Multi-Factor Deep Learning Model for Sea Surface Temperature Forecasting

Abstract

Accurately predicting sea surface temperature (SST) is crucial for marine environmental monitoring and climate research. However, existing ocean model approaches often struggle to capture complex spatiotemporal patterns and are limited by their reliance on thermodynamic equations to impose oceanographic constraints. To address these challenges, we propose a multi-sensor SST prediction model that integrates Long Short-Term Memory (LSTM) networks, convolutional neural networks (CNNs), and an attention mechanism to directly incorporate physical variables such as temperature, salinity, density, and current velocity. By bypassing the need for explicit physical equation constraints, our model effectively learns complex relationships from multi-source data. Experimental results show that our approach significantly improves predictive accuracy across various ocean regions, providing a robust solution for both short-term and long-term SST forecasting.

1. Introduction

Temperature is a crucial parameter in the Earth’s climate system [1], acting as a major driver of climate change. Specifically, variations in sea surface temperature (SST) significantly affect global weather patterns [2,3,4], including monsoons, cyclones, and precipitation events, directly impacting disaster preparedness and response strategies. Accurate SST predictions not only improve the management of extreme weather events but also support climate adaptation planning and sustainable marine resource utilization [5,6]. What is more, SST variations impact the transfer of heat and moisture across the air–sea interface, play a critical role in phenomena like El Niño–Southern Oscillation (ENSO) and La Niña [7,8]. These processes, in turn, regulate global heat redistribution and carbon cycling [9,10], making SST an essential factor in understanding climate variability and forecasting climate change. Furthermore, SST affects marine ecosystems, with changes in surface temperature impacting biodiversity, altering fish migration patterns, and contributing to the degradation of coral reefs. In recent years, more frequent mesoscale ocean phenomena like ocean fronts and eddies, and their ecological consequences, have further underscored the importance of monitoring and predicting SST accurately.

From an application perspective, the variation in SST has profound effects on the marine environment and a variety of economic activities that depend on marine resources [11]. For instance, SST predictions play a pivotal role in disaster management by improving the prediction of extreme weather events like hurricanes and typhoons. They are also critical for fisheries management, facilitating the sustainability of marine ecosystems in regions where temperature variations influence fish migration patterns and coral reef health [12,13]. Additionally, SST prediction contributes to maritime operations, including the optimization of shipping routes, and informs decision-making in offshore industries such as oil and gas exploration. The integration of SST prediction into climate prediction models further highlights their relevance, as they provide scientific insights necessary for developing strategies to adapt to the effects of global warming.

Despite its significance, SST prediction remains a challenge due to the complex interplay of physical, chemical, and biological processes that govern temperature variations at the ocean surface layer. These processes are distributed across various spatial and temporal scales and are influenced by multiple factors, including ocean currents, salinity, density, and vertical mixing in the water. Moreover, climate change has intensified the variability of SST, introducing new patterns of extreme events and nonlinear dynamics that existing prediction models often struggle to capture. Given these challenges, there is an urgent need for innovative approaches to improve SST prediction. Advances in observational technologies, such as satellite remote sensing and in situ measurements, have made multi-source data more accessible, providing opportunities to better capture the latent forces driving SST variability. In the study of sea surface temperature prediction, deep learning methods have been widely applied to process oceanographic data in the form of images [14], particularly in the use of satellite imagery for environmental monitoring and forecasting. Recently, the increasing availability of observation resources has enabled models to integrate multi-source data. These advancements not only promise improved accuracy in SST prediction but also provide new potentials for understanding the underlying mechanisms of air–sea interactions.

Building on leveraging multi-source data and advanced modeling techniques, in this paper, we introduce a model that aims to address these challenges while offering insights into the dynamics of SST variability. Specifically, we propose a multi-factor SST prediction model that utilizes 3D-CNN, BiLSTM, and an attention mechanism to process multi-source remote sensing data, including sea surface temperature, salinity, density, mixed layer depth, and current velocity. By utilizing physical factors, our model satisfies the need for essential physical information, leading to enhanced prediction performance across different test regions. This approach not only addresses the challenge associated with traditional methods but also leverages the adaptability of data-driven models, ultimately contributing to more reliable and effective SST prediction. The rest of this paper is organized as follows: Section 2 provides a comprehensive review of existing SST prediction methods, highlighting their limitations and motivating our proposed approach. Section 3 introduces the proposed hybrid model, detailing its theoretical foundation, architecture, and implementation. Section 4 describes the multi-source dataset and outlines the experimental design, including ablation and comparison studies. Section 5 focuses on evaluating the contributions of individual model components, validating the model performance across different temporal and spatial conditions, and benchmarking the proposed method against state-of-the-art approaches. Section 6 analyzes the prediction accuracy and provides insights into the comparative performance of the models. Finally, Section 7 summarizes the findings and discusses future research directions.

2. Related Work

SST prediction is a challenging task due to the highly dynamic nature of ocean systems and the interaction of multiple physical factors. Existing SST prediction methodologies are generally divided into two categories: numerical models and data-driven approaches. Numerical models, such as the Regional Ocean Modeling System (ROMS) and Hybrid Coordinate Ocean Model (HYCOM), rely on solving complex physical equations to simulate ocean dynamics [15,16] and provide physically interpretable results. These methods simulate ocean dynamics by solving mathematical equations that describe physical processes like heat exchange and circulation. While these models provide high accuracy under stable conditions and are physically interpretable, they rely heavily on precise initial and boundary conditions, limiting their practicality in rapidly changing or poorly observed marine environments. These limitations make them less practical for real-time predictions in dynamic marine environments [17,18,19,20]. Notably, these models excel in long-term predictions by leveraging well-established physical principles. However, their reliance on precise initial and boundary conditions limits their adaptability in capturing the rapidly changing and highly variable nature of dynamic marine environments.

