Articles | Volume 16, issue 23
https://doi.org/10.5194/gmd-16-7075-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-16-7075-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A finite-element framework to explore the numerical solution of the coupled problem of heat conduction, water vapor diffusion, and settlement in dry snow (IvoriFEM v0.1.0)
Julien Brondex
CORRESPONDING AUTHOR
Université Grenoble Alpes, Université de Toulouse, Météo-France, CNRS, CNRM, Centre d’Études de la Neige, 38000 Grenoble, France
Kévin Fourteau
Université Grenoble Alpes, Université de Toulouse, Météo-France, CNRS, CNRM, Centre d’Études de la Neige, 38000 Grenoble, France
Marie Dumont
Université Grenoble Alpes, Université de Toulouse, Météo-France, CNRS, CNRM, Centre d’Études de la Neige, 38000 Grenoble, France
Pascal Hagenmuller
Université Grenoble Alpes, Université de Toulouse, Météo-France, CNRS, CNRM, Centre d’Études de la Neige, 38000 Grenoble, France
Neige Calonne
Université Grenoble Alpes, Université de Toulouse, Météo-France, CNRS, CNRM, Centre d’Études de la Neige, 38000 Grenoble, France
François Tuzet
Université Grenoble Alpes, Université de Toulouse, Météo-France, CNRS, CNRM, Centre d’Études de la Neige, 38000 Grenoble, France
Henning Löwe
WSL Institute for Snow and Avalanche Research SLF, Flüelastr. 11, 7260 Davos, Switzerland
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EGUsphere, https://doi.org/10.5194/egusphere-2025-3039, https://doi.org/10.5194/egusphere-2025-3039, 2025
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Transport processes like rocks carried by ice flow and damage evolution – a proxy for crevasses – are key in ice sheet modeling and should occur without diffusion. Yet, standard numerical methods often blur these features. We explore a particle-based Semi-Lagrangian approach, comparing it to a Discontinuous Galerkin method, and show it can accurately simulate such transport when run at high enough resolution.
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We investigate crevasse initiation by analyzing the artificial drainage of a water-filled cavity at Tête Rousse Glacier (Mont Blanc, France). Using a numerical model, we compute stress fields in response to water level variations in the cavity and compare them to observed crevasse patterns. Results show that a non-linear viscous rheology and a maximum principal stress criterion (with a stress threshold of 100–130 kPa) best predict crevasse occurrence.
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Geosci. Model Dev., 17, 1903–1929, https://doi.org/10.5194/gmd-17-1903-2024, https://doi.org/10.5194/gmd-17-1903-2024, 2024
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In this paper, we provide a novel numerical implementation for solving the energy exchanges at the surface of snow and ice. By combining the strong points of previous models, our solution leads to more accurate and robust simulations of the energy exchanges, surface temperature, and melt while preserving a reasonable computation time.
Fanny Brun, Owen King, Marion Réveillet, Charles Amory, Anton Planchot, Etienne Berthier, Amaury Dehecq, Tobias Bolch, Kévin Fourteau, Julien Brondex, Marie Dumont, Christoph Mayer, Silvan Leinss, Romain Hugonnet, and Patrick Wagnon
The Cryosphere, 17, 3251–3268, https://doi.org/10.5194/tc-17-3251-2023, https://doi.org/10.5194/tc-17-3251-2023, 2023
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The South Col Glacier is a small body of ice and snow located on the southern ridge of Mt. Everest. A recent study proposed that South Col Glacier is rapidly losing mass. In this study, we examined the glacier thickness change for the period 1984–2017 and found no thickness change. To reconcile these results, we investigate wind erosion and surface energy and mass balance and find that melt is unlikely a dominant process, contrary to previous findings.
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Transport processes like rocks carried by ice flow and damage evolution – a proxy for crevasses – are key in ice sheet modeling and should occur without diffusion. Yet, standard numerical methods often blur these features. We explore a particle-based Semi-Lagrangian approach, comparing it to a Discontinuous Galerkin method, and show it can accurately simulate such transport when run at high enough resolution.
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EGUsphere, https://doi.org/10.5194/egusphere-2025-2947, https://doi.org/10.5194/egusphere-2025-2947, 2025
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A new scheme has been developed in the SURFEX/ISBA-Crocus model, to consider the impact of liquid water dynamics on bare ice, including albedo feedback and refreezing. When applied to the Mera Glacier in Nepal, the model reveals strong seasonal effects on the energy and mass balance, with increased melting in dry seasons and significant refreezing during the monsoon. This development improves mass balance modeling under increasing rainfall and bare ice exposure due to climate warming.
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EGUsphere, https://doi.org/10.5194/egusphere-2025-2903, https://doi.org/10.5194/egusphere-2025-2903, 2025
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A quasi-static model is used to simulate the distribution of liquid water in the pore space of snow for various water contents. Liquid water is gradually introduced and then removed from a set of 34 3D tomography snow images by capillarity during wetting and drying simulations. This work constitutes an exploratory numerical work (i) to study the water retention curves and (ii) the effective transport properties of wet snow and how they are influenced by the water distribution at the pore scale.
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EGUsphere, https://doi.org/10.5194/egusphere-2025-444, https://doi.org/10.5194/egusphere-2025-444, 2025
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Saharan dust deposits frequently color alpine glaciers orange. Mineral dust reduces snow albedo and increases snow and glaciers melt rate. Using physical modeling, we quantified the impact of dust on the Argentière Glacier over the period 2019–2022. We found that that the contribution of mineral dust to the melt represents between 6 and 12 % of Argentière Glacier summer melt. At specific locations, the impact of dust over one year can rise to an equivalent of 1 meter of melted ice.
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The Cryosphere, 18, 4379–4397, https://doi.org/10.5194/tc-18-4379-2024, https://doi.org/10.5194/tc-18-4379-2024, 2024
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The Cryosphere, 18, 4285–4313, https://doi.org/10.5194/tc-18-4285-2024, https://doi.org/10.5194/tc-18-4285-2024, 2024
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Four different macroscopic heat and mass transfer models have been derived for a large range of condensation coefficient values by an upscaling method. A comprehensive evaluation of the models is presented based on experimental datasets and numerical examples. The models reproduce the trend of experimental temperature and density profiles but underestimate the magnitude of the processes. Possible causes of these discrepancies and potential improvements for the models are suggested.
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The Cryosphere, 18, 3787–3805, https://doi.org/10.5194/tc-18-3787-2024, https://doi.org/10.5194/tc-18-3787-2024, 2024
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This paper presents the evaluation of a numerical discrete element method (DEM) by simulating cone penetration tests in different snow samples. The DEM model demonstrated a good ability to reproduce the measured mechanical behaviour of the snow, namely the force evolution on the cone and the grain displacement field. Systematic sensitivity tests showed that the mechanical response depends not only on the microstructure of the sample but also on the mechanical parameters of grain contacts.
