U.S. Dept. of Commerce / NOAA / OAR / PMEL / Publications


Forcing of intraseasonal Kelvin waves in the equatorial Pacific

William S. Kessler and Michael J. McPhaden

Pacific Marine Environmental Laboratory, NOAA, Seattle, Washington

Klaus M. Weickmann

Climate Diagnostics Center, NOAA, Boulder, Colorado

J. Geophys. Res., 100(C6), 10,613-10,631 (1995)
This paper is not subject to U.S. copyright. Published in 1995 by the American Geophysical Union.

3. Results

3.1. Description

The intraseasonal Kelvin waves are clearly seen as sloped bands of high and low values in the longitude-time plot of 20C depth along the equator (Figure 3). We show the 4-year period from mid 1989 to mid 1993 because there were sufficient buoys to reliably perform the zonal interpolation and because the waves were relatively well developed at this time. The previous 3 years were dominated by the El Nio/La Nia seesaw of 1986-1988 and have been discussed by McPhaden and Hayes [1990].

Figure 3. Longitude-time plot of 20C depth on the equator. The contours and shading show the depth of the 20C isotherm, zonally interpolated between the buoy positions (see text). Contour interval is 20 m, and deeper thermocline depths are darker shades. The slanted lines show identified downwelling Kelvin wave ray paths (see text) and represent a speed of 2.4 m s-1. The heavy line at top shows the time series of zonal winds averaged over 165E-180 (scale at upper right). Both time series have been smoothed with a 17-day triangle filter (see text).

Observed changes to the mean thermocline slope and depth during the 4 years shown in Figure 3 were order 1; while the mean zonal thermocline slope in the central Pacific is close to 10-5 (1 m per 100 km), the standard deviation is about 0.7 10-5 and the large-scale slope both doubled and vanished on occasion during this period. Similarly, the mean depth of 20C at 140W during 1989-1993 was about 125 m, but values ranged between 80 m and 170 m, and displacements of more than 8 m day-1 were observed during Kelvin wave passage.

It is clear from Figure 3 that the intraseasonal Kelvin waves form a major component of equatorial thermocline depth variability. Slanted lines have been overplotted to show the downwelling waves; their slope represents a speed of 2.4 m s-1, which is the average speed found from the phase of the coherence in the intraseasonal band (see section 3.2) and is similar to other estimates [e.g., Johnson and McPhaden, 1993a]. The amplitudes are seen to be roughly 20 m in the central Pacific, and the zonal wavelengths of the intraseasonal Kelvin waves are at least 10,000 km (the east-west width of Figure 3 is about 9500 km); a simple calculation = cT gives 12,400 km for a speed of 2.4 m s-1 and period of 60 days.

There is a close visual coherence between zonal winds over the far western Pacific (heavy line at the top of Figure 3) and thermocline depth in the east/central Pacific. Figure 3 shows that virtually every western Pacific wind fluctuation was reproduced in 20C depth signals propagating across the basin at Kelvin-like speeds of 2 to 3 m s-1. The correlation of zonal winds at 165E with 20C depth at 140W was greater than 0.7 at a lag of 29 days corresponding to 2.4 m s -1 phase speed. The local correlation between zonal winds and 20C depth at 140W was zero, so remote forcing is clearly dominant. Intraseasonal westerly wind events were concentrated during the boreal fall/winter season, and during the past 4 years typically produced two to four downwelling Kelvin waves about 60 days apart each year. The duration of the series of downwelling waves each year effectively defines the annual thermocline deepening, and the El Nio event of 1991-1992 appears as a more intense version of the usual fall/winter deepening.

The corresponding longitude-time plot of surface zonal winds along the equator (Figure 4) suggests that the zonal wind has a shorter zonal coherence scale than either 20C depth or SST. Typically the strongest trades in the central Pacific occur during boreal fall/winter, which is when westerly events are most prominent in the far west. This out-of-phase relation between central and western Pacific is associated with the westward propagation of the annual cycle of zonal winds across the basin [e.g., Meyers, 1979; Lukas and Firing, 1985; Gent, 1985; Kessler and McCreary, 1993]. The result is that the correlation of winds along the equator has a relatively short zonal scale and becomes negative after a few thousand kilometers. The short zonal scales are consistent with those observed for deep tropical convection [Waliser et al., 1993].

