Long-wavelength annual Rossby waves are important in the adjustment of the equatorial pycnocline to seasonal and interannual wind stress fluctuations. With phase lines extending downward, annual Rossby waves carry surface signatures into the deep ocean and exert major influence on the circulation system of the equatorial Pacific Ocean, including the Equatorial Undercurrent(EUC)(Phil and er, 1979), the North Equatorial Countercurrent(NECC)(Busalacchi and O’Brien, 1980), the Equatorial Intermediate Current(EIC)(Marin et al., 2010), and the equatorial warm water volume(Bosc and Delcroix, 2008).

Observational studies of equatorial Rossby waves have been based on Expendable Bathythermograph data(XBT), Mechanical Bathythermograph data(MBT), as well as ship measurements(Meyers, 1979; Kessler and McCreary, 1993, hereafter KM93; Yu and McPhaden, 1999). Results are mostly descriptive and detailed wave properties, especially the vertical structure, are difficult to distinguish due to the paucity of observations. For example, KM93 analyzed the seasonal temperature variation across the equatorial Pacific and interpreted the thermal signal along 4°N as vertically propagating annual Rossby waves. The hydrographic profiles they used, however, are inadequate to resolve the horizontal structure of Rossby waves. The resultant vertical structure is also noisy because historical casts tend to be seasonally biased and often have quality problem in deep depths.

The rapid accumulation of Argo floats since the past decade makes it possible to study the detailed structure of equatorial Rossby waves. Up to now about 3 800 Argo floats have been deployed in the ocean, producing more than 100 000 profiles each year. Unlike traditional hydrographic surveys, Argo floats cover the entire tropical Pacific Ocean without seasonal bias(Fig. 1).

Fig. 1 a. distribution of 130 600 Argo profiles during 2001-2013, superimposed with the mean dynamic height field(sea surface relative to 2 000 dbar)derived from the MOAA-GPV data. Pentagrams represent the TRITON moorings; b. histogram of the Argo profiles by month

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We plan to extend KM93’s wave analysis to new Argo data. The paper is organized as follows. Section 2 gives a brief description of the Argo gridded dataset. Results of annual harmonic analysis and lagcorrelation tracing are described in Section 3. The mechanism of equatorward shift of annual Rossby wave is then discussed in Section 4.

The MOAA-GPV data(Grid Point Value of the Monthly Objective Analysis using the Argo data)are used to analyze the seasonal variations of the equatorial Pacific Ocean. The dataset is a global grid of monthly temperature and salinity from January 2001 to December 2013, constructed mainly with Argo profiles. For each month, original Argo profiles are vertically interpolated onto st and ard pressure levels from¹⁰ to 2 000 dbar and then gridded into 1°× 1° fields using two-dimensional optimal interpolation(OI)method. Details of gridding process and error estimation of MOAA-GPV data are given in Hosoda et al.(2008). To avoid error contamination only data in the upper 1 500 m are used, because Argo floats make fewer measurements in the deeper water.

In this study, the seasonal signal of temperature is described by its annual harmonic T, a complex function of amplitude and phase. Following KM93, we estimate the isotherm vertical displacement at each depth by , where T _z is the mean vertical gradient of potential temperature. The Argo gridded data are interpolated onto regular depths of 10 m interval using 1-D cubic spline method. In KM93, historical hydrographic casts(CTD and Nansen)were used to calculate climatological monthly-mean temperature fields, to which annual harmonic analysis is applied. We perform similar annual harmonic analysis on the Argo gridded temperature data and compare the results with KM93.

Figure 2 shows the annual harmonic amplitude of isotherm vertical displacement ζ at four typical depths. There are two noticeable features. Firstly, the amplitude exhibits significant hemispheric asymmetry, with greater values in the Northern Hemisphere. There are several mechanisms that potentially cause the phenomenon, including asymmetry of wind stress curl(Meyers, 1979), crossequatorial southerly winds(Lukas and Firing, 1985), and background mean flow shear(Perez et al., 2005). Secondly, the maximal amplitude increases by 20 m from³⁰⁰ m to 1 000 m, which is associated with the weak stratification in the deep ocean.

