equations for the wind field are

$$u_a^s(\hat{x}, \hat{y}, t) = U_s \sin^2(2\pi\hat{x}) \sin(4\pi\hat{y}) \cdot \gamma(t) \cdot U_{\text{mask}}, \quad (B2)$$

$$v_a^s(\hat{x}, \hat{y}, t) = -U_s \sin^2(2\pi\hat{y}) \sin(4\pi\hat{x}) \cdot \gamma(t) \cdot U_{\text{mask}} + U^b, \quad (B3)$$

$$u_a^d(\hat{x}, \hat{y}, t) = U_d \sin^2(2\pi\hat{x}) \sin(4\pi\hat{y}) \cdot \gamma(t) \cdot U_{\text{mask}}, \quad (B4)$$

$$v_a^d(\hat{x}, \hat{y}, t) = U_d \sin^2(2\pi\hat{x}) \sin(4\pi\hat{y}) \cdot \gamma(t) \cdot U_{\text{mask}}, \quad (B5)$$

with $U_d = 0.1 \text{ m s}^{-1}$ as the magnitude of the divergent wind, $U_s = 22 \text{ m s}^{-1}$ as the maximum solenoidal wind speed and $U^b = 2 \text{ m s}^{-1}$ as the background wind field. To simulate a sequence of storms generating and dissipating, we introduce the time-dependent term, $\gamma(t)$, that controls the strength of the storm:

$$\gamma(t) = 1 - \exp\left(-a\left|\sin\left(\pi \frac{t}{T}\right)\right|^b\right), \quad (B6)$$

where $T$ is the period of the storm and $a = 10$ and $b = 2$ are parameters that control the shape of the curve and in turn the rate at which the storm is generated, maintains its maximum strength and then dissipates. In Eqs. (B2)–(B5), the spatial coordinate, $(\hat{x}_t, \hat{y}_t)$, is time-dependent. This simulates the passing of the storm across the domain.

$$\hat{x}_t = \hat{x}_{t-1} + \Delta\hat{x}_t, \quad (B7)$$

$$\hat{y}_t = \hat{y}_{t-1} - v_c \Delta t / L, \quad (B8)$$

where $\Delta t$ is the forcing frequency, $v_c$ is the speed at which the storm passes across the domain (from the bottom to top), $L = L_{\text{max}} - L_{\text{min}}$ and $\Delta \hat{x}_t$ is a random perturbation that allows us to send the storm on a random walk. The initial position of each storm is given by

$$\hat{x}_0 = \frac{(x - x_c) - L_{\text{min}}}{L} - \frac{1}{4}, \quad (B9)$$

$$\hat{y}_0 = \frac{(y - y_c) - L_{\text{min}}}{L} - \frac{1}{4}, \quad (B10)$$

where $(x_c, y_c)$ is the initial position of the storm centre. The choice of $T$; $v_c$; and $x_c, y_c$ is given in Table 2, and the $\Delta \hat{x}_t$ related to the random walk is specified in Eq. (4).

With these setups, each storm is approximately half the width of the domain. The sine and cosine equations can generate four storms in the domain, and $U_{\text{mask}}$ is used to ensure only one storm is in the domain at any time:

$$U_{\text{mask}} = (1 - \lfloor x \rfloor - 2 \lfloor \frac{x}{2} \rfloor) H(\sin(2\pi x) H(\sin(2\pi y)), \quad (B11)$$

where $\lfloor x \rfloor$ is the integral part function and $H(x)$ is a Heaviside step function.

*Code and data availability.* The code for the data assimilation scheme and experiment setup can be found at https://doi.org/10.5281/zenodo.8224997 (Chen, 2023). The dynamics-only sea-ice model is available upon request.

*Author contributions.* YC conducted the experiments, performed the data analysis and wrote the paper. PS developed the wind field perturbation. AC, IP, LB and VD contributed to conceptualisation of the work, to discussion and to the paper writing. MB contributed with the DA codes and to the writing. This paper builds on VD’s MEB model. TSF and YC modified I/O routines and boundary conditions for the purposes of simulations. All authors contributed to the experiment’s design, interpreting the results, the discussion and writing the paper.

*Competing interests.* The contact author has declared that none of the authors has any competing interests.

*Disclaimer.* Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

*Acknowledgements.* The authors acknowledge the support of the Scale-Aware Sea Ice Project (SASIP) funded by Schmidt Futures – a philanthropic initiative that seeks to improve societal outcomes through the development of emerging science and technologies. CEREA is a member of the Institut Pierre-Simon Laplace (IPSL). The authors thank Yvonne Ruckstuhl and the anonymous reviewer for their help in improving this paper.

*Financial support.* This research has been supported by the UK National Environment Research Council’s support for the National Centre for Earth Observation (contract no. PR140015) and the Schmidt Family Foundation (grant no. 353).

*Review statement.* This paper was edited by Yevgeny Aksenov and reviewed by Yvonne Ruckstuhl and one anonymous referee.

## References

Aksoy, A., Zhang, F., and Nielsen-Gammon, J.: Ensemble-based simultaneous state and parameter estimation in a two-dimensional sea-breeze model, Mon. Weather Rev., 134, 2951–2969, https://doi.org/10.1175/MWR3224.1, 2006.

