查看“︁冰盖模型”︁的源代码

'''冰盖模型'''是采用[[数值方法]]模拟[[冰盖]]的演变、动力学和热力学过程的[[气候模型]]，包括[[格陵兰冰盖]]、[[南极冰盖]]或北半球[[末次冰期]]大冰盖的模拟。它们被用于研究过去[[大冰期|冰期-间冰期循环]]中冰川的作用、预测未来[[全球变暖]]条件下冰盖衰变等。

== 历史 ==
对冰盖的研究始于18世纪中叶。<ref name=":02"/>自《冰川学杂志》（{{lang|en|''Journal of Glaciology''}}）创刊以来，物理学家一直在发表有关冰川力学的研究成果。<ref name=":02" />
[[File:Barnes_Ice_Cap_432_pan_merge_crop_15_(31109130474).jpg|thumb|巴恩斯冰帽]]
第一个三维冰盖模型被用于{{le|巴恩斯冰帽|Barnes Ice Cap}}模拟。<ref name=":02"/>1988年，首个涵盖[[冰架]]、冰盖/冰架过渡、膜应力梯度、冰川床等静力调整、{{le|基底滑动|Basal sliding}}的热力学耦合模型诞生，并被用于南极冰盖。<ref name=":02" />该模型的空间分辨率为40公里，并分为10个垂直层。<ref name=":02" />

1990年[[IPCC第一次评估报告]]发布时，冰盖并非是气候系统模型的主动组成部分，其演化预测基于全球温度与地表物质平衡之间的关联。<ref name=":6">{{Cite journal |last=Shepherd |first=Andrew |last2=Nowicki |first2=Sophie |date=October 2017 |title=Improvements in ice-sheet sea-level projections |url=http://www.nature.com/articles/nclimate3400 |journal=Nature Climate Change |language=en |volume=7 |issue=10 |page=672–674 |bibcode=2017NatCC...7..672S |doi=10.1038/nclimate3400 |issn=1758-678X |access-date=2023-12-15 |archive-date=2023-05-07 |archive-url=https://web.archive.org/web/20230507053414/https://www.nature.com/articles/nclimate3400 |dead-url=no }}</ref>到1996年[[IPCC第二次评估报告]]发布时，冰盖的二维和三维建模已加入其中。<ref name=":6" />1990年代还涌现出了多种计算模型，并诞生了欧洲冰盖建模计划（{{lang|en|European Ice Sheet Modelling Initiative}}，简称{{lang|en|EISMINT}}）。<ref name=":02">{{Cite journal |last=Blatter |first=Heinz |last2=Greve |first2=Ralf |last3=Abe-Ouchi |first3=Ayako |date=2010 |title=A short history of the thermomechanical theory and modeling of glaciers and ice sheets |journal=Journal of Glaciology |language=en |volume=56 |issue=200 |page=1087–1094 |bibcode=2010JGlac..56.1087B |doi=10.3189/002214311796406059 |issn=0022-1430 |hdl=2115/46879 |doi-access=free |hdl-access=free}}</ref><ref name=":1">{{Cite book|last=Philippe|first=Huybrechts|url=https://epic.awi.de/id/eprint/6776/1/Huy1998b.pdf|title=Report of the Third EISMINT Workshop on Model Intercomparison|year=1997|access-date=2023-12-15|archive-date=2024-04-05|archive-url=https://web.archive.org/web/20240405074706/https://epic.awi.de/id/eprint/6776/1/Huy1998b.pdf|dead-url=no}}</ref>EISMINT在1990年代组织了多次国际研讨会，比较了格陵兰冰盖、南极冰盖、冰架、热力机械、基线（{{lang|en|grounding line}}）等多种模型。<ref name=":1" />

首个集成完整[[斯托克斯定理|斯托克斯动力学]]一阶近似的冰盖模型于2000年代提出。<ref name=":02"/>[[IPCC第四次评估报告]]展示了冰盖模型的快速动力响应预测，并提供冰量显著减少的证据。<ref name=":6"/>

