3Dfrom2D: Using theories of the ocean variability for linking the 3D ocean structure to 2D surface observations
- (University of Reading)
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 flat-bottom 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 large-scale waves from the meso-scale and submeso-scale 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 too-fast' 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 self-adjoint, 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 bottom-trapped 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 meso-scale 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 large-scale background mean flow, meso-scale eddies, westward propagating signals, and residuals. We will seek to isolate the meso-scale 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 surface-intensified 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 self-adjoint part of the GLT eigenvalue problem can be used to define alternative inner-products to compute empirical orthogonal functions, which are key reduction techniques in data assimilation strategies.