A method for reconstructing three-dimensional temperature field of ocean based on physical guidance and space-time enhancement

Abstract

The application discloses a kind of ocean three-dimensional temperature field reconstruction methods based on physical guidance's space-time enhancement, belong to marine environment monitoring and marine data processing technical field.The application constructs the network model of physical guidance's frequency domain and spatial clustering enhancement;Model includes physical priori guidance branch, satellite remote sensing data branch, Argo data processing branch and decoding branch;Through the spatial clustering modulation module of physical guidance, the self-adapting spatial clustering and dynamic deformation feature extraction are carried out to remote sensing feature using physical priori characteristics, through the frequency domain separation enhancement module, the multi-band separation and self-adapting enhancement are carried out to the extracted features, through Argo dynamic correction module, the layer-by-layer dynamic correction is carried out to three-dimensional reconstruction features using Argo profile characteristics, and finally output three-dimensional ocean temperature field.The application effectively improves the reconstruction precision of three-dimensional temperature field in mesoscale process active sea area, and can be used in marine environment monitoring, marine dynamic process analysis and underwater engineering support and other application fields.

Description

Technical Field

[0001] This invention belongs to the field of marine environmental monitoring and marine data processing technology, and specifically relates to a method for reconstructing a three-dimensional marine temperature field based on physical guidance and frequency-space enhancement. Background Technology

[0002] Three-dimensional ocean temperature fields are crucial foundational data for understanding ocean dynamics, enhancing climate change prediction capabilities, and ensuring the safety of underwater engineering projects. The upper ocean, from 0 to 500 meters, is the region with the most active air-sea interactions and mesoscale processes; obtaining high-precision three-dimensional temperature fields within this depth range has significant scientific value and application implications.

[0003] Currently, obtaining ocean internal temperature profiles mainly relies on in-situ observation methods such as Argo buoys, underway drop-out thermo-depth meters, and moored buoys. Due to limitations in deployment and maintenance costs, these observation stations are spatially unevenly distributed and have low temporal sampling frequencies, making it difficult to directly support continuous reconstruction of high-resolution three-dimensional temperature fields.

[0004] With the development of satellite remote sensing technology, multi-source remote sensing data such as sea surface temperature, sea surface height anomalies, sea surface salinity, and sea surface wind fields can be continuously acquired, providing a data foundation for three-dimensional temperature field reconstruction. Three-dimensional temperature reconstruction methods have evolved from statistical methods and dynamic numerical models to machine learning and deep learning. Early methods, such as empirical orthogonal functions, multiple linear regression, and dynamic inversion models based on physical governing equations, are highly sensitive to dynamic backgrounds and parameterization schemes, limiting their cross-regional applicability. While traditional machine learning methods have improved nonlinear fitting capabilities, shallow architectures struggle to fully extract the complex spatiotemporal topological features of ocean data.

[0005] In recent years, deep learning technology has made progress in the reconstruction of three-dimensional ocean temperature fields. Researchers have used models such as convolutional neural networks and Transformer architectures to achieve the inversion of subsurface temperature fields. However, existing deep learning models generally suffer from the following problems: First, most models rely on ocean reanalysis datasets such as HYCOM, SODA, GLORYS, or ECCO as real labels during the training phase. However, the reanalysis data itself contains systematic errors such as imperfect model parameterization and data assimilation bias. The model will inherit or even amplify these biases during the learning process, leading to error propagation.

[0006] Secondly, when relying solely on sparse and discrete measured data for reconstruction, the lack of high-density 3D label supervision makes it easy for the fixed spatial sampling mechanism of conventional networks to violate the physical continuity of fluids. Introducing prior physical data to constrain and guide the network is particularly important for improving the physical rationality of the reconstruction.

[0007] Third, multi-source satellite remote sensing fusion data of the sea surface simultaneously contains large-scale background circulation, mesoscale disturbances and high-frequency noise. Signals of different scales are superimposed in the spatial domain, lacking effective frequency domain separation and targeted enhancement mechanisms, which affects the network's ability to focus on extracting key ocean dynamic features.

[0008] Fourth, the ocean contains various dynamic flow patterns such as eddies, fronts, and background waters, which follow different evolutionary laws. Using globally shared network parameters to process all sea areas will cause mutual interference of features and reduce the accuracy of reconstruction.

[0009] Therefore, there is a need to provide a method for reconstructing the three-dimensional ocean temperature field that can integrate multi-source satellite remote sensing data, physical prior data and Argo profile data, in order to overcome the dependence on reanalysis data, and improve the reconstruction accuracy of the three-dimensional temperature field in mesoscale active sea areas through physical-guided spatial clustering and frequency domain enhancement mechanisms. Summary of the Invention

[0010] To address the aforementioned technical problems, this invention provides a physical-guided frequency-space enhancement method for reconstructing three-dimensional ocean temperature fields, aiming to improve the accuracy of three-dimensional temperature field reconstruction in mesoscale active sea areas.

[0011] To achieve the above objectives, the technical solution of the present invention is as follows: A physically guided, spacetime-enhanced method for reconstructing a three-dimensional ocean temperature field includes the following steps: Step 1: Acquire multi-source satellite remote sensing fusion data, Argo profile data, and physical prior data, and perform preprocessing. Step 2: Construct a physics-guided, frequency-space-enhanced three-dimensional ocean temperature field reconstruction model. This model includes a physics-guided branch, a satellite remote sensing data branch, an Argo data processing branch, and a decoding branch. The physics-guided branch extracts multi-scale features from the physics-guided data, outputting physics-guided features at multiple scales. Each processing level of the satellite remote sensing data branch includes a physics-guided spatial clustering modulation module and a frequency domain separation enhancement module. The physics-guided spatial clustering modulation module uses the physics-guided features to perform adaptive spatial clustering and dynamic deformation feature extraction on the input multi-source satellite remote sensing fusion data. The frequency domain separation enhancement module performs frequency domain feature separation and enhancement on the extracted features, outputting two-dimensional surface features at multiple scales. The Argo data processing branch extracts spatiotemporal dependencies from the Argo profile data, outputting Argo feature sequences. The decoding branch includes an Argo dynamic correction module, which uses a cross-attention mechanism to dynamically correct the input two-dimensional surface features and Argo feature sequences layer by layer and outputs a three-dimensional temperature field. Step 3: Input the multi-source satellite remote sensing fusion data, the physical prior data and part of the Argo profile data into the model, use the remaining Argo profile data in the same spatiotemporal window as the real labels to calculate the reconstruction loss, and train the model until the convergence condition is met. Step 4: Input the multi-source satellite remote sensing fusion data, physical prior data and corresponding Argo profile data of the area to be reconstructed into the trained model. After being processed by the physical prior guidance branch, satellite remote sensing data branch, Argo data processing branch and decoding branch in sequence, the three-dimensional temperature field of the ocean is output.