Figure 4. Longitude-time plot of zonal winds on the equator. The plot has the same format as Figure 3 for 20C depth. The contours and shading show the zonal wind at a contour interval of 3 m s-1. Westerlies are darker shades. The heavy curve at top show the time series of OLR averaged between 160E and 170E on the equator, with values below 220 W m-2 darkened (scale at upper right). Both time series have been smoothed with a 17-day triangle filter.

Western Pacific westerly winds often appear as a series of roughly month-long events, rather than a simple annual sinusoid (Figure 4). Unlike 20C depth (Figure 3) there is only weak evidence of eastward propagation of the individual intraseasonal wind events, but successive events often extend farther to the east than did the preceding one. The 1991-1992 El Nio is evident in the zonal wind time series as a stronger-than-usual period of westerly events, which extended further east than in the preceding years (Figure 4). This low-frequency signal was disrupted by the intraseasonal waves, and between the strong westerly events the western Pacific winds returned to more normal conditions with easterlies or very weak westerlies (Figure 4). With the first of the series of MJOs in September 1991, substantial weakening of the trades west of about 170W was observed (Figure 4). The "collapse of the trades" occurred during January 1992, when westerly winds were seen as far east as 140W for about 3 weeks (although winds at 110W remained seasonally normal according to the Comprehensive Ocean-Atmosphere Data Set (COADS) climatology).

The occurrence of western Pacific westerly events corresponded closely to low values of OLR, which indicate the presence of intense tropical convection (heavy line at the top of Figure 4). At 0, 165E, the largest lag correlation of zonal winds and OLR was 0.7, with OLR leading the winds by about 5 days. The lag is approximate since OLR is processed to 5-day averages but is consistent with westerly winds following on the west side of eastward-propagating convective activity. An annual cycle showing low values in boreal fall/winter is evident in the OLR record, but the highly intraseasonal nature of particularly the low-OLR events is obvious in the time series at the top of Figure 4 (see section 3.2).

The corresponding longitude-time plot of sea surface temperature (SST) along the equator (Figure 5) shows a very different character of variability. Whereas thermocline depth and western Pacific zonal winds demonstrated large-amplitude intraseasonal fluctuations, SST variations were largely of lower frequency. An annual cycle was prominent east of about 170W, and in the eastern Pacific the annual occurrence of warm SSTs lagged the deepest thermocline (Figure 3) by 2-3 months. During the ENSO warm event of 1991-1992 the 29C isotherm moved east from its usual position near the date line to about 140W, and maximum SST at 110W reached 28C, about 1-2C warmer than the annual maxima of the previous 2 years. Before the 1991-1992 event, in 1989 and 1990 the cold tongue (defined roughly as the SST less than 25C) persisted through January of the following year east of 140W. However, in September-October 1991 a relatively abrupt warming took place across the basin, which roughly coincided with the first of the four downwelling Kelvin waves of this event and terminated the annual cold period about 3 months earlier than usual (Figure 5). While the SST was warming to its peak in the eastern Pacific during March 1992, the western Pacific at 165E cooled below 29C for the first time since 1989. Superimposed on these low-frequency changes of SST in Figure 5 are 500-1000 km bumps on the SST contours that appear to have an intraseasonal timescale. In section 4 we will argue that these are the result of zonal advection by the intraseasonal Kelvin waves, and further, that in some cases these advective SST anomalies can provide a significant feedback to the atmosphere in an eastward-propagating coupled interaction.

Figure 5. Longitude-time plot of SST on the equator. The plot has the same format as Figures 3 and 4. The contours and shading show the SST (actually, the 1-m temperature) at a contour resolution of 1C, with supplementary shading at 29.5C. Darker shades show warmer SST. The slanted lines are the same Kelvin wave paths shown in Figure 3.

3.2. Spectral Characteristics

Spectra of OLR and zonal winds in the western Pacific, and 20C depth and zonal current at the undercurrent level in the central Pacific are shown in Figure 6. The spectra were calculated for the 10-year period April 1983-April 1993 for all quantities except the zonal wind, for which only the seven years July 1986-July 1993 are available. The spectra were estimated from the raw periodogram amplitudes by smoothing in six frequency bands, with breaks at 600-, 225-, 110-, 45-, and 20-day periods, corresponding roughly to interannual, annual, semiannual, intraseasonal, monthly and submonthly variability. Within each of these bands the periodogram estimates were smoothed with a triangle filter whose length was constant within the band; however, a longer filter length was used to give greater smoothing in the higher-frequency bands. The resulting degrees of freedom (DF) were estimated according to the procedure of Bloomfield [1976, Chapter 8]; these range from 5 DF in the interannual band, to about 20 DF in the intraseasonal band and to about 60 DF for periods less than 20 days. The same frequency bands and smoothing were used to estimate the 95% confidence limits on the squared coherence amplitude and phase shown in Figures 7 and 8.

