MOSAiC现场观测期间海冰厚度季节变化模拟误差分析

陆洋; 赵海波; 赵嘉炜; 王晓春; 何宜军; 雷瑞波; 喻小勇

doi:10.12284/hyxb2024065

MOSAiC现场观测期间海冰厚度季节变化模拟误差分析

doi: 10.12284/hyxb2024065

陆洋^1,,
赵海波¹,
赵嘉炜¹,
王晓春¹,
何宜军^{1, 2, ,},
雷瑞波³,
喻小勇⁴

1.
南京信息工程大学海洋科学学院，江苏南京 210044
2.
三亚海洋实验室，海南三亚 572024
3.
中国极地研究中心自然资源部极地科学重点实验室，上海 200136
4.
无锡学院大气与遥感学院，江苏无锡 214105

基金项目: 国家重点研发计划（2021YFC2803301，2018YFA0605904）；国家自然科学基金委项目（42376200）；高分辨率南海海洋动力环境要素构建技术研究（SOLZSKY2024005）。

详细信息

作者简介:
陆洋（1995—），男，江苏省泰州市人，博士生，主要从事海冰模拟研究。E-mail：202411090011@nuist.edu.cn

通讯作者:
何宜军（1963—），男，湖南省临湘市人，教授，博士生导师，研究方向为海洋微波遥感。E-mail：yjhe@nuist.edu.cn

中图分类号: P731.15
计量
- 文章访问数: 101
- HTML全文浏览量: 83
- PDF下载量: 30
- 被引次数: 0
出版历程
- 收稿日期: 2024-02-06
- 修回日期: 2024-05-17
- 网络出版日期: 2024-07-12
- 刊出日期: 2024-06-01

Simulation error diagnosis of the seasonal evolution of sea ice thickness during MOSAiC in-situ observation

1.
School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China
2.
SANYA Oceanographic Laboratory, Sanya 572024, China
3.
Key Laboratory of Polar Science, Ministry of Natural Resources, Polar Research Institute of China, Shanghai 200136, China
4.
School of Atmosphere and Remote Sensing, Wuxi University, Wuxi 214105, China

摘要

摘要: 北极气候研究多学科漂流观测计划（Multidisciplinary drifting Observatory for the Study of Arctic Climate, MOSAiC）于2019年10月至2020年9月开展，期间获得了变量完整的大气、海洋、海冰厚度及积雪厚度观测，为海冰模式的发展提供了新的契机。本研究利用两个完整观测时段（2019年11月1日至2020年5月7日、2020年6月26日至7月27日）的大气和海洋强迫场，驱动一维海冰柱模式ICEPACK，模拟了MOSAiC期间海冰厚度的季节演变，同海冰厚度观测进行了对比，并诊断分析了海冰厚度模拟误差的原因。结果表明，在冬春季节，模式可以再现海冰厚度增长过程，但由于模式在春季高估了积雪向海冰的转化及对海冰物质平衡的贡献，模拟的春季海冰厚度偏厚。在夏季期间，2种热力学方案及3种融池方案的组合都表明模式高估了海冰表层的消融过程，导致模拟结束阶段的海冰厚度偏薄。我们的研究表明，使用变量完整的MOSAiC大气和海洋强迫场可以诊断目前海冰模式中的问题，为海冰模式的改进奠定基础。
- MOSAiC观测计划 /
- 热力学方案 /
- 融池方案 /
- ICEPACK海冰模式 /
- 海冰厚度 /
- 积雪深度 /
- 北冰洋
Abstract: The Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) was conducted from October 2019 to September 2020, yielding complete observations of atmosphere, ocean, sea ice thickness (SIT), and snow thickness. These observations provide new opportunities for the development of sea ice models. In this study, the seasonal evolution of SIT during MOSAiC was simulated using the ICEPACK sea ice model and atmospheric and oceanic forcing observations from two periods without missing data (from November 1, 2019 to May 7, 2020; from June 26 to July 27, 2020). The simulation was compared with SIT observation and the reasons for SIT simulation errors were diagnosed. The results show that, in the winter and spring seasons, the model can reproduce the increase in SIT, but overestimates the transition from submerged snow to sea ice and its contribution to sea ice mass balance. This causes the overestimation of SIT in spring. During the summer season, the combination of two thermodynamic schemes and three melt pond schemes indicates that the model overestimates the sea ice surface melting, resulting in thinner SIT at the end of simulation period. Our research demonstrates that the MOSAiC atmospheric and oceanic observation with all variables needed to force ICEPACK can be used to diagnose current sea ice models and very useful for their future improvements.
- MOSAiC /
- thermodynamic scheme /
- melt pond scheme /
- ICEPACK sea ice model /
- sea ice thickness /
- snow thickness /
- Arctic Ocean