[0012] In the above scheme, the physically guided spatial clustering modulation module performs the following operations: The physical prior features are processed in two ways. The first path of physical prior features is fused after multi-scale physical information is extracted by parallel 3×3 standard convolution and 3×3 dilated convolution. Then, spatial offset and modulation weight are generated by 3×3 average pooling. This drives three sets of parallel deformable convolution operators to adaptively sample the output features of the multi-source satellite remote sensing fusion data or the output features of the previous level max pooling layer, and output deformable features. The second physical prior features are processed by the dynamic spatial clustering module, and then passed through a 3×3 convolution, a batch normalization layer, a ReLU activation function and a 1×1 convolution layer in sequence, and finally through a Softmax layer to output the clustering probability distribution map of different ocean dynamic flow states to which each spatial location belongs; The clustering probability distribution map is used as a linear modulation weight and multiplied element-wise with the deformation features output by the three sets of deformable convolution operators. The three modulated and weighted features are then aggregated by adding them element-wise to output the two-dimensional features modulated by physical prior.

[0013] In the above scheme, the frequency domain separation enhancement module performs the following operations: The features output by the physically guided spatial clustering modulation module are synchronously fed into three parallel discrete cosine transform layers for specific frequency band separation, resulting in feature components of three different frequency bands. Each frequency band feature component undergoes deep nonlinear mapping via its corresponding multilayer perceptron layer. The physical prior features are used to generate a spatially gated weight map covering three frequency band channels through a dynamic spatial clustering module and a Sigmoid activation function. The spatial gated weight map is multiplied element-wise with the features output from the three multilayer perceptron layers to achieve adaptive weighting of the features; The weighted multi-band features are aggregated by adding them element by element, and then added to the original input features through residual connections to output the enhanced features.

[0014] In the above scheme, the Argo dynamic correction module performs the following operations: The three-dimensional feature vector of the current processing level of the decoding branch is reshaped into a one-dimensional spatial sequence feature through the feature flattening layer, and used as the query vector; The Argo feature sequence is used as a key-value pair and input together with the query vector into the cross-attention mechanism layer to calculate spatial similarity. A binary mask matrix is ​​introduced in the cross-attention calculation to force the attention score of the region without Argo observations to be negative infinity; After cross-attention weighting and multi-head feature aggregation, the output features are remapped back to the three-dimensional tensor dimension through the feature restoration layer; The obtained 3D features are added element-wise to the original 3D tensor before entering the Argo dynamic correction module, and the corrected 3D features are output.

[0015] In the above scheme, the physical prior guidance branch contains four levels. The first level contains two consecutive 3×3 convolutional layers and a ReLU activation function. The subsequent three levels are each composed of a maximum pooling layer, a 3×3 convolutional layer and a ReLU activation function connected in sequence. The physical prior features of different scales are output to the corresponding levels with the same receptive field scale in the satellite remote sensing data branch step by step.

[0016] In the above scheme, the satellite remote sensing data branch includes four levels. The first three levels are each composed of the physically guided spatial clustering modulation module, the frequency domain separation enhancement module, and the max pooling layer in sequence. The last level is composed of the physically guided spatial clustering modulation module and the frequency domain separation enhancement module. The multi-source satellite remote sensing fusion data is used as the initial input to the physically guided spatial clustering modulation module of the first level. The output of the max pooling layer in the subsequent levels is used as the input of the current level. Each level outputs two-dimensional surface features at the corresponding scale.

[0017] In the above scheme, the Argo data processing branch uses the time encoding layer, the position encoding layer, and the temperature normalization layer as parallel initial inputs. The position features output by the position encoding layer and the time features output by the time encoding layer are concatenated in the channel dimension and then mapped to a high-dimensional space by the first multilayer perceptron. The temperature features output by the temperature normalization layer are mapped to a high-dimensional space by the second multilayer perceptron. The two are concatenated again in the channel dimension and then fed into the Transformer encoder layer and the fully connected layer in sequence to output a 128-dimensional Argo feature sequence.

[0018] In the above scheme, the decoding branch includes a front-end upscaling mapping layer, three decoding modules in the middle, and an output structure at the tail end. Each decoding module consists of an upsampling layer, two 3×3×3 convolutional layers, a batch normalization layer, a ReLU activation function, and the Argo dynamic correction module connected in sequence. The two-dimensional surface features output from the last level of the satellite remote sensing data branch are converted into an initial three-dimensional feature tensor by the upscaling mapping layer and processed by three decoding modules. In each decoding process, the upsampled features are spliced ​​in the channel dimension with the three-dimensional feature tensor obtained by the upscaling mapping layer of the two-dimensional surface features of the corresponding level of the satellite remote sensing data branch through skip connections. The tail output structure consists of a 3×3×3 convolutional layer and a 1×1×1 convolutional layer connected in series, projecting the high-dimensional features onto a single-channel output three-dimensional temperature field.

[0019] In the above scheme, the multi-source satellite remote sensing fusion data includes sea surface temperature data, sea surface salinity data, absolute dynamic topography data, sea surface wind field data, and geostrophic data; the physical prior data includes absolute dynamic topography data, eddy energy data, front intensity data, and front frequency data. The front intensity data is obtained by performing bilateral filtering preprocessing on sea surface temperature data followed by Sobel operator convolution operation; the front frequency data is obtained by performing multi-level threshold segmentation and time-dimensional cumulative statistics on front intensity data; and the eddy energy data is calculated based on the geostrophic velocity anomaly component.

[0020] In the above scheme, the data acquisition and preprocessing steps include: bilinear interpolation of the multi-source satellite remote sensing fusion data to unify the spatial resolution to 0.25°×0.25° and the temporal resolution to daily average data, and performing max-min normalization; retaining the sea surface to 500-meter depth range for the Argo profile data, interpolating along the vertical direction to one data point every 10 meters, and matching it with the satellite remote sensing data using a spatiotemporal nearest neighbor matching strategy, with the matching conditions being that the latitude and longitude difference does not exceed 0.25° and the time difference does not exceed 24 hours; and using trigonometric functions to continuously and periodically encode the data dates to generate time sine and time cosine features as time prior input networks.

[0021] Through the above technical solution, the ocean three-dimensional temperature field reconstruction method based on physical guidance and frequency-space enhancement provided by the present invention has the following beneficial effects: (i) Through the collaborative design of a physically guided spatial clustering modulation module (PSCM) and a frequency domain separation enhancement module (FSEM), adaptive feature extraction and effective separation of multi-scale signals for different dynamic flow states are achieved. This invention incorporates two core modules, PSCM and FSEM, at each processing level of the satellite remote sensing data branch. PSCM utilizes physical prior features to allocate input features to different dynamic flow regimes through Dynamic Spatial Clustering (DSC), while simultaneously driving a Deformable Convolutional Operator (DCN) to adaptively adjust the sampling grid, ensuring the receptive field adapts to the spatial heterogeneity and morphological evolution of ocean fronts and eddies. FSEM, on the other hand, decomposes features into different frequency band components through Discrete Cosine Transform and generates a spatially gated weight map using physical prior features. In dynamically active regions, high-frequency weights are increased to enhance mesoscale features, while in calm background sea areas, high-frequency weights are suppressed to filter out data noise. The combined efforts of these two modules effectively solve the problems of mutual interference between features from different sea areas caused by globally shared parameters in traditional networks, as well as the spatial aliasing of multi-scale signals.

