scholarly journals The Equation of Continuity and its Application to the Ice Sheet Near “byrd” Station, Antarctica

1977 ◽  
Vol 18 (80) ◽  
pp. 359-371 ◽  
Author(s):  
I. M. Whillans
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Ice Sheet ◽  
Ice Thickness ◽  
Surface Mass Balance ◽  
Velocity Measurements ◽  
Ice Flow ◽  
Measured Velocity ◽  
Surface Mass ◽  
Ice Velocity

AbstractThe continuity relationship that is often used in the study of ice sheets and ice shelves is developed by integrating the equation of continuity through the ice thickness. This equation is then integrated again with respect to horizontal distance from an ice divide, showing that the difference between the true ice velocity and the balance velocity, which is defined, is a measure of the time chance of the mass of a column through the ice thickness.The relationship is applied using data from along the “Byrd” station strain network, Antarctica. This region is found to be thinning slowly (0.03 m a−1 of ice of mean density) and uniformly, but it is still close to steady-state. The calculations would show a larger thinning rate if bottom sliding contributed more to the ice movement and integral shear contributed less, but the “Byrd” station bore-hole tilting results of Garfield and Ueda (1975, 1976), together with surface velocity measurements at “Byrd” station, indicate that most of the ice flow is by deformation within the ice mass. This large amount of internal deformation is more than that predicted by most “flow laws”, probably because of the strongly oriented ice-crystal fabric in the ice sheet. The cause of ice thinning is probably decreased surface mass balance beginning before A.D. 1550.The consistent relationship between measured velocity and balance velocity indicates that the ice flow is simple and that flow lines are in the same direction at depth as at the surface when considered smoothed over a distance of 10 km. Because the ice sheet is at present thinning, the balance velocity, calculated only from flow line and surface mass-balance data, and the somewhat mistaken assumption of steady-state is 15% less than the true ice velocity. This rather small difference confirms the use of balance-velocity estimates where velocity measurements are not available.

scholarly journals The Equation of Continuity and its Application to the Ice Sheet Near “byrd” Station, Antarctica

1977 ◽  
Vol 18 (80) ◽  
pp. 359-371 ◽  
Author(s):  
I. M. Whillans
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Ice Sheet ◽  
Ice Thickness ◽  
Surface Mass Balance ◽  
Velocity Measurements ◽  
Ice Flow ◽  
Measured Velocity ◽  
Surface Mass ◽  
Ice Velocity

Abstract The continuity relationship that is often used in the study of ice sheets and ice shelves is developed by integrating the equation of continuity through the ice thickness. This equation is then integrated again with respect to horizontal distance from an ice divide, showing that the difference between the true ice velocity and the balance velocity, which is defined, is a measure of the time chance of the mass of a column through the ice thickness. The relationship is applied using data from along the “Byrd” station strain network, Antarctica. This region is found to be thinning slowly (0.03 m a−1 of ice of mean density) and uniformly, but it is still close to steady-state. The calculations would show a larger thinning rate if bottom sliding contributed more to the ice movement and integral shear contributed less, but the “Byrd” station bore-hole tilting results of Garfield and Ueda (1975, 1976), together with surface velocity measurements at “Byrd” station, indicate that most of the ice flow is by deformation within the ice mass. This large amount of internal deformation is more than that predicted by most “flow laws”, probably because of the strongly oriented ice-crystal fabric in the ice sheet. The cause of ice thinning is probably decreased surface mass balance beginning before A.D. 1550. The consistent relationship between measured velocity and balance velocity indicates that the ice flow is simple and that flow lines are in the same direction at depth as at the surface when considered smoothed over a distance of 10 km. Because the ice sheet is at present thinning, the balance velocity, calculated only from flow line and surface mass-balance data, and the somewhat mistaken assumption of steady-state is 15% less than the true ice velocity. This rather small difference confirms the use of balance-velocity estimates where velocity measurements are not available.

