Deep learning based high-resolution downscaling reconstruction method for south china sea subsurface temperature structure

Abstract

The application belongs to the field of ocean subsurface temperature structure reconstruction, and in particular to a South China Sea subsurface temperature structure high-resolution downscaling reconstruction method based on deep learning. The method comprises the following steps: 1) obtaining South China Sea ocean surface data and subsurface data respectively and preprocessing the data; 2) constructing an ocean downscaling model based on a Transformer architecture and training the model using the preprocessed data; 3) dividing the South China Sea sea surface variable data in a 1 / 4° step using an input window of the same size as in the training stage, inputting the divided data into the trained ocean downscaling model, and then obtaining the subsurface temperature field with a resolution of 1 / 4° at the corresponding spatial position of the sea surface. The application can directly output a 1 / 4° resolution subsurface temperature field by adjusting the division method of the input data, significantly enhancing the performance of the mesoscale features in the South China Sea temperature field.

Description

Technical Field

[0001] This invention belongs to the field of marine subsurface temperature structure reconstruction, specifically a high-resolution downscaling reconstruction method for the South China Sea subsurface temperature structure based on deep learning. Background Technology

[0002] Ocean temperature is a key physical quantity characterizing the ocean's thermal state and energy distribution, and its structure directly determines ocean stratification, circulation systems, and air-sea interactions. Variations in ocean temperature not only reflect the thermodynamic response driven by external forcing such as monsoons, thermal radiation, and wind stress, but also reveal the changing characteristics of internal dynamic processes such as upwelling and eddies. Located at the intersection of tropical and subtropical zones, the South China Sea is influenced by a complex monsoon system and circulation structure, resulting in significant spatiotemporal heterogeneity in its temperature variations. In summer, under the influence of the southwest monsoon, sea surface temperatures rise, forming a significant strong stratification structure; while in winter, dominated by the northeast monsoon, surface cooling and enhanced vertical mixing lead to a significant weakening of the vertical temperature gradient. This seasonal shift not only regulates the changes in ocean heat content (OHC) in the South China Sea, but also profoundly impacts the climate variability of the western Pacific by influencing regional air-sea fluxes and energy redistribution processes. Therefore, systematically revealing the spatiotemporal evolution characteristics of the high-resolution temperature field in the South China Sea is of great scientific significance for deepening the understanding of regional ocean thermodynamic processes and their climate feedback mechanisms, and has broad application prospects in regional ocean dynamics research under the background of climate change.

[0003] Previous studies have primarily reconstructed the structure of subsurface ocean temperature using three main methods: observation-driven methods, numerical simulation methods, and statistical methods. The first method relies on measured data from buoys and CTDs, obtaining a gridded ocean element field through objective analysis techniques such as optimal interpolation. While this method directly reflects observational data, the spatial resolution of the objective analysis product is low, typically only 1°, due to the sparsity and non-uniform distribution of the observational data in space and time, making it difficult to resolve small- to medium-scale structures. The second method is based on ocean numerical models that incorporate data assimilation. These models simulate internal ocean flows and thermohaline transport processes by solving ocean dynamics and thermodynamic governing equations, and then incorporate observational information into the model system through data assimilation, thereby reconstructing high-resolution subsurface temperatures. Although numerical models have advantages in dynamic constraints and physical interpretability, their results are highly sensitive to initial fields, boundary conditions, and parameterization schemes, and computational costs increase significantly with resolution, limiting their feasibility for long-term and large-scale applications. The third method is a statistical approach that learns statistical mapping relationships between multiple ocean elements based on historical data to obtain the continuous spatiotemporal distribution of subsurface ocean elements. Some studies have also achieved inferences from high-resolution information by constructing empirical mappings between large-scale or sea-surface variables and regional / subsurface structures. These methods are computationally efficient and can, to some extent, compensate for data gaps caused by sparse observations. However, they typically rely on assumptions of linearity and stationarity, making it difficult to capture complex nonlinear dynamic responses in ocean systems. Their applicability is limited, especially in regions with complex dynamic processes, such as the South China Sea.

[0004] In recent years, with the rapid development of machine learning and deep learning technologies, researchers in the ocean and atmosphere fields have begun to gradually apply these advanced methods to subsurface temperature reconstruction and downscaling studies. Unlike traditional statistical methods based on linear assumptions, deep learning methods, through representation learning and end-to-end optimization, can automatically capture high-dimensional nonlinear mapping relationships between variables, exhibiting greater advantages in reconstruction accuracy and generalization. Therefore, deep learning methods have gradually become one of the important technical approaches for ocean subsurface reconstruction.

[0005] Despite significant progress made by deep learning in ocean downscaling tasks, two key challenges remain. First, many existing studies use “high-resolution” interpolated data, numerical model outputs, or reanalysis products as training labels, which often exhibit systematic biases against the true subsurface structure, potentially propagating errors into the model's learned mappings. Second, directly transferring the super-resolution framework from computer vision to Earth's fluid systems often overlooks the complex physical constraints and thermodynamic characteristics of ocean processes, thus weakening the physical reliability of the results. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes a high-resolution downscaling reconstruction method for the South China Sea subsurface temperature structure based on deep learning. This method learns the mapping relationship between high-resolution sea surface elements and the ocean subsurface structure, applying this relationship during the inference stage to achieve downscaling of the three-dimensional temperature structure. To this end, this invention proposes an efficient ocean downscaling model—Ocean Downscaling Transformer (ODT). This model integrates multi-scale feature extraction and cross-variable representation capabilities, effectively capturing the spatial structure of high-resolution sea surface elements and achieving high-precision reconstruction of the subsurface temperature structure. The ODT model, without relying on high-resolution subsurface datasets or using image super-resolution techniques, utilizes 1° resolution EN4 data as training labels to achieve a 1 / 4° South China Sea subsurface temperature reconstruction. This method provides an efficient and scalable technical approach for downscaling the South China Sea subsurface temperature, possessing significant scientific and applied value and broadly applicable to research on regional ocean dynamic processes and climate variability.

