A physical gradient-guided and constrained reconstruction model of three-dimensional temperature and salinity fields in the ocean

Abstract

This invention discloses a physical gradient-guided and constrained three-dimensional temperature-salinity field reconstruction model for the ocean, belonging to the field of marine technology. First, historical sea surface temperature, sea surface height anomalies, sea surface wind fields, and three-dimensional reanalysis temperature-salinity datasets are collected, and daily three-dimensional reanalysis climatological mean temperature-salinity fields are calculated. Then, the MOEF-Net-PTS three-dimensional temperature-salinity reconstruction model is designed. Regarding reconstruction accuracy, the model fully explores and integrates the correlations between multi-source sea surface observation elements through self-attention and mutual attention mechanisms, thereby enhancing the inference ability of subsurface structures. Regarding physical characteristics, the three-dimensional temperature-salinity climatological mean is used as prior gradient knowledge to guide the model, and horizontal and vertical gradient loss functions are designed to constrain the gradient distribution of the model output, making it more consistent with the characteristics of ocean processes. The model constructed in this invention significantly enhances the rationality and stability of spatial structure while ensuring numerical accuracy, achieving a balance between statistical fitting ability and physical consistency.

Description

Technical Field

[0001] This invention belongs to the field of marine technology, specifically relating to a three-dimensional marine temperature and salinity field reconstruction model guided and constrained by physical gradients. Background Technology

[0002] The subsurface thermohaline structure of the ocean is a crucial physical foundation driving global climate system evolution and internal ocean dynamics. The vertical distribution of temperature and salinity not only determines seawater density structure and stratification but also directly influences vertical energy and mass exchange processes in the ocean, playing a key role in global heat redistribution, regulation of air-sea interactions, and maintenance of marine ecosystem productivity. Therefore, obtaining large-scale, high-resolution three-dimensional thermohaline field information is a vital foundation for physical oceanography, climatology, and marine resource development.

[0003] Currently, ocean three-dimensional observation data still mainly rely on in-situ methods such as Argo buoys, CTD profiles, and moored observations. These methods have relatively sparse spatial distribution and discontinuous temporal coverage, making it difficult to meet the needs of high-resolution operational applications. In contrast, satellite remote sensing can provide large-scale, continuous ocean observation information. However, limited by the attenuation characteristics of electromagnetic waves propagating in seawater, remote sensing can only acquire surface variables such as sea surface temperature (SST), sea surface salinity (SSS), sea surface height (SSH), and wind field, and cannot directly detect underwater three-dimensional structures. Numerous studies have shown that changes in sea surface conditions are influenced to some extent by the expansion effect and density changes of the subsurface thermohaline structure, thus forming a complex nonlinear coupling relationship between the sea surface and the subsurface. This provides a theoretical basis for using sea surface remote sensing information to invert the subsurface three-dimensional thermohaline structure and has become an important direction in ocean three-dimensional reconstruction research in recent years.

[0004] Traditional methods for inverting subsurface temperature, salinity, and volume (TTC) structures using sea surface remote sensing information mainly include statistical methods, dynamic methods, and empirical methods based on sound propagation time. Statistical methods typically achieve inversion by establishing empirical relationships between sea surface observation factors and subsurface TTC structures. Among these, the Empirical Orthogonal Function Decomposition (EOF) method extracts the principal modes of the TTC profile and establishes a regression relationship between the mode amplitudes and sea surface variables, thereby achieving three-dimensional structure reconstruction. Dynamic methods introduce physical constraints and solve the nonlinear equations between surface information and subsurface structures through numerical models, such as MODAS and the SQG method based on quasi-geostrophic theory. Empirical methods based on sound propagation time utilize the influence of TTC on sound speed to indirectly estimate underwater structures by establishing an empirical model between sound propagation time and TTC structures. While these methods have some inversion capability in open deep-sea areas, their core still relies on empirical assumptions or physically simplified models, making it difficult to directly characterize the complex nonlinear mapping relationship between the sea surface and the subsurface. When dealing with multi-scale dynamic processes, areas with significant regional differences, or areas with strong nonlinear characteristics, there are often problems such as insufficient accuracy and limited generalization ability.