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The Cryosphere, 18, 3741–3763, https://doi.org/10.5194/tc-18-3741-2024, https://doi.org/10.5194/tc-18-3741-2024, 2024
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Ice core δO2/N2 records are useful dating tools due to their local insolation pacing. A precise understanding of the physical mechanism driving this relationship, however, remain ambiguous. By compiling data from 15 polar sites, we find a strong dependence of mean δO2/N2 on accumulation rate and temperature in addition to the well-documented insolation dependence. Snowpack modelling is used to investigate which physical properties drive the mechanistic dependence on these local parameters.
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The Cryosphere, 18, 3633–3652, https://doi.org/10.5194/tc-18-3633-2024, https://doi.org/10.5194/tc-18-3633-2024, 2024
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The topmost layer of a snowpack forms the interface to the atmosphere and is critical for the reflectance of solar radiation and avalanche formation. The effect of wind on the surface snow microstructure during precipitation events is poorly understood and quantified. We performed controlled lab experiments in a ring wind tunnel to systematically quantify the snow microstructure for different wind speeds, temperatures and precipitation intensities and to identify the relevant processes.
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The Cryosphere, 18, 3081–3116, https://doi.org/10.5194/tc-18-3081-2024, https://doi.org/10.5194/tc-18-3081-2024, 2024
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The Cryosphere, 18, 2831–2846, https://doi.org/10.5194/tc-18-2831-2024, https://doi.org/10.5194/tc-18-2831-2024, 2024
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Understanding the settling of snow under its own weight has applications from avalanche forecasts to ice core interpretations. We study how this settling can be modeled using 3D images of the internal structure of snow and ice deformation mechanics. We found that classical ice mechanics, as used, for instance, in glacier flow, explain the compaction of dense polar snow but not that of lighter seasonal snow. How, exactly, the ice deforms during light snow compaction thus remains an open question.
Julien Meloche, Melody Sandells, Henning Löwe, Nick Rutter, Richard Essery, Ghislain Picard, Randall K. Scharien, Alexandre Langlois, Matthias Jaggi, Josh King, Peter Toose, Jérôme Bouffard, Alessandro Di Bella, and Michele Scagliola
EGUsphere, https://doi.org/10.5194/egusphere-2024-1583, https://doi.org/10.5194/egusphere-2024-1583, 2024
Preprint archived
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Sea ice thickness is essential for climate studies. Radar altimetry has provided sea ice thickness measurement, but uncertainty arises from interaction of the signal with the snow cover. Therefore, modelling the signal interaction with the snow is necessary to improve retrieval. A radar model was used to simulate the radar signal from the snow-covered sea ice. This work paved the way to improved physical algorithm to retrieve snow depth and sea ice thickness for radar altimeter missions.
Anna Braun, Kévin Fourteau, and Henning Löwe
The Cryosphere, 18, 1653–1668, https://doi.org/10.5194/tc-18-1653-2024, https://doi.org/10.5194/tc-18-1653-2024, 2024
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The specific surface of snow dictates key physical properties and continuously evolves in natural snowpacks. This is referred to as metamorphism. This work develops a rigorous physical model for this evolution, which is able to reproduce X-ray tomography measurements without using unphysical tuning parameters. Our results emphasize that snow crystal growth at the micrometer scale ultimately controls the pace of metamorphism.
Kavitha Sundu, Johannes Freitag, Kévin Fourteau, and Henning Löwe
The Cryosphere, 18, 1579–1596, https://doi.org/10.5194/tc-18-1579-2024, https://doi.org/10.5194/tc-18-1579-2024, 2024
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Ice crystals often show a rod-like, vertical orientation in snow and firn; they are said to be anisotropic. The stiffness in the vertical direction therefore differs from the horizontal, which, for example, impacts the propagation of seismic waves. To quantify this anisotropy, we conducted finite-element simulations of 391 snow, firn, and ice core microstructures obtained from X-ray tomography. We then derived a parameterization that may be employed for advanced seismic studies in polar regions.
Kévin Fourteau, Julien Brondex, Fanny Brun, and Marie Dumont
Geosci. Model Dev., 17, 1903–1929, https://doi.org/10.5194/gmd-17-1903-2024, https://doi.org/10.5194/gmd-17-1903-2024, 2024
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In this paper, we provide a novel numerical implementation for solving the energy exchanges at the surface of snow and ice. By combining the strong points of previous models, our solution leads to more accurate and robust simulations of the energy exchanges, surface temperature, and melt while preserving a reasonable computation time.
Amy R. Macfarlane, Henning Löwe, Lucille Gimenes, David N. Wagner, Ruzica Dadic, Rafael Ottersberg, Stefan Hämmerle, and Martin Schneebeli
The Cryosphere, 17, 5417–5434, https://doi.org/10.5194/tc-17-5417-2023, https://doi.org/10.5194/tc-17-5417-2023, 2023
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Snow acts as an insulating blanket on Arctic sea ice, keeping the underlying ice "warm", relative to the atmosphere. Knowing the snow's thermal conductivity is essential for understanding winter ice growth. During the MOSAiC expedition, we measured the thermal conductivity of snow. We found spatial and vertical variability to overpower any temporal variability or dependency on underlying ice type and the thermal resistance to be directly influenced by snow height.
Samuel Morin, Hugues François, Marion Réveillet, Eric Sauquet, Louise Crochemore, Flora Branger, Étienne Leblois, and Marie Dumont
Hydrol. Earth Syst. Sci., 27, 4257–4277, https://doi.org/10.5194/hess-27-4257-2023, https://doi.org/10.5194/hess-27-4257-2023, 2023
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Ski resorts are a key socio-economic asset of several mountain areas. Grooming and snowmaking are routinely used to manage the snow cover on ski pistes, but despite vivid debate, little is known about their impact on water resources downstream. This study quantifies, for the pilot ski resort La Plagne in the French Alps, the impact of grooming and snowmaking on downstream river flow. Hydrological impacts are mostly apparent at the seasonal scale and rather neutral on the annual scale.
Jean Emmanuel Sicart, Victor Ramseyer, Ghislain Picard, Laurent Arnaud, Catherine Coulaud, Guilhem Freche, Damien Soubeyrand, Yves Lejeune, Marie Dumont, Isabelle Gouttevin, Erwan Le Gac, Frédéric Berger, Jean-Matthieu Monnet, Laurent Borgniet, Éric Mermin, Nick Rutter, Clare Webster, and Richard Essery
Earth Syst. Sci. Data, 15, 5121–5133, https://doi.org/10.5194/essd-15-5121-2023, https://doi.org/10.5194/essd-15-5121-2023, 2023
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Forests strongly modify the accumulation, metamorphism and melting of snow in midlatitude and high-latitude regions. Two field campaigns during the winters 2016–17 and 2017–18 were conducted in a coniferous forest in the French Alps to study interactions between snow and vegetation. This paper presents the field site, instrumentation and collection methods. The observations include forest characteristics, meteorology, snow cover and snow interception by the canopy during precipitation events.
