Abstract
We study the impact of synthesizing ocean and sea ice concentration data with a global, eddying coupled sea ice-ocean configuration of the Massachusetts Institute of Technology general circulation model with the goal of reproducing the 2004 three-dimensional time-evolving ice-ocean state. This work builds on the state estimation framework developed in the Estimating the Circulation and Climate of the Ocean consortium by seeking a reconstruction of the global sea ice-ocean system that is simultaneously consistent with (1) a suite of in situ and remotely-sensed ocean and ice data and (2) the physics encoded in the numerical model. This dual consistency is successfully achieved here by adjusting only the model’s initial hydrographic state and its atmospheric boundary conditions such that misfits between the model and data are minimized in a least-squares sense. We show that synthesizing both ocean and sea ice concentration data is required for the model to adequately reproduce the observed details of the sea ice annual cycle in both hemispheres. Surprisingly, only modest adjustments to our first-guess atmospheric state and ocean initial conditions are necessary to achieve model-data consistency, suggesting that atmospheric reanalysis products remain a leading source of errors for sea ice-ocean model hindcasts and reanalyses. The synthesis of sea ice data is found to ameliorate misfits in the high latitude ocean, especially with respect to upper ocean stratification, temperature, and salinity. Constraining the model to sea ice concentration modestly reduces ICESat-derived Arctic ice thickness errors by improving the temporal and spatial evolution of seasonal ice. Further increases in the accuracy of global sea ice thickness in the model likely require the direct synthesis of sea ice thickness data.
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Notes
Formally interpreting the normalized cost as the Chi-square metric requires knowledge of the number of degrees of freedom associated with the fitting the nonlinear OGCM to the data. The number of degrees of freedom for this problem is unknown and the common assumption that the number of degrees of freedom issue can be ignored when evaluating state estimate consistency appears to be a common ad hoc assumption within the community.
References
Adcroft A, Campin JM, Hill C, Marshall J (2004) Implementation of an atmosphere-ocean general circulation model on the expanded spherical cube. Mon Weather Rev 132(12):2845–2863. doi:10.1175/MWR2823.1
Antonov JI, Seidov D, Boyer TP, Locarnini RA, Mishonov AV, Garcia HE, Baranova OK, Zweng MM, Johnson DR (2010) World Ocean Atlas 2009. In: Levitus S (ed) Salinity, NOAA Atlas NESDIS 69, vol 2. U.S. Government Printing Office, Washington, D.C., p 184
Bertino L, Lisaæter K (2008) The TOPAZ monitoring and prediction system for the Atlantic and Arctic Oceans. J Oper Oceanogr 1(2):15–19. doi:10.1080/1755876X.2008.11020098
Bitz CM, Holland MM, Hunke EC, Moritz RE (2005) Maintenance of the sea-ice edge. J Clim 18(15):2903–2921. doi:10.1175/JCLI3428.1
Bitz CM, Gent PR, Woodgate RA, Holland MM, Lindsay R (2006) The influence of sea ice on ocean heat uptake in response to increasing \(\text{ CO }_2\). J Clim 19:2437–2450. doi:10.1175/JCLI3756.1
Boé J, Hall A, Qu X (2009) September sea-ice cover in the Arctic Ocean projected to vanish by 2100. Nat Geosci 2(5):341–343. doi:10.1038/natg467
