Short-term space-time sea ice thickness prediction method and system based on ETrans deep learning model

Abstract

The invention relates to the technical field of sea ice thickness prediction, in particular to a short-term space-time sea ice thickness prediction method and system based on an ETmeans deep learning model, and the method comprises the steps: decomposing the space-time data of the sea ice thickness into a space mode EOFs and a corresponding principal component PCs in a space-time decomposition stage; in the prediction stage, a Transform model is used for fitting nonlinear time sequence change of the sea ice thickness, so that a principal component PCs containing future space-time change information of the ice thickness is obtained; and in a reconstruction stage, fusing the space mode EOFs obtained in the space-time decomposition stage and the principal component PCs output in the prediction stage, reconstructing ice thickness data, and obtaining a final ice thickness prediction result. According to the ETrs deep learning model provided by the invention, the mining capability of an empirical orthogonal function (EOF) on overall change characteristics and the description capability of Transform on a time sequence context relation are considered, and the short-term and high-precision sea ice thickness is predicted from sea ice observation data through sea ice thickness (SIT) space-time decomposition and prediction and reconstruction.

Description

Technical Field

[0001] The present invention relates to the technical field of sea ice thickness prediction, and particularly relates to a short-term spatio-temporal sea ice thickness prediction method and system based on an ETrans deep learning model. Background Art

[0002] With global warming, the ablation rate of Arctic sea ice has accelerated, and its average thickness has decreased by 20% compared to 2010. The sharp reduction in sea ice extent and thickness provides potential opportunities for opening Arctic shipping lanes, extending operation exploration time, and carrying out scientific research activities. Compared with sea ice extent, the observation and reanalysis of sea ice thickness are more difficult, resulting in relatively scarce thickness data, and the research on short-term prediction of sea ice thickness is still in its infancy. In addition, the rapid changes in sea ice thickness in time and space pose higher requirements for the timeliness and accuracy of the current prediction of ice thickness spatio-temporal distribution. The research on short-term ice thickness prediction using remote sensing models can not only provide efficient support for human activities in the Arctic region, but also promote the harmonious coexistence of humans and the polar natural environment.

[0003] The simple climate models Persistence and Climatology were first proposed. The Persistence model assumes that the current state will continuously affect the future ice thickness condition, while the Climatology model predicts the future ice thickness condition based on average historical data. Subsequently, short-term sea ice forecasts based on numerical models were proposed. According to the ocean thermodynamics and sea ice dynamic processes, the numerical model solves partial differential equations to master, simulate, and predict the change of ice thickness over time and space. Although the numerical model was the first to reveal the trend of sea ice thickness change, it still cannot meet the short-term prediction requirements, and the error of short-term forecasts is significant. This is because the numerical model needs to be coupled with other models, and the complex physical processes of sea ice make it difficult for the numerical model to describe the thermodynamics and dynamics processes in detail. In addition, the prediction accuracy of ice thickness based on the numerical model is highly correlated with the setting of initial parameters and changing boundaries, and different initial-boundary conditions will lead to obvious differences in the results. Under the influence of various environmental factors such as temperature, wind speed, ocean circulation, and solar radiation, the numerical model can predict the overall change trend of ice thickness, but it is still difficult to accurately depict the spatio-temporal distribution of sea ice in the short term.

[0004] The method based on machine learning has achieved accurate prediction of ice thickness spatio-temporal changes, and the rapid development of deep learning (DL) makes it promising to further explore the latent spatio-temporal correlations of sea ice. DL was first applied to sea ice concentration (SIC). However, there are still limitations in the deep learning model in mining the spatio-temporal correlation features of sea ice and describing the ice thickness time context relationship. Summary of the Invention

[0005] The present invention aims to solve the problem that the short-term changes of sea ice are rapid, and the current spatio-temporal prediction models have limitations in describing the spatial global characteristics of sea ice thickness and mining the temporal context correlations. A short-term spatio-temporal sea ice thickness prediction method and system based on the ETrans deep learning model are proposed. The ETrans deep learning model takes into account the ability of the Empirical Orthogonal Function (EOF) to mine the overall change characteristics and the ability of the Transformer to describe the temporal context relationship. Through the spatio-temporal decomposition, prediction, and reconstruction of the sea ice thickness (SIT), short-term and high-precision sea ice thickness is predicted from the sea ice observation data.

