Articles | Volume 4, issue 4
Geosci. Model Dev., 4, 1133–1149, 2011
https://doi.org/10.5194/gmd-4-1133-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Geosci. Model Dev., 4, 1133–1149, 2011
https://doi.org/10.5194/gmd-4-1133-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Development and technical paper 19 Dec 2011
Development and technical paper | 19 Dec 2011
Improved convergence and stability properties in a three-dimensional higher-order ice sheet model
J. J. Fürst et al.
Related subject area
Cryosphere
Snow profile alignment and similarity assessment for aggregating, clustering, and evaluating snowpack model output for avalanche forecasting
Improvements in one-dimensional grounding-line parameterizations in an ice-sheet model with lateral variations (PSUICE3D v2.1)
Implementation of the RCIP scheme and its performance for 1-D age computations in ice-sheet models
COSIPY v1.3 – an open-source coupled snowpack and ice surface energy and mass balance model
Using Arctic ice mass balance buoys for evaluation of modelled ice energy fluxes
Impact of the ice thickness distribution discretization on the sea ice concentration variability in the NEMO3.6–LIM3 global ocean–sea ice model
Simulating the Early Holocene demise of the Laurentide Ice Sheet with BISICLES (public trunk revision 3298)
Extended enthalpy formulations in the Ice-sheet and Sea-level System Model (ISSM) version 4.17: discontinuous conductivity and anisotropic streamline upwind Petrov–Galerkin (SUPG) method
The Community Firn Model (CFM) v1.0
A Framework for Ice Sheet – Ocean Coupling (FISOC) V1.1
CrocO_v1.0 : a Particle Filter to assimilate snowpack observations in a spatialised framework
Description and validation of the ice-sheet model Yelmo (version 1.0)
A fully coupled Arctic sea ice-ocean-atmosphere model (ArcIOAM v1.0) based on C-Coupler2: model description and preliminary results
Multi-Scale Sea Ice Kinematics Modeling with a Grid Hierarchy in Community Earth System Model (version 1.2.1)
Evaluating integrated surface/subsurface permafrost thermal hydrology models in ATS (v0.88) against observations from a polygonal tundra site
SICOPOLIS-AD v1: an open-source adjoint modeling framework for ice sheet simulation enabled by the algorithmic differentiation tool OpenAD
On the calculation of normalized viscous–plastic sea ice stresses
Modelling thermomechanical ice deformation using an implicit pseudo-transient method (FastICE v1.0) based on graphical processing units (GPUs)
Version 1 of a sea ice module for the physics-based, detailed, multi-layer SNOWPACK model
A module to convert spectral to narrowband snow albedo for use in climate models: SNOWBAL v1.2
On the discretization of the ice thickness distribution in the NEMO3.6-LIM3 global ocean–sea ice model
Scientific workflows applied to the coupling of a continuum (Elmer v8.3) and a discrete element (HiDEM v1.0) ice dynamic model
A rapidly converging initialisation method to simulate the present-day Greenland ice sheet using the GRISLI ice sheet model (version 1.3)
Assessment of sub-shelf melting parameterisations using the ocean–ice-sheet coupled model NEMO(v3.6)–Elmer/Ice(v8.3)
CSIB v1 (Canadian Sea-ice Biogeochemistry): a sea-ice biogeochemical model for the NEMO community ocean modelling framework
LIVVkit 2.1: automated and extensible ice sheet model validation
ATAT 1.1, the Automated Timing Accordance Tool for comparing ice-sheet model output with geochronological data
The Open Global Glacier Model (OGGM) v1.1
Description and evaluation of the Community Ice Sheet Model (CISM) v2.1
Implementation and performance of adaptive mesh refinement in the Ice Sheet System Model (ISSM v4.14)
A continuum model (PSUMEL1) of ice mélange and its role during retreat of the Antarctic Ice Sheet
ESM-SnowMIP: assessing snow models and quantifying snow-related climate feedbacks
The GRISLI ice sheet model (version 2.0): calibration and validation for multi-millennial changes of the Antarctic ice sheet
CVPM 1.1: a flexible heat-transfer modeling system for permafrost
Dynamically coupling full Stokes and shallow shelf approximation for marine ice sheet flow using Elmer/Ice (v8.3)
The NASA Eulerian Snow on Sea Ice Model (NESOSIM) v1.0: initial model development and analysis
MPAS-Albany Land Ice (MALI): a variable-resolution ice sheet model for Earth system modeling using Voronoi grids
BrAHMs V1.0: a fast, physically based subglacial hydrology model for continental-scale application
SHAKTI: Subglacial Hydrology and Kinetic, Transient Interactions v1.0
SMRT: an active–passive microwave radiative transfer model for snow with multiple microstructure and scattering formulations (v1.0)
PIC v1.3: comprehensive R package for computing permafrost indices with daily weather observations and atmospheric forcing over the Qinghai–Tibet Plateau
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
Implementation of higher-order vertical finite elements in ISSM v4.13 for improved ice sheet flow modeling over paleoclimate timescales
Intercomparison of Antarctic ice-shelf, ocean, and sea-ice interactions simulated by MetROMS-iceshelf and FESOM 1.4
The sea ice model component of HadGEM3-GC3.1
A JavaScript API for the Ice Sheet System Model (ISSM) 4.11: towards an online interactive model for the cryosphere community
Implementation of a physically based water percolation routine in the Crocus/SURFEX (V7.3) snowpack model
Evaluating the performance of coupled snow–soil models in SURFEXv8 to simulate the permafrost thermal regime at a high Arctic site
Sea-ice evaluation of NEMO-Nordic 1.0: a NEMO–LIM3.6-based ocean–sea-ice model setup for the North Sea and Baltic Sea
A vertical representation of soil carbon in the JULES land surface scheme (vn4.3_permafrost) with a focus on permafrost regions
Florian Herla, Simon Horton, Patrick Mair, and Pascal Haegeli
Geosci. Model Dev., 14, 239–258, https://doi.org/10.5194/gmd-14-239-2021, https://doi.org/10.5194/gmd-14-239-2021, 2021
Short summary
Short summary
The adoption of snowpack models in support of avalanche forecasting has been limited. To promote their operational application, we present a numerical method for processing multivariate snow stratigraphy profiles of mixed data types. Our algorithm enables applications like dynamical grouping and summarizing of model simulations, model evaluation, and data assimilation. By emulating the human analysis process, our approach will allow forecasters to familiarly interact with snowpack simulations.
David Pollard and Robert M. DeConto
Geosci. Model Dev., 13, 6481–6500, https://doi.org/10.5194/gmd-13-6481-2020, https://doi.org/10.5194/gmd-13-6481-2020, 2020
Short summary
Short summary
Buttressing by floating ice shelves at ice-sheet grounding lines is an
important process that affects ice retreat and whether structural failure
occurs in deep bathymetry. Here, we use a simple algorithm to better
represent 2-D grounding-line curvature in an ice-sheet model. Along with other
enhancements, this improves the performance in idealized-fjord intercomparisons
and enables better diagnosis of potential structural failure at future
retreating Antarctic grounding lines.
