A method for spatio-temporal prediction of three-dimensional temperature and salinity field in ocean based on Gaussian filter

Abstract

The application discloses a kind of Gauss filtering-based ocean three-dimensional temperature and salinity field space-time prediction method, specifically comprising: first, collect multi-source sea surface data and ocean three-dimensional reanalysis dataset, and after pre-processing, division is obtained Model training dataset;Then, for the ocean three-dimensional temperature and salinity field under the continuous time step, frequency decomposition is carried out using Gaussian filtering, to obtain the corresponding high, low frequency component respectively;Using low frequency component and multi-source sea surface data to construct end-to-end prediction path, using high frequency component to construct autoregressive prediction path, and the mapping relationship between the historical time window and the future target state is obtained by fusion;Based on this, build Gaussian filtering double-path neural network GDP-Net and train;Finally, three-dimensional temperature and salinity initial field and 10 days of multi-source sea surface observation data are input into the trained GDP-Net model, and the future 10 days of ocean three-dimensional temperature and salinity field space-time prediction results are restored. The application improves the prediction accuracy and alleviates the problem of blurring and smoothing of the prediction results.

Description

Technical Field

[0001] This invention discloses a spatiotemporal prediction method for three-dimensional temperature and salinity fields in the ocean based on Gaussian filtering, belonging to the field of marine technology. Background Technology

[0002] The three-dimensional temperature and salinity field of the ocean is an important physical variable characterizing the ocean's thermohaline structure, density stratification, and internal dynamic processes. Its spatiotemporal evolution directly affects ocean circulation, air-sea interaction, heat transport, mass exchange, and small- to medium-scale dynamic processes. Therefore, accurate prediction of the three-dimensional temperature and salinity field of the ocean is of great significance for marine environmental forecasting, climate change research, and marine resource development.

[0003] Existing methods for predicting the three-dimensional temperature and salinity field of the ocean include traditional numerical solutions and data-driven methods based on deep learning:

[0004] Traditional numerical methods are based on ocean dynamics and thermodynamics equations. They simulate the spatiotemporal evolution of temperature and salinity fields by discretizing and solving momentum equations, mass conservation equations, energy conservation equations, and salinity transport equations. These methods have a clear physical basis, but they are highly dependent on the initial field, boundary conditions, external forcing field, and parameterization scheme. Furthermore, they consume a lot of computational resources in high-resolution three-dimensional prediction tasks, making it difficult to meet the needs of fast and efficient operational prediction.

[0005] Data-driven methods based on deep learning utilize historical ocean data to learn the spatiotemporal evolution patterns of temperature and salinity fields, establishing a nonlinear mapping relationship between historical and future states. These methods offer advantages such as high computational efficiency, strong nonlinear expressive power, and strong multi-source data fusion capabilities.

[0006] However, the three-dimensional temperature and salinity field of the ocean has significant multi-scale characteristics, including large-scale background fields, stratified structures, and slowly varying dynamic processes, as well as high-frequency details such as fronts, vortex boundaries, local anomalies, and thermocline disturbances. Existing deep learning methods typically model the original temperature and salinity field as a whole, failing to adequately distinguish different spatial frequency components, which can easily lead to mutual interference between information at different scales and increase the difficulty of model learning.

[0007] Existing methods for predicting the three-dimensional temperature and salinity field of the ocean using deep learning models mainly fall into two categories: end-to-end prediction and autoregressive prediction.

[0008] End-to-end prediction can directly output results for multiple future time steps, exhibiting good long-term stability and making it suitable for characterizing large-scale, low-frequency, and slowly changing background evolution processes. However, this type of method usually aims to minimize the overall error, which can easily lead to over-smoothing, resulting in the weakening of high-frequency structures such as fronts, vortex boundaries, and local anomalies.

[0009] Autoregressive prediction predicts future states through a step-by-step recursive approach, which helps to preserve local details and continuous evolution characteristics. However, the prediction results depend on the output of the previous step, which can easily lead to error accumulation and affect the long-term prediction stability.

[0010] Furthermore, multi-source sea surface information, such as sea surface temperature, sea surface height anomalies, and sea surface wind fields, can reflect large-scale ocean state changes and has a certain coupling relationship with the subsurface temperature-salinity structure. However, sea surface remote sensing information mainly characterizes the two-dimensional surface state, while the three-dimensional temperature-salinity field has obvious vertical structure and stratification characteristics. Existing methods mostly use simple stitching to fuse multi-source sea surface variables, which makes it difficult to fully establish an effective mapping relationship between two-dimensional sea surface information and three-dimensional temperature-salinity structure. At the same time, sea surface observation information has a strong indicative role in large-scale background evolution, but its ability to directly characterize local high-frequency disturbances and sub-mesoscale details is limited.

[0011] Therefore, the existing technology still has the following shortcomings: First, it does not fully distinguish between low-frequency background fields and high-frequency detail fields, resulting in mixed modeling of information at different scales; second, end-to-end prediction is prone to smoothing of high-frequency details, and autoregressive prediction is prone to error accumulation; third, the coupling mapping ability between two-dimensional sea surface information and three-dimensional temperature and salinity structure is insufficient; and fourth, the ability to preserve key structures such as fronts, vortex boundaries, and thermoclines is limited. Summary of the Invention

[0012] To address the aforementioned issues, this invention proposes a spatiotemporal prediction method for three-dimensional ocean temperature and salinity fields based on Gaussian filtering. By using Gaussian filtering, the original three-dimensional temperature and salinity field is decomposed into low-frequency background signals and high-frequency detail signals. Prediction paths are constructed for different frequency components, and finally, the paths are fused to achieve a complete prediction of the future three-dimensional ocean temperature and salinity field. This improves the prediction accuracy and alleviates the problems of fuzziness and smoothing in the prediction results.

[0013] The specific steps are as follows:

[0014] Step 1: Collect sea surface temperature, sea surface height anomaly, sea surface wind field, and three-dimensional ocean temperature and salinity datasets, and divide them into training sets after preprocessing;

[0015] Preprocessing includes bilinear interpolation, default value replacement, etc.

[0016] Step 2: Targeting the three-dimensional temperature and salinity field of the ocean under continuous time steps Gaussian filtering is used to perform frequency decomposition at each time point to obtain the corresponding high and low frequency components.

[0017] The three-dimensional temperature and salinity field of the ocean is defined as:

[0018]

[0019] in, , and These represent the spatial dimensions of latitude, longitude, and depth, respectively, while t represents time.

[0020] Frequency decomposition refers to the process of directly obtaining low-frequency components from the initial three-dimensional temperature-salt field at time t through Gaussian filtering. The remaining field consists of high-frequency components. ;

[0021] Step 3: Combining the preprocessed data, construct an end-to-end prediction path using low-frequency components and an autoregressive prediction path using high-frequency components, and fuse them to obtain the mapping relationship between historical time windows and future target states.

[0022] The low-frequency path expression is:

[0023]

[0024] Where h represents the historical input length and f represents the prediction step size. This represents an end-to-end prediction model;

[0025] These represent historical sea surface temperature, sea surface height, and sea surface wind field information for a consecutive h time periods.

