Articles | Volume 10, issue 6
https://doi.org/10.5194/tc-10-2887-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/tc-10-2887-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
24 Nov 2016
Research article |
| 24 Nov 2016
Effects of local advection on the spatial sensible heat flux variation on a mountain glacier
Climate System Research Group, Institute of Geography, Friedrich-Alexander University Erlangen-Nürnberg (FAU), Erlangen, Germany
Institute of Atmospheric and Cryospheric Sciences, University of Innsbruck, Innsbruck, Austria
Stephan Peter Galos
Institute of Atmospheric and Cryospheric Sciences, University of Innsbruck, Innsbruck, Austria
Related authors
Wilhelm Furian and Tobias Sauter
EGUsphere, https://doi.org/10.5194/egusphere-2025-50, https://doi.org/10.5194/egusphere-2025-50, 2025
This preprint is open for discussion and under review for Natural Hazards and Earth System Sciences (NHESS).
Short summary
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Glacial lake outburst floods (GLOFs) continue to threaten high-mountain communities in Nepal. We simulate potential GLOF events from five glacial lakes in the Everest region during the 21st century using a 3D flood model and several breach and SSP scenarios. Large GLOFs could extend over 100 km and inundate 80 to 100 km of roads, 735 to 1,989 houses and between 0.85 and 3.52 km2 of agricultural land. The results help to assess the changing GLOF impacts and support more accurate risk assessments.
Annelies Voordendag, Brigitta Goger, Rainer Prinz, Tobias Sauter, Thomas Mölg, Manuel Saigger, and Georg Kaser
The Cryosphere, 18, 849–868, https://doi.org/10.5194/tc-18-849-2024, https://doi.org/10.5194/tc-18-849-2024, 2024
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Wind-driven snow redistribution affects glacier mass balance. A case study of Hintereisferner glacier in Austria used high-resolution observations and simulations to model snow redistribution. Simulations matched observations, showing the potential of the model for studying snow redistribution on other mountain glaciers.
Franziska Temme, David Farías-Barahona, Thorsten Seehaus, Ricardo Jaña, Jorge Arigony-Neto, Inti Gonzalez, Anselm Arndt, Tobias Sauter, Christoph Schneider, and Johannes J. Fürst
The Cryosphere, 17, 2343–2365, https://doi.org/10.5194/tc-17-2343-2023, https://doi.org/10.5194/tc-17-2343-2023, 2023
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Calibration of surface mass balance (SMB) models on regional scales is challenging. We investigate different calibration strategies with the goal of achieving realistic simulations of the SMB in the Monte Sarmiento Massif, Tierra del Fuego. Our results show that the use of regional observations from satellite data can improve the model performance. Furthermore, we compare four melt models of different complexity to understand the benefit of increasing the processes considered in the model.
Tobias Sauter, Anselm Arndt, and Christoph Schneider
Geosci. Model Dev., 13, 5645–5662, https://doi.org/10.5194/gmd-13-5645-2020, https://doi.org/10.5194/gmd-13-5645-2020, 2020
Short summary
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Glacial changes play a key role from a socioeconomic, political, and scientific point of view. Here, we present the open-source coupled snowpack and ice surface energy and mass balance model, which provides a lean, flexible, and user-friendly framework for modeling distributed snow and glacier mass changes. The model provides a suitable platform for sensitivity, detection, and attribution analyses for glacier changes and a tool for quantifying inherent uncertainties.
Tobias Sauter
Hydrol. Earth Syst. Sci., 24, 2003–2016, https://doi.org/10.5194/hess-24-2003-2020, https://doi.org/10.5194/hess-24-2003-2020, 2020
Short summary
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Patagonia is thought to be one of the wettest – if not the wettest – places on Earth. The plausibility of these numbers has never been carefully scrutinized, despite the significance of this topic to our understanding of observed environmental changes, such as glacier recession. The revised precipitation values are significantly smaller than the previously reported values, thus opening up a new perspective on the Patagonian glaciers' response to climate change.
T. Sauter, M. Möller, R. Finkelnburg, M. Grabiec, D. Scherer, and C. Schneider
The Cryosphere, 7, 1287–1301, https://doi.org/10.5194/tc-7-1287-2013, https://doi.org/10.5194/tc-7-1287-2013, 2013
Wilhelm Furian and Tobias Sauter
EGUsphere, https://doi.org/10.5194/egusphere-2025-50, https://doi.org/10.5194/egusphere-2025-50, 2025
This preprint is open for discussion and under review for Natural Hazards and Earth System Sciences (NHESS).
Short summary
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Glacial lake outburst floods (GLOFs) continue to threaten high-mountain communities in Nepal. We simulate potential GLOF events from five glacial lakes in the Everest region during the 21st century using a 3D flood model and several breach and SSP scenarios. Large GLOFs could extend over 100 km and inundate 80 to 100 km of roads, 735 to 1,989 houses and between 0.85 and 3.52 km2 of agricultural land. The results help to assess the changing GLOF impacts and support more accurate risk assessments.
Annelies Voordendag, Brigitta Goger, Rainer Prinz, Tobias Sauter, Thomas Mölg, Manuel Saigger, and Georg Kaser
The Cryosphere, 18, 849–868, https://doi.org/10.5194/tc-18-849-2024, https://doi.org/10.5194/tc-18-849-2024, 2024
Short summary
Short summary
Wind-driven snow redistribution affects glacier mass balance. A case study of Hintereisferner glacier in Austria used high-resolution observations and simulations to model snow redistribution. Simulations matched observations, showing the potential of the model for studying snow redistribution on other mountain glaciers.
Franziska Temme, David Farías-Barahona, Thorsten Seehaus, Ricardo Jaña, Jorge Arigony-Neto, Inti Gonzalez, Anselm Arndt, Tobias Sauter, Christoph Schneider, and Johannes J. Fürst
The Cryosphere, 17, 2343–2365, https://doi.org/10.5194/tc-17-2343-2023, https://doi.org/10.5194/tc-17-2343-2023, 2023
Short summary
Short summary
Calibration of surface mass balance (SMB) models on regional scales is challenging. We investigate different calibration strategies with the goal of achieving realistic simulations of the SMB in the Monte Sarmiento Massif, Tierra del Fuego. Our results show that the use of regional observations from satellite data can improve the model performance. Furthermore, we compare four melt models of different complexity to understand the benefit of increasing the processes considered in the model.
