The description of grounding line migration in a two-dimensional mathematical model of an ice sheet

Contemporary thinning of the marine-based areas of ice sheets is believed to be the consequence of the grounding line retreat caused mainly by ocean gradual warming beneath the ice shelves. In order to estimate potential contribution of ice sheets into the future sea-level rise grounding line migrat...

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Published in:Ice and Snow
Main Authors: O. Rybak O., E. Rybak A., О. Рыбак О., Е. Рыбак А.
Format: Article in Journal/Newspaper
Language:Russian
Published: IGRAS 2015
Subjects:
Antarctica Ice Sheet;climatic variations;grounding line;ice flow;ice shelf;mathematical model
Annals of Glaciology
Antarc*
Antarctica
Berichte zur Polarforschung
Ice Sheet
Ice Shelf
Ice Shelves
Polarforschung
The Cryosphere
Online Access:https://ice-snow.igras.ru/jour/article/view/111
https://doi.org/10.15356/2076-6734-2013-3-5-11
id ftjias:oai:oai.ice.elpub.ru:article/111
record_format openpolar
institution Open Polar
collection Ice and Snow (E-Journal)
op_collection_id ftjias
language Russian
topic Antarctica Ice Sheet;climatic variations;grounding line;ice flow;ice shelf;mathematical model
spellingShingle Antarctica Ice Sheet;climatic variations;grounding line;ice flow;ice shelf;mathematical model
O. Rybak O.
E. Rybak A.
О. Рыбак О.
Е. Рыбак А.
The description of grounding line migration in a two-dimensional mathematical model of an ice sheet
topic_facet Antarctica Ice Sheet;climatic variations;grounding line;ice flow;ice shelf;mathematical model
description Contemporary thinning of the marine-based areas of ice sheets is believed to be the consequence of the grounding line retreat caused mainly by ocean gradual warming beneath the ice shelves. In order to estimate potential contribution of ice sheets into the future sea-level rise grounding line migration must be accurately described in the mathematical models. We incorporated an algorithm based on application of the boundary condition on the mass flux across the grounding line into a two-dimensional ice flow model. In the numerical experiments, externally forced ice sheet returns to its initial equilibrium state after termination of the external forcing (either accumulation rate or sea-level change anomalies). In future, the model will be modified to incorporate buttressing effect. Объём ледниковых щитов, основание которых лежит ниже уровня моря, сокращается главным образом в результате смещения линии налегания в глубь континентальной области предположительно в результате потепления окружающих его вод океана. Для оценки потенциального вклада ледниковых щитов в будущее увеличение уровня моря в математических моделях необходимо как можно точнее описывать процесс миграции линии налегания. В статье рассматривается алгоритм миграции, в основе которого лежит задание граничного условия потока массы на линии налегания. В численных экспериментах ледниковый щит, будучи выведенным из равновесия внешним воздействием, возвращается к своему первоначальному состоянию при прекращении действия внешней силы. После соответствующей доработки алгоритм можно применять в комплексных моделях ледниковых щитов.
format Article in Journal/Newspaper
author O. Rybak O.
E. Rybak A.
О. Рыбак О.
Е. Рыбак А.
author_facet O. Rybak O.
E. Rybak A.
О. Рыбак О.
Е. Рыбак А.
author_sort O. Rybak O.
