1. Introduction
Although internal atmospheric variability has been proposed as a major source of the stochastic forcing that drives El Niño–Southern Oscillation (ENSO; see Lau 1985; Vallis 1988; Penland and Sardeshmukh 1995; Thompson and Battisti 2000; Penland et al. 2000; Philander and Fedorov 2003; Flügel et al. 2004), there is little coherent understanding of the underlying physical processes that link internal atmospheric variability to ENSO. Recent studies have linked the onset of ENSO to extratropical atmospheric variability (Vimont et al. 2003; Pierce et al. 2001), which is, to a large extent, driven by the internal dynamics of atmosphere (Saravanan 1998; Kushnir et al. 2002). However, the separation of internal atmospheric variability from external components, both based on observational data and in the global climate model, remains a difficult and controversial task. Therefore, further studies in making use of coupled GCMs to study the role of internal atmospheric variability of ENSO are needed. Recently, Chang et al. (2007) introduced a noise-filtering technique to a newly developed coupled global climate model and demonstrated the effectiveness of the filter in reducing the influence of atmospheric internal variability on ENSO variability. This paper extends Chang et al. (2007) by explaining the noise-filtering technique in more detail and by further exploring the role of atmospheric internal variability in maintaining the Pacific meridional mode (MM) variability, and consequently ENSO.
This paper covers two interrelated topics. The first is a discussion of a “noise filter,” which is constructed from a set of signal-to-noise optimals (Venzke et al. 1999), ordered by the ratio of externally forced (e.g., sea surface temperatures) variability to internal atmospheric variability. The second topic is the utilization of the noise filter in the coupled model to remove the internal atmospheric variability, so that its effect on ENSO can be further quantified. We also study the different impacts on ENSO from the different components (heat flux and wind stress) of the internal atmospheric variability.
The approach used here assumes that atmospheric variability can be divided into the following two parts: an internal part resulting from intrinsic atmospheric dynamics (hereafter referred to as the noise), which is independent of anomalous sea surface temperature (SST) forcing, and an external part (hereafter referred to as the signal), which is forced by the imposed boundary condition (SST forcing). One major difficulty in using a coupled global climate model (CGCM) for the study of the stochastic ENSO mechanism is how to isolate the coupled signal from the noise reliably so that the coupled feedback can be extracted and examined separately. It is challenging because 1) the signal and noise are integral parts of the atmospheric variability, and 2) the coupled signal is often weak compared to the internal atmospheric variability, allowing the signal to be easily contaminated by the noise (Chang et al. 2000). Until very recently, the available CGCMs did not have the ability to discriminate between these two components.
The traditional technique for isolating the signal resulting from boundary forcing from noise is to use an ensemble average of many atmospheric realizations, subject to the same boundary forcing. In this approach, an ensemble of atmospheric global climate model (AGCM) runs with slightly different initial conditions, forced, for example, with observed SST, is first performed. Then, a first-order estimate of the signal can be obtained by taking an ensemble average of these runs. The noise can be defined as the departure from the ensemble mean. This simple technique works well provided that the ensemble size is sufficiently large. Extending this idea to a coupled model, Kirtman and Shukla (2002) proposed the use of an interactive coupled ensemble strategy within a CGCM to separate signal fields from noise fields. A practical limitation of this method is that for a finite size ensemble, the ensemble mean provides a biased estimate of the signal. This noise contamination problem can be severe if the ensemble size is small.
The appealing feature of our noise-filtering procedure is that it presents an unbiased estimate of the signal, and thus gives a better treatment of signal–noise separation, even when the ensemble size is relatively small. It is also computationally more efficient because the filter is predetermined based on AGCM Atmospheric Model Intercomparison Project (AMIP) runs. The objective of the paper is not to demonstrate that our filtering approach is superior over the interactive coupled ensemble approach introduced by Kirtman and Shukla (2002), or vise versa. Instead, our main objective is to investigate the effect of atmospheric internal variability on ENSO via the effective “noise-reduction filter” procedure.
