Physics-enhanced deep learning for sea surface temperature forecasting via multi-scale feature integration

Abstract

Accurate prediction of sea surface temperature (SST) is essential for marine environmental monitoring and climate forecasting. However, most existing deep-learning-based approaches rely heavily on data-driven methodologies and lack sufficient integration of physical mechanisms, thereby limiting their physical consistency and interpretability. To overcome this limitation, this study introduces a multi-source coupled prediction neural network (MSCPNN), which incorporates temperature, salinity, and current dynamics into a multi-scale feature learning framework. Built upon the multi-feature physical neural network (MFPNN), the proposed model integrates a convolutional block attention module (CBAM), where channel attention adaptively models the multi-factor coupling among temperature, salinity, and currents, and spatial attention captures multi-scale spatial patterns in SST. Using high-resolution reanalysis data from the South China Sea spanning 2011 to 2020, comprehensive experiments were conducted comparing MSCPNN with MFPNN and PCL-MFPNN. The results demonstrate that MSCPNN significantly outperforms the baseline models across multiple evaluation metrics—including RMSE, correlation coefficient, PSNR, and SSIM—achieving an average reduction in RMSE of 17% and an increase in correlation coefficient of 0.035, which reflects higher predictive accuracy and improved physical consistency. Ablation studies further validate the superiority of multi-factor coupling over single-factor alternatives and clarify the distinct contributions of salinity and currents to SST prediction. Overall, MSCPNN advances the accuracy and stability of long-term SST forecasting while providing a more interpretable framework for intelligent ocean prediction.

1 Introduction

Sea surface temperature (SST), as a critically important marine parameter, has become a key research focus in the development of marine science and technology. SST prediction plays a significant role in maritime navigation, fisheries, disaster prevention, military planning, and many other fields (Woo et al., 2018). In recent years, intelligent forecasting methods based on deep learning have demonstrated advantages in medium- to long-term SST prediction. By virtue of its strong nonlinear modeling capability and efficient data fitting, deep learning provides an effective methodological foundation for forecasting complex spatiotemporal variations such as those in ocean temperature fields (Wunsch, 2002). Essentially an innovation within the statistical forecasting framework, this approach learns from large volumes of historical data to extract spatiotemporal statistical patterns. Compared with traditional numerical forecasting and statistical methods, it offers notable advantages such as high computational efficiency, simple model structures, and strong generalization ability. Artificial neural networks (Jamil et al., 2023) have shown great potential in forecasting marine variables—for instance, early studies applied neural networks to achieve seasonal and interannual predictions of sea temperature in the Mediterranean Sea (Landman and Mason, 2001). Models such as fuzzy neural networks (Collins et al., 2004), backpropagation (BP) networks (Repelli and Nobre, 2004), and nonlinear autoregressive (NAR) networks (Abhigna et al., 2017) were successively introduced, significantly improving the prediction accuracy. In recent years, long short-term memory (LSTM) networks (Zhang et al., 2017) and their variants, such as ConvLSTM (Jonnakuti and Bhaskar, 2020) and CNN-LSTM (Zhang et al., 2020), have further integrated spatiotemporal feature extraction capabilities, overcoming the limitations of traditional point-wise prediction in capturing spatiotemporal coupling patterns. These models have exhibited superior performance in forecasting sea temperature and sea surface height in regions such as the East China Sea and the Pacific Ocean (Daw et al., 2022). Moreover, novel architectures like attention mechanisms (Yang et al., 2018), U-Net (Jia et al., 2019), and PredRNN (Colman and Davey, 2003) have been introduced, further enhancing the forecasting accuracy and image reconstruction quality.

However, these methods predominantly rely on data-driven approaches, lacking guidance from physical mechanisms, which makes it difficult to ensure the physical consistency of the results. Since 2017, research on physically enhanced and physics-guided neural networks has shown vigorous development. Initially, Karpatne et al (Raissi et al., 2019). proposed the physics-guided neural networks (PGNNs) for modeling lake temperature, demonstrating their ability to reduce errors and maintain consistency with physical characteristics. Subsequently, Raissi et al (Wei et al., 2020). introduced physics-informed neural networks (PINNs), providing a novel framework for solving partial differential equations, which has been widely applied in fields such as fluid dynamics. Meanwhile, improved models for time-series forecasting have continued to emerge, such as physics-guided recurrent neural networks (PGRNNs) (Xue and Leetmaa, 2000) and physically enhanced long short-term memory networks (Jiang et al., 2019). These have demonstrated superior performance over purely data-driven models in forecasting tasks such as lake temperature and rainfall runoff, particularly showing robustness when training data is limited.

After 2020, research deepened further, and methods became more diverse: Kashinath et al (Zhu et al., 2022). incorporated partial differential equations through differentiable projection layers, enhancing the realism of turbulence forecasting; Zhu et al (Cho and Kim, 2022). explored physics-based deep learning parameterization schemes to improve climate simulations. Furthermore, models such as the WRF HydroLSTM integrating hydrological physical processes (Willard et al., 2020), convolutional network-based post-processing methods for precipitation forecasting (Zhang, 2023), and the combined approach of transfer learning with physics-informed networks (TL-PINN) (Imani et al., 2014) for three-dimensional temperature field reconstruction have all validated the effectiveness of integrating physical knowledge in different scenarios. Collectively, these studies indicate that the incorporation of physical mechanisms not only improves prediction accuracy and efficiency but also enhances model generalizability and reduces reliance on massive training datasets. Domestic studies have also begun incorporating physical processes into networks—for instance, by integrating oceanic heat advection processes with deep learning models (e.g., the physical coupling layer in PCL-MFPNN) (Chen et al., 2021), which has improved the plausibility of the results to some extent. However, due to the reliance on incorporating only a single physical variable, such methods still exhibit limitations in characterizing complex coupled thermal–salinity–current mechanisms and multi-scale features, resulting in the limited enhancement of forecast accuracy and physical interpretability.

Sea surface temperature forecasting is influenced by the complex nonlinear coupling of multiple physical variables such as ocean currents and salinity, which involve diverse physical laws and multi-scale characteristics (Cai et al., 2021). Consequently, relying on a single physical factor is often insufficient to provide stable guidance for intelligent forecasting models and cannot adequately explain the impact of multi-variable coupling on prediction outcomes. Moreover, gradient conflicts arising from incorporating multiple physical equations as hard constraints (e.g., in loss functions) tend to undermine the training stability of neural network models, while the nonlinear interactions among variables significantly hinder convergence efficiency (Patel et al., 2022). At present, research on multi-factor, multi-scale physically-enhanced intelligent forecasting in the field of SST remains relatively underdeveloped. Thus, a key challenge in physics-aware intelligent forecasting lies in effectively integrating multiple physical mechanisms and multi-scale features to improve physically guided SST prediction.