[0007] The technical solution adopted by the present invention to achieve the above objectives is as follows:

[0008] A high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning includes the following steps:

[0009] 1) Acquire surface and subsurface ocean data from the South China Sea and preprocess them;

[0010] 2) Construct an ocean downscaling model based on the Transformer architecture and train the model using preprocessed data;

[0011] 3) The same input window size as the training phase is used, and the South China Sea surface variable data is divided into subdivisions with a step size of 1 / 4°. The subdivision data is then input into the trained ocean downscaling model to obtain the subsurface temperature field with a resolution of 1 / 4° at the corresponding spatial location of the sea surface.

[0012] Step 1) includes the following steps:

[0013] 2.1) Unify all surface and sub-surface data into monthly average data;

[0014] 2.2) Keeping the original EN4 1° grid unchanged, a 1 / 4° target grid corresponding to the original EN4 grid is constructed by interpolation, and this is used as the unified spatial reference grid;

[0015] 2.3) All ocean surface data were unified into a spatial reference grid through resampling;

[0016] 2.4) Remove grid points with missing data values ​​in the area to be reconstructed, and normalize the processed data.

[0017] The ocean downscaling model includes:

[0018] Spatial Feature Extraction Layer: This layer extracts spatial features from the preprocessed local neighborhood data using two-dimensional convolution, and then rearranges the convolutional two-dimensional spatial features into a sequence of length [length missing]. The spatial sequence is then processed by linear mapping and layer normalization to obtain the spatial sequence representation. ,in, Indicates batch size, Indicates the total number of spatial locations. This represents the feature dimension of the model, used to indicate the length of the embedded feature vector corresponding to each spatial location;

[0019] Cross-attention layer for variables: Based on multi-temporal sample data, learn the mapping law between sea surface variables and subsurface temperature structure, and use attention mechanism to enhance the modeling ability of non-neighboring spatial location correlation features within the local window;

[0020] Position-aware Transformer encoding layer: Encodes the fused features obtained from the variable cross-attention layer through relative position encoding;

[0021] Attention aggregation layer: The encoded feature matrix is ​​converted into a single-point matrix using the attention aggregation mechanism, and then point-by-point regression prediction is performed through a multilayer perceptron to output the temperature estimate of the target depth layer.

[0022] The spatial feature extraction layer performs the following steps:

[0023] Preprocessed local neighborhood sea surface multivariate data Perform two-dimensional convolution operations to extract local spatial features:

[0024]

[0025] in, This indicates that the input is multivariate sea table data. Indicates batch size, Indicates the number of input variables. and These represent the height and width of the local neighborhood window, respectively. This represents the spatial features extracted by convolution;

[0026] The convolutional two-dimensional spatial features are rearranged into a sequence of length [length missing]. Spatial sequence representation:

[0027]

[0028] in, This represents the spatial sequence characteristics after rearrangement. Indicates the total number of spatial locations. Indicates the dimension of the convolution output features;

[0029] By performing linear mapping and layer normalization on the spatial sequence features, we obtain the spatial sequence representation:

[0030]

[0031] in, Represents the linear mapping weight matrix. Indicates the bias term. This represents the spatial sequence representation output by the spatial feature extraction layer. This represents the feature dimension of the model, used to indicate the length of the embedded feature vector corresponding to each spatial location.

[0032] The variable cross-attention layer performs the following steps:

[0033] Calculate the variable weights based on the original data variables:

[0034]

[0035] in, Indicates the first The input variable in the th... The value at each spatial location Indicates the first Importance coefficients of each variable; representation of spatial sequences Perform linear mapping on each variable to obtain the feature representation of each variable:

[0036]

[0037] in, Indicates the first Feature representation of input variables after linear mapping Indicates the first The linear mapping weight matrix corresponding to each input variable;

[0038] Weighted fusion of feature variables based on their weights:

[0039]

[0040] in, Indicates fusion characteristics, Given the number of input variables; a multi-head self-attention mechanism is used to model long-range spatial dependencies:

[0041]

[0042] Among them, attention mechanism parameters Depend on Linear mapping yields, The key vector dimension is represented by a linear transformation applied to the attention output features and then compared with the input features. By performing residual connections and layer normalization, the output features of the multivariate cross-attention module are obtained:

[0043]

[0044] in, This represents the linear mapping matrix corresponding to the attention output. This represents the output feature of the multivariate cross-attention module.

[0045] The location-aware Transformer coding layer performs the following steps:

[0046]

[0047] in, This represents the encoded features after processing by the position-aware Transformer coding layer. This refers to the Transformer encoding module. This indicates a relative position encoding.

[0048] The attention aggregation layer performs the following steps:

[0049] Let the aggregate weights be:

[0050]

[0051] in, Represents the aggregate weight vector. This represents the learnable attention projection matrix. This represents the center position offset vector. If the learnable bias term is represented, then the single-point spatial representation... for:

[0052]

[0053] in, Indicates the first The encoded features corresponding to each spatial location This represents the spatial features of a single point after aggregation;

[0054] The aggregated spatial features are analyzed using a multilayer perceptron. Perform pointwise regression prediction:

[0055]

[0056] in, Indicates the prediction result. This represents a multilayer perceptron.

[0057] Training the model using the preprocessed data includes the following steps:

[0058] Based on EN4 grid data, the corresponding sea surface input location is determined, and a mapping relationship between sea surface information and subsurface temperature is constructed as a label dataset;

[0059] Target depth based on ocean Constructing a composite weighted loss function ;

[0060] Using labeled datasets and The ocean downscaling model was trained.

[0061] The mapping relationship between sea surface information and subsurface temperature is constructed as follows:

[0062] (1) Taking each EN4 grid point as the center, extract the 1 / 4° resolution sea surface data within a 7×7 range around it as the input window, and use the subsurface temperature at the corresponding location as the label value;

[0063] (2) Slide the input window in space with a step size of 1°, that is, 4 1 / 4° grid points, and extract the next set of "input-label" samples. Slide the input window and extract samples in sequence until all EN4 surface temperature data are covered.

[0064] (3) Use the extracted samples to construct a sea surface input and subsurface temperature label dataset.