Asch, M., Bocquet, M., and Nodet, M.: Data Assimilation: Methods, Algorithms, and Applications, Fundamentals of Algorithms, SIAM, Philadelphia, ISBN 978-1-611974-53-9, https://doi.org/10.1137/1.9781611974546, 2016.

Aydoğdu, A., Currass, A., Guider, C. T., Jones, C. K. R. T., and Rampal, P.: Data assimilation using adaptive, non-conservative, moving mesh models, Nonlin. Processes Geophys., 26, 175–193, https://doi.org/10.5194/npg-26-175-2019, 2019.
equations for the wind field are

$$u_a^s(\hat{x}, \hat{y}, t) = U_s \sin^2(2\pi\hat{x}) \sin(4\pi\hat{y}) \cdot \gamma(t) \cdot U_{\text{mask}}, \quad (B2)$$

$$v_a^s(\hat{x}, \hat{y}, t) = -U_s \sin^2(2\pi\hat{y}) \sin(4\pi\hat{x}) \cdot \gamma(t) \cdot U_{\text{mask}} + U^b, \quad (B3)$$

$$u_a^d(\hat{x}, \hat{y}, t) = U_d \sin^2(2\pi\hat{x}) \sin(4\pi\hat{y}) \cdot \gamma(t) \cdot U_{\text{mask}}, \quad (B4)$$

$$v_a^d(\hat{x}, \hat{y}, t) = U_d \sin^2(2\pi\hat{x}) \sin(4\pi\hat{y}) \cdot \gamma(t) \cdot U_{\text{mask}}, \quad (B5)$$

with $U_d = 0.1 \text{ m s}^{-1}$ as the magnitude of the divergent wind, $U_s = 22 \text{ m s}^{-1}$ as the maximum solenoidal wind speed and $U^b = 2 \text{ m s}^{-1}$ as the background wind field. To simulate a sequence of storms generating and dissipating, we introduce the time-dependent term, $\gamma(t)$, that controls the strength of the storm:

$$\gamma(t) = 1 - \exp\left(-a\left|\sin\left(\pi\frac{t}{T}\right)\right|^b\right), \quad (B6)$$

where $T$ is the period of the storm and $a = 10$ and $b = 2$ are parameters that control the shape of the curve and in turn the rate at which the storm is generated, maintains its maximum strength and then dissipates. In Eqs. (B2)–(B5), the spatial coordinate, $(\hat{x}_t, \hat{y}_t)$, is time-dependent. This simulates the passing of the storm across the domain.

$$\hat{x}_t = \hat{x}_{t-1} + \Delta\hat{x}_t, \quad (B7)$$

$$\hat{y}_t = \hat{y}_{t-1} - v_c \Delta t / L, \quad (B8)$$

where $\Delta t$ is the forcing frequency, $v_c$ is the speed at which the storm passes across the domain (from the bottom to top), $L = L_{\text{max}} - L_{\text{min}}$ and $\Delta \hat{x}_t$ is a random perturbation that allows us to send the storm on a random walk. The initial position of each storm is given by

$$\hat{x}_0 = \frac{(x - x_c) - L_{\text{min}}}{L} - \frac{1}{4}, \quad (B9)$$

$$\hat{y}_0 = \frac{(y - y_c) - L_{\text{min}}}{L} - \frac{1}{4}, \quad (B10)$$

where $(x_c, y_c)$ is the initial position of the storm centre. The choice of $T$; $v_c$; and $x_c, y_c$ is given in Table 2, and the $\Delta \hat{x}_t$ related to the random walk is specified in Eq. (4).

With these setups, each storm is approximately half the width of the domain. The sine and cosine equations can generate four storms in the domain, and $U_{\text{mask}}$ is used to ensure only one storm is in the domain at any time:

$$U_{\text{mask}} = (1 - \lfloor x \rfloor - 2 \lfloor \frac{x}{2} \rfloor) H(\sin(2\pi x) H(\sin(2\pi y)), \quad (B11)$$

where $\lfloor x \rfloor$ is the integral part function and $H(x)$ is a Heaviside step function.

*Code and data availability.* The code for the data assimilation scheme and experiment setup can be found at https://doi.org/10.5281/zenodo.8224997 (Chen, 2023). The dynamics-only sea-ice model is available upon request.

*Author contributions.* YC conducted the experiments, performed the data analysis and wrote the paper. PS developed the wind field perturbation. AC, IP, LB and VD contributed to conceptualisation of the work, to discussion and to the paper writing. MB contributed with the DA codes and to the writing. This paper builds on VD’s MEB model. TSF and YC modified I/O routines and boundary conditions for the purposes of simulations. All authors contributed to the experiment’s design, interpreting the results, the discussion and writing the paper.

*Competing interests.* The contact author has declared that none of the authors has any competing interests.

*Disclaimer.* Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

*Acknowledgements.* The authors acknowledge the support of the Scale-Aware Sea Ice Project (SASIP) funded by Schmidt Futures – a philanthropic initiative that seeks to improve societal outcomes through the development of emerging science and technologies. CEREA is a member of the Institut Pierre-Simon Laplace (IPSL). The authors thank Yvonne Ruckstuhl and the anonymous reviewer for their help in improving this paper.

*Financial support.* This research has been supported by the UK National Environment Research Council’s support for the National Centre for Earth Observation (contract no. PR140015) and the Schmidt Family Foundation (grant no. 353).