Xavier Faïn, David M. Etheridge, Kévin Fourteau, Patricia Martinerie, Cathy M. Trudinger, Rachael H. Rhodes, Nathan J. Chellman, Ray L. Langenfelds, Joseph R. McConnell, Mark A. J. Curran, Edward J. Brook, Thomas Blunier, Grégory Teste, Roberto Grilli, Anthony Lemoine, William T. Sturges, Boris Vannière, Johannes Freitag, and Jérôme Chappellaz
Clim. Past, 19, 2287–2311, https://doi.org/10.5194/cp-19-2287-2023, https://doi.org/10.5194/cp-19-2287-2023, 2023
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We report on a 3000-year record of carbon monoxide (CO) levels in the Southern Hemisphere's high latitudes by combining ice core and firn air measurements with modern direct atmospheric samples. Antarctica [CO] remained stable (–835 to 1500 CE), decreased during the Little Ice Age, and peaked around 1985 CE. Such evolution reflects stable biomass burning CO emissions before industrialization, followed by growth from CO anthropogenic sources, which decline after 1985 due to improved combustion.
Lisa Bouvet, Neige Calonne, Frédéric Flin, and Christian Geindreau
The Cryosphere, 17, 3553–3573, https://doi.org/10.5194/tc-17-3553-2023, https://doi.org/10.5194/tc-17-3553-2023, 2023
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This study presents two new experiments of temperature gradient metamorphism in a snow layer using tomographic time series and focusing on the vertical extent. The results highlight two little known phenomena: the development of morphological vertical heterogeneities from an initial uniform layer, which is attributed to the temperature range and the vapor pressure distribution, and the quantification of the mass loss at the base caused by the vertical vapor fluxes and the dry lower boundary.
Fanny Brun, Owen King, Marion Réveillet, Charles Amory, Anton Planchot, Etienne Berthier, Amaury Dehecq, Tobias Bolch, Kévin Fourteau, Julien Brondex, Marie Dumont, Christoph Mayer, Silvan Leinss, Romain Hugonnet, and Patrick Wagnon
The Cryosphere, 17, 3251–3268, https://doi.org/10.5194/tc-17-3251-2023, https://doi.org/10.5194/tc-17-3251-2023, 2023
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The South Col Glacier is a small body of ice and snow located on the southern ridge of Mt. Everest. A recent study proposed that South Col Glacier is rapidly losing mass. In this study, we examined the glacier thickness change for the period 1984–2017 and found no thickness change. To reconcile these results, we investigate wind erosion and surface energy and mass balance and find that melt is unlikely a dominant process, contrary to previous findings.
Marie Dumont, Simon Gascoin, Marion Réveillet, Didier Voisin, François Tuzet, Laurent Arnaud, Mylène Bonnefoy, Montse Bacardit Peñarroya, Carlo Carmagnola, Alexandre Deguine, Aurélie Diacre, Lukas Dürr, Olivier Evrard, Firmin Fontaine, Amaury Frankl, Mathieu Fructus, Laure Gandois, Isabelle Gouttevin, Abdelfateh Gherab, Pascal Hagenmuller, Sophia Hansson, Hervé Herbin, Béatrice Josse, Bruno Jourdain, Irene Lefevre, Gaël Le Roux, Quentin Libois, Lucie Liger, Samuel Morin, Denis Petitprez, Alvaro Robledano, Martin Schneebeli, Pascal Salze, Delphine Six, Emmanuel Thibert, Jürg Trachsel, Matthieu Vernay, Léo Viallon-Galinier, and Céline Voiron
Earth Syst. Sci. Data, 15, 3075–3094, https://doi.org/10.5194/essd-15-3075-2023, https://doi.org/10.5194/essd-15-3075-2023, 2023
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Saharan dust outbreaks have profound effects on ecosystems, climate, health, and the cryosphere, but the spatial deposition pattern of Saharan dust is poorly known. Following the extreme dust deposition event of February 2021 across Europe, a citizen science campaign was launched to sample dust on snow over the Pyrenees and the European Alps. This campaign triggered wide interest and over 100 samples. The samples revealed the high variability of the dust properties within a single event.
Léo Viallon-Galinier, Pascal Hagenmuller, and Nicolas Eckert
The Cryosphere, 17, 2245–2260, https://doi.org/10.5194/tc-17-2245-2023, https://doi.org/10.5194/tc-17-2245-2023, 2023
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Avalanches are a significant issue in mountain areas where they threaten recreationists and human infrastructure. Assessments of avalanche hazards and the related risks are therefore an important challenge for local authorities. Meteorological and snow cover simulations are thus important to support operational forecasting. In this study we combine it with mechanical analysis of snow profiles and find that observed avalanche data improve avalanche activity prediction through statistical methods.
Oscar Dick, Léo Viallon-Galinier, François Tuzet, Pascal Hagenmuller, Mathieu Fructus, Benjamin Reuter, Matthieu Lafaysse, and Marie Dumont
The Cryosphere, 17, 1755–1773, https://doi.org/10.5194/tc-17-1755-2023, https://doi.org/10.5194/tc-17-1755-2023, 2023
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Saharan dust deposition can drastically change the snow color, turning mountain landscapes into sepia scenes. Dust increases the absorption of solar energy by the snow cover and thus modifies the snow evolution and potentially the avalanche risk. Here we show that dust can lead to increased or decreased snowpack stability depending on the snow and meteorological conditions after the deposition event. We also show that wet-snow avalanches happen earlier in the season due to the presence of dust.
Pyei Phyo Lin, Isabel Peinke, Pascal Hagenmuller, Matthias Wächter, M. Reza Rahimi Tabar, and Joachim Peinke
The Cryosphere, 16, 4811–4822, https://doi.org/10.5194/tc-16-4811-2022, https://doi.org/10.5194/tc-16-4811-2022, 2022
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Characterization of layers of snowpack with highly resolved micro-cone penetration tests leads to detailed fluctuating signals. We used advanced stochastic analysis to differentiate snow types by interpreting the signals as a mixture of continuous and discontinuous random fluctuations. These two types of fluctuation seem to correspond to different mechanisms of drag force generation during the experiments. The proposed methodology provides new insights into the characterization of snow layers.
