A method and system for joint prediction of concentration and thickness of arctic sea ice

Abstract

This invention belongs to the field of sea ice state prediction, specifically relating to a method and system for jointly predicting the concentration and thickness of Arctic sea ice. The method involves acquiring daily data on Arctic sea ice concentration and thickness, preprocessing them to obtain spatiotemporally aligned sea ice concentration and thickness sequences, extracting historical input sequences, constructing trend channels based on sea ice thickness differences, and forming extended input sequences. Feature mapping, attention enhancement, and multi-stage encoding are then performed to obtain multi-scale features and bottleneck features. The bottleneck features undergo bidirectional cross-attention processing, and multi-scale features are fused based on gating weights. Decoding yields the sea ice concentration and thickness prediction fields. Physical consistency processing is performed based on the sea ice concentration of the last day. This invention can utilize the coupling relationship between sea ice concentration and thickness, as well as the thickness change trend, to improve the spatial consistency and physical rationality of the joint prediction, providing a basis for Arctic navigation planning and ice condition risk early warning.

Description

Technical Field

[0001] This invention belongs to the field of sea ice state prediction, specifically relating to a method and system for jointly predicting the concentration and thickness of Arctic sea ice. Background Technology

[0002] Arctic sea ice is a crucial environmental factor influencing the polar marine environment, shipping safety, and climate change. Sea ice concentration characterizes the proportion of sea ice covering a unit of ocean area, reflecting the extent of the ice zone and the location of the ice edge. Sea ice thickness characterizes the vertical scale of sea ice, reflecting its volume, carrying capacity, and stability. With the increasing navigation activities along Arctic shipping routes, the development of marine resources, and polar scientific research operations, timely prediction of changes in sea ice coverage, ice edge location, and sea ice thickness over the next few days has become a critical technical requirement for polar shipping route planning, vessel scheduling, determining operational windows, and providing early warnings of ice conditions. Especially during the summer melt season and in the ice edge zone, sea ice conditions change rapidly, and relying solely on current satellite observations is insufficient to meet the practical operational needs for predicting short-term ice condition trends.

[0003] Existing methods for predicting Arctic sea ice mainly include numerical modeling methods based on physical processes and data-driven methods based on historical observation data. Numerical models typically construct predictive models based on sea ice thermodynamics, dynamics, and ocean-atmosphere interactions, and combine initial sea ice field, atmospheric field, and ocean field to extrapolate future ice conditions. Data-driven methods utilize historical sea ice concentration and thickness data obtained from satellite remote sensing, and extract spatiotemporal variation characteristics of sea ice through convolutional neural networks, recurrent neural networks, Transformers, or other deep learning networks, and predict sea ice conditions for the next few days accordingly. In recent years, with the accumulation of satellite remote sensing data and the development of deep learning technology, the application of data-driven methods in short-term sea ice prediction has gradually increased. However, many existing schemes still model sea ice concentration and sea ice thickness independently, or mainly use sea ice concentration as the prediction object, failing to fully utilize the correlation between sea ice concentration and sea ice thickness.

[0004] However, in the actual evolution of Arctic sea ice, sea ice concentration and sea ice thickness are not independent. Ice expansion, melting, convergence, divergence, and ice edge movement all simultaneously affect the spatial distribution and temporal variations of both. If predictions are made based solely on a single sea ice element, the predictions are prone to significant deviations in rapidly changing ice edge regions, thin ice areas, and during the summer melting season. Conversely, predicting sea ice concentration and thickness separately makes it difficult to utilize their interrelationships, potentially resulting in predicted sea ice concentrations below ice-forming conditions while corresponding locations still exhibit substantial sea ice thickness—inconsistencies with actual physical conditions. Furthermore, satellite-retrieved sea ice concentration and thickness data may suffer from differences in spatial resolution, inconsistent grid orientations, and missing polar observations. Directly inputting these into prediction models can easily lead to spatial location errors or insufficient utilization of relevant information. These issues further affect the reliability of predictions regarding ice edge location, ice area extent, and thick ice regions, impacting navigation safety. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a method and system for jointly predicting the concentration and thickness of Arctic sea ice, which can provide more complete ice information for ships in polar regions, enabling navigation planning to simultaneously consider the presence and thickness of sea ice, thereby providing a more complete short-term forecast basis for Arctic route selection, ship ice avoidance, determination of offshore operation windows, and ice risk warning.

[0006] A method for jointly predicting the concentration and thickness of Arctic sea ice includes: Obtain daily data on Arctic sea ice concentration and daily data on Arctic sea ice thickness; Preprocessing the daily data of Arctic sea ice concentration and the daily data of Arctic sea ice thickness yields a spatiotemporally aligned sea ice concentration sequence and sea ice thickness sequence. Data for a consecutive preset number of days are extracted from the sea ice concentration sequence and the sea ice thickness sequence to obtain the historical input sequence of sea ice concentration and the historical input sequence of sea ice thickness. Based on the sea ice thickness difference at different times in the historical input sequence of sea ice thickness, the sea ice thickness trend channel is obtained. The historical input sequence of sea ice thickness is concatenated with the trend channel of sea ice thickness to obtain the extended input sequence of sea ice thickness. Feature embedding processing is performed on the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness respectively to obtain initial embedding features of sea ice concentration and initial embedding features of sea ice thickness. Attention enhancement is then performed on the initial embedding features of sea ice concentration and initial embedding features of sea ice thickness to obtain enhanced features of sea ice concentration and enhanced features of sea ice thickness. Then, multi-stage encoding is performed to obtain multi-scale features of sea ice concentration, bottleneck features of sea ice concentration, multi-scale features of sea ice thickness, and bottleneck features of sea ice thickness. Bidirectional cross-attention processing is performed on the bottleneck features of sea ice concentration and sea ice thickness to obtain bottleneck coupling features; Gating weights are generated based on the multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness. The multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness are then weighted and fused using the gating weights to obtain multi-scale coupled features. The bottleneck coupling features and the multi-scale coupling features are decoded respectively to obtain the sea ice concentration prediction field and the initial sea ice thickness prediction field for the next preset number of days. Based on the sea ice concentration of the last day in the historical input sequence of sea ice concentration, the initial sea ice thickness prediction field is subjected to physical consistency processing. The sea ice thickness prediction value corresponding to the pixel position where the sea ice concentration is lower than the preset threshold is set to zero to obtain the sea ice thickness prediction field. The sea ice concentration prediction field and the sea ice thickness prediction field are used as the joint short-term forecast result of Arctic sea ice.

[0007] Feature embedding processing is performed on the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness, respectively, to obtain initial embedding features of sea ice concentration and initial embedding features of sea ice thickness. Attention enhancement is then applied to the initial embedding features of sea ice concentration and initial embedding features of sea ice thickness, respectively, to obtain enhanced features of sea ice concentration and enhanced features of sea ice thickness. Then, multi-stage encoding is performed to obtain multi-scale features of sea ice concentration, bottleneck features of sea ice concentration, multi-scale features of sea ice thickness, and bottleneck features of sea ice thickness, including: Image block segmentation and feature dimension mapping are performed on the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness, respectively, to obtain the initial embedding features of sea ice concentration and the initial embedding features of sea ice thickness. The initial embedding features of sea ice concentration are enhanced using channel attention and spatial attention to obtain enhanced sea ice concentration features; the initial embedding features of sea ice thickness are enhanced using channel attention and spatial attention to obtain enhanced sea ice thickness features. The sea ice concentration enhancement features are encoded in multiple stages to obtain sea ice concentration multi-scale features and sea ice concentration bottleneck features; the sea ice thickness enhancement features are encoded in multiple stages to obtain sea ice thickness multi-scale features and sea ice thickness bottleneck features.

[0008] Optionally, the daily sea ice concentration data and the daily sea ice thickness data are preprocessed to obtain spatiotemporally aligned sea ice concentration sequences and sea ice thickness sequences, including: The daily Arctic sea ice concentration data were numerically normalized to obtain normalized sea ice concentration data. The normalized sea ice concentration data is downsampled to obtain downsampled sea ice concentration data with the same spatial resolution as the daily Arctic sea ice thickness data. Based on the grid coordinate axis correspondence between the downsampled sea ice concentration data and the daily Arctic sea ice thickness data, the downsampled sea ice concentration data is subjected to matrix transpose and coordinate axis flipping to obtain grid-aligned sea ice concentration data that is in the same polar projection grid as the daily Arctic sea ice thickness data. Missing value connected component detection was performed on the grid-aligned sea ice concentration data and the daily Arctic sea ice thickness data to obtain the missing sea ice concentration region and the missing sea ice thickness region. Nearest neighbor interpolation is performed using the effective pixels around the missing sea ice concentration region and the effective pixels around the missing sea ice thickness region to obtain the missing sea ice concentration data and missing sea ice thickness data after filling the missing values. By using an active grid mask, effective ocean regions are selected from the sea ice concentration data and sea ice thickness data after missing value filling, respectively, to obtain spatiotemporally aligned sea ice concentration sequences and sea ice thickness sequences.

