A surface-aware projection basis for quasigeostrophic flow

A number of recent studies have demonstrated that altimetric observations of the ocean's mesoscale wave and eddy field reflect the combined influence of both surface buoyancy anomalies and interior potential vorticity anomalies. The former are associated with surface-trapped modes, with an exponentially-decaying vertical structure, and the latter with the standard baroclinic modes, which are the oscillating eigenfunctions of the quasigeostrophic potential vorticity stretching operator. In order to assess the relative importance of the two contributions to the signal, one would like to project the observed field onto a set of complete modes that separates the influence of each aspect of the dynamics in a natural way. However, because the surface-trapped modes are dependent on horizontal wavenumber, they are not, in general, orthogonal to the (wavenumber-independent) interior baroclinic modes, thus any projection will contain energetic overlaps.

Here we propose a modal decomposition that results from the simulateous diagonalization of two quadratic forms: the energy and a generalization of potential enstrophy that includes contributions from the surface buoyancy variances. These modes provide an orthonormal basis that represents surface and interior components in a natural way. A special case of these modes, which applies to flows with an active upper surface and a quiescent bottom boundary, will be explained and applied to a simulation of midlatitude oceanic mesoscale eddies. The new basis reveals that a significant portion of the energy is in the surface mode. Moreover, far fewer modes are required to capture the majority of the energy than with the traditional projection. Implications for inferring the vertical structure of eddies and waves from satellite observations will be discussed.