*Review statement.* This paper was edited by Yevgeny Aksenov and reviewed by Yvonne Ruckstuhl and one anonymous referee.

## References

Aksoy, A., Zhang, F., and Nielsen-Gammon, J.: Ensemble-based simultaneous state and parameter estimation in a two-dimensional sea-breeze model, Mon. Weather Rev., 134, 2951–2969, https://doi.org/10.1175/MWR3224.1, 2006.

Asch, M., Bocquet, M., and Nodet, M.: Data Assimilation: Methods, Algorithms, and Applications, Fundamentals of Algorithms, SIAM, Philadelphia, ISBN 978-1-611974-53-9, https://doi.org/10.1137/1.9781611974546, 2016.

Aydoğdu, A., Currass, A., Guider, C. T., Jones, C. K. R. T., and Rampal, P.: Data assimilation using adaptive, non-conservative, moving mesh models, Nonlin. Processes Geophys., 26, 175–193, https://doi.org/10.5194/npg-26-175-2019, 2019.
Bannister, R. N.: A review of operational methods of variational and ensemble-variational data assimilation, Q. J. Roy. Meteor. Soc., 143, 607–633, https://doi.org/10.1002/qj.2982, 2017.

Bertino, L. and Holland, M. M.: Coupled ice-ocean modeling and predictions, J. Marine Res., 75, 839–875, 2017.

Blockley, E. W. and Peterson, K. A.: Improving Met Office seasonal predictions of Arctic sea ice using assimilation of CryoSat-2 thickness, The Cryosphere, 12, 3419–3438, https://doi.org/10.5194/tc-12-3419-2018, 2018.

Bocquet, M.: Parameter field estimation for atmospheric dispersion: Application to the Chernobyl accident using 4D-Var, Q. J. Roy. Meteor. Soc., 138, 664–681, https://doi.org/10.1002/qj.961, 2012.

Bocquet, M.: Localization and the iterative ensemble Kalman smoother, Q. J. Roy. Meteor. Soc., 142, 1075–1089, https://doi.org/10.1002/qj.2711, 2016.

Bocquet, M. and Sakov, P.: Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems, Nonlin. Processes Geophys., 19, 383–399, https://doi.org/10.5194/npg-19-383-2012, 2012.

Bocquet, M. and Sakov, P.: Joint state and parameter estimation with an iterative ensemble Kalman smoother, Nonlin. Processes Geophys., 20, 803–818, https://doi.org/10.5194/npg-20-803-2013, 2013.

Bocquet, M. and Sakov, P.: An iterative ensemble Kalman smoother, Q. J. Roy. Meteor. Soc., 140, 1521–1535, https://doi.org/10.1002/qj.2236, 2014.

Bocquet, M., Farchi, A., and Malartic, Q.: Online learning of both state and dynamics using ensemble Kalman filters, Foundations of Data Science, 3, 305–330, https://doi.org/10.3934/fods.2020015, 2021.

Bouillon, S. and Rampal, P.: Presentation of the dynamical core of neXtSIM, a new sea ice model, Ocean Model., 91, 23–37, https://doi.org/10.1016/j.ocemod.2015.04.005, 2015.

Boutin, G., Ólason, E., Rampal, P., Regan, H., Lique, C., Talandier, C., Brodeau, L., and Ricker, R.: Arctic sea ice mass balance in a new coupled ice-ocean model using a brittle rheology framework, The Cryosphere, 17, 617–638, https://doi.org/10.5194/tc-17-617-2023, 2023.

Carrassi, A., Bocquet, M., Bertino, L., and Evensen, G.: Data assimilation in the geosciences: An overview of methods, issues, and perspectives, WIREs Climate Change, 9, e535, https://doi.org/10.1002/wcc.535, 2018.

Chen, Y.: Multivariate state and parameter estimation with data assimilation on sea-ice models using a Maxwell- Elasto-Brittle rheology, Zenodo [code and data set], https://doi.org/10.5281/zenodo.8224997, 2023.

Cheng, S., Aydoğdu, A., Rampal, P., Carrassi, A., and Bertino, L.: Probabilistic forecasts of sea ice trajectories in the Arctic: impact of uncertainties in surface wind and ice cohesion, Oceans, 1, 326–342, https://doi.org/10.3390/oceans1040022, 2020.

Cheng, S., Chen, Y., Aydoğdu, A., Bertino, L., Carrassi, A., Rampal, P., and Jones, C. K. R. T.: Arctic sea ice data assimilation combining an ensemble Kalman filter with a novel Lagrangian sea ice model for the winter 2019–2020, The Cryosphere, 17, 1735–1754, https://doi.org/10.5194/tc-17-1735-2023, 2023.

Dansereau, V.: Are sea-ice model parameters independent of convergence and resolution?, master's thesis, McGill University, 2011.

Dansereau, V.: A Maxwell-Elasto-Brittle model for the drift and deformation of sea ice, Theses, Université Grenoble Alpes, https://theses.hal.science/tel-01316987 (last access: 8 May 2024), 2016.

Dansereau, V., Weiss, J., Saramito, P., and Lattes, P.: A Maxwell elasto-brittle rheology for sea ice modelling, The Cryosphere, 10, 1339–1359, https://doi.org/10.5194/tc-10-1339-2016, 2016.