[0009] Optionally, a sea ice thickness trend channel is obtained based on the sea ice thickness difference at different times in the historical input sequence of sea ice thickness, including: Using the current moment in the historical input sequence of sea ice thickness as a benchmark, the difference between the sea ice thickness at the current moment and the sea ice thickness at at least two different historical moments is calculated to obtain the sea ice thickness trend characteristics corresponding to different time scales. Each of the aforementioned sea ice thickness trend characteristics is used as a sea ice thickness trend channel to characterize the thickening or thinning trend of sea ice thickness at different time scales.

[0010] Optionally, image patching and feature dimension mapping are performed on the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness, respectively, to obtain initial embedding features of sea ice concentration and initial embedding features of sea ice thickness, including: The historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness are respectively divided into multiple non-overlapping image blocks; Each non-overlapping image patch is subjected to feature projection to transform it to a preset feature dimension, thereby obtaining the initial embedding features of sea ice concentration and the initial embedding features of sea ice thickness.

[0011] Optionally, attention enhancement is applied to the initial embedding features of sea ice concentration and the initial embedding features of sea ice thickness, respectively, to obtain enhanced features of sea ice concentration and enhanced features of sea ice thickness, including: The initial sea ice concentration embedding features are aggregated along the channel dimension to obtain a first channel aggregation result. A first channel attention weight is generated based on the channel aggregation result. The initial sea ice concentration embedding features are then weighted using the first channel attention weight to obtain enhanced sea ice concentration channel features. Spatial dimension feature aggregation is performed on the sea ice concentration channel enhancement features to obtain a first feature aggregation result. A first spatial attention weight is generated based on the feature aggregation result. The sea ice concentration channel enhancement features are weighted using the first spatial attention weight to obtain the sea ice concentration enhancement features. The initial sea ice thickness embedding features are aggregated along the channel dimension to obtain a second channel aggregation result. A second channel attention weight is generated based on the second channel aggregation result. The initial sea ice thickness embedding features are then weighted using the second channel attention weight to obtain the sea ice thickness channel enhancement features. Spatial feature aggregation is performed on the sea ice thickness channel enhancement features to obtain a second feature aggregation result. A second spatial attention weight is generated based on the second feature aggregation result. The sea ice thickness channel enhancement features are then weighted using the second spatial attention weight to obtain the sea ice thickness enhancement features.

[0012] Optionally, multi-stage encoding is performed to obtain multi-scale features of sea ice concentration, bottleneck features of sea ice concentration, multi-scale features of sea ice thickness, and bottleneck features of sea ice thickness, including: The sea ice concentration enhancement feature and the sea ice thickness enhancement feature are respectively used as the initial coding features of the corresponding coding branches; In each encoding stage, the current encoded features are divided into rectangular attention windows with different widths and heights, and self-attention operations are performed on the current encoded features within each rectangular attention window to obtain window attention features; The window attention features are shifted to enable feature interaction between adjacent rectangular attention windows, thus obtaining the interaction features of the current stage. The interaction features of the current stage are downsampled to obtain the encoding features of the next encoding stage; The coding features obtained in each intermediate coding stage are respectively used as the corresponding multi-scale features of sea ice concentration or multi-scale features of sea ice thickness, and the coding features obtained in the final coding stage are respectively used as the bottleneck features of sea ice concentration or the bottleneck features of sea ice thickness.

[0013] Optionally, the bidirectional cross-attention processing of the sea ice concentration bottleneck feature and the sea ice thickness bottleneck feature to obtain the bottleneck coupling feature includes: Using the sea ice concentration bottleneck feature as the query feature, and the sea ice thickness bottleneck feature as the key feature and value feature, a first cross-attention process is performed to obtain the first cross-field interaction feature. Using the sea ice thickness bottleneck feature as the query feature, and the sea ice density bottleneck feature as the key feature and value feature, a second cross-attention process is performed to obtain the second cross-field interaction feature. The bottleneck coupling feature is obtained by fusing the first cross-field interaction feature and the second cross-field interaction feature.

[0014] A joint prediction system for Arctic sea ice concentration and thickness, comprising: The data acquisition module is used to acquire daily data on Arctic sea ice concentration and daily data on Arctic sea ice thickness. The data preprocessing module is used to preprocess the daily data of Arctic sea ice concentration and the daily data of Arctic sea ice thickness to obtain a spatiotemporally aligned sea ice concentration sequence and sea ice thickness sequence. The sequence and trend extraction module is used to extract data for a consecutive preset number of days from the sea ice concentration sequence and the sea ice thickness sequence, respectively, to obtain the historical input sequence of sea ice concentration and the historical input sequence of sea ice thickness. Based on the sea ice thickness difference at different times in the historical input sequence of sea ice thickness, the sea ice thickness trend channel is obtained. The sequence expansion module is used to concatenate the historical input sequence of sea ice thickness with the trend channel of sea ice thickness to obtain the expanded input sequence of sea ice thickness. The feature processing module is used to perform feature embedding processing on the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness respectively to obtain initial embedded features of sea ice concentration and initial embedded features of sea ice density and thickness; to perform attention enhancement on the initial embedded features of sea ice concentration and initial embedded features of sea ice density and thickness respectively to obtain enhanced features of sea ice concentration and enhanced features of sea ice thickness; and then to perform multi-stage encoding to obtain multi-scale features of sea ice concentration, bottleneck features of sea ice concentration, multi-scale features of sea ice thickness, and bottleneck features of sea ice thickness. The bottleneck feature coupling module is used to perform bidirectional cross-attention processing on the sea ice concentration bottleneck feature and the sea ice thickness bottleneck feature to obtain the bottleneck coupling feature. The multi-scale feature fusion module is used to generate gating weights based on the multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness, and to use the gating weights to perform weighted fusion of the multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness to obtain multi-scale coupled features. The feature decoding and prediction module is used to decode the bottleneck coupling feature and the multi-scale coupling feature respectively to obtain the sea ice concentration prediction field and the initial sea ice thickness prediction field for the next preset number of days. The physical consistency correction module is used to perform physical consistency processing on the initial sea ice thickness prediction field based on the sea ice concentration of the last day in the historical input sequence of sea ice concentration. The predicted sea ice thickness value corresponding to the pixel position where the sea ice concentration is lower than a preset threshold is set to zero to obtain the sea ice thickness prediction field. The sea ice concentration prediction field and the sea ice thickness prediction field are used as the joint short-term forecast result of Arctic sea ice.

[0015] A terminal device includes a memory and a processor. The memory stores a computer program that can run on the processor. When the processor loads and executes the computer program, it employs a joint prediction method for the concentration and thickness of Arctic sea ice.

[0016] A computer-readable storage medium storing a computer program that, when loaded and executed by a processor, employs a method for jointly predicting the concentration and thickness of Arctic sea ice.

[0017] The beneficial effects of this invention are: 1. By performing spatial grid alignment, missing value imputation, and effective ocean area screening on daily data of Arctic sea ice concentration and thickness, a correspondence can be established between sea ice concentration and thickness data with different spatial resolutions and grid arrangements at a unified spatial location. Compared to directly using remote sensing data from different sources for prediction, this reduces input errors caused by inconsistent spatial resolution, grid misalignment, and missing polar observations, improves the spatial consistency and effectiveness of the data used in subsequent joint predictions, and provides a more reliable data foundation for short-term Arctic sea ice prediction.

[0018] 2. A sea ice thickness trend channel is constructed based on the sea ice thickness differences at different times in the historical sea ice thickness input sequence. This historical input sequence and the trend channel are then used together for feature extraction. This allows the prediction process to utilize not only the absolute spatial distribution of sea ice thickness but also the thickening or thinning trends at different time scales. Compared to existing methods that rely solely on continuous historical sea ice thickness values, this approach enhances the ability to identify slow changes in sea ice thickness. It is particularly beneficial for improving the characterization of short-term trends during freezing and melting periods, as well as in areas of continuous ice thickness variation, thereby increasing the sea ice thickness prediction results' ability to reflect actual ice condition changes.

[0019] 3. Sea ice concentration and thickness are feature-encoded separately, and the two bottleneck features are coupled through bidirectional cross-attention. Simultaneously, gating weights are used to adaptively fuse sea ice concentration and thickness features at different spatial scales. Compared to existing techniques that predict sea ice concentration and thickness independently, this method retains the inherent characteristics of both sea ice elements while leveraging their interrelationship. This allows the model to adaptively select sea ice concentration or thickness information based on different regions and spatial scales, thereby improving the adaptability of the joint prediction results to spatial differences in ice conditions across different Arctic regions.

