DSpace Collection: 2009-12
http://hdl.handle.net/2115/45402
2009-122024-03-28T11:47:34ZCombined Analysis of Water Stable Isotopes ($H_{2}^{16}O, H_{2}^{17}O, H_{2}^{18}O, HD^{16}O$) in Ice Cores
http://hdl.handle.net/2115/45457
Title: Combined Analysis of Water Stable Isotopes ($H_{2}^{16}O, H_{2}^{17}O, H_{2}^{18}O, HD^{16}O$) in Ice Cores
Authors: Landais, Amaelle; Barkan, Eugeni; Vimeux, Françoise; Masson-Delmotte, Valérie; Luz, Boaz
Abstract: Water stable isotopes are currently measured in polar ice cores. The long records of $δ_{18}O$ and δD provide unique information on the past polar temperature while the combination of $δ_{18}O$ and δD constrains the evolution of the oceanic evaporative regions. Recently, new analytical developments have made it possible to measure with high precision a new isotopic ratio in water, $δ_{17}O$. As for δD and $δ_{18}0$, the combination of $δ_{17}0$ and $δ_{18}0$ shows a high dependence with the climatic conditions during evaporation. Based on measurements of the different isotopic ratios in Antarctica surface snow, we show that while the combination of $δ_{18}0$ and δD in the so-called d-excess displays variation with local climatic conditions in the polar regions in addition to the influence of the evaporative regions, the combination of $δ_{17}0$ and $δ_{18}0$ in the so-called $^{17}O_{excess}$ is not modified during the air mass transportation above the polar regions. This makes $^{17}O_{excess}$ a simpler parameter than d-excess to constrain the evolution of the oceanic evaporative regions. Finally, records of d-excess and $^{17}O_{excess}$ over the deglaciation in the Vostok ice core suggest significant changes in the evaporative regions. Our interpretation is that the relative humidity over the ocean was higher during the glacial period than today and that reevaporation increased over the deglaciation.
Description: IV. Chemical properties and isotopes2009-11-30T15:00:00ZLandais, AmaelleBarkan, EugeniVimeux, FrançoiseMasson-Delmotte, ValérieLuz, BoazWater stable isotopes are currently measured in polar ice cores. The long records of $δ_{18}O$ and δD provide unique information on the past polar temperature while the combination of $δ_{18}O$ and δD constrains the evolution of the oceanic evaporative regions. Recently, new analytical developments have made it possible to measure with high precision a new isotopic ratio in water, $δ_{17}O$. As for δD and $δ_{18}0$, the combination of $δ_{17}0$ and $δ_{18}0$ shows a high dependence with the climatic conditions during evaporation. Based on measurements of the different isotopic ratios in Antarctica surface snow, we show that while the combination of $δ_{18}0$ and δD in the so-called d-excess displays variation with local climatic conditions in the polar regions in addition to the influence of the evaporative regions, the combination of $δ_{17}0$ and $δ_{18}0$ in the so-called $^{17}O_{excess}$ is not modified during the air mass transportation above the polar regions. This makes $^{17}O_{excess}$ a simpler parameter than d-excess to constrain the evolution of the oceanic evaporative regions. Finally, records of d-excess and $^{17}O_{excess}$ over the deglaciation in the Vostok ice core suggest significant changes in the evaporative regions. Our interpretation is that the relative humidity over the ocean was higher during the glacial period than today and that reevaporation increased over the deglaciation.Formation of the Ice Core Isotopic Composition
http://hdl.handle.net/2115/45456
Title: Formation of the Ice Core Isotopic Composition
Authors: Ekaykin, Alexey A.; Lipenkov, Vladimir Ya.
Abstract: Main processes of the ice core isotopic composition formation are overviewed. Theory of isotope-temperature relationship is discussed and confirmed by a number of experimental data. The factors related to wind-driven spatial snow redistribution and post-depositional isotopic changes that may alter or weaken this relationship, are also considered. For high-resolution isotopic time-series obtained at sites with low accumulation of snow, the signal-to-noise ratio is shown to be as low as 0.25, which means that noise accounts for about 80 % of the total variance. It is demonstrated that "classical isotopic method" (based on the present-day geographical isotope-temperature slope) underestimates the amplitude of past temperature changes in Antarctica. The most likely reason for the discrepancy is the change in the moisture source conditions. After correction for the latter, the paleo-temperature reconstructions produced by the isotopic method become consistent with those obtained from borehole temperature measurements. We show that in the case of the Vostok ice core, both approaches lead to the same temperature shift of 10℃ between LGM and the present time. The isotopic composition of the basal part of the Vostok ice core, comprising frozen subglacial Lake Vostok water, is also discussed.