[0026] The high-frequency path expression is:

[0027]

[0028]

[0029] in, This represents an autoregressive prediction model, where k represents the number of times the data has been regressed by the model.

[0030] The prediction results of the low-frequency path and the high-frequency path are fused to obtain the three-dimensional temperature and salinity field prediction results for the next f time steps. The calculation formula is as follows:

[0031]

[0032] This indicates that the temperature-salinity field at time t is subjected to Gaussian filtering.

[0033] Step 4: Construct a Gaussian-filtered dual-path neural network, GDP-Net, consisting of an end-to-end prediction branch and an autoregressive prediction branch;

[0034] The end-to-end prediction branch consists of a 2D encoder, a Trans-Conv module, a 3D encoder, a 3D decoder, and a dual-path multi-scale global spatiotemporal attention module (DMG-STA).

[0035] The autoregressive prediction branch consists of a 2D encoder, a 2D decoder, and a dual-channel gated attention module (DCG-A).

[0036] The specific principles behind GDP-Net are as follows:

[0037] First, the end-to-end prediction branch performs predictions on low-frequency three-dimensional temperature and salinity data, specifically as follows:

[0038] Step 401: The preprocessed multi-source sea surface feature data and three-dimensional temperature, salinity and low-frequency data are processed through 2D coding structure and 3D coding structure respectively. The multi-source sea surface feature features are extracted and transformed by the Trans-Conv module to be unified to the same five dimensions as the three-dimensional temperature, salinity and low-frequency data. They are then sent to the two gated attention branches of the dual-path multi-scale global spatiotemporal attention module (DMG-STA) for feature fusion.

[0039] Step 402: Each branch undergoes feature normalization and channel mapping sequentially using BatchNorm 3D and PW Conv 3D to obtain its corresponding features. ;

[0040] The formula is expressed as:

[0041] in, and This represents the feature input of multi-source sea surface data and three-dimensional temperature and salinity data; BN3D represents the feature normalization function; PWConv3D is a 3D convolution function with a convolution sum of 1;

[0042] Step 403: The two features enter the dual-gated attention module DG-A to enhance the features of the multi-source sea surface data and the three-dimensional temperature and salinity features respectively;

[0043] The formulas for calculating the dual-gated features g1 and g2 after DG-A are:

[0044]

[0045] Enhanced output is:

[0046]

[0047]

[0048] Step 404: Enhance the dual-gated features and Multi-scale features are obtained by fusing multiple scale MLPs. ;

[0049] First, two-way features and First, the channel transformation is completed through PW Conv 3D, and then it enters the MSDW-Conv 3D module for multi-scale three-dimensional depth convolution modeling.

[0050] Subsequently, nonlinear mapping and channel integration are performed using the GELU activation function and PW Conv 3D, and then combined with the original features. and Fusion yields multi-scale features ;

[0051] The formula is expressed as:

[0052] +

[0053] Step 405: Combine the fused multi-scale features Entering the global spatiotemporal attention modeling stage, the output of DMG-STA is obtained. The fused features will be used to reconstruct the low-frequency three-dimensional temperature and salinity features for the next n consecutive days using a 3D decoder.

[0054] The global spatiotemporal attention modeling process involves transforming the five-dimensional features (B, C, L', H', W') into (B, P, N, D) through a Rearrange operation. This is followed by a multi-head attention mechanism, and the output is then restored to (B, C, L', H', W') through a Linear layer and another Rearrange operation. Finally, channel integration and local spatial information supplementation are performed using PW Conv 3D to obtain the final output of DMG-STA.

[0055]

[0056] in,

[0057]

[0058] Then, the autoregressive prediction branch performs predictions on high-frequency three-dimensional temperature and salinity data, specifically:

[0059] Step 406: The high-frequency three-dimensional temperature and salinity data is first processed by a 2D encoder to obtain high-frequency features. , will feature First, the data is normalized and channel-mapped using BatchNorm 2D and PW Conv 2D, then it enters the DCG-A dual-path attention mechanism to output features. :

[0060] In the dual-path attention mechanism, one path uses the multi-head attention mechanism in Transformer to establish global spatial relationships between patches; the other path uses a large-kernel convolutional gating structure.

[0061] The expression is:

[0062]

[0063] GELU is the activation function, and DCG-A represents the dual-path attention module.

[0064] Step 407, Global Attention Features The input enters the MSDW-Conv 2D multi-scale convolution module, and then undergoes nonlinear mapping and feature fusion via GELU and PWConv 2D to output the features. :

[0065]

[0066] Step 408: Output features After restoring the high-frequency three-dimensional temperature and salinity features using a 2D decoder, the changes in the high-frequency three-dimensional temperature and salinity features over the next n consecutive days are predicted using an autoregressive prediction method.

[0067] n takes the value of an integer within the range of computing power support and data support;

[0068] Finally, the high-frequency 3D temperature and salinity data predicted by the end-to-end branch for n days and the low-frequency 3D temperature and salinity data predicted by the autoregressive branch are added together to perform feature fusion and reconstruct the 3D temperature and salinity field for the next n consecutive days.

[0069] Step 5: Train the Gaussian-filtered dual-path neural network GDP-Net using the training set;

[0070] First, the initial 3D temperature and salinity field of the training data is decomposed by Gaussian filtering to obtain low-frequency background components and high-frequency detail components; and then the 3D temperature and salinity reanalysis label data corresponding to the future time step is set.

[0071] Then, the low-frequency background component is input into the end-to-end prediction path, and the high-frequency detail component is input into the autoregressive prediction path. The prediction results are fused to obtain the complete three-dimensional temperature and salinity field prediction results, which are then compared with the corresponding three-dimensional temperature and salinity reanalysis label data.

[0072] The loss function is used to simultaneously calculate the numerical reconstruction error and spatial gradient error between the model's prediction results and the labeled data. Based on the calculation results of the loss function, the error is backpropagated to each network layer of the model, and the Adam optimizer is used to iteratively update the model parameters.

[0073] Step 6: Input the initial three-dimensional temperature and salinity field, as well as the sea surface temperature, sea surface height anomaly, and sea surface wind field data for n consecutive days, into the trained GDP-Net model to reconstruct the spatiotemporal prediction results of the ocean's three-dimensional temperature and salinity field for the next n consecutive days.

[0074] The GDP-Net model first decomposes the temperature and salinity field into high- and low-frequency information using Gaussian filtering. Then, it predicts the background changes of the ocean temperature and salinity field through the low-frequency path and the local detailed changes through the high-frequency path, and then superimposes the prediction results of the two paths.

[0075] The advantages of this invention are:

[0076] (1) This invention achieves decoupling of high- and low-frequency spatial information of the three-dimensional temperature-salinity field based on Gaussian filtering, and constructs a dual-path spatiotemporal prediction framework by using autoregressive prediction and end-to-end prediction respectively. Among them, the low-frequency path maintains the long-term evolution trend and overall stability of the low-frequency temperature-salinity field, while the high-frequency path enhances the ability to characterize local details and small-scale dynamic processes, thereby improving prediction accuracy and alleviating the problems of fuzziness and smoothing in the mid-to-late stage of prediction.

