Abstract

The interannual, equatorial Pacific, 20°C isotherm depth variability since 1980 is dominated by two empirical orthogonal function (EOF) modes: the “tilt” mode, having opposite signs in the eastern and western equatorial Pacific and in phase with zonal wind forcing and El Niño–Southern Oscillation (ENSO) indices, and a second EOF mode of one sign across the Pacific. Because the tilt mode is of opposite sign in the eastern and western equatorial Pacific while the second EOF mode is of one sign, the second mode has been associated with the warm water volume (WWV), defined as the volume of water above the 20°C isotherm from 5°S to 5°N, 120°E to 80°W. Past work suggested that the WWV led the tilt mode by about 2–3 seasons, making it an ENSO predictor. But after 1998 the lead has decreased and WWV-based predictions of ENSO have failed. The authors constructed a sea level–based WWV proxy back to 1955, and before 1973 it also exhibited a smaller lead. Analysis of data since 1980 showed that the decreased WWV lead is related to a marked increase in the tilt mode contribution to the WWV and a marked decrease in second-mode EOF amplitude and its contribution. Both pre-1973 and post-1998 periods of reduced lead were characterized by “mean” La Niña–like conditions, including a westward displacement of the anomalous wind forcing. According to recent theory, and consistent with observations, such westward displacement increases the tilt mode contribution to the WWV and decreases the second-mode amplitude and its WWV contribution.

1. Introduction

Numerical models (Zebiak 1989) and theoretical results (Jin 1997) suggest that the warm water volume (WWV) plays a crucial role in El Niño–Southern Oscillation (ENSO) dynamics [see also section 7.3 of Clarke (2008)]. These results were confirmed by observations reported by Meinen and McPhaden (2000) who analyzed monthly variations of the tropical Pacific 20°C isotherm depth (D20), a proxy for the thermocline depth for the period 1980–99. Meinen and McPhaden (2000) found that anomalies (i.e., departures from the seasonal cycle) of this depth could be well described by two empirical orthogonal function (EOF) modes of comparable variance. The first mode, sometimes called the “tilt” mode, involved a zonal tilt of the 20°C isotherm along the equator so that eastern and western equatorial Pacific isotherm depths were of the opposite sign. The principal component of this mode was in phase with anomalous, positive, eastern equatorial Pacific sea surface temperature (SST) and anomalous, positive D20 there (see Fig. 1). The second EOF mode was of one spatial sign and, for the 1980–99 data Meinen and McPhaden (2000) had available, led the tilt mode by 9 months with a maximum correlation r = 0.77. Meinen and McPhaden (2000) associated the second EOF mode with the discharge and recharge of warm water in the near-equatorial Pacific and defined a WWV as the volume of water above the 20°C isotherm in the equatorial Pacific region 5°S–5°N, 120°E–80°W (www.pmel.noaa.gov/tao/elnino/WWV/).

Fig. 1.

(top left) Tilt (first EOF) and (top right) second EOF modes of the monthly D20 anomalies (m). (bottom) The corresponding PCs have been normalized so that their root-mean-square (RMS) value is . This means that the spatial EOFs at the top display the amplitude of the monthly D20 anomalies (m). The letters T, K, and A correspond to the locations of Tabuaeran Island (formerly Fanning Island), Kiritimati Island (formerly Christmas Island), and Abariringa Island (formerly Kanton Island), respectively. The first EOF explains 52% of the variance and is highly correlated with negative ESOI [r = 0.97; rcrit (95%) = 0.44], while the second mode explains 33% of the variance and is highly correlated with WWV [r = 0.95; rcrit (95%) = 0.45]. The third mode (not shown) explains 6% of the variance. Here and elsewhere in this paper rcrit is based on the analysis of Ebisuzaki (1997).

Fig. 1.

(top left) Tilt (first EOF) and (top right) second EOF modes of the monthly D20 anomalies (m). (bottom) The corresponding PCs have been normalized so that their root-mean-square (RMS) value is . This means that the spatial EOFs at the top display the amplitude of the monthly D20 anomalies (m). The letters T, K, and A correspond to the locations of Tabuaeran Island (formerly Fanning Island), Kiritimati Island (formerly Christmas Island), and Abariringa Island (formerly Kanton Island), respectively. The first EOF explains 52% of the variance and is highly correlated with negative ESOI [r = 0.97; rcrit (95%) = 0.44], while the second mode explains 33% of the variance and is highly correlated with WWV [r = 0.95; rcrit (95%) = 0.45]. The third mode (not shown) explains 6% of the variance. Here and elsewhere in this paper rcrit is based on the analysis of Ebisuzaki (1997).

Note, however, that the equivalence between the second mode and WWV depends on the zonal cancellation of the opposite-signed tilt mode as well as the one-signed second mode having a variance comparable to the tilt mode. Recent theory (Clarke 2010; Fedorov 2010) does not guarantee such equivalence. If, in fact, there were incomplete zonal cancellation of the tilt mode and the second mode were to weaken decadally compared to the tilt mode, then both modes would make a contribution to the WWV. Here we want to make clear the distinction between the second EOF mode of D20 and the WWV since, as we will prove, their variability is not always equivalent.

Physically, the tilt mode is due to the zonal equatorial wind stress tilting the thermocline along the equator in accordance with an approximate balance between the zonal pressure gradient and zonal wind stress forcing (Kessler 1990; Jin 1997). Because of this we expect the principle component (PC) of the tilt mode to be highly correlated, at zero lag, with the zonal equatorial wind stress integrated from one side of the Pacific to the other. Such an integration has been shown dynamically to be proportional to the surface atmospheric pressure difference between the eastern and western equatorial Pacific (Clarke and Lebedev 1996) or, more precisely, a weighted surface atmospheric pressure difference between the eastern and western equatorial Pacific (Bunge and Clarke 2009). This surface pressure difference has been called the equatorial Southern Oscillation index (ESOI) since it is along the equator and, like the SOI, it is a surface atmospheric pressure difference between the eastern and western Pacific. Because of its direct and simple dynamical relationship to the tilt mode, we will use the ESOI (www.cpc.ncep.noaa.gov/data/indices/) as our ENSO index.