Ghislain Picard, Henning Löwe, and Christian Mätzler
The Cryosphere, 16, 3861–3866, https://doi.org/10.5194/tc-16-3861-2022, https://doi.org/10.5194/tc-16-3861-2022, 2022
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Microwave satellite observations used to monitor the cryosphere require radiative transfer models for their interpretation. These models represent how microwaves are scattered by snow and ice. However no existing theory is suitable for all types of snow and ice found on Earth. We adapted a recently published generic scattering theory to snow and show how it may improve the representation of snows with intermediate densities (~500 kg/m3) and/or with coarse grains at high microwave frequencies.
Leung Tsang, Michael Durand, Chris Derksen, Ana P. Barros, Do-Hyuk Kang, Hans Lievens, Hans-Peter Marshall, Jiyue Zhu, Joel Johnson, Joshua King, Juha Lemmetyinen, Melody Sandells, Nick Rutter, Paul Siqueira, Anne Nolin, Batu Osmanoglu, Carrie Vuyovich, Edward Kim, Drew Taylor, Ioanna Merkouriadi, Ludovic Brucker, Mahdi Navari, Marie Dumont, Richard Kelly, Rhae Sung Kim, Tien-Hao Liao, Firoz Borah, and Xiaolan Xu
The Cryosphere, 16, 3531–3573, https://doi.org/10.5194/tc-16-3531-2022, https://doi.org/10.5194/tc-16-3531-2022, 2022
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Snow water equivalent (SWE) is of fundamental importance to water, energy, and geochemical cycles but is poorly observed globally. Synthetic aperture radar (SAR) measurements at X- and Ku-band can address this gap. This review serves to inform the broad snow research, monitoring, and application communities about the progress made in recent decades to move towards a new satellite mission capable of addressing the needs of the geoscience researchers and users.
Georg Lackner, Florent Domine, Daniel F. Nadeau, Matthieu Lafaysse, and Marie Dumont
The Cryosphere, 16, 3357–3373, https://doi.org/10.5194/tc-16-3357-2022, https://doi.org/10.5194/tc-16-3357-2022, 2022
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We compared the snowpack at two sites separated by less than 1 km, one in shrub tundra and the other one within the boreal forest. Even though the snowpack was twice as thick at the forested site, we found evidence that the vertical transport of water vapor from the bottom of the snowpack to its surface was important at both sites. The snow model Crocus simulates no water vapor fluxes and consequently failed to correctly simulate the observed density profiles.
Matthieu Vernay, Matthieu Lafaysse, Diego Monteiro, Pascal Hagenmuller, Rafife Nheili, Raphaëlle Samacoïts, Deborah Verfaillie, and Samuel Morin
Earth Syst. Sci. Data, 14, 1707–1733, https://doi.org/10.5194/essd-14-1707-2022, https://doi.org/10.5194/essd-14-1707-2022, 2022
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This paper introduces the latest version of the freely available S2M dataset which provides estimates of both meteorological and snow cover variables, as well as various avalanche hazard diagnostics at different elevations, slopes and aspects for the three main French high-elevation mountainous regions. A complete description of the system and the dataset is provided, as well as an overview of the possible uses of this dataset and an objective assessment of its limitations.
Bertrand Cluzet, Matthieu Lafaysse, César Deschamps-Berger, Matthieu Vernay, and Marie Dumont
The Cryosphere, 16, 1281–1298, https://doi.org/10.5194/tc-16-1281-2022, https://doi.org/10.5194/tc-16-1281-2022, 2022
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The mountainous snow cover is highly variable at all temporal and spatial scales. Snow cover models suffer from large errors, while snowpack observations are sparse. Data assimilation combines them into a better estimate of the snow cover. A major challenge is to propagate information from observed into unobserved areas. This paper presents a spatialized version of the particle filter, in which information from in situ snow depth observations is successfully used to constrain nearby simulations.
Xavier Faïn, Rachael H. Rhodes, Philip Place, Vasilii V. Petrenko, Kévin Fourteau, Nathan Chellman, Edward Crosier, Joseph R. McConnell, Edward J. Brook, Thomas Blunier, Michel Legrand, and Jérôme Chappellaz
Clim. Past, 18, 631–647, https://doi.org/10.5194/cp-18-631-2022, https://doi.org/10.5194/cp-18-631-2022, 2022
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Carbon monoxide (CO) is a regulated pollutant and one of the key components determining the oxidizing capacity of the atmosphere. In this study, we analyzed five ice cores from Greenland at high resolution for CO concentrations by coupling laser spectrometry with continuous melting. By combining these new datasets, we produced an upper-bound estimate of past atmospheric CO abundance since preindustrial times for the Northern Hemisphere high latitudes, covering the period from 1700 to 1957 CE.
Neige Calonne, Alexis Burr, Armelle Philip, Frédéric Flin, and Christian Geindreau
The Cryosphere, 16, 967–980, https://doi.org/10.5194/tc-16-967-2022, https://doi.org/10.5194/tc-16-967-2022, 2022
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Modeling gas transport in ice sheets from surface to close-off is key to interpreting climate archives. Estimates of the diffusion coefficient and permeability of snow and firn are required but remain a large source of uncertainty. We present a new dataset of diffusion coefficients and permeability from 20 to 120 m depth at two Antarctic sites. We suggest predictive formulas to estimate both properties over the entire 100–850 kg m3 density range, i.e., anywhere within the ice sheet column.
Konstantin Schürholt, Julia Kowalski, and Henning Löwe
The Cryosphere, 16, 903–923, https://doi.org/10.5194/tc-16-903-2022, https://doi.org/10.5194/tc-16-903-2022, 2022
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This companion paper deals with numerical particularities of partial differential equations underlying 1D snow models. In this first part we neglect mechanical settling and demonstrate that the nonlinear coupling between diffusive transport (heat and vapor), phase changes and ice mass conservation contains a wave instability that may be relevant for weak layer formation. Numerical requirements are discussed in view of the underlying homogenization scheme.
Georg Lackner, Florent Domine, Daniel F. Nadeau, Annie-Claude Parent, François Anctil, Matthieu Lafaysse, and Marie Dumont
The Cryosphere, 16, 127–142, https://doi.org/10.5194/tc-16-127-2022, https://doi.org/10.5194/tc-16-127-2022, 2022
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The surface energy budget is the sum of all incoming and outgoing energy fluxes at the Earth's surface and has a key role in the climate. We measured all these fluxes for an Arctic snowpack and found that most incoming energy from radiation is counterbalanced by thermal radiation and heat convection while sublimation was negligible. Overall, the snow model Crocus was able to simulate the observed energy fluxes well.
Anna Simson, Henning Löwe, and Julia Kowalski
The Cryosphere, 15, 5423–5445, https://doi.org/10.5194/tc-15-5423-2021, https://doi.org/10.5194/tc-15-5423-2021, 2021
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This companion paper deals with numerical particularities of partial differential equations underlying one-dimensional snow models. In this second part we include mechanical settling and develop a new hybrid (Eulerian–Lagrangian) method for solving the advection-dominated ice mass conservation on a moving mesh alongside Eulerian diffusion (heat and vapor) and phase changes. The scheme facilitates a modular and extendable solver strategy while retaining controls on numerical accuracy.