Fuyuki Saito, Takashi Obase, and Ayako Abe-Ouchi
Geosci. Model Dev., 13, 5875–5896, https://doi.org/10.5194/gmd-13-5875-2020, https://doi.org/10.5194/gmd-13-5875-2020, 2020
Short summary
Short summary
The present study introduces the rational function-based constrained interpolation profile (RCIP) method for use in 1 d dating computations in ice sheets and demonstrates the performance of the scheme. Comparisons are examined among the RCIP schemes and the first- and second-order upwind schemes. The results show that, in particular, the RCIP scheme preserves the pattern of input histories, in terms of the profile of internal annual layer thickness, better than the other schemes.
Tobias Sauter, Anselm Arndt, and Christoph Schneider
Geosci. Model Dev., 13, 5645–5662, https://doi.org/10.5194/gmd-13-5645-2020, https://doi.org/10.5194/gmd-13-5645-2020, 2020
Short summary
Short summary
Glacial changes play a key role from a socioeconomic, political, and scientific point of view. Here, we present the open-source coupled snowpack and ice surface energy and mass balance model, which provides a lean, flexible, and user-friendly framework for modeling distributed snow and glacier mass changes. The model provides a suitable platform for sensitivity, detection, and attribution analyses for glacier changes and a tool for quantifying inherent uncertainties.
Alex West, Mat Collins, and Ed Blockley
Geosci. Model Dev., 13, 4845–4868, https://doi.org/10.5194/gmd-13-4845-2020, https://doi.org/10.5194/gmd-13-4845-2020, 2020
Short summary
Short summary
This study calculates sea ice energy fluxes from data produced by ice mass balance buoys (devices measuring ice elevation and temperature). It is shown how the resulting dataset can be used to evaluate a coupled climate model (HadGEM2-ES), with biases in the energy fluxes seen to be consistent with biases in the sea ice state and surface radiation. This method has potential to improve sea ice model evaluation, so as to better understand spread in model simulations of sea ice state.
Eduardo Moreno-Chamarro, Pablo Ortega, and François Massonnet
Geosci. Model Dev., 13, 4773–4787, https://doi.org/10.5194/gmd-13-4773-2020, https://doi.org/10.5194/gmd-13-4773-2020, 2020
Short summary
Short summary
Climate models need to capture sea ice complexity to represent it realistically. Here we assess how distributing sea ice in discrete thickness categories impacts how sea ice variability is simulated in the NEMO3.6–LIM3 model. Simulations and satellite observations are compared by using k-means clustering of sea ice concentration in winter and summer between 1979 and 2014 at both poles. Little improvements in the modeled sea ice lead us to recommend using the standard number of five categories.
Ilkka S. O. Matero, Lauren J. Gregoire, and Ruza F. Ivanovic
Geosci. Model Dev., 13, 4555–4577, https://doi.org/10.5194/gmd-13-4555-2020, https://doi.org/10.5194/gmd-13-4555-2020, 2020
Short summary
Short summary
The Northern Hemisphere cooled by several degrees for a century 8000 years ago due to the collapse of an ice sheet in North America that released large amounts of meltwater into the North Atlantic and slowed down its circulation. We numerically model the ice sheet to understand its evolution during this event. Our results match data thanks to good ice dynamics but depend mostly on surface melt and snowfall. Further work will help us understand how past and future ice melt affects climate.
Martin Rückamp, Angelika Humbert, Thomas Kleiner, Mathieu Morlighem, and Helene Seroussi
Geosci. Model Dev., 13, 4491–4501, https://doi.org/10.5194/gmd-13-4491-2020, https://doi.org/10.5194/gmd-13-4491-2020, 2020
Short summary
Short summary
We present enthalpy formulations within the Ice-Sheet and Sea-Level System model that show better performance than earlier implementations. A first experiment indicates that the treatment of discontinuous conductivities of the solid–fluid system with a geometric mean produce accurate results when applied to coarse vertical resolutions. In a second experiment, we propose a novel stabilization formulation that avoids the problem of thin elements. This method provides accurate and stable results.
C. Max Stevens, Vincent Verjans, Jessica M. D. Lundin, Emma C. Kahle, Annika N. Horlings, Brita I. Horlings, and Edwin D. Waddington
Geosci. Model Dev., 13, 4355–4377, https://doi.org/10.5194/gmd-13-4355-2020, https://doi.org/10.5194/gmd-13-4355-2020, 2020
Short summary
Short summary
Understanding processes in snow (firn), including compaction and airflow, is important for calculating how much mass the ice sheets are losing and for interpreting climate records from ice cores. We have developed the open-source Community Firn Model to simulate these processes. We used it to compare 13 different firn compaction equations and found that they do not agree within 10 %. We also show that including firn compaction in a firn-air model improves the match with data from ice cores.
Rupert Gladstone, Benjamin Galton-Fenzi, David Gwyther, Qin Zhou, Tore Hattermann, Chen Zhao, Lenneke Jong, Yuwei Xia, Xiaoran Guo, Konstantinos Petrakopoulos, Thomas Zwinger, Daniel Shapero, and John Moore
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-206, https://doi.org/10.5194/gmd-2020-206, 2020
Revised manuscript accepted for GMD
Short summary
Short summary
Retreat of the Antarctic Ice Sheet, and hence its contribution to sea level rise, is highly sensitive to melting of its floating ice shelves. This melt is caused by warm ocean currents coming into contact with the ice. Computer models used for future ice sheet projections are not able to realistically evolve these melt rates. We describe a new coupling framework to enable ice sheet and ocean computer models to interact, allowing projection of the evolution of melt and its impact on sea level.
Bertrand Cluzet, Matthieu Lafaysse, Emmanuel Cosme, Clément Albergel, Louis-François Meunier, and Marie Dumont
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-130, https://doi.org/10.5194/gmd-2020-130, 2020
Revised manuscript accepted for GMD
Short summary
Short summary
In mountainous areas, snowpack models suffer from large errors and observations are scarce, a challenge for data assimilation. Here, we develop two variants of the Particle Filter in order to propagate the information content of observations over a complex topography. By adjusting observation errors and exploiting background correlation patterns, these variants demonstrate the potential for partial observations of snow depth and surface reflectance to improve model accuracy in a whole domain.
Alexander Robinson, Jorge Alvarez-Solas, Marisa Montoya, Heiko Goelzer, Ralf Greve, and Catherine Ritz
Geosci. Model Dev., 13, 2805–2823, https://doi.org/10.5194/gmd-13-2805-2020, https://doi.org/10.5194/gmd-13-2805-2020, 2020
Short summary
Short summary
Here we describe Yelmo v1.0, an intuitive and state-of-the-art hybrid ice sheet model. The model design and physics are described, and benchmark simulations are provided to validate its performance. Yelmo is a versatile ice sheet model that can be applied to a wide variety of problems.
