Global Prediction of Whitecap Coverage Using Transfer Learning and Satellite-Derived Data

Abstract

Whitecaps formed by breaking waves and air entrainment are readily visible on the ocean surface, with their high albedo significantly impacting the accuracy of remote sensing retrievals. While most traditional whitecap parameterizations rely only on wind speed, these approaches fail to explain complex variations in whitecap coverage. Satellite-derived whitecap data, based on brightness temperature variations from the WindSat radiometer, provide valuable global observations of whitecap coverage. To effectively utilize these satellite-derived data, we propose a transfer learning approach for predicting global whitecap coverage. The model is first pre-trained using modeling data based on statistical wave-breaking theory and subsequently fine-tuned with satellite-derived observations. The fine-tuned model demonstrates significant improvements over both the pre-trained model and traditional wind speed parameterizations when evaluated on independent satellite-derived test data. Through explainable deep learning methods, we identify that whitecap coverage is modulated by various atmospheric and wave parameters. The variable contribution analysis reveals the significant impacts of wind–wave interaction, wave states, and atmospheric stability on whitecap formation and coverage.

1. Introduction

Wave breaking induces a series of highly complex phenomena across the air–sea interface, which have important implications for weather and climate change [1]. Wave crests torn by strong winds generate spume droplets [2], while bubble-bursting processes produce films [3] and jet drops [4,5]. These droplets are responsible for the mass, energy, gas, and moisture exchange through their suspension and interaction with the atmosphere. During wave breaking, air is entrained into the upper ocean layer, creating surface foams and subsurface bubble clouds. Within their finite lifespan, these foams and bubble clouds manifest in what we observe as whitecaps. While Andreas and Monahan [6] found that whitecap bubbles themselves play a minimal direct role in air–sea heat and moisture exchange at common wind speeds, the overall whitecapping process plays a significant role in the production of sea spray and the alteration of surface properties. Distinctly different from the quiescent air–sea interface, these whitecaps transform the sea surface layer approximately into a blackbody for both microwave and acoustic radiation. Thus, whitecap coverage (W) emerges as an important physical parameter in both wind retrieval and oceanic remote sensing.

The parameterizations of whitecap coverage stem from fitting as a function of 10 m wind speed (U₁₀), most of which are derived based on limited, in situ observation data. Thus, large gaps can be found by comparing different empirical parameterizations under the same wind speed [7,8]. Emerging studies suggest that wind speed alone is not able to render accurate parameterization, as whitecaps are also influenced by various other factors, including air and sea surface temperature [9], wave characteristics [10], ocean currents [11], surfactant concentration [12,13], and sea state [14,15]. Complex and changeable wave states could be one of the key factors inhibiting wind-speed-only parameterizations from accurately modeling the global whitecap distribution [8]. This has led subsequent studies to consider both wind and wave factors in modeling whitecap coverage globally. Yuan et al. [10] proposed the statistical modeling of whitecap coverage and entrainment depth with real sea wave states incorporated, which was later improved by Wang et al. [16] based on the ratio of breaking wave kinetic to potential energy. The improved model has been validated leveraging satellite-derived data and shows better performance than other parameterizations, particularly in regions with rough winds and waves [17]. Further validation using data from the High Wind Speed Gas Exchange Study (HiWinGS) demonstrated generally good agreement between model predictions and observational data across various sites with high wind speeds and complex mixed-wave fields [18].