[0005] With the development of machine learning and deep learning technologies, researchers have begun to introduce data-driven models to establish nonlinear mapping relationships between sea surface remote sensing factors and subsurface temperature and salinity structures. Early studies used fully connected neural networks (FNNs) and multilayer perceptron (MLP) models to reconstruct subsurface temperature fields, validating the potential of neural networks in characterizing complex nonlinear relationships. Subsequently, research gradually introduced convolutional neural networks (CNNs) to enhance spatial feature extraction capabilities and combined them with multi-source remote sensing factors (SST, SSS, SSH, wind stress, etc.) to improve model expressive power. In recent years, the Transformer structure, due to its excellent global dependency modeling capabilities, has been introduced into ocean 3D reconstruction tasks, effectively improving the modeling effect of long-distance spatial correlations. At the same time, deep networks based on U-Net, attention mechanisms, and multi-scale structure optimization have emerged, significantly improving the overall numerical accuracy of remote sensing information inversion of 3D temperature and salinity fields. Overall, data-driven methods, through network structure optimization and attention mechanism enhancement, have gradually improved the ability to model nonlinear mappings from the sea surface to the subsurface, providing a new technical path for ocean 3D temperature and salinity reconstruction.

[0006] Despite significant progress in overall error metrics, existing deep learning methods still face several key challenges:

[0007] (1) Existing models mainly rely on sea surface remote sensing variables as input and lack prior knowledge of the three-dimensional background structure. When relying solely on surface information, the models cannot accurately depict the overall stratified structure and vertical distribution characteristics of the temperature and salinity field.

[0008] (2) Most methods take the minimization of global error as the optimization objective and lack explicit constraints on temperature-salinity gradients and spatial continuity. Although they can achieve overall numerical fitting, random numerical distributions are prone to occur in local regions, resulting in unreasonable horizontal or vertical gradients and spatial artifacts.

[0009] (3) In the absence of structural constraints, key marine dynamic structures such as fronts and thermoclines are prone to feature weakening or morphological distortion, which affects the physical consistency and application reliability of the reconstruction results.

[0010] In essence, existing purely data-driven methods often focus on optimizing numerical accuracy, while giving insufficient consideration to the guidance of three-dimensional structural knowledge and physical gradient constraints, making it difficult to ensure both error accuracy and physical rationality and structural stability. Summary of the Invention

[0011] To address the shortcomings of existing methods in reconstructing three-dimensional temperature and salinity fields (TSTs) of the sea surface, which lack sufficient consideration of three-dimensional constraints and gradient guidance, this invention proposes a physical gradient-guided and constrained TST reconstruction model for the ocean's three-dimensional TST, constructing the MOEF-Net-PTS three-dimensional TST reconstruction model. MOEF-Net (Multi-Source Ocean Element Fusion Network) aims to achieve efficient feature extraction and deep fusion among multi-source ocean surface elements.

[0012] A method for constructing a three-dimensional marine temperature-salinity field reconstruction model guided and constrained by physical gradients includes the following steps:

[0013] Step 1: Collect publicly available sea surface temperature, sea surface height anomalies, sea surface wind fields, and three-dimensional ocean reanalysis datasets for the same sea area over several years to construct a sample database and a three-dimensional climatological mean temperature and salinity field;

[0014] The process of constructing the sample database is as follows:

[0015] Satellite remote sensing data and 3D reanalysis data of the same sea area within n years are used as the sample database. The historical data of sea surface temperature, sea surface height anomaly and sea surface wind speed of the day are combined as input data, and the 3D reanalysis data of layers 1-32 are used as the label dataset.

[0016] The data in the sample database was divided into grids as follows: First, the input data and label data were subjected to max-min normalization. Then, the input sea surface element data was divided into (B, C, H, W) format, the climatological temperature and salinity mean was divided into (B, C, L, H, W) format, and the label data was divided into (B, C, L, H', W') format. 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 of the remote sensing data at the study latitude and longitude, and H' and W' correspond to the number of grid points of the reanalysis data at the study latitude and longitude.

