  We expand on a recent determination of the first global energy spectrum of
the ocean's surface geostrophic circulation (Storer et al., 2022) 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.
