Multiple westward propagating signals in South

Pacific sea level anomalies

A. M. Maharaj,1 N. J. Holbrook,2 and P. Cipollini3

Received 19 February 2008; revised 4 July 2009; accepted 20 August 2009; published 11 December 2009.

[1] The characteristics of multiple westward propagating signals in the satellite observedSouth Pacific sea level anomalies (SLA) between 10�S and 50�S are analyzed using thetwo-dimensional Radon transform (2D-RT). We test the hypothesis that these signals aremost likely to be the signature of the first few baroclinic Rossby wave modes. Thisinvolves a comparison of the estimated phase speeds of the 2D-RT peaks against the firstfour baroclinic mode Rossby wave speeds predicted from the extended theory. The 2D-RTanalysis typically identified up to three propagating signals in the SLA and veryoccasionally, a fourth. The first Radon transform (RT) peak phase speeds correspondedvery well with first baroclinic mode Rossby wave phase speed estimates from lineartheory between 15�S and 25�S and the extended theory phase speed estimates poleward of25�S. RT peak 2 speeds were less coherent but fell within the range of extended theoryestimates of the first four baroclinic Rossby wave modes, consistent with large-scaleRossby wave dynamics. The relationship between peaks 3 and 4 and the extended theoryhigher-order baroclinic mode speed estimates varied markedly across the basin. Regionalvariability in the spectral characteristics of the peaks suggests that different dynamicalregimes dominate north and south of 30�S in the South Pacific basin. The presence ofsecondary peaks in the middle to high latitudes suggests that higher-order modes may playa role in these regions.

Citation: Maharaj, A. M., N. J. Holbrook, and P. Cipollini (2009), Multiple westward propagating signals in South Pacific sea level

anomalies, J. Geophys. Res., 114, C12016, doi:10.1029/2008JC004799.

1. Introduction

[2] Westward propagating signals are clearly visible inlongitude-time (also known as Hovmoller) plots of sea levelanomalies (SLA) throughout the World Ocean. Due to theirubiquity, low-frequency, and long wavelengths, these signalshave generally been interpreted as the surface signature oflong planetary (Rossby) waves. Long wavelength baroclinicRossby waves are considered to be the main oceanic responseto large-scale (O [1000 km]), low-frequency (O [1 year])changes in atmospheric forcing and consequently are anindicator of the ocean’s memory, i.e., the length of time thatanomalous conditions persist [Gill, 1982]. However, theirsmall sea surface signature O [0.1m] and slow propagationspeeds O [0.1 ms�1] required the advent of high-precisionsatellite altimetry (in the early 1990s) before they could beclearly observed. With more than a decade of high-precisionaltimeter data from the TOPEX/Poseidon (T/P) satellite andother missions, it is now possible to examine these signals at

the basin wide or global scale with centimeter accuracy. Dueto an almost systematic discrepancy between the predictedand observed speeds of these westward propagating signalsin the midlatitudes, there has been much debate in theliterature on the exact interpretation of the observationsand the validity of the classical linear theory (see Fu andChelton [2001] for a review). Recently, Chelton et al.[2007] have suggested that the signals are in fact a super-position of large long-lived eddies (predominant polewardof 25� latitude) and larger-scale Rossby waves.[3] To analyze the characteristics of these propagating

signals, Hovmoller plots can be subjected to various signalprocessing techniques to gain latent information. Twocommon signal processing techniques used to this end arethe two-dimensional Fourier Transform (2D-FT) and two-dimensional Radon transform (2D-RT). Both of these tech-niques provide an objective means of determining the peakpropagating signals in Hovmoller plots. The Radon trans-form objectively determines the angle of propagation andthe associated speed of propagating features in the datawhile the Fourier Transform detects the spectral (frequency)components of the propagating signal. Further detail on theRadon transform is provided in section 3.2.[4] Previous studies have suggested that multiple peaks in

sea surface height (SSH) or SLA and sea surface tempera-ture (SST) spectra may be the surface signature of higher-order baroclinic Rossby wave modes in the ocean. Forexample, Subrahmanyam et al. [2001] examined T/P altim-

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1Department of Environment and Geography, Macquarie University,Sydney, New South Wales, Australia.

2School of Geography and Environmental Studies, University ofTasmania, Hobart, Tasmania, Australia.

3National Oceanography Centre, Southampton, University of South-ampton, Southampton, UK.

Copyright 2009 by the American Geophysical Union.0148-0227/09/2008JC004799$09.00

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eter data for the equatorial Indian Ocean with Fast FourierTransform (FFT) techniques and found three energeticpeaks in the spectra which were comparable in their speedsto estimates of the first three baroclinic modes from amodified theory for Rossby waves [Killworth et al.,1997]. The authors found that the T/P data resolved thesecond baroclinic mode Rossby waves in the Indian Oceanmore clearly than the first and third modes. This conclusionwas corroborated in the same study by results from a 31

2layer wind driven, reduced gravity model for the regionwhich showed stronger second baroclinic mode Rossbywaves than the first mode. The energy of the Rossby andKelvin waves were found to be related to the Monsoonstrength. Cipollini et al. [1997] found three peak signatureswith distinct speeds in T/P SSH data and ERS-1 SST datanear 34�N using Fourier Transform techniques. The SSHand SST signals were found to be in phase around 34�N butthe agreement between the SSH and SST field reducedaway from this latitude. However, the consistency in thevariance, phase and speeds between the three peaks in bothvariables led the authors to contend that the fastest propa-gating signal corresponds to the first baroclinic Rossbywave vertical mode, and more tentatively, that the twoslower signals correspond to the second and third baroclinicmodes. There is some debate about how to interpret SLA dataand consequently whether multiple propagating signals in-deed reflect higher-ordermodes of nondispersive longRossbywaves. For instance, in the Fourier analysis conducted byZang and Wunsch [1999] on six years of North Pacific T/Pdata, all peaks found appear to belong to the same dispersioncurve. Nevertheless, the previous studies mentioned aboveand the availability of higher resolution merged data setsprovide the impetus to continue to test this hypothesis.[5] While these studies have shown that there are multi-