Tobias Sauter, Anselm Arndt, and Christoph Schneider
Geosci. Model Dev., 13, 5645–5662, https://doi.org/10.5194/gmd-13-5645-2020, https://doi.org/10.5194/gmd-13-5645-2020, 2020
Short summary
Short summary
Glacial changes play a key role from a socioeconomic, political, and scientific point of view. Here, we present the open-source coupled snowpack and ice surface energy and mass balance model, which provides a lean, flexible, and user-friendly framework for modeling distributed snow and glacier mass changes. The model provides a suitable platform for sensitivity, detection, and attribution analyses for glacier changes and a tool for quantifying inherent uncertainties.
Tobias Sauter
Hydrol. Earth Syst. Sci., 24, 2003–2016, https://doi.org/10.5194/hess-24-2003-2020, https://doi.org/10.5194/hess-24-2003-2020, 2020
Short summary
Short summary
Patagonia is thought to be one of the wettest – if not the wettest – places on Earth. The plausibility of these numbers has never been carefully scrutinized, despite the significance of this topic to our understanding of observed environmental changes, such as glacier recession. The revised precipitation values are significantly smaller than the previously reported values, thus opening up a new perspective on the Patagonian glaciers' response to climate change.
Tobias Zolles, Fabien Maussion, Stephan Peter Galos, Wolfgang Gurgiser, and Lindsey Nicholson
The Cryosphere, 13, 469–489, https://doi.org/10.5194/tc-13-469-2019, https://doi.org/10.5194/tc-13-469-2019, 2019
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A mass and energy balance model was subjected to sensitivity and uncertainty analysis on two different Alpine glaciers. The global sensitivity analysis allowed for a mass balance measurement independent assessment of the model sensitivity and functioned as a reduction of the model free parameter space. A novel approach of a multi-objective optimization estimates the uncertainty of the simulated mass balance and the energy fluxes. The final model uncertainty is up to 1300 kg m−3 per year.
Christoph Klug, Erik Bollmann, Stephan Peter Galos, Lindsey Nicholson, Rainer Prinz, Lorenzo Rieg, Rudolf Sailer, Johann Stötter, and Georg Kaser
The Cryosphere, 12, 833–849, https://doi.org/10.5194/tc-12-833-2018, https://doi.org/10.5194/tc-12-833-2018, 2018
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This study presents a reanalysis of the glacier mass balance record at Hintereisferner, Austria, for the period 2001 to 2011. We provide a year-by-year comparison of glaciological and geodetic mass balances obtained from annual airborne laser scanning data. After applying a series of corrections, a comparison of the methods reveals major differences for certain years. We thoroughly discuss the origin of these discrepancies and implications for future glaciological mass balance measurements.
Stephan Peter Galos, Christoph Klug, Fabien Maussion, Federico Covi, Lindsey Nicholson, Lorenzo Rieg, Wolfgang Gurgiser, Thomas Mölg, and Georg Kaser
The Cryosphere, 11, 1417–1439, https://doi.org/10.5194/tc-11-1417-2017, https://doi.org/10.5194/tc-11-1417-2017, 2017
Paolo Gabrielli, Carlo Barbante, Giuliano Bertagna, Michele Bertó, Daniel Binder, Alberto Carton, Luca Carturan, Federico Cazorzi, Giulio Cozzi, Giancarlo Dalla Fontana, Mary Davis, Fabrizio De Blasi, Roberto Dinale, Gianfranco Dragà, Giuliano Dreossi, Daniela Festi, Massimo Frezzotti, Jacopo Gabrieli, Stephan P. Galos, Patrick Ginot, Petra Heidenwolf, Theo M. Jenk, Natalie Kehrwald, Donald Kenny, Olivier Magand, Volkmar Mair, Vladimir Mikhalenko, Ping Nan Lin, Klaus Oeggl, Gianni Piffer, Mirko Rinaldi, Ulrich Schotterer, Margit Schwikowski, Roberto Seppi, Andrea Spolaor, Barbara Stenni, David Tonidandel, Chiara Uglietti, Victor Zagorodnov, Thomas Zanoner, and Piero Zennaro
The Cryosphere, 10, 2779–2797, https://doi.org/10.5194/tc-10-2779-2016, https://doi.org/10.5194/tc-10-2779-2016, 2016
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New ice cores were extracted from Alto dell'Ortles, the highest glacier of South Tyrol in the Italian Alps, to check whether prehistoric ice, which is coeval to the famous 5300-yr-old Tyrolean Iceman, is still preserved in this region. Dating of the ice cores confirms the hypothesis and indicates the drilling site has been glaciated since the end of the Northern Hemisphere Climatic Optimum (7000 yrs BP). We also infer that an unprecedented acceleration of the glacier flow has recently begun.
T. Sauter, M. Möller, R. Finkelnburg, M. Grabiec, D. Scherer, and C. Schneider
The Cryosphere, 7, 1287–1301, https://doi.org/10.5194/tc-7-1287-2013, https://doi.org/10.5194/tc-7-1287-2013, 2013
Related subject area
Alpine Glaciers
Reconstructed glacier area and volume changes in the European Alps since the Little Ice Age
Separating snow and ice melt using water stable isotopes and glacio-hydrological modelling: towards improving the application of isotope analyses in highly glacierized catchments
Distributed surface mass balance of an avalanche-fed glacier
Recent observations and glacier modeling point towards near complete glacier loss in western Austria (Ötztal and Stubai mountain range) if 1.5 °C is not met
Unprecedented 21st century glacier loss on Mt. Hood, Oregon, USA
Brief communication: On the potential of seismic polarity reversal to identify a thin low-velocity layer above a high-velocity layer in ice-rich rock glaciers
Mapping and characterization of avalanches on mountain glaciers with Sentinel-1 satellite imagery
The Glaciers of the Dolomites: last 40 years of melting
Spectral characteristics of seismic ambient vibrations reveal subglacial hydraulic changes beneath Glacier de la Plaine Morte, Switzerland
Automated snow cover detection on mountain glaciers using space-borne imagery
Brief communication: Recent estimates of glacier mass loss for western North America from laser altimetry
The Aneto glacier's (Central Pyrenees) evolution from 1981 to 2022: ice loss observed from historic aerial image photogrammetry and remote sensing techniques
Modelling point mass balance for the glaciers of the Central European Alps using machine learning techniques
Consistent histories of anthropogenic western European air pollution preserved in different Alpine ice cores
Brief communication: Non-linear sensitivity of glacier mass balance to climate attested by temperature-index models
Halving of Swiss glacier volume since 1931 observed from terrestrial image photogrammetry
Land- to lake-terminating transition triggers dynamic thinning of a Bhutanese glacier
Brief communication: A framework to classify glaciers for water resource evaluation and management in the Southern Andes
Strong acceleration of glacier area loss in the Greater Caucasus between 2000 and 2020
Ice volume and basal topography estimation using geostatistical methods and ground-penetrating radar measurements: application to the Tsanfleuron and Scex Rouge glaciers, Swiss Alps
Significant mass loss in the accumulation area of the Adamello glacier indicated by the chronology of a 46 m ice core
Brief communication: Do 1.0, 1.5, or 2.0 °C matter for the future evolution of Alpine glaciers?