[0077] (2) The present invention designs a multi-source element fusion spatiotemporal prediction neural network, which comprehensively utilizes multi-source sea surface observation information such as sea surface temperature, sea surface height and climate state over n historical days, learns the nonlinear coupling relationship between multi-source sea surface elements and the three-dimensional temperature and salinity field of the ocean, enhances the model's ability to express the evolution of complex ocean spatiotemporal structure and cross-scale dynamic processes, and thus further improves the prediction accuracy of the three-dimensional temperature and salinity field of the ocean.

[0078] (3) This invention reduces the modeling complexity of the original ocean field by Gaussian filtering decomposition, so that different prediction paths only need to focus on the dynamic evolution characteristics within a specific frequency range, which helps to reduce the interference of high-frequency disturbances on long-term prediction stability and enhances the model's ability to learn spatiotemporal change characteristics. Attached Figure Description

[0079] Figure 1 This is a flowchart of a spatiotemporal prediction method for three-dimensional marine temperature and salinity fields based on Gaussian filtering according to the present invention.

[0080] Figure 2 The spatial weight distribution variation of the Gaussian kernel in this invention corresponds to different smoothing scales;

[0081] Figure 3 This is a structural diagram of the GDP-Net model of the present invention;

[0082] Figure 4 This is the core module unit in the GDP-Net model of this invention; Detailed Implementation

[0083] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0084] This invention proposes a spatiotemporal prediction method for three-dimensional ocean temperature and salinity fields based on Gaussian filtering, using an artificial intelligence algorithm. It employs a dual-path prediction model, GDP-Net (Gaussian Decomposition Dual-path Prediction Network), to improve the accuracy of three-dimensional ocean temperature and salinity field prediction while preserving local high-frequency detail information in the prediction results as much as possible. Specifically, GDP-Net decomposes the original three-dimensional temperature and salinity field into low-frequency background signals and high-frequency detail signals using Gaussian filtering, and constructs corresponding prediction paths based on the different frequency components of the two types of signals. The low-frequency path integrates multi-source sea surface spatiotemporal observation information to predict dominant ocean state changes in an end-to-end manner; the high-frequency path uses an autoregressive approach to characterize the continuous evolution of local detail information. Finally, the prediction results of the two paths are combined to obtain a complete three-dimensional temperature and salinity field prediction result. In application, the initial three-dimensional temperature and salinity field and multi-source sea surface observation data for n consecutive days are input into the trained GDP-Net model to achieve spatiotemporal prediction of the ocean's three-dimensional temperature and salinity field for the next n consecutive days. This method can effectively integrate multi-source sea surface information with three-dimensional temperature, salinity and structural features, improving prediction accuracy while enhancing the ability to characterize local details, thus providing technical support for intelligent forecasting of the marine environment and analysis of marine dynamic processes.

[0085] like Figure 1 As shown, the specific steps are as follows:

[0086] Step 1: Collect and construct the multi-source sea surface observation data and the three-dimensional ocean temperature and salinity dataset required for the experiment; perform preprocessing and then divide the training set;

[0087] The multi-source sea surface data includes information such as sea surface temperature, sea surface height anomalies, and sea surface wind fields.

[0088] Subsequently, bilinear interpolation was performed on the multi-source sea surface observation data to ensure that it maintained the same spatial resolution as the three-dimensional temperature and salinity data, and preprocessing operations such as default value replacement were performed on all collected data.

[0089] Finally, a training dataset is constructed using a windowed data partitioning method to provide a data foundation for model training.

[0090] Step 2: Targeting the three-dimensional temperature and salinity field of the ocean under continuous time steps Gaussian filtering is used to perform frequency decomposition at each time point to obtain the corresponding high and low frequency components.

[0091] To address the issue of mixed large-scale background variations and local detail variations in the three-dimensional temperature-salinity field of the ocean, a Gaussian filtering method is employed to perform spatial frequency decomposition on the initial three-dimensional temperature-salinity field, yielding low-frequency background signals and high-frequency detail signals. The low-frequency signals are used to characterize the ocean background field, stratification structure, and slowly varying dynamic processes; the high-frequency signals are used to characterize fronts, vortex boundaries, local anomalies, and small-scale rapidly changing structures. This decomposition method reduces mutual interference between information at different scales, providing clearer input features for subsequent dual-path prediction.

[0092] Let the three-dimensional temperature-salinity field of the ocean at continuous time steps be defined as:

[0093]

[0094] in, , and These represent the spatial dimensions of latitude, longitude, and depth, respectively, while t represents time.

[0095] Since the three-dimensional temperature-salinity field of the ocean contains both high- and low-frequency spatial information at different scales of variation, Gaussian filtering is first used to perform frequency decomposition on the initial three-dimensional temperature-salinity field at time t:

[0096]

[0097] This represents the low-frequency component obtained after Gaussian filtering, which mainly describes the background field and the slowly varying process; Representing high-frequency components, through It is used to characterize local details, small-to-medium scale dynamic structures, and rapidly changing information.

[0098] The Gaussian filtering algorithm can be expressed as follows: For any position (i, j) in two-dimensional space, its low-frequency component can be represented as a neighborhood weighted normalization result:

[0099]

[0100] The Gaussian weighting function is defined as follows:

[0101]

[0102] In the formula, (i, j) represents the position of the center grid point to be filtered; m and n represent the offsets relative to the center grid point in the latitudinal and longitudinal directions, respectively, that is, the position of the neighboring grid point is (i+m, j+n). This represents the weighting coefficient of the offset position (m, n) with respect to the center grid point; σ is the standard deviation of the Gaussian kernel, used to control the filtering scale and determine the spatial influence radius of the smoothing range. When When the value is increased, the filtering result is smoother, corresponding to a stronger low-pass characteristic; when When reduced, there is a greater tendency to preserve local structures. For example... Figure 2 The diagram shows the Gaussian kernel at σ = 0, 2, and 5, and illustrates the changes in spatial weight distribution corresponding to different smoothing scales. It can be seen from the diagram that when σ = 0, no Gaussian smoothing is performed, and the original field is used directly as input information, which can serve as a baseline for direct prediction or no-decomposition conditions. As σ increases, the smoothing scale becomes larger, and the corresponding low-pass characteristics become stronger.

[0103] Step 3: Combining the preprocessed data, construct an end-to-end prediction path using low-frequency components and an autoregressive prediction path using high-frequency components. Combine the initial temperature and salinity information and multi-source sea surface observation elements to obtain the mapping relationship between historical time windows and future target states.

[0104] To address the dynamic characteristics of different frequency components, a dual-path prediction strategy is adopted: the low-frequency component uses an end-to-end approach to fuse multi-source sea surface information to maintain the long-term evolution stability of the background field; the high-frequency component uses an autoregressive approach to characterize continuous changes in local details, thereby enhancing the ability to express small- and medium-scale dynamic structures. Finally, by fusing the high- and low-frequency prediction results, a complete prediction of the future three-dimensional ocean temperature and salinity field is achieved, thereby improving prediction accuracy and mitigating the problems of fuzziness and smoothing in the prediction results.

[0105] The low-frequency path expression is:

[0106]

[0107] Where h represents the historical input length and f represents the prediction step size. This represents an end-to-end prediction model;

[0108] These represent historical sea surface temperature, sea surface height, and sea surface wind field information for a consecutive h time periods.

