scholarly journals Estimating the ice thickness of mountain glaciers with a shape optimization algorithm using surface topography and mass-balance

2014 ◽  
Vol 22 (6) ◽  
Author(s):  
Laurent Michel ◽  
Marco Picasso ◽  
Daniel Farinotti ◽  
Andreas Bauder ◽  
Martin Funk ◽  
...  
Keyword(s):  
Shape Optimization ◽  
Mass Balance ◽  
Surface Topography ◽  
Optimization Algorithm ◽  
Moving Boundary ◽  
Thickness Distribution ◽  
Ice Thickness ◽  
Surface Geometry ◽  
Mountain Glacier ◽  
Surface Mass

AbstractWe present a shape optimization algorithm to estimate the ice thickness distribution within a two-dimensional, non-sliding mountain glacier, given a transient surface geometry and a mass-balance distribution. The approach is based on the minimization of the surface topography misfit at the end of the glacier's evolution in the shallow ice approximation of ice flow. Neither filtering of the surface topography where its gradient vanishes nor interpolation of the basal shear stress is involved. Novelty of the presented shape optimization algorithm is the use of surface topography and mass-balance only within a time-dependent Lagrangian approach for moving-boundary glaciers. On real-world inspired geometries, it is shown to produce estimations of even better quality in smaller time than the recently proposed steady and transient inverse methods. A sensitivity analysis completes the study and evinces the method's higher susceptibility to perturbations in the surface topography than in surface mass-balance or rate factor.

Estimating the ice thickness of shallow glaciers from surface topography and mass-balance data with a shape optimization algorithm

2014 ◽  
Vol 66 ◽  
pp. 182-199 ◽  
Author(s):  
Laurent Michel ◽  
Marco Picasso ◽  
Daniel Farinotti ◽  
Martin Funk ◽  
Heinz Blatter
Keyword(s):  
Shape Optimization ◽  
Mass Balance ◽  
Surface Topography ◽  
Optimization Algorithm ◽  
Ice Thickness

Combining SAR interferometry and the equation of continuity to estimate the three-dimensional glacier surface-velocity vector

1999 ◽  
Vol 45 (151) ◽  
pp. 533-538 ◽  
Author(s):  
Niels Reeh ◽  
Søren Nørvang Madsen ◽  
Johan Jakob Mohr
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Vertical Velocity ◽  
Velocity Vector ◽  
Thickness Distribution ◽  
Vertical Surface ◽  
Horizontal Velocity ◽  
Sar Interferometry ◽  
Surface Velocity ◽  
Ice Thickness

AbstractUntil now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from synthetic aperture radar interferometry. We discuss this assumption, which neglects the influence of the local mass balance and a possible contribution to the vertical velocity arising if the glacier is not in steady state. We find that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreover, the vertical velocity contribution arising if the ice sheet is not in steady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizontal velocity vector. This equation, valid for both steady-state and non-steady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between the surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.

scholarly journals Ice thickness and volume of the Renland Ice Cap, East Greenland

2021 ◽  
pp. 1-13
Author(s):  
Iben Koldtoft ◽  
Aslak Grinsted ◽  
Bo M. Vinther ◽  
Christine S. Hvidberg
Keyword(s):  
Surface Topography ◽  
Climate Model ◽  
Thickness Distribution ◽  
High Elevation ◽  
Surface Velocity ◽  
Ice Thickness ◽  
Model Parameters ◽  
East Greenland ◽  
Ice Volume ◽  
Ice Cap

Abstract To assess the amount of ice volume stored in glaciers or ice caps, a method to estimate ice thickness distribution is required for glaciers where no direct observations are available. In this study, we use an existing inverse method to estimate the bedrock topography and ice thickness of the Renland Ice Cap, East Greenland, using satellite-based observations of the surface topography. The inverse approach involves a procedure in which an ice dynamical model is used to build-up an ice cap in steady state with climate forcing from a regional climate model, and the bedrock is iteratively adjusted until the modelled and observed surface topography match. We validate our model results against information from airborne radar data and satellite observed surface velocity, and we find that the inferred ice thickness and thereby the stored total volume of the ice cap is sensitive to the assumed ice softness and basal slipperiness. The best basal model parameters for the Renland Ice Cap are determined and the best estimated total ice volume of 384 km3 is found. The Renland Ice Cap is particularly interesting because of its location at a high elevation plateau and hence assumed low sensitivity to climate change.

