Data-Driven Probabilistic Air-Sea Flux Parameterization

Accurately quantifying air-sea fluxes is important for understanding air-sea interactions and improving coupled weather and climate systems. This study introduces a probabilistic framework to represent the highly variable nature of air-sea fluxes, which is missing in deterministic bulk algorithms. Assuming Gaussian distributions conditioned on the input variables, we use artificial neural networks and eddy-covariance measurement data to estimate the mean and variance by minimizing negative log-likelihood loss. The trained neural networks provide alternative mean flux estimates to existing bulk algorithms, and quantify the uncertainty around the mean estimates. Stochastic parameterization of air-sea turbulent fluxes can be constructed by sampling from the predicted distributions. Tests in a single-column forced upper-ocean model suggest that changes in flux algorithms influence sea surface temperature and mixed layer depth seasonally. The ensemble spread in stochastic runs is most pronounced during spring restratification.

💡 Research Summary

The paper presents a novel probabilistic framework for parameterizing air‑sea momentum and heat fluxes, addressing the lack of uncertainty representation in traditional deterministic bulk algorithms. Using a dataset of roughly 10,000 eddy‑covariance (EC) measurements collected by NOAA’s Physical Sciences Laboratory, the authors train two artificial neural networks (ANNs) to predict, for each flux component (τx, τy, QS, QL), the conditional mean μ(X) and variance σ²(X) given five readily available input variables: wind speed, atmospheric temperature, sea‑surface temperature, relative humidity, and surface pressure. The mean‑ANN is first trained on a mean‑square‑error loss to capture the basic functional relationship, then both networks are jointly optimized by minimizing the negative log‑likelihood (NLL) loss, ensuring that the variance predictions remain positive (via an exponential output activation).

The conditional Gaussian assumption (each flux follows N(μ(X), σ²(X))) allows the model to quantify the spread of observed EC data around the deterministic prediction. Evaluation against the state‑of‑the‑art COARE 3.6 bulk algorithm shows that the ANN‑based mean predictions achieve comparable or slightly higher R² values for τx and QL, while QS remains difficult for both methods, especially in tropical regimes where its variance is small. τy, lacking a directional input, is predicted as near zero, but the framework still provides a variance estimate that captures its uncertainty. Regional analysis reveals that predictive skill varies with the distribution of input variables, underscoring the importance of diverse training data.

To demonstrate the practical impact of the probabilistic parameterization, the authors embed the learned flux models into the General Ocean Turbulence Model (GOTM), a single‑column ocean model forced by realistic atmospheric conditions. Two experiment sets are performed: (i) deterministic runs using only the predicted means, and (ii) stochastic runs where fluxes are sampled from the predicted Gaussian distributions at each time step. While deterministic runs produce sea‑surface temperature (SST) and mixed‑layer depth (MLD) trajectories similar to those obtained with COARE, the stochastic ensemble exhibits markedly larger spread, especially during the spring restratification period. The ensemble variance in SST and MLD can be two to three times larger than in the deterministic case, indicating that flux uncertainty propagates to oceanic state variables in a seasonally dependent manner.

Key contributions of the study include: (1) a data‑driven method that simultaneously delivers accurate mean flux estimates and a principled quantification of their uncertainty; (2) a demonstration that even with a modest dataset, conditional Gaussian ANNs can be trained robustly using a two‑stage loss‑function strategy; (3) evidence that stochastic air‑sea flux parameterizations can enhance the realism of ocean model variability, particularly during periods of rapid thermodynamic change.

The paper also acknowledges limitations: the input set does not contain sea‑state information or vertical wind profiles, which restricts the ability to predict τy sign and may bias variance estimates; the training data are heavily weighted toward tropical cruises, potentially limiting extrapolation to high‑latitude conditions; and the Gaussian assumption may not fully capture skewness or heavy tails observed in EC flux distributions. Future work is suggested to incorporate additional latent variables (Z), explore non‑Gaussian mixture models or Bayesian neural networks, and apply the stochastic flux scheme in coupled climate models to assess its impact on large‑scale circulation and climate variability. Overall, the study provides a compelling proof‑of‑concept that probabilistic, machine‑learning‑based flux parameterizations can bridge the gap between sparse in‑situ measurements and the needs of Earth system models for both accurate means and realistic uncertainty representations.