the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Feb 2025
Four-dimensional variational data assimilation with a sea-ice thickness emulator
Abstract. Developing operational data assimilation systems for sea-ice models is challenging, especially using a variational approach due to the absence of adjoint models. NeXtSIM, a sea-ice model based on a brittle rheology paradigm, enables high-fidelity simulations of sea-ice dynamics at mesoscale resolution (~10 km) but lacks an adjoint. By training a neural network as an Arctic-wide emulator for sea-ice thickness based on mesoscale simulations with neXtSIM, we gain access to an adjoint. Building on this emulator and its adjoint, we introduce a four-dimensional variational (4D–Var) data assimilation system to correct the emulator's bias and to better position the marginal ice zone (MIZ). Firstly, we perform twin experiments to demonstrate the capabilities of this 4D–Var system and to evaluate two approximations of the background covariance matrix. These twin experiments demonstrate that the assimilation improves the positioning of the MIZ and enhances the forecast quality, achieving an average reduction in sea-ice thickness root-mean-squared error of 0.8 m compared to the free run. Secondly, we assimilate real CS2SMOS satellite retrievals with this system. While the assimilation of these rather smooth retrievals amplifies the loss of small-scale information in our system, it effectively corrects the forecast bias. The forecasts of our 4D–Var system achieve a similar performance as the operational sea-ice forecasting system neXtSIM-F. These results pave the way to the use of deep learning-based emulators for 4D–Var systems to improve sea-ice modeling.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(1771 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1771 KB) - Metadata XML
- BibTeX
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-4028', Anonymous Referee #1, 17 Mar 2025
- AC1: 'Reply on RC1', Charlotte Durand, 05 May 2025
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RC2: 'Comment on egusphere-2024-4028', Anonymous Referee #2, 20 Mar 2025
- AC2: 'Reply on RC2', Charlotte Durand, 05 May 2025
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-4028', Anonymous Referee #1, 17 Mar 2025
The manuscript "Four-dimensional variational data assimilation with a sea-ice thickness emulator" by Durand et al presents an evaluation of a 4D-Var data assimilation framework using a data-driven sea ice thickness emulator of the neXtSIM sea ice model. The authors show how, through the emulator's back-propagation capabilities, sea ice thickness observations (both idealized and real) can be assimilated into the emulator using 4D-Var, effectively reducing the emulator bias. I very much enjoyed reading this manuscript and think it's a nice contribution to the literature. In fact, most of the comments I had noted down by the time of the discussion were then answered in the discussion, so thanks! My comments were overall minor, and I think the manuscript is almost ready for publication with a few small edits (see below).
General question regarding methodology
Could you just clarify something about the methodology for me. Are the EOFs used for the background covariance static over the course of the DA simulation? My concern early on was the ability of the EOF approach to capture flow-dependent processes, given the strong seasonal cycle of sea ice (you do mention this in the discussion). Is there some expectation that the minimization figures out which EOFs are most important and dynamically weights them (in time) according to w? I would be very interested to see how the approach compares to an Ensemble Kalman Filter (as you also say in the discussion).Comments
L112: I suggest adding a citation to show an example of where observations are typically log-normal. E.g Landy et al 2020.
L117 and elsewhere: change “In average,” to “On average,”
L129 - L132: Somewhere in this section it might be worth highlighting a recent paper (Nab et al. 2025) which quantified the effect on DA-derived analysis fields due to varying observational uncertainty on sea ice thickness measurements—Turns out to be quite sensitive.
Figures 3 and 7: Missing text in all labels
L258: Doesn’t the RMSE in Fig 5 peak in July? I guess the bias error peaks just before May and then rises again in December? Maybe changing L258 to “from Fig. 5 top” to make it clear which panel in Fig 5 we are looking at
L306-310 : Can you borrow some info from data-driven NWP models which retain sharpness by augmenting loss function
L350 : Might be worth highlighting here that there are ongoing developments in this space. For example Chen et al and Gregory et al both show ML-based approaches for deriving complete daily sea ice and ocean fields from satellite altimetry at 5 km grid resolution. Both of these approaches model the spatio-temporal covariance of daily fields, rather than simply averaging through time. Although these studies show sea ice freeboard, it is conceivable that daily sea ice thickness observations are on the horizon.
L400: I thought neXtSIM-F was initialized through nudging and not EnKF (L274/275)?Appendix B: Can you quantify the time change in the 4D-var minimization when increasing the truncation index m? For example, on L324 you say it's 155 seconds for m=7000. What is the time if m is halved to 3500? I guess I'm wondering what is the cost-accuracy tradeoff.
