Title: SIFusion: A Unified Fusion Framework for Multi-granularity Arctic Sea Ice Forecasting
Venue: NeurIPS 2025
Accepted: yes
Keywords: Arctic Sea Ice Forecasting

Multi-granularity Fusion
Abstract: Arctic sea ice performs a vital role in global climate and has paramount impacts on both polar ecosystems and coastal communities. In the last few years, multiple deep learning based pan-Arctic sea ice concentration (SIC) forecasting methods have emerged and showcased superior performance over physics-based dynamical models. However, previous methods forecast SIC at a fixed temporal granularity, e.g. sub-seasonal or seasonal, thus only leveraging inter-granularity information and overlooking the plentiful inter-granularity correlations. SIC at various temporal granularities exhibits cumulative effects and are naturally consistent, with short-term fluctuations potentially impacting long-term trends and long-term trends provides effective hints for facilitating short-term forecasts in Arctic sea ice. Therefore, in this study, we propose to cultivate temporal multi-granularity that naturally derived from Arctic sea ice reanalysis data and provide a unified perspective for modeling SIC via our Sea Ice Fusion framework. SIFusion is delicately designed to leverage both intra-granularity and inter-granularity information for capturing granularity-consistent representations that promote forecasting skills. Our extensive experiments show that SIFusion outperforms off-the-shelf deep learning models for their specific temporal granularity.

SIFusion: A Unified Fusion Framework for Multi-granularity Arctic Sea Ice Forecasting

Abstract

Arctic sea ice performs a vital role in global climate and has paramount impacts on both polar ecosystems and coastal communities. In the last few years, multiple deep learning based pan-Arctic sea ice concentration (SIC) forecasting methods have emerged and showcased superior performance over physics-based dynamical models. However, previous methods forecast SIC at a fixed temporal granularity, e.g. sub-seasonal or seasonal, thus only leveraging intra-granularity information and overlooking the plentiful inter-granularity correlations. Specifically, intergranularity correlations mean that SIC at various temporal granularities exhibits cumulative effects and are naturally consistent, with short-term fluctuations potentially impacting long-term trends and long-term trends provide effective hints for facilitating short-term forecasts in Arctic sea ice. Therefore, in this study, we propose to cultivate temporal multi-granularity that naturally derived from Arctic sea ice reanalysis data and provide a unified perspective for modeling SIC via our S ea I ce Fusion framework. SIFusion is delicately designed to leverage intra-granularity and inter-granularity information to capture granularity-consistent representations that promote forecasting skills. Our extensive experiments indicate that SIFusion outperforms off-the-shelf fixed temporal granularity SIC forecasting deep learning models for their specific temporal granularity.

1 Introduction

Arctic sea ice has a profound influence on both local and global climate systems. The near-surface air temperature of Arctic regions has increased at a speed that is two to nearly four times faster than the global average from 1979 to 2021, a phenomenon known as 'Arctic amplification' [1, 2]. This accelerated temperature rise performs a key role in the unprecedented rapid diminishing of Arctic sea ice which has extensive consequences that could transcend the polar area. For example, the accelerated reduction of Arctic sea ice could not only jeopardize the survival of species residing in polar regions but also pose adverse effects on local communities whose livelihoods and well-being depend on those animals; it could substantially affect mid-latitude summer weather by weakening the storm tracks [3]; and it will bring new opportunities for marine transportation and new access to natural resources like fossil fuels [4].

Due to the vital role of Arctic sea ice in coastal communities, global climate, and potential impacts on the world's economy, numerical and statistical models have been proposed to forecast pan-Arctic sea ice concentration (SIC) ranging from sub-seasonal to seasonal scale [5, 6]. However, numerical

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and statistical models usually rely on high-performance computing on CPU clusters and often lead to complex debugging processes and uncertain parameterization, which limits their performance in forecasting long-term SIC changes. With the advent of deep learning models and their powerful capability in capturing complex patterns within high dimensional data, recent studies have developed end-to-end SIC forecasting models based on deep learning approaches and have presented a promising performance that exceeds previous numerical and statistical methods [7, 8]. Considering existing deep learning-based methods mainly focus on predicting SIC at a specific temporal granularity, e.g., 7 days or 6 months' averages, the intra-granularity correlations are well captured while the inter-granularity information that contains intrinsic annual cyclic trend and intra-seasonal predictability of Arctic sea ice [9] are overlooked.