A new automatic approach for extracting glacier centerlines based on Euclidean allocation
Spatially and temporally resolved ice loss in High Mountain Asia and the Gulf of Alaska observed by CryoSat-2 swath altimetry between 2010 and 2019
Crystallographic analysis of temperate ice on Rhonegletscher, Swiss Alps
Modal sensitivity of rock glaciers to elastic changes from spectral seismic noise monitoring and modeling
Debris cover and the thinning of Kennicott Glacier, Alaska: in situ measurements, automated ice cliff delineation and distributed melt estimates
Small-scale spatial variability in bare-ice reflectance at Jamtalferner, Austria
Numerical modeling of the dynamics of the Mer de Glace glacier, French Alps: comparison with past observations and forecasting of near-future evolution
Monitoring the seasonal changes of an englacial conduit network using repeated ground-penetrating radar measurements
Possible biases in scaling-based estimates of glacier change: a case study in the Himalaya
Spatial and temporal variations in glacier aerodynamic surface roughness during the melting season, as estimated at the August-one ice cap, Qilian mountains, China
Strong changes in englacial temperatures despite insignificant changes in ice thickness at Dôme du Goûter glacier (Mont Blanc area)
Supra-glacial debris cover changes in the Greater Caucasus from 1986 to 2014
Glacier thickness estimations of alpine glaciers using data and modeling constraints
Unravelling the evolution of Zmuttgletscher and its debris cover since the end of the Little Ice Age
Modelling the future evolution of glaciers in the European Alps under the EURO-CORDEX RCM ensemble
Robust uncertainty assessment of the spatio-temporal transferability of glacier mass and energy balance models
Impacts of topographic shading on direct solar radiation for valley glaciers in complex topography
19th century glacier retreat in the Alps preceded the emergence of industrial black carbon deposition on high-alpine glaciers
Iron oxides in the cryoconite of glaciers on the Tibetan Plateau: abundance, speciation and implications
Numerical reconstructions of the flow and basal conditions of the Rhine glacier, European Central Alps, at the Last Glacial Maximum
Relative performance of empirical and physical models in assessing the seasonal and annual glacier surface mass balance of Saint-Sorlin Glacier (French Alps)
Geodetic reanalysis of annual glaciological mass balances (2001–2011) of Hintereisferner, Austria
The European mountain cryosphere: a review of its current state, trends, and future challenges
Brief communication: The Khurdopin glacier surge revisited – extreme flow velocities and formation of a dammed lake in 2017
The Greater Caucasus Glacier Inventory (Russia, Georgia and Azerbaijan)
Impact of impurities and cryoconite on the optical properties of the Morteratsch Glacier (Swiss Alps)
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Recent geodetic mass balance of Monte Tronador glaciers, northern Patagonian Andes
Johannes Reinthaler and Frank Paul
The Cryosphere, 19, 753–767, https://doi.org/10.5194/tc-19-753-2025, https://doi.org/10.5194/tc-19-753-2025, 2025
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Since the end of the Little Ice Age (LIA) around 1850, glaciers in the European Alps have melted considerably. We collected LIA glacier extents, calculated changes using geoinformatics, and found a 57 % decrease in area (4244 km² to 1806 km²) and a 64 % decrease in volume (280 km³ to 100 km³) by 2015. The average glacier surface lowering was 44 m. After 2000, elevation change rates tripled. Over 1938 glaciers melted away completely, impacting entire regions.
Tom Müller, Mauro Fischer, Stuart N. Lane, and Bettina Schaefli
The Cryosphere, 19, 423–458, https://doi.org/10.5194/tc-19-423-2025, https://doi.org/10.5194/tc-19-423-2025, 2025
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Based on extensive field observations in a highly glacierized catchment in the Swiss Alps, we develop a combined isotopic and glacio-hydrological model. We show that water stable isotopes may help to better constrain model parameters, especially those linked to water transfer. However, we highlight that separating snow and ice melt for temperate glaciers based on isotope mixing models alone is not advised and should only be considered if their isotopic signatures have clearly different values.
Marin Kneib, Amaury Dehecq, Adrien Gilbert, Auguste Basset, Evan S. Miles, Guillaume Jouvet, Bruno Jourdain, Etienne Ducasse, Luc Beraud, Antoine Rabatel, Jérémie Mouginot, Guillem Carcanade, Olivier Laarman, Fanny Brun, and Delphine Six
The Cryosphere, 18, 5965–5983, https://doi.org/10.5194/tc-18-5965-2024, https://doi.org/10.5194/tc-18-5965-2024, 2024
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Avalanches contribute to increasing the accumulation on mountain glaciers by redistributing snow from surrounding mountains slopes. Here we quantified the contribution of avalanches to the mass balance of Argentière Glacier in the French Alps, by combining satellite and field observations to model the glacier dynamics. We show that the contribution of avalanches locally increases the accumulation by 60–70 % and that accounting for this effect results in less ice loss by the end of the century.
Lea Hartl, Patrick Schmitt, Lilian Schuster, Kay Helfricht, Jakob Abermann, and Fabien Maussion
EGUsphere, https://doi.org/10.5194/egusphere-2024-3146, https://doi.org/10.5194/egusphere-2024-3146, 2024
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We use regional observations of glacier area and volume change to inform glacier evolution modeling in the Ötztal and Stubai range (Austrian Alps) until 2100 in different climate scenarios. Glaciers in the region lost 23 % of their volume between 2006 and 2017. Under current warming trajectories, glacier loss in the region is expected to be near total by 2075. We show that integrating regional calibration and validation data in glacier models is important to improve confidence in projections.