Photographs and video recordings used to retrieve in situ whitecap coverage still pose challenges for extrapolating to large-scale whitecap coverage modeling due to limited data volume and varying sea states [19]. Remote sensing has shown its potential and capability in obtaining global whitecap fractions from satellite observations. Microwave radiometry, such as WindSat, has advantages including global coverage, day/night observation capability, all-weather operation, and performance under extreme wind conditions [20]. By building the correlation between whitecap coverage and brightness temperature variations, Anguelova et al. [7,21] developed the W(T_B) algorithm to retrieve the whitecap fraction from WindSat measurements, providing an additional important data source for observational whitecaps. Optical remote sensing methods, such as Sentinel-2 MSI, provide high spatial resolution for regional and coastal studies, though their utility for global-scale whitecap observations is constrained by their dependency on cloud-free and daylight conditions [22]. Future availability of validated, high-resolution global whitecap datasets from optical sensors could potentially complement microwave observations and serve as valuable datasets for transfer learning methods. Coupled with machine learning methods, a multivariate whitecap fraction model has been proposed that utilizes deep neural networks trained on satellite-derived whitecap data [23]. Qi et al. (2024) leveraged machine learning to nudge the statistical modeling of whitecap coverage with the latest satellite-derived whitecap data [24]. However, all the above studies mainly consider one daily or monthly averaged satellite-derived global whitecap fraction to train, validate, and test the model. Specifically, the monthly averaged data utilized in previous studies are from the original version of the W(T_B) algorithm, which is subject to limited global whitecap fraction retrieval and lower accuracy compared with the latest version of the W(T_B) algorithm [14,21]. It could therefore be argued that the trained model based on a single monthly map likely cannot generalize well to other seasonal patterns of whitecaps due to limited satellite data availability.

The whitecap dataset volume from in situ and satellite observations is limited, but statistical modeling is capable of providing a comparably large dataset. In this study, we leverage the transfer learning method [25] to propose a new data-driven whitecap coverage parameterization with improved accuracy. First, we pre-train our deep learning model using data modeled through the statistical theory of whitecap coverage, which was proposed by Yuan et al. [10] and subsequently improved by Wang et al. [16]. Further, we employ transfer learning techniques to fine-tune the pre-trained models with satellite data from Salisbury et al. [14] and Anguelova et al. [21]. Independent satellite-derived whitecap data are utilized to validate the proposed model. Through transfer learning, we enable the deep learning model to capture general patterns of whitecap coverage during the pre-training phase and perform domain adaptation on satellite-derived data through fine-tuning. By providing more accurate and temporally resolved whitecap coverage predictions, our method can assist in optimizing the whitecapping dissipation parameters that are critical for calibrating wave models, thus reducing uncertainties in wave height predictions and associated morphodynamic modeling [26,27].

2. Data and Methods

2.1. Statistical Theory Derived Modeling of Whitecap Coverage

Wave breaking is typically associated with wind waves, so it ought to be more dependent on wave states, which are dominated by steeper waves instead of the mean wave system [8]. Therefore, wave characteristics need to be considered for modeling whitecap coverage rather than solely modeling atmospheric parameters. Yuan et al. [10] suggested that the whitecap coverage for a general state could be written as follows:

$$\varpi =C_{en}{F}_T{\displaystyle \frac{g^{\frac{1}{2}}\rho }{4{\pi }^{\frac{3}{2}}\alpha U_B}}{\left({\displaystyle \frac{\overline{L}}{\lambda }}\right)}^{{\displaystyle \frac{1}{2}}}{\left[\left(1+\theta \right){\displaystyle \frac{{\alpha }^2{\pi }^2{\lambda }^2}{{4\rho }^2}}{\left({\displaystyle \frac{H_S}{\overline{L}}}\right)}^2\right]}^n\times \exp \left[-{\displaystyle \frac{{\rho }^2}{2{\alpha }^2{\pi }^2{\lambda }^2}}{\left({\displaystyle \frac{\overline{L}}{H_S}}\right)}^2{\varphi }_0^2\right]$$

(1)

where:

$${\varphi }_0^2={\left(1-0.55{\displaystyle \frac{1}{\rho }}\sqrt{2\pi \alpha \lambda C_D{\displaystyle \frac{U_{10}^2}{g\overline{L}}}}\right)}^4$$

(2)

Here, C_en and n are the undetermined constants, F_T is the integral of bubble accumulation, and g is the gravitational acceleration. ρ is a parameter associated with the spectrum width, α is set to 1 due to the weakly nonlinear behavior before wave breaks, and θ, which represents the ratio of breaking wave kinetic to potential energy, is also set to 1. Wave parameters include wavelength $\overline{L}$ and significant wave height H_s. The Neumann spectrum gives the coefficient $\lambda =2/3$. U₁₀ is the wind speed at 10 m above the sea surface. U_B is set to 0.25 m/s, which represents the minimum terminal rise velocity for the group of bubbles. C_D is the drag coefficient and is considered to be 1.5 × 10⁻³.