Accordingly, this paper proposes an intelligent forecasting method named the multi-source coupled prediction neural network (MSCPNN), which integrates multi-scale feature learning with multi-physical coupling. Building upon the MFPNN framework, this method incorporates the CBAM attention mechanism: channel attention is utilized to adaptively model the influence of factors such as temperature, salinity, and currents on SST features, while spatial attention is employed to highlight multi-scale spatial differences in the temperature field, thereby achieving a natural integration of physical mechanisms and deep feature learning. Through comparative experiments and ablation analysis involving MFPNN and the single physical coupling model PCL-MFPNN, the effectiveness of multi-factor coupling in improving forecasting accuracy and physical consistency is validated, and the distinct physical contributions of various factors on SST forecasting characteristics are analyzed, achieving the goal of enhancing the physical interpretability of intelligent forecasting.

This chapter first elaborates on the research significance of sea surface temperature forecasting and then reviews the current state of research both domestically and internationally in statistical forecasting, deep-learning-based intelligent forecasting, and physically enhanced neural network forecasting, providing a clear analysis and summary of the existing issues and shortcomings in traditional statistical forecasting, deep learning-based intelligent forecasting, and the integration of physical mechanisms with data-driven forecasting. Building on this foundation, the key scientific problems addressed in this study and the main research contents are proposed. Section 2 introduces an intelligent SST forecasting method based on temperature–salinity–current multi-variable coupling and multi-scale modeling, designs a multi-source coupled forecasting network MSCPNN incorporating the CBAM attention mechanism, and explains the principle of how CBAM integrates the multi-factor physical coupling of temperature, salinity, and currents; it also describes the experimental data and evaluation metrics used in this study. Section 3 presents comparative experiments between MSCPNN and PCL-MFPNN, along with ablation experiments on various coupling components of MSCPNN, to validate the performance improvement achieved by multi-factor joint coupling and analyze the specific physical contributions of individual factors on SST forecasting characteristics, thereby achieving the objective of enhancing the physical interpretability of intelligent forecasting. Section 4 discusses the experimental results and summarizes the research limitations and potential directions for future work.

2 Materials and methods

Salinity and ocean currents significantly influence sea surface temperature (SST) variability through complex, coupled interactions among these three physical elements. Conventional integration approaches, which often rely on linear superposition, generally fail to ensure physical consistency and may adversely affect forecast accuracy (Farea et al., 2024). To address these limitations, this study introduces a novel multi-physical coupling framework. By leveraging an attention mechanism to adaptively fuse multi-factor features, the proposed method enhances both the physical interpretability and predictive accuracy of data-driven SST forecasts.

2.1 Multi-feature physical neural network design

The MSCPNN architecture, designed with temperature–salinity–current multi-source coupling, comprises two primary components: a data-driven MFPNN intelligent forecasting network and a physical coupling module. The MFPNN network is primarily responsible for extracting the multi-scale spatiotemporal features of sea surface temperature and generating preliminary predictions. The physical coupling module integrates salinity and ocean current data, leveraging the seawater equation of state and heat conduction equation to generate multi-physical coupled residual feature tensors that reflect the interactions among temperature, salinity, and currents (Cuomo et al., 2022). The overall schematic architecture of the MFPNN network is illustrated in Figure 1.

Figure 1

In this design, the heat conduction equation is employed to describe the propagation of thermal energy within the ocean. Within this equation, the temporal variation of seawater temperature is intrinsically coupled with its spatial variation, wherein spatial gradients in each direction are modulated by the corresponding components of ocean current velocity. Consequently, these coupled dynamics govern the temporal evolution of temperature at any given spatial location. Given that the predictive target of this study consists of two-dimensional sea surface temperature fields, the heat conduction equation must be appropriately reformulated to be effectively integrated into the physical coupling layer. Accordingly, specific design adaptations are implemented to accommodate the dimensional and structural requirements of the coupling formulation.

Since seawater heat conduction is influenced not only by ocean currents but also closely related to physical factors such as temperature, salinity, and pressure, the heat conduction equation strengthens the physical guidance capability of the network by establishing the relationship between seawater temperature variations across space and time. Specifically, the spatiotemporal variations in the heat conduction equation are tightly coupled with ocean current velocity; therefore, the horizontal components of ocean currents exert a significant influence on the spatiotemporal characteristics of sea surface temperature. To simplify the computation, vertical heat conduction effects are neglected, with primary consideration given to heat conduction in the horizontal direction. The governing equation is formulated as Equation 1:

First, the seawater equation of state and the heat conduction equation are transformed into a unified spatiotemporal differential equation. By computing the heat conduction residual feature equation, as expressed in Equation 2, and applying normalization processing, a coupled physical feature tensor is obtained, which reflects the coupling relationships among temperature, salinity, and ocean currents. This residual tensor highlights the magnitude of deviations between the sea surface temperature forecast results and the heat conduction law in terms of spatiotemporal characteristics, thereby enabling the forecasting network to enhance its representation of heat conduction physical features through loss propagation during the training process. For grid data in the two-dimensional Cartesian coordinate plane, both first-order and second-order differential calculations in space can be discretized using the central difference method. The computation of the first-order temperature gradient is shown in Equation 3, and the formula for the temperature Laplacian operator is presented in Equation 4. Differential calculations in the temporal dimension are performed using the forward difference method, as illustrated in Equation 5.

In this process, the heat conduction equation serves to provide an idealized description of heat conduction, thereby enabling the neural network to learn how to integrate the interactions among ocean currents, temperature dynamics, and salinity into the prediction model (Liao et al., 2008).

Subsequently, the physical coupling tensor is concatenated with the sea surface temperature feature maps output by the MFPNN network along the channel dimension, yielding a multi-channel physical feature representation. To leverage these multi-dimensional features more effectively, the network incorporates the convolutional block attention module (CBAM) (Wang et al., 2020), which applies adaptive weighting across both channel and spatial dimensions. Specifically, the channel attention mechanism identifies feature channels that contribute most significantly to the prediction task, while the spatial attention mechanism accentuates salient regional patterns. This enables the network to adaptively emphasize critical physical relationships while simultaneously suppressing noise.