Nicolas Bakken-French, Stephen J. Boyer, B. Clay Southworth, Megan Thayne, Dylan H. Rood, and Anders E. Carlson
The Cryosphere, 18, 4517–4530, https://doi.org/10.5194/tc-18-4517-2024, https://doi.org/10.5194/tc-18-4517-2024, 2024
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Repeat photography, field mapping, and remote sensing find that glaciers on Mt. Hood, Oregon, have lost about 25 % of their area in the first 2 decades of the 21st century and 17 % of their area in the last 7–8 years. The 21st century recession rate is more than 3 times faster than the 20th century average and 1.9 times faster than the fastest period of retreat within the 20th century. This unprecedented retreat corresponds to regional summer warming of 1.7–1.8°C relative to the early 1900s.
Jacopo Boaga, Mirko Pavoni, Alexander Bast, and Samuel Weber
The Cryosphere, 18, 3231–3236, https://doi.org/10.5194/tc-18-3231-2024, https://doi.org/10.5194/tc-18-3231-2024, 2024
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Reversal polarity is observed in rock glacier seismic refraction tomography. We collected several datasets observing this phenomenon in Switzerland and Italy. This phase change may be linked to interferences due to the presence of a thin low-velocity layer. Our results are confirmed by the modelling and analysis of synthetic seismograms to demonstrate that the presence of a low-velocity layer produces a polarity reversal on the seismic gather.
Marin Kneib, Amaury Dehecq, Fanny Brun, Fatima Karbou, Laurane Charrier, Silvan Leinss, Patrick Wagnon, and Fabien Maussion
The Cryosphere, 18, 2809–2830, https://doi.org/10.5194/tc-18-2809-2024, https://doi.org/10.5194/tc-18-2809-2024, 2024
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Avalanches are important for the mass balance of mountain glaciers, but few data exist on where and when they occur and which glaciers they affect the most. We developed an approach to map avalanches over large glaciated areas and long periods of time using satellite radar data. The application of this method to various regions in the Alps and High Mountain Asia reveals the variability of avalanches on these glaciers and provides key data to better represent these processes in glacier models.
Andrea Securo, Costanza Del Gobbo, Giovanni Baccolo, Carlo Barbante, Michele Citterio, Fabrizio De Blasi, Marco Marcer, Mauro Valt, and Renato R. Colucci
EGUsphere, https://doi.org/10.5194/egusphere-2024-1357, https://doi.org/10.5194/egusphere-2024-1357, 2024
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We have reconstructed the multi-decadal (1980s–2023) cumulative mass balance for all the current mountain glaciers in the Italian Dolomites. We used historical aerial imagery, drone surveys and airborne LiDAR to fill the existing gap of glaciological data for the region. We observed an alarming decline in both glaciers area and volume, with some of them showing lower losses due to local topography and debris cover feedback. We strongly encourage more specific monitoring for these small glaciers.
Janneke van Ginkel, Fabian Walter, Fabian Lindner, Miroslav Hallo, Matthias Huss, and Donat Fäh
EGUsphere, https://doi.org/10.5194/egusphere-2024-646, https://doi.org/10.5194/egusphere-2024-646, 2024
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This study on Glacier de la Plaine Morte in Switzerland employs various passive seismic analysis methods to identify complex hydraulic behaviours at the ice-bedrock interface. In 4 months of seismic records, we detect spatiotemporal variations in the glacier's basal interface, following the drainage of an ice-marginal lake. We identify a low-velocity layer, whose properties are determined using modeling techniques. This low-velocity layer results from temporary water storage within the glacier.
Rainey Aberle, Ellyn Enderlin, Shad O'Neel, Caitlyn Florentine, Louis Sass, Adam Dickson, Hans-Peter Marshall, and Alejandro Flores
EGUsphere, https://doi.org/10.5194/egusphere-2024-548, https://doi.org/10.5194/egusphere-2024-548, 2024
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Tracking seasonal snow on glaciers is critical for understanding glacier health. However, current snow detection methods struggle to distinguish seasonal snow from glacier ice. To address this, we developed a new automated workflow for tracking seasonal snow on glaciers using satellite imagery and machine learning. Applying this method can help provide insights into glacier health, water resources, and the effects of climate change on snow cover over broad spatial scales.
Brian Menounos, Alex Gardner, Caitlyn Florentine, and Andrew Fountain
The Cryosphere, 18, 889–894, https://doi.org/10.5194/tc-18-889-2024, https://doi.org/10.5194/tc-18-889-2024, 2024
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Glaciers in western North American outside of Alaska are often overlooked in global studies because their potential to contribute to changes in sea level is small. Nonetheless, these glaciers represent important sources of freshwater, especially during times of drought. We show that these glaciers lost mass at a rate of about 12 Gt yr-1 for about the period 2013–2021; the rate of mass loss over the period 2018–2022 was similar.
Ixeia Vidaller, Eñaut Izagirre, Luis Mariano del Rio, Esteban Alonso-González, Francisco Rojas-Heredia, Enrique Serrano, Ana Moreno, Juan Ignacio López-Moreno, and Jesús Revuelto
The Cryosphere, 17, 3177–3192, https://doi.org/10.5194/tc-17-3177-2023, https://doi.org/10.5194/tc-17-3177-2023, 2023
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The Aneto glacier, the largest glacier in the Pyrenees, has shown continuous surface and ice thickness losses in the last decades. In this study, we examine changes in its surface and ice thickness for 1981–2022 and the remaining ice thickness in 2020. During these 41 years, the glacier has shrunk by 64.7 %, and the ice thickness has decreased by 30.5 m on average. The mean ice thickness in 2022 was 11.9 m, compared to 32.9 m in 1981. The results highlight the critical situation of the glacier.
Ritu Anilkumar, Rishikesh Bharti, Dibyajyoti Chutia, and Shiv Prasad Aggarwal
The Cryosphere, 17, 2811–2828, https://doi.org/10.5194/tc-17-2811-2023, https://doi.org/10.5194/tc-17-2811-2023, 2023
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Our analysis demonstrates the capability of machine learning models in estimating glacier mass balance in terms of performance metrics and dataset availability. Feature importance analysis suggests that ablation features are significant. This is in agreement with the predominantly negative mass balance observations. We show that ensemble tree models typically depict the best performance. However, neural network models are preferable for biased inputs and kernel-based models for smaller datasets.
