A method to estimate the ice volume and ice-thickness distribution of alpine glaciers

AbstractSound knowledge of the ice volume and ice-thickness distribution of a glacier is essential for many glaciological applications. However, direct measurements of ice thickness are laborious, not feasible everywhere and necessarily restricted to a small number of glaciers. In this paper, we present a method to estimate the ice-thickness distribution and the total ice volume of alpine glaciers. This method is based on glacier mass turnover and principles of ice-flow mechanics. The required input data are the glacier surface topography, the glacier outline and a set of borders delineating different ‘ice-flow catchments’. Three parameters describe the distribution of the ‘apparent mass balance’, which is defined as the difference between the glacier surface mass balance and the rate of ice-thickness change, and two parameters define the ice-flow dynamics. The method was developed and validated on four alpine glaciers located in Switzerland, for which the bedrock topography is partially known from radio-echo soundings. The ice thickness along 82 cross-profiles can be reproduced with an average deviation of about 25% between the calculated and the measured ice thickness. The cross-sectional areas differ by less than 20% on average. This shows the potential of the method for estimating the ice-thickness distribution of alpine glaciers without the use of direct measurements.

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The ice thickness distribution of Flask Glacier, Antarctic Peninsula, determined by combining radio-echo soundings, surface velocity data and flow modelling

Annals of Glaciology ◽

10.3189/2013aog63a603 ◽

2013 ◽

Vol 54 (63) ◽

pp. 18-24 ◽

Cited By ~ 20

Author(s):

Daniel Farinotti ◽

Hugh Corr ◽

G.Hilmar Gudmundsson

Keyword(s):

Antarctic Peninsula ◽

Thickness Distribution ◽

Surface Velocity ◽

Ice Thickness ◽

Ice Shelf ◽

Ice Flow ◽

Ice Volume ◽

Flow Modelling ◽

Bedrock Topography ◽

Sparse Measurements

AbstractAn interpolated bedrock topography is presented for Flask Glacier, one of the tributaries of the remnant part of the Larsen B ice shelf, Antarctic Peninsula. The ice thickness distribution is derived by combining direct but sparse measurements from airborne radio-echo soundings with indirect estimates obtained from ice-flow modelling. The ice-flow model is applied to a series of transverse profiles, and a first estimate of the bedrock is iteratively adjusted until agreement between modelled and measured surface velocities is achieved. The adjusted bedrock is then used to reinterpret the radio-echo soundings, and the recovered information used to further improve the estimate of the bedrock itself. The ice flux along the glacier center line provides an additional and independent constraint on the ice thickness. The resulting bedrock topography reveals a glacier bed situated mainly below sea level with sections having retrograde slope. The total ice volume of 120 ±15 km3 for the considered area of 215 km2 corresponds to an average ice thickness of 560 ± 70 m.

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Using surface velocities to calculate ice thickness and bed topography: a case study at Columbia Glacier, Alaska, USA

Journal of Glaciology ◽

10.3189/2012jog11j249 ◽

2012 ◽

Vol 58 (212) ◽

pp. 1151-1164 ◽

Cited By ~ 76

Author(s):

R.W. Mcnabb ◽

R. Hock ◽

S. O’Neel ◽

L.A. Rasmussen ◽

Y. Ahn ◽

...

Keyword(s):

Thickness Distribution ◽

Computational Time ◽

Ice Thickness ◽

Thickness Change ◽

Bed Topography ◽

Surface Data ◽

Direct Measurements ◽

The Mean ◽

Time Required

AbstractInformation about glacier volume and ice thickness distribution is essential for many glaciological applications, but direct measurements of ice thickness can be difficult and costly. We present a new method that calculates ice thickness via an estimate of ice flux. We solve the familiar continuity equation between adjacent flowlines, which decreases the computational time required compared to a solution on the whole grid. We test the method on Columbia Glacier, a large tidewater glacier in Alaska, USA, and compare calculated and measured ice thicknesses, with favorable results. This shows the potential of this method for estimating ice thickness distribution of glaciers for which only surface data are available. We find that both the mean thickness and volume of Columbia Glacier were approximately halved over the period 1957–2007, from 281 m to 143 m, and from 294 km3 to 134 km3, respectively. Using bedrock slope and considering how waves of thickness change propagate through the glacier, we conduct a brief analysis of the instability of Columbia Glacier, which leads us to conclude that the rapid portion of the retreat may be nearing an end.

