Articles | Volume 3, issue 2 
            
                
                    
            
            
            https://doi.org/10.5194/tc-3-217-2009
                    © Author(s) 2009. 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-3-217-2009
                    © Author(s) 2009. This work is distributed under 
the Creative Commons Attribution 3.0 License.
                the Creative Commons Attribution 3.0 License.
Diagnostic and prognostic simulations with a full Stokes model accounting for superimposed ice of Midtre Lovénbreen, Svalbard
T. Zwinger
                                            CSC – IT Center for Science Ltd., Espoo, Finland
                                        
                                    J. C. Moore
                                            Arctic Centre, University of Lapland, Rovaniemi, Finland
                                        
                                    
                                            Thule Institute, University of Oulu, Oulu, Finland
                                        
                                    
                                            College of Global Change and Earth System Science, Beijing Normal University, China
                                        
                                    Related subject area
            Numerical Modelling
            
                    
                        
                            
                            
                                     
                                Antarctic sensitivity to oceanic melting parameterizations
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Analytical solutions for the advective–diffusive ice column in the presence of strain heating
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Ice viscosity governs hydraulic fracture that causes rapid drainage of supraglacial lakes
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Microstructure-based modelling of snow mechanics: experimental evaluation of the cone penetration test
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Snow redistribution in an intermediate-complexity snow hydrology modelling framework
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Increasing numerical stability of mountain valley glacier simulations: implementation and testing of free-surface stabilization in Elmer/Ice
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Analyzing the sensitivity of a blowing snow model (SnowPappus) to precipitation forcing, blowing snow, and spatial resolution
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Exploring non-Gaussian sea ice characteristics via observing system simulation experiments
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Past and future of the Arctic sea ice in High-Resolution Model Intercomparison Project (HighResMIP) climate models
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Biases in ice sheet models from missing noise-induced drift
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                            
                                     
                                Application of a regularised Coulomb sliding law to Jakobshavn Isbræ, West Greenland
                                
                                        
                                            
                                    
                            
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                A 3D glacier dynamics–line plume model to estimate the frontal ablation of Hansbreen, Svalbard
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                            
                                     
                                Sensitivity of Future Projections of the Wilkes Subglacial Basin Ice Sheet to Grounding Line Melt Parameterizations
                                
                                        
                                            
                                    
                            
                            
                            
                        
                    
                    
                        
                            
                            
                            
                                     
                                Brief communication: Stalagmite damage by cave-ice flow quantitatively assessed by fluid-structure-interaction simulations
                                
                                        
                                            
                                    
                            
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Data-driven surrogate modeling of high-resolution sea-ice thickness in the Arctic
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Using Icepack to reproduce ice mass balance buoy observations in landfast ice: improvements from the mushy-layer thermodynamics
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Modeling the timing of Patagonian Ice Sheet retreat in the Chilean Lake District from 22–10 ka
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Understanding the influence of ocean waves on Arctic sea ice simulation: a modeling study with an atmosphere–ocean–wave–sea ice coupled model
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Sea ice cover in the Copernicus Arctic Regional Reanalysis
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                            
                                     
                                How Many Parameters are Needed to Represent Polar Sea Ice Surface Patterns and Heterogeneity?
                                
                                        
                                            
                                    
                            
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Regime shifts in Arctic terrestrial hydrology manifested from impacts of climate warming
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Smoothed particle hydrodynamics implementation of the standard viscous–plastic sea-ice model and validation in simple idealized experiments
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                            
                                     
                                Modelling snowpack on ice surfaces with the ORCHIDEE land surface model: Application to the Greenland ice sheet
                                
                                        
                                            
                                    
                            
                            
                            
                        
                    
                    
                        
                            
                            
                            
                                     
                                Simulating lake ice phenology using a coupled atmosphere-lake model at Lake Nam Co, a typical deep alpine lake on the Tibetan Plateau
                                
                                        
                                            
                                    
                            
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Coupled thermo–geophysical inversion for permafrost monitoring
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Using specularity content to evaluate eight geothermal heat flow maps of Totten Glacier
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                            
                                     
                                Exploring the decision-making process in model development: focus on the Arctic snowpack
                                
                                        
                                            
                                    
                            
                            
                            
                        
                    
                    
                        
                            
                            
                            
                                     
                                Modeling the effect of free convection on permafrost melting-rates in frozen rock-clefts
                                
                                        
                                            
                                    
                            
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Surging of a Hudson Strait-scale ice stream: subglacial hydrology matters but the process details mostly do not
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                            
                                     
                                Exploring the potential of forest snow modelling at the tree and snowpack layer scale
                                
                                        
                                            
                                    
                            
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Impact of the Nares Strait sea ice arches on the long-term stability of the Petermann Glacier ice shelf
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Quantifying the uncertainty in the Eurasian ice-sheet geometry at the Penultimate Glacial Maximum (Marine Isotope Stage 6)
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Simulating ice segregation and thaw consolidation in permafrost environments with the CryoGrid community model
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Reconciling ice dynamics and bed topography with a versatile and fast ice thickness inversion
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                The stability of present-day Antarctic grounding lines – Part 2: Onset of irreversible retreat of Amundsen Sea glaciers under current climate on centennial timescales cannot be excluded
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                The stability of present-day Antarctic grounding lines – Part 1: No indication of marine ice sheet instability in the current geometry
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Phase-field models of floe fracture in sea ice
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Exploring the ability of the variable-resolution Community Earth System Model to simulate cryospheric–hydrological variables in High Mountain Asia
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Investigating the thermal state of permafrost with Bayesian inverse modeling of heat transfer
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Modelling the development and decay of cryoconite holes in northwestern Greenland
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                The effect of partial dissolution on sea-ice chemical transport: a combined model–observational study using poly- and perfluoroalkylated substances (PFASs)
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Deep learning subgrid-scale parametrisations for short-term forecasting of sea-ice dynamics with a Maxwell elasto-brittle rheology
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Representation of soil hydrology in permafrost regions may explain large part of inter-model spread in simulated Arctic and subarctic climate
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Impact of atmospheric forcing uncertainties on Arctic and Antarctic sea ice simulations in CMIP6 OMIP models
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Arctic sea ice mass balance in a new coupled ice–ocean model using a brittle rheology framework
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Snow cover prediction in the Italian central Apennines using weather forecast and land surface numerical models
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Geothermal heat flux is the dominant source of uncertainty in englacial-temperature-based dating of ice rise formation
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Simulating the current and future northern limit of permafrost on the Qinghai–Tibet Plateau
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
                        