Florent Veillon, Marie Dumont, Charles Amory, and Mathieu Fructus
Geosci. Model Dev., 14, 7329–7343, https://doi.org/10.5194/gmd-14-7329-2021, https://doi.org/10.5194/gmd-14-7329-2021, 2021
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In climate models, the snow albedo scheme generally calculates only a narrowband or broadband albedo. Therefore, we have developed the VALHALLA method to optimize snow spectral albedo calculations through the determination of spectrally fixed radiative variables. The development of VALHALLA v1.0 with the use of the snow albedo model TARTES and the spectral irradiance model SBDART indicates a considerable reduction in calculation time while maintaining an adequate accuracy of albedo values.
Zacharie Barrou Dumont, Simon Gascoin, Olivier Hagolle, Michaël Ablain, Rémi Jugier, Germain Salgues, Florence Marti, Aurore Dupuis, Marie Dumont, and Samuel Morin
The Cryosphere, 15, 4975–4980, https://doi.org/10.5194/tc-15-4975-2021, https://doi.org/10.5194/tc-15-4975-2021, 2021
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Since 2020, the Copernicus High Resolution Snow & Ice Monitoring Service has distributed snow cover maps at 20 m resolution over Europe in near-real time. These products are derived from the Sentinel-2 Earth observation mission, with a revisit time of 5 d or less (cloud-permitting). Here we show the good accuracy of the snow detection over a wide range of regions in Europe, except in dense forest regions where the snow cover is hidden by the trees.
Marie Dumont, Frederic Flin, Aleksey Malinka, Olivier Brissaud, Pascal Hagenmuller, Philippe Lapalus, Bernard Lesaffre, Anne Dufour, Neige Calonne, Sabine Rolland du Roscoat, and Edward Ando
The Cryosphere, 15, 3921–3948, https://doi.org/10.5194/tc-15-3921-2021, https://doi.org/10.5194/tc-15-3921-2021, 2021
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The role of snow microstructure in snow optical properties is only partially understood despite the importance of snow optical properties for the Earth system. We present a dataset combining bidirectional reflectance measurements and 3D images of snow. We show that the snow reflectance is adequately simulated using the distribution of the ice chord lengths in the snow microstructure and that the impact of the morphological type of snow is especially important when ice is highly absorptive.
Sebastian Hellmann, Melchior Grab, Johanna Kerch, Henning Löwe, Andreas Bauder, Ilka Weikusat, and Hansruedi Maurer
The Cryosphere, 15, 3507–3521, https://doi.org/10.5194/tc-15-3507-2021, https://doi.org/10.5194/tc-15-3507-2021, 2021
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In this study, we analyse whether ultrasonic measurements on ice core samples could be employed to derive information about the particular ice crystal orientation in these samples. We discuss if such ultrasonic scans of ice core samples could provide similarly detailed results as the established methods, which usually destroy the ice samples. Our geophysical approach is minimally invasive and could support the existing methods with additional and (semi-)continuous data points along the ice core.
Kévin Fourteau, Florent Domine, and Pascal Hagenmuller
The Cryosphere, 15, 2739–2755, https://doi.org/10.5194/tc-15-2739-2021, https://doi.org/10.5194/tc-15-2739-2021, 2021
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The thermal conductivity of snow is an important physical property governing the thermal regime of a snowpack and its substrate. We show that it strongly depends on the kinetics of water vapor sublimation and that previous experimental data suggest a rather fast kinetics. In such a case, neglecting water vapor leads to an underestimation of thermal conductivity by up to 50 % for light snow. Moreover, the diffusivity of water vapor in snow is then directly related to the thermal conductivity.
Daniela Krampe, Frank Kauker, Marie Dumont, and Andreas Herber
The Cryosphere Discuss., https://doi.org/10.5194/tc-2021-100, https://doi.org/10.5194/tc-2021-100, 2021
Manuscript not accepted for further review
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Reliable and detailed Arctic snow data are limited. Evaluation of the performance of atmospheric reanalysis compared to measurements in northeast Greenland generally show good agreement. Both data sets are applied to an Alpine snow model and the performance for Arctic conditions is investigated: Simulated snow depth evolution is reliable, but vertical snow profiles show weaknesses. These are smaller with an adapted parametrisation for the density of newly fallen snow for harsh Arctic conditions.
Bertrand Cluzet, Matthieu Lafaysse, Emmanuel Cosme, Clément Albergel, Louis-François Meunier, and Marie Dumont
Geosci. Model Dev., 14, 1595–1614, https://doi.org/10.5194/gmd-14-1595-2021, https://doi.org/10.5194/gmd-14-1595-2021, 2021
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In the mountains, the combination of large model error and observation sparseness is a challenge for data assimilation. Here, we develop two variants of the particle filter (PF) in order to propagate the information content of observations into unobserved areas. By adjusting observation errors or exploiting background correlation patterns, we demonstrate the potential for partial observations of snow depth and surface reflectance to improve model accuracy with the PF in an idealised setting.
Nora Helbig, Yves Bühler, Lucie Eberhard, César Deschamps-Berger, Simon Gascoin, Marie Dumont, Jesus Revuelto, Jeff S. Deems, and Tobias Jonas
The Cryosphere, 15, 615–632, https://doi.org/10.5194/tc-15-615-2021, https://doi.org/10.5194/tc-15-615-2021, 2021
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The spatial variability in snow depth in mountains is driven by interactions between topography, wind, precipitation and radiation. In applications such as weather, climate and hydrological predictions, this is accounted for by the fractional snow-covered area describing the fraction of the ground surface covered by snow. We developed a new description for model grid cell sizes larger than 200 m. An evaluation suggests that the description performs similarly well in most geographical regions.
Kévin Fourteau, Florent Domine, and Pascal Hagenmuller
The Cryosphere, 15, 389–406, https://doi.org/10.5194/tc-15-389-2021, https://doi.org/10.5194/tc-15-389-2021, 2021
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There has been a long controversy to determine whether the effective diffusion coefficient of water vapor in snow is superior to that in free air. Using theory and numerical modeling, we show that while water vapor diffuses more than inert gases thanks to its interaction with the ice, the effective diffusion coefficient of water vapor in snow remains inferior to that in free air. This suggests that other transport mechanisms are responsible for the large vapor fluxes observed in some snowpacks.