This paper is divided into five sections: Section 2 discusses the design of the noise filter and tests its effectiveness. Section 3 describes the implementation of the noise filter with the coupled system and the noise-filtered coupled experiment. Section 4 examines the relative importance of dynamic and thermodynamic noise forcing. Section 5 provides a summary and discussion.
2. Design and testing of the noise filter
a. Concept of the noise filter
The solution of the generalized eigenvalue problem requires inverting the noise covariance matrix. In practice, the noise covariance 𝗖N must be estimated from data as the covariance of the departure from the ensemble mean and is often singular or has small, poorly estimated eigenvalues. If 𝗖N is singular, there are directions in state space that do not project onto the noise so the maximum signal-to-noise ratio is infinite. This issue can be avoided by projecting the problem onto the leading well-estimated EOFs of the noise, scaling each projection by the standard deviation of the noise principle component. This is sometimes called a “whitening” transformation because the transformation makes the noise spatially homogeneous and uncorrelated. In addition to regularizing the problem, this change of variable simplifies the calculation of the filter patterns, because after the whitening transformation, the noise covariance matrix is the identity matrix. Then, optimizing the ratio in (7) simply requires finding the principle components of the whitened ensemble mean.
In summary, the construction of the noise filter consists of the following three steps: 1) projection of the problem on the leading noise EOFs (whitening), 2) principle component analysis of the whitened ensemble mean, and 3) inversion of the whitening transformation to obtain the filter weights and patterns. A signal estimate is obtained by applying the filter to an individual ensemble member.
There are two truncations in this process: the first is to determine how many noise EOFs are kept in the whitening transformation, and the second is to determine how many signal-to-noise weights and patterns are kept in the filter. We tested the sensitivity of the noise filter to truncation variations in a certain range of EOF modes, and took the patterns that are robust with respect to the truncations. It should be pointed out that the filter is time independent, and there is no filtering in time.
b. Test of the noise filter
The noise filter is designed to remove the noise from an individual ensemble member and provide a good estimate of the SST-forced response from a single realization of the AGCM. To illustrate the effectiveness of the filter, an ensemble of 10 Community Climate Model, version 3 (CCM3), integrations, forced with global monthly averaged observed SSTs (Smith et al. 1996) from January 1950 to December 1994, was used to construct a noise filter using the EOFs of the noise covariance of the zonal wind stress derived from these 45-yr integrations; the data from all of the months were used to construct a single, annually invariant filter. We then applied the filter to the zonal wind stress anomaly from an arbitrary ensemble member.
Figure 1 shows the leading EOF of the zonal wind stress in the tropical Pacific and the associated time series of the leading EOF (Figs. 1a,b) for the signal estimate. The signal estimate is derived from the 10-member ensemble mean using the Eq. (11). Also shown in Fig. 1 is the leading EOF (Figs. 1c,d) for an arbitrarily chosen ensemble member. The spatial pattern of the individual ensemble member shows a very weak structure in the tropics and is clearly dominated by the variability in the North Pacific, compared with the signal pattern (Figs. 1a,b). Figures 1e,f depicts the leading EOF of the signal variance of the same individual ensemble member estimated by using the noise filter in Eq. (12). The leading EOF over the tropical Pacific basin exhibits a spatial pattern that is virtually identical to that of the signal. The correlation between the time series associated with the leading EOF of the ensemble-mean-estimated signal variance (Fig. 1b) and of the single-ensemble-member-estimated signal variance (Fig. 1f) is 0.71, while the correlation between that of the ensemble-mean-estimated signal and that of the individual ensemble member (Fig. 1d) is only 0.28. This suggests that the noise filter is capable of extracting the forced signal from the individual ensemble member.
To illustrate this point further, in Fig. 2 we show the time series associated with the leading EOF of the zonal wind stress for the 10 individual ensemble members (gray lines in Fig. 2a), the corresponding noise-filtered ones (gray lines in Fig. 2b), and the ensemble-mean-estimated signal (black line in Figs. 2a,b, as with Fig. 1b). The 10 noise-filtered time series agree much better with the time series estimated using the ensemble mean than the unfiltered time series. There is a considerable spread among 10 unfiltered time series of the individual ensemble members. The time series associated with the first EOFs of the 10 individual ensemble members show some seasonal variation, suggesting that the filter would work even better if we take seasonal variation into consideration.
