Thanks for the comment.

We have uploaded the exact input data, output data, and the well-trained model weights to the new Zenodo repository with a DOI: https://doi.org/10.5281/zenodo.14561423. We have added detail introductions for the upload files to make sure the model can be run:

1. The codes of the model are in the model_utils folders.
2. The jupyter file "SICNet_season_training.ipynb" contains the flow of loading data, defining a model, and training the model.
3. The jupyter file "SICNet_season_evaluating.ipynb" includes evaluating the trained model and drawing the ACC/BACC result.
4. The training and testing data are in the Data/Data.zip file and can be loaded for training and evaluation of the model. The files "SIC_1979_2020_Jan_May_96.npy", "SIT_1979_2020_Jan_May_96.npy", "SIC_climate_mean_96.npy", and "mask_96.npy" are input data for model training. The "Output data" file contains the predicted results output by SICNetseason model, "Predicted_SIC_output.npy". The "Ground_SIC_output.npy" in this file is the ground truth from NSIDC.
5. The Model_SICNet.zip contains the saved well-trained models. Please unpackage the zip file and copy the  .h5 files to the corresponding file path "/Result/Model_SICNet". Then, the "SICNet_season_evaluating.ipynb" can be run to genernate the predicted values by the well-trained models. 

We also revised the “Code and data availability” session as follow:

The satellite-observed sea ice concentration is obtained from the following site https://nsidc.org/data/NSIDC-0081/versions/1 (Cavalieri et al., 1996). The reanalysis of sea ice thickness data is open access (http://psc.apl.uw.edu/research/projects/arctic-sea-ice-volume-anomaly/data/model_grid) (Zhang and Rothrock, 2003). The seasonal predictions of SEAS5 are obtained from the ECMWF (https://cds.climate.copernicus.eu/cdsapp#!/dataset/seasonal-monthly-single-levels?tab=form) (Johnson et al., 2019). The code, the exact input/output data, and the saved well-trained weights of the developed model SICNetseason are available at https://doi.org/10.5281/zenodo.14561423.

We upload the revised manuscript with the new “Code and data availability”  section as supplement.

Summary

The manuscript "SICNet_season V1.0: a transformer-based deep learning model for seasonal Arctic sea ice prediction by incorporating sea ice thickness data" by Ren et al presents a seasonal forecast model for Arctic sea ice, based on deep learning. This paper presents a novel approach to training DL models for sea ice prediction, by integrating a loss function which considers spatial information (the Integrated Ice Edge Error), as well as the standard Mean-Squred Error (MSE). The authors claim that, by including PIOMAS sea ice thickness reanalysis in their training, SICNet_season is able to "optimize" the spring predictability barrier, improving forecasts of September sea ice made before June 1st. These forecasts are benchmarked against a damped persistence forecast, and the ECMWF SEAS5 seasonal prediction system. Overall the paper is well written and is a nice contribution to the sea ice prediction literature. I recommend minor revisions before publication.

Response: Thanks for the comment.

General comments

Comment 1: One small comment I have relates to how the Spring Predictability Barrier (SBP) is motivated and referenced throughout the manuscript. I suggest changing statements like "optimize the SPB" to "optimize predictions around the SPB", and remove statements such as "overcome the SPB" on L60 and elsewhere. I think it's important to make it clear to the reader that the SPB is an inherent characteristic of Arctic sea ice that cannot be overcome by better data, as it relates to how physical sea ice mass anomalies are locked in by ice-albedo feedbacks at the date of melt onset. Having thickness data before the SPB is of limited use because thickness anomalies in winter-spring are primarily driven by export (and moderated by negative ice growth feedbacks), hence these anomalies do not persist for long.

Response: Agreed and revised. We revised statements like "optimize the SPB" or "overcome the SPB" to "optimize predictions around the SPB."