ple signals in the SLA data that are worthy of investigation,only specific locations have been explored leaving openquestions regarding the spatial extent and overall impor-tance of these multiple signals on a basin-wide scale. Toaddress this, Maharaj et al. [2007] recently conducted asystematic analysis of the westward propagating signalsacross the width of the South Pacific Ocean between 10�Sand 50�S using 2D-FT analysis. From this analysis, esti-mates of the energetic contribution of the first four baro-clinic Rossby wave modes were produced and discussed. Itwas found that the first three modes contributed significantlyto the total Rossby wave energy in the SLA data, althoughthe third mode was seen to be very localized in spatialextent and could be ignored at the large scale. The contri-bution from the fourth mode was found to be negligible. Inorder to distinguish the various modes, dispersion relation-ships for each baroclinic mode were determined a priori andprojected in frequency-wavenumber (w – k) space based onthe classical linear theory [LeBlond and Mysak, 1978] andthe extended theory [Killworth and Blundell, 2003a, 2003b,2004, 2005]. The variance of the observed westward prop-agating signal in the SLA was then projected and comparedagainst these model dispersion curves.[6] A more direct method for detecting multiple signals

propagating at different speeds in the SLA is the 2D-RT[Deans, 1983; Polito and Cornillon, 1997]. The 2D-RTprovides an objective estimate of the orientation of lines inHovmoller plots (that is, the diagonally aligned ridges and

troughs in the SLA field characteristic of westward Rossbywave propagation) in order to determine the speeds of thewestward propagating signals. While the 2D-FT and 2D-RTmethods are mathematically related, in practice they aretwo very different approaches to examining the SLA spectra.These differences are explained further in section 3. Insummary, the inherent differences between the twoapproaches means that if one technique yields similar resultsto the other, it serves as confirmation that the calculatedspeeds are consistent. Nevertheless, one technique mightalso usefully reveal valuable information that was notapparent in the other.[7] This study aims to quantify the relative contributions

from the multiple westward propagating signals in theoceanic Rossby wave signature using a 2D-RT analysis ofthe South Pacific SLA data determined from a merged dataset of multimission altimeter observations between October1992 and September 2007 (almost 15 years). The primaryaim is to objectively determine the spectral characteristicsand distribution of the propagating signals from the 2D-RTanalysis and then to test the hypothesis that these signalsactually characterize various vertical baroclinic Rossbywave modes. We focus on the long wave hypothesis forthe following reasons: First, the Chelton et al. [2007]analysis of eddy identification and tracking found feweddies in the midlatitude South Pacific. We anticipate,therefore, that much of the westward propagating signaldetected will be of long Rossby waves and that the wavesignal will be ‘‘cleaner’’ than in other ocean basins wherelong-lived eddies were found to be abundant. In fact, sincethe combination of purely sinusoidal wave signals withslightly different phases (and phase speeds) in adjacentlatitudes can generate eddy-like signals, the presence ofeddies does not necessarily exclude the presence of longwaves. We will revisit this point later in the discussion ofour results. Secondly, our analysis technique has a tendencyto homogenize the signal and is more appropriate for larger-scale processes such as long waves. We choose an analysiswindow which is larger than the expected diameter of largeeddies but not so wide as to lose regional variability in longRossby waves which may potentially be caused by the meanflow or bottom topography. This is explained in detail insection 3. Our secondary aim in this study is to determinewhether the results from the 2D-RT approach lead us tosimilar conclusions about the prevalence and importance ofhigher-order baroclinic modes as Maharaj et al. [2007]came to using the 2D-FT approach.[8] This paper is structured as follows. Section 2

describes the SLA altimeter data set. Section 3 brieflydetails the data treatment and the 2D-RT methodology.Section 4 provides the results of the multiple westwardpropagating signals as detected by the 2D-RT. Section 5presents a discussion of the results and compares the out-comes of this study to those drawn from the 2D-FTapproach as reported by Maharaj et al. [2007]. Conclusionsare provided in section 6.

2. Data

[9] The merged Maps of Sea Level Anomaly (MSLA)data set consists of altimeter observations from T/P, Jason 1ERS-1/2, GFO and Envisat for the period from 14 October

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1992 to 26 September 2007 and are provided by theDeveloping Use of Altimetry for Climate Studies(DUACS), the Collecte Localisation Satellites (CLS) nearreal time multimission altimeter data processing system.This optimally interpolated and gridded data set providesthe highest quality of sampling for all satellites for anygiven time and is ideal for spatial analysis examiningregional variability. The advantage of such merged multi-mission data sets is that the estimates of the mesoscalesignals in the SLA are significantly improved [Le Traon etal., 2001] which facilitates a more accurate estimation ofspectral signatures in the data. Data processing and mappingdetails can be found in Le Traon et al. [1995] and Le Traonand Ogor [1998]. Maps are provided on a 1

4� spatial grid and

the time resolution is 7 days. This study focuses on extra-equatorial Rossby wave variability in the South PacificOcean between 10�S and 50�S.

3. Method

3.1. Data Treatment

[10] We extract Hovmoller plots of the MSLA, h(x, t),which were analyzed in a running window 20� wide inlongitude and shifted by 1� in space (latitude and longitude)from 10�S to 50�S. Windows (or data blocks) with landwere filled with a Gaussian interpolation scheme if the gapwidth was less than 10% of the window. Otherwise, the landwas left in. Spikes and outliers (values more than threestandard deviations away from the mean) in the data blockswere removed and interpolated using a 2-D Gaussianprocess with the full width at half maximum set to 2

3� in

space and 1.4 days in time and the search radius set to 1�in space and 7 days in time. Figure 1a is an example of a20� Hovmoller plot centred on 30�S and 116�W (244�E).The main positive (crests) and negative (troughs) bands ofSLA are aligned tilting left indicating that these featuresare propagating westward in time. However, close exam-ination also reveals some standing (near vertically, orhorizontally aligned) signals, such as the seasonal cycleof the SLA, and some small-scale eastward propagatingfeatures, which tilt to the right.[11] Each window or data block was passed through what

we refer to as the ‘‘westward-only’’ filter [Cipollini et al.,2001, 2006]. This filter removes stationary and eastwardpropagating signals by removing any signals in the secondand fourth quadrants in the frequency-wavenumber space.This leaves only westward propagating signals (the first andthird quadrants) and removes the annual standing signal. Afew more spectral bins around the annual peak are alsoforced to zero to effectively remove any stationary quasian-nual signals. The percentage of signal removed depends onthe percentage of annual and standing signals present in anygiven region. Maharaj et al. [2005] discuss the regionalvariability of the unfiltered versus filtered signal for theSouth Pacific basin.[12] Figure 1b is a Hovmoller plot of the same data as

Figure 1a after these have been passed through the west-ward filter. A comparison with Figure 1a shows that onlywestward propagating features remain in the filtered data(Figure 1b). Note that even by eye, more than one angle ofalignment can be seen in the filtered data. Multiple propa-gating features like these are characteristic of many of the

Hovmoller plots examined in our region of study. The 2D-RT analysis was then carried out and is detailed insection 3.2.

