scholarly journals Constraints on glacier flow from temperature-depth profiles in the ice. Application to EPICA Dome C.

2016 ◽  
Author(s):  
Ignacio Hermoso de Mendoza ◽  
Jean-Claude Mareschal ◽  
Hugo Beltrami
Keyword(s):  
Heat Flux ◽  
Velocity Profile ◽  
Boundary Conditions ◽  
Temperature Profile ◽  
East Antarctica ◽  
Surface Velocity ◽  
Function Parameter ◽  
Unknown Parameters ◽  
Conduction Model ◽  
Ice Flow

Abstract. A one-dimensional (1-D) ice flow and heat conduction model is used to calculate the temperature and heat flux profiles in the ice and to constrain the parameters characterizing the ice flow and the thermal boundary conditions at the Dome C drilling site in East Antarctica. We use the reconstructions of ice accumulation, glacier height and air surface temperature histories as boundary conditions to calculate the ice temperature profile. The temperature profile also depends on a set of poorly known parameters, the ice velocity profile and magnitude, basal heat flux, and air-ice surfaces temperature coupling. We use Monte Carlo methods to search the parameters' space of the model, compare the model output with the temperature data, and find probability distributions for the unknown parameters. We could not determine the sliding ratio because it has no effect on the thermal profile, but we could constrain the flux function parameter p that determines the velocity profile. We determined the basal heat flux qb = 49.0  ± 2.7 (2σ)m W m−2, almost equal to the apparent value. We found an ice surface velocity of vsur = 2.6 ± 1.9 (2σ)m y−1 and an air-ice temperature coupling of 0.8 ± 1.0(2σ)K. Our study confirms that the heat flux is low and does not destabilize the ice sheet in east Antarctica.

Modelling ice rise englacial temperature profiles to constrain past ice-sheet dynamics

2020 ◽  
Author(s):  
Aleksandr Montelli ◽  
Jonathan Kingslake
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Ross Sea ◽  
Accumulation Rate ◽  
Ice Sheet ◽  
Temperature Profiles ◽  
Measured Temperature ◽  
Ice Dynamics ◽  
Ice Flow ◽  
Thickness Change

<p>Present-day englacial temperatures are the product of the millennial-scale histories of ice flow and thermal boundary conditions experienced by an ice sheet. Vertical englacial temperature profiles extracted from boreholes drilled at ice divides record past ice dynamics and changing external forcings. Bindschadler (1990) estimated the timing of grounding of Crary Ice Rise, Ross Sea, by minimizing the mismatch between modelled and measured temperature profiles. This approach has huge potential if future boreholes are drilled at Antarctic ice rises in locations suspected of undergoing significant dynamics change. Yet, the uncertainties inherent in this approach must be carefully assessed to target and maximize the utility of borehole drilling. Here, using a 1D vertical heat flux model, we simulate the evolution of temperature as a function of depth in six locations with slow-flowing, cold-based ice in the Weddell and Ross Sea sectors of the West Antarctic Ice Sheet. The locations were chosen using output from the Parallel Ice Sheet Model (PISM) as which are most likely to have ungrounded and regrounded during the last deglaciation (i.e., through last 20 k.y.). We use the shallow ice approximation assuming horizontally isothermal ice and no basal sliding. Several parameters, accounting for timing and duration of grounding/ungrounding events, surface temperature evolution, accumulation rate, ice-thickness change, geothermal heat flux and vertical velocity, are varied to generate a range of different temperature profile outputs. Uncertainties associated with each parameter are then evaluated using a Monte-Carlo approach, yielding a statistical account of model sensitivity to key variables. We highlight that the precision needed to infer timing of grounding increases with the duration of grounded ice flow. Results presented here can help in choosing future ice drilling sites, and provide useful constraints on inferring past forcings and changing boundary conditions from in-situ temperature-depth measurements.</p>

scholarly journals Ice flow across a warm-based/cold-based transition at a glacier margin

2009 ◽  
Vol 50 (52) ◽  
pp. 1-8 ◽  
Author(s):  
Peter L. Moore ◽  
Neal R. Iverson ◽  
Denis Cohen
Keyword(s):  
Boundary Conditions ◽  
Structural Features ◽  
Surface Velocity ◽  
Stress Concentrations ◽  
Longitudinal Compression ◽  
Ice Flow ◽  
Vertical Extension ◽  
Model Flow ◽  
Polythermal Glacier ◽  
Slip Transition

AbstractWhere polythermal glaciers have frozen margins that buttress otherwise temperate-based sliding ice, longitudinal compression can strongly influence ice-flow trajectory, and consequently sediment transport paths. Past efforts to model flow in the vicinity of a basal thermal transition (BTT) have generally relied on simplified boundary conditions or rheological idealizations, making these model results difficult to apply to real glacier termini. Herein, we present results of numerical simulations using a power-law rheology and with boundary conditions that better represent the frozen margin. Model results indicate that a transition to a non-sliding frozen margin causes a decline in surface velocity made possible by upward ice flow, implying either enhanced ablation for steady-state simulations or the formation of a surface bulge. Permitting ice loss by ablation combined with numerical smoothing of the basal slip transition subdues basal stress concentrations and thereby inhibits development of structural discontinuities such as thrust faults. Upward ice flow is accommodated by vertical extension up-glacier of the BTT. This strain regime can potentially account for key structural features in polythermal glacier termini without appealing to thrusting.