Description: IV. Chemical properties and isotopes2009-11-30T15:00:00ZEkaykin, Alexey A.Lipenkov, Vladimir Ya.Main processes of the ice core isotopic composition formation are overviewed. Theory of isotope-temperature relationship is discussed and confirmed by a number of experimental data. The factors related to wind-driven spatial snow redistribution and post-depositional isotopic changes that may alter or weaken this relationship, are also considered. For high-resolution isotopic time-series obtained at sites with low accumulation of snow, the signal-to-noise ratio is shown to be as low as 0.25, which means that noise accounts for about 80 % of the total variance. It is demonstrated that "classical isotopic method" (based on the present-day geographical isotope-temperature slope) underestimates the amplitude of past temperature changes in Antarctica. The most likely reason for the discrepancy is the change in the moisture source conditions. After correction for the latter, the paleo-temperature reconstructions produced by the isotopic method become consistent with those obtained from borehole temperature measurements. We show that in the case of the Vostok ice core, both approaches lead to the same temperature shift of 10℃ between LGM and the present time. The isotopic composition of the basal part of the Vostok ice core, comprising frozen subglacial Lake Vostok water, is also discussed.Ion Fractionation and Percolation in Ice Cores with Seasonal Melting
http://hdl.handle.net/2115/45455
Title: Ion Fractionation and Percolation in Ice Cores with Seasonal Melting
Authors: Moore, John C.; Grinsted, Aslak
Abstract: We examine the impact that post-depositional change has on ion concentrations in ice cores that suffer limited seasonal melting. We show that the impact in the case of at least one Svalbard ice core is limited to decreasing resolution of signals to about 3 years - a similar accuracy as the best dating can usually provide. We model various effects such as percolation and washout of ions, and show how they can be used to construct useful ice core proxies. The sulfate profile shows how post depositional effects lead to magnesium and nitrate being excellent predictors under normal conditions for sulfate - indicating a difference in the properties of acidic and neutral salt sulfate components. The approach leads to an objective method of detecting volcanic signals in sulfate, even when the signals are much smaller than the sulfate variability caused by other factors. We emphasis the importance of correct statistical analysis the interpretation of ion profiles, taking into account how measurement errors and the distribution of ion chromatography data affects how statistical modelling should be done.
Description: IV. Chemical properties and isotopes2009-11-30T15:00:00ZMoore, John C.Grinsted, AslakWe examine the impact that post-depositional change has on ion concentrations in ice cores that suffer limited seasonal melting. We show that the impact in the case of at least one Svalbard ice core is limited to decreasing resolution of signals to about 3 years - a similar accuracy as the best dating can usually provide. We model various effects such as percolation and washout of ions, and show how they can be used to construct useful ice core proxies. The sulfate profile shows how post depositional effects lead to magnesium and nitrate being excellent predictors under normal conditions for sulfate - indicating a difference in the properties of acidic and neutral salt sulfate components. The approach leads to an objective method of detecting volcanic signals in sulfate, even when the signals are much smaller than the sulfate variability caused by other factors. We emphasis the importance of correct statistical analysis the interpretation of ion profiles, taking into account how measurement errors and the distribution of ion chromatography data affects how statistical modelling should be done.Chemical Compounds of Water-Soluble Impurities in Dome Fuji Ice Core
http://hdl.handle.net/2115/45453
Title: Chemical Compounds of Water-Soluble Impurities in Dome Fuji Ice Core
Authors: Iizuka, Yoshinori; Ohno, Hiroshi; Sakurai, Toshimitsu; Horikawa, Shinichiro; Hondoh, Takeo
Abstract: The amounts of water-soluble impurities in ice cores have been widely discussed in past research on prehistoric climates; in those studies, the analysis of the soluble-aerosol signals of several ion concentrations took place after the ice cores were melted. However, the chemical compounds of the impurities being studied were unclear, due to the ionization of the impurities being caused by the melting of the ice cores. In this paper, the chemical compounds of water-soluble impurities in Dome Fuji ice core are discussed and analyzed using micro-Raman spectroscopy and ion chromatography. Raman spectroscopy helped identify micro-inclusions within ice grains as water-soluble impurities made up primarily of sodium sulfate formed in warm periods and calcium sulfate in cold periods. The major chemical compounds of the water-soluble impurities (sodium sulfate and calcium sulfate) were deduced by examining ion concentrations and the stability of chemical compounds. The amounts of impurities reflect the differences in climatic time periods, as the environment was acidic during warm times and reductive during cold.