Over the last few decades, the Arctic sea ice extent (SIE, where SIC value is larger than 15%) has exhibited a continuous declining trend and a clear recurrent variational pattern. For example, the annual pan-Arctic sea ice edge usually starts to expand after the summer melting season in September (Figure 1(b)). Given these patterns, concurrently utilizing inter-granularity and intragranularity information and employing a unified fusion framework could be mutually beneficial for modeling each granularity. For instance, long-term trends in weekly granularity could be helpful in calibrating short-term daily predictions, and finer granularity features could provide more accurate initial conditions to facilitate seasonal forecasting. Besides, the essence of predicting future SIC is to forecast spatially correlated time series. Their sequentially varying nature requires effective modeling of SIC sequences. However, the most commonly utilized U-Net architecture [10] in previous work [7] implicitly fulfills sequential modeling by channel-wise fusion operations which could be ill-posed for sequence modeling for two reasons: (1) The expansion and contraction of channels in the up-sampling and down-sampling steps disturb the intrinsic sequential feature and complicates the capturing of sequential correlations. (2) When jointly modeling with climate variables, for instance sea surface temperature, fusing different variable channels all together could further corrupt the modeling of spatially correlated time series. Alternatively, adopting explicit modeling of SIC sequences based on sufficiently extracted spatial features could facilitate the spatio-temporal forecasting task.

Based on the above-mentioned motivations, we propose a unified fusion framework for multigranularity Arctic S ea I ce Fusion forecasting based on Transformer backbone ( SIFusion ). Unlike previous approaches (as demonstrated in Figure 2), we propose to independently tokenize spatial features, explicitly extract sequential information and jointly model three granularities: daily, weekly average, and monthly average. Specifically, SIFusion first embeds SIC from each temporal granularity into independent spatial tokens and sequentially concatenates them to represent temporal fluctuations within each granularity. Then, we treat these independent sequences as correlated granularity variates and utilize the attention mechanism in conjunction with the feed-forward network (FFN) for extracting both intra-granularity and inter-granularity correlations. By incorporating multi-granularity representation, SIFusion could simultaneously generate future SIC in three different temporal scales, boosting not only the performance in a specific temporal scale but also the overall forecasting skill. Our contributions are three-fold:

We revisit the potentially overlooked inter-granularity information by previous methods for Arctic SIC forecasting and explore the effectiveness of independent spatial tokens representation of SIC for facilitating accurate predictions.

We propose SIFusion that leverages independent spatial tokenization of SIC and effectively unifies three temporal granularities that cover from sub-seasonal to seasonal scale for better overall representation and improved forecasting performance.

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The comprehensive experiments demonstrate that by adopting the approach of multigranularity fusion, our SIFusion achieves state-of-the-art on prediction in each granularity, which advances toward a more practical Arctic sea ice forecasting system.

2 Related Works

Sea ice concentration forecasting. Researchers have proposed various approaches to forecasting SIC, encompassing numerical and statistical models [11, 12]. However, numerical and statistical models usually rely on the high-performance computing of the CPU cluster and tend to result in complex debugging processes and uncertain parameterization. Recently, deep learning models have drawn the attention of sea ice research communities and have been widely investigated for Arctic sea ice forecasting [13, 14, 15, 16]. These methods utilize U-Net-based architectures to solve daily (SICNet [8], or monthly (IceNet [7], MT-IceNet [16]) SIC forecasting. However, although these UNet-based architectures are built on top of LSTM [17] or CNN [7], the temporal information inherent in sea ice modeling can not be fully exploited. Moreover, these methods and the latest Transformerbased model [18] concentrate on single-granularity SIC forecasting, where the inter-granularity information from multi-granularity sea ice modeling is overlooked.

Multi-scale representative learning. The multi-scale phenomenon is common in vision tasks, while it is always overlooked in sea ice modeling. To exploit the information in multi-scale sources, multi-scale features are commonly exploited by using spatial pyramids [19], dense sampling of windows [20], and the combination of them [21] in the vision community. The learning of CNNbased multi-scale representations is typically approached in two ways: utilizing external factors like multi-scale kernel architectures and multi-scale input architectures [22], or designing internal network layers with skip and dense connections [23]. Recently, there has been a surge of interest in applying transformer-based architectures to computer vision tasks, with the Vision Transformer (ViT) being particularly successful in balancing global and local features compared to CNNs [24]. When revisiting the task of forecasting sea ice concentration, its multiscale features stem from different temporal resolutions. Existing methods focus on a single scale, such as daily, weekly, or monthly. However, different temporal resolutions are inherently connected, and treating them as a single scale for modeling would increase the complexity of network learning.

3 SIFusion for Multi-granularity Arctic Sea Ice Forecasting

Given historical Arctic SIC records Y = { X T -L -1 , ..., X T -1 , X T } ∈ [0% , 100%] L × H × W , where L is the input length of a specific granularity which includes the given observation time step T , H

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and W denotes the rectangle pan-Arctic region, the forecasting model predicts the subsequent SIC values ˆ Y = { X T +1 , ..., X T + P -1 , X T + P } ∈ [0% , 100%] P × H × W with forecasting lead times of P . In this study, our SIFusion jointly models three granularities, i.e., daily, weekly average, and monthly average SIC values that cover both sub-seasonal and seasonal variations, and simultaneously forecasts on all these temporal scales. For each temporal granularity, the input length L equals the forecasting lead times P . The overview of the proposed SIFusion architecture is presented Figure 3. The shared spatial encoder and decoder perform SIC tokenization and restoration while multi-granularity fusion explicitly extracts sequential information.

