scholarly journals Glacier–plume or glacier–fjord circulation models? A 2-D comparison for Hansbreen–Hansbukta system, Svalbard

2021 ◽  
pp. 1-14
Author(s):  
Eva De Andrés ◽  
Jaime Otero ◽  
Francisco J. Navarro ◽  
Waldemar Walczowski
Keyword(s):  
Water Depth ◽  
Seasonal Variations ◽  
Stress Fields ◽  
Two Dimensional ◽  
Coupled Models ◽  
Fjord Circulation ◽  
Glacier Front ◽  
Iceberg Calving ◽  
Best Fit ◽  
Frontal Ablation

Abstract Up to 30% of the current tidewater mass loss in Svalbard corresponds to frontal ablation through submarine melting and calving. We developed two-dimensional (2-D) glacier–line–plume and glacier–fjord circulation coupled models, both including subglacial discharge, submarine melting and iceberg calving, to simulate Hansbreen–Hansbukta system, SW Svalbard. We ran both models for 20 weeks, throughout April–August 2010, using different scenarios of subglacial discharge and crevasse water depth. Both models showed large seasonal variations of submarine melting in response to transient fjord temperatures and subglacial discharges. Subglacial discharge intensity and crevasse water depth influenced calving rates. Using the best-fit configuration for both parameters our two coupled models predicted observed front positions reasonably well (±10 m). Although the two models showed different melt-undercutting front shapes, which affected the net-stress fields near the glacier front, no significant effects on the simulated glacier front positions were found. Cumulative calving (91 and 94 m) and submarine melting (108 and 118 m) along the simulated period showed in both models (glacier–plume and glacier–fjord) a 1:1.2 ratio of linear frontal ablation between the two mechanisms. Overall, both models performed well on predicting observed front positions when best-fit subglacial discharges were imposed, the glacier–plume model being 50 times computationally faster.

scholarly journals A two-dimensional glacier–fjord coupled model applied to estimate submarine melt rates and front position changes of Hansbreen, Svalbard

2018 ◽  
Vol 64 (247) ◽  
pp. 745-758 ◽  
Author(s):  
E. DE ANDRÉS ◽  
J. OTERO ◽  
F. NAVARRO ◽  
A. PROMIŃSKA ◽  
J. LAPAZARAN ◽  
...  
Keyword(s):  
Coupled Model ◽  
Small Scale ◽  
Two Dimensional ◽  
Time Step ◽  
Software Packages ◽  
Front Position ◽  
Circulation Patterns ◽  
Glacier Front ◽  
Order Of Magnitude ◽  
Frontal Ablation

ABSTRACTWe have developed a two-dimensional coupled glacier–fjord model, which runs automatically using Elmer/Ice and MITgcm software packages, to investigate the magnitude of submarine melting along a vertical glacier front and its potential influence on glacier calving and front position changes. We apply this model to simulate the Hansbreen glacier–Hansbukta proglacial–fjord system, Southwestern Svalbard, during the summer of 2010. The limited size of this system allows us to resolve some of the small-scale processes occurring at the ice–ocean interface in the fjord model, using a 0.5 s time step and a 1 m grid resolution near the glacier front. We use a rich set of field data spanning the period April–August 2010 to constrain, calibrate and validate the model. We adjust circulation patterns in the fjord by tuning subglacial discharge inputs that best match observed temperature while maintaining a compromise with observed salinity, suggesting a convectively driven circulation in Hansbukta. The results of our model simulations suggest that both submarine melting and crevasse hydrofracturing exert important controls on seasonal frontal ablation, with submarine melting alone not being sufficient for reproducing the observed patterns of seasonal retreat. Both submarine melt and calving rates accumulated along the entire simulation period are of the same order of magnitude, ~100 m. The model results also indicate that changes in submarine melting lag meltwater production by 4–5 weeks, which suggests that it may take up to a month for meltwater to traverse the englacial and subglacial drainage network.