scholarly journals Local surface mass-balance reconstruction from a tephra layer – a case study on the northern slope of Mýrdalsjökull, Iceland

2016 ◽  
Vol 63 (237) ◽  
pp. 79-87 ◽  
Author(s):  
CHRISTOPH MAYER ◽  
JULIA JAENICKE ◽  
ASTRID LAMBRECHT ◽  
LUDWIG BRAUN ◽  
CHRISTOF VÖLKSEN ◽  
...  
Keyword(s):  
Mass Balance ◽  
Volcanic Eruptions ◽  
Surface Mass Balance ◽  
Ablation Zone ◽  
Tephra Layer ◽  
Surface Geometry ◽  
High Accumulation ◽  
Surface Mass ◽  
Ice Caps ◽  
Ice Cap

ABSTRACTMost Icelandic glaciers show high-accumulation rates during winter and strong surface melting during summer. Although it is difficult to establish and maintain mass-balance programs on these glaciers, mass-balance series do exist for several of the ice caps (Björnsson and others, 2013). We make use of the frequent volcanic eruptions in Iceland, which cause widespread internal tephra layers in the ice caps, to reconstruct the surface mass balance (SMB) in the ablation zone. This method requires information about surface geometry and ice velocity, derived from remote-sensing information. In addition, the emergence angle of the tephra layer needs to be known. As a proof-of-concept, we utilize a prominent tephra layer of the Mýrdalsjökull Ice Cap to infer local SMB estimates in the ablation area back to 1988. Using tephra-layer outcrop locations across the glacier at different points in time it is possible to determine local mass changes (loss and redistribution) for a large part of the ablation zone, without the use of historic elevation models, which often are not available.

Combining SAR interferometry and the equation of continuity to estimate the three-dimensional glacier surface-velocity vector

1999 ◽  
Vol 45 (151) ◽  
pp. 533-538 ◽  
Author(s):  
Niels Reeh ◽  
Søren Nørvang Madsen ◽  
Johan Jakob Mohr
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Vertical Velocity ◽  
Velocity Vector ◽  
Thickness Distribution ◽  
Vertical Surface ◽  
Horizontal Velocity ◽  
Sar Interferometry ◽  
Surface Velocity ◽  
Ice Thickness

AbstractUntil now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from synthetic aperture radar interferometry. We discuss this assumption, which neglects the influence of the local mass balance and a possible contribution to the vertical velocity arising if the glacier is not in steady state. We find that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreover, the vertical velocity contribution arising if the ice sheet is not in steady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizontal velocity vector. This equation, valid for both steady-state and non-steady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between the surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.

scholarly journals Characteristics of ice rises and ice rumples in Dronning Maud Land and Enderby Land, Antarctica

2020 ◽  
Vol 66 (260) ◽  
pp. 1064-1078
Author(s):  
Vikram Goel ◽  
Kenichi Matsuoka ◽  
Cesar Deschamps Berger ◽  
Ian Lee ◽  
Jørgen Dall ◽  
...  
Keyword(s):  
Mass Balance ◽  
Ice Cores ◽  
Ice Thickness ◽  
Ice Shelf ◽  
Ice Dynamics ◽  
Surface Mass ◽  
Ice Shelves ◽  
The Past ◽  
Dronning Maud Land ◽  
The Antarctic

AbstractIce rises and rumples, locally grounded features adjacent to ice shelves, are relatively small yet play significant roles in Antarctic ice dynamics. Their roles generally depend upon their location within the ice shelf and the stage of the ice-sheet retreat or advance. Large, long-stable ice rises can be excellent sites for deep ice coring and paleoclimate study of the Antarctic coast and the Southern Ocean, while small ice rises tend to respond more promptly and can be used to reveal recent changes in regional mass balance. The coasts of Dronning Maud Land (DML) and Enderby Land in East Antarctica are abundant with these features. Here we review existing knowledge, presenting an up-to-date status of research in these regions with focus on ice rises and rumples. We use regional datasets (satellite imagery, surface mass balance and ice thickness) to analyze the extent and surface morphology of ice shelves and characteristic timescales of ice rises. We find that large parts of DML have been changing over the past several millennia. Based on our findings, we highlight ice rises suitable for drilling ice cores for paleoclimate studies as well as ice rises suitable for deciphering ice dynamics and evolution in the region.