3.2. Two-Dimensional Radon transform

[13] The 2D-RT is a useful tool to objectively estimate theorientation of lines in a Hovmoller plot, and hence, toobjectively estimate the speed of the propagating signalsin the image. The 2D-RT, p(x0, f) is a projection of theimage intensity along a direction normal to the angle fwhere x0 is the projected coordinate [Deans, 1983; Politoand Cornillon, 1997; Challenor et al., 2001] and is given by

p x0;fð Þ ¼Zy0f x; yð Þj x ¼ x0 cos f � y0 sin f

y ¼ x0 sin f þ y0 cos f

dy0: ð1Þ

[14] Diagonal alignments of the features in longitude-timespace, as illustrated in Figure 1b, are lines of constant speed.When f is orthogonal to the direction of the alignments inthe plot, the Radon energy (expressed as the variance ofp(x0) at a given f) is maximum. Computing the RT of aHovmoller diagram for a range of values of f, and then itsenergy, allows one to find the value of f for which theenergy is maximum. This objectively determines the angleof the predominant signal in the filtered data. Thecorresponding speed can then be readily calculated from fusing simple trigonometry, being proportional to tan(f)[Cipollini et al., 2006]. The Radon transform is related tothe Fourier Transform via the projection slice theorem inthat p(x0, f) equals the inverse of the 1-D Fourier Transformof a section (or slice) at the angle f in frequency-wave-number space. Hence, computing the RT energy from aHovmoller diagram for a range of f is the equivalent ofcomputing the FT energy along the same range of angles inFourier space [Cipollini et al., 2006].[15] The 2D-RT was calculated from each Hovmoller

diagram for f ranging between 0� and 90� at 0.25� intervals,i.e., corresponding to orientations of westward propagation.It is worth noting here that because of the aspect ratio of theHovmoller plots (i.e., that they are longer than they arewide), the Radon transform must be normalized. This isachieved by dividing the Radon transform of the Hovmollerof length(l, t) by the standard deviation of the RT of a matrix(of the same size) of ones. Figures 1c and 1d show theRadon transform and standard deviation (arbitrary units),respectively, determined from the westward filtered Hov-moller diagram (Figure 1b). One large maximum at aboutf = 40� can be seen in Figure 1d along with some minorpeaks between 0 and 15�. The peaks were detected byexamining the first and second derivatives of the standarddeviation of the Radon energy. The first derivative wassmoothed with a five point Boxcar filter before computingthe second derivative. This translates to a smoothing of thefirst derivative over 5�. In the case of our example plot, thisyielded three peaks. The resulting angles of propagation aredrawn as white lines on the filtered image (Figure 1e). Theshallower angle is obvious. The two steeper angles are lessclear, but nevertheless apparent. The latter angles of propa-gation can be detected by eye in the lower half of the plot.Note, however, that detection by eye is not a necessarycondition for predominance or significance of propagation

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as the advantage of the RTalgorithm is that it can detect linesaccurately in a noisy image [Toft, 1996; Hill et al., 2000]. Itis also noteworthy that a fundamental property of the RT ishomogeneity [Deans, 1983]. This is required to identifydistinct peaks in the propagating features of the Hovmollerdiagram. Consequently, the data must be broken down intosubdomains where the speed of the waves (regardless ofperiodicity) must be reasonably constant [Challenor et al.,2001]. We achieve this by our choice of a 20� analysiswindow.[16] Figure 1e demonstrates the ability of the 2D-RT

analysis to detect the angle of propagation in an objective

manner. We note, however, that not all the peaks detected bythis technique may be important and some form of peakscreening is warranted. We achieve this by two methods.First, to determine whether the peaks found by the RTanalysis are significant (i.e., whether the signal can beconsidered a ‘‘real’’ low-frequency signal in the ocean),we set a threshold based on a mean ‘‘reference’’ spectrumfor the global ocean. This is based on a global frequency-wavenumber spectrum of global temporal variability fromTOPEX/POSEIDON data [Wunsch and Stammer, 1995].Peaks must lie more than one standard deviation above thereference spectrum to pass. We create a Gaussian white

Figure 1. Stages of the data processing and method. (a) A Hovmoller plot of SLA data centered on30�S, 244�E (m), (b) same as Figure 1a but westward filtered (m), (c) radon energy over a range of angles(arbitrary units), (d) standard deviation of the radon energy (arbitrary units), and (e) same as Figure 1b butwith three peak angles of propagation detected by the RT.

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process shaped with the reproduced spectrum, invert it toproduce a Hovmoller plot, then compute its Radon trans-form and variance. A hundred such simulations allows forthe calculation of a reference mean and standard deviationof the RT variances (Figure 2). The reasoning here is that ifa peak in the observed RT variance lies above this referenceRT variance plus one standard deviation, it may be consid-ered as significant and will consequently be accepted as areal low-frequency signal. Figure 3 shows an examplerealization of a Hovmoller plot with the reference spectrumand a coherent periodic (600 km) 2-D wave (longitude,time)signal, traveling at 3.8 km/d, with an amplitude of 1 cm.The green curve in Figure 2 is the RT variance of this plotand the peak readily stands out (around 33�) above thereference +1 standard deviation threshold.[17] The second peak screening we perform is to deter-

mine the relative height of each peak. This is a ratio of thestandard deviation of the peak to the mean standard devi-ation value as used and defined by Hill et al. [2000]. Peaksbelow a relative height of unity (i.e., those peaks that weresmaller than the average standard deviation in the plot) werediscarded. This value infers how dominant the angle ofpropagation detected by the peak is against the localbackground SLA in the 20� Hovmoller plot. Finally, thespeeds are computed for the peak angles which passed thescreening, multiplying tan(f) with the ratio of the longituderesolution and time resolution.[18] The estimated westward speeds, the Radon energy,

relative heights and relative distances for up to the first fourpeaks are investigated in section 4. The zonal mean speedswere calculated for every latitude and for each peak andcompared against long Rossby wave speed estimates for the

first four baroclinic modes determined from the extendedRossby wave theory [Killworth and Blundell, 2003a,2003b]. This extended theory has been shown to be animprovement over classical linear theory outside the tropics

Figure 2. RT variances from a Hovmoller realization generated with a Gaussian white process and thereference spectrum (blue), with a 1 cm amplitude westward propagating signal (green), the meanreference spectrum after filtering (solid red), and one standard deviation (dashed red).

