Data Driven Air Entrainment Velocity Parameterization by Breaking Waves

TL;DR

Air-sea exchange is strongly influenced by wave breaking, but traditional parameterizations of the air-entrainment velocity $V_a$ miss sea-state variability. The authors train a four-layer $\text{MLP}$ to predict $V_a$ from seven physically motivated predictors using a 43-year WW3 hindcast that diagnoses the breaker-front distribution $\Lambda(c)$, achieving close reproduction of the spectral reference with RMSE $=0.11$ cm h$^{-1}$ and $R=0.999$. Validation against HiWinGS shows reasonable skill ($R=0.76$) in real ocean conditions, with limitations under non-equilibrium regimes. When propagated to bubble-mediated gas transfer velocity $k_b$ and sea-salt emissions, the ML-based $V_a$ substantially reduces regional biases compared with wind-only or semi-bulk schemes, improving climate-relevant flux estimates and enabling efficient, global, sea-state dependent air-sea flux representations in Earth-system models.

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.

Figures (4)

• Figure 1: Schematic of the machine-learning framework used to parameterize the air-entrainment velocity ($V_a$). Seven physically based predictors are derived from WAVEWATCH III simulations: significant wave height ($H_s$), 10-m wind speed ($U_{10}$), cosine and sine of wind direction ($\cos\theta_w$, $\sin\theta_w$), wave age ($c_p/U_{10}$), wave steepness ($k_pH_s/2$), and water depth ($d$). These inputs are processed through a multilayer perceptron (MLP) with four hidden layers (512 neurons each, GELU activation, and $10\%$ dropout) to predict the target variable $V_a$. The architecture captures nonlinear relationships between wind forcing, sea-state parameters, and air entrainment, forming the basis for a global machine-learning parameterization of wave-breaking-induced air–sea fluxes.
• Figure 2: Annual mean air-entrainment velocity $V_a$ in $cm/hour$ from 2019–2022 for different parameterizations. Panels (a–d) show $V_a$ computed from (a) the spectral model $V_a^{Spec}$, (b) the machine-learning model $V_a^{ML}$, (c) the semi-empirical formulation $V_a^{Semi}$, and (d) the wind-speed-based parameterization $V_a^{U_{10}}$. Panel (e) presents the zonal-mean profiles for each scheme. Panels (f–h) display spatial differences relative to the spectral reference $V_a^{Spec}$. The machine-learning parameterization reproduces the large-scale structure and magnitude of the spectral model while substantially reducing biases in mid-latitude storm tracks and swell-dominated regions.
• Figure 3: Comparison between predicted and observed air-entrainment velocity ($V_a$) from the HiWinGS field campaign Brumer2017. Colors indicate wave steepness ($H_s k_p/2$).
• Figure 4: a) The global zonal monthly bubble mediated gas transfer velocity from the wave spectrum model predicted air entrainment velocity $k_b^{spec}$ from 2019 to 2022. b) The difference of bubble mediated gas transfer velocity from air entrainment velocity based on different model, the difference between machine learning model and wave spectrum model. c) The difference between semi-bulk model based on significant wave height and wave spectrum model. d) The difference between bulk model based on wind speed only and wave spectrum model. Panels (e) to (h) similar to the previous panels, but for the sea salt emissions with droplet diameter less than $10 \mu m$.