SIFusion: A Unified Fusion Framework for Multi-granularity Arctic Sea Ice Forecasting
Authors: Jingyi Xu
Shengnan Wang
Weidong Yang
Keyi Liu
Yeqi Luo
Ben Fei
LEI BAI
Venue: NeurIPS 2025 poster ()
Keywords: Arctic Sea Ice Forecasting
Multi-granularity Fusion
Primary area: machine_learning_for_sciences

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
Jingyi Xu Shengnan Wang" ,Weidong Yang .t, Keyi Liu', Yeqi Luo', Ben Fei Lei Bai College of Computer Science and Artificial Intellegence, Fudan University Shanghai Artificial Intelligence Laboratory, *Chinese University of Hong Kong
jyxu220m. f fudan. edu. en, wdyangåfudan, edu. en, benfei einfeilen frcfek, edu. hk, baisanshi@gmail. com
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 a fixed temporal granularity, e.g. sub-seasonal or seasonal, thus only leveraging intra- aatra-raanllartty information and overlooking the plentiful inter- enter-gramularity correlations. Specifically, inter- granularity correlations mean that SIC at various temporal granularities exhibits cumulative effects and naturally consistent, with short-term fluctuations poten- tially impacting long-term trends and long-term trends provide effective hints for facilitating short-term forecasts in Arctic ice. Therefore, in this study, pro- pose to cultivate temporal multi-granularity that naturally derived from Arctic sea ice reanalysis data and provide unified perspective for modeling SIC via Sea Ice Fusion framework. SIFusion is delicately designed to leverage intra- untra-granularity and unter-granularity information capture granularity-consisee 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.
Introduction
Arctic sea ice has profound influence on both local and global climate systems. The near-surface air temperature of Arctic regions has increased speed that two to nearly four times faster than the global average from 1979 to 2021, phenomenon known as "Arctic amplification" 2 This accelerated temperature rise performs 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 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: 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 [ 6). However, numerical
Equaal Contributions.
Corresponding Authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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13
Annual
Average
SIE Average
Annual
4.5
SiE (mil mmlkkmm3
15
SIE (mil.km²))
SIC (96)
4
SIC
10
4.0
11
3.5
1997 2004 2011 2018
Mar
Jun
Sep
Dec
Mar
Jun
Sep
Dec
(a)
(b)
(c)
Figure 1: Visualization of Aretic sea ice trends. (h) annual average SIC and SIE trend over the last 35 years (1987-2023); the monthly cyclic trend of SIC (b) and SIE (c). Note that the averaged
SIC values are calculated over the entire pan-Arctic region, which could only be used to observe the trend.
and statistical models usually rely on high- peefrorrffrmmece 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 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-Aretic sea ice edge usually starts to expand after the summer melting season in September (Figure bb). Given these patterns. concurrently utilizing inter- anter-granulartty and intra- granularity 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- 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 mbove-mentioned motivations, we propose unified fusion framework for multi- granularity Aretic Sea Ice 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, 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-gran grannaranularity and -nter-granularity correlations. By incorporating -uati-grayularity 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- granulaaauyrrtty information by previous methods for Arctic SIC forecasting and explore the effectiveness of independent spatial tokens representation 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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(a)
Single-Granularin
Single-Granulariy SIC Output
SIC Input
U-Net
Based Architecture
Channel-wise Fusion
(b)
Multi-Granulartt
Embedded
Multi-Granulartty SIC Output
Tokens
SIC Input
Spatial
Grandarity
Varioles
Sequential Modeling
Spatial Decoder
Encoder
Multi-Grauulrity Representation
Figure 2: The main differences between (a) existing mainstream SIC forecasting approaches and (b) our SIFusion are follows: (1) Previous models take a channel-wise fusion to jointly extract spatial features, e.g., utilizing 2D convolution to expand and downsample SIC channels. In our case, we focus on capturing an effective spatial tokens representation of SIC by the shared spatial encoder. (2) The correlation among input SIC sequence is implicitly modeled via the U-Net-based architecture in (a) while SIFusion explicitly captures untra-granulariyy and anter-granularis correlation via sequential modeling. (3) We propose leveraging multi multi-granularity information that is naturally derived from the SIC and embedding it into granularity variates to improve overall forecasting skills.
The comprehensive experiments demonstrate that by adopting the approach of multi- gramularity fusion, our SIFusion achieves state-of-the th-te-rrt on prediction in each granularity, which advances toward 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 122. 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 113 14 15 16). These methods utilize U-Net-based architectures to solve daily (SICNet [8], monthly (IceNet 77. M'T-IeeNet (16) SIC forecasting. However, although these U- Net-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 Transformer- based model [8] concentrate on Lunle-granularigg SIC forecasting, where the inter-granularity information from multi-granulariyy 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 [9)] dense sampling of windows (20), and the combination of them [11 in the vision community. The learning of CNN- based multi-scale representations is typically approached in two ways: utilizing external factors like multi-scale kernel architectures and multi-scale input architectures (22), designing internal network layers with skip and dense connections
(23]. Recently, there has been a surge interest in architectures to computer vision tasks, with the Vision Transformer (ViT) being particularly successful in balancing global and local features compared to CNNs (44 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.
applying transformer-basee
3 SIFusion for Multi-granularity Arctic Sea Ice Forecasting
Given historical Arctic SIC records = (X7-1-1,,.. X7-1,77) E [0%, 100%] where L is the input length of a specific granularity which includes the given observation time step T, H
3

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Hords
Sequential Feature Skip Connection
Moritt
Shared Spatial Encoder
Shared Spatial Decoder
Multi-Granulaitt Fusion
Xi
(6:la4484304)
(eals
Fltton
iReshape
Ree
Rio
(hxd2
Xis
(i-1004)
0445222286
Xu
Nia
Spatial Feature Skip Connection
Figure 3: Overview of proposed SIFusion, which comprises three main components: (1) The shared spatial encoder first independently extracts spatial features of input SIC from each granularity (i.e. days, 8 weeks' averages and 6 months' averages) to obtain spatial tokens, and then concatenates these spatial tokens accordingly. (2) The embedded spatial tokens are subsequently flattened with respect to their granularity and linearly projected into the same length. We propose utilize encoder- only transformer backbone to perform multi-granularity fusion which explicitly captures both inter-grat guteu-rranllartty and intra- aataulrraullrrty sequential features. (3) Lastly, the predicted multi-granullnn features are restored to the shape of the input via linear transformation and the shared spatial decoder.
and W denotes the rectangle pan-Arctic region, the forecasting model predicts the subsequent SIC values y [XT+1..... X1+r-1, Xr+r) )) E [0%, 100%]*x**** with forecasting lead times of P. In this study, our SIFusion jointly models three granularities, i.c., daily, weekly average, and monthly average SIC values that cover both sub-scasonal and seasonal variations, and simultancously 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-grame mullt-graauularity 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 downsam- pling that extracts both spatial features and tem- poral dependencies. How- ever, since U-Net-based models are not specif- ically designed for se- quence modeling (27), the joint spatial-channel fusion of SIC and im- plicit sequence modeling could be ill-posed prop- erties for spatio-temporal forecasting tasks. In this regard, we propose to in- dependently tokenize spa- tial features at first, which could disentangle the above ill-posed problem and be beneficial for SIC forecasting.
Variate Tedsens
Attention ever Variste Torens
FFN Variates Retresentalinn
(b)
Tina Swips
Attenton ever Temporal Tokens
FFN on Nubbarratee Representatios
Mulvariates
Cranuaatt Voride
Chermate
NLP Layen1 for Tokan Mixing
Toleus
NLP Layen for Miain
Tolero
Figure 4: Comparison between different backbones for temporal se- quence modeling: (a) Our proposed SIFusion sequentially concatenates independent SIC tokens that are derived from each temporal scale as a granularity variate and applies an attention mechanism over the embed- ded variate tokens. The FFN transforms the variate representation for the input of the next layer: (b) For vanilla Transformer architecture (25) applies attention mechanism over temporal tokens and FFN is applied on multivariate representations; (c) The MLP-mixer (26 approach first performs token-wise mixing, then transposes the extracted features to apply channel-wise mixing. The vanilla Transformer and MI.P-ixer both fall short of modeling the sequential information of sea ice.
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