Figure 3. Example Hovmoller plot of SLA (cm) incorpor-ating the reference spectrum and a westward propagatingperiodic 2-D wave of 1 cm amplitude.

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[Maharaj et al., 2007], and takes account of the vorticityeffects of the baroclinic background mean flow andbathymetry on long Rossby wave propagation. Rossbywave speeds predicted from this theory agree well withsatellite observations, which are larger (by a factor of two)than classical linear theory predicts in the mid latitudes[Chelton and Schlax, 1996]. We also include mean clas-sical linear theory estimates for the first baroclinic mode inthis analysis. The extended theory has been further gener-alized recently to a full (two-dimensional) dispersionrelationship [Killworth and Blundell, 2005] allowing esti-mates of shorter wavelengths. The long wave estimates,however, remain similar to the global results presented inKillworth and Blundell [2003a, 2003b] which are usedhere.

4. Results

[19] From our analysis of the peaks in the 2D-RT, we findthat secondary (or higher order) peaks are successively hardto find. Generally only up to three distinct and predominantwestward propagating signatures can be detected across thebasin with the fourth peak being present over only about3.5% of the total South Pacific domain. Consequently, wefocus on the results for the first two peaks but provide abrief discussion on peaks 3 and 4 for consistency andcomparison with results presented in recent previous studies[Maharaj et al., 2007]. It is also worth noting at this pointthat these spectral results are derived from the filtered SLAso the peaks, and consequently their significance, are

determined relative to the total westward propagating signaland not the overall (i.e., including eastward and stationary)signal which may include the signature of various otheroceanic processes. Some of these signals may well dominatethe westward propagating signal over parts of the basin[Maharaj et al., 2005]. On average, across the basin, thewestward propagating signal makes up 66% of the variancein the total signal, accounting for almost all the variancebetween 15� and 30�S. The westward propagating compo-nent makes up 30–40% of the total signal between 10� and15�S and there is significant variability south of 30�Sranging from 20–90%. The spatial variability of the west-ward propagating signal often appears to reflect the under-lying bathymetry of the South Pacific basin. This isdiscussed in some detail by Maharaj et al. [2005].[20] We characterize the results of the RT analysis in the

first part of this section and then examine the issue ofwhether these spectral signals may be the signature of longbaroclinic waves in the second half. Figures 4 and 5 showthe westward phase speeds, the RT standard deviation andrelative heights for peaks 1 and 2. Recall that the relativeheight is the ratio of the peak standard deviation to meanstandard deviation value and quantifies how dominant thepeak is (i.e., how well the wave signal in the MSLA standsout over the background signal). Only peaks which lieabove one standard deviation of the reference spectrum(as per Figure 2) and with a relative height of greater thanunity are presented. The first (dominant) peak estimatescover more than half the South Pacific domain (55%). Thefirst peak RT estimates of the speeds and standard deviation

Figure 4. The (a) speeds (cm/s), (b) standard deviations of the RT energy (arbitrary units), and(c) relative heights (nondimensional units) for peak 1 estimated from the 2D-RT analysis. Missing valuesdenote that no first peak was present.

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(Figures 4a and 4b) are similar to the long Rossby wavephase speed estimates and standard deviations of the west-ward filtered SLA reported by Maharaj et al. [2005,Figure 1]. In general, the westward phase speeds decreasepoleward from around 25 cms�1 at 10�S to approximately2 cms�1 at 50�S and tend to accelerate in the western side ofthe basin. These characteristics are consistent with theliterature on long Rossby wave propagation [Chelton andSchlax, 1996; Cipollini et al., 2006]. A small region ofanomalously fast speed estimates can be seen just southeastof New Zealand (50�S, 170�E–175�W). The most promi-nent feature from the standard deviations of the first peakenergy spectrum (Figure 4b) is the zonal band of highenergetic variability in the western half of the basin. Thelargest relative heights (Figure 4c) are across the subtropicswith values ranging from 1.8 to 2.3 between 150�–80�Wand 22�–50�S. The lowest relative heights are in thesouthwest of the basin and are close to unity, indicatingthat these peaks do not differ much from the mean value.Low relative heights for peak 1 indicate that secondarypeaks at these locations may carry a similar contribution ofthe Radon energy and, therefore, may be as important as thefirst peak in explaining the dominant propagating signals inthe SLA.[21] The second peak can be found over 20% of the South

Pacific domain, mostly in the midlatitudes (Figure 5). Peak2 westward phase speeds (Figure 5a) also decrease pole-ward but are generally much slower, O[<5 cms�1], thanpeak 1. There are some exceptions, such as in the southeastcorner of the domain and the region southeast of NewZealand mentioned in the discussion of peak 1. The relative

heights are between 1 and 1.5 (Figure 5c) in this area andare comparable to the results for peak 1 in the samelocation, again indicating that the second peak here is asimportant as the first peak. Across the basin, peak 2standard deviations (Figure 5b) have a similar distributionto those of peak 1 albeit with lower amplitudes. Only 10%of the South Pacific domain is estimated to include a thirdRT peak contribution and occur mostly poleward of 35�S(not shown). The westward phase speeds are mostly veryslow (<5 cms�1). Finally, we note here that the fourth peak(not shown) in the 2D-RT exists over only 3.3% of thedomain which is insufficient for drawing any definitiveconclusions.[22] The results from our analysis suggest that there are

regions (such as in the southern part of the basin) wheresecondary peaks detected by the 2D-RT may hold as muchenergy as the primary peak. Figure 6 shows the ratio of theenergy ratios of peak 1 against peak 2. The energy ratios areexpressed as the variance explained by a given peak overthe total westward propagating variance. Peak 2 effectivelyaccounts for as much of the total westward energy as peak 1where ratios are equal to 1. We find that up to 60% of peak 2values correspond to this value and are, therefore, asdominant as peak 1.[23] To further compare the variability in the RT energy

across the basin, we have extracted the distribution of theprescreened RT variance (in arbitrary units) over the rangeof angles (f) computed in this study for nine separatelocations (i.e., Hovmoller plots) across the basin (Figure 7).These locations are located at 12�S, 30�S and 45�S and are20� long, centered on longitudes between 155�–165�E,

Figure 5. Same as Figure 4 but for peak 2.