On the other hand, data-driven models, such as Long Short-Term Memory (LSTM) networks and convolutional neural networks (CNNs), exhibit excellent performance in extracting temporal and spatial features from historical data and effectively mapping input features to predictions [21,22]. However, these methods often focus solely on historical SST data and overlook the influence of critical physical factors such as salinity, density, and current velocity. In dynamic ocean regions, where such factors play a significant role, this limitation results in suboptimal predictions. Data-driven models, particularly Long Short-Term Memory (LSTM) and Convolutional LSTM (ConvLSTM), have been successfully applied to time series prediction tasks, including SST prediction [23,24]. LSTM networks show an advantage in capturing long-term temporal dependencies; for example, Jia et al. [22] achieved improvements in prediction performance by leveraging LSTM. ConvLSTM further enhances prediction performance by integrating spatial correlations with temporal dependencies. For instance, Wanigasekara et al. [25] employed ConvLSTM for SST prediction, exhibiting superior prediction performance compared to traditional LSTM models. These models are inherently more adaptable to complex and diverse ocean conditions, making them well suited for handling variations in currents, temperature fronts, and other dynamic factors. However, they often lack physical interpretability and struggle with long-term predictions due to their limited ability to incorporate the underlying physical equations governing ocean dynamics.

These complementary strengths and weaknesses highlight the necessity for a more robust network that satisfies the dual needs of long-term prediction capability and adaptability to dynamic ocean environments. To address this challenge, we propose a multi-factor SST prediction model that integrates essential physical factors into a hybrid deep learning framework, combining the strengths of numerical and data-driven approaches to achieve enhanced prediction performance. Recent studies in time series prediction try to combine physical constraints with data-driven models to enhance prediction performance [26,27,28]. Hybrid approaches have emerged as a promising direction by combining physical constraints with data-driven techniques. For instance, Schmidt et al. [29] explored the application of physics-informed neural networks (PINNs) for ocean dynamics prediction, improving the interpretability of data-driven models. While PINNs have demonstrated success in simulating ocean dynamics, they face limitations in generalizing across diverse ocean regions due to the high variability in physical processes [26]. Additionally, recent works in deep learning have introduced attention mechanisms, which enable models to dynamically focus on critical features during prediction, enhancing their prediction performance [30,31,32]. These mechanisms have been shown to enhance performance in tasks requiring the integration of hybrid approaches, by prioritizing the most relevant temporal or spatial features. For example, Xie et al. [33] demonstrated the effectiveness of combining attention mechanisms with recurrent networks for enhancing model forecasting performance.

In this study, we try to address the aforementioned challenges by incorporating key physical factors, which can influence SST variation, into the prediction process, enabling our model to learn from data without requiring explicit physical constraints. Our method acknowledges the limitations of numerical models and data-driven techniques, trying to leverage the advantages of both to enhance model prediction performance across different ocean regions. Unlike numerical models, our approach avoids the dependency on precise initial and boundary conditions, and, unlike purely data-driven models, it incorporates physical insights to improve interpretability. By leveraging the strengths of hybrid approaches and introducing an attention mechanism for dynamic feature prioritization, our model enhances predictive performance across diverse and complex ocean regions.

3. Methodology

Grounded in fundamental physical principles, including the First Law of Thermodynamics, the heat conduction equation, and stratification theory, the proposed model integrates multiple physical factors, such as temperature, salinity, and density. These factors play pivotal roles in vertical mixing and stratification, which are essential for accurately modeling heat exchange dynamics. For instance, the heat conduction equation governs both horizontal advection $U·\nabla T$ and vertical diffusion $K_z{\displaystyle \frac{{\partial }^{2}T}{\partial z^2}}$, providing a robust theoretical framework for predicting SST variations. The integration of these factors into the CNN-LSTM–attention framework allows the model to dynamically adjust its focus on the most impactful variables, enhancing predictive performance. The proposed model integrates three key components: CNN for spatial feature extraction, LSTM for temporal dependencies, and an attention mechanism for feature prioritization. The CNN outputs spatial features, which are fed into LSTM layers to model temporal dependencies. The attention mechanism dynamically assigns weights, prioritizing the most relevant features at each time step. This integration enables the model to adaptively focus on critical physical factors, enhancing predictive accuracy across dynamic marine environments.

3.1. Multi-Factor Consideration for SST Prediction

Sea surface temperature (SST) is influenced by a complex interplay of various physical factors, particularly affected by heat exchange processes, salinity and density variations, ocean currents, and atmospheric conditions. SST is primarily regulated by thermodynamic processes involving the heat exchange between the atmosphere and ocean, as well as lateral mixing driven by ocean currents. Physical factors such as salinity and density have a significant impact on heat exchange by the water stratification and vertical mixing mechanisms [34]. Thermodynamic principles, such as the First Law of Thermodynamics, the heat conduction equation, and stratification theory, provide a robust theoretical foundation for understanding SST dynamics and guiding model design.

The First Law of Thermodynamics is a fundamental physical principle universally applicable to thermodynamic systems [35]. Its application in oceanography is primarily aimed at describing the transfer and balance of heat. The First Law of Thermodynamics states that the change in internal energy $\mathsf{\Delta }U$ of a system is equal to the heat added to the system Q minus the work done by the system W. This can be mathematically represented as follows:

(1)$\mathsf{\Delta }U=Q-W$

The ocean heat balance equation, derived from the application of the First Law of Thermodynamics, is widely used to describe the relationship between ocean heat fluxes and internal energy changes [36]. This equation is particularly significant in studies of surface ocean heat balance. Taking into account factors such as heat absorption from solar radiation, heat lost through evaporation, and the work done by horizontal and vertical mixing, the heat exchanges in SST can be described as follows:

(2)$\mathsf{\Delta }U=Q_{\mathrm{in}}-Q_{\mathrm{out}}-W$

where $Q_{\mathrm{in}}$ refers to the heat absorbed, such as solar radiation, $Q_{\mathrm{out}}$ refers to the heat lost, such as through evaporation, and W represents the work done by lateral and vertical mixing. These components account for processes such as solar radiation, evaporation, and oceanic currents, which are critical to SST variability.