Comment 2: Another comment relates to how SICNet_season is trained and evaluated. I think in the sea ice prediction community we would probably consider this leave-one-out evaluation as "cheating", as you have optimized the weights of the network using future data. As you say on L148, for a testing year 2000, you train using data from 1979-1999 and 2001-2019. Meanwhile If you were really making this forecast in 2000, you would only have had access to data from 1979-1999. Your model therefore has a much better understanding of sea ice variability and trends than it should have in the year 2000. This ultimately makes me question how fair it is to  compare this model to damped persistence, unless you computed the damped persistence forecast in a similar leave-one-out way? For example, for a damped persistence forecast in the year 2000, are the anomalies at the chosen lead time based on a linear trend climatology computed over the period 1979-1999, or 1979-2019? The same question for the anomaly standard deviation and correlations. In any case, I think what would be most preferable is if the damped persistence forecasts were generated using only past data, and SICNetseason is trained for each forecast year, using only past data. Otherwise, I feel the only forecast evaluations I can consider "fair" are those over 2020-2023.

Response: Thanks for the comment. The main reason for using the leave-one-out strategy is to evaluate the model's performance in a long time series with limited samples, which reviewers of a previous submission suggested. The sample volume for seasonal scale predictions with monthly mean data is not large. So, some statistical models [1-2] adopted the "leave-one-out" cross-validation to maximize the sample volume while obtaining a multi-year evaluation. Especially for deep learning models, the sample volume is vital for model training. If we train the model using data from 1979 to 1999 for the 2000 evaluation, the volume of training samples will be reduced by half. When we use the leave-one-out strategy, we randomly shuffle all samples for each training epoch to eliminate the influence of trends. The sea ice trends from the past have been disrupted. In this instance, the model can not learn the long-term trend. Besides, the ACC we calculated is the detrended ACC. These measures eliminate the contribution of the long-term trend to the model skill. Therefore, we have to utilize the "leave-one-out" strategy and try our best to eliminate the influence of the sea ice trend.

We used the Anomaly Persistence baseline, not the Damped Anomaly Persistence. Sorry for the misleading statement. We have clarified this point in the revision; see following Comment 12. As referred to in Yuan's papers [1], Persistence prediction is calculated using the current anomaly plus the climatology at the target time to estimate the future state. The climatology is the mean state of 1979-2019, excluding the target year.

[1] Yuan, X., Chen, D., Li, C., Wang, L., and Wang, W.: Arctic sea ice seasonal prediction by a linear markov model, J Clim, 29, 8151–8173, https://doi.org/10.1175/JCLI-D-15-0858.s1, 2016.

[2] Wang, Y., Yuan, X., Bi, H., Bushuk, M., Liang, Y., Li, C., and Huang, H.: Reassessing seasonal sea ice predictability of the Pacific-Arctic sector using a Markov model, Cryosphere, 16, 1141–1156, https://doi.org/10.5194/tc-16-1141-2022, 2022.

Comment 3: Lastly, I have concerns about the comparison with ICENet. On L268-271 you describe how you have changed ICENet's training procedure and architecture to be similar to SICNet_season to make it a fairer comparison. I actually feel like this is less fair to ICENet. The original ICENet architecture, loss function, and inputs were optimized for the task outlined in the Andersson 2021 paper, and changing these may result in sub-optimal predictions. Effectively, you're no longer using ICENet. I suggest in this section you make a fair comparison to the original (unchanged) ICENet model, or you change the labelling to say you're comparing SICNet_season with an (ICENet-inspired) U-Net architecture.

Response: Thanks for the comment. Agreed. The original IceNet treated the sea ice prediction (regression task) as a classification task. Here, we implemented the same backbone as the original IceNet and changed the classification output layer to a regression one. We adopted the comment and revised the "IceNet" labeling as "U-Net (IceNet-inspired)."

Minor comments

Comment 1 L11: suggest changing "predictions made later than May" to "predictions made later than the date of melt onset (roughly May)."

Response: Agreed and revised.

Comment 2 L17: suggest stating explicitly that the ECMWF model is the SEAS5 model

Response: Agreed and revised.

Comment 3 L30: instead of referencing Andersson et al., 2021 here, I would reference papers specifically focused on ice-free timing, like Jahn et al 2024 and Kim et al 2023.

Response: Agreed and revised.

Comment 4 L31: suggest changing to "it may weaken the stratospheric polar vortex", as actually Blackport et al., 2019 suggests that it likely does not.

Response: Agreed and revised.