Note that negative ESOI corresponds to higher equatorial surface atmospheric pressure in the west, westerly wind anomalies blowing down the zonal pressure gradient, reduced equatorial upwelling and eastward movement of the western equatorial Pacific warm pool, and warmer water in the eastern equatorial Pacific. We note that often used ENSO SST indices like Niño-3.4 and Niño-3 are highly positively correlated with the negative ESOI and the tilt mode at zero lag. Our results do not change if we use these SST indices instead of the negative ESOI.

The WWV has been said to be due to off-equatorial Sverdrup transport associated with Rossby waves (Jin 1997). Clarke et al. (2007) showed how long Rossby wave dynamics give rise to a meridional transport different from that proposed by Sverdrup dynamics, and Bosc and Delcroix (2008) suggested that WWV changes could largely be explained by net convergence and divergence of geostrophic meridional flow. However, Brown and Fedorov (2010) used a comprehensive numerical model to show that both zonal and meridional convergence were crucial to WWV variability. Clarke (2010) also argued for the order-one importance of zonal convergence using an analytical model. He further suggested (see also Fedorov 2010) that the WWV not in phase with the tilt mode, and having a one-signed horizontal structure similar to the second EOF, was crucially dependent on the rapid decrease of Rossby wave speed with increasing latitude. Because of this, long-wave energy generated in the equatorial Pacific during (say) an El Niño does not reach the western boundary at the same time. Reflection from the boundary results in a “nonequilibrium” mode in that it is π/2 out of phase with the wind forcing and the tilt mode. The nonequilibrium mode is of one sign across the Pacific and so the larger its amplitude, the more it contributes to the WWV. The theory suggests that if the wind forcing is closer to the western boundary, then the energy reaching the western boundary at different latitudes will arrive more nearly in phase and the amplitude of the nonequilibrium part of the WWV will be decreased. This idea will be used later in this paper to explain decadal changes in the second EOF mode, that is, the decadal changes in the variability not in equilibrium with the tilt mode and ENSO.

Although the WWV was a good ENSO predictor before the turn of the century (Ji and Leetmaa 1997; Clarke and Van Gorder 2003; McPhaden 2003), after 1998 the lead between the indices decreased (Fig. 2), reducing the utility of the WWV as an ENSO predictor (McPhaden 2012; Horii et al. 2012). Tang and Deng (2010) suggested that low ENSO predictability also occurred before 1980 based on data-assimilated heat content in the upper 250 m of certain regions of the equatorial Pacific. We examined the relationship of anomalous WWV to anomalous upper-ocean heat content before and after 1980 using data from the Simple Ocean Data Assimilation–Parallel Ocean Program (SODA–POP; Carton and Giese 2008) reanalysis. However, our results using these data differed enough from a SODA–POP reanalysis index of upper-ocean heat content that we adopted a different approach.

Fig. 2.

Lead (months) of the WWV over negative ESOI (solid) and the corresponding correlation (dashed). The lead was calculated by correlating the WWV with ESOI at different leads and, month by month, saving the leads at max correlation and the corresponding max correlation. The plot shows these leads and max correlations based on sliding 10-yr segments that are labeled according to the starting year of the segment. For example, the results for 1980 correspond to the 10-yr interval 1980–89.

Fig. 2.

Lead (months) of the WWV over negative ESOI (solid) and the corresponding correlation (dashed). The lead was calculated by correlating the WWV with ESOI at different leads and, month by month, saving the leads at max correlation and the corresponding max correlation. The plot shows these leads and max correlations based on sliding 10-yr segments that are labeled according to the starting year of the segment. For example, the results for 1980 correspond to the 10-yr interval 1980–89.

Specifically, we constructed a WWV proxy using sea level and precipitation data from Kiritimati Island (1°59′N, 157°28′W). The difference between this index and previous WWV/heat content reconstructions (Rajeevan and McPhaden 2004; Tang and Deng 2010) is that it does not depend on sophisticated interpolation schemes or model input. The WWV proxy we constructed is highly correlated with the WWV during their period of overlap, and when correlated with the ESOI has three distinguishable periods: 1955–72, 1973–98, and 1999–2012. The first and last periods have decreased leads compared with the period in between. Further analysis indicated that the decreased WWV lead is related to a marked increase in the tilt mode contribution to the WWV and a marked decrease in second-mode EOF amplitude and its contribution to the WWV. Both pre-1973 and post-1998 periods of reduced lead were characterized by “mean” La Niña–like conditions. During these periods the wind was more westward on average, the eastern edge of the western equatorial Pacific warm pool was displaced westward, and the interannual wind forcing was displaced westward. An explanation for why decreased lead should be associated with interannual wind forcing situated farther to the west can be found in the context of a recent theory by Clarke (2010) and Fedorov (2010).

Our paper is organized as follows. Section 2 explains the basics for the construction of the WWV proxy. Section 3 compares the WWV and WWV proxy indices with the ESOI and establishes that reduced lead also occurred before 1980. Sections 4 and 5 analyze why decadal changes in the lead occurred, and a final section 6 summarizes and discusses the main results.