The cause of isothermal displacement is often attributed to the wind-driven downward flux of momentum. As seen in Fig. 2, the track of maximalamplitude core is quite similar from³⁰⁰ m to 1 000 m, shifting equatorward from the eastern equatorial Pacific near 10°N to the western equatorial Pacific. Such zonal asymmetry prompts us to conduct seasonal analysis along the track of maximal amplitude, rather than along constant latitude as KM93 did. For simplicity, we will use the track at 800 m to represent the vertical-mean position of maximal amplitude.

Fig. 2 Amplitude of annual harmonic of isotherm displacement in meters at(a)300 m, (b)500 m, (c)800 m, and (d)1 000 m The dashline connects the maximal-amplitude core at each longitude.

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In KM93, the seasonal analysis was conducted along 4°N(see their Fig. 2). In Fig. 3 we do the same and plot annual harmonic properties along 4°N. It shows similar spatial pattern of amplitude and phase as in KM93. Generally speaking, the distribution of amplitude and phase is divided into two regimes by a line extending from¹¹⁰°W at sea surface to 150°W at 1 500 m. Above and to the west of this separation line, the pattern of amplitude and phase suggests a westward propagating annual Rossby wave. To the east of this line, a Rossby wave shadow zone is located in the deep water of the eastern equatorial Pacific, where seasonal signal is quite weak.

Fig. 3 (a)amplitude(meters);(b)phase; and (c)variance percentage of annual harmonic of isotherm displacement along 4°N

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Superimposed are stationary seasonal signal and its percentage variance ratio R. Compared with KM93, the wave pattern obtained in this study has less noise and appears to be more organized, because much more temperature profiles are now used. To measure how much temperature variance is explained by the seasonal signal, a percentage ratio can be calculated as

Click Browse formula

As seen in Fig. 2, the 4°N latitude line does not always coincide with the maximal-amplitude core. A better path to examine annual Rossby waves is along the maximal-amplitude track, which is given in Fig. 4. The phase pattern in the western and central Pacific is similar to that along 4°N, and both amplitude and percentage ratio are higher along the track. Significant discrepancy appears in the eastern equatorial Pacific, where phase lines are now vertically distributed and the seasonal amplitude is no longer small. The phenomenon is caused by the large seasonal variance near 10°N, which is associated with local Ekman pumping, eastern boundary reflection of Kelvin wave, and the mountain-gap wind jet(Kessler, 2006). Meanwhile the percentage ratio in Fig. 4c suggests that the thermal variations below 500 m along the entire maximal-amplitude track are dominated by seasonal signal.

Fig. 4 Similar to Fig. 3, but along the maximal-amplitudetrack at 800 m in Fig. 2

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The westward and downward propagation of annual Rossby waves thus produces a unique phenomenon in the western equatorial Pacific: seasonal signal dominates the thermohaline variation in the deep water rather than near the surface. This peculiar feature can be directly verified by mooring observations. The temperature records from the Triangle Trans-Ocean Buoy Network(TRITON)buoy at 2°N, 138°E, as plotted in Fig. 5, show that stationary seasonal signal explains more than 60% of deep thermal variance, but the ratio is only 20% in the shallow water above 500 m.

Fig. 5 Temperature record from the TRITON mooring at2°N, 138°E

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So far we have diagnosed the vertical structure of annual Rossby waves using annual harmonic analysis. The maximal-amplitude track in Fig. 2 and the phaseline pattern in Fig. 4b both suggest there is seasonal signal propagating southwestward from the eastern equatorial Pacific to the western equatorial Pacific. To investigate the spatial structure of annual Rossby wave, we apply lag-correlation analysis to the 13-year MOAA-GPV monthly time series to find the source region of the sub-thermocline seasonal signal in the western Pacific.

