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\begin{document}

\title{Global Patterns of Bias in Ocean Mixing Parameterization Identified
Through Unsupervised Machine Learning}



\author[1]{Ratnaksha Lele}%
\author[2]{Sarah G. Purkey}%
\author[3]{Jennifer A MacKinnon}%
\author[4]{Jonathan D Nash}%
\affil[1]{Scripps Institution of Oceanography, UC San Diego}%
\affil[2]{Scripps Institution of Oceanography, UCSD}%
\affil[3]{Scripps Institution of Oceanography}%
\affil[4]{Oregon State University}%


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  \date{June 13, 2024}


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\begin{abstract}
Turbulent mixing in the ocean is often parameterized in terms of the
downscale energy transfer by internal waves. Expressed in terms of the
vertical wavenumber spectrum of oceanic velocity shear (\$V\^{}2\_z \$)
and isopycnal strain (\$ \textbackslash{}zeta\^{}2\_z \$), the
``finescale parameterization'' relies on several parameters, including
key assumptions relating to the spectral properties. Here we use an
unsupervised learning model to identify spatial correlations between
embedded parameters of the finescale parameterization based upon data
from 1875 full-depth hydrographic profiles from 15 sections traversing
the global ocean. The clustered patterns along the sections have marked
horizontal and vertical spatial dependence associated with distinct
modes of spectral variation. Two clustered regions are identified where
the underlying spectra deviate significantly from the canonical
Garrett-Munk (GM) spectrum, suggesting potential departures from
implicit assumptions about the downscale energy cascade. Spectral
composites in these two regions show intensification of variance in the
low and high wavenumber regimes respectively, as well as distinction in
overall spectral levels and geographic prevalence. Furthermore, these
clusters are found to be associated with regions where parameterized
estimates of the turbulent dissipation rate \$\textbackslash{}epsilon\$
differ significantly (exceeding a factor of 5) from co-located in-situ
observations measured using \$\textbackslash{}chi\$-pod temperature
microstructure. Extending the methodology to other hydrographic datasets
has the potential to reveal reasons for this parameterization bias and
to identify the dynamical underpinnings leading to more robust
parameterizations of oceanic turbulent mixing.ere%
\end{abstract}%



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