During the training process, the network compares the predicted outputs with the ground-truth sea surface temperature fields to compute prediction errors and adjusts network parameters through the backpropagation mechanism. This enables the network to continuously learn and adapt to multi-element physical laws. Ultimately, through multi-source coupled joint training, the resulting network model not only achieves more accurate sea surface temperature predictions but also exhibits enhanced physical interpretability. This design ensures that the model can deliver reliable forecasting results under varying oceanic environmental conditions while also providing robust support for the subsequent analysis of physical mechanisms.

2.2 Multi-factor coupled feature fusion based on CBAM attention mechanism

Attention mechanisms draw computational inspiration from the human visual system, enabling models to automatically identify and prioritize the most informative features. The convolutional block attention module (CBAM) is a lightweight yet highly efficient architecture that substantially enhances feature representation capacity and generalization performance without adding significant computational complexity (Winkler and Mohandas, 2008; Palubinskas, 2017). The module consists of two core components operating sequentially: the channel attention module (CAM) and the spatial attention module (SAM).

The channel attention module (CAM) learns the relative importance of each channel in multi-channel feature maps, thereby discriminating the contributions of different physical elements (Kim et al., 2015). Specifically, the input features undergo both global average pooling and max pooling along the spatial dimension, yielding two distinct channel descriptors that capture global contextual information and salient local features, respectively. These descriptors are fed into a shared network to generate channel attention weights. A sigmoid activation function is then applied to produce the final channel attention coefficients (Newbold, 1983). By performing channel-wise multiplication with the original features, this mechanism adaptively enhances informative channels while suppressing less relevant ones. The structure of the channel attention module is illustrated in Figure 2.

Figure 2

The spatial attention module (SAM) enhances discriminative capacity by identifying spatially salient regions within feature maps. Taking the channel-refined features as input, SAM applies both average pooling and max pooling along the channel dimension to generate two complementary 2D spatial feature maps (Chen, 2017). These maps are concatenated and processed through a 7 × 7 convolutional layer to produce a spatial attention map, with the convolutional kernel size specifically chosen to expand the receptive field for capturing long-range spatial dependencies. By element-wise multiplying of the spatial attention weights with the input features, SAM generates refined feature representations, yielding features that integrate both channel-refined and spatially weighted information (Patil et al., 2013). The architectural design of SAM is illustrated in Figure 3.

Figure 3

Experimental results demonstrate that applying channel attention prior to spatial attention achieves superior performance. This sequential design is effective because the channel attention module first suppresses less informative channels, thereby reducing interference in subsequent processing, while the spatial attention module subsequently highlights salient spatial regions based on the refined feature set. The combination of both attention mechanisms collectively enhances the discriminative capacity of the multi-factor coupled feature representations.

2.3 Overview of experimental data

The dataset used in this study was sourced from multiple marine data products provided by the Copernicus Marine Environment Monitoring Service (CMEMS). Specifically, the selected data consist of daily updated global ocean physical reanalysis fields with a spatial resolution of 1/12°. This product is generated through the assimilation and reanalysis of marine environmental variables using a European numerical model. The dataset offers comprehensive global ocean environmental parameters, characterized by extensive geographical coverage and diverse variables. Furthermore, its daily update frequency ensures both substantial data volume and strong timeliness, enhancing its representativeness for analysis.

The environmental element data were extracted from the daily global ocean physical reanalysis dataset as daily averaged sea surface temperature, salinity, and current gridded data for the South China Sea. This gridded dataset covers the period from January 1, 2011 to December 31, 2020, comprising a total of 3,653 daily samples. Spatially, the data encompass most of the South China Sea region, specifically within the geographical bounds of 106° E to 120° E longitude and 8° N to 22° N latitude.

To ensure consistency across different physical variables and accelerate model convergence, standard preprocessing steps were applied prior to neural network training. The data were spatially resampled to a resolution of 1/4° × 1/4° using bilinear interpolation while maintaining the daily temporal resolution. Subsequently, all input variables were normalized to a range of [0, 1] using min–max scaling to eliminate dimensional discrepancies among temperature, salinity, and current data.

2.4 Evaluation indicators of the experiment

To comprehensively evaluate the prediction performance of different models, this study adopts four standard evaluation metrics: root mean square error (RMSE), Pearson correlation coefficient (r), peak signal-to-noise ratio (PSNR) (Shen et al., 2004), and structural similarity index measure (SSIM) (Niedzielski and Kosek, 2005). The root mean square error (RMSE) is employed to quantify the quantitative deviation between predicted and observed values, rendering it particularly appropriate for assessing errors between predicted SST images and corresponding actual SST data. RMSE serves as an indicator of the model’s fitting precision: a lower RMSE value signifies that the model’s predictions are closer to the true data, thereby indicating a higher forecasting accuracy. The mathematical expression for RMSE is provided in Equation 6:

where x is the observed data value, is the forecast data value.

The correlation coefficient r is a standard statistical measure used to quantify the strength and direction of the linear relationship between two random variables. Its calculation formula is given in Equation 7:

where Cov is the covariance, σ represents the standard deviation, and X_i and Y_i are the observed values from the sample data.

The peak signal-to-noise ratio (PSNR) is a full-reference image quality metric used to evaluate the fidelity of the predicted images by quantifying their difference from ground truth images. Expressed in decibels (dB), PSNR reflects the magnitude of deviation between reconstructed and reference images. Consistent with the behavior of MSE and RMSE, a higher PSNR value indicates smaller deviations between the reconstructed and true images, thereby demonstrating superior precision of the forecasting model (Chapman et al., 2015). The calculation formula for PSNR is provided in Equation 8:

where MSE is the mean squared error between the forecasted image and the ground-truth image, and RMSE is the root mean squared error between the forecasted image and the ground-truth image.

Structural similarity index measure (SSIM) assesses image similarity through three comparative dimensions: luminance, contrast, and structural information. The SSIM function is symmetric, bounded between 0 and 1. A value closer to 1 indicates higher perceptual image quality, greater resemblance to the reference image, and more accurate forecasting performance. The SSIM calculation is given in Equation 9:

where x denotes the forecasted image, y denotes the ground-truth image, and α, β, and γ are positive weights assigned to luminance, contrast, and structural information, respectively.

