In this paper, the zonal and meridional sea surface height (SSH) wavenumber spectra are systematically calculated using along-track and gridded altimeter products, and the slopes of the SSH wavenumber spectra over the mesoscale band, which is defined by the characteristic length scale of mesoscale signals, are estimated. The results show that the homogeneous spectral slopes calculated from the along-track and gridded altimeter datasets have a similar spatial pattern, but the spectral slopes from gridded altimeter data are generally steeper than that from the along-track data with an averaged difference of 1.5. Significant differences are found between the zonal and meridional spectra, which suggest that SSH wavenumber spectra are indeed anisotropic. Furthermore, the anisotropy exhibits strong regional contrast: in the equatorial region, the zonal spectrum is steeper than its corresponding meridional spectrum, while in the eastward-flowing high EKE regions the meridional spectrum is steeper than its zonal counterpart. The anisotropy of SSH wavenumber spectral slopes implies that EKE distributes anisotropically in different directions, and this distribution is closely associated with the generation and nonlinear evolution of mesoscale movements.

The geographic character of the inverse cascade is analyzed based on the spectral kinetic energy flux calculated in the global ocean, using sea surface height (SSH) data from satellites, reanalysis data, and model outputs. It is shown that the strongest inverse cascade occurs mostly in high-energy eastward-flowing currents, such as the Antarctic Circumpolar Current (ACC), the Kuroshio Extension, and the Gulf Stream, which matches the global distribution pattern of the eddy kinetic energy (EKE). Hence, the eddy scales predicted by the local linear baroclinic instability L bci and from the altimeter observation L eddy are mapped out and compared with the energy injection scale L inj and the arrest-start scale L arrest2start of the inverse cascade, respectively. Generally, L bci agrees well with L inj in the midlatitude and high-latitude oceans, especially in the Northern Hemisphere. L eddy falls within the arrest ranges of the inverse cascade and is quite close to L arrest2start . Finally, the depth dependence and the anisotropy of the inverse kinetic energy cascade are also diagnosed in the global ocean. We have found that the strength of the inverse cascades decreases with increasing depth, but the global pattern of the strength is nearly invariable. Meanwhile, the variations in depth hardly affect the L inj and L arrest2start . After considering the anisotropy in the spectral flux calculation, a possible inertial range for the zonal spectral kinetic energy flux is expected, where the cascade magnitude will keep a nearly constant negative value associated with the oceanic zonal jets.