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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 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 by 2 window size for the patch partition. Then, the patch tokens are further transformed by the first two Swin Transformer blocks. The multi-scal 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 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:
2 LN(WMSA( - 1)) 2
2 = (N(ML)((2) + 2
2, b+1 LN MSA(²²)) +2
2b1 -L((MLP(())) 2/.
(1)
where 2 and 2 represents the output spatial feature of the (Shifted) Window- Mann-MMulthhaa Self Attention module and the MLP module for block respectively: LN denotes the layer normalization operation [3I]. 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 pro- cedure is symmetrical to the encoding process, except that the patch merging operation replaced by the patch expanding operation 32). While patch merging downsamples the input spatial fea- ture 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 add 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
3.2 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 ID tokens. These individual spatial tokens are then concatenated sequen- tially based their granularity respectively and utilized to form the multi-granularigg 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 derived from daily SIC values, we choose to tokenize those sequences further and align their feature dimensions with the length of daily input using linear transformation follows:
g Linear
(2)
where granularity E [daily, weekly, monthly]. gr is the aligned granularity feature, xT Tokenizer is the shared Swin Transformer spatial encoder:Thh generated quati-granullarity variates are subsequently fed into the sequential modeling backbone. Encouraged by prior work 33 we propose adopt an encoder-only Transformer architecture as the sequential modeling backbone for grati-granullrity fusion in Figure 3 that: (1) applies multi-head self-attention the embedded granularity variate
5

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tokens to explicitly capture inter- anter-granularig correlations; (2) each granularity variate is independently processed by FFN to extract intra-gran catra-granllartty information (as depicted Figure Fa)) 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 4b). 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-granularig correlations. Experimentally. we will show in Section (.2 that by adopting our sequential modeling, the overall performance is superior 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 pro- cess could introduce unintended noise that deteriorates the modeling of intra- aatra-gramularity correlation. To compensate for the antraggraullarie information and reduce the potential impact that impairs sequential skip
inter- uieer-ranularity modeling, we propose to utilize the cross cross-attention mechanism 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.
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 25th 1978 and provides the coverage of the pan-Arctic region (N:89.8,, S:31.1 E:180", W:-180), Each daily SIC data formed of 448 x 304 pixels and each pixel corresponds the area of 25km 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 25th 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.
The official data was preserved in the NetCDF format. We use the open-source Python package 'netCDF4" 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_seaicceconc" to the API.
Data curation.
Evaluation metrics. This study employs root mean square error (RMSE) and mean absolute error (MAE) to assess forecasting accuracy, along with the R² 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,i)) calculates the absolute discrepancy between predicted and observed ice area (in millions of km²²). The Nash-Sutcliffe Efficiency [35] further evaluates prediction quality by comparing model performance to baseline mean. The detailed calculations could be found in the Appendix
A.1 A.1
4.1 Multi-granularity forecasting
Baselines. Since our SIFusion simultaneously generates predictions of three granularities, we select corresponding forecasting deep learning-basee models for comparison. Specifically, we re- implemented 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 SICNetoo (36), IceFormer (18), and scasonal forecasting methods IceNet [7],

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Table 1: Quantitative results of SIC forecasting. We compare the performance of SIFusion in each
temporal granularity with the corresponding deep learning based methods.
Temporal Scale
Lead Times
Methods
RMSE,
MAE]
R²t
NSE1
DEEL
STE
SICNer [8]
0,0490
0.0100
0.982
0.979
976
0.0718
ConvLSTMM
37
0.0881
0.0263
Days (Daily)
PredRNN
38
0.0594
0,0220
0.977
Sub-scasonal
SimVP
39
0.0640
0.0238
0,974
SIFusion
0.0429
0,985
0,0380
45 Days (Daly)
leeFormer [8]
0.0660
0,0201
0,960
90 Days (Dail)
SICNoooo
36
0XU112
Weeks Average (Weekly)
SIFusion
0.0625
0.0140
0.973
0.968
1600
0.1541
IeeNet [2]
0.1820
0.0916
0.567
Scasonal
Months Average (Monthly)
MT-IoeNet
16
0.0777
0.0197
0,915
SIFusion
0.0692
0.0166
0.917
2156
0.2083
MT-IceNNt [6] that reported in the original paper for reference. We also include ConvLSTM 37
PredRNN 38 and SimVP for comparison.
The overall performance of SIFusion and baseline methods is listed in 1 The lower RMSE/MAE indicates a more accurate forecast SIC values. Methods with lower IEE//TE are more capable of identifying the edge of sea ice while higher R²/NSE suggests that the predicted spatial patterns are closer to the truth of the ground. Our proposed method achieves the best performance in all metries for forecasting 7 days SIC, establishes new state-of-the-ate 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, verifies the effectiveness of the proposed approach for multi-granularity forecasting.
Main results.
Qualitative analysis. To visu- ally verify the forecasting skills of SIFusion, we select the end of the melting season in Septem- ber 2022. From Figure Ta) (a) we observe that the annual Are- tie sea ice in 2022 has increased by 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 be- fore 2014. Starting from Septem- ber 1st we calculate the averaged SIC of 7 days, weeks and month that correspond to three temporal granularities of SIFu- sion. The ground truth of calcu- lated average SIC along with the ground truth and predicted SIE are visualized in Figure 5 The fore- casting results in the lower row are produced by SIFusion and the upper row represents predictions generated by three variants of SI- Fusion that only leverage single- granularity SIC, we will discuss later in Section 4.2
Singlo
SFusion
Forecast P Period See 1-), 2022
crecastPenod
ForecastPeno: Sep 1-30, 2022 (1 Month ave rage)
[A]
(b)
Sep 1-28, 2022
(7 Days Average)
(4 Wooks Average!
Figure 5: Qualitative analysis of SIE prediction. The derived SIE ground truth and prediction generated by SIFusion and three models (one for each temporal granularity) over: (a) The first week of September; (b) 4 weeks; (c) month. Considering the abnormal increase of Aretic sea ice in 2022, our proposed method could still produce reasonable forecasts that keep the similar overall shape of Arctic SIE.
Despite the inconsistent annual trend of Arctic SIC in 2022, our
7