2016年，{{le|耦合模型比对计划|Coupled Model Intercomparison Project
}}第6阶段提出了“”冰盖模型比对计划”（{{lang|en|Ice Sheet Model Intercomparison Project}}），为与冰盖建模相关的所有变量定义了标准。<ref>{{Cite journal |last=Nowicki |first=Sophie M. J. |last2=Payne |first2=Anthony |last3=Larour |first3=Eric |last4=Seroussi |first4=Helene |last5=Goelzer |first5=Heiko |last6=Lipscomb |first6=William |last7=Gregory |first7=Jonathan |last8=Abe-Ouchi |first8=Ayako |last9=Shepherd |first9=Andrew |date=2016-12-21 |title=Ice Sheet Model Intercomparison Project (ISMIP6) contribution to CMIP6 |journal=Geoscientific Model Development |language=en |volume=9 |issue=12 |page=4521–4545 |bibcode=2016GMD.....9.4521N |doi=10.5194/gmd-9-4521-2016 |issn=1991-9603 |pmc=5911933 |pmid=29697697 |doi-access=free}}</ref>该计划促进了冰盖模型在数值与物理方法两方面的改进。<ref>{{Cite journal |last=Pattyn |first=Frank |date=December 2018 |title=The paradigm shift in Antarctic ice sheet modelling |journal=Nature Communications |language=en |volume=9 |issue=1 |page=2728 |bibcode=2018NatCo...9.2728P |doi=10.1038/s41467-018-05003-z |issn=2041-1723 |pmc=6048022 |pmid=30013142}}</ref>

== 模型 ==
=== 冰流 ===
==== 浅冰近似 ====
浅冰近似（{{lang|en|Shallow Ice Approximation}}，简称{{lang|en|SIA}}）是一种模拟冰流的简单方法，无需求解完整的斯托克斯方程。<ref name=":2">{{Cite journal |last=Oerlemans |first=J. |date=December 1982 |title=Glacial cycles and ice-sheet modelling |url=http://link.springer.com/10.1007/BF02423468 |journal=Climatic Change |language=en |volume=4 |issue=4 |page=353–374 |bibcode=1982ClCh....4..353O |doi=10.1007/BF02423468 |issn=0165-0009 |hdl=1874/21024 |s2cid=189889177 |hdl-access=free}}</ref>这一近似方法适用于深宽比较小、滑移很少且冰川床地形简单的冰盖。<ref name=":82">{{Cite web|last=Davies|first=Bethan|date=22 June 2020|title=A hierarchy of ice-sheet models|url=http://www.antarcticglaciers.org/glaciers-and-climate/numerical-ice-sheet-models/hierarchy-ice-sheet-models-introduction/|access-date=2021-10-18|website=AntarcticGlaciers.org|language=en-US|archive-date=2023-10-04|archive-url=https://web.archive.org/web/20231004153314/https://www.antarcticglaciers.org/glaciers-and-climate/numerical-ice-sheet-models/hierarchy-ice-sheet-models-introduction/|dead-url=no}}</ref>浅冰近似假设[[冰盖动力学#基底剪应力|基底剪应力]]在冰盖运动中占主导地位，没有考虑其他许多受力，可以被视为一种零阶模型。<ref name=":82" /><ref name=":9">{{Cite journal |last=Van Den Berg |first=J. |last2=Van De Wal |first2=R.S.W. |last3=Oerlemans |first3=J. |date=2006 |title=Effects of spatial discretization in ice-sheet modelling using the shallow-ice approximation |journal=Journal of Glaciology |language=en |volume=52 |issue=176 |page=89–98 |bibcode=2006JGlac..52...89V |doi=10.3189/172756506781828935 |issn=0022-1430 |doi-access=free}}</ref>它还假设基底剪应力与冰的重力推动力相互平衡。<ref name=":82" />该方法计算成本较低。<ref name=":9" />