title The description of grounding line migration in a two-dimensional mathematical model of an ice sheet
title_short The description of grounding line migration in a two-dimensional mathematical model of an ice sheet
title_full The description of grounding line migration in a two-dimensional mathematical model of an ice sheet
title_fullStr The description of grounding line migration in a two-dimensional mathematical model of an ice sheet
title_full_unstemmed The description of grounding line migration in a two-dimensional mathematical model of an ice sheet
title_sort description of grounding line migration in a two-dimensional mathematical model of an ice sheet
publisher IGRAS
publishDate 2015
url https://ice-snow.igras.ru/jour/article/view/111
https://doi.org/10.15356/2076-6734-2013-3-5-11
genre Annals of Glaciology
Antarc*
Antarctica
Berichte zur Polarforschung
Ice Sheet
Ice Shelf
Ice Shelves
Polarforschung
The Cryosphere
genre_facet Annals of Glaciology
Antarc*
Antarctica
Berichte zur Polarforschung
Ice Sheet
Ice Shelf
Ice Shelves
Polarforschung
The Cryosphere
op_source Ice and Snow; Том 53, № 3 (2013); 5-11
Лёд и Снег; Том 53, № 3 (2013); 5-11
2412-3765
2076-6734
10.15356/2076-6734-2013-3
op_relation Grosswald M.G. Pokrovnye ledniki kontinentalnykh shelfov. Ice sheets of continental shelves. Moscow: Nauka, 1983: 216 с. [In Russian].
Danilyuk I.I. On the Stephan problem. Uspekhi matematicheskikh nauk. Successes of Mathematical Sciences. 1985, 40, 5 (245):133–185. [In Russian].
Rybak O.O. Modeling of migration of marine ice sheet border in the simple numerical model. Izvestiya vyzov. Severo-Kavkazskiy region. Estestvennye nauki. Proc. of vuzov. North-Caucasian region. Natural Sciences. 2010, 4: 126–130. [In Russian].
Rybak O.O. Migration of marine ice sheet border in the numerical model. Vestnik Yuzhnogo nauchnogo tsentra RAN. Herald of the South Scientific Center of the Russian Academy of Sciences. 2010, 4: 50–56. [In Russian].
Arakawa A., Lamb V. Computational design of the basic dynamical processes of the UCLA general circulation model. Methods in Computational Physics. V. 17. Еd. J. Chang. San Francisco: Academic Press, 1977: 174–267.
Bueler E. Brown J. Shallow shelf approximation as a «sliding law» in a thermomechanically coupled ice sheet model. Journ. of Geophys. Research. 2009, 114: F03008. doi:10.1029/2008JF001179.
Docquier D., Perichon L., Pattyn F. Representing grounding line dynamics in numerical ice sheet models: Recent advances and outlook. Surveys in Geophysics. 2011, 32: 417–435.
Fowler A.C. A theoretical treatment of sliding of glaciers in absence of cavitation. Philosophical Transactions of the Royal Society: Series A. 1981, 298: 637–685.
Hindmarsh R.C.A. Stability of ice rises and uncoupled marine ice sheets. Annals of Glaciology. 1996, 23: 105–115.
Hindmarsh R.C.A. The role of membrane-like stresses in the determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion.Philosophical Transactions of the Royal Society: Series A. 2006, 364: 1733–1767. doi:10.1098/rsta.2006.1797.
Hutter K. Theoretical Glaciology: material science of ice and the mechanics of glaciers and ice sheets. Dordrecht: D. Reidel, 1983: 510 p.
Huybrechts P. The Antarctic ice sheet and environmental change. Berichte zur Polarforschung. 1992, 99: 241 p.
MacAyeal D.R., Rommelaere V., Huybrechts P. Hulbe C.L., Determann J., Ritz C. An ice-shelf model test based on the Ross ice shelf. Annals of Glaciology. 1996, 23: 46–51.
Oppenheimer M. Global warming and the stability of the West Antarctic Ice Sheet. Nature. 1998, 393: 325–332.
Paterson W.S.B. The physics of glaciers. Oxford: Elsevier, 1994. 480 p.
Pattyn F., Huyghe A., De Brabander S., De Smedt B. Role of transition zones in marine ice sheet dynamics. Journ. of Geophys. Research. 2006, 111: F02004. doi:10.1029/2005JF000.
Pattyn F., Schoof C., Perichon L., Hindmarsh R.C.A., Bueler E., de Fleurian B., Durand G., Gagliardini O., Gladstone R., Goldberg D., Gudmundsson G.H., Huybrechts P., Lee V., Nick F. M., Payne A. J., Pollard D., Rybak O., Saito F., Vieli A. Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP. The Cryosphere. 2012, 6: 573–588.