                            
                            
                                     
                                Improving interpretation of sea-level projections through a machine-learning-based local explanation approach
                                
                                        
                                            
                                    
                            
                            
                        
                    
                    
            
        
        Antonio Juarez-Martinez, Javier Blasco, Alexander Robinson, Marisa Montoya, and Jorge Alvarez-Solas
                                    The Cryosphere, 18, 4257–4283, https://doi.org/10.5194/tc-18-4257-2024, https://doi.org/10.5194/tc-18-4257-2024, 2024
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                                                We present sea level projections for Antarctica in the context of ISMIP6-2300 with several forcings but extend the simulations to 2500, showing that more than 3 m of sea level contribution could be reached. We also test the sensitivity on a basal melting parameter and determine the timing of the loss of ice in the west region. All the simulations were carried out with the ice sheet model Yelmo.
                                            
                                            
                                        Daniel Moreno-Parada, Alexander Robinson, Marisa Montoya, and Jorge Alvarez-Solas
                                    The Cryosphere, 18, 4215–4232, https://doi.org/10.5194/tc-18-4215-2024, https://doi.org/10.5194/tc-18-4215-2024, 2024
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                                                Our study tries to understand how the ice temperature evolves in a large mass as in the case of Antarctica. We found a relation that tells us the ice temperature at any point. These results are important because they also determine how the ice moves. In general, ice moves due to slow deformation (as if pouring honey from a jar). Nevertheless, in some regions the ice base warms enough and melts. The liquid water then serves as lubricant and the ice slides and its velocity increases rapidly.
                                            
                                            
                                        Tim Hageman, Jessica Mejía, Ravindra Duddu, and Emilio Martínez-Pañeda
                                    The Cryosphere, 18, 3991–4009, https://doi.org/10.5194/tc-18-3991-2024, https://doi.org/10.5194/tc-18-3991-2024, 2024
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                                                Due to surface melting, meltwater lakes seasonally form on the surface of glaciers. These lakes drive hydrofractures that rapidly transfer water to the base of ice sheets. This paper presents a computational method to capture the complicated hydrofracturing process. Our work reveals that viscous ice rheology has a great influence on the short-term propagation of fractures, enabling fast lake drainage, whereas thermal effects (frictional heating, conduction, and freezing) have little influence.
                                            
                                            
                                        Clémence Herny, Pascal Hagenmuller, Guillaume Chambon, Isabel Peinke, and Jacques Roulle
                                    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.
                                            
                                            
                                        Louis Quéno, Rebecca Mott, Paul Morin, Bertrand Cluzet, Giulia Mazzotti, and Tobias Jonas
                                    The Cryosphere, 18, 3533–3557, https://doi.org/10.5194/tc-18-3533-2024, https://doi.org/10.5194/tc-18-3533-2024, 2024
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                                                Snow redistribution by wind and avalanches strongly influences snow hydrology in mountains. This study presents a novel modelling approach to best represent these processes in an operational context. The evaluation of the simulations against airborne snow depth measurements showed remarkable improvement in the snow distribution in mountains of the eastern Swiss Alps, with a representation of snow accumulation and erosion areas, suggesting promising benefits for operational snow melt forecasts.
                                            
                                            
                                        André Löfgren, Thomas Zwinger, Peter Råback, Christian Helanow, and Josefin Ahlkrona
                                    The Cryosphere, 18, 3453–3470, https://doi.org/10.5194/tc-18-3453-2024, https://doi.org/10.5194/tc-18-3453-2024, 2024
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                                                This paper investigates a stabilization method for free-surface flows in the context of glacier simulations. Previous applications of the stabilization on ice flows have only considered simple ice-sheet benchmark problems; in particular the method had not been tested on real-world glacier domains. This work addresses this shortcoming by demonstrating that the stabilization works well also in this case and increases stability and robustness without negatively impacting computation times.
                                            
                                            
                                        Ange Haddjeri, Matthieu Baron, Matthieu Lafaysse, Louis Le Toumelin, César Deschamps-Berger, Vincent Vionnet, Simon Gascoin, Matthieu Vernay, and Marie Dumont
                                    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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                                                Our study addresses the complex challenge of evaluating distributed alpine snow simulations with snow transport against snow depths from Pléiades stereo imagery and snow melt-out dates from Sentinel-2 and Landsat-8 satellites. Additionally, we disentangle error contributions between blowing snow, precipitation heterogeneity, and unresolved subgrid variability. Snow transport enhances the snow simulations at high elevations, while precipitation biases are the main error source in other areas.
                                            
