Over the past 10 to 15 years, satellite altimeter data have become an integral part of the data assimilation strategies that are key to the success of operational oceanography. From a practical viewpoint, the usefulness of sea surface height (SSH) (as well as of all of the other remotely observed properties, such as sea surface temperature (SST), sea surface color or sea surface salinity (SSS)) ultimately relies on the information content of surface properties with regard to constraining part of the threedimensional structure of the ocean circulation and its variability. In an operational context, each data assimilation strategy has its own way, usually based on some form of multivariate analysis, to project the surface information provided by satellite on the vertical, so that it may affect the underlying threedimensional structure.
From a fundamental viewpoint, much of our theoretical understanding of how the surface information may constrain the underlying threedimensional structure of the interior ocean variability has relied on the socalled standard linear theory (SLT). Indeed, this states that under idealized conditions, the ocean variability can be decomposed into normal mode solutions that are the product of a horizontal part solution of the shallowwater equations times a vertical normal mode structure solution of a classical Sturm Liouville problem. Thus, it is the SLT that is at the origin of the wellknown concepts of barotropic and baroclinic modes. It is now clear, however, that the background mean flow, varying bottom topography, and nonlinearities that are neglected in the SLT have a profound influence on physical normal modes, and that these need to be accounted for in realistic applications. The Generalized Linear Theory (GLT) is perhaps the simplest and most natural extension of the SLT that accounts for its main neglected effects. Unlike the SLT, however, the eigenproblem considered by GLT is non selfadjoint, and its eigenmodes differ in many important respects from that of the SLT. Indeed, whereas the SLT eigenmodes form a complete orthonormal basis, that are all stable and energy conserving, the GLT modes include stable as well as unstable discrete modes, surface and bottomtrapped eigenmodes, and a continuous spectrum of solutions.
Research carried out as part of the last three OSTST cycles has established that the GLT eigenmodes were helpful in rationalizing the ‘toofast’ Rossby waves observed in satellite altimeter data, as well as in interpreting the vertical structures of Rossby waves simulated by highresolution numerical model simulations. It also established that the assumption that vertical normal modes are useful to interpret ocean variability appears to be verified in ocean models, at least as far as Rossby waves are concerned. From a practical viewpoint, however, the physical modes predicted by the GLT appear increasingly impractical for actual attempts at reconstructing or constraining the ocean interior circulation from surface data. As a result, the research that is proposed for the next OSTST cycle will aim at identifying suitable hybrid statistical/physical strategies for constructing modes that are empirical/statistical modes in nature but informed by physical considerations. This will be done by exploring various ways to define the innerproduct underlying the construction of any EOFs, by using as innerproducts those arising from the symmetric part of the linear operators of the GLT, an approach that has been previously used with some success in the atmospheric literature for constructed empirical normal modes that are as close as practical to physical modes. We will also seek to identify the relative importance of spatial and temporal filtering for teasing out vertical structures. We are still planning to use Kevin Hodges methodology to document the vertical structure of ocean eddies, which has been successfully applied to that end in the atmosphere.
 Left panel) Minimum number of vertical structures (based on EOFs) required to explain 99% of the variability of the zonal component of a 20 years long 1/12 degree resolution realistic NEMO model simulation. (Right panel) Same as left panel but for the meridional velocity component. The relative information content of Sea Surface Height (SSH) and Sea Surface Temperature (SST) relative to interior observations in constraining the full 3D ocean circulation is a priori much higher in the ACC and western boundary regions than elsewhere. 