[0006] To achieve the above object, the technical solution adopted is as follows:

[0007] The present invention proposes a short-term spatio-temporal sea ice thickness prediction method based on the ETrans deep learning model, which is divided into a spatio-temporal decomposition stage, a prediction stage, and a reconstruction stage;

[0008] In the spatio-temporal decomposition stage, the spatio-temporal data of the sea ice thickness is decomposed into spatial modes EOFs and corresponding principal components PCs;

[0009] In the prediction stage, the Transformer model is used to fit the non-linear temporal variation of the sea ice thickness, so as to obtain the principal components PCs containing the future spatio-temporal change information of the ice thickness;

[0010] In the reconstruction stage, the spatial modes EOFs obtained in the spatio-temporal decomposition stage and the principal components PCs output in the prediction stage are fused to reconstruct the ice thickness data, and the final ice thickness prediction result is obtained.

[0011] According to the short-term spatio-temporal sea ice thickness prediction method based on the ETrans deep learning model of the present invention, further, decomposing the spatio-temporal data of the sea ice thickness into spatial modes EOFs and corresponding principal components PCs includes: projecting the sea ice thickness observation into the covariance matrix through covariance matrix calculation, and decomposing the sea ice thickness observation varying with time into EOFs not varying with time and PCs depending on time variation through eigenvalue decomposition EVD.

[0012] According to the short-term spatio-temporal sea ice thickness prediction method based on the ETrans deep learning model of the present invention, further, decomposing the sea ice thickness observation varying with time into EOFs not varying with time and PCs depending on time variation through eigenvalue decomposition EVD specifically includes:

[0013] First, calculate the sea ice thickness observation of the covariance matrix C S×S :

[0014]

[0015] Among them, S represents the number of spatial points of sea ice thickness on a certain day, T represents the number of time series at a certain location, and ob represents the observation;

[0016] Then, the spatial eigenvector EOF of the spatio-temporal data of sea ice thickness is obtained through EVD decomposition S×S and its corresponding time coefficients (λ 1 , …, λ S ):

[0017] C S×S × EOF S×S = EOF S×S × Λ S×S

[0018] Among them, Λ S×S is a diagonal matrix in which the time coefficients (λ 1 , …, λ S ) are arranged from large to small;

[0019] Finally, the time component PC S×S corresponding to EOF S×S is obtained through matrix multiplication:

[0020]

[0021] According to the short-term spatio-temporal sea ice thickness prediction method based on the ETrans deep learning model of the present invention, further, the Transformer model includes a plurality of encoders and decoders; the encoder is used to generate the context representation of the sea ice thickness time series, and each encoder includes a multi-head attention mechanism and a feed-forward neural network, and each sub-layer is followed by a residual connection and layer normalization; the decoder is used to predict the PCs at future moments according to the context representation of the sea ice thickness time series generated by the encoder and the predicted PCs, and each decoder includes a masked multi-head attention mechanism, a multi-head attention mechanism and a feed-forward neural network.

[0022] According to the short-term spatio-temporal sea ice thickness prediction method based on the ETrans deep learning model of the present invention, further, in the encoder, the multi-head attention mechanism is used to generate the context representation Context ice :

[0023] Context ice = MH-Attention(Q ice , K ice , V ice )

[0024] Among them, MH-Attention is the multi-head attention mechanism, and Q ice , K ice , V iceThey are the query vector, key vector, and value vector respectively;

[0025] The feed-forward neural network applies a non-linear transformation to Context ice The expression is:

[0026] nolin_Context ice = FFN(Context ice )

[0027] where FFN is the feed-forward neural network.

[0028] According to the short-term spatio-temporal sea ice thickness prediction method based on the ETrans deep learning model of the present invention, further, in the decoder, the masked multi-head attention mechanism is used to collect the context information of the predicted PCs:

[0029] tar_Context ice = MMH-Attention(Tar gets ice )

[0030] where Targets ice represents the predicted PCs in the sequence to be predicted, and tar_Context ice represents the context representation of the predicted PCs in the sequence to be predicted;

[0031] The decoder uses the multi-head attention mechanism and the feed-forward neural network to generate the prediction result of the next future moment's PCs from nolin_Context ice and tar_Context ice :

[0032] PC_pred = FFN(MH-Attention(nolin_Context ice , tar_Context ice ))

[0033] where MH-Attention is the multi-head attention mechanism and FFN is the feed-forward neural network;

[0034] The PC_pred at each moment in the sequence to be predicted is passed through the output layer to obtain the final result PC_output:

[0035] PC_output = Linear&Softmax(PC_pred).

