The effects of dispersion on the propagation and amplitude variations of baroclinic Rossby waves

Ten years ago, Chelton and Schlax (1996) questioned the validity of the linear standard theory (LST) for Rossby waves by showing that observed westward propagating signals seemed to propagate about two to three times faster than predicted at mid-and high-latitudes, using 4 years of TOPEX/Poseidon satellite altimeter data. To account for the discrepancy, two main theories were initially proposed: 1) the zonal mean flow theory of Killworth et al. (1997), which emphasized the importance of the background zonal flow in modifying the planetary vorticity gradient; 2) the bottom-pressure compensated theory of Tailleux and McWilliams (2001), which emphasized the decoupling roles of steep/rough topography, friction, and nonlinearities in decoupling the bottom and upper layers, thus surface-intensifiying the modal structure of the waves and thereby speeding them up. Both theories improved upon the LST, but they nevertheless systematically underestimated and overestimated observations respectively. Furthermore, both theories neglected dispersive effects, owing to the the wavelengths initially observed being much larger than the Rossby radius of deformation. Since then, the merging of various satellite altimeter datasets have led to a significant increase in spatial resolution. This in turn led to an improved description of westward propagation, revealing finer details and a higher concentration of energy at smaller scales than previously thought, prompting the need for a theoretical re-examination of the respective roles of nonlinearities and dispersion on the observed features. To that end, I will present a dispersive extension of the bottom-pressure compensated theory of Tailleux and McWilliams (2001), and discuss its links with the dispersive theory of Killworth and Blundell in presence of mean flow and topography. I will also compare the performance of the theory compared to empirically-determined dispersion relations, as well as discuss the important role of dispersion on the westward penetration of Rossby waves excited along eastern boundaries.