[0017] The first n-1 years of the split input data are used as the training set, 20% as the validation set, and the data from the nth year is used as the test set.

[0018] Using historical 3D reanalysis datasets, a daily 3D climatological mean temperature and salinity field is constructed as 3D gradient guiding information. The specific process is as follows:

[0019] Three-dimensional reanalysis data for each year in the training set were collected. Each year's data was treated as an independent time unit. The data were aligned and summed year by year along the time dimension and divided by the year fraction to obtain 366 daily three-dimensional climatological mean temperature and salinity fields.

[0020] Step 2: Using convolutional neural networks and the gSTA large kernel attention mechanism, based on the spatial distribution characteristics of multi-source sea surface element data and the spatial distribution characteristics of the three-dimensional climatological mean temperature and salinity field, construct the MOEF-Net-PTS model architecture;

[0021] The specific process is as follows:

[0022] ①Equal-distance downsampling (Downsample to patches)

[0023] To address the differences in grid resolution among multi-source sea surface feature data, an equidistant grid sampling method is adopted to unify the grid, retain all features of the original data, and construct input data with a consistent structure.

[0024] ② Autoencoder and Self-Attention Module (gSTA)

[0025] The autoencoder extracts data features from multi-source sea surface data and the 3D climatological temperature and salinity mean field using convolution, GroupNorm, and SiLU units. The 3D climatological temperature and salinity mean field is then used by a downsampling encoder to extract 3D structural information. Subsequently, the self-attention module combines large-kernel convolution and gated attention to learn the key features within each element, while the large-kernel convolution learns the spatial distribution features of the data over a wider range.

[0026] ③ Multi-source Information Interaction Block

[0027] Multi-source feature fusion is achieved by using mutual encoders and mutual attention mechanisms, and nonlinear spatial correlations between multi-source features are captured by cross-branch jump connections, thus realizing multi-feature coupled modeling.

[0028] ④ Decoder

[0029] Composed of convolutional, GroupNorm, and SiLU units, the model employs pixel-level resampling to restore spatial resolution. The main branch reconstructs and fuses features, while the residual branch incorporates original sea surface and climatological information to supplement details and reduce the risk of model overfitting.

[0030] Step 3: Train the MOEF-Net-PTS model using the constructed multi-source sea surface feature data, the ocean three-dimensional climatological mean field, and the ocean reanalysis training dataset, and introduce physical gradient constraints during the training process.

[0031] The model training process is as follows:

[0032] The feature dataset of the training dataset is input into the MOEF-Net-PTS model. The direct difference and gradient difference between the reconstruction result of the model and the label data are calculated through the loss function. The difference is backpropagated to the model. The optimal solution of the model is determined by the validation set, and the model parameter file is saved.

[0033] Step 4: Combine the sea surface temperature, sea surface height anomaly, sea surface wind field, and three-dimensional reanalysis climatological mean temperature and salinity field of the day and input them into the trained model to obtain the reconstructed subsurface three-dimensional temperature and salinity field data.

[0034] The advantages and beneficial effects of this invention are as follows:

[0035] (1) A three-dimensional temperature-salinity field reconstruction method guided and constrained by physical gradient is proposed.

[0036] A physical gradient constraint mechanism is constructed, and a climatological three-dimensional background field is introduced as a structural prior to achieve effective connection between satellite sea surface spatiotemporal information and three-dimensional temperature and salinity structure characteristics, thereby improving the physical consistency and spatial continuity of the reconstruction results.

[0037] (2) Design a multi-source element fusion model framework

[0038] Leveraging the superior spatial feature learning capabilities of convolutional neural networks, a gSTA large kernel attention mechanism is introduced to construct a multi-element self-attention and mutual attention interaction framework, thereby enhancing the coupling modeling capabilities among multi-source ocean elements and significantly improving the model's ability to characterize complex ocean states and their multi-scale structural features.

[0039] (3) Significantly improves the performance of three-dimensional temperature and salinity field reconstruction

[0040] Compared with existing methods, this method significantly enhances the rationality and stability of spatial structure while ensuring numerical accuracy, achieving a better balance between statistical fitting ability and physical consistency. Attached Figure Description

[0041] Figure 1 The flowchart illustrates the construction process of a physical gradient-guided and constrained three-dimensional marine temperature and salinity field reconstruction model for this invention.