scholarly journals Quantifying mass balance processes on the Southern Patagonia Icefield

2015 ◽  
Vol 9 (1) ◽  
pp. 25-35 ◽  
Author(s):  
M. Schaefer ◽  
H. Machguth ◽  
M. Falvey ◽  
G. Casassa ◽  
E. Rignot
Keyword(s):  
Mass Balance ◽  
Reanalysis Data ◽  
Ice Thickness ◽  
Surface Mass Balance ◽  
Mass Balances ◽  
Surface Mass ◽  
Mass Losses ◽  
Southern Patagonia ◽  
Spatially Distributed ◽  
The Individual

Abstract. We present surface mass balance simulations of the Southern Patagonia Icefield (SPI) driven by downscaled reanalysis data. The simulations were evaluated and interpreted using geodetic mass balances, measured point balances and a complete velocity field of the icefield for spring 2004. The high measured accumulation of snow of up to 15.4 m w.e. yr−1 (meters water equivalent per year) as well as the high measured ablation of up to 11 m w.e. yr−1 is reproduced by the model. The overall modeled surface mass balance was positive and increasing during 1975–2011. Subtracting the surface mass balance from geodetic balances, calving fluxes were inferred. Mass losses of the SPI due to calving were strongly increasing from 1975–2000 to 2000–2011 and higher than losses due to surface melt. Calving fluxes were inferred for the individual glacier catchments and compared to fluxes estimated from velocity data. Measurements of ice thickness and flow velocities at the glaciers' front and spatially distributed accumulation measurements can help to reduce the uncertainties of the different terms in the mass balance of the Southern Patagonia Icefield.

Surface mass balance modeling of mountain glaciers in the Caucasus and in the High Mountain Asia

2020 ◽  
Author(s):  
Oleg Rybak ◽  
Elena Rybak ◽  
Victor Popovnin ◽  
Afanasy Gubanov ◽  
Rysbek Satylkanov ◽  
...  
Keyword(s):  
Energy Balance ◽  
Mass Balance ◽  
Tien Shan ◽  
Surface Mass Balance ◽  
Mountain Glacier ◽  
Model Calculations ◽  
Suggested Approach ◽  
Surface Mass ◽  
Mountain Glaciers ◽  
Energy Balance Approach

<p> </p><p>            The most significant quantity characterizing current state of a mountain glacier is its surface mass balance (SMB). SMB responds to changing climatic conditions and therefore determines present and future behavior of the glacier. Formulation of SMB in terms of a mathematical model allows better understanding complex processes of the atmospheric impact on glacier dynamics. After several decades of development, common universal modeling principles and approaches have been elaborated. At present, most of the newly developed models are quite similar with only varying details mostly concerning parameterization of heat fluxes.</p><p>SMB is an interplay between positive (accumulation) and negative (ablation) components. Ablation is formulated either using temperature-index (positive degree day) approach or surface energy balance calculation (or combination of both). Both these approaches are based on genuine physical principles and that is why they can be easily transformed into computational algorithms. Results of ablation model calculations are relatively easily constrained by observations. In contrast, evaluation of accumulation is much more dependent on poorly constrained factors such as local atmospheric circulation, snow-storm transport (including post-depositional) and avalanche feeding.</p><p>Our approach to simulate components of SMB is based on energy balance approach and emulation of meteorological conditions using a simple stochastic weather generator. To validate the model, we use observed SMB data from several mountain glaciers in different environmental conditions – Djankuat (Central Caucasus), Tuyuksu (Zailiyski Alatau), Sary-Tor and Karabatkak (Inner Tien Shan). Suggested approach allows to easily construct an ensemble of numerical experiments and implement Monte Carlo method for the SMB evaluation. This possibility is especially significant for simulation of future states of glaciers according to one or another climatic scenario on a coupled ice flow-SMB model.</p><p>The reported study was funded by RFBR, project number 20-05-00681 (“Evolution of glaciation of Inner Tien Shan under climate change and technogenic influence”)</p>

scholarly journals Estimating surface mass balance patterns from unoccupied aerial vehicle measurements in the ablation area of the Morteratsch–Pers glacier complex (Switzerland)

