Data-Driven Uncertainty-Aware Forecasting of Sea Ice Conditions in the Gulf of Ob Based on Satellite Radar Imagery

Response to questions:

1. Novelty of Contributions. Our contributions include: the development of task-specific augmentations combining physical and geometric transformations to address missing data issues in satellite imagery; implementation of an uncertainty-aware pipeline using heterogeneous ensembles, demonstrating their effectiveness in geophysical contexts.
2. Model Adaptations. Models were adapted to handle missing values, a common issue in satellite-derived data (lines 341-343 and Figure 3 in the manuscript). All models were extended to work with multiple geophysical data channels, departing from the traditional RGB-focused implementations.
3. Evaluation of Practical Significance. It is challenging to assess the direct practical benefits of these forecasts without conducting a thorough practical study and onboarding the proposed methods for operational use by captains. However, this requires substantial additional work, which we believe lies beyond the scope of this paper. Initially we have consulted the icebreaker first mate who said that the satellite image direct operational forecasts could be of big help for route planning and that’s one of the reasons why we have made this study.
4. Generalizability. Our approach is expected to generalize well to regions of other Arctic rivers, however, we acknowledge that numerical models may be superior in regions with free sea surfaces. The challenges in sea ice modeling, such as limited satellite coverage and the dynamic nature of ice sheets, make this task uniquely demanding. Also, it would be interesting to apply the approach to glacier movement analysis and forecast. The explored techniques can be helpful in a broad range of geophysical applications, such as ocean biochemistry, ocean plastic pollution, and atmospheric pollution modelling.

We thank the reviewer for their constructive feedback. We appreciate the acknowledgment of the novelty of the task and the importance of the introduced augmentations. Below, we address the specific concerns and questions raised in the review:

Response to weaknesses:

1. Lack of Novel Methodological Contributions. We consider our main methodological contribution the proposed uncertainty quantification and uncertainty aware model switching scheme leveraging different ML models’ strengths and flaws. In particular we have shown that the ensemble of different ML methods produces a good uncertainty estimate for the complex geophysical task of sattelite radar image forecasting and the use of this estimate can improve the quality of the resulting prediction by switching between the models. We have improved the Contributions section to reflect this better. As a secondary contribution, we developed augmentations that combine physical and geometrical transformations to better align with geophysical characteristics and include handling irregularly missing values due to satellite coverage limitations.
2. Engineering Focus Over Research Innovation. We introduce data filtration and task-specific augmentations, which combine physical and geometrical transformations, and leverages the problem of irregularly missing values due to limitation of satellite coverage; we develop the uncertainty-aware pipeline, which results in performance improvement and provide uncertainty quantification, and proof the efficacy of heterogeneous ensemble in geophysical applications. We argue that our work enhances the connection between video prediction and the challenging task of high-resolution sea ice forecasting, which alignes well with ICLR relevant topics, such as applications of DL in geophysical and climate sciences.
3. Improvements Over Baselines. The improvements we achieved (1.5-2x better than baselines) are significant in the context of Arctic sea ice forecasting, where even small gains translate to operational benefits. The uncertainty estimation, being an additional result of the proposed approach, is also useful for the practical tasks such as icebreaker caravan route planning with risks consideration We also included an ablation study to explore the contribution of various techniques, such as uncertainty modeling and specialized augmentations, which helped achieve these improvements. Also Figure 6 in Appendix provides a brief analyis, showing that modern NWPs, like that producing GLORYS product struggle to forecast sea ice conditions in the Golf of Ob as well.
4. Theoretical Analysis. We acknowledge the importance of theoretical analysis and have provided additional context in the revised manuscript. The performance of optical flow estimation and prediction, an essential architecture feature of video prediction models, is limited in low-variability ice sheet regions and due to complexity of stochastic physics (see Appendix C). These insights highlight why video prediction models struggle in this domain, providing a foundation for future research. While a deeper theoretical analysis of model behavior is valuable, we note that this falls outside the primary scope of this work, which is centered on applying and adapting ML models for a novel and challenging task.

