Ice flow localisation enhanced by composite ice rheology 

2021 ◽  
Author(s):  
Ludovic Räss ◽  
Thibault Duretz
Keyword(s):  
Grain Size ◽  
Strain Rate ◽  
Surface Velocity ◽  
Total Strain ◽  
Ice Dynamics ◽  
Ice Flow ◽  
Creep Mechanisms ◽  
Size Evolution ◽  
Flow Law ◽  
Total Strain Rate

<p>Ice’s predominantly viscous rheology exhibits a significant temperature and strain-rate dependence, commonly captured as a single deformation mechanism by Glen's flow law. However, Glen’s power-law relationship may fail to capture accurate stress levels at low and elevated strain-rates ultimately leading to velocity over- and under-estimates, respectively. Alternative more complex flow laws such as Goldsby rheology combine various creep mechanisms better accounting for micro-scale observations resulting in enhanced localisation of ice flow at glacier scales and internal sliding.</p><p>The challenge in implementing Goldsby rheology arises with the need of computing an accurate partitioning of the total strain-rate among the active creep mechanisms. Some of these mechanisms exhibit grain-size evolution sensitivity potentially impacting the larger scale ice dynamics.</p><p>We here present a consistent way to compute the effective viscosity of the ice using Goldsby rheology for temperature and strain-rate ranges relevant to ice flow. We implement a local iteration procedure to ensure accurate implicit partitioning of the total strain-rate among the active creep mechanisms including grain-size evolution. We discuss the composite deformation maps and compare the results against Glen's flow law. We incorporate our implicit rheology solver into an implicit 2D thermo-mechanical ice flow solver to investigate localisation of ice flow over variable topography and in shear margin configurations. We quantify discrepancies  in surface velocity patterns when using Goldsby rheology instead of Glen's flow law.</p>

scholarly journals The role of grain size evolution in the rheology of ice: implications for reconciling laboratory creep data and the Glen flow law

2021 ◽  
Vol 15 (9) ◽  
pp. 4589-4605
Author(s):  
Mark D. Behn ◽  
David L. Goldsby ◽  
Greg Hirth
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Stress Exponent ◽  
Ice Sheets ◽  
Grain Boundary Sliding ◽  
Dislocation Creep ◽  
Ice Flow ◽  
Size Evolution ◽  
Boundary Sliding ◽  
Flow Law

Abstract. Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain rate with a stress exponent n ∼ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ∼ 4) nor grain boundary sliding (n ∼ 1.8) have stress exponents that match the value of n ∼ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ∼ 3 dependence of the Glen law by using the “wattmeter” to model grain size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone and (2) as a function of depth within an ice sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.

scholarly journals Influence of anisotropy on velocity and age distribution at Scharffenbergbotnen blue ice area

2014 ◽  
Vol 8 (2) ◽  
pp. 607-621 ◽  
Author(s):  
T. Zwinger ◽  
M. Schäfer ◽  
C. Martín ◽  
J. C. Moore
Keyword(s):  
Initial Conditions ◽  
Model Simulation ◽  
Age Distribution ◽  
Late Glacial ◽  
Glacial Maximum ◽  
Surface Velocity ◽  
Ice Dynamics ◽  
Ice Flow ◽  
Flow Law ◽  
The Impact

Abstract. We use a full-Stokes thermo-mechanically coupled ice-flow model to study the dynamics of the glacier inside Scharffenbergbotnen valley, Dronning Maud Land, Antarctica. The domain encompasses a high accumulation rate region and, downstream, a sublimation-dominated bare ice ablation area. The ablation ice area is notable for having old ice at its surface since the vertical velocity is upwards, and horizontal velocities are almost stagnant there. We compare the model simulation with field observations of velocities and the age distribution of the surface ice. No satisfactory match using an isotropic flow law could be found because of too high vertical velocities and much too high horizontal ones in simulations despite varying enhancement factor, geothermal heat flux and surface temperatures over large ranges. However, the existence of a pronounced ice fabric may explain the observed present-day surface velocity and mass balance distribution in the inner Scharffenbergbotnen blue ice area. Near absence of data on the temporal evolution of Scharffenbergbotnen since the Late Glacial Maximum necessitates exploration of the impact of anisotropy using prescribed ice fabrics: isotropic, single maximum, and linear variation with depth, in both two-dimensional and three-dimensional flow models. The realistic velocity field simulated with a noncollinear orthotropic flow law, however, produced surface ages in significant disagreement with the few reliable age measurements and suggests that the age field is not in a steady state and that the present distribution is a result of a flow reorganization at about 15 000 yr BP. In order to fully understand the surface age distribution, a transient simulation starting from the Late Glacial Maximum including the correct initial conditions for geometry, age, fabric and temperature distribution would be needed. This is the first time that the importance of anisotropy has been demonstrated in the ice dynamics of a blue ice area and demonstrates the need to understand ice flow in order to better interpret archives of ancient ice for paleoclimate research.