3 Experiments and results

This chapter presents a series of comparative experiments designed to evaluate the MSCPNN method, with a focus on examining the seasonal feature forecasting performance and quantified evaluation metrics of MSCPNN in comparison with PCL-MFPNN and MFPNN.

3.1 Correlation analysis between salinity–current and sea surface temperature

To investigate the correlation among salinity, ocean currents, and temperature, a comparative analysis was conducted to examine their annual-scale correlation characteristics. The study utilized the 2011–2020 temperature–salinity–current reanalysis dataset from the Copernicus Marine Service, consistent with previous research. The spatial distributions of the annual mean correlation coefficients among salinity, ocean currents, and temperature are presented in Figure 4, while the spatial patterns of the correlation strength are shown in Figure 5.

Figure 4

Figure 5

A comparison of Figure 4 and 5 reveals distinct correlation characteristics across the study region. Overall, salinity exhibits a stronger linear association with temperature than ocean currents do. Furthermore, the spatial distribution of the correlation coefficients between salinity and temperature demonstrates greater uniformity and concentration, whereas the correlation between ocean currents and temperature appears more scattered spatially.

The strongest positive correlation between salinity and temperature (r ≈ 0.6) occurs in the coastal waters off north-central Vietnam. A similarly strong positive correlation is observed in the southeastern South China Sea. Conversely, a pronounced negative correlation (r ≈ −0.6) is evident in east of Hainan Island in the northern basin, with this negative correlation zone extending southward along the Vietnamese coast to the Mekong Delta region.

For ocean current-temperature relationships, the highest positive correlation (r ≈ 0.5) appears in waters from Guangdong to the vicinity of Hainan Island. Strong negative correlations are observed adjacent to these highly positive regions, extending southward along the Vietnamese coast, with the most significant negative correlation (r ≈ −0.6) occurring in the southern Mekong Delta waters.

The dynamics of temperature, salinity, and ocean currents in the South China Sea are strongly influenced by monsoonal forcing and exhibit pronounced seasonal characteristics. To further investigate the correlation among salinity, ocean currents, and temperature across different seasons, a comparative analysis of their seasonal-scale correlation characteristics was conducted. The spatial distributions of seasonal correlation coefficients among these variables are presented in Figure 6, while the spatial patterns of correlation strength are shown in Figure 7.

Figure 6

Figure 7

A comparison of Figure 6 and 7 reveals that the correlation patterns among salinity, ocean currents, and temperature remain broadly consistent with those shown in Figure 4 and 5. Salinity continues to exhibit a stronger and more spatially coherent correlation with temperature, whereas the relationship between ocean currents and temperature remains comparatively weaker and more scattered.

The sea surface temperature (SST) in the South China Sea follows a distinct seasonal cycle: it gradually increases from spring to summer, reaching its annual peak, and then declines from autumn to winter, falling to its annual minimum. This seasonal progression provides a useful framework for interpreting the correlation patterns. In spring, a strong negative correlation between salinity and temperature emerges in the northern South China Sea, largely attributable to increased Pearl River discharge delivering large volumes of low-salinity freshwater as temperatures rise. In summer, a strong positive correlation appears in the southeastern region, where peak seasonal temperatures coincide with heightened evaporation, increasing both temperature and salinity. By autumn, the positive correlation weakens in the southeast, as stronger monsoon transition winds enhance evaporation, while precipitation and river inflow diminish, raising the surface salinity and altering the temperature–salinity relationship. In winter, a pronounced negative correlation occurs in the western basin, where the northeast monsoon drives evaporation exceeding precipitation and promotes the advection of high-salinity water toward the coast.

Regarding ocean current–temperature correlations, a notable feature is the South China Sea Warm Current, which flows northeastward along the coasts of Hainan Island and Guangdong. Its velocity peaks in winter, weakens in summer, and changes most rapidly during spring and autumn. Accordingly, the spatial outline of this current is clearly delineated in the positive correlation maps for spring and autumn. These seasonal correlation characteristics align well with the broader patterns shown in Figure 4 and 5.

The comparative experiments above demonstrate that the influences of salinity and ocean currents on temperature are markedly distinct, with complex correlations in both spatial distribution and seasonal characteristics. Consequently, simply superimposing multi-element physical variables cannot effectively capture the multi-scale characteristics of temperature, as such an approach may obscure both the coupled interactions and individual contributions of each factor, thereby limiting the effectiveness of physics-guided intelligent forecasting. The correlation analysis among salinity, ocean currents, and sea surface temperature not only confirms the challenges in coupling multi-element physical properties with the multi-scale features of SST but also provides a robust basis for the subsequent analysis in this chapter on integrating these two physical elements to enhance the forecasting performance of sea surface temperature fields.

3.2 Analysis of the plan view of experimental forecast results

This experiment compares the forecasting performance of the MSCPNN, PCL-MFPNN, and MFPNN networks to evaluate how multi-factor joint coupling, single-factor physical coupling, and purely data driven approaches affect the prediction of spatiotemporal variation characteristics across seasons. The study further assesses MSCPNN’s applicability for seasonal forecasting.

The experiment was designed to evaluate 15-day forecasts generated by the MSCPNN, PCL-MFPNN, and MFPNN algorithms, initialized on seasonal representative dates in 2020: January 20 (winter), April 29 (spring), July 23 (summer), and September 16 (autumn). The spatial distribution of sea surface temperature (SST) predictions from each model at days 1, 5, 10, and 15, respectively, are shown in Figure 8.

Figure 8

As shown in Figure 8, the multi-factor coupled algorithm MSCPNN achieves superior forecasting performance compared to PCL-MFPNN, exhibiting a higher accuracy and an improved ability to capture and reconstruct physical features—for instance, on forecast day 10, the intensity and spatial distribution of cold/warm waters along the Vietnamese coastal area near 16° N, and on day 15, the thermal characteristics of the central Vietnamese coastal waters as well as the spatial extent and thermal structure of a warm water mass near 114° E, 16° N—these key physical features are more accurately represented by MSCPNN and align more closely with the ground truth. Although PCL-MFPNN outperforms MFPNN, it still shows relatively larger errors in feature prediction compared to MSCPNN.