Wang et al. [16] improved the statistical model by determining the constants of C_en, n and F_T and gave the updated form as follows:

$$\varpi ={\displaystyle \frac{3\rho }{4\pi }}{\left({\displaystyle \frac{3g\overline{L}}{2\pi }}\right)}^{1/2}{\times 0.1777\left[\left(1+\theta \right){\displaystyle \frac{{\pi }^2}{{9\rho }^2}}{\left({\displaystyle \frac{H_S}{\overline{L}}}\right)}^2\right]}^{-1.713}\times \mathit{exp}\left[-{\displaystyle \frac{{9\rho }^2}{8{\pi }^2}}{\left({\displaystyle \frac{\overline{L}}{H_S}}\right)}^2{\varphi }_0^2\right]$$

(3)

where θ was determined under varied wave states.

The related wind speed, significant wave height, and zero-crossing wave period parameters from the fifth-generation European Centre for Medium-Range Weather Forecasts reanalysis data (ERA5) are leveraged to calculate global whitecap coverage data from 2012 to 2021. The wind speed spatial resolution is ${0.25}^{°}\times {0.25}^{°}$, which we upscaled and matched to the same resolution as wave parameters at ${0.5}^{°}\times {0.5}^{°}$. The constructed modeling dataset contains 10 years of whitecap coverage variations and is used for the model’s pre-training process.

2.2. Satellite-Derived Whitecap Coverage

Following a similar digitalization method as Wang et al. [17] and Zhou et al. [23], we first collected the satellite-derived whitecap data from Salisbury et al. [14], which are the WindSat-retrieved whitecap data from October 2006, with a spatial resolution of ${0.5}^{°}\times {0.5}^{°}$. Then, we collected two daily maps of satellite-derived whitecap coverage data from Anguelova et al. [21], which are the whitecap fraction data from 27 December 2006 and 19 March 2014. Importantly, compared with the former, the latest 2014 data were obtained with a newly released version of the W(T_B) algorithm using WindSat SDRs and an updated forward model v2. It mitigates the issue of data loss and limited coverage of whitecap retrieval. The two sources of W data from 2006 are leveraged to fine-tune the pre-trained model to fulfill the purpose of domain knowledge adaptation. We leveraged the W data from 2014 to test the model’s performance.

Figure 1 shows the W estimate results from statistical theory modeling and the satellite-derived algorithm using WindSat data. Figure 1a shows continuous global coverage from the modeling results, revealing high W concentrations in the North Atlantic and Southern Ocean. Figure 1b shows the satellite-derived observations with characteristic orbit tracks from the WindSat Radiometer. Both datasets capture similar large-scale features and latitude variations, as shown in the side panels. The highest whitecap coverage concentrations appear in the mid-to-high latitudes in both hemispheres, while tropical regions show consistently lower values. The latitude-averaged profiles demonstrate good agreement in the overall meridional distribution pattern, though the modeling results overestimate whitecap coverage in the North Atlantic compared to observations.

2.3. Transfer Learning Model

The transfer learning method was initially proposed for resolving few shot learning problems, where collecting labels is quite expensive for some real-world applications. The assumption that training and test datasets share the same distribution and patterns does not always hold [25]. Transfer learning enables knowledge transfer between related domains, allowing models to maintain performance even when test data distributions differ from training data.

Here, we leverage a transfer learning technique to resolve the problem of limited observational W data. Ten years of statistical modeling W data reflect the general evolution patterns of whitecaps based on the theoretical parameterizations incorporated with both atmospheric and wave characteristics. However, these data still differ from the observational data; for example, they contain overestimation in certain regions, as shown in Figure 1. Nevertheless, the general large-scale pattern indicates the validity of the modeling data and their potential to be adapted to the target domain. Thus, we pre-train the model using the modeling data and then fine-tune the pre-trained model with the satellite-derived data.

The model architecture is shown in Figure 2, which incorporates three stages:

• Data preprocessing

For the input processing layer, we input the raw atmospheric features, including 10 m wind speed (WS), wind direction (WD), boundary layer height (BLH), 2 m temperature (T2M), and surface pressure (SP), as well as wave parameters such as significant wave height (SWH), mean wave direction (MWD), mean wave period (MWP), and mean wave zero-crossing period (MP2). The sea surface temperature (SST) and geographical features of latitude and longitude were also considered. We designed three tailored modifications in the feature engineering part to capture the physical implications of wind and wave states on whitecaps. First, the pairwise feature cross module is adopted to capture physical interactions related to combined wave effects (WS and SWH), and wave steepness (MWP and SWH). The following batch normalization is utilized to stabilize training with varying wind and wave conditions.

