  The decomposition of oceanic flow into its balanced and unbalanced motions
carries theoretical and practical significance for the oceanographic community.
These two motions have distinct dynamical characteristics and affect the
transport of tracers differently from one another. The launch of Surface Water
and Ocean Topography (SWOT) satellite provides a prime opportunity to diagnose
the surface balanced and unbalanced motions on a global scale at an
unprecedented spatial resolution. Here, we apply dynamic-mode decomposition
(DMD), a linear-algebraic data-driven method, to a tidally-forced numerical
simulation and one-day-repeat SWOT observations of sea-surface height (SSH) in
the Gulf Stream extension. DMD is able to separate out the spatial modes
associated with sub-inertial periods from super-inertial periods. The
sub-inertial modes of DMD can be used to extract geostrophically balanced
motions from SSH fields, which have an imprint of internal tides.