Chaudhuri AH, Ponte RM, Nguyen AT (2014) A comparison of atmospheric reanalysis products for the Arctic Ocean and implications for uncertainties in air–sea fluxes. J Clim 27(14):5411–5421. doi:10.1175/JCLI-D-13-00424.1
Comiso J (2000, updated 2014) Bootstrap sea ice concentrations from Nimbus-7 SMMR and DMSP SSM/I-SSMIS. Version 2. [Daily Jan 1, 2004–Dec 31, 2004]. Digital media, NASA DAAC at the National Snow and Ice Data Center, Boulder, Colorado USA
Condron A, Winsor P (2011) A subtropical fate awaited freshwater discharged from glacial Lake Agassiz. Geophys Res Lett 38(3):L03,705. doi:10.1029/2010GL046011
Condron A, Windsor P, Hill C, Menemenlis D (2009) Simulated response of the Arctic freshwater budget to extreme NAO wind forcing. J Clim 22(9):2422–2437. doi:10.1175/2008JCLI2626.1
de Lavergne C, Palter JB, Galbraith ED, Bernardello R, Marinov I (2014) Cessation of deep convection in the open Southern Ocean under anthropogenic climate change. Nat Clim Change 4(4):278–282. doi:10.1038/NCLIMATE2132
Duffy P, Eby M, Weaver AJ (1999) Effects of sinking of salt rejected during formation of sea ice on results of an ocean-atmosphere-sea ice climate model. Geophys Res Lett 26(12):1739–1742. doi:10.1029/1999GL900286
Fenty I, Heimbach P (2013a) Coupled sea ice–ocean state estimation in the Labrador Sea and Baffin Bay. J Phys Oceanogr 43:884–904. doi:10.1175/JPO-D-12-065.1
Fenty I, Heimbach P (2013b) Hydrographic preconditioning for seasonal sea ice anomalies in the Labrador Sea. J Phys Oceanogr 43:863–883. doi:10.1175/JPO-D-12-064.1
Forget G (2010) Mapping ocean observations in a dynamical framework: a 2004–06 ocean atlas. J Phys Oceanogr 40:1201–1221. doi:10.1175/2009JPO4043.1
Forget G, Wunsch C (2007) Estimated global hydrographic variability. J Phys Oceanogr 37:1997–2008. doi:10.1175/JPO3072.1
Forget G, Campin JM, Heimbach P, Hill CN, Ponte RM, Wunsch C (2015) ECCO version 4: an integrated framework for non-linear inverse modeling and global ocean state estimation. Geosci Model Dev Discuss 8:3653–3743. doi:10.5194/gmdd-8-3653-2015
Fukumori I, Wang O, Llovel W, Fenty I, Forget G (2015) A near-uniform fluctuation of ocean bottom pressure and sea level across the deep ocean basins of the Arctic Ocean and the Nordic Seas. Prog Oceanogr 134:152–172. doi:10.1016/j.pocean.2015.01.013
Giering R, Kaminski T, Slawig T (2005) Generating efficient derivative code with TAF: adjoint and tangent linear Euler flow around an airfoil. Future Gener Comput Syst 21(8):1345–1355. doi:10.1016/j.future.2004.11.003
Griffies SM, Biastoch A, Böning C, Bryan F, Danabasoglu G, Chassignet EP, England MH, Gerdes R, Haak H, Hallberg RW, Hazeleger W, Jungclaus J, Large WG, Madec G, Pirani A, Samuels BL, Scheinert M, Gupta AS, Severijns CA, Simmons HL, Treguier AM, Winton M, Yeager S, Yin J (2009) Coordinated ocean-ice reference experiments (COREs). Ocean Model 26(1–2):1–46. doi:10.1016/j.ocemod.2008.08.007
Heimbach P, Losch M (2012) Adjoint sensitivities of sub-ice shelf melt rates to ocean circulation under Pine Island Ice Shelf, West Antarctica. Ann Glaciol 53(60):59–69. doi:10.3189/2012/AoG60A025
Heimbach P, Menemenlis D, Losch M, Campin JM, Hill C (2010) On the formulation of sea-ice models. Part 2: lessons from multi-year adjoint sea ice export sensitivities through the Canadian Arctic Archipelago. Ocean Model 33(1–2):145–158. doi:10.1016/j.ocemod.2010.02.002
Hibler WD (1979) A dynamic thermodynamic sea ice model. J Phys Oceanogr 9(4):815–846. doi:10.1175/1520-0485(1979)009<0815:ADTSIM>2.0.CO;2
Hibler WD (1980) Modeling a variable thickness sea ice cover. Mon Weather Rev 108(12):1943–1973. doi:10.1175/1520-0493(1980)108<1943:MAVTSI>2.0.CO;2
