Spatio-temporal coarse-graining decomposition of the global ocean
geostrophic kinetic energy
Abstract
We expand on a recent determination of the first global energy spectrum
of the ocean’s surface geostrophic circulation
\cite{Storer2022} using a coarse-graining (CG) method.
We compare spectra from CG to those from spherical harmonics by treating
land in a manner consistent with the boundary conditions. While the two
methods yield qualitatively consistent domain-averaged results,
spherical harmonics spectra are too noisy at gyre-scales
($>1000 $km). More importantly, spherical harmonics are
inherently global and cannot provide local information connecting scales
with currents geographically. CG shows that the extra-tropics mesoscales
(100–500 km) have a root-mean-square (rms) velocity of
$\sim15 $cm/s, which increases to
$\sim30$–40 cm/s locally in the Gulf Stream and
Kuroshio and to $\sim16$–28 cm/s in the ACC. There is
notable hemispheric asymmetry in mesoscale energy-per-area, which is
higher in the north due to continental boundaries. We estimate that
$\approx25$–50\% of total geostrophic
energy is at scales smaller than 100 km, and is un(der)-resolved by
pre-SWOT satellite products. Spectra of the time-mean component show
that most of its energy (up to $70\%$) resides in
stationary mesoscales ($<500 $km), highlighting the
preponderance of ‘standing’ small-scale structures in the global ocean.
By coarse-graining in space and time, we compute the first
spatio-temporal global spectrum of geostrophic circulation from AVISO
and NEMO. These spectra show that every length-scale evolves over a wide
range of time-scales with a consistent peak at
$\approx200$ km and $\approx2$–3
weeks.