HTML全文

图 1 本研究使用的MOSAiC期间大气、海洋、海冰观测点的漂移轨迹

箭头指示了本研究中冬春季节模拟和夏季模拟的起始点，背景为水深

Fig. 1 Drift trajectories of MOSAiC atmospheric, oceanic and sea ice observation stations used in this research

Arrows denotes the starting points of winter-spring simulation and summer simulation in this study. Background color shows the bottomtopography

下载: 全尺寸图片幻灯片

图 2 MOSAiC提供的大气强迫数据序列（2019年10月11日至2020年10月31日）

a. 风速; b. 湿度; c. 气温; d. 短波辐射; e. 长波辐射; f. 降水

Fig. 2 Atmospheric forcing data provided by MOSAiC (October 11, 2019 to October 31, 2020)

a. Wind speed; b. humidity; c. temperature; d. short wave radiation; e. long wave radiation; f. precipitation

下载: 全尺寸图片幻灯片

图 3 MOSAiC提供的海洋强迫数据序列（2019年11月1日至2020年8月5日）

a. 海水温度; b. 海水盐度

Fig. 3 Oceanic forcing data provided by MOSAiC (November 1, 2019 to August 5, 2020)

a. Sea water temperature; b. sea water salinity

下载: 全尺寸图片幻灯片

图 4 2019年11月1日至2020年5月7日海冰厚度模拟与MOSAiC浮标观测对比

Fig. 4 Comparison of simulated sea ice thickness and MOSAiC buoy observations from November 1, 2019 to May 7, 2020

下载: 全尺寸图片幻灯片

图 5 2019年11月1日至2020年5月7日模拟和观测的累积海冰厚度变化（a, b），模拟的逐日海冰厚度变化（c, d）与模拟的逐日雪转换成的海冰厚度（e, f）的比较

a, c, e. 使用BL99热力学方案; b, d, f. 使用Mushy热力学方案

Fig. 5 Simulatedand observed cumulative sea ice thickness growth(a, b), simulated daily changes in sea ice thickness (c, d) and snow converted ice thickness (e, f) from November 1, 2019 to May 7, 2020

a, c, e.Simulation using BL99 thermodynamic scheme; b, d, f.simulation using Mushy thermodynamic scheme

下载: 全尺寸图片幻灯片

图 6 2019年11月1日至2020年5月7日积雪厚度模拟与MOSAiC浮标观测对比

Fig. 6 Comparison of simulated snow thickness and MOSAiC buoy observations from November 1, 2019 to May 7, 2020

下载: 全尺寸图片幻灯片

图 7 2019年11月1日至2020年5月7日模拟和观测的海洋表面辐射对比（向下为正，向上为负）

a. 使用BL99热力学方案的模拟结果; b. 使用Mushy热力学方案的模拟结果

Fig. 7 Comparison of simulated and observed ocean surface radiation from November 1, 2019 to May 7, 2020 (downward radiation is positive, upward radiation is negative)

a. Simulation using BL99 thermodynamic scheme; b. simulation using Mushy thermodynamic scheme

