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\begin{document}

\title{Reconstruction of Surface Kinematics from Sea Surface Height Using
Neural Networks}



\author[1]{Qiyu Xiao}%
\author[2]{Dhruv Balwada}%
\author[3]{C Spencer Jones}%
\author[4]{Mario Herrero-Gonzalez}%
\author[1]{K. Shafer Smith}%
\author[5]{Ryan Abernathey}%
\affil[1]{New York University}%
\affil[2]{Lamont-Doherty Earth Observatory, Columbia University}%
\affil[3]{Texas A\&M University}%
\affil[4]{Ecole Nationale Superieure de Techniques Avancees}%
\affil[5]{Columbia University}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{abstract}
The Surface Water and Ocean Topography (SWOT) satellite is expected to
observe the sea surface height (SSH) down to scales of ~10-15
kilometers. While SWOT will reveal submesoscale SSH patterns that have
never before been observed on global scales, how to extract the
corresponding velocity fields and underlying dynamics from this data
presents a new challenge. At these soon-to-be-observed scales,
geostrophic balance is not sufficiently accurate, and the SSH will
contain strong signals from inertial gravity waves --- two problems that
make estimating surface velocities non-trivial. Here we show that a
data-driven approach can be used to estimate the surface flow,
particularly the kinematic signatures of smaller scales flows, from SSH
observations, and that it performs significantly better than directly
using the geostrophic relationship. We use a Convolution Neural Network
(CNN) trained on submesoscale-permitting high-resolution simulations to
test the possibility of reconstructing surface vorticity, strain, and
divergence from snapshots of SSH. By evaluating success using pointwise
accuracy and vorticity-strain joint distributions, we show that the CNN
works well when inertial gravity wave amplitudes are weak. When the wave
amplitudes are strong, the model may produce distorted results; however,
an appropriate choice of loss function can help filter waves from the
divergence field, making divergence a surprisingly reliable field to
reconstruct in this case. We also show that when applying the CNN model
to realistic simulations, pretraining a CNN model with simpler
simulation data improves the performance and convergence, indicating a
possible path forward for estimating real flow statistics with limited
observations.%
\end{abstract}%



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