a. Change in ENSO amplitude

The ENSO amplitude has been changing in the past century as shown in Fig. 1a. The standard deviation (SD) of Niño-3 SST anomaly is around 0.7°C before 1900. It reaches the minimum (0.6°C) during the 1940s and then increases to around 0.9°C during the past two decades, showing a nearly 50% increase in the ENSO variability. This increase in ENSO amplitude is significant and passes the Student’s t test of 95% significant level, although it does not appear as a smooth increase and exhibits some decadal variability. It is noticed that there is a suspicious SD “spike” near year 2000 (Fig. 1a). This is influenced by the strong El Niño event in 1997/98, because the SD is calculated with an 11-yr sliding window. We also calculated the SD with 21- and 31-yr sliding window (figure not shown). The rising in ENSO amplitude after 1940s is remarkable and is insensitive to the width of the sliding window. The increasing interannual variabilities can be also seen in the mixed layer depth, the thermocline temperature, and the upper-ocean heat content in JEDAC-XBT data (Fig. 1a).

b. Changes in mean climate

Consistent with the enhancing ENSO amplitude since 1940s, the Pacific equatorial thermocline also shows a strengthening trend (Fig. 1b). The warming rate of tropical SST in the past 50 yr is generally over 1°C century⁻¹; it reaches 1.5°C century⁻¹ in the eastern equatorial Pacific. This big surface warming, however, does not appear to penetrate downward into the thermocline, where a cooling trend occurs instead. The cooling rate in the western equatorial Pacific reaches as much as −2°C century⁻¹. Although the cooling rate in the eastern thermocline is not as significant as that in the west, the overall vertical temperature gradient is enhanced substantially during the past 50 yr. In contrast to the thermocline strength, the observation shows a clear reduction in the mean depth of equatorial thermocline (Z_tc) during the same period (Fig. 1c). The shoaling trend of Z_tc is not uniform along the equator. It is more notable in the western equatorial Pacific than in the east. This pattern also suggests a flattening in the east–west tilt of the equatorial Pacific thermocline.

The strengthened thermocline appears to be responsible for the shift in ENSO amplitude as suggested by many coupled model studies (e.g., Meehl et al. 2001; Collins 2000; Timmermann et al. 1999). The shoaling of Z_tc is likely to increase the SST sensitivity to the thermocline, especially in the Niño-3 region (Philip and van Oldenborgh 2006). A shallower Z_tc in the equatorial Pacific suggests that the local mode or SST mode, resulting from local SST–wind interaction in the central-east Pacific, may play a relatively important role in generating ENSO variability (Fedorov and Philander 2001; Guilyardi 2006). This local mode is described as the anomalous upwelling of the mean temperature gradient (−w′T_z) in the SST equation. A shallower Z_tc means the thermocline water would be easier to affect the SST through the anomalous upwelling (w′). A stronger thermocline (T_z) means a bigger impact on SST. Here, the w′ is closely related to the local wind variability and bridges the mean thermocline with the SST variability. The observation shows that the mean SST increases the most in the Niño-3 region (Fig. 1b), where an increasing response of winds to SST variability is expected (Philip and van Oldenborgh 2006). Therefore, the shallower and stronger thermocline could result in an enhanced ENSO variability because of the positive feedback among the wind variability, anomalous upwelling, and SST variability in the central-east Pacific. This speculative discussion will be examined thoroughly in the next section through term balance analyses on coupled model experiments.

The shoaling and flattening of the equatorial thermocline can be attributed to the weakened trade wind, and thus the weakening of tropical Walker circulation (Vecchi et al. 2006; Vecchi and Soden 2007). Coupled models’ studies have suggested that these changes in atmosphere in the past century may result from anthropogenic forcing (Vecchi et al. 2006). A consequence of the weakened trade wind is to stabilize the tropical atmosphere–ocean coupling system (Vecchi et al. 2006; Meehl et al. 2001; Neelin et al. 1992; Clarke and Lebedev 1996), which would result in the suppression of the ENSO variability. Many sensitivity studies of linear and coupled models (Fedorov and Philander 2001; Meehl et al. 2001) have shown the similar conclusions.