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-0666
-0.2
0.4
0.8
Forecast Period
Forecast Period
Forecast
(a)
Sep 1-7, 2022 (7 Days Average)
(b) Sep 1-28, 2022 (4 Weeks Average)
(c)
Sep 1-30, 2022
(1 Month average)
Figure 6: Spatial residual of predicted SIC. We examine the spatial patterns of forecasting results
over the same period presented in Figure SIFusion could generate consistent daily forecasts (a). Considering the abnormal Arctic SIC change in 2022, the annual trend could be different than the SIC data on which the model was trained, SIFusion could still predict weekly (b) and monthly (c) average SIC with a bounded residual region rather than scattered forecasting results. The spatial residual calculated by using predicted SIC to subtract the ground truth value.
Trasffm
SIC SIC RMSE (%)
Hiphixx
10
Single
3
5
6
2.0
3.0
SIC MAE (3)
2.0
2.5
1.5
2.0
1.0
1.5
2
4
6
2 3
4
6
7
2
4 5
Forecasting Lead Days
Forecasting Lead in Weeks
Forecasting Lead Months
Figure 7: Averaged intra-granularity forecasting granularity and single-granularity SIC and plot RMSE and MAE of each lead time step in three temporal granularities the test dataset.
We evaluate models trained multi-
method could still generate forecasts that are consistent with the average SIE in the first week of September (Figure S(a)), and the general shape in both 4 weeks' average (Figure 5]) and 1-month average (Figure (()).. Compared to models with a similar backbone of SIFusion but only leveraging
single-granularig 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 B(a), SIFusion could accurately predict the first week of SIC, while coarser weekly average granularity our SIFusion tends to slightly underestimate in Arctic sea ice edge areas 6 b)). For the predicted monthly average of September 2022, the overall shape of SIE resembles the observation but overestimates SIC along the boundary.

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Table 2: Effectiveness of multi-granularity representation. Multi represents the proposed SIFusion
and Single stands for models with similar backbone but trained solely on
data.
Temporal Scale
Lead Time
Granularity
RMSEL
MAEL
R²t
NSE
HIEE
SlEaf
Single
0.0704
0.0148
0.982
0.979
I0I8
0.0509
7 Days
Multi
0.0429
0.0096
0.987
0.985
926
0.0380
Sub-scasonal
Single
0.0771
0.0163
0.962
0.954
2208
0.3301
8 Weeks Average
Multi
0.0625
0.0140
0.973
0.968
1600
0.1541
Single
0.0721
0.0191
0.882
0.873
2482
0.4298
Seasonal
6 Months Average
Multi
0.0692
0.0166
0.917
0.910
2156
0.2083
Table 3: Effectiveness of proposed approach for multi-granularity fusion. We adopt conventional utilization of the Transformer and the recent trend in leveraging full MLP-based backbone [26) for temporal sequence modeling as counterparts of our proposed sequential backbone.
Temporal Scale
Lead Time
Method
RMSEL
MAEL
Rºt
NSEt
IEEL
STE
MI.P Mixing
0.0506
0.0117
0.984
0.981
1153
0.1265
7 Days
Transformer
0.0633
0.0159
0.970
0.965
1519
0.2338
SIFusion
0.0429
0.0096
0.987
0.985
926
0.0380
Sub-scasonal
MLP Mixing
0.0689
0.0169
0.969
0.963
2222
0.3839
8 Weeks Average
Transformer
0.0771
0.0206
0.970
0.964
1718
0,2028
SlFusion
0.0625
0.0140
0,973
0.968
1600
0.1541
MLP Mixing
0.0775
0,0206
0.857
0,845
2477
0,3837
Seasonal
6 Months Average
Transformer
0.0913
0.262
0.833
0.821
3490
0.4902
SIFusion
0.0692
0.0166
0.917
0.910
2156
0.2083
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.c., three single-granularity models that respectively utilize temporal granularities in SIFusion, and two multi-granularity forecasting models with different backbones to perform the multi-granulaan fusion.
Effectiveness of multi-granularity modeling. We first verify our proposed muuli-granularigg 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-gran granuiataanlarrtyy 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
data (as shown in Figure
Alternative backbone for multi-granularity fusion. To validate the effectiveness of our proposed multi- multi-granularitien fusion and sequential modeling approach, we compare the performance of our SIFusion with two other variants that are trained on the identical multi 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-ge qulli-granularity variants, indicating the effectiveness of multi- multi-granularity SIC variates for sequential modeling. As shown in Table 3 our SIFusion outperforms these variants by a great margin, demonstrating the intra-granularig 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 multi- granularity fusion framework is generic for different temporal scales, it is essential to further explore (I) 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 mask token, and then extended the daily scale from 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 kinle-granulariin 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 Days, we could find that the daily and monthly figures close, but the

---

Table 4: Application to missing daily observation and different temporal scale. To further explore the capability of our multi-granun granularity fusion framework, we randomly masked daily training data Mal) and extended the daily input from 7 days 10 days (SIFusion Days). Metrics for SIFusionno Days are calculated using the first 7-day prediction.
Temporal Scale
Lead Time
Method
RMSEL
MAEL
R²'
NSE1
IEEL
SlEarr
0.0633
0.0141
0,975
0.971
1280
0.0941
7 Days
SIFusionio-Dey
0.0643
0.0140
0.977
0.974
1292
0.0978
STFusion
0,0429
0.0096
0.987
0.985
926
0.0380
Sub-seasonal
SIFusion
0.0639
0.0162
0.969
0.963
2214
0.2674
8 Weeks Average
Sll'usion1o Days
0.0664
0.0155
0.958
0.950
2335
0.3472
SlFusion
0.0625
0.0140
0,973
0.968
1600
0,1541
SiFusion stank
0.0719
0.0166
0.871
0.862
2258
0,3075
Seasonal
6 Months Average
SlFusionto- Daye
0.0663
0,0153
0.887
0.879
2169
0,2950
SlFusion 0.0692
0.0166
0.917
0.910
2156
0.2083
identification of sea ice extent on the weekly scale suffers larger performance drop. Since 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 beneficial. As to the 8 weeks' average at the weekly scale, the time span of 8 weeks is still within month, so that one one-month token could represent the information of the weekly scale.
Conclusion and Future Work
In this paper, we propose SIFusion, a transformer-based sea ice concentration forecasting framework that unifies guatilgran covering from sub-seasonal to seasonal scale enhance the forecasting skills. Specifically, we propose to explore the independent spatial tokens representation of SIC and explicitly modeling intra-gramin granulataall information. These spatial tokens are sequentially concatenated within their own granularity and go through multi-granularrty fusion to effectively capture the inter- granularity correlations. Experiments demonstrate that our SIFusion achieves skillful forecasting in each granularity and outperforms methods trained on 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 SlFusion 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 a promising candidate to fulfill the challenging and critical sub-seasone to seasonal (S2S) sea ice forecast.
SIC and climate data,
Acknowledgments
This research was supported by Shanghai's Key Technology Development Program, under the project 'Intelligent Integrated Aretic Sce-Snow-Atmospher Observation Platform and Short- to Medium- Term High-Precision Sea Ice Forecasting' (Grant No. 25DZ3 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 R2 score evaluate the performance:
RSS
R²
(3)
TSS'
where RSS represents the sum of squares of residuals and TSS denotes the total sum of squares. The Integrated lce-Edge Error score (34 is introduced to evaluate the prediction of SIE:
HEEE = 0 +U
(4)
Σ (Mar(STFF, - STF,,))),
(5)
U = Σ (Maz(STF, - -SIEp: 0)),
(6)
1,5' 15
STE,, 0,SIC - 15
where O and U represent the overestimated and underestimated SIE between the prediction (S1 E,) and the ground truth E5),,,, respectively. The difference between the forecasted and ground truth sea ice area (in millions of km?) is calculated as follows:
E(STEE, - STF,)) 25 25
S1Eaf
(8)
1000000
We also adopt the Nash-Sutcliffe Efficiency 35
further evaluate the predicted quality:
NSE 1 ((STC, -STC)),
(9)
[(SIC, - Meam(S();)))
A.2 The details of sequential feature skip connection
CrossAttention (Q, V) softmax( QKT
V.
vd
W/ = K W predt V W 2pred
(10)
where denotes each granularity. 29 29 prred
E R 1xd, represents the sequential features before linear projection and the prediction, respectively. W W W Raxds 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.
14

