Estimation of surface viscous stress from wave profiles using deep neural networks*

The air-sea momentum and scalar exchanges are contingent on small-scale interfacial dynamics, which are crucial for climate and weather forecasting, significantly impacting many aspects of human life. To improve the predictive abilities of numerical models, it is essential to understand the behavior of wind stress, i.e., the sum of skin friction and form drag, at the ocean surface. Although skin friction contributes considerably to the total surface stress up to moderate wind speeds, it is notoriously challenging to measure and/or predict using classical physics-based numerical simulations.

Here, we present a supervised machine learning model to estimate the skin-friction drag of wind waves only 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 experiments. The model consists of several convolutional neural network blocks with non-linear activation functions. Results show that the model can accurately predict the overall distribution of viscous stress; it captures the peak of viscous stress at/near the crest and its dramatic drop to almost null just past the crest, which is a robust indicator of airflow separation.