[0022] (ii) Through the Argo Dynamic Correction Module (ADCM), the layer-by-layer dynamic correction of 3D reconstruction features based on sparse measured data was realized. This invention incorporates ADCM in each decoding module of the decoding branch, using continuous 3D spatial features as query vectors to actively match sparse Argo observation point sequences (Key / Value). A cross-attention mechanism dynamically corrects the 3D reconstructed features. Simultaneously, a binarized mask matrix is ​​introduced, forcibly assigning negative infinity to the attention scores of unobserved areas, ensuring that correction only applies to areas with measured information. This mechanism effectively solves the problem of accumulated errors that easily occur when reconstructing from multi-source satellite remote sensing data of the sea surface, allowing sparse Argo profile data to fully play its calibration role in the deep temperature field.

[0023] (iii) Direct supervision of training through measured data effectively avoids the transmission of systematic biases in reanalysis data. This invention uses Argo measured temperature profiles as real labels to calculate reconstruction loss for model training. Unlike traditional methods that rely on reanalysis datasets such as HYCOM, SODA, GLORYS, or ECCO as training labels, the training labels of this invention are directly derived from field measured data. This fundamentally avoids the problem of systematic errors such as incomplete model parameterization and data assimilation bias in reanalysis data being inherited and amplified by the model, effectively improving the realism and reliability of the reconstruction results.

[0024] (iv) Ablation experiments verified the effectiveness of each module and the synergistic gain effect. This invention quantitatively evaluates the contribution of each module to reconstruction performance through ablation experiments on key components of PFSC-Net. Experimental results show that introducing the PSCM module alone on the baseline network reduces RMSE from 0.703 to 0.593 and MAE from 0.462 to 0.377; introducing the FSEM module alone reduces RMSE to 0.594 and MAE to 0.379; introducing the ADCM module alone reduces RMSE to 0.552 and MAE to 0.358. When all three modules are integrated simultaneously, the model achieves optimal reconstruction performance, with RMSE decreasing to 0.510, MAE decreasing to 0.333, and the coefficient of determination (R²) decreasing significantly. 2 The value was increased to 0.995. This indicates that there is a significant synergistic gain effect among PSCM, FSEM, and ADCM, which can effectively integrate multi-source satellite remote sensing data, physical prior data, and sparse observation data into the model.

[0025] (v) Possesses excellent spatial reconfiguration capabilities in complex marine dynamic environments. Visual verification results of this invention in the Kuroshio Extension (KE) and Kuroshio-Oyashio Confluence (KOC) regions of the Northwest Pacific Ocean show that the reconstructed three-dimensional temperature field clearly presents the flow pattern of the Kuroshio main axis, the core of warm eddies, and the bending morphology of the fronts in the horizontal direction; and accurately captures the downward V-shaped undulations of large warm eddies and the inverted V-shaped bulges of upwelling cold eddies in the vertical direction, as well as the intense vertical water exchange and zonal evolution characteristics unique to the KOC frontal zone. The reconstruction results conform to objective ocean dynamic laws, indicating that this invention can provide a high-precision technical solution for reconstructing subsurface ocean temperatures. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0027] Figure 1 This is a flowchart illustrating the algorithm implementation of the physical-guided frequency-space-enhanced three-dimensional ocean temperature field reconstruction method of the present invention. Figure 2 This is a diagram showing the overall network architecture of the PFSC-Net model of this invention; Figure 3 This is a detailed architecture diagram of the physical prior guiding branch in this invention; Figure 4 This is a detailed architecture diagram of the satellite remote sensing data branch in this invention; Figure 5 This is a detailed architecture diagram of the Argo data processing branch in this invention; Figure 6 This is a detailed architecture diagram of the decoding branch in this invention; Figure 7 This is a detailed architecture diagram of the Physically Guided Spatial Clustering Modulation Module (PSCM) in this invention; Figure 8 This is a detailed architecture diagram of the frequency domain separation enhancement module (FSEM) of the present invention; Figure 9 This is a detailed architecture diagram of the Argo Dynamic Correction Module (ADCM) in this invention. Detailed Implementation

[0028] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0029] This invention provides a physical-guided frequency-domain and spatial clustering enhancement method for reconstructing the three-dimensional temperature field of the ocean. By constructing a PFSC-Net (Physics-guided Frequency-domain and Spatial Clustering Enhancement Network) model and fusing multi-source satellite remote sensing data, physical prior data and Argo profile data, a high-precision reconstruction of the three-dimensional temperature field in the Northwest Pacific Ocean at a depth range of 0 to 500 meters (51 layers in total) can be achieved.

[0030] like Figure 1 As shown, the method of the present invention generally includes the following steps: preprocessing multi-source satellite remote sensing fusion data and Argo profile data; acquiring and calculating the physical prior data required for the model; dividing the dataset into training, validation, and test sets; constructing the PFSC-Net model; training the model using the training set, evaluating it using the validation set, and adjusting the parameters; and evaluating the model's generalization ability and reconstruction accuracy on the test set. The following describes each step in detail with reference to the accompanying drawings.

[0031] I. Data Acquisition and Preprocessing The study area selected in this embodiment is the Northwest Pacific Ocean (25°N~60°N, 120°E~180°E).

[0032] 1. Multi-source satellite remote sensing data fusion This embodiment utilizes five remote sensing fusion products from 2019 to 2022: sea surface temperature (SST), sea surface salinity (SSS), absolute dynamic topography (ADT), sea surface wind field (SSW), and geostrophic current (U / Vgos) data. The SST dataset is a CMEMSOSTIA product with a daily temporal resolution and a spatial resolution of 0.05° × 0.05°. The SSS product is published by CMEMS with a spatial resolution of 0.125° × 0.125°. The ADT and U / Vgos products are provided by CMEMS with a daily temporal resolution and a spatial resolution of 0.125° × 0.125°. The SSW data comes from the CCMP wind dataset, including U and V winds at 10 meters, with a 6-hour temporal resolution and a spatial resolution of 0.25° × 0.25°.

[0033] To eliminate the differences in spatiotemporal resolution and sampling mechanisms between multi-source heterogeneous data, this embodiment employs bilinear interpolation to uniformly interpolate multi-source satellite remote sensing fusion data with different spatial resolutions onto a 0.25°×0.25° resolution grid, ensuring spatial pixel consistency. Temporally, the data is uniformly processed into daily average data. Subsequently, max-min normalization is performed on the data from all channels to eliminate network gradient fluctuations caused by differences in units. The calculation formula is as follows: ; In the formula, These are the original observations. These are the normalized eigenvalues. and These represent the minimum and maximum values ​​of the variable within the dataset, respectively.

[0034] Furthermore, considering the seasonal cycles of ocean systems, trigonometric functions are used to continuously and periodically encode data dates, as shown in the following formula: ; ; In the formula, This represents the day's number within the year; 365.25 is the average number of days in a year, including leap years. and These are the generated time sine and cosine feature components, respectively. This periodic feature uses the co-normalized year feature as a stable time prior input network to help the model capture deep physical correlations.