Description: IV. Chemical properties and isotopes2009-11-30T15:00:00ZIizuka, YoshinoriOhno, HiroshiSakurai, ToshimitsuHorikawa, ShinichiroHondoh, TakeoThe amounts of water-soluble impurities in ice cores have been widely discussed in past research on prehistoric climates; in those studies, the analysis of the soluble-aerosol signals of several ion concentrations took place after the ice cores were melted. However, the chemical compounds of the impurities being studied were unclear, due to the ionization of the impurities being caused by the melting of the ice cores. In this paper, the chemical compounds of water-soluble impurities in Dome Fuji ice core are discussed and analyzed using micro-Raman spectroscopy and ion chromatography. Raman spectroscopy helped identify micro-inclusions within ice grains as water-soluble impurities made up primarily of sodium sulfate formed in warm periods and calcium sulfate in cold periods. The major chemical compounds of the water-soluble impurities (sodium sulfate and calcium sulfate) were deduced by examining ion concentrations and the stability of chemical compounds. The amounts of impurities reflect the differences in climatic time periods, as the environment was acidic during warm times and reductive during cold.Seasonal Variations of Isotope Ratios and CO2 Concentrations in Firn Air
http://hdl.handle.net/2115/45452
Title: Seasonal Variations of Isotope Ratios and CO2 Concentrations in Firn Air
Authors: Weiler, Karin; Schwander, Jakob; Leuenberger, Markus; Blunier, Thomas; Mulvaney, Robert; Anderson, Philip S.; Salmon, Rhian; Sturges, William T.
Abstract: A first year-round firn air sampling carried out at the British Antarctic station Halley in 2003 shows isotope and CO2 changes owing to diffusive mixing driven by seasonal variations of surface temperature, and gas composition of the atmosphere. Seasonal firn temperatures are well reproduced from the atmospheric temperature history. Based on these profiles thermal diffusion is forced with thermal diffusion factors αT with respect to air. Application of the available literature data for αT (15N14 / N2) leads to a proper prediction of the seasonal thermal amplitude during the entire year. By forcing thermal fractionation with αT as derived from two different model approaches and taking into account literature data reasonable results can be achieved for CO2 but not for thermal fractionation of 18016O and 16O2 in air. The latter is attributed to an inappropriate reproduction of the intermolecular interaction forces by either model. Neither thermal diffusion nor annual variations in the atmospheric CO2 concentration seem to have a substancial effect on the CO2 concentration finally conserved in air bubbles at the close-off level.