Figure 6. Variance-preserving spectra of OLR at 165E, zonal wind at 165E, 20C depth at 140W, and equatorial undercurrent speed at 140W, 120 m depth, all at the equator. Each variable has a separate scale as indicated. The spectra are calculated for the 10-year period April 1983-April 1993 for all quantities except the zonal wind, for which only the 7 years July 1986-July 1993 are available.

The spectra given in Figure 6 show that the intraseasonal band was a prominent feature of the variability of all these quantities, as expected from previous results and the plots discussed in section 3.1. The longitudes chosen for Figure 6 are roughly at the maximum amplitude of intraseasonal variability for OLR and 20C depth; in the case of zonal wind this amplitude increased toward the west and may have been larger to the west of 165E. The amplitude of zonal winds and OLR in this band dropped off rapidly east of the date line, so much of the oceanic intraseasonal variability in the eastern Pacific must have been remotely forced. The intraseasonal band variability in the atmospheric quantities shown (OLR and zonal wind) was skewed toward the high-frequency end of the band near 45-day or shorter periods, while the oceanic variability (20C depth and undercurrent speed) peaked near 60- to 75-day or longer periods (Figure 6). There was little oceanic energy in the central Pacific at periods shorter than 50 days, even though there was such energy in OLR and the wind forcing. This discrepancy is reflected in the fact that many of the papers discussing intraseasonal variability in the atmosphere refer to "30-60 day" or "40-50 day" fluctuations [e.g., Madden and Julian, 1972; Weickmann et al., 1985; Lau and Chan, 1985, 1986; Zhu and Wang, 1993], but the ocean seems to selectively respond to the lower-frequency part of the intraseasonal forcing. We discuss this question further in section 4.6.

In addition to the intraseasonal peak, major spectral peaks are also seen at 3- to 4-year periods associated with the ENSO cycle, and at the annual period (Figure 6). Weak semiannual variability was indicated for all four quantities, with only slightly higher energy levels than neighboring frequencies. It is noteworthy, but beyond the scope of this paper, that although there have been large changes, even reversals, of the equatorial undercurrent in the central Pacific associated with El Nio [e.g., Firing et al., 1983; Halpern, 1987], these events were short lived and did not compose a very large fraction of the variance, so there was no interannual spectral peak of zonal current at 120 m depth at 140W during 1983-1993, unlike the other quantities studied (Figure 6).

All four quantities shown in Figure 6 were coherent at periods longer than 1 or 2 months. Figure 7 shows the coherence squared of western Pacific OLR and zonal wind, and central Pacific undercurrent speed, with 20C depth at 0, 140W. Coherence significant at the 95% level is seen in the intraseasonal band, at the annual and semiannual periods, and at interannual periods. In the absence of local intraseasonal atmospheric forcing at 140W (the zonal wind amplitude in the intraseasonal band at 140W is about one-fourth that shown in Figure 7 at 165E), this coherence demonstrates the remotely forced nature of the central Pacific oceanic signals. The intraseasonal coherence peaks appear at the low-frequency end of the band (Figure 7), which again suggests that, although the intraseasonal convection occurs at periods down to about 35 days, the ocean response is dominated by periods of 60 days or longer.

Figure 7. Squared coherence amplitude of OLR at 165E, zonal wind at 165E and zonal current at 140W with 20C depth at 140W; 95% confidence levels are indicated by the thin horizontal lines, which also show the frequency bands used to smooth the raw periodograms (see text).