                                            
                                        Christopher Riedel and Jeffrey Anderson
                                    The Cryosphere, 18, 2875–2896, https://doi.org/10.5194/tc-18-2875-2024, https://doi.org/10.5194/tc-18-2875-2024, 2024
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                                                Accurate sea ice conditions are crucial for quality sea ice projections, which have been connected to rapid warming over the Arctic. Knowing which observations to assimilate into models will help produce more accurate sea ice conditions. We found that not assimilating sea ice concentration led to more accurate sea ice states. The methods typically used to assimilate observations in our models apply assumptions to variables that are not well suited for sea ice because they are bounded variables.
                                            
                                            
                                        Julia Selivanova, Doroteaciro Iovino, and Francesco Cocetta
                                    The Cryosphere, 18, 2739–2763, https://doi.org/10.5194/tc-18-2739-2024, https://doi.org/10.5194/tc-18-2739-2024, 2024
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                                                Climate models show differences in sea ice representation in comparison to observations. Increasing the model resolution is a recognized way to improve model realism and obtain more reliable future projections. We find no strong impact of resolution on sea ice representation; it rather depends on the analysed variable and the model used. By 2050, the marginal ice zone (MIZ) becomes a dominant feature of the Arctic ice cover, suggesting a shift to a new regime similar to that in Antarctica.
                                            
                                            
                                        Alexander A. Robel, Vincent Verjans, and Aminat A. Ambelorun
                                    The Cryosphere, 18, 2613–2623, https://doi.org/10.5194/tc-18-2613-2024, https://doi.org/10.5194/tc-18-2613-2024, 2024
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                                                The average size of many glaciers and ice sheets changes when noise is added to the system. The reasons for this drift in glacier state is intrinsic to the dynamics of how ice flows and the bumpiness of the Earth's surface. We argue that not including noise in projections of ice sheet evolution over coming decades and centuries is a pervasive source of bias in these computer models, and so realistic variability in glacier and climate processes must be included in models.
                                            
                                            
                                        Matt Trevers, Antony J. Payne, and Stephen L. Cornford
                                        EGUsphere, https://doi.org/10.5194/egusphere-2024-1040, https://doi.org/10.5194/egusphere-2024-1040, 2024
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                                                The form of the friction law which determines the speed of ice sliding over the bedrock remains a major source of uncertainty in ice sheet model projections of future sea level rise. Jakobshavn Isbræ, the fastest flowing glacier in Greenland which has undergone significant changes in the last few decades, is an ideal case for testing sliding laws. We find that a regularised Coulomb friction law reproduces the large seasonal and interannual flow speed variations most accurately.
                                            
                                            
                                        José M. Muñoz-Hermosilla, Jaime Otero, Eva De Andrés, Kaian Shahateet, Francisco Navarro, and Iván Pérez-Doña
                                    The Cryosphere, 18, 1911–1924, https://doi.org/10.5194/tc-18-1911-2024, https://doi.org/10.5194/tc-18-1911-2024, 2024
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                                                A large fraction of the mass loss from marine-terminating glaciers is attributed to frontal ablation. In this study, we used a 3D ice flow model of a real glacier that includes the effects of calving and submarine melting. Over a 30-month simulation, we found that the model reproduced the seasonal cycle for this glacier. Besides, the front positions were in good agreement with observations in the central part of the front, with longitudinal differences, on average, below 15 m.
                                            
                                            
                                        Yu Wang, Chen Zhao, Rupert Gladstone, Thomas Zwinger, Ben Galton-Fenzi, and Poul Christoffersen
                                        EGUsphere, https://doi.org/10.5194/egusphere-2024-1005, https://doi.org/10.5194/egusphere-2024-1005, 2024
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                                                Our research delves into the future ice loss in Antarctica’s Wilkes Subglacial Basin (WSB) and its impact on sea level rise, focusing on how basal melt is implemented at the grounding line in ice flow models. According to our best model results, under high-emission scenarios, the WSB ice sheet could undergo massive and rapid retreat between 2200 and 2300, potentially raising global sea levels by up to 0.34 m by 2500.
                                            
                                            
                                        Alexander H. Jarosch, Paul Hofer, and Christoph Spötl
                                        EGUsphere, https://doi.org/10.5194/egusphere-2024-751, https://doi.org/10.5194/egusphere-2024-751, 2024
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                                                Mechanical damage to stalagmites is commonly observed in mid-latitude caves. In this study we investigate ice flow along the cave bed as a possible mechanism for stalagmite damage. Utilizing models which simulate forces created by ice flow we study the structural integrity of different stalagmite geometries. Our results suggest that structural failure of stalagmites caused by ice flow is possible, albeit unlikely.
                                            
                                            
                                        Charlotte Durand, Tobias Sebastian Finn, Alban Farchi, Marc Bocquet, Guillaume Boutin, and Einar Ólason
                                    The Cryosphere, 18, 1791–1815, https://doi.org/10.5194/tc-18-1791-2024, https://doi.org/10.5194/tc-18-1791-2024, 2024
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                                                This paper focuses on predicting Arctic-wide sea-ice thickness using surrogate modeling with deep learning. The model has a predictive power of 12 h up to 6 months. For this forecast horizon, persistence and daily climatology are systematically outperformed, a result of learned thermodynamics and advection. Consequently, surrogate modeling with deep learning proves to be effective at capturing the complex behavior of sea ice.
                                            
                                            
                                        Mathieu Plante, Jean-François Lemieux, L. Bruno Tremblay, Adrienne Tivy, Joey Angnatok, François Roy, Gregory Smith, Frédéric Dupont, and Adrian K. Turner
                                    The Cryosphere, 18, 1685–1708, https://doi.org/10.5194/tc-18-1685-2024, https://doi.org/10.5194/tc-18-1685-2024, 2024
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                                                We use a sea ice model to reproduce ice growth observations from two buoys deployed on coastal sea ice and analyze the improvements brought by new physics that represent the presence of saline liquid water in the ice interior. We find that the new physics with default parameters degrade the model performance, with overly rapid ice growth and overly early snow flooding on top of the ice. The performance is largely improved by simple modifications to the ice growth and snow-flooding algorithms.
                                            