下载: 全尺寸图片幻灯片

图 8 2020年春季海冰表面反照率

Fig. 8 The surface albedo of spring sea ice in 2020

下载: 全尺寸图片幻灯片

图 9 2020年6月26日至7月27日海冰厚度模拟与MOSAiC浮标观测对比

Fig. 9 Comparison of simulated sea ice thickness and MOSAiC buoy observations from June 26 to July 27, 2020

下载: 全尺寸图片幻灯片

图 10 2020年6月26日至7月27日模拟的海冰表面融化、底部融化与观测的对比

图中标注了对应方案组合，RMSE (top)为表面融化的均方根误差，RMSE(bot)为底部融化的均方根误差

Fig. 10 Comparison of simulated and observed sea ice surface and bottom melting from June 26 to July 27, 2020

The specific combination of schemesis marked in the figure. RMSE (top) represents the root mean square error of surface melting and RMSE (bot) represents the root mean square error of bottom melting

下载: 全尺寸图片幻灯片

图 11 2020年6月26日至7月27日模拟的海洋表面辐射与观测的对比

向下为正，向上为负，图中标注了对应方案组合

Fig. 11 Comparison of simulated and observed ocean surface radiation from June 26 to July 27, 2020

Downward radiation is positive, upward radiation is negative. The specific combination of schemes is marked in the figure

下载: 全尺寸图片幻灯片

图 12 2020年6月26日至7月27日模拟的海冰反照率与观测的对比

Fig. 12 Comparison of simulated and observed sea ice albedo from June 26 to July 27, 2020

下载: 全尺寸图片幻灯片

表 1 ICEPACK模式试验设置

Tab. 1 Configuration of ICEPACK model experiments

试验名	模拟时间范围	热力学方案	融池方案	初始冰厚/m	初始雪厚/m	初始融池覆盖率/%	初始融池深度/m
冬春季节模拟	2019-11-01至2020-05-07	BL99	TOPO	0.44	0.12	0	0.0
		Mushy	TOPO	0.44	0.12	0	0.0
夏季模拟	2020-06-26至2020-07-27	BL99	CESM	1.60	0.06	10	0.1
			TOPO	1.60	0.06	10	0.1
			LVL	1.60	0.06	10	0.1
		Mushy	CESM	1.60	0.06	10	0.1
			TOPO	1.60	0.06	10	0.1
			LVL	1.60	0.06	10	0.1

下载: 导出CSV

表 2 海冰厚度模拟与观测之间的均方根误差

Tab. 2 Root mean square error between simulation and observation of sea ice thickness

融池方案	BL99热力学方案	Mushy热力学方案
CESM	0.070 m	0.066 m
TOPO	0.074 m	0.088 m
LVL	0.067 m	0.066 m

下载: 导出CSV

表 3 夏季模拟结束时累积表面融化、底部融化模拟与观测之间的偏差（正值代表模式高估，负值代表模式低估）

Tab. 3 Bias between simulation and observation of cumulative sea ice surface and bottom melting at the end of the summer simulation (positive values represent overestimation of the model, while negative values represent underestimation of the model)

方案组合	表面融化偏差/m	底部融化偏差/m
BL99 + CESM	0.268	−0.137
BL99 + TOPO	0.201	−0.158
BL99 + LVL	0.218	−0.134
Mushy + CESM	0.183	−0.114
Mushy + TOPO	0.110	−0.127
Mushy + LVL	0.235	−0.117

下载: 导出CSV

表 4 夏季模拟与观测的净长波辐射、净短波辐射的平均值（向下为正，向上为负）

Tab. 4 The summer average of simulated and observed net longwave radiation and net shortwave radiation (downward radiation is positive, upward radiation is negative)

方案组合	净长波辐射/(W/m²)	净短波辐射/(W/m²)
BL99 + CESM	11.476	97.085
BL99 + TOPO	19.168	88.846
BL99 + LVL	9.089	91.306
Mushy + CESM	13.731	84.542
Mushy + TOPO	15.316	74.751
Mushy + LVL	12.322	89.113
MOSAiC	-8.447	76.539