[0065] The composite weighted loss function Specifically:

[0066]

[0067] in, Indicates depth The actual value of the subsurface temperature at that location. This represents the reconstruction result of the model. For single-point absolute error, parameters and This represents a hyperparameter used to control the relative importance of the two weighting factors. This represents the vertical structure weighting factor used to enhance the vertical gradient information in the EN4 subsurface temperature profile. Indicates the weighting factor based on sea surface spatial variability:

[0068]

[0069]

[0070] in, This represents the difference in subsurface temperature label values ​​between adjacent depth layers. Indicates the depth interval between adjacent depth layers. Indicates depth The magnitude of the vertical temperature gradient at that location. express The average value of the inner horizontal gradient magnitude, This indicates the sea surface temperature data within the input window. and Both represent normalization functions.

[0071] The present invention has the following beneficial effects and advantages:

[0072] 1. This invention enables high-resolution downscaling reconstruction of the subsurface temperature structure in the South China Sea without relying on high-resolution subsurface temperature tag data;

[0073] 2. This invention can effectively improve the accuracy and stability of the subsurface temperature structure reconstruction in the South China Sea;

[0074] 3. While maintaining the consistency of large-scale temperature distribution, this invention can enhance the ability to express the details of mesoscale temperature structures;

[0075] 4. This invention has good physical consistency and can more reasonably reflect the spatial distribution characteristics of the subsurface temperature structure in the South China Sea. Attached Figure Description

[0076] Figure 1 Schematic diagram of the model training and downscaling process;

[0077] Figure 2 RMSE box plots for four selected regions of RNN, CNN, and ODT models in 2024;

[0078] Figure 3 Ri of four selected regions in 2024 Ri for RNN, CNN, and ODT models 2 Box-type diagram;

[0079] Figure 4 RMSE (left axis) and Ri of subsurface temperature reconstruction at different depths in the South China Sea using RNN, CNN, and ODT models in 2024. 2 (Right axis) Comparison diagram. Detailed Implementation

[0080] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0081] A high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning includes the following steps:

[0082] 1) Acquire surface and subsurface ocean data from the South China Sea and preprocess them;

[0083] The ocean surface data includes: absolute dynamic height data (ADT), sea surface temperature data (SST), wind stress curl data (WSC), location information, time information, and climatological data. All sea surface data are preprocessed and unified to a spatial resolution of 1 / 4°. The subsurface data is three-dimensional temperature data with a spatial resolution of 1° from the EN4 dataset, which is used as a supervision label during the model training phase.

[0084] 2) Construct an ocean downscaling model based on the Transformer architecture and train the model using preprocessed data;

[0085] 3) The same input window size as the training phase is used, and the South China Sea surface variable data is divided into subdivisions with a step size of 1 / 4°. The subdivision data is then input into the trained ocean downscaling model to obtain the subsurface temperature field with a resolution of 1 / 4° at the corresponding spatial location of the sea surface.

[0086] Example

[0087] 1. Data and Methods

[0088] 1.1 Data

[0089] Based on previous research, this invention selects absolute dynamic topography (ADT), sea surface temperature (SST), wind stress curl (WSC), as well as location information (latitude and longitude), time information, and climatological data as input variables for the model.

[0090] The ADT data comes from a satellite altimeter fusion product provided by the Copernicus Marine Environment Monitoring Service (CMEMS), which integrates sea surface height observations from multiple satellite missions to generate a globally gridded absolute dynamic height field. The SST data comes from the Optimal Interpolation Sea Surface Temperature (OISST) high-resolution grid product from the National Oceanic and Atmospheric Administration (NOAA), which integrates multi-source observation data. The WSC data is calculated from the meridional (NSSW) and zonal (ESSW) wind vector components of the Sea Surface Wind (SSW). The SSW data uses a Cross-Calibrated Multi-Platform (CCMP) wind field dataset, which integrates multiple satellite observations to generate a globally unified and spatiotemporally consistent wind field product. The formula for calculating WSC is:

[0091]

[0092]

[0093]

[0094]

[0095] in For wind stress, air density, The drag coefficient, For the sea surface wind speed component, The wind speed is used. All sea surface variables are at a 1 / 4° spatial resolution to ensure the model can resolve the mesoscale features required to reconstruct the high-resolution subsurface temperature structure. The target label is the subsurface temperature (1° grid) from the EN4 monthly-scale objective analysis product provided by the UK Met Office Hadley Centre. This dataset integrates multi-source observational data from Argo, XBT, CTD, etc. To evaluate the accuracy of the downscaling results, this invention also selected high-resolution products from GLORYS12V1, ORAS5, ARMOR3D, and ECCO2 as control data. The introduction of multi-source data products provides a more comprehensive perspective for model validation and helps improve the reliability of the evaluation. A summary of all data products used in this invention is shown in Table 1.

[0096] Table 1 Summary of data used in the study

[0097]

[0098] To maintain consistency between model input and output over time, this invention first converts all data to monthly averages. For spatial processing, given the subsequent need to downscale and reconstruct subsurface temperature, all sea surface variables are unified to the same 1 / 4° regular grid. It should be noted that although the spatial resolution of each original sea surface data product is 1 / 4°, their grid construction methods differ; without unification, this would lead to coordinate position deviations. Therefore, while maintaining the original 1° EN4 grid, this invention constructs a corresponding 1 / 4° target grid through interpolation, using this grid system as a unified spatial reference. This step is only used to establish a unified spatial coordinate framework and does not directly use the interpolated EN4 data for model training. Based on this, all sea surface input variables are resampled to this 1 / 4° target grid, ensuring spatial consistency among input variables and complete coverage of the 1° EN4 grid. Grid points with missing values ​​within the study area are removed. Finally, to improve training efficiency and promote model convergence, all variables are normalized before training.

