds. Sea-level rise leading to reduced effective pressures under ice streams is shown to be a feasible mechanism for producing postglacial West Antarctic ice-sheet retreat but is inconsistent with borehole evidence. Warming thins the ice sheet by reducing the average viscosity but does not lead to grounding-line retreat. Internal oscillations either specified or generated via a MacAyeal–Payne thermal mechanism promote migration. This is a noise-induced drift phenomenon stemming from the neutral equilibrium property of marine ice sheets. This migration occurs at quite slow rates, but these are sufficiently large to have possibly played a role in the dynamics of the West Antarctic ice sheet after the glacial maximum. Numerical experiments suggest that it is generally true that while significant changes in thickness can be caused by spatially uniform changes, spatial variability coupled with dynamical variability is needed to cause margin movement.

scholarly journals Investigating the evolution of major Northern Hemisphere ice sheets during the last glacial-interglacial cycle

2009 ◽  
Vol 5 (3) ◽  
pp. 329-345 ◽  
Author(s):  
S. Bonelli ◽  
S. Charbit ◽  
M. Kageyama ◽  
M.-N. Woillez ◽  
G. Ramstein ◽  
...  
Keyword(s):  
Northern Hemisphere ◽  
Climate Model ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Co2 Concentration ◽  
Atmospheric Co2 ◽  
Glacial Cycle ◽  
Last Glacial ◽  
Atmospheric Co2 Concentration ◽  
The Last Glacial

Abstract. A 2.5-dimensional climate model of intermediate complexity, CLIMBER-2, fully coupled with the GREMLINS 3-D thermo-mechanical ice sheet model is used to simulate the evolution of major Northern Hemisphere ice sheets during the last glacial-interglacial cycle and to investigate the ice sheets responses to both insolation and atmospheric CO2 concentration. This model reproduces the main phases of advance and retreat of Northern Hemisphere ice sheets during the last glacial cycle, although the amplitude of these variations is less pronounced than those based on sea level reconstructions. At the last glacial maximum, the simulated ice volume is 52.5×1015 m3 and the spatial distribution of both the American and Eurasian ice complexes is in reasonable agreement with observations, with the exception of the marine parts of these former ice sheets. A set of sensitivity studies has also been performed to assess the sensitivity of the Northern Hemisphere ice sheets to both insolation and atmospheric CO2. Our results suggest that the decrease of summer insolation is the main factor responsible for the early build up of the North American ice sheet around 120 kyr BP, in agreement with benthic foraminifera δ18O signals. In contrast, low insolation and low atmospheric CO2 concentration are both necessary to trigger a long-lasting glaciation over Eurasia.

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