The intraseasonal coherence among OLR, west Pacific winds and central Pacific thermocline is not surprising, but it is important because the OLR events are known to propagate eastward into the Pacific from the Indian Ocean as part of the Madden-Julian Oscillation [Weickmann et al., 1985; Rui and Wang, 1990]. The Indian-Pacific connection is shown by high coherence in the intraseasonal band between OLR at 90E in the eastern Indian Ocean and 20C depth at 140W, 14,500 km to the east in the central Pacific (Figure 8). The intraseasonal coherence peak is found at 74.2 days and is significant at more than the 95% level (Figure 8, top). The coherence phase (Figure 8, bottom) indicates a lag of about 75 days for negative OLR (strong convection) leading positive (deeper) 20C depth; a lag that encompasses propagation of the OLR signal from the Indian Ocean across the Indonesian Archipelago and over the Pacific, the forcing of the Kelvin waves by winds associated with the tropical convection, and the propagation of the Kelvin waves across the Pacific. It is worth noting that the existence of large-amplitude intraseasonal variability of OLR over the Indian Ocean suggests that similar oceanic Kelvin waves may be observed there as well. Since the speed of OLR propagation across the Indian Ocean can be similar to the oceanic first baroclinic mode Kelvin speed [Rui and Wang, 1990], the forcing may be nearly resonant and the wave amplitude may be found to be large. McPhaden [1982] observed 30- to 60-day fluctuations of temperature and zonal velocity at Gan Island in the central Indian Ocean, which he interpreted as an equatorial Kelvin wave corresponding to the MJO. It is unlikely that such resonant intraseasonal forcing is a strong influence on the Pacific because the MJO fetch there is usually fairly short and because the propagation speed of the wind tends to speed up over the Pacific [Rui and Wang, 1990].

Figure 8. Squared coherence amplitude (top) and phase (bottom) of OLR at 90E with 20C depth at 140W. The intraseasonal peak is centered at 74 days. Positive phase indicates deep 20C depth leads low OLR. (Top) 95% confidence limits on the coherence amplitude are shown by the thin horizontal lines; 95% confidence limits on the phase are shown as "error bars," in each of the five frequency intervals in which the coherence (top panel) is significant above the 95% level. The phase limits are an average over each such interval and are plotted at the center of the intervals.

The Pacific Ocean Kelvin wave speed itself is found from Figure 9, which shows the squared coherence amplitude and phase of 20C depth across the equatorial band, averaged over periods of 55-65 days. The coherence is significant above the 95% level everywhere except 175E, where it is slightly smaller, and the phase variation is nearly linear, with a slope indicating a speed of 2.43 m s-1. This speed is used to draw the Kelvin wave lines in Figure 3. The speed is remarkably consistent over a wide region of the Pacific, despite the large range of mean thermocline depth (161 m at 165E to 58 m at 110W), and the order 1 changes in thermocline depth during this period (Figure 3). Similar calculations using other longitudes and bands give estimates between 2.2 and 2.8 m s-1, which suggests that 0.3 m s-1 is a rough measure of the uncertainty of the Kelvin speed estimate. Although one might expect that the first baroclinic mode Kelvin wave speed would vary zonally in concert with the thermocline depth across the Pacific, our results to the contrary are borne out by calculation of the baroclinic modal parameters using the mean full-depth temperature profiles compiled from historical data archives studied by Kessler and McCreary [1993]. The baroclinic modes are defined by a phase speed cn and a vertical structure function n(z) [Cane, 1984; Kessler and McPhaden, 1995a]. When these quantities are calculated from the mean historical profiles at different locations along the equator in the Pacific, it is found that the first-mode speed c1 varies only from about 2.8 m s-1 west of 150E to 2.3 m s-1 east of 120W, in approximate agreement with the present results. However, the structure functions n(z) show considerably more zonal variation, which might be expected to result in wave reflections and interactions between modes [Gill and King, 1985; Long and Chang, 1990]. One can interpret the nearly constant phase speed in a reduced gravity representation (where the phase speed is c2 = g(/)H, with the density contrast across the interface and H the mean interface depth). Although the thermocline shoals in the east, the vertical density contrast increases in the cold tongue region, and the two compensate to produce a net change in c that is less than would occur due to thermocline depth variations alone.

Figure 9. Squared coherence amplitude and phase of 20C depth over the zonal extent of the buoy array with that at 140W, averaged in the frequency band 55-65 days. The solid line shows the coherence amplitude (identically 1 at 140W), and the light dashed horizontal line is the 95% confidence level (scale at left). The heavy dashed line is the phase, expressed as a lag in days with the phase at 140W (scale at right). The thin solid line along the phase is a best fit straight line to the phase and represents a speed of 2.43 m s-1. This fit is the basis for the slope of the slant lines in Figures 3 and 5.