[0099] 1.2 Methods

[0100] To overcome the limitations of traditional convolutional networks in long-range dependency modeling and multivariate collaborative representation, this invention constructs an ODT model based on the Transformer architecture for downscaling reconstruction of subsurface temperature. The model focuses on local... Using a multivariable sea surface field as input, an end-to-end mapping from a two-dimensional sea surface matrix to the vertical temperature structure at the target point is achieved. Let the input tensor be... ,in For batch size, The number of input variables includes ADT, SST, wind stress curl, longitude, latitude, cos(month), sin(month), and climatological temperature. The spatial window scale is used. First, spatial features are extracted from the local neighborhood using two-dimensional convolution:

[0101]

[0102] in, This represents the activation function. Subsequently, the convolutional two-dimensional spatial features are rearranged into a sequence of length [length missing]. Spatial sequence representation Furthermore, spatial sequence features are obtained by projecting them onto a unified feature space through linear mapping and layer normalization. :

[0103]

[0104] in, This represents a spatial sequence obtained by rearranging two-dimensional spatial features. Indicates batch size, The model's feature dimension represents the length of the embedded feature vector corresponding to each spatial location. Through the above process, the model achieves the transformation from a two-dimensional local neighborhood matrix to a high-dimensional spatial sequence representation.

[0105] To characterize the relative contributions of different physical variables in the reconstruction process, the model introduces a multivariate cross-attention mechanism based on spatial features. First, the variable weights are calculated based on the original variable field.

[0106]

[0107] in, Indicates the first The input variable in the th ... The value at each spatial location Indicates the first The importance coefficients of each variable are then obtained through a variable-specific linear mapping path.

[0108]

[0109] in, Indicates the first The linear mapping weight matrix corresponds to each variable. Weighted fusion is then performed based on the weights.

[0110]

[0111] in, Indicates the number of input variables. This represents the weighted fusion of features. Based on this, a multi-head self-attention mechanism is used to model long-range spatial dependencies.

[0112]

[0113] in, Depend on Linear mapping yields, This represents the dimension of the key vector. To further enhance feature representation and maintain training stability, the attention output is linearly transformed and then compared with the input features. By performing residual connections and layer normalization, the output features of the variable cross-attention layer are obtained:

[0114]

[0115] in, This represents the linear mapping matrix corresponding to the attention output. This structure combines variable-level weighting with spatial self-attention, enabling adaptive collaborative modeling of multi-source ocean elements, and is one of the important structural features of the model.

[0116] To enhance the ability to express local structural morphology, relative position encoding is introduced in the Transformer encoding process. The encoding process, which describes the offset relationship of each spatial position relative to the center point, can be represented as follows:

[0117]

[0118] in, This represents the feature representation after processing by the location-aware Transformer encoding layer. By introducing relative location encoding, the model enhances its sensitivity to local mesoscale spatial structures while maintaining its ability to model global dependencies. After completing global modeling, the model achieves the transformation from a matrix to a single point through a learnable attention aggregation mechanism. Let the aggregation weights be...

[0119]

[0120] in For aggregate weight vectors, For learnable attention projection matrix, This represents the learnable bias term. Let be the center position bias vector, used to enhance the importance of the neighborhood features of the target point. Then, the single-point space is represented as:

[0121]

[0122] in, Indicates the first The encoded features correspond to each spatial location. This mechanism has stronger spatial focusing capabilities compared to traditional average pooling. Finally, the aggregated spatial features... Pointwise regression prediction using a multilayer perceptron:

[0123]

[0124] in, This indicates the temperature prediction results for the target depth layer. This represents a multilayer perceptron.

[0125] Overall, the ODT model achieves cross-scale modeling and effective integration of multivariate information on the local sea surface through a hierarchical structure including spatial feature extraction, variable cross-attention, location-aware Transformer encoding, and attention aggregation. While maintaining the ability to model global dependencies, it enhances the ability to analyze spatial details, thereby significantly improving the accuracy and physical consistency of subsurface temperature downscaling reconstruction.

[0126] 1.3 Experimental Design

[0127] This invention applies the proposed ODT model to reconstruction and downscaling tasks. The overall process includes three key steps: data processing, model training and evaluation, and model downscaling.

[0128] During the model training phase, this invention first determines the corresponding sea surface input location based on EN4 grid data, thereby constructing a mapping relationship between sea surface information and subsurface temperature. Specifically, as... Figure 1 As shown in diagram a, for each EN4 grid point, sea surface data with a 1 / 4° resolution within a 7×7 area around it is extracted as model input, and the corresponding subsurface temperature is used as the label value. Then, this input window slides spatially in steps of 1° (i.e., four 1 / 4° grid points), sequentially extracting the next set of "input-label" samples, and so on, until all EN4 subsurface temperature data is covered. Finally, the constructed sea surface input and subsurface temperature label dataset is used for model training, thereby achieving the mapping learning from sea surface variables to subsurface temperature.

[0129] To further enhance the ability to downscale subsurface temperature using high-resolution sea surface data, this invention targets the target depth. A composite weighted loss function was constructed. This is to enhance the model's ability to characterize key structural layers. The loss function is defined as follows:

[0130]

[0131] in, Indicates depth The actual value of the subsurface temperature at that location. This represents the reconstruction result of the model. This is the single-point absolute error, serving as the basic point-by-point error metric. Parameters and These are hyperparameters that control the relative importance of the two weighting factors.

[0132] in, The vertical structure weighting factor is used to enhance the vertical gradient information in the EN4 subsurface temperature profile. Its expression is as follows:

[0133]

[0134] In the formula, Indicates depth The magnitude of the vertical temperature gradient at that location. This is the normalization function. This weight can enhance the model's attention to significant levels of vertical temperature gradients (especially in the latitudinal regions), thereby improving its ability to characterize the complex latitudinal structures and their evolution.

[0135] Simultaneously, a weighting factor based on sea surface spatial variability is introduced. To characterize the input 1 / 4° resolution sea surface data block (denoted as...) The horizontal gradient feature in () is defined as follows:

[0136]

[0137] in, express The average value of the inner horizontal gradient magnitude, This is the normalization function. During training, this weight highlights complex regions of the surface dynamic process, guiding the model to pay more attention to subsurface responses with strong spatial non-uniformity, thereby improving the model's generalization ability and reconstruction accuracy under dynamically active and extreme environmental conditions.