[0035] 2. Argo profile data The ocean temperature in-situ observation data used in this embodiment comes from the international Argo project (Array for Real-time Geostrophic Oceanography). This observation network acquires upper ocean temperature and salinity profiles through global autonomous profiling buoys, and the data center is operated and maintained by the French Institute for the Development of the Sea (Ifremer).

[0036] For discrete Argo profiles, Argo profile data within the region is retained, with the depth range maintained from sea surface to 500m below sea level. In the quality control phase, only temperature and depth data with quality indicators of 1 (good data) and 2 (potentially good data) are retained, and profiles with fewer than 3 vertical recording points are discarded. Subsequently, the temperature profile is interpolated vertically to one data point every 10m.

[0037] To match satellite remote sensing data with Argo profile data, this embodiment employs a spatiotemporal nearest neighbor matching strategy: a successful match is determined when the latitude and longitude difference between the satellite remote sensing grid points and the Argo profile data does not exceed 0.25° and the time difference is controlled within 24 hours. A total of 15,208 profile data points were successfully matched.

[0038] 3. Physical prior data The physical prior data used in this embodiment are generated from ADT, as well as eddy kinetic energy (EKE) calculated based on U / Vgos and front intensity and frequency calculated based on SST. These fundamental physical parameters characterizing ocean mesoscale dynamics serve as prior knowledge for the Physically Guided Spatial Clustering Modulation Module (PSCM), effectively capturing and reflecting the evolutionary behavior and intrinsic physical properties of mesoscale phenomena such as eddies and fronts.

[0039] Frontal intensity data: First, data quality control was performed on the SST data. Nearest neighbor interpolation was used to fill in missing values ​​to construct a spatially continuous temperature field. Bilateral filtering was employed for noise suppression. An adaptive filter kernel was constructed by multiplying a spatial Gaussian kernel function with a similarity weight in the value range, effectively smoothing uniform regions while preserving the geometric features of the frontal edges. The preprocessed temperature field was then convolved using the Sobel operator, as shown in the following formula: ; ; ; In the formula, , These represent the horizontal and vertical gradients at the current coordinate point, respectively. This is the 3×3 neighborhood matrix of the current coordinate point. This represents the convolution operation. This represents the gradient value at the current coordinate point.

[0040] Front frequency data: Front intensity data is transformed into binary front detection results through multi-level threshold segmentation and morphological optimization algorithms, where 1 represents the area where a front exists and 0 represents a non-front area. Based on this, front frequency analysis adopts a time-dimensional cumulative statistical method, spatially aligning and accumulating the daily binary front masks within each month to generate the cumulative number of days that each grid cell was identified as a front within the statistical period.

[0041] Eddy Kinetic Energy Data: Eddy kinetic energy (EKE) data is a key indicator used to measure eddy intensity and activity. It is calculated from geostrophic velocity component anomaly data, and the calculation formula is as follows: ; In the formula, , This refers to the abnormal velocity component of the geostrophic flow.

[0042] II. PFSC-Net Model Structure To reconstruct the three-dimensional temperature field from 0 to 500 meters (51 layers) in the Northwest Pacific Ocean, this embodiment constructs a multi-source data collaboratively driven network model, PFSC-Net. For example... Figure 2 As shown, the model mainly consists of four branches: the physical prior guidance branch, the satellite remote sensing data branch, the Argo data processing branch, and the decoding branch.

[0043] The physical prior guidance branch takes physical prior data as input and outputs physical prior features at different scales. Its output is unidirectionally connected to the satellite remote sensing data branch. Its main function is to extract and provide multi-scale constraint signals conforming to physical laws to guide feature extraction in the satellite remote sensing data branch. The satellite remote sensing data branch takes multi-source satellite remote sensing fusion data and physical prior features as input and outputs two-dimensional surface features at different scales. This branch is responsible for adaptive clustering and frequency domain enhancement extraction of features under the guidance of physical prior data, achieving adaptive feature extraction from multi-source satellite remote sensing fusion data. The Argo data processing branch takes Argo profile data as input and outputs Argo feature sequences rich in contextual information. This branch transforms discrete observation data into a unified feature sequence by extracting the spatiotemporal dependencies of the non-mesh profile data, thus providing a reliable dynamic correction benchmark for subsequent layer-by-layer reconstruction of 3D space. The decoding branch receives the input two-dimensional surface features and Argo feature sequences. This branch outputs a reconstructed 3D temperature field by fully fusing shallow spatial details and correcting reconstruction errors in the deep temperature field layer by layer, achieving cross-dimensional reconstruction and dynamic correction from two-dimensional to three-dimensional.

[0044] 1. Physics-Prior Guiding Branch like Figure 3 As shown, the physical prior guidance branch consists of four levels. The first level contains two consecutive 3×3 convolutional layers and a ReLU activation function; the subsequent three levels each consist of a max pooling layer, a 3×3 convolutional layer, and a ReLU activation function connected in sequence.

[0045] The input physical prior data first passes through two 3×3 convolutional layers and a ReLU activation function to extract shallow physical prior features 1 containing local details. Subsequently, these shallow features flow through three downsampling modules consisting of a max-pooling layer, a 3×3 convolutional layer, and a ReLU activation function. As the spatial resolution gradually decreases, the receptive field gradually increases, outputting physical prior features (physical prior features 2 to 4) at different scales. These multi-scale features, as the final output of this branch, are then input step-by-step into the corresponding layers with the same receptive field scale in the satellite remote sensing data branch.

[0046] 2. Satellite Remote Sensing Data Branch like Figure 4 As shown, the satellite remote sensing data branch comprises four levels. The first three levels contain, in turn, a Physically Guided Spatial Clustering Modulation Module (PSCM), a Frequency Domain Separation Enhancement Module (FSEM), and a Max Pooling Layer; the last level consists only of PSCM and FSEM.

[0047] PSCM utilizes physical prior information to guide the adaptive spatial clustering and dynamic deformation feature extraction of multi-source satellite remote sensing data features; FSEM achieves adaptive enhancement of feature information in different frequency bands in the frequency domain dimension. Multi-source satellite remote sensing data serves as the initial input to the first-level PSCM; in subsequent processing levels, the output features of the previous level's max-pooling layer serve as the input to the current level's PSCM. Within each processing level, physical prior features from the corresponding scale in the physical prior guidance branch are injected into the current level's PSCM and FSEM, respectively. Guided by the physical prior features, PSCM performs adaptive clustering and modulation of the input features; subsequently, the PSCM output enters the FSEM, where, guided by physical prior features of the same scale, further feature separation and enhancement at the frequency domain scale are performed. After FSEM processing, the first three levels output two-dimensional surface feature 1, two-dimensional surface feature 2, and two-dimensional surface feature 3 sequentially, and the last level outputs two-dimensional surface feature 4, completing all feature extraction for this branch.