下载: 导出CSV

参考文献(55)

[1]	WMO. WMO Sea-Ice Nomenclature[R]. Geneva: WMO, 2014.
[2]	Comiso J C, Parkinson C L, Gersten R, et al. Accelerated decline in the Arctic sea ice cover[J]. Geophysical Research Letters, 2008, 35(1): L01703.
[3]	Kwok R, Rothrock D A. Decline in Arctic sea ice thickness from submarine and ICESat records: 1958–2008[J]. Geophysical Research Letters, 2009, 36(15): L15501.
[4]	Maslanik J A, Fowler C, Stroeve J, et al. A younger, thinner Arctic ice cover: increased potential for rapid, extensive sea-ice loss[J]. Geophysical Research Letters, 2007, 34(24): L24501.
[5]	Parkinson C L, Digirolamo N E. Sea ice extents continue to set new records: Arctic, Antarctic, and global results[J]. Remote Sensing of Environment, 2021, 267: 112753. doi: 10.1016/j.rse.2021.112753
[6]	Stroeve J C, Markus T, Boisvert L, et al. Changes in Arctic melt season and implications for sea ice loss[J]. Geophysical Research Letters, 2014, 41(4): 1216−1225. doi: 10.1002/2013GL058951
[7]	Kim Y H, Min S K, Gillett N P, et al. Observationally-constrained projections of an ice-free Arctic even under a low emission scenario[J]. Nature Communications, 2023, 14(1): 3139. doi: 10.1038/s41467-023-38511-8
[8]	Walter N M, National S, Julienne S. An updated assessment of the changing arctic sea ice cover[J]. Oceanography, 2022, 35(3/4): 10−19.
[9]	Lindsay R, Schweiger A. Arctic sea ice thickness loss determined using subsurface, aircraft, and satellite observations[J]. The Cryosphere, 2015, 9(1): 269−283. doi: 10.5194/tc-9-269-2015
[10]	Kwok R. Arctic sea ice thickness, volume, and multiyear ice coverage: losses and coupled variability (1958–2018)[J]. Environmental Research Letters, 2018, 13(10): 105005. doi: 10.1088/1748-9326/aae3ec
[11]	Hibler W D. Modeling a variable thickness sea ice cover[J]. Monthly Weather Review, 1980, 108(12): 1943−1973. doi: 10.1175/1520-0493(1980)108<1943:MAVTSI>2.0.CO;2
[12]	邱博, 张录军, 储敏, 等. 气候系统模式对于北极海冰模拟分析[J]. 极地研究, 2015, 27(1): 47−55. Qiu Bo, Zhang Lujun, Chu Min, et al. Performance analysis of Arctic sea ice simulation in climate system models[J]. Chinese Journal of Polar Research, 2015, 27(1): 47−55.
[13]	朱清照, 闻新宇. 中国CMIP5模式对未来北极海冰的模拟偏差[J]. 气候变化研究进展, 2016, 12(4): 276−285. Zhu Qingzhao, Wen Xinyu. Performance of Chinese climate models in simulating Arctic sea-ice in CMIP5 experiments[J]. Climate Change Research, 2016, 12(4): 276−285.
[14]	Liu Jiping, Song Mirong, Horton R M, et al. Reducing spread in climate model projections of a September ice-free Arctic[J]. Proceedings of the National Academy of Sciences of the United States of America, 2013, 110(31): 12571−12576.
[15]	Zhang Jinlun, Rothrock D A. Modeling global sea ice with a thickness and enthalpy distribution model in generalized curvilinear coordinates[J]. Monthly Weather Review, 2003, 131(5): 845−861. doi: 10.1175/1520-0493(2003)131<0845:MGSIWA>2.0.CO;2