Dansereau, V., Weiss, J., Saramito, P., Lattes, P., and Coche, E.: Ice bridges and ridges in the Maxwell-EB sea ice rheology, The Cryosphere, 11, 2033–2058, https://doi.org/10.5194/tc-11-2033-2017, 2017.

Evensen, G.: The ensemble Kalman filter: Theoretical formulation and practical implementation, Ocean Dynam., 53, 343–367, https://doi.org/10.1007/s10236-003-0036-9, 2003.

Evensen, G., Vossepoel, F. C., and van Leeuwen, P. J.: Data assimilation fundamentals: A unified formulation of the state and parameter estimation problem, Springer Nature, ISBN 978-3-030-96708-6, 2022.

Fiedler, E. K., Martin, M. J., Blockley, E., Mignac, D., Fournier, N., Ridout, A., Shepherd, A., and Tilling, R.: Assimilation of sea ice thickness derived from CryoSat-2 along-track freeboard measurements into the Met Office's Forecast Ocean Assimilation Model (FOAM), The Cryosphere, 16, 61–85, https://doi.org/10.5194/tc-16-61-2022, 2022a.

Fiedler, E. K., Martin, M. J., Blockley, E., Mignac, D., Fournier, N., Ridout, A., Shepherd, A., and Tilling, R.: Assimilation of sea ice thickness derived from CryoSat-2 along-track freeboard measurements into the Met Office's Forecast Ocean Assimilation Model (FOAM), The Cryosphere, 16, 61–85, https://doi.org/10.5194/tc-16-61-2022, 2022b.

Grudzien, C., Carrassi, A., and Bocquet, M.: Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error, Nonlin. Processes Geophys., 25, 633–648, https://doi.org/10.5194/npg-25-633-2018, 2018.

Guemas, V., Blanchard-Wrigglesworth, E., Chevallier, M., Day, J. J., Déqué, M., Doblas-Reyes, F. J., Fučkar, N. S., Germe, A., Hawkins, E., Keeley, S., Koenigk, T., Salas y Mélia, D., and Tietsche, S.: A review on Arctic sea-ice predictability and prediction on seasonal to decadal time-scales, Q. J. Roy. Meteor. Soc., 142, 546–561, https://doi.org/10.1002/qj.2401, 2016.

Haussaire, J.-M. and Bocquet, M.: A low-order coupled chemistry meteorology model for testing online and offline data assimilation schemes: L95-GRS (v1.0), Geosci. Model Dev., 9, 393–412, https://doi.org/10.5194/gmd-9-393-2016, 2016.

Heorton, H. D. B. S., Tsamados, M., Cole, S. T., Ferreira, A. M. G., Berbellini, A., Fox, M., and Armitage, T. W. K.: Retrieving sea ice drag coefficients and turning angles from in situ and satellite observations using an inverse modeling framework, J. Geophys. Res.-Oceans, 124, 6388–6413, https://doi.org/10.1029/2018JC014881, 2019.

Hunke, E. C., Lipscomb, W. H., Turner, A. K., Jeffery, N., and Elliott, S.: Cice: the los alamos sea ice model documentation and software user's manual version 4.1 la-cc-06-012, T-3 Fluid Dynamics Group, Los Alamos National Laboratory, 675, 500, 2010.

Jakobson, E., Vihma, T., Palo, T., Jakobson, L., Keernik, H., and Jaagus, J.: Validation of atmospheric reanalyses over the central Arctic Ocean, Geophys. Res. Lett., 39, L10802, https://doi.org/10.1029/2012GL051591, 2012.

Lauritzen, P. H., Skamarock, W. C., Prather, M. J., and Taylor, M. A.: A standard test case suite for two-dimensional lin-
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Bertino, L. and Holland, M. M.: Coupled ice-ocean modeling and predictions, J. Marine Res., 75, 839–875, 2017.

Blockley, E. W. and Peterson, K. A.: Improving Met Office seasonal predictions of Arctic sea ice using assimilation of CryoSat-2 thickness, The Cryosphere, 12, 3419–3438, https://doi.org/10.5194/tc-12-3419-2018, 2018.

Bocquet, M.: Parameter field estimation for atmospheric dispersion: Application to the Chernobyl accident using 4D-Var, Q. J. Roy. Meteor. Soc., 138, 664–681, https://doi.org/10.1002/qj.961, 2012.

Bocquet, M.: Localization and the iterative ensemble Kalman smoother, Q. J. Roy. Meteor. Soc., 142, 1075–1089, https://doi.org/10.1002/qj.2711, 2016.

Bocquet, M. and Sakov, P.: Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems, Nonlin. Processes Geophys., 19, 383–399, https://doi.org/10.5194/npg-19-383-2012, 2012.

Bocquet, M. and Sakov, P.: Joint state and parameter estimation with an iterative ensemble Kalman smoother, Nonlin. Processes Geophys., 20, 803–818, https://doi.org/10.5194/npg-20-803-2013, 2013.

Bocquet, M. and Sakov, P.: An iterative ensemble Kalman smoother, Q. J. Roy. Meteor. Soc., 140, 1521–1535, https://doi.org/10.1002/qj.2236, 2014.

Bocquet, M., Farchi, A., and Malartic, Q.: Online learning of both state and dynamics using ensemble Kalman filters, Foundations of Data Science, 3, 305–330, https://doi.org/10.3934/fods.2020015, 2021.