[0036] According to the short-term spatio-temporal sea ice thickness prediction method based on the ETrans deep learning model of the present invention, further, the spatial modes EOFs obtained in the spatio-temporal decomposition stage and the principal components PCs output in the prediction stage are fused to reconstruct the ice thickness data, and the final ice thickness prediction result is obtained, including:

[0037] Multiply the spatial EOFs in the spatio-temporal decomposition stage by the temporal PCs in the prediction stage, and then add the benchmark To obtain the sea ice thickness prediction result

[0038]

[0039] Furthermore, the present invention also proposes a short-term spatio-temporal sea ice thickness prediction system based on the ETrans deep learning model, which is used to implement the short-term spatio-temporal sea ice thickness prediction method based on the ETrans deep learning model as described above. The system includes a spatio-temporal decomposition module, a prediction module, and a reconstruction module, wherein:

[0040] The spatio-temporal decomposition module is used to decompose the spatio-temporal data of the sea ice thickness into spatial modes EOFs and the corresponding principal components PCs;

[0041] The prediction module is used to fit the non-linear time series change of the sea ice thickness by using the Transformer model, so as to obtain the principal components PCs containing the future spatio-temporal change information of the ice thickness;

[0042] The reconstruction module is used to fuse the spatial modes EOFs obtained in the spatio-temporal decomposition stage and the principal components PCs output in the prediction stage, reconstruct the ice thickness data, and obtain the final ice thickness prediction result.

[0043] By adopting the above technical solutions, the beneficial effects obtained are:

[0044] Under the action of global warming, the downward trend of sea ice thickness has accelerated significantly. In this case, accurate short-term sea ice thickness (SIT) prediction will provide more reliable guarantee for human activities. However, the current spatio-temporal prediction model lacks effective mining of the spatial global characteristics and time context information of sea ice thickness, and the prediction accuracy of short-term sea ice thickness needs to be improved. To overcome this limitation, the present invention proposes an ETrans model that can use the observed data of past sea ice thickness to predict the short-term sea ice thickness change within 21 days. Since EOF has the ability to mine spatial global characteristics and Transformer has the ability to describe temporal context relationships, ETrans fuses the empirical orthogonal function (EOF) and Transformer, and realizes the accurate prediction of SIT spatio-temporal changes through spatio-temporal decomposition, prediction and reconstruction. Description of the Drawings

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments of the present invention will be briefly introduced below. Among them, the accompanying drawings are only used to show some embodiments of the present invention, rather than limiting all embodiments of the present invention thereto.

[0046] Figure 1 is a schematic flow chart of the short-term spatio-temporal sea ice thickness prediction method based on the ETrans deep learning model in the embodiments of the present invention;

[0047] Figure 2 is a research area map of the embodiments of the present invention, which shows the SMOS L3 SIT data on January 12, 2019, and the research locations in the Beaufort Sea are marked with red boxes;

[0048] Figure 3 is an architecture diagram of the Transformer model in the embodiments of the present invention;

[0049] Figure 4 is the prediction accuracy among Etrans, numerical models and benchmark models in the embodiments of the present invention, where (a) is the comparison result of RMSE and (b) is the comparison result of Corr;

[0050] Figure 5 is the result of Etrans in the embodiments of the present invention. From left to right are the predicted ice thickness, the observed value, and the root mean square error between them; from top to bottom are the results of the 7th day, 14th day and 21st day;

[0051] Figure 6 is the performance comparison of ETrans and other deep learning models at different preset times in the embodiments of the present invention; from left to right are RMSE, MAE and Corr;

[0052] Figure 7 is the prediction results of ETrans and ConvLSTM on the 21st day in the embodiments of the present invention. From left to right are the ETrans ice thickness prediction, observation and ConvLSTM ice thickness prediction. Detailed implementation manners

[0053] In the following, the exemplary solutions of the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings of the specific embodiments of the present invention. Unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meaning understood by those of ordinary skill in the art.

