Structure-preserving stochastic parameterization of a barotropic coupled ocean-atmosphere model with Ornstein--Uhlenbeck noise

TL;DR

This paper applies the SALT framework to a coupled ocean-atmosphere model, introducing Ornstein-Uhlenbeck noise to better capture autocorrelation in unresolved transport processes, and demonstrates improved ensemble forecast performance.

Contribution

It is the first to incorporate Ornstein-Uhlenbeck processes into SALT for coupled models, preserving geometric structure and enhancing forecast skill.

Findings

OU processes effectively model autocorrelation in unresolved transport.

Stochastic ensembles outperform deterministic ones in forecast skill.

Ensemble spread-error is well-matched over 10-15 time units.

Abstract

We present the first application of the stochastic advection by Lie transport (SALT) framework to an idealized coupled ocean-atmosphere system. SALT derives stochastic fluid equations from Hamilton's variational principle under a stochastic Lagrangian kinematic assumption, thereby preserving the geometric structure -- Kelvin circulation theorem, Lie-derivative advection operators, and local conservation laws -- of the underlying deterministic equations. The atmospheric component is rendered stochastic while the ocean remains deterministic, following Hasselmann's paradigm of a fast stochastic atmosphere driving a slow climate. The spatial correlation vectors encoding unresolved subgrid transport are estimated from high-resolution simulations via EOF analysis of Lagrangian trajectory differences. A central contribution is the replacement of the standard white-noise temporal model with Ornstein-Uhlenbeck (OU) processes, motivated by strong autocorrelation (decorrelation times of 50-150 time steps) in the dominant EOF modes; the OU process is the unique stationary Gaussian Markov process capable of capturing this temporal memory with a single parameter. Ensemble forecasts exhibit good spread-error agreement over 10-15 time units. Evaluated via the Continuous Ranked Probability Score -- a strictly proper scoring rule measuring discrepancy between the forecast measure and the true conditional distribution -- the stochastic ensemble consistently outperforms a size-matched deterministic ensemble, despite carrying higher RMSE. Well-posedness of the coupled stochastic system is identified as an important open problem.