Mixed layer depth significantly influences the coupling efficiency between surface heat fluxes ($Q_{\mathrm{in}}$ and $Q_{\mathrm{out}}$) and the internal heat distribution. When the mixed layer is deep, the heat capacity per unit volume of seawater increases, allowing absorbed heat to be more widely distributed, thereby constricting surface temperature variations. Conversely, in shallow mixed layers, the absorbed heat remains concentrated near the surface; thereby, SST is more sensitive to heat input. The heat conduction equation, incorporating an advection term, is one of the fundamental equations governing SST spatiotemporal distribution, characterizing the temporal and spatial evolution of heat, including processes of horizontal advection and vertical diffusion [37,38]. It can be mathematically represented as follows:

(3)${\displaystyle \frac{\partial T}{\partial t}}+U·\nabla T=K_z{\displaystyle \frac{{\partial }^{2}T}{\partial z^2}}+H$

where T is the temperature, $U·\nabla T$ represents horizontal advection driven by ocean currents, $K_z{\displaystyle \frac{{\partial }^{2}T}{\partial z^2}}$ represents vertical heat diffusion determined by the vertical mixing coefficient $K_z$, and H accounts for external heat sources such as solar radiation. Mixed layer depth directly affects the vertical diffusion coefficient $K_z$. In shallow mixed layers, vertical diffusion is constrained, and surface temperature variations are primarily governed by horizontal advection and surface fluxes. In contrast, in deep mixed layers, vertical mixing becomes more pronounced, enabling heat to be transferred more effectively to deeper layers. Additionally, in regions with strong ocean currents, such as the Kuroshio Current, horizontal advection plays a dominant role, whereas in more low-dynamic regions, vertical mixing prevails. This equation provides the basis for understanding how heat is distributed both horizontally and vertically in the ocean.

The pure diffusion heat conduction equation, compared to the heat conduction equation, does not include the horizontal advection term [39]. This formulation is often used in static or experimental scenarios where the effects of ocean currents or horizontal movements on temperature changes are negligible. The pure heat conduction equation is given by

(4)${\displaystyle \frac{\partial T}{\partial t}}=\alpha {\nabla }^{2}T+H$

where ${\displaystyle \frac{\partial T}{\partial t}}$ is the change rate of temperature at each time step, $\alpha$ is the thermal diffusivity, which measures how quickly heat diffuses through water, and ${\nabla }^{2}T$ is the Laplacian of the temperature field, representing the lateral and vertical distribution of temperature.

For regions with strong ocean currents, the heat conduction equation is employed to emphasize the effects of advection. Conversely, in areas where temperature diffusion dominates and horizontal motion is minimal, the pure diffusion heat conduction equation can be used, highlighting the roles of diffusion and localized heat sources. In the context of SST prediction, the heat conduction equation is more applicable, as it accounts for both heat diffusion and horizontal advection, a crucial factor in complex oceanic regions, such as those where ocean fronts form.

The density equation is one of the core equations in ocean hydrodynamics, describing the effects of temperature and salinity on seawater density [40]. Salinity and density play critical roles in SST dynamics by affecting vertical stratification and mixing processes. The density of seawater can be expressed as follows:

(5)$\rho ={\rho }_0\left(1-{\beta }_T(T-T_0)+{\beta }_S(S-S_0)\right)$

where ${\rho }_0$ is a reference density, T and S are temperature and salinity, ${\beta }_T$ and ${\beta }_S$ are the thermal expansion and salinity contraction coefficients, and $T_0$ and $S_0$ are reference values. Variations in salinity and density influence the stratification of ocean layers and vertical mixing, which are crucial for heat redistribution.

The Brunt–Väisälä frequency is a critical formula in fluid dynamics used to characterize stratification stability, and it finds broad applications in oceanography [41]. Stratification strength can be quantified using the Brunt-Väisälä frequency:

(6)$N^2=-{\displaystyle \frac{g}{{\rho }_0}}{\displaystyle \frac{\partial \rho }{\partial z}}$

where $N^2$ represents the stratification frequency, g is the gravitational acceleration, and ${\displaystyle \frac{\partial \rho }{\partial z}}$ is the vertical density gradient. Stronger stratification (higher $N^2$) reduces vertical mixing, trapping heat in surface layers and amplifying SST gradients. Furthermore, mixed layer depth is both an outcome and a determinant of water column stratification stability. Shallow mixed layers are typically associated with strong stratification (high $N^2$ values), which restricts vertical mixing. In contrast, deep mixed layers correspond to weaker stratification (low $N^2$ values), facilitating enhanced vertical heat exchange.

Building on these theoretical principles, the proposed multi-factor SST prediction model incorporates key physical factors such as temperature, salinity, density, mixed layer depth, and current velocity. By embedding these factors into a hybrid deep learning framework comprising CNN, LSTM, and attention mechanisms, the model dynamically captures critical spatiotemporal relationships. This approach ensures that the model not only learns from data but also respects the physical processes governing SST dynamics, leading to enhanced predictive performance across diverse marine environments.

3.2. Model Architecture

The proposed multi-factor SST prediction model effectively addresses the challenges of ocean front prediction by leveraging a hybrid architecture grounded in robust theoretical principles. Building on these theoretical principles, the proposed multi-factor SST prediction model integrates key physical factors such as temperature, salinity, density, mixed layer depth, and current velocity, ensuring a comprehensive representation of the physical processes driving SST dynamics. The use of density and salinity directly relates to stratification effects and vertical mixing, while current velocity captures horizontal advection; both are crucial for accurately predicting SST variation. As displayed in Figure 1, the proposed SST prediction model integrates three key components: convolutional neural networks (CNNs), Long Short-Term Memory (LSTM) networks, and an attention mechanism. The CNN is designed to efficiently model the temporal dependencies of SST variations, LSTM is designed to extract critical spatial features, and the attention mechanism is designed to dynamically adjust the importance of different input variables. Together, these three components enable to capture complex spatiotemporal relationships from multi-factor data. This integration ensures that the model respects physical processes governing SST dynamics while leveraging data-driven learning, resulting in enhanced predictive performance and interpretability across diverse marine environments.

3.3. Convolutional Neural Network for Spatial Feature Extraction

The CNN module is primarily responsible for extracting spatial features from multi-source SST-related data. Local receptive fields in the convolutional filters detect spatial patterns such as thermal fronts and eddies, which are critical for understanding heat distribution [42,43]. To enhance generalization and prevent overfitting, a dropout layer is applied during training. The dense layer further integrates these spatial features, ensuring that the model captures the essential characteristics necessary for the following temporal modeling.

Our CNN module is composed of a Conv2D layer, a dropout layer, and a dense layer. The CNN module provides a balance of effective spatial feature extraction, regularization, and robust decision-making. Conv2D excels in extracting spatial features from 2D data, while maintaining computational efficiency and avoiding overfitting to extraneous dimensions. In contrast, Conv3D often introduces excessive model complexity, leading to suboptimal results, specifically when the third dimension contains noise or irrelevant variations.