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Single
-0.4
-0.2
0.0
0.2
0.6
SiFusion
Forecast Period
Forecast P Period Sep 1-28, 2022 (4 Weeks Average)
Forecast P eriod
(a)
Sep 1-7, 2022
(b)
(c)
Sep 1-30, 2022 (1 Month average)
(7 Days Average)
Figure 8: Spatial residual comparison. We compare the spatial patterns of forecasting results
produced by SIFusion and single-granularity variants.
15

---

-0666
-0.2
Residual
0.2
0.6
0.0
GT
Pred
0.2
SIC (96)
0.6
0.8
1.0
Forecast Period Mar 1-7, 2017 (Daily Granularity)
Forecast Period 1-28, 2017 (Weekly Granularity)
Forecast Period 1-30, 2017 (Monthly Granularity)
(a)
(b)
(c)
Figure 9: Spatial residual and predicted SIE quality of Mar 2017.
16

---

-066
-0.2
Residual
0.2
0.6
0.0
GT
Pred
0.2
SIC (%)
0.6
0.8
Forecast Sep 1-7, 2017 (Daily Granularity)
Forecast Period
Forecast Period (c) Sep 1-30, 2017 (Monthly Granularity)
1.0
(a)
(b)
Sep 1-28, 2017 (Weekly Granularity)
Figure 10: Spatial residual and predicted SIE quality of Sep 2017.
17

---

-0066
-0.2
Residual
0.2
0.6
0.0
GT
Pred
0.2
SIC (%6)
0.6
0.8
1.0
Forecast Mar 1-7, 2018 (Daily Granularity)
Forecast Period
Forecast Period 1-30, 2018 (Monthly Granularity
(a)
(b)
1-28, 2018 (Weekly Granularity)
(c)
Figure 11: Spatial residual and predicted SIE quality of Mar 2018.
18

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-066
-0.2
Residual
0.2
0.6
0.0
GT
Pred
0.2
SIC (%)
0.6
0.8
1.0
Forecast Period Sep 1-7, 2018 (Daily Granularity)
Forecast Period
Forecast Period (c) Sep 1-30, 2018 (Monthly Granularity
(a)
(b)
Sep 1-28, 2018 (Weekly Granularity)
Figure 12: Spatial residual and predicted SIE quality of Sep 2018
19

---

-0666
-0.2
Residual
0.0
0.2
0.6
0.0
GT
Pred
0.2
SIC (96)
0.6
0.8
1.0
Forecast Mar 1-7, 2019 (Daily Granularity)
Forecast Period
Forecast Period 1-30, 2019 (Monthly Granularity
(a)
(b)
1-28, 2019 (Weekly Granularity)
(c)
Figure 13: Spatial residual and predicted SIE quality of Mar 2019.
20

---

-066
-0.2
Residual
0.0
0.2
0.6
0.0
GT
Pred
0.2
SIC (%)
0.6
0.8
1.0
Forecast Sep 1-7, 2021 (Daily Granularity)
Forecast Period
Forecast Period (c) Sep 1-30, 2021 (Monthly Granularity
(a)
(b)
Sep 1-28, 2021 (Weekly Granularity)
Figure 14: Spatial residual and predicted SIE quality of Sep 2021.
21