[0042] Figure 2 The structure diagram of the MOEF-Net-PTS model constructed in this invention;

[0043] Figure 3 This is a structural diagram of the main modules in the MOEF-Net-PTS model of this invention. Detailed Implementation

[0044] The present invention will now be described in further detail with reference to the accompanying drawings.

[0045] Unlike previous simple channel fusion mechanisms, the MOEF-Net proposed in this invention enhances the coupling modeling capability between multi-source elements through self-attention and mutual attention mechanisms, thereby improving the model's ability to characterize complex ocean states. Simultaneously, the model incorporates a climatological 3D mean temperature and salinity field into the input, providing stable background 3D structural information and crucial 3D structural priors, guiding the model to learn more reasonable vertical and horizontal structural features during training. Building upon this, the model introduces physical gradient loss during reconstruction, constraining the gradient and spatial continuity of the reconstructed temperature and salinity to improve the physical consistency and structural stability of the reconstruction results. Through the synergistic effect of structural design and physical constraints, the model effectively improves the rationality and stability of the reconstruction results while maintaining numerical accuracy, achieving a better balance between statistical fitting ability and physical consistency.

[0046] A physical gradient-guided and constrained model for reconstructing a three-dimensional ocean temperature-salinity field is constructed as follows: Figure 1 As shown, the specific steps are as follows:

[0047] Step 1: Obtain the required sea surface temperature (SST), sea surface height anomaly (SLA), sea surface wind field (SSW), and ocean 3D reanalysis datasets from internationally available data platforms. Based on multi-year historical 3D reanalysis data, construct the sample data needed for model training.

[0048] A three-dimensional reanalysis dataset spanning 12 years from 2007 to 2018 (the training set in this embodiment) was used. Each year's data was treated as an independent time unit (365 days in a common year and 366 days in a leap year). The 12 annual sequences were then aligned along the time dimension and summed. Finally, the sum was divided by the number of years (12) to calculate 366 daily three-dimensional climatological mean temperature and salinity fields, which served as the three-dimensional structural prior and gradient guidance information for the model. Based on this, a complete experimental training data sample library was established to provide data support for model training and validation.

[0049] In this embodiment, satellite remote sensing data and reanalysis data from 2007 to 2022, totaling 16 years, are used as the dataset. Historical daily satellite remote sensing data on sea surface temperature, sea surface height anomalies, and sea surface wind speed are combined as input data. Three-dimensional reanalysis data from layers 1-32 are used as the label dataset. The dataset is partitioned as follows: before partitioning, the input and label data are subjected to min-max normalization. The input sea surface element data is partitioned into (B, C, H, W) format, the climatological temperature and salinity mean is partitioned into (B, C, L, H, W), and the label data is partitioned into (B, C, L, H', W') format, 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 partitioning, 80% of the data from the first 15 years is used as the training set, 20% as the validation set, and the entire year of 2022 is used as the test set for testing.

[0050] Step 2: Using convolutional neural networks and the gSTA large kernel attention mechanism, based on the spatial distribution characteristics of sea surface temperature, wind field and other data and the spatial distribution characteristics of the three-dimensional temperature and salinity field, the basic architecture of the MOEF-Net-PTS model for multi-source sea surface element fusion is constructed.

[0051] like Figure 2 As shown, the MOEF-Net-PTS model uses multi-source sea surface data as input, including SST, SLA, SSW, and climatological mean values ​​of subsurface temperature and salinity. The main idea behind model construction is to adopt the currently mainstream multi-element fusion strategy, employing a logical structure of "self-encoding-self-attention-mutual encoding-mutual attention-fusion decoding" for multiple elements. First, the multi-source sea surface elements are downsampled at equal intervals to unify the grid resolution. Then, single-element features are extracted through an autoencoder, and local and global spatial features are captured by a self-attention module. The climatological three-dimensional temperature and salinity are extracted using a downsampling encoder for structural priors. Subsequently, the features of each modality are concatenated and fused through a multi-source information interaction module. Finally, the fusion result is input into the decoding structure to reconstruct the three-dimensional temperature and salinity field of the ocean, achieving high-precision three-dimensional temperature and salinity field reconstruction through the coupling of multiple elements. Since the model mainly performs spatial nonlinear fitting, a model structure based on convolutional neural networks is more conducive to capturing the spatial mapping relationships of the data. For the attention mechanism, this invention adopts the gSTA structure based on pure convolutional neural networks, focusing on the spatial features of the data.