scholarly journals Simulating ice thickness and velocity evolution of Upernavik Isstrøm 1849–2012 by forcing prescribed terminus positions in ISSM

2018 ◽  
Vol 12 (4) ◽  
pp. 1511-1522 ◽  
Author(s):  
Konstanze Haubner ◽  
Jason E. Box ◽  
Nicole J. Schlegel ◽  
Eric Y. Larour ◽  
Mathieu Morlighem ◽  
...  
Keyword(s):  
Mass Loss ◽  
Mass Balance ◽  
Surface Mass Balance ◽  
Position Change ◽  
Ice Flow ◽  
Surface Mass ◽  
Total Mass Loss ◽  
Negative Surface ◽  
Ice Velocity ◽  
Glacier Velocity

Abstract. Tidewater glacier velocity and mass balance are known to be highly responsive to terminus position change. Yet it remains challenging for ice flow models to reproduce observed ice margin changes. Here, using the Ice Sheet System Model (Larour et al., 2012), we simulate the ice velocity and thickness changes of Upernavik Isstrøm (north-western Greenland) by prescribing a collection of 27 observed terminus positions spanning 164 years (1849–2012). The simulation shows increased ice velocity during the 1930s, the late 1970s and between 1995 and 2012 when terminus retreat was observed along with negative surface mass balance anomalies. Three distinct mass balance states are evident in the reconstruction: (1849–1932) with near zero mass balance, (1932–1992) with ice mass loss dominated by ice dynamical flow, and (1998–2012), when increased retreat and negative surface mass balance anomalies led to mass loss that was twice that of any earlier period. Over the multi-decadal simulation, mass loss was dominated by thinning and acceleration responsible for 70 % of the total mass loss induced by prescribed change in terminus position. The remaining 30 % of the total ice mass loss resulted directly from prescribed terminus retreat and decreasing surface mass balance. Although the method can not explain the cause of glacier retreat, it enables the reconstruction of ice flow and geometry during 1849–2012. Given annual or seasonal observed terminus front positions, this method could be a useful tool for evaluating simulations investigating the effect of calving laws.

scholarly journals Greenland ice sheet contribution to sea-level rise from a new-generation ice-sheet model

2012 ◽  
Vol 6 (6) ◽  
pp. 1561-1576 ◽  
Author(s):  
F. Gillet-Chaulet ◽  
O. Gagliardini ◽  
H. Seddik ◽  
M. Nodet ◽  
G. Durand ◽  
...  
Keyword(s):  
Mass Balance ◽  
Sea Level Rise ◽  
Sea Level ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Mass Balance ◽  
Ice Flow ◽  
Surface Mass ◽  
Continental Scale ◽  
New Generation

Abstract. Over the last two decades, the Greenland ice sheet (GrIS) has been losing mass at an increasing rate, enhancing its contribution to sea-level rise (SLR). The recent increases in ice loss appear to be due to changes in both the surface mass balance of the ice sheet and ice discharge (ice flux to the ocean). Rapid ice flow directly affects the discharge, but also alters ice-sheet geometry and so affects climate and surface mass balance. Present-day ice-sheet models only represent rapid ice flow in an approximate fashion and, as a consequence, have never explicitly addressed the role of ice discharge on the total GrIS mass balance, especially at the scale of individual outlet glaciers. Here, we present a new-generation prognostic ice-sheet model which reproduces the current patterns of rapid ice flow. This requires three essential developments: the complete solution of the full system of equations governing ice deformation; a variable resolution unstructured mesh to resolve outlet glaciers and the use of inverse methods to better constrain poorly known parameters using observations. The modelled ice discharge is in good agreement with observations on the continental scale and for individual outlets. From this initial state, we investigate possible bounds for the next century ice-sheet mass loss. We run sensitivity experiments of the GrIS dynamical response to perturbations in climate and basal lubrication, assuming a fixed position of the marine termini. We find that increasing ablation tends to reduce outflow and thus decreases the ice-sheet imbalance. In our experiments, the GrIS initial mass (im)balance is preserved throughout the whole century in the absence of reinforced forcing, allowing us to estimate a lower bound of 75 mm for the GrIS contribution to SLR by 2100. In one experiment, we show that the current increase in the rate of ice loss can be reproduced and maintained throughout the whole century. However, this requires a very unlikely perturbation of basal lubrication. From this result we are able to estimate an upper bound of 140 mm from dynamics only for the GrIS contribution to SLR by 2100.