[0020] 4. It can simultaneously obtain sea ice concentration and thickness prediction fields for a predetermined number of days in the future. This not only reflects the future sea ice coverage and ice edge location, but also further reflects the sea ice thickness distribution in different regions. Compared to methods that only provide a single sea ice concentration or thickness prediction result, it can provide more complete ice information for polar vessels, enabling navigation planning to consider both the presence and thickness of sea ice. This provides a more complete short-term forecast basis for Arctic route selection, ship ice avoidance, determination of offshore operation windows, and ice risk warning. It helps reduce the probability of vessels entering high-risk thick ice areas or abruptly changing ice edge areas, improving the safety and scheduling efficiency of polar navigation and offshore operations. Attached Figure Description

[0021] Figure 1 This is a lead-wise MAE curve of SIC and SIT in this invention; Figure 2 This is a bar chart showing the average SIC and SITMAE for each month from January to December of this invention; Figure 3 This is a comparison chart of Lead+1 day MAE for various sea areas according to the present invention; Figure 4 Heatmaps of average MAE (Lead 1–7 days) for SIC and SIT in various sea areas and months in 2021 are provided. Figure 4(a) is a heatmap of the average MAE of SIC in 2021. Figure 4 (b) is a heatmap of the average MAE of SIT in 2021; Figure 5 Heatmaps of average MAE (Lead 1–7 days) for SIC and SIT in various sea areas and months in 2022, including... Figure 5 (a) is a heatmap of the average MAE of SIC in 2022. Figure 5 (b) is a heat map of the average MAE of SIT in 2022. Detailed Implementation

[0022] A method for jointly predicting the concentration and thickness of Arctic sea ice includes: S1. Obtain daily data on Arctic sea ice concentration and daily data on Arctic sea ice thickness; Specifically, Sea Ice Concentration (SIC) represents the proportion of sea ice coverage area to the total area of ​​a spatial grid cell. In this embodiment, the original sea ice concentration can be expressed as a percentage, which can be normalized to a value range of 0 to 1.

[0023] Sea ice thickness (SIT): represents the thickness of sea ice in the vertical direction. In this embodiment, sea ice thickness is expressed in meters and can be normalized according to a preset scale factor before training.

[0024] Daily data: refers to sea ice spatial field data formed at one-day intervals, with each day corresponding to a two-dimensional grid.

[0025] Daily sea ice concentration data were retrieved from the Fengyun-3 MWRI microwave imager, with an original spatial resolution of 12.5 km. The original sea ice concentration was expressed as a percentage from 0 to 100. Daily sea ice thickness data were generated from a multi-source fused sea ice thickness product formed by combining Fengyun-3 MWRI data with CryoSat-2 / SMOS altimeter data, with a spatial resolution of 25 km. The common time range of both types of products can be used to establish a continuous joint dataset of sea ice concentration and sea ice thickness.

[0026] Both types of data can be projected using EPSG:3411 Arctic polar projection, but even with the same projection identifier, the row and column arrangement of the original grid may still be inconsistent. For example, in this embodiment, the sea ice concentration grid size is 896×608, and the sea ice thickness grid size is 304×448. The two have different spatial resolutions and coordinate axis arrangements, so grid alignment needs to be performed.

[0027] S2. Preprocess the daily data of Arctic sea ice concentration and the daily data of Arctic sea ice thickness to obtain a spatiotemporally aligned sea ice concentration sequence and sea ice thickness sequence. Preprocessing the daily sea ice concentration data and the daily sea ice thickness data yields spatiotemporally aligned sea ice concentration and thickness sequences, including: The daily Arctic sea ice concentration data were numerically normalized to obtain normalized sea ice concentration data. The normalized sea ice concentration data is downsampled to obtain downsampled sea ice concentration data with the same spatial resolution as the daily Arctic sea ice thickness data. Based on the grid coordinate axis correspondence between the downsampled sea ice concentration data and the daily Arctic sea ice thickness data, the downsampled sea ice concentration data is subjected to matrix transpose and coordinate axis flipping to obtain grid-aligned sea ice concentration data that is in the same polar projection grid as the daily Arctic sea ice thickness data. Missing value connected component detection was performed on the grid-aligned sea ice concentration data and the daily Arctic sea ice thickness data to obtain the missing sea ice concentration region and the missing sea ice thickness region. Nearest neighbor interpolation is performed using the effective pixels around the missing sea ice concentration region and the effective pixels around the missing sea ice thickness region to obtain the missing sea ice concentration data and missing sea ice thickness data after filling the missing values. By using an active grid mask, effective ocean regions are selected from the sea ice concentration data and sea ice thickness data after missing value filling, respectively, to obtain spatiotemporally aligned sea ice concentration sequences and sea ice thickness sequences.

[0028] Specifically, spatiotemporal alignment refers to establishing a correspondence between sea ice concentration data and sea ice thickness data in terms of date, spatial resolution, grid orientation, grid position, and effective computation area, so that the same pixel represents the same spatial location.

[0029] The polar projection grid refers to a regular grid formed by projecting the latitude and longitude coordinates of the Arctic region onto a plane. The data in this embodiment uses the EPSG:3411 Arctic polar projection.

[0030] Downsampling refers to reducing the spatial resolution or grid size of two-dimensional data so that high-resolution data and low-resolution data have the same or comparable spatial scale.

[0031] Matrix transpose refers to swapping the row and column axes of a two-dimensional matrix, used to correct inconsistencies in the grid principal axis directions between different data products.

[0032] Axis flipping refers to reversing the pixel arrangement order along a specified axis of a two-dimensional grid, used to make different data products consistent in geographical direction.

[0033] A missing value connected region refers to a continuous area formed by adjacent missing pixels. After identifying this region, the fill value can be obtained from the valid pixels at the region's edge.

[0034] Nearest neighbor interpolation is a method that fills in missing pixels by selecting the nearest valid pixel value in terms of spatial distance.

[0035] First, the original sea ice concentration values ​​are normalized. In this embodiment, the percentage sea ice concentration from 0 to 100 is divided by 100 to convert it to a range of 0 to 1, resulting in normalized sea ice concentration data. Sea ice thickness can also be normalized by a preset scale factor during model training; in this embodiment, it can be divided by 5 to make its numerical range closer to that of sea ice concentration.

[0036] Secondly, the normalized sea ice concentration data is downsampled to make its spatial resolution the same as that of the sea ice thickness data. In this embodiment, local window mean pooling can be used to reduce the high-resolution sea ice concentration grid to a spatial scale corresponding to the sea ice thickness grid. The purpose of downsampling is to ensure that the two types of data have pixel correspondence in spatial resolution.

[0037] Next, based on the coordinate axis correspondence between the two types of grids, the downsampled sea ice concentration data is subjected to matrix transpose and corresponding coordinate axis flipping, so that sea ice concentration pixels and sea ice thickness pixels represent the same geographical location. The alignment result can be verified by the latitude and longitude positions of grid corner points or several control points.

[0038] For observation holes in high-latitude regions, connected component detection is first performed on NaN or other missing pixel markers to identify continuous missing blocks located at the grid center or other regions. Then, nearest neighbor filling is performed using the valid pixels at the edges of the missing blocks. By performing connected component detection followed by filling, polar observation holes can be distinguished from grids with different meanings, such as zero sea ice values ​​or land areas.

[0039] After handling missing values, a pre-established active grid mask is used to filter valid ocean regions. The active grid mask can be pre-calculated by month to distinguish between land, open sea, and sea ice activity areas that need to participate in model learning. After the above processing, sea ice concentration and sea ice thickness sequences with consistent dates, spatial grids, and valid regions are obtained.

[0040] An active grid mask is a spatial mask used to identify effective ocean grids participating in training or prediction calculations. It can be used to exclude land, long-term invalid areas, or areas that do not participate in loss calculations.

[0041] S3. Extract data for a consecutive preset number of days from the sea ice concentration sequence and the sea ice thickness sequence to obtain the historical input sequence of sea ice concentration and the historical input sequence of sea ice thickness. Based on the sea ice thickness difference at different times in the historical input sequence of sea ice thickness, obtain the sea ice thickness trend channel. Based on the sea ice thickness differences at different times in the historical input sequence of sea ice thickness, a sea ice thickness trend channel is obtained, including: Using the current moment in the historical input sequence of sea ice thickness as a benchmark, the difference between the sea ice thickness at the current moment and the sea ice thickness at at least two different historical moments is calculated to obtain the sea ice thickness trend characteristics corresponding to different time scales. Each of the aforementioned sea ice thickness trend characteristics is used as a sea ice thickness trend channel to characterize the thickening or thinning trend of sea ice thickness at different time scales.