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Reviews:
[{"review_id": "9t1HiTuQss", "reviewer": "Reviewer_73pK", "summary": "Thanks 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.", "questions": "My 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?", "limitations": "Yes. The authors have discussed the limitations.", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths-\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", "was_revised": true, "final_justification": "The authors provided clarification for the multi-temporal granularity and explained their implementation of independent spatial tokenization in the discussion period. However, lacking a direct comparison with the existing prominent deep learning models is still a concerning issue. I increased my score to acknowledge their efforts in providing detailed clarifications.", "rebuttal": "Thanks for your valuable review and comments of our work.\n___\n\n>**Response to Q1: Additional climatic variables.** \n\nThanks for your insightful question. Adding multiple climatic variables could be effective and beneficial, as you suggested, but it also poses a non-trivial challenge for the model to learn multiple variables. We implement the integration of variable correlation to the variation of Arctic sea ice for verification based on the SIFusion architecture. We choose three atmospheric ERA5 variables, i.e., air temperature of 2 meters (t2m), u component of 10 meter wind (u10), and v component of 10 meter wind (v10), to investigate the impact of integrating them into our proposed architecture.\n\nWe conduct additional experiments under the following settings:\n1. Training set period: from the year 2000 to 2013; validation and test period remain unchanged.\n2. We download hourly global ERA5 data (with resolution of 128 x 256) and average 24-hour files into daily values. To geophysically align global ERA5 with pan-Arctic SIC data, we regrid and interpolate those variables to the same Arctic grid.\n3. We trained baselines of three single granularities and SIFusion with all three time scales on the training dataset.\n4. We utilize two sets of spatial encoder-decoders, one for SIC data and the other for encoding three ERA5 variables. The sequential backbone is the same as SIFusion. The input and prediction length of all ERA5 data and SIC are identical, i.e., 7 days. The additional variables are normalized to [0,1]. We denote this model as Model-1.\n\n**Experiment Results:**\n\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| Model-1: Trained with Selected ERA5 Variables (7 Days Daily Performance)|  0.0800 |  0.0462  | 0.9337  |  0.9157  |  0.401  |\n| 7 Days Daily  Baseline  |0.0823 | 0.0200 |0.9670|0.9613|0.285|\n| SIFusion (Daily Scale)  |**0.0261**| **0.0132**|**0.9883**|**0.9862**|**0.087**|\n\nComparing the performance of Model-1 with 7 Days daily baseline, we find that adding ERA5 variables could lead to a slightly lower RMSE but a much higher MAE. Considering the lower R Squared, NSE, and larger SIE difference, the prediction error could be around the 15% sea ice concentration threshold for determining sea ice extent. Adding additional variables to the model could be challenging, especially when the spatio-temporal distribution of the variables is unique from each other. We will further investigate the effective integration of extra climatic variables.\n\n\n> **Response to Q2: Dataset pre-processing.**\n \nThanks for your kind suggestion. We provide a brief summary of our pre-processing procedure to curate the AI-ready dataset and will open-source the data pre-processing code to facilitate reproduction.\n1. We download the NOAA/NSIDC Climate Data Record of Passive Microwave Sea Ice Concentration G02202 Version 4 dataset from the official website.\n2. The official data was preserved in the NetCDF format. We use the open-sourced python package “netCDF4” to read data from the file with “.nc” suffix.\n3. The “netCDF4” package provides us an API to extract sea ice concentration data by providing the official variable name, i.e., “cdr_seaice_conc”.\n4. Since the acquired SIC data contains mask values that stand for land, ocean, and lake, we filter out these values with special meanings. \n5. We calculate the weekly and monthly average of SIC based on daily values to generate the AI-ready dataset.\nWe will add a brief summary of data curation to the dataset section.\n\n> **Response to Q3: Intra and inter-gruanularity.**\n\nThanks for raising this point. In our SIFusion architecture, the modeling of intra-granularity is naturally achieved by two steps:\n1. Spatial patterns of sea ice are tokenized for each time step within a specific granularity.\n2. Temporally concatenated spatial tokens are further embedded as one holistic token that represents the temporal pattern of the sea ice sequence.\n\nFor inter-granularity modeling, sea ice variations of each temporal granularity are first independently embedded as a single token. Then the multi-head self-attention is applied across the granularity dimension to explicitly capture pairwise correlations.\n\n>**Response to Q4: Change of the temporal granularities.**\n\nThanks for your intriguing question. Firstly, we choose to investigate the fusion of daily, weekly, and monthly granularity based on the literature of sea ice research. Since these three granularities are commonly studied scales, our motivation is to further exploit the inter-granularity between those time scales and to achieve simultaneous forecasting at all scales. Secondly, to further investigate the sensitivity of different granularity and quantitatively enhance the understanding of adding or removing specific granularity, we perform model training of three combinations: Daily-Weekly (Model-2), Weekly-Monthly (Model-3), and Daily-Monthly (Model-4). The overall architecture is similar to SIFusion, only that one granularity is removed from the modeling process. The experiment results are organized as follows:\n\n**Performance at Daily Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| Model-2: Daily-Weekly (7 Days Daily)|0.0667 |  **0.0120**|**0.9884**|**0.9863**|0.109|\n| Model-4: Daily-Monthly (7 Days Daily) |0.0610 |0.0139|0.9861|0.9836|0.129 |\n| 7 Days Daily  Baseline | 0.0823 |0.0200| 0.9670|  0.9613|0.285|\n| SIFusion (Daily Scale) |**0.0261**|0.0132|0.9883 |0.9862|**0.087**|\n\nAdding long-term predictions to the daily time scale could improve the performance of daily forecasts. Since both weekly and monthly data contain previous long-term trends, it is expected to be useful and to facilitate initialization of the Arctic sea ice state. Considering the lower SIE error and higher R Squared for Model-2, it could suggest that the 7-day weekly data aligns more naturally to weekly granularity.\n\n**Performance at Weekly Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| Model-2: Daily-Weekly (8 Weeks' Average)   | 0.0658| 0.0160|**0.9743** |**0.9693**|0.269|\n| Model-3: Weekly-Monthly (8 Weeks' Average) |0.0719|0.0154|0.9697|0.9638|0.203| \n| 8 Weeks' Average Baseline| 0.0775|0.0177|0.9671|0.9624|0.291|\n| SIFusion (Weekly Scale)|  **0.0639** |**0.0132**|0.9650|0.9582|**0.253**|\n\nWe could find that predicting at a weekly time scale, along with shorter or longer time scales, could both be effective for improving the overall performance. This could be the benefit of additional training data. By combining weekly and monthly granularity together, Model-3 could offer RMSE and MAE performance close to the SIFusion model and could achieve more accurate sea ice extent identification. \n\n** Performance at Monthly Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| Model-3: Weekly-Monthly (6 Months' Average)|0.0698|0.0190|**0.9144**|**0.9075**|0.299|\n| Model-4: Daily-Monthly  (6 Months' Average)|**0.0589**|  **0.0121**|0.8499|0.8393|0.315|\n| 6 Months' Average Baseline|0.0714|0.0167|0.8859|0.8766|0.346|\n| SIFusion (Monthly Scale)|0.0640|0.0133|0.8870|0.8788|**0.251**|\n\nFor the forecasting at the monthly scale, we could find that adding daily granularity was slightly less significant than adding weekly averages prediction to the model. Lastly, from the above experiments, we could find that longer-term temporal granularity tends to provide useful information to help improve the overall performance. Adding an extra time scale to the model could be rewarding and verify our proposed approach.\n\n> **Response to Q5: Using pre-trained weather model.