However, the enhanced ENSO variability suggests that the stabilizing effect of atmosphere does not seem to compensate the destabilizing effect of the enhanced thermocline completely in the past half century. We therefore speculate that the ocean, particularly the subsurface ocean, may play a more important role in the long-term changes of ENSO properties. Some studies have shown a poor relationship between the shift in ENSO activity and the mean climate change during the last millennium (Cobb et al. 2003). Yet the mean climate change in the past century is so obvious that its impact on the ENSO behaviors should be paid attention sufficiently. The mean climate change in the ocean may even overwhelm the influence of atmosphere change, as implied in the observations.

The ENSO behavior during the transient warming period, like the twentieth century, does not imply that it will behave the same in a warmed climate. Although the mean atmosphere climate during the transient period and equilibrium period could be very similar because of quick response of atmosphere to external forcings, the mean ocean climate could be very different because of the huge thermal inertia of the ocean. This could result in a different ENSO in a warmed climate. Our questions are: would the ENSO be changing in the whole global warming period? If so, how would the ENSO change? What does the role of the ocean play in the ENSO change? Next we will check the ENSO behavior in our coupled model experiments.

a. Changes in mean climate and ENSO amplitude

The equatorial SST increases almost linearly under the forcing of the transient increasing of CO₂ (Fig. 2a) as expected in most coupled models. At year 70 when the CO₂ concentration is doubled, the equatorial SST has been warmed by about 1°C. Afterward, under the forcing of fixed double CO₂, the SST changes very slowly and is only warmed by about 0.4°C from year 71 to year 220. In contrast to the SST, the equatorial thermocline is only warmed by about 0.3°C during the transient forcing period (Fig. 2b). This warming rate is obviously much smaller than that in SST. However, during the equilibrium forcing period, the warming rate in the thermocline is, in turn, much larger than that in SST. The thermocline temperature has been warmed by about 0.8°C from year 71 to 220. This situation suggests that the ocean climate change will persist for a much longer time than the atmosphere, even after the external forcings stop changing. It further implies that the ocean–atmosphere coupled variabilities, which are closely related to the mean states of both the atmosphere and ocean, may behave differently during the different stages of climate change.

The coupled tropical variabilities, for example, the ENSO variability, do show big variations during the whole global warming period (Fig. 3). Compared with the control run, the time evolution of the tropical temperature SD shows a much bigger oscillation (An et al. 2008). During the transient period, the Niño-3 SST SD appears to increase with time (Fig. 3a). The mean SST SD averaged over years 50–70 is around 0.64°C, showing a near 16% increase in amplitude when compared to the mean variability in control run (0.55°C). During the equilibrium period, the Niño-3 SST variability is, in turn, reduced significantly. The mean SD averaged over the last 50 yr (years 170–220) is about 0.53°C, showing a 4% reduction when compared to the control run, or a 17% reduction when compared to that in the transient period (0.64°C). The same situation also occurs in the equatorial thermocline, such as the temperature variability at the mean thermocline depth Z_tc (Fig. 3b), as well as the thermocline variability (Fig. 3c) defined as the SD of the thermocline depth anomaly (Z_tc′). They both show a modest increase in the transient stage and a clear decrease in the equilibrium stage when compared to those in the control run.

The turnaround in the interannual variability, enhancing during the transient stage and then weakening during the stable stage, occurs almost in the entire tropical Pacific. In normal conditions, the ENSO variability shows bigger amplitude in the eastern equatorial Pacific for both the SST and thermocline in our control run (Figs. 4a,b). During the transient stage of global warming, the SST variability is enhanced significantly in the tropics, despite the nonuniformity in the spatial pattern (Fig. 4c). The thermocline depth variability shows a modest increase in the eastern and southern Pacific and a weak decrease in the western equatorial Pacific (Fig. 4d). During the equilibrium stage the remarkable decrease in ENSO variability occurs in the thermocline (Fig. 4f), showing a 20% reduction relative to control run. The SST variability also shows a 5%–10% decrease in the eastern Pacific (Fig. 4e).

The spatial pattern of ENSO mode simulated in our model appears to be unaffected, despite the notable changes in ENSO time-scale variability. The ENSO mode is defined as the first EOF mode of the tropical SST anomaly within 25° of the equator, which accounts for about 18% of the total SST variance (Fig. 5a) and has a principal period of around 30 months in the control run (Fig. 5b). The ENSO mode has the maximum amplitude located in the central equatorial Pacific (Fig. 5a), which is partly due to the overwestward spread of the equatorial cold tongue in our coupled model. This pattern does not change in 2CO2T and 2CO2E (figure not shown). The first EOF mode in Fig. 5a can be thought as the “real” ENSO mode, while the SD of tropical SST in Fig. 4a can be thought of as ENSO time-scale variability. These two are not exactly the same. The latter is clearly changed in the CO₂ experiments as shown in Figs. 4c,e, which may result from the changes in the higher-order modes of the tropical SST. These higher-order modes still have time scales within 5–85 months.