Shihe Ren, Xi Liang, Qizhen Sun, Hao Yu, L. Bruno Tremblay, Xiaoping Mai, Fu Zhao, Ming Li, Na Liu, Zhikun Chen, and Yunfei Zhang
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-95, https://doi.org/10.5194/gmd-2020-95, 2020
Preprint under review for GMD
Short summary
Short summary
Sea ice plays a crucial role in global energy and water budge. To get a better simulation of seaice, we coupled seaice model with atmospheric and ocean model to form a fully coupled system. The seaice simulation results of coupled system demonstrated two-way coupled model has better performance in terms of sea ice, especially in summer. This indicates that sea ice-ocean-atmosphere interaction takes a crucial role in controlling Arctic summertime sea ice distribution.
Shiming Xu, Jialiang Ma, Lu Zhou, Yan Zhang, Jiping Liu, and Bin Wang
Geosci. Model Dev. Discuss., https://doi.org/10.5194/gmd-2020-160, https://doi.org/10.5194/gmd-2020-160, 2020
Revised manuscript accepted for GMD
Short summary
Short summary
A multi-resolution tripolar grid hierarchy is constructed and integrated in CESM (version 1.2.1). The resolution range includes 0.45-deg, 0.15-deg, and 0.05-deg. Based on atmospherically forced sea ice experiments, we show that the model simulates reasonable sea ice kinematics and scaling properties. Besides, landfast ice thickness can be systematically shifted due to non-convergent solutions to EVP rheology. This work serve as a framework of multi-scale modeling of ocean and sea ice with CESM.
Ahmad Jan, Ethan T. Coon, and Scott L. Painter
Geosci. Model Dev., 13, 2259–2276, https://doi.org/10.5194/gmd-13-2259-2020, https://doi.org/10.5194/gmd-13-2259-2020, 2020
Short summary
Short summary
Computer simulations are important tools for understanding the response of Arctic permafrost to a warming climate. To build confidence in an emerging class of permafrost simulators, we evaluated the Advanced Terrestrial Simulator against field observations from a frozen tundra site near Utqiaġvik (formerly Barrow), Alaska. The 3-year simulations agree well with observations of snow depth, summer water table, soil temperature at multiple locations, and spatially averaged evaporation.
Liz C. Logan, Sri Hari Krishna Narayanan, Ralf Greve, and Patrick Heimbach
Geosci. Model Dev., 13, 1845–1864, https://doi.org/10.5194/gmd-13-1845-2020, https://doi.org/10.5194/gmd-13-1845-2020, 2020
Short summary
Short summary
A new capability has been developed for the ice sheet model SICOPOLIS (SImulation COde for POLythermal Ice Sheets) that enables the generation of derivative code, such as tangent linear or adjoint models, by means of algorithmic differentiation. It relies on the source transformation algorithmic (AD) differentiation tool OpenAD. The reverse mode of AD provides the adjoint model, SICOPOLIS-AD, which may be applied for comprehensive sensitivity analyses as well as gradient-based optimization.
Jean-François Lemieux and Frédéric Dupont
Geosci. Model Dev., 13, 1763–1769, https://doi.org/10.5194/gmd-13-1763-2020, https://doi.org/10.5194/gmd-13-1763-2020, 2020
Short summary
Short summary
Sea ice dynamics plays an important role in shaping the sea cover in polar regions. Winds and ocean currents exert large stresses on the sea ice cover. This can lead to the formation of long cracks and ridges, which strongly impact the exchange of heat, momentum and moisture between the atmosphere and the ocean. It is therefore crucial for a sea ice model to be able to represent these features. This article describes how internal sea ice stresses should be diagnosed from model simulations.
Ludovic Räss, Aleksandar Licul, Frédéric Herman, Yury Y. Podladchikov, and Jenny Suckale
Geosci. Model Dev., 13, 955–976, https://doi.org/10.5194/gmd-13-955-2020, https://doi.org/10.5194/gmd-13-955-2020, 2020
Short summary
Short summary
Accurate predictions of future sea level rise require numerical models that predict rapidly deforming ice. Localised ice deformation can be captured numerically only with high temporal and spatial resolution. This paper’s goal is to propose a parallel FastICE solver for modelling ice deformation. Our model is particularly useful for improving our process-based understanding of localised ice deformation. Our solver reaches a parallel efficiency of 99 % on GPU-based supercomputers.
Nander Wever, Leonard Rossmann, Nina Maaß, Katherine C. Leonard, Lars Kaleschke, Marcel Nicolaus, and Michael Lehning
Geosci. Model Dev., 13, 99–119, https://doi.org/10.5194/gmd-13-99-2020, https://doi.org/10.5194/gmd-13-99-2020, 2020
Short summary
Short summary
Sea ice is an important component of the global climate system. The presence of a snow layer covering sea ice can impact ice mass and energy budgets. The detailed, physics-based, multi-layer snow model SNOWPACK was modified to simulate the snow–sea-ice system, providing simulations of the snow microstructure, water percolation and flooding, and superimposed ice formation. The model is applied to in situ measurements from snow and ice mass-balance buoys installed in the Antarctic Weddell Sea.
Christiaan T. van Dalum, Willem Jan van de Berg, Quentin Libois, Ghislain Picard, and Michiel R. van den Broeke
Geosci. Model Dev., 12, 5157–5175, https://doi.org/10.5194/gmd-12-5157-2019, https://doi.org/10.5194/gmd-12-5157-2019, 2019
Short summary
Short summary
Climate models are often limited to relatively simple snow albedo schemes. Therefore, we have developed the SNOWBAL module to couple a climate model with a physically based wavelength dependent snow albedo model. Using SNOWBAL v1.2 to couple the snow albedo model TARTES with the regional climate model RACMO2 indicates a potential performance gain for the Greenland ice sheet.
François Massonnet, Antoine Barthélemy, Koffi Worou, Thierry Fichefet, Martin Vancoppenolle, Clément Rousset, and Eduardo Moreno-Chamarro
Geosci. Model Dev., 12, 3745–3758, https://doi.org/10.5194/gmd-12-3745-2019, https://doi.org/10.5194/gmd-12-3745-2019, 2019
Short summary
Short summary
Sea ice thickness varies considerably on spatial scales of several meters. However, contemporary climate models cannot resolve such scales yet. This is why sea ice models used in climate models include an ice thickness distribution (ITD) to account for this unresolved variability. Here, we explore with the ocean–sea ice model NEMO3.6-LIM3 the sensitivity of simulated mean Arctic and Antarctic sea ice states to the way the ITD is discretized.