Bouillon, S. and Rampal, P.: Presentation of the dynamical core of neXtSIM, a new sea ice model, Ocean Model., 91, 23–37, https://doi.org/10.1016/j.ocemod.2015.04.005, 2015.

Boutin, G., Ólason, E., Rampal, P., Regan, H., Lique, C., Talandier, C., Brodeau, L., and Ricker, R.: Arctic sea ice mass balance in a new coupled ice-ocean model using a brittle rheology framework, The Cryosphere, 17, 617–638, https://doi.org/10.5194/tc-17-617-2023, 2023.

Carrassi, A., Bocquet, M., Bertino, L., and Evensen, G.: Data assimilation in the geosciences: An overview of methods, issues, and perspectives, WIREs Climate Change, 9, e535, https://doi.org/10.1002/wcc.535, 2018.

Chen, Y.: Multivariate state and parameter estimation with data assimilation on sea-ice models using a Maxwell- Elasto-Brittle rheology, Zenodo [code and data set], https://doi.org/10.5281/zenodo.8224997, 2023.

Cheng, S., Aydoğdu, A., Rampal, P., Carrassi, A., and Bertino, L.: Probabilistic forecasts of sea ice trajectories in the Arctic: impact of uncertainties in surface wind and ice cohesion, Oceans, 1, 326–342, https://doi.org/10.3390/oceans1040022, 2020.

Cheng, S., Chen, Y., Aydoğdu, A., Bertino, L., Carrassi, A., Rampal, P., and Jones, C. K. R. T.: Arctic sea ice data assimilation combining an ensemble Kalman filter with a novel Lagrangian sea ice model for the winter 2019–2020, The Cryosphere, 17, 1735–1754, https://doi.org/10.5194/tc-17-1735-2023, 2023.

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Dansereau, V.: A Maxwell-Elasto-Brittle model for the drift and deformation of sea ice, Theses, Université Grenoble Alpes, https://theses.hal.science/tel-01316987 (last access: 8 May 2024), 2016.

Dansereau, V., Weiss, J., Saramito, P., and Lattes, P.: A Maxwell elasto-brittle rheology for sea ice modelling, The Cryosphere, 10, 1339–1359, https://doi.org/10.5194/tc-10-1339-2016, 2016.

Dansereau, V., Weiss, J., Saramito, P., Lattes, P., and Coche, E.: Ice bridges and ridges in the Maxwell-EB sea ice rheology, The Cryosphere, 11, 2033–2058, https://doi.org/10.5194/tc-11-2033-2017, 2017.

Evensen, G.: The ensemble Kalman filter: Theoretical formulation and practical implementation, Ocean Dynam., 53, 343–367, https://doi.org/10.1007/s10236-003-0036-9, 2003.

Evensen, G., Vossepoel, F. C., and van Leeuwen, P. J.: Data assimilation fundamentals: A unified formulation of the state and parameter estimation problem, Springer Nature, ISBN 978-3-030-96708-6, 2022.

Fiedler, E. K., Martin, M. J., Blockley, E., Mignac, D., Fournier, N., Ridout, A., Shepherd, A., and Tilling, R.: Assimilation of sea ice thickness derived from CryoSat-2 along-track freeboard measurements into the Met Office's Forecast Ocean Assimilation Model (FOAM), The Cryosphere, 16, 61–85, https://doi.org/10.5194/tc-16-61-2022, 2022a.

Fiedler, E. K., Martin, M. J., Blockley, E., Mignac, D., Fournier, N., Ridout, A., Shepherd, A., and Tilling, R.: Assimilation of sea ice thickness derived from CryoSat-2 along-track freeboard measurements into the Met Office's Forecast Ocean Assimilation Model (FOAM), The Cryosphere, 16, 61–85, https://doi.org/10.5194/tc-16-61-2022, 2022b.

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Guemas, V., Blanchard-Wrigglesworth, E., Chevallier, M., Day, J. J., Déqué, M., Doblas-Reyes, F. J., Fučkar, N. S., Germe, A., Hawkins, E., Keeley, S., Koenigk, T., Salas y Mélia, D., and Tietsche, S.: A review on Arctic sea-ice predictability and prediction on seasonal to decadal time-scales, Q. J. Roy. Meteor. Soc., 142, 546–561, https://doi.org/10.1002/qj.2401, 2016.

Haussaire, J.-M. and Bocquet, M.: A low-order coupled chemistry meteorology model for testing online and offline data assimilation schemes: L95-GRS (v1.0), Geosci. Model Dev., 9, 393–412, https://doi.org/10.5194/gmd-9-393-2016, 2016.

Heorton, H. D. B. S., Tsamados, M., Cole, S. T., Ferreira, A. M. G., Berbellini, A., Fox, M., and Armitage, T. W. K.: Retrieving sea ice drag coefficients and turning angles from in situ and satellite observations using an inverse modeling framework, J. Geophys. Res.-Oceans, 124, 6388–6413, https://doi.org/10.1029/2018JC014881, 2019.

Hunke, E. C., Lipscomb, W. H., Turner, A. K., Jeffery, N., and Elliott, S.: Cice: the los alamos sea ice model documentation and software user's manual version 4.1 la-cc-06-012, T-3 Fluid Dynamics Group, Los Alamos National Laboratory, 675, 500, 2010.