[0109] High-frequency paths employ an autoregressive prediction strategy, using a stepwise recursive approach to predict rapidly changing local high-frequency spatial information.

[0110]

[0111]

[0112] in, This represents an autoregressive prediction model, where k represents the number of times the data has been regressed by the model.

[0113] The prediction results of the low-frequency path and the high-frequency path are fused to obtain the three-dimensional temperature and salinity field prediction results for the next f time steps. The calculation formula is as follows:

[0114]

[0115] This indicates that the temperature-salinity field at time t is subjected to Gaussian filtering.

[0116] Step 4: Construct a Gaussian-filtered dual-path neural network, GDP-Net, consisting of an end-to-end prediction branch and an autoregressive prediction branch, which are composed of multi-source data fusion.

[0117] like Figure 3 As shown, several key modules in the GDP-Net model are illustrated.

[0118] The end-to-end prediction branch consists of a 2D encoder, a Trans-Conv module, a 3D encoder, a 3D decoder, and a dual-path multi-scale global spatiotemporal attention module (DMG-STA). It is used to model the spatiotemporal coupling relationship between the 3D temperature and salinity field and multi-source remote sensing observation information, enabling end-to-end prediction of low-frequency varying 3D fields. Its feature dimensions can be expressed as (B, T, L, H, W), where B represents the batch size, T represents the time series length, L represents the depth layer number, and H and W represent the latitudinal and meridional grid sizes, respectively.

[0119] The autoregressive prediction branch consists of a 2D encoder, a 2D decoder, and a multi-scale global attention module (MG-STA); its overall structure is similar to that of the end-to-end prediction branch, but it differs in convolutional dimension and decoding method.

[0120] The input to the autoregressive branch contains only high-frequency temperature and salinity information at a single time step. Its main task is to characterize the spatial variation features at different depths, with feature dimensions of (B, L, H, W). Compared to the three-dimensional spatiotemporal structure (B, T, L, H, W), it does not involve multi-time step information modeling. Therefore, this branch of research uses multi-channel 2D convolution for encoding, decoding, and decoding to transform the predicted content into multi-channel spatial variation modeling.

[0121] In terms of overall functionality, the encoder is used for deep feature extraction from the input data, while the decoder is responsible for restoring the high-dimensional features to the spatial resolution of the target data. The DMG-STA module is mainly used for the fusion modeling of 3D temperature and salinity field and multi-source remote sensing observation data, and can simultaneously capture local spatial structure, vertical variation features, and long-distance dependencies. The MG-STA module focuses on enhancing the model's ability to globally correlate high-frequency temperature and salinity structures and to represent local multi-scale details, thereby improving the capture effect of small-scale perturbation information.

[0122] Furthermore, the Dual-Gated Attention Module (DG-A), Dual-Path Gated Attention Module (DCG-A), and Multi-Scale Depthically Separable Convolutional Module (MSDW-Conv 3D) further enhance the model's ability to model multi-scale spatial structures, dependencies between variables, and complex ocean dynamic features. The Trans-Conv module is used to map two-dimensional sea surface spatial features to a three-dimensional feature space, thereby achieving efficient fusion of multi-source sea surface feature features and three-dimensional temperature and salinity field features.

[0123] Specifically as follows:

[0124] (a) Encoder and Decoder

[0125] The encoder is used to extract features from the input data; in this embodiment, the encoder consists of two stacked coding blocks, each of which includes a convolutional layer, a grouped normalization layer, and a SiLU activation function. Depending on the form of the input data, both a 3D encoder and a 2D encoder are designed for the model.

[0126] The input dimensions of the 3D encoder are (B, T, L, H, W), which are mainly used to extract the spatiotemporal distribution features of the three-dimensional temperature-salinity field under continuous time steps. The output results are used as the input for the subsequent spatiotemporal fusion and transformation of the DMG-STA module.

[0127] The input dimension of the 2D encoder is (B, L, H, W). Since the autoregressive high-frequency prediction branch only inputs high-frequency temperature and salt information of a single time step each time and does not involve temporal modeling of multiple time steps, this branch uses 2D convolution to extract horizontal spatial features at different depth layers.

[0128] The 2D encoder maintains the same basic structure as the 3D encoder, with the main difference being the replacement of 3D convolution with 2D convolution. After encoding, the output of the 2D encoder is used by the MG-STA module to enhance the modeling of high-frequency spatial features.

[0129] The decoder is used to restore the high-dimensional features after spatiotemporal transformation to the spatial resolution of the target data. Similar to the encoder, the decoder is also composed of two stacked decoding blocks. It mainly receives the feature output from the DMG-STA or MG-STA module and gradually restores the data size.

[0130] The 3D decoder is used for the end-to-end low-frequency prediction branch, and finally outputs the three-dimensional temperature-salinity field for multiple future time steps; the 2D decoder is used for the autoregressive high-frequency prediction branch, and finally outputs the high-frequency temperature-salinity field for a single time step.

[0131] In the 3D decoder, this embodiment further introduces a spatiotemporal adjustment mechanism, Conv-FC, to enhance the model's ability to express multi-step spatiotemporal changes. Specifically, the features generated by the decoder are first processed by convolution with a kernel of 1 to adjust channel and spatiotemporal information, then normalized by Layernorm, and nonlinearly transformed by Tanh activation function. Subsequently, a Linear layer is used separately for the time dimension to perform nonlinear mapping of the temporal dimension T.

[0132] The core function of this mechanism is to establish the spatiotemporal relationship between multi-source remote sensing observation information and the future three-dimensional temperature and salinity field, thereby enhancing the model's ability to express the nonlinear evolution of the temperature and salinity field under different prediction step sizes.

[0133] The 2D decoder primarily focuses on local detail recovery of high-frequency components. Since high-frequency components contain significant information about frontal boundaries, local anomalies, and small-scale perturbations, ordinary linear interpolation can easily smooth out structural details. Therefore, this embodiment employs a pixel reshaping method instead of linear interpolation in the 2D decoder to improve the recovery capability of small-scale spatial structures. Furthermore, since the autoregressive high-frequency branch does not involve multi-step temporal prediction, the Conv-FC operation used in the 3D decoder for multi-step spatiotemporal modeling is removed from the 2D decoder.

[0134] Overall, the 3D encoder and decoder are mainly used for the end-to-end low-frequency prediction branch, focusing on modeling the spatiotemporal mapping relationship between the 3D temperature and salinity field and multi-source remote sensing observation information at continuous time steps; the 2D encoder and decoder are mainly used for the autoregressive high-frequency prediction branch, focusing on extracting and restoring local spatial details in high-frequency temperature and salinity signals. Both maintain a consistent basic coding structure, but are differentiated in convolution dimension, decoding method, and spatiotemporal transformation mechanism according to the different requirements of low-frequency background evolution and high-frequency detail restoration.

[0135] (b) Trans-conv

[0136] The feature evolution module (Trans-conv) primarily transforms multi-source sea surface data features (B, C, H, W) into three-dimensional temperature and salinity data features (B, C', L, H, W). The principle is to generate depth layer information from channel information through two-dimensional convolution, transforming the original (B, C, H, W) into (B, C'×L, H, W). Then, the depth information is separated from the channels to obtain (B, C', L, H, W), which is then activated by Groupnorm and SiLU. Here, C represents the number of channels in the multi-source sea surface data feature, L represents the depth layer, and C' represents the number of channels matching the three-dimensional temperature and salinity data feature.