Shahbaz Memon, Dorothée Vallot, Thomas Zwinger, Jan Åström, Helmut Neukirchen, Morris Riedel, and Matthias Book
Geosci. Model Dev., 12, 3001–3015, https://doi.org/10.5194/gmd-12-3001-2019, https://doi.org/10.5194/gmd-12-3001-2019, 2019
Short summary
Short summary
Scientific workflows enable complex scientific computational scenarios, which include data intensive scenarios, parametric executions, and interactive simulations. In this article, we applied the UNICORE workflow management system to automate a formerly hard-coded coupling of a glacier flow model and a calving model, which contain many tasks and dependencies, ranging from pre-processing and data management to repetitive executions on heterogeneous high-performance computing (HPC) resources.
Sébastien Le clec'h, Aurélien Quiquet, Sylvie Charbit, Christophe Dumas, Masa Kageyama, and Catherine Ritz
Geosci. Model Dev., 12, 2481–2499, https://doi.org/10.5194/gmd-12-2481-2019, https://doi.org/10.5194/gmd-12-2481-2019, 2019
Short summary
Short summary
To provide reliable projections of the ice-sheet contribution to future sea-level rise, ice sheet models must be able to simulate the observed ice sheet present-day state. Using a low computational iterative minimisation procedure, based on the adjustment of the basal drag coefficient, we rapidly minimise the errors between the simulated and the observed Greenland ice thickness and ice velocity, and we succeed in stabilising the simulated Greenland ice sheet state under present-day conditions.
Lionel Favier, Nicolas C. Jourdain, Adrian Jenkins, Nacho Merino, Gaël Durand, Olivier Gagliardini, Fabien Gillet-Chaulet, and Pierre Mathiot
Geosci. Model Dev., 12, 2255–2283, https://doi.org/10.5194/gmd-12-2255-2019, https://doi.org/10.5194/gmd-12-2255-2019, 2019
Short summary
Short summary
The melting at the base of floating ice shelves is the main driver of the Antarctic ice sheet current retreat. Here, we use an ideal set-up to assess a wide range of melting parameterisations depending on oceanic properties with regard to a new ocean–ice-sheet coupled model, published here for the first time. A parameterisation that depends quadratically on thermal forcing in both a local and a non-local way yields the best results and needs to be further assessed with more realistic set-ups.
Hakase Hayashida, James R. Christian, Amber M. Holdsworth, Xianmin Hu, Adam H. Monahan, Eric Mortenson, Paul G. Myers, Olivier G. J. Riche, Tessa Sou, and Nadja S. Steiner
Geosci. Model Dev., 12, 1965–1990, https://doi.org/10.5194/gmd-12-1965-2019, https://doi.org/10.5194/gmd-12-1965-2019, 2019
Short summary
Short summary
Ice algae, the primary producer in sea ice, play a fundamental role in shaping marine ecosystems and biogeochemical cycling of key elements in polar regions. In this study, we developed a process-based numerical model component representing sea-ice biogeochemistry for a sea ice–ocean coupled general circulation model. The model developed can be used to simulate the projected changes in sea-ice ecosystems and biogeochemistry in response to on-going rapid decline of the Arctic.
Katherine J. Evans, Joseph H. Kennedy, Dan Lu, Mary M. Forrester, Stephen Price, Jeremy Fyke, Andrew R. Bennett, Matthew J. Hoffman, Irina Tezaur, Charles S. Zender, and Miren Vizcaíno
Geosci. Model Dev., 12, 1067–1086, https://doi.org/10.5194/gmd-12-1067-2019, https://doi.org/10.5194/gmd-12-1067-2019, 2019
Short summary
Short summary
A robust validation of ice sheet models is presented using LIVVkit, version 2.1. It targets ice sheet and coupled Earth system models, and handles datasets and operations that require high-performance computing and storage. We apply LIVVkit to a Greenland ice sheet simulation to show the degree to which it captures the surface mass balance. LIVVkit identifies a positive bias due to insufficient melting compared to observations that is focused largely around Greenland's southwest region.
Jeremy C. Ely, Chris D. Clark, David Small, and Richard C. A. Hindmarsh
Geosci. Model Dev., 12, 933–953, https://doi.org/10.5194/gmd-12-933-2019, https://doi.org/10.5194/gmd-12-933-2019, 2019
Short summary
Short summary
During the last 2.6 million years, the Earth's climate has cycled between cold glacials and warm interglacials, causing the growth and retreat of ice sheets. These ice sheets can be independently reconstructed using numerical models or from dated evidence that they leave behind (e.g. sediments, boulders). Here, we present a tool for comparing numerical model simulations with dated ice-sheet material. We demonstrate the utility of this tool by applying it to the last British–Irish ice sheet.
Fabien Maussion, Anton Butenko, Nicolas Champollion, Matthias Dusch, Julia Eis, Kévin Fourteau, Philipp Gregor, Alexander H. Jarosch, Johannes Landmann, Felix Oesterle, Beatriz Recinos, Timo Rothenpieler, Anouk Vlug, Christian T. Wild, and Ben Marzeion
Geosci. Model Dev., 12, 909–931, https://doi.org/10.5194/gmd-12-909-2019, https://doi.org/10.5194/gmd-12-909-2019, 2019
Short summary
Short summary
Mountain glaciers are one of the few remaining subsystems of the global climate system for which no globally applicable community-driven model exists. Here we present the Open Global Glacier Model (OGGM; www.oggm.org), developed to provide a modular and open-source numerical model framework for simulating past and future change of any glacier in the world.
William H. Lipscomb, Stephen F. Price, Matthew J. Hoffman, Gunter R. Leguy, Andrew R. Bennett, Sarah L. Bradley, Katherine J. Evans, Jeremy G. Fyke, Joseph H. Kennedy, Mauro Perego, Douglas M. Ranken, William J. Sacks, Andrew G. Salinger, Lauren J. Vargo, and Patrick H. Worley
Geosci. Model Dev., 12, 387–424, https://doi.org/10.5194/gmd-12-387-2019, https://doi.org/10.5194/gmd-12-387-2019, 2019
Short summary
Short summary
This paper describes the Community Ice Sheet Model (CISM) version 2.1. CISM solves equations for ice flow, heat conduction, surface melting, and other processes such as basal sliding and iceberg calving. It can be used for ice-sheet-only simulations or as the ice sheet component of the Community Earth System Model. Model solutions have been verified for standard test problems. CISM can efficiently simulate the whole Greenland ice sheet, with results that are broadly consistent with observations.
Thiago Dias dos Santos, Mathieu Morlighem, Hélène Seroussi, Philippe Remy Bernard Devloo, and Jefferson Cardia Simões
Geosci. Model Dev., 12, 215–232, https://doi.org/10.5194/gmd-12-215-2019, https://doi.org/10.5194/gmd-12-215-2019, 2019
Short summary
Short summary
The reduction of numerical errors in ice sheet modeling increases the results' accuracy reliability. We improve numerical accuracy by better capturing grounding line dynamics, while maintaining a low computational cost. We implement an adaptive mesh refinement (AMR) technique in the Ice Sheet System Model and compare AMR simulations with uniformly refined meshes. Our results show that the computational time with AMR is significantly shorter than for uniformly refined meshes for a given accuracy.