2021 ◽  
Vol 15 (9) ◽  
pp. 4445-4464
Author(s):  
Lander Van Tricht ◽  
Philippe Huybrechts ◽  
Jonas Van Breedam ◽  
Alexander Vanhulle ◽  
Kristof Van Oost ◽  
...  
Keyword(s):  
Mass Balance ◽  
Continuity Equation ◽  
Spatial Scales ◽  
Equation Method ◽  
Ice Thickness ◽  
Constant Density ◽  
Surface Mass Balance ◽  
High Resolution Data ◽  
Surface Mass ◽  
Aerial Vehicle

Abstract. The surface mass balance (SMB) of a glacier provides the link between the glacier and the local climate. For this reason, it is intensively studied and monitored. However, major efforts are required to determine the point SMB at a sufficient number of locations to capture the heterogeneity of the SMB pattern. Furthermore, because of the time-consuming and costly nature of these measurements, detailed SMB measurements are carried out on only a limited number of glaciers. In this study, we investigate how to accurately determine the SMB in the ablation zone of Vadret da Morteratsch and Vadret Pers (Engadin, Switzerland) using the continuity equation method, based on the expression of conservation of mass for glacier flow with constant density. An elaborate dataset (spanning the 2017–2020 period) of high-resolution data derived from unoccupied aerial vehicle (UAV) measurements (surface elevation changes and surface velocities) is combined with reconstructed ice thickness fields (based on radar measurements). To determine the performance of the method, we compare modelled SMB with measured SMB values at the position of stakes. Our results indicate that with annual UAV surveys, it is possible to obtain SMB estimates with a mean absolute error smaller than 0.5 m of ice equivalent per year. Yet, our study demonstrates that to obtain these accuracies, it is necessary to consider the ice flow over spatial scales of several times the local ice thickness, accomplished in this study by applying an exponential decay filter. Furthermore, our study highlights the crucial importance of the ice thickness, which must be sufficiently well known in order to accurately apply the method. The latter currently seems to complicate the application of the continuity equation method to derive detailed SMB patterns on regional to global scales.

scholarly journals Anomalously-dense firn in an ice-shelf channel revealed by wide-angle radar

2015 ◽  
Vol 9 (5) ◽  
pp. 5647-5680
Author(s):  
R. Drews ◽  
J. Brown ◽  
K. Matsuoka ◽  
E. Witrant ◽  
M. Philippe ◽  
...  
Keyword(s):  
Mass Balance ◽  
Propagation Speed ◽  
Radar Data ◽  
Temporal Variations ◽  
Ice Thickness ◽  
Wide Angle ◽  
Ice Shelf ◽  
Surface Mass ◽  
Density Anomaly ◽  
Similar Density

Abstract. The thickness of ice shelves, a basic parameter for mass balance estimates, is typically inferred using hydrostatic equilibrium for which knowledge of the depth-averaged density is essential. The densification from snow to ice depends on a number of local factors (e.g. temperature and surface mass balance) causing spatial and temporal variations in density–depth profiles. However, direct measurements of firn density are sparse, requiring substantial logistical effort. Here, we infer density from radio-wave propagation speed using ground-based wide-angle radar datasets (10 MHz) collected at five sites on Roi Baudouin Ice Shelf (RBIS), Dronning Maud Land, Antarctica. Using a novel algorithm including traveltime inversion and raytracing with a prescribed shape of the depth–density relationship, we show that the depth to internal reflectors, the local ice thickness and depth-averaged densities can reliably be reconstructed. For the particular case of an ice-shelf channel, where ice thickness and surface slope change substantially over a few kilometers, the radar data suggests that firn inside the channel is about 5 % denser than outside the channel. Although this density difference is at the detection limit of the radar, it is consistent with a similar density anomaly reconstructed from optical televiewing, which reveals 10 % denser firn inside compared to outside the channel. The denser firn in the ice-shelf channel should be accounted for when using the hydrostatic ice thickness for determining basal melt rates. The radar method presented here is robust and can easily be adapted to different radar frequencies and data-acquisition geometries.

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