To capture spatially periodic patterns in oceanic and atmospheric fields, we apply the Fourier transform spatially across grid points [28]. For a two-dimensional spatial field, the discrete two-dimensional Fourier transform is computed as follows:

$$F\left(u,v\right)=\sum _{x=0}^{M-1} \sum _{y=0}^{N-1}f\left(x,y\right)e^{-i2\pi ({\displaystyle \frac{ux}{M}}+{\displaystyle \frac{vy}{N}})}$$

(4)

where $u$ and $v$ represent spatial frequencies in longitude and latitude directions, respectively, and $M$,$N$ are the spatial grid dimensions. This transformation converts spatial data into the frequency domain, characterizing periodic spatial structures at different spatial scales. The resulting frequency components capture organized patterns in wind–wave interactions that could potentially influence whitecap formation.

Finally, the statistical moments are utilized to capture the central tendency, variability, asymmetry, and extreme conditions that might influence whitecap formation [29]. The $n^{th}$ statistical moment for the mean ($u$) for a spatial field, $X$, is computed as follows:

$$m_n={\displaystyle \frac{1}{N}}\sum _{i=1}^N{\left(X_i-u\right)}^n$$

(5)

where $n=1, 2, 3, 4$ represent mean-centered moments, and $N$ is the total number of spatial grid points. These moments quantify different characteristics of data distribution: variance ($n=2$) measures the spread of values, skewness ($n=3$) indicates distribution asymmetry, and kurtosis ($n=4$) reveals the presence of extreme values or outliers.

Thus, we considered the feature interactions, periodic behaviors, and statistical properties of input features by introducing the above modifications, to better account for the wave state and wind–wave interaction effects.

2.

Model Pre-training

The main network architecture consists of three key components designed to capture complex relationships in wind and wave data. First, an input projection layer maps the tailored features to a higher-dimensional space, employing layer normalization and dropout for training stability. This is followed by multiple residual blocks, each containing dual linear transformations with layer normalization and ReLU activations, connected by skip connections to allow for deep feature processing while preventing gradient degradation, following the key concept of ResNet [30]. The architecture then incorporates a multi-head self-attention module, which enables the model to dynamically weight the importance of different features and their interactions based on the input context. The attention layer is particularly valuable for capturing long-range dependencies and complex interactions between input parameters that might influence whitecap formation during varying conditions. The output processing pathway implements a skip connection that concatenates the deeply processed features with original input features, ensuring the model maintains access to both raw physical parameters and their learned representations. This concatenated representation undergoes a gradual dimension reduction through a series of linear transformations with ReLU activations and dropout regularization. The final layer produces the whitecap fraction prediction. We leverage this main network to obtain the pre-trained model based on statistical modeling data.

3.

Model Fine-tuning

This stage focuses on adapting the pre-trained model to satellite-derived observations through transfer learning. In this stage, the model, which has already learned fundamental physical relationships from statistical modeling, is fine-tuned using satellite-derived whitecap observations. The pre-trained model serves as the foundation, where the learned feature maps from ERA parameters are preserved, while the final layers are adjusted to better align with the satellite observations.

Given the different scales of input features, we applied standardization to each input variable, enhancing the convergence rates for the following training. The whole dataset generated by statistical theory modeling, which spans from 2012 to 2021, is divided into training and validation subsets with a ratio of 8:2. The satellite-derived data from WindSat for October 2006 and 27 December 2006 are utilized for fine-tuning the pre-trained model, while retaining the retrieved data on 19 March 2014 as the independent test dataset. The hyperparameters are set as follows: the batch size is 128, the epoch is set to 200, and the dropout ratio for preventing overfitting is set to 0.2. We also implemented an adaptive learning method in which the initial learning rate is set to $2\times {10}^{-3}$ with the weight decay rate set to 0.05, to improve the generalization of the model [31]. For the multi-head attention module, we set the number of multi-heads to 5, the head size to 256, and the number of transform blocks to 4.