David Pollard, Robert M. DeConto, and Richard B. Alley
Geosci. Model Dev., 11, 5149–5172, https://doi.org/10.5194/gmd-11-5149-2018, https://doi.org/10.5194/gmd-11-5149-2018, 2018
Short summary
Short summary
Around the margins of ice sheets in contact with the ocean, calving of icebergs can generate large amounts of floating ice debris called "mélange". In major Greenland fjords, mélange significantly slows down ice flow from upstream. Our study applies numerical models to past and possible future episodes of rapid Antarctic Ice Sheet retreat. We find that, due to larger spatial scales, Antarctic mélange does not significantly impede flow or slow ice retreat and associated sea level rise.
Gerhard Krinner, Chris Derksen, Richard Essery, Mark Flanner, Stefan Hagemann, Martyn Clark, Alex Hall, Helmut Rott, Claire Brutel-Vuilmet, Hyungjun Kim, Cécile B. Ménard, Lawrence Mudryk, Chad Thackeray, Libo Wang, Gabriele Arduini, Gianpaolo Balsamo, Paul Bartlett, Julia Boike, Aaron Boone, Frédérique Chéruy, Jeanne Colin, Matthias Cuntz, Yongjiu Dai, Bertrand Decharme, Jeff Derry, Agnès Ducharne, Emanuel Dutra, Xing Fang, Charles Fierz, Josephine Ghattas, Yeugeniy Gusev, Vanessa Haverd, Anna Kontu, Matthieu Lafaysse, Rachel Law, Dave Lawrence, Weiping Li, Thomas Marke, Danny Marks, Martin Ménégoz, Olga Nasonova, Tomoko Nitta, Masashi Niwano, John Pomeroy, Mark S. Raleigh, Gerd Schaedler, Vladimir Semenov, Tanya G. Smirnova, Tobias Stacke, Ulrich Strasser, Sean Svenson, Dmitry Turkov, Tao Wang, Nander Wever, Hua Yuan, Wenyan Zhou, and Dan Zhu
Geosci. Model Dev., 11, 5027–5049, https://doi.org/10.5194/gmd-11-5027-2018, https://doi.org/10.5194/gmd-11-5027-2018, 2018
Short summary
Short summary
This paper provides an overview of a coordinated international experiment to determine the strengths and weaknesses in how climate models treat snow. The models will be assessed at point locations using high-quality reference measurements and globally using satellite-derived datasets. How well climate models simulate snow-related processes is important because changing snow cover is an important part of the global climate system and provides an important freshwater resource for human use.
Aurélien Quiquet, Christophe Dumas, Catherine Ritz, Vincent Peyaud, and Didier M. Roche
Geosci. Model Dev., 11, 5003–5025, https://doi.org/10.5194/gmd-11-5003-2018, https://doi.org/10.5194/gmd-11-5003-2018, 2018
Short summary
Short summary
This paper presents the GRISLI (Grenoble ice sheet and land ice) model in its newest revision. We present the recent model improvements from its original version (Ritz et al., 2001), together with a discussion of the model performance in reproducing the present-day Antarctic ice sheet geometry and the grounding line advances and retreats during the last 400 000 years. We show that GRISLI is a computationally cheap model, able to reproduce the large-scale behaviour of ice sheets.
Gary D. Clow
Geosci. Model Dev., 11, 4889–4908, https://doi.org/10.5194/gmd-11-4889-2018, https://doi.org/10.5194/gmd-11-4889-2018, 2018
Short summary
Short summary
CVPM is a modular heat-transfer modeling system designed for scientific and engineering studies in permafrost terrain, and as an educational tool. CVPM implements the heat-transfer equations in both Cartesian and cylindrical coordinates. To accommodate a diversity of geologic settings, a variety of materials can be specified within the model domain. CVPM can be used over a broad range of depth, temperature, porosity, water saturation, and solute conditions on either Earth or Mars.
Eef C. H. van Dongen, Nina Kirchner, Martin B. van Gijzen, Roderik S. W. van de Wal, Thomas Zwinger, Gong Cheng, Per Lötstedt, and Lina von Sydow
Geosci. Model Dev., 11, 4563–4576, https://doi.org/10.5194/gmd-11-4563-2018, https://doi.org/10.5194/gmd-11-4563-2018, 2018
Short summary
Short summary
Ice flow forced by gravity is governed by the full Stokes (FS) equations, which are computationally expensive to solve. Therefore, approximations to the FS equations are used, especially when modeling an ice sheet on long time spans. Here, we report a combination of an approximation with the FS equations that allows simulating the dynamics of ice sheets over long time spans without introducing artifacts caused by application of approximations in parts of the domain where they are not valid.
Alek A. Petty, Melinda Webster, Linette Boisvert, and Thorsten Markus
Geosci. Model Dev., 11, 4577–4602, https://doi.org/10.5194/gmd-11-4577-2018, https://doi.org/10.5194/gmd-11-4577-2018, 2018
Matthew J. Hoffman, Mauro Perego, Stephen F. Price, William H. Lipscomb, Tong Zhang, Douglas Jacobsen, Irina Tezaur, Andrew G. Salinger, Raymond Tuminaro, and Luca Bertagna
Geosci. Model Dev., 11, 3747–3780, https://doi.org/10.5194/gmd-11-3747-2018, https://doi.org/10.5194/gmd-11-3747-2018, 2018
Short summary
Short summary
MPAS-Albany Land Ice (MALI) is a new variable-resolution land ice model that uses unstructured grids on a plane or sphere. MALI is built for Earth system modeling on high-performance computing platforms using existing software libraries. MALI simulates the evolution of ice thickness, velocity, and temperature, and it includes schemes for simulating iceberg calving and the flow of water beneath ice sheets and its effect on ice sliding. The model is demonstrated for the Antarctic ice sheet.
Mark Kavanagh and Lev Tarasov
Geosci. Model Dev., 11, 3497–3513, https://doi.org/10.5194/gmd-11-3497-2018, https://doi.org/10.5194/gmd-11-3497-2018, 2018
Short summary
Short summary
We present and validate BrAHMs (BAsal Hydrology Model): a new
physically based basal hydrology model, which captures the two main
types of subglacial drainage systems (high-pressure distributed systems and
low-pressure channelized systems). BrAHMs is designed for continental
glacial cycle scale contexts, for which computational speed is
essential. This speed is accomplished, in part, by numerical methods
novel to basal hydrology contexts.