[0137] (c) DMG-STA

[0138] The DMG-STA module is used to achieve fusion modeling and spatiotemporal relationship transformation between the spatiotemporal characteristics of multi-source sea surface elements and 3D temperature and salinity field characteristics. By progressively enhancing the fusion expression capability of remote sensing features and 3D temperature and salinity features through dual-gated attention, multi-scale MLP fusion, and multi-head attention, it simultaneously establishes local structure, multi-scale spatial relationships, and global spatiotemporal dependencies.

[0139] Before entering this module, the two types of features are unified to the same dimension through encoding structure and dimensional transformation, represented as (B, C, L', H', W'). The module first feeds the spatiotemporal features of multi-source sea surface elements and the three-dimensional temperature and salinity features into two parallel gated attention branches. Each branch is then processed by BatchNorm 3D and PW Conv 3D (ordinary convolution with a kernel of 1) for feature normalization and channel mapping. This process does not change the spatial scale of the features, and the output remains (B, C, L', H', W').

[0140] Subsequently, the two feature streams enter the dual-gated attention module DG-A. This module expands the spatial receptive field through large-kernel convolution and generates adaptive weights using a gating mechanism to enhance the features of multi-source sea surface data and the 3D temperature and salinity features, respectively. For the remote sensing branch, large-kernel convolution helps capture large-scale spatial variations in sea surface variables such as SST, SLA, and SSW; for the 3D temperature and salinity branch, this structure can enhance information such as vertical stratification, thermocline changes, and local anomaly structures. After gating modulation, the spatiotemporal information of the data is highlighted, redundant features are suppressed, and the dimensions of its output features remain (B, C, L', H', W'). This part is expressed by the formula:

[0141]

[0142]

[0143] in, and This represents the feature input from multi-source sea surface data and 3D temperature and salinity data. BN3D represents the feature normalization function BatchNorm 3D; PWConv3D is a 3D convolution function with a convolution sum of 1; DG-A is a dual-gated attention module; g1 and g2 are dual-gated features passed through DG-A.

[0144] The output of the attention structure can then be expressed as:

[0145]

[0146]

[0147] After completing the dual-gating enhancement, and The features are further fused using a multi-scale MLP.

[0148] Specifically, the features are first transformed using PW Conv 3D, and then entered into the MSDW-Conv 3D module for multi-scale 3D depth convolution modeling. This process can extract local details and large-scale spatial context information under different receptive fields, thus simultaneously representing the background field structure at multiple scales. Afterwards, the features undergo nonlinear mapping and channel integration using the GELU activation function and PWConv 3D to obtain a fused multi-scale feature representation, thereby establishing a multi-scale nonlinear coupling relationship between sea surface remote sensing observations and subsea 3D temperature and salinity structures. This part can be expressed by the following formula:

[0149] +

[0150] Finally, the fused features Entering the global spatiotemporal attention modeling stage.

[0151] The module first transforms the five-dimensional features from (B, C, L', H', W') to (B, P, N, D) using a Rearrange operation. Then, a multi-head attention mechanism further models the global dependencies between different times, depths, and spatial locations, enabling the model to capture large-scale background evolution, mesoscale perturbation propagation, and long-distance connections between different spatial locations. The attention output is then restored to (B, C, L', H', W') through a Linear layer and a Rearrange operation. Finally, PWConv 3D is used for channel integration and local spatial information supplementation to obtain the final output of DMG-STA.

[0152] Overall, DMG-STA enhances the fusion and representation capabilities of remote sensing features and 3D temperature and salinity features through dual-gated attention, multi-scale MLP fusion, and multi-head attention, thereby simultaneously establishing local structure, multi-scale spatial relationships, and global spatiotemporal dependencies. This part can be expressed by the following formula:

[0153]

[0154] in,

[0155]

[0156] (d) MG-STA

[0157] The MG-STA module is designed primarily for feature enhancement of high-frequency temperature and salinity signals obtained through Gaussian filtering.

[0158] High-frequency components include fronts, vortex boundaries, local anomalies, and small-scale rapidly changing structures, resulting in more dramatic spatial variations. Therefore, it is necessary to capture both local details and spatial correlations over a larger area.

[0159] After the high-frequency data feature F is output from the encoding structure, the data dimension remains (B, C, H', W'). Before entering this module, the data feature is first normalized and channel-mapped by BatchNorm 2D and PW Conv 2D to make the feature distribution more stable. Then it enters the DCG-A dual-path attention mechanism: one path uses the multi-head attention mechanism in Transformer to establish global spatial associations between patches, enhancing the model's ability to express long-distance grid relationships; the other path uses a large-kernel convolutional gating structure, expands the receptive field through DW-Conv and dilated depth convolution to capture continuous spatial relationships between adjacent grids and over a larger range, and highlights key regions and suppresses redundant perturbations through Sigmoid gating. Finally, the output dimension remains (B, C, H', W').

[0160] These two pathways are complementary. Multi-head attention models the relationships between corresponding grids in the global patch, but it lacks detail in depicting local continuity and the overlapping regions of adjacent blocks. Large-kernel convolution, on the other hand, can supplement the spatial continuity within the grid neighborhood and the correlation of local structural overlap. Combining the two, the module can establish global spatial connections for high-frequency signals while preserving local spatial connections between blocks. This part can be expressed by the following formula:

[0161]

[0162] GELU is the activation function, DCG-A represents the dual-path attention module, F represents the high-frequency data features of the encoder output, DCG-A represents the dual-path attention module, and Fa represents the dual-path attention output.

[0163] Subsequently, global attention features The module then enters the MSDW-Conv 2D multi-scale convolution module. This module extracts multi-receptive field features through depthwise convolutions at different scales. Small-scale branches are used to capture frontal boundaries and local disturbances, while large-scale branches are used to perceive a wider range of spatial background. Finally, GELU and PW Conv 2D are used to complete nonlinear mapping and feature fusion, enhancing the representation of high-frequency spatial features. The final output features can be expressed as:

[0164]

[0165] BN2D stands for Batchnorm2D; MSDWConv2D stands for Multi-Scale Convolutional Module; GELU stands for Activation Function; Fout stands for Output Feature;

[0166] Step 5: Input the preprocessed training dataset into the GDP-Net model for training;

[0167] First, training data is constructed, including multi-source sea surface feature data, three-dimensional temperature and salinity initial field, low-frequency background components and high-frequency detail components obtained by Gaussian filtering decomposition, and three-dimensional temperature and salinity reanalysis label data corresponding to future time steps.

[0168] Then, during the training process, the low-frequency background component is input into the end-to-end prediction path to fuse multi-source sea surface element information and predict the low-frequency three-dimensional temperature and salinity background field at future time steps; the high-frequency detail component is input into the autoregressive prediction path to progressively predict the high-frequency local detail field at future time steps.

[0169] Subsequently, the low-frequency prediction results and high-frequency prediction results are fused to obtain a complete three-dimensional temperature and salinity field prediction result, which is then compared with the corresponding three-dimensional temperature and salinity reanalysis label data.