scholarly journals Inferred basal friction and surface mass balance of the Northeast Greenland Ice Stream using data assimilation of ICESat (Ice Cloud and land Elevation Satellite) surface altimetry and ISSM (Ice Sheet System Model)

2014 ◽  
Vol 8 (6) ◽  
pp. 2335-2351 ◽  
Author(s):  
E. Larour ◽  
J. Utke ◽  
B. Csatho ◽  
A. Schenk ◽  
H. Seroussi ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Mass Balance ◽  
Ice Sheet ◽  
System Model ◽  
Surface Mass Balance ◽  
Altimetry Data ◽  
Ice Flow ◽  
Surface Mass ◽  
Ice Cloud ◽  
Basal Friction

Abstract. We present a new data assimilation method within the Ice Sheet System Model (ISSM) framework that is capable of assimilating surface altimetry data from missions such as ICESat (Ice Cloud and land Elevation Satellite) into reconstructions of transient ice flow. The new method relies on algorithmic differentiation to compute gradients of objective functions with respect to model forcings. It is applied to the Northeast Greenland Ice Stream, where surface mass balance and basal friction forcings are temporally inverted, resulting in adjusted modeled surface heights that best fit existing altimetry. This new approach allows for a better quantification of basal and surface processes and a better understanding of the physical processes currently missing in transient ice-flow models to better capture the important intra- and interannual variability in surface altimetry. It also demonstrates that large spatial and temporal variability is required in model forcings such as surface mass balance and basal friction, variability that can only be explained by including more complex processes such as snowpack compaction at the surface and basal hydrology at the bottom of the ice sheet. This approach is indeed a first step towards assimilating the wealth of high spatial resolution altimetry data available from EnviSat, ICESat, Operation IceBridge and CryoSat-2, and that which will be available in the near future with the launch of ICESat-2.

scholarly journals Greenland Ice Sheet contribution to sea-level rise from a new-generation ice-sheet model

2012 ◽  
Vol 6 (4) ◽  
pp. 2789-2826 ◽  
Author(s):  
F. Gillet-Chaulet ◽  
O. Gagliardini ◽  
H. Seddik ◽  
M. Nodet ◽  
G. Durand ◽  
...  
Keyword(s):  
Mass Balance ◽  
Sea Level Rise ◽  
Sea Level ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Mass Balance ◽  
Ice Flow ◽  
Surface Mass ◽  
Continental Scale ◽  
New Generation

Abstract. Over the last two decades, the Greenland Ice Sheet (GrIS) has been losing mass at an increasing rate, enhancing its contribution to sea-level rise. The recent increases in ice loss appear to be due to changes in both the surface mass balance of the ice sheet and ice discharge (ice flux to the ocean). Rapid ice flow directly affects the discharge, but also alters ice-sheet geometry and so affects climate and surface mass balance. The most usual ice-sheet models only represent rapid ice flow in an approximate fashion and, as a consequence, have never explicitly addressed the role of ice discharge on the total GrIS mass balance, especially at the scale of individual outlet glaciers. Here, we present a new-generation prognostic ice-sheet model which reproduces the current patterns of rapid ice flow. This requires three essential developments: the complete solution of the full system of equations governing ice deformation; an unstructured mesh to usefully resolve outlet glaciers and the use of inverse methods to better constrain poorly known parameters using observations. The modelled ice discharge is in good agreement with observations on the continental scale and for individual outlets. By conducting perturbation experiments, we investigate how current ice loss will endure over the next century. Although we find that increasing ablation tends to reduce outflow and on its own has a stabilising effect, if destabilisation processes maintain themselves over time, current increases in the rate of ice loss are likely to continue.