3. Results

3.1. Model Evaluation

The evaluation metrics, including bias (Bias), root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²), are utilized to evaluate the model’s performance. Bias is defined as the modeling error minus the ground truth satellite-derived W value at a given location, which demonstrates systematic errors of the model’s overestimation or underestimation. RMSE is sensitive to large values of errors, and MAE provides a linear weighting of errors. The correlation coefficient indicates the linear relationship between predicted and actual values, while R² shows explained variance.

Figure 3 shows a comparative analysis of pre-trained and fine-tuned model performance with a focus on prediction accuracy and bias distribution. As shown in Figure 3a, the pre-trained model demonstrates greater scatter, with an RMSE of 1.608%, an MAE of 1.343%, and an R² of 0.551, indicating moderate predictive capability. Conversely, the fine-tuned model exhibits markedly improved performance, with RMSE and MAE reducing to 0.601% and 0.441%, and an improved R² of 0.83, which suggests enhanced generalizability using transfer learning. The bias distribution plots (Figure 3c,d) show distinct error patterns between the two models. The pre-trained model exhibits a systematic positive bias trend, particularly pronounced at lower predicted values, suggesting consistent underestimation in the low W value range. However, the fine-tuned model shows a more symmetric pattern in the mid-range values, indicating improved model calibration through domain adaptation. Through the density distribution, the W data are concentrated in the lower value range, and this poses significant challenges for the prediction of extreme values due to limited data points. Importantly, we do not observe increased scatter for the fine-tuned model in the range of large W values, while the pre-trained model shows a tendency toward systematic overestimation at higher values. This highlights the good generalizability of the fine-tuned model in predicting increased W values during complex wave states. Further, the test dataset we adopted here comes from an independent satellite-derived dataset. We avoid the issues of potential overfitting by not training and testing on the same satellite image, which differs from previous studies [23,24] that used data splitting from a single satellite image.

3.2. Spatial Error Patterns

Figure 4 illustrates the potential prediction improvements with the spatial distributions and biases of the pre-trained and fine-tuned models by utilizing the transfer learning technique, based on global whitecap fraction data from 19 March 2014. The pre-trained model captures the large-scale spatial patterns but overpredicts the magnitude of W values at the mid to large values range and underestimates W values in tropical regions (Figure 4b,d). Further, it lacks the sensitivity to detect the fluctuating values in transition areas. After the model is fine-tuned with the satellite image, the proposed deep learning model correctly reduces the magnitude of the peak W value, particularly in the high latitudes near the North Atlantic and Southern Ocean (Figure 4f). Additionally, the model mitigates the issue of underestimation around the tropical regions. Figure 4e shows the performance of the fine-tuned model with the least biases, which demonstrates that the transfer learning technique leads to more accurate modeling.

We further use the RMSE and spatial Pearson correlation (PC) metrics to evaluate the error patterns for these models besides the bias. The RMSE is calculated at each grid point as the square root of the squared difference between predicted and observed whitecap fraction values. For the PC, we compute a single correlation coefficient for each latitude band by correlating the predicted and observed whitecap values across all longitudes within that band, providing insight into how well the models capture longitudinal patterns at different latitudes. These metrics were computed using global whitecap fraction data from 19 March 2014.

The largest sources of pre-trained model prediction error occur predominantly in locations with elevated W data values. This indicates that complex wave states under strong winds constitute the larger error fraction. The RMSE field is dominated by random errors and conditional biases, as shown by comparing Figure 4f and Figure 5a for the pre-trained model, but this error has been greatly reduced by the fine-tuned model, which shows more consistent error patterns. The highest levels of Pearson correlation occur in the mid-range latitude regions for the pre-trained model and mid to high latitude range regions for the fine-tuned model, with low values observed in tropical regions for both. This may be associated with the distribution of low W values with mild variation patterns around the tropical regions, which include lower predictability. The latitudinal band of high predictability exists in the high latitude regions with the elevated wave breaking event-induced whitecap coverage for both. The fine-tuned model demonstrates significant improvements in the high latitude regions compared with low latitude regions.

3.3. Comparison with Wind Speed Parameterizations

Brumer et al. [8] compiled the parameterizations of whitecap fraction using wind speed at 10 m above the surface since 2004. Here, we adopt some of those parameterizations, which depend on wind speed only since 2011.