[0054] In order to achieve accurate prediction of sea ice thickness at the daily scale, this solution proposes a short-term spatio-temporal sea ice thickness prediction method based on the ETrans deep learning model, as Figure 1 shown. This method is divided into a spatio-temporal decomposition stage, a prediction stage and a reconstruction stage, which are specifically as follows:

[0055] In the spatio-temporal decomposition stage, the spatio-temporal data of sea ice thickness is decomposed into spatial modes EOFs and corresponding principal components PCs to capture the spatial distribution pattern of ice thickness in the spatio-temporal domain and its changing trend over time.

[0056] In the prediction stage, the Transformer model is used to fit the non-linear temporal variation of sea ice thickness, thereby obtaining the principal components PCs containing the future spatio-temporal change information of ice thickness. At the same time, the attention mechanism is introduced in this stage, and by dynamically assigning weights to each time step in the ice thickness sequence, ETrans can focus on the temporal features affecting the change of ice thickness.

[0057] In the reconstruction stage, the spatial modes EOFs obtained in the spatio-temporal decomposition stage and the principal components PCs output in the prediction stage are fused to reconstruct the ice thickness data and obtain the final sea ice thickness prediction result.

[0058] As Figure 2 shown, the study site and data are selected: The Arctic Beaufort Sea region (longitude: 135° - 168°W, latitude: 72° - 79°N) is selected as the study area. This study site has a relatively high latitude, and the cold Beaufort Bay current ensures that there is a large area of first-year sea ice and multi-year sea ice in this region, which can fully verify the performance of the prediction model.

[0059] The SMOS satellite was launched by the European Space Agency (ESA), and the L-band two-dimensional synthetic aperture microwave radiometer carried on it can observe the polar ice thickness. The SMOS Level3 Sea Ice Thickness (SMOS L3 SIT) product released by the Alfred Wegener Institute (AWI) has a high resolution in both time and space, making short-term refined prediction possible. The spatial resolution of L3 SIT is 12.5 km, and the data range covers the Arctic region up to 85°N. In addition, AWI provides the daily SMOS SIT observation results from the freezing season since 2010 and can be downloaded open source. The present invention collects the SMOS L3 SIT data from October 15 of each year to January 15 of the following year for short-term prediction of sea ice thickness.

[0060] (1) Spatio-temporal decomposition

[0061] The atmosphere, ocean, and sea ice are coupled and interact with each other, resulting in the non-independence of sea ice thickness changes in space. Current research focuses on characterizing the local changes of SIT, while the redundancy of observational data in spatial distribution characteristics and temporal change trends poses challenges to the description of the global characteristics of SIT. Spatio-temporal decomposition can decompose the SIT spatio-temporal data set and identify and separate temporal and spatial information from it, helping to understand the internal mechanism of sea ice thickness and describe the change characteristics.

[0062] AsFigure 1 As shown in (a), the sea ice thickness observations are projected into the covariance matrix through covariance matrix calculation, and the time-varying sea ice thickness observations are decomposed into time-invariant EOFs and time-dependent PCs through eigenvalue decomposition (EVD).

[0063] Assume that S represents the number of spatial points of SIT on a certain day, T represents the number of time series at a certain location, and ob represents the observation. Then the SIT observation can be expressed as To eliminate the influence of the long-term state in the SIT change, the anomaly matrix is calculated according to formula (1)

[0064]

[0065] Then can be expressed as:

[0066]

[0067] where the element x st represents the SIT observation at the t-th time point and the s-th spatial point.

[0068] From the SIT covariance matrix C S×S can be obtained:

[0069]

[0070] Furthermore, the spatial eigenvector EOF of the sea ice thickness spatio-temporal data is obtained through EVD decomposition S×s and its corresponding time coefficients (λ 1 , …, λ S ):

[0071] C S×S × EOF S×S = EOF S×S × Λ S×S (4)

[0072] where Λ S×S is a diagonal matrix of the time coefficients (λ 1 , …, λ S ) arranged from largest to smallest:

[0073] Λ S×S = diag(λ 1 , …, λ S ) (5)

[0074] Finally, the time component PC S×S corresponding to EOF S×S is obtained through matrix multiplication:

[0075]

[0076] Regarding the SIT observations at a certain moment as a linear combination of multiple spatial modes with different weights, the spatio-temporal decomposition decomposes the SIT observations into EOFs and PCs. Thus, the SIT variations are transformed into spatial modes that do not change with time and different time series components, which helps to describe its internal mechanism.