Aleah Sommers, Harihar Rajaram, and Mathieu Morlighem
Geosci. Model Dev., 11, 2955–2974, https://doi.org/10.5194/gmd-11-2955-2018, https://doi.org/10.5194/gmd-11-2955-2018, 2018
Short summary
Short summary
Meltwater drainage beneath glaciers and ice sheets influences how fast they move and is complicated and constantly changing. Most models distinguish between
fastand
slowdrainage with different equations for each system. The SHAKTI model allows for the ice–water drainage arrangement to transition naturally between different types of flow. This model can be used to understand how drainage affects glacier speeds and the associated ice loss to further inform predictions of sea level rise.
Ghislain Picard, Melody Sandells, and Henning Löwe
Geosci. Model Dev., 11, 2763–2788, https://doi.org/10.5194/gmd-11-2763-2018, https://doi.org/10.5194/gmd-11-2763-2018, 2018
Short summary
Short summary
The Snow Microwave Radiative Transfer (SMRT) is a novel model developed to calculate how microwaves are scattered and emitted by snow. The model is built from separate, interconnecting modules to make it easy to compare different aspects of the theory. SMRT is the first model to allow a choice of how to represent the microstructure of the snow, which is extremely important, and has been used to unite multiple previous studies. This model will ultimately be used to observe snow from space.
Lihui Luo, Zhongqiong Zhang, Wei Ma, Shuhua Yi, and Yanli Zhuang
Geosci. Model Dev., 11, 2475–2491, https://doi.org/10.5194/gmd-11-2475-2018, https://doi.org/10.5194/gmd-11-2475-2018, 2018
Short summary
Short summary
Based on the current situation of permafrost modeling in the Qinghai–Tibet Plateau (QTP), a software PIC was developed to evaluate the temporal–spatial change trends of permafrost, which allows us to automatically compute permafrost indices with daily weather and atmospheric forcing datasets. The main features include computing, visualization, and statistics. The software will serve engineering applications and can be used to assess the impact of climate change on permafrost over the QTP.
Alexandra Touzeau, Amaëlle Landais, Samuel Morin, Laurent Arnaud, and Ghislain Picard
Geosci. Model Dev., 11, 2393–2418, https://doi.org/10.5194/gmd-11-2393-2018, https://doi.org/10.5194/gmd-11-2393-2018, 2018
Short summary
Short summary
We introduced a new module of water vapor diffusion into the snowpack model Crocus. Vapor transport locally modifies the density of snow layers, possibly influencing compaction. It also affects the original isotopic signature of snow layers. We also introduced water isotopes (𝛿18O) in the model. Over 10 years, the modeled attenuation of isotopic variations due to vapor diffusion is 7–18 % lower than the observations. Thus, other processes are required to explain the total attenuation.
Joshua K. Cuzzone, Mathieu Morlighem, Eric Larour, Nicole Schlegel, and Helene Seroussi
Geosci. Model Dev., 11, 1683–1694, https://doi.org/10.5194/gmd-11-1683-2018, https://doi.org/10.5194/gmd-11-1683-2018, 2018
Short summary
Short summary
This paper details the implementation of higher-order vertical finite elements in the Ice Sheet System Model (ISSM). When using higher-order vertical finite elements, fewer vertical layers are needed to accurately capture the thermal structure in an ice sheet versus a conventional linear vertical interpolation, therefore greatly improving model runtime speeds, particularly in higher-order stress balance ice sheet models. The implications for paleoclimate ice sheet simulations are discussed.
Kaitlin A. Naughten, Katrin J. Meissner, Benjamin K. Galton-Fenzi, Matthew H. England, Ralph Timmermann, Hartmut H. Hellmer, Tore Hattermann, and Jens B. Debernard
Geosci. Model Dev., 11, 1257–1292, https://doi.org/10.5194/gmd-11-1257-2018, https://doi.org/10.5194/gmd-11-1257-2018, 2018
Short summary
Short summary
MetROMS and FESOM are two ocean/sea-ice models which resolve Antarctic ice-shelf cavities and consider thermodynamics at the ice-shelf base. We simulate the period 1992–2016 with both models, and with two options for resolution in FESOM, and compare output from the three simulations. Ice-shelf melt rates, sub-ice-shelf circulation, continental shelf water masses, and sea-ice processes are compared and evaluated against available observations.
Jeff K. Ridley, Edward W. Blockley, Ann B. Keen, Jamie G. L. Rae, Alex E. West, and David Schroeder
Geosci. Model Dev., 11, 713–723, https://doi.org/10.5194/gmd-11-713-2018, https://doi.org/10.5194/gmd-11-713-2018, 2018
Short summary
Short summary
The sea ice component of the Met Office coupled climate model, HadGEM3-GC3.1, is presented and evaluated. We determine that the mean state of the sea ice is well reproduced for the Arctic; however, a warm sea surface temperature bias over the Southern Ocean results in a low Antarctic sea ice cover.
Eric Larour, Daniel Cheng, Gilberto Perez, Justin Quinn, Mathieu Morlighem, Bao Duong, Lan Nguyen, Kit Petrie, Silva Harounian, Daria Halkides, and Wayne Hayes
Geosci. Model Dev., 10, 4393–4403, https://doi.org/10.5194/gmd-10-4393-2017, https://doi.org/10.5194/gmd-10-4393-2017, 2017
Short summary
Short summary
This work presents a new way of carrying out simulations using the C++ based Ice Sheet System Model (ISSM) within a web page. This allows for a new generation of websites that can rely on the entire code of a climate model, without compromising or simplifying the physics implemented in such a model. We believe this approach will enable better education/outreach websites as well as improve access to complex climate models without compromising their integrity.
Christopher J. L. D'Amboise, Karsten Müller, Laurent Oxarango, Samuel Morin, and Thomas V. Schuler
Geosci. Model Dev., 10, 3547–3566, https://doi.org/10.5194/gmd-10-3547-2017, https://doi.org/10.5194/gmd-10-3547-2017, 2017
Short summary
Short summary
We present a new water percolation routine added to the Crocus model. The new routine is physically based, describing motion of water through a layered snowpack considering capillary-driven and gravity flow. We tested the routine on two data sets. Wet-snow layers were able to reach higher saturations than the empirical routine. Meaningful applicability is limited until new and better parameterizations of water retention are developed, and feedbacks are adjusted to handle higher saturations.
Mathieu Barrere, Florent Domine, Bertrand Decharme, Samuel Morin, Vincent Vionnet, and Matthieu Lafaysse
Geosci. Model Dev., 10, 3461–3479, https://doi.org/10.5194/gmd-10-3461-2017, https://doi.org/10.5194/gmd-10-3461-2017, 2017
Short summary
Short summary
Global warming projections still suffer from a limited representation of the permafrost–carbon feedback. This study assesses the capacity of snow-soil coupled models to simulate the permafrost thermal regime at Bylot Island, a high Arctic site. Significant flaws are found in the description of Arctic snow properties, resulting in erroneous heat transfers between the soil and the snow in simulations. Improved snow schemes are needed to accurately predict the future of permafrost.