scholarly journals Eemian Greenland ice sheet simulated with a higher-order model shows strong sensitivity to surface mass balance forcing

2019 ◽  
Vol 13 (8) ◽  
pp. 2133-2148
Author(s):  
Andreas Plach ◽  
Kerim H. Nisancioglu ◽  
Petra M. Langebroek ◽  
Andreas Born ◽  
Sébastien Le clec'h
Keyword(s):  
Mass Balance ◽  
Sea Level Rise ◽  
Sea Level ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Higher Order ◽  
Interglacial Period ◽  
Surface Mass Balance ◽  
Ice Flow ◽  
Surface Mass

Abstract. The Greenland ice sheet contributes increasingly to global sea level rise. Its history during past warm intervals is a valuable reference for future sea level projections. We present ice sheet simulations for the Eemian interglacial period (∼130 000 to 115 000 years ago), a period with warmer-than-present summer climate over Greenland. The evolution of the Eemian Greenland ice sheet is simulated with a 3-D higher-order ice sheet model, forced with a surface mass balance derived from regional climate simulations. Sensitivity experiments with various surface mass balances, basal friction, and ice flow approximations are discussed. The surface mass balance forcing is identified as the controlling factor setting the minimum in Eemian ice volume, emphasizing the importance of a reliable surface mass balance model. Furthermore, the results indicate that the surface mass balance forcing is more important than the representation of ice flow for simulating the large-scale ice sheet evolution. This implies that modeling of the future contribution of the Greenland ice sheet to sea level rise highly depends on an accurate surface mass balance.

scholarly journals Surface Mass-Balance Gradients From Elevation and Ice Flux Data in the Columbia Basin, Canada

2021 ◽  
Vol 9 ◽  
Author(s):  
Ben M. Pelto ◽  
Brian Menounos
Keyword(s):  
Mass Balance ◽  
Numerical Models ◽  
Large Mass ◽  
Surface Elevation ◽  
Surface Velocity ◽  
Ice Thickness ◽  
Surface Mass Balance ◽  
Ice Dynamics ◽  
Surface Mass ◽  
Ice Velocity

The mass-balance—elevation relation for a given glacier is required for many numerical models of ice flow. Direct measurements of this relation using remotely-sensed methods are complicated by ice dynamics, so observations are currently limited to glaciers where surface mass-balance measurements are routinely made. We test the viability of using the continuity equation to estimate annual surface mass balance between flux-gates in the absence of in situ measurements, on five glaciers in the Columbia Mountains of British Columbia, Canada. Repeat airborne laser scanning surveys of glacier surface elevation, ice penetrating radar surveys and publicly available maps of ice thickness are used to estimate changes in surface elevation and ice flux. We evaluate this approach by comparing modeled to observed mass balance. Modeled mass-balance gradients well-approximate those obtained from direct measurement of surface mass balance, with a mean difference of +6.6 ± 4%. Regressing modeled mass balance, equilibrium line altitudes are on average 15 m higher than satellite-observations of the transient snow line. Estimates of mass balance over flux bins compare less favorably than the gradients. Average mean error (+0.03 ± 0.07 m w.e.) between observed and modeled mass balance over flux bins is relatively small, yet mean absolute error (0.55 ± 0.18 m w.e.) and average modeled mass-balance uncertainty (0.57 m w.e.) are large. Mass conservation, assessed with glaciological data, is respected (when estimates are within 1σ uncertainties) for 84% of flux bins representing 86% of total glacier area. Uncertainty on ice velocity, especially for areas where surface velocity is low (<10 m a−1) contributes the greatest error in estimating ice flux. We find that using modeled ice thicknesses yields comparable modeled mass-balance gradients relative to using observations of ice thickness, but we caution against over-interpreting individual flux-bin mass balances due to large mass-balance residuals. Given the performance of modeled ice thickness and the increasing availability of ice velocity and surface topography data, we suggest that similar efforts to produce mass-balance gradients using modern high-resolution datasets are feasible on larger scales.