                                            
                                        Joshua Cuzzone, Matias Romero, and Shaun A. Marcott
                                    The Cryosphere, 18, 1381–1398, https://doi.org/10.5194/tc-18-1381-2024, https://doi.org/10.5194/tc-18-1381-2024, 2024
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                                                We simulate the retreat history of the Patagonian Ice Sheet (PIS) across the Chilean Lake District from 22–10 ka. These results improve our understanding of the response of the PIS to deglacial warming and the patterns of deglacial ice margin retreat where gaps in the geologic record still exist, and they indicate that changes in large-scale precipitation during the last deglaciation played an important role in modulating the response of ice margin change across the PIS to deglacial warming.
                                            
                                            
                                        Chao-Yuan Yang, Jiping Liu, and Dake Chen
                                    The Cryosphere, 18, 1215–1239, https://doi.org/10.5194/tc-18-1215-2024, https://doi.org/10.5194/tc-18-1215-2024, 2024
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                                                We present a new atmosphere–ocean–wave–sea ice coupled model to study the influences of ocean waves on Arctic sea ice simulation. Our results show (1) smaller ice-floe size with wave breaking increases ice melt, (2) the responses in the atmosphere and ocean to smaller floe size partially reduce the effect of the enhanced ice melt, (3) the limited oceanic energy is a strong constraint for ice melt enhancement, and (4) ocean waves can indirectly affect sea ice through the atmosphere and the ocean.
                                            
                                            
                                        Yurii Batrak, Bin Cheng, and Viivi Kallio-Myers
                                    The Cryosphere, 18, 1157–1183, https://doi.org/10.5194/tc-18-1157-2024, https://doi.org/10.5194/tc-18-1157-2024, 2024
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                                                Atmospheric reanalyses provide consistent series of atmospheric and surface parameters in a convenient gridded form. In this paper, we study the quality of sea ice in a recently released regional reanalysis and assess its added value compared to a global reanalysis. We show that the regional reanalysis, having a more complex sea ice model, gives an improved representation of sea ice, although there are limitations indicating potential benefits in using more advanced approaches in the future.
                                            
                                            
                                        Joseph Fogarty, Elie Bou-Zeid, Mitchell Bushuk, and Linette Boisvert
                                        EGUsphere, https://doi.org/10.5194/egusphere-2024-532, https://doi.org/10.5194/egusphere-2024-532, 2024
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                                                We hypothesize that using a broad set of surface characterization metrics for polar sea ice surfaces will lead to more accurate representations in general circulation models – but the first step is to identify that minimum set of metrics. We show via numerical simulations that sea ice surface patterns can play a crucial role in determining boundary-layer structure, then statistically analyze a set of high-resolution sea ice surface images to obtain said minimal set of parameters.
                                            
                                            
                                        Michael A. Rawlins and Ambarish V. Karmalkar
                                    The Cryosphere, 18, 1033–1052, https://doi.org/10.5194/tc-18-1033-2024, https://doi.org/10.5194/tc-18-1033-2024, 2024
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                                                Flows of water, carbon, and materials by Arctic rivers are being altered by climate warming. We used simulations from a permafrost hydrology model to investigate future changes in quantities influencing river exports. By 2100 Arctic rivers will receive more runoff from the far north where abundant soil carbon can leach in. More water will enter them via subsurface pathways particularly in summer and autumn. An enhanced water cycle and permafrost thaw are changing river flows to coastal areas.
                                            
                                            
                                        Oreste Marquis, Bruno Tremblay, Jean-François Lemieux, and Mohammed Islam
                                    The Cryosphere, 18, 1013–1032, https://doi.org/10.5194/tc-18-1013-2024, https://doi.org/10.5194/tc-18-1013-2024, 2024
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                                                We developed a standard viscous–plastic sea-ice model based on the numerical framework called smoothed particle hydrodynamics. The model conforms to the theory within an error of 1 % in an idealized ridging experiment, and it is able to simulate stable ice arches. However, the method creates a dispersive plastic wave speed. The framework is efficient to simulate fractures and can take full advantage of parallelization, making it a good candidate to investigate sea-ice material properties.
                                            
                                            
                                        Sylvie Charbit, Christophe Dumas, Fabienne Maignan, Catherine Ottlé, Nina Raoult, and Xavier Fettweis
                                        EGUsphere, https://doi.org/10.5194/egusphere-2024-285, https://doi.org/10.5194/egusphere-2024-285, 2024
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                                                The evolution of the Greenland ice sheet is highly dependent on surface melting and therefore on the processes operating at the snow-atmosphere interface and within the snow cover. Here we present new developments to apply a snow model to the Greenland ice sheet. The performance of this model is analysed in terms of its ability to simulate ablation processes. Our analysis shows that the model performs well when compared with the MAR regional polar atmospheric model.
                                            
                                            
                                        Xu Zhou, Binbin Wang, Xiaogang Ma, Zhu La, and Kun Yang
                                        EGUsphere, https://doi.org/10.5194/egusphere-2023-2455, https://doi.org/10.5194/egusphere-2023-2455, 2024
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                                                Simulating the ice phenology of Nam Co by WRF model is investigated. Compared with default model, improving the key model schemes, such as water surface roughness length and the shortwave radiation transfer for lake ice, can better simulate the lake ice phenology. The still existing errors in the spatial patterns of lake ice phenology imply that challenges still exist in modelling key lake and non-lake physics such as grid-scale water circulation, snowfall and snow related processes.
                                            