For the prediction of summer sea surface temperature (SST) fields in the South China Sea, MSCPNN similarly demonstrates a higher forecasting accuracy than both PCL-MFPNN and MFPNN—for instance, in forecasting the warm water mass southeast of Hainan Island on days 1 and 5, both MFPNN and PCL-MFPNN exhibit relatively large errors in predicting its spatial distribution and show considerable inaccuracy in estimating the thermal characteristics of the cold eddy current near Vietnam. On days 10 and 15, MFPNN and PCL-MFPNN significantly underestimate both the intensity and spatial extent of warm waters in the Beibu Gulf and around Hainan Island. In contrast, MSCPNN produces predictions that align more closely with the true characteristics for all the aforementioned features.

For the autumn sea surface temperature (SST) field in the South China Sea, MSCPNN maintains superior forecasting accuracy compared to both PCL-MFPNN and MFPNN. In predicting the cold water intensity in the northern South China Sea on day 5, although MSCPNN, MFPNN, and PCL-MFPNN all exhibit underestimation, MSCPNN demonstrates the smallest error among them. Regarding the spatial distribution of cold water in the northern region and warm water in the southeastern region on days 10 and 15, MFPNN shows the largest forecasting deviation, followed by PCL-MFPNN, while MSCPNN yields the most accurate predictions.

Similarly, for the winter sea surface temperature (SST) field in the South China Sea, MSCPNN again demonstrates superior forecasting accuracy over both PCL-MFPNN and MFPNN. In predicting the annular warm current structure southeast of Hainan Island and the distribution of warm water masses along the southwestern coast of Hainan Island from day 5 to day 15, MFPNN exhibits the greatest degree of blurring and spatial inaccuracy, PCL-MFPNN shows intermediate performance, and MSCPNN achieves the highest spatial precision and pattern fidelity.

In summary, a comparative analysis of forecasting results across all seasons demonstrates that the multi-source coupled intelligent forecasting algorithm MSCPNN yields the most accurate predictions. It effectively mitigates the problem of accumulated statistical feature errors that typically emerge in the later stages of the MFPNN forecasts. These findings indicate that MSCPNN’s multi-factor coupling capability is more robust than the single-factor physical coupling approach employed by PCL-MFPNN. Furthermore, the results confirm the consistent performance and general applicability of the MSCPNN forecasting algorithm across different seasonal conditions throughout the year.

3.3 Analysis of experimental forecast results

The spatial forecast results across the four seasons visually confirm the superior prediction accuracy of MSCPNN. To further evaluate the performance of the MSCPNN method in a quantitative manner, MSCPNN, PCL-MFPNN, and MFPNN were applied to conduct full-temporal-domain forecasting experiments on the South China Sea SST field during spring, summer, autumn, and winter. The RMSE, correlation coefficient (r), PSNR, and SSIM metrics were computed by comparing the predicted SST values against corresponding observational data. These metrics were then averaged on a seasonal basis to obtain the seasonal-scale performance of each forecasting algorithm, as summarized in Tables 1–4. This methodology allows for a more straightforward and quantitative comparison of the coupled forecasting algorithms across different seasons.

Furthermore, to more intuitively assess and compare the performance improvements achieved by multi-factor joint coupling versus single-factor coupling in the MFPNN framework, the results are further analyzed to quantify the comparative effectiveness of different physical enhancement strategies.

As shown in the preceding tables, MSCPNN achieves superior performance over both PCL-MFPNN and MFPNN across all evaluation metrics—RMSE, r, PSNR, and SSIM. Furthermore, the forecasting improvement attained by the multi-factor coupled MSCPNN over the baseline MFPNN substantially exceeds that of the single-factor coupled PCL-MFPNN. Consistent performance gains are observed across spring, summer, autumn, and winter, confirming MSCPNN’s ability to capture seasonal variations and its broad applicability throughout the year.

To further assess the annual-scale forecasting performance of the physically enhanced algorithms, a year-long averaged forecasting experiment was conducted for the entire year of 2020, producing an averaged 15-day extended forecast. The same evaluation metrics—RMSE, r, PSNR, and SSIM—were employed to compare the annual average 15-day forecasts of each algorithm over the South China Sea SST field. The results are presented in Figure 9, depicting the temporal evolution of RMSE, r, and PSNR throughout the 15-day forecasting horizon.

Figure 9

As illustrated by the evaluation metric curves in Figure 9, which compare the annual average 15-day forecasts of MSCPNN, PCL-MFPNN, and MFPNN, both MSCPNN and PCL-MFPNN exhibit RMSE trends from day 1 to day 15 that are generally consistent with MFPNN—characterized by increasing values over time, with a gradually decelerating growth rate. However, MSCPNN achieves a substantially larger RMSE reduction relative to MFPNN than PCL-MFPNN does. Furthermore, this error reduction becomes more pronounced over extended forecast horizons, indicating a progressively stronger physical guidance of MSCPNN on the network’s forecasts. This finding aligns with the earlier comparisons based on spatial forecast feature maps. Similar trends are observed in the correlation coefficient (r), PSNR, and SSIM metrics, which exhibit comparative patterns aligned with the RMSE curves. Consequently, MSCPNN consistently surpasses PCL-MFPNN across all evaluation metrics, demonstrating superior capability in maintaining physical consistency in forecasts. Furthermore, the performance advantage of MSCPNN becomes increasingly pronounced as the forecast horizon extends. Moreover, to assess the uncertainty and stability of forecasts generated by different coupled prediction algorithms, a comparative experiment was designed based on the root mean square error (RMSE) of the forecast results. This evaluation incorporated uncertainty metrics including RMSE extremes (minimum and maximum error), the range of RMSE distribution (error interval width), and the dispersion degree of RMSE distribution (standard deviation of error). Using daily forecast results from 2019 to 2020 (a 2-year period) generated by each physically enhanced prediction algorithm, the corresponding RMSE values served as experimental test data. Metric calculations yielded a comparative table of RMSE uncertainty metrics for the temperature forecasts of each coupled prediction algorithm, as presented in Table 5.

As can be observed from Table 5, the MSCPNN forecasting algorithm achieves the smallest values across all evaluated metrics—minimum error, maximum error, error interval range, and standard deviation of error—when compared with both MFPNN and PCL-MFPNN. These results not only confirm the superior stability and accuracy of the MSCPNN network in sea surface temperature prediction but also demonstrate that incorporating multi-factor physical coupling to guide the training of the intelligent forecasting network effectively enhances its robustness against environmental variations. Having evaluated the forecasting accuracy and stability of the coupled prediction algorithms, we further compare their computational efficiency and resource requirements. Table 6 presents the computational performance of each evaluated forecasting algorithm, including processing speed and resource utilization measured in both software and hardware environments.

