Ocean general circulation models (OGCMs) are often used at horizontal resolutions that preclude the appearance of mesoscale eddies. The ocean mesoscale constitutes a significant component of ocean variability, and OGCMs whose resolutions are too coarse to represent the mesoscale are necessarily lacking this variability. In addition to being variable, the ocean mesoscale also induces variability on larger scales that could be resolved on a coarse grid, but coarse OGCMs often lack this variability too. This paper develops a stochastic parameterization that adds small increments to an OGCM’s lateral velocity field, which excites natural modes of variability in the model. The rate at which these velocity increments add energy to the flow is tied to the rate at which the Gent-McWilliams parameterization – a popular parameterization of the effect of mesoscale eddies on tracer transport – removes potential energy from the resolved scales. The stochastic parameterization is implemented in a non-eddying OGCM, where it is shown to increase the variability significantly.

Air-sea flux variability has contributions from both ocean and atmosphere at different spatio-temporal scales. Atmospheric synoptic scales and the air-sea turbulent heat flux that they drive are well represented in climate models, but ocean mesoscales and their associated variability are often not well resolved due to non-eddy-resolving spatial resolutions of current climate models. We deploy a physics-based stochastic subgrid-scale parameterization for ocean density, that reinforces the lateral density variations due to oceanic eddies, and examine its effect on air-sea heat flux variability in a comprehensive coupled climate model. The stochastic parameterization substantially modifies sea surface temperature (SST) and latent heat flux (LHF) variability and their co-variability, primarily at scales near the resolution of the ocean model grid. Enhancement in the SST-LHF anomaly covariance, and correlations, indicate that the ocean-intrinsic component of the air-sea heat flux variability improves with respect to high-resolution satellite observations, especially in Gulf Stream region.

Biased, incomplete models are often used for forecasting states of complex dynamical systems by mapping an estimate of a “true’ initial state into model phase space, making a forecast, and then mapping back to the “true’ space. While advances have been made to reduce errors associated with model initialization and model forecasts, we lack a general framework for discovering optimal mappings between the reference dynamical system and the model phase space. Here, we propose using a data-driven approach to infer these maps. Our approach consistently reduces errors in the Lorenz-96 system with an imperfect model constructed to produce significant model errors compared to a reference configuration. Optimal pre- and post-processing transforms leverage “shocks’ and “drifts’ in the imperfect model to make more skillful forecasts of the reference system. The implemented machine learning architecture using neural networks constructed with a custom analog-adjoint layer makes the approach generalizable to numerous applications.

Imperfect models are often used for forecasting and state estimation of complex dynamical systems, typically by mapping a reference initial state into model phase space, making a forecast, and then mapping back to the reference space. In many cases these mappings are implicit, and forecast errors thus reflect a combination of model forecast errors and mapping errors. Techniques to infer parameterizations and parameters to reduce model bias have been the subject of intense scrutiny; however, we lack a general framework for discovering optimal mappings between system and model attractors. Here we propose a novel Machine Learning paradigm for inferring cross-attractor transformations (CATs) that minimize forecast error. CATs are pairs of transformations from the phase space of a reference system to the phase space of a model and vice versa that serve as a bridge between the attractors of a true system and an imperfect model. A computationally efficient analog approximation to tangent linear and adjoint models is developed to enable efficient stochastic gradient descent algorithms to train CAT parameters. Neural networks constructed with a custom analog-adjoint layer permit specification of affine transformations as well as more general nonlinear transformations.

Air-sea flux variability has contributions from both ocean and atmosphere at different spatio-temporal scales. Atmospheric synoptic scales and the air-sea turbulent heat flux that they drive are well represented in climate models, but ocean mesoscales and their associated variability are often not well resolved due to non-eddy-resolving spatial resolutions of current climate models. We deploy a physics-based stochastic subgrid-scale parameterization for ocean density, that reinforces the lateral density variations due to oceanic eddies, and examine its effect on air-sea heat flux variability in a comprehensive coupled climate model. The stochastic parameterization substantially modifies sea surface temperature (SST) and latent heat flux (LHF) variability and their correlations, primarily at scales near the resolution of the ocean model grid. Changes in the SST-LHF anomaly correlations indicate that the ocean-intrinsic component of the air-sea heat flux variability improves with respect to the satellite observational product, especially in western boundary current extensions.