[Paper Review] Data Driven Air Entrainment Velocity Parameterization by Breaking Waves

Xiaohui Zhou, Anton Darmenov+1 more|arXiv (Cornell University)|Feb 3, 2026

Ocean Waves and Remote Sensing0 citations

TL;DR

The paper trains a four-layer MLP to predict air-entrainment velocity Va from seven sea-state predictors, achieving a global, physics-informed surrogate for spectral Va and improving upon wind-only and semi-bulk schemes; it is validated with HiWinGS data and applied to bubble-mediated gas transfer and sea-salt emission.

ABSTRACT

Wave breaking injects turbulence and bubbles into the upper ocean, modulating air-sea exchange of momentum, heat, gases, and sea-spray aerosols. These fluxes depend nonlinearly on sea state but remain poorly represented in coupled atmosphere-wave-ocean models, where air-entrainment velocity is often parameterized using wind speed or significant wave height alone. We develop a global machine-learning parameterization of Va trained on a 43-year WAVEWATCH III simulation that resolves the breaker-front distribution and associated energetics. A multilayer perceptron with seven physically motivated predictors (wind speed, wave height, wave age, steepness, direction, and depth) reproduces spectral-reference Va with high skill. The model reduces longstanding biases in bulk formulas, notably overestimation in swell-dominated low latitudes and underestimation in storm tracks. Applied globally, it improves bubble-mediated CO2 transfer velocity and sea-salt aerosol emission, reducing errors by an order of magnitude. Validation against independent HiWinGS observations supports robust deep-water performance.

Motivation & Objective

• Motivate the need for sea-state dependent air-entrainment velocity (Va) representations in atmosphere–ocean models.
• Develop a physically interpretable ML surrogate for Va trained on a 43-year WW3 hindcast that resolves breaker dynamics.
• Demonstrate global Va performance and validation against independent observations.
• Show implications of Va improvements for bubble-mediated gas transfer and sea-salt emissions.

Proposed method

• Diagnose the breaking-crest distribution Lambda(c) in WW3 to compute Va as Va = B~ ∫ S(k)^{3/2} c^3/g Lambda(c) dc with B~ = 0.1.
• Train a multilayer perceptron with four hidden layers (512 neurons each) to map seven predictors (Hs, U10, wind-direction, wave age cp/U10, wave steepness kpHs/2, depth) to Va.
• Use Adam optimization (lr 1e-3, weight decay 1e-4) with dropout 0.1, on 1980–2022 data split into training/validation/testing (80/10/10).
• Evaluate against withheld WW3 references and HiWinGS observations using RMSE, bias, and correlation.
• Compare ML Va to semi-empirical (Va based on Cp, u*, Hs) and wind-only (Va based on U10) parameterizations.

Experimental results

Research questions

• RQ1 Can a machine-learning surrogate reproduce spectral-based Va across global sea states using routinely available predictors?
• RQ2 Does the ML Va reduce regional biases seen in wind-only or semi-bulk Va parameterizations, especially in storm tracks and swell regimes?
• RQ3 How does the ML Va propagate to bubble-mediated gas transfer velocity (kb) and sea-salt emission (Msalt) compared to traditional schemes?
• RQ4 Is the ML Va robust when validated against independent HiWinGS observations?
• RQ5 What are the limitations and regime of validity of the Va ML parameterization?

Key findings

• Va predicted by the ML model reproduces the spectral reference Va with small bias (-0.018 cm h^-1), RMSE 0.11 cm h^-1, NRMSE 0.08, and R=0.999 for 2019–2022.
• ML Va shows improved global spatial pattern and magnitude versus Va based on wind speed (U10) or a semi-empirical scheme, with reduced biases in mid-latitude storm tracks and swell regions.
• HiWinGS validation yields R=0.76, RMSE=64.2 cm h^-1, and bias=53.7 cm h^-1, indicating skill under high-wind, steep-wave conditions but some overestimation under low-wind conditions.
• Applying ML Va to kb and Msalt reduces global biases relative to spectral Va, with kb bias ~0.1–0.4 cm h^-1 (about 1% relative difference) and Msalt differences showing up to ~30% biases for non-ML schemes.
• The ML parameterization provides similar global emission patterns to spectral estimates, whereas wind- or Hs-based schemes overestimate in some regions and underestimate in others.
• Validation suggests the approach is robust in deep-water, high-wind conditions and can be retrained as more non-equilibrium/shallow-water data become available.