What Vertical Mode Does the Altimeter Reflect? On the Decomposition in Baroclinic Modes and on a Surface-Trapped Mode

This study is motivated by the ongoing debate on the dynamical properties of surface motions at mesoscales that are measured by altimetry [for sea surface height (SSH)] and microwave [for sea surface temperature (SST)]. The mesoscale signal obtained by the altimeter is often considered to be associated with the first baroclinic mode, but recent results indicate that SST spectra and surface kinetic energy spectra derived from SSH have the same slope, which is not consistent with this hypothesis. Moreover, baroclinic modes are associated by definition with vanishing buoyancy anomalies at the ocean surface, which is obviously not the case. Here a careful derivation of the vertical modes is done using the concepts of quasigeostrophic potential vorticity (QGPV) theory. Since the surface buoyancy can be interpreted as a Dirac function in PV, the traditional baroclinic modes have to be completed by a surface-trapped mode with no interior QGPV. The possible contribution of each mode is quantified in a realistic simulation of the North Atlantic Ocean. The surface mode is found to give the largest contribution in terms of surface energy in most of the Atlantic. Its relative importance compared to the other modes is determined at first order by the large-scale forcing of PV and surface buoyancy. These results emphasize the necessity for a new interpretation of satellite measurements of sea surface temperature or height.