Abstract
Abstract. Tests of the new Rossby wave theories that have been developed over the past decade to account for discrepancies between theoretical wave speeds and those observed by satellite altimeters have focused primarily on the surface signature of such waves. It appears, however, that the surface signature of the waves acts only as a rather weak constraint, and that information on the vertical structure of the waves is required to better discriminate between competing theories. Due to the lack of 3-D observations, this paper uses high-resolution model data to construct realistic vertical structures of Rossby waves and compares these to structures predicted by theory. The meridional velocity of a section at 24° S in the Atlantic Ocean is pre-processed using the Radon transform to select the dominant westward signal. Normalized profiles are then constructed using three complementary methods based respectively on: (1) averaging vertical profiles of velocity, (2) diagnosing the amplitude of the Radon transform of the westward propagating signal at different depths, and (3) EOF analysis. These profiles are compared to profiles calculated using four different Rossby wave theories: standard linear theory (SLT), SLT plus mean flow, SLT plus topographic effects, and theory including mean flow and topographic effects. Our results support the classical theoretical assumption that westward propagating signals have a well-defined vertical modal structure associated with a phase speed independent of depth, in contrast with the conclusions of a recent study using the same model but for different locations in the North Atlantic. The model structures are in general surface intensified, with a sign reversal at depth in some regions, notably occurring at shallower depths in the East Atlantic. SLT provides a good fit to the model structures in the top 300 m, but grossly overestimates the sign reversal at depth. The addition of mean flow slightly improves the latter issue, but is too surface intensified. SLT plus topography rectifies the overestimation of the sign reversal, but overestimates the amplitude of the structure for much of the layer above the sign reversal. Combining the effects of mean flow and topography provided the best fit for the mean model profiles, although small errors at the surface and mid-depths are carried over from the individual effects of mean flow and topography respectively. Across the section the best fitting theory varies between SLT plus topography and topography with mean flow, with, in general, SLT plus topography performing better in the east where the sign reversal is less pronounced. None of the theories could accurately reproduce the deeper sign reversals in the west. All theories performed badly at the boundaries. The generalization of this method to other latitudes, oceans, models and baroclinic modes would provide greater insight into the variability in the ocean, while better observational data would allow verification of the model findings.
Highlights
Advances in the satellite observation of the ocean surface have led to significant progress in our theoretical understanding of oceanic Rossby waves, most notably on the “too-fast”Published by Copernicus Publications on behalf of the European Geosciences Union.F
The amplitude of the Radon transform of the meridional velocity anomalies at 24◦ S before filtering is shown in Fig. 2a at a number of selected depths; each line is normalized by its maximum so that the lines are on the same scale, as the amplitude decreases with depth
The phase speed at which the amplitude is maximum is indicated with a vertical black line and it is clear that while the maximum of every layer does not necessarily lie on this line, there is always at least a local maximum in the same location
Summary
Advances in the satellite observation of the ocean surface have led to significant progress in our theoretical understanding of oceanic Rossby waves, most notably on the “too-fast”. Vertical structures found by decomposition of the data into eigenfunctions yielded surface intensification of the waves that was more prominent the further north the section and which reduced in magnitude with depth, slightly increasing in speed at the ocean bottom and showing no reversal of velocity in the profile, contrary to the expectations from standard linear theory for the first baroclinic mode. It was occasionally found that the dominant speed at a particular level would differ from that exhibited by the surface level; in general, the Radon power would exhibit a secondary peak corresponding to the dominant surface speed, in which case the Gaussian filter would be applied to the secondary peak, rather than to the dominant peak, in order to isolate a vertical Rossby wave structure associated with vertically coherent propagation, as is usually assumed in WKB theories of Rossby wave propagation This procedure was repeated for two sub-domains representing the east and west Atlantic basins, spanning −37.75◦ to −16.42◦, down to 4000 m and −9.91◦ to 4.42◦, down to 4200 m respectively, to find the dominant phase speed in each basin. The coefficient of determination or R2 is used to determine the proportion of the variance in the RMSE that can be explained by a variable, if all the variance can be explained R2 has a value of 1, if none of the variance can be explained the value is zero
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