Table 1. Whitecap fraction parameterizations as a function of wind speed only, with the range of wind speed applied.

Reference	Formula	Wind Speed Range
Scanlon and Ward [32]	$W=7.84\times {10}^{-4}{\left(U_{10}-2.56\right)}^3$	${1<U}_{10}\le 21$
Schwendeman and Thomson [33]	$W=2.81\times {10}^{-3}{\left(U_{10}-3.87\right)}^{2.76}$	${1<U}_{10}\le 21$
Sablisbury et al. [14]	$W=4.6\times {10}^{-3}{U}_{10}^{1.26}$	${2<U}_{10}\le 20$
Goddijn-Murphy et al. [34]	$W=15.9\times {10}^{-4}{U}_{10}^{2.7}$	${4.6<U}_{10}\le 23.09$

shows these selected parameterization formulas and their applied wind range scope.

The quantitative evaluation metrics for both deep learning models and established parameterizations are presented in

Table 2. Evaluation metrics of deep learning models and wind speed parameterizations. The metrics demonstrate the relative performance of each approach in estimating W.

Predictor	RMSE (%)	CRMSE (%)	MAE (%)	PC
Pre-trained Model	1.61	1.46	1.34	0.70
Fine-tuned Model	0.60	0.58	0.44	0.86
Scanlon and Ward [32]	3.07	1.47	2.7	0.55
Schwendeman and Thomson [33]	3.37	1.31	3.1	0.49
Sablisbury et al. [14]	3.36	1.58	2.96	0.60
Goddijn-Murphy et al. [34]	3.01	1.31	2.72	0.53

. The fine-tuned model demonstrates superior performance across all metrics, achieving the lowest RMSE of 0.60%, a CRMSE of 0.58%, and an MAE of 0.44%, while maintaining the highest Pearson correlation coefficient of 0.86. Among the wind-speed-only parameterizations, the Goddijn-Murphy et al. [34] formulation exhibits relatively better performance with an RMSE of 3.01%, though this is still substantially higher than both ML models. The pre-trained model shows intermediate performance with an RMSE of 1.61% and PC of 0.7, outperforming all parameterizations but falling short of the fine-tuned model accuracy. All parameterizations demonstrate similar performance, with RMSE values ranging from 3.01% to 3.37% and PC values between 0.49 and 0.60, suggesting consistent limitations in their ability to capture the complexity of W variations without the incorporation of wave characteristics. We also introduce the centered root mean square error (CRMSE) here to evaluate the capability of models in capturing the data variability, which focuses on errors after removing the mean ($\sqrt{RMS{E}^2-Bia{s}^2}$). The significantly lower CRMSE values compared to RMSE indicate that systematic biases largely account for the prediction errors.

3.4. Validation in the Westerly Zone of the Southern Hemisphere

The distribution pattern of whitecap coverage in the test data reveals a pronounced spatial variability, with comparatively minimum values in tropical regions and notably higher values occurring predominantly in the westerly zone of the Southern Hemisphere (30°S–60°S). This westerly belt is characterized by persistent strong westerly winds throughout the annual cycle, which induce more frequent and intense wave breaking events. Thus, we conducted a focused analysis of this region to further validate the fine-tuned model performance under the high-wind-speed conditions.

The fine-tuned model demonstrates general improvement across multiple error metrics, as shown in Figure 6. Post fine-tuning, both RMSE and CRMSE values decreased at the majority of grid points and exhibited similar spatial error patterns, suggesting a notable contribution from systematic errors (Figure 6b,c). Further, the spatial distribution of differences in Bias and RMSE between fine-tuned and pre-trained model predictions indicates improvement across most locations within the westerly zone (Figure 6d,e).

The PC field exhibited the least improvement among the evaluated metrics. Notably, regions with lower PC improvement values were predominantly located in regions with comparatively higher wind speeds. This pattern was also present in other error metrics, albeit less prominently than the PC field. For instance, the region spanning 40°S–60°S and 20°E–40°E, characterized by wind speeds reaching up to 16 m/s, demonstrated minimal improvement compared with other regions. One explanation for this is the underestimation of wind speeds in the ERA5 reanalysis data during high-wave-state conditions [35], which introduces systematic errors in the simulation data utilized for model training. This finding suggests that the generalizability of the model could be further improved through integration of more accurate input data, particularly under high-wave-state conditions.