2. Basic idea and feasibility of the WWV proxy

a. Basic idea

The spatial structure of the tilt and second EOF modes (Fig. 1), given by the first two EOFs of the 20°C isotherm depth, were obtained using data from the Australian Bureau of Meteorology Research Centre (BMRC) ocean analyses (Smith 1995a,b). The data are monthly and span 1980–2010. Figure 1 shows that the tilt mode has minimum variability in the central equatorial Pacific where the second EOF mode is near its maximum. This suggests that the local D20 data, or perhaps a proxy local D20 data in the form of long sea level records from islands in the region, might be used to obtain a long record of the WWV. Kiritimati (formerly Christmas) Island (1°59′N, 157°28′W) is in the region of interest (see Fig. 1) and has a monthly sea level record that begins in 1955.

b. Relationship between WWV anomalies and local Kiritimati D20 anomalies

Monthly D20 anomalies near Kiritimati were well correlated with monthly WWV anomalies. The correlation coefficient for the raw monthly anomalies is r = 0.86; rcrit (95%) = 0.35, confirming that local D20 near Kiritimati Island is an accurate proxy for the WWV. [Correlation significance in this paper will be determined following Ebisuzaki (1997).] The correlation is even higher [r = 0.93, rcrit (95%) = 0.45; see Fig. 3] if the series are low-pass filtered so that only interannual and lower frequencies are present. Here and elsewhere in this paper we used a Trenberth (1984) 11-point monthly symmetric filter as the low-pass filter; it passes more than 80% of the amplitude at periods of 24 months and longer and less than 10% at periods shorter than 8 months.

Fig. 3.

Trenberth-filtered monthly time series of D20 at Kiritimati (thick gray) and WWV (thin black). Each time series was normalized by its std dev. The correlation between the time series is r = 0.93 [rcrit (95%) = 0.45].

Fig. 3.

Trenberth-filtered monthly time series of D20 at Kiritimati (thick gray) and WWV (thin black). Each time series was normalized by its std dev. The correlation between the time series is r = 0.93 [rcrit (95%) = 0.45].

c. D20 and sea level anomalies

It is generally accepted that low-frequency sea level variability is a good proxy for thermocline displacement in the tropical Pacific. This result has a physical basis. If the low-frequency variability is predominantly wind driven, and therefore predominantly confined to the upper ocean above the thermocline, then pressure variations beneath the thermocline are comparatively small. This implies that, in principle, a local increase in sea level should be coincident with an increased depth of the lighter upper-ocean water (as monitored by D20) to keep the local pressure variations beneath the thermocline small. This in turn implies that sea level and D20 should be highly correlated at zero lag. Satellite estimates of sea surface height (SSH) available from Archiving, Validation, and Interpretation of Satellite Oceanographic data (AVISO; www.aviso.oceanobs.com) enable us to check this relationship for the equatorial Pacific (see Fig. 4, top). While the correlation is generally high, there are also regions where the correlation between interannual D20 and SSH is low. Kiritimati, marked K on the map in Fig. 4 (top), is on the edge of one of these regions in the western equatorial Pacific. The correlation at Kiritimati is 0.77, the same correlation as the interannual, in situ, tide gauge sea level at Kiritimati.

Fig. 4.

(top) Correlation between SSH and D20. Prior to the analysis, the data were converted to anomalies and filtered with a Trenberth (1984) filter. Correlation at Kiritimati (indicated by “K”) is 0.77. (middle) OLR std dev (W m−2). (bottom) As in (top), but D20 was replaced by ASSH + BPP [see (1) of the text]. The correlation at K increased to 0.83.

Fig. 4.

(top) Correlation between SSH and D20. Prior to the analysis, the data were converted to anomalies and filtered with a Trenberth (1984) filter. Correlation at Kiritimati (indicated by “K”) is 0.77. (middle) OLR std dev (W m−2). (bottom) As in (top), but D20 was replaced by ASSH + BPP [see (1) of the text]. The correlation at K increased to 0.83.

The large equatorial region of low correlation between interannual SSH and D20 is approximately coincident with the region of large interannual rainfall variability as delineated (see Fig. 4, middle) by minus the outgoing longwave radiation (−OLR), a proxy for deep atmospheric convection. A. J. Clarke and L. Bunge (2014, unpublished manuscript) have proposed that the observed uncorrelated SSH signal is due to the near-surface mixing of heavy rainfall over the western equatorial Pacific warm pool and the pool’s back and forth zonal movement during El Niño/La Niña.

We improved our representation of D20 by using negative OLR as a tropical proxy precipitation (PP) and by writing

 
formula

where A and B are multiplicative constants determined by a least squares fit. We used the interpolated satellite OLR data available online (http://www.esrl.noaa.gov/psd/data/gridded/data.interp_OLR.html). Equivalent results can be obtained using merged precipitation data products [global monthly merged precipitation analyses of the Global Precipitation Climatology Project (GPCP) and the Xie–Arkin Climate Prediction Center (CPC) merged monthly precipitation data].

Figure 4c shows that taking into account the effect of rainfall on SSH using (1) dramatically improves the representation of D20 in the region of large interannual rainfall variability in the western equatorial Pacific. In the heart of the region of interannual rainfall on the equator near the date line, the correlation improves from about 0.38 to 0.89. At Kiritimati, near the edge of the strong rainfall variability, the correlation increase is small, from 0.77 to 0.83. In this location the correction by precipitation affects mostly the lag between the variables; it sets the best correlation to be at zero lag.

The above analysis has shown that a linear combination of satellite-derived SSH and negative OLR can be used to estimate D20, suggesting that longer records of sea level and rainfall can be used to estimate D20 at Kiritimati. The  appendix confirms that this can be done with the aid of island sea level and precipitation records back to 1955. Since D20 anomalies at Kiritimati are well correlated with WWV anomalies, it is possible to construct a Kiritimati proxy WWV index since 1955 (see the  appendix). This index, hereafter called the Kiritimati index, will be used to examine the relationship between WWV and ENSO before 1980.

3. Relationship of the WWV and Kiritimati proxy WWV with the ESOI

In this section we check the correlation and lead between the ENSO index ESOI and the WWV and Kiritimati proxy WWV index, the latter constructed in the previous section. The differences in lead are important because, as mentioned in the introduction, since the beginning of this century, when data are plentiful, the lead between the WWV and the ESOI has decreased (McPhaden 2012; Horii et al. 2012; see also Fig. 2). As noted earlier, this has meant that the WWV has not been a useful El Niño predictor recently and raises questions as to why the lead has decreased and whether the lead has been stable in the past.