The power spectrum of the time series of the first ENSO mode (Fig. 5b) is also checked. The principal period of 30 months in control run does not change in 2CO2T, but it seems to shift toward both the longer and shorter period in 2CO2E. Moreover, in 2CO2T, besides the 30-month period, there is another significant peak at about 20 months. In addition, the global warming seems to favor more high-frequency variabilities with periods shorter than 20 months. Figure 5b also shows that the power of ENSO mode in 2CO2E is less than that in 2CO2T and control, consistent with the discussions in Figs. 3 and 4. The frequency change itself in response to global warming is a very complex problem. It is unlikely to elucidate this problem in our current work. We will study this question with more ensemble experiments and more coupled models in the near future.

In general, our coupled model experiments show a big variation in ENSO amplitude during the entire global warming period. Previous studies have established a robust connection between the ENSO properties and the tropical mean ocean–atmosphere climate, particularly between the ENSO amplitude and the equatorial thermocline strength as shown in the observations (Fig. 1). The model experiments show a strengthened vertical stratification along the equator in 2CO2T (Fig. 6c) consistent with the enhanced ENSO amplitude. It is seen that, in this stage, the warming effect of the atmosphere forcing has very limited downward penetration. Most of the warming is confined in the upper thermocline above 200-m depth. The temperature in the lower thermocline is only slightly increased. There is even a small cooling at 200–300 m in the western Pacific. After another 150-yr evolution, the lower thermocline finally warms up and the temperature rises by 0.9°C (Fig. 6d). During the equilibrium stage, the sea surface is only warmed by 0.2°C (Figs. 6a,b), while the lower thermocline is warmed by 0.7°C. Therefore, the equatorial vertical stratification is, in turn, weakened considerably, which is consistent with the weakened ENSO amplitude in this stage.

The cooling or minimum warming in the western thermocline (Figs. 6c,d), which is also clear in the observation (Fig. 1b), may result from both the equatorial and off-equatorial processes. The weakened trade winds cause the flattening of the east–west thermocline slope, resulting in an upward movement of the deeper colder water. This may involve equatorial wave processes that span the width of the basin. In the global warming situation, there could also generate cold Rossby waves in the off equator, propagating westward and southward along the mean potential vorticity contours and cooling the western equatorial thermocline (Yang et al. 2005). Other coupled models forced by increasing GHGs have also shown the cooling thermocline in the equator (Timmermann et al. 1999; Zhang et al. 2008).

The tropical atmosphere in our experiments experiences reductions in the east–west sea level pressure (SLP) gradient and equatorial trade winds (Fig. 7). This suggests a slowdown of Walker circulation during the entire global warming period, similar to that in observation and other models (Vecchi et al. 2006; Vecchi and Soden 2007). The pattern in Fig. 7b is very similar to that in Fig. 7c, except small differences in the magnitude of SLP and wind anomalies. This is understandable because the atmosphere and the SST change swiftly in response to the CO₂ forcing so that they can reach dynamical equilibrium in a short time. These mean climate change in atmosphere are thought as to suppress the ENSO variability in many studies. Therefore, the turnaround of the ENSO amplitude can be due to the delayed response of the ocean to global warming (An et al. 2008). This increases the complexity and uncertainty when assessing the ENSO behaviors in global climate change.

The above descriptions on the ENSO amplitude change in different global warming stages are highly qualitative. Next we will investigate the mechanisms and the dynamic processes through term balance analyses on the equation of temperature variance.

a. Term balance analyses for control run

To identify the dynamic processes that are responsible for the temperature change, the terms in the temperature equation are carefully examined (see the appendix). The temperature tendency is controlled by advection terms, external forcing terms, and damping terms. For the equilibrium state, the mean temperature change is nearly zero, so the terms above are well balanced. For the equatorial Pacific surface, the downward heating of the surface net heat flux (Q_F > 0) is mainly balanced by the cooling effects of poleward heat transport of the Ekman flow (−T_y < 0) and the Ekman upwelling (−wT_z < 0). For the subsurface ocean, the temperature is maintained by the equatorward heat transport of the geostrophic flow (−T_y > 0), the Ekman upwelling (−wT_z < 0), and the vertical temperature diffusion (A_υT_zz < 0). These have been discussed in Yang and Liu (2005).