[0042] Specifically, data for a predetermined number of consecutive days is extracted from the spatiotemporally aligned sea ice concentration and sea ice thickness sequences using a sliding window approach to form the historical input for a prediction sample. In one embodiment, the historical window length is 30 days, the prediction target is the following 7 days, and the sliding step size is 1 day. Thus, each sample includes a 30-day historical input sequence of sea ice concentration and a 30-day historical input sequence of sea ice thickness.

[0043] Sea ice thickness is a relatively slowly changing state variable, and the absolute thickness values ​​may be similar over several consecutive days. To enable the model to directly obtain the direction of thickness increase or decrease, this embodiment constructs two trend channels in addition to the historical input sequence of sea ice thickness. The trend channels are defined as follows:

[0044] Where SIT represents sea ice thickness; t represents the current moment in the historical input sequence, that is, the last moment of the historical window; SIT t This represents the spatial field representing the current sea ice thickness. This represents the spatial field of sea ice thickness 7 days prior to the current moment; This represents the spatial field of sea ice thickness corresponding to the 29th day prior to the current moment; This indicates the characteristics of sea ice thickness variation over a shorter timescale; This indicates the characteristics of sea ice thickness changes covering the entire historical window. A positive difference indicates an overall increase in sea ice thickness at the corresponding location, while a negative difference indicates an overall decrease in sea ice thickness at the corresponding location.

[0045] The historical sea ice thickness input sequence is concatenated with one or more sea ice thickness trend channels along the channel dimension to obtain the extended sea ice thickness input sequence. In the 30-day embodiment described above, the sea ice thickness branch can consist of 30 historical thickness channels and 2 trend channels; the sea ice concentration branch uses 30 historical concentration channels.

[0046] S4. The historical input sequence of sea ice thickness is concatenated with the trend channel of sea ice thickness to obtain the extended input sequence of sea ice thickness. Specifically, historical input sequence refers to a series of consecutive days of data selected from the spatiotemporally aligned daily sequence, which serves as the historical observation input for predicting future sea ice conditions.

[0047] Sea ice thickness trend channel: refers to a two-dimensional feature channel obtained by subtracting the current sea ice thickness from the sea ice thickness at one or more historical times, used to explicitly represent the trend of sea ice thickening or thinning.

[0048] Extended input sequence for sea ice thickness: refers to the input data obtained by concatenating the historical input sequence of sea ice thickness with one or more sea ice thickness trend channels along the feature channel dimension.

[0049] S5. Perform image block segmentation and feature dimension mapping on the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness respectively to obtain the initial embedding features of sea ice concentration and the initial embedding features of sea ice thickness. Image patching and feature dimension mapping are performed on the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness, respectively, to obtain initial embedding features of sea ice concentration and initial embedding features of sea ice thickness, including: The historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness are respectively divided into multiple non-overlapping image blocks; Each non-overlapping image patch is subjected to feature projection to transform it to a preset feature dimension, thereby obtaining the initial embedding features of sea ice concentration and the initial embedding features of sea ice thickness.

[0050] Specifically, an image patch refers to a local spatial unit obtained by dividing a two-dimensional spatial field. Multiple image patches serve as the basic spatial units for subsequent transformation network processing.

[0051] Feature dimension mapping refers to projecting the numerical information in the original image patch onto a feature representation space of a preset dimension, so that each image patch has a unified feature dimension.

[0052] Initial embedded features refer to the features obtained after the historical input sequence is divided into image blocks and the feature dimension is mapped. They are the initial inputs for attention enhancement and multi-stage encoding in the coding branch.

[0053] Specifically, the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness are respectively fed into their respective coding branches. The parameters of the two coding branches are independent of each other, allowing sea ice concentration and sea ice thickness to retain their respective physical field characteristics.

[0054] The input spatial field of each branch is divided into non-overlapping image patches, and feature projection is performed on each image patch to map the original numerical channels to a unified embedding dimension, thereby obtaining the initial embedding features of sea ice concentration and sea ice thickness. In one embodiment, image patch division and dimension mapping can be performed using convolution, with the initial embedding dimension set to 32.

[0055] S6. Enhance the initial embedding features of sea ice concentration using channel attention and spatial attention to obtain enhanced sea ice concentration features; enhance the initial embedding features of sea ice thickness using channel attention and spatial attention to obtain enhanced sea ice thickness features. The initial embedding features of sea ice concentration are enhanced using channel attention and spatial attention to obtain enhanced sea ice concentration features; the initial embedding features of sea ice thickness are enhanced using channel attention and spatial attention to obtain enhanced sea ice thickness features, including: The initial sea ice concentration embedding features are aggregated along the channel dimension to obtain a first channel aggregation result. A first channel attention weight is generated based on the channel aggregation result. The initial sea ice concentration embedding features are then weighted using the first channel attention weight to obtain enhanced sea ice concentration channel features. Spatial dimension feature aggregation is performed on the sea ice concentration channel enhancement features to obtain a first feature aggregation result. A first spatial attention weight is generated based on the feature aggregation result. The sea ice concentration channel enhancement features are weighted using the first spatial attention weight to obtain the sea ice concentration enhancement features. The initial sea ice thickness embedding features are aggregated along the channel dimension to obtain a second channel aggregation result. A second channel attention weight is generated based on the second channel aggregation result. The initial sea ice thickness embedding features are then weighted using the second channel attention weight to obtain the sea ice thickness channel enhancement features. Spatial feature aggregation is performed on the sea ice thickness channel enhancement features to obtain a second feature aggregation result. A second spatial attention weight is generated based on the second feature aggregation result. The sea ice thickness channel enhancement features are then weighted using the second spatial attention weight to obtain the sea ice thickness enhancement features.

[0056] Specifically, channel attention refers to a processing method that generates weights based on the responses of different feature channels and uses these weights to adjust the contribution level of each channel. In this paper, the TSAM channel branch operates on the feature channels and does not perform convolution directly on the time axis.

[0057] Spatial attention refers to generating spatial weights based on responses at different spatial locations and using these weights to highlight spatial locations that are more important for prediction.

[0058] TSAM is an abbreviation for Temporal-Spatial Attention Module, which is a feature enhancement module composed of channel attention branches and spatial attention branches connected in series.

[0059] Specifically, in each coding branch, the initial embedded features are sequentially subjected to channel attention and spatial attention. These two attention processes can be implemented using TSAM.

[0060] During channel attention processing, global max pooling and global average pooling are performed on the initial embedded features along the spatial dimension to obtain two sets of channel description information. These two sets of channel description information are then processed by multi-scale one-dimensional dilated convolutions. The convolution results are summed and activated by a sigmoid function to obtain the channel attention weights corresponding to each feature channel. These weights are then used to recalibrate the original initial embedded features channel by channel to obtain the channel-enhanced features.

[0061] In this embodiment, the channel attention branch can employ multi-layer one-dimensional dilated convolutions, with the dilation rate varying cyclically across multiple scales to broaden the scope of channel dependency modeling. It should be noted that the "Temporal" in TSAM derives from its borrowed temporal convolutional structure, but this branch actually operates on feature channels, rather than directly performing convolution along the 30-day time axis.

[0062] In spatial attention processing, max pooling and average pooling are performed along the channel dimension for the channel enhancement features, resulting in two spatial description maps. These two spatial description maps are then concatenated and followed by convolution and sigmoid activation to generate a spatial attention map. This spatial attention map is then used to recalibrate different spatial locations of the channel enhancement features, yielding sea ice concentration enhancement features or sea ice thickness enhancement features. This process enables the model to pay closer attention to ice edges, high-gradient regions, and other spatial structures relevant to the prediction.

[0063] TSAM can be embedded using a residual method, which preserves the original input features in the attention-enhanced features, thereby enhancing important features while reducing the loss of original information.

[0064] S7. Perform multi-stage encoding on the sea ice concentration enhancement features to obtain sea ice concentration multi-scale features and sea ice concentration bottleneck features; perform multi-stage encoding on the sea ice thickness enhancement features to obtain sea ice thickness multi-scale features and sea ice thickness bottleneck features. The process of multi-stage encoding the sea ice concentration enhancement features yields multi-scale sea ice concentration features and sea ice concentration bottleneck features; the process of multi-stage encoding the sea ice thickness enhancement features yields multi-scale sea ice thickness features and sea ice thickness bottleneck features, including: The sea ice concentration enhancement feature and the sea ice thickness enhancement feature are respectively used as the initial coding features of the corresponding coding branches; In each encoding stage, the current encoded features are divided into rectangular attention windows with different widths and heights, and self-attention operations are performed on the current encoded features within each rectangular attention window to obtain window attention features; The window attention features are shifted to enable feature interaction between adjacent rectangular attention windows, thus obtaining the interaction features of the current stage. The interaction features of the current stage are downsampled to obtain the encoding features of the next encoding stage; The coding features obtained in each intermediate coding stage are respectively used as the corresponding multi-scale features of sea ice concentration or multi-scale features of sea ice thickness, and the coding features obtained in the final coding stage are respectively used as the bottleneck features of sea ice concentration or the bottleneck features of sea ice thickness.