Figure 5 is analogous to Fig. 2, except that it includes the Kiritimati index and so shows results from 1955 rather than from 1980. For the period of overlap the Kiritimati index agrees qualitatively with the standard WWV in that both show reduced lead over negative ESOI after 1998. In addition, the Kiritimati index shows relatively smaller leads before the early 1970s, suggesting that the lead between the WWV and the tilt mode is not stable; that not only has the lead decreased in recent years, but it was also small in the past. Tang and Deng (2010) also found decadal changes in lead before 1980 based on upper-ocean heat content of different regions in the equatorial Pacific as a WWV index. In their case, data before 1980 were obtained from an ocean general circulation model with an ensemble Kalman filter of historic SST. However, for the period of overlap from 1955 to 1980, our results differed from theirs; they found good predictability (large leads) since1960, and our results show large leads from 1973. In the next two sections, we explore why the decadal lead changes we observe occur.

Fig. 5.

(a) 10-yr running max correlation between the WWV and the negative ESOI (gray) and the Kiritimati WWV index and the negative ESOI (black). The 10-yr correlation is labeled according to the starting year of the segment. The correlation is a max of all possible lead and lag correlations of the WWV or its Kiritimati proxy with the negative ESOI. (b) Lead at max correlation, a positive lead meaning that the WWV (gray) or the WWV Kiritimati proxy (black) leads the negative ESOI. The different indices were filtered with a Trenberth (1984) filter before the correlations were calculated.

Fig. 5.

(a) 10-yr running max correlation between the WWV and the negative ESOI (gray) and the Kiritimati WWV index and the negative ESOI (black). The 10-yr correlation is labeled according to the starting year of the segment. The correlation is a max of all possible lead and lag correlations of the WWV or its Kiritimati proxy with the negative ESOI. (b) Lead at max correlation, a positive lead meaning that the WWV (gray) or the WWV Kiritimati proxy (black) leads the negative ESOI. The different indices were filtered with a Trenberth (1984) filter before the correlations were calculated.

4. Why does the lead of the WWV over the negative ESOI change?

a. Is a reduction in lead due to a change in ENSO periodicity?

Past theory and observations indicate that the WWV is not in phase with the wind forcing, and the WWV leads the tilt mode by about a quarter of a period (Cane and Zebiak 1985; Zebiak and Cane 1987; Jin 1997; Meinen and McPhaden 2000; Clarke et al. 2007). Therefore, one possible explanation for the changes in the lead of WWV over ENSO would be that ENSO periodicity has changed with time; before 1973 and after 1998 ENSO periodicity is shorter than during 1973–98. We checked this hypothesis by calculating the local wavelet power spectrum (Torrence and Compo 1998) of WWV index and ESOI (not shown) and found no clear changes in periodicity during these time intervals.

b. Is a reduction in lead due to a larger fraction of the WWV being due to the tilt mode?

As discussed in the introduction, another explanation for the reduction in lead takes into account the 5°S–5°N zonal average definition of the WWV and the spatial structures of the tilt and second EOF modes. The second EOF mode is essentially of one sign, while the tilt mode has opposite signs in the eastern and western equatorial Pacific. Therefore, for equal tilt and second-mode amplitudes, the second mode would dominate the contribution to the WWV. However, if the second-mode amplitude is small compared to the tilt mode, the tilt mode could contribute substantially to the WWV since its spatial average, both observationally and theoretically (Clarke 2010; Fedorov 2010), is usually not exactly zero. Since the tilt mode is in phase with negative ESOI, this would result in a decreased lead of WWV over the negative ESOI.

We checked this hypothesis by doing a separate EOF analysis of D20 for decades when the lead was reduced and when it was not. Only since 1980 are the D20 observations adequate, so we limit our analysis to the periods 1980–98 and 1999–2010. Results are very different for each period (Fig. 6), the main differences being 1) the relative amount of explained variance by the first two modes (48% and 39% in the first period in contrast with 66% and 13% for the second period) and 2) a westward shift of the main spatial structures in the second period. We note that the first principal component is highly correlated with negative ESOI in both periods [r = 0.94; rcrit (95%) = 0.55 and r = 0.98; rcrit (95%) = 0.60]. However, while the second principal component is highly correlated with the WWV in the first period [r = 0.98; rcrit (95%) = 0.56], this is not the case for the second period [r = 0.61; rcrit (95%) = 0.49]. The correlation in the second period improves to r = 0.81 [rcrit (95%) = 0.51] if the principal component leads the WWV by 3 months. This suggests that the reduced WWV lead in the second period may be due to an increased contribution to the WWV by the dominant tilt mode during that time since the tilt mode is in phase with negative ESOI.

Fig. 6.

(top left) Tilt (first EOF) and (top right) second EOF modes of the monthly D20 anomalies (m) for the period 1980–98. (middle left and right) As in top left and right, but for 1999–2010. The percentages in the upper left corners are the explained variances for each of the modes. (bottom) The corresponding PCs (blue) have been normalized so that their RMS value is . This means that the spatial EOFs at the top and middle display the amplitude of the monthly D20 anomalies (m). The letter K corresponds to the location Kiritimati Island. The first EOF explains 48% of the variance in the period 1980–98 and 66% variance in the period 1999–2010. The PC in both periods is highly correlated with minus ESOI [r = 0.94; rcrit (95%) = 0.55 and r = 0.98; rcrit (95%) = 0.60]. The second EOF explains 39% of the variance in the period 1980–98 and only 13% variance in the period 1999–2010. The PC is highly correlated with WWV in the first period [r = 0.98; rcrit (95%) = 0.56] but not in the second period [r = 0.61; rcrit (95%) = 0.49]. The correlation increases to r = 0.81 [rcrit (95%) = 0.51] if the PC leads WWV by 3 months. The third modes (not shown) explain 5% and 7% of the variance.