In our CNN module, the input of Conv2D is spatial slices of the multi-factor data. The CNN module aligns with the heat conduction equation ${\nabla }^{2}T$, as it captures lateral variations and gradients in temperature fields, essential for identifying the boundaries and transitions characteristic of ocean fronts. The performance of a convolutional neural network on multi-factor data may degrade due to increased model complexity, potential noise sensitivity, and the inability to effectively disentangle spatial and inter-factor relationships, leading to suboptimal feature extraction and generalization. To solve this problem, we applied a dropout layer and dense layer to the convolution result. The dropout layer further improves generalization by preventing overfitting, while the dense layer effectively integrates extracted features for precise predictions.

3.4. Long Short-Term Memory for Temporal Dependencies

LSTM networks utilize memory cells and gates to regulate the flow of information over time. The ability of LSTM networks to remember information over time relies on their use of forget, input, and output gates, which can regulate information preservation and elimination. This mechanism is crucial for accurately capturing temporal patterns and long-term and short-term changes in SST data [34]. This architecture reduces the risk of gradient explosion caused by backpropagation through long sequences, allowing the network retain long-term temporal dependencies. Additionally, time series analysis emphasizes the importance of modeling SST dynamics in the temporal dimension, supporting the suitability of LSTM networks for SST prediction.

Figure 2 illustrates a neural network architecture designed for sequential data prediction, leveraging the strengths of bidirectional Long Short-Term Memory (BiLSTM) layers, dropout layers, and dense layers. The input data are first processed through multiple LSTM layers, where each layer captures temporal dependencies in both forward and backward directions, enhancing the model’s ability to learn contextual relationships. Outputs from these layers are concatenated to integrate diverse feature representations, ensuring robust learning. Dropout layers are strategically placed to mitigate overfitting, promoting better generalization on unseen data. Finally, the dense layer serves as a fully connected module, consolidating the extracted features to produce the final prediction. This architecture demonstrates a sophisticated approach to modeling complex temporal dynamics in sequential datasets.

3.5. Heat Transport and Attention Mechanisms

Ocean currents and vertical mixing govern heat transport, influencing SST distribution. The heat conduction equation highlights the critical roles of horizontal advection and vertical diffusion. These processes are regionally variable, with horizontal advection dominating in high-current areas (e.g., the Kuroshio Current) and vertical diffusion playing a greater role in more stable regions. Incorporating attention mechanisms within the proposed hybrid model aligns with these principles. The attention mechanism dynamically prioritizes physical factors such as salinity, temperature, and current velocity based on their relevance to specific spatial and temporal contexts. For example, in regions with strong stratification (high $N^2$), the model focuses more on surface temperature and salinity. Conversely, in high-advection regions, the attention mechanism emphasizes horizontal velocity and its influence on heat transport ($U·\nabla T$).

The attention mechanism is inspired by cognitive processes that prioritize relevant information. When applied in neural networks, the attention mechanism allows the model to focus on specific parts of the input data dynamically, enhancing its ability to learn and make predictions based on the most relevant features [44]. The attention mechanism dynamically adjusts the importance of input features at each time step, ensuring the model focuses on the most relevant physical factors for SST prediction. Mathematically, the attention weights $\mathrm{Attention}(Q,K,V)$ are computed as follows:

(7)$\mathrm{Attention}(Q,K,V)=\mathrm{softmax}\left({\displaystyle \frac{Q{K}^{\top }}{\sqrt{d_k}}}\right)V$

where $Q,K,V$ represent the query, key, and value matrices derived from input features, and $d_k$ is a scaling factor equal to the dimension of the key vectors, used to normalize the dot product. The attention mechanism dynamically weights the importance of physical factors (e.g., salinity, density, or current velocity) based on their relevance at each time step, ensuring that the model focuses on the most influential factors.

The attention mechanism is built upon the idea of weighted aggregation, where the extracted features are assigned varying weights based on their relevance. This is particularly useful in SST prediction, as the influence of physical factors like sea surface salinity and density on SST can change over time. SST is influenced by localized phenomena such as strong currents or density gradients. By prioritizing these variables when they are most influential, the attention mechanism respects the principles of heat transport and stratification ($U·\nabla T$ and $K_z{\displaystyle \frac{{\partial }^{2}T}{\partial z^2}}$). By focusing on specific variables, the attention mechanism enhances the predictive performance of the model, allowing it to adapt effectively to the conditions that change at each time step. In this study, we design the attention mechanism to prioritize the most recent days, allowing the model to focus on the most relevant and timely information. Additionally, we introduce a concatenation layer to integrate outputs from different components of the model, including the CNN module, LSTM module, attention mechanism, and original input data. This fusion of feature representations enhances the model’s ability to learn complex patterns.

4. Experiments

4.1. Dataset and Experimental Setup

The dataset includes multi-source physical factors, including sea surface temperature, mixed layer depth, sea surface salinity, sea surface density, and current velocity in two directions. Incorporating these factors aligns with the First Law of Thermodynamics, the heat conduction equation, and stratification theory, enabling the model to capture critical heat exchange processes and vertical mixing dynamics. These variables are derived from high-resolution satellite and in situ observations, which can offer an important understanding of the physical processes that affect SST variations [34].

The study area spans from $5^{\circ }\mathrm{N}$ to $5^{\circ }\mathrm{S}$ in latitude and from ${160}^{\circ }\mathrm{W}$ to ${170}^{\circ }\mathrm{W}$ in longitude, belonging to Kuroshio Current. The data used have a spatial resolution of $0.05$ degrees and cover a time span from 2002 to 2021, comprising 5475 SST images, each with $200\times 200$ pixels. These are Near-Real-Time (NRT) observations obtained from a combination of satellite and in situ measurements published by Copernicus Marine Service. Before being input into our model, the remote sensing data undergo a preprocessing pipeline. The preprocessing pipeline standardizes the multi-source data for consistency and compatibility. Firstly, normalization scales each variable to a [0, 1] range, facilitating efficient training. Secondly, spatial resampling ensures a uniform resolution of $0.05$ degrees, aligning satellite and in situ data. Finally, data fusion combines different data sources using a weighted averaging method, addressing gaps and inconsistencies in individual datasets. These steps ensure robust feature extraction and improve model generalization. The preprocessed data are then split into training, validation, and test sets, covering diverse temporal and spatial conditions to evaluate the model’s adaptability.