Glacier-plume or glacier-fjord circulation models? A model intercomparison for Hansbreen-Hansbukta system, Svalbard

2020 ◽  
Author(s):  
Eva De Andrés ◽  
Jaime Otero ◽  
Francisco Navarro
Keyword(s):  
Information Exchange ◽  
Computational Cost ◽  
Coupled Model ◽  
High Sensitivity ◽  
Coupled Models ◽  
Plume Model ◽  
Fjord Circulation ◽  
Iceberg Calving ◽  
Front Shape ◽  
Set Up

<p> <span>Up to 30% of the global tidewater mass loss corresponds to frontal ablation through submarine melting and calving. However, the glacier-fjord interactions remain poorly understood and challenging to constrain in the models. We have developed a 2D glacier flowline-plume coupled model that includes subglacial discharge, submarine melting and iceberg calving to simulate Hansbreen-Hansbukta system (SW Svalbard). We run the model for 20 weeks, from April to September of 2010, with weekly information exchange between glacier and plume models. The same set up and constraints of a previous glacier-fjord </span><span>circulation </span><span>model are used here, making the results of both simulations comparable. We consider a 200 m-width subglacial discharging channel, which was found to be a good approximation in the previous glacier-fjord model. Submarine melt rates show high sensitivity to the subglacial-discharge and ambient fjord-temperature intraseasonal evolution. Calving rates are highly dependent on both submarine melting and crevasse water depth. Glacier-plume and glacier-fjord coupled models differ in vertically-accumulated submarine melt rates (up to 30 % higher for the glacier-plume model) and show different melt-undercutting front shapes, which have an influence on the net stress fields near the glacier front. The quasi-linear melt-undercutting morphology exhibited by the glacier-plume model promotes higher calving rates than the quasi-parabolic front shape resulting from the glacier-fjord model, although both models predict similar front positions. Given that the glacier-plume model diminishes the computational cost by a factor of >50, we think that it is a good option for projection studies, as long as we apply appropriate constraints to subglacial discharge fluxes and ambient fjord temperatures.</span></p>

scholarly journals Two Calving Laws for Grounded Iceberg-Calving Glaciers (Abstract only)

1983 ◽  
Vol 4 ◽  
pp. 295 ◽  
Author(s):  
C. S. Brown ◽  
W. G. Sikonia ◽  
Austin Post ◽  
L. A. Rasmussen ◽  
M. F. Meier
Keyword(s):  
Water Depth ◽  
Variance Reduction ◽  
Coefficient Of Determination ◽  
Time Intervals ◽  
Cross Sectional ◽  
Glacial Stream ◽  
Iceberg Calving ◽  
Average Water ◽  
Image Position ◽  
Best Fit

Prediction of the future retreat of Columbia Glacier, Alaska, required a calving law for the boundary condition at the terminus. Qualitative observations on the variations of all major iceberg-calving glaciers of Alaska suggest that calving is high whenever glaciers terminate in deep water, and greatly reduced whenever they terminate in shallow water. Calving relations were investigated based on calculations of calving speed, defined as the volume rate of iceberg discharge from the terminus divided by the cross-sectional area of the terminus. The calving speed was determined for 12 glaciers for which measurements of glacier speed, advance and retreat rates, and other variables were obtained. To extend the range of data, four additional periods of rapid retreat were examined. Values for the terminus characteristics of water depth, cliff height, and thickness of the terminus, averaged over the width of the glacier and over a year, were then examined in relation to the calculated speeds of calving. A statistical analysis to determine the form and coefficients of an empirical calving relation that approximates the data shows that calving speed is best fitted by a simple proportionality to average water depth at the terminus: 1 where v c is the calving speed and h w the water depth, both averaged over the width and over a year, and c a constant of proportionality. This gives a variance reduction fraction (similar to the coefficient of determination r2) of 0.90. To investigate seasonal changes in calving, data based on shorter time intervals were obtained at the head of embayments from Columbia Glacier. At intervals of approximately two months, the following expression fits intra-yearly calving at Columbia Glacier: 2 where D is the meltwater discharge from the glacier, hj is the height of the ice column unsupported by water buoyancy, a, b, c are constants, and vc and hu are evaluated at the embayment head. D was determined by correlation with a nearby glacial stream, and hu = h _ hw PW/PJ, where h is glacier thickness and pi and pw the densities of ice and water. Best-fit values of b and c are approximately 0.5 and -2, respectively. This yields a variance reduction fraction r2 of 0.83. Equation (2) does not fit data averaged over a year and over the width of the glacier and Equation (1) does not fit data obtained over shorter periods at the head of the embayment. Although the two equations are different in form, for similar or average values of D and h - hw (ice-cliff height), they give approximately similar results over the present range of the geometry of the terminus of Columbia Glacier. Whether this will be true after rapid retreat begins remains to be seen.