3.1 Sea ice concentration tokenization

Existing mainstream deep learning-based methods for SIC forecasting adopt U-Net architectures and leverage 2D convolution to perform channel-wise expansion and downsampling that extracts both spatial features and temporal dependencies. However, since U-Net-based models are not specifically designed for sequence modeling [27], the joint spatial-channel fusion of SIC and implicit sequence modeling could be ill-posed properties for spatio-temporal forecasting tasks. In this regard, we propose to independently tokenize spatial features at first, which

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could disentangle the above ill-posed problem and be beneficial for SIC forecasting.

Independent spatial embedding. Since we aim to simultaneously model SIC derived from three temporal granularities, encoding their spatial features into shared embedding space not only yields

consistent representation but also reduces the number of trainable parameters. Inspired by prior works [28, 29], we utilize Swin Transformer V2 [30] as the backbone for both shared spatial encoder and decoder.

Specifically, each SIC input is independently fed into the shared spatial encoder and partitioned by a non-overlapped window to generate patch representation [24] with 32 spatial channels (the original SIC data has only one channel). To preserve local SIC information, we choose the smallest 2 by 2 window size for the patch partition. Then, the patch tokens are further transformed by the first two Swin Transformer blocks. The multi-scale spatial features are extracted through the subsequent hierarchical encoder layers which comprise a patch merging operation and two Swin Transformer blocks. The patch merging operation first concatenates the spatial feature of each group of 2 by 2 adjacent patch representations from the previous encoder layer. The calculation of each pair of two consecutive Swin Transformer blocks in encoder layers can be described as follows:

where z b s and z b represents the output spatial feature of the ( S hifted) W indowM ulti-head S elf A ttention module and the MLP module for block b , respectively; LN denotes the layer normalization operation [31]. The attention mechanism with a shifted window could effectively extract neighboring SIC information and sufficiently represent the local correlation of sea ice. After all input SIC are independently encoded into 2D spatial features, we apply linear projection to generate 1D tokens for each SIC to obtain compact spatial representation for sequential modeling.

The shared spatial decoder adopts an identical Swin Transformer backbone and the decoding procedure is symmetrical to the encoding process, except that the patch merging operation is replaced by the patch expanding operation [32]. While patch merging downsamples the input spatial feature dimension and increases the embedding channels, patch expanding symmetrically restores the resolution of the feature map and merges channels via linear transformation.

Spatial feature skip connection. Since the SIC features encoded by Swin Transformer blocks will be tokenized into highly compact sequence representation, the spatial SIC information should be maximally preserved during the sequential modeling. Besides, our proposed sequential modeling backbone comprises deep encoding layers which might lead to loss of embedded spatial features. To preserve spatial SIC information and avoid insufficient restoration, we propose to add a skip connection between the output of the last pair of Swin Transformer blocks in the spatial encoder and the input of the first block in the shared decoder (see in Figure 3).

3.2 Multi-granularity fusion

We propose to jointly model three granularities that cover sub-seasonal to seasonal scale, i.e., 7 days, 8 weeks averages, and 6 months averages, and explicitly capture inter-granularity correlation and intra-granularity sequential information.

Modeling granularity variates. As mentioned in Section 3.1 the shared spatial encoder transforms each SIC into independent 1D tokens. These individual spatial tokens are then concatenated sequentially based on their granularity respectively and utilized to form the multi-granularity representation. As each granularity incorporates a different time span, the dimensions of concatenated granularity sequences are mismatched. Considering that both the weekly average and monthly average are derived from daily SIC values, we choose to tokenize those sequences further and align their feature dimensions with the length of daily input using a linear transformation as follows:

where granularity ∈ [daily, weekly, monthly], g f is the aligned granularity feature, vTokenizer is the shared Swin Transformer spatial encoder.The generated multi-granularity variates are subsequently fed into the sequential modeling backbone. Encouraged by prior work [33], we propose to adopt an encoder-only Transformer architecture as the sequential modeling backbone for multi-granularity fusion in Figure 3 that: (1) applies multi-head self-attention on the embedded granularity variate

tokens to explicitly capture inter-granularity correlations; (2) each granularity variate is independently processed by FFN to extract intra-granularity information (as depicted Figure 4(a)). As for the conventional usage of vanilla Transformer in sequence prediction, the attention mechanism is applied on embedded temporal tokens which comprise variate information collected from the same time step (as in Figure 4(b)). The vanilla Transformer is challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Furthermore, the temporal token embeddings incorporate multiple variates that represent distinct physical measurements, which may struggle to capture variate-specific representations and potentially lead to the generation of incoherent attention maps. However, in sea ice modeling, each dimension of the tokenized granularity variate incorporates SIC features that come from a different time span. This could lead to poor representation of sequential SIC features and restrict the effective modeling of inter-granularity correlations. Experimentally, we will show in Section 4.2 that by adopting our sequential modeling, the overall performance is superior to alternative backbones. After each SIC granularity variate token is properly fused and encoded, the final prediction of future granularity variate features is generated through a linear projection layer.

