Articles | Volume 18, issue 23
https://doi.org/10.5194/gmd-18-9451-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-18-9451-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
03 Dec 2025
Development and technical paper |
| 03 Dec 2025
| 03 Dec 2025
Adjoint-based simultaneous state and parameter estimation in an Arctic Sea Ice-Ocean Model using MITgcm (c63m)
Guokun Lyu
Key Laboratory for Polar Science, Polar Research Institute of China, Ministry of Natural Resources, Shanghai, 200136, China
Shanghai Key Laboratory of Polar Life and Environment Sciences, School of Oceanography, Shanghai Jiao Tong University, Shanghai, 200230, China
Longjiang Mu
Laoshan Laboratory, Qingdao, 266100, China
Armin Koehl
Center for Earth System Research and Sustainability (CEN), Universität Hamburg, Hamburg, 54662, Germany
Key Laboratory for Polar Science, Polar Research Institute of China, Ministry of Natural Resources, Shanghai, 200136, China
Key Laboratory of Marine Hazards Forecasting, National Marine Environmental Forecasting Center, Ministry of Natural Resources, Beijing, 100081, China
Chuanyu Liu
Key Laboratory of Ocean Observation and Forecasting, and Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao, 266000, China
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Data assimilation techniques are important for combining observations with numerical models. Here, we approximate the adjoint of viscous-plastic dynamics (adjoint-VP) to replace the adjoint of free-drift dynamics (adjoint-FD) for developing an advanced Arctic Ocean and sea ice modeling and adjoint-based assimilation system. We find that adjoint-VP provides a better ocean and sea ice estimation than adjoint-FD, considering the residual errors and adjustments of the atmospheric states.
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Quantification of ice deformation is useful for understanding of the role of ice dynamics in climate change. Using data of 32 buoys, we characterized spatiotemporal variations in ice kinematics and deformation in the Pacific sector of Arctic Ocean for autumn–winter 2018/19. Sea ice in the south and west has stronger mobility than in the east and north, which weakens from autumn to winter. An enhanced Arctic dipole and weakened Beaufort Gyre in winter lead to an obvious turning of ice drifting.
Shihe Ren, Xi Liang, Qizhen Sun, Hao Yu, L. Bruno Tremblay, Bo Lin, Xiaoping Mai, Fu Zhao, Ming Li, Na Liu, Zhikun Chen, and Yunfei Zhang
Geosci. Model Dev., 14, 1101–1124, https://doi.org/10.5194/gmd-14-1101-2021, https://doi.org/10.5194/gmd-14-1101-2021, 2021
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Sea ice plays a crucial role in global energy and water budgets. To get a better simulation of sea ice, we coupled a sea ice model with an atmospheric and ocean model to form a fully coupled system. The sea ice simulation results of this coupled system demonstrated that a two-way coupled model has better performance in terms of sea ice, especially in summer. This indicates that sea-ice–ocean–atmosphere interaction plays a crucial role in controlling Arctic summertime sea ice distribution.
Xuewei Li, Qinghua Yang, Lejiang Yu, Paul R. Holland, Chao Min, Longjiang Mu, and Dake Chen
The Cryosphere Discuss., https://doi.org/10.5194/tc-2020-359, https://doi.org/10.5194/tc-2020-359, 2021
Preprint withdrawn
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The Arctic sea ice thickness record minimum is confirmed occurring in autumn 2011. The dynamic and thermodynamic processes leading to the minimum thickness is analyzed based on a daily sea ice thickness reanalysis data covering the melting season. The results demonstrate that the dynamic transport of multiyear ice and the subsequent surface energy budget response is a critical mechanism actively contributing to the evolution of Arctic sea ice thickness in 2011.
Chao Min, Qinghua Yang, Longjiang Mu, Frank Kauker, and Robert Ricker
The Cryosphere, 15, 169–181, https://doi.org/10.5194/tc-15-169-2021, https://doi.org/10.5194/tc-15-169-2021, 2021
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An ensemble of four estimates of the sea-ice volume (SIV) variations in Baffin Bay from 2011 to 2016 is generated from the locally merged satellite observations, three modeled sea ice thickness sources (CMST, NAOSIM, and PIOMAS) and NSIDC ice drift data (V4). Results show that the net increase of the ensemble mean SIV occurs from October to April with the largest SIV increase in December, and the reduction occurs from May to September with the largest SIV decline in July.