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The bedrock topography of Gries- and Findelengletscher

Geographica Helvetica ◽

10.5194/gh-73-1-2018 ◽

2018 ◽

Vol 73 (1) ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Nadine Feiger ◽

Matthias Huss ◽

Silvan Leinss ◽

Leo Sold ◽

Daniel Farinotti

Keyword(s):

Spatial Interpolation ◽

Thickness Distribution ◽

Estimation Method ◽

Ice Thickness ◽

Glacier Surface ◽

Ice Flow ◽

Bedrock Topography ◽

Abstract Knowledge ◽

Ground Penetrating ◽

Item Item

Abstract. Knowledge of the ice thickness distribution of glaciers is important for glaciological and hydrological applications. In this contribution, we present two updated bedrock topographies and ice thickness distributions for Gries- and Findelengletscher, Switzerland. The results are based on ground-penetrating radar (GPR) measurements collected in spring 2015 and already-existing data. The GPR data are analysed using ReflexW software and interpolated by using the ice thickness estimation method (ITEM). ITEM calculates the thickness distribution by using principles of ice flow dynamics and characteristics of the glacier surface. We show that using such a technique has a significance advantage compared to a direct interpolation of the measurements, especially for glacier areas that are sparsely covered by GPR data. The uncertainties deriving from both the interpretation of the GPR signal and the spatial interpolation through ITEM are quantified separately, showing that, in our case, GPR signal interpretation is a major source of uncertainty. The results show a total glacier volume of 0.28±0.06 and 1.00±0.34 km3 for Gries- and Findelengletscher, respectively, with corresponding average ice thicknesses of 56.8±12.7 and 56.3±19.6 m.

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Changes in ice thickness and flow velocity of Yala Glacier, Langtang Himal, Nepal, from 1982 to 2009

Annals of Glaciology ◽

10.3189/2013aog64a111 ◽

2013 ◽

Vol 54 (64) ◽

pp. 157-162 ◽

Cited By ~ 18

Author(s):

Shin Sugiyama ◽

Kotaro Fukui ◽

Koji Fujita ◽

Kenta Tone ◽

Satoru Yamaguchi

Keyword(s):

Flow Velocity ◽

Surface Elevation ◽

Ice Thickness ◽

Glacier Surface ◽

Ice Flow ◽

Ice Volume ◽

Glacier Changes ◽

Ice Velocity ◽

Ground Penetrating ◽

Thinning Rate

Abstract To investigate recent glacier changes in the Himalayan region, we carried out GPS and ground-penetrating radar (GPR) measurements at Yala Glacier, a benchmark glacier in Nepal. Glacier surface elevation and ice thickness were surveyed along a 1.5 km profile from the glacier top to the terminus. Ice flow velocity was measured at five locations by surveying stakes for either 1 year or 4 day periods. Obtained surface elevation and ice velocity were compared with those measured in 1982 and 1996. The mean ice thickness along the radar profile was 36 m in 2009 and the ice has been thinning at rates of-0.69 ±0.25 and -0.75 ± 0.24 m a-1 during the periods 1982-96 and 1996-2009, respectively. The thinning rate increases down-glacier, reaching a magnitude up to -1.8 m a-1 near the terminus from 1996 to 2009. The ice velocity has reduced by >70% from 1982 to 2009 in the lower half of the glacier. By assuming a constant driving stress over the glacier, the total ice volume in 2009 was estimated as 0.061 km3. Our results indicate that Yala Glacier has lost ∼40% of its ice volume over the last 27 years and that the rate of the mass loss has accelerated over the last decade.