[0065] Specifically, multi-stage coding refers to a coding process that involves performing feature extraction and spatial downsampling in multiple stages, gradually reducing the spatial resolution of features and gradually improving their semantic level.

[0066] SwinV2: refers to the Swin Transformer V2 structure. In this implementation, the window self-attention and shift window mechanism are used to extract local and cross-window spatial relationships.

[0067] Rectangular attention window: refers to a local attention window with unequal width and height, used to adapt to the scale difference of polar projection grids in two spatial directions.

[0068] Shifting window: refers to changing the starting position of the window division during the adjacent attention calculation stage, so that features that were originally in different windows can interact with each other.

[0069] Multi-scale features: refer to a set of features output from different intermediate encoding stages, with different spatial resolutions and different semantic levels.

[0070] Bottleneck features: These are deep features output from the last coding stage of a coding branch. Their spatial resolution is lower than that of features from intermediate stages, but they have a larger effective receptive range.

[0071] Specifically, the sea ice concentration enhancement features and sea ice thickness enhancement features are fed into a parameter-independent hierarchical shift window transform coding network. Each coding branch includes multiple coding stages. The current stage receives the output features from the previous stage, extracts spatial correlations within a local window, and performs downsampling between stages to gradually reduce the spatial size and gradually increase the feature dimension.

[0072] In each encoding stage, the current encoded features are divided into multiple rectangular attention windows. SwinV2 self-attention processing is performed within each rectangular window to extract spatial relationships within the window range. Subsequently, the window division positions are changed, causing windows in adjacent stages to shift. Features that were originally in different windows participate in attention calculation together under the new window division, thereby achieving cross-window information interaction.

[0073] The width and height of the rectangular attention window are unequal to accommodate the scale differences of the polar projection grid in different spatial directions. In one embodiment, the window size can be set to 19×28, with a diagonal shift of approximately half the window size. This specific value is only one implementation method, and can be adjusted according to the input grid size and polar projection characteristics in practical applications.

[0074] The encoding branch can include four levels. Taking this embodiment as an example, the spatial dimensions of the outputs of the four stages are 152×224, 76×112, 38×56, and 19×28, respectively, with the corresponding feature dimensions increasing sequentially. The different spatial scale features retained in the first three stages are used as multi-scale features for subsequent decoding; the deep features output in the last encoding stage are used as bottleneck features. Therefore, the multi-scale features and bottleneck features are not two independent results generated simultaneously in the same stage, but rather come from the intermediate encoding stage and the final encoding stage, respectively.

[0075] S8. Perform bidirectional cross-attention processing on the sea ice concentration bottleneck feature and the sea ice thickness bottleneck feature to obtain the bottleneck coupling feature; The bidirectional cross-attention processing of the sea ice concentration bottleneck feature and the sea ice thickness bottleneck feature yields bottleneck coupling features, including: Using the sea ice concentration bottleneck feature as the query feature, and the sea ice thickness bottleneck feature as the key feature and value feature, a first cross-attention process is performed to obtain the first cross-field interaction feature. Using the sea ice thickness bottleneck feature as the query feature, and the sea ice density bottleneck feature as the key feature and value feature, a second cross-attention process is performed to obtain the second cross-field interaction feature. The bottleneck coupling feature is obtained by fusing the first cross-field interaction feature and the second cross-field interaction feature.

[0076] Specifically, bidirectional cross-attention refers to two cross-attention paths: one querying sea ice thickness features using sea ice concentration features, and the other querying sea ice concentration features using sea ice thickness features.

[0077] Bottleneck coupling features refer to the deep dual-field interaction features formed after the fusion of cross-attention results from two directions.

[0078] Gating weights refer to the weights generated by the same-scale sea ice concentration feature and sea ice thickness feature, used to determine the fusion ratio of the two types of features.

[0079] Specifically, the bottleneck features of sea ice concentration and sea ice thickness share the same spatial scale and feature dimension, allowing for bidirectional cross-attention interaction at the bottleneck layer. Let these two be respectively... and All of these can be flattened into a spatial position sequence. Bidirectional asymmetric cross-attention employs independent parameterization in two directions.

[0080] Taking the direction of querying sea ice thickness features based on sea ice concentration features as an example, the h-th attention head first forms the query, key, and value respectively:

[0081] in, This indicates the bottleneck characteristics of sea ice concentration; The bottleneck characteristic of sea ice thickness is represented; h represents the h-th attention head in multi-head attention; This represents the query features obtained by projecting the bottleneck features of sea ice concentration. and These represent the bond features and value features obtained by projecting the bottleneck features of sea ice thickness, respectively. , and These represent the query projection matrix, key projection matrix, and value projection matrix corresponding to the attention head, respectively.

[0082]

[0083] in, The h-th attention head represents the interactive output along the direction from sea ice concentration to sea ice thickness; softmax represents the normalization function; ) Represents the transpose of the key feature; The dimension representing the key features in a single attention head; This is used to scale the dot product of the query feature and the key feature. The correlation between the query feature and the key feature, after being normalized by softmax, is used for weighted aggregation of the value features.

[0084]

[0085] in, The first cross-field interaction feature represents the cross-field interaction feature from sea ice concentration to sea ice thickness; H represents the total number of attention heads; the symbol ⊕ indicates concatenation along the feature dimension; This indicates that the concatenated result of multiple attention heads is projected back into the output projection matrix of the target feature dimension.

[0086] The reverse path uses sea ice thickness bottleneck features as the query and sea ice concentration bottleneck features as the key and value, and is defined as follows:

[0087] in, The cross-field interaction feature (second cross-field interaction feature) represents the cross-attention processing along the direction from sea ice thickness to sea ice concentration; Q, K, and V represent query, key, and value, respectively. The parameters in this direction are independent of those in the previous direction.

[0088] The results of the interactions in both directions are summed and merged, and represented as:

[0089] in, This indicates bottleneck coupling characteristics; This indicates the first cross-field interaction feature; This represents the second cross-field interaction feature. This coupling feature simultaneously includes information from sea ice concentration-driven queries for sea ice thickness and information from sea ice thickness-driven queries for sea ice concentration.

[0090] In one embodiment, four attention heads can be set. When the bottleneck feature dimension is 256, the dimension of each attention head is 64. The above parameters are for an embodiment and are not intended to limit the scope of protection of this invention.

[0091] S9. Generate gate weights based on the multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness, and use the gate weights to perform weighted fusion of the multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness to obtain multi-scale coupled features. Specifically, multi-scale coupled features refer to the feature set obtained by fusing sea ice concentration features and sea ice thickness features at multiple intermediate coding scales using gating weights respectively.

[0092] Specifically, in addition to the deep interactions at the bottleneck layer, the decoding process also needs to utilize the multi-scale features retained in the intermediate encoding stage. To avoid fusing sea ice concentration and thickness features at a fixed ratio across all regions, gating fusion is implemented at the same spatial scale.

[0093] Specifically, at the k-th scale, the multi-scale features of sea ice concentration and sea ice thickness at that scale are concatenated. A gating weight is obtained through linear mapping and Sigmoid activation. Then, the two types of features are weighted and summed according to the gating weight. The gating fusion relationship is as follows:

[0094] Where k represents the coding level corresponding to the multi-scale feature; This represents the multi-scale characteristic of sea ice concentration at the k-th scale; This represents the multi-scale feature of sea ice thickness at the k-th scale; the symbol ⊕ indicates feature concatenation. This represents the learnable linear mapping parameter corresponding to the k-th scale; This represents the Sigmoid activation function; The gating weights for the k-th scale are represented, with values ​​between 0 and 1; the symbol ⊙ indicates element-wise multiplication. This represents the multi-scale coupling feature obtained at the k-th scale. This represents the complementary weights assigned to the sea ice thickness feature.

[0095] Gated networks at multiple scales can operate independently. This allows for different dual-field fusion ratios at different scales and spatial locations. For example, shallow scales can retain more ice perimeter texture and local boundary information, while deep scales can better utilize the spatial modes of sea ice thickness. The actual fusion ratio is determined by the trained gating weights, without requiring a pre-set fixed ratio.

[0096] S10. Decode the bottleneck coupling feature and the multi-scale coupling feature respectively to obtain the sea ice concentration prediction field and the initial sea ice thickness prediction field for the next preset number of days. Specifically, the bottleneck coupling features are input into the sea ice concentration decoding branch and the sea ice thickness decoding branch, respectively. The two decoding branches share the bottleneck coupling information and the corresponding multi-scale coupling features, but each has independent decoding parameters to adapt to the different output numerical features of sea ice concentration and sea ice thickness.