Fig. 6.

(top left) Tilt (first EOF) and (top right) second EOF modes of the monthly D20 anomalies (m) for the period 1980–98. (middle left and right) As in top left and right, but for 1999–2010. The percentages in the upper left corners are the explained variances for each of the modes. (bottom) The corresponding PCs (blue) have been normalized so that their RMS value is . This means that the spatial EOFs at the top and middle display the amplitude of the monthly D20 anomalies (m). The letter K corresponds to the location Kiritimati Island. The first EOF explains 48% of the variance in the period 1980–98 and 66% variance in the period 1999–2010. The PC in both periods is highly correlated with minus ESOI [r = 0.94; rcrit (95%) = 0.55 and r = 0.98; rcrit (95%) = 0.60]. The second EOF explains 39% of the variance in the period 1980–98 and only 13% variance in the period 1999–2010. The PC is highly correlated with WWV in the first period [r = 0.98; rcrit (95%) = 0.56] but not in the second period [r = 0.61; rcrit (95%) = 0.49]. The correlation increases to r = 0.81 [rcrit (95%) = 0.51] if the PC leads WWV by 3 months. The third modes (not shown) explain 5% and 7% of the variance.

We tested this idea by calculating the time series of the tilt and second EOF mode contributions to the WWV in each period. Figure 7 shows that the relative contributions to the WWV in each period are strikingly different. Consistent with our hypothesis, during 1980–98 the tilt mode and second mode are comparable in strength and the WWV is almost entirely due to the second EOF mode. However, during 1999–2010, the tilt mode dominates and both tilt and the second EOF modes make a comparable contribution to WWV. Indeed, if both contributions are taken into account, the correlation with the WWV is r = 0.99 compared to r = 0.61 if only the second EOF mode contributes.

Fig. 7.

WWV contribution by the tilt EOF mode (thin black) and nonequilibrium second EOF mode (thick gray) for the periods 1980–98 and 1999–2010. The WWV has been divided by its equatorial Pacific area 120°E–80°W and 5°N–5°S, so the WWV units are meters. As measured by times the std dev, the amplitude of the WWV due to the tilt mode increases from 0.4 m during 1980–98 to 3.8 m during 1999–2010, but the contribution of the nonequilibrium second EOF mode to the WWV decreases from 8.3 to 3.1 m.

Fig. 7.

WWV contribution by the tilt EOF mode (thin black) and nonequilibrium second EOF mode (thick gray) for the periods 1980–98 and 1999–2010. The WWV has been divided by its equatorial Pacific area 120°E–80°W and 5°N–5°S, so the WWV units are meters. As measured by times the std dev, the amplitude of the WWV due to the tilt mode increases from 0.4 m during 1980–98 to 3.8 m during 1999–2010, but the contribution of the nonequilibrium second EOF mode to the WWV decreases from 8.3 to 3.1 m.

Note that the reduced lead and comparable tilt and second EOF mode contributions to WWV in 1999–2010 are due to both the reduced amplitude of the second EOF mode and the increased contribution to the WWV by the tilt mode (see Fig. 7). As mentioned earlier in the introduction, the tilt mode is due to an approximate balance between the equatorial zonal pressure gradient and zonal wind stress (Kessler 1990; Jin 1997), so changes in zonal structure of the tilt mode and associated changes in WWV contribution should be related to changes in the zonal equatorial wind stress.

c. Changes in wind stress structure and the tilt mode

We examined changes in the zonal wind stress using zonal wind stress data from the European Centre for Medium-Range Weather Forecasts (ECMWF) Ocean Re-Analysis System 3 (ORA-S3) (Balmaseda et al. 2008; available online at http://apdrc.soest.hawaii.edu/datadoc/ecmwf_oras3.php). The data are monthly, have a spatial resolution of 1°, and span from 1959 to 2009. Monthly wind stress anomalies were low-pass filtered with a Trenberth (1984) filter before obtaining the standard deviation plots shown in Fig. 8. Even though the equatorial zonal interannual wind stress forcing is, if anything, greater during 1973–98 than 1999–2009 (cf. Fig. 8, middle and bottom), the tilt mode contribution to the WWV is still enhanced in 1999–2009. The greater contribution is due to the changed structure of the zonal wind stress forcing rather than its amplitude. Specifically, because the interannual wind stress forcing is much farther to the west during 1999–2010, the zonal tilt along the equator is farther to the west then. As a result, the zonal average of the tilt mode will have a greater contribution from the region east of the tilt that is in phase with negative ESOI and D20. Consequently, the tilt mode contribution to the WWV increases when the interannual wind stress forcing is displaced westward. This physics is consistent with the increased WWV tilt mode contribution from essentially zero in 1980–98 to a substantial positive contribution in 1999–2010 (Fig. 7).

Fig. 8.

Std dev of zonal wind stress anomalies for (top) 1959–72, (middle) 1973–98, and (bottom) 1999–2009. The series were filtered with a Trenberth (1984) filter before the std dev were calculated. Units are Pa.

Fig. 8.

Std dev of zonal wind stress anomalies for (top) 1959–72, (middle) 1973–98, and (bottom) 1999–2009. The series were filtered with a Trenberth (1984) filter before the std dev were calculated. Units are Pa.

As documented earlier, it is not just the change in the tilt mode contribution to the WWV that results in a reduced lead of the WWV over the tilt mode and negative ESOI and ENSO indices. It is also that the second EOF mode amplitude is small during 1999–2010 (Fig. 6), and therefore the second mode’s contribution to the WWV during this period decreases. Recent theory (Fedorov 2010; Clarke 2010) enables a physical explanation for the second EOF mode, amplitude reduction when the wind forcing is displaced westward. We will discuss this further in section 5.

