Spatio‐Temporal Coarse‐Graining Decomposition of the Global Ocean Geostrophic Kinetic Energy

We expand on a recent determination of the first global energy spectrum of the ocean's surface geostrophic circulation (Storer et al., 2022, https://doi.org/10.1038/s41467-022-33031-3) 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 (>1,000 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 ∼15 cm/s, which increases to ∼30–40 cm/s locally in the Gulf Stream and Kuroshio and to ∼16–28 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 ≈25%–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 circulation show that most of its energy (up to 70%) resides in stationary eddies with characteristic scales smaller than (<500 km). This highlights the preponderance of “standing” small-scale structures in the global ocean due to the temporally coherent forcing by boundaries. 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 ≈200 km and ≈2–3 weeks.