[16]	Chen Lanying, Wu Renhao, Shu Qi, et al. The Arctic sea ice thickness change in CMIP6’s historical simulations[J]. Advances in Atmospheric Sciences, 2023, 40(12): 2331−2343. doi: 10.1007/s00376-022-1460-4
[17]	王梓琦. 我国CMIP6模式北极海冰厚度比较及误差来源分析[D]. 南京: 南京信息工程大学, 2023. Wang Ziqi. Comparison and error source analysis of Arctic sea ice thickness in China’s CMIP6 models[D]. Nanjing: Nanjing University of Information Science and Technology, 2023.
[18]	Hunke E, Allard R, Bailey D A, et al. CICE-Consortium/CICE: CICE version 6.0. 0[EB/OL]. https://doi.org/10.5281/zenodo.1900639,2018-10-04/2024-02-04.
[19]	Long Mengyuan, Zhang Lujun, Hu Siyu, et al. Multi-aspect assessment of CMIP6 models for Arctic sea ice simulation[J]. Journal of Climate, 2021, 34(4): 1515−1529. doi: 10.1175/JCLI-D-20-0522.1
[20]	Xu Mengliu, Li Junde. Assessment of sea ice thickness simulations in the CMIP6 models with CICE components[J]. Frontiers in Marine Science, 2023, 10: 1223772. doi: 10.3389/fmars.2023.1223772
[21]	Hunke E, Allard R, Bailey D, et al. CICE Consortium/Icepack version 1.1.0[EB/OL]. http://doi.org/10.5281/zenodo.1891650,2018-10-03/2024-02-04.
[22]	Gu Fengguan, Yang Qinghua, Kauker F, et al. The sensitivity of landfast sea ice to atmospheric forcing in single-column model simulations: a case study at Zhongshan Station, Antarctica[J]. The Cryosphere, 2022, 16(5): 1873−1887. doi: 10.5194/tc-16-1873-2022
[23]	曹淑涛, 苏洁, 李涛, 等. 基于Icepack海冰柱模式的融池反照率模拟研究[J]. 海洋学报, 2021, 43(7): 63−74. Cao Shutao, Su Jie, Li Tao, et al. Study on melt pond albedo based on Icepack sea ice column model[J]. Haiyang Xuebao, 2021, 43(7): 63−74.
[24]	Plante M, Lemieux J F, Tremblay L B, et al. Using icepack to reproduce ice mass balance buoy observations in landfast ice: improvements from the mushy-layer thermodynamics[J]. The Cryosphere, 2024, 18(4): 1685−1708. doi: 10.5194/tc-18-1685-2024
[25]	肖峰, 张胜凯, 李佳星, 等. 基于CryoSat-2卫星测高数据的北极海冰厚度变化研究[J]. 中国科学: 地球科学, 2021, 51(7): 1059-1069. Xiao Feng, Zhang Shengkai, Li Jiaxing, et al. Arctic sea ice thickness variations from CryoSat-2 satellite altimetry data[J]. Science China Earth Sciences, 2021, 64(7): 1080-1089.
[26]	Shupe M D, Rex M, Blomquist B, et al. Overview of the MOSAiC expedition: atmosphere[J]. Elementa: Science of the Anthropocene, 2022, 10(1): 00060. doi: 10.1525/elementa.2021.00060
[27]	Nicolaus M, Perovich D K, Spreen G, et al. Overview of the MOSAiC expedition: snow and sea ice[J]. Elementa: Science of the Anthropocene, 2022, 10(1): 000046. doi: 10.1525/elementa.2021.000046
[28]	Rabe B, Heuzé C, Regnery J, et al. Overview of the MOSAiC expedition: physical oceanography[J]. Elementa: Science of the Anthropocene, 2022, 10(1): 00062. doi: 10.1525/elementa.2021.00062
[29]	雷瑞波. 我国参与MOSAiC气候多学科漂流冰站计划的概况[J]. 极地研究, 2020, 32(4): 596−600. Lei Ruibo. Contributions to the MOSAIC from China[J]. Chinese Journal of Polar Research, 2020, 32(4): 596−600.