[0170] The loss function simultaneously calculates the numerical reconstruction error and spatial gradient error between the model's predictions and the labeled data. The main loss function uses mean squared error (MSE) to constrain the overall prediction accuracy, while the spatial gradient error constrains the horizontal and vertical gradient structures of the temperature-salinity field to reduce over-smoothing and local structural distortion. Based on the loss function calculation results, the error is backpropagated to each network layer of the model, and the Adam optimizer is used to iteratively update the model parameters.

[0171] Step 6: Input the three-dimensional initial temperature and salinity field, as well as the sea surface temperature, sea surface height anomaly, and sea surface wind field data for n consecutive days, into the trained GDP-Net model for prediction.

[0172] First, the temperature and salinity field is decomposed into high- and low-frequency information through Gaussian filtering. Then, the background changes of the ocean temperature and salinity field are predicted by the low-frequency path and the local detailed changes are predicted by the high-frequency path. The prediction results of the two paths are superimposed to restore the spatiotemporal prediction results of the ocean three-dimensional temperature and salinity field for the next n consecutive days.

[0173] Example:

[0174] Step 1: Collect multi-source sea surface information and ocean three-dimensional reanalysis temperature and salinity datasets required for the experiment through internationally available public data websites.

[0175] The experiment used 16 years of satellite remote sensing data from 2007 to 2022, along with reanalysis data, as the dataset. It combined historical data on sea surface temperature, sea surface height anomalies, and sea surface wind speed over 10 consecutive days as multi-source sea surface data. The current day's 3D temperature-salinity reanalysis field served as the initial 3D temperature-salinity field, and these were used as the input dataset. The label dataset consisted of reanalysis data from layers 1-32 over the next 10 consecutive days. A sliding window approach was used for data partitioning. Before partitioning, the input and label data underwent max-min normalization. The input sea surface features were partitioned into (B, T, C, H, W) forms, while the initial 3D data and label data were partitioned into (B, T, C, L, H, W) forms, where B is the batch size, C is the number of variables, L is the ocean depth layer, H and W correspond to the number of grid points in the remote sensing data at the studied latitude and longitude, and H and W correspond to the number of grid points in the reanalysis data at the studied latitude and longitude. After splitting, 70% is used as the training set, 20% as the validation set, and 10% as the test set for testing.

[0176] Step 2: Based on the idea of ​​Gaussian filtering decomposition, the three-dimensional temperature-salinity initial field is decomposed by Gaussian filtering to obtain low-frequency background signals and high-frequency detail signals. Combining artificial intelligence algorithms such as convolutional neural networks, Transformers and large kernel gating attention mechanisms, a dual-path prediction model GDP-Net based on Gaussian filtering decomposition is constructed.

[0177] Based on the different characteristics of low-frequency background signals and high-frequency detail signals, the model designs low-frequency prediction paths and high-frequency prediction paths respectively. The low-frequency path is used to fuse multi-source sea surface spatiotemporal information such as sea surface temperature, sea surface height anomalies, and sea surface wind fields to predict dominant ocean state changes in an end-to-end manner; the high-frequency path is used to characterize the continuous evolution of local high-frequency detail information using an autoregressive approach.

[0178] Based on multi-source sea surface element data and ocean 3D temperature and salinity reanalysis data, a dual-path ocean 3D temperature and salinity field spatiotemporal prediction model, GDP-Net, based on Gaussian filter decomposition, is constructed. This model first decomposes the 3D temperature and salinity field into low-frequency background signals and high-frequency detail signals using Gaussian filtering. Then, based on the dynamic characteristics of the two types of signals, a low-frequency end-to-end prediction path and a high-frequency autoregressive prediction path are constructed respectively. Finally, the prediction results of the two paths are superimposed to obtain the 3D temperature and salinity field prediction results for future continuous time steps.

[0179] The GDP-Net model takes as input a 3D initial temperature and salinity field, multi-source sea surface element data, and sea surface driving information for future continuous time steps. First, Gaussian filtering is used to decompose the 3D temperature and salinity field into high- and low-frequency components. The low-frequency component mainly represents the large-scale background field and slowly varying dynamic processes, while the high-frequency component mainly represents local small-scale changes, frontal structures, vortex boundaries, and complex dynamic disturbances. To address the different characteristics of the low-frequency and high-frequency signals, GDP-Net constructs separate low-frequency and high-frequency prediction branches. The low-frequency prediction branch integrates multi-source sea surface information such as sea surface temperature, sea surface height anomalies, and sea surface wind fields, predicting the background state evolution of the 3D temperature and salinity field in an end-to-end manner. The high-frequency prediction branch does not introduce additional multi-source sea surface information but instead uses an autoregressive approach to predict based on the decomposed historical high-frequency temperature and salinity signals. Finally, the model adds the low-frequency and high-frequency prediction results to form a complete spatiotemporal prediction of the ocean's 3D temperature and salinity field.

[0180] The low-frequency end-to-end prediction branch is primarily used to predict the large-scale background state evolution of the 3D temperature and salinity field. This branch is based on the low-frequency 3D temperature and salinity initial field and integrates multi-source sea surface element information such as sea surface temperature, sea surface height anomalies, and sea surface wind fields. First, a 2D encoder extracts the spatial features of the multi-source sea surface data, and the Trans-Conv module maps these 2D features to a 3D feature space. Simultaneously, a 3D encoder extracts the spatiotemporal structural features of the low-frequency 3D temperature and salinity field. Then, a dual-path, multi-scale global spatiotemporal attention module, DMG-STA, is used to fuse and model the multi-source sea surface features and 3D temperature and salinity features, capturing the coupling relationship between sea surface processes and subsea temperature and salinity structures. Finally, a 3D decoder outputs the predicted low-frequency 3D temperature and salinity background field for multiple future time steps.

[0181] The high-frequency autoregressive prediction branch is primarily used to predict the continuous evolution of local high-frequency details. Since high-frequency signals typically correspond to complex dynamic processes such as frontal propagation, vortex boundaries, local anomalies, and small-scale disturbances, which are difficult to capture completely directly from sea surface remote sensing observations, this branch does not introduce additional multi-source sea surface elements. Instead, it uses historical high-frequency temperature and salinity signals as input and iteratively extrapolates high-frequency changes for future time steps through an autoregressive approach. This branch employs a two-dimensional encoder to extract horizontal spatial features at different depth layers and enhances the model's ability to express local details and global spatial correlations through the multi-scale global attention module MG-STA. Finally, a two-dimensional decoder is used to recover the spatial structure of the high-frequency temperature and salinity field, thereby improving the model's ability to preserve small-scale details and local disturbances.

[0182] GDP-Net introduces different attention enhancement structures in its low-frequency and high-frequency branches. In the low-frequency branch, the DMG-STA module fuses multi-source sea surface features and 3D temperature and salinity field features, capturing local spatial structure, vertical variation characteristics, and long-distance spatiotemporal dependencies through gated attention, multi-scale convolution, and global spatiotemporal attention mechanisms. In the high-frequency branch, the MG-STA module primarily targets high-frequency temperature and salinity signals, enhancing the model's ability to characterize frontal boundaries, local anomalies, small-scale disturbances, and global spatial connections through multi-head attention mechanisms and large-kernel gated convolution structures. These modules improve the model's ability to represent ocean dynamic characteristics at different scales.