Description: III. Firn densification, close-off and chronology2009-11-30T15:00:00ZWeiler, KarinSchwander, JakobLeuenberger, MarkusBlunier, ThomasMulvaney, RobertAnderson, Philip S.Salmon, RhianSturges, William T.A first year-round firn air sampling carried out at the British Antarctic station Halley in 2003 shows isotope and CO2 changes owing to diffusive mixing driven by seasonal variations of surface temperature, and gas composition of the atmosphere. Seasonal firn temperatures are well reproduced from the atmospheric temperature history. Based on these profiles thermal diffusion is forced with thermal diffusion factors αT with respect to air. Application of the available literature data for αT (15N14 / N2) leads to a proper prediction of the seasonal thermal amplitude during the entire year. By forcing thermal fractionation with αT as derived from two different model approaches and taking into account literature data reasonable results can be achieved for CO2 but not for thermal fractionation of 18016O and 16O2 in air. The latter is attributed to an inappropriate reproduction of the intermolecular interaction forces by either model. Neither thermal diffusion nor annual variations in the atmospheric CO2 concentration seem to have a substancial effect on the CO2 concentration finally conserved in air bubbles at the close-off level.A Probabilistic Method to Construct an Optimal Ice Chronology for Ice Cores
http://hdl.handle.net/2115/45451
Title: A Probabilistic Method to Construct an Optimal Ice Chronology for Ice Cores
Authors: Lemieux-Dudon, Benedicte; Frederic, Parrenin; Blayo, Eric
Abstract: Accurate ice chronologies are needed for the interpretation of paleoclimate reconstructions inferred from ice cores. Several methods are used to provide chronological information: identification of dated horizons along the cores, synchronization to other dated paleoclimatic records, counting of annual layers or modelling of the ice flow. These methods are relevant for different parts of the core and enable to reach various levels of accuracy. We present a probabilistic approach based on inverse techniques which aims at building an optimal ice core chronology by using all the available chronological information. It consists in identifying the accumulation rate and the thinning function along the core 1) which are as close as possible to the flow model simulations and 2) so that the corresponding ice chronology is as close as possible to independent dating information. This probabilistic approach enables to evaluate confidence intervals on the optimal age scale as well as on the accumulation and the thinning estimates. We test the new method on the EPICA Dome C ice core. The necessary prior accumulation rate and thinning function as well as a set of dated horizons are provided by a previous work aiming at the EDC3 age scale reconstruction. We further discuss the sensitivity of the obtaincd optimal solution with respect to the necessary prior information. This probabilistic approach could be used in the future to build a common and optimal chronology for several ice cores simultaneously.
Description: III. Firn densification, close-off and chronology2009-11-30T15:00:00ZLemieux-Dudon, BenedicteFrederic, ParreninBlayo, EricAccurate ice chronologies are needed for the interpretation of paleoclimate reconstructions inferred from ice cores. Several methods are used to provide chronological information: identification of dated horizons along the cores, synchronization to other dated paleoclimatic records, counting of annual layers or modelling of the ice flow. These methods are relevant for different parts of the core and enable to reach various levels of accuracy. We present a probabilistic approach based on inverse techniques which aims at building an optimal ice core chronology by using all the available chronological information. It consists in identifying the accumulation rate and the thinning function along the core 1) which are as close as possible to the flow model simulations and 2) so that the corresponding ice chronology is as close as possible to independent dating information. This probabilistic approach enables to evaluate confidence intervals on the optimal age scale as well as on the accumulation and the thinning estimates. We test the new method on the EPICA Dome C ice core. The necessary prior accumulation rate and thinning function as well as a set of dated horizons are provided by a previous work aiming at the EDC3 age scale reconstruction. We further discuss the sensitivity of the obtaincd optimal solution with respect to the necessary prior information. This probabilistic approach could be used in the future to build a common and optimal chronology for several ice cores simultaneously.Impact of Local Insolation on Snow Metamorphism and Ice Core Records
http://hdl.handle.net/2115/45450
Title: Impact of Local Insolation on Snow Metamorphism and Ice Core Records
Authors: Hutterli, Manuel A.; Schneebeli, Martin; Freitag, Johannes; Kipfstuhl, Josef; Röthlisberger, Regine
Abstract: Local insolation is a major component of the energy balance at the surface of an ice sheet and causes temperature gradient metamorphism (TGM) of snow and firn. TGM is one of the dominant processes changing the structure of dry snow. We present a physically based model that calculates insolation-induced relative changes in TGM in the past. The results indicate that TGM at Dome Fuji varied by up to a factor of 2 over the past 350ka, and is driven predominately by the precession-band variability in local summer solstice insolation. At Dome Fuji, the impact of glacial-interglacial temperature changes on TGM is almost fully compensated by synchronous, opposite changes in accumulation rate, which determines the exposure time of a snow layer to TGM. Even small remaining temperature signals in TGM can cause phase shifts between TGM and local summer solstice insolation of several ka. This directly affects the accuracy of orbitally tuned ice core time scales using O2/N2 or total air content records, as this dating method is based on the assumption of synchronicity between TGM and insolation. It must be assumed that the strong variability in TGM will also be reflected in physical and chemical ice core records by e.g. modulating the volatilization of reversibly deposited species including the stable isotopes of water. Sublimation and thus accumulation rates are also closely linked to TGM, affecting the concentrations also of irreversibly deposited non-volatile impurities. Thus, the effect of a local, post-depositional contribution of TGM on ice core records must be quantified prior to their interpretation in terms of larger scale climate variability in the orbital frequency bands.