[0138] This invention targets each target depth layer in the EN4 dataset. Each model constructs its own independent training sample set and trains a corresponding ODT model with parameters for each depth. The model parameters for each depth are independent of each other, with no parameter sharing across depths. This strategy allows each model to focus on learning the mapping relationship between sea surface variables and subsurface temperature at a specific depth, thereby achieving optimal reconstruction performance at different depths.

[0139] To verify whether the model effectively learns the physically meaningful sea surface-subsurface mapping and to demonstrate its reliability in downscaling reconstruction applications, a systematic evaluation was conducted on the model after training, considering multiple perspectives including horizontal spatial distribution characteristics, vertical structural characteristics, and monthly variation characteristics. By comparing the consistency and error characteristics of the reconstruction results and labeled data across different depths, time scales, and spatial regions, the model's ability to characterize the subsurface temperature structure was comprehensively analyzed. In the downscaling stage, such as... Figure 1 As shown in b, the input window of the same size as in the training phase is used, and the sea surface variables are divided into input data with a step size of 1 / 4°. Subsequently, the divided sea surface data are sequentially input into the trained model, outputting the subsurface temperature field at the corresponding spatial location with a resolution of 1 / 4°. Through this process, the model achieves subsurface temperature downscaling by constructing a mapping relationship between high-resolution sea surface data and subsurface structure.

[0140] 2 Results

[0141] 2.1 Comparison of CNN, RNN, and ODT models

[0142] To systematically evaluate the performance of the ODT model in reconstructing the subsurface temperature structure of the South China Sea, this invention selected 2024 data as an independent test set and compared it with traditional RNN and CNN models. The three models were compared under identical datasets and experimental configurations to ensure the comparability and objectivity of the evaluation results. Overall, the ODT model performed best, with a regional average RMSE of 0.27℃ and an R... 2 The efficiency score was 0.998, significantly better than RNN (0.52℃ / 0.9888) and CNN (0.46℃ / 0.9898). To further verify the applicability of the model under different dynamic environments, this invention selected four typical sub-regions (ADs) in the South China Sea for performance evaluation. Region A (115°-117°E, 18°-20°N) is located in the shelf-slope transition zone of the northern South China Sea, and is affected by shelf slope topography, nearshore upwelling, and slope eddies, resulting in active dynamic processes. Region B (116°-118°E, 15°-17°N) corresponds to the Luzon eddy active zone and is significantly affected by the intrusion of the Kuroshio tributary. Region C (113°-115°E, 10°-12°N) is located at the edge of the deep water area in the central and southern South China Sea, and eddy activity is frequent under the combined influence of wind fields and large-scale circulation. Region D (110°–112°E, 12°–14°N) is located in the upwelling zone off the central coast of Vietnam, where the coastal upwelling driven by the summer southwest monsoon is significantly coupled with mesoscale eddies. Evaluation results show that ODT outperforms RNN and CNN models in all four sub-regions, exhibiting lower RMSE and higher R-values. 2 For example, in region D, the average RMSE of the ODT model is approximately 0.19 °C, and R0.05... 2 The RMSE was 0.9987, while the RNN and CNN models were 0.37 ℃ / 0.9959 and 0.33 ℃ / 0.9964, respectively. Similar performance improvements were observed in regions A, B, and C. Furthermore, the sub-region RMSE and R... 2 Box plot analysis ( Figure 2 and Figure 3 This verified the above differences: ODT not only had a smaller overall error in most regions, but also lower inter-sample dispersion, and higher stability and consistency (R²). 2 (Greater than 0.996, RMSE less than 0.6 ℃). Overall, the ODT model exhibits higher reconstruction accuracy and stronger robustness than traditional deep learning models under various marine dynamic backgrounds.

[0143] After evaluating the horizontal reconstruction performance, this invention further calculated the RMSE and Ri of the reconstruction results at different depths in the South China Sea in 2024. 2 This is to verify the model's consistency and stability in the vertical direction. For example... Figure 4 As shown, the vertical error trends of the three models are generally similar. Figure 4 It includes the ODT model (blue), RNN model (yellow), and CNN model (red). Figure 4 The horizontal axis represents depth, the bar chart represents RMSE (°C, left axis), and the line chart represents R. 2 (Right axis) As shown in the figure, RMSE gradually increases from the surface downwards, reaching a peak around 110m, and then slowly decreases towards 1800m; R 2 The value decreases from the sea surface downwards, reaching its lowest point around 100m, and then gradually increases with increasing depth. It is worth noting that the ODT model performs better across the entire depth range, with its advantages being most pronounced within the thermocline, exhibiting lower RMSE and higher R0. 2 Compared to RNNs and CNNs, it shows a significant improvement. Overall, the ODT model achieved the lowest vertical mean RMSE (0.31℃) and the highest R... 2 (0.9411), and its standard deviation with depth is the smallest (RMSE is 0.18℃, R 2 The value of 0.045 indicates that its vertical reconstruction results are smoother and more consistent, with stronger stability and robustness. In contrast, the reconstruction errors of RNN and CNN models fluctuate more in the vertical direction, and their accuracy and consistency are relatively weaker.

[0144] To test the robustness of the models across time scales, this invention evaluated their reconstruction performance month by month in 2024. The results show that the seasonal variation characteristics of the three models are generally consistent, but the ODT model exhibits superior performance and higher stability throughout the year. Regarding RMSE, the RMSE of RNN and CNN is typically between 0.35 and 0.55 °C, while the ODT model remains relatively stable between 0.2 and 0.35 °C, with the most significant improvement observed in April and May, reducing the error by approximately 0.2 to 0.25 °C. Regarding R... 2 In terms of RNN and CNN, R... 2 Most RNNs and CNNs scored between 0.985 and 0.995, while the ODT model consistently scored above 0.995, reaching as high as 0.998. It's worth noting that the performance of RNNs and CNNs declined during January-March (R² = 0.985). 2 During the period of approximately 0.985, ODT remained above 0.993. Overall, the ODT model achieved lower errors and higher correlations in all months of the year, demonstrating better temporal consistency and stability.