References
Landy et al. Sea Ice Roughness Overlooked as a Key Source of Uncertainty in CryoSat‐2 Ice Freeboard Retrievals. JGR Oceans. 2020
Nab et al. Sensitivity to Sea Ice Thickness Parameters in a Coupled Ice‐Ocean Data Assimilation System. JAMES. 2025
Chen et al. Deep random features for scalable interpolation of spatiotemporal data. ICLR (arXiv). 2024
Gregory et al. Scalable interpolation of satellite altimetry data with probabilistic machine learning. Nature Communications. 2024Citation: https://doi.org/10.5194/egusphere-2024-4028-RC1 - AC1: 'Reply on RC1', Charlotte Durand, 05 May 2025
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RC2: 'Comment on egusphere-2024-4028', Anonymous Referee #2, 20 Mar 2025
- AC2: 'Reply on RC2', Charlotte Durand, 05 May 2025
Peer review completion
Journal article(s) based on this preprint
Data sets
Post-processed dataset Charlotte Durand https://doi.org/10.5281/zenodo.14418068
Model code and software
Python Code Charlotte Durand https://doi.org/10.5281/zenodo.14418068
Weights of the neural network Charlotte Durand https://doi.org/10.5281/zenodo.14418068
Interactive computing environment
Notebook to reproduce the figures Charlotte Durand https://doi.org/10.5281/zenodo.14418068
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- 1
Charlotte Durand
Tobias Sebastian Finn
Alban Farchi
Marc Bocquet
Julien Brajard
Laurent Bertino
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1771 KB) - Metadata XML
The manuscript "Four-dimensional variational data assimilation with a sea-ice thickness emulator" by Durand et al presents an evaluation of a 4D-Var data assimilation framework using a data-driven sea ice thickness emulator of the neXtSIM sea ice model. The authors show how, through the emulator's back-propagation capabilities, sea ice thickness observations (both idealized and real) can be assimilated into the emulator using 4D-Var, effectively reducing the emulator bias. I very much enjoyed reading this manuscript and think it's a nice contribution to the literature. In fact, most of the comments I had noted down by the time of the discussion were then answered in the discussion, so thanks! My comments were overall minor, and I think the manuscript is almost ready for publication with a few small edits (see below).
General question regarding methodology
Could you just clarify something about the methodology for me. Are the EOFs used for the background covariance static over the course of the DA simulation? My concern early on was the ability of the EOF approach to capture flow-dependent processes, given the strong seasonal cycle of sea ice (you do mention this in the discussion). Is there some expectation that the minimization figures out which EOFs are most important and dynamically weights them (in time) according to w? I would be very interested to see how the approach compares to an Ensemble Kalman Filter (as you also say in the discussion).
Comments
L112: I suggest adding a citation to show an example of where observations are typically log-normal. E.g Landy et al 2020.
L117 and elsewhere: change “In average,” to “On average,”
L129 - L132: Somewhere in this section it might be worth highlighting a recent paper (Nab et al. 2025) which quantified the effect on DA-derived analysis fields due to varying observational uncertainty on sea ice thickness measurements—Turns out to be quite sensitive.
Figures 3 and 7: Missing text in all labels
L258: Doesn’t the RMSE in Fig 5 peak in July? I guess the bias error peaks just before May and then rises again in December? Maybe changing L258 to “from Fig. 5 top” to make it clear which panel in Fig 5 we are looking at
L306-310 : Can you borrow some info from data-driven NWP models which retain sharpness by augmenting loss function
L350 : Might be worth highlighting here that there are ongoing developments in this space. For example Chen et al and Gregory et al both show ML-based approaches for deriving complete daily sea ice and ocean fields from satellite altimetry at 5 km grid resolution. Both of these approaches model the spatio-temporal covariance of daily fields, rather than simply averaging through time. Although these studies show sea ice freeboard, it is conceivable that daily sea ice thickness observations are on the horizon.
L400: I thought neXtSIM-F was initialized through nudging and not EnKF (L274/275)?
Appendix B: Can you quantify the time change in the 4D-var minimization when increasing the truncation index m? For example, on L324 you say it's 155 seconds for m=7000. What is the time if m is halved to 3500? I guess I'm wondering what is the cost-accuracy tradeoff.
References
Landy et al. Sea Ice Roughness Overlooked as a Key Source of Uncertainty in CryoSat‐2 Ice Freeboard Retrievals. JGR Oceans. 2020
Nab et al. Sensitivity to Sea Ice Thickness Parameters in a Coupled Ice‐Ocean Data Assimilation System. JAMES. 2025
Chen et al. Deep random features for scalable interpolation of spatiotemporal data. ICLR (arXiv). 2024
Gregory et al. Scalable interpolation of satellite altimetry data with probabilistic machine learning. Nature Communications. 2024