**\n\nWe sincerely appreciate your insightful inquiry. Indeed, it is an innovative and quite promising idea to leverage pre-trained weather and climate foundation models to boost the overall performance. Specifically, the hidden atmospheric and oceanic dynamics learned by these foundation models are coupled with sea ice changes, and they could be leveraged to improve the forecasting skill. We will definitely look into the transfer of knowledge embedded in climate foundation models to SIC forecasting. We will add this to the discussion of future work.\n\n> **Response to Q6: Independent spatial tokenization.**\n\nThanks for your question. Most of prior works that leverage the U-Net architecture will concatenate variables from different time step to construct input batch with a dimension of [B,C,H,W], where B is the batch size, C stands for the total number of concatenated daily/weekly/monthly SIC data, H and W represents the shape of SIC data. There are no independent spatial and temporal encoding processes, since the data are concatenated along the time axis, and it will be transformed altogether by U-Net encoder. Different from prior approach, the shape of our proposed SIFusion has a [B,C,1,H,W]. This means that C stays unchanged during spatial feature extraction, i.e., \"independent spatial tokenization\", and we will get spatial tokens with dimension of [B,C,Feats]. This allows us to explicitly extract useful intra-granularity information that would benefit forecasting changes of sea ice. Moreover, we could further model inter-granularity correlations.\n\n> **Response to weakness.**\n\nThanks for your question. Since prior sea ice frameworks mainly focus on forecasting at single granularity, we evaluate the proposed framework by comparing their reported results.\n\n**Response to Formatting Issues.**\n\nWe sincerely thank you for bringing these issues to our attention.\n\n1. We will revise the heading to 'Introduction'.\n2. We will adjust the spacing of Figure 4 to produce a consistent line of text on page 5.\n___\nOnce more, sincere thanks for your review, and grateful for your insightful query. We look forward to your active participation in the discussion and we will respond promptly."}, {"review_id": "Vy4Sc6N9Km", "reviewer": "Reviewer_YeEK", "summary": "This paper introduces SIFusion, a unified deep learning framework for multi-granularity Arctic Sea Ice Concentration (SIC) forecasting. \nThe 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.", "questions": "Maybe I missed it, how Swim transformer is selected? Is that a crucial part for the performance?\n\nIs this method applicable to time series with missings?\n\nIs 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.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "The paper is rather complete, positions itself as a worth-trying method on NSIDC data.\n\nThere are improved performance in SIC forecasting area. \n\nThe 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?", "was_revised": true, "final_justification": "The authors addressed my concerns about the application on missingness and granularities. I therefore increased my rating to 4.", "rebuttal": "Thanks for your dedication to reviewing our work.\n___\n\n> **Response to Q1: Choice of Swin Transformer.**\n\nThanks for your question. We select Swin transformer as our spatial encoder mainly due to the following reasons:\na. Swin transformer uses a shifted window strategy that helps the model to effectively capture spatial correlations and features between the neighboring local Arctic regions.\nb. Swin transformer builds a hierarchical feature map by merging neighboring sea ice map patches. This design could preserve local detail while effectively extracting the global feature of the pan-Arctic region, which would facilitate the model to more accurately capture the overall distribution of sea ice extent.\n\n> **Response to Q2: Application for missing time series.**\n\nThanks for your insightful question.To verify whether our method is applicable to missing time series, we conduct additional experiments under the following settings:\n 1. Training set period: from the year 2000 to 2013; validation and test period remain unchanged.\n 2. Decreased model parameters for a shorter training set period due to the limited computational resources and time.\n 3. We trained baselines of three single granularities and SIFusion with all three time scales on the training dataset without masking.\n 4. We randomly mask the input of SIFusion at a daily scale, and the number of applied daily masks N in [1,3].\n\nWe report the results as follows.\n\n**Performance at Daily Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| 7 Days Daily  Baseline  |  0.0823 |  0.0200  |  0.9670  |  0.9613  |  0.285  |\n| SIFusion   |  **0.0261** |  **0.0132** |  **0.9883**  |  **0.9862**  |  **0.087**  |\n| SIFusion (Masked at Daily Scale)   |  0.0633 |  0.0141  |  0.9751  |  0.9713  |  0.094  |\n\nWe could find that when training SIFusion with randomly masked daily values, the performance slightly drops, but still outperforms the daily baseline.\n\n**Performance at Weekly Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| 8 Weeks' Average Baseline    |  0.0775 |  0.0177  |  **0.9671**  |  **0.9624**  |  0.291  |\n| SIFusion   |  **0.0639** |  **0.0132**  |  0.9650  |  0.9582  |  **0.253**  |\n| SIFusion (Masked at Daily Scale)   |  0.0679 |  0.0162  |  0.9688  |  0.9627  |  0.267  |\n\n**Performance at Monthly Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| 6 Months' Average Baseline   |  0.0714 |  0.0167  |  0.8859  |  0.8766  |  0.346  |\n| SIFusion |  **0.0640** |  **0.0133**  | **0.8870** |  **0.8788**  | **0.251**  |\n| SIFusion (Masked at Daily Scale)   |  0.0719 |  0.0166  |  0.8711  |  0.8612  |  0.307  |\n\nSimilarly, the performance at the weekly and monthly scales also drops slightly, but they still perform better than the baselines. This could indicate that our SIFusion is still applicable to missing time series. \n\n> **Response to Q3: Change of temporal scale.**\n\nWe appreciate your insightful inquiry. Incorporating a more temporal scale contributes to the improvement of SIFusion's forecasting skills. We agree that incorporating weekly/monthly scales is a natural choice. The main reason why we specifically use 7 days on a daily scale is that the 7 days time naturally aligns with one week's time. This alignment with tokens in the weekly scale could facilitate the learning of the model. We perform a revised version of SIFusion with 10 days daily forecast time.\n\n**Performance at Daily Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| 7 Days Daily  Baseline  |  0.0823 |  0.0200  |  0.9670  |  0.9613  |  0.285  |\n| SIFusion   |  **0.0261** |  **0.0132**  |  **0.9883**  |  **0.9862**  |  **0.087** |\n| SIFusion (Trained with 10 Days at Daily Scale)   |  0.0643 |  0.0140  |  0.9772  |  0.9739  |  0.098  |\n\n**Performance at Weekly Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| 8 Weeks' Average Baseline    |  0.0775 |  0.0177  |  **0.9671**  |  **0.9624**  |  0.291  |\n| SIFusion   |  **0.0639** |  **0.0132**  |  0.9650  |  0.9582  |  **0.253**  |\n| SIFusion (Trained with 10 Days at Daily Scale)   |  0.0664 |  0.0155  |  0.9579  |  0.9498  |  0.347  |\n\n**Performance at Monthly Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| 6 Months' Average Baseline   |  0.0714 |  0.0167  |  0.8859  |  0.8766  |  0.346  |\n| SIFusion |  **0.0640** |  **0.0133**  |  **0.8870**  |  **0.8788**  |  **0.251**  |\n| SIFusion (Trained with 10 Days at Daily Scale)  |  0.0663 |  0.0153  |  0.8874  |  0.8789  |  0.295  |\n\n By comparing the variance of performance between SIFusion and SIFusion trained with 10 10-day leads at the daily scale, we could find that the daily and monthly figures are close, but the identification of sea ice extent at the weekly scale suffers a larger performance drop. This 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.\n\n\n> **Response to Weaknesses: Valuable application beyond this problem.**\n\nMany thanks for raising this point. Our model is capable of capturing the variation of sea ice across multiple temporal scales, thereby enhancing overall forecasting skill. Specifically, the monthly scale incorporates important seasonal trends for predicting future sea ice. At the onset of the melt season, for example, monthly prediction of SIFusion provides guidance that could subsequently steer shorter-range forecasts based on the expected long-term trend. Moreover, the historical monthly means fed into the model carry the imprint of winter ice volume and its variability information intimately linked to pan-Arctic albedo strength and energy exchange, thereby facilitating short-term predictions with a more accurate initial state.