3.5. Variable Importance

We employ the permutation importance (PI) technique, which evaluates feature importance by individually shuffling each variable and measuring the resulting model performance degradation [36]. Features causing greater performance decline are deemed more influential for model predictions. The PI of feature $i$ is given as follows:

$$I\left(x_i\right)=E\left[L\left(y,f\left({\tilde{X}}^i\right)\right)\right]-E\left[L\left(y,f\left(X\right)\right)\right]$$

(6)

where $I\left(x_i\right)$ is the permutation importance of feature $i$, $E\left[L\left(y,f\left(X\right)\right)\right]$ is the expected loss of the model on the original dataset, $E\left[L\left(y,f\left({\tilde{X}}^i\right)\right)\right]$ is the expected loss after permuting $i$, ${\tilde{X}}^i$ represents the dataset with feature $i$ randomly shuffled, $y$ represents the true target values, and $f$ is the trained model.

Complementing this approach, we utilize SHAP (Shapley Additive Explanations) values to quantify the contribution of each feature to individual predictions, allowing for both the global and local models’ interpretability [37,38]. SHAP applies game theory principles to machine learning interpretation by assigning importance values to each feature for specific predictions. Derived from Shapley values in cooperative game theory, this method demonstrates how individual features influence model outputs by measuring their marginal contributions across all possible feature combinations. By implementing SHAP analysis, we uncover the key drivers behind whitecap coverage predictions, addressing our research objective of identifying the relative importance of various physical parameters in whitecap formation processes. The Shapley value ${\varphi }_i$ for feature $i$ can be expressed as follows:

$${\varphi }_i\left(f,x\right)=\sum _{S\subseteq x^{\prime }}{\displaystyle \frac{\left|S\right|!\left(n-\left|S\right|-1\right)!}{n!}}[f_x\left(S\cup \left\{i\right\}\right)-f_x(S)]$$

(7)

where $x^{\prime }$ is the set of all features, $n$ is the total number of features, $f_x(S$) is the model prediction using only the feature subset $S$, and $x$ is the specific data instance.

Figure 7a shows that wind-related parameters demonstrate predominant influence. Wind speed exhibits the highest relative permutation importance of 32.02%, followed by BLH of 12.83% and T2M of 9.27%. The geographical variables show moderate importance, suggesting regional variations in W patterns. Wave variables demonstrate a secondary but notable influence, together explaining 19.95% of the total variance.

The SHAP summary plot (Figure 7b) shows consistent findings with permutation methods while providing additional insights. Wind speed demonstrates a strong positive correlation with model output, particularly at higher values. BLH shows a complex and nonlinear relationship, with its influence varying significantly across different atmospheric conditions. The geographical parameters exhibit distinct regional patterns, indicating similar regional variation pattern impacts. Wind speed shows a clear positive correlation with predicted W, exhibiting an approximately linear relationship at moderate winds and increased variance at higher speeds (Figure 7c). The BLH SHAP dependence plot reveals a threshold effect (Figure 7d), while SWH demonstrates a positive but saturating effect at higher values (Figure 7e). SST displays an inverse relationship with W, particularly pronounced at higher temperatures, suggesting thermal effects on the wave breaking process (Figure 7f).

From the combined analysis of permutation importance and SHAP values, our model captures the complex interaction between physical factors impacting whitecap coverage: the wave state influence is shown by the variance explained by wave parameters including SWH, MWD, MP2, and MWP, while atmospheric stability effects are reflected in the substantial importance of BLH and T2M. This strong influence of atmospheric stability aligns with previous field studies [15,39] that found atmospheric stability significantly impacts whitecap formation, with unstable conditions enhancing wave breaking and stable conditions suppressing it, an effect driven by air–sea temperature differences. The wind–wave interaction is further demonstrated by the high importance of WS coupled with wave parameters, which is consistent with previous findings that wave state acts as an important factor in whitecap formation [8,10].