Although data are not as readily available before 1980, the WWV proxy predicts a decreased lead during 1959–72, so we checked whether the interannual zonal wind stress was located farther westward in accordance with the more recent period since 1998. Figure 8 indicates that the zonal wind stress anomalies during 1959–72 are indeed, on average, farther westward than those in 1973–98. They are also weaker, and we wondered whether this might be due to error in the data. But the negative ESOI, a measure of the zonal wind stress averaged along the equator, also consistently has lower amplitude then, so we think that the lower-amplitude zonal equatorial wind stress during 1959–72 is realistic.

Westward displacement of anomalous zonal wind forcing (Fig. 8) is usually associated with La Niña conditions and a westward displacement of the eastern edge of the western equatorial Pacific warm pool [see, e.g., Fig. 1 of Shu and Clarke (2002)]. If this were to apply on a decadal time scale, then on average during 1955–72 and 1999–2010 the eastern edge of the western equatorial Pacific warm pool should be displaced westward compared to 1973–98, and the mean conditions during the first and last periods should be more La Niña–like than 1973–98. We checked the decadal changes in the strength of anomalous winds and average position of the eastern edge of the warm pool by calculating the 10-yr running mean of the negative ESOI and the zonal displacement of the equatorial 28.5°C isotherm at the sea surface (see Fig. 9). The results in the three periods are qualitatively consistent with the westward warm pool displacement, reduced lead, and La Niña–like average conditions during the early and more recent periods compared to the middle period.

Fig. 9.

(a) 10-yr running mean of negative ESOI (dashed) and lead at max correlation between Kiritimati WWV index and negative ESOI (solid). A positive lead means that the Kiritimati index leads negative ESOI. The 10-yr segments are labeled according to the starting year of the segment. (b) 10-yr running mean of the zonal displacement of the 28.5°C isotherm, a proxy of the eastern edge of the warm pool (dashed), and lead at max correlation between Kiritimati index and the zonal 28.5°C isotherm displacement (solid). A positive lead means that the Kiritimati WWV index leads the zonal 28.5°C isotherm displacement. The lead calculations were based on the monthly time series filtered with the Trenberth (1984) filter.

Fig. 9.

(a) 10-yr running mean of negative ESOI (dashed) and lead at max correlation between Kiritimati WWV index and negative ESOI (solid). A positive lead means that the Kiritimati index leads negative ESOI. The 10-yr segments are labeled according to the starting year of the segment. (b) 10-yr running mean of the zonal displacement of the 28.5°C isotherm, a proxy of the eastern edge of the warm pool (dashed), and lead at max correlation between Kiritimati index and the zonal 28.5°C isotherm displacement (solid). A positive lead means that the Kiritimati WWV index leads the zonal 28.5°C isotherm displacement. The lead calculations were based on the monthly time series filtered with the Trenberth (1984) filter.

5. Why is the WWV mode amplitude reduced when the zonal equatorial interannual wind stress forcing is displaced westward?

In the previous section, we explained the increased contribution of the tilt mode to the WWV when the wind stress forcing is farther westward, but we did not explain the corresponding reduction in second EOF mode amplitude. While box models and observations (e.g., Meinen and McPhaden 2000, 2001; Clarke et al. 2007; Bosc and Delcroix 2008), conceptual models (e.g., Jin 1997), and general circulation ocean models (e.g., Brown and Fedorov 2010) have all been used to help us understand the role of WWV in ENSO, it is not obvious from these studies whether or not there would be a change in the second EOF mode amplitude if the zonal equatorial interannual wind stress forcing were displaced westward. In view of this uncertainty, it is useful to examine what analytical linear theory from first principles can tell us about the low-frequency equatorial ocean response. A basic understanding of how WWV is generated according to large-scale linear dynamics is foundational to understanding the WWV, a large-scale physical variable.

Fedorov (2010) and Clarke (2010) have both considered such theory for interannual and lower-frequency idealized wind stress forcing and have examined the tilt and WWV. Key to their analyses was the recognition that at low frequencies the sum of the wind-forced long equatorial Kelvin and equatorial Rossby waves (e.g., Gill and Clarke 1974) is in the form of a westward-propagating long Rossby wave having a speed of

 
formula

where β is the northward gradient of the Coriolis parameter f, and c is the long internal gravity wave speed for a given vertical ocean mode (see also Clarke 1983). We emphasize that (2) applies even at the equator. Because of the strong latitudinal speed dependence of γ, when energy reaches the western ocean boundary, a signal generated by the wind will not be in phase in time. Clarke (2010) emphasized (see also Fedorov 2010) that it is this phase difference at the western ocean boundary that gives rise to variability that is not in equilibrium with the wind stress forcing and the negative ESOI. Therefore, the further these waves are generated from the western boundary, the bigger the phase differences will be at that boundary and hence, other things being equal, the bigger the reflected interannual variability that is not in equilibrium with the wind forcing. More comprehensive numerical models are required to obtain quantitative results, but the analytical theory has shown that key components of the nonequilibrium physics are likely to be the strong variations of the Rossby wave speed γ with latitude and the distance of wave generation from the western ocean boundary.

According to the EOF analysis, almost all the low-frequency variability is described by the tilt mode, which is in phase with the negative ESOI and zonal wind forcing, and the nonequilibrium second EOF mode. So, theory and observations are consistent in the sense that the nonequilibrium second EOF mode is smaller in amplitude during 1959–72 and 1999–2010 when the wind forcing is farther westward and therefore closer to the western ocean boundary.

6. Summary and discussion

Analysis of the 20°C isotherm depth suggests that in the central equatorial Pacific, D20 might be used to represent the WWV. Knowing that monthly central equatorial sea level records are available at Kiritimati Island since 1955, and that sea level should be related to D20, we built a WWV proxy based on sea level data from the central equatorial Pacific Island of Kiritimati. The construction of this index also involved precipitation data there since precipitation appears to influence the observed sea level. The motivation for constructing this index was to see if periods of low ENSO predictability, like that in the new millennium, also occurred before 1980. By calculating the lead of maximum correlation between the Kiritimati WWV index and the negative ESOI, we were able to identify roughly three periods, namely, before 1973, 1973–98, and after 1998, with the first and last period showing reduced WWV lead over ENSO compared to the period in between.