Description: III. Firn densification, close-off and chronology2009-11-30T15:00:00ZHutterli, Manuel A.Schneebeli, MartinFreitag, JohannesKipfstuhl, JosefRöthlisberger, RegineLocal insolation is a major component of the energy balance at the surface of an ice sheet and causes temperature gradient metamorphism (TGM) of snow and firn. TGM is one of the dominant processes changing the structure of dry snow. We present a physically based model that calculates insolation-induced relative changes in TGM in the past. The results indicate that TGM at Dome Fuji varied by up to a factor of 2 over the past 350ka, and is driven predominately by the precession-band variability in local summer solstice insolation. At Dome Fuji, the impact of glacial-interglacial temperature changes on TGM is almost fully compensated by synchronous, opposite changes in accumulation rate, which determines the exposure time of a snow layer to TGM. Even small remaining temperature signals in TGM can cause phase shifts between TGM and local summer solstice insolation of several ka. This directly affects the accuracy of orbitally tuned ice core time scales using O2/N2 or total air content records, as this dating method is based on the assumption of synchronicity between TGM and insolation. It must be assumed that the strong variability in TGM will also be reflected in physical and chemical ice core records by e.g. modulating the volatilization of reversibly deposited species including the stable isotopes of water. Sublimation and thus accumulation rates are also closely linked to TGM, affecting the concentrations also of irreversibly deposited non-volatile impurities. Thus, the effect of a local, post-depositional contribution of TGM on ice core records must be quantified prior to their interpretation in terms of larger scale climate variability in the orbital frequency bands.Snow/Firn Densification in Polar Ice Sheets
http://hdl.handle.net/2115/45449
Title: Snow/Firn Densification in Polar Ice Sheets
Authors: Salamatin, Andrey N.; Lipenkov, Vladimir Ya.; Barnola, Jean Marc; Hori, Akira; Duval, Paul; Hondoh, Takeo
Abstract: A sophisticated physical model of the dry snow/firn densification process in ice sheets is proposed. Macroscopically, snow and firn undergo vertical uniaxial compression with non-zero deviatoric stresses and strain rates. The present mathematical description of densificntion includes dilatancy and "force-chain" effects in snow and develops previous concepts of ice-particle rearrangement by grain-boundary sliding and sintering by power-law creep under overburden pressure. Both densification mechanisms work together during the first snow stage until the closest packing of ice grains is reached at critical densities of 0.7-0.76 and the firn stage controlled only by the dislocation creep sets on. In addition to the ice-grain coordination number and the slope of the radial distribution function, a new structural parameter is introduced to account for grain bonding (agglomeration) effects. The model is constrained and validated on direct stereological observations of ice core structures and a representative set of snow/firn density-depth profiles covering a wide range of present-day climatic conditions (-57.5 to -10℃ and ice accumulation at 2.15 to 330 cm yr^[-1] ). Simple equations are derived for predicting the depth of pore closure in firn and the ice age at close-off. The paleoclimatic evolution of quasi-stationary density-depth profiles and close-off characteristics at Vostok Station (East Antarctica) are simulated and discussed.
Description: III. Firn densification, close-off and chronology2009-11-30T15:00:00ZSalamatin, Andrey N.Lipenkov, Vladimir Ya.Barnola, Jean MarcHori, AkiraDuval, PaulHondoh, TakeoA sophisticated physical model of the dry snow/firn densification process in ice sheets is proposed. Macroscopically, snow and firn undergo vertical uniaxial compression with non-zero deviatoric stresses and strain rates. The present mathematical description of densificntion includes dilatancy and "force-chain" effects in snow and develops previous concepts of ice-particle rearrangement by grain-boundary sliding and sintering by power-law creep under overburden pressure. Both densification mechanisms work together during the first snow stage until the closest packing of ice grains is reached at critical densities of 0.7-0.76 and the firn stage controlled only by the dislocation creep sets on. In addition to the ice-grain coordination number and the slope of the radial distribution function, a new structural parameter is introduced to account for grain bonding (agglomeration) effects. The model is constrained and validated on direct stereological observations of ice core structures and a representative set of snow/firn density-depth profiles covering a wide range of present-day climatic conditions (-57.5 to -10℃ and ice accumulation at 2.15 to 330 cm yr^[-1] ). Simple equations are derived for predicting the depth of pore closure in firn and the ice age at close-off. The paleoclimatic evolution of quasi-stationary density-depth profiles and close-off characteristics at Vostok Station (East Antarctica) are simulated and discussed.Ice Flow Line Modeling and Ice Core Data Interpretation : Vostok Station (East Antarctica)
http://hdl.handle.net/2115/45448
Title: Ice Flow Line Modeling and Ice Core Data Interpretation : Vostok Station (East Antarctica)
Authors: Salamatin, Andrey N.; Tsyganova, Elena A.; Popov, Sergey V.; Lipenkov, Vladimir Ya.