[0048] 3. Argo Data Processing Branch like Figure 5As shown, the Argo data processing branch uses the time encoding layer, the location encoding layer, and the temperature normalization layer as parallel initial inputs. After the back end completes the high-dimensional mapping of features through a multilayer perceptron (MLP), it is sequentially connected to the Transformer encoder layer and the fully connected layer at the end.

[0049] Specifically, the input Argo profile data is simultaneously fed into three parallel feature processing branches. The location encoding layer receives the latitude and longitude coordinates of each Argo point, the time encoding layer receives the date stamp of the corresponding profile point, and the temperature normalization layer receives the temperature value. The feature vectors output by the location and time encoding layers are first concatenated along the channel dimension. Subsequently, the concatenated spatiotemporal features and temperature features are mapped to a high-dimensional feature space through their respective independent MLP layers, and then concatenated again along the channel dimension. The integrated feature vector is fed into the Transformer encoder layer, which uses a multi-head self-attention mechanism to capture the complex spatiotemporal dependencies within and between profiles. Finally, the discrete profile features processed by the Transformer encoder layer are projected and aligned along the feature dimension through a fully connected layer at the end, outputting a 128-dimensional Argo feature sequence rich in contextual information.

[0050] 4. Decoding Branch like Figure 6 As shown, the decoding branch mainly consists of a front-end upscaling mapping layer, three decoding modules in the middle, and an output structure at the rear, all connected in series. The front-end upscaling mapping layer connects to the satellite remote sensing data branch and makes cross-branch connections with each subsequent decoding module.

[0051] Each decoding module consists of an upsampling layer, two 3×3×3 convolutional layers, a batch normalization layer, a ReLU activation function, and an Argo Dynamic Correction Module (ADCM) connected sequentially. Within the decoding module, the end of the upsampling layer is concatenated with the end of the upsampling layer on one side to the front of the first 3×3×3 convolutional layer, followed by the second 3×3×3 convolutional layer, the batch normalization layer, the ReLU activation function, and the ADCM module. The terminal structure of each branch consists of a 3×3×3 convolutional layer and a 1×1×1 convolutional layer connected in series.

[0052] Specifically, this branch first receives the 2D surface feature 4 from the last level output of the satellite remote sensing data branch, and converts it into an initial 3D feature tensor through an upsampling layer. It then proceeds to three decoding processes sequentially. In each decoding process, the received 3D feature is first expanded in spatial scale through an upsampling layer; simultaneously, the 2D surface features 1, 2, and 3 from the first three levels of the satellite remote sensing data branch are also expanded into 3D feature tensors through independent upsampling layers. After each upsampling, the current 3D feature is concatenated with the 3D feature tensor obtained from the upsampling of the corresponding level's 2D surface features via skip connections in the channel dimension to fuse shallow spatial details. The concatenated multi-scale features are then continuously processed through two 3×3×3 convolutional layers for depth feature extraction, and after batch normalization and ReLU activation, are input into ADCM. ADCM dynamically corrects the 3D reconstruction result by injecting Argo feature sequences into the decoding branch, enabling each position in the 3D feature tensor to be adaptively calibrated based on its most relevant Argo observation information. The final output features are projected onto a single-channel space through a 3×3×3 convolutional layer and a 1×1×1 convolutional layer, realizing a three-dimensional temperature reconstruction of the active mesoscale processes in the Northwest Pacific from 0 to 500m.

[0053] III. Detailed Design of Core Modules (a) Physically Guided Spatial Clustering Modulation Module (PSCM) In existing studies on 3D ocean temperature field reconstruction, models typically employ standard convolutional neural networks with shared weights to extract features uniformly across the entire spatial domain. However, the real ocean environment exhibits strong spatial heterogeneity, with gentle background currents and drastically changing mesoscale phenomena showing vastly different spatial distribution patterns. Without high-density 3D label supervision, down-reconstruction based solely on 2D sea surface satellite remote sensing data easily leads to feature smoothing, thereby compromising the spatial continuity and accuracy of the 3D temperature field. To address this feature extraction problem and achieve constrained training on unlabeled regions, this method proposes a Physically Prior Data-Guided Spatial Clustering Modulation Module (PSCM) (see...). Figure 7 ).

[0054] In terms of structure, the PSCM has two input ends: multi-source satellite remote sensing fusion data and physical prior features. The physical prior feature input end is divided into two branches: the upper branch has a parallel 3×3 convolutional layer and a 3×3 dilated convolutional layer at its front end, and the output is connected to a 3×3 average pooling layer through an addition operation; the lower branch has a Dynamic Spatial Clustering (DSC) module at its front end, which consists of a 3×3 convolutional layer, a batch normalization layer, a ReLU activation layer, and a 1×1 convolutional layer connected in sequence, with the end of the DSC module directly connected to a Softmax layer. At the rear end of the upper branch, there are three DCN operator layers. The front ends of these three DCN operator layers are connected to both the multi-source satellite remote sensing fusion data input end and the end of the 3×3 average pooling layer in the upper branch, to achieve feature convergence and dynamic modulation between the satellite remote sensing data branch and the physical prior guidance branch.

[0055] Internally, the PSCM receives physical prior features from the physical prior guidance branch, which are then processed in two ways: The first path involves feeding the data into parallel 3×3 standard convolutions and dilated convolutions (with a dilation rate of 3) to extract smaller-scale ocean disturbances and macroscopic ocean circulation information. The output physical features are fused element-wise and then smoothed and dimensionality-reduced using 3×3 average pooling to calculate continuous spatial offsets and modulation weights. Multi-source satellite remote sensing fusion data is directly fed into three sets of parallel deformable convolution operators (DCNs). Driven by the physical spatial offsets and modulation weights, the DCN operators dynamically adjust their sampling grid for the multi-source satellite remote sensing fusion data, enabling their receptive fields to accurately adapt to the spatial heterogeneity of ocean fronts and eddies, extracting deformation features representing different ocean dynamic flow regimes.

[0056] The second approach involves entering the Dynamic Spatial Clustering (DSC) module. Within this module, features are sequentially processed through a 3×3 convolution, a batch normalization layer, a ReLU activation function, and a 1×1 convolutional layer to generate initial clustering results. These results are then processed by a Softmax layer to output a clustering probability distribution map representing the different ocean dynamic current states at each spatial location. Finally, the output clustering probability distribution map is used as linear modulation weights and multiplied element-wise with the deformation features output from the three DCN operators to achieve adaptive extraction of the dominant dynamic features for the current region. Finally, the three modulated and weighted features are aggregated element-wise to output a two-dimensional feature modulated by physical prior guidance.

[0057] This module first calculates spatial location based on prior physical features. Pixels at that location are assigned Clustering probability of parallel branches The specific calculation formula is as follows: ; In the formula, For position The physical prior characteristics of the location. and For learnable mapping weights, This represents the total number of parallel branches.

[0058] Each parallel branch uses the parameters mapped from the physical features to guide the deformable convolution operator, the th Parallel branches at position Output features at The calculation formula is as follows: ; In the formula, This represents the total number of sampling points for the convolution kernel. For the corresponding convolution weights, Feature inputs provided for the satellite observation branch For standard grid space indexing, It is the spatial offset generated by mapping physical features after parallel processing of standard convolution and dilated convolution.