[0052] After the data is input, it first undergoes equidistant point sampling downsampling to process the sea surface elements of different data sources into the same size through equidistant grid point sampling. After processing, it first goes through an encoder for self-encoding to extract their respective data features. After extraction, it enters the self-attention mechanism big core attention module gSTA to realize self-attention of the elements.

[0053] The subsurface temperature, salinity, and climatological mean values ​​are then downsampled using encoder downsampling to extract three-dimensional structural features. The size is reduced to the same as that of sea surface elements. Similarly, a self-attention mechanism is used to achieve self-attention of the three-dimensional temperature, salinity, and climatological structure.

[0054] Each modality is concatenated after autoencoding and self-attention in the model, and then mutual attention is performed. The multi-source information interaction module is composed of the mutual encoding module, which fuses information from multiple feature elements and extracts the interdependencies between information. Specifically, this invention defines the output of the self-attention mechanism of the SST channel as x, the output of the self-attention mechanism of the SLA channel as y, and the output of the self-attention mechanism of the SSW channel as z. These are then interacted and fused with the climatological mean encoding output w to form a multi-channel mutual attention mechanism to accommodate the weighting relationships between features. Finally, the concatenated data from multiple mutual attention results is fed into the decoding module to obtain the reconstructed three-dimensional temperature and salinity field.

[0055] The equidistant point downsampling, encoder, decoder, gSTA attention mechanism, and multi-source information interaction module can be specifically expressed as follows:

[0056] ① Downsample to patches at equal intervals

[0057] Because multi-source sea surface data exhibit variations in grid resolution, many studies have employed interpolation to unify the resolution of the original data. However, interpolation introduces more spurious information, thus affecting the accuracy of data reconstruction. To preserve more of the original data's characteristics, this study uses an equidistant grid sampling method, specifically as follows: Figure 3 As shown.

[0058] The grid resolution of multi-source sea surface element data is standardized. Specifically, each data source is sampled according to a uniform grid interval in the latitude and longitude directions, so that they correspond to the same resolution standard in spatial scale, thereby constructing input grid data with a consistent structure. The advantage of this approach is that it preserves the data characteristics of the original data, eliminates the need for interpolation, and improves the utilization rate of the original data.

[0059] ② Autoencoder and self-attention module (gSTA)

[0060] like Figure 3As shown, the autoencoder part is mainly responsible for extracting data features of different elements from multi-source sea surface data (SST, SLA, SSW) and the three-dimensional temperature and salinity field. This module mainly consists of (3,3)-sized convolutions, combined with Groupnorm and SiLU, forming a small coding unit. Ns represents the number of coding units. The Encoder block contains 4 units, where the downsampling steps n1 and n2 are both 1, and no downsampling processing is required. The Encoder down also contains 4 units, where the downsampling steps n1 and n2 are set to 3 and 2 respectively, performing downsampling processing on the climatological three-dimensional temperature and salinity field to extract three-dimensional structural information.

[0061] Encoded data features are directly input into the self-attention gSTA module. This self-attention mechanism effectively learns key features within each element, providing more representative single-element feature representations for subsequent mutual attention tasks. This attention module primarily combines large-kernel attention with gated attention, considering both local details and the global picture, selectively learning key features, performing spatial mapping transformations, and improving the model's generalization ability.