Anja Eichler, Michel Legrand, Theo M. Jenk, Susanne Preunkert, Camilla Andersson, Sabine Eckhardt, Magnuz Engardt, Andreas Plach, and Margit Schwikowski
The Cryosphere, 17, 2119–2137, https://doi.org/10.5194/tc-17-2119-2023, https://doi.org/10.5194/tc-17-2119-2023, 2023
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We investigate how a 250-year history of the emission of air pollutants (major inorganic aerosol constituents, black carbon, and trace species) is preserved in ice cores from four sites in the European Alps. The observed uniform timing in species-dependent longer-term concentration changes reveals that the different ice-core records provide a consistent, spatially representative signal of the pollution history from western European countries.
Christian Vincent and Emmanuel Thibert
The Cryosphere, 17, 1989–1995, https://doi.org/10.5194/tc-17-1989-2023, https://doi.org/10.5194/tc-17-1989-2023, 2023
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Temperature-index models have been widely used for glacier mass projections in the future. The ability of these models to capture non-linear responses of glacier mass balance (MB) to high deviations in air temperature and solid precipitation has recently been questioned by mass balance simulations employing advanced machine-learning techniques. Here, we confirmed that temperature-index models are capable of detecting non-linear responses of glacier MB to temperature and precipitation changes.
Erik Schytt Mannerfelt, Amaury Dehecq, Romain Hugonnet, Elias Hodel, Matthias Huss, Andreas Bauder, and Daniel Farinotti
The Cryosphere, 16, 3249–3268, https://doi.org/10.5194/tc-16-3249-2022, https://doi.org/10.5194/tc-16-3249-2022, 2022
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How glaciers have responded to climate change over the last 20 years is well-known, but earlier data are much more scarce. We change this in Switzerland by using 22 000 photographs taken from mountain tops between the world wars and find a halving of Swiss glacier volume since 1931. This was done through new automated processing techniques that we created. The data are interesting for more than just glaciers, such as mapping forest changes, landslides, and human impacts on the terrain.
Yota Sato, Koji Fujita, Hiroshi Inoue, Akiko Sakai, and Karma
The Cryosphere, 16, 2643–2654, https://doi.org/10.5194/tc-16-2643-2022, https://doi.org/10.5194/tc-16-2643-2022, 2022
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We investigate fluctuations in Bhutanese lake-terminating glaciers focusing on the dynamics change before and after proglacial lake formation at Thorthormi Glacier (TG) based on photogrammetry, satellite, and GPS surveys. The thinning rate of TG became double compared to before proglacial lake formation, and the flow velocity has also sped up considerably. Those changes would be due to the reduction in longitudinal ice compression by the detachment of the glacier terminus from the end moraine.
Nicole Schaffer and Shelley MacDonell
The Cryosphere, 16, 1779–1791, https://doi.org/10.5194/tc-16-1779-2022, https://doi.org/10.5194/tc-16-1779-2022, 2022
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Over the last 2 decades the importance of Andean glaciers, particularly as water resources, has been recognized in both scientific literature and the public sphere. This has led to the inclusion of glaciers in environmental impact assessment and the development of glacier protection laws. We propose three categories that group glaciers based on their environmental sensitivity to hopefully help facilitate the effective application of these measures and evaluation of water resources in general.
Levan G. Tielidze, Gennady A. Nosenko, Tatiana E. Khromova, and Frank Paul
The Cryosphere, 16, 489–504, https://doi.org/10.5194/tc-16-489-2022, https://doi.org/10.5194/tc-16-489-2022, 2022
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The new Caucasus glacier inventory derived from manual delineation of glacier outlines based on medium-resolution (Landsat, Sentinel) and high-resolution (SPOT) satellite imagery shows the accelerated glacier area loss over the last 2 decades (2000–2020). This new glacier inventory will improve our understanding of climate change impacts at a regional scale and support related modelling studies by providing high-quality validation data.
Alexis Neven, Valentin Dall'Alba, Przemysław Juda, Julien Straubhaar, and Philippe Renard
The Cryosphere, 15, 5169–5186, https://doi.org/10.5194/tc-15-5169-2021, https://doi.org/10.5194/tc-15-5169-2021, 2021
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We present and compare different geostatistical methods for underglacial bedrock interpolation. Variogram-based interpolations are compared with a multipoint statistics approach on both test cases and real glaciers. Using the modeled bedrock, the ice volume for the Scex Rouge and Tsanfleuron glaciers (Swiss Alps) was estimated to be 113.9 ± 1.6 million cubic meters. Complex karstic geomorphological features are reproduced and can be used to improve the precision of underglacial flow estimation.
Daniela Festi, Margit Schwikowski, Valter Maggi, Klaus Oeggl, and Theo Manuel Jenk
The Cryosphere, 15, 4135–4143, https://doi.org/10.5194/tc-15-4135-2021, https://doi.org/10.5194/tc-15-4135-2021, 2021
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In our study we dated a 46 m deep ice core retrieved from the Adamello glacier (Central Italian Alps). We obtained a timescale combining the results of radionuclides 210Pb and 137Cs with annual layer counting derived from pollen and refractory black carbon concentrations. Our results indicate that the surface of the glacier is older than the drilling date of 2016 by about 20 years, therefore revealing that the glacier is at high risk of collapsing under current climate warming conditions.
Loris Compagno, Sarah Eggs, Matthias Huss, Harry Zekollari, and Daniel Farinotti
The Cryosphere, 15, 2593–2599, https://doi.org/10.5194/tc-15-2593-2021, https://doi.org/10.5194/tc-15-2593-2021, 2021
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Recently, discussions have focused on the difference in limiting the increase in global average temperatures to below 1.0, 1.5, or 2.0 °C compared to preindustrial levels. Here, we assess the impacts that such different scenarios would have on both the future evolution of glaciers in the European Alps and the water resources they provide. Our results show that the different temperature targets have important implications for the changes predicted until 2100.
Dahong Zhang, Xiaojun Yao, Hongyu Duan, Shiyin Liu, Wanqin Guo, Meiping Sun, and Dazhi Li
The Cryosphere, 15, 1955–1973, https://doi.org/10.5194/tc-15-1955-2021, https://doi.org/10.5194/tc-15-1955-2021, 2021
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Glacier centerlines are crucial input for many glaciological applications. We propose a new algorithm to derive glacier centerlines and implement the corresponding program in Python language. Application of this method to 48 571 glaciers in the second Chinese glacier inventory automatically yielded the corresponding glacier centerlines with an average computing time of 20.96 s, a success rate of 100 % and a comprehensive accuracy of 94.34 %.