[0145] 2.2 Performance Evaluation of ODT Model Reconstruction

[0146] The above evaluation results show that the ODT model proposed in this invention outperforms RNN and CNN models in the South China Sea region, exhibiting higher reconstruction accuracy and robustness. To further verify the model's performance, this section will conduct an in-depth analysis of the ODT model from multiple perspectives, focusing on whether it has learned physically meaningful sea surface-subsurface mapping relationships, thereby demonstrating its effectiveness in downscaling reconstruction applications.

[0147] To evaluate the spatial reconstruction performance of the model, this invention compared the subsurface temperature field reconstructed by the ODT model at different depths in 2024 with the EN4 data distribution. These depths cover the main water layers from the surface mixing layer, through the thermocline, to the deep water, and can comprehensively reflect the model's stability and accuracy in each vertical layer. Overall, the ODT model can reproduce the main horizontal structures in EN4 and the vertical characteristic of decreasing temperature with increasing depth. Overall, the reconstructed temperature field maintains high consistency with EN4 at all depths with small errors, indicating that the model has good spatial reconstruction performance. At 5 m, the seawater temperature is approximately 28-30 ℃, showing a significant warm-north pattern, with the northern shelf and nearshore waters being relatively cold, and the spatial distribution is basically consistent with the EN4 data; the errors are mainly distributed along the eastern shelf coast, with amplitudes mostly less than ±0.5 ℃. At 45 m, the transition between warm and cold distributions is clearer, forming a significant temperature gradient from west to east, with the eastern waters slightly warmer due to warm water intrusion. At 98 m, the cold water region in the central South China Sea further expands, with two significant cold water masses forming along the coasts of Vietnam and Luzon Island, respectively. Errors are mainly concentrated in the area where cold and warm water masses converge. At 165 m, the cold water region in the central South China Sea expands significantly, with temperatures around 16-19 °C. The eastern continental slope and surrounding waters are relatively cold, while the waters near Palawan Island in the southeast and the Luzon Strait in the northeast are slightly warmer. At 315 m, the cold water structure further strengthens and extends southward, forming a persistent low-temperature zone in the northeastern South China Sea, with temperatures dropping to around 11-11.5 °C. At 1868 m, the temperature range narrows further to around 2.5-3.5 °C, and the overall horizontal gradient weakens significantly, indicating that the temperature structure gradually becomes more homogeneous and stable with increasing depth. Furthermore, the temperature reconstructed by the ODT model shows a significant linear relationship with EN4 at all depths, with the scatter points closely distributed near the 1:1 line, indicating high consistency and small systematic bias. R0 at each depth... 2 All values ​​exceeded 0.975, further demonstrating that the model can accurately reproduce the main spatial distribution characteristics of temperature variation with depth.

[0148] To more comprehensively evaluate the performance of the ODT model, this invention further analyzes the spatiotemporal variation characteristics of the reconstruction results throughout 2024. Overall, the RMSE was below 0.7 °C for most months and within the depth range throughout the year, and R...2 A value above 0.85 indicates that the ODT model maintains high accuracy and robustness in subsurface temperature reconstruction. It should be noted that the RMSE distribution shows that errors are mainly concentrated in the 110-200 m depth range, particularly during the monsoon transition from February to June, with a peak value of approximately 0.6-0.7 ℃, corresponding to the transition from winter to summer in the upper South China Sea. During this period, the vertical temperature gradient changes drastically, increasing the difficulty of model fitting and resulting in larger errors. With increasing depth, the RMSE decreases rapidly and tends to stabilize, generally falling below 0.2 ℃ below 200 m, indicating that the model's reconstruction of deep-layer temperature structures is more stable and reliable. 2 Further analysis shows that the model maintains a high correlation (greater than 0.85) across most depths and months, accurately reproducing the spatiotemporal variations of the South China Sea temperature structure. However, the surface correlation slightly decreases from June to October; and a slight decrease also occurs near a depth of approximately 100 m from January to March. This may be related to seasonal dynamic processes: increased solar radiation in summer leads to greater surface sea surface temperature variability, while stronger winds in winter exacerbate vertical mixing, increasing fluctuations in the subsurface temperature structure and thus raising the difficulty of model fitting. Overall, the ODT model exhibits high consistency throughout the year and across all vertical levels, demonstrating its robustness and stability to temperature variations across different seasons and depths.

[0149] 2.3 Evaluation of ODT Model Downscaling Performance

[0150] A core innovation of this invention lies in its downscaling capability during the model inference stage: using only 1° resolution EN4 data as training labels, the ODT model, combined with the input data segmentation strategy proposed above, can directly output a subsurface temperature field with 1 / 4° resolution during the inference stage. The performance of this downscaling reconstruction result is evaluated below.

[0151] To verify the model's downscaling performance at different depths in the South China Sea, this invention selected July 2024 for comparative analysis. This period coincides with the peak of the summer southwest monsoon, characterized by active wind stress and upwelling processes in the South China Sea, resulting in the most significant subsurface temperature structure features. Overall, the temperature distribution obtained by downscaling the ODT model is highly consistent with the EN4 temperature field in terms of large-scale spatial patterns, and can accurately reproduce the temperature structure characteristics at different depths. Specifically, at the surface (approximately 5 m), both the model and EN4 exhibit a north-cold, south-warm distribution pattern, with the northern continental shelf and coastal waters being relatively cold and the eastern region relatively warm, resulting in a small overall horizontal temperature difference (less than 2 °C). At 45 m, the location of the cold-warm transition zone closely matches EN4, and the model can reproduce the significant temperature gradient in the Beibu Gulf cold water area and the northeastern continental slope region. At 165 m and 315 m, the spatial extent of the cold water area is almost identical to the EN4 data, with temperatures mainly distributed between approximately 11-17 °C. At a deeper depth of 1868 m, the temperature distribution of the model largely overlaps with EN4, with the temperature range further narrowing to approximately 2-2.5 °C. Overall, the model not only maintains consistency with the large-scale spatial structure of EN4 at different depths but also reasonably reflects the decreasing vertical temperature characteristics with depth, indicating high reliability and physical consistency in the downscaling reconstruction of the South China Sea subsurface temperature. It should be noted that, limited by the low spatial resolution of EN4, its ability to characterize mesoscale dynamic processes and temperature gradient details is limited, with the warm and cold boundaries often appearing as diffuse transitions. In contrast, the ODT downscaling results show a significant advantage in resolving mesoscale temperature structures: frontal boundaries are clearer, horizontal gradients are steeper, and it can reveal the smoothed mesoscale temperature details and structural features in EN4. Overall, the ODT model, while maintaining the consistency of large-scale temperature distribution, significantly enhances its ability to express mesoscale structures, further demonstrating its effectiveness and application potential in downscaling reconstruction of the South China Sea subsurface temperature.