[0077] (2) Spatio-temporal prediction of sea ice thickness

[0078] Characterizing the temporal variation characteristics of SIT is the guarantee for accurate short-term spatio-temporal prediction of SIT, while existing studies lack the consideration of the context characteristics of SIT temporal variation. Compared with other deep learning models, Transformer can construct the correlation between any two elements in the time series through the attention mechanism, characterize the variation characteristics of the SIT time series, and is not affected by the length of the dataset. As Figure 1 (b) shows, Transformer is introduced and used to construct the context characteristics of SIT PCs in the time series. The PCs obtained from the SIT observations are input into Transformer, and the predicted PCs are obtained through the encoder and decoder.

[0079] Figure 3 Figure (a) shows the encoder-decoder architecture of the Transformer model. The encoder is used to generate the context representation of the sea ice thickness time series. The encoder consists of multiple identical layers, and each layer contains a multi-head attention mechanism and a feed-forward neural network. Each sub-layer is followed by a residual connection and layer normalization to alleviate the vanishing gradient and stabilize the model training. The decoder is used to predict the PCs at future moments based on the context representation of the sea ice thickness time series generated by the encoder and the already predicted PCs. The decoder also consists of multiple identical layers, and each layer contains a masked multi-head attention mechanism, a multi-head attention mechanism, and a feed-forward neural network.

[0080] Establishing the dependence between different parts of the SIT PCs in the time series and capturing the relationship between different positions rely on the multi-head (MH) attention mechanism. Figure 3 (c) shows the multi-head attention mechanism used, which contains multiple parallel attention mechanisms to capture different features and relationships in the input SIT observations:

[0081] MH-Attention(Q ice ,K ice ,B ice ) = Concat(head 1 , … head h )W H (7)

[0082] Among them, W H is the weight matrix, and the nth attention mechanism head in the cascade n = Attention(Q ice n , K ice n , V ice n ) can be expressed as:

[0083]

[0084] Among them, is the scaling factor, and the constituent elements Q ice , K ice , V ice of the attention mechanism are obtained by the SIT PCs through three different linear transformation layers respectively.

[0085] Therefore, when using the Transformer for SIT spatio-temporal prediction, the SIT PCs after position encoding are input into the encoder:

[0086] Inputs = PCs + Position Encoding(PCs) (9)

[0087] The multi-head attention mechanism realizes the focusing on the important positions of the SIT PCs input by mining the complex dependencies at different positions, thereby generating the context representation Context of the sea ice time series ice :

[0088] Context ice = MH-Attention(Q ice , K ice , V ice ) (10)

[0089] Among them, MH-Attention is the multi-head attention mechanism, and Q ice , K ice , V ice are the query vector, key vector, and value vector respectively.

[0090] The feed-forward neural network applies a non-linear transformation to Context ice to increase the expression ability of the Transformer for SIT PCs:

[0091] nolin_Context ice = FFN(Context ice ) (11)

[0092] Among them, FFN is a feed-forward neural network.

[0093] In the decoder, the masked multi-head attention mechanism is used to collect the context information of the predicted PCs:

[0094] tar_Context ice = MMH-Attention(Targets ice ) (12)

[0095] Among them, Targets ice represents the predicted PCs in the sequence to be predicted, and tar_Context ice represents the context representation of the predicted PCs in the sequence to be predicted. Compared with the multi-head attention mechanism, the masked multi-head attention mechanism ensures that the model can only access the information before the current moment and cannot obtain the information of future moments when processing the context information of PCs through the masking mechanism, thus ensuring the temporal prediction ability of the model.

[0096] The decoder uses the multi-head attention mechanism and the feed-forward neural network to generate the prediction result of the PCs at the next future moment from nolin_Context ice and tar_Context ice :

[0097] PC_pred = FFN(MH-Attention(nolin_Context ice , tar_Context ice )) (13)

[0098] Iterate formulas (12) and (13), and pass the PC_pred at each moment in the sequence to be predicted through the output layer to obtain the final result PC_output:

[0099] PC_output = Linear&Softmax(PC_pred) (14)

[0100] Through the above process, Transformer can use the context information contained in the SIT PCs for the prediction of SIT.

