
Decomposition of the sea surface height altimeter signal into a linear Rossby wave component and eddy component, for the 12th June 2001, using the method detailed in Thomas, Cipollini, Benveniste and Tailleux (2013, submitted to GRL). Panels: (a) Full signal (b) Linear Rossby wave component (c) eddy component. The decomposition suggests that linear Rossby waves are important at low latitudes, but that their importance decreases as latitudes increase. Figure created by Matthew Thomas. 
Over the past ten 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 being able to constrain the threedimensional structure of the ocean circulation upon which the temporal variability, and hence forecasting skill, rely. In an operational context, different data assimilation strategies are used, usually based on some form of multivariate covariance to project the surface information onto the vertical, so that it may affect the underlying threedimensional structure. However, vertical covariances may be position, time and state dependent and can be hard to determine from an entirely statistical approach. Fundamentally, much of the theoretical understanding of how the surface reflects the underlying threedimensional structure has relied on the results from the socalled standard linear theory (SLT), which 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 multiplied by a vertical normal mode structure solution of a classical SturmLiouville problem. The SLT predicts the existence of a barotropic mode and an infinite set of baroclinic modes, whose surface signature decreases with the order of the mode.
The SLT has played and still plays a considerable role in physical oceanography, since it forms the basis for our theoretical understanding of the forced and free variability of the oceans, for which a key part is a basic description of oceanic Rossby waves in a flatbottom ocean in the absence of a mean flow. It is also the framework that defines such important and fundamental length scales as the barotropic and baroclinic Rossby radii of deformation, which are traditionally regarded as the scales separating linear largescale waves from the mesoscale and submesoscale variability. Given that the SLT neglects such important effects as the background mean flow and topography, its validity has always been uncertain, but it is only with the advent of satellite altimetry that its validity has started to be systematically questioned, following the realization that the observed propagation characteristics of westward propagating signals that are ubiquitous in SSH data in all ocean basins at nearly all latitudes often differ significantly from predictions (The toofast' Rossby wave problem). This realization prompted a renewal of interest in the Generalized Linear Theory (GLT), which is the natural extension of the SLT accounting for a background mean flow and topography. The GLT, as the SLT, defines dynamical modes that are approximately separable solutions of the linearized equations of motion, and whose vertical structure is the solution of a generalized eigenvalue problem. Unlike in the SLT, however, the GLT eigenproblem 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 each conserving their energy, the GLT eigenmodes include stable as well as unstable discrete modes, surface and bottomtrapped eigenmodes, and a continuous spectrum of solutions.
Research funded by the last two OSTST cycles focused on improving our understanding of the structure of the GLT eigenmodes, and of their relevance to account for the observed propagation characteristics of westward propagating signals, and of their vertical structures. An important result was to convince ourselves that the ocean variability organizes itself into vertically coherent structures, which therefore supports the idea that thinking of the ocean variability in terms of modes is justified. Moreover, our research as well as that of others suggested that the first baroclinic GLT eigenmode can account for part of the vertical structure of westward propagation, and that the properties of the baroclinically unstable GLT eigenmodes can account, qualitatively and partly quantitatively, for the observed structure of the mesoscale ocean variability. The research proposed for the next funding cycle January 2013 December 2016 will continue to develop the theoretical understanding of the GLT eigenmodes, and of their relevance to account for the observed features of the free and forced variability. To make progress, significant effort will be devoted to test the usefulness of the GLT eigenmodes to account for the observed vertical structure of the variability. We will make progress towards achieving a meaningful decomposition of the variability into largescale background mean flow, mesoscale eddies, westward propagating signals, and residuals. We will seek to isolate the mesoscale eddy field by using the automated tracking of features method developed in Reading, and that has been successful so far in providing insights into the structure of the storm tracks in the atmosphere. This will parallel a similar effort undertaken by Dudley Chelton as part of his own OSTST proposal submitted to NASA. We will seek to identify the degree to which the part of the ocean variability having a surface signature is coupled with the part of the ocean variability lacking such a signature, as has been shown to occur between surfaceintensified and bottom trapped modes, using mode conversion theory. The vertical structure of the GLT eigenmodes will be evaluated by comparison with the largest current meter database. We will test whether the selfadjoint part of the GLT eigenvalue problem can be used to define alternative innerproducts to compute empirical orthogonal functions, which are key reduction techniques in data assimilation strategies.