Holland PR, Kwok R (2012) Wind-driven trends in Antarctic sea-ice drift. Nat Geosci 5(12):872–875. doi:10.1038/natg1627
Howat IM, Box JE, Ahn Y, Herrington A, McFadden EM (2010) Seasonal variability in the dynamics of marine-terminating outlet glaciers in Greenland. J Glaciol 56(198):601–613. doi:10.3189/002214310793146232
Isaac T, Petra N, Stadler G, Ghattas O (2015) Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet. J Comput Phys 296:348–368. doi:10.1016/j.jcp.2015.04.047
Jahn A, Holland MM (2013) Implications of Arctic sea ice changes for North Atlantic deep convection and the meridional overturning circulation in CCSM4-CMIP5 simulations. Geophys Res Lett 40(6):1206–1211. doi:10.1002/grl.50183
Jakobson E, Vihma T, Palo T, Jakobson L, Keernik H, Jaagus J (2012) Validation of atmospheric reanalyses over the central Arctic Ocean. Geophys Res Lett 39(10):L10,802. doi:10.1029/2012GL051591
Johnson M, Proshutinsky A, Aksenov Y, Nguyen AT, Lindsay R, Haas C, Zhang J, Diansky N, Kwok R, Maslowski W, Häkkinen S, Ashik I, de Cuevas B (2012) Evaluation of Arctic sea ice thickness simulated by Arctic Ocean Model Intercomparison Project models. J Geophys Res Oceans 117(C3):C00D13. doi:10.1029/2011JC007257
Kalmikov AG, Heimbach P (2014) A Hessian-based method for uncertainty quantification in global ocean state estimation. SIAM J Sci Comput 36(5):S267–S295. doi:10.1137/130925311
Köhl A (2015) Evaluation of the GECCO2 ocean synthesis: transports of volume, heat and freshwater in the Atlantic. Q J R Meteorol Soc 141(686):166–181. doi:10.1002/qj.2347
Koldunov NV, Koehl A, Stammer D (2013) Properties of adjoint sea ice sensitivities to atmospheric forcing and implications for the causes of the long term trend of Arctic sea ice. Clim Dyn 41(2):227–241. doi:10.1007/s00382-013-1816-7
Kwok R, Cunningham GF (2008) ICESat over Arctic sea ice: estimation of snow depth and ice thickness. J Geophys Res Oceans 113(C8):C08,010. doi:10.1029/2008JC004753
Kwok R, Cunningham GF (2015) Variability of Arctic sea ice thickness and volume from CryoSat-2. Phil Trans R Soc A 373(2045):20140157. doi:10.1098/rsta.2014.0157
Kwok R, Maksym T (2014) Snow depth of the Weddell and Bellingshausen sea ice covers from IceBridge surveys in 2010 and 2011: an examination. J Geophys Res Oceans 119(7):4141–4167. doi:10.1002/2014JC009943
Kwok R, Cunningham GF, Pang SS (2004a) Fram Strait sea ice outflow. J Geophys Res 109(C1):C01,009. doi:10.1029/2003JC001785
Kwok R, Zwally HJ, Yi D (2004b) Icesat observations of arctic sea ice: a first look. Geophys Res Lett 31(16):L16,401. doi:10.1029/2004GL020309
Kwok R, Cunningham G, Zwally H, Yi D (2006) ICESat over Arctic sea ice: interpretation of altimetric and reflectivity profiles. J Geophys Res Oceans 111(C6):C06,006. doi:10.1029/2005JC003175
Kwok R, Hunke E, Maslowski W, Menemenlis D, Zhang J (2008) Variability of sea ice simulations assessed with RGPS kinematics. J Geophys Res 131(C11):C11,012. doi:10.1029/2008JC004783
Kwok R, Cunningham GF, Wensnahan M, Rigor I, Zwally HJ, Yi D (2009) Thinning and volume loss of Arctic sea ice: 2003–2008. J Geophys Res 114(C7):C07,005. doi:10.1029/2009JC005312
Large W, Yeager S (2004) Diurnal to decadal global forcing for ocean and sea-ice models: thedata sets and flux climatologies. NCAR technical note: NCAR/TN-460+STR, CGD Division of the National Center for Atmospheric Research
Large W, McWilliams J, Doney S (1994) Oceanic vertical mixing: a review and a model with nonlocal boundary layer parameterization. Rev Geophys 32(4):363–403. doi:10.1029/94RG01872