[0101] (3) Spatiotemporal reconstruction of sea ice thickness

[0102] The PCs obtained in the spatiotemporal prediction stage contain the future spatiotemporal change information of ice thickness, while the spatial distribution pattern of ice thickness is contained in the EOFs output in the spatiotemporal decomposition stage. As Figure 1 (c) shows, in actual calculation, multiply the spatial EOFs in the spatiotemporal decomposition stage by the temporal PCs in the prediction stage, and then add the reference the sea ice thickness prediction results can be obtained

[0103]

[0104] Correspondingly to the above method, this embodiment also proposes a short-term spatio-temporal sea ice thickness prediction system based on the ETrans deep learning model. The system includes a spatio-temporal decomposition module, a prediction module, and a reconstruction module, where:

[0105] The spatio-temporal decomposition module is used to decompose the spatio-temporal data of the sea ice thickness into spatial modes EOFs and corresponding principal components PCs.

[0106] The prediction module is used to fit the non-linear time series change of the sea ice thickness by using the Transformer model, so as to obtain the principal components PCs containing the future spatio-temporal change information of the ice thickness.

[0107] The reconstruction module is used to fuse the spatial modes EOFs obtained in the spatio-temporal decomposition stage and the principal components PCs output in the prediction stage, reconstruct the ice thickness data, and obtain the final ice thickness prediction result.

[0108] To verify the effectiveness of this solution, further explanations will be given below in combination with experimental data.

[0109] (1) Verification strategies and metrics

[0110] The SMOS L3 SIT dataset contains 14 years of data. Among them, the data from 2010 to 2019 are used as the training set, the data from 2020 to 2021 are used as the validation set, and the data from 2022 to 2023 are used as the test set. Among them, the first 18 PCs are retained as training samples after the spatio-temporal decomposition of the sea ice, and their cumulative explained variance ratio is 95%. The PCs of the validation set and the test set are obtained from the EOFs of the training set according to formula (6). During the calculation process, the mean square error (MSE) is used as the loss function, and the model parameters are optimized by iterating 100 time steps and backpropagating the gradient.

[0111]

[0112] where M is the number of training samples, pred i 、true i are the i-th predicted value and the observed value respectively.

[0113] ETrans uses the SIT observations of the past 7 days to predict the SIT for the next consecutive 21 days. The root mean square error (RMSE), mean absolute error (MAE), and Pearson correlation coefficient (Corr) between the observed value and the predicted value are used to evaluate the model performance.

[0114]

[0115] Among them, N is the number of predicted points in the study area, and represent the mean values of the predicted value and the true value respectively. At the same time, the Persistence model, Climatology model, TOPAZ5 model, CNN, and ConvLSTM are introduced to verify the performance of ETrans relative to the benchmark model, numerical model, and DL model.

[0116] (2) Accuracy of SIT prediction

[0117] Figure 4 Shows the ice thickness prediction error and correlation of ETrans at different lead times (in days, i.e., the time from the current moment to the predicted moment). Except for the first and second days, the RMSE of ETrans prediction is better than that of the numerical model and the benchmark model. Similarly, the overall correlation of ETrans in predicting SIT is also better than that of other models. As the number of days increases, the prediction ability of all models decreases, but the performance of ETrans decreases the least, showing good stability. Therefore, the comprehensive performance of ETrans is the best, followed by Climatology, and the performance of TOPAZ5 and Persistence decreases in turn.

[0118] Figure 5 Compares the differences between the ETrans prediction results and the actual observations in space and time. The prediction results show obvious spatial characteristics. As the latitude increases, the SIT predicted by ETrans gradually increases to 1.7 m. Thanks to the ability of EOF to describe the overall characteristics of ice thickness, the results of ETrans are close to the actual observations and can accurately predict the spatial distribution of SIT. From the time dimension, the prediction errors on the 7th, 14th, and 21st days gradually increase. Although the error of ETrans prediction increases with time, the spatial distribution of SIT depicted by it is still consistent with the actual observations. The description of the temporal context relationship of SIT PCs by ETrans ensures its performance at larger lead times.

[0119] (3) Performance comparison with other deep learning models

[0120] Although ETrans has better performance compared to the benchmark model and numerical model, its performance relative to other deep learning models needs to be further compared. Table 1 compares the average performance of ETrans, CNN, and ConvLSTM in short-term (within 21 days) spatio-temporal prediction of sea ice using RMSE, MAE, and Corr as evaluation metrics. ETrans is optimal in all metrics, with an average RMSE of only 0.1716 m, an average MAE of 0.1313 m, and a correlation of 0.8771. In contrast, ConvLSTM has the second-best performance, while CNN has the worst performance.