Comment 5 L43: suggest changing "before or on May" to "before or at the timing of melt onset"

Response: Agreed and revised.

Comment 6 L45/46: Actually many statistical and dynamical models do beat damped persistence on these timescales. See the recent review paper by Bushuk et al 2024.

Response: Agreed. We delete this sentence in the revision.

Comment 7 L61: suggest clarifying what you mean here by "mainstream" sea ice prediction

Response: Thanks for the comment. We revised the sentence as "numerical models are widely used in operationally sea ice predicting."

Comment 8 L76: Clarify that this is the SEAS5 model

Response: Agreed and revised.

Comment 9 L84: Is there a reason you don't use the more up-to-date (version 2) NSIDC sea ice concentration data set? https://doi.org/10.5067/MPYG15WAA4WX

Response: Thanks for the comment. We used the version 2 data set and made a wrong citation. We replaced the old reference with the following new one in the revision.

[1] DiGirolamo, N., Parkinson, C. L., Cavalieri, D. J., Gloersen, P. & Zwally, H. J. (2022). Sea Ice Concentrations from Nimbus-7 SMMR and DMSP SSM/I-SSMIS Passive Microwave Data. (NSIDC-0051, Version 2). [Data Set]. Boulder, Colorado USA. NASA National Snow and Ice Data Center Distributed Active Archive Center.

Comment 10 L89: suggest adding that PIOMAS generally overestimates thin ice and underestimates thick ice regions

Response: Agreed and revised.

Comment 11 L97: Just to clarify, the inputs to the network are monthly-mean fields, and you are predicting monthly-mean fields? So a Lead 4 prediction of September-mean SIC is based on monthly-mean May data?

Response: Agreed and revised. We added "the inputs to the network are monthly-mean fields" in the revision. The input length of the monthly mean SIC/SIT is six/three. So, a lead four prediction of September-mean SIC is based on monthly-mean SIC/SIT of Dec.-May/Mar.-May. We explain more about the input factors and their lengths in the revised Section 3.1.

Comment 12 L167: suggest clarifying that by "Persistence model" you mean "Damped Anomaly Persistence"

Response: Thanks for the comment. The "Persistence model" we used is "Anomaly Persistence," not the "Damped Anomaly Persistence." It is calculated, referred to in Yuan's paper [1], using the current anomaly plus the climatology at the target time to estimate the future state. As Yuan's studies show, the ACCs of "Anomaly Persistence" and "Damped Anomaly Persistence" in subseasonal are very similar, so we used "Anomaly Persistence" in our study. We clarify this point in the revision:

The Persistence is the anomaly persistence model. It assumes the anomaly constant in time and estimates the target SIC values by adding the current anomaly to the climate mean state at the target time, widely adopted as a benchmark for sea ice prediction (Wang et al., 2016).

[1] Wang, L., Yuan, X., Ting, M., and Li, C.: Predicting summer arctic sea ice concentration intraseasonal variability using a vector autoregressive model, J Clim, 29, 1529–1543, https://doi.org/10.1175/JCLI-D-15-0313.1, 2016.

Comment 13 L204: Can you speculate here whether the lead 1 and 2 predictions from ECWMF are better because of their good atmospheric initialization? Certainly in Bushuk et al 2024, ECMWF SEAS5 beats all other dynamical forecast systems for Jun 1 to Sep 1 initializations, possibly for this reason. Did you test including atmospheric variables in your training?

Response: Thanks for the comment. Yes, that may be a reason. Zampieri et al. (2018) revealed that the ECMWF outperforms the climatology and many dynamical models in predicting SIC 0-45 days [1]. Bushuk et al. (2024) also showed that the RMSE of SEAS5 is lower than that of most statical models in Agu./Sep. 1 initialization [2]. These results demonstrate that the atmospheric initialization of SEAS5 may provide performance in sub-seasonal scale prediction. We did not include atmospheric variables in this study because an ablation experiment with different variables requires a lot of work and 20 years of testing. We have another paper focusing on evaluating the contributions of atmospheric variables (SAT, SST, surface radiation, SLP, etc.), which is under revision now. We revised the L204 as follows:

When the lead month is one, the MAE of SEAS5 is slightly better than that of Persistence and SICNet_season, indicating that the SEAS5 model performs well in monthly predicting. This result may be due to the good atmospheric initialization in SEAS5, which beat many machine learning and dynamical models in sub-seasonal scale SIC prediction (Bushuk et al., 2024).