scholarly journals Two Calving Laws for Grounded Iceberg-Calving Glaciers (Abstract only)

1983 ◽  
Vol 4 ◽  
pp. 295-295 ◽  
Author(s):  
C. S. Brown ◽  
W. G. Sikonia ◽  
Austin Post ◽  
L. A. Rasmussen ◽  
M. F. Meier
Keyword(s):  
Water Depth ◽  
Variance Reduction ◽  
Coefficient Of Determination ◽  
Time Intervals ◽  
Cross Sectional ◽  
Glacial Stream ◽  
Iceberg Calving ◽  
Average Water ◽  
Image Position ◽  
Best Fit

Prediction of the future retreat of Columbia Glacier, Alaska, required a calving law for the boundary condition at the terminus. Qualitative observations on the variations of all major iceberg-calving glaciers of Alaska suggest that calving is high whenever glaciers terminate in deep water, and greatly reduced whenever they terminate in shallow water. Calving relations were investigated based on calculations of calving speed, defined as the volume rate of iceberg discharge from the terminus divided by the cross-sectional area of the terminus. The calving speed was determined for 12 glaciers for which measurements of glacier speed, advance and retreat rates, and other variables were obtained. To extend the range of data, four additional periods of rapid retreat were examined. Values for the terminus characteristics of water depth, cliff height, and thickness of the terminus, averaged over the width of the glacier and over a year, were then examined in relation to the calculated speeds of calving. A statistical analysis to determine the form and coefficients of an empirical calving relation that approximates the data shows that calving speed is best fitted by a simple proportionality to average water depth at the terminus: 1 where vc is the calving speed and hw the water depth, both averaged over the width and over a year, and c a constant of proportionality. This gives a variance reduction fraction (similar to the coefficient of determination r2) of 0.90.To investigate seasonal changes in calving, data based on shorter time intervals were obtained at the head of embayments from Columbia Glacier. At intervals of approximately two months, the following expression fits intra-yearly calving at Columbia Glacier: 2 where D is the meltwater discharge from the glacier, hj is the height of the ice column unsupported by water buoyancy, a, b, c are constants, and vc and hu are evaluated at the embayment head. D was determined by correlation with a nearby glacial stream, and hu = h _ hw PW/PJ, where h is glacier thickness and pi and pw the densities of ice and water. Best-fit values of b and c are approximately 0.5 and -2, respectively. This yields a variance reduction fraction r2 of 0.83.Equation (2) does not fit data averaged over a year and over the width of the glacier and Equation (1) does not fit data obtained over shorter periods at the head of the embayment. Although the two equations are different in form, for similar or average values of D and h - hw (ice-cliff height), they give approximately similar results over the present range of the geometry of the terminus of Columbia Glacier. Whether this will be true after rapid retreat begins remains to be seen.

scholarly journals Exotic spin phases in two-dimensional spin-orbit coupled models: Importance of quantum effects

2017 ◽  
Vol 96 (11) ◽  
Author(s):  
Chao Wang ◽  
Ming Gong ◽  
Yongjian Han ◽  
Guangcan Guo ◽  
Lixin He
Keyword(s):  
Quantum Effects ◽  
Spin Orbit ◽  
Two Dimensional ◽  
Coupled Models

Unstable Squat from Lateral Motion of Ships in Shallow Water

1974 ◽  
Vol 18 (01) ◽  
pp. 50-55
Author(s):  
E. O. Tuck
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Critical Value ◽  
Lateral Motion ◽  
Two Dimensional ◽  
Theoretical Possibility ◽  
Dimensional Flow ◽  
Ship Maneuvers ◽  
Depth Ratio ◽  
Two Dimensional Flow

The theoretical possibility of instability exists in two-dimensional or nearly two-dimensional flow involving ship sections in shallow water, whenever the clearance is very low. This squat instability, which causes the ship to hit the bottom, occurs only for speeds greater than a certain critical value which varies as the three-halves power of the clearance/water depth ratio. Some applications to lateral ship maneuvers, as in tug-assisted docking, are discussed.