We thank the reviewer for their time and constructive feedback. We appreciate the acknowledgment of the novelty of the task and the importance of the introduced augmentations. Below, we address the specific concerns and questions raised in the review:

Response to weaknesses:

1. Overparameterization and performance. We agree on that the task is challenging. However, it is so for numerical models as well, as we point out in the paper. There are two reasons to choose large NN models: firstly, high resolution effectively increases amount of data (one can split the image into patches) and necessitates the usage of model with perception window large enough to capture global dynamics; что secondly, overparameterized models are widely used nowadays because of the specific properties giving them ability to converge to good solutions (probably suboptimal) as demonstrated in many works (e.g. https://www.sciencedirect.com/science/article/pii/S106352032100110X).
2. Text clarity. We updated the manuscript to improve clarity.
3. Contributions. We think that our main contribution is also the developed uncertainty-aware pipeline, which results in performance improvement and provides uncertainty quantification, and proof the efficacy of heterogeneous ensemble in geophysical applications. We argue that our work enhances the connection between video prediction and the challenging task of high-resolution sea ice forecasting, which aligns well with ICLR defined scopes.
4. Novelty. We argue that the task of vegetation forecasting is simpler due to absence of movement, the sea ice dynamics is much more complex. Moreover, our study incorporates the combination of physical and geometrical augmentations and develops the uncertainty-aware pipeline based on UNet, modified for autoregressive forecast and handling missing values (see Figure 3), DMVFN and heterogeneous ensemble.
5. Forecast resolution. Thanks for a good point and interesting proposal. We selected this resolution because it is at the frontier of modern research on sea ice forecasting and highlights the techniques that would be essential for the increase of resolution in further studies. The 1 km resolution is just enough for planning the icebraker caravan routes in the challenging conditions of the Gulf of Ob which we consider as one of the possible practical uses of our results.
6. Ensemble evaluation. We study the spread-error correlation of ensembles (see Figure 13). Up to 87% of variance is explained, which proves the heterogeneous ensemble to be efficient in geophysical application. We reckon that further investigation is out of scope of the study.
7. Formulations clarity. Thank you for pointing out these problematic moments! We fixed the aforementioned comments in the updated manuscript.
8. Related works. We consciously reduced the scope of related works. We firstly refer to one of the first data-driven sea ice forecasting models, then discuss most relevant modern models, specifically for short-term forecast in one kilometer resolution, and finally discuss works related to uncertainty quantification and gap filling. The study by Palermo et al is focused on 12.5km resolution and hence is out of scope.

Response to questions:

1. How do you split the different samples in the training period? We include sequences started at every date, so most of the images are inputs in some sequences and targets in others. The models never see the test subset, so we consider the provided metrics to be sound.
2. How do you do the backward forecast? For backward forecasting we reverse the input sequences and change the sign of winds and ocean currents. The second law of thermodynamics is obviously broken, however in the short-term timespan it still improves the performance of the gap filling as the diffusion lengthscale (including turbulent diffusion) is under the pixel size on these times.
3. Augmentation strategy. Yes, the same strategy is applied to train all models.
4. Sentinel-1 Product details. We use Sentinel-1 in Extra Wide (EW) mode to maximize coverage. Terrain radiometric correction on topography doesn’t affect sea surface, while the land surface is masked with zeros in terms to learn strictly sea ice dynamics.
5. IIEE. We agree that the definition and formula of this metric is important and added it in the Appendix, see line 867.
6. Could you explain the filtration in other words again? The filtration is realized via linear projection operator, which removes the part of additive noise with specific patterns (scalloping). The patterns were gathered from summer periods when there is no ice in the target region and were calibrated such that filtration would not modify the neutral image (the left one in Figure 1c).
7. Why specific loss? It is a heuristic solution. This combination enhanced the convergence in early experiments.
8. How do you feed missing inputs to your models? Missing values are filled with zeros for UNet and IAM4V. Other models impute the missing values with their intermediate forecast. We updated the manuscript to make it more clear (see Figure 3 and lines 341-343).
9. The variation of missing data ratio. The Sentinel satellite has power limitation, hence does not operate contagiously. We suggest that changes in the powering schedule might be the reason.
10. Have you compared to a climatology? We compared with climatologies, the proposed pipeline beats them by a wide margin. We provide our results bellow. However, we doubt that averaging over 9 years with lots of missing values provides a valuable baseline. ||MSE|IIEE@15|IIEE@30|IIEE@50|IIEE@75| |---|---|---|---|---|---| |monthly climatology|10.9|15.3|9.4|13.7|10.3| |weekly climatology|9.2|14.0|10.2|11.6|8.6| |our pipeline|6.8|10.0|9.0|9.2|5.3|
11. Evaluated pipeline. Forecast of the tested models were replaced with one of the DMVFN at dates with high uncertainty. Each model in the table is mixed with DMVFN except baselines and the DMVFN itself. Metrics without such mixture are provided in appendix at Table 8.