[1] Zampieri, L., Goessling, H. F., and Jung, T.: Bright Prospects for Arctic Sea Ice Prediction on Subseasonal Time Scales, Geophys Res Lett, 45, 9731–9738, https://doi.org/10.1029/2018GL079394, 2018.

[2] Bushuk et al. Predicting September Arctic Sea Ice: A Multimodel Seasonal Skill Comparison. BAMS (2024).

Comment 14 L228/229: change "cycles" to "circles."

Response: Agreed and revised.

Comment 15 L253: change "generalization ability" to "generalization."

Response: Agreed and revised.

Comment 16 Figures: I think generally the figures throughout the manuscript are quite small and it's difficult to read the numbers in the ACC/BACC plots (especially when the manuscript is printed). Also some of the spatial maps like Figure 7 are very busy with many panels, and it's hard to distinguish between contour lines without really zooming in (also please choose a different color for contours other than red and green for color blind readers). In figure 7 I suggest just showing one or two example lead months, so that the individual panels can be made bigger and easier to see.

Response: Agreed and revised. In the revision, we plotted the figures using a large font size. We deleted some panels and kept only nine in Figure 7, lead months 4-6 of 2020, 2021, and 2023. The panels in Figure 7 are easier to read than before. The green and red lines have also been replaced by cyan and orange. Some new figures are shown as follows:

Figure 2. Detrend ACC of SIE, BACC of SIE, and their differences of Persistence, SEAS5, and SICNet_season from Jun. to Sep., averaged by 2000-2019. (a)-(c) Detrend ACC of three models. Two detrend SIE series (predicted and observed) calculate each value. (d)-(e) Detrend ACC differences between SICNet_season and Persistence/SEAS5. (f)-(h) BACC of three models. Each BACC is a mean value during 20 testing years. (i)-(j) BACC differences of SICNet_season and Persistence/SEAS5. The black line indicates the SPB: a maximum decrease between two adjacent lead months. The red signifies a high/improvement in ACC/BACC, and the blue signifies a decrease.

Figure 4. Detrended ACC of SICNet_{season_nosit} (a) and SICNet_season (b). (c) ACC difference obtained by SICNet_season minus SICNet_{season_nosit}. BACC of SICNet_{season_nosit} (d) and SICNet_season (e). (f) BACC difference like (c).  The red signifies a high/improvement in ACC/BACC, and the blue signifies a decrease.

Figure 6. BACC of 2020-2023. (a) Persistence, (b) SEAS5, and (c) SICNet_season. Each value is a mean value of the four testing years. The horizontal axis represents the six lead months, and the vertical axis represents the target months, Jun. to Sep. The red signifies a high/improvement in ACC/BACC, and the blue signifies a decrease.

Figure 7. Predicted Sep. SIEs and their BACCs of 2020/2022/2023 in four to six months lead by Persistence, SEAS5, and SICNet_season. (a)-(c) 2020, (d)-(f) 2022, and (g)-(i) 2023.

Figure 8. Detrended ACC of IceNet (a) and SICNet_season (b). (c) ACC difference obtained by SICNet_season minus U-Net (IceNet-inspired). BACC of U-Net (IceNet-inspired)(d) and SICNet_season (e). (f) BACC difference like (c).  The red signifies a high/improvement in ACC/BACC, and the blue signifies a decrease.

Figure 9. The predicted Sep. SIEs of U-Net (IceNet-inspired) and SICNet_season in six months' lead: (a) 2012, (b) 2017, (c) 2018, and (d) 2019.

References



Jahn et al. Projections of an ice-free Arctic Ocean. Nature Reviews Earth and Environment (2024).

Kim et al. Observationally-constrained projections of an ice-free Arctic even under a low emissions scenario. Nature Communications (2023).

Bushuk et al. Predicting September Arctic Sea Ice: A Multimodel Seasonal Skill Comparison.BAMS(2024).

Response: Thanks. We cite these references in the revision.