An EOF analysis of D20 divided in two periods, 1980–98 and 1999–2010, when adequate subsurface temperature data are available, showed that in the more recent period, the main structures of the tilt and WWV modes have shifted westward and the amplitude of the WWV is dramatically reduced. We were able to demonstrate that this westward shift leads to a marked reduction in second EOF mode amplitude and a marked increase in the tilt mode contribution to the WWV (see Fig. 7 and Table 1). Consequently, the WWV lead over the tilt mode (and the ENSO indices in phase with it) is reduced; the WWV is no longer a good ENSO predictor because it contains not only nonequilibrium mode variability, but also tilt mode variability.

Table 1.

Percentage of explained D20 anomaly variance by each of the first three EOFs for 1980–98 and the reduced lead period 1999–2010.

Percentage of explained D20 anomaly variance by each of the first three EOFs for 1980–98 and the reduced lead period 1999–2010.
Percentage of explained D20 anomaly variance by each of the first three EOFs for 1980–98 and the reduced lead period 1999–2010.

The physical reason for the tilt mode’s increased contribution to the WWV in the more recent period 1999–2010 is that when the zonal wind forcing is displaced westward, so is the tilt (see Fig. 6). Consequently, the zonal average of the tilt and its contribution to the WWV changes (see Fig. 7). The physical reason for the marked reduction in the amplitude of the second EOF mode is suggested by large-scale linear dynamics (Clarke 2010; Fedorov 2010). The more the ENSO wind forcing is displaced westward, the more the large-scale westward-propagating energy is in phase with that ENSO wind forcing when the energy reaches the western ocean boundary and therefore the smaller the amplitude of the nonequilibrium second EOF mode. Our analysis for the period of reduced lead before 1973 is consistent with the more recent reduced lead period 1999–2010 in that both involve a westward displacement of the eastern edge of the western equatorial Pacific warm pool and interannual wind forcing associated with “mean” decadal La Niña–like conditions (Figs. 8 and 9).

Since the WWV index may not always be a good ENSO predictor, can we use the second EOF mode as an ENSO predictor? There are difficulties in doing this. One is that even if the principal component time series of the second EOF mode were the ideal ENSO predictor, since we do not know in advance how the decadal structure of the second EOF mode is changing, we cannot calculate the principal component predictor. Another difficulty is that the EOF analysis may not accurately pick out the ideal ENSO predictor. This is because EOF analysis results in modes that must be uncorrelated with each other in both time and space, and this may not match the physics. The theoretical results of Clarke (2010) suggest that this is indeed the case; the nonequilibrium variability, while uncorrelated with the tilt mode and zonal wind forcing in time, need not be uncorrelated in space. Consequently, the second EOF may not efficiently capture all the coherent nonequilibrium variability that is useful for prediction.

Evidence for this can be found in the separate EOF analysis of the 1980–98 and 1999–2010 periods. In both periods the first EOF mode was the tilt mode with its principal component highly correlated with the negative ESOI, and in both periods the second principal component was maximally correlated with the first at a lead of 7 months. However, the maximum correlation at this lead fell from r = 0.70 [rcrit (95%) = 0.49] for the 1980–98 period to only r = 0.52 [rcrit (95%) = 0.49] for the 1999–2010 period. The lower correlation and therefore decreased prediction capability in the more recent period may have been caused by noise contamination of the low-amplitude second EOF signal, which would have been boosted if more of the nonequilibrium predictor had been found.

Note that the idea that, other things being equal, wind stress forcing farther from the western ocean boundary generates larger-amplitude nonequilibrium mode variability than wind stress forcing closer to the western boundary may be relevant to other discharge–recharge oscillator behavior. Specifically, on an interannual time scale the zonal equatorial wind forcing is typically several thousand kilometers closer to the western ocean boundary than during El Niño [see, e.g., Fig. 1 of Shu and Clarke (2002)]. This suggests that following an El Niño, the nonequilibrium mode is large, while following a La Niña the nonequilibrium mode should be reduced in amplitude, perhaps too small to permit the continuation of the discharge–recharge oscillator. Kessler (2002) found evidence for such a breakdown in his analysis.

A reviewer of our manuscript suggested that we comment on the relationship of our findings to recent work, based largely on SST, suggesting that El Niño has been changing from an eastern equatorial Pacific phenomenon to a central equatorial Pacific phenomenon. For example, Yeh et al. (2009) suggest that central equatorial Pacific El Niños have been more frequent since 1990. This does not correspond to our decadal changes (smaller lead in 1955–72 and after 1998 than in 1973–98) so it is not clear that these phenomena are strongly connected. A thorough investigation would be necessary to discuss this connection and, in order to keep our results here as clear and direct as possible, we have chosen not to pursue this possible connection.

Copies of the monthly anomalous Kiritimati WWV index (January 1955–2012) are available from our websites (http://ocean.fsu.edu/~bunge/ or http://eoas.fsu.edu/people/faculty/dr-allan-j-clarke).

Acknowledgments

The altimeter products were produced by SSALTO/DUACS and distributed by AVISO, with support from CNES (http://www.aviso.oceanobs.com/duacs/). Wind velocity data reanalysis ECMWF ORA-S3 were made available by the Asia–Pacific Data-Research Center. Interpolated OLR data were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, from their website (http://www.esrl.noaa.gov/psd/). We thank Neville Smith and BMRC for the D20 data, the TAO Project Office of NOAA/PMEL for the WWV index, and the NOAA Climate Prediction Center for the ESOI. We gratefully acknowledge the National Science Foundation and Naval Research Laboratory for financial support (Grants OCE-1155257 and N00173-11-2-C901).

