On the appropriateness of the baroclinic mode or the SQG dynamics to describe the surface mesoscale motions

The mesoscale signal obtained by the altimeter is often considered to be associated with the first baroclinic mode, but no studies has investigated this assumption using realistic simulations.The baroclinic modes are modes that capture the potential vorticity (PV) anomalies in the ocean interior and are derived using an assumption of vanishing buoyancy anomalies at the ocean surface (which is obviously not the case). The surface Quasi-Geostrophic (SQG) theory present an alternative framework since it consists of a fluid with uniform PV but with non-uniform surface density anomalies.

Here we examine how surface motions are related to baroclinic modes and SQG dynamics. A complete decomposition of the mesoscale signal is done using realistic numerical simulations of the World Ocean. The contribution of each solution (baroclinic and SQG) is measured in different regions of the ocean. The SQG solution is found to give the largest contribution in terms of surface energy in many parts of the ocean. Its relative importance compared to baroclinic modes is determined at first order by the large-scale forcing of PV and surface buoyancy. Also, the error committed by the SQG method when reconstructing currents through depth is smaller than when reconstructing using the first baroclinic mode. These results are consistent with the fact that the SQG theory applies for the ocean surface and explain why density (or SST) variance spectra are similar to kinetic energy spectra at ocean surface. It means that the ocean surface reflects more the SQG dynamics than the first baroclinic mode.