[0152] To further verify the model's ability to downscale and reconstruct the vertical temperature structure, this invention compares the ODT downscaling results with EN4 observations using two cross-sections: one is a zonal cross-section (along 16°N, extending from 108°E to 121°E), and the other is a meridional cross-section (along 117°E, extending from 7°N to 20°N). Overall, the temperature profiles downscaled by the ODT model and the EN4 observations maintain a high degree of consistency in spatial distribution and vertical gradient, indicating that the model can accurately reproduce the characteristics of the subsurface temperature structure in the South China Sea. In the zonal cross-section, the surface water temperature is approximately 28-30 °C, gradually increasing from west to east; the thermocline is mainly located at 50-150 m, with a clear tilting structure, and the water temperature drops below 10 °C at 200 m. The ODT model reproduces this layered structure and its depth range well. On the meridional profile, a significant tropical-subtropical difference is visible in the north-south direction: the surface temperature is relatively warmer in the south (approximately 10°N), while it is slightly lower in the north (approximately 20°N). The ODT downscaling results almost perfectly match the isotherm distribution observed in EN4. Overall, the ODT downscaling results maintain good consistency with EN4 in terms of large-scale spatial distribution, while also exhibiting richer mesoscale structural information compared to the original EN4 field, characterized by more detailed isotherms and clearer temperature gradients, demonstrating the model's strong analytical and reconstructive capabilities for vertical structures and mesoscale thermal variability.

[0153] To evaluate the advantages of the proposed downscaling method over traditional interpolation methods, this invention downscales EN4 data using linear interpolation, cubic spline interpolation, and Kriging interpolation. The results are then compared with those from multiple independent high-resolution datasets (ARMOR3D, ECCO2, GLORYS12V1, and ORAS5) in terms of data consistency. The results show that the downscaled product of the ODT model maintains higher consistency with the high-resolution data in terms of spatial patterns and feature changes, exhibiting higher correlation and lower error. This advantage stems from the methodological difference between interpolation and reconstruction: traditional interpolation is essentially a smoothing / weighted averaging process based on the spatial continuity of neighboring grid points, making it difficult to introduce additional dynamic constraint information; while the ODT downscaling model can fully utilize the mesoscale physical information contained in sea surface variables, achieving a more physically consistent subsurface temperature reconstruction by learning the nonlinear mapping relationship between these variables and the subsurface structure.

[0154] This invention proposes an ODT model based on the Transformer architecture. This model utilizes 1 / 4° sea surface features (SST, ADT, WSC) along with geographic location, time, and climatological information to reconstruct high-resolution subsurface temperature in the South China Sea by learning the statistical mapping relationship between the sea surface and the subsurface layer. Through the synergistic effect of multi-source information fusion and multi-scale feature extraction, the ODT model significantly outperforms RNN and CNN models in both accuracy and stability (RMSE of 0.27℃, R...). 2 The accuracy is 0.998, and it exhibits consistent reconstruction performance across vertical and temporal variations. Based on the comprehensive evaluation results of horizontal, vertical, and monthly data, the ODT model can robustly reproduce the key spatial structure and stratification features of the South China Sea.

[0155] By adjusting the sliding step size of the input window, this invention successfully improved the subsurface temperature spatial resolution of the EN4 dataset from 1° to 1 / 4°. The results show that the downscaling significantly enhances the resolution of mesoscale structures while maintaining the large-scale distribution characteristics of the original EN4 dataset, and can more clearly depict the horizontal temperature gradient and detailed structural features that are difficult to present in low-resolution data. Compared with traditional interpolation methods such as linear interpolation, cubic spline interpolation, and Kriging interpolation, the ODT downscaling results achieved higher R-values ​​in tests using various high-resolution datasets (GLORYS12V1, ORAS5, ARMOR3D, and ECCO2) as references. 2 The lower RMSE further demonstrates its advantages in physical consistency and mesoscale variability feature reduction.

[0156] In summary, the downscaling model proposed in this invention can effectively reconstruct the high-resolution subsurface temperature structure of the South China Sea, maintaining high accuracy across different time ranges and vertical depths. This not only deepens our understanding of the spatiotemporal variability of the South China Sea temperature structure but also provides a feasible approach for inferring high-resolution subsurface structures from sea surface elements. It should be noted that the current model is still a purely data-driven statistical method, with limited ability to characterize complex dynamic processes; its training labels are derived from objective analysis products, and interpolation errors and systematic biases may exist in sparsely observed regions. Future work could introduce explicit physical constraints into the model structure or loss function to enhance the model's reconstruction and generalization capabilities in regions with strong physical processes; simultaneously, introducing measured profile data as training or validation labels could further improve the independence and physical reliability of the results.

Claims

1. A high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning, characterized in that, Includes the following steps: 1) Acquire surface and subsurface ocean data from the South China Sea and preprocess them; 2) Construct an ocean downscaling model based on the Transformer architecture and train the model using preprocessed data; 3) The same input window size as the training phase is used, and the South China Sea surface variable data is divided into subdivisions with a step size of 1 / 4°. The subdivision data is then input into the trained ocean downscaling model to obtain the subsurface temperature field with a resolution of 1 / 4° at the corresponding spatial location of the sea surface.