Qian Shi, Qinghua Yang, Longjiang Mu, Jinfei Wang, François Massonnet, and Matthew R. Mazloff
The Cryosphere, 15, 31–47, https://doi.org/10.5194/tc-15-31-2021, https://doi.org/10.5194/tc-15-31-2021, 2021
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The ice thickness from four state-of-the-art reanalyses (GECCO2, SOSE, NEMO-EnKF and GIOMAS) are evaluated against that from remote sensing and in situ observations in the Weddell Sea, Antarctica. Most of the reanalyses can reproduce ice thickness in the central and eastern Weddell Sea but failed to capture the thick and deformed ice in the western Weddell Sea. These results demonstrate the possibilities and limitations of using current sea-ice reanalysis in Antarctic climate research.
Cited articles
Annan, J. D., Hargreaves, J. C., Edwards, N. R., and Marsh, R.: Parameter estimation in an intermediate complexity earth system model using an ensemble Kalman filter, Ocean Modelling, 8, 135–154, https://doi.org/10.1016/j.ocemod.2003.12.004, 2005.
Branstator, G. and Teng, H.: Two Limits of Initial-Value Decadal Predictability in a CGCM, Journal of Climate, 23, 6292–6311, https://doi.org/10.1175/2010JCLI3678.1, 2010.
Bretherton, C. S., Henn, B., Kwa, A., Brenowitz, N. D., Watt-Meyer, O., McGibbon, J., Perkins, W. A., Clark, S. K., and Harris, L.: Correcting Coarse-Grid Weather and Climate Models by Machine Learning From Global Storm-Resolving Simulations, Journal of Advances in Modeling Earth Systems, 14, e2021MS002794, https://doi.org/10.1029/2021MS002794, 2022.
Chen, Y., Lei, R., Zhao, X., Wu, S., Liu, Y., Fan, P., Ji, Q., Zhang, P., and Pang, X.: A new sea ice concentration product in the polar regions derived from the FengYun-3 MWRI sensors, Earth Syst. Sci. Data, 15, 3223–3242, https://doi.org/10.5194/essd-15-3223-2023, 2023.
Data Unification and Altimeter Combination System (DUACS) Team: Global Ocean Along Track L 3 Sea Surface Heights Reprocessed 1993 Ongoing Tailored For Data Assimilation, Copernicus Marine Data Store [data set], https://doi.org/10.48670/moi-00146, 2025.
European Space Agency: SMOS-CryoSat L4 Sea Ice Thickness, Version 206, European Space Agency [data set], https://doi.org/10.57780/sm1-4f787c3, 2023.
Forget, G., Campin, J.-M., Heimbach, P., Hill, C. N., Ponte, R. M., and Wunsch, C.: ECCO version 4: an integrated framework for non-linear inverse modeling and global ocean state estimation, Geosci. Model Dev., 8, 3071–3104, https://doi.org/10.5194/gmd-8-3071-2015, 2015.
Fenty, I. and Heimbach, P.: Coupled Sea Ice–Ocean-State Estimation in the Labrador Sea and Baffin Bay, Journal of Physical Oceanography, 43, 884–904, https://doi.org/10.1175/JPO-D-12-065.1, 2013.
Fenty, I., Menemenlis, D., and Zhang, H.: Global coupled sea ice-ocean state estimation, Climate Dynamics, 49, 931–956, https://doi.org/10.1007/s00382-015-2796-6, 2017.
Gentemann, C. L., Wentz, F. J., Mears, C. A., and Smith, D. K.: In situ validation of Tropical Rainfall Measuring Mission microwave sea surface temperatures, Journal of Geophysical Research: Oceans, 109, C04021, https://doi.org/10.1029/2003JC002092, 2004 (data available at: https://data.remss.com/SST/daily/mw_ir/v05.1/netcdf/, last access: 25 November 2025).
Giering, R. and Kaminski, T.: Recipes for adjoint code construction, ACM Transactions on Mathematical Software (TOMS), 24, 437–474, https://doi.org/10.1145/293686.293695, 1998.