[30]	Wagner D N, Shupe M D, Cox C, et al. Snowfall and snow accumulation during the MOSAiC winter and spring seasons[J]. The Cryosphere, 2022, 16(6): 2373−2402. doi: 10.5194/tc-16-2373-2022
[31]	Rinke A, Cassano J J, Cassano E N, et al. Meteorological conditions during the MOSAiC expedition: normal or anomalous?[J]. Elementa: Science of the Anthropocene, 2021, 9(1): 00023. doi: 10.1525/elementa.2021.00023
[32]	Hoppmann M, Kuznetsov I, Fang Y C, et al. Mesoscale observations of temperature and salinity in the Arctic Transpolar Drift: a high-resolution dataset from the MOSAiC Distributed Network[J]. Earth System Science Data, 2022, 14(11): 4901−4921. doi: 10.5194/essd-14-4901-2022
[33]	Jackson K, Wilkinson J, Maksym T, et al. A novel and low-cost sea ice mass balance buoy[J]. Journal of Atmospheric and Oceanic Technology, 2013, 30(11): 2676−2688. doi: 10.1175/JTECH-D-13-00058.1
[34]	赵杰臣, 杨清华, 程斌, 等. 基于温度链浮标获取南极普里兹湾积雪和固定冰厚度的研究[J]. 海洋学报, 2017, 39(11): 115−127. Zhao Jiechen, Yang Qinghua, Cheng Bin, et al. Snow and land-fast sea ice thickness derived from thermistor chain buoy in the Prydz Bay, Antarctic[J]. Haiyang Xuebao, 2017, 39(11): 115−127.
[35]	郝光华, 杨清华, 赵杰臣, 等. 2016年南极中山站固定冰冰厚观测分析[J]. 海洋学报, 2019, 41(9): 26−39. Hao Guanghua, Yang Qinghua, Zhao Jiechen, et al. Observation and analysis of landfast ice arounding Zhongshan Station, Antarctic in 2016[J]. Haiyang Xuebao, 2019, 41(9): 26−39.
[36]	Lei Ruibo, Cheng B, Hoppmann M, et al. Seasonality and timing of sea ice mass balance and heat fluxes in the Arctic transpolar drift during 2019–2020[J]. Elementa: Science of the Anthropocene, 2022, 10(1): 000089. doi: 10.1525/elementa.2021.000089
[37]	Webster M A, Holland M, Wright N C, et al. Spatiotemporal evolution of melt ponds on Arctic sea ice: MOSAiC observations and model results[J]. Elementa: Science of the Anthropocene, 2022, 10(1): 000072. doi: 10.1525/elementa.2021.000072
[38]	Niehaus H, Spreen G, Birnbaum G, et al. Sea ice melt pond fraction derived from Sentinel-2 data: along the MOSAiC drift and Arctic-wide[J]. Geophysical Research Letters, 2023, 50(5): e2022GL102102. doi: 10.1029/2022GL102102
[39]	Oggier M, Salganik E, Whitmore L, et al. First-year sea-ice salinity, temperature, density, oxygen and hydrogen isotope composition from the main coring site (MCS-FYI) during MOSAiC legs 1 to 4 in 2019/2020[EB/OL]. https://doi.pangaea.de/10.1594/PANGAEA.956732,2024-02-04.
[40]	Thorndike A S, Rothrock D A, Maykut G A, et al. The thickness distribution of sea ice[J]. Journal of Geophysical Research, 1975, 80(33): 4501−4513. doi: 10.1029/JC080i033p04501
[41]	Semtner Jr A J. A model for the thermodynamic growth of sea ice in numerical investigations of climate[J]. Journal of Physical Oceanography, 1976, 6(3): 379−389. doi: 10.1175/1520-0485(1976)006<0379:AMFTTG>2.0.CO;2
[42]	Bitz C M, Lipscomb W H. An energy-conserving thermodynamic model of sea ice[J]. Journal of Geophysical Research: Oceans, 1999, 104(C7): 15669−15677. doi: 10.1029/1999JC900100