[0097] During decoding, upsampling is performed step by step, starting from the bottleneck spatial scale. At each decoding stage, the current upsampled features are combined with multi-scale coupled features of the corresponding scale to supplement the spatial details preserved during the encoding process. After continuous spatial recovery, the final decoded features are mapped to the preset number of output channels.

[0098] In one embodiment, a sample directly outputs the results for the next 7 days, where the sea ice concentration decoding branch outputs 7 future sea ice concentration channels, and the sea ice thickness decoding branch outputs 7 future sea ice thickness channels. This method is a one-time multi-day mapping, which does not require using the output of the previous prediction day to continue rolling to generate the next prediction day, thereby avoiding the accumulation of daily errors caused by autoregressive rolling.

[0099] S11. Based on the sea ice concentration of the last day in the historical input sequence of sea ice concentration, perform physical consistency processing on the initial sea ice thickness prediction field, set the sea ice thickness prediction value corresponding to the pixel position where the sea ice concentration is lower than the preset threshold to zero, obtain the sea ice thickness prediction field, and use the sea ice concentration prediction field and the sea ice thickness prediction field as the joint short-term forecast result of Arctic sea ice.

[0100] Specifically, physical consistency processing refers to the process of correcting the initial prediction results of the model based on the fundamental constraint that there should be no normal sea ice thickness in ice-free areas.

[0101] Specifically, sea ice thickness should be zero in open sea areas. To ensure the model output conforms to this fundamental physical relationship, pixels in open sea areas are identified based on the sea ice concentration of the last day in the historical input sequence of sea ice concentration. For locations where the sea ice concentration is below a preset threshold, the corresponding initial sea ice thickness prediction value is set to zero, resulting in the final sea ice thickness prediction field.

[0102] In one embodiment, a preset threshold of 15% sea ice concentration is used. This threshold can also serve as a criterion for distinguishing between sea ice areas and open sea areas. After physical consistency processing, the predicted future sea ice concentration field and the predicted sea ice thickness field are combined as a joint short-term forecast result.

[0103] During model training, sea ice concentration loss and sea ice thickness loss can be calculated only on physically meaningful valid sea ice pixels, thereby reducing interference from land and invalid regions. An adaptive mask mean square error is employed. Taking sea ice concentration as an example, it is defined as:

[0104] in, This indicates training losses related to sea ice concentration; This represents the set of valid pixels used in the calculation of sea ice concentration loss. This indicates the number of pixels in the set of valid pixels; Indicates the pixel position in a two-dimensional grid; Represents pixels Predicted sea ice concentration at the location; Σ represents the target value of sea ice concentration at the same pixel location; Σ represents the summation of the squared errors within the effective pixel set. The sea ice thickness loss can be expressed in the same way, using the target sea ice thickness value to determine the corresponding effective pixel set.

[0105] The total loss is the sum of sea ice concentration loss and sea ice thickness loss, i.e. .in, This represents the total loss of the model. Indicates the loss of sea ice concentration. This represents the loss in sea ice thickness. To ensure that the two types of losses are on similar numerical scales, the sea ice thickness can be normalized using a preset scale factor before training.

[0106] In one embodiment, the model can be trained using the AdamW optimizer, employing a cosine annealing learning rate strategy and a warm-up phase. Gradient clipping can be used during training, and early stopping can be performed based on the mean absolute error of sea ice thickness on the validation set. The above training method is provided to illustrate one feasible configuration of the present invention and does not constitute a limitation on the core structure of the prediction method.

[0107] After obtaining the sea ice concentration prediction field and the sea ice thickness prediction field, two-dimensional forecast products can be output daily according to the date. The sea ice concentration prediction field can be used to determine the future sea ice coverage and ice edge changes, while the sea ice thickness prediction field can be used to determine the distribution of ice thickness. The combination of the two can form a joint forecast of Arctic sea ice status for a predetermined number of days in the future, providing data support for polar navigation planning, maritime operation arrangements, and ice condition monitoring.

[0108] experiment: To convert the daily aligned data into a sample format trainable by the model, a sliding window method is used: each sample takes 30 consecutive days of SIC and SIT as input, and the next 7 days as the prediction target, with a sliding step of 1 day. SIC and SIT are concatenated along the channel dimension to form an input tensor with dimensions (60, 304, 448), where the first 30 channels represent SIC history and the last 30 channels represent SIT history; the output dimension is (14, 304, 448), with the first 7 channels representing SIC prediction and the last 7 channels representing SIT prediction. The SIT value range is approximately... During training, the data was normalized to the [0, 1] interval by dividing by 5. To fully utilize the data and avoid the loss of year boundary information caused by dividing by year, samples were continuously spliced ​​across year boundaries. The final dataset is divided by year, as shown in Table 1. The training set contains 2,152 samples, the validation set contains 330 samples, and the test set contains 694 samples. The test set was selected from 2021–2022 to ensure the timeliness and independence of the evaluation.

[0109] Table 1 Dataset Partitioning Scheme

[0110] Figure 1 and Figure 2 The overall error assessment results for the test set (2021–2022) are presented. Figure 1 Lead-wise MAE curves (Lead 1–7 days) for SIC and SIT. Figure 2 Bar charts showing the average SIC and SITMAE for each month from January to December. Table 2 summarizes the numerical results for the key lead days.

[0111] Table 2: Summary of MAE for Key Lead Days in the Test Set

[0112] The lead-wise curve reveals the following characteristics: (1) The MAE of SIC smoothly increases from 0.032 on Lead+1 day to 0.055 on Lead+7 day, with an average daily growth rate of approximately The cumulative error is well controlled, indicating that the model has a strong ability to capture the short-term evolution of SIC; (2) The MAE of SIT is from Rise to The thickness prediction error within 7 days remained at Within, taking into account The observation error of the SIT inversion product itself on the grid is usually also present. The magnitude of this level of accuracy is of practical value for business applications; (3) the absolute value of the SIT error ( ) is much larger than SIC ( This reflects the inherent difference in the difficulty of predicting SIT: concentration is mainly controlled by horizontal and thermodynamic processes, and its short-term changes are relatively regular, while thickness is affected by the coupling of multiple factors and its absolute value of change is larger.

[0113] Significant seasonal dependence can be observed from the monthly error bar chart: (1) The SIC and SIT errors in winter (December-February) and spring (March-May) are at their lowest levels throughout the year, reflecting the characteristics of stable ice conditions and slow changes in the ice edge during the freezing period; (2) The error gradually increases from June, reaching its peak in August-September. SICMAE rises from approximately 0.03 in winter to approximately 0.07 in summer, while SITMAE rises from approximately... Rise to approximately The increase was nearly double, which is highly consistent with the physical processes of rapid summer sea ice melting, significant northward retreat of the ice edge, and interference of melt pools with SIT inversion signals; (3) The error dropped rapidly after October, corresponding to the transition period of autumn refreezing and rapid expansion of the ice sheet.

[0114] To finely evaluate the model's performance in different Arctic sea areas, this paper divides the Arctic into 12 main sea areas based on a predefined fine-grained region mask. Figure 3 The bar chart shows the comparison of SIC and SITMAE for each sea area at Lead+1 day.

[0115] Regional analysis revealed significant spatial heterogeneity: (1) The SIC and SIT errors were lowest in the Central North Pole (14) and Beaufort Sea (15) (SICMAE). SITMAE These areas are covered by thick ice all year round, resulting in the most stable ice conditions with minimal seasonal variations and uniform spatial distribution. (2) The Barents Sea (No. 13) and Greenland Sea (No. 9) had the highest errors (SICMAE>0.08, SITMAE>0.30m). The main reason is that these sea areas are located in the periglacial zone, the sea ice coverage varies drastically with the seasons, and are strongly influenced by the North Atlantic Current (Norwegian Current). The ice-sea interaction is complex and the prediction difficulty is much greater than that of the inland ice zone. (3) The Bering Sea (No. 6) and the Sea of ​​Okhotsk are located south of the Arctic Circle. They only have seasonal sea ice during the winter half-year. The ice is relatively thin and the ice conditions change drastically, so the model's predictive ability is limited.

[0116] Figures 4 to 5 It shows the division of the Arctic Ocean (left half) and the MAE heat map of each ocean area × each month. Each year includes two heat maps, SIC and SIT, for a total of 4 sub-maps.

