An evaluation of the classical and extended Rossby wave theories in explaining spectral estimates of the first few baroclinic modes in the South Pacific Ocean

Abstract

Previous literature has suggested that multiple peaks in sea level anomalies (SLA) detected by twodimensional Fourier Transform (2D-FT) analysis are spectral components of multiple propagating signals, which may correspond to different baroclinic Rossby wave modes. We test this hypothesis in the South Pacific Ocean by applying a 2D-FT analysis to the long Rossby wave signal determined from filtered TOPEX/Poseidon and European Remote Sensing-1/2 satellite altimeter derived SLA. The first four baroclinic mode dispersion curves for the classical linear wave theory and the Killworth and Blundell extended theory are used to determine the spectral signature and energy contributions of each mode. South of 17°S, the first two extended theory modes explain up to 60% more of the variance in the observed power spectral energy than their classical linear theory counterparts. We find that Rossby wave modes 2-3 contribute to the total Rossby wave energy in the SLA data. The second mode contributes significantly over most of the basin. The third mode is also evident in some localized regions of the South Pacific but may be ignored at the large scale. Examination of a selection of case study sites suggests that bathymetric effects may dominate at longer wavelengths or permit higher order mode solutions, but mean flow tends to be the more influential factor in the extended theory. We discuss the regional variations in frequency and wave number characteristics of the extended theory modes across the South Pacific basin.

Depth dependence of westward-propagating North Atlantic features diagnosed from altimetry and a numerical 1/6° model

“…While the extended theories appear to do better than the SLT at reducing the discrepancy with observations, e.g., Maharaj et al (2007), this does not necessarily mean that they do so for the correct reasons. This is because the extended theories, despite their apparent success, still rely on a number of assumptions whose validity can neither be directly checked against observations, nor rigorously proven mathematically.…”

“…Challenor et al (2001) applied a 3-D RT on altimeter data in the North Atlantic and showed that the meridional phase speed was negligible in many places; this justifies why only the 2-D RT is used here. Some authors (Subrahmanyam et al, 2000;Osychny and Cornillon, 2004;Maharaj et al, 2007) have used the 2-D Fourier Transform instead of the 2-D RT. This alternative approach highlights the spectral components of the data in time and space and provides a different estimate of superimposed phase speeds.…”

Eddy Heat Flux in the Southern Ocean: Response to Variable Wind Forcing

“…Second, a three-layer model is the simplest that will capture modal interactions correctly [see Dewar and Morris (2000), who explicitly advocate the use of three-layer models]. Third, Maharaj et al (2007) have shown that, at least in the South Pacific, two baroclinic modes suffice to explain almost all the observed variability of sea surface height. They see hardly any third mode, which would in any case be very poorly resolved on the 10-km grid used in this study.…”

On the Generalized Eigenvalue Problem for the Rossby Wave Vertical Velocity in the Presence of Mean Flow and Topography

“…The main objective of this paper is twofold: 1) to clarify the nature of the error and show how to redress it and 2) to understand how the error affects some of KB04's conclusions regarding the nature of the dispersion relation of Rossby waves in the presence of a background mean flow and topography. The issue is important to clarify because it also affects KB05's results and KB07's discussion of forced modes and baroclinic instability and is expected to alter some of the conclusions of the comparison of the KB04 theoretical dispersion relations against observations recently carried out by Maharaj et al (2007Maharaj et al ( , 2009.…”