The coupled CCM3–reduced gravity ocean (RGO) model used for this study consists of the National Center for Atmospheric Research (NCAR) CCM3 and an extended 1.5-layer RGO model. This model reproduces many salient features of observed ENSO and also captures the boreal spring MM variability and its relation to ENSO [more details can be found in Chang et al. (2007)]. The anomaly-coupling approach is used in this coupled model, which minimizes the coupled model drifts and systematic biases. This allows us to use AGCM-only runs to separate the signal from the noise. To make the signal–noise separation more consistent between the AGCM runs and coupled runs, we used a 45-yr-long SST record from the coupled model control simulation to force an ensemble of 12 AGCM-only runs. The noise filter is constructed from this ensemble of AGCM only runs. Because the SST is taken from the coupled model, the noise and signal patterns are consistent with the coupled system. To take into consideration the strong seasonal dependence, 12 filters, one for each of the calendar months, were constructed for each of the coupled variables, including wind stress, surface heat flux, and solar radiation.
Figure 3 displays the time series associated with the first EOFs of the zonal wind stress for January before (Fig. 3a) and after (Fig. 3b) applying the noise filter. It is obvious that unfiltered members show a considerable spread and are barely correlated among each other, but the filtered members are strongly correlated among each other with average correlation value of 0.997.
In terms of the total noise variance that is removed by the filter, Fig. 3 compares the variance maps of the January zonal wind stress anomalies of one unfiltered (Fig. 3c) and filtered (Fig. 3d) individual ensemble member. It clearly shows that much of the variance in the extratropics is reduced dramatically in the unfiltered case, while within the tropical region most of the variance is retained. This is expected because the tropical atmosphere is much more sensitive to SST forcing than the extratropics. Therefore, we would expect behavior of the control run to be different from the coupled experiments with filtered surface wind stress and heat flux.
3. Coupled experiments with noise filter
As demonstrated in the previous section, the noise filter is effective in suppressing internal atmosphere variability, and is readily applied to the anomalously coupled CCM3–RGO model. Four atmospheric variables (zonal and meridional wind stress, net heat flux, and solar radiation) are passed to the ocean at each coupling step (once a day). The noise filter was implemented in the coupled model by simply applying the filter to all four variables at each coupling step (every day), and then combining these filtered fields with the corresponding observed climatology before passing them onto the ocean model. The way that the SST anomaly was passed to the atmosphere model remained unchanged. In so doing, the noise filter acts to reduce the effect of the internal atmospheric variability on the ocean–atmosphere coupling.
A 100-yr coupled simulation is conducted where the noise filter is applied to the four atmospheric variables. Hereafter, we refer to this experiment as the fully filtered run. The following discussion is devoted to the comparison between the first 100-yr CCM3–RGO control run and this fully filtered run.
a. ENSO variance
The first issue to be addressed concerns the role of atmospheric internal variability in maintaining ENSO variance. Figure 4 compares the SST anomaly variance in the tropical Pacific region from the two experiments. There is a major reduction in SST variance of the fully filtered experiment in comparison with the control run. Furthermore, the structure of SST variance in the Pacific becomes narrower and more confined to the equatorial zone in the fully filtered run than in the control run.
This reduction in SST variance can be further seen in Fig. 5, where the time series, power spectra, and autocorrelation of the Niño-3 index are displayed for the first 100-yr control run and the 100-yr fully filtered run. When the filter is applied, the peak-to-peak variation of the Niño-3 index falls within one standard deviation of the control run (dashed line in Figs. 5a,b), though its periodicity does not change substantially (Figs. 5c,d). Another interesting difference between the two runs is that the Niño-3 SST index in the fully filtered experiment (blue) shows a more regular oscillation than in the control run (red). However, it may be difficult to pinpoint in exactly which regime the model ENSO resides. This is because the noise filter can only reduce the influence of atmospheric noise, but cannot remove it completely