A WKB analysis of the surface signature and vertical structure of long extratropical baroclinic Rossby waves over topography

WKB theory has been used recently to construct global approximations of purely periodic long extratropical baroclinic Rossby waves in a continuously stratified ocean, with the goal of building a global theoretical framework that can serve to interpret observed features of the waves, such as sea surface height wave activity and anomalous propagation. This study adopts the same approach in the idealized context of an ocean with constant buoyancy frequency N and longitudinally varying Gaussian topography, to gain insight into issues that have received little or no attention so far, namely: (a) the nature of the links between the vertical structure of the wave field and its surface signature, and the extent to which constraints on the interior dynamics can be derived solely from observing the surface; (b) which of the phase/amplitude variations determine the visual impression of westward propagation, addressed by constructing longitude/time plots of the signal in the attempt to mimic more closely the way the satellite SSH data of TOPEX/Poseidon are analyzed; (c) the validity and accuracy of the classical leading order WKB theory, addressed by estimating the residual a posteriori by computing the next-order term of the formal WKB series expansion. To a lesser extent, this also serves to assess the validity of the planetary geostrophic equations used to describe the dynamics of long Rossby waves. in results are that: (a) faster propagation is unambiguously related to the surface intensification of the waves, while slower propagation is associated with a vertical structure intermediate between that of the first and second standard baroclinic modes; (b) westward propagation is dominated by the phase variations; (c) the residual is inversely proportional to the frequency (or equivalently the wavelength by dividing by the phase speed), and is found to vary strongly with position. The hilltop is where the residual is the highest, and hence where WKB is the most likely to breakdown, in agreement with recent published predictions of mode conversion theory in a two-layer model setting.