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\begin{document}

\title{Stochastic Deep Learning parameterization of Ocean Momentum Forcing}



\author[1]{Arthur Guillaumin}%
\author[1]{Laure Zanna}%
\affil[1]{New York University}%


\vspace{-1em}



  
  \date{May 21, 2024}


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\begin{abstract}
Coupled climate simulations that span several hundred years cannot be
run at a high-enough spatial resolution to resolve mesoscale ocean
dynamics. These mesoscale dynamics backscatter to macroscales. Recently,
several studies have considered Deep Learning to parameterize subgrid
forcing within macroscale ocean equations using data from idealized
simulations. In this manuscript, we present a stochastic Deep Learning
parameterization that is trained on data generated by CM2.6, a
high-resolution state-of-the-art coupled climate model with nominal
resolution 1/10\selectlanguage{ngerman}° . We train a Convolutional Neural Network for the
subgrid momentum forcing using macroscale surface velocities from a few
selected subdomains. At each location and each time step of the coarse
grid, rather than predicting a single number, we predict the mean and
standard deviation of a Gaussian probability distribution. This approach
requires training our neural network to minimize a negative
log-likelihood loss function rather than the Mean Square Error, which
has been the standard in applications of Deep Learning to the problem of
parameterizations. Each prediction of the mean subgrid forcing can be
associated with an uncertainty estimate and can form the basis for a
stochastic subgrid parameterization. Offline tests show that our
parameterization generalizes well to the global oceans, and a climate
with increased CO2 levels, without further training. We test our
stochastic parameterization in an idealized shallow water model. The
implementation is stable and improves some statistics of the flow. Our
work demonstrates the potential of combining Deep Learning tools with a
probabilistic approach in parameterizing unresolved ocean dynamics.%
\end{abstract}\selectlanguage{ngerman}%



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