4. Discussion

4.1. Domain Adaptation and Model Generalization

In this study, we demonstrate that the transfer learning technique can achieve domain adaptation from the statistical model data to the satellite-derived observational data. Importantly, the fine-tuned model demonstrates good generalization on the independent satellite-derived test dataset. Thus, this study fills the gap in addressing the potential overfitting and inability to test model generalization, since previous studies [23,24] were limited to one single daily or monthly satellite-derived dataset for the whole dataset’s training and testing. This basically assumes the same data distribution for the training and testing datasets, which does not hold true for most real cases. The pre-training based on statistical modeling data initializes weights by capturing the large-scale spatiotemporal patterns, while fine-tuning on the satellite-derived data helps incorporate the nuanced patterns and nudge the models toward improved accuracy.

Nevertheless, more available satellite-derived data across different seasons in the future would obviously improve and help evaluate the model more thoroughly. Our transfer learning methodology demonstrates promising results in bridging the gap between statistical models and observational data. The ability to generalize effectively to independent test data from a different time period and updated W(T_B) algorithm generation suggests our approach mitigates potential overfitting concerns. Nevertheless, additional validation with more diverse whitecap coverage datasets would further strengthen these conclusions. With more W observation data available in the future, the model architecture could be refined with additional deep learning modules, beyond attention mechanisms, to capture more complex and higher-dimensional relationships between input parameters and W.

4.2. Variables Importance on W

Most traditional parameterizations of W are established by considering only wind speed, which simplifies the whitecap generation process. Emerging research shows that many other factors, beyond wind speed, also significantly influence the whitecap fraction. This has been analyzed in this study as well. Leveraging explainable deep learning methods (XDL), we show that the wave state, wind–wave interaction, SST, and atmospheric stability variables all influence the prediction of W. The combined variable importance is consistent with previous findings [39,40,41]. Our results highlight that atmospheric layer properties have emerged as influential factors, accounting for 20% of the explained variance in whitecap coverage, exceeding the contribution of wave parameters (17%). This aligns with findings from Myrhaug and Holmedal [39], who demonstrated that whitecap coverage dependence on air stability is generally an order of magnitude larger than its dependence on wave age. Their research established that unstable air conditions promote and enhance wave breaking, thereby increasing whitecap coverage for a given wind speed, while stable conditions suppress it. Similarly, Jia and Zhao [15] quantified this relationship and showed that whitecap coverage decreases exponentially with increased atmospheric stability. These findings collectively emphasize that atmospheric-stability-related variables show great potential for use in W estimates, which could be explored further in future research.

4.3. Comparison with In Situ Observation Data

Besides the satellite-derived data from WindSat, whitecap data can also be obtained through field observations using cameras and image processing algorithms. However, in situ observation data might be sparse, intermittent, and limited. Although the current limited volume of in situ observation data makes them challenging to use as a training dataset, they could serve as a valuable test source due to their high accuracy. By incorporating field observation data, we could further analyze error patterns, which could refine the transfer learning model with more physical implications. Thus, a physics-guided neural network could be combined to predict whitecap coverage with improved accuracy [42]. Further, validating the model under more extreme events and across diverse oceanic regions through incorporation of in situ observations would be valuable for testing model generalizability and region-specific performance [43,44].

5. Conclusions

The paper explored the utility of a transfer learning model to predict the global whitecap fraction and interpret it with XDL methods. We demonstrate that transfer learning techniques can be utilized to improve the model prediction of W by adapting the knowledge learned from statistical modeling to satellite observations. The fine-tuned model yields significant accuracy improvement across all evaluation metrics, compared with the pre-trained model and traditional wind-dependent parameterizations. Ongoing work focuses on collecting more satellite-derived and in situ observation data to further improve the model’s accuracy and better quantify uncertainty.

The XDL method was leveraged here to interpret the contributions of model inputs. Consistent with emerging studies, whitecap fraction modeling requires the involvement of additional atmospheric and wave parameters, rather than relying solely on wind speed. The traditional single wind-related parameterizations inevitably introduce large errors and are unable to effectively model whitecap fraction under complex sea states. Our results revealed that wind speed shows a positive correlation with whitecap coverage with increased variance at higher wind speeds, atmospheric stability significantly influences whitecap formation through boundary layer height and air–sea temperature interactions, and SWH demonstrates a positive but saturating effect at higher values, aligning with a physical understanding of wave breaking processes. While pure data-driven methods achieved relatively good performance in this study, integrating underlying physical mechanisms with neural networks could further improve the model predictive ability and interpretability.