[43]	Turner A K, Hunke E C, Bitz C M. Two modes of sea-ice gravity drainage: a parameterization for large-scale modeling[J]. Journal of Geophysical Research: Oceans, 2013, 118(5): 2279−2294. doi: 10.1002/jgrc.20171
[44]	Holland M M, Bailey D A, Briegleb B P, et al. Improved sea ice shortwave radiation physics in CCSM4: the impact of melt ponds and aerosols on Arctic sea ice[J]. Journal of Climate, 2012, 25(5): 1413−1430. doi: 10.1175/JCLI-D-11-00078.1
[45]	Flocco D, Feltham D L. A continuum model of melt pond evolution on Arctic sea ice[J]. Journal of Geophysical Research: Oceans, 2007, 112(C8): C08016.
[46]	Flocco D, Feltham D L, Turner A K. Incorporation of a physically based melt pond scheme into the sea ice component of a climate model[J]. Journal of Geophysical Research: Oceans, 2010, 115(C8): C08012.
[47]	Flocco D, Schroeder D, Feltham D L, et al. Impact of melt ponds on Arctic sea ice simulations from 1990 to 2007[J]. Journal of Geophysical Research: Oceans, 2012, 117(C9): C09032.
[48]	Flocco D, Feltham D L, Bailey E, et al. The refreezing of melt ponds on Arctic sea ice[J]. Journal of Geophysical Research: Oceans, 2015, 120(2): 647−659. doi: 10.1002/2014JC010140
[49]	Hunke E C, Hebert D A, Lecomte O. Level-ice melt ponds in the Los Alamos sea ice model, CICE[J]. Ocean Modelling, 2013, 71: 26−42. doi: 10.1016/j.ocemod.2012.11.008
[50]	Huwald H, Tremblay L B, Blatter H. Reconciling different observational data sets from Surface Heat Budget of the Arctic Ocean (SHEBA) for model validation purposes[J]. Journal of Geophysical Research: Oceans, 2005, 110(C5): C05009.
[51]	张慧敏, 金梅兵, 祁第. 常数和变化积雪密度方案诊断计算积雪厚度的敏感性研究[J]. 海洋学报, 2022, 44(7): 47−57. Zhang Huimin, Jin Meibing, Qi Di. Sensitivity study of constant and variable snow density schemes in diagnosing and calculating snow depth[J]. Haiyang Xuebao, 2022, 44(7): 47−57.
[52]	尹豪, 苏洁, Cheng Bin. 积雪密度演变对北极积雪深度模拟的影响[J]. 海洋学报, 2021, 43(7): 75−89. Yin Hao, Su Jie, Cheng Bin. The effect of snow density evolution on modelled snow depth in the Arctic[J]. Haiyang Xuebao, 2021, 43(7): 75−89.
[53]	Turner A K, Hunke E C. Impacts of a mushy-layer thermodynamic approach in global sea-ice simulations using the CICE sea-ice model[J]. Journal of Geophysical Research: Oceans, 2015, 120(2): 1253−1275. doi: 10.1002/2014JC010358
[54]	Brandt R E, Warren S G, Worby A P, et al. Surface albedo of the Antarctic sea ice zone[J]. Journal of Climate, 2005, 18(17): 3606−3622. doi: 10.1175/JCLI3489.1
[55]	杨清华, 刘骥平, 孙启振, 等. 2010年春季南极固定冰反照率变化特征及其影响因子[J]. 地球物理学报, 2013, 56(7): 2177−2184. doi: 10.6038/cjg20130705 Yang Qinghua, Liu Jiping, Sun Qizhen, et al. Surface albedo variation and its influencing factors over costal fast ice around Zhongshan station, Antarcticain austral spring of 2010[J]. Chinese Journal of Geophysics, 2013, 56(7): 2177−2184. doi: 10.6038/cjg20130705