Jakobson, E., Vihma, T., Palo, T., Jakobson, L., Keernik, H., and Jaagus, J.: Validation of atmospheric reanalyses over the central Arctic Ocean, Geophys. Res. Lett., 39, L10802, https://doi.org/10.1029/2012GL051591, 2012.

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Lisæter, K. A., Rosanova, J., and Evensen, G.: Assimilation of ice concentration in a coupled ice–ocean model, using the Ensemble Kalman filter, Ocean Dynam., 53, 368–388, https://doi.org/10.1007/s10236-003-0049-4, 2003.

Malartic, Q., Farchi, A., and Bocquet, M.: State, global, and local parameter estimation using local ensemble Kalman filters: Applications to online machine learning of chaotic dynamics, Q. J. Roy. Meteor. Soc., 148, 2167–2193, https://doi.org/10.1002/qj.4297, 2022.

Massonnet, F., Goosse, H., Fichefet, T., and Counillon, F.: Calibra-
tion of sea ice dynamic parameters in an ocean-sea ice model
using an ensemble Kalman filter, J. Geophys. Res.-Oceans, 119,
4168–4184, https://doi.org/10.1002/2013JC009705, 2014.

Massonnet, F., Fichefet, T., and Goosse, H.: Prospects for improved seasonal Arctic sea ice predictions from multivariate data assimilation, Ocean Model., 88, 16–25, https://doi.org/10.1016/j.ocemod.2014.12.013, 2015.

Meier, W. N.: Losing Arctic sea ice: observations of the recent decline and the long-term context, chap. 11, 290–303, John Wiley & Sons, Ltd, ISBN 9781118778371, https://doi.org/10.1002/9781118778371.ch11, 2017.

Miller, P. A., Laxon, S. W., Feltham, D. L., and Cresswell, D. J.: Optimization of a sea ice model using basinwide observations of Arctic sea ice thickness, extent, and velocity, J. Climate, 19, 1089–1108, https://doi.org/10.1175/JCLI3648.1, 2006.

Mioduszewski, J. R., Vavrus, S., Wang, M., Holland, M., and Lan-
drum, L.: Past and future interannual variability in Arctic sea
ice in coupled climate models, The Cryosphere, 13, 113–124,
https://doi.org/10.5194/tc-13-113-2019, 2019.

Flood inundation model updating using an ensemble Kalman fil-
ter and spatially distributed measurements, J. Hydrol., 336, 401–
415, https://doi.org/10.1016/j.jhydrol.2007.01.012, 2007.

Park, S. K. and Zupanski, M.: Principles of Data Assimilation,
Cambridge University Press, ISBN 9781108924238, 2022.

Pasmans, I., Chen, Y., Carrassi, A., and Jones, C. K. R. T.: TAI-
loring data assimilation to discontinuous Galerkin models, arXiv
[preprint], https://doi.org/10.48550/arXiv.2305.02950, 2023.

Rabatel, M., Rampal, P., Carrassi, A., Bertino, L., and Jones, C. K. R. T.: Impact of rheology on probabilistic forecasts of sea ice trajectories: application for search and rescue operations in the Arctic, The Cryosphere, 12, 935–953, https://doi.org/10.5194/tc-12-935-2018, 2018.

Rampal, P., Bouillon, S., Ólason, E., and Morlighem, M.: neXtSIM: a new Lagrangian sea ice model, The Cryosphere, 10, 1055–1073, https://doi.org/10.5194/tc-10-1055-2016, 2016.

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.

Ruckstuhl, Y. M. and Janjić, T.: Parameter and state estimation with ensemble Kalman filter based algorithms for convective-

scale applications, Q. J. Roy. Meteor. Soc., 144, 826–841,
https://doi.org/10.1002/qj.3257, 2018.

Ruiz, J. J., Pulido, M., and Miyoshi, T.: Estimating model parameters with ensemble-based data assimilation: a review, J. Meteorol. Soc. Jpn. Ser. II, 91, 79–99, https://doi.org/10.2151/jmsj.2013-201, 2013.

Sakov, P., Counillon, F., Bertino, L., Lisæter, K. A., Oke, P. R., and Korablev, A.: TOPAZ4: an ocean-sea ice data assimilation system for the North Atlantic and Arctic, Ocean Sci., 8, 633–656, https://doi.org/10.5194/os-8-633-2012, 2012a.

Sakov, P., Oliver, D. S., and Bertino, L.: An iterative EnKF for strongly nonlinear systems, Mon. Weather Rev., 140, 1988–2004, https://doi.org/10.1175/MWR-D-11-00176.1, 2012b.

Sampson, C., Carrassi, A., Aydoğdu, A., and Jones, C. K.: Ensemble Kalman filter for nonconservative moving mesh solvers with a joint physics and mesh location update, Q. J. Roy. Meteor. Soc., 147, 1539–1561, https://doi.org/10.1002/qj.3980, 2021.

Scheffler, G., Carrassi, A., Ruiz, J., and Pulido, M.: Dynamical ef-
fects of inflation in ensemble-based data assimilation under the
presence of model error, Q. J. Roy. Meteor. Soc., 148, 2368–
2383, https://doi.org/10.1002/qj.4307, 2022.