Sequential feature skip connection. Considering the concatenated sequence of SIC features are linearly transformed and aligned to form the multi-granularity variate representation, the significant original sequential feature needs appropriate preservation. Besides, the deep sequence encoding process could introduce unintended noise that deteriorates the modeling of intra-granularity correlation. To compensate for the intra-granularity information and reduce the potential impact that impairs inter-granularity modeling, we propose to utilize the cross-attention mechanism as a sequential skip connection (in Figure 3), where the latent query features are sourced from the concatenated sequence token before the linear projection and the predicted SIC sequence generates both key and value latent representations. The details about this process can be found in Appendix.

4 Experiments

In this section, we evaluate the forecasting performance of our SIFusion over 8 years of SIC data and compare it with other deep learning models. The implementation details and evaluation metrics calculation of our SIFusion are provided in Appendix.

Datasets. We evaluate our proposed SIFusion framework on the G02202 Version 4 dataset from the National Snow and Ice Data Center (NSIDC). It records daily SIC data starting from October 25 th 1978 and provides the coverage of the pan-Arctic region (N: 89 . 8 ◦ , S: 31 . 1 ◦ , E: 180 ◦ , W: -180 ◦ ). Each daily SIC data is formed of 448 x 304 pixels and each pixel corresponds to the area of a 25km x 25km grid. The SIC data has a range of 0% to 100% and areas where SIC value is greater than 15% indicate the SIE. We choose data from October 25 th 1978 to the end of 2013 as the training dataset, the years 2014 and 2015 are selected as the validation set, and data collected from 2016 to 2023 are used to test models.

Data curation. The official data was preserved in the NetCDF format. We use the open-source Python package 'netCDF4' to read data from the file with the suffix '.nc'. The sea ice concentration data can then be extracted by applying the official variable name, i.e., 'cdr_seaice_conc', to the API.

Evaluation metrics. This study employs root mean square error (RMSE) and mean absolute error (MAE) to assess forecasting accuracy, along with the R 2 score to quantify model performance. For SIE prediction, the Integrated Ice-Edge Error score [34] metric is used, which decomposes errors into overestimation (O) and underestimation (U) components. Additionally, the SIE difference (SIE dif ) calculates the absolute discrepancy between predicted and observed ice area (in millions of km 2 ). The Nash-Sutcliffe Efficiency [35] further evaluates prediction quality by comparing model performance to a baseline mean. The detailed calculations could be found in the Appendix A.1.

4.1 Multi-granularity forecasting

Baselines. Since our SIFusion simultaneously generates predictions of three granularities, we select corresponding forecasting deep learning-based models for comparison. Specifically, we reimplemented SICNet [8] and trained under an identical environment for direct comparison on 7 days SIC forecasting; Due to dataset and code accessibility, we adopt performance of sub-seasonal forecasting methods as SICNet 90 [36], IceFormer [18], and seasonal forecasting methods IceNet [7],

MT-IceNet [16] that reported in the original paper for reference. We also include ConvLSTM [37], PredRNN [38] and SimVP [39] for comparison.

Main results. The overall performance of SIFusion and baseline methods is listed in 1. The lower RMSE/MAE indicates a more accurate forecast in SIC values. Methods with lower IIEE/SIE dif are more capable of identifying the edge of sea ice while higher R 2 /NSE suggests that the predicted spatial patterns are closer to the truth of the ground. Our proposed method achieves the best performance in all metrics for forecasting 7 days SIC, establishes a new state-of-the-art method for sub-seasonal weekly average prediction, and presents superior seasonal SIC forecasting capability. Considering the fact that baseline methods, except for SICNet, utilize several additional atmospheric and oceanic variables to facilitate forecasting, and our SIFusion only leverages SIC data with carefully extracted intrinsic inter-granularity correlation, it verifies the effectiveness of the proposed approach for multi-granularity forecasting.