Livia Jakob, Noel Gourmelen, Martin Ewart, and Stephen Plummer
The Cryosphere, 15, 1845–1862, https://doi.org/10.5194/tc-15-1845-2021, https://doi.org/10.5194/tc-15-1845-2021, 2021
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Glaciers and ice caps are currently the largest contributor to sea level rise. Global monitoring of these regions is a challenging task, and significant differences remain between current estimates. This study looks at glacier changes in High Mountain Asia and the Gulf of Alaska using a new technique, which for the first time makes the use of satellite radar altimetry for mapping ice mass loss over mountain glacier regions possible.
Sebastian Hellmann, Johanna Kerch, Ilka Weikusat, Andreas Bauder, Melchior Grab, Guillaume Jouvet, Margit Schwikowski, and Hansruedi Maurer
The Cryosphere, 15, 677–694, https://doi.org/10.5194/tc-15-677-2021, https://doi.org/10.5194/tc-15-677-2021, 2021
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We analyse the orientation of ice crystals in an Alpine glacier and compare this orientation with the ice flow direction. We found that the crystals orient in the direction of the largest stress which is in the flow direction in the upper parts of the glacier and in the vertical direction for deeper zones of the glacier. The grains cluster around this maximum stress direction, in particular four-point maxima, most likely as a result of recrystallisation under relatively warm conditions.
Antoine Guillemot, Laurent Baillet, Stéphane Garambois, Xavier Bodin, Agnès Helmstetter, Raphaël Mayoraz, and Eric Larose
The Cryosphere, 15, 501–529, https://doi.org/10.5194/tc-15-501-2021, https://doi.org/10.5194/tc-15-501-2021, 2021
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Among mountainous permafrost landforms, rock glaciers are composed of boulders, fine frozen materials, water and ice in various proportions. Displacement rates of active rock glaciers can reach several m/yr, contributing to emerging risks linked to gravitational hazards. Thanks to passive seismic monitoring, resonance effects related to seasonal freeze–thawing processes of the shallower layers have been monitored and modeled. This method is an accurate tool for studying rock glaciers at depth.
Leif S. Anderson, William H. Armstrong, Robert S. Anderson, and Pascal Buri
The Cryosphere, 15, 265–282, https://doi.org/10.5194/tc-15-265-2021, https://doi.org/10.5194/tc-15-265-2021, 2021
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Many glaciers are thinning rapidly beneath debris cover (loose rock) that reduces melt, including Kennicott Glacier in Alaska. This contradiction has been explained by melt hotspots, such as ice cliffs, scattered within the debris cover. However, at Kennicott Glacier declining ice flow explains the rapid thinning. Through this study, Kennicott Glacier is now the first glacier in Alaska, and the largest glacier globally, where melt across its debris-covered tongue has been rigorously quantified.
Lea Hartl, Lucia Felbauer, Gabriele Schwaizer, and Andrea Fischer
The Cryosphere, 14, 4063–4081, https://doi.org/10.5194/tc-14-4063-2020, https://doi.org/10.5194/tc-14-4063-2020, 2020
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When glaciers become snow-free in summer, darker glacier ice is exposed. The ice surface is darker than snow and absorbs more radiation, which increases ice melt. We measured how much radiation is reflected at different wavelengths in the ablation zone of Jamtalferner, Austria. Due to impurities and water on the ice surface there are large variations in reflectance. Landsat 8 and Sentinel-2 surface reflectance products do not capture the full range of reflectance found on the glacier.
Vincent Peyaud, Coline Bouchayer, Olivier Gagliardini, Christian Vincent, Fabien Gillet-Chaulet, Delphine Six, and Olivier Laarman
The Cryosphere, 14, 3979–3994, https://doi.org/10.5194/tc-14-3979-2020, https://doi.org/10.5194/tc-14-3979-2020, 2020
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Alpine glaciers are retreating at an accelerating rate in a warming climate. Numerical models allow us to study and anticipate these changes, but the performance of a model is difficult to evaluate. So we compared an ice flow model with the long dataset of observations obtained between 1979 and 2015 on Mer de Glace (Mont Blanc area). The model accurately reconstructs the past evolution of the glacier. We simulate the future evolution of Mer de Glace; it could retreat by 2 to 6 km by 2050.
Gregory Church, Melchior Grab, Cédric Schmelzbach, Andreas Bauder, and Hansruedi Maurer
The Cryosphere, 14, 3269–3286, https://doi.org/10.5194/tc-14-3269-2020, https://doi.org/10.5194/tc-14-3269-2020, 2020
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In this field study, we repeated ground-penetrating radar measurements over an active englacial channel network that transports meltwater through the glacier. We successfully imaged the englacial meltwater pathway and were able to delimitate the channel's shape. Meltwater from the glacier can impact the glacier's dynamics if it reaches the ice–bed interface, and therefore monitoring these englacial drainage networks is important to understand how these networks behave throughout a season.
Argha Banerjee, Disha Patil, and Ajinkya Jadhav
The Cryosphere, 14, 3235–3247, https://doi.org/10.5194/tc-14-3235-2020, https://doi.org/10.5194/tc-14-3235-2020, 2020
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Simple models of glacier dynamics based on volume–area scaling underestimate climate sensitivity and response time of glaciers. Consequently, they may predict a faster response and a smaller long-term glacier loss. These biases in scaling models are established theoretically and are analysed in detail by simulating the step response of a set of 703 Himalayan glaciers separately by three different models: a scaling model, a 2-D shallow-ice approximation model, and a linear-response model.
Junfeng Liu, Rensheng Chen, and Chuntan Han
The Cryosphere, 14, 967–984, https://doi.org/10.5194/tc-14-967-2020, https://doi.org/10.5194/tc-14-967-2020, 2020
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Glacier surface roughness during melting season was observed by manual and automatic photogrammetry. Surface roughness was larger at the snow and ice transition zone than in fully snow- or ice-covered areas. Persistent snowfall and rainfall both reduce surface roughness. High or rising turbulent heat as a component of surface energy balance tended to produce a smooth ice surface; low or decreasing turbulent heat tended to produce a rougher surface.