Inferring ice rheology in Antarctic ice shelves from remotely sensed observations

2021 ◽  
Author(s):  
Joanna Millstein ◽  
Brent Minchew
Keyword(s):  
Stress Exponent ◽  
Ice Sheets ◽  
Remotely Sensed ◽  
Creep Mechanism ◽  
Surface Velocity ◽  
Dislocation Creep ◽  
Ice Flow ◽  
Ice Shelves ◽  
Creep Mechanisms ◽  
Flow Law

<p>Glaciers and ice sheets flow as a consequence of ice rheology. At the temperatures and pressures found on Earth, several creep mechanisms allow glacier ice to flow as a non-Newtonian (shear-thinning) viscous fluid. The semi-empirical constitutive relation known as Glen’s Flow Law is often used to describe ice flow and to provide a simple expression for an effective viscosity that decreases with increasing stress and deformation rate. Glen’s Flow Law is a power-law relation between effective strain rate and deviatoric stress, with two parameters defining the rheology of ice: a rate factor, A, and stress exponent, n. The rate factor depends on features such as temperature and grain size, while the stress exponent is primarily representative of the creep mechanism. Neither A nor n are well constrained in natural ice, and the stress exponent is typically assumed to be n = 3 everywhere. Here, we take advantage of recent improvements in remotely sensed observations of surface velocity and ice shelf thickness to infer the values of A and n in Antarctic ice shelves. We focus on areas of ice shelves that flow in a purely extensional regime, where extensional stresses are proportional to observed ice thickness, drag at the base of the ice is negligible, and extensional strain-rates are calculated from the gradients of observed surface velocity fields. In this manner, we use independent observational data to derive spatially dependent constraints on the rate factor A and stress exponent n in Glen's Flow Law. The robust spatial variability provides insights into the creep mechanisms of ice, thereby capturing rheological properties from satellite observations. Our analysis indicates that n ≈ 4 in most fast-flowing areas in an extensional regime, contrary to the prototypical value of n = 3. This finding implies higher non-linearity in ice flow than typically prescribed, influencing calculations of mass flux and the response of ice sheets to perturbations. Additionally, This result suggests that dislocation creep is the dominant creep mechanism in extensional regimes of Antarctic ice shelves, indicative of tertiary creep. This analysis unites theoretical work and synoptic-scale observations of ice flow, providing insights into the rheology and stress-states of ice shelves in Antarctica.</p>

scholarly journals The role of grain-size evolution on the rheology of ice: Implications for reconciling laboratory creep data and the Glen flow law

2020 ◽  
Author(s):  
Mark D. Behn ◽  
David L. Goldsby ◽  
Greg Hirth
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Stress Exponent ◽  
Ice Sheets ◽  
Grain Boundary Sliding ◽  
Dislocation Creep ◽  
Ice Flow ◽  
Size Evolution ◽  
Boundary Sliding ◽  
Flow Law

Abstract. Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain-rate with a stress exponent n ~ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain-size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ~ 4) nor grain boundary sliding (n ~ 1.8) have stress exponents that match the value of n ~ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ~ 3 dependence of the Glen law by using the wattmeter to model grain-size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone, and (2) as a function of depth within an ice-sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.

scholarly journals Influence of anisotropy on velocity and age distribution at Scharffenbergbotnen blue ice area

2013 ◽  
Vol 7 (3) ◽  
pp. 3059-3093 ◽  
Author(s):  
T. Zwinger ◽  
M. Schäfer ◽  
C. Martín ◽  
J. C. Moore
Keyword(s):  
Initial Conditions ◽  
Model Simulation ◽  
Age Distribution ◽  
Late Glacial ◽  
Glacial Maximum ◽  
Surface Velocity ◽  
Ice Dynamics ◽  
Ice Flow ◽  
Flow Law ◽  
The Impact