                                            
                                        Soňa Tomaškovičová and Thomas Ingeman-Nielsen
                                    The Cryosphere, 18, 321–340, https://doi.org/10.5194/tc-18-321-2024, https://doi.org/10.5194/tc-18-321-2024, 2024
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                                                We present the results of a fully coupled modeling framework for simulating the ground thermal regime using only surface measurements to calibrate the thermal model. The heat conduction model is forced by surface ground temperature measurements and calibrated using the field measurements of time lapse apparent electrical resistivity. The resistivity-calibrated thermal model achieves a performance comparable to the traditional calibration of borehole temperature measurements.
                                            
                                            
                                        Yan Huang, Liyun Zhao, Michael Wolovick, Yiliang Ma, and John C. Moore
                                    The Cryosphere, 18, 103–119, https://doi.org/10.5194/tc-18-103-2024, https://doi.org/10.5194/tc-18-103-2024, 2024
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                                                Geothermal heat flux (GHF) is an important factor affecting the basal thermal environment of an ice sheet and crucial for its dynamics. But it is poorly defined for the Antarctic ice sheet. We simulate the basal temperature and basal melting rate with eight different GHF datasets. We use specularity content as a two-sided constraint to discriminate between local wet or dry basal conditions. Two medium-magnitude GHF distribution maps rank well, showing that most of the inland bed area is frozen.
                                            
                                            
                                        Cecile B. Menard, Sirpa Rasmus, Ioanna Merkouriadi, Gianpaolo Balsamo, Annett Bartsch, Chris Derksen, Florent Domine, Marie Dumont, Dorothee Ehrich, Richard Essery, Bruce C. Forbes, Gerhard Krinner, David Lawrence, Glen Liston, Heidrun Matthes, Nick Rutter, Melody Sandells, Martin Schneebeli, and Sari Stark
                                        EGUsphere, https://doi.org/10.5194/egusphere-2023-2926, https://doi.org/10.5194/egusphere-2023-2926, 2024
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                                                Computer models, like those used in climate change studies, are written by modelers who have to decide how best to construct the models in order to satisfy the purpose they serve. Using snow modeling as an example, we examine the process behind the decisions to understand what motivates or limits modelers in their decision-making. We found that the context in which research is undertaken is often more crucial than scientific limitations. We argue for more transparency into our research practice.
                                            
                                            
                                        Amir Sedaghatkish, Frédéric Doumenc, Pierre-Yves Jeannin, and Marc Luetscher
                                        EGUsphere, https://doi.org/10.5194/egusphere-2023-2349, https://doi.org/10.5194/egusphere-2023-2349, 2024
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                                                We developed a model to simulate the natural convection of water within frozen rock crevices subject to daily warming in mountain permafrost regions. Traditional models relying on conduction and latent heat flux typically overlook the free convection. The results reveal that free convection can significantly accelerate the melting rate by an order of magnitude higher than conduction-based models. Our results are important for assessing the impact of climate change on mountain infrastructures.
                                            
                                            
                                        Matthew Drew and Lev Tarasov
                                    The Cryosphere, 17, 5391–5415, https://doi.org/10.5194/tc-17-5391-2023, https://doi.org/10.5194/tc-17-5391-2023, 2023
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                                                The interaction of fast-flowing regions of continental ice sheets with their beds governs how quickly they slide and therefore flow. The coupling of fast ice to its bed is controlled by the pressure of meltwater at its base. It is currently poorly understood how the physical details of these hydrologic systems affect ice speedup. Using numerical models we find, surprisingly, that they largely do not, except for the duration of the surge. This suggests that cheap models are sufficient.
                                            
                                            
                                        Giulia Mazzotti, Jari-Pekka Nousu, Vincent Vionnet, Tobias Jonas, Rafife Nheili, and Matthieu Lafaysse
                                        EGUsphere, https://doi.org/10.5194/egusphere-2023-2781, https://doi.org/10.5194/egusphere-2023-2781, 2023
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                                                As many boreal and alpine forests have seasonal snow, models are needed to predict forest snow under future environmental conditions. We have created a new forest snow model by combining existing, very detailed model components for the canopy and the snowpack. We applied it to forests in Switzerland and Finland and showed how complex forest cover leads to a snowpack layering that is very variable in space and time, because different processes prevail at different locations in the forest.
                                            
                                            
                                        Abhay Prakash, Qin Zhou, Tore Hattermann, and Nina Kirchner
                                    The Cryosphere, 17, 5255–5281, https://doi.org/10.5194/tc-17-5255-2023, https://doi.org/10.5194/tc-17-5255-2023, 2023
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                                                Sea ice arch formation in the Nares Strait has shielded the Petermann Glacier ice shelf from enhanced basal melting. However, with the sustained decline of the Arctic sea ice predicted to continue, the ice shelf is likely to be exposed to a year-round mobile and thin sea ice cover. In such a scenario, our modelled results show that elevated temperatures, and more importantly, a stronger ocean circulation in the ice shelf cavity, could result in up to two-thirds increase in basal melt.
                                            
                                            
                                        Michael Wolovick, Angelika Humbert, Thomas Kleiner, and Martin Rückamp
                                    The Cryosphere, 17, 5027–5060, https://doi.org/10.5194/tc-17-5027-2023, https://doi.org/10.5194/tc-17-5027-2023, 2023
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                                                The friction underneath ice sheets can be inferred from observed velocity at the top, but this inference requires smoothing. The selection of smoothing has been highly variable in the literature. Here we show how to rigorously select the best smoothing, and we show that the inferred friction converges towards the best knowable field as model resolution improves. We use this to learn about the best description of basal friction and to formulate recommended best practices for other modelers.
                                            