[0117] The heat map reveals the following seasonal patterns: (1) The errors of SIC and SIT are generally lower in winter (November-February) and spring (March-May) because the Arctic sea ice coverage is the largest, the ice layer is the thickest, the ice edge position is relatively stable, and the freezing process is dominant at this time. (2) The error increases significantly in summer (June-September), especially in July-September in shelf waters such as the Laptev Sea and the East Siberian Sea, where the SIT MAE can reach [missing information]. The error is 2-3 times that of winter, which is directly related to the rapid melting of the ice sheet in summer, the large northward retreat of the ice edge, and the interference of the melt pool on the SIT inversion signal. (3) The comparison between years shows that the error distribution patterns in 2021 and 2022 are basically the same, indicating that the model has a good generalization ability for sea ice change patterns in different years.

[0118] September is typically the month with the smallest Arctic sea ice extent, representing the peak of annual sea ice melt, and is also the most challenging period for sea ice forecasting.

[0119] Analysis of SIT prediction error sources: In this study, the SIT MAE (0.17–0.26m) was significantly higher than the SIC MAE (0.03–0.06). This difference is not a flaw in the model design, but rather reflects the fundamentally different predictability of the two variables. The SIT prediction error mainly originates from the following three aspects: (1) Uncertainty in observational data. Satellite SIT inversion itself contains significant errors. The CryoSat-2 radar altimeter experiences severe signal attenuation under summer meltwater coverage, leading to a significant decrease in the accuracy of high-latitude summer SIT inversion; the SMOSL band radiometer is sensitive to thin ice (<0.5m) but has limited penetration capability through thick ice. These uncertainties propagate directly to the labels in supervised learning, constituting irreducible basis errors.

[0120] (2) Multi-factor coupling control. Unlike SIC, which is mainly controlled by periglacial advection and surface thermal processes, SIT variation involves the coupling of multiple processes such as ice internal stress accumulation and release (ridge formation and cracking), bottom melting of ocean heat flux, insulation effect of snow depth, and ice age effect. Relying solely on the two-dimensional fields of SIC and SIT over a historical 30 days, the model may lack sufficient information to fully infer the combined effects of these underlying processes.

[0121] (3) Polar observation voids. SIT data north of 87°N is completely missing. This paper attempts to fill the void using nearest-neighbor interpolation, but the accuracy of the filled area is naturally lower than the actual observation area. Although the void area only accounts for approximately [percentage missing] of the entire grid... (60 pixels / 136, 192 pixels), but this region happens to be located in the high-concentration thick ice zone in the center of the Arctic, which has a certain influence on the characterization of the spatial distribution of SIT.

[0122] A joint prediction system for Arctic sea ice concentration and thickness, comprising: The data acquisition module is used to acquire daily data on Arctic sea ice concentration and daily data on Arctic sea ice thickness. The data preprocessing module is used to preprocess the daily data of Arctic sea ice concentration and the daily data of Arctic sea ice thickness to obtain a spatiotemporally aligned sea ice concentration sequence and sea ice thickness sequence. The sequence and trend extraction module is used to extract data for a consecutive preset number of days from the sea ice concentration sequence and the sea ice thickness sequence, respectively, to obtain the historical input sequence of sea ice concentration and the historical input sequence of sea ice thickness. Based on the sea ice thickness difference at different times in the historical input sequence of sea ice thickness, the sea ice thickness trend channel is obtained. The sequence expansion module is used to concatenate the historical input sequence of sea ice thickness with the trend channel of sea ice thickness to obtain the expanded input sequence of sea ice thickness. The feature processing module is used to perform feature embedding processing on the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness respectively to obtain initial embedded features of sea ice concentration and initial embedded features of sea ice density and thickness; to perform attention enhancement on the initial embedded features of sea ice concentration and initial embedded features of sea ice density and thickness respectively to obtain enhanced features of sea ice concentration and enhanced features of sea ice thickness; and then to perform multi-stage encoding to obtain multi-scale features of sea ice concentration, bottleneck features of sea ice concentration, multi-scale features of sea ice thickness, and bottleneck features of sea ice thickness. The bottleneck feature coupling module is used to perform bidirectional cross-attention processing on the sea ice concentration bottleneck feature and the sea ice thickness bottleneck feature to obtain the bottleneck coupling feature. The multi-scale feature fusion module is used to generate gating weights based on the multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness, and to use the gating weights to perform weighted fusion of the multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness to obtain multi-scale coupled features. The feature decoding and prediction module is used to decode the bottleneck coupling feature and the multi-scale coupling feature respectively to obtain the sea ice concentration prediction field and the initial sea ice thickness prediction field for the next preset number of days. The system also includes a physical consistency correction module, which performs physical consistency processing on the initial sea ice thickness prediction field based on the sea ice concentration of the last day in the historical input sequence of sea ice concentration. The system sets the predicted sea ice thickness value corresponding to the pixel position where the sea ice concentration is lower than a preset threshold to zero, thereby obtaining the sea ice thickness prediction field. The sea ice concentration prediction field and the sea ice thickness prediction field are used as the joint short-term forecast result for Arctic sea ice.

[0123] This application also discloses a terminal device, including a memory and a processor. The memory stores a computer program that can run on the processor. When the processor loads and executes the computer program, it uses a method for jointly predicting the concentration and thickness of Arctic sea ice.

[0124] The terminal device can be a computer device such as a desktop computer, a laptop computer, or a cloud server. The terminal device includes, but is not limited to, a processor and a memory. For example, the terminal device may also include input / output devices, network access devices, and buses.

[0125] The processor can be a central processing unit (CPU). Of course, depending on the actual use, it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc., and this application does not limit it.

[0126] The memory can be an internal storage unit of the terminal device, such as a hard disk or RAM of the terminal device, or an external storage device of the terminal device, such as a plug-in hard disk, smart memory card (SMC), secure digital card (SD), or flash memory card (FC) equipped on the terminal device. Furthermore, the memory can be a combination of internal storage units and external storage devices of the terminal device. The memory is used to store computer programs and other programs and data required by the terminal device. The memory can also be used to temporarily store data that has been output or will be output. This application does not limit this.

[0127] In this terminal device, the method for jointly predicting the concentration and thickness of Arctic sea ice in the above embodiments is stored in the memory of the terminal device and loaded and executed on the processor of the terminal device for convenient use.

[0128] This application also discloses a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it employs a method for jointly predicting the concentration and thickness of Arctic sea ice as described in the above embodiments.

[0129] The computer program can be stored in a computer-readable medium. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or certain middleware. The computer-readable medium includes any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the computer-readable medium includes, but is not limited to, the above-mentioned components.

[0130] The method for jointly predicting the concentration and thickness of Arctic sea ice in the above embodiments is stored in the computer-readable storage medium and loaded and executed on the processor to facilitate the storage and application of the above method.

[0131] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of protection of this application is limited to these examples; within the framework of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of one or more embodiments of this application as described above, which are not provided in detail for the sake of brevity.

[0132] One or more embodiments in this application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of this application. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of one or more embodiments in this application should be included within the protection scope of this application.

Claims

1. A method for joint prediction of concentration and thickness of Arctic sea ice, characterized in that, include: Obtain daily data on Arctic sea ice concentration and daily data on Arctic sea ice thickness; Preprocessing the daily data of Arctic sea ice concentration and the daily data of Arctic sea ice thickness yields a spatiotemporally aligned sea ice concentration sequence and sea ice thickness sequence. Data for a consecutive preset number of days are extracted from the sea ice concentration sequence and the sea ice thickness sequence to obtain the historical input sequence of sea ice concentration and the historical input sequence of sea ice thickness. Based on the sea ice thickness difference at different times in the historical input sequence of sea ice thickness, the sea ice thickness trend channel is obtained. The historical input sequence of sea ice thickness is concatenated with the trend channel of sea ice thickness to obtain the extended input sequence of sea ice thickness. The historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness are respectively subjected to feature embedding processing to obtain the initial embedding features of sea ice concentration and the initial embedding features of sea ice thickness. Attention enhancement is applied to the initial embedding features of sea ice concentration and the initial embedding features of sea ice thickness respectively to obtain enhanced features of sea ice concentration and enhanced features of sea ice thickness. Then, multi-stage encoding is performed to obtain multi-scale features of sea ice concentration, bottleneck features of sea ice concentration, multi-scale features of sea ice thickness, and bottleneck features of sea ice thickness. Bidirectional cross-attention processing is performed on the bottleneck features of sea ice concentration and sea ice thickness to obtain bottleneck coupling features; Gating weights are generated based on the multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness. The multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness are then weighted and fused using the gating weights to obtain multi-scale coupled features. The bottleneck coupling features and the multi-scale coupling features are decoded respectively to obtain the sea ice concentration prediction field and the initial sea ice thickness prediction field for the next preset number of days. Based on the sea ice concentration of the last day in the historical input sequence of sea ice concentration, the initial sea ice thickness prediction field is subjected to physical consistency processing. The sea ice thickness prediction value corresponding to the pixel position where the sea ice concentration is lower than the preset threshold is set to zero to obtain the sea ice thickness prediction field. The sea ice concentration prediction field and the sea ice thickness prediction field are used as the joint short-term forecast result of Arctic sea ice.