==== 浅冰架近似 ====
浅冰架近似（{{lang|en|Shallow Shelf Approximation}}，简称{{lang|en|SSA}}）是另一种模拟冰流的方法，特别适用于描述浮冰的薄膜型流动或者在基底上滑动的冰流。<ref>{{Cite web|title=Two stress balance models: SIA and SSA – PISM, a Parallel Ice Sheet Model 1.2.1 documentation|url=https://pism-docs.org/sphinx/manual/highlevelview/stress-balance-models.html|access-date=2021-10-19|website=pism-docs.org|archive-date=2021-10-19|archive-url=https://web.archive.org/web/20211019054924/https://pism-docs.org/sphinx/manual/highlevelview/stress-balance-models.html|dead-url=no}}</ref>SSA也称为膜模型（{{lang|en|membrane model}}），类似于流体动力学中的自由膜模型。<ref>{{Cite journal |last=Schoof |first=Christian |last2=Hewitt |first2=Ian |date=2013-01-03 |title=Ice-Sheet Dynamics |url=https://www.annualreviews.org/doi/10.1146/annurev-fluid-011212-140632 |journal=Annual Review of Fluid Mechanics |language=en |volume=45 |issue=1 |page=217–239 |bibcode=2013AnRFM..45..217S |doi=10.1146/annurev-fluid-011212-140632 |issn=0066-4189 |access-date=2023-12-15 |archive-date=2022-03-07 |archive-url=https://web.archive.org/web/20220307174359/https://www.annualreviews.org/doi/10.1146/annurev-fluid-011212-140632 |dead-url=no }}</ref>与浅冰近似相反，浅冰架近似适用于轴向力较强的冰流，而不考虑基底剪应力。<ref name=":82"/>该方法也是一种零阶模型。<ref name=":82" />

==== 完整斯托克斯方程 ====
冰是一种粘性流体，因而可以用流体力学中的[[纳维-斯托克斯方程]]来描述，这一控制方程考虑到了冰上的所有受力。<ref name=":2"/>在流速很低时，纳维-斯托克斯方程可以被简化为[[斯托克斯方程]]。其计算成本较高，不易大规模使用，通常只用基线等于特定场景。<ref name=":8">{{Cite web|last=Davies|first=Bethan|date=22 June 2020|title=A hierarchy of ice-sheet models|url=http://www.antarcticglaciers.org/glaciers-and-climate/numerical-ice-sheet-models/hierarchy-ice-sheet-models-introduction/|access-date=2021-10-18|website=AntarcticGlaciers.org|language=en-US|archive-date=2023-10-04|archive-url=https://web.archive.org/web/20231004153314/https://www.antarcticglaciers.org/glaciers-and-climate/numerical-ice-sheet-models/hierarchy-ice-sheet-models-introduction/|dead-url=no}}</ref>
[[File:Illustration-of-the-mass-change-of-ice-sheets-and-key-processes-that-are-specific-to-ice-sheet-model-evaluation-or-forci.png|thumb|冰盖与冰架示意图]]

=== 与其他气候条件的相互作用 ===
冰盖与周围的大气、海洋和冰下地层相互作用。<ref name=":4">{{Cite journal |last=Goelzer |first=Heiko |last2=Robinson |first2=Alexander |last3=Seroussi |first3=Helene |last4=van de Wal |first4=Roderik S.W. |date=December 2017 |title=Recent Progress in Greenland Ice Sheet Modelling |journal=Current Climate Change Reports |language=en |volume=3 |issue=4 |page=291–302 |bibcode=2017CCCR....3..291G |doi=10.1007/s40641-017-0073-y |issn=2198-6061 |pmc=6959375 |pmid=32010550}}</ref>为了建立全面的冰盖模型，所有这些部分都需要被纳入考虑。<ref name=":4" />

基底条件在决定冰盖行为方面发挥着重要作用。然而基底热状态（冰融化或冻结）和基底地形数据都很难获得。<ref name=":4"/>最常用的方法是应用质量守恒约束。<ref name=":4" />