[0062] ③ Multi-source Information Interaction block

[0063] like Figure 2 As shown, the multi-source information interaction module is the core of the entire model structure, mainly composed of a mutual encoder and a mutual attention mechanism. Its internal core structure is the same as that of the autoencoder and self-attention mechanism, and its main function is to establish interactive fusion between multiple oceanographic elements through convolution. By introducing cross-layer skip connections, the multi-source sea surface information features extracted by the autoencoder and self-attention mechanism are concatenated with the climatological 3D temperature and salinity field features in the convolutional channel dimension. The multi-source sea surface data features (SST, SLA, SSW) are denoted as x, y, and z variables, respectively, and the climatological 3D temperature and salinity structure features are denoted as w variables. These are concatenated into xyw, xzw, yzw, and combinations of different data features. The mutual encoder learns and fuses these different combinations of features, and then performs mutual attention on the fused features to learn the key features of the fused data. Finally, the different fused features are weighted and input into the decoder for decoding.

[0064] ④ Decoder

[0065] like Figure 3As shown, the decoder consists of multiple identical decoding units, each containing a (3×3) convolutional layer, a GroupNorm normalization layer, and a SiLU activation function. For feature upsampling, the decoder employs UnConv units, using pixel reshaping to improve the spatial resolution of the data and restore it to the same spatial scale as the original 3D temperature and salinity field. This module primarily undertakes the task of reconstructing a high-resolution 3D temperature and salinity field from the fused multi-source features. Its structure includes three key branches: the main branch is responsible for decoding and reconstructing the multi-source information fused through a mutual attention mechanism; the two residual branches respectively introduce the original input sea surface remote sensing data and climatological 3D temperature and salinity field information into the decoding process to supplement details and enhance generalization ability, effectively suppressing model overfitting.

[0066] Step (3): The prediction model is trained using the constructed multi-source sea surface element data, the ocean three-dimensional climate mean field and the ocean reanalysis training dataset, and physical gradient constraints are introduced during the training process.

[0067] Specific training process: Due to the different distribution patterns of temperature and salinity, a dual-loss function constraint model is adopted to capture the distribution patterns of temperature and salinity data separately. Both loss functions are MSE. To constrain the performance of the model prediction results in terms of spatial consistency and physical rationality, the loss function in this study mainly consists of two aspects: the temperature and salinity field reconstruction loss function (ReconstructLoss) and the physical feature consistency loss function (Gradient Consistency Loss). The weighted combination of the two constitutes the overall optimization objective.

[0068] (1) Temperature-salinity field reconstruction loss function ( )

[0069] This loss function is primarily used to constrain the model's accuracy in reconstructing the temperature-salinity field. After extracting a mask of non-aquatic grid points from the label data, invalid data from non-aquatic grid points in the mask is removed from both the reconstructed field and the label values ​​to avoid affecting their inclusion in the model's loss calculation and interfering with model convergence. After processing, the mean squared error of the temperature-salinity reconstruction results and the model label data is calculated separately.

[0070]

[0071]

[0072] The temperature-salinity field reconstruction loss function can then be expressed as:

[0073]

[0074] in , Represents the reconstruction of the subsurface temperature and salinity. , This indicates the subsurface temperature and salinity of the reanalysis data.

[0075] (2) Gradient consistency loss function )

[0076] This loss function aims to constrain the consistency between the model's predicted field and the true field in the vertical and horizontal gradients. During the calculation, the true and predicted fields are first masked using NaN (NaN masking) to eliminate invalid or missing values. Then, the gradient differences of the 3D field in three directions (vertical z, longitudinal x, and latitudinal y) are calculated respectively.

[0077]

[0078]

[0079] in, , , These represent the gradient fields of the predicted field in the vertical, longitudinal, and latitudinal directions, respectively. , , This represents the true gradient field of the label. Note that Δx, Δy, and Δz are taken as grid distances, not true distances. The mask positions are then replaced with 0 values. Finally, the mean squared error (MSE) is used to measure the difference between the predicted and true gradients. The gradient losses in the vertical, longitudinal, and latitudinal directions can then be expressed as:

[0080]

[0081]

[0082]

[0083] The gradient loss is then expressed as:

[0084]

[0085] Where e represents the reconstructed element. The reconstruction temperature gradient loss is... The salinity loss during reconstruction is The total gradient loss for reconstructing temperature and salinity is:

[0086]

[0087] Here, sbt represents the loss for reconstructing the subsurface temperature field, and sbs represents the loss for reconstructing the subsurface salinity field. This loss helps maintain the continuity and physical plausibility of the model output in three-dimensional space during the optimization process.