Simon, E. and Bertino, L.: Application of the Gaussian anamorpho-
sis to assimilation in a 3-D coupled physical-ecosystem model
of the North Atlantic with the EnKF: a twin experiment, Ocean
Sci., 5, 495–510, https://doi.org/10.5194/os-5-495-2009, 2009.

Simon, E. and Bertino, L.: Gaussian anamorphosis extension of the DEnKF for combined state parameter estimation: Application to a 1D ocean ecosystem model, J. Marine Syst., 89, 1–18, https://doi.org/10.1016/j.jmarsys.2011.07.007, 2012.

Stark, J. D., Donlon, C. J., Martin, M. J., and McCulloch, M. E.: OS-
TIA: An operational, high resolution, real time, global sea sur-
face temperature analysis system, in: OCEANS 2007 – Europe,
1–4, https://doi.org/10.1109/OCEANSE.2007.4302251, 2007.

Toyoda, T., Fujii, Y., Yasuda, T., Usui, N., Ogawa, K., Kuragano, T., Tsujino, H., and Kamachi, M.: Data assimilation of sea ice concentration into a global ocean–sea ice model with corrections for atmospheric forcing and ocean temperature fields, J. Oceanogr., 72, 235–262, https://doi.org/10.1007/s10872-015-0326-0, 2016.

Weiss, J. and Dansereau, V.: Linking scales in sea ice mechanics, Philos. T. Roy. Soc. A, 375, 20150352, https://doi.org/10.1098/rsta.2015.0352, 2017.

Xie, J., Bertino, L., Counillon, F., Lisæter, K. A., and Sakov, P.: Quality assessment of the TOPAZ4 reanalysis in the Arctic over the period 1991–2013, Ocean Sci., 13, 123–144, https://doi.org/10.5194/os-13-123-2017, 2017.

Xie, J., Counillon, F., and Bertino, L.: Impact of assimilat-
ing a merged sea-ice thickness from CryoSat-2 and SMOS
in the Arctic reanalysis, The Cryosphere, 12, 3671–3691,
https://doi.org/10.5194/tc-12-3671-2018, 2018.

Zuo, H., Balmaseda, M. A., Tietsche, S., Mogensen, K., and Mayer, M.: The ECMWF operational ensemble reanalysis–analysis system for ocean and sea ice: a description of the system and assessment, Ocean Sci., 15, 779–808, https://doi.org/10.5194/os-15-779-2019, 2019.

Zupanski, M.: Maximum likelihood ensemble filter: theo-
retical aspects, Mon. Weather Rev., 133, 1710–1726,
https://doi.org/10.1175/MWR2946.1, 2005.
ear transport on the sphere, Geosci. Model Dev., 5, 887–901,
https://doi.org/10.5194/gmd-5-887-2012, 2012.

Lea, D. J., Mirouze, I., Martin, M. J., King, R. R., Hines, A., Wal-
ters, D., and Thurlow, M.: Assessing a new coupled data as-
similation system based on the Met Office coupled atmosphere–
land–ocean–sea ice model, Mon. Weather Rev., 143, 4678–4694,
https://doi.org/10.1175/MWR-D-15-0174.1, 2015.

Lisæter, K. A., Rosanova, J., and Evensen, G.: Assimilation of ice concentration in a coupled ice–ocean model, using the Ensemble Kalman filter, Ocean Dynam., 53, 368–388, https://doi.org/10.1007/s10236-003-0049-4, 2003.

Malartic, Q., Farchi, A., and Bocquet, M.: State, global, and local parameter estimation using local ensemble Kalman filters: Applications to online machine learning of chaotic dynamics, Q. J. Roy. Meteor. Soc., 148, 2167–2193, https://doi.org/10.1002/qj.4297, 2022.

Massonnet, F., Goosse, H., Fichefet, T., and Counillon, F.: Calibra-
tion of sea ice dynamic parameters in an ocean-sea ice model
using an ensemble Kalman filter, J. Geophys. Res.-Oceans, 119,
4168–4184, https://doi.org/10.1002/2013JC009705, 2014.

Massonnet, F., Fichefet, T., and Goosse, H.: Prospects for improved seasonal Arctic sea ice predictions from multivariate data assimilation, Ocean Model., 88, 16–25, https://doi.org/10.1016/j.ocemod.2014.12.013, 2015.

Meier, W. N.: Losing Arctic sea ice: observations of the recent decline and the long-term context, chap. 11, 290–303, John Wiley & Sons, Ltd, ISBN 9781118778371, https://doi.org/10.1002/9781118778371.ch11, 2017.

Miller, P. A., Laxon, S. W., Feltham, D. L., and Cresswell, D. J.: Optimization of a sea ice model using basinwide observations of Arctic sea ice thickness, extent, and velocity, J. Climate, 19, 1089–1108, https://doi.org/10.1175/JCLI3648.1, 2006.

Mioduszewski, J. R., Vavrus, S., Wang, M., Holland, M., and Lan-
drum, L.: Past and future interannual variability in Arctic sea
ice in coupled climate models, The Cryosphere, 13, 113–124,
https://doi.org/10.5194/tc-13-113-2019, 2019.

Flood inundation model updating using an ensemble Kalman fil-
ter and spatially distributed measurements, J. Hydrol., 336, 401–
415, https://doi.org/10.1016/j.jhydrol.2007.01.012, 2007.

