  Subgrid parameterizations of mesoscale eddies continue to be in demand for
climate simulations. These subgrid parameterizations can be powerfully designed
using physics and/or data-driven methods, with uncertainty quantification. For
example, Guillaumin and Zanna (2021) proposed a Machine Learning (ML) model
that predicts subgrid forcing and its local uncertainty. The major assumption
and potential drawback of this model is the statistical independence of
stochastic residuals between grid points. Here, we aim to improve the
simulation of stochastic forcing with generative models of ML, such as
Generative adversarial network (GAN) and Variational autoencoder (VAE).
Generative models learn the distribution of subgrid forcing conditioned on the
resolved flow directly from data and they can produce new samples from this
distribution. Generative models can potentially capture not only the spatial
correlation but any statistically significant property of subgrid forcing. We
test the proposed stochastic parameterizations offline and online in an
idealized ocean model. We show that generative models are able to predict
subgrid forcing and its uncertainty with spatially correlated stochastic
forcing. Online simulations for a range of resolutions demonstrated that
generative models are superior to the baseline ML model at the coarsest
resolution.