[0088] (3) Temperature-salinity double loss function

[0089] Taking into account both the temperature-salinity field reconstruction error and the spatial gradient error, the total loss function is defined as:

[0090]

[0091] in and This is a balancing coefficient used to adjust the trade-off between physical consistency constraints and reconstruction accuracy. Here, and Through experiments, we tried setting the value to 1 and 0.1 respectively, and obtained higher accuracy reconstruction results.

[0092] In this embodiment, the initial learning rate for model training is set to 0.001, and OneCycleLR is used to update the learning rate, continuously adjusting the network's learning rate to find the optimal solution for the model. The number of training iterations is set to 100, and the optimizer is Adam.

Claims

1. A physical gradient-guided and constrained three-dimensional marine temperature-salinity field reconstruction model, characterized in that, Its construction method includes the following steps: Step 1: Collect publicly available sea surface temperature, sea surface height anomalies, sea surface wind fields, and three-dimensional ocean reanalysis datasets for the same sea area over several years to construct a sample database and a three-dimensional climatological mean temperature and salinity field. The process of constructing the sample database is as follows: Satellite remote sensing data and 3D reanalysis data of the same sea area within n years are used as the sample database. The historical data of sea surface temperature, sea surface height anomaly and sea surface wind speed of the day are combined as input data, and the 3D reanalysis data of layers 1-32 are used as the label dataset. The data in the sample database is divided into grids. 80% of the first n-1 years of the divided input data is used as the training set, 20% as the validation set, and the data from the nth year is used as the test set. Using historical 3D reanalysis datasets, a daily 3D climatological mean temperature and salinity field is constructed as 3D gradient guiding information; Step 2: Using convolutional neural networks and the gSTA large kernel attention mechanism, based on the spatial distribution characteristics of multi-source sea surface element data and the spatial distribution characteristics of the three-dimensional climatological mean temperature and salinity field, construct the MOEF-Net-PTS model architecture. The specific process is as follows: ①Equal-distance downsampling To address the differences in grid resolution among multi-source sea surface feature data, an equidistant grid sampling method is adopted to unify the grid, retain all features of the original data, and construct input data with a consistent structure. ② Autoencoder and self-attention module gSTA The autoencoder extracts data features of each element from multi-source sea surface data and three-dimensional climatological temperature and salinity mean field through convolution, GroupNorm and SiLU units. The three-dimensional climatological temperature and salinity mean field is then used to extract three-dimensional structural information through downsampling encoder. Subsequently, the self-attention module combines large kernel convolution and gated attention to learn the key features inside each element. ③ Multi-source information interaction module By using mutual encoders and mutual attention mechanisms, the features of multi-source sea surface element data and the three-dimensional climatological temperature and salinity mean features are fused. Combined with cross-branch jump connections, the nonlinear spatial correlation between multi-source elements is captured, realizing multi-element coupled modeling. ④ Decoder Composed of convolution, GroupNorm and SiLU units, it uses pixel reshaping upsampling method to restore spatial resolution and reconstructs the fused multi-source features into a high-resolution three-dimensional temperature and salinity field. Step 3: Train the MOEF-Net-PTS model using the constructed multi-source sea surface feature data, the ocean three-dimensional climatological mean field, and the ocean reanalysis training dataset; The specific model training process is as follows: The feature dataset of the training dataset is input into the MOEF-Net-PTS model. The direct difference and gradient difference between the reconstruction result of the model and the label data are calculated through the loss function. The difference is backpropagated to the model. The optimal solution of the model is determined through the validation set, and the model parameter file is saved. Step four: Combine the sea surface temperature, sea surface height anomaly, sea surface wind field, and three-dimensional reanalysis climatological mean temperature and salinity field of the day and input them into the trained MOEF-Net-PTS model to obtain the reconstructed subsurface three-dimensional temperature and salinity field data.