Gilbert, J. C. and Lemaréchal, C.: The module M1QN3, https://who.rocq.inria.fr/Jean-Charles.Gilbert/modulopt/optimization-routines/m1qn3/m1qn3.html (last access: 25 November 2025), 2023.
Good, S. A., Martin, M. J., and Rayner, N. A.: EN4: Quality controlled ocean temperature and salinity profiles and monthly objective analyses with uncertainty estimates, Journal of Geophysical Research: Oceans, 118, 6704-6716, https://doi.org/10.1002/2013jc009067, 2013 (data available at: https://www.metoffice.gov.uk/hadobs/en4/, last access: 25 November 2025).
Heimbach, P., Menemenlis, D., Losch, M., Campin, J.-M., and Hill, C.: On the formulation of sea-ice models. Part 2: Lessons from multi-year adjoint sea-ice export sensitivities through the Canadian Arctic Archipelago, Ocean Modelling, 33, 145–158, https://doi.org/10.1016/j.ocemod.2010.02.002, 2010.
Hibler, W.: A Dynamic Thermodynamic Sea Ice Model, Journal of Physical Oceanography, 9, 815–846, https://doi.org/10.1175/1520-0485(1979)009<0815:adtsim>2.0.co;2, 1979.
Hibler, W.: Modeling a Variable Thickness Sea Ice Cover, Monthly Weather Review, 108, 1943–1973, https://doi.org/10.1175/1520-0493(1980)108<1943:mavtsi>2.0.co;2, 1980.
Horvat, C. and Roach, L. A.: WIFF1.0: a hybrid machine-learning-based parameterization of wave-induced sea ice floe fracture, Geosci. Model Dev., 15, 803–814, https://doi.org/10.5194/gmd-15-803-2022, 2022.
Hourdin, F., Mauritsen, T., Gettelman, A., Golaz, J.-C., Balaji, V., Duan, Q., Folini, D., Ji, D., Klocke, D., Qian, Y., Rauser, F., Rio, C., Tomassini, L., Watanabe, M., and Williamson, D.: The Art and Science of Climate Model Tuning, Bulletin of the American Meteorological Society, 98, 589–602, https://doi.org/10.1175/BAMS-D-15-00135.1, 2017.
Hu, X.-M., Zhang, F., and Nielsen-Gammon, J. W.: Ensemble-based simultaneous state and parameter estimation for treatment of mesoscale model error: A real-data study, Geophysical Research Letters, 37, L08802, https://doi.org/10.1029/2010GL043017, 2010.
Hunke, E. C., Allard, R., Bailey, D. A., Blain, P., Craig, A., Dupont, F., and Winton, M.: CICE-Consortium/CICE: CICE version 6.1.2 (version 6.1.2), Zenodo [code], https://doi.org/10.5281/zenodo.3888653, 2020.
Jackson, C. S., Sen, M. K., Huerta, G., Deng, Y., and Bowman, K. P.: Error Reduction and Convergence in Climate Prediction, Journal of Climate, 21, 6698–6709, https://doi.org/10.1175/2008JCLI2112.1, 2008.
Kaleschke, L., Lüpkes, C., Vihma, T., Haarpaintner, J., Bochert, A., Hartmann, J., and Heygster, G.: SSM/I Sea Ice Remote Sensing for Mesoscale Ocean-Atmosphere Interaction Analysis, Journal of Remote Sensing, 27, 526–537, https://doi.org/10.1080/07038992.2001.10854892, 2001.
Kim, J. G., Hunke, E. C., and Lipscomb, W. H.: Sensitivity analysis and parameter tuning scheme for global sea-ice modeling, Ocean Modelling, 14, 61–80, https://doi.org/10.1016/j.ocemod.2006.03.003, 2006.
Kochkov, D., Yuval, J., Langmore, I., Norgaard, P., Smith, J., Mooers, G., Klöwer, M., Lottes, J., Rasp, S., Düben, P., Hatfield, S., Battaglia, P., Sanchez-Gonzalez, A., Willson, M., Brenner, M. P., and Hoyer, S.: Neural general circulation models for weather and climate, Nature, 632, 1060–1066, https://doi.org/10.1038/s41586-024-07744-y, 2024.
Koldunov, N. V., Köhl, A., Serra, N., and Stammer, D.: Sea ice assimilation into a coupled ocean–sea ice model using its adjoint, The Cryosphere, 11, 2265–2281, https://doi.org/10.5194/tc-11-2265-2017, 2017.