Abstract. We use a full-Stokes thermo-mechanically coupled ice-flow model to study the dynamics of the glacier inside Scharffenbergbotnen valley, Dronning Maud Land, Antarctica. The domain encompasses a high accumulation rate region and, downstream a sublimation-dominated bare ice ablation area. The ablation ice area is notable for having old ice at its surface since the vertical velocity is upwards, and horizontal velocities are almost stagnant there. We compare the model simulation with field observations of velocities and the age distribution of the surface ice. A satisfactory match with simulations using an isotropic flow law was not found because of too high horizontal velocities and too slow vertical ones. However, the existence of a pronounced ice fabric may explain the present day surface velocity distribution in the inner Scharffenbergbotnen blue ice area. Near absence of data on the temporal evolution of Scharffenbergbotnen since the Late Glacial Maximum necessitates exploration of the impact of anisotropy using prescribed ice fabrics: isotropic, single maximum, and linear variation with depth, in both two-dimensional and three dimensional flow models. The realistic velocity field simulated with a non-collinear orthotropic flow law, however produced surface ages in significant disagreement with the few reliable age measurements and suggests that the age field is not in a steady state and that the present distribution is a result of a flow reorganization at about 15 000 yr BP. In order to fully understand the surface age distribution a transient simulation starting from the Late Glacial Maximum including the correct initial conditions for geometry, age, fabric and temperature distribution would be needed. It is the first time that the importance of anisotropy has been demonstrated in the ice dynamics of a blue ice area. This is useful to understand ice flow in order to better interpret archives of ancient ice for paleoclimate research.

scholarly journals Temperature and strain controls on ice deformation mechanisms: insights from the microstructures of samples deformed to progressively higher strains at −10, −20 and −30 °C

2020 ◽  
Author(s):  
Sheng Fan ◽  
Travis Hager ◽  
David J. Prior ◽  
Andrew J. Cross ◽  
David L. Goldsby ◽  
...  
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Strain Rate ◽  
Microstructural Evolution ◽  
Deformation Mechanisms ◽  
Opening Angle ◽  
Ice Flow ◽  
Grain Rotation ◽  
Subgrain Rotation ◽  
Small Grains

Abstract. Understanding ice deformation mechanisms is crucial for understanding the dynamic evolution of terrestrial and planetary ice flow. To understand better the deformation mechanisms, we document the microstructural evolution of ice with increasing strain. We include data from deformation at relatively low temperature (−20 and −30 °C) where the microstructural evolution has never before been documented. Polycrystalline pure water ice was deformed under a constant displacement rate (equal to the strain rate of ~1.0×10−5 s−1) at temperatures of −10, −20 and −30 °C to progressively higher true axial strains (~ 3, 5, 8, 12 and 20 %). Mechanical data show peak and steady-state stresses are larger at colder temperatures as expected from the temperature dependency of creep. Cryo-electron backscattered diffraction (EBSD) analyses show distinct sub-grain boundaries in all deformed samples, suggesting activation of recovery and subgrain rotation. Deformed ice samples are characterised by big grains interlocking with small grains. For each temperature series, we separated big grains from small grains using a threshold grain size, which equals to the square mean root diameter at ~ 12 % strain. Big grains are more lobate at −10 °C than at colder temperatures, suggesting grain boundary migration (GBM) is more prominent at warmer temperatures. The small grains are smaller than subgrains at −10 °C and they become similar in size at −20 and −30 °C, suggesting bulge nucleation facilitates the recrystallization process at warmer temperature and subgrain rotation recrystallization is the nucleation mechanism at colder temperatures. At temperatures warmer than −15 °C, c-axes develop a crystallographic preferred orientation (CPO) characterized by a cone (i.e., small circle) around the compression axis. We suggest the c-axis cone forms as a result of selective growth of grains at easy slip orientations (i.e., ~ 45° to shortening direction) by strain-energy driven GBM. This particular finding is consistent with previous works. The opening-angle of the c-axis cone decreases with strain, suggesting strain-induced GBM is balanced by grain rotation. Furthermore, the opening-angle of the c-axis cone decreases with temperature. At −30 °C, the c-axis CPO transits from a narrow cone to a cluster, parallel to compression, with increasing strain. This closure of the c-axis cone is interpreted as the result of a more active grain rotation together with a less effective GBM. As the temperature decreases, the overall CPO intensity decreases, facilitated by the CPO weakening in small grains. We suggest the grain size sensitivity of grain boundary sliding (GBS) favours a faster strain rate in small grains and leads to the CPO weakening at cold temperatures. CPO development cannot provide a uniform explanation for the mechanical weakening (enhancement) after peak stress. Grain size reduction, which can be observed in all deformed samples, is most likely to cause weakening (enhancement) and should be considered to have a significant control on the rheology of natural ice flow.