THE STUDIES OF SURFACE MASS BALANCE AND ICE FLOW ON GLACIERS AUSTRELOVéNBREEN AND PEDERSENBREEN, SVALBARD, ARCTIC

2010 ◽  
Vol 22 (1) ◽  
pp. 10-22 ◽  
Author(s):  
Mingxing Xu ◽  
Ming Yan ◽  
Jiawen Ren ◽  
Songtao Ai ◽  
Jiancheng Kang ◽  
...  
Keyword(s):  
Mass Balance ◽  
Surface Mass Balance ◽  
Ice Flow ◽  
Surface Mass

Contemporary (1960–2012) Evolution of the Climate and Surface Mass Balance of the Greenland Ice Sheet

2013 ◽  
Vol 35 (5) ◽  
pp. 1155-1174 ◽  
Author(s):  
J. H. van Angelen ◽  
M. R. van den Broeke ◽  
B. Wouters ◽  
J. T. M. Lenaerts
Keyword(s):  
Mass Balance ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Mass Balance ◽  
Surface Mass

scholarly journals Simulation of the future sea level contribution of Greenland with a new glacial system model

2018 ◽  
Vol 12 (10) ◽  
pp. 3097-3121 ◽  
Author(s):  
Reinhard Calov ◽  
Sebastian Beyer ◽  
Ralf Greve ◽  
Johanna Beckmann ◽  
Matteo Willeit ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Surface Temperature ◽  
Mass Balance ◽  
Sea Level Rise ◽  
Sea Level ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
System Model ◽  
Surface Mass Balance ◽  
Surface Mass

Abstract. We introduce the coupled model of the Greenland glacial system IGLOO 1.0, including the polythermal ice sheet model SICOPOLIS (version 3.3) with hybrid dynamics, the model of basal hydrology HYDRO and a parameterization of submarine melt for marine-terminated outlet glaciers. The aim of this glacial system model is to gain a better understanding of the processes important for the future contribution of the Greenland ice sheet to sea level rise under future climate change scenarios. The ice sheet is initialized via a relaxation towards observed surface elevation, imposing the palaeo-surface temperature over the last glacial cycle. As a present-day reference, we use the 1961–1990 standard climatology derived from simulations of the regional atmosphere model MAR with ERA reanalysis boundary conditions. For the palaeo-part of the spin-up, we add the temperature anomaly derived from the GRIP ice core to the years 1961–1990 average surface temperature field. For our projections, we apply surface temperature and surface mass balance anomalies derived from RCP 4.5 and RCP 8.5 scenarios created by MAR with boundary conditions from simulations with three CMIP5 models. The hybrid ice sheet model is fully coupled with the model of basal hydrology. With this model and the MAR scenarios, we perform simulations to estimate the contribution of the Greenland ice sheet to future sea level rise until the end of the 21st and 23rd centuries. Further on, the impact of elevation–surface mass balance feedback, introduced via the MAR data, on future sea level rise is inspected. In our projections, we found the Greenland ice sheet to contribute between 1.9 and 13.0 cm to global sea level rise until the year 2100 and between 3.5 and 76.4 cm until the year 2300, including our simulated additional sea level rise due to elevation–surface mass balance feedback. Translated into additional sea level rise, the strength of this feedback in the year 2100 varies from 0.4 to 1.7 cm, and in the year 2300 it ranges from 1.7 to 21.8 cm. Additionally, taking the Helheim and Store glaciers as examples, we investigate the role of ocean warming and surface runoff change for the melting of outlet glaciers. It shows that ocean temperature and subglacial discharge are about equally important for the melting of the examined outlet glaciers.

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