[0183] The low-frequency prediction branch generates low-frequency temperature and salinity field predictions for future consecutive time steps using a 3D decoder, while the high-frequency prediction branch generates high-frequency temperature and salinity field predictions for future time steps progressively using a 2D decoder. To reduce the smoothing problem of high-frequency details during the restoration process, the high-frequency branch uses pixel reshaping for spatial restoration to enhance the ability to restore local structures.

[0184] Finally, the low-frequency background field prediction results are added to the high-frequency detail field prediction results to obtain the complete three-dimensional ocean temperature and salinity field prediction results for multiple consecutive time steps in the future. This dual-path fusion mechanism can improve the model's ability to predict local high-frequency structures and complex dynamic disturbances while maintaining the long-term evolution stability of the background field.

[0185] like Figure 4 As shown, the dual-path spatiotemporal prediction framework GDP-Net first uses Gaussian filtering to decouple high- and low-frequency spatial information of the three-dimensional ocean temperature-salinity field. The low-frequency components mainly characterize the large-scale background field and slowly varying dynamic processes, while the high-frequency components reflect local small-scale rapid changes, frontal structures, and complex dynamic disturbances. To address the issue of differentiated dynamic characteristics across different frequency components, this paper designs corresponding spatiotemporal prediction paths for each.

[0186] For low-frequency spatial signals, which primarily describe the evolution of the ocean background field and typically exhibit strong stationarity and predictability, an end-to-end prediction approach is employed for modeling. This path uses the low-frequency components of the historical 3D temperature and salinity field as the initial state and integrates multi-source sea surface remote sensing observation information such as SST, SLA, and SSW-U / V. A multi-source element fusion prediction network is used to establish a coupled mapping relationship between sea surface information and subsea temperature and salinity structure, enabling the prediction of the future multi-timestep 3D temperature and salinity field background state. The introduction of multi-source sea surface observation information in the low-frequency path is due to the limitations of current ocean observation systems' spatial resolution and detection capabilities. Sea surface remote sensing information more readily reflects large-scale ocean state changes and can better characterize the statistical correlation between sea surface processes and the subsea background field, thus providing effective spatiotemporal information for low-frequency background state prediction.

[0187] In contrast, high-frequency spatial signals typically correspond to rapidly changing local small-scale processes, whose evolution is more controlled by local nonlinear hydrodynamic processes, including vortex boundaries, frontal propagation, and local topographic structures. However, due to limitations in current observation resolution, these high-frequency dynamic details, such as mesoscale or sub-mesoscale local boundary changes, are difficult to capture directly from sea surface remote sensing observations and can currently only be simulated through boundary adjustment and hydrodynamic equations.

[0188] Therefore, instead of introducing additional multi-source sea surface observation information into the high-frequency prediction path, an autoregressive prediction method is adopted, which gradually extrapolates the local spatiotemporal evolution characteristics based on historical high-frequency temperature and salinity signals. This enhances the model's ability to characterize small- and medium-scale dynamic processes and detailed structures, and alleviates the fuzziness and smoothing problems that easily occur in the mid-to-late stages of end-to-end prediction.

[0189] Finally, GDP-Net fuses the predictions of high- and low-frequency paths to obtain a complete three-dimensional ocean temperature and salinity field prediction for future time steps. This framework can improve the model's ability to represent local detailed structures and high-frequency dynamic processes while maintaining the long-term evolution stability of the background field, thus balancing overall prediction accuracy with spatial detail preservation.

[0190] Step 3: Train the GDP-Net model using the constructed multi-source sea surface feature data, the three-dimensional temperature and salinity initial field decomposition results, and the ocean three-dimensional reanalysis temperature and salinity training dataset.

[0191] The model training process specifically includes:

[0192] The completed training dataset is input into the 3D temperature and salinity field spatiotemporal prediction model GDP-Net. The model is used to predict the 3D temperature and salinity field at future time steps, and the prediction results are compared with the corresponding 3D temperature and salinity reanalysis label data.

[0193] During training, the loss function simultaneously calculates the numerical reconstruction error and spatial gradient error between the model's predictions and the labeled data, constraining the model to maintain the spatial structural characteristics of the temperature and salinity field while improving overall prediction accuracy. Subsequently, the loss error is backpropagated to each network layer of the model, and the Adam optimizer is used to iteratively optimize the model parameters. The model performance under different training epochs is evaluated using a validation set, and the validation set loss or prediction accuracy is used as the basis for model selection. The parameter file of the best-performing model is saved for subsequent continuous spatiotemporal prediction of the three-dimensional ocean temperature and salinity field.

[0194] The initial learning rate for model training was set to 0.001, and the OneCycleLR learning rate scheduling strategy was used to dynamically adjust the learning rate to improve model convergence efficiency and find optimal parameters. The model training iterations were set to 50 times. After each training round, the model performance was evaluated using a validation set, and the validation set loss or prediction accuracy was used as the criterion for selecting the optimal model. The parameter file of the model with the best performance was saved. To verify the impact of Gaussian filtering decomposition scale on model prediction performance, comparative ablation experiments were conducted on the graphics card with σ = 0, 2, and 5 respectively. σ = 0 represents no Gaussian smoothing, serving as a baseline experiment under the condition of no high- and low-frequency decomposition. σ = 2 and σ = 5 were used to analyze the high- and low-frequency decomposition experiments under different smoothing scales, i.e., the model's ability to preserve low-frequency background evolution and high-frequency details. After training, the model with the best performance on the validation set was selected for subsequent continuous spatiotemporal prediction of the three-dimensional marine temperature and salinity field.

[0195] Step 4: Input the initial 3D temperature and salinity field, as well as the sea surface temperature, sea surface height anomaly, and sea surface wind field data for 10 consecutive days, into the trained GDP-Net model. Predict the background changes of the ocean temperature and salinity field through the low-frequency path and predict the local detailed changes through the high-frequency path. Then, superimpose the prediction results of the two paths to reconstruct the spatiotemporal prediction results of the ocean 3D temperature and salinity field for the next 10 consecutive days.