Qualitative analysis. To visually verify the forecasting skills of SIFusion, we select the end of the melting season in September 2022. From Figure 1(a) we can observe that the annual Arctic sea ice in 2022 has increased by a considerable margin, which is against the persisting long-term declining trend. This unusual rise makes SIC and SIE difficult for our model to predict since it only learns from the data collected before 2014. Starting from September 1 st , we calculate the averaged SIC of 7 days, 4 weeks and 1 month that correspond to three temporal granularities of SIFusion. The ground truth of calculated average SIC along with the ground truth and predicted SIE are visualized in Figure 5. The forecasting results in the lower row are produced by SIFusion and the upper row represents predictions generated by three variants of SIFusion that only leverage singlegranularity SIC, we will discuss later in Section 4.2.

Despite the inconsistent annual trend of Arctic SIC in 2022, our

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method could still generate forecasts that are consistent with the average SIE in the first week of September (Figure 5(a)), and the general shape in both 4 weeks' average (Figure 5(b)) and 1-month average (Figure 5(c)). Compared to models with a similar backbone of SIFusion but only leveraging single-granularity SIC, the prediction of SIE is noticeably different from the ground truth, indicating that SIFusion could effectively leverage multi-granularity SIC to improve forecasting skills.

We plot spatial residuals to further investigate the learned spatial patterns of our SIFusion. In Figure 6(a), SIFusion could accurately predict the first week of SIC, while in coarser weekly average granularity our SIFusion tends to slightly underestimate in Arctic sea ice edge areas (Figure 6(b)). For the predicted monthly average of September 2022, the overall shape of SIE resembles the observation but overestimates SIC along the boundary.

4.2 Ablation study

To further analyze the performance of our proposed method, we trained five additional variants of SIFusion (as in Figure 7), i.e., three single-granularity models that respectively utilize temporal granularities in SIFusion, and two multi-granularity forecasting models with different backbones to perform the multi-granularity fusion.

Effectiveness of multi-granularity modeling. We first verify our proposed multi-granularity modeling approach by comparing SIFusion with models that comprise a similar model architecture but only adopt single granularity SIC data. Comprehensive experiments in Table 2 show that by leveraging the naturally derived multi-granularity SIC, the overall performance in all temporal scales can be promoted by a significant margin. For each individual forecasting lead time, SIFusion consistently outperforms models solely trained on single-granularity data (as shown in Figure 7).

Alternative backbone for multi-granularity fusion. To validate the effectiveness of our proposed multi-granularities fusion and sequential modeling approach, we compare the performance of our SIFusion with two other variants that are trained on the identical multi-granularity data with different sequential backbones, i.e., Transformer and MLP mixer [26, 40]. Considering intra-granularity performance in Figure 7, SIFusion presents superior forecasting skill in each time step of daily, weekly average and monthly average when compared to multi-granularity variants, indicating the effectiveness of multi-granularity SIC variates for sequential modeling. As shown in Table 3, our SIFusion outperforms these variants by a great margin, demonstrating the intra-granularity and inter-granularity correlations inherent in the sea ice modeling benefits for the forecasting.

Adaptation to missing observations and change in temporal scale. Considering our multigranularity fusion framework is generic for different temporal scales, it is essential to further explore (1) whether SIFusion applies to missing SIC observations and (2) if it still works when the input temporal scale varies. We first randomly masked the daily scale, i.e., select one of the 7 days and set the input SIC values to a mask token, and then extended the daily scale from 7 days to 10 days. The evaluation of these two variants is presented in Table 4. For the scenario with missing values and changed input daily scale, the performance of all three temporal scales slightly drops, but still outperforms the single-granularity baseline in terms of RMSE and MAE. This could indicate that our SIFusion is applicable to missing observations. By comparing the performance variance between SIFusion and SIFusion 10 -Days , we could find that the daily and monthly figures are close, but the

identification of sea ice extent on the weekly scale suffers a larger performance drop. Since we use 7 days on a daily scale, i.e., the 7-day time naturally aligns with one week, the results could indicate that keeping this alignment between the daily scale and a one-week token is beneficial. As to the 8 weeks' average at the weekly scale, the time span of 8 weeks is still within a month, so that one one-month token could represent the information of the weekly scale.

5 Conclusion and Future Work

In this paper, we propose SIFusion, a transformer-based sea ice concentration forecasting framework that unifies multi-granularity covering from sub-seasonal to seasonal scale to enhance the forecasting skills. Specifically, we propose to explore the independent spatial tokens representation of SIC and explicitly modeling intra-granularity information. These spatial tokens are sequentially concatenated within their own granularity and go through multi-granularity fusion to effectively capture the intergranularity correlations. Experiments demonstrate that our SIFusion achieves skillful forecasting in each granularity and outperforms methods trained on single-granularity SIC and climate data. Limitation. Despite the effectiveness of only using SIC as the input, the absence of climate variables could still limit the performance of the proposed approach for modeling Arctic sea ice. The weekly average granularity at sub-seasonal scale was not fully aligned with existing models, but it provides critical correlations for bridging the gap between short-term and long-term forecasting, our SIFusion sets up a new baseline for future explorations. Since our proposed framework is versatile, the climate information could be easily incorporated in future work. The joint modeling of climate variables and SIC using SIFusion from a multi-granularity perspective could provide a more comprehensive understanding of climate change both within and beyond the Arctic region. Besides, leveraging the hidden knowledge of atmospheric and oceanic dynamics embedded in pre-trained weather and climate foundation models could enhance the forecasting skill and boost the overall performance. Lastly, the capability of SIFusion to simultaneously forecast Arctic SIC at multiple granularities could make it a promising candidate to fulfill the challenging and critical sub-seasonal to seasonal (S2S) sea ice forecast.