Christian Vincent, Adrien Gilbert, Bruno Jourdain, Luc Piard, Patrick Ginot, Vladimir Mikhalenko, Philippe Possenti, Emmanuel Le Meur, Olivier Laarman, and Delphine Six
The Cryosphere, 14, 925–934, https://doi.org/10.5194/tc-14-925-2020, https://doi.org/10.5194/tc-14-925-2020, 2020
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We observed very low glacier thickness changes over the last decades at very-high-elevation glaciated areas on Mont Blanc. Conversely, measurements performed in deep boreholes since 1994 reveal strong changes in englacial temperature reaching 1.5 °C at a depth of 50 m. We conclude that at such very high elevations, current changes in climate do not lead to visible changes in glacier thickness but cause invisible changes within the glacier in terms of englacial temperatures.
Levan G. Tielidze, Tobias Bolch, Roger D. Wheate, Stanislav S. Kutuzov, Ivan I. Lavrentiev, and Michael Zemp
The Cryosphere, 14, 585–598, https://doi.org/10.5194/tc-14-585-2020, https://doi.org/10.5194/tc-14-585-2020, 2020
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We present data of supra-glacial debris cover for 659 glaciers across the Greater Caucasus based on satellite images from the years 1986, 2000 and 2014. We combined semi-automated methods for mapping the clean ice with manual digitization of debris-covered glacier parts and calculated supra-glacial debris-covered area as the residual between these two maps. The distribution of the supra-glacial debris cover differs between northern and southern and between western, central and eastern Caucasus.
Lisbeth Langhammer, Melchior Grab, Andreas Bauder, and Hansruedi Maurer
The Cryosphere, 13, 2189–2202, https://doi.org/10.5194/tc-13-2189-2019, https://doi.org/10.5194/tc-13-2189-2019, 2019
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We have developed a novel procedure for glacier thickness estimations that combines traditional glaciological modeling constraints with ground-truth data, for example, those obtained with ground-penetrating radar (GPR) measurements. This procedure is very useful for determining ice volume when only limited data are available. Furthermore, we outline a strategy for acquiring GPR data on glaciers, such that the cost/benefit ratio is optimized.
Nico Mölg, Tobias Bolch, Andrea Walter, and Andreas Vieli
The Cryosphere, 13, 1889–1909, https://doi.org/10.5194/tc-13-1889-2019, https://doi.org/10.5194/tc-13-1889-2019, 2019
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Debris can partly protect glaciers from melting. But many debris-covered glaciers change similar to debris-free glaciers. To better understand the debris influence we investigated 150 years of evolution of Zmutt Glacier in Switzerland. We found an increase in debris extent over time and a link to glacier flow velocity changes. We also found an influence of debris on the melt locally, but only a small volume change reduction over the whole glacier, also because of the influence of ice cliffs.
Harry Zekollari, Matthias Huss, and Daniel Farinotti
The Cryosphere, 13, 1125–1146, https://doi.org/10.5194/tc-13-1125-2019, https://doi.org/10.5194/tc-13-1125-2019, 2019
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Glaciers in the European Alps play an important role in the hydrological cycle, act as a source for hydroelectricity and have a large touristic importance. We model the future evolution of all glaciers in the Alps with a novel model that combines both ice flow and melt processes. We find that under a limited warming scenario about one-third of the present-day ice volume will still be present by the end of the century, while under strong warming more than 90 % of the volume will be lost by 2100.
Tobias Zolles, Fabien Maussion, Stephan Peter Galos, Wolfgang Gurgiser, and Lindsey Nicholson
The Cryosphere, 13, 469–489, https://doi.org/10.5194/tc-13-469-2019, https://doi.org/10.5194/tc-13-469-2019, 2019
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A mass and energy balance model was subjected to sensitivity and uncertainty analysis on two different Alpine glaciers. The global sensitivity analysis allowed for a mass balance measurement independent assessment of the model sensitivity and functioned as a reduction of the model free parameter space. A novel approach of a multi-objective optimization estimates the uncertainty of the simulated mass balance and the energy fluxes. The final model uncertainty is up to 1300 kg m−3 per year.
Matthew Olson and Summer Rupper
The Cryosphere, 13, 29–40, https://doi.org/10.5194/tc-13-29-2019, https://doi.org/10.5194/tc-13-29-2019, 2019
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Solar radiation is the largest energy input for most alpine glaciers. However, many models oversimplify the influence of topographic shading. Also, no systematic studies have explored the variable impact of shading on glacier ice. We find that shading can significantly impact modeled solar radiation, particularly at low elevations, at high latitudes, and for glaciers with a north/south orientation. Excluding the effects of shading will overestimate modeled solar radiation for alpine glaciers.
Michael Sigl, Nerilie J. Abram, Jacopo Gabrieli, Theo M. Jenk, Dimitri Osmont, and Margit Schwikowski
The Cryosphere, 12, 3311–3331, https://doi.org/10.5194/tc-12-3311-2018, https://doi.org/10.5194/tc-12-3311-2018, 2018
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The fast retreat of Alpine glaciers since the mid-19th century documented in photographs is used as a symbol for the human impact on global climate, yet the key driving forces remain elusive. Here we argue that not industrial soot but volcanic eruptions were responsible for an apparently accelerated deglaciation starting in the 1850s. Our findings support a negligible role of human activity in forcing glacier recession at the end of the Little Ice Age, highlighting the role of natural drivers.
Zhiyuan Cong, Shaopeng Gao, Wancang Zhao, Xin Wang, Guangming Wu, Yulan Zhang, Shichang Kang, Yongqin Liu, and Junfeng Ji
The Cryosphere, 12, 3177–3186, https://doi.org/10.5194/tc-12-3177-2018, https://doi.org/10.5194/tc-12-3177-2018, 2018
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Cryoconites from glaciers on the Tibetan Plateau and surrounding area were studied for iron oxides. We found that goethite is the predominant iron oxide form. Using the abundance, speciation and optical properties of iron oxides, the total light absorption was quantitatively attributed to goethite, hematite, black carbon and organic matter. Such findings are essential to understand the relative significance of anthropogenic and natural impacts.