François Tuzet, Marie Dumont, Ghislain Picard, Maxim Lamare, Didier Voisin, Pierre Nabat, Mathieu Lafaysse, Fanny Larue, Jesus Revuelto, and Laurent Arnaud
The Cryosphere, 14, 4553–4579, https://doi.org/10.5194/tc-14-4553-2020, https://doi.org/10.5194/tc-14-4553-2020, 2020
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This study presents a field dataset collected over 30 d from two snow seasons at a Col du Lautaret site (French Alps). The dataset compares different measurements or estimates of light-absorbing particle (LAP) concentrations in snow, highlighting a gap in the current understanding of the measurement of these quantities. An ensemble snowpack model is then evaluated for this dataset estimating that LAPs shorten each snow season by around 10 d despite contrasting meteorological conditions.
Maxim Lamare, Marie Dumont, Ghislain Picard, Fanny Larue, François Tuzet, Clément Delcourt, and Laurent Arnaud
The Cryosphere, 14, 3995–4020, https://doi.org/10.5194/tc-14-3995-2020, https://doi.org/10.5194/tc-14-3995-2020, 2020
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Terrain features found in mountainous regions introduce large errors into the calculation of the physical properties of snow using optical satellite images. We present a new model performing rapid calculations of solar radiation over snow-covered rugged terrain that we tested over a site in the French Alps. The results of the study show that all the interactions between sunlight and the terrain should be accounted for over snow-covered surfaces to correctly estimate snow properties from space.
César Deschamps-Berger, Simon Gascoin, Etienne Berthier, Jeffrey Deems, Ethan Gutmann, Amaury Dehecq, David Shean, and Marie Dumont
The Cryosphere, 14, 2925–2940, https://doi.org/10.5194/tc-14-2925-2020, https://doi.org/10.5194/tc-14-2925-2020, 2020
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We evaluate a recent method to map snow depth based on satellite photogrammetry. We compare it with accurate airborne laser-scanning measurements in the Sierra Nevada, USA. We find that satellite data capture the relationship between snow depth and elevation at the catchment scale and also small-scale features like snow drifts and avalanche deposits. We conclude that satellite photogrammetry stands out as a convenient method to estimate the spatial distribution of snow depth in high mountains.
Cited articles
Adams, E. E. and Brown, R. L.: A mixture theory for evaluating heat and mass transport processes in nonhomogeneous snow, Continuum Mech. Therm., 2, 31–63, https://doi.org/10.1007/BF01170954, 1990. a
Albert, M. R. and McGilvary, W. R.: Thermal effects due to air flow and vapor transport in dry snow, J. Glaciol., 38, 273–281, https://doi.org/10.1017/S0022143000003683, 1992. a
Bader, H.-P. and Weilenmann, P.: Modeling temperature distribution, energy and mass flow in a (phase-changing) snowpack. I. Model and case studies, Cold Reg. Sci. Technol., 20, 157–181, https://doi.org/10.1016/0165-232X(92)90015-M, 1992. a, b, c, d
Barrere, M., Domine, F., Decharme, B., Morin, S., Vionnet, V., and Lafaysse, M.: Evaluating the performance of coupled snow–soil models in SURFEXv8 to simulate the permafrost thermal regime at a high Arctic site, Geosci. Model Dev., 10, 3461–3479, https://doi.org/10.5194/gmd-10-3461-2017, 2017. a
Bourbatache, M. K., Le, T. D., Millet, O., and Moyne, C.: Limits of Classical Homogenization Procedure for Coupled Diffusion-Heterogeneous Reaction Processes in Porous Media, Transport Porous Med., 140, 437–457, https://doi.org/10.1007/s11242-021-01683-2, 2021. a, b
Bouvet, L., Calonne, N., Flin, F., and Geindreau, C.: Heterogeneous grain growth and vertical mass transfer within a snow layer under a temperature gradient, The Cryosphere, 17, 3553–3573, https://doi.org/10.5194/tc-17-3553-2023, 2023. a
Brondex, J., Fourteau, K., Dumont, M., Hagenmuller, P., Calonne, N., Tuzet, F., and Löwe, H.: Supplementary to “A finite-element framework to explore the numerical solution of the coupled problem of heat conduction, water vapor diffusion and settlement in dry snow (IvoriFEM v0.1.0)”, Zenodo [code and data set], https://doi.org/10.5281/zenodo.7941767, 2023. a, b
Brun, E., Martin, E., Simon, V., Gendre, C., and Coléou, C.: An energy and mass model of snow cover suitable for operational avalanche forecasting, J. Glaciol., 35, 333–342, https://doi.org/10.1017/S0022143000009254, 1989. a, b, c
Brun, E., David, P., Sudul, M., and Brunot, G.: A numerical model to simulate snow-cover stratigraphy for operational avalanche forecasting, J. Glaciol., 38, 13–22, https://doi.org/10.1017/S0022143000009552, 1992. a, b
Calonne, N., Flin, F., Morin, S., Lesaffre, B., du Roscoat, S. R., and Geindreau, C.: Numerical and experimental investigations of the effective thermal conductivity of snow, Geophys. Res. Lett., 38, L23501, https://doi.org/10.1029/2011gl049234, 2011. a, b
Casulli, V. and Zanolli, P.: A nested Newton-type algorithm for finite volume methods solving Richards' equation in mixed form, SIAM J. Sci. Comput., 32, 2255–2273, https://doi.org/10.1137/100786320, 2010. a, b
Ciarlet, P.: Maximum principle and uniform convergence for the finite element method, Comput. Method. Appl. M., 2, 17–31, https://doi.org/10.1016/0045-7825(73)90019-4, 1973. a
Decharme, B., Boone, A., Delire, C., and Noilhan, J.: Local evaluation of the Interaction between Soil Biosphere Atmosphere soil multilayer diffusion scheme using four pedotransfer functions, J. Geophys. Res.-Atmos., 116, D20126, https://doi.org/10.1029/2011JD016002, 2011. a
Domine, F., Barrere, M., and Sarrazin, D.: Seasonal evolution of the effective thermal conductivity of the snow and the soil in high Arctic herb tundra at Bylot Island, Canada, The Cryosphere, 10, 2573–2588, https://doi.org/10.5194/tc-10-2573-2016, 2016. a