scholarly journals Surface Velocity Determination on Large Polar Glaciers by Aerial Photogrammetry

1986 ◽  
Vol 8 ◽  
pp. 22-26 ◽  
Author(s):  
H. H. Brecher
Keyword(s):  
Strain Rate ◽  
Flow Regime ◽  
Surface Velocity ◽  
Control Points ◽  
West Antarctica ◽  
Ice Flow ◽  
Elapsed Time ◽  
Aerial Photogrammetry ◽  
Ice Surface ◽  
Ice Stream B

Aerial photogrammetric block triangulation, a standard and well-developed technique for extending accurate control for mapping into the interior of a region from a few points of known position on its perimeter, can be readily adapted to determine surface velocities on bodies of ice which are too large, and often too crevassed, to be studied effectively by conventional ground surveying. Velocities are calculated from the changes in positions of the same natural surface features determined from photography of two (or more) epochs and the elapsed time. This method is capable of providing many uniformly-spaced measurements over the whole, moving, ice surface, thus allowing the production of maps of velocity and strain-rate, which are valuable in analyzing the ice-flow regime. Results from measurements completed some years ago on Byrd Glacier, one of the largest outlet glaciers from the East Antarctic plateau, are presented as an example of what the method can yield. By means of Doppler satellite surveying, relative positions of control points for each photography epoch can be determined with sub-meter accuracy, making the technique suitable also in regions where no fixed land features exist. A brief description of a project under way in such an area, on Ice Stream B in West Antarctica, is given.

scholarly journals Ice flow modelling to constrain the surface mass balance and ice discharge of San Rafael Glacier, Northern Patagonia Icefield

2018 ◽  
Vol 64 (246) ◽  
pp. 568-582 ◽  
Author(s):  
GABRIELA COLLAO-BARRIOS ◽  
FABIEN GILLET-CHAULET ◽  
VINCENT FAVIER ◽  
GINO CASASSA ◽  
ETIENNE BERTHIER ◽  
...  
Keyword(s):  
Mass Balance ◽  
Flow Model ◽  
Surface Velocity ◽  
Shear Stresses ◽  
Surface Mass Balance ◽  
Ice Dynamics ◽  
Ice Flow ◽  
Surface Mass ◽  
Northern Patagonia ◽  
San Rafael

ABSTRACTWe simulate the ice dynamics of the San Rafael Glacier (SRG) in the Northern Patagonia Icefield (46.7°S, 73.5°W), using glacier geometry obtained by airborne gravity measurements. The full-Stokes ice flow model (Elmer/Ice) is initialized using an inverse method to infer the basal friction coefficient from a satellite-derived surface velocity mosaic. The high surface velocities (7.6 km a−1) near the glacier front are explained by low basal shear stresses (<25 kPa). The modelling results suggest that 98% of the surface velocities are due to basal sliding in the fast-flowing glacier tongue (>1 km a−1). We force the model using different surface mass-balance scenarios taken or adapted from previous studies and geodetic elevation changes between 2000 and 2012. Our results suggest that previous estimates of average surface mass balance over the entire glacier (Ḃ) were likely too high, mainly due to an overestimation in the accumulation area. We propose that most of SRG imbalance is due to the large ice discharge (−0.83 ± 0.08 Gt a−1) and a slightly positiveḂ(0.08 ± 0.06 Gt a−1). The committed mass-loss estimate over the next century is −0.34 ± 0.03 Gt a−1. This study demonstrates that surface mass-balance estimates and glacier wastage projections can be improved using a physically based ice flow model.

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