Thermal instability in a horizontal fluid layer: effect of boundary conditions and non-linear temperature profile

1964 ◽  
Vol 18 (4) ◽  
pp. 513-528 ◽  
Author(s):  
E. M. Sparrow ◽  
R. J. Goldstein ◽  
V. K. Jonsson
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Boundary Conditions ◽  
Temperature Profile ◽  
Fluid Layer ◽  
Bounding Surface ◽  
Fixed Temperature ◽  
Linear Temperature ◽  
Lower Bounding ◽  
Horizontal Fluid Layer

An investigation is carried out to determine the conditions marking the onset of convective motion in a horizontal fluid layer in which a negative temperature gradient occurs somewhere within the layer. In such cases, fluid of greater density is situated above fluid of lesser density. Consideration is given to a variety of thermal and hydrodynamic boundary conditions at the surfaces which bound the fluid layer. The thermal conditions include fixed temperature and fixed heat flux at the lower bounding surface, and a general convective-radiative exchange at the upper surface which includes fixed temperature and fixed heat flux as special cases. The hydrodynamic boundary conditions include both rigid and free upper surfaces with a rigid lower bounding surface. It is found that the Rayleigh number marking the onset of motion is greatest for the boundary condition of fixed temperature and decreases monotonically as the condition of fixed heat flux is approached. Non-linear temperature distributions in the fluid layer may result from internal heat generation. With increasing departures from the linear temperature profile, it is found that the fluid layer becomes more prone to instability, that is, the critical Rayleigh number decreases.

scholarly journals Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

2016 ◽  
Author(s):  
Hongyu Zhu ◽  
Noemi Petra ◽  
Georg Stadler ◽  
Tobin Isaac ◽  
Thomas J. R. Hughes ◽  
...  
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Optimization Problem ◽  
Premature Termination ◽  
Adjoint Equations ◽  
Surface Velocity ◽  
Geothermal Heat ◽  
Ice Flow ◽  
Cost Functional ◽  
The Cost

Abstract. We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using an instantaneous thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations, which then determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well-posed. We derive adjoint-based gradient and Hessian expressions for the resulting PDE-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases, and that small wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems — i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian — we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

scholarly journals Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

2016 ◽  
Vol 10 (4) ◽  
pp. 1477-1494 ◽  
Author(s):  
Hongyu Zhu ◽  
Noemi Petra ◽  
Georg Stadler ◽  
Tobin Isaac ◽  
Thomas J. R. Hughes ◽  
...  
Keyword(s):  
Heat Flux ◽  
Inverse Problem ◽  
Optimization Problem ◽  
Premature Termination ◽  
Adjoint Equations ◽  
Surface Velocity ◽  
Geothermal Heat ◽  
Ice Flow ◽  
Cost Functional ◽  
The Cost

Abstract. We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

scholarly journals COMPILING TECHNIQUES FOR EAST ANTARCTIC ICE VELOCITY MAPPING BASED ON HISTORICAL OPTICAL IMAGERY

2018 ◽  
Vol XLII-3 ◽  
pp. 2625-2628
Author(s):  
X. Li ◽  
R. Li ◽  
G. Qiao ◽  
Y. Cheng ◽  
W. Ye ◽  
...  
Keyword(s):  
Flow Velocity ◽  
Image Matching ◽  
Landsat Imagery ◽  
East Antarctica ◽  
Surface Velocity ◽  
Velocity Mapping ◽  
Large Space ◽  
Ice Flow ◽  
Ice Velocity ◽  
Optical Imagery

Ice flow velocity over long time series in East Antarctica plays a vital role in estimating and predicting the mass balance of Antarctic Ice Sheet and its contribution to global sea level rise. However, there is no Antarctic ice velocity product with large space scale available showing the East Antarctic ice flow velocity pattern before the 1990s. We proposed three methods including parallax decomposition, grid-based NCC image matching, feature and gird-based image matching with constraints for estimation of surface velocity in East Antarctica based on ARGON KH-5 and LANDSAT imagery, showing the feasibility of using historical optical imagery to obtain Antarctic ice motion. Based on these previous studies, we presented a set of systematic method for developing ice surface velocity product for the entire East Antarctica from the 1960s to the 1980s in this paper.

scholarly journals ICE FLOW VELOCITY MAPPING OF EAST ANTARCTICA FROM 1963 TO 1989