As indicated by the performance comparison in Table 6, MSCPNN incurs the highest computational overhead and the longest execution time among the evaluated models. This can be attributed to its more complex network architecture and the greater volume of multi-source physical data involved compared to the other two approaches, which consequently lowers computational efficiency and increases resource demands. Nonetheless, MSCPNN remains fully operable on conventional laboratory hardware platforms. Thus, although MSCPNN is moderately less efficient in terms of computational load and speed, its superior forecasting accuracy and stability are clearly demonstrated. Future work will focus on further optimizing the network architecture to enhance its computational performance.

3.4 Coupling ablation experiment analysis

To further examine the effects of salinity coupling, current coupling, and their combined application in the multi-source coupled forecasting algorithm MSCPNN on sea surface temperature (SST) field characteristics, an ablation experiment was designed for the MSCPNN network. This experiment systematically compares three configurations: temperature–salinity coupling only (T–S), temperature–current coupling only (T–C), and the full joint coupling (MSCPNN). Specifically, the baseline MFPNN along with the three physically enhanced variants—MSCPNN (T-S), MSCPNN (T-C), and the complete MSCPNN—was applied to generate 15-day extended forecasts for each season of 2020. The resulting SST forecast fields on days 1, 5, 10, and 15 are visualized through planar maps to illustrate the performance of each ablated configuration. The following analysis assesses the forecasting capability of each MSCPNN variant based on the spatiotemporal characteristics observed during spring, summer, autumn, and winter.

Figure 10 presents a planar comparison of forecast results from the MSCPNN ablation experiments across spring, summer, autumn, and winter. For the spring season, although both the temperature–salinity coupled MSCPNN and the temperature–current coupled MSCPNN achieve more accurate predictions than the baseline MFPNN, their performance remains inferior to the fully coupled MSCPNN—for instance, in forecasting the warm water features along the Vietnamese coast at 16° N on day 10 and the spatial distribution and thermal characteristics of the warm water mass near 114° E and 16° N on day 15, the temperature–salinity coupled MSCPNN demonstrates a higher accuracy than the temperature–current coupled MSCPNN. The jointly coupled MSCPNN further improves the representation of these features, producing temperature values that align more closely with observations. Conversely, for the cold water trajectory extending from the Vietnamese coast at 14° N toward the central South China Sea on day 15, the temperature–current coupled MSCPNN yields more accurate predictions than the temperature–salinity coupled MSCPNN. The complete MSCPNN algorithm further refines this feature, delivering enhanced spatial detail and precision in the forecast. In the summer results, the prediction of cold-water intensity and spatial trajectory features in the northeastern South China Sea on days 5 and 10 demonstrated progressive improvement in the full MSCPNN, achieved through strengthened coupling of the temperature–salinity and temperature–current features. By day 15, both the temperature–salinity coupled MSCPNN and the temperature–current coupled MSCPNN mitigated the overestimation of cold-water extent in the northern South China Sea exhibited by MFPNN, with this bias correction effect being further enhanced in the fully coupled MSCPNN. In the autumn forecasting results, the movement path of the cold eddy near Vietnam on day 5 is more accurately captured by the temperature–current coupled MSCPNN than by the temperature–salinity coupled MSCPNN. However, in the full MSCPNN forecast, the representation of this feature is not limited by the shortcomings of the temperature–salinity coupled MSCPNN; rather, the cold eddy characterization based on the temperature–current coupled MSCPNN is further refined. For the distribution of warm-water features along the Vietnamese coast at 16° N on days 10 and 15, the temperature–salinity coupled MSCPNN delivers more accurate predictions compared to the temperature–current coupled MSCPNN, and the complete MSCPNN framework further enhances the feature representation initially achieved by the temperature–salinity coupled MSCPNN. In the winter forecast results, a crown-shaped spreading pattern of the cold water current along the Vietnamese coast near 14° N on day 10 is captured by the temperature–current coupled MSCPNN but remains absent in the temperature–salinity coupled MSCPNN. The full MSCPNN, however, successfully retains this feature in its final output. Regarding the spatial outline of warm water southeast of Hainan Island on days 10 and 15, the temperature–salinity coupled MSCPNN yields a clearer prediction than the temperature–current coupled MSCPNN, and the complete MSCPNN further refines the thermal characteristics while reducing numerical deviations in the predicted values.

Figure 10

Based on the comparative analysis of the experimental results, it can be concluded that MSCPNN demonstrates significantly superior performance over both single-factor coupled variants, namely, the temperature–current coupled MSCPNN and the temperature–salinity coupled MSCPNN, in jointly utilizing salinity and current data to enhance sea surface temperature forecasts. Moreover, the temperature–current coupled MSCPNN and the temperature–salinity coupled MSCPNN exhibit distinct physical guidance effects, with varying effectiveness across different spatial features. The multi-factor coupling mechanism in MSCPNN organically integrates the physical influences of salinity and currents on temperature via an attention mechanism, which enhances the representation of beneficial features while suppressing ineffective or erroneous ones. This results in a more accurate characterization of the detailed physical properties. To evaluate the annual-scale performance of the MSCPNN ablation experiments, this study calculated the average daily forecasts for 2020 and assessed their performance using RMSE, correlation coefficient r, PSNR, and SSIM metrics.

As shown in Figure 11, the MSCPNN model demonstrates overall superior performance compared to the baseline MFPNN model. Among the physically enhanced variants, the temperature–salinity coupled MSCPNN exhibits a slightly better performance than the temperature–current coupled MSCPNN. This advantage can be attributed to several factors: salinity is directly coupled with the density field through the equation of state, enabling a more effective representation of thermohaline circulation’s regulation on heat transfer; its parameter universality and stability surpass those of empirical parameterizations used in ocean current heat conduction models. Meanwhile, the spatiotemporal variations of salinity remain relatively stable with lower observational uncertainty, thereby providing more reliable boundary conditions during training.

Figure 11

In contrast, single-factor coupling demonstrates limited predictive capability, whereas the multi-source coupled MSCPNN model achieves optimal performance in both accuracy and consistency, outperforming the simple combination of the temperature–salinity coupled MSCPNN and the temperature–current coupled MSCPNN (Halmova et al., 2016). These results indicate that the CBAM attention mechanism effectively achieves adaptive fusion of salinity and ocean current features, enhancing both physical rationality and prediction accuracy while highlighting the necessity and advantages of multi-factor joint coupling in intelligent forecasting systems.