Acknowledgments

This research was supported by Shanghai's Key Technology Development Program, under the project 'Intelligent Integrated Arctic Ice-Snow-Atmosphere Observation Platform and Short- to Medium-Term High-Precision Sea Ice Forecasting' (Grant No. 25DZ3102600), Shanghai Artificial Intelligence Laboratory, and the JC STEM Lab of AI for Science and Engineering, funded by The Hong Kong Jockey Club Charities Trust, the Research Grants Council of Hong Kong (Project No. CUHK14213224).

We want to express our sincere gratitude to Professor Xiaojun Yuan from the Lamont-Doherty Earth Observatory, Columbia University, for her insightful and invaluable help and discussion. We also extend our gratitude to Professor Lei Wang from the Institute of Atmospheric Sciences, Fudan University, whose advice has been instrumental in our study.

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A Appendix

A.1 Evaluation Metrics

To evaluate SIFusion, we select widely used root mean square error (RMSE) and mean absolute error (MAE) for comparison of forecasting accuracy. We also leverage R 2 score to evaluate the performance:

where RSS represents the sum of squares of residuals and TSS denotes the total sum of squares. The Integrated Ice-Edge Error score [34] is introduced to evaluate the prediction of SIE:

where O and U represent the overestimated and underestimated SIE between the prediction ( SIE p ) and the ground truth ( SIE t ), respectively. The difference between the forecasted and ground truth sea ice area (in millions of km 2 ) is calculated as follows:

We also adopt the Nash-Sutcliffe Efficiency [35] to further evaluate the predicted quality:

A.2 The details of sequential feature skip connection

where g denotes each granularity. z g in , z g pred ∈ R 1 × d z represents the sequential features before linear projection and the prediction, respectively. W g Q , W g K , W g V ∈ R d × d z are the query, key and value projection matrices.

A.3 Visualization of forecasting results

In this section, we will present more visualization of forecasting results generated by SIFusion.

GT

Pred

Forecast Period

Sep 1~7, 2022

(7 Days Average)

Forecast Period

Sep 1~28, 2022

(4 Weeks Average)

Forecast Period

Sep 1~30, 2022

(1 Month average)

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(c)

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SIFusion

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Forecast Period

Mar 1~30, 2017

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Sep 1~7, 2017

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Forecast Period

Sep 1~28, 2017

(Weekly Granularity)

Forecast Period

Sep 1~30, 2017

(Monthly Granularity)

(a)

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Mar 1~7, 2018

(Daily Granularity)

Forecast Period

(Weekly Granularity)

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Mar 1~30, 2018

(Monthly Granularity)

(a)

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Pred

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Sep 1~7, 2018

(Daily Granularity)

Forecast Period

Sep 1~28, 2018

(Weekly Granularity)

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Sep 1~30, 2018

(Monthly Granularity)

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Mar 1~7, 2019

(Daily Granularity)

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Mar 1~30, 2019

(Monthly Granularity)

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Pred

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Sep 1~7, 2021

(Daily Granularity)

Forecast Period

Sep 1~28, 2021

(Weekly Granularity)

Forecast Period

Sep 1~30, 2021

(Monthly Granularity)

(a)