From the temperature anomaly equation (A3), the relative importance of the terms on the right side of (A3) can be identified in principle. However, since all the anomalous terms in (A3) oscillate around their own mean values over the time, the time means of these terms tend to be zero. Thus in practice it is inconvenient to assess the time-averaged contributions of the terms to the amplitude of temperature anomaly. Here we derive the equation for temperature variance (A7), in which the anomalous terms are nonlinear so that their time means are nonzero. Based on (A7), the contributions of each term to the temperature amplitude can be explicitly estimated. The dominant mechanisms of the temperature amplitude change can thus be easily pinpointed.

Different from the processes controlling the mean temperature, the temperature amplitude change is mainly determined by the balance between the vertical temperature advection, the vertical temperature diffusion, as well as the meridional advection and diffusion terms. Here we first discuss the results from the control run. The most important driving mechanism for the amplitude of Niño-3 temperature anomaly is the vertical advection term [−T ′(w′T_z + wT ′_z)] (Fig. 8a). The largest damping effect comes from the vertical temperature diffusion [A_υT ′T ′_zz]. The secondary damping processes are the meridional advection term [−T ′(υ′T_y + T ′_y)] and diffusion term [A_hT ′T ′_yy]. The zonal advection and diffusion terms are very small and negligible. For a steady state without amplitude change, these terms have to be balanced. Here we would like to emphasize that the terms in Fig. 8 are calculated at the time mean thermocline depth Z_tc. Before the calculation, all variables, including the derived quantity like vertical temperature gradient T_z, have been interpolated to the depth Z_tc. The term balance at Z_tc can also represent the situation above the thermocline, except the thin sea surface level. The vertical advection term is underestimated on the sea surface (figure not shown), because both the vertical movement w and the vertical temperature gradient T_z are very small at the sea surface. The small w is resulted from the rigid-lid approximation in the ocean model. The T_z is small because, technically, it is calculated within the mixed layer. But physically both the T_z and upwelling w are important to the SST, at least in the eastern equatorial Pacific.

The above analyses are valid for the most of the equatorial Pacific. An exception occurs in the warm pool region, in which the vertical term is very small while the meridional advection term dominates the amplitude change of temperature anomaly (Fig. 8c), because both the upwelling and temperature stratification here is much weaker than in the east. However, the vertical advection term is the most important destabilizing factor to the changes in the amplitude of the temperature variability for the equatorial Pacific Ocean on the whole (Figs. 8a,b,d).

Here let’s focus on the dynamic effect of the vertical advection term on the amplitude of interannual variability in the equatorial Pacific. This term can be further decomposed into three subterms: 1) the local term which depicts the anomalous upwelling of the mean temperature [−T ′w′T_z] (see the appendix; Fedorov and Philander 2001; Guilyardi 2006), 2) the remote term which represents the mean upwelling of the anomalous temperature gradient [−T ′wT ′_z] (Fedorov and Philander 2001), and 3) the nonlinear term [−T ′w′T ′_z]. These subterms are closely related to the vertical temperature gradient.

For the FOAM control run, in the Niño-3 region the local term dominates over the remote term and plays a more important role in the amplitude of the temperature variability. Figure 9a clearly shows that the time evolution of the local term (gray line) follows tightly with that of the total vertical advection term (black). It acts as a positive factor that favors an increase in temperature variability around the thermocline. The remote term (dashed black) varies in the vicinity of zero and its time mean value is slightly less than zero, which acts as a weak damping effect. The nonlinear term (dashed gray), as expected, is negligible.