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170�–160�W (190�–200�E), and 120�–110�W (240�–250�E) as depicted in Figure 7. The mid-point longitudefalls within a range of 10� to avoid sections with land whichmay contaminate the data, missing values, and to be morestatistically representative of the east, west or midbasin. Thereference spectrum +1 standard deviation is also shown togive an idea of where the variance is significant and peaksare also labeled.[24] The distribution of the RT energy displays significant

variability across the basin. Along 12�S (Figure 7 (top)), thevariance curve is skewed toward larger angles (equating tofaster speeds). The variance in the eastern tropical sector isalso mostly lower than the reference variance though theactual peak does exceed the reference +1 standard deviationthreshold. This area of the study domain displayed almost

no secondary peaks in Figure 5. At 30�S (Figure 7 (mid-dle)), we see a more distinct ‘‘Gaussian-like’’ RT distribu-tion as a function of the angle f, with a prominent primarypeak that is more easily identifiable. The RT energy in thewestern basin case study region is different to both theeastern and midbasin examples at 30�S, with higher energymore akin to the western tropics. Along 45�S (Figure 7(bottom)), the energy plateaus across a wide range of anglesso that the peaks are not prominent against the background.As expected from the previous results shown in the study,the secondary peak contains almost as much energeticcontribution as the primary peak even when they exist atdifferent ends of the spectrum. This suggests that a range ofpropagating features exist at the higher latitudes of equalenergetic contribution (but different propagating speeds)

Figure 6. The ratio of the energy ratios of peak 1 against peak 2.

Figure 7. Variance of RT energy (arbitrary units) for nine case studies.

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and makes it difficult for the RT analysis to discern adominant mode of propagation in the Hovmoller plots.[25] Figures 4–7 confirm that secondary peaks exist in

the South Pacific basin. It is also intriguing that thesecondary peaks appear almost exclusively at mid to highlatitudes. The basin wide analysis of the peak characteristicsand the variance distribution of the westward propagatingsignal both suggest that there may be two distinct dynamical

regimes in the South Pacific basin: one dominating thetropics to subtropics (equatorward of 30�S) and anotherdominating the mid to high latitudes (poleward of 30�S).Our initial hypothesis was that multiple peaks in the Radontransform were most likely to correspond to respectivebaroclinic Rossby wave modes. If our hypothesis is correct,then our analysis suggests higher-order baroclinic modesplay a large role in the Rossby wave dynamics, selectively,in the higher latitudes. Many studies in the literature haveeluded to this, from the inability of a linear vorticity(Rossby wave) model to replicate thermocline depth vari-ability poleward of 30� [e.g., Perkins and Holbrook, 2001]to the direct investigation of higher-order mode contribu-tions to the mean flow field and its effect on long Rossbywave propagation [e.g., Killworth et al., 1997; Dewar,1998]. This does not exclude the possibility that we maybe seeing the signature of other mechanisms present at theselatitudes such as nonlinear eddies but since our results thusfar do not contradict our initial hypothesis we proceed totest our hypothesis further.[26] We compare the mean westward phase speeds esti-

mated from the 2D-RT peaks at each latitude across theSouth Pacific domain with the speed estimates of the first tothird baroclinic mode Rossby waves based on the extendedtheory of Killworth and Blundell [2003a, 2003b]. In theprevious results, it was clear that some of the secondarypeaks accounted for as much variance as the primary peakwhich casts doubt on the dominance of the primary peak.Consequently, we have reordered the peaks based onpropagation speed. The reasoning here is that the fastestpropagating signal is most likely to be the signature of thelowest-order baroclinic Rossby wave. Our results are illus-trated in Figure 8. Note that these plots have a logarithmicscale on the y axis in order to show the detail on the slowerend of the range of speeds. We also include estimates of thefirst baroclinic mode Rossby wave speeds based on classicallinear theory for reference.[27] Southward of 25�S, the mean speeds for peak 1 from

the 2D-RT analysis generally follow the extended theorymode 1 speeds very closely (Figure 8a). Equatorward of15�S, the RT peak speeds are significantly slower, evenslower than the first mode linear theory estimates and closerto the extended theory second mode estimates. The meanspeeds for peak 2 (Figure 8b) between 10�S and 18�S areslower than the theoretical higher-order mode estimates(<1 cms�1) then increase to within the higher-order modeestimates between 18�S and 33�S with a consistent patternof decreasing speeds with increasing latitude to around

Figure 8. Comparison of the Killworth and Blundell[2003a, 2003b] extended theory baroclinic Rossby wavemean phase speed estimates against the mean phase speedsof peaks (a) 1, (b) 2, and (c) 3 from the 2D-RT analysis. Theextended theory mode 1 Rossby wave speeds are denotedby the bold solid line, mode 2 Rossby wave speeds aredenoted by the dot-dashed line, mode 3 Rossby wavespeeds are denoted by the dashed line, and mode 4 Rossbywave speeds are denoted by the dotted line. The firstbaroclinic Rossby wave speed estimates from classicallinear theory are also included as the thin solid line. The RTpeak speeds are denoted by the asterisks.

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25�S. Poleward of this, the peak 2 mean speed estimates fallmost closely to the classical theory first mode. An importantpoint to note from Figure 8 is that the higher-order theoret-ical estimates are all very close together. With respect toobservations, peak 2 and 3 speed estimates are very similarat latitudes greater than 30�S. Since some of the peaksdetected are from a very broad shaped distribution(Figure 7), many of these peaks 2 and 3 fall within thesame margin of error. As we are uncertain of whether thedata resolution or the RT technique can determine speedswith a high enough accuracy to distinguish between eachmode, we will focus our discussion on whether the observedphase speeds are consistent with the first baroclinic modespeed estimates or are in the range of higher-order modes.[28] The third peak in the 2D-RT (Figure 8c) again

displays poleward increasing speeds between observationsand theory. Peaks propagate slower than the extended mode4 estimates equatorward of 20�S and then fall between theclassical theory first mode predictions and extended theoryhigher-order mode range of predictions poleward of 20�S.The phase speeds across most latitudes are generally con-sistent around approximately 1 cms�1 and are indistinguish-able from peak 2 poleward of 30�S. These meridionallyaveraged estimates all fall below the classical theory firstmode but display no discernible pattern or structure. Wenote that the mean speed estimates for peak 3 are based on avery small number of values.[29] In summary, peaks 1 and 2 (Figure 8) describe