2. The three-dimensional marine temperature and salinity field reconstruction model guided and constrained by physical gradients according to claim 1, characterized in that, The data in the sample database was divided into grids as follows: First, the input data and label data were subjected to max-min normalization. Then, the input sea surface element data was divided into (B, C, H, W) format, the climatological temperature and salinity mean was divided into (B, C, L, H, W) format, and the label data was divided into (B, C, L, H', W') format. 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 of the remote sensing data at the study latitude and longitude, and H' and W' correspond to the number of grid points of the reanalysis data at the study latitude and longitude.

3. The three-dimensional marine temperature and salinity field reconstruction model guided and constrained by physical gradients according to claim 1, characterized in that, Using historical 3D reanalysis datasets, a daily 3D climatological mean temperature and salinity field is constructed as 3D gradient guiding information. The specific process is as follows: Three-dimensional reanalysis data for each year in the training set were collected. Each year's data was treated as an independent time unit. The data were aligned and summed year by year along the time dimension and divided by the year fraction to obtain 366 daily three-dimensional climatological mean temperature and salinity fields.

4. The three-dimensional marine temperature and salinity field reconstruction model guided and constrained by physical gradients according to claim 1, characterized in that, The working process of the multi-source information interaction module is as follows: The multi-source sea surface feature data extracted by the autoencoder and self-attention modules are concatenated with the climatological 3D temperature and salinity structure features in the convolutional channel dimension. Specifically, the data features of the multi-source sea surface data SST, SLA, and SSW are denoted as x, y, and z variables, respectively, and the climatological 3D temperature and salinity structure features are denoted as w variables. These are concatenated into different combinations of data features: xyw, xzw, yzw, and xyzw. Then, the different combinations of features are learned and fused through the inter-encoder. The fused features are then subjected to mutual attention learning to learn the key features of the fused data. Finally, the different fused features are weighted and input into the decoder.

5. The three-dimensional marine temperature and salinity field reconstruction model guided and constrained by physical gradients according to claim 1, characterized in that, The decoder includes three branches: the main branch is responsible for decoding and reconstructing the multi-source information features fused through the mutual attention mechanism; the two residual branches introduce the original input sea surface remote sensing data and the climatological three-dimensional temperature and salinity field information into the decoding process, respectively.

6. The three-dimensional marine temperature and salinity field reconstruction model guided and constrained by physical gradients according to claim 1, characterized in that, The loss function consists of a temperature-salinity field reconstruction loss function and a physical feature consistency loss function. The weighted combination of the two constitutes the overall optimization objective, specifically: (1) Temperature-salinity field reconstruction loss function After extracting the non-aquatic grid point mask from the label data, invalid data of non-aquatic grid points in the mask are removed from the reconstructed field and label values. Then, the mean square error of the temperature-salinity reconstruction results and the model label data are calculated respectively. The temperature-salt field reconstruction loss function is then expressed as: in , Represents the reconstruction of the subsurface temperature and salinity. , This represents the subsurface temperature and salinity of the reanalysis data; (2) Gradient consistency loss function First, NaN masks are applied to both the real and predicted fields to eliminate invalid or missing values. Then, the gradient differences of the three-dimensional temperature-salinity field in the vertical, meridional, and latitudinal directions are calculated respectively. in, , , These represent the gradient fields of the predicted field in the vertical, longitudinal, and latitudinal directions, respectively. , , This represents the true gradient field of the labels, where Δx, Δy, and Δz are the grid distances; Then, the mask positions are replaced with 0 values. Finally, the difference between the predicted gradient and the true gradient is measured by the mean squared error (MSE). The gradient loss in the vertical, longitudinal, and latitudinal directions is expressed as follows: The gradient loss is then expressed as: Where e represents the reconstructed element; the reconstruction temperature gradient loss is... The salinity loss during reconstruction is The gradient consistency loss function for reconstructing temperature and salinity is: (3) Taking into account both the temperature-salinity field reconstruction loss and the gradient consistency loss, the total loss function is defined as: in and This is a balancing coefficient used to adjust the trade-off between physical consistency constraints and reconstruction accuracy.

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