APPENDIX

Construction of a Proxy WWV Index Based on Kiritimati Sea Level and Precipitation

To obtain monthly WWV anomalies from 1955, we need to obtain continuous monthly records of sea level and precipitation at Kiritimati. The monthly Kiritimati time series have gaps, so we had to rely on data from nearby islands or satellite data to fill them in. In this appendix we explain how this was done.

a. Reconstructing the precipitation time series for Kiritimati

The precipitation record at Kiritimati (available at ftp://ftp.ncdc.noaa.gov/pub/data/ghcn/v2/) begins in 1921 and ends in 2000. Because there are large gaps toward the end of the series and because the series ends in 2000, we patched the gaps and ended the series with interpolated OLR data (Liebmann and Smith 1996). Except for one gap in 1978, the OLR data are available from 1974. For the period of overlap, the correlation between the raw monthly Kiritimati anomalous rainfall and the raw negative OLR anomalies over Kiritimati Island is r = 0.71 with rcrit (95%) = 0.25. The interannual correlation is likely higher than r = 0.71 because there appears to be considerable high-frequency noise.

To construct the single long precipitation record, the series were first normalized by the standard deviation of the points shared by both records. When both normalized records were available, they were averaged. To recover precipitation units, the resultant time series was then multiplied by the precipitation standard deviation.

Five gaps still remained in the series; three of them were 3 months or less, one was 5 months, and the largest was 8 months. To fill those gaps we used rainfall data from Tabuaeran Island (3°52′N, 159°22′W), the closest island to Kiritimati. Correlation between the monthly anomaly Tabuaeran and Kiritimati Island time series since 1950 is 0.54 [rcrit (95%) = 0.18].

b. Reconstructing the sea level time series for Kiritimati

The monthly sea level record in Kiritimati starts in 1955 and ends in 2003. The record is divided into two parts; one from 1955 to 1972 and the other from 1974 to 2003, both parts with different and unknown reference levels. Monthly anomalies were obtained by removing a separate mean for each part, then calculating a common annual cycle and removing it from the entire time series. We are aware that this simple procedure may introduce an error into decadal and longer variability. However, we found that the resultant anomalous time series, divided by its standard deviation, before 1972 and after 1974 well matched equivalent, equatorial, sea level anomaly time series normalized by their respective standard deviations at the nearby Tabuaeran and Abariringa Islands (see Fig. 1 for island locations and Fig. A1 showing the match).

Fig. A1.

Sea level at Kiritimati (solid black line), Abariringa (thick gray line), and Tabuaeran (dashed black line) Islands. The Abariringa and Tabuaeran series were divided by their std dev (calculated from the points they shared in common with the Kiritimati series) and then multiplied by the std dev of the Kiritimati record, calculated separately in each case from the points shared with the Abariringa and Tabuaeran series, respectively.

Fig. A1.

Sea level at Kiritimati (solid black line), Abariringa (thick gray line), and Tabuaeran (dashed black line) Islands. The Abariringa and Tabuaeran series were divided by their std dev (calculated from the points they shared in common with the Kiritimati series) and then multiplied by the std dev of the Kiritimati record, calculated separately in each case from the points shared with the Abariringa and Tabuaeran series, respectively.

In addition to adjusting for reference level, we also must fill in the gaps in the sea level record and extend it to the present. Besides the large gap of 23 months between March 1972 and January 1974 discussed above, there is also a large gap of 19 months between December 1963 and June 1964. The sea level records at the nearby Tabuaeran and Abariringa Islands (Fig. A1) were used to fill in these large gaps. The sea level record from Tabuaeran, the nearest island to Kiritimati, has a correlation of 0.87 [rcrit (95%) = 0.41] with the record in Kiritimati (Fig. A1). However, the Tabuaeran record is of limited utility since it is short, starting in April 1973 and ending in December 1989, and it also does not completely cover the 23-month gap discussed above from March 1972 to January 1974. The sea level record at Abariringa Island, the next nearest island with a long record, has a slightly lower correlation of 0.77 [rcrit (95%) = 0.32] and will be used.

To fill in gaps in the Kiritimati sea level record before 1992 we used monthly sea level anomaly data from Tabuaeran Island and, when that was not available, monthly sea level data from Abariringa Island. After October 1992, we filled in gaps using monthly anomalous AVISO satellite SSH. The correlation between the overlapping monthly anomaly Kiritimati sea level and SSH records was 0.97 [rcrit (95%) = 0.53]. The proxy records were inserted into the Kiritimati record in each case by first dividing by the standard deviation of the proxy record, calculated only for the points the proxy record and Kiritimati records had in common, then multiplying the gap-filling points by the standard deviation of the Kiritimati record, again estimated from the points the proxy and Kiritimati records had in common (Fig. A1). When this process was completed, the resulting monthly anomaly record had only two gaps, one of 1 month and the other of 2 months. These gaps were filled by linear interpolation.

c. Finding the A and B coefficients in (1)

To obtain our estimate of monthly anomaly D20 at Kiritimati back to 1955, we used the observed anomalous monthly D20 grid point near Kiritimati since 1980 and the overlapping (in time) monthly anomalous Kiritimati precipitation and sea level records, determined in the appendix sections above, to find A and B in (1) from a least squares fit. We obtained A = 164.4 and B = 5.8 months. Since our constructed sea level and precipitation records are available from January 1955, we have a way to estimate monthly D20 at Kiritimati and WWV back till then. For the period of overlap our estimate from (1) was well correlated with the observed D20 gridpoint data {r = 0.83 [rcrit (95%) = 0.31]} and with the WWV {r = 0.79 [rcrit (95%) = 0.33]}. If we filter the data with the Trenberth filter so that only interannual and lower frequencies are present, the correlations improve to r = 0.86 [rcrit (95%) = 0.44] in the D20 case and r = 0.85 [rcrit (95%) = 0.43] for the WWV index case.

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