coherent westward propagating signals consistent withlarge-scale, basin-wide planetary wave propagation asdepicted by the classical and extended theories. The resem-blance of the RT first peak speeds to the extended theoryfirst baroclinic mode Rossby wave speeds in the midlati-tudes is compelling. The peak 2 speeds show excellentcorrespondence with the range of higher-order theoreticalspeeds between 18� and 33�S but are unconvincing outsideof this zone. The meridional distribution of the third peak isfairly similar to the second peak, also falling within thehigher-order mode speeds poleward of 20�S. The speedshere are significantly slower than low-order Rossby wave

speed estimates in the tropics (to about 15�S), within therange of speeds for the higher-order modes in the sub-tropics and lower midlatitudes (to about 39�S), then followthe classical theory mean speeds. The first peak speedestimates, at any given latitude, are significantly differentto the secondary speed estimates at the same latitude. Asthe outliers in the secondary RT peaks do not conform tothe classical or extended theory mean speeds, this suggeststhat they may well be sea surface signatures of otherwestward propagating features such as locally forced longwaves, short waves or nonlinear eddies. Further work isnecessary to confirm the exact mechanisms underlyingthese westward propagating signals.[30] As mentioned earlier, the RT is related to the FT via

the projection slice theorem and both should yield similarphase speeds for the dominant peak in the data. It would bean interesting exercise to test whether this occurs in practiceby confirming that both the RT and FT analyses producedsimilar results. We cannot do this by direct comparison ofthe speeds estimated from the FT analysis of Maharaj et al.[2007] as their results had undergone further analysis whichsegmented portions (which amounts to a range of angle (f)projections rather than a single angle projection as deter-mined here) of the frequency-wavenumber space into var-ious baroclinic modes. Clearly, these will not correspond toany individual RT angles.[31] In order to appropriately test the RT analysis against

the FT analysis, we performed a 2D-FT of the SLA dataunder the same conditions (using a 20� analysis window)and estimated the phase speeds of the peak westwardpropagating signals in the spectra by dividing the peakfrequency by the peak wavenumber. We found an inherentdifference in the results from the two techniques. While theRT analysis readily detected the multiple propagating fea-tures, it was difficult to discern secondary peaks with anycertainty in the FT results through an automated algorithmover the entire basin. The primary signal in the FT frequency-wavenumber space could be detected relatively easily but,due to spectral leakage into surrounding bins, it was verydifficult to ascertain whether subsequent maxima in the FTenergy were due to leakage of the main peak or independentsecondary peaks. Assessing each frequency-wavenumberplot by eye would yield better estimates of which peakswere independent of the primary peak but this would add anelement of subjectivity to the analysis and is unfeasible forsuch a large spatial domain. Furthermore, to detect spectralpeaks unambiguously in the FT analysis, waves mustdisplay a clear periodicity and the sampling must besufficient to resolve the wave. The difficulties of ascertain-ing meaningful information from Fourier Transforms withrespect to Rossby waves is further discussed by Hill et al.[2000]. For our immediate purposes, we confine our anal-ysis to the first FT peak.[32] The speed estimates for the first peak in the FT

results generally agree well with the RT results. Figure 9shows the meridional distribution of median phase speedsfrom the 2D-FT analysis of the South Pacific westwardfiltered SLA data against phase speed predictions of the firstto fourth baroclinic Rossby wave modes from the extendedtheory as well as the classical linear theory first mode. Thedistribution is remarkably similar to the first RT peakmedian speeds (not shown). Between 20�S and 50�S,

Figure 9. Westward phase speed estimates from FTanalysis. Lines are as in Figure 8.

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median phase speeds are very close to the extended theoryfirst mode. Equatorward of 20�S, the FT speeds are signif-icantly slower than either theoretical first mode estimates,falling within the range of the extended higher-order modes.[33] For further comparison, the median speeds estimated

for the RT first peaks were plotted against the medianspeeds estimated from the primary FT peaks (Figure 10).There is a strong linear correspondence between the twoanalysis results up to a speed of around 5 cms�1 after whichthe FT estimates deviate significantly from the RT estimates.The FT speeds plateau at �7 cms�1 while the RT resolvesspeeds of up to 15 cms�1. This discrepancy occurs in thelow latitudes from 10 to 20�S. Poleward of this, the RT andFT speeds compare well, validating that the RT and FTapproaches lead to similar results for the most dominantpropagating signal in the SLA.

5. Discussion

[34] The discrepancy between the Fourier and the Radonresults is curious, even more so that it occurs selectively atlower latitudes. If there was an overall discrepancy acrossall latitudes one could assume that there was an error in theimplementation of the transforms or that the projection slicetheorem does not hold true in the discrete case. An exam-ination of the propagation angles in low-latitude Hovmollerplots indicates that the Radon transform speed estimates areaccurate so it would seem that the Fourier results fall short.[35] Maharaj et al. [2007] argue that the 20� analysis

window, as used here, is insufficient to resolve the wave-length of long Rossby waves in the low latitudes. Furtherexamination of the FT analysis at low latitudes indicates thatthe speed estimates improve with a much larger analysiswindow. For example, at 12�S a window width of around80� was needed to accurately resolve the annual Rossbywave signal and speed. The asymptotic-like behavior of theFT speeds is most likely due to this. The wavelengths ofRossby waves in the low latitudes are more than half thewidth of the South Pacific basin. Hence the FT analysis islikely to be invalid at such large scales as the method

assumes homogeneity over the analysis window. Conversely,while the RT peak 1 estimates fall short of the extendedtheory first mode estimates in the low latitudes, and themethod is also bound by some similar limitations as the FTtechnique (such as homogeneity), the RT technique appearsto effectively detect the longer waves by their angle ofpropagation rather than by attempting to resolve the spectralcomponents of the moving signals.[36] It would appear that while the two transforms work

on the same underlying assumptions, the FT is moresensitive to these assumptions than the RT. The FT high-lights single sinusoidal components, as identified by distinctwavenumber frequencies; whereas the RT effectively‘‘groups’’ together all features propagating at the samespeed (which correspond to peaks lying on a line in FourierSpace). Therefore, if the profile of the propagating featuresis not perfectly sinusoidal, i.e., each feature is made ofseveral components all propagating at the same speed (quiteplausible, given the broadbanded Fourier spectra that isnormally observed [e.g., Fu and Chelton, 2001; Maharaj etal., 2007]), then the RT will still ‘‘count’’ all that energyunder the one mode. In other words, the RT can detectnonsinusoidally-shaped features propagating coherently.Hence, for the purposes of detecting westward propagatingfeatures in SLA, the possibility for error is much larger in theFT as it actually attempts to resolve the spectral componentsof the signal while the RT only has to accurately determinethe predominant angle of propagation in the signal.[37] In summary, we find that the primary RT and FT

peaks compare well to each other and to the (long wavelimit of the) extended theory first baroclinic mode polewardof 20�S. Second and third RT peaks, and very rarely fourthpeaks, have been detected in the South Pacific data but theirmean phase speeds do not correspond as clearly with any ofthe first to fourth extended theory baroclinic mode estimateseven though they fall within this range of speed estimates.[38] We now provide a short discussion of how well the