Koo, Y., Lei, R., Cheng, Y., Cheng, B., Xie, H., Hoppmann, M., Kurtz, N. T., Ackley, S. F., and Mestas-Nuñez, A. M.: Estimation of thermodynamic and dynamic contributions to sea ice growth in the Central Arctic using ICESat-2 and MOSAiC SIMBA buoy data, Remote Sensing of Environment, 267, 112730, https://doi.org/10.1016/j.rse.2021.112730, 2021.
Krishfield, R. A., Proshutinsky, A., Tateyama, K., Williams, W. J., Carmack, E. C., McLaughlin, F. A., and Timmermans, M.-L.: Deterioration of perennial sea ice in the Beaufort Gyre from 2003 to 2012 and its impact on the oceanic freshwater cycle, Journal of Geophysical Research: Oceans, 119, 1271–1305, https://doi.org/10.1002/2013JC008999, 2014.
Lavergne, T., Eastwood, S., Teffah, Z., Schyberg, H., and Breivik, L.-A.: Sea ice motion from low-resolution satellite sensors: An alternative method and its validation in the Arctic, Journal of Geophysical Research: Oceans, 115, C10032, https://doi.org/10.1029/2009JC005958, 2010.
Lavergne, T., Sørensen, A. M., Kern, S., Tonboe, R., Notz, D., Aaboe, S., Bell, L., Dybkjær, G., Eastwood, S., Gabarro, C., Heygster, G., Killie, M. A., Brandt Kreiner, M., Lavelle, J., Saldo, R., Sandven, S., and Pedersen, L. T.: Version 2 of the EUMETSAT OSI SAF and ESA CCI sea-ice concentration climate data records, The Cryosphere, 13, 49–78, https://doi.org/10.5194/tc-13-49-2019, 2019.
Lei, R., Cheng, B., Hoppmann, M., Zhang, F., Zuo, G., Hutchings, J. K., Lin, L., Lan, M., Wang, H., Regnery, J., Krumpen, T., Haapala, J., Rabe, B., Perovich, D. K., and Nicolaus, M.: Seasonality and timing of sea ice mass balance and heat fluxes in the Arctic transpolar drift during 2019–2020, Elementa: Science of the Anthropocene, 10, 000089, https://doi.org/10.1525/elementa.2021.000089, 2022.
Li, Z., Chao, Y., McWilliams, J. C., and Ide, K.: A Three-Dimensional Variational Data Assimilation Scheme for the Regional Ocean Modeling System, Journal of Atmospheric and Oceanic Technology, 25, 2074–2090, https://doi.org/10.1175/2008JTECHO594.1, 2008.
Lindsay, R. W. and Zhang, J.: Assimilation of Ice Concentration in an Ice–Ocean Model, Journal of Atmospheric and Oceanic Technology, 23, 742–749, https://doi.org/10.1175/jtech1871.1, 2006.
Liu, C., Köhl, A., and Stammer, D.: Adjoint−Based Estimation of Eddy-Induced Tracer Mixing Parameters in the Global Ocean, Journal of Physical Oceanography, 42, 1186–1206, https://doi.org/10.1175/jpo-d-11-0162.1, 2012.
Liu, X. and Zhang, L.: Study on optimization of sea ice concentration with adjoint method, Journal of Coastal Research, 84, 44–50, https://doi.org/10.2112/SI84-006.1, 2018.
Locarnini, R. A., Mishonov, A. V., Baranova, O. K., Boyer, T. P., Zweng, M. M., Garcia, H. E., Reagan, J. R., Seidov, D., Weathers, K. W., Paver, C. R., and Smolyar, I. V.: World Ocean Atlas 2018, Volume 1: Temperature, Levitus, edited by: Mishonov, A., NOAA Atlas NESDIS, 82, 52 pp., https://doi.org/10.25923/e5rn-9711, 2018.
Losch, M., Menemenlis, D., Campin, J.-M., Heimbach, P., and Hill, C.: On the formulation of sea–ice models. Part 1: Effects of different solver implementations and parameterizations, Ocean Modelling, 33, 129–144, https://doi.org/10.1016/j.ocemod.2009.12.008, 2010.