Pattyn F., Perichon L., Durand G., Favier L., Gagliardini O., Hindmarsh R.C.A., Zwinger T., Abrecht T., Cornford S., Docquier D., Fürst J.J., Goldberg D., Gudmundsson G.H., Humbert A., Hütten M., Huybrechts P., Jouvet G., Kleiner T., Larour E., Martin D., Morlighem M., Payne A.J., Pollard D., Rückamp M., Rybak O., Seroussi H., Thoma M., Wilkens N. Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison. Journ. of Glaciology. 2013, 59: 410–422.
Pollard D., DeConto R. Modeling West Antarctic Ice Sheet growth and collapse through the last 5 million years. Nature. 2009, 458: 329–332. doi:10.1038/nature07809.
Schoof C. Ice sheet grounding line dynamics: steady states, stability and hysteresis. Journ. of Geophys. Research. 2007, 112: F03S28. doi:10.1029/2006JF000664.
Shepherd A., Wingham D., Rignot E. Warm ocean is eroding West Antarctic Ice. Geophys. Research Letters. 2004, 31: L23402. doi:10.1029/2004GL021106.
Shumskiy P.A., Krass M.S. Mathematical models of ice shelves. Journ. of Glaciology. 1976, 17: 419–432.
Thomas R.H., Bentley C.R. A model for Holocene retreat of the West Antarctic ice sheet. Quaternary Research. 1978, 10: 150–170.
Weertman J. Stability of the junction of an ice sheet and an ice shelf. Journ. of Glaciology. 1974, 13: 3–11.
Wilchinsky A.V., Chugunov V.A. Ice-stream-ice-shelf transition: theoretical analysis of two-dimensional flow. Annals of Glaciology. 2000, 30: 153–162.
https://ice-snow.igras.ru/jour/article/view/111
doi:10.15356/2076-6734-2013-3-5-11
op_rights Authors who publish with this journal agree to the following terms:Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Авторы, публикующие статьи в данном журнале, соглашаются на следующее:Авторы сохраняют за собой авторские права и предоставляют журналу право первой публикации работы, которая по истечении 6 месяцев после публикации автоматически лицензируется на условиях Creative Commons Attribution License , что позволяет другим распространять данную работу с обязательным сохранением ссылок на авторов оригинальной работы и оригинальную публикацию в этом журнале.Редакция журнала будет размещать принятую для публикации статью на сайте журнала до выхода её в свет (после утверждения к печати редколлегией журнала). Авторы также имеют право размещать их работу в сети Интернет (например в институтском хранилище или персональном сайте) до и во время процесса рассмотрения ее данным журналом, так как это может привести к продуктивному обсуждению и большему количеству ссылок на данную работу (См. The Effect of Open Access).
op_rightsnorm CC-BY
op_doi https://doi.org/10.15356/2076-6734-2013-3-5-11
https://doi.org/10.15356/2076-6734-2013-3
https://doi.org/10.1029/2008JF001179
https://doi.org/10.1098/rsta.2006.1797
https://doi.org/10.1029/2005JF000
https://doi.org/10.1038/nature07809
https://
container_title Ice and Snow
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spelling ftjias:oai:oai.ice.elpub.ru:article/111 2023-05-15T13:29:49+02:00 The description of grounding line migration in a two-dimensional mathematical model of an ice sheet Описание миграции линии налегания в двумерной математической модели ледникового щита O. Rybak O. E. Rybak A. О. Рыбак О. Е. Рыбак А. 2015-04-02 https://ice-snow.igras.ru/jour/article/view/111 https://doi.org/10.15356/2076-6734-2013-3-5-11 ru rus IGRAS Grosswald M.G. Pokrovnye ledniki kontinentalnykh shelfov. Ice sheets of continental shelves. Moscow: Nauka, 1983: 216 с. [In Russian]. Danilyuk I.I. On the Stephan problem. Uspekhi matematicheskikh nauk. Successes of Mathematical Sciences. 1985, 40, 5 (245):133–185. [In Russian]. Rybak O.O. Modeling of migration of marine ice sheet border in the simple numerical model. Izvestiya vyzov. Severo-Kavkazskiy region. Estestvennye nauki. Proc. of vuzov. North-Caucasian region. Natural Sciences. 