RT results (Figures 4 and 5) presented here compare withestimates of the first four baroclinic modes using 2D-FTtechniques. The 2D-FT analysis by Maharaj et al. [2007]involved projecting dispersion curves for the first four bar-oclinic modes from the extended theory onto the frequency-wavenumber space and then estimating the energeticcontribution of each mode thereby quantifying the propora-tion of variance in the power spectrum of the SLA that couldbe explained by the extended theory (see their Figure 3).[39] First, it is noteworthy that as with the number of

peaks detected in the 2D-RT analysis here, the first threemodes from the Maharaj et al. [2007] 2D-FT analysis madeimportant contributions to the overall variance while thefourth mode was negligible. The 2D-RT results suggest thatthe second and third peaks are not ubiquitous over the basin.On the contrary, higher-order peaks are successively harderto find. This corroborates the Maharaj et al. [2007] results,further demonstrating that only up to three modes are likelyto be important for representing Rossby wave propagation.[40] To more directly compare these results, we estimated

the energy ratio of the RT peaks (Figure 11). If we assumethat each RT peak is a baroclinic mode, the energeticcontribution of each mode is the ratio of the peak inquestion to the sum of all the (westward propagating)energy estimated by the 2D-RT. While this is not the same

Figure 10. Phase speeds from the RT peak 1 versus phasespeeds from the FT peak 1.

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as the energy ratios reported by Maharaj et al [2007], thiscalculation nevertheless provides an indication of the rela-tive contribution of each peak. Hence, we can attempt tocompare the distribution as well as the energetic contribu-tion between the Maharaj et al. [2007] FT results and theRT results presented here.[41] Both the FT and RT results are similar in that peaks

occur just south of 20�S. The Maharaj et al. [2007] FTmode 1 gives high energy ratios throughout most of thebasin south of 20�S while the RT peak 1 results show thehighest energy ratios eastward of 150�W, particularly in thenortheast (Figure 11a). The RT peak 2 results also showhigh energy ratios across the basin but also show values ofsignificantly lower energetic contribution (�0.1). The dis-tribution of peak 2 in the midlatitudes is similar to theMaharaj et al. [2007] FT mode 2 but they also found largeenergy ratios in the northwest part of the basin. In thepresent study, we do not detect any significant peaks in thisarea. Also, the energetic variability of the RT peak 2 is morescattered across the basin while the Maharaj et al. [2007]FT mode 2 shows a distinct gyre-scale circulation pattern.The RT peaks 3 and 4 (not shown) occur over more of theocean basin than their FT mode 3 and 4 counterparts,although some of the locations for the third RT peakcoincide with the FT mode 3. The energy contribution ofthe RT peaks 3 and 4 (mostly around 0.2–0.4) are alsoslightly higher than their respective FT modes.[42] In summary, while the number of peaks detected in

the RT in the present study and the number of modesdetected by the FT analysis by Maharaj et al. [2007]coincide, the spatial distribution and relative contributionof these are not always consistent. The FT modes given by

Maharaj et al. [2007] were determined from extendedtheory dispersion curves for the first four baroclinic modes.We find that some similarities exist in the spatial distribu-tion and energetic contribution of RT peaks 1 and 2presented here and the FT modes 1 and 2 presented byMaharaj et al. [2007], although the similarities betweenpeaks 3 and 4 and modes 3 and 4 are more equivocal.Again, this reinforces our conclusions that peak 1 and, moretentatively, peak 2 between 18�S and 30�S in the RT arevery likely to be the signature of the first and second Rossbywave modes, but no such conclusions can drawn for peaks 3and 4 in any region of the study domain.

6. Conclusions

[43] This study has investigated the characteristics ofwestward propagating features apparent in longitude-timeplots of satellite altimeter sensed SLA across the SouthPacific basin using the two-dimensional Radon transform(2D-RT). Our main hypothesis was that the multiple peaksestimated by the 2D-RT technique from the westwardfiltered SLA are the signature of the first few baroclinicRossby wave modes. We tested this by comparing theestimated phase speeds of the 2D-RT peaks against Rossbywave speed predictions corresponding to the extendedtheory first four baroclinic modes. The extended theoryprojections are based on modeled Rossby wave speedestimates that include the effects of baroclinic backgroundmean flow and the underlying bathymetry on long Rossbywave propagation, and agree well with satellite observationsof Rossby wave speeds [Killworth and Blundell, 2003a].

Figure 11. Energy ratios for RT peaks (a) 1, (b) 2, and (c) 3.

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[44] Generally, up to three separate propagating signals(the fourth occurring very rarely) were detected with sec-ondary (higher order) peaks being successively less appar-ent or important. Dominant and solitary peaks mostlyoccurred in the low-latitude north-eastern parts of the SouthPacific while multiple signatures of comparable amplitudeexisted mostly in the high latitudes. The highest variancewas found in the western basin. These characteristics agreewell with the observations given by Maharaj et al. [2005].Furthermore, in their FT analysis, Maharaj et al. [2007]found that the classical theory explained a significantlylarger proportion of the energy in the eastern tropicswhile the extended theory performed significantly betterin the eastern subtropics and midlatitudes. Their estimatesfor the midbasin did not meet the significance criteriawhile the western end of the basin showed mixed results.Maharaj et al. [2007] suggest that, in contrast to themultiple processes that may be occurring at the westernside of the basin, the dynamics on the eastern side of theSouth Pacific are essentially limited to first baroclinicmode Rossby waves generated at the eastern boundaryand propagating in the presence of mean flow andbathymetry. While that study demonstrated east-westdifferences across the basin, the present study highlightsnorth-south differences on either side of 30�S. The mainimplications suggested by this result is that the mechanicsof ocean adjustment in the tropics and subtropics arelargely dominated by the first baroclinic mode whilehigher-order modes and other westward propagating sig-nals discernably contribute to the dynamics in the mid tohigh latitudes.[45] In the present study, the strongest primary peaks

