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\begin{document}

\title{Probabilistic Machine Learning Estimation of Ocean Mixed Layer Depth
from Dense Satellite and Sparse In-Situ Observations}



\author[1]{Dallas Foster}%
\author[2]{David John Gagne}%
\author[3]{Daniel Bridger Whitt}%
\affil[1]{Oregon State University}%
\affil[2]{NCAR}%
\affil[3]{National Center for Atmospheric Research}%


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  \date{June 14, 2024}


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\begin{abstract}
The ocean mixed layer plays an important role in subseasonal climate
dynamics because it can exchange large amounts of heat with the
atmosphere, and it evolves significantly on subseasonal timescales.
Estimation of the subseasonal variability of the ocean mixed layer is
therefore important for subseasonal to seasonal prediction and analysis.
The increasing coverage of in-situ Argo ocean profile data allows for
greater analysis of the aseasonal ocean mixed layer depth (MLD)
variability on subseasonal and interannual timescales; however, current
sampling rates are not yet sufficient to fully resolve subseasonal MLD
variability. Other products, including gridded MLD estimates, require
optimal interpolation, a process that often ignores information from
other oceanic variables. We demonstrate how satellite observations of
sea surface temperature, salinity, and height facilitate MLD estimation
in a pilot study of two regions: the mid-latitude southern Indian and
the eastern equatorial Pacific Oceans. We construct multiple machine
learning architectures to produce weekly 1/2 degree gridded MLD anomaly
fields (relative to a monthly climatology) with uncertainty estimates.
We test multiple traditional and probabilistic machine learning
techniques to compare both accuracy and probabilistic calibration. We
find that incorporating sea surface data through a machine learning
model improves the performance of MLD estimation over traditional
optimal interpolation in terms of both mean prediction error and
uncertainty calibration. These preliminary results provide a promising
first step to greater understanding of aseasonal MLD phenomena and the
relationship between the MLD and sea surface variables. Extensions to
this work include global and temporal analyses of MLD.%
\end{abstract}%



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