2010, 4: 126–130. [In Russian]. Rybak O.O. Migration of marine ice sheet border in the numerical model. Vestnik Yuzhnogo nauchnogo tsentra RAN. Herald of the South Scientific Center of the Russian Academy of Sciences. 2010, 4: 50–56. [In Russian]. Arakawa A., Lamb V. Computational design of the basic dynamical processes of the UCLA general circulation model. Methods in Computational Physics. V. 17. Еd. J. Chang. San Francisco: Academic Press, 1977: 174–267. Bueler E. Brown J. Shallow shelf approximation as a «sliding law» in a thermomechanically coupled ice sheet model. Journ. of Geophys. Research. 2009, 114: F03008. doi:10.1029/2008JF001179. Docquier D., Perichon L., Pattyn F. Representing grounding line dynamics in numerical ice sheet models: Recent advances and outlook. Surveys in Geophysics. 2011, 32: 417–435. Fowler A.C. A theoretical treatment of sliding of glaciers in absence of cavitation. Philosophical Transactions of the Royal Society: Series A. 1981, 298: 637–685. Hindmarsh R.C.A. Stability of ice rises and uncoupled marine ice sheets. Annals of Glaciology. 1996, 23: 105–115. Hindmarsh R.C.A. The role of membrane-like stresses in the determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion.Philosophical Transactions of the Royal Society: Series A. 2006, 364: 1733–1767. doi:10.1098/rsta.2006.1797. Hutter K. Theoretical Glaciology: material science of ice and the mechanics of glaciers and ice sheets. Dordrecht: D. Reidel, 1983: 510 p. Huybrechts P. The Antarctic ice sheet and environmental change. Berichte zur Polarforschung. 1992, 99: 241 p. MacAyeal D.R., Rommelaere V., Huybrechts P. Hulbe C.L., Determann J., Ritz C. An ice-shelf model test based on the Ross ice shelf. Annals of Glaciology. 1996, 23: 46–51. Oppenheimer M. Global warming and the stability of the West Antarctic Ice Sheet. Nature. 1998, 393: 325–332. Paterson W.S.B. The physics of glaciers. Oxford: Elsevier, 1994. 480 p. Pattyn F., Huyghe A., De Brabander S., De Smedt B. Role of transition zones in marine ice sheet dynamics. Journ. of Geophys. Research. 2006, 111: F02004. doi:10.1029/2005JF000. Pattyn F., Schoof C., Perichon L., Hindmarsh R.C.A., Bueler E., de Fleurian B., Durand G., Gagliardini O., Gladstone R., Goldberg D., Gudmundsson G.H., Huybrechts P., Lee V., Nick F. M., Payne A. J., Pollard D., Rybak O., Saito F., Vieli A. Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP. The Cryosphere. 2012, 6: 573–588. Pattyn F., Perichon L., Durand G., Favier L., Gagliardini O., Hindmarsh R.C.A., Zwinger T., Abrecht T., Cornford S., Docquier D., Fürst J.J., Goldberg D., Gudmundsson G.H., Humbert A., Hütten M., Huybrechts P., Jouvet G., Kleiner T., Larour E., Martin D., Morlighem M., Payne A.J., Pollard D., Rückamp M., Rybak O., Seroussi H., Thoma M., Wilkens N. Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison. Journ. of Glaciology. 2013, 59: 410–422. Pollard D., DeConto R. Modeling West Antarctic Ice Sheet growth and collapse through the last 5 million years. Nature. 2009, 458: 329–332. doi:10.1038/nature07809. Schoof C. Ice sheet grounding line dynamics: steady states, stability and hysteresis. Journ. of Geophys. Research. 2007, 112: F03S28. doi:10.1029/2006JF000664. Shepherd A., Wingham D., Rignot E. Warm ocean is eroding West Antarctic Ice. Geophys. Research Letters. 2004, 31: L23402. doi:10.1029/2004GL021106. Shumskiy P.A., Krass M.S. Mathematical models of ice shelves. Journ. of Glaciology. 1976, 17: 419–432. Thomas R.H., Bentley C.R. A model for Holocene retreat of the West Antarctic ice sheet. Quaternary Research. 1978, 10: 150–170. Weertman J. Stability of the junction of an ice sheet and an ice shelf. Journ. of Glaciology. 