4 Conclusion

This study addresses two critical challenges in long-term intelligent forecasting of sea surface temperature, hereafter referred to as SST: first, existing deep learning methods are heavily reliant on purely data-driven paradigms and lack an explicit integration of physical mechanisms, which compromises both physical consistency and model interpretability; second, the effective coupling of multi-physical properties with multi-scale spatiotemporal features remains difficult, leading to insufficient prediction accuracy and temporal stability. To overcome these limitations, we propose the multi-source coupled prediction neural network MSCPNN and systematically evaluate its performance through a hierarchy of comparative experiments.

The experimental results demonstrate that MSCPNN achieves an average root mean square error of 0.347°C, representing a 17% reduction compared to PCL-MFPNN, and attains a correlation coefficient of 0.935. The model also consistently outperforms all baseline approaches in terms of PSNR and SSIM. When benchmarked against the baseline MFPNN, MSCPNN exhibits substantial improvements across all evaluation metrics, including RMSE, correlation coefficient, PSNR, and SSIM. Notably, these advantages become increasingly pronounced in forecasts extending beyond 10 days, underscoring the model’s superior capability in long-range prediction.

Ablation experiments reveal that salinity coupling—owing to its direct connection with seawater density stratification and mixed-layer dynamics—contributes more consistently to SST prediction and exhibits robust physical guidance effects across both interannual and seasonal timescales.

A further analysis of the error distributions shows that MSCPNN achieves optimal performance across multiple uncertainty metrics, including minimum and maximum errors, error range, and standard deviation. These results confirm that the model not only enhances predictive accuracy but also improves robustness in the face of seasonal transitions, shifts in local circulation patterns, and other abrupt environmental perturbations. Despite the considerable advances in prediction performance and physical consistency attained by MSCPNN, some limitations persist. Future research can be extended in several directions: first, while the current experiments focus on the South China Sea, subsequent studies could expand to larger regions or global scales, incorporating higher-resolution data products to validate model generalizability; second, beyond salinity and currents, additional physical factors such as wind stress and heat fluxes could be integrated to develop more comprehensive physics–data hybrid models; third, closer integration with numerical models and physical mechanism studies is necessary to refine physical coupling strategies and interpretability frameworks, thereby advancing the application of intelligent forecasting methods in climate prediction and marine disaster warning. In summary, by synergistically combining multi-source physical coupling with multi-scale feature learning, MSCPNN effectively bridges data-driven flexibility and physical rigor. Its marked improvements in accuracy, stability, and physical plausibility underscore the promise of attention-guided, physics-informed fusion strategies to advance intelligent ocean forecasting. This work establishes a viable framework to develop physically consistent deep learning models and provides a foundation for next-generation marine prediction systems.

References

• 1

  AbhignaP.JerrittaS.SrinivasanR.RajendranV. (2017). “ Analysis of feed forward and recurrent neural networks in predicting the significant wave height at the moored buoys in bay of bengal,” in Proceedings of the 2017 International Conference on Communication and Signal Processing (ICCSP). 1856–1860 (Chennai, India: IEEE). doi: 10.1109/ICCSP.2017.8286717

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 2

  CaiS.MaoZ.WangZ.YinM.KarniadakisG. E. (2021). Physics-informed neural networks (PINNs) for fluid mechanics: A review. Acta Mech. Sin.37, 1727–1738. doi: 10.1007/s10409-021-01148-1. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 3

  ChapmanD.CaneM. A.HendersonN.LeeD. E.ChenC. (2015). A vector autoregressive ENSO prediction model. J. Clim.28, 8511–8520. doi: 10.1175/JCLI-D-15-0306.1. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 4

  ChenY.-C. (2017). A tutorial on kernel density estimation and recent advances. Biostatistics Epidemiol.1, 161–187. doi: 10.1080/24709360.2017.1396742. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 5

  ChenZ.LiuY.SunH. (2021). Physics-informed learning of governing equations from scarce data. Nat. Commun.12, 6136. doi: 10.1038/s41467-021-26434-1. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 6

  ChoK.KimY. (2022). Improving streamflow prediction in the WRF-Hydro model with LSTM networks. J. Hydrol605, 127297. doi: 10.1016/j.jhydrol.2021.127297. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 7

  CollinsD. C.ReasonC. J. C.TangangF. (2004). Predictability of Indian ocean sea surface temperature using canonical correlation analysis. Clim. Dyn22, 481–497. doi: 10.1007/s00382-004-0390-4. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 8

  ColmanA. W.DaveyM. K. (2003). Statistical prediction of global sea-surface temperature anomalies. Int. J. Climatol.23, 1677–1697. doi: 10.1002/joc.956. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 9

  CuomoS.Di ColaV. S.GiampaoloF.RozzaG.RaissiM.PiccialliF. (2022). Scientific machine learning through physics informed neural networks: Where we are and what’s next. J. Sci. Comput.92, 88. doi: 10.1007/s10915-022-01939-z. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 10

  DawA.KarpatneA.WatkinsW. D.ReadJ. S.KumarV. (2022). “ Physics-guided neural networks (PGNN): An application in lake temperature modeling,” in Knowledge guided machine learning ( Chapman and Hall/CRC, Boca Raton, FL, USA), 353–372. doi: 10.1201/9781003143376-15

  • CrossRef
  • Google Scholar

• 11

  FareaA.Yli-HarjaO.Emmert-StreibF. (2024). Understanding physics-informed neural networks: Techniques, applications, trends, and challenges. AI5, 1534–1557. doi: 10.3390/ai5030083. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 12

  HalmovaD.PekarovaP.PekarJ.KucarovaK. (2016). The simulation of the water temperature rising using ARIMA models. Measurements58, 4.

  • Pubmed Abstract
  • Google Scholar

• 13

  ImaniM.YouR.-J.KuoC.-Y. (2014). Caspian sea level prediction using satellite altimetry by artificial neural networks. Int. J. Environ. Sci. Technol.11, 1035–1042. doi: 10.1007/s13762-013-0287-z. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 14

  JamilF.AliH. M.KhiadaniM. (2023). Concise summary of existing correlations with thermophysical properties of seawater with applications: A recent review. Appl. Therm Eng227, 120404. doi: 10.1016/j.applthermaleng.2023.120404. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 15

  JiaX.WillardJ.KarpatneA.ReadJ.ZwartJ.SteinbachM.et al. (2019). “ Physics guided RNNs for modeling dynamical systems: a case study in simulating lake temperature profiles,” in Proceedings of the 2019 SIAM International Conference on Data Mining. (Philadelphia, PA: SIAM), 558–566. doi: 10.1137/1.9781611975673.63

  • CrossRef
  • Google Scholar

• 16

  JiangC. M.KashinathK.PrabhatMarcusP. (2019). “ Enforcing physical constraints in CNNs through differentiable PDE layer,” in Proceedings of the ICLR 2020 Workshop on Integration of Deep Neural Models and Differential Equations (Addis Ababa, Ethiopia: ICLR).