[0059] Finally, the module aggregates the output features of all branches using the initially generated clustering probabilities, and the aggregated features... The calculation formula is as follows: ; In the formula, These are the corresponding spatial clustering probability weights. Local deformation features extracted for each branch.

[0060] Through the PSCM module, the network obtains indicative gradient guidance during backpropagation, enabling effective constrained training even under conditions where the measured data is relatively sparse, thus ensuring the accuracy of feature reconstruction in complex dynamic sea areas.

[0061] (ii) Frequency Domain Separation Enhancement Module (FSEM) Multi-scale dynamic phenomena in the ocean exhibit significant frequency differences: broad background currents are predominantly present in the low-frequency domain, mesoscale eddies are concentrated in the mid-frequency domain, while narrow ocean fronts and observational noise often coexist as high-frequency features. Traditional networks typically process this information in a mixed manner within the spatial domain when extracting features, which can easily lead to frequency aliasing of features at different scales, thus neglecting crucial physical information. Furthermore, blindly enhancing the high frequencies globally on feature maps can easily amplify local observational errors in the data. To achieve effective separation and targeted processing of multi-scale ocean features in the frequency dimension, this invention proposes a frequency domain separation enhancement module, FSEM (see...). Figure 8This module combines Discrete Cosine Transform (DCT) with the Dynamic Spatial Clustering (DSC) module in PSCM to dynamically control the flow of information at different frequencies using physical prior features.

[0062] In terms of structure, the FSEM front end has two inputs: the PSCM output and the physical prior features. The PSCM output is divided into three processing branches and one cross-layer direct connection branch. Each processing branch consists of a DCT layer and an MLP layer connected sequentially. The branch containing the physical prior features is formed by connecting a DSC layer and a Sigmoid activation function sequentially.

[0063] In practice, the features output from the PSCM are simultaneously fed into three parallel DCT layers for specific frequency band separation. Each frequency band feature is then mapped using the corresponding MLP layer for deep nonlinear mapping. Simultaneously, the physical prior features input to the FSEM are used by the DSC module and a sigmoid activation function to generate a spatially gated weight map covering the three frequency band channels. This weight map is then element-wise multiplied with the output features of the three MLP layers to achieve adaptive weighting. The weighted multi-frequency band features are then aggregated through element-wise addition, and finally added to the original input features via residual connections to output the final enhanced features. This mechanism utilizes physical field features as spatial guidance, increasing high-frequency weights in dynamically active regions to preserve and enhance corresponding features, while suppressing high-frequency weights in calm background sea areas to filter data noise, thus adaptively adjusting specific frequency features according to local physical sea conditions.

[0064] The frequency domain transform of this module relies on channel-by-channel constructed DCT basis functions, in spatial location The first The formula for calculating each channel is as follows: ; In the formula, The matrix coefficients are the basis functions of the discrete cosine transform. and Spatial location coordinates, For channel index, and This is the frequency reference index corresponding to this channel. and The height and width of the input feature map are given. The normalization constant is used to ensure the orthogonality of the discrete cosine transform.

[0065] The input features are decomposed into components of different frequency bands by a filter. The formula is as follows: ; In the formula, For input spatial features, For grid indexing, It is a nonlinear function. This represents a mapping network that learns the criticality of different frequency channels. This is the set of filters for this frequency band.

[0066] After obtaining the components of different frequency bands, the module uses DSC to evaluate the dynamic characteristic distribution of the current spatial location and calculates the spatial weight matrix for each frequency component based on the input physical guidance features. After obtaining the feature components of each frequency band, these components are multiplied by their corresponding weights, and the adjusted results are added to the initial spatial features. Through this physically guided frequency domain gating mechanism, the network can adaptively retain mid-to-high frequency information in strong eddy current regions and focus on the flow of low-frequency background information in calm sea areas, thus improving the physical rationality of the ocean temperature field reconstruction results.

[0067] (III) Argo Dynamic Correction Module (ADCM) In existing ocean temperature field reconstruction studies, the irregular and sparse distribution of Argo profile data in time and space makes it difficult for models to directly process discrete profile information using conventional convolution. To overcome this limitation and capture the physical correlation between surface and deep water, this invention proposes the Argo Dynamic Correction Module (ADCM) (see...). Figure 9 The core of this module is to use continuous three-dimensional spatial features as query vectors to actively match sparse Argo observation point sequences (Key / Value), and to dynamically correct the three-dimensional reconstruction features through a cross-attention mechanism layer. In the absence of globally dense labels, the reconstructed field is calibrated using sparse measured points to solve the problem of accumulated errors that easily occur when reconstructing from sea surface satellite remote sensing data alone.

[0068] Structurally, ADCM comprises three core units connected in series: a feature flattening layer, a cross-attention mechanism layer, and a feature restoration layer. The module's front end has three input terminals: a 3D feature vector, a spatial mask matrix, and an Argo feature sequence. The 3D feature vector input terminal is divided into a main branch and a cross-layer direct connection branch. The feature flattening layer at the beginning of the main branch performs dimensionality reduction and serialization transformation of the feature space, and its front end is connected to the aforementioned 3D feature vector. The cross-attention mechanism layer in the middle is responsible for guiding the main features to perform dynamic context correction using measured data, and its front end is connected to the end of the feature flattening layer, the spatial mask matrix input terminal, and the Argo feature sequence input terminal. The feature restoration layer at the end restores the 3D feature dimension, and its front end is connected to the cross-attention mechanism layer. Simultaneously, the cross-layer direct connection branch directly connects the 3D feature vector to the feature restoration layer, which is used to add the original 3D features and the cross-attention corrected features element-wise after feature restoration, forming a residual connection structure.

[0069] During the specific forward propagation process, the module receives the concatenated three-dimensional feature vector from the front-end network, whose tensor dimension is... To meet the attention mechanism's requirement for a one-dimensional sequence format input, the feature vector first needs to pass through a feature flattening layer to perform spatial feature flattening, thus being reshaped into spatial sequence features. (in (This represents the total number of 3D spatial grids). Subsequently, the flattened 3D spatial sequence and dimensions are... Argo feature sequences ( The maximum number of observation points is input into the cross-attention mechanism layer. Inside this layer, the flattened 3D features serve as the query vector, actively calculating the spatial similarity with Argo profile features (Key / Value). Considering the extreme sparsity of Argo observation data, a binarized mask matrix with dimensions of [dimension missing] is introduced in this calculation step. The attention score for the unobserved region is forcibly assigned negative infinity. After cross-attention weighting and multi-head feature aggregation, the output features enter the feature restoration layer for spatial feature restoration, and are remapped back to the initial three-dimensional tensor dimension. Finally, the obtained 3D features are added element-wise to the initial 3D tensor entering ADCM, and the corrected 3D features are output.

[0070] Through this module, the network achieves layer-by-layer dynamic correction of three-dimensional features by discrete profile information, effectively mitigating the smoothing error when inverting deep structures from sea surface input data.