\n\nConsidering the surface ocean directly contacts with the sea ice and the oceanic variable, e.g., sea surface salinity, which impacts the concentration of sea ice, our model could be extended to the prediction of oceanic variables and the joint modeling of multiple sea-ice-related variables.\n\n> **Response to Formatting Issues.**\n\nThanks for you for bringing formatting issues to our attention.\nWe will revise Figure 5 and the caption to make a clearer description that it represents the comparison between single daily time scale and our proposed SIFusion.\n___\nOnce again, sincere thanks for your review and insightful questions. We look forward to your active participation in the discussion and we will respond promptly."}, {"review_id": "NhJwrDsw3K", "reviewer": "Reviewer_vhuq", "summary": "Sea 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.", "questions": "It 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.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\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.", "was_revised": true, "final_justification": "I thought this was a good contribution and the authors did quite an impressive amount of work during the rebuttal period.", "rebuttal": "Thanks for valuing our work and acknowledging the effectiveness of the proposed approach.\n___\n> **Response to Q1: The main contributing time scale.**\n\nWe totally agree with your opinion that longer-term predictions contribute more to the improvement of overall performance. For instance, assuming that our model forecasts at the beginning of a melting season, on the one hand, the prediction of the monthly average sea ice could provide critical hints that the extent of sea ice is about to drop drastically, which would facilitate the short-term predictions. On the other hand, the input of historical monthly average also provides the model with information about the amount and variation of sea ice and during the winter season, which is correlated to the strength of albedo and the energy exchange in the pan-Arctic region. This helps the short-term prediction to set up a correct initial state.\n\n> **Response to Q2: Exploring pre-training and fine-tuning.**\n\nWe appreciate your insightful question, and we fully agree that the pre-train and fine-tune approach is definitely worth exploring. Hence, we set up the following experiment for further investigation:\n 1. Training set period: from the year 2000 to 2013; validation and test periods remain unchanged.\n 2. Decreased model parameters for a shorter training set period due to the limited computational resources and time.\n 3. Baselines of three single granularities and SIFusion with all three time scales.\n 4. Pre-train and fine-tune experiments design:\n      - a. Pre-train a 7 days single granularity model, then fine-tune on 6 months' average data.\n      - b. Pre-train a 8 weeks' average model, then fine-tune on 6 months' average data.\n 5. We additionally trained two models for comparison: the SIFusion and the single-granularity model that performs at a monthly scale.\n\nWe report our experiment as follows:\n**Performance at Monthly Scale**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|-|-|-|-|-|-|\n| Pre-train on 7 Days and Fine-tune on 6 Months' Average|  0.1147 |  0.0396  |  0.5630  |  0.5362  |  1.89  |\n| Pre-train on 8 Weeks' Average and Fine-tune on 6 Months Average |  **0.0544** |  **0.0129**  |  **0.9441**  |  **0.9400**  |  0.283  |\n| 6 Months' Average Baseline   |  0.0714 |  0.0167  |  0.8859  |  0.8766  |  0.346  |\n| SIFusion (Monthly Scale) |  0.0640 |  0.0133  |  0.8870  |  0.8788  |  **0.251**  |\n\nWe could find that pre-training a 7 days forecasting model then fine-tuning on monthly data, suffers a performance drop in all metrics. This could be caused by the temporal distribution of daily and monthly scales, which are distinct from each other; hence fine-tuning the pre-trained model on monthly data could be difficult to converge. For the other setting, pre-training a 7 days forecasting model then fine-tuning for predicting 6 months' averages could improve the performance on most evaluation metrics, except that the identification of sea ice extent is inferior. The success of fine-tuning the model in this setting could indicate that the temporal distribution of medium range and seasonal time scales is closer than the distribution between daily and monthly scales, hence the forecasting skill could be further improved.\nWe will continue investigating this approach and fully exploit the potential of the proposed pretrain-finetune architecture.\n\n> **Response Weaknesses: Description of proposed architecture and performance of physical models.**\n\nSincere thanks for your kind suggestion.\n\n1. Improve the description of the model:\n\nWe agree that explaining our proposed architecture in plain text is hard to get through. We think the description of the model could be improved by providing an equation or example of the manipulation of the input data dimension. This could facilitate the understanding of the difference between our multi-granularity fusion module and the previously used vanilla Transformer. \n\n2. Regarding the physical model:\n   \n Considering the sea ice forecasting physical model SEAS5 [1] only provides prediction of the binary index, which indicates the sea ice extent, from the first date of each month, it could only provide limited evalation metrics (for reference, we applied for the SEAS5 to forecast the first 216 days of 2016, the calculated SIE difference is 0.3359 millions of square killometers). We choose a surrogate model [2] that is usually utilized to benchmark dynamical sea ice forecasting models to provide more evaluation metrics. We train the model from the dynamical model benchmark under our experimental setting and compare it with our model. From the following table, we can find that the dynamical model benchmark performs well at the recent time scale, and the performance drops as the prediction horizon extends to the seasonal scale.\n\n**Comparison with Dynamical Model Benchmark**\n**Performance at Daily Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ |\n|-|-|-|-|-|\n| Dynamical Model Benchmark  |  0.0476 |  0.0081  |  0.9735  |  0.9705  |\n| 7 Days Daily  Baseline     |  0.0823 |  0.0200  |  0.9670  |  0.9613  |\n| SIFusion (Daily Scale)   |  **0.0261** |  **0.0132**  |  **0.9883**  |  **0.9862**  |\n\n**Performance at Weekly Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | \n|-|-|-|-|-|\n| Dynamical Model Benchmark   |  0.0897 |  0.0190  |  0.9008  |  0.8902  |\n| 8 Weeks' Average Baseline    |  0.0775 |  0.0177  |  **0.9671**  |  **0.9624**  | \n| SIFusion (Weekly Scale)  |  **0.0639** |  **0.0132**  |  0.9650  |  0.9582  |\n\n**Performance at Monthly Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ |\n|-|-|-|-|-|\n| Dynamical Model Benchmark   |  0.1020 |  0.0219  |  **0.8892**  |  0.8758  |\n| 6 Months' Average Baseline   |  0.0714 |  0.0167  |  0.8859  |  0.8766  |\n| SIFusion (Monthly Scale) |  **0.0640** |  **0.0133**  |  0.8870 |  **0.8788** |\n\n3. Indeed, our initial intention in the limitation section is to discuss the potential of leveraging sea ice correlated meteorological and oceanic variables to facilitate forecasting. We will revise the expression to a more precise version.\n\n\n>**Response to Minor Comments**\n\nThanks you for kindly bringing these issues to our attention. We will accordingly revise the expression in line 84, 89, 122, 215, 236 and the use of term “variate”.\n\n**Reference**\n\n[1] Johnson, S. J.; Stockdale, T. N.; Ferranti, L.; Balmaseda, M. A.; Molteni, F.; Magnusson, L.; Tietsche, S.; Decremer, D.; Weisheimer, A.; Balsamo, G.; et al. 2019. SEAS5: the new ECMWF seasonal forecast system. Geoscientific Model\nDevelopment, 12(3): 1087–1117.\n\n[2] Niraula, B.; and Goessling, H. F. 2021. Spatial damped\nanomaly persistence of the sea ice edge as a benchmark for\ndynamical forecast systems. Journal of Geophysical Re-\nsearch: Oceans, 126(12): e2021JC017784.\n___\nWe thank you once again and warmly invite you to engage in the ongoing discussion. We will response promtly."}, {"review_id": "2hYCcZx6OA", "reviewer": "Reviewer_X1aA", "summary": "This 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.", "questions": "Please refer to the three questions raised in Weaknesses.", "limitations": "Yes.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**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 $\\mathrm{SIC}_{diff}$.", "was_revised": true, "final_justification": "This paper addresses forecasting pan-Arctic sea ice concentration (SIC). Unlike prior (deep learning-based) methods, the proposed method considers several time scales from short-term fluctuations and long-term trends. 