We thank the reviewer for constructive feedback. We appreciate the acknowledgment of the importance and novelty of our work. Below, we address the specific concerns and questions raised in the review:

Response to weaknesses:

1. SAR parameters. We directly use SAR HV and HH polarizations from Sentinel-1 extra-wide product. The preprocessing includes: conservative interpolation to the target resolution, normalization, and filtration. Processed SAR imagery is used as both input and target for neural networks.
2. Models. We have included more thorough models descriptions and the schematic visuals of the models and whole pipeline (please see Figure 3, lines 248-312 of the updated manuscript). In general, the input consists of described data channels sampled at sequential seven days (ten for IAM4VP), the outputs are predicted SAR images at the following three days. rUNet and all SISO models apply recurrently, the prediction is produced in the autoregressive manner (see Figure 3c).
3. IIEE. We added the definition of the integrated ice-edge error to the appendix (line 866)
4. Preprocessing. The projection operator is learnt once. Only the projecting should be evaluated to remove the artifacts. The computational complexity of evaluation a single image is O(h*w) where ‘h’ is height and ‘w’ is width in pixels. One can derive the complexity from the fact that the projection is a linear operator over the image space.

Response to minor comments:

1. Typos. We fixed the typo, thanks for pointing them out!
2. Map. We added a map of the target area to the main body of the paper (see Figure 1a of the updated manuscript).

Response to questions:

1. Is the SAR video prediction and end in itself in this work? SAR video prediction is an output of the developed pipeline. It was selected in collaboration with marine captains, who regard this data as a convenient and reliable source for assessing sea ice conditions. Additionally, the missing values imputation and uncertainty quantification are the byproducts of our forecasts and can be used as well.
2. Preprocessing demonstration. We added the examples of the filtration algorithm to the main body of the paper (see Figure 1c). The quantitative evaluation is out of scope of the paper, however we verify its importance via ablation study (appendix, Table 6)
3. Is there a way to incorporate ice-dynamics in this video prediction approach? The ice dynamics can be interpolated as specific parameterization of the neural ODE model or via addition of PINN-loss. However, the quality data on sea ice parameters, which is necessary to incorporate their dynamics, is unavailable in the target region due to its complex environmental conditions.
4. How sensitive would any approach be to location? We expect the pipeline to generalize well to other arctic rivers. However we acknowledge that the application over regions of the free sea surface might result in suboptimal performance in comparison with numerical models.

We thank the reviewer for valuable feedback and comments. We appreciate the recognition of the importance and potential of the work. Below, we address the specific concerns raised in the review:

1. Model descriptions. We added a section with enhanced model descriptions (lines 248 – 312) and a schematic figure to represent how autoregressive and non-autoregressive approaches manage data and missing values.
2. Representations of the task. We include a schematic of the overall pipeline (see Figure 3a), the visualization of the target region, examples of the input SAR imagery to represent the problems of missing values and scalloping, and results of filtration to the main body of the paper.
3. Paper structure. We restructured the paper to shift focus on the task, applied models and the developed pipeline, and moved part of the data description into appendix.
4. Target. As a target we use HV polarization of SAR imagery. The same preprocessing applies both to input and target images: interpolation, normalization, filtration.
5. Minor comments. We fixed all typos. Both GLORYS and meteostations are daily-averaged to decrease computational burden of the models. SAR imagery is interpolated conservatively, line 206 was a typo. “Nor noise” meant that further apllication of the filtration won’t modify images; we removed these labels to avoid misunderstanding.