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The Causes of Debris-Covered Glacier Thinning: Evidence for the Importance of Ice Dynamics From Kennicott Glacier, Alaska

Frontiers in Earth Science ◽

10.3389/feart.2021.680995 ◽

2021 ◽

Vol 9 ◽

Author(s):

Leif S. Anderson ◽

William H. Armstrong ◽

Robert S. Anderson ◽

Dirk Scherler ◽

Eric Petersen

Keyword(s):

Mass Balance ◽

Flow Direction ◽

Surface Velocity ◽

Glacier Surface ◽

Ice Dynamics ◽

Ice Flow ◽

Thickness Change ◽

Air Temperatures ◽

Compressive Flow ◽

Wide Range

The cause of debris-covered glacier thinning remains controversial. One hypothesis asserts that melt hotspots (ice cliffs, ponds, or thin debris) increase thinning, while the other posits that declining ice flow leads to dynamic thinning under thick debris. Alaska’s Kennicott Glacier is ideal for testing these hypotheses, as ice cliffs within the debris-covered tongue are abundant and surface velocities decline rapidly downglacier. To explore the cause of patterns in melt hotspots, ice flow, and thinning, we consider their evolution over several decades. We compile a wide range of ice dynamical and mass balance datasets which we cross-correlate and analyze in a step-by-step fashion. We show that an undulating bed that deepens upglacier controls ice flow in the lower 8.5 km of Kennicott Glacier. The imposed velocity pattern strongly affects debris thickness, which in turn leads to annual melt rates that decline towards the terminus. Ice cliff abundance correlates highly with the rate of surface compression, while pond occurrence is strongly negatively correlated with driving stress. A new positive feedback is identified between ice cliffs, streams and surface topography that leads to chaotic topography. As the glacier thinned between 1991 and 2015, surface melt in the study area decreased, despite generally rising air temperatures. Four additional feedbacks relating glacier thinning to melt changes are evident: the debris feedback (negative), the ice cliff feedback (negative), the pond feedback (positive), and the relief feedback (positive). The debris and ice cliff feedbacks, which are tied to the change in surface velocity in time, likely reduced melt rates in time. We show this using a new method to invert for debris thickness change and englacial debris content (∼0.017% by volume) while also revealing that declining speeds and compressive flow led to debris thickening. The expansion of debris on the glacier surface follows changes in flow direction. Ultimately, glacier thinning upvalley from the continuously debris-covered portion of Kennicott Glacier, caused by mass balance changes, led to the reduction of flow into the study area. This caused ice emergence rates to decline rapidly leading to the occurrence of maximum, glacier-wide thinning under thick, insulating debris.

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

Journal of Glaciology ◽

10.3189/s0022143000001398 ◽

1999 ◽

Vol 45 (151) ◽

pp. 533-538 ◽

Cited By ~ 2

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.

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Ice thickness distribution of all Swiss glaciers based on extended ground-penetrating radar data and glaciological modeling

Journal of Glaciology ◽

10.1017/jog.2021.55 ◽

2021 ◽

pp. 1-19

Author(s):

Melchior Grab ◽

Enrico Mattea ◽

Andreas Bauder ◽

Matthias Huss ◽

Lasse Rabenstein ◽

...

Keyword(s):

Ground Penetrating Radar ◽

Thickness Distribution ◽

Radar Data ◽

Tourism Industry ◽

Swiss Alps ◽

Ice Thickness ◽

Hazard Management ◽

Bed Topography ◽

Ice Volume ◽

Ground Penetrating

Abstract Accurate knowledge of the ice thickness distribution and glacier bed topography is essential for predicting dynamic glacier changes and the future developments of downstream hydrology, which are impacting the energy sector, tourism industry and natural hazard management. Using AIR-ETH, a new helicopter-borne ground-penetrating radar (GPR) platform, we measured the ice thickness of all large and most medium-sized glaciers in the Swiss Alps during the years 2016–20. Most of these had either never or only partially been surveyed before. With this new dataset, 251 glaciers – making up 81% of the glacierized area – are now covered by GPR surveys. For obtaining a comprehensive estimate of the overall glacier ice volume, ice thickness distribution and glacier bed topography, we combined this large amount of data with two independent modeling algorithms. This resulted in new maps of the glacier bed topography with unprecedented accuracy. The total glacier volume in the Swiss Alps was determined to be 58.7 ± 2.5 km3 in the year 2016. By projecting these results based on mass-balance data, we estimated a total ice volume of 52.9 ± 2.7 km3 for the year 2020. Data and modeling results are accessible in the form of the SwissGlacierThickness-R2020 data package.