1974, 13: 3–11. Wilchinsky A.V., Chugunov V.A. Ice-stream-ice-shelf transition: theoretical analysis of two-dimensional flow. Annals of Glaciology. 2000, 30: 153–162. https://ice-snow.igras.ru/jour/article/view/111 doi:10.15356/2076-6734-2013-3-5-11 Authors who publish with this journal agree to the following terms:Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access). Авторы, публикующие статьи в данном журнале, соглашаются на следующее:Авторы сохраняют за собой авторские права и предоставляют журналу право первой публикации работы, которая по истечении 6 месяцев после публикации автоматически лицензируется на условиях Creative Commons Attribution License , что позволяет другим распространять данную работу с обязательным сохранением ссылок на авторов оригинальной работы и оригинальную публикацию в этом журнале.Редакция журнала будет размещать принятую для публикации статью на сайте журнала до выхода её в свет (после утверждения к печати редколлегией журнала). Авторы также имеют право размещать их работу в сети Интернет (например в институтском хранилище или персональном сайте) до и во время процесса рассмотрения ее данным журналом, так как это может привести к продуктивному обсуждению и большему количеству ссылок на данную работу (См. The Effect of Open Access). CC-BY Ice and Snow; Том 53, № 3 (2013); 5-11 Лёд и Снег; Том 53, № 3 (2013); 5-11 2412-3765 2076-6734 10.15356/2076-6734-2013-3 Antarctica Ice Sheet;climatic variations;grounding line;ice flow;ice shelf;mathematical model info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 2015 ftjias https://doi.org/10.15356/2076-6734-2013-3-5-11 https://doi.org/10.15356/2076-6734-2013-3 https://doi.org/10.1029/2008JF001179 https://doi.org/10.1098/rsta.2006.1797 https://doi.org/10.1029/2005JF000 https://doi.org/10.1038/nature07809 https:// 2022-12-20T13:30:26Z Contemporary thinning of the marine-based areas of ice sheets is believed to be the consequence of the grounding line retreat caused mainly by ocean gradual warming beneath the ice shelves. In order to estimate potential contribution of ice sheets into the future sea-level rise grounding line migration must be accurately described in the mathematical models. We incorporated an algorithm based on application of the boundary condition on the mass flux across the grounding line into a two-dimensional ice flow model. In the numerical experiments, externally forced ice sheet returns to its initial equilibrium state after termination of the external forcing (either accumulation rate or sea-level change anomalies). In future, the model will be modified to incorporate buttressing effect. Объём ледниковых щитов, основание которых лежит ниже уровня моря, сокращается главным образом в результате смещения линии налегания в глубь континентальной области предположительно в результате потепления окружающих его вод океана. Для оценки потенциального вклада ледниковых щитов в будущее увеличение уровня моря в математических моделях необходимо как можно точнее описывать процесс миграции линии налегания. В статье рассматривается алгоритм миграции, в основе которого лежит задание граничного условия потока массы на линии налегания. В численных экспериментах ледниковый щит, будучи выведенным из равновесия внешним воздействием, возвращается к своему первоначальному состоянию при прекращении действия внешней силы. После соответствующей доработки алгоритм можно применять в комплексных моделях ледниковых щитов. Article in Journal/Newspaper Annals of Glaciology Antarc* Antarctica Berichte zur Polarforschung Ice Sheet Ice Shelf Ice Shelves Polarforschung The Cryosphere Ice and Snow (E-Journal) Ice and Snow 123 3 5

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