                                            
                                        Oliver G. Pollard, Natasha L. M. Barlow, Lauren J. Gregoire, Natalya Gomez, Víctor Cartelle, Jeremy C. Ely, and Lachlan C. Astfalck
                                    The Cryosphere, 17, 4751–4777, https://doi.org/10.5194/tc-17-4751-2023, https://doi.org/10.5194/tc-17-4751-2023, 2023
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                                                We use advanced statistical techniques and a simple ice-sheet model to produce an ensemble of plausible 3D shapes of the ice sheet that once stretched across northern Europe during the previous glacial maximum (140,000 years ago). This new reconstruction, equivalent in volume to 48 ± 8 m of global mean sea-level rise, will improve the interpretation of high sea levels recorded from the Last Interglacial period (120 000 years ago) that provide a useful perspective on the future.
                                            
                                            
                                        Juditha Aga, Julia Boike, Moritz Langer, Thomas Ingeman-Nielsen, and Sebastian Westermann
                                    The Cryosphere, 17, 4179–4206, https://doi.org/10.5194/tc-17-4179-2023, https://doi.org/10.5194/tc-17-4179-2023, 2023
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                                                This study presents a new model scheme for simulating ice segregation and thaw consolidation in permafrost environments, depending on ground properties and climatic forcing. It is embedded in the CryoGrid community model, a land surface model for the terrestrial cryosphere. We describe the model physics and functionalities, followed by a model validation and a sensitivity study of controlling factors.
                                            
                                            
                                        Thomas Frank, Ward J. J. van Pelt, and Jack Kohler
                                    The Cryosphere, 17, 4021–4045, https://doi.org/10.5194/tc-17-4021-2023, https://doi.org/10.5194/tc-17-4021-2023, 2023
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                                                Since the ice thickness of most glaciers worldwide is unknown, and since it is not feasible to visit every glacier and observe their thickness directly, inverse modelling techniques are needed that can calculate ice thickness from abundant surface observations. Here, we present a new method for doing that. Our methodology relies on modelling the rate of surface elevation change for a given glacier, compare this with observations of the same quantity and change the bed until the two are in line.
                                            
                                            
                                        Ronja Reese, Julius Garbe, Emily A. Hill, Benoît Urruty, Kaitlin A. Naughten, Olivier Gagliardini, Gaël Durand, Fabien Gillet-Chaulet, G. Hilmar Gudmundsson, David Chandler, Petra M. Langebroek, and Ricarda Winkelmann
                                    The Cryosphere, 17, 3761–3783, https://doi.org/10.5194/tc-17-3761-2023, https://doi.org/10.5194/tc-17-3761-2023, 2023
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                                                We use an ice sheet model to test where current climate conditions in Antarctica might lead. We find that present-day ocean and atmosphere conditions might commit an irreversible collapse of parts of West Antarctica which evolves over centuries to millennia. Importantly, this collapse is not irreversible yet.
                                            
                                            
                                        Emily A. Hill, Benoît Urruty, Ronja Reese, Julius Garbe, Olivier Gagliardini, Gaël Durand, Fabien Gillet-Chaulet, G. Hilmar Gudmundsson, Ricarda Winkelmann, Mondher Chekki, David Chandler, and Petra M. Langebroek
                                    The Cryosphere, 17, 3739–3759, https://doi.org/10.5194/tc-17-3739-2023, https://doi.org/10.5194/tc-17-3739-2023, 2023
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                                                The grounding lines of the Antarctic Ice Sheet could enter phases of irreversible retreat or advance. We use three ice sheet models to show that the present-day locations of Antarctic grounding lines are reversible with respect to a small perturbation away from their current position. This indicates that present-day retreat of the grounding lines is not yet irreversible or self-enhancing.
                                            
                                            
                                        Huy Dinh, Dimitrios Giannakis, Joanna Slawinska, and Georg Stadler
                                    The Cryosphere, 17, 3883–3893, https://doi.org/10.5194/tc-17-3883-2023, https://doi.org/10.5194/tc-17-3883-2023, 2023
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                                                We develop a numerical method to simulate the fracture in kilometer-sized chunks of floating ice in the ocean. Our approach uses a mathematical model that balances deformation energy against the energy required for fracture. We study the strength of ice chunks that contain random impurities due to prior damage or refreezing and what types of fractures are likely to occur. Our model shows that crack direction critically depends on the orientation of impurities relative to surrounding forces.
                                            
                                            
                                        René R. Wijngaard, Adam R. Herrington, William H. Lipscomb, Gunter R. Leguy, and Soon-Il An
                                    The Cryosphere, 17, 3803–3828, https://doi.org/10.5194/tc-17-3803-2023, https://doi.org/10.5194/tc-17-3803-2023, 2023
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                                                We evaluate the ability of the Community Earth System Model (CESM2) to simulate cryospheric–hydrological variables, such as glacier surface mass balance (SMB), over High Mountain Asia (HMA) by using a global grid (~111 km) with regional refinement (~7 km) over HMA. Evaluations of two different simulations show that climatological biases are reduced, and glacier SMB is improved (but still too negative) by modifying the snow and glacier model and using an updated glacier cover dataset.
                                            
                                            
                                        Brian Groenke, Moritz Langer, Jan Nitzbon, Sebastian Westermann, Guillermo Gallego, and Julia Boike
                                    The Cryosphere, 17, 3505–3533, https://doi.org/10.5194/tc-17-3505-2023, https://doi.org/10.5194/tc-17-3505-2023, 2023
                                    Short summary
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                                                It is now well known from long-term temperature measurements that Arctic permafrost, i.e., ground that remains continuously frozen for at least 2 years, is warming in response to climate change. Temperature, however, only tells half of the story. In this study, we use computer modeling to better understand how the thawing and freezing of water in the ground affects the way permafrost responds to climate change and what temperature trends can and cannot tell us about how permafrost is changing.
                                            