occurred in the northern and eastern parts of the SouthPacific basin while the weakest primary peaks occurred inthe southern and western portion of this basin. This indi-cates that in the latter region, the second peak carries asmuch energy as the first. An important conclusion drawnfrom this study is that the entire variance distribution in thewestward propagating signal needs to be considered beforethe dominance of a peak can be determined. Accordingly,we reordered the peaks based on speeds rather than variancebefore comparing to theoretical estimates. The first RT peakphase speeds corresponded very well with the classicaltheory first baroclinic mode Rossby wave phase speedestimates, between 15�S and 25�S, and with the extendedtheory first mode estimates in the midlatitudes. RT peak 2speeds also showed some coherency, falling within therange of extended theory estimates for the first four bar-oclinic Rossby wave modes. In general, the relationshipbetween the secondary peaks and the extended theoryhigher-order baroclinic mode speed estimates varied mark-edly across the basin with little coherency (such as, forexample, a latitudinal dependency) to indicate that they maybe the signal of a single dynamical process.[46] It is worth pointing out that one must be careful not

to assess the dynamics behind propagating features solelyon their speeds. The meridional distribution of speedestimates corresponding to the third and fourth peaks, whileseemingly at odds, may still be a characteristic signature ofRossby waves. The thermocline slope associated with themean geostrophic flow can dramatically influence Rossbywave phase speeds. While the extended theory should take

into account these effects and the theoretical speed estimatesdo not show these tendencies, the WKB assumptions of aslowly varying mean flow in this theory may explain someof the discrepancies. The problem of identifying the surfacesignature of higher-order modes is further confounded byother theoretical considerations. For instance, higher-orderbaroclinic modes are increasingly affected by the mean flow[Liu, 1999] and consequently their signatures may notpropagate purely westward, they may disappear wheninteracting with a critical level [Colin de Verdiere andTailleux, 2005] or special (e.g., bottom trapped) solutionscan exist in parts of the ocean [Maharaj et al., 2007]. Someof the secondary peaks detected here may well be thesignature of other processes such as nonlinear eddies. Acomparison of the spatial distribution of our peaks to thespatial distribution of eddies as found by Chelton et al.[2007] shows that our peak screening removes much of thesignal in some areas which they find to be eddy rich (e.g.,20�–30�S in the western Pacific) and our second peaklargely exists in some regions which they find to havelow eddy activity (e.g., 30�–50�S, east of 180�). Our 20�,15 year data blocks in the RT analysis are effectivelylooking for features of much longer wavelength and lifetimethan the mesoscale eddies. However, if such eddies occurredregularly and followed the same path (‘‘eddy highways’’)then their signal may well be captured by the RT. Also, thespeeds of the second peak are comparable to the estimatededdy speeds provided by the authors. Therefore, while onthe surface it may appear that our secondary peak results aredifferent to the eddy results of Chelton et al. [2007], takinginto consideration the techniques used in both the studies, itis very likely that the results could be different if the eddytracking or 2D-RT parameters were changed. Therefore, it isdifficult to confidently assign any significance to thesepatterns without further investigation of subsurface data orundertaking a separate comprehensive modeling study.[47] We have also investigated whether the results from

this analysis corroborate the conclusions of Maharaj et al.[2007] who use a different (Fourier) technique. We foundsome inherent differences between the RT and FT analysisresults. First, while the Radon transform appears to easilycapture multiple propagating signals in Hovmoller dia-grams, the Fourier Transform largely identifies the mostdominant signal. Secondly, though the two methods arerelated, in practice, the Fourier Transform seems to be moresensitive to the wavelength of this signal and resolution ofthe data set. Despite this, both the primary RT and FT peaksgenerally compared well to each other and to the extendedtheory first baroclinic mode over most of the South Pacificdomain with the exception of the low latitudes.[48] A comparison of these results with the energy ratios

for the first four baroclinic modes calculated by Maharaj etal. [2007] showed that while the number of modes in theirFT results and peaks in the RT analysis performed herecoincided, the spatial distribution and relative contributionof these results was not as consistent. The results suggestthat our initial hypothesis stands for the first two peaksdetected by the RT analysis but does not hold for subsequentpeaks.[49] We conclude that the first peak and selective regions

of the second peak in the RT most likely represent thesignature of long Rossby waves, but the dynamics behind

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subsequent RT peaks is unclear. Our observations providethe impetus for further investigation into the dynamics toadequately explain the regional variability of westwardpropagating signals in ocean basins. Explorations of Rossbywave theory, modeling investigations and subsurface dataare imperative to achieve a better understanding of theseobservations. For example, one important source of vortic-ity which has not been given due attention in the extendedtheory of Killworth and Blundell [2003a, 2003b, 2005] isthe local wind forcing. The extended theory does a good jobof explaining the SLA variance in the midlatitudes withoutincorporating this vorticity source, though it often underperforms at the shorter wavelengths [Maharaj et al., 2007].The effects of both local and remote (i.e., forced Rossbywaves) wind forcing may be the key to fully resolving thissignal as has been suggested in a number of studies[Holbrook and Bindoff, 1999; Chen and Qiu, 2004; Bowenet al., 2006].

[50] Acknowledgments. The altimeter products were produced bySSALTO/DUACS and distributed by AVISO with support from CNES. Theauthors are grateful to Jeff Blundell and the late Peter Killworth forproviding the extended theory speed estimates. We are indebted to Peter’sgenerosity with his data and insights over the course of this study. Theauthors would also like to thank Remi Tailleux and two anonymousreviewers for their valuable suggestions on a previous version of thismanuscript.

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�����������������������P. Cipollini, National Oceanography Centre, Southampton, University of

Southampton, Waterfront Campus, European Way, Southampton SO143ZH, UK. (cipo@noc.soton.ac.uk)N. J. Holbrook, School of Geography and Environmental Studies,

University of Tasmania, Hobart Campus, Geography-Geology Building,Room 319, Hobart, TAS 7001, Australia. (neil.holbrook@utas.edu.au)A. M. Maharaj, Department of Environment and Geography, Macquarie

University, Sydney, NSW 2109, Australia. (angela.maharaj@mq.edu.au)

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