Lu, Y., Wang, X., and Dong, J.: Melt Pond Scheme Parameter Estimation Using an Adjoint Model, Advances in Atmospheric Sciences, 38, 1525–1536, https://doi.org/10.1007/s00376-021-0305-x, 2021.
Lyu, G.: MITgcm model developed for state and parameter estimation in a pan-Arctic ocean and sea ice model, Zenodo [code], https://doi.org/10.5281/zenodo.14584929, 2025.
Lyu, G., Koehl, A., Serra, N., and Stammer, D.: Assessing the current and future Arctic Ocean observing system with observing system simulating experiments, Quarterly Journal of the Royal Meteorological Society, 147, 2670–2690, https://doi.org/10.1002/qj.4044, 2021a.
Lyu, G., Koehl, A., Serra, N., Stammer, D., and Xie, J.: Arctic ocean–sea ice reanalysis for the period 2007–2016 using the adjoint method, Quarterly Journal of the Royal Meteorological Society, 147, 1908–1929, https://doi.org/10.1002/qj.4002, 2021b.
Lyu, G., Köhl, A., Matei, I., and Stammer, D.: Adjoint-Based Climate Model Tuning: Application to the Planet Simulatorm Journal of Advances in Modeling Earth Systems, 10, 207–222, https://doi.org/10.1002/2017MS001194, 2018.
Lyu, G., Koehl, A., Wu, X., Zhou, M., and Stammer, D.: Effects of including the adjoint sea ice rheology on estimating Arctic Ocean–sea ice state, Ocean Sci., 19, 305–319, https://doi.org/10.5194/os-19-305-2023, 2023.
Lyu, G., Mu, L., Koehl, A., Lei, R., Liang, X., and Liu, C.: MITgcm model developed for state and parameter estimation in a pan-Arctic ocean and sea ice model using MITgcm (c63m), Zenodo [data set], https://doi.org/10.5281/zenodo.14584780, 2025.
Marshall, J., Adcroft, A., Hill, C., Perelman, L., and Heisey, C.: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers, Journal of Geophysical Research: Oceans, 102, 5753–5766, https://doi.org/10.1029/96JC02775, 1997.
Massonnet, F., Goosse, H., Fichefet, T., and Counillon, F.: Calibration of sea ice dynamic parameters in an ocean-sea ice model using an ensemble Kalman filter, Journal of Geophysical Research: Oceans, 119, 4168–4184, https://doi.org/10.1002/2013JC009705, 2014.
Mauritsen, T., Stevens, B., Roeckner, E., Crueger, T., Esch, M., Giorgetta, M., Haak, H., Jungclaus, J., Klocke, D., Matei, D., Mikolajewicz, U., Notz, D., Pincus, R., Schmidt, H., and Tomassini, L.: Tuning the climate of a global model, Journal of Advances in Modeling Earth Systems, 4, M00A01, https://doi.org/10.1029/2012MS000154, 2012.
Miller, P. A., Laxon, S. W., and Feltham, D. L.: Improving the spatial distribution of modeled Arctic sea ice thickness, Geophysical Research Letters, 32, L18503, https://doi.org/10.1029/2005GL023622, 2005.
Mu, L., Losch, M., Yang, Q., Ricker, R., Losa, S. N., and Nerger, L.: Arctic-Wide Sea Ice Thickness Estimates From Combining Satellite Remote Sensing Data and a Dynamic Ice-Ocean Model with Data Assimilation During the CryoSat-2 Period, Journal of Geophysical Research: Oceans, 123, 7763–7780, https://doi.org/10.1029/2018JC014316, 2018.
Murphy, J. M., Sexton, D. M. H., Barnett, D. N., Jones, G. S., Webb, M. J., Collins, M., and Stainforth, D. A.: Quantification of modelling uncertainties in a large ensemble of climate change simulations, Nature, 430, 768–772, https://doi.org/10.1038/nature02771, 2004.
Nie, Y., Li, C., Vancoppenolle, M., Cheng, B., Boeira Dias, F., Lv, X., and Uotila, P.: Sensitivity of NEMO4.0-SI3 model parameters on sea ice budgets in the Southern Ocean, Geosci. Model Dev., 16, 1395–1425, https://doi.org/10.5194/gmd-16-1395-2023, 2023.