Abstract: This work, originally based on a series of the authors' publications [101 , 102, 104, 112, 130, 131], considers general questions of ice-sheet flow modeling as related to ice core records interpretation. It reviews the previous results and, using new geographical, geophysical and glaciological data, continues the study aimed at solving the twofold problem of ice core age dating and paleoclimatic reconstructions from the isotopic content measurements in the deep ice cores from Vostok Station located in central East Antarctica, above the vast subglacial lake. The principal idea of the paper is to develop a general approach to past climate investigation by means of an improved thermo-mechanical ice flow line model, involving a wide spectra of supplementary data such as borehole-temperature, radio-echo-sounding reflection layers, and air-bubble measurements.
Description: II. Ice-sheet flow model2009-11-30T15:00:00ZSalamatin, Andrey N.Tsyganova, Elena A.Popov, Sergey V.Lipenkov, Vladimir Ya.This work, originally based on a series of the authors' publications [101 , 102, 104, 112, 130, 131], considers general questions of ice-sheet flow modeling as related to ice core records interpretation. It reviews the previous results and, using new geographical, geophysical and glaciological data, continues the study aimed at solving the twofold problem of ice core age dating and paleoclimatic reconstructions from the isotopic content measurements in the deep ice cores from Vostok Station located in central East Antarctica, above the vast subglacial lake. The principal idea of the paper is to develop a general approach to past climate investigation by means of an improved thermo-mechanical ice flow line model, involving a wide spectra of supplementary data such as borehole-temperature, radio-echo-sounding reflection layers, and air-bubble measurements.A Review of Anisotropic Polar Ice Models : from Crystal to Ice-Sheet Flow Models
http://hdl.handle.net/2115/45447
Title: A Review of Anisotropic Polar Ice Models : from Crystal to Ice-Sheet Flow Models
Authors: Gagliardini, Olivier; Gillel-Chaulet, Fabien; Montagnat, Maurine
Abstract: The ice single crystal is one of the most anisotropic natural materials and the resulting viscous behaviour of polycrystalline ice can also be strongly anisotropic and is a function of the distribution of the crystal c-axis orientations, i.e. its fabric. Such a strong and strain-dependant anisotropy of the ice polycrystal certainly affects the general flow of polar ice. The aim of this paper is to present an exhaustive overview of most of the glaciological efforts made from more than two decades to account for polar ice anisotropy in ice flow modelling, from the crystal to the ice-sheets scale. We first recall the deformation and recrystallization proccsses occurring within ice-sheets and their respective effect on the polar ice textures. Then, the different models developed to describe the behaviour of the ice crystal and the polycrystal are presented, with a special emphasis on homogenization methods and fabric description. Finally, existing anisotropic ice flow models and their applications are reviewed.
Description: II. Ice-sheet flow model2009-11-30T15:00:00ZGagliardini, OlivierGillel-Chaulet, FabienMontagnat, MaurineThe ice single crystal is one of the most anisotropic natural materials and the resulting viscous behaviour of polycrystalline ice can also be strongly anisotropic and is a function of the distribution of the crystal c-axis orientations, i.e. its fabric. Such a strong and strain-dependant anisotropy of the ice polycrystal certainly affects the general flow of polar ice. The aim of this paper is to present an exhaustive overview of most of the glaciological efforts made from more than two decades to account for polar ice anisotropy in ice flow modelling, from the crystal to the ice-sheets scale. We first recall the deformation and recrystallization proccsses occurring within ice-sheets and their respective effect on the polar ice textures. Then, the different models developed to describe the behaviour of the ice crystal and the polycrystal are presented, with a special emphasis on homogenization methods and fabric description. Finally, existing anisotropic ice flow models and their applications are reviewed.