2. The high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning as described in claim 1, characterized in that, Step 1) includes the following steps: 2.1) Unify all surface and sub-surface data into monthly average data; 2.2) Keeping the original EN4 1° grid unchanged, a 1 / 4° target grid corresponding to the original EN4 grid is constructed by interpolation, and this is used as the unified spatial reference grid; 2.3) All ocean surface data were unified into a spatial reference grid through resampling; 2.4) Remove grid points with missing data values ​​in the area to be reconstructed, and normalize the processed data.

3. The high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning according to claim 1, characterized in that, The ocean downscaling model includes: Spatial Feature Extraction Layer: This layer extracts spatial features from the preprocessed local neighborhood data using two-dimensional convolution, and then rearranges the convolutional two-dimensional spatial features into a sequence of length [length missing]. The spatial sequence is then processed by linear mapping and layer normalization to obtain the spatial sequence representation. ,in, Indicates batch size, Indicates the total number of spatial locations. This represents the feature dimension of the model, used to indicate the length of the embedded feature vector corresponding to each spatial location; Cross-attention layer for variables: Based on multi-temporal sample data, learn the mapping law between sea surface variables and subsurface temperature structure, and use attention mechanism to enhance the modeling ability of non-neighboring spatial location correlation features within the local window; Position-aware Transformer encoding layer: Encodes the fused features obtained from the variable cross-attention layer through relative position encoding; Attention aggregation layer: The encoded feature matrix is ​​converted into a single-point matrix using the attention aggregation mechanism, and then point-by-point regression prediction is performed through a multilayer perceptron to output the temperature estimate of the target depth layer.

4. The high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning according to claim 3, characterized in that, The spatial feature extraction layer performs the following steps: Preprocessed local neighborhood sea surface multivariate data Perform two-dimensional convolution operations to extract local spatial features: in, This indicates that the input is multivariate sea table data. Indicates batch size, Indicates the number of input variables. and These represent the height and width of the local neighborhood window, respectively. This represents the spatial features extracted by convolution; The convolutional two-dimensional spatial features are rearranged into a sequence of length [length missing]. Spatial sequence representation: in, This represents the spatial sequence characteristics after rearrangement. Indicates the total number of spatial locations. Indicates the dimension of the convolution output features; By performing linear mapping and layer normalization on the spatial sequence features, we obtain the spatial sequence representation: in, Represents the linear mapping weight matrix. Indicates the bias term. This represents the spatial sequence representation output by the spatial feature extraction layer. This represents the feature dimension of the model, used to indicate the length of the embedded feature vector corresponding to each spatial location.

5. The high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning according to claim 3, characterized in that, The variable cross-attention layer performs the following steps: Calculate the variable weights based on the original data variables: in, Indicates the first The input variable in the th... The value at each spatial location Indicates the first Importance coefficients of each variable; representation of spatial sequences Perform linear mapping on each variable to obtain the feature representation of each variable: in, Indicates the first Feature representation of input variables after linear mapping Indicates the first The linear mapping weight matrix corresponding to each input variable; Weighted fusion of feature variables based on their weights: in, Indicates fusion characteristics, Given the number of input variables; a multi-head self-attention mechanism is used to model long-range spatial dependencies: Among them, attention mechanism parameters Depend on Linear mapping yields, The key vector dimension is represented by a linear transformation applied to the attention output features and then compared with the input features. By performing residual connections and layer normalization, the output features of the multivariate cross-attention module are obtained: in, This represents the linear mapping matrix corresponding to the attention output. This represents the output feature of the multivariate cross-attention module.

6. The high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning according to claim 3, characterized in that, The location-aware Transformer coding layer performs the following steps: in, This represents the encoded features after processing by the position-aware Transformer coding layer. This refers to the Transformer encoding module. This indicates a relative position encoding.

7. The high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning according to claim 3, characterized in that, The attention aggregation layer performs the following steps: Let the aggregate weights be: in, Represents the aggregate weight vector. This represents the learnable attention projection matrix. This represents the center position offset vector. If the learnable bias term is represented, then the single-point spatial representation... for: in, Indicates the first The encoded features corresponding to each spatial location This represents the spatial features of a single point after aggregation; The aggregated spatial features are analyzed using a multilayer perceptron. Perform pointwise regression prediction: in, Indicates the prediction result. This represents a multilayer perceptron.

8. The high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning according to claim 1, characterized in that, Training the model using the preprocessed data includes the following steps: Based on EN4 grid data, the corresponding sea surface input location is determined, and a mapping relationship between sea surface information and subsurface temperature is constructed as a label dataset; Target depth based on ocean Constructing a composite weighted loss function ; Using labeled datasets and The ocean downscaling model was trained.

9. The high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning according to claim 8, characterized in that, The mapping relationship between sea surface information and subsurface temperature is constructed as follows: (1) Using each EN4 grid point as the center, extract the 1 / 4° resolution sea surface data within a 7×7 range around it as the input window, and use the subsurface temperature at the corresponding location as the label value; (2) Slide the input window in space with a step size of 1°, that is, 4 1 / 4° grid points, and extract the next set of "input-label" samples. Slide the input window and extract samples in sequence until all EN4 surface temperature data are covered. (3) Use the extracted samples to construct a sea surface input and subsurface temperature label dataset.

10. The high-resolution downscaling reconstruction method for the subsurface temperature structure of the South China Sea based on deep learning according to claim 8, characterized in that, The composite weighted loss function Specifically: in, Indicates depth The actual value of the subsurface temperature at that location. This represents the reconstruction result of the model. For single-point absolute error, parameters and This represents a hyperparameter used to control the relative importance of the two weighting factors. This represents the vertical structure weighting factor used to enhance the vertical gradient information in the EN4 subsurface temperature profile. Indicates the weighting factor based on sea surface spatial variability: in, This represents the difference in subsurface temperature label values ​​between adjacent depth layers. Indicates the depth interval between adjacent depth layers. Indicates depth The magnitude of the vertical temperature gradient at that location. express The average value of the inner horizontal gradient magnitude, This indicates the sea surface temperature data within the input window. and Both represent normalization functions.

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