The local term is proportional to the mean vertical temperature gradient (T_z), where the latter plays as a “background” of the perturbation quantities such like the anomalous upwelling (w′) and temperature anomaly (T ′). Figure 9d shows that, although the w′ and T ′ themselves oscillate around zero over the time, the product of w′ and T ′ (−w′T ′, thick black), after a low-pass filtering, is well elevated from the zero. Therefore, besides the background temperature gradient (T_z), the −w′T ′ is also crucial to the sign and the final magnitude of the local term. Here the positive −w′T ′ in Niño-3 region can be understood as follows. Under the background of positive temperature gradient (T_z > 0), an anomalous upwelling (w′ > 0) can bring cold water at depth upward, and cause a negative temperature anomaly tendency (T ′_t < 0) based on Eq. (A3). For an initially cold water (T ′ < 0), an anomalous upwelling (w′ > 0) can enhance the initial anomaly so that the −w′T ′ > 0. An anomalous downwelling (w′ < 0) can damp the initial cold anomaly quickly and finally produce a warm anomaly (T ′ > 0). The further check on the relationship between w′ and T ′ confirms that they are negatively correlated (Fig. 10, black). The peak correlation occurs when T ′ lags w′ by 3 months, with the maximum correlation of about −0.5. This suggests that the upwelling (downwelling) can cause cold (warm) anomaly. Although there is a time lag between w′ and T ′, the low-pass filtered −w′T ′ is generally above the zero. The −w′T ′ can be somehow thought as the vertical heat flux and should also correlate positively with the mean temperature gradient. The local upwelling w′ is closely related to the wind-driven Ekman pumping w′_e, that is, the zonal wind stress anomaly τ′_x. Figure 10 shows that there is no time lag between w′ and w′_e (dashed black line). The maximum positive correlation is about 0.4.

The remote term is determined by the product of the mean upwelling (w), temperature anomaly (T ′) and the anomalous vertical temperature gradient (T ′_z). Although the w is much larger than the w′ in the local term, the T ′_z is much smaller than the T_z in the local term. The ratios of w′/w and T_z/T ′_z are usually around 10⁻² and 10², respectively. The remote term and the local term could be comparable if the T_z is not that strong. In our experiments, the mean depth of the equatorial thermocline is relatively shallow, particularly in the eastern Pacific (dashed thick line in Fig. 6c). This is usually associated with a strong T_z, and favors an easy and quick interaction between the local surface air and the thermocline water. The equatorial unstable modes can be thus thought as the local modes or the SST mode that have been discussed in Fedorov and Philander (2001; i.e., the modes in the vicinity of point E in their Fig. 4). The local term, or the local air–sea coupling plays a dominant role in the temperature variation. This can also explain why the T ′ and w′ in Niño-3 region tends to be out of phase despite the time lag between them (Figs. 9d and 10). A deep thermocline, however, means that the T_z near the surface would be very weak so that the remote term wT ′_z has to be dominant (Fedorov and Philander 2001).

b. Changes in term balance under global warming

The enhanced ENSO variability during the transient period of global warming results from the bigger local term. Figures 9b and 11a explicitly show the elevated vertical advection term and its local component. Compared with the mean value (0.43) in the control run, the local term is increased by 21% to 0.52 in 2CO2T (gray line in Fig. 9b). The contributions to the increased local term come from the mean vertical temperature gradient T_z, which is enhanced by 7% to 0.61 in 2CO2T (Figs. 9e and 11a) from 0.57 in control run (Fig. 9d), as well as the “virtual vertical heat flux” −w′T ′, which is increased by 17% to 0.21 in 2CO2T from 0.18 in control run. (For simplicity the values discussed here are the plotted values in Fig. 9. The real values should be multiplied by certain constants. See the Fig. 9 caption for the details.) It is noticed that the contribution of −w′T ′ to the increased local term is clearly larger than that of T_z. This does not have to impair the critical role of T_z in ENSO amplitude change. Because the T_z can be viewed as the background state of −w′T ′, and, the magnitude of −w′T ′ should be positively correlated to the strength of T_z.

The reduced ENSO amplitude during the equilibrium stage is associated with the reduced local term (Fig. 9c). The mean values of the local term, T_z and −w′T ′ over the last 50 yr of 2CO2E are 0.40, 0.57, and 0.17 (Fig. 9f), which are reduced by 23%, 7%, and 19%, respectively, when compared with those in 2CO2T. It is noticed that these terms change little when compared with the control run (Fig. 11a). It is unnecessary that they should be smaller than those in the control run. In this study we focus on the different behaviors of ENSO in different stages of global warming. The ocean in the 2CO2E does act differently from that in the 2CO2T.

