Reconstruction of skin friction drags for surface waves using convolutional neural network

To improve the predictive abilities of weather and climate models, it is essential to understand the behavior of wind stress at the ocean surface. Wind stress is contingent on small-scale interfacial dynamics typically not directly resolved in numerical models. Although skin friction contributes considerably to the total stress up to moderate wind speeds, it is notoriously challenging to measure and predict using physics-based approaches. This work proposes a supervised machine learning (ML) model that estimates the spatial distributions of the skin friction drag over wind waves from wave profiles and 10 m wind speeds, which are relatively easy to acquire. The input-output pairs are high-resolution wave profiles and their corresponding surface viscous stresses collected from laboratory experiments. The ML model is built upon a convolutional neural network architecture that incorporates the Mish non-linearity as its activation function. Results show that the model can accurately predict the overall distribution of viscous stresses; it captures the peak of viscous stress at/near the crest and its dramatic drop to almost null just past the crest, which can be an indicator of airflow separation. The predicted area-aggregate skin friction is also in excellent agreement with the corresponding measurements. The proposed method offers a fruitful pathway for estimating both local and area-aggregate skin friction and can be easily integrated into existing numerical models for air-sea interaction.