Per Pemberton, Ulrike Löptien, Robinson Hordoir, Anders Höglund, Semjon Schimanke, Lars Axell, and Jari Haapala
Geosci. Model Dev., 10, 3105–3123, https://doi.org/10.5194/gmd-10-3105-2017, https://doi.org/10.5194/gmd-10-3105-2017, 2017
Short summary
Short summary
The Baltic Sea is seasonally ice covered with intense wintertime ship traffic and a sensitive ecosystem. Understanding the sea-ice pack is important for climate effect studies and forecasting. A NEMO-LIM3.6-based model setup for the North Sea/Baltic Sea is introduced, including a method for ice in the coastal zone. We evaluate different sea-ice parameters and overall find that the model agrees well with the observation though deformed ice is more challenging to capture.
Eleanor J. Burke, Sarah E. Chadburn, and Altug Ekici
Geosci. Model Dev., 10, 959–975, https://doi.org/10.5194/gmd-10-959-2017, https://doi.org/10.5194/gmd-10-959-2017, 2017
Short summary
Short summary
There is a large amount of relatively inert organic carbon locked into permafrost soils. In a warming climate the permafrost will thaw and this organic carbon will become vulnerable to decomposition. This process is not typically included within Earth system models (ESMs). This paper describes the development of a vertically resolved soil organic carbon decomposition model which, in the future, can be included within the UKESM to quantify the response of the climate to permafrost carbon loss.
Cited articles
Albrecht, T., Martin, M., Haseloff, M., Winkelmann, R., and Levermann, A.: Parameterization for subgrid-scale motion of ice-shelf calving fronts, The Cryosphere, 5, 35–44, https://doi.org/10.5194/tc-5-35-2011, 2011.
Benn, D. I., Warren, C. R., and Mottram, R. H.: Calving processes and the dynamics of calving glaciers, Earth-Sci. Rev., 82, 143–179, https://doi.org/10.1016/j.earscirev.2007.02.002, 2007.
Berman, A. and Plemmons, R. J.: Nonnegative Matrices in the Mathematical Sciences, Society for Industrial and Applied Mathematics (SIAM), ISBN:978-0898713213, 1994.
Blatter, H.: Velocity and stress fields in grounded glaciers: a simple algorithm for including deviatoric stress gradients, J. Glaciol., 41, 333–344, 1995.
Bueler, E. and Brown, J.: Shallow shelf approximation as a "sliding law" in a thermomechanically coupled ice sheet model, J. Geophys. Res.-Earth, 114(F03008), 21 pp., https://doi.org/10.1029/2008JF001179, 2009.
Colinge, J. and Blatter, H.: Stress and velocity fields in glaciers: Part I. Finite-difference schemes for higher-order glacier models, J. Glaciol., 44), 448–456, 1998.
De Smedt, B., Pattyn F., and De Groen, P.: Using the unstable manifold correction in a Picard iteration to solve the velocity field in higher-order ice-flow models, J. Glaciol., 56, 257–261, https://doi.org/10.3189/002214310791968395, 2010.
Dukowicz, J. K., Price, S. F., and Lipscomb, W. H.: Consistent approximations and boundary conditions for ice-sheet dynamics from a principle of least action, J. Glaciol., 56, 480–496, https://doi.org/10.3189/002214310792447851, 2010.
Ferziger, J. H. and Perić, M.: Computational Methods for Fluid Dynamics, Springer Verlag, 3, ISBN:978-3540594345, 2002.
Fowler, A. C. and Larson, D. A.: The uniqueness of steady state flows of glaciers and ice sheets, Geophys. J. Roy. Astr. S., 63, 333–345, https://doi.org/10.1111/j.1365-246X.1980.tb02624.x, 1980.
Gagliardini, O., Duran, G., Zwinger, T., Hindmarsh, R. C. A., and Le Meur, E.: Coupling of ice-shelf melting and buttressing is a key process in ice-sheet dynamics, Geophys. Res. Lett., 37, 24 pp., https://doi.org/10.1029/2010GL043334, 2010.
Goldberg, D., Holland, D. M., and Schoof, C.: Grounding line movement and ice shelf buttressing in marine ice sheets, J. Geophys. Res.-Earth, 114, 23 pp., https://doi.org/10.1029/2008JF001227, 2009.
Harlow, F. and Welch, J.: Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8, 2182–2189, https://doi.org/10.1063/1.1761178, 1965.
Hindmarsch, R. C. A.: A numerical comparison of approximations to the Stokes equations used in ice sheet and glacier modelling, J. Geophys. Res.-Earth, 109, F01012, https://doi.org/10.1029/2003JF000065, 2004.
Hindmarsch, R. C. A.: The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion, Philos. T. Roy. Soc. A., 364, 1733–1767, https://doi.org/10.1098/rsta.2006.1797, 2006.
Hindmarsch, R. C. A. and Payne, A. J.: Time-step limits for stable solutions of the ice-sheet equation, Ann. Glaciol., 23, 74–85, 1996.
Hutter, K.: Theoretical glaciology. Material science of ice and the mechanics of glaciers and ice sheets, Reidel, Dordrecht, Netherlands, ISBN:978-9027714732, 1983.
Huybrechts, P. and de Wolde, J.: The dynamic response of the Greenland and Antarctic ice sheets to multiple-century climatic warming, J. Climate, 12, 2169–2188, https://doi.org/10.1175/1520-0442(1999)012<2169:TDROTG>2.0.CO;2 , 1999.
Johnson, J. and Fastook, J. L.: Northern Hemisphere glaciation and its sensitivity to basal melt water, Quatern. Int., 95–96, 65–74, https://doi.org/10.1016/S1040-6182(02)00028-9, 2002.
Jouvet, G., Huss, M., Blatter, H., Picasso, M., and Rappaz, J.: Numerical simulation of Rhonegletscher from 1824 to 2100, J. Comput. Phys., 228, 6426–6439, https://doi.org/10.1016/j.jcp.2009.05.033, 2009.
LeVeque, R. J.: Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, Philadelphia, ISBN: 978-0898716290, 2007.
MacAyeal, D. R.: Large-Scale Ice Flow Over a Viscous Basal Sediment: Theory and Application to Ice Stream B, Antarctica, J. Geophys. Res.-Solid, 94, 4071–4087, https://doi.org/10.1029/JB094iB04p04071, 1989.
Mattheij, R. M. M., Rienstra, S. W., and ten Thije Boonkamp, J. H. M.: Partial differential equations: modeling, analysis, computation, SIAM, Philadelphia, ISBN:978-0898715941, 2005.
Morland, L. W.: Unconfined ice-shelf flow, in: Dynamics of the West Antarctic ice sheet, dited by: van der Veen, C. J. and Oerlemans, J., Kluwer Academic Publishers, 99–116, ISBN:978-9027723703, 1986.