Results of signal tracing at 800 m depth are plotted in Fig. 6. The first base point A ₀ is at 2°N, 138°E, near the western end of the maximal-amplitude track. We calculate the correlation between the time series of ζ at the base point and each grid point in the tropical Pacific that leads A ₀ by one month. The position of maximal correlation is found at A 1. Statistically A 1 is the most likely place where seasonal signal propagates to A ₀ after one month. Similar procedure is repeated with increasing lead period to find the successive source points A _i(i =1, 2, 3 …)until the signal source reaches 120°W. All together, the seasonal signal at A ₀ is traced back by nine months to the eastern equatorial Pacific with correlation values above the 95% confidence level. The resultant signal path nearly coincides with the maximal-amplitude track in Fig. 2c, suggesting that seasonal signal indeed propagates along the maximal-amplitude track.Similar tracing results are obtained for other subthermocline depths, and small variation of the initial base point does not change the signal path very much. It means our lag-correlation tracing procedure is convergent. The westward propagation of seasonal signal along this tracing path, in the form of annual Rossby wave, is further illustrated in a longitude-time plot(Fig. 7). The seasonal signal propagates across the Pacific basin with a period of 11 months and a mean westward speed of 0.52 m/s.

Fig. 6 Maps of lag-correlation(>95% confidence level)between isotherm displacements at the base point 2°N, 138°E and every other grid points in the tropical Pacific at 800 m The tropical field leads the base point by 1-9 months as labeled.

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Fig. 7 Longitude-time plot of the annual cycle of isotherm displacement along the maximal-amplitude track The dashlines represent the phase lines for wave crest and trough.

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The study suggests that there is seasonal signal propagating below the equatorial thermocline from the eastern Pacific to the western Pacific in the form of annual Rossby waves, and the wave track exhibits an equatorward shift. Kessler(2006)also found southwestward phase propagation of thermocline variation in the equatorial Pacific near the Central American coast. He argued that long-wavelength Rossby waves propagate due west and attributed the equatorward phase shift to the sum of seesawing waves. The mechanism, however, does not seem applicable to the Pacific basin which has a width of 15 000 km: if there are Rossby waves propagating westward at diff erent latitudes, their phase lines would distort too much over such a long distance. Diagnosis of satellite altimeter data has shown that Rossby wave propagation is not restricted to latitudinal circle, and sometimes meridional deviation exists as a response to topography change(Challenor et al., 2001, their Fig. 5a). In Fig. 8 we see that ocean depth becomes shallower toward the western equatorial Pacific. Whether this incurs a topographic beta eff ect that shifts the Rossby wave propagation southward is an interesting question.

Fig. 8 Bathymetry of tropical Pacific Ocean from ETOPO5 Superimposed is the maximal-amplitude track at 800 m in Fig. 2c.

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Meanwhile both theoretical and numerical analyses have demonstrated that background current shear, such as that associated with the EUC or EIC, could distort zonal wave propagation(Philander, 1979; Proehl, 1990). As seen in Fig. 3 of Durl and et al.(2011), the peak of long Rossby wave is shifted equatorward in the presence of a westward jet. Nevertheless, more study is needed in order to determine which mechanism causes the path-shift phenomenon.

The present study is focused on annual signal because it is significant throughout the whole water column. As shown in Fig. 4c, more than 50% of total thermal variance in the equatorial Pacific is explained by annual signal. Semiannual signal is very weak in comparison, especially in the deep ocean. Harmonic analysis of the TRITON temperature records at 700 m in Fig. 5 yields a percentage variance ratio of 62% for annual signal and merely 3% for semiannual signal. For the broader tropical region, the altimetric SSH analysis by Qu et al.(2008)shows that the amplitude of semi-annual signal is only 1/5-1/3 of that of annual signal(see their Fig. 1a-b).

Annual Rossby waves are important in modulating the thermohaline structure in the equatorial Pacific Ocean. Based on new Argo gridded data, we diagnose the seasonal variation of temperature in the subthermocline equatorial Pacific through annual harmonic analysis and lag-correlation tracing. Two major findings can be summarized: 1)the maximalamplitude track of annual Rossby wave in the equatorial Pacific exhibits a southwestward shift and deviates from latitudinal circle. Compared with KM93, both amplitude and percentage variance ratio are higher along this equatorward track; 2)in the western equatorial Pacific, seasonal signal dominates the sub-thermocline temperature variance below 500 m and lag-correlation tracing shows that the signal originates from the eastern equatorial Pacific.

The MOAA-GPV datasets are downloaded from JAMSTEC websites:(http://www.jamstec.go.jp/ARGO). The encouragement and helpful comments from two anonymous reviewers are greatly appreciated.