Nguyen, A. T., Menemenlis, D., and Kwok, R.: Arctic ice-ocean simulation with optimized model parameters: Approach and assessment, Journal of Geophysical Research: Oceans, 116, C04025, https://doi.org/10.1029/2010JC006573, 2011.
Nguyen, A. T., Pillar, H., Ocaña, V., Bigdeli, A., Smith, T. A., and Heimbach, P.: The Arctic Subpolar Gyre sTate Estimate: Description and Assessment of a Data-Constrained, Dynamically Consistent Ocean-Sea Ice Estimate for 2002–2017, Journal of Advances in Modeling Earth Systems, 13, e2020MS002398, https://doi.org/10.1029/2020MS002398, 2021.
OSI SAF: Global Low Resolution Sea Ice Drift – Multimission, EUMETSAT SAF on Ocean and Sea Ice [data set], https://doi.org/10.15770/EUM_SAF_OSI_NRT_2007, 2010.
OSI SAF: Global Sea Ice Concentration Climate Data Record v3.0 – Multimission, EUMETSAT SAF on Ocean and Sea Ice [data set], https://doi.org/10.15770/EUM_SAF_OSI_0013, 2022.
Panteleev, G., Yaremchuk, M., Stroh, J. N., Francis, O. P., and Allard, R.: Parameter optimization in sea ice models with elastic–viscoplastic rheology, The Cryosphere, 14, 4427–4451, https://doi.org/10.5194/tc-14-4427-2020, 2020.
Perovich, D., Richter-Menge, J., and Polashenski, C.: Observing and understanding climate change: Monitoring the mass balance, motion, and thickness of Arctic sea ice, IMB CRREL Dartmouth [data set], http://imb-crrel-dartmouth.org/results/ (last access: 25 November 2025), 2025.
Pujol, M.-I., Faugère, Y., Taburet, G., Dupuy, S., Pelloquin, C., Ablain, M., and Picot, N.: DUACS DT2014: the new multi-mission altimeter data set reprocessed over 20 years, Ocean Sci., 12, 1067–1090, https://doi.org/10.5194/os-12-1067-2016, 2016.
Richter-Menge, J. A., Perovich, D. K., Elder, B. C., Claffey, K., Rigor, I., and Ortmeyer, M.: Ice mass-balance buoys: a tool for measuring and attributing changes in the thickness of the Arctic sea-ice cover, Annals of Glaciology, 44, 205–210, https://doi.org/10.3189/172756406781811727, 2006.
Ricker, R., Hendricks, S., Kaleschke, L., Tian-Kunze, X., King, J., and Haas, C.: A weekly Arctic sea-ice thickness data record from merged CryoSat-2 and SMOS satellite data, The Cryosphere, 11, 1607–1623, https://doi.org/10.5194/tc-11-1607-2017, 2017.
Spreen, G., Kaleschke, L., and Heygster, G.: Sea ice remote sensing using AMSR-E 89-GHz channels, Journal of Geophysical Research: Oceans, 113, 14 pp., https://doi.org/10.1029/2005jc003384, 2008.
Sumata, H., Kauker, F., Karcher, M., and Gerdes, R.: Simultaneous Parameter Optimization of an Arctic Sea Ice–Ocean Model by a Genetic Algorithm, Monthly Weather Review, 147, 1899–1926, https://doi.org/10.1175/mwr-d-18-0360.1, 2019.
Taburet, G., Sanchez-Roman, A., Ballarotta, M., Pujol, M.-I., Legeais, J.-F., Fournier, F., Faugere, Y., and Dibarboure, G.: DUACS DT2018: 25 years of reprocessed sea level altimetry products, Ocean Sci., 15, 1207–1224, https://doi.org/10.5194/os-15-1207-2019, 2019.
Taylor, K. E.: Summarizing multiple aspects of model performance in a single diagram, Journal of Geophysical Research: Atmospheres, 106, 7183–7192, https://doi.org/10.1029/2000JD900719, 2001.
