Eddy kinetic energy and small-scale sea level height variability

A mathematical connection is established between the ocean near-surface geostrophic kinetic energy and the small-scale variance of its surface height. The latter is defined as the spatial variance of sea surface height inside a given grid box and represents a basic statistical characteristic of the field, necessary for estimating its vulnerability to sampling error. The former is also computed from sea surface height fields and, being an important dynamical attribute of the ocean, is often used to describe its mesoscale variability, or eddy energy. Under the condition of isotropic distribution of mesoscale energy, simple formulas connecting the two are obtained for the longand short-wave (compared to the grid scale) portions of the ocean power spectrum. Without these simplifying assumptions, a factor depending on the actual location-dependent two-dimensional wavenumber power spectrum enters the equation. Approximations based on the Stammer (1997) one-dimensional power spectrum estimates are developed. They are verified by application to the Ducet et al. (2000) gridded satellite altimetry fields.