The image shown in Figure 3 illustrates the spatial distribution of the experimental regions chosen for this study. It depicts the methodology for selecting nine experimental regions from a $200\times 200$ image. Each experimental region is a $5\times 5$ patch, selected to ensure diverse spatial coverage. The selected experimental regions include the following: (1) four regions located at the corners of the image, representing the outermost areas; (2) four regions situated at the midpoints of the diagonals from the outer corners to the image center; and (3) one central region at the exact center of the image. This selection method achieves a balanced spatial coverage while maintaining sufficient independence and representativeness.

To evaluate the proposed model, we conducted experiments using multi-source data from nine regions, representing diverse oceanographic conditions such as strong currents and thermal fronts. The experiments are designed to validate the model’s robustness in spatial variability, temporal prediction lengths (1-day, 3-day, 7-day, and 1-month), and performance compared to state-of-the-art methods. The dataset was split into training (70%), validation (10%), and test (20%) subsets, ensuring temporal and spatial independence. The model was trained using the Adam optimizer with a learning rate of 0.001, and the performance was evaluated using RMSE (Root Mean Square Error) metrics. This setup allows for a comprehensive assessment through ablation and comparison experiments.

To evaluate the predictive performance of our model, we employ the RMSE as the primary metric. RMSE is a widely used statistical measure for quantifying the difference between predicted values and observed values. The formula for RMSE is defined as follows:

(8)$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\left(y_i-{\widehat{y}}_i\right)}^2},$

where N is the total number of samples in the training/validation batch, $y_i$ represents the ground truth value for sample i, and ${\widehat{y}}_i$ denotes the predicted value for sample i.

RMSE provides a comprehensive assessment of model accuracy by penalizing larger errors more heavily than smaller ones, owing to the squaring operation. This property makes RMSE particularly suitable for evaluating SST prediction. In the context of our experiments, lower RMSE values indicate better model performance, signifying closer alignment between predicted and observed SST values. The metric is computed across different spatial regions and predictive lengths to provide an overall evaluation of the model’s robustness and adaptability.

4.2. Ablation Study

To systematically evaluate the contributions of individual components (CNN, LSTM, and attention) within the proposed model, an ablation study is conducted. Each module is removed separately to assess its specific impact on critical tasks such as spatial feature extraction, temporal dependency modeling, and dynamic feature weighting. The experimental results, as shown in Figure 4, provide insights into the individual contributions of the CNN, LSTM, and attention modules to the overall model performance.

Removing the CNN module: The exclusion of the CNN module diminished the model’s ability to capture spatial patterns, resulting in a $0.0223$ increase in RMSE. This result validates the vital role of spatial feature extraction in SST prediction, particularly in regions with complex ocean dynamics where spatial variability significantly influences SST. Temporal dependencies alone are insufficient to model SST effectively in regions where spatial interactions dominate. These findings validate the necessity of each component in achieving robust predictions.

Removing the LSTM module: Replacing the LSTM module with a convolutional neural network reduced the model’s capacity for temporal dependency modeling, causing a $0.1017$ increase in RMSE. The LSTM module effectively captures long-term dependencies in SST data, which are essential for predicting SST variation over time. The absence of LSTM module resulted in a reduction in the model’s ability to capture crucial temporal information, leading to a decrease in model’s long-term predictive performance.

Removing the attention module: The absence of the attention mechanism diminished the model’s ability to dynamically weight input features over time, leading to a $0.1563$ increase in RMSE. The attention mechanism dynamically assigns weights to input features based on their importance at each time step, which allows the model to adaptively focus on the most relevant physical factors. Without it, the model assigns equal importance to all features, cause a decrease in the model’s predictive performance, particularly in regions where specific variables such as salinity, density, or current velocity dominate.

Overall, the results show that removing the CNN increases the RMSE by $0.0223$, indicating its ability to capture spatial patterns. Similarly, the exclusion of the LSTM leads to a $0.1017$ increase in RMSE, highlighting the importance of temporal modeling. The removal of the attention mechanism causes the highest increase in RMSE of $0.1563$, demonstrating its pivotal role in dynamically prioritizing input features based on their relevance.

4.3. Comparison Experiments

To evaluate the effectiveness of the proposed model, we compared its performance with several state-of-the-art methods, including VAE (Variational AutoEncoder Network) [45], Conv3D (Three-Dimensional Convolution Network) [46], LSTM (Long Short-Term Memory network) [47], ConvLSTM (Convolutional Long Short-Term Memory Network) [48], and Transformer Network [49]. These methods were chosen for their diverse architectural designs and proven applications in spatiotemporal prediction tasks. The results indicate that our model achieves the lowest RMSE across all prediction lengths, with a notable improvement over Transformer Network by 0.0226 for 1-day forecasts and 0.0334 for 1-month forecasts. While Transformer benefits from its self-attention mechanism, it lacks the integration of physical factors, limiting its generalizability. Conv3D demonstrates strong spatial modeling capabilities but struggles with parameter complexity, leading to overfitting in dynamic ocean conditions.

The proposed model consistently achieved the lowest RMSE across all temporal lengths, demonstrating its superior ability to integrate spatiotemporal dynamics and physical factors. For instance, the Transformer Network performed competitively due to its self-attention mechanism, yet its lack of explicit spatial modeling limited its performance in regions with complex spatial variability. Conv3D exhibited strong spatial feature extraction but struggled with parameter complexity, leading to overfitting in regions with sparse data. The LSTM and ConvLSTM models effectively captured temporal patterns but underperformed in leveraging multi-source physical factors, resulting in higher RMSE values. These findings highlight the importance of combining spatial, temporal, and physical modeling, as achieved by our hybrid architecture.

5. Comparative Analysis of Model Performance

We performed comparison experiment on nine different spatial locations, namely, P1, P2,..., P9; the experimental results are analyzed in Section 5.1. In addition, we analyze the results for different temporal lengths, namely, one-day, three-days, seven-days, and one-month in Section 5.2. Moreover, to evaluate the effectiveness of the proposed model, we compared its performance with several state-of-the-art methods, including VAE, Conv3D, LSTM, ConvLSTM, and Transformer Network, and the results are analyzed in Section 5.3.