[0071] IV. Model Training 1. Division of training, validation, and test sets This embodiment employs a center-aligned matching strategy, matching each profile with a 40×40 grid of remote sensing satellite data windows and a physical prior data window. These paired samples are then fed into the model for training, resulting in 15208 paired samples. The sample set is divided into training, validation, and test sets in an 8:1:1 ratio. The training set is used to train the model, the validation set is used for hyperparameter tuning and early stopping mechanism monitoring, and the test set is used to test the model's generalization ability.

[0072] To train the model's reconstruction capability under sparse observations, 50% of the Argo profiles falling within each 40×40 sample window in the training set are randomly selected as measured features and input into the network along with other features. The remaining 50% of the profiles are used as the true labels to calculate the reconstruction loss.

[0073] 2. Training Configuration The deep learning framework of this invention is built on the PyTorch deep learning framework, and runs on a Windows 10 operating system and Python 3.9. All training and testing inference are performed on a single NVIDIA GeForce RTX 4090D GPU. The batch size for model training is set to 16, and the maximum number of training epochs is set to 100.

[0074] This embodiment uses the AdamW optimizer for network weight iteration and combines it with a cosine annealing strategy to dynamically decay the learning rate. This strategy causes the learning rate to decrease smoothly along a cosine curve as the training progresses, which helps the network converge quickly in the early stages and find the optimal solution stably in the later stages.

[0075] To prevent overfitting in spatial feature fitting, an early stopping mechanism is introduced during training. After each training epoch, the reconstruction error of the validation set is calculated. If the validation set error does not decrease further within 20 consecutive training epochs, training is automatically terminated and the best-performing weights from the validation set are loaded, thus ensuring that the reconstructed model has good generalization ability.

[0076] 3. Evaluation Indicators To quantitatively evaluate the model's accuracy in reconstructing the three-dimensional ocean temperature field, this embodiment selects the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination. () as an evaluation indicator.

[0077] RMSE is a sample standard deviation used to measure the deviation between reconstructed values ​​and true values. It is highly sensitive to local significant errors, and its calculation formula is as follows: ; In the formula, To assess the total number of spatial grid points within the region, For the first The actual ocean temperature observation values ​​at each location This represents the reconstructed temperature value predicted by the model.

[0078] MAE reflects the average level of the absolute error between predicted and actual values, and can effectively assess the overall prediction bias of the model. The calculation formula is as follows: ; In the formula, To assess the total number of spatial grid points within the region, For the first The actual ocean temperature observation values ​​at each location This represents the reconstructed temperature value predicted by the model.

[0079] This value is used to characterize the extent to which the model's predictions explain the spatial variance of the real physical field. The closer the value is to 1, the better the model's spatial fit. The calculation formula is as follows: ; In the formula, The numerator represents the spatial population mean of the actual temperature observations, the denominator represents the sum of squares of the residuals predicted by the model, and the denominator represents the total sum of squares of the actual data.

[0080] V. Experimental Results 1. Module validity verification This embodiment uses ablation experiments on key components of PFSC-Net to evaluate the contributions of FSEM, PSCM, and ADCM to the model's performance in reconstructing 3D ocean temperature. Six sets of experiments were designed: Baseline, Baseline+ADCM, Baseline+PSCM, Baseline+FSEM, Baseline+FSEM+PSCM, and the complete model including all components: Baseline+FSEM+PSCM+ADCM. All models were trained and tested under the same experimental conditions to quantitatively analyze the impact of each module on reconstruction accuracy. The ablation experiment results are shown in Table 1. Table 1 Ablation Experiment Results

[0081] As can be seen from the results in Table 1, compared to the base model, the introduction of corresponding feature enhancement or correction modules resulted in varying degrees of decrease in both RMSE and MAE. The improvement indicates that all of the above modules have a positive effect on the model's ability to reconstruct the ocean's three-dimensional temperature.

[0082] In the ablation experiment using a single module, the baseline model had an RMSE of 0.703 and a MAE of 0.462. The value was 0.990. After introducing the PSCM module separately, the RMSE decreased to 0.593 and the MAE decreased to 0.377. Improved to 0.993; after introducing the FSEM module separately, RMSE decreased to 0.594 and MAE decreased to 0.379. The RMSE was 0.993; after introducing the ADCM module separately, the RMSE dropped to 0.552 and the MAE dropped to 0.358. It is 0.994.

[0083] The FSEM module separates and enhances the large-scale background trend of the sea surface temperature field from the mesoscale ocean phenomena through a multi-band adaptive decomposition mechanism, which helps the model extract multi-scale features of the ocean. The PSCM module uses dynamic spatial clustering to distinguish different dynamic regions such as background field, eddies and fronts, and guides deformable convolution operators to adapt to the spatial distribution differences of different ocean elements, effectively improving the model's temperature reconstruction effect in dynamically active regions. The ADCM module uses sparse Argo profile data and performs local correction of backbone features in the vertical direction through cross-attention mechanism and dynamic masking to achieve dynamic constraints of observation data on three-dimensional features.

[0084] In the combined experiment, the RMSE of Baseline+FSEM+PSCM was 0.540, and the MAE was 0.357. The RMSE was 0.994, outperforming the single module, indicating a certain complementarity between frequency domain separation enhancement and the physically prior-guided spatial clustering mechanism in the feature extraction process. When ADCM was further added to form the complete model, the RMSE decreased to 0.510 and the MAE decreased to 0.333. The value was increased to 0.995, and the synergistic effect of multiple modules enabled the model to achieve optimal reconstruction performance.

[0085] It can be seen that by introducing FSEM, PSCM and ADCM modules, multi-source satellite remote sensing fusion data, physical prior data and sparse observation data can be well integrated into the model, which can effectively improve the model's ability to characterize the spatiotemporal changes and spatial heterogeneity of the three-dimensional sea surface temperature field, and provide a feasible optimization approach for the reconstruction of ocean subsurface temperature.

[0086] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for reconstructing a three-dimensional ocean temperature field based on physical-guided frequency-space enhancement, characterized in that, Includes the following steps: Step 1: Acquire multi-source satellite remote sensing fusion data, Argo profile data, and physical prior data, and perform preprocessing. Step 2: Construct a physics-guided, frequency-space-enhanced three-dimensional ocean temperature field reconstruction model. This model includes a physics-guided branch, a satellite remote sensing data branch, an Argo data processing branch, and a decoding branch. The physics-guided branch extracts multi-scale features from the physics-guided data, outputting physics-guided features at multiple scales. Each processing level of the satellite remote sensing data branch includes a physics-guided spatial clustering modulation module and a frequency domain separation enhancement module. The physics-guided spatial clustering modulation module uses the physics-guided features to perform adaptive spatial clustering and dynamic deformation feature extraction on the input multi-source satellite remote sensing fusion data. The frequency domain separation enhancement module performs frequency domain feature separation and enhancement on the extracted features, outputting two-dimensional surface features at multiple scales. The Argo data processing branch extracts spatiotemporal dependencies from the Argo profile data, outputting Argo feature sequences. The decoding branch includes an Argo dynamic correction module, which uses a cross-attention mechanism to dynamically correct the input two-dimensional surface features and Argo feature sequences layer by layer and outputs a three-dimensional temperature field. Step 3: Input the multi-source satellite remote sensing fusion data, the physical prior data and part of the Argo profile data into the model, use the remaining Argo profile data in the same spatiotemporal window as the real labels to calculate the reconstruction loss, and train the model until the convergence condition is met. Step 4: Input the multi-source satellite remote sensing fusion data, physical prior data and corresponding Argo profile data of the area to be reconstructed into the trained model. After being processed by the physical prior guidance branch, satellite remote sensing data branch, Argo data processing branch and decoding branch in sequence, the three-dimensional temperature field of the ocean is output.