The remote term exerts a weak damping effect on the ENSO amplitude. It is much smaller than the local term (Figs. 9a–c). Consistent with the changes in mean trade wind (Fig. 7), the mean upwelling w in the remote term is reduced to 0.38 in the 2CO2T, and further to 0.35 in the 2CO2E (Figs. 9g–i and 11b) from 0.40 in the control run. The weak mean upwelling implies a weak interaction between the thermocline and the surface. The −T ′T ′_z in the remote term, which can be rewritten as −(T ′²/2)_z, represents the vertical gradient of the temperature variability. Usually the (T ′²)_z > 0 because the temperature variability in the shallower layer is larger than that in the deeper layer (Figs. 3a,b), so −(T ′²/2)_z < 0 as shown in Figs. 9g–i. Here it is plausible that the (T ′²)_z determines the sign and size of the remote term. However, under the background of weak mean upwelling, the weak interaction between the thermocline and the surface would result in a large vertical gradient of the temperature variability (T ′²)_z. The (T ′²)_z appears to be determined by and very sensitive to the w. Therefore, although the weaker w tends to reduce the damping effect of the remote term and favors an increase in the temperature variability, the much stronger (T ′²)_z can ultimately result in the stronger damping, where the background w determines the magnitude of (T ′²)_z. It is clearly seen that in Fig. 11b the w is reduced by 5% in the 2CO2T and 13% in the 2CO2E, while the magnitude of −T ′T ′_z is increased by 23% in the 2CO2T and 54% in the 2CO2E, when compared with the control run. This increases the magnitude of remote term by 13% in the 2CO2T and 50% in the 2CO2E. Here the physical process of the remote term can be understood as that the mean upwelling brings the low variability water upward and thus causes a reduction in the magnitude of surface variability. In this sense the remote term tends to always play a damping role in the surface variabilities. Since the mean upwelling w is closely related to the large-scale atmosphere, for instance, the mean surface trade winds and the Walker circulation, the remote term, to some extent, manifests the effect of atmosphere change on the temperature variability in the tropics.

The relative changes of the vertical temperature advection and its subterms in global warming experiments are summarized in Fig. 11. In general, the enhanced ENSO variability in the 2CO2T results from the strengthened equatorial thermocline because of the sluggish subsurface ocean. This overwhelms the damping effect of the weakened equatorial trade winds or the mean upwelling. The turnaround in ENSO variability in the 2CO2E occurs because of the turnaround of the T_z and the bigger damping effect from the remote term as well. The ocean virtually plays a deterministic role in the ENSO amplitude in the whole global warming period.

The ocean role can be further understood from the sensitivity analyses on the tropical air–sea coupling (Fig. 12). The atmospheric sensitivity—the sensitivity of central equatorial zonal wind stress anomalies to the Niño-3 SST anomalies in the 2CO2T—changes little when compared with the control run (gray and dashed black lines in Fig. 12a). The atmospheric sensitivity in the 2CO2E over the last 50 yr even shows a decreasing trend (black line in Fig. 12a). Despite its decadal variation the mean value over the last 50 yr is very close to the control run. The oceanic sensitivity—the sensitivity of Niño-3 SST anomalies to the central equatorial zonal wind stress anomalies—increases in the 2CO2T (dashed black line in Fig. 12b). During the equilibrium period of global warming, the oceanic sensitivity is again reduced over the last 50 yr. These are well consistent with our conclusion that the ocean dynamics arising from the changing thermocline is responsible for the enhanced ENSO variability and its turnaround afterward. To further check the coupling between the surface SST and the thermocline, the sensitivity of Niño-3 SST to thermocline temperature anomalies and the contrary are calculated. The thermocline sensitivity to the Niño-3 SST changes little during the whole global warming period (dashed black and black lines in Fig. 12c). However, as expected, the sensitivity of Niño-3 SST to the thermocline temperature is enhanced in the 2CO2T and 2CO2E (Fig. 12d). These further highlight the deterministic role of the thermocline dynamics on the surface variability in the Niño-3 region. These sensitivities are calculated based on the zero lag correlation among SST, wind stress, and thermocline temperature. We have also calculated the sensitivities based on nonzero lag correlation (figure not shown). The largest sensitivities are found at the zero lag, and the sensitivities will reduce substantially and even become negative for nonzero lag correlations among them.

The discussions above explicitly relate the vertical temperature gradient to the amplitude of the ENSO variability, in which we highlight the dominant role of the local term. However, the vertical temperature gradient in the equator does not have to be completely locally determined. It has to involve the meridional overturning circulation. As noted in the discussions in Liu and Yang (2003) and Yang and Liu (2005), the tropical–extratropical interaction affects the equatorial vertical thermocline structure to a great extent, particularly for the subsurface ocean where the mean advection mechanism plays an important role.