scholarly journals Testing the effect of water in crevasses on a physically based calving model

2012 ◽  
Vol 53 (60) ◽  
pp. 90-96 ◽  
Author(s):  
S. Cook ◽  
T. Zwinger ◽  
I.C. Rutt ◽  
S. O'Neel ◽  
T. Murray
Keyword(s):  
Finite Element ◽  
Water Depth ◽  
Surface Mass Balance ◽  
Two Dimensional ◽  
Finite Element Code ◽  
Surface Mass ◽  
Starting Point ◽  
Physically Based ◽  
Calving Rate

AbstractA new implementation of a calving model, using the finite-element code Elmer, is presented and used to investigate the effects of surface water within crevasses on calving rate. For this work, we use a two-dimensional flowline model of Columbia Glacier, Alaska. Using the glacier’s 1993 geometry as a starting point, we apply a crevasse-depth calving criterion, which predicts calving at the location where surface crevasses cross the waterline. Crevasse depth is calculated using the Nye formulation. We find that calving rate in such a regime is highly dependent on the depth of water in surface crevasses, with a change of just a few metres in water depth causing the glacier to change from advancing at a rate of 3.5 kma–1 to retreating at a rate of 1.9 km a–1. These results highlight the potential for atmospheric warming and surface meltwater to trigger glacier retreat, but also the difficulty of modelling calving rates, as crevasse water depth is difficult to determine either by measurement in situ or surface mass-balance modelling.

scholarly journals Large spatial variations in the flux balance along the front of a Greenland tidewater glacier

2019 ◽  
Vol 13 (3) ◽  
pp. 911-925 ◽  
Author(s):  
Till J. W. Wagner ◽  
Fiamma Straneo ◽  
Clark G. Richards ◽  
Donald A. Slater ◽  
Laura A. Stevens ◽  
...  
Keyword(s):  
High Resolution ◽  
Spatial Variability ◽  
Ocean Model ◽  
Complex Interplay ◽  
Flux Balance ◽  
Tidewater Glacier ◽  
Glacier Front ◽  
The Individual ◽  
High Spatial Variability ◽  
Frontal Ablation

Abstract. The frontal flux balance of a medium-sized tidewater glacier in western Greenland in the summer is assessed by quantifying the individual components (ice flux, retreat, calving, and submarine melting) through a combination of data and models. Ice flux and retreat are obtained from satellite data. Submarine melting is derived using a high-resolution ocean model informed by near-ice observations, and calving is estimated using a record of calving events along the ice front. All terms exhibit large spatial variability along the ∼5 km wide ice front. It is found that submarine melting accounts for much of the frontal ablation in small regions where two subglacial discharge plumes emerge at the ice front. Away from the subglacial plumes, the estimated melting accounts for a small fraction of frontal ablation. Glacier-wide, these estimates suggest that mass loss is largely controlled by calving. This result, however, is at odds with the limited presence of icebergs at this calving front – suggesting that melt rates in regions outside of the subglacial plumes may be underestimated. Finally, we argue that localized melt incisions into the glacier front can be significant drivers of calving. Our results suggest a complex interplay of melting and calving marked by high spatial variability along the glacier front.

scholarly journals CALCULATION OF THE RATE OF NET ON-OFFSHORE SEDIMENT TRANSPORT ON THE BASIS OF FLUX CONCEPT

1984 ◽  
Vol 1 (19) ◽  
pp. 91 ◽  
Author(s):  
Ichiro Deguchi ◽  
Toru Sawaragi
Keyword(s):  
Sediment Transport ◽  
Water Depth ◽  
Sediment Concentration ◽  
Suspended Load ◽  
Spatial Variations ◽  
Sediment Flux ◽  
Bed Load ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Dimensional Model

Time and spatial variations of sediment concentration of both bed load and suspended load in the process of two-dimensional beach deformation were investigated experimentally. At the same time, the relation between the velocities of water-particle and sediment migration was analyzed theoretically. By using those results,a net rate of on-offshore sediment_ transport in the process of two-dimensional model beach deformation qf was calculated on the basis of sediment flux. It is found that Qf coincides fairly well with .the net rate of on-offshore sediment transport calculated from the change of water depth.

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