5.1. Spatial Comparison

We conducted validation experiments using multi-factor data from nine experiment regions. These regions are influenced by various environmental factors such as strong ocean currents, thermal fronts, and seasonal variations, making them ideal test areas for evaluating the robustness of our SST prediction model. From an oceanographic perspective, including physical factors such as salinity, density, sea level, and seawater flow velocity significantly enhances the model’s capacity to capture the complex physical processes driving SST variations. Specifically, by incorporating flow velocity data, our model captures the effect of heat advection, with the attention mechanism enabling the model to prioritize areas influenced by ocean currents like the Kuroshio Current and Gulf Stream.

Density, which is influenced by both temperature and salinity, affects the ocean’s vertical structure and the extent of mixing between surface and deeper waters. Vertical mixing plays a crucial role in impacting surface temperatures. By integrating density variations into the model, we enhance its ability to predict SST changes driven by these processes. Overall, the inclusion of key physical factors captures the spatiotemporal complexity of SST dynamics, ensuring more reliable predictions across different ocean environments.

To evaluate the performance of our model across different spatial regions, we conducted comparative experiments at nine distinct locations. The nine locations were chosen to represent different spatial conditions, including regions with high spatial variability and regions with relatively uniform conditions. The goal of this comparison study is to verify the model’s robustness under various spatial conditions. The model’s performance at each location was evaluated using RMSE.

Table 1 shows the RMSE achieved at each location. The results indicate that the proposed model achieved a relatively uniform RMSE across all locations. Notably, the RMSE at position P1 achieves an average value of 0.1760, at position P2 achieves an average value of 0.1810, at position P3 achieves an average value of 0.1803, at position P4 achieves an average value of 0.1777, at position P5 achieves an average value of 0.1786, at position P6 achieves an average value of 0.1714, at position P7 achieves an average value of 0.1755, at position P8 achieves an average value of 0.1797, and at position P9 achieves an average value of 0.1837. The RMSE values achieved across the nine selected regions range from 0.1760 to 0.1837, with an average of 0.1782. This narrow range demonstrates the model’s robust generalizability across diverse marine environments, including high-current areas such as the Kuroshio Current. The inclusion of physical factors, such as flow velocity and salinity, ensures that the model effectively captures region-specific spatiotemporal dynamics, leading to consistent predictive performance.

5.2. Temporal Comparison

To evaluate the proposed model’s effectiveness across various time periods, we conducted experiments with different predictive lengths: 1 day, 3 days, 7 days, and 1 month. These experiments aimed to validate the model’s performance on both short-term and long-term predictions, which are critical for practical applications.

For each predictive length, the model is trained and tested separately at the nine spatial regions. Table 1 presents the RMSE values for different predictive lengths. The results indicate that the model achieves high predictive performance for short-term predictions. Our model achieves RMSE ranges from 0.1208 to 0.1468, with an average of 0.1306, for one-day prediction, 0.1554 to 0.1637, with an average of 0.1600, for three-day prediction, and maintains reasonable performance for longer time periods, though errors increase with predictive lengths. Our model achieves RMSE ranges from 0.1763 to 0.1861, with an average of 0.1806, for seven-day prediction, and 0.2228 to 0.2617, with an average of 0.2416, for one-month prediction.

Our proposed model excels in both short-term and long-term SST predictions, demonstrating its ability to effectively capture the temporal and spatial complexities inherent in SST variations. Predicting SST is particularly challenging due to the influence of both short-term processes, such as daily temperature fluctuations, and long-term phenomena, such as seasonal cycles. Short-term prediction tends to be less challenging as the SST changes within shorter time periods are generally smoother and more predictable. However, long-term predictions are more difficult due to the influence of complex oceanographic processes, such as seasonal variability, ocean currents, and climate cycles, which introduce greater uncertainty.

In the short term, such as 1-day and 3-day prediction, SST is influenced by daily or weekly changes in atmospheric conditions, solar radiation, and local oceanographic processes. Our model’s combination of CNN and LSTM allows it to effectively capture both spatial and temporal patterns, ensuring high performance even over short time periods. The CNN extracts detailed spatial features from the input data, while the LSTM tracks the evolution of these patterns over time, enabling the model to make precise short-term predictions.

Long-term SST predicting is more complex due to the influence of slower processes, such as seasonal temperature shifts, ocean currents, and climate oscillations such as ENSO events. For longer time periods, such as 7-day and 1-month prediction, performance gradually declines due to the accumulation of prediction errors and increased uncertainty in temporal dependencies. Our model’s bidirectional LSTM captures long-range temporal dependencies, allowing it to retain important information across longer periods.

Bidirectional LSTM significantly outperformed unidirectional LSTM, particularly in long-term SST prediction tasks. This is because bidirectional LSTM processes the input data in both forward and backward directions, enabling the model to capture dependencies that extend both into the past and the future. The bidirectional LSTM improved accuracy of the model, especially in regions where SST is influenced by both historical and future data patterns, such as areas with strong ocean currents or seasonal variations.

Additionally, the attention mechanism plays a crucial role by dynamically adjusting the model’s focus on the most relevant physical factors at each time step, ensuring that long-term trends and key environmental drivers are accurately reflected in the predictions. The attention mechanism further enhances the model’s predictive performance by dynamically adjusting the weight of various physical factors in response to rapidly changing oceanographic conditions. Overall, the attention mechanism, combined with the feature extraction capabilities of the CNN and the temporal learning abilities of the LSTM, allows our model to provide highly reliable SST predictions. The combination of bidirectional LSTM, the attention mechanism, and the multi-scale CNN allows our model to effectively capture both short-term fluctuations and long-term trends in SST data.

5.3. Method Comparison

To evaluate the effectiveness of the proposed model, we conducted comparative experiments using five different prediction methods: VAE, Conv3D, LSTM, ConvLSTM, and Transformer Network. These methods represent diverse architectures commonly used for spatiotemporal prediction. We evaluate the performance of each method across different predictive lengths, which are 1 day, 3 days, 7 days, and 1 month.