2. The method of claim 1, wherein the method is characterized by, Preprocessing the daily sea ice concentration data and the daily sea ice thickness data yields spatiotemporally aligned sea ice concentration and thickness sequences, including: The daily Arctic sea ice concentration data were numerically normalized to obtain normalized sea ice concentration data. The normalized sea ice concentration data is downsampled to obtain downsampled sea ice concentration data with the same spatial resolution as the daily Arctic sea ice thickness data. Based on the grid coordinate axis correspondence between the downsampled sea ice concentration data and the daily Arctic sea ice thickness data, the downsampled sea ice concentration data is subjected to matrix transpose and coordinate axis flipping to obtain grid-aligned sea ice concentration data that is in the same polar projection grid as the daily Arctic sea ice thickness data. Missing value connected component detection was performed on the grid-aligned sea ice concentration data and the daily Arctic sea ice thickness data to obtain the missing sea ice concentration region and the missing sea ice thickness region. Nearest neighbor interpolation is performed using the effective pixels around the missing sea ice concentration region and the effective pixels around the missing sea ice thickness region to obtain the missing sea ice concentration data and missing sea ice thickness data after filling the missing values. By using an active grid mask, effective ocean regions are selected from the sea ice concentration data and sea ice thickness data after missing value filling, respectively, to obtain spatiotemporally aligned sea ice concentration sequences and sea ice thickness sequences.

3. The method for jointly predicting the concentration and thickness of Arctic sea ice according to claim 1, characterized in that, Based on the sea ice thickness differences at different times in the historical input sequence of sea ice thickness, a sea ice thickness trend channel is obtained, including: Using the current moment in the historical input sequence of sea ice thickness as a benchmark, the difference between the sea ice thickness at the current moment and the sea ice thickness at at least two different historical moments is calculated to obtain the sea ice thickness trend characteristics corresponding to different time scales. Each of the aforementioned sea ice thickness trend characteristics is used as a sea ice thickness trend channel to characterize the thickening or thinning trend of sea ice thickness at different time scales.

4. The method for jointly predicting the concentration and thickness of Arctic sea ice according to claim 1, characterized in that, Image patching and feature dimension mapping are performed on the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness, respectively, to obtain initial embedding features of sea ice concentration and initial embedding features of sea ice thickness, including: The historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness are respectively divided into multiple non-overlapping image blocks; Each non-overlapping image patch is subjected to feature projection to transform it to a preset feature dimension, thereby obtaining the initial embedding features of sea ice concentration and the initial embedding features of sea ice thickness.

5. The method for jointly predicting the concentration and thickness of Arctic sea ice according to claim 1, characterized in that, Attention enhancement is applied to the initial embedding features of sea ice concentration and sea ice thickness, respectively, to obtain enhanced sea ice concentration features and enhanced sea ice thickness features, including: The initial sea ice concentration embedding features are aggregated along the channel dimension to obtain a first channel aggregation result. A first channel attention weight is generated based on the channel aggregation result. The initial sea ice concentration embedding features are then weighted using the first channel attention weight to obtain enhanced sea ice concentration channel features. Spatial dimension feature aggregation is performed on the sea ice concentration channel enhancement features to obtain a first feature aggregation result. A first spatial attention weight is generated based on the feature aggregation result. The sea ice concentration channel enhancement features are weighted using the first spatial attention weight to obtain the sea ice concentration enhancement features. The initial sea ice thickness embedding features are aggregated along the channel dimension to obtain a second channel aggregation result. A second channel attention weight is generated based on the second channel aggregation result. The initial sea ice thickness embedding features are then weighted using the second channel attention weight to obtain the sea ice thickness channel enhancement features. Spatial feature aggregation is performed on the sea ice thickness channel enhancement features to obtain a second feature aggregation result. A second spatial attention weight is generated based on the second feature aggregation result. The sea ice thickness channel enhancement features are then weighted using the second spatial attention weight to obtain the sea ice thickness enhancement features.

6. The method for jointly predicting the concentration and thickness of Arctic sea ice according to claim 1, characterized in that, Multi-stage encoding was performed to obtain multi-scale features of sea ice concentration, bottleneck features of sea ice concentration, multi-scale features of sea ice thickness, and bottleneck features of sea ice thickness, including: The sea ice concentration enhancement feature and the sea ice thickness enhancement feature are respectively used as the initial coding features of the corresponding coding branches; In each encoding stage, the current encoded features are divided into rectangular attention windows with different widths and heights, and self-attention operations are performed on the current encoded features within each rectangular attention window to obtain window attention features; The window attention features are shifted to enable feature interaction between adjacent rectangular attention windows, thus obtaining the interaction features of the current stage. The interaction features of the current stage are downsampled to obtain the encoding features of the next encoding stage; The coding features obtained in each intermediate coding stage are respectively used as the corresponding multi-scale features of sea ice concentration or multi-scale features of sea ice thickness, and the coding features obtained in the final coding stage are respectively used as the bottleneck features of sea ice concentration or the bottleneck features of sea ice thickness.

7. The method for jointly predicting the concentration and thickness of Arctic sea ice according to claim 1, characterized in that, The bidirectional cross-attention processing of the sea ice concentration bottleneck feature and the sea ice thickness bottleneck feature yields bottleneck coupling features, including: Using the sea ice concentration bottleneck feature as the query feature, and the sea ice thickness bottleneck feature as the key feature and value feature, a first cross-attention process is performed to obtain the first cross-field interaction feature. Using the sea ice thickness bottleneck feature as the query feature, and the sea ice density bottleneck feature as the key feature and value feature, a second cross-attention process is performed to obtain the second cross-field interaction feature. The bottleneck coupling feature is obtained by fusing the first cross-field interaction feature and the second cross-field interaction feature.

8. A joint prediction system for Arctic sea ice concentration and thickness, characterized in that, include: The data acquisition module is used to acquire daily data on Arctic sea ice concentration and daily data on Arctic sea ice thickness. The data preprocessing module is used to preprocess the daily data of Arctic sea ice concentration and the daily data of Arctic sea ice thickness to obtain a spatiotemporally aligned sea ice concentration sequence and sea ice thickness sequence. The sequence and trend extraction module is used to extract data for a consecutive preset number of days from the sea ice concentration sequence and the sea ice thickness sequence, respectively, to obtain the historical input sequence of sea ice concentration and the historical input sequence of sea ice thickness. Based on the sea ice thickness difference at different times in the historical input sequence of sea ice thickness, the sea ice thickness trend channel is obtained. The sequence expansion module is used to concatenate the historical input sequence of sea ice thickness with the trend channel of sea ice thickness to obtain the expanded input sequence of sea ice thickness. The feature processing module is used to perform feature embedding processing on the historical input sequence of sea ice concentration and the extended input sequence of sea ice thickness respectively to obtain the initial embedded features of sea ice concentration and the initial embedded features of sea ice thickness. Attention enhancement is applied to the initial embedding features of sea ice concentration and the initial embedding features of sea ice thickness to obtain enhanced features of sea ice concentration and enhanced features of sea ice thickness. Then, multi-stage encoding is performed to obtain multi-scale features of sea ice concentration, bottleneck features of sea ice concentration, multi-scale features of sea ice thickness, and bottleneck features of sea ice thickness. The bottleneck feature coupling module is used to perform bidirectional cross-attention processing on the sea ice concentration bottleneck feature and the sea ice thickness bottleneck feature to obtain the bottleneck coupling feature. The multi-scale feature fusion module is used to generate gating weights based on the multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness, and to use the gating weights to perform weighted fusion of the multi-scale features of sea ice concentration and the multi-scale features of sea ice thickness to obtain multi-scale coupled features. The feature decoding and prediction module is used to decode the bottleneck coupling feature and the multi-scale coupling feature respectively to obtain the sea ice concentration prediction field and the initial sea ice thickness prediction field for the next preset number of days. The physical consistency correction module is used to perform physical consistency processing on the initial sea ice thickness prediction field based on the sea ice concentration of the last day in the historical input sequence of sea ice concentration. The predicted sea ice thickness value corresponding to the pixel position where the sea ice concentration is lower than a preset threshold is set to zero to obtain the sea ice thickness prediction field. The sea ice concentration prediction field and the sea ice thickness prediction field are used as the joint short-term forecast result of Arctic sea ice.

9. A terminal device, comprising a memory and a processor, characterized in that, The memory stores a computer program that can run on a processor, and when the processor loads and executes the computer program, it employs the method described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is loaded and executed by the processor, it employs the method described in any one of claims 1 to 7.

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