[0121] Table 1 Performance comparison of ETrans, CNN, and ConvLSTM

[0122]

[0123] Figure 6 Further shows the performance of deep learning models in predicting SIT at different lead times. At all lead times, the RMSE and MAE of ETrans are better than those of CNN and ConvLSTM. Although the errors of DL models increase with time, the increase rate of ETrans is also the smallest. For the correlation coefficient, ETrans is lower than ConvLSTM on the 1st, 2nd, and 3rd days. Overall, ETrans has better performance than CNN and ConvLSTM.

[0124] CNN lacks consideration of time series data, so its prediction performance is the worst at all lead times. Although ConvLSTM takes into account the time series characteristics of SIT, it is difficult to describe the global spatial characteristics and ignores the connection of SIT time series context. In contrast, decomposing SIT into spatial EOFs and temporal PCs enables ETrans to overcome the challenges of short-term sea ice prediction.

[0125] In fact, describing the global spatial characteristics and mining the connection of time series context helps to more precisely depict the spatio-temporal distribution of sea ice. Therefore, Figure 7 Further shows the performance advantage of ETrans over ConvLSTM at the 21st day. By comparison, it is found that the results of ETrans in predicting the area above 75°N are closer to the actual observations, and the spatio-temporal variation characteristics of sea ice can be accurately described. ConvLSTM overestimates the SIT in the same area and wrongly draws the thin ice area thicker. The overall trend of the SIT predicted by ConvLSTM is also similar to the actual observations, but it struggles in the detailed description.

[0126] The experimental results in the Beaufort Sea of the Arctic show that the average RMSE, average MAE, and average Corr of ETrans are 0.1716m, 0.1313m, and 0.8771 respectively. Compared with the benchmark model, numerical model, and other DL models, ETrans has better comprehensive performance at different preset times and depicts the local changes of sea ice more accurately and meticulously.

[0127] Unless otherwise specifically stated, the components, steps, numerical expressions, and values set forth in these embodiments do not limit the scope of the present invention.

[0128] Each embodiment in this specification is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and reference can be made to the description in the method part for the relevant parts.

[0129] The units and method steps of the examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. To clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described according to their functions in the above description. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Those of ordinary skill in the art can use different methods to implement the described functions for each specific application, but such implementation is not considered to exceed the scope of the present invention.

[0130] Those of ordinary skill in the art can understand that all or part of the steps in the above methods can be completed by instructing relevant hardware through a program, and the program can be stored in a computer-readable storage medium, such as a read-only memory, a magnetic disk, or an optical disc, etc. Optionally, all or part of the steps of the above embodiments can also be implemented using one or more integrated circuits. Correspondingly, each module / unit in the above embodiments can be implemented in the form of hardware or in the form of a software functional module. The present invention is not limited to any specific form of the combination of hardware and software.

[0131] Finally, it should be noted that the above-described embodiments are only specific embodiments of the present invention, used to illustrate the technical solutions of the present invention, rather than limiting it. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that any person skilled in the art within the technical scope disclosed by the present invention can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A short-term spatiotemporal sea ice thickness prediction method based on the ETrans deep learning model, characterized in that: It is divided into the spatiotemporal decomposition phase, the prediction phase and the reconstruction phase; In the spatiotemporal decomposition stage, the spatiotemporal data of sea ice thickness are decomposed into spatial modal EOFs and corresponding principal components PCs; In the prediction stage, the Transformer model is used to fit the nonlinear time series changes of sea ice thickness, so as to obtain the principal components PCs containing the information of future spatiotemporal changes of ice thickness. In the reconstruction stage, the spatial modal EOFs obtained in the spatiotemporal decomposition stage and the principal components PCs output in the prediction stage are fused to reconstruct the ice thickness data and obtain the final ice thickness prediction result.

2. The short-term spatiotemporal sea ice thickness prediction method based on the ETrans deep learning model according to claim 1 is characterized in that: The spatiotemporal data of sea ice thickness are decomposed into spatial modal EOFs and corresponding principal components PCs, including: projecting the sea ice thickness observations into the covariance matrix through covariance matrix calculation, and decomposing the time-varying sea ice thickness observations into time-invariant EOFs and time-dependent PCs through eigenvalue decomposition (EVD).