As shown in Table 2, the proposed method consistently outperformed the other approaches, achieving the lowest RMSE across different predictive lengths. For 1-day prediction, the proposed method achieved an RMSE of 0.1306, 0.0226 lower than that achieved by Transformer Network and significantly lower than that achieved by VAE, Conv3D, LSTM, and ConvLSTM, which is 0.2414, 0.2372, 0.1252, and 0.2461, respectively. For 3-day prediction, the proposed method achieved an RMSE of 0.1600, 0.0034 lower than that achieved by Transformer Network abd significantly lower than that achieved by VAE, Conv3D, LSTM, and ConvLSTM, which is 0.222, 0.2627, 0.113, and 0.3687, respectively. For 7-day prediction, the proposed method achieved an RMSE of 0.1806, 0.028 lower than that achieved by Transformer Network and significantly lower than that achieved by VAE, Conv3D, LSTM, and ConvLSTM, which is 0.2274, 0.699, 0.1914, and 0.4588, respectively. For 1-month prediction, the proposed method achieved an RMSE of 0.2416, 0.0334 lower than that achieved by Transformer Network and significantly lower than that achieved by VAE, Conv3D, LSTM, and ConvLSTM, which is 0.5354, 0.6388, 0.2404, and 0.4548, respectively.

For short-term predictions (1 day and 3 days), the proposed method achieved superior performance due to its ability to effectively integrate spatial and temporal features through the combination of CNN, LSTM, and attention mechanisms. In contrast, Conv3D struggled to capture fine-grained temporal dynamics, and VAE’s reconstruction-focused architecture limited its predictive accuracy.

For long-term predictions (7 days and 1 month), the proposed model achieved a relatively low RMSE, demonstrating its robustness in handling long-term dependencies. While Transformer Network exhibited competitive performance due to its self-attention mechanism, it was slightly outperformed by our method, likely because our architecture better integrates spatial patterns with temporal dynamics through the concatenaiton module.

VAE, while effective for data reconstruction, lacks the temporal modeling capability required for accurate predictions over extended time periods. Conv3D, despite capturing spatiotemporal features, tends to overfit due to high parameter complexity. LSTM and ConvLSTM showed strong temporal modeling capabilities but failed to fully leverage spatial correlations, particularly in regions with complex dynamics. In contrast, the proposed method achieves a balance between spatial and temporal modeling, enhanced by the attention mechanism’s ability to dynamically prioritize relevant features.

The comparative experiments across different predictive lengths validate that the proposed model outperforms existing methods in both short-term and long-term predictions. By effectively integrating spatiotemporal features and dynamically weighting input relevance, our method achieves superior predictive performance and robustness.

6. Discussion and Insights from Model Performance Comparison

We introduce a discussion on the model’s performance, focusing on the overall prediction accuracy observed during the prediction process across different time periods and prediction errors estimated across different methods. The discussion provides an insight into how the model’s predictions align with expected patterns.

6.1. Prediction Performance Compared Across Time Periods

By comparing the model’s prediction accuracy over different time periods, we try to delve deeper into the experimental results, evaluating the model’s performance using two key metrics: prediction accuracy and RMSE. Prediction accuracy provides a comprehensive assessment of the model’s reliability in terms of correct predictions, while the RMSE boxplot illustrates the magnitude of the prediction errors. These metrics provide complementary perspectives on the model’s ability to make accurate predictions.

6.1.1. Experimental Results Evaluated by Prediction Accuracy

The experimental results are presented in Figure 5; the x-axis of the figure represents the number of test samples, while the y-axis shows the normalized SST values. The displayed prediction and true values are calculated by summing up the prediction values over the entire prediction time period. For example, the 1-month prediction result is the summation of the predicted values for each of the 30 days in the prediction time period.

The prediction values for 1 day and 3 days, as presented in Figure 5a,b, show relatively good alignment with the true values, with a small discrepancy. As the prediction time period increases, the discrepancy between prediction values and true values becomes more pronounced. The largest discrepancy occurs in the 1-month predictions, showing a clear increase in the prediction discrepancy. The prediction accuracy appears to decrease as the prediction time period increases, for predictions are inherently more uncertain due to the cumulation of SST variation. This is reflected in the growing discrepancies between prediction values and true values for the 7-day and 1-month predictions, as presented in Figure 5c,d.

6.1.2. Experimental Results Evaluated by Root Mean Squared Error

Figure 6 shows the performance distributions for different predictive time periods. The vertical axis of the boxplot represents performance evaluated by RMSE; the horizontal axis represents the predictive time periods. The boxplots for the 1-day, 3-day, and 7-day prediction exhibit a narrow interquartile range (IQR) and short whiskers, indicating low variability in RMSE. Meanwhile, the boxplot for the 1-month prediction shows the widest IQR and longest whiskers, indicating an increase in RMSE variability. The results demonstrate that the proposed method performs effectively across various time scales.

However, a clear trend of increasing RMSE with longer prediction periods is observed, as longer periods introduce greater complexity and uncertainty. The boxplots appear symmetric for shorter time periods (1 day and 3 days), indicating balanced RMSE distributions around the median. For longer time periods (7 days and 1 month), slight asymmetry is visible, suggesting a tendency for the model to occasionally overpredict, likely due to the complexity of long-term dynamics. For overprediction, the predicted values tend to exceed true values more frequently, which may indicate that the model is overly sensitive to trend variations in certain variables. This is particularly obvious in long-term predictions, where variations in trend estimates may be exaggerated.

6.2. Prediction Performance Compared Across Methods

To further analyze the variability and stability of the prediction results, we employ boxplot visualizations. These visualizations provide insights into the distribution, outliers, and interquartile ranges of the RMSE across different methods. Figure 7 illustrates the performance distributions of various prediction methods, including VAE, LSTM, Transformer, Conv3D, ConvLSTM, and the proposed method. The vertical axis of the boxplot represents performance evaluated by RMSE, while each box indicates the interquartile range (IQR).