Morland, L. W. and Johnson, I. R.: Steady Motion of Ice Sheets, J. Glaciol., 25, 229–246, 1980.
Manguoglu, M., Sameh, A. H., Saied, F., Tezduyar, T. E., and Sathe, S.: Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows, J. Appl. Mech., 76, 7 pp., https://doi.org/10.1115/1.3059576, 2009.
Otero, J., Navarro, F. J., Martin, C., Cuadrado, M. L., and Corcuera, M. I.: A three-dimensional calving model: numerical experiments on Johnsons Glacier, Livingston Island, Antarctica, J. Glaciol., 56, 200–214, https://doi.org/10.3189/002214310791968539, 2010.
Pattyn, F.: A new three-dimensional higher-order thermomechanical ice sheet model: Basic sensitivity, ice stream development, and ice flow across subglacial lakes, J. Geophys. Res.-Sol. Earth, 108, 2382, https://doi.org/10.1029/2002JB002329, 2003.
Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson, G. H., Hindmarsh, R. C. A., Hubbard, A., Johnson, J. V., Kleiner, T., Konovalov, Y., Martin, C., Payne, A. J., Pollard, D., Price, S., Rückamp, M., Saito, F., Soucček, O., Sugiyama, S., and Zwinger, T.: Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIPHOM), The Cryosphere, 2, 95–108, http://dx.doi.org/10.5194/tc-2-95-2008https://doi.org/10.5194/tc-2-95-2008, 2008.
Pimentel, S., Flowers, G. E., and Schoof, C. G.: A hydrologically coupled higher-order flow-band model of ice dynamics with a Coulomb friction sliding law, J. Geophys. Res.-Earth, 115, F04023, https://doi.org/10.1029/2009JF001621, 2010.
Pollard, D. and DeConto, R. M.: Modelling West Antarctic ice sheet growth and collapse through the past five million years, Nature, 458, 7236, 329–332, https://doi.org/10.1038/nature07809, 2009.
Press, W. H., Teukoslky, S. A., Vetterling, W. T., and Flannery, B. P.: Numerical Recipes in Fortran, Second Edition: The Art of Scientific Computing, Volume 1 of Fortran Numerical Recipes, Cambridge University Press, New York, ISBN:978-0521430647, 2003.
Pritchard, H. D., Arthern, R. J., Vaughan, D. G., and Edwards, L. A.: Extensive dynamic thinning on the margins of the Greenland and Antarctic ice sheets, Nature, 461, 7266, https://doi.org/10.1038/nature08471, 2009.
Ritz, C., Rommelaere, V., and Dumas, C.: Modeling the evolution of Antarctic ice sheet over the last 420,000 years: Implications for altitude changes in the Vostok region, J. Geophys. Res.-Atmos., 106, 31943–31964, https://doi.org/10.1029/2001JD900232, 2001.
Saad, Y. and Schultz, M. H.: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM, Philadelphia, 7, 856–869, https://doi.org/10.1137/0907058, 1986.
Schoof, C.: A variational approach to ice streams flow, J. Fluid. Mech., 556, 227–251, https://doi.org/10.1017/S0022112006009591, 2006.
Schoof, C.: Ice sheet grounding line dynamics: Steady states, stability, and hysteresis, J. Geophys. Res., 112, F03S28, https://doi.org/10.1029/2006JF000664, 2007.
Schoof, C. and Hindmarsh, R. C. A.: Thin-Film Flows with Wall Slip: An Asymptotic Analysis of Higher Order Glacier Flow Models, Q. J. Mech. Appl. Math., 63, 73–114, https://doi.org/10.1093/qjmam/hbp025, 2010.
Shepherd, A. and Wingham, D.: Recent sea-level contributions of the Antarctic and Greenland ice sheets, Science, 315, 1529–1532, https://doi.org/10.1126/science.1136776, 2007.
Sleijpen, G. L. G. and van Gijzen, M. B.: Exploiting BiCGstab($l)$ Strategies to Induce Dimension Reduction, SIAM, Philadelphia, 32, 2687–2709, https://doi.org/10.1137/090752341, 2010.
Sonneveld, P. and Van Gijzen, M. B.: IDR(s): a family of simple and fast algorithms for solving large nonsymmetric systems of linear equations, SIAM, Philadelphia, 31, 1053–1062, https://doi.org/10.1137/070685804, 2008.
Trottenberg, U., Oosterlee, C. W. and Schüller, A.: Multigrid, Academic Press, ISBN: 978-0127010700, 2001.
Truffer, M. and Fahnestock, M.: Rethinking ice sheet time scales, Science, 315, 1508–1510, https://doi.org/10.1126/science.1140469, 2007.
Tulaczyk, S., Kamb, W. B., and Engelhardt, H. F.: Basal mechanics of Ice Stream B, West Antarctica 1. Till mechanics, J. Geophys. Res.-Sol. Earth, 105, 463–481, 2000.
van Gijzen, M. B. and Sonneveld, P.: An elegant IDR(s) variant that efficiently exploits bi-orthogonality properties, Technical Report 10-16, Department of Applied Mathematical Analysis, Delft University of Technology, Delft, 2010.
Van Der Veen, C. J.: A Numerical Scheme for Calculating Stresses and Strain Rates in Glacier, Math. Geol., 21, 363–377, https://doi.org/10.1007/BF00893696, 1989.
Van Der Veen, C. J.: Fundamentals of Glacier Dynamics, edited by: Balkema, A. A., Rotterdam, Netherlands, ISBN: 978-9054104704, 1999.
Van der Vorst, H. A.: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems, SIAM, Philadelphia, https://doi.org/10.1137/0913035, 1992.
Vaughan, D. G. and Arthern, R.: Why is it hard to predict the future of ice sheets?, Science, 315, 1503–1504, https://doi.org/10.1126/science.1141111, 2007.
Veldman, A. E. P. and Rinzema, K.: Playing with nonuniform grids, J. Eng. Math., 26, 119–130, https://doi.org/10.1007/BF00043231, 1992.
Weis, M., Greve, R., and Hutter, K.: Theory of shallow ice shelves, Continuum Mech. Therm., 11, 15–50, https://doi.org/10.1007/s001610050102, 1999.
Wesseling, P. and Sonneveld, P.: Numerical Experiments with a Multiple Grid and a Preconditioned Lanczos Type Method, Lecture Notes in Mathematics 771, Springer Verlag, 543–562, 1980.
Yeung, M.-C. and Chan, T. F.: ML($K)$BiCGSTAB: A BiCGSTAB Variant based on Multiple Lanczos Starting Vectors, SIAM, Philadelphia, 21, 1263–1290, https://doi.org/10.1137/S1064827597321581, 1999.
Zwinger, T., Greve, R., Gagliardini, O., Takayuki, S., 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, https://doi.org/10.3189/172756407782282543, 2007.