Denis Cohen, Fabien Gillet-Chaulet, Wilfried Haeberli, Horst Machguth, and Urs H. Fischer
The Cryosphere, 12, 2515–2544, https://doi.org/10.5194/tc-12-2515-2018, https://doi.org/10.5194/tc-12-2515-2018, 2018
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As part of an integrative study about the safety of repositories for radioactive waste under ice age conditions in Switzerland, we modeled the flow of ice of the Rhine glacier at the Last Glacial Maximum to determine conditions at the ice–bed interface. Results indicate that portions of the ice lobes were at the melting temperature and ice was sliding, two conditions necessary for erosion by glacier. Conditions at the bed of the ice lobes were affected by climate and also by topography.
Marion Réveillet, Delphine Six, Christian Vincent, Antoine Rabatel, Marie Dumont, Matthieu Lafaysse, Samuel Morin, Vincent Vionnet, and Maxime Litt
The Cryosphere, 12, 1367–1386, https://doi.org/10.5194/tc-12-1367-2018, https://doi.org/10.5194/tc-12-1367-2018, 2018
Christoph Klug, Erik Bollmann, Stephan Peter Galos, Lindsey Nicholson, Rainer Prinz, Lorenzo Rieg, Rudolf Sailer, Johann Stötter, and Georg Kaser
The Cryosphere, 12, 833–849, https://doi.org/10.5194/tc-12-833-2018, https://doi.org/10.5194/tc-12-833-2018, 2018
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This study presents a reanalysis of the glacier mass balance record at Hintereisferner, Austria, for the period 2001 to 2011. We provide a year-by-year comparison of glaciological and geodetic mass balances obtained from annual airborne laser scanning data. After applying a series of corrections, a comparison of the methods reveals major differences for certain years. We thoroughly discuss the origin of these discrepancies and implications for future glaciological mass balance measurements.
Martin Beniston, Daniel Farinotti, Markus Stoffel, Liss M. Andreassen, Erika Coppola, Nicolas Eckert, Adriano Fantini, Florie Giacona, Christian Hauck, Matthias Huss, Hendrik Huwald, Michael Lehning, Juan-Ignacio López-Moreno, Jan Magnusson, Christoph Marty, Enrique Morán-Tejéda, Samuel Morin, Mohamed Naaim, Antonello Provenzale, Antoine Rabatel, Delphine Six, Johann Stötter, Ulrich Strasser, Silvia Terzago, and Christian Vincent
The Cryosphere, 12, 759–794, https://doi.org/10.5194/tc-12-759-2018, https://doi.org/10.5194/tc-12-759-2018, 2018
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This paper makes a rather exhaustive overview of current knowledge of past, current, and future aspects of cryospheric issues in continental Europe and makes a number of reflections of areas of uncertainty requiring more attention in both scientific and policy terms. The review paper is completed by a bibliography containing 350 recent references that will certainly be of value to scholars engaged in the fields of glacier, snow, and permafrost research.
Jakob F. Steiner, Philip D. A. Kraaijenbrink, Sergiu G. Jiduc, and Walter W. Immerzeel
The Cryosphere, 12, 95–101, https://doi.org/10.5194/tc-12-95-2018, https://doi.org/10.5194/tc-12-95-2018, 2018
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Glaciers that once every few years or decades suddenly advance in length – also known as surging glaciers – are found in many glaciated regions in the world. In the Karakoram glacier tongues are additionally located at low altitudes and relatively close to human settlements. We investigate a very recent and extremely rapid surge in the region that has caused a lake to form in the main valley with possible risks for downstream communities.
Levan G. Tielidze and Roger D. Wheate
The Cryosphere, 12, 81–94, https://doi.org/10.5194/tc-12-81-2018, https://doi.org/10.5194/tc-12-81-2018, 2018
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This is one of the first papers containing the Greater Caucasus glacier area and number change over the 1960–2014 period by individual river basins and countries. During the research we used old topographical maps and Corona imagery from the 1960s, and Landsat/ASTER imagery from 1986/2014. The separate sections and slopes have been revealed where there are the highest indices of the reduction in the area of the glaciers.
Biagio Di Mauro, Giovanni Baccolo, Roberto Garzonio, Claudia Giardino, Dario Massabò, Andrea Piazzalunga, Micol Rossini, and Roberto Colombo
The Cryosphere, 11, 2393–2409, https://doi.org/10.5194/tc-11-2393-2017, https://doi.org/10.5194/tc-11-2393-2017, 2017
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In the paper, we demonstrate the potential of field and satellite hyperspectral reflectance data in characterizing the spatial distribution of impurities on the Morteratsch Glacier. In situ reflectance spectra showed that impurities reduced ice reflectance in visible wavelengths by 80–90 %. Satellite data also showed the outcropping of dust during the melting season in the upper parts of the glacier. Laboratory measurements of cryoconite showed the presence of elemental and organic carbon.
Douglas I. Benn, Sarah Thompson, Jason Gulley, Jordan Mertes, Adrian Luckman, and Lindsey Nicholson
The Cryosphere, 11, 2247–2264, https://doi.org/10.5194/tc-11-2247-2017, https://doi.org/10.5194/tc-11-2247-2017, 2017
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This paper provides the first complete view of the drainage system of a large Himalayan glacier, based on ice-cave exploration and satellite image analysis. Drainage tunnels inside glaciers have a major impact on melting rates, by providing lines of weakness inside the ice and potential pathways for melt-water, and play a key role in the response of debris-covered glaciers to sustained periods of negative mass balance.
Lucas Ruiz, Etienne Berthier, Maximiliano Viale, Pierre Pitte, and Mariano H. Masiokas
The Cryosphere, 11, 619–634, https://doi.org/10.5194/tc-11-619-2017, https://doi.org/10.5194/tc-11-619-2017, 2017
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Our paper assesses the glacier mass change in the northern Patagonian Andes of Argentina and Chile, which is crucial to understanding how climate change is affecting them. We have found that between 2000 and 2012, glaciers in this region were slightly out of balance, with larger valley glaciers losing more mass than smaller mountain glaciers. The slightly negative mass balance of the northern Patagonian Andes contrasts with the highly negative mass balance of the Patagonian ice fields.
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Short summary
The paper deals with the micrometeorological conditions on mountain glaciers. We use idealized large-eddy simulations to study the heat transport associated with the local wind systems and its impact on the energy exchange between atmosphere and glaciers. Our results demonstrate how the sensible heat flux variablility on glaciers is related to topographic effects and that the energy surplus is strong enough to significantly increase the local glacier melting rates.
The paper deals with the micrometeorological conditions on mountain glaciers. We use idealized...