                                            
                                        Yukihiko Onuma, Koji Fujita, Nozomu Takeuchi, Masashi Niwano, and Teruo Aoki
                                    The Cryosphere, 17, 3309–3328, https://doi.org/10.5194/tc-17-3309-2023, https://doi.org/10.5194/tc-17-3309-2023, 2023
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                                                We established a novel model that simulates the temporal changes in cryoconite hole (CH) depth using heat budgets calculated independently at the ice surface and CH bottom based on hole shape geometry. The simulations suggest that CH depth is governed by the balance between the intensity of the diffuse component of downward shortwave radiation and the wind speed. The meteorological conditions may be important factors contributing to the recent ice surface darkening via the redistribution of CHs.
                                            
                                            
                                        Max Thomas, Briana Cate, Jack Garnett, Inga J. Smith, Martin Vancoppenolle, and Crispin Halsall
                                    The Cryosphere, 17, 3193–3201, https://doi.org/10.5194/tc-17-3193-2023, https://doi.org/10.5194/tc-17-3193-2023, 2023
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                                                A recent study showed that pollutants can be enriched in growing sea ice beyond what we would expect from a perfectly dissolved chemical. We hypothesise that this effect is caused by the specific properties of the pollutants working in combination with fluid moving through the sea ice. To test our hypothesis, we replicate this behaviour in a sea-ice model and show that this type of modelling can be applied to predicting the transport of chemicals with complex behaviour in sea ice.
                                            
                                            
                                        Tobias Sebastian Finn, Charlotte Durand, Alban Farchi, Marc Bocquet, Yumeng Chen, Alberto Carrassi, and Véronique Dansereau
                                    The Cryosphere, 17, 2965–2991, https://doi.org/10.5194/tc-17-2965-2023, https://doi.org/10.5194/tc-17-2965-2023, 2023
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                                                We combine deep learning with a regional sea-ice model to correct model errors in the sea-ice dynamics of low-resolution forecasts towards high-resolution simulations. The combined model improves the forecast by up to 75 % and thereby surpasses the performance of persistence. As the error connection can additionally be used to analyse the shortcomings of the forecasts, this study highlights the potential of combined modelling for short-term sea-ice forecasting.
                                            
                                            
                                        Philipp de Vrese, Goran Georgievski, Jesus Fidel Gonzalez Rouco, Dirk Notz, Tobias Stacke, Norman Julius Steinert, Stiig Wilkenskjeld, and Victor Brovkin
                                    The Cryosphere, 17, 2095–2118, https://doi.org/10.5194/tc-17-2095-2023, https://doi.org/10.5194/tc-17-2095-2023, 2023
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                                                The current generation of Earth system models exhibits large inter-model differences in the simulated climate of the Arctic and subarctic zone. We used an adapted version of the Max Planck Institute (MPI) Earth System Model to show that differences in the representation of the soil hydrology in permafrost-affected regions could help explain a large part of this inter-model spread and have pronounced impacts on important elements of Earth systems as far to the south as the tropics.
                                            
                                            
                                        Xia Lin, François Massonnet, Thierry Fichefet, and Martin Vancoppenolle
                                    The Cryosphere, 17, 1935–1965, https://doi.org/10.5194/tc-17-1935-2023, https://doi.org/10.5194/tc-17-1935-2023, 2023
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                                                This study provides clues on how improved atmospheric reanalysis products influence sea ice simulations in ocean–sea ice models. The summer ice concentration simulation in both hemispheres can be improved with changed surface heat fluxes. The winter Antarctic ice concentration and the Arctic drift speed near the ice edge and the ice velocity direction simulations are improved with changed wind stress. The radiation fluxes and winds in atmospheric reanalyses are crucial for sea ice simulations.
                                            
                                            
                                        Guillaume Boutin, Einar Ólason, Pierre Rampal, Heather Regan, Camille Lique, Claude Talandier, Laurent Brodeau, and Robert Ricker
                                    The Cryosphere, 17, 617–638, https://doi.org/10.5194/tc-17-617-2023, https://doi.org/10.5194/tc-17-617-2023, 2023
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                                                Sea ice cover in the Arctic is full of cracks, which we call leads. We suspect that these leads play a role for atmosphere–ocean interactions in polar regions, but their importance remains challenging to estimate. We use a new ocean–sea ice model with an original way of representing sea ice dynamics to estimate their impact on winter sea ice production. This model successfully represents sea ice evolution from 2000 to 2018, and we find that about 30 % of ice production takes place in leads.
                                            
                                            
                                        Edoardo Raparelli, Paolo Tuccella, Valentina Colaiuda, and Frank S. Marzano
                                    The Cryosphere, 17, 519–538, https://doi.org/10.5194/tc-17-519-2023, https://doi.org/10.5194/tc-17-519-2023, 2023
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                                                We evaluate the skills of a single-layer (Noah) and a multi-layer (Alpine3D) snow model, forced with the Weather Research and Forecasting model, to reproduce snowpack properties observed in the Italian central Apennines. We found that Alpine3D reproduces the observed snow height and snow water equivalent better than Noah, while no particular model differences emerge on snow cover extent. Finally, we observed that snow settlement is mainly due to densification in Alpine3D and to melting in Noah.
                                            