夏季日照是温度变化的主要原因，影响到冰盖的融化速度和质量平衡。<ref name=":5">{{Cite book|last=Ruddiman|first=William|title=Earth's Climate: Past and Future|url=https://archive.org/details/earthsclimatepas03edrudd|publisher=W.H. Freeman and Company|year=2014|isbn=978-1-4292-5525-7|location=New York}}</ref>例如，冰体体积与夏季日照的依赖关系可以表示为<math>{d(I) \over d(t)} = {1 \over T} (S - I)</math>，其中I是冰体体积，<math>{d(I) \over d(t)}</math>是单位时间内体积的变化率，T是冰盖的响应时间，S是日照信号。<ref name=":5" />

空气温度在冰盖模型中也是必需的，因为它可以反映表面融化率和径流速度。<ref name=":10">{{Cite journal |last=Albrecht |first=Torsten |last2=Winkelmann |first2=Ricarda |last3=Levermann |first3=Anders |date=2020-02-14 |title=Glacial-cycle simulations of the Antarctic Ice Sheet with the Parallel Ice Sheet Model (PISM) – Part 1: Boundary conditions and climatic forcing |url=https://tc.copernicus.org/articles/14/599/2020/ |journal=The Cryosphere |language=en |volume=14 |issue=2 |page=599–632 |bibcode=2020TCry...14..599A |doi=10.5194/tc-14-599-2020 |issn=1994-0424 |doi-access=free |access-date=2023-12-15 |archive-date=2024-04-23 |archive-url=https://web.archive.org/web/20240423102254/https://tc.copernicus.org/articles/14/599/2020/ |dead-url=no }}</ref>例如，可以用纬度、海拔高度''h''来估算年平均温度：<ref name=":10" /><math>T_{aml} = T - c_1 * max(h, 1000) - c_2 * lat </math>，其中假设冰架表面温度与海拔1千米处一样寒冷。<ref name=":10" />

降水量与气温直接相关，并取决于冰盖上方和周围的湿度。<ref name=":10" />降水在冰盖融化和堆积过程中也起着重要作用。<ref name=":10" />

=== 崩解 ===
崩解是冰盖模型研究的一个活跃领域。<ref name=":4" />潮汐、基底裂缝、与冰山的碰撞、厚度和温度等不同因素都会影响到崩解过程。<ref>{{Cite journal |last=Alley |first=Richard B. |last2=Horgan |first2=Huw J. |last3=Joughin |first3=Ian |last4=Cuffey |first4=Kurt M. |last5=Dupont |first5=Todd K. |last6=Parizek |first6=Byron R. |last7=Anandakrishnan |first7=Sridhar |last8=Bassis |first8=Jeremy |date=2008-11-28 |title=A Simple Law for Ice-Shelf Calving |url=https://www.science.org/doi/full/10.1126/science.1162543 |journal=Science |volume=322 |issue=5906 |page=1344 |bibcode=2008Sci...322.1344A |doi=10.1126/science.1162543 |pmid=19039129 |s2cid=206514828}}</ref>近年来{{le|海洋冰盖不稳定性|Marine Ice Sheet Instability}}、{{le|海洋冰崖不稳定性|Marine Ice Cliff Instability}}等概念的发展促进了对冰盖崩解过程更全面的理解。<ref>{{Cite journal |last=Pattyn |first=Frank |last2=Favier |first2=Lionel |last3=Sun |first3=Sainan |last4=Durand |first4=Gaël |date=2017-09-01 |title=Progress in Numerical Modeling of Antarctic Ice-Sheet Dynamics |url=https://doi.org/10.1007/s40641-017-0069-7 |journal=Current Climate Change Reports |language=en |volume=3 |issue=3 |page=174–184 |bibcode=2017CCCR....3..174P |doi=10.1007/s40641-017-0069-7 |issn=2198-6061 |s2cid=134517464}}</ref>

== 参见 ==
* [[冰盖动力学]]
* [[海平面上升]]

== 参考文献 ==
{{reflist}}

[[Category:氣候模式]]
[[Category:冰蓋]]
[[Category:冰川学]]