2019 ◽  
Vol XLII-2/W13 ◽  
pp. 1735-1739
Author(s):  
Y. Cheng ◽  
X. Li ◽  
G. Qiao ◽  
W. Ye ◽  
Y. Huang ◽  
...  
Keyword(s):  
Flow Velocity ◽  
East Antarctica ◽  
Surface Velocity ◽  
Velocity Mapping ◽  
Landsat Images ◽  
Ice Flow ◽  
Continental Scale ◽  
Optical Images ◽  
Long Time ◽  
Surface Ice

<p><strong>Abstract.</strong> Long-time serial observation of surface ice flow velocity in Antarctic is a crucial component in estimating the mass balance of Antarctic ice sheet. However, there is a lack of historical continental scale velocity maps of Antarctica before the 1990s. Historical optical images such as ARGON and Landsat images before 1990s are difficult to be used for ice flow velocity mapping, due to the fact that they are mostly not strictly geo-processed (e.g., ortho-rectified) and the image quality is lower than those of recent sensors. This paper presents a systematic framework for developing a surface velocity map of East Antarctica from 1963 to 1989 based on historical ARGON and Landsat images, followed by analysis of spatial-temporal changes of the ice flow velocity in some major glaciers, as well as the dynamic changes. The preliminary comparison with existing products suggests that the glaciers in Wilkes Land experienced an increasing trend with obvious fluctuations during the past &amp;sim;50 years, while the glaciers near Transantarctic Mountains tended to be stable or slightly fluctuating to a certain degree.</p>

scholarly journals The role of subglacial hydrology in ice streams with elevated geothermal heat flux

2020 ◽  
Vol 66 (256) ◽  
pp. 303-312
Author(s):  
Silje Smith-Johnsen ◽  
Basile de Fleurian ◽  
Kerim H. Nisancioglu
Keyword(s):  
Heat Flux ◽  
Ice Sheet ◽  
Complex Surface ◽  
Surface Velocity ◽  
Ice Streams ◽  
Geothermal Heat ◽  
Ice Flow ◽  
Ice Stream ◽  
The Impact

AbstractThe spatial distribution of geothermal heat flux (GHF) under ice sheets is largely unknown. Nonetheless, it is an important boundary condition in ice-sheet models, and suggested to control part of the complex surface velocity patterns observed in some regions. Here we investigate the effect of including subglacial hydrology when modelling ice streams with elevated GHF. We use an idealised ice stream geometry and a thermomechanical ice flow model coupled to subglacial hydrology in the Ice Sheet System Model (ISSM). Our results show that the dynamic response of the ice stream to elevated GHF is greatly enhanced when including the interactive subglacial hydrology. On the other hand, the impact of GHF on ice temperature is reduced when subglacial hydrology is included. In conclusion, the sensitivity of ice stream dynamics to GHF is likely to be underestimated in studies neglecting subglacial hydrology.

scholarly journals ICE VELOCITY MEASUREMENT IN EAST ANTARCTICA FROM 1960s TO 1980s BASED ON ARGON AND LANDSAT IMAGERY

2017 ◽  
Vol XLII-2/W7 ◽  
pp. 1535-1539 ◽  
Author(s):  
R. Li ◽  
X. Ma ◽  
Y. Cheng ◽  
W. Ye ◽  
S. Guo ◽  
...  
Keyword(s):  
Flow Velocity ◽  
Feature Matching ◽  
Geometric Model ◽  
East Antarctica ◽  
Surface Velocity ◽  
Time Interval ◽  
Stereo Pair ◽  
Landsat Images ◽  
Ice Flow ◽  
Ice Velocity

Ice flow velocity is a vital parameter for estimating the ice mass balance of glaciers in Antarctica. Especially long time serial observation of the surface velocity is of great significance to assessing the relationship between Antarctic ice materials and global climate change. However, the existing research on Antarctic ice velocity based on remote sensing data since 1970s due to the harsh climate in Antarctica. This paper presents an ice flow velocity estimating method includes image pre-processing, geometric model reconstruction, image ortho-rectification and feature matching by using ARGON images token in 1963 and Landsat images collected form 1973 to 1989.Considering the temporal-spatial distributions of ARGON images and Landsat images in Antarctica, two different methods respectively based on ortho-photos pair and Non-Ortho photos are adopted in this paper. More specifically, when there exist two stereo pairs taken in different time in the glacier region, after being ortho-rectified, the stereo pairs can be used to calculate ice flow velocity based on feature matching method. Otherwise, a parallax decomposition method that separates the effect of the terrain relief from the ice flow motion is applied when there only exists one stereo pair with a certain time interval. With this method, glacier surface velocity is available in the glacier region lacked enough stereo pairs. The methods mentioned above for estimating ice flow velocity are applied in Totten, Amery and Fimbul, etc. in eastern Antarctica. Furthermore, a 1960-80s ice flow speed map in the main glaciers of East Antarctica is produced for the first time.

Sign in / Sign up

Export Citation Format

Share Document