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Measuring and inferring the ice thickness distribution of four glaciers in the Tien Shan, Kyrgyzstan

Journal of Glaciology ◽

10.1017/jog.2020.104 ◽

2020 ◽

pp. 1-18

Author(s):

Lander Van Tricht ◽

Philippe Huybrechts ◽

Jonas Van Breedam ◽

Johannes J. Fürst ◽

Oleg Rybak ◽

...

Keyword(s):

Cross Validation ◽

Thickness Distribution ◽

Tien Shan ◽

Ice Thickness ◽

Ice Volume ◽

In Situ Data ◽

Radio Echo Sounding ◽

Thickness Measurements ◽

Tien Shan Mountains

Abstract Glaciers in the Tien Shan mountains contribute considerably to the fresh water used for irrigation, households and energy supply in the dry lowland areas of Kyrgyzstan and its neighbouring countries. To date, reconstructions of the current ice volume and ice thickness distribution remain scarce, and accurate data are largely lacking at the local scale. Here, we present a detailed ice thickness distribution of Ashu-Tor, Bordu, Golubin and Kara-Batkak glaciers derived from radio-echo sounding measurements and modelling. All the ice thickness measurements are used to calibrate three individual models to estimate the ice thickness in inaccessible areas. A cross-validation between modelled and measured ice thickness for a subset of the data is performed to attribute a weight to every model and to assemble a final composite ice thickness distribution for every glacier. Results reveal the thickest ice on Ashu-Tor glacier with values up to 201 ± 12 m. The ice thickness measurements and distributions are also compared with estimates composed without the use of in situ data. These estimates approach the total ice volume well, but local ice thicknesses vary substantially.

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

Journal of Glaciology ◽

10.1017/jog.2021.11 ◽

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.

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Sea ice deformation and thickness in the Western Ross Sea

10.5194/egusphere-egu21-10607 ◽

2021 ◽

Author(s):

Wolfgang Rack ◽

Daniel Price ◽

Christian Haas ◽

Patricia J. Langhorne ◽

Greg H. Leonard

Keyword(s):

Sea Ice ◽

Satellite Images ◽

Ross Sea ◽

Thickness Distribution ◽

Ice Thickness ◽

Ice Dynamics ◽

Sea Ice Thickness ◽

Ice Volume ◽

Terra Nova Bay ◽

Western Ross Sea

Sea ice cover is arguably the longest and best observed climate variable from space, with over four decades of highly reliable daily records of extent in both hemispheres. In Antarctica, a slight positive decadal trend in sea ice cover is driven by changes in the western Ross Sea, where a variation in weather patterns over the wider region forced a change in meridional winds. The distinguishing wind driven sea ice process in the western Ross Sea is the regular occurrence of the Ross Sea, McMurdo Sound, and Terra Nova Bay polynyas. Trends in sea ice volume and mass in this area unknown, because ice thickness and dynamics are particularly hard to measure.Here we present the first comprehensive and direct assessment of large-scale sea-ice thickness distribution in the western Ross Sea. Using an airborne electromagnetic induction (AEM) ice thickness sensor towed by a fixed wing aircraft (Basler BT-67), we observed in November 2017 over a distance of 800 km significantly thicker ice than expected from thermodynamic growth alone. By means of time series of satellite images and wind data we relate the observed thickness distribution to satellite derived ice dynamics and wind data. Strong southerly winds with speeds of up to 25 ms-1 in early October deformed the pack ice, which was surveyed more than a month later.We found strongly deformed ice with a mean and maximum thickness of 2.0 and 15.6 m, respectively. Sea-ice thickness gradients are highest within 100-200 km of polynyas, where the mean thickness of the thickest 10% of ice is 7.6 m. From comparison with aerial photographs and satellite images we conclude that ice preferentially grows in deformational ridges; about 43% of the sea ice volume in the area between McMurdo Sound and Terra Nova Bay is concentrated in more than 3 m thick ridges which cover about 15% of the surveyed area. Overall, 80% of the ice was found to be heavily deformed and concentrated in ridges up to 11.8 m thick.Our observations hold a link between wind driven ice dynamics and the ice mass exported from the western Ross Sea. The sea ice statistics highlighted in this contribution forms a basis for improved satellite derived mass balance assessments and the evaluation of sea ice simulations.

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