                                            
                                        Aleksandr Montelli and Jonathan Kingslake
                                    The Cryosphere, 17, 195–210, https://doi.org/10.5194/tc-17-195-2023, https://doi.org/10.5194/tc-17-195-2023, 2023
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                                                Thermal modelling and Bayesian inversion techniques are used to evaluate the uncertainties inherent in inferences of ice-sheet evolution from borehole temperature measurements. We show that the same temperature profiles may result from a range of parameters, of which geothermal heat flux through underlying bedrock plays a key role. Careful model parameterisation and evaluation of heat flux are essential for inferring past ice-sheet evolution from englacial borehole thermometry.
                                            
                                            
                                        Jianting Zhao, Lin Zhao, Zhe Sun, Fujun Niu, Guojie Hu, Defu Zou, Guangyue Liu, Erji Du, Chong Wang, Lingxiao Wang, Yongping Qiao, Jianzong Shi, Yuxin Zhang, Junqiang Gao, Yuanwei Wang, Yan Li, Wenjun Yu, Huayun Zhou, Zanpin Xing, Minxuan Xiao, Luhui Yin, and Shengfeng Wang
                                    The Cryosphere, 16, 4823–4846, https://doi.org/10.5194/tc-16-4823-2022, https://doi.org/10.5194/tc-16-4823-2022, 2022
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                                                Permafrost has been warming and thawing globally; this is especially true in boundary regions. We focus on the changes and variability in permafrost distribution and thermal dynamics in the northern limit of permafrost on the Qinghai–Tibet Plateau (QTP) by applying a new permafrost model. Unlike previous papers on this topic, our findings highlight a slow, decaying process in the response of permafrost in the QTP to a warming climate, especially regarding areal extent.
                                            
                                            
                                        Jeremy Rohmer, Remi Thieblemont, Goneri Le Cozannet, Heiko Goelzer, and Gael Durand
                                    The Cryosphere, 16, 4637–4657, https://doi.org/10.5194/tc-16-4637-2022, https://doi.org/10.5194/tc-16-4637-2022, 2022
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                                                To improve the interpretability of process-based projections of the sea-level contribution from land ice components, we apply the machine-learning-based 
                                            
                                        SHapley Additive exPlanationsapproach to a subset of a multi-model ensemble study for the Greenland ice sheet. This allows us to quantify the influence of particular modelling decisions (related to numerical implementation, initial conditions, or parametrisation of ice-sheet processes) directly in terms of sea-level change contribution.
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                        Eisen, O., Wilhelms, F., Nixdorf, U., and Miller, H.: Identifying isochrones in GPR profiles from DEP-based forward modelling, Ann. Glaciol., 37, 344–350, 2003.
                    
                
                        
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                        Hagen, J. O., Melvold, K., Pinglot, F., and Dowdeswell, J. A.: On the net balance of the glaciers and ice caps in Svalbard, Norwegian Arctic, Arct. Antarct. Alp. Res., 35(2), 264–270, 2003.
                    
                
                        
                        Hubbard, A. W., Lawson, W., Anderson, B., Hubbard, B., and Blatter, H.: Evidence for subglacial ponding across Taylor Glacier, Dry Valleys, Antarctica, Ann. Glaciol., 39, 79–84, 2005.
                    
                
                        
                        Kohler, J., Nordli, Ø., Brandt, O., Isaksson, E., Pohjola, V., Martma, T., and Aas, H. F.: Svalbard temperature and precipitation, late 19th century to the present. Final report on ACIA-funded project, Norwegian Polar Institute, Oslo, Norway, 2002.
                    
                
                        
                        Kohler, J., James, T. D., Murray, T., Nuth, C., Brandt, O., Barrand, N. E., Aas, H. F., and Luckman, A.: Acceleration in thinning rate on western Svalbard glaciers, Geophys. Res. Lett., 34, L18502, https://doi.org/10.1029/2007GL030681, 2007.
                    
                
                        
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                        Pälli, A., Kohler, J., Isaksson, E., Moore, J. C, Pinglot, J.-F., Pohjola, V., and Samuelsson, H.: Spatial and temporal variability of snow accumulation using ground-penetrating radar and ice cores on a Svalbard glacier, J. Glaciol., 48(162), 417–424, 2003.
                    
                
                        
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                        Rippin, D., Willis, I., Arnold, N., Hodson, A., Moore, J., Kohler, J., and Björnsson, H.: Changes in geomety and subglacial drainage of Midre Lovénbreen, Svalbard, determined from digital elevation models, Earth Surf. Proc. Land., 28(3), 273–298, 2003.
                    
                
                        
                        Sinisalo, A., Grinsted, A., Moore, J. C., Meijer, H., and Martma, T.: Inferences from stable water isotopes on the Holocene evolution of Scharffenbergbotnen blue ice area, East Antarctica, J. Glaciol., 53(182), 427–433, 2007.
                    
                
                        
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                        Wadham, J., Kohler, J., Hubbard, A., Nuttall, A.-M., and Rippin, D.: Superimposed ice regime of a high arctic glacier inferred using GPR, flow modelling, and ice-cores, J. Geophys. Res., 111, F01007, https://doi.org/10.1029/2004JF000144, 2006.
                    
                
                        
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                        Wright, A. P., Wadham, J. L., Siegert, M. J., Luckman, A., Kohler, J., and Nuttall, A. M.: Modeling the refreezing of meltwater as superimposed ice on a high Arctic glacier: A comparison of approaches, J. Geophys. Res., 112, F04016, https://doi.org/10.1029/2007JF000818, 2007.
                    
                
                        
                        Zwinger, T., Greve, R., Gagliardini, O., Shiraiwa, T., and Lyly, M.: A full Stokes-flow thermo-mechanical model for firn and ice applied to the Gorshkov crater glacier, Kamchatka, Ann. Glaciol., 45, 29–37, 2007.
                    
                 
 
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
                        
                                         
             
             
             
            