The proposed model exhibits a lower median RMSE and smaller IQR compared to other methods across all predictive lengths, indicating higher accuracy and stability. Transformer and LSTM methods also achieve a relatively low median RMSE of approximately 0.19 and 0.32, respectively, but remain inferior to our proposed method. Meanwhile, VAE displays more outliers, indicating its sensitivity to temporal dependencies, particularly for longer predictions. The variability in characteristics across time steps amplifies fluctuations in model predictions. Compared to VAE, ConvLSTM and Conv3D achieve fewer outliers, demonstrating their robustness, whereas a median RMSE higher than VAE suggests poor predictive performance. ConvLSTM and Conv3D may fail to leverage the interplay between all input variables, especially lacking the complexity required to capture the nonlinear relationship of the physical factors.

The proposed method achieves superior performance not only in terms of a lower median RMSE but also a narrow IQR, highlighting its reliability across diverse experimental conditions. The Transformer and LSTM methods, while achieving performance levels close to the proposed method, exhibit a larger IQR, indicating potential sensitivity to certain conditions such as strong ocean currents or extreme weather. Conversely, Conv3D and ConvLSTM demonstrate significant performance instability, as evidenced by their broader IQR distributions, indicating their sensitivity to the complexity of spatial features. The variability in characteristics across various test regions demonstrates wider error distributions in these regions, suggesting difficulties in handling spatiotemporal complexities. The boxplot analysis strongly supports the superiority of the proposed method. Its combination of a high median performance and narrow IQR distribution demonstrates robustness, stability, and adaptability to complex predictive scenarios, making it the most reliable among the compared methods.

7. Conclusions

This paper presents a novel multi-factor SST prediction model that integrates CNN, LSTM, and an attention mechanism. By dynamically adjusting the weights on the extracted features, the attention mechanism plays a critical role in allowing the model to adapt to the rapidly changing conditions of marine environments. By leveraging essential physical factors such as sea surface temperature, sea surface salinity, sea surface density, sea level, and seawater flow velocity, the model effectively addresses some of the constraints of traditional methods, which often fail to consider the complex interactions in oceanographic processes, such as those described by the First Law of Thermodynamics, the heat conduction equation, and stratification theory. The model significantly enhances predictive performance by effectively capturing both the spatial and temporal complexities of oceanographic processes while adapting to rapidly changing environmental conditions.

Our findings demonstrate that the model consistently outperforms traditional approaches, including VAE, Conv3D, LSTM, ConvLSTM, and Transformer Network, across multiple ocean regions, excelling in both short-term and long-term predictions. Experimental results demonstrate significant improvements in predictive accuracy across diverse ocean regions, outperforming state-of-the-art methods. The impact of seasonal variability on the model’s performance remains an important area for further exploration. Future research could focus on incorporating seasonal patterns into the model, exploring whether different seasons require different model adjustments, and whether season-specific training could improve performance. This could be an important direction for advancing SST prediction accuracy, especially in operational settings where seasonal forecasting is critical. Furthermore, by incorporating physical factors, the model bridges the gap between numerical and data-driven approaches. Future research will focus on incorporating additional environmental variables, including wind patterns, atmospheric pressure, and ocean heat content, to enhance the model’s capability in capturing complex air–sea interactions, further advancing the reliability of SST predictions. Moreover, extending the application scope to global climate systems can provide deeper insights into large-scale phenomena, such as the El Niño–Southern Oscillation (ENSO).

Author Contributions

Conceptualization, Y.J. and J.D.; methodology, Y.Y.; software, Y.Y.; validation, Y.Y.; formal analysis, Y.J., J.D. and K.-M.L.; investigation, Y.J., J.D. and K.-M.L.; resources, Y.J. and J.D.; data creation, Y.Y., Y.J. and J.D.; writing—original draft preparation, Y.Y.; writing—review and editing, K.-M.L.; visualization, Y.J. and Y.Y.; supervision, Y.J. and J.D.; project administration, Y.J. and J.D.; funding acquisition, Y.J., J.D. and K.-M.L. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The datasets analyzed in this study are publicly available at [https://dx.doi.org/10.21227/5ntd-nt58], accessed on 20 November 2024.

Acknowledgments

This study benefited from the data provided by the Copernicus Marine Service, for which we are deeply grateful.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. The architecture of the proposed multi-factor deep learning model. The proposed model is composed of a CNN module, an LSTM module, an attention module, and a concatenation layer.

Figure 2. Architecture of a BiLSTM-based model with dropout and dense layers for capturing temporal dependencies and generating accurate sequential predictions.

Figure 3. Experimental regions selected for analysis. Nine regions are marked and labeled blue, indicating specific areas of interest.

Figure 4. The model’s performance with and without CNN, LSTM, and attention modules evaluated by RMSE for 3-day SST prediction.

Figure 5. The prediction accuracy across time periods. The prediction values and true values for (a) 1 day, (b) 3 days, (c) 7 days, and (d) 1 month provide insight into the performance of the model over different prediction time periods.

Figure 6. Comparison of model performance using boxplots across time periods. The orange line within the box represents the median (Q2) of the RMSE. The blue box spans the first quartile (Q1) to the third quartile (Q3), and the blue whiskers extend from the box to the minimum and maximum values within 1.5 times the interquartile range (IQR).

Figure 7. Comparison of model performance using boxplots across prediction methods.

Table 1

Prediction performances on different positions.

Prediction Length	Positions
	P1	P2	P3	P4	P5	P6	P7	P8	P9
1-day	0.1468	0.1341	0.1311	0.1289	0.1293	0.1208	0.1300	0.1313	0.1233
3-days	0.1581	0.1554	0.1588	0.1622	0.1631	0.1587	0.1599	0.1601	0.1637
7-days	0.1763	0.1806	0.1807	0.1815	0.1824	0.1775	0.1812	0.1794	0.1861
1-month	0.2228	0.2538	0.2505	0.2381	0.2397	0.2285	0.2310	0.2480	0.2617
Mean	0.1760	0.1810	0.1803	0.1777	0.1786	0.1714	0.1755	0.1797	0.1837

Table 2

Prediction performances using different methods.

Prediction Length	Methods
	VAE	Conv3D	LSTM	ConvLSTM	Transformer	Our
1 day	0.3719	0.3678	0.2558	0.3767	0.1532	0.1306
3 days	0.3820	0.4227	0.2730	0.5287	0.1634	0.1600
7 days	0.4080	0.8796	0.3720	0.6394	0.2086	0.1806
1 month	0.7770	0.8804	0.4820	0.6964	0.2750	0.2416

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