Domine, F., Picard, G., Morin, S., Barrere, M., Madore, J.-B., and Langlois, A.: Major Issues in Simulating Some Arctic Snowpack Properties Using Current Detailed Snow Physics Models: Consequences for the Thermal Regime and Water Budget of Permafrost, J. Adv. Model. Earth Sy., 11, 34–44, https://doi.org/10.1029/2018MS001445, 2019. a
El-Mikkawy, M. and Atlan, F.: Algorithms for solving linear systems of equations of tridiagonal type via transformations, Applied Mathematics, 5, 413–422, https://doi.org/10.4236/am.2014.53042, 2014. a
Essery, R., Rutter, N., Pomeroy, J., Baxter, R., Stähli, M., Gustafsson, D., Barr, A., Bartlett, P., and Elder, K.: SNOWMIP2: An Evaluation of Forest Snow Process Simulations, B. Am. Meteorol. Soc., 90, 1120–1135, https://doi.org/10.1175/2009BAMS2629.1, 2009. a
Etchevers, P., Martin, E., Brown, R., Fierz, C., Lejeune, Y., Bazile, E., Boone, A., Dai, Y.-J., Essery, R., Fernandez, A., Gusev, Y., Jordan, R., Koren, V., Kowalczyk, E., Nasonova, N. O., Pyles, R. D., Schlosser, A., Shmakin, A. B., Smirnova, T. G., Strasser, U., Verseghy, D., Yamazaki, T., and Yang, Z.-L.: Validation of the energy budget of an alpine snowpack simulated by several snow models (Snow MIP project), Ann. Glaciol., 38, 150–158, https://doi.org/10.3189/172756404781814825, 2004. a
Formaggia, L. and Scotti, A.: Positivity and conservation properties of some integration schemes for mass action kinetics, SIAM J. Numer. Anal., 49, 1267–1288, https://doi.org/10.1137/100789592, 2011. a
Fourteau, K., Domine, F., and Hagenmuller, P.: Macroscopic water vapor diffusion is not enhanced in snow, The Cryosphere, 15, 389–406, https://doi.org/10.5194/tc-15-389-2021, 2021. a, b
Gagliardini, O., Zwinger, T., Gillet-Chaulet, F., Durand, G., Favier, L., de Fleurian, B., Greve, R., Malinen, M., Martín, C., Råback, P., Ruokolainen, J., Sacchettini, M., Schäfer, M., Seddik, H., and Thies, J.: Capabilities and performance of Elmer/Ice, a new-generation ice sheet model, Geosci. Model Dev., 6, 1299–1318, https://doi.org/10.5194/gmd-6-1299-2013, 2013. a
Gupta, A. S., Jourdain, N. C., Brown, J. N., and Monselesan, D.: Climate Drift in the CMIP5 Models, J. Climate, 26, 8597–8615, https://doi.org/10.1175/JCLI-D-12-00521.1, 2013. a
Hagenmuller, P., Flin, F., Dumont, M., Tuzet, F., Peinke, I., Lapalus, P., Dufour, A., Roulle, J., Pézard, L., Voisin, D., Ando, E., Rolland du Roscoat, S., and Charrier, P.: Motion of dust particles in dry snow under temperature gradient metamorphism, The Cryosphere, 13, 2345–2359, https://doi.org/10.5194/tc-13-2345-2019, 2019. a
Hobbs, W., Palmer, M. D., and Monselesan, D.: An Energy Conservation Analysis of Ocean Drift in the CMIP5 Global Coupled Models, J. Climate, 29, 1639–1653, https://doi.org/10.1175/JCLI-D-15-0477.1, 2016. a
Irving, D., Hobbs, W., Church, J., and Zika, J.: A Mass and Energy Conservation Analysis of Drift in the CMIP6 Ensemble, J. Climate, 34, 3157–3170, https://doi.org/10.1175/JCLI-D-20-0281.1, 2021. a
Jaafar, H. and Picot, J. J. C.: Thermal Conductivity of Snow by a Transient State Probe Method, Water Resour. Res., 6, 333–335, https://doi.org/10.1029/WR006i001p00333, 1970. a
Jafari, M., Gouttevin, I., Couttet, M., Wever, N., Michel, A., Sharma, V., Rossmann, L., Maass, N., Nicolaus, M., and Lehning, M.: The impact of diffusive water vapor transport on snow profiles in deep and shallow snow covers and on sea ice, Frontiers in Earth Science, 8, 249, https://doi.org/10.3389/feart.2020.00249, 2020. a, b, c, d
Jia, J. and Jiang, Y.: Two symbolic algorithms for solving general periodic pentadiagonal linear systems, Comput. Math. Appl., 69, 1020–1029, https://doi.org/10.1016/j.camwa.2015.03.009, 2015. a
John, V. and Schmeyer, E.: Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion, Comput. Method. Appl. M., 198, 475–494, https://doi.org/10.1016/j.cma.2008.08.016, 2008. a, b, c
Krinner, G., Derksen, C., Essery, R., Flanner, M., Hagemann, S., Clark, M., Hall, A., Rott, H., Brutel-Vuilmet, C., Kim, H., Ménard, C. B., Mudryk, L., Thackeray, C., Wang, L., Arduini, G., Balsamo, G., Bartlett, P., Boike, J., Boone, A., Chéruy, F., Colin, J., Cuntz, M., Dai, Y., Decharme, B., Derry, J., Ducharne, A., Dutra, E., Fang, X., Fierz, C., Ghattas, J., Gusev, Y., Haverd, V., Kontu, A., Lafaysse, M., Law, R., Lawrence, D., Li, W., Marke, T., Marks, D., Ménégoz, M., Nasonova, O., Nitta, T., Niwano, M., Pomeroy, J., Raleigh, M. S., Schaedler, G., Semenov, V., Smirnova, T. G., Stacke, T., Strasser, U., Svenson, S., Turkov, D., Wang, T., Wever, N., Yuan, H., Zhou, W., and Zhu, D.: ESM-SnowMIP: assessing snow models and quantifying snow-related climate feedbacks, Geosci. Model Dev., 11, 5027–5049, https://doi.org/10.5194/gmd-11-5027-2018, 2018. a, b
Libbrecht, K. G.: Physical properties of ice, http://www.cco.caltech.edu/~atomic/snowcrystals/ice/ice.htm, (last access: 2023-03-29), 1999. a
Magnusson, J., Wever, N., Essery, R., Helbig, N., Winstral, A., and Jonas, T.: Evaluating snow models with varying process representations for hydrological applications, Water Resour. Res., 51, 2707–2723, https://doi.org/10.1002/2014WR016498, 2015. a
Menard, C. B., Essery, R., Krinner, G., Arduini, G., Bartlett, P., Boone, A., Brutel-Vuilmet, C., Burke, E., Cuntz, M., Dai, Y., Decharme, B., Dutra, E., Fang, X., Fierz, C., Gusev, Y., Hagemann, S., Haverd, V., Kim, H., Lafaysse, M., Marke, T., Nasonova, O., Nitta, T., Niwano, M., Pomeroy, J., Schädler, G., Semenov, V. A., Smirnova, T., Strasser, U., Swenson, S., Turkov, D., Wever, N., and Yuan, H.: Scientific and Human Errors in a Snow Model Intercomparison, B. Am. Meteorol. Soc., 102, E61–E79, https://doi.org/10.1175/BAMS-D-19-0329.1, 2021. a, b
Milly, P. C. D.: A mass-conservative procedure for time-stepping in models of unsaturated flow, Adv. Water Resour., 8, 32–36, https://doi.org/10.1016/0309-1708(85)90078-8, 1985. a