2. The method according to claim 1, characterized in that, The physically guided spatial clustering modulation module performs the following operations: The physical prior features are processed in two ways. The first path of physical prior features is fused after multi-scale physical information is extracted by parallel 3×3 standard convolution and 3×3 dilated convolution. Then, spatial offset and modulation weight are generated by 3×3 average pooling. This drives three sets of parallel deformable convolution operators to adaptively sample the output features of the multi-source satellite remote sensing fusion data or the output features of the previous level max pooling layer, and output deformable features. The second physical prior features are processed by the dynamic spatial clustering module, and then passed through a 3×3 convolution, a batch normalization layer, a ReLU activation function and a 1×1 convolution layer in sequence, and finally through a Softmax layer to output the clustering probability distribution map of different ocean dynamic flow states to which each spatial location belongs; The clustering probability distribution map is used as a linear modulation weight and multiplied element-wise with the deformation features output by the three sets of deformable convolution operators. The three modulated and weighted features are then aggregated by adding them element-wise to output the two-dimensional features modulated by physical prior.

3. The method according to claim 1, characterized in that, The frequency domain separation enhancement module performs the following operations: The features output by the physically guided spatial clustering modulation module are synchronously fed into three parallel discrete cosine transform layers for specific frequency band separation, resulting in feature components of three different frequency bands. Each frequency band feature component undergoes deep nonlinear mapping via its corresponding multilayer perceptron layer. The physical prior features are used to generate a spatially gated weight map covering three frequency band channels through a dynamic spatial clustering module and a Sigmoid activation function. The spatial gated weight map is multiplied element-wise with the features output from the three multilayer perceptron layers to achieve adaptive weighting of the features; The weighted multi-band features are aggregated by adding them element by element, and then added to the original input features through residual connections to output the enhanced features.

4. The method according to claim 1, characterized in that, The Argo dynamic correction module performs the following operations: The three-dimensional feature vector of the current processing level of the decoding branch is reshaped into a one-dimensional spatial sequence feature through the feature flattening layer, and used as the query vector; The Argo feature sequence is used as a key-value pair and input together with the query vector into the cross-attention mechanism layer to calculate spatial similarity. A binary mask matrix is ​​introduced in the cross-attention calculation to force the attention score of the region without Argo observations to be negative infinity; After cross-attention weighting and multi-head feature aggregation, the output features are remapped back to the three-dimensional tensor dimension through the feature restoration layer; The obtained 3D features are added element-wise to the original 3D tensor before entering the Argo dynamic correction module, and the corrected 3D features are output.

5. The method according to claim 1, characterized in that, The physical prior guidance branch contains four levels. The first level contains two consecutive 3×3 convolutional layers and a ReLU activation function. The subsequent three levels are each composed of a maximum pooling layer, a 3×3 convolutional layer, and a ReLU activation function connected in sequence. The physical prior features of different scales are output to the corresponding levels with the same receptive field scale in the satellite remote sensing data branch step by step.

6. The method according to claim 1, characterized in that, The satellite remote sensing data branch comprises four levels. The first three levels are each composed of the physically guided spatial clustering modulation module, the frequency domain separation enhancement module, and the max pooling layer in sequence. The last level is composed of the physically guided spatial clustering modulation module and the frequency domain separation enhancement module. Multi-source satellite remote sensing fusion data is used as the initial input to the physically guided spatial clustering modulation module of the first level. The output of the max pooling layer in subsequent levels is used as the input of the current level. Each level outputs two-dimensional surface features at the corresponding scale.

7. The method according to claim 1, characterized in that, The Argo data processing branch uses a time encoding layer, a position encoding layer, and a temperature normalization layer as parallel initial inputs. The position features output by the position encoding layer and the time features output by the time encoding layer are concatenated in the channel dimension and then mapped to a high-dimensional space by a first multilayer perceptron. The temperature features output by the temperature normalization layer are mapped to a high-dimensional space by a second multilayer perceptron. The two are concatenated again in the channel dimension and then fed into the Transformer encoder layer and the fully connected layer in sequence, outputting a 128-dimensional Argo feature sequence.

8. The method according to claim 1, characterized in that, The decoding branch comprises a front-end upscaling mapping layer, three middle decoding modules, and a tail-end output structure. Each decoding module consists of an upsampling layer, two 3×3×3 convolutional layers, a batch normalization layer, a ReLU activation function, and the Argo dynamic correction module connected in sequence. The two-dimensional surface features output from the last level of the satellite remote sensing data branch are converted into an initial three-dimensional feature tensor by the upscaling mapping layer. After being processed by three decoding modules, in each decoding process, the upsampled features are spliced ​​in the channel dimension with the three-dimensional feature tensor obtained by the upscaling mapping layer from the two-dimensional surface features of the corresponding level of the satellite remote sensing data branch through skip connections. The tail-end output structure consists of a 3×3×3 convolutional layer and a 1×1×1 convolutional layer connected in series, projecting the high-dimensional features onto a single-channel output three-dimensional temperature field.

9. The method according to claim 1, characterized in that, The multi-source satellite remote sensing fusion data includes sea surface temperature data, sea surface salinity data, absolute dynamic topography data, sea surface wind field data, and geostrophic data; the physical prior data includes absolute dynamic topography data, eddy energy data, front intensity data, and front frequency data. The front intensity data is obtained by performing bilateral filtering preprocessing on sea surface temperature data followed by Sobel operator convolution operation. The front frequency data is obtained by performing multi-level threshold segmentation and time-dimensional cumulative statistics on front intensity data. The eddy energy data is calculated based on the geostrophic velocity anomaly component.

10. The method according to claim 1, characterized in that, In the data acquisition and preprocessing steps: the multi-source satellite remote sensing fusion data is bilinearly interpolated to unify the spatial resolution to 0.25°×0.25° and the temporal resolution to daily average data, and max-min normalization is performed; the Argo profile data retains the sea surface to a depth range of 500 meters, interpolates along the vertical direction to one data point every 10 meters, and is matched with the satellite remote sensing data using a spatiotemporal nearest neighbor matching strategy, with the matching conditions being that the latitude and longitude difference does not exceed 0.25° and the time difference does not exceed 24 hours; trigonometric functions are used to continuously and periodically encode the data dates to generate time sine and time cosine features as time prior input networks.

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