Park, S. K. and Zupanski, M.: Principles of Data Assimilation,
Cambridge University Press, ISBN 9781108924238, 2022.

Pasmans, I., Chen, Y., Carrassi, A., and Jones, C. K. R. T.: TAI-
loring data assimilation to discontinuous Galerkin models, arXiv
[preprint], https://doi.org/10.48550/arXiv.2305.02950, 2023.

Rabatel, M., Rampal, P., Carrassi, A., Bertino, L., and Jones, C. K. R. T.: Impact of rheology on probabilistic forecasts of sea ice trajectories: application for search and rescue operations in the Arctic, The Cryosphere, 12, 935–953, https://doi.org/10.5194/tc-12-935-2018, 2018.

Rampal, P., Bouillon, S., Ólason, E., and Morlighem, M.: neXtSIM: a new Lagrangian sea ice model, The Cryosphere, 10, 1055–1073, https://doi.org/10.5194/tc-10-1055-2016, 2016.

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.

Ruckstuhl, Y. M. and Janjić, T.: Parameter and state estimation with ensemble Kalman filter based algorithms for convective-

scale applications, Q. J. Roy. Meteor. Soc., 144, 826–841,
https://doi.org/10.1002/qj.3257, 2018.

Ruiz, J. J., Pulido, M., and Miyoshi, T.: Estimating model parameters with ensemble-based data assimilation: a review, J. Meteorol. Soc. Jpn. Ser. II, 91, 79–99, https://doi.org/10.2151/jmsj.2013-201, 2013.

Sakov, P., Counillon, F., Bertino, L., Lisæter, K. A., Oke, P. R., and Korablev, A.: TOPAZ4: an ocean-sea ice data assimilation system for the North Atlantic and Arctic, Ocean Sci., 8, 633–656, https://doi.org/10.5194/os-8-633-2012, 2012a.

Sakov, P., Oliver, D. S., and Bertino, L.: An iterative EnKF for strongly nonlinear systems, Mon. Weather Rev., 140, 1988–2004, https://doi.org/10.1175/MWR-D-11-00176.1, 2012b.

Sampson, C., Carrassi, A., Aydoğdu, A., and Jones, C. K.: Ensemble Kalman filter for nonconservative moving mesh solvers with a joint physics and mesh location update, Q. J. Roy. Meteor. Soc., 147, 1539–1561, https://doi.org/10.1002/qj.3980, 2021.

Scheffler, G., Carrassi, A., Ruiz, J., and Pulido, M.: Dynamical ef-
fects of inflation in ensemble-based data assimilation under the
presence of model error, Q. J. Roy. Meteor. Soc., 148, 2368–
2383, https://doi.org/10.1002/qj.4307, 2022.

Simon, E. and Bertino, L.: Application of the Gaussian anamorpho-
sis to assimilation in a 3-D coupled physical-ecosystem model
of the North Atlantic with the EnKF: a twin experiment, Ocean
Sci., 5, 495–510, https://doi.org/10.5194/os-5-495-2009, 2009.

Simon, E. and Bertino, L.: Gaussian anamorphosis extension of the DEnKF for combined state parameter estimation: Application to a 1D ocean ecosystem model, J. Marine Syst., 89, 1–18, https://doi.org/10.1016/j.jmarsys.2011.07.007, 2012.

Stark, J. D., Donlon, C. J., Martin, M. J., and McCulloch, M. E.: OS-
TIA: An operational, high resolution, real time, global sea sur-
face temperature analysis system, in: OCEANS 2007 – Europe,
1–4, https://doi.org/10.1109/OCEANSE.2007.4302251, 2007.

Toyoda, T., Fujii, Y., Yasuda, T., Usui, N., Ogawa, K., Kuragano, T., Tsujino, H., and Kamachi, M.: Data assimilation of sea ice concentration into a global ocean–sea ice model with corrections for atmospheric forcing and ocean temperature fields, J. Oceanogr., 72, 235–262, https://doi.org/10.1007/s10872-015-0326-0, 2016.

Weiss, J. and Dansereau, V.: Linking scales in sea ice mechanics, Philos. T. Roy. Soc. A, 375, 20150352, https://doi.org/10.1098/rsta.2015.0352, 2017.

Xie, J., Bertino, L., Counillon, F., Lisæter, K. A., and Sakov, P.: Quality assessment of the TOPAZ4 reanalysis in the Arctic over the period 1991–2013, Ocean Sci., 13, 123–144, https://doi.org/10.5194/os-13-123-2017, 2017.

Xie, J., Counillon, F., and Bertino, L.: Impact of assimilat-
ing a merged sea-ice thickness from CryoSat-2 and SMOS
in the Arctic reanalysis, The Cryosphere, 12, 3671–3691,
https://doi.org/10.5194/tc-12-3671-2018, 2018.

Zuo, H., Balmaseda, M. A., Tietsche, S., Mogensen, K., and Mayer, M.: The ECMWF operational ensemble reanalysis–analysis system for ocean and sea ice: a description of the system and assessment, Ocean Sci., 15, 779–808, https://doi.org/10.5194/os-15-779-2019, 2019.

Zupanski, M.: Maximum likelihood ensemble filter: theoreti-
cal aspects, Mon. Weather Rev., 133, 1710–1726,
https://doi.org/10.1175/MWR2946.1, 2005.