Morin, S., Horton, S., Techel, F., Bavay, M., Coléou, C., Fierz, C., Gobiet, A., Hagenmuller, P., Lafaysse, M., Ližar, M., Mitterer, C., Monti, F., Müller, K., Olefs, M., Snook, J. S., van Herwijnen, A., and Vionnet, V.: Application of physical snowpack models in support of operational avalanche hazard forecasting: A status report on current implementations and prospects for the future, Cold Reg. Sci. Technol., 170, 102910, https://doi.org/10.1016/j.coldregions.2019.102910, 2020. a
Patankar, S. V.: Numerical heat transfer and fluid flow, 1st edn., CRC Press, https://doi.org/10.1201/9781482234213, 1980. a
Pepper, D. W. and Heinrich, J. C.: The finite element method: basic concepts and applications, Taylor & Francis, https://doi.org/10.1201/9781315395104, 2005. a
Pfeffer, W. T. and Mrugala, R.: Temperature gradient and initial snow density as controlling factors in the formation and structure of hard depth hoar, J. Glaciol., 48, 485–494, 2002. a
Pinzer, B. R., Schneebeli, M., and Kaempfer, T. U.: Vapor flux and recrystallization during dry snow metamorphism under a steady temperature gradient as observed by time-lapse micro-tomography, The Cryosphere, 6, 1141–1155, https://doi.org/10.5194/tc-6-1141-2012, 2012. a
Protter, M. H. and Weinberger, H. F.: Maximum principles in differential equations, Springer Science & Business Media, ISBN 9781461252825, 2012. a
Riche, F. and Schneebeli, M.: Thermal conductivity of snow measured by three independent methods and anisotropy considerations, The Cryosphere, 7, 217–227, https://doi.org/10.5194/tc-7-217-2013, 2013. a
Sauter, T., Arndt, A., and Schneider, C.: COSIPY v1.3 – an open-source coupled snowpack and ice surface energy and mass balance model, Geosci. Model Dev., 13, 5645–5662, https://doi.org/10.5194/gmd-13-5645-2020, 2020. a, b
Schürholt, K., Kowalski, J., and Löwe, H.: A numerical solver for heat and mass transport in snow based on FEniCS, EnviDat [code and data set], https://doi.org/10.16904/envidat.298, 2022a. a, b, c
Schürholt, K., Kowalski, J., and Löwe, H.: Elements of future snowpack modeling – Part 1: A physical instability arising from the nonlinear coupling of transport and phase changes, The Cryosphere, 16, 903–923, https://doi.org/10.5194/tc-16-903-2022, 2022b. a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, aa, ab, ac, ad, ae, af, ag, ah, ai
Simson, A., Löwe, H., and Kowalski, J.: Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes, The Cryosphere, 15, 5423–5445, https://doi.org/10.5194/tc-15-5423-2021, 2021. a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, aa, ab, ac, ad, ae, af, ag, ah, ai, aj
Slater, A. G., Schlosser, C. A., Desborough, C. E., Pitman, A. J., Henderson-Sellers, A., Robock, A., Vinnikov, K. Y., Mitchell, K., Boone, A., Braden, H., Chen, F., Cox, P. M., de Rosnay, P., Dickinson, R. E., Dai, Y. J., Duan, Q., Entin, J., Etchevers, P., Gedney, N., Gusev, Y. M., Habets, F., Kim, J., Koren, V., Kowalczyk, E. A., Nasonova, O. N., Noilhan, J., Schaake, S., Shmakin, A. B., Smirnova, T. G., Verseghy, D., Wetzel, P., Xue, Y., Yang, Z. L., and Zeng, Q.: The Representation of Snow in Land Surface Schemes: Results from PILPS 2(d), J. Hydrometeorol., 2, 7–25, https://doi.org/10.1175/1525-7541(2001)002<0007:TROSIL>2.0.CO;2, 2001. a
Sturm, M. and Benson, C. S.: Vapor transport, grain growth and depth-hoar development in the subarctic snow, J. Glaciol., 43, 42–59, https://doi.org/10.1017/S0022143000002793, 1997. a
Sturm, M. and Johnson, J. B.: Thermal conductivity measurements of depth hoar, J. Geophys. Res.-Sol. Ea., 97, 2129–2139, https://doi.org/10.1029/91JB02685, 1992. a, b
Thomée, V.: On positivity preservation in some finite element methods for the heat equation, in: Numerical Methods and Applications: 8th International Conference, NMA 2014, Borovets, Bulgaria, 20–24 August 2014, Revised Selected Papers 8, Springer, 13–24, https://doi.org/10.1007/978-3-319-15585-2_2, 2015. a
Touzeau, A., Landais, A., Morin, S., Arnaud, L., and Picard, G.: Numerical experiments on vapor diffusion in polar snow and firn and its impact on isotopes using the multi-layer energy balance model Crocus in SURFEX v8.0, Geosci. Model Dev., 11, 2393–2418, https://doi.org/10.5194/gmd-11-2393-2018, 2018. a, b, c, d, e, f
Tubini, N., Gruber, S., and Rigon, R.: A method for solving heat transfer with phase change in ice or soil that allows for large time steps while guaranteeing energy conservation, The Cryosphere, 15, 2541–2568, https://doi.org/10.5194/tc-15-2541-2021, 2021. a, b, c, d
van Pelt, W. J. J., Oerlemans, J., Reijmer, C. H., Pohjola, V. A., Pettersson, R., and van Angelen, J. H.: Simulating melt, runoff and refreezing on Nordenskiöldbreen, Svalbard, using a coupled snow and energy balance model, The Cryosphere, 6, 641–659, https://doi.org/10.5194/tc-6-641-2012, 2012. a
Vionnet, V., Brun, E., Morin, S., Boone, A., Faroux, S., Le Moigne, P., Martin, E., and Willemet, J.-M.: The detailed snowpack scheme Crocus and its implementation in SURFEX v7.2, Geosci. Model Dev., 5, 773–791, https://doi.org/10.5194/gmd-5-773-2012, 2012. a, b, c, d
Wiese, M. and Schneebeli, M.: Snowbreeder 5: a Micro-CT device for measuring the snow-microstructure evolution under the simultaneous influence of a temperature gradient and compaction, J. Glaciol., 63, 355–360, https://doi.org/10.1017/jog.2016.143, 2017. a
Short summary
Vapor diffusion is one of the main processes governing snowpack evolution, and it must be accounted for in models. Recent attempts to represent vapor diffusion in numerical models have faced several difficulties regarding computational cost and mass and energy conservation. Here, we develop our own finite-element software to explore numerical approaches and enable us to overcome these difficulties. We illustrate the capability of these approaches on established numerical benchmarks.
Vapor diffusion is one of the main processes governing snowpack evolution, and it must be...