3.3. Complex Demodulation

The spectral representations shown in Figures 6, 7, 8, and 9 depict the average variability over the whole record lengths. Complex demodulation is a simple technique that gives time series of the amplitude and phase of the variability within a frequency band (see section 2.1) and thus allows examination of the temporal modulation of energy content of a particular band. Demodulation of the time series of 20C depth at 140W, at a central period of 60 days (Figure 10a) shows that the intraseasonal energy is largely concentrated in the boreal fall/winter season, as could be inferred from Figure 3. During most years, the 60-day amplitude approximately triples during this season, from a base of about 5 m to 15-20 m (Figure 10a). Smaller midyear peaks are also sometimes found, most prominently in 1986, 1987, and 1989. These three midyear peaks represent a single strong Kelvin event in each year. Weak midyear bumps also occur in other years, indicating that some semiannual variation of 60-day 20C depth amplitude is a normal part of the seasonal cycle. Construction of an average year of the 10 years of demodulated amplitude in Figure 10a shows largest values at the end of January and a weaker midyear peak 6 months later (Figure 11).

Figure 10. Time-varying amplitude of the intraseasonal variability obtained through complex demodulation of (a) 20C depth at 0, 140W, (b) zonal winds at 165E, and (c) OLR at 165E. The demodulation is performed about a central frequency of 60 days, with half-power between 42 and 108 days. The dashed line overlaid is a 1-year running mean of each demodulated time series.

Figure 11. Average year of 60-day amplitude of 20C depth at 0, 140W (meters, solid line, scale at left; data from Figure 10a), zonal winds at 165E (meters per second, dashed line, scale at right; data from Figure 10b) and OLR at 165E (W m-2, dotted line, scale at left; data from Figure 10c).

In late 1988 a sharp peak of 60-day amplitude occurred that did not represent the usual annual downwelling Kelvin waves associated with MJO convection and westerlies in the western Pacific, despite the fact that it appears to fit the annual pattern of maxima (Figure 10a). Instead, this event was a strong upwelling signal that was generated by a fairly confined patch of easterly winds near the date line [Picaut and Delcroix, 1995] and marked the maximum cooling of the La Nia of 1988 (Figure 2). If we omit the non-MJO 1988 peak, the largest intraseasonal signals of 20C depth are found at the beginnings of 1987 and 1992 (Figure 10a), both associated with the El Nio events of those years, and these appear as enhancements of the deep-thermocline phase of the annual cycle.

The corresponding demodulation of zonal wind at 165E is shown in Figure 10b. As in the case of 20C depth, a strong annual signal of 60-day variability is seen, with peaks roughly 3 times larger than the background occurring at the end of each year. The average annual and semiannual variation of 60-day wind amplitude (Figure 11) is very similar to that for 20C depth, with the western Pacific winds leading 140W 20C depth by 1-2 months, consistent with Kelvin propagation. Also in agreement with the thermocline signals, the strongest years of zonal wind 60-day amplitude were late 1986 and late 1991, preceding the two El Nio events of this period. In 1988, the usual year-end maximum was the weakest of any observed (Figure 10b), consistent with the interpretation given above that there were no MJOs over the Pacific that year. Picaut and Delcroix [1995] showed that the easterly wind event that forced the sharp SST cooling of November 1988 occurred primarily east of 165E, and thus this signal does not appear in the demodulation of the buoy winds at that location. The unusually large midyear peak in 1987 is also in good agreement with the 20C history. The correlation between the amplitude time series for 20C depth (Figure 10a) and that of 165E zonal wind (Figure 10b) is 0.68 at a 38-day lag, indicating an average propagation speed of 1.9 m s-1.

The corresponding demodulation of the OLR time history averaged over 160-170E on the equator is shown in Figure 10c. Again, for most years the OLR intraseasonal variability peaked in boreal fall/winter with an amplitude 2 to 3 times the background. The average year of OLR 60-day amplitude (Figure 11) shows peak amplitude in February-March, 1-2 months later than either the winds or 20C depth. This does not seem compatible with a simple relation between winds and convection, but it is nevertheless an accurate summary of even most of the years with strong intraseasonal waves (e.g., 1987, 1988, and 1991 in Figure 10c). Consistent with the 165E zonal winds, late 1988 appears especially weak in intraseasonal OLR variability, and the four most recent years were the most regular. The extra midyear peak in mid-1987 was very similar to the other two quantities, indicating that MJO convection and winds continued to affect the west Pacific even through boreal summer during the warm event. The periods of the 1986-1987 and 1991-1992 El Nios were amplitude maxima (also 1982 is a maximum not shown), although there are other large peaks, and the two El Nio years are not as distinctive in OLR intraseasonal variance as in western Pacific zonal winds or central Pacific thermocline depth. The 1-year running mean amplitude time series (dashed line in Figure 10c) shows that, even if the particular El Nio years were not necessarily the largest values, the low-frequency trend of OLR intraseasonal energy was maximum at the warm phase of the ENSO cycle.


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