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\nThe rebuttal and discussion clarified my major concerns regarding the ablation study, providing evidence for the value of introducing independent time scales. Through the discussion, I understood that the proposed architecture does not offer computational efficiency gains. However, I do not consider this a critical limitation, and I therefore recommend that this work be accepted to the conference.", "rebuttal": "Thanks for acknowledging the value of our work and our effort to explore effective neural network architecture for polar scientific research.\n___\n\n> **Response to Q1: Training on a mixture of temporal scales.**\n\nThanks for your question. Indeed, training prior U-Net-based approaches with a dataset that contains a mixture of time scales is an intriguing idea. Considering that the temporal distribution of different time scales is not identical, this could lead to inferior performance of those models. It could be elaborated by a succinct example. If we set the input length of the model to 7, i.e., the temporal step equals 7.  The model will simultaneously learn the evolving Arctic sea ice pattern from 7 days, 7 weeks’ average, and 7 months’ average values. The mixture of mean and variance derived from the above three different time scales would generate a misleading data distribution that causes forecasting error.\n\nIn contrast, our proposed architecture mitigates this non-trivial issue by explicitly mapping encoded input sea ice data sequences from different temporal scales into independent sequential tokens. Therefore, the unique temporal variation pattern of a specific time scale is preserved rather than mixed with patterns from other time scales.  Additionally, by adopting the proposed approach, our model could exploit inter-granularity correlations to improve the overall performance.\n\n\n> **Response to Q2: Embedding vectors of different time scales.**\n\nMany thanks for raising this point. Based on the analysis from Q1, we know that the temporal distributions of different time scales are distinctive from each other. On the contrary, the spatial structure across different time scales is similar. For instance, given a monthly average of sea ice maps and a sampled daily sea ice map from the same month, it would be difficult to tell which one stands for the averaged value and which one represents the daily value. This also applies to the comparison between daily value and weekly average, or between monthly average and weekly average. It is because all time scales spatially represent the identical pan-Arctic area. The variation caused by averaging along the time axis will not drastically change the spatial structure and impede the learning of spatial embedding. Therefore, we adopt the shared spatial encoder approach, which is sufficient for compressing sea ice data derived from different time scales into a latent feature space. Additional benefits would be the simpler architecture and a reduction in overall parameters.\n\n> **Response to Q3: Complement of different time scales.**\n\nWe appreciate your insightful question. To further validate the importance of a specific time scale, we conduct experiments under the following settings:\n 1. Training set period: from the year 2000 to 2013; validation and test period remain unchanged.\n 2. We trained baselines of three single granularities and SIFusion with all three time scales on the training dataset.\n 3. We perform model training of three combinations: Daily-Weekly (Model-1), Weekly-Monthly (Model-2), and Daily-Monthly (Model-3). The overall architecture is similar to SIFusion, only that one granularity is removed from the modeling process. \n\nThe experiment results are organized as following:\n\n**Performance at Daily Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|----------|-----------|---------|-----------------|---------|---------|\n| Model-1: Daily-Weekly (7 Days Daily)  |  0.0667 |  **0.0120**  |  **0.9884**  |  **0.9863**  |  0.109  |\n| Model-3: Daily-Monthly (7 Days Daily) |  0.0610 |  0.0139  |  0.9861  |  0.9836  |  0.129  |\n| 7 Days Daily  Baseline     |  0.0823 |  0.0200  |  0.9670  |  0.9613  |  0.285  |\n| SIFusion (Daily Scale)   |  **0.0261** |  0.0132  |  0.9883  |  0.9862  |  **0.087**  |\n\nAdding long-term predictions to the daily time scale could improve the performance of daily forecasts. Since both weekly and monthly data contain previous long-term trends, it is expected to be useful and to facilitate initialization of the Arctic sea ice state. Considering the lower SIE error and higher R Squared for Model-1, it could suggest that the 7-day weekly data aligns more naturally with weekly granularity.\n\n**Performance at Weekly Scale:**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|----------|-----------|---------|-----------------|---------|---------|\n| Model-1: Daily-Weekly (8 Weeks' Average)   |  0.0658 |  0.0160  |  **0.9743**  |  **0.9693**  |  0.269  |\n| Model-2: Weekly-Monthly (8 Weeks' Average) |  0.0719 |  0.0154  |  0.9697  |  0.9638  |  **0.203**  | \n| 8 Weeks' Average Baseline    |  0.0775 |  0.0177  |  0.9671  |  0.9624  |  0.291  |\n| SIFusion (Weekly Scale)  |  **0.0639** |  **0.0132**  |  0.9650  |  0.9582  |  0.253  |\n\nWe could find that predicting at a weekly time scale, along with shorter or longer time scales, could both be effective for improving the overall performance. This could be the benefit of additional training data. By combining weekly and monthly granularity together, Model-2 could offer RMSE and MAE performance close to the SIFusion model, and it could achieve more accurate sea ice extent identification. \n\n**Performance at Monthly Scale**\n| **Model** | **RMSE** ↓ | **MAE** ↓ | **R Squared** ↑ | **NSE** ↑ | **SIE Difference** ↓|\n|----------|-----------|---------|-----------------|---------|---------|\n| Model-2: Weekly-Monthly (6 Months' Average)   |  0.0698 |  0.0190  |  **0.9144**  |  **0.9075**  |  0.299  |\n| Model-3: Daily-Monthly (6 Months' Average)    |  **0.0589** |  **0.0121**  |  0.8499  |  0.8393  |  0.315  |\n| 6 Months' Average Baseline   |  0.0714 |  0.0167  |  0.8859  |  0.8766  |  0.346  |\n| SIFusion (Monthly Scale) |  0.0640 |  0.0133  |  0.8870  |  0.8788 |  **0.251**  |\n\nFor the forecasting at monthly scale, we could find that adding daily granularity was slightly less significant than adding weekly averages prediction to the model.\n\nOverall, from the above experiments, we could find that longer-term temporal granularity tends to provide useful information to help improve the overall performance. Adding an extra time scale to the model could be rewarding and verify our proposed approach.\n\n>**Response to the Increased Training Time**\n\nBased on the above experiments, we collect the training time of all models to assess the increased training time by introducing extra temporal scales:\n\n**Training Time of Experiments**\n| **Model** | **Training Time** (GPU hours) |\n|-|-|\n| 7 Days Daily  Baseline     | 16.6 | \n| 8 Weeks' Average Baseline    | 18.3 |\n| 6 Months' Average Baseline   | 14.5  | \n| Daily-Weekly | 38.9  |\n| Weekly-Monthly | 33.1  |\n| Daily-Monthly | 31.9  |\n| SIFusion (All three time scales)| 49.3 |\n\nFrom the above table, we can see that, as temporal granularity increases, the training time almost linearly increases, which could be reasonable since the models are calculating with more data.\n\n> **Response to Minor Comments**\n\nThanks for your kind suggestion. We will revise the italic fonts in equations to accurately convey their meanings.\n\n___\n\n\nOnce more, thank you for acknowledging the contribution of our work. We look forward to your active participation in the discussion. We will respond promptly."}]

Author rebuttal:

Meta-review: This paper introduces SIFusion, a transformer-based framework for Arctic sea ice concentration (SIC) forecasting that addresses the limitation of existing deep learning models, which typically operate at a fixed temporal resolution and overlook dependencies across time scales. By independently embedding spatial features from daily, weekly, and monthly SIC data and fusing them through a multi-head attention-based transformer, SIFusion captures both intra- and inter-granularity correlations. Empirical results on pan-Arctic datasets show that SIFusion achieves improved accuracy, robustness to anomalies (e.g., 2022 SIC trends), and better generalization compared to strong baselines.
Overall, while the contribution may be somewhat application-specific, the paper presents a well-executed study with convincing empirical evidence.
Decision: Accept (poster)