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1.0

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses forecasting pan-Arctic sea ice concentration (SIC). Unlike prior (deep learning-based) methods, the proposed method takes into account several time scales from short-term fluctuations and long-term trends. Particularly, it embeds time-series data of three time scales independently, which are then processed by Transformer encoders. The attention block of the Transformer encoder captures interactions between time scales, while the subsequent feedforward network applies a nonlinear transformation to each time scale independently. The experiments show that the proposed method better predicts the sea ice extent (SIE) even when unusual increases in Arctic sea ice occur. The quantitative evaluations also exhibit the superiority of the proposed method.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n- The proposed method is designed with a clear awareness of the weakness of prior methods, namely, not considering the distinct contributions from different time scales.\n- A new deep model based on Transformer encoders with input and output embedding networks is proposed so that several time scales can be taken into account with their interplay.\n- The experiments demonstrate that the explicit introduction of multiple time scales significantly improves SIC forecasting. Table 1 shows that the proposed method (SIFusion) outperforms baseline methods that are specialized to specific time scales.\n\n---\n\n**Weaknesses**\n\nOverall, this work is solid and appears to have no significant weaknesses. I raise the following questions to improve this work further.\n\nThe idea of introducing multiple time scales is intuitive, but deeper analysis may provide valuable insights. Namely:\n1. The prior U-Net-based methods only use single-granularity input, but what if we train a model on datasets containing multiple time scales in a mixture? Does it still encounter non-trivial challenges? Why can the proposed model resolve it?\n2. The embedding of input of different time scales is done by a shared spatial encoder. Are there any differences in the embedding vectors between time scales?\n3. Which time scales are more important than others? For the task with 7 7-day lead time, does the longest time scale really help? Table 2 shows that training on single-granularity is insufficient, but it would be more interesting to know how other time scales complement the target time scale to predict.\n\nThe time complexity is also of interest. Generally speaking, taking into account multiple scales is more expensive than using a single scale.\n\n**Minor comments.** Please be aware of the implication of the italic fonts in math. For example, in Eq. (1), $LN$ can be viewed as a product of two variables $L$ and $N$. If authors want to mean any abbreviation of words, e.g., Layer Normalization (LN), it should be presented in the roman font $\\mathrm{LN}$. Same applies to $MLP$, $z_s$, and $\\mathrm{SIC}_{diff}$.\n\nQUESTIONS:\nPlease refer to the three questions raised in Weaknesses.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nSea ice forecasting is critically important geopolitically, for transport, for ecosystems, and because of its effect on the long-term climate. AI models for sea ice forecasting have recently been developed over multiple different time scales (medium-range, sub-seasonal, and seasonal) which are competitive with, or outperform, the traditional physics-based modelling approaches at orders of magnitude smaller computational cost. Previous AI approaches have largely focussed on a single forecasting lead time and they have used inputs of just one temporal granularity. Due to the multiple time-scales of relevance for sea-ice forecasting, this paper takes a different approach, using inputs with a range of different granularities (daily, weekly or monthly averages of sea ice concentration) and predicting at medium-range, sub-seasonal, and seasonal time scales. The approach improves over strong baselines in several sea ice forecasting tests.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\nI enjoyed reading the paper. I like the central idea of a single model operating across all time-scales and granularities. I found the results in the paper impressive. \nI like the figures — it’s clear that a lot of work has gone into them — figure 3 is especially helpful for understanding the architecture. It was good that the paper compared alternatives to their multi-granular fusion module. The paper was pretty clear.\n\nWeaknesses\n\nI found the description of the architecture quite dense and hard to get through. The figure definitely helped, but I felt that the architecture involved many standard deep learning blocks arranged in a sensible way, rather than a major innovation. To be clear, I don’t see this as an issue — I think the major contribution is the idea to model many different temporal scales jointly and to show substantial improvement in the experiments — rather than a specific architecture that is necessarily the only one capable of doing this. However, I wonder whether the model description could be improved.\n\nI might have expected some comparison to physical models in the results section. I suspect that in some cases the baseline AI approaches which are compared to have been shown to go beyond the physical models already, and so improving on the AI models entails further improvement over the physical models, but it would be useful to state what is known about this.\n\nIn the limitations section, there is a reference to climate variables. I think rather the authors may mean that the model predictions could be improved by coupling the sea ice models to medium range, sub-seasonal and seasonal weather forecasts. Meteorological variables, particularly wind speed and temperature, could be added as input variables. I would interpret climate as referring to time-scales beyond 1 year\n\nMinor comments\n\nline 84 \"models usually rely on the high-performance computing of the CPU cluster “ -> \"models usually require a high-performance CPU cluster”\n\nline 89 \"the temporal information inherent in sea ice modeling can not be fully exploited” - I think that this needs to be justified or backed up with a citation\n\nline 93 - I found the discussion of multi-scale representations a bit confusing. On the one hand there is discussion of modelling multiple “spatial” scales in vision. Then this is connected to modelling multiple temporal scales for sea ice, but isn't it also important to capture multiple spatial scales in sea ice modelling? I’m not sure why this isn’t mentioned as it appears to be the more natural connection. Moreover, in weather modelling which is also arguably a similar multi-scale phenomenon, state-of-the-art models like GenCast or Aurora only condition on the last two six-hour snapshots of the atmosphere, but there are of course a range of temporal dynamical behaviour with different spatial scales which these methods capture (e.g. from tropical cyclones to the MJO). So it’s not strictly necessary to explicitly have multi-resolution temporal information in the input. At least in principle, as the physics are Markovian, if we did have the complete state, then it wouldn’t be necessary to have access to other inputs. In the light of this, I think the argumentation needs to be tightened up in this section.   \n\nline 122 \"ill-posed properties” this isn’t the right term here - perhaps just say that the UNet is “ill-suited” to sequence modeling and spatial-channel fusion\n\nline 215 \"provided in Appendix” -> \"provided in the Appendix” \n\nline 236 \"we adopt performance of sub-seasonal forecasting methods as SICNet90 [36], IceFormer [18], and seasonal forecasting methods IceNet [7], MT-IceNet [16] that reported in the original paper for reference.” -> \"we use the performance of sub-seasonal forecasting methods SICNet90 [36] and IceFormer [18], and seasonal forecasting methods IceNet [7] and MT-IceNet [16] that is reported in the original papers.\"\n\nThe term “variate” is a bit over-used in my opinion and “variable” would be simpler, clearer, and more usual.\n\nQUESTIONS:\nIt seems to me that there are at least two different reasons why the model might be performing well. First, the multi-scale information contains more information than one modality alone and this improves forecasts. Second, training across multiple different temporal scales learns a better shared representation of sea ice which facilitates better prediction. Do we know which one of these is the main contribution? E.g. I could imagine for the longer term predictions, the second reason might be the dominant one — would pre-training at medium range and fine-tuning to seasonal time-scales be an even better approach in this case, a bit like the Aurora model used for weather? I think this experiment is outside of the scope of the paper, but thinking through whether there is evidence of how the model is operating and whether the pre-train and fine-tune approach would be worse, would be fruitful.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