  • Google Scholar

• 17

  JonnakutiP. K.BhaskarT. V. S. U. (2020). “ A hybrid CNN LSTM based model for the prediction of sea surface temperature using time series satellite data,” in EGU General Assembly Conference Abstracts (Vienna, Austria: Copernicus GmbH on behalf of the European Geosciences Union), 817.

  • Google Scholar

• 18

  KimK. Y.HamlingtonB.NaH. (2015). Theoretical foundation of cyclostationary EOF analysis for geophysical and climatic variables: Concepts and examples. Earth Sci. Rev.150, 201–218. doi: 10.1016/j.earscirev.2015.06.003. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 19

  LandmanW. A.MasonS. J. (2001). Forecasts of near-global sea surface temperatures using canonical correlation analysis. J. Clim.14, 3819–3833. doi: 10.1175/1520-0442(2001)014<3819:FONGSS>2.0.CO;2

  • CrossRef
  • Google Scholar

• 20

  LiaoD.-C.WangQ.ZhouY.-H.LiaoX. (2008). Prediction of the sea surface temperature anomaly by neural networks. Ann. Shanghai Astronomical Observatory Chin. Acad. Sci.37, 11–20.

  • Google Scholar

• 21

  NewboldP. (1983). ARIMA model building and the time series analysis approach to forecasting. J. Forecasting2, 23–35. doi: 10.1002/for.3980020104. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 22

  NiedzielskiT.KosekW. (2005). Multivariate stochastic prediction of the global mean sea level anomalies based on TOPEX/Poseidon satellite altimetry. Artif. Satellites40, 185–198.

  • Pubmed Abstract
  • Google Scholar

• 23

  PalubinskasG. (2017). Image similarity/distance measures: What is really behind MSE and SSIM? Int. J. Image Data Fusion8, 32–53. doi: 10.1080/19479832.2016.1273259. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 24

  PatelR. S.BhartiyaS.GudiR. D. (2022). Physics-constrained learning in neural network based modeling. IFAC-PapersOnLine55, 79–85. doi: 10.1016/j.ifacol.2022.07.425. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 25

  PatilK.DeoM. C.GhoshS.RavichandranM. (2013). Predicting sea surface temperatures in the north Indian ocean with nonlinear auto-regressive neural networks. Int. J. Oceanography2013, 63–64. doi: 10.1155/2013/302479

  • CrossRef
  • Google Scholar

• 26

  RaissiM.PerdikarisP.KarniadakisG. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys.378, 686–707. doi: 10.1016/j.jcp.2018.10.045. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 27

  RepelliC. A.NobreP. (2004). Statistical prediction of sea-surface temperature over the tropical atlantic. Int. J. Climatol.24, 45–55. doi: 10.1002/joc.982. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 28

  ShenS. S. P.BasistA. N.LiG.WilliamsC.KarlT. (2004). Prediction of sea surface temperature from the global historical climatology network data. Environmetrics15, 233–249. doi: 10.1002/env.638. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 29

  WangQ.MaY.ZhaoK.YingjieT. (2022). A comprehensive survey of loss functions in machine learning. Ann. Data Sci. 9, 187–212. doi: 10.1007/s40745-020-00253-5. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 30

  WeiL.GuanL.QuL.GuoD. (2020). Prediction of sea surface temperature in the China seas based on long short-term memory neural networks. Remote Sens12, 2697. doi: 10.3390/rs12172697. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 31

  WillardJ.JiaX.XuS.SteinbachM.KumarV. (2022). Integrating scientific knowledge with machine learning for engineering and environmental systems. ACM Comput. Surv.55, 1–37. doi: 10.1145/3514228

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 32

  WinklerS.MohandasP. (2008). The evolution of video quality measurement: From PSNR to hybrid metrics. IEEE Trans. Broadcast54, 660–668. doi: 10.1109/TBC.2008.2000733. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 33

  WooS.ParkJ.LeeJ.-Y.KweonI. S. (2018). “ Convolutional block attention module,” in Proceedings of the European Conference on Computer Vision (ECCV). 3–19 (Munich, Germany: Springer). doi: 10.1007/978-3-030-01234-2_1

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 34

  WunschC. (2002). What is the thermohaline circulation? Science298, 1179–1181. doi: 10.1126/science.1079329. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 35

  XueY.LeetmaaA. (2000). Forecasts of tropical pacific SST and sea level using a Markov model. Geophys. Res. Lett.27, 2701–2704. doi: 10.1029/1999GL011107. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 36

  YangY.DongJ.SunX.LimaE.MuQ.WangX. (2018). A CFCC-LSTM model for sea surface temperature prediction. IEEE Geosci. Remote Sens Lett.15, 207–211. doi: 10.1109/LGRS.2017.2780843. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 37

  ZhangK.GengX.YanX.-H. (2020). Prediction of 3-d ocean temperature by multilayer convolutional LSTM. IEEE Geosci. Remote Sens Lett.17, 1303–1307. doi: 10.1109/LGRS.2019.2947170. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 38

  ZhangQ.WangH.DongJ.SunX. (2017). Prediction of sea surface temperature using long short-term memory. IEEE Geosci. Remote Sens Lett.14, 1745–1749. doi: 10.1109/LGRS.2017.2733548. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 39

  ZhangY. (2023). Encoder–decoder models in sequence-to-sequence learning: A survey of RNN and LSTM approaches. Appl. Computing Eng.22, 218–226. doi: 10.54254/2755-2721/22/20231220. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar

• 40

  ZhuY.ZhangR.-H.MoumJ. N.WangF.LiX.LiD. (2022). Physics-informed deep-learning parameterization of ocean vertical mixing improves climate simulations. Natl. Sci. Rev.9, nwac044. doi: 10.1093/nsr/nwac044. PMID:

  • Pubmed Abstract
  • CrossRef
  • Google Scholar