Quantifying the Degree of Eddy Quasi‐Geostrophy by Generalizing Rossby Deformation

Abstract The quasi‐geostrophy (QG) of oceanic eddies is scientifically challenging and observationally puzzling because of its marginally balanced yet resolvable nature. Here a quantitative analysis on the degree of eddy QG is carried out using altimetric sea surface height data from multiple missions. We propose a metric of Rossby period of deformation (Td) as an extension to the Rossby radius of deformation (Rd) and its related phase speed of the first baroclinic Rossby wave (Cd) which satisfies Td = Rd/Cd, implying that any robust eddy with a length scale of ∼Rd is supposed to survive for a period longer than the Rossby period ∼Td under an average propagation speed of ∼Cd if a quasi‐geostrophic balance can be maintained. In terms of a generalized Rossby deformation with regards to Rd, Td, and Cd, three indices are defined as baselines to characterize the spatial, temporal, and dynamic aspects of eddy QG according to their effective size, actual lifetime, and propagation speed, respectively.