Claims

1. A spatiotemporal prediction method for three-dimensional ocean temperature-salinity field based on Gaussian filtering, characterized in that, The specific steps are as follows: Step 1: Collect sea surface temperature, sea surface height anomaly, sea surface wind field, and three-dimensional ocean temperature and salinity datasets, and divide them into training sets after preprocessing; Step 2: Targeting the three-dimensional temperature and salinity field of the ocean under continuous time steps By using Gaussian filtering to perform frequency decomposition at each time point, the corresponding high-frequency components are obtained. and low frequency components ; Step 3: Combining the preprocessed data, construct an end-to-end prediction path using low-frequency components and an autoregressive prediction path using high-frequency components, and fuse them to obtain the mapping relationship between historical time windows and future target states. The low-frequency path expression is: Where h represents the historical input length and f represents the prediction step size. This represents an end-to-end prediction model; These represent historical sea surface temperature, sea surface height, and sea surface wind field information for h consecutive time periods; The high-frequency path expression is: in, This represents an autoregressive prediction model, where k represents the number of times the data has been regressed by the model. The prediction results of the low-frequency path and the high-frequency path are fused to obtain the three-dimensional temperature and salinity field prediction results for the next f time steps. The calculation formula is as follows: This indicates that the temperature-salinity field at time t is subjected to Gaussian filtering. Step 4: Construct a Gaussian-filtered dual-path neural network, GDP-Net, consisting of an end-to-end prediction branch and an autoregressive prediction branch; The specific principle of GDP-Net is as follows: First, the end-to-end prediction branch predicts low-frequency three-dimensional temperature and salinity data; then, the autoregressive prediction branch predicts high-frequency three-dimensional temperature and salinity data; finally, the high-frequency three-dimensional temperature and salinity data predicted by the end-to-end branch for n days and the low-frequency three-dimensional temperature and salinity data predicted by the autoregressive branch are added together to perform feature fusion and restore the three-dimensional temperature and salinity field for the next n consecutive days. n takes the value of an integer within the range of computing power support and data support; Step 5: Train the Gaussian-filtered dual-path neural network GDP-Net using the training set; Step 6: Input the initial three-dimensional temperature and salinity field, as well as the sea surface temperature, sea surface height anomaly, and sea surface wind field data for n consecutive days, into the trained GDP-Net model to reconstruct the spatiotemporal prediction results of the ocean's three-dimensional temperature and salinity field for the next n consecutive days.

2. The prediction method as described in claim 1, characterized in that, In step one, the preprocessing includes bilinear interpolation of the sea surface temperature, sea surface height anomaly, and sea surface wind field data to ensure that they are consistent with the spatial resolution of the three-dimensional temperature and salinity data, and replacing all collected data with default values; then, a training dataset is constructed by using a window-based data partitioning method.

3. The prediction method as described in claim 1, characterized in that, In step two, the three-dimensional temperature and salinity field of the ocean is defined as: in, , and These represent the spatial dimensions of latitude, longitude, and depth, respectively, and t represents time. Frequency decomposition refers to the process of directly obtaining low-frequency components from the initial three-dimensional temperature-salt field at time t through Gaussian filtering. The remaining field consists of high-frequency components. .

4. The prediction method as described in claim 1, characterized in that, In step four, the end-to-end prediction branch consists of a 2D encoder, a Trans-Conv module, a 3D encoder, a 3D decoder, and a dual-path multi-scale global spatiotemporal attention module. The autoregressive prediction branch consists of a 2D encoder, a 2D decoder, and a dual-path gated attention module.

5. The prediction method as described in claim 4, characterized in that, In step four, the end-to-end prediction branch performs prediction of low-frequency three-dimensional temperature and salinity data, specifically as follows: Step 401: The preprocessed multi-source sea surface feature data and three-dimensional temperature, salinity and low-frequency data are processed through 2D coding structure and 3D coding structure respectively. The multi-source sea surface feature features are extracted and transformed by the Trans-Conv module to be unified to the same five dimensions as the three-dimensional temperature, salinity and low-frequency data. They are then sent to the two gated attention branches of the dual-path multi-scale global spatiotemporal attention module for feature fusion. Step 402: Each branch undergoes feature normalization and channel mapping sequentially using BatchNorm 3D and PW Conv 3D to obtain its corresponding features. ; The formula is expressed as: in, and This represents the feature input of multi-source sea surface data and three-dimensional temperature and salinity data; BN3D represents the feature normalization function; PWConv3D is a 3D convolution function with a convolution sum of 1; Step 403: The two features enter the dual-gated attention module DG-A to enhance the features of the multi-source sea surface data and the three-dimensional temperature and salinity features respectively; The formulas for calculating the dual-gated features g1 and g2 after DG-A are: Enhanced output is: Step 404: Enhance the dual-gated features and Multi-scale features are obtained by fusing multiple scale MLPs. ; First, two-way features and First, the channel transformation is completed through PW Conv 3D, and then it enters the MSDW-Conv 3D module for multi-scale three-dimensional depth convolution modeling. Subsequently, nonlinear mapping and channel integration are performed using the GELU activation function and PW Conv 3D, and then combined with the original features. and Fusion yields multi-scale features ; The formula is expressed as: + Step 405: Combine the fused multi-scale features Entering the global spatiotemporal attention modeling stage, the output of DMG-STA is obtained. The fused features will be used to reconstruct the low-frequency three-dimensional temperature and salinity features for the next 10 consecutive days using a 3D decoder. The global spatiotemporal attention modeling process involves transforming the five-dimensional features (B, C, L', H', W') into (B, P, N, D) through a Rearrange operation. This is followed by a multi-head attention mechanism, and the output is then restored to (B, C, L', H', W') through a Linear layer and another Rearrange operation. Finally, PW Conv 3D is used for channel integration and local spatial information supplementation to obtain the final output of DMG-STA. in, .

6. The prediction method as described in claim 4, characterized in that, In step four, the autoregressive prediction branch performs predictions on high-frequency three-dimensional temperature and salinity data, specifically as follows: Step 406: The high-frequency three-dimensional temperature and salinity data is first processed by a 2D encoder to obtain high-frequency features. , will feature First, the data is normalized and channel-mapped using BatchNorm 2D and PW Conv 2D, then it enters the DCG-A dual-path attention mechanism to output features. : In the dual-path attention mechanism, one path uses the multi-head attention mechanism in Transformer to establish global spatial relationships between patches; the other path uses a large-kernel convolutional gating structure. The expression is: GELU is the activation function, and DCG-A represents the dual-path attention module. Step 407, Global Attention Features The input enters the MSDW-Conv 2D multi-scale convolution module, and then undergoes nonlinear mapping and feature fusion via GELU and PWConv 2D to output the features. : Step 408: Output features After restoring the high-frequency three-dimensional temperature and salinity characteristics using a 2D decoder, the changes in the high-frequency three-dimensional temperature and salinity characteristics over the next 10 consecutive days are predicted using an autoregressive prediction method.

7. The prediction method as described in claim 1, characterized in that, In step five, firstly, the initial three-dimensional temperature and salinity field of the training data is decomposed by Gaussian filtering to obtain low-frequency background components and high-frequency detail components; and then the three-dimensional temperature and salinity reanalysis label data corresponding to the future time step is set. Then, the low-frequency background component is input into the end-to-end prediction path, and the high-frequency detail component is input into the autoregressive prediction path. The prediction results are fused to obtain the complete three-dimensional temperature and salinity field prediction results, which are then compared with the corresponding three-dimensional temperature and salinity reanalysis label data. The loss function is used to simultaneously calculate the numerical reconstruction error and spatial gradient error between the model's prediction results and the labeled data. Based on the calculation results of the loss function, the error is backpropagated to each network layer of the model, and the Adam optimizer is used to iteratively update the model parameters.

8. The prediction method as described in claim 1, characterized in that, In step six, the GDP-Net model first decomposes the temperature and salinity field into high and low frequency information through Gaussian filtering, then predicts the background changes of the ocean temperature and salinity field through the low-frequency path and predicts the local detailed changes through the high-frequency path, and then superimposes the prediction results of the two paths.

Images