comments: SUMMARY:
This paper introduces SIFusion, a unified deep learning framework for multi-granularity Arctic Sea Ice Concentration (SIC) forecasting. 
The proposed method addresses the problem of fixed temporal granularity in existing works, and proposes to cultivate temporal multi-granularity (daily, weekly, and monthly specifically). The effectiveness is demonstrated empirically on real-world datasets.

STRENGTHS AND WEAKNESSES:
The paper is rather complete, positions itself as a worth-trying method on NSIDC data.

There are improved performance in SIC forecasting area. 

The major concern is that the significance of this work is not enough for this venue. The paper lacks theoretical investigation on understanding how the method improves the performance. The setup seems pretty much tailored to SIC forecasting. Is there any idea that might be valuable beyond this problem?

QUESTIONS:
Maybe I missed it, how Swim transformer is selected? Is that a crucial part for the performance?

Is this method applicable to time series with missings?

Is the choice of daily, weekly,  monthly crucial? I can see the choice of daily is natural, for weekly/monthly, is there any specific reason about not using a different scale, say 5 days, 10 days, etc?

LIMITATIONS:
yes.
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-03

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThanks to the authors for their contributions. \n\nThis paper proposes the SIFusion or Sea Ice Fusion framework, a transformer-based forecasting framework that unifies multi-granularity Arctic sea ice concentration (SIC) prediction. The authors claim that the existing deep learning models typically forecast SIC at a fixed temporal resolution (e.g., daily or seasonal), missing the inter-granularity dependencies that may exist between different temporal scales. SIFusion introduces a novel design that independently embeds spatial features from daily, weekly, and monthly SIC data, then fuses them through a multi-head attention-based transformer backbone. The architecture models both intra- and inter-granularity dependencies. Extensive experiments on pan-Arctic SIC data are presented. Additionally, the model demonstrates robustness under abnormal SIC trends (e.g., 2022 anomalies) and superior generalization over unseen conditions.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths-\n\n* A novel contribution for Sea Ice Forecasting comprising of fusing multi-temporal information \n* Practical solution to a relevant problem, considering multi-time stamp input and multi-scale analysis for climate applications\n* Comprehensive documentation of the ablation study\n\nWeaknesses-\n\n* No benchmarking with the existing multi-temporal modeling frameworks is present\n\nQUESTIONS:\nMy questions are inline below-\n\n* It is not clear to me how the model will perform if additional climatic variables are added for the analysis. Do the authors perform any such ablation study to compare it with the baseline models?\n* How was the AI-ready dataset curated? It is recommended to explain the data curation steps properly for the reproducibility of research. \n* If the contribution is fusion of inter and intra-granularity, then how does the transformer architecture accommodate this? \n* What is the reason behind selecting only these time-stamps for temporal granularities? Will the model still perform if I change the temporal granularities? I'm curios to see how sensitive the model is for different multi-temporal granularities.\n* If the idea is to use transformer architecture for leveraging multi-temporal granularity information, why did the authors not consider using pre-trained weather and climate foundation models (FM)? Is it possible to use any of the existing pre-trained FMs and map it for SIC? \n* It is hard to assess the novelty in the proposed method since it seems like a conventional spatio-temporal processing, which many transformer networks are capable of doing. How is the \"independent spatial tokenization\" mentioned in the contribution different?\n\nLIMITATIONS:\nYes. The authors have discussed the limitations.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}