Lindsay R (2010) New unified sea ice thickness climate data record. EOS Trans AGU 91(44):405–406. doi:10.1029/2010EO440001
Lindsay R, Schweiger A (2015) Arctic sea ice thickness loss determined using subsurface, aircraft, and satellite observations. The Cryosphere 9(1):269–283. doi:10.5194/tc-9-269-2015
Lindsay R, Haas C, Hendricks S, Hunkeler P, Kurtz N, Paden J, Panzer B, Sonntag J, Yungel J, Zhang J (2012) Seasonal forecasts of Arctic sea ice initialized with observations of ice thickness. Geophys Res Lett 39(21):L21,502. doi:10.1029/2012GL053576
Lindsay RW, Zhang J (2006) Assimilation of ice concentration in an ice-ocean model. J Atmos Ocean Technol 23(5):742–749. doi:10.1175/JTECH1871.1
Liu J, Curry JA, Rossow WB, Key JR, Wang X (2005) Comparison of surface radiative flux data sets over the Arctic Ocean. J Geophys Res Oceans 110(C2):C02,015. doi:10.1029/2004JC002381
Locarnini RA, Mishonov AV, Antonov JI, Boyer TP, Garcia HE, Baranova OK, Zweng MM, Johnson DR (2010) World Ocean Atlas 2009. In: Levitus S (ed) Temperature, NOAA Atlas NESDIS 69, vol 1. U.S. Government Printing Office, Washington, D.C., p 184
Losch M, Heimbach P (2007) Adjoint sensitivity of an ocean general circulation model to bottom topography. J Phys Oceanogr 37(2):377–393. doi:10.1175/JPO3017.1
Losch M, Herlufsen S, Timmermann R (2006) Effects of heterogeneous surface boundary conditions on parameterized oceanic deep convection. Ocean Model 13(2):156–165. doi:10.1016/j.ocemod.2005.12.003
Losch M, Menemenlis D, Campin JM, Heimbach P, Hill C (2010) On the formulation of sea-ice models. Part 1: effects of different solver implementations and parameterizations. Ocean Model 33(1–2):129–144. doi:10.1016/j.ocemod.2009.12.008
Manizza M, Follows MJ, Dutkiewicz S, Menemenlis D, McClelland JW, Hill CN, Peterson BJ, Key RM (2011) A model of the Arctic Ocean carbon cycle. J Geophys Res Oceans 116(C12):C12,020. doi:10.1029/2011JC006998
Marshall J, Adcroft A, Hill C, Perelman L, Heisey C (1997a) A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J Geophys Res Oceans 102(C3):5753–5766. doi:10.1029/96JC02775
Marshall J, Hill C, Perelman L, Adcroft A (1997b) Hydrostatic, quasi-hydrostatic, and nonhydrostatic ocean modeling. J Geophys Res Oceans 102(C3):5733–5752
Mazloff M, Heimbach P, Wunsch C (2010) An eddy-permitting Southern Ocean state estimate. J Phys Oceanogr 40(5):880–899. doi:10.1175/2009JPO4236.1
McGuire A (2010) An analysis of the carbon balance of the Arctic Basin from 1997 to 2006. Tellus B 62(5):455–474. doi:10.1111/j.1600-0889.2010.00497.x
Menemenlis D, Fukumori I, Lee T (2005) Using Green’s functions to calibrate an ocean general circulation model. Mon Weather Rev 133(5):1224–1240. doi:10.1175/MWR2912.1
Menemenlis D, Campin J, Heimbach P, Hill C, Lee T, Nguygen A, Schodlock M, Zhang H (2008) ECCO2: high resolution global ocean and sea ice data synthesis. Mercat Ocean Q Newsl 31:13–21
Miller MD, Adkins JF, Menemenlis D, Schodlok MP (2012) The role of ocean cooling in setting glacial southern source bottom water salinity. Paleoceanography 27(3):PA3207. doi:10.1029/2012PA002297
Naeije M, Schrama E, Scharroo R (2000) The radar altimeter database system project rads. In: Geoscience and remote sensing symposium, 2000. Proceedings of IGARSS 2000. IEEE 2000 international, IEEE, vol 2, pp 487–490
Nguyen A, Menemenlis D, Kwok R (2009) Improved modeling of the Arctic halocline with a sub-grid-scale brine rejection parameterization. J Geophys Res 114(C11):C11,014. doi:10.1029/2008JC005121
Nguyen AT, Kwok R, Menemenlis D (2012) Source and pathway of the Western Arctic upper halocline in a data-constrained coupled ocean and sea ice model. J Phys Oceanogr 42(5):802–823. doi:10.1175/JPO-D-11-040.1
Onogi K, Tslttsui J, Koide H, Sakamoto M, Kobayashi S, Hatsushika H, Matsumoto T, Yamazaki N, Kaalhori H, Takahashi K, Kadokura S, Wada K, Kato K, Oyama R, Ose T, Mannoji N, Taira R (2007) The JRA-25 reanalysis. J Meteorol Soc Jpn 85(3):369–432. doi:10.2151/jmsj.85.369
Overland JE, Wang M (2007) Future regional Arctic sea ice declines. Geophys Res Lett 34(17):L17,705. doi:10.1029/2007GL030808
Parkinson C, Cavalieri D (2008) Arctic sea ice variability and trends, 1979–2006. J Geophys Res 113(C07):C07,003. doi:10.1029/2007JC004558
Parkinson CL, Cavalieri DJ (2012) Antarctic sea ice variability and trends, 1979–2010. The Cryosphere 6(4):871–880. doi:10.5194/tc-6-871-2012
Renfrew IA, Moore GWK, Guest PS, Bumke K (2002) A Comparison of surface layer and surface turbulent flux observations over the Labrador Sea with ECMWF analyses and NCEP reanalyses. J Phys Oceanogr 32(2):383–400. doi:10.1175/1520-0485(2002)032<0383:ACOSLA>2.0.CO;2
Rignot E, Fenty I, Menemenlis D, Xu Y (2012) Spreading of warm ocean waters around Greenland as a possible cause for glacier acceleration. Ann Glaciol 53(60):257–266. doi:10.3189/2012AoG60A136
Schodlok MP, Menemenlis D, Rignot E, Studinger M (2012) Sensitivity of the ice shelf/ocean system to the sub-ice-shelf cavity shape measured by NASA IceBridge in Pine Island Glacier, West Antarctica. Ann Glaciol 53(60):156–162. doi:10.3189/2012AoG60A073
Screen JA, Simmonds I (2010) The central role of diminishing sea ice in recent Arctic temperature amplification. Nature 464(7293):1334–1337. doi:10.1038/nature09051
Semtner A (1976) A Model for the thermodynamic growth of sea ice in numerical investigations of climate. J Phys Oceanogr 6(3):379–389. doi:10.1175/1520-0485%281976%29006<0379%AAMFTTG>2.0.CO%3B2
Shimada K, Kamoshida T, Itoh M, Nishino S, Carmack E, McLaughlin F, Zimmermann S, Proshutinsky A (2006) Pacific Ocean inflow: influence on catastrophic reduction of sea ice cover in the Arctic Ocean. Geophys Res Lett 33(8):L08,605. doi:10.1029/2005GL025624
Spreen G, Kwok R, Menemenlis D (2011) Trends in Arctic sea ice drift and role of wind forcing: 1992–2009. Geophys Res Lett 38(19):4097–4100. doi:10.1029/2011GL048970
Squire V (2007) Of ocean waves and sea-ice revisited. Cold Reg Sci Technol 49(2):110–133. doi:10.1016/j.coldregions.2007.04.007
Stammer D, Ueyoshi K, Köhl A, Large WG, Josey SA, Wunsch C (2004) Estimating air–sea fluxes of heat, freshwater, and momentum through global ocean data assimilation. J Geophys Res Oceans 109(C5):C05,023. doi:10.1029/2003JC002082
Stroeve J, Holland MM, Meier W, Scambos T, Serreze M (2007) Arctic sea ice decline: faster than forecast. Geophys Res Lett 34(9):L09,501. doi:10.1029/2007GL029703
Stroeve J, Hamilton LC, Bitz CM, Blanchard-Wrigglesworth E (2014) Predicting September sea ice: ensemble skill of the SEARCH sea ice outlook 2008–2013. Geophys Res Lett 41(7):2411–2418. doi:10.1002/2014GL059388
Stroeve JC, Kattsov V, Barrett A, Serreze M, Pavlova T, Holland M, Meier WN (2012a) Trends in Arctic sea ice extent from CMIP5, CMIP3 and observations. Geophys Res Lett 39(16):L16,502. doi:10.1029/2012GL052676
Stroeve JC, Serreze MC, Holland MM, Kay JE, Malanik J, Barrett AP (2012b) The Arctic’s rapidly shrinking sea ice cover: a research synthesis. Clim Change 110(3–4):1005–1027. doi:10.1007/s10584-011-0101-1
Vaughan GL, Bennetts LG, Squire VA (2009) The decay of flexural-gravity waves in long sea ice transects. Phil Trans R Soc A 465(2109):2785–2812. doi:10.1098/rspa.2009.0187
Vihma T (2014) Effects of Arctic sea ice decline on weather and climate: a review. Surv Geophys 35(5):1175–1214. doi:10.1007/s10712-014-9284-0
Visbeck M, Fischer J, Schott F (1995) Preconditioning the Greenland Sea for deep convection: ice formation and ice drift. J Geophys Res Oceans 100(C9):18,489–18,502. doi:10.1029/95JC01611
Wang M, Overland JE (2009) A sea ice free summer Arctic within 30 years? Geophys Res Lett 36(7):L07,502. doi:10.1029/2009GL037820
Wunsch C (2006) Discrete inverse and state estimation problems: with geophysical fluid applications. Cambridge University Press, Cambridge
Wunsch C, Heimbach P (2006) Estimated decadal changes in the North Atlantic meridional overturning circulation and heat flux 1993–2004. J Phys Oceanogr 36(11):2012–2024. doi:10.1175/JPO2957.1
Wunsch C, Heimbach P (2007) Practical global oceanic state estimation. Phys D Nonlinear Phenom 230(1–2):197–208. doi:10.1016/j.physd.2006.09.040
Wunsch C, Heimbach P (2013) Ocean circulation and climate, 2nd edn. Elsevier, chap Dynamically and kinematically consistent global ocean circulation state estimates with land and sea ice, pp 553–579
Wunsch C, Heimbach P (2014) Bidecadal thermal changes in the abyssal ocean. J Phys Oceanogr 44(8):2013–2030. doi:10.1175/JPO-D-13-096.1
Wunsch C, Heimbach P, Ponte R, Fukumori I (2009) The global general circulation of the oceans estimated by the ECCO-consortium. Oceanography 22(2):88–103. doi:10.5670/oceanog.2009.41
Zhang J, Hibler WD (1997) On an efficient numerical method for modeling sea ice dynamics. J Geophys Res Oceans 102(C4):8691–8702. doi:10.1029/96JC03744
Zhang J, Thomas DR, Rothrock DA, Lindsay RW, Yu Y, Kwok R (2003) Assimilation of ice motion observations and comparisons with submarine ice thickness data. J Geophys Res Oceans 108(C6):3170. doi:10.1029/2001JC001041
Zwally HJ, Schutz B, Abdalati W, Abshire J, Bentley C, Brenner A, Bufton J, Dezio J, Hancock D, Harding D, Herring T, Minster B, Quinn K, Palm S, Spinhirne J, Thomas R (2002) ICESat’s laser measurements of polar ice, atmosphere, ocean, and land. J Geodyn 34(3–4):405–445. doi:10.1016/S0264-3707(02)00042-X
Acknowledgments
The research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Support was provided by an appointment to the NASA Postdoctoral Program which is administered by Oak Ridge Associated Universities through a contract with NASA; the NASA Cryosphere program; and the NASA Modeling, Analysis, and Prediction program. We thank our ECCO partners, the MITgcm development group, the various data centers and the helpful comments of our reviewers. Computations were carried out at NASA Advanced Supercomputing (NAS) facilities.
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This paper is a contribution to the special issue on Ocean estimation from an ensemble of global ocean reanalyses,consisting of papers from the Ocean Reanalyses Intercomparsion Project (ORAIP), coordinated by CLIVAR-GSOP and GODAE OceanView. The special issue also contains specific studies using single reanalysis systems.
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Fenty, I., Menemenlis, D. & Zhang, H. Global coupled sea ice-ocean state estimation. Clim Dyn 49, 931–956 (2017). https://doi.org/10.1007/s00382-015-2796-6
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DOI: https://doi.org/10.1007/s00382-015-2796-6