3. The short-term spatiotemporal sea ice thickness prediction method based on the ETrans deep learning model according to claim 2 is characterized in that: The time-varying sea ice thickness observations are decomposed into EOFs that do not vary with time and PCs that depend on time through eigenvalue decomposition (EVD), including: First calculate the sea ice thickness observation The covariance matrix C S×S : Among them, S represents the number of spatial points of sea ice thickness on a certain day, T represents the number of time series at a certain location, and ob represents observation; Then the spatial characteristic vector EOF of the spatiotemporal data of sea ice thickness is obtained by EVD decomposition. S×S and its corresponding time coefficients (λ1,…,λ S ): C S×S ×EOF S×S =EOF S×S ×Λ S×S Among them, Λ S×S is the time coefficient (λ1,…,λ S )A diagonal matrix arranged from large to small; Finally, we get the matrix multiplication with EOF S×S The corresponding time component PC S×S :

4. The short-term spatiotemporal sea ice thickness prediction method based on the ETrans deep learning model according to claim 1 is characterized in that: The Transformer model includes several encoders and decoders; the encoder is used to generate a contextual representation of the sea ice thickness time series, each encoder includes a multi-head attention mechanism and a feedforward neural network, and each sublayer is followed by a residual connection and layer normalization; The decoder is used to predict PCs at future moments based on the contextual representation of the sea ice thickness time series generated by the encoder and the predicted PCs. Each decoder contains a masked multi-head attention mechanism, a multi-head attention mechanism, and a feedforward neural network.

5. The short-term spatiotemporal sea ice thickness prediction method based on the ETrans deep learning model according to claim 4 is characterized in that: In the encoder, a multi-head attention mechanism is used to generate the context representation of the sea ice thickness time series. ice : Context ice =MH-Attention(Q ice ,K ice ,V ice ) Among them, MH-Attention is a multi-head attention mechanism, Q ice , K ice 、V ice They are query vector, key vector and value vector respectively; Feedforward Neural Network to Context ice Applying nonlinear transformation, the expression is: nolin_Context ice =FFN(Context ice ) Among them, FFN is a feed-forward neural network.

6. The short-term spatiotemporal sea ice thickness prediction method based on the ETrans deep learning model according to claim 5 is characterized in that: In the decoder, a masked multi-head attention mechanism is used to collect contextual information of the predicted PCs: tar_Context ice =MMH-Attention(Targets ice ) Among them, Targets ice Indicates the predicted PCs in the sequence to be predicted, tar_Context ice Represents the context representation of the predicted PCs in the sequence to be predicted; The decoder uses a multi-head attention mechanism and a feed-forward neural network to extract the nolin_Context ice and tar_Context ice Generate the PCs prediction results for the next future moment: PC_pred=FFN(MH-Attention(nolin_Context ice ,tar_Context ice )) Among them, MH-Attention is a multi-head attention mechanism, and FFN is a feedforward neural network; The PC_pred at each moment in the sequence to be predicted is passed through the output layer to obtain the final result PC_output: PC_output=Linear&Softmax(PC_pred).

7. The short-term spatiotemporal sea ice thickness prediction method based on the ETrans deep learning model according to claim 6 is characterized in that: The spatial modal EOFs obtained in the spatiotemporal decomposition stage and the principal components PCs output in the prediction stage are fused to reconstruct the ice thickness data and obtain the final ice thickness prediction results, including: Multiply the spatial EOFs of the spatiotemporal decomposition phase and the temporal PCs of the prediction phase, and add the benchmark Get the sea ice thickness prediction results 8. A short-term spatiotemporal sea ice thickness prediction system based on the ETrans deep learning model, characterized in that: The method for predicting the short-term spatiotemporal sea ice thickness based on the ETrans deep learning model according to any one of claims 1 to 7 comprises a spatiotemporal decomposition module, a prediction module and a reconstruction module, wherein: The spatiotemporal decomposition module is used to decompose the spatiotemporal data of sea ice thickness into spatial modal EOFs and corresponding principal components PCs; The prediction module is used to fit the nonlinear time series changes of sea ice thickness using the Transformer model, so as to obtain the principal components PCs containing the information of future spatiotemporal changes of ice thickness; The reconstruction module is used to fuse the spatial modal EOFs obtained in the spatiotemporal decomposition stage and the principal components PCs output in the prediction stage to reconstruct the ice thickness data and obtain the final ice thickness prediction result.

9. A computer device comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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