Uotila, P., O'Farrell, S., Marsland, S. J., and Bi, D.: A sea-ice sensitivity study with a global ocean-ice model, Ocean Modelling, 51, 1–18, https://doi.org/10.1016/j.ocemod.2012.04.002, 2012.
von Albedyll, L., Hendricks, S., Grodofzig, R., Krumpen, T., Arndt, S., Belter, H. J., Birnbaum, G., Cheng, B., Hoppmann, M., Hutchings, J., Itkin, P., Lei, R., Nicolaus, M., Ricker, R., Rohde, J., Suhrhoff, M., Timofeeva, A., Watkins, D., Webster, M., and Haas, C.: Thermodynamic and dynamic contributions to seasonal Arctic sea ice thickness distributions from airborne observations, Elementa: Science of the Anthropocene, 10, 00074, https://doi.org/10.1525/elementa.2021.00074, 2022.
Weaver, A. T. and Mirouze, I.: On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation, Quarterly Journal of the Royal Meteorological Society, 139, 242–260, https://doi.org/10.1002/qj.1955, 2013.
Williamson, D., Goldstein, M., Allison, L., Blaker, A., Challenor, P., Jackson, L., and Yamazaki, K.: History matching for exploring and reducing climate model parameter space using observations and a large perturbed physics ensemble, Climate Dynamics, 41, 1703–1729, https://doi.org/10.1007/s00382-013-1896-4, 2013.
Wu, X., Zhang, S., Liu, Z., Rosati, A., Delworth, T. L., and Liu, Y.: Impact of Geographic-Dependent Parameter Optimization on Climate Estimation and Prediction: Simulation with an Intermediate Coupled Model, Monthly Weather Review, 140, 3956–3971, https://doi.org/10.1175/MWR-D-11-00298.1, 2012.
Yang, B., Qian, Y., Lin, G., Leung, L. R., Rasch, P. J., Zhang, G. J., McFarlane, S. A., Zhao, C., Zhang, Y., Wang, H., Wang, M., and Liu, X.: Uncertainty quantification and parameter tuning in the CAM5 Zhang-McFarlane convection scheme and impact of improved convection on the global circulation and climate, Journal of Geophysical Research: Atmospheres, 118, 395–415, https://doi.org/10.1029/2012JD018213, 2013.
Zampieri, L., Kauker, F., Fröhle, J., Sumata, H., Hunke, E. C., and Goessling, H. F.: Impact of Sea-Ice Model Complexity on the Performance of an Unstructured-Mesh Sea-Ice/Ocean Model under Different Atmospheric Forcings, Journal of Advances in Modeling Earth Systems, 13, e2020MS002438, https://doi.org/10.1029/2020MS002438, 2021.
Zhang, F., Pang, X., Lei, R., Zhai, M., Zhao, X., and Cai, Q.: Arctic sea ice motion change and response to atmospheric forcing between 1979 and 2019, International Journal of Climatology, 42, 1854–1876, https://doi.org/10.1002/joc.7340, 2022.
Zhang, J. and Hibler, W. D.: On an efficient numerical method for modeling sea ice dynamics, Journal of Geophysical Research: Oceans, 102, 8691–8702, https://doi.org/10.1029/96JC03744, 1997.
Zhang, S.: A Study of Impacts of Coupled Model Initial Shocks and State–Parameter Optimization on Climate Predictions Using a Simple Pycnocline Prediction Model, Journal of Climate, 24, 6210–6226, https://doi.org/10.1175/JCLI-D-10-05003.1, 2011.
Zweng, M. M., Reagan, J. R., Seidov, D., Boyer, T. P., Locarnini, R. A., Garcia, H. E., Mishonov, A. V., Baranova, O. K., Weathers, K. W., Paver, C. R., and Smolyar, I. V.: World Ocean Atlas 2018, Volume 2: Salinity. Levitus, edited by: Mishonov, A., NOAA Atlas NESDIS, 82, 50 pp., https://doi.org/10.25923/9pgv-1224, 2018.
Short summary
In the sea ice-ocean models, errors in the parameters and missing spatiotemporal variations contribute to the deviations between the simulations and the observations. We extended an adjoint method to optimize spatiotemporally varying parameters together with the atmosphere forcing and the initial conditions using satellite and in-situ observations. Seasonally, this scheme demonstrates a more prominent advantage in mid-autumn and show great potential for accurately reproducing the Arctic changes.
In the sea ice-ocean models, errors in the parameters and missing spatiotemporal variations...
