scholarly journals Wave Ogives

1986 ◽  
Vol 32 (112) ◽  
pp. 325-334 ◽  
Author(s):  
E.D. Waddington
Keyword(s):  
Mass Balance ◽  
Method Of Characteristics ◽  
Wave Pattern ◽  
Wave Excitation ◽  
Ice Flow ◽  
Forcing Function ◽  
Excitation Potential ◽  
Ice Velocity ◽  
Balance Functions ◽  
Velocity Channel

AbstractWave ogives arise in a solution of the continuity equation by the method of characteristics. Steady ice flow is assumed. Ice velocity, channel width, and mass-balance functions combine to form a wave-excitation potential that yields the forcing function for wave ogives. This linear-systems formulation extends the ogive theory of Nye. Convolution of the temporal cumulative mass balance and spatial forcing functions gives the total wave pattern below an ice fall. Many ice falls do not generate ogives because the wave amplitude is modulated by a factor related to ice-fall length. The wave ogives at Austerdalsbreen, Norway, are due almost entirely to ice acceleration at the top of the ice-fall, i.e. the same zone that King and Lewis showed was responsible for forming Forbes bands.

scholarly journals Wave Ogives

1986 ◽  
Vol 32 (112) ◽  
pp. 325-334 ◽  
Author(s):  
E.D. Waddington
Keyword(s):  
Mass Balance ◽  
Method Of Characteristics ◽  
Wave Pattern ◽  
Wave Excitation ◽  
Ice Flow ◽  
Forcing Function ◽  
Excitation Potential ◽  
Ice Velocity ◽  
Balance Functions ◽  
Velocity Channel

AbstractWave ogives arise in a solution of the continuity equation by the method of characteristics. Steady ice flow is assumed. Ice velocity, channel width, and mass-balance functions combine to form a wave-excitation potential that yields the forcing function for wave ogives. This linear-systems formulation extends the ogive theory of Nye. Convolution of the temporal cumulative mass balance and spatial forcing functions gives the total wave pattern below an ice fall. Many ice falls do not generate ogives because the wave amplitude is modulated by a factor related to ice-fall length. The wave ogives at Austerdalsbreen, Norway, are due almost entirely to ice acceleration at the top of the ice-fall, i.e. the same zone that King and Lewis showed was responsible for forming Forbes bands.

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 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 Modelling mass balance using photogrammetric and geophysical data: a pilot study at Griesgletscher, Swiss Alps

1999 ◽  
Vol 45 (151) ◽  
pp. 575-583 ◽  
Author(s):  
Andreas Kääb ◽  
Martin Funk
Keyword(s):  
Pilot Study ◽  
Mass Balance ◽  
Surface Strain ◽  
Swiss Alps ◽  
Surface Velocity ◽  
Glacier Mass Balance ◽  
Glacier Surface ◽  
Ice Flow ◽  
Applied Model ◽  
Ice Velocity

AbstractThe kinematic boundary condition al the glacier surface can be used to give glacier mass balance at a point as a function of changes in the surface elevation, and of the horizontal and vertical velocities. Vertical velocity can in turn be estimated from basal slope, basal ice velocity and surface strain. In a pilot study on the tongue of Griesgletscher, Swiss Alps, the applicability of the relation for modelling area-wide ice flow and mass-balance distribution is tested. The key input of the calculations, i.e. the area-wide surface velocity field, is obtained using a newly developed photogrammetric technique. Ice thickness is derived from radar-echo soundings. Error estimates and comparisons with stake measurements show an average accuracy of approximately ±0.3 ma-1for the calculated vertical ice velocity at the surface and ±0.7 ma-1for the calculated mass balance. Due to photogrammetric restrictions and model-inherent sensitivities the applied model appeared to be most suitable for determining area-wide mass balance and ice flow on flat-lying ablation areas, but is so far not very well suited for steep ablation areas and most parts of accumulation areas. Nevertheless, the study on Griesgletscher opens a new and promising perspective for the monitoring of spatial and temporal glacier mass-balance variations.

scholarly journals Numerical simulation of fluctuations of Hintereisferner, Ötztal Alps, since AD 1850

1997 ◽  
Vol 24 ◽  
pp. 199-202 ◽  
Author(s):  
Elisabeth Schlosser
Keyword(s):  
Mass Balance ◽  
Flow Model ◽  
Grid Point ◽  
Mass Balances ◽  
Specific Mass ◽  
Ice Flow ◽  
One Dimensional ◽  
Temperature And Precipitation ◽  
Forcing Function ◽  
Point Distance

A one-dimensional ice flow model was adapted to reconstruct fluctuations of Hintereisferner, Ötztal Alps, since the last postglacial maximum in the mid-19th century. Both front positions and longitudinal ice thickness profiles were considered.As forcing function the specific mass balance was used. The model was calibrated with the period 1953–91, because since 1953 the mass balance has been determined directly. For the period before 1953, as a first step so-called dendro-mass balances (derived from tree rings) were used. Then the mass balance was also parameterized as a function of temperature and precipitation from adjacent climate stations. With both forcings Hintereisferner could be reconstructed back to about 1850 with an accuracy that lies within the accuracy of the model (200 m grid-point distance).

scholarly journals ICE FLOW VELOCITY MAPPING IN EAST ANTARCTICA USING HISTORICAL IMAGES FROM 1960s TO 1980s: RECENT PROGRESS

2021 ◽  
Vol XLIII-B3-2021 ◽  
pp. 491-496
Author(s):  
S. Luo ◽  
Y. Cheng ◽  
Z. Li ◽  
Y. Wang ◽  
K. Wang ◽  
...  
Keyword(s):  
Mass Balance ◽  
Flow Velocity ◽  
East Antarctica ◽  
Input Output ◽  
Velocity Mapping ◽  
Ice Flow ◽  
Optical Images ◽  
Elevation Changes ◽  
Ice Velocity ◽  
Surface Ice

Abstract. Recent research indicates that the estimated elevation changes and associated mass balance in East Antarctica are of some degree of uncertainty; a light accumulation has occurred in its vast inland regions, while mass loss in Wilkes Land appears significant. It is necessary to study the mass change trend in the context of a long period of the East Antarctic Ice Sheet (EAIS). The input-output method based on surface ice flow velocity and ice thickness is one of the most important ways to estimate the mass balance, which can provide longer-term knowledge of mass balance because of the availability of the early satellites in 1960s. In this study, we briefly describe the method of extracting ice velocity based on the historical optical images from 1960s to 1980s. Based on the draft ice velocity map of the EAIS using this method, we conduct a series of validation experiments, including comparisons with in-situ measurement, existing historical maps and rock outcrop dataset. Finally, we use the input-output method to estimate mass balance in some regions of EAIS using the generated velocity map.

Corner Reflectors for Validation of Ice Flow Velocity Derived from SAR Images along the CHINARE-Route in Antarctica

2020 ◽  
Author(s):  
Gang Qiao ◽  
Rongxing Li ◽  
Tong Hao ◽  
Xiaohua Tong ◽  
Yanjun Li ◽  
...  
Keyword(s):  
Mass Balance ◽  
Flow Velocity ◽  
Incident Angle ◽  
Surface Shape ◽  
Sar Images ◽  
Ice Flow ◽  
Ground Truth Data ◽  
Radar Images ◽  
Ice Velocity

<p>Ice flow velocity is an important parameter for evaluating the stability of Antarctic ice shelves and analyzing the mass balance of the ice sheet. Large scale ice flow maps can be produced from satellite images with ground control and validation. Among various ground targets, corner reflectors show distinct intensity characteristics on SAR images due to its highly reflective surface shape and have been used for calibration and validation. This paper focuses on design and implementation of a set of corner reflectors to obtain the first-hand data of in-situ ice flow velocity for SAR image based ice velocity maps. The results should further help evaluate mass balance changes in East Antarctica using the input-output method.</p><p>Generally, the remote sensing method uses airborne or satellite optical and radar images from multiple periods to map ice flow velocity fields. The ground truth data are often sparse due to the harsh environment in the polar region. The annual Chinese Antarctic Research Expedition (CHINARE) makes it possible to obtain period field data of ice velocity within its campaign regions. The ~1200 km CHINARE-Route runs from Zhongshan Station to Kunlun Station along which the ice flow velocity varies from a few meters per year to 100s meters per year. 5 corner reflectors have been designed and installed along the 31st CHINARE-Route in 2015 and the 35th CHINARE-Route in 2019 (M1, M2 and M3 in the 31st CHINARE, A1and A2 in the 35th CHINARE). The ice flow velocities at the installation locations are of different orders of magnitude, about 44 m per year at the locations of M1 and A1, 93 m per year at M2 and M3 and 73 m per year at A2. The satellite orbit inclination, incident angle and the installation location were used to calculate the azimuth and elevation angles of the corner reflectors for installation. At all reflector locations GPS positions were collected at the time of installation. After that, the second time GPS coordinates of M3 in the 34th CHINARE in 2018, the third time GPS coordinates of M3, the second time GPS coordinates of A1 and A2 in the 36th CHINARE at the end of 2019 were measured respectively. TerraSAR-X was used to image the reflectors.</p><p>The results show that the mean in-situ ice flow velocity of M3 is 96.83 m per year between Feb. 2015 and Dec. 2019, with 97.51 m per year between Feb. 2015 and Jan. 2018 and 95.81m per year between Jan. 2018 and Dec. 2019. The in-situ ice flow velocity is 54.9 m per year at A1 between Jan. 2019 and Dec. 2019 and 86.92 m per year at A2 between Feb. 2019 and Dec. 2019. More TerraSAR-X and COSMO-SkyMed data will be used to extract the ice velocity corresponding to GPS measurements. The detailed information will be presented at the meeting.</p>

scholarly journals Predicted time-scales for GISP2 and GRIP boreholes at Summit, Greenland

1992 ◽  
Vol 38 (128) ◽  
pp. 162-168 ◽  
Author(s):  
Christine Schøtt ◽  
E. D. Waddington ◽  
C. F. Raymond
Keyword(s):  
Mass Balance ◽  
Time Scales ◽  
Ice Core ◽  
Ice Cores ◽  
Balance Model ◽  
Momentum Balance ◽  
Regional Survey ◽  
Ice Flow ◽  
The Past ◽  
Ice Velocity

AbstractTwo deep-drilling projects (GISP2 and GRIP) in central Greenland will provide ice cores for paleoclimate studies. Drilling decisions and preliminary interpretations require age-depth curves (time-scales). Using a finite-element momentum-balance model, we calculate the modern ice-flow pattern on the flowline through the two drill sites. Our model appears to require relatively soft ice either throughout the ice sheet or below the Wisconsinan-Holocene transition in order to match the modern geometry and mass balance. By scaling the ice velocity to an assumed mass-balance history throughout the past 200 000 years, we estimate the time-scales at both sites. At GISP2, a flank site, we place the 10 000 years BP isochrone (representing the Wisconsinan-Holocene transition) at 1535 m ice-equivalent depth. At GRIP, on the ice divide, the corresponding depth is 1377 m. Our calculations show ice older than 200 000 years at 100 m above the bed at both coring sites. The time-scale calculation can be used for drilling decisions and preliminary interpretations. It should be refined as more regional-survey and ice-core data become 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

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 Modelling mass balance using photogrammetric and geophysical data: a pilot study at Griesgletscher, Swiss Alps

1999 ◽  
Vol 45 (151) ◽  
pp. 575-583 ◽  
Author(s):  
Andreas Kääb ◽  
Martin Funk
Keyword(s):  
Pilot Study ◽  
Mass Balance ◽  
Surface Strain ◽  
Swiss Alps ◽  
Surface Velocity ◽  
Glacier Mass Balance ◽  
Glacier Surface ◽  
Ice Flow ◽  
Applied Model ◽  
Ice Velocity

AbstractThe kinematic boundary condition al the glacier surface can be used to give glacier mass balance at a point as a function of changes in the surface elevation, and of the horizontal and vertical velocities. Vertical velocity can in turn be estimated from basal slope, basal ice velocity and surface strain. In a pilot study on the tongue of Griesgletscher, Swiss Alps, the applicability of the relation for modelling area-wide ice flow and mass-balance distribution is tested. The key input of the calculations, i.e. the area-wide surface velocity field, is obtained using a newly developed photogrammetric technique. Ice thickness is derived from radar-echo soundings. Error estimates and comparisons with stake measurements show an average accuracy of approximately ±0.3 ma-1 for the calculated vertical ice velocity at the surface and ±0.7 ma-1 for the calculated mass balance. Due to photogrammetric restrictions and model-inherent sensitivities the applied model appeared to be most suitable for determining area-wide mass balance and ice flow on flat-lying ablation areas, but is so far not very well suited for steep ablation areas and most parts of accumulation areas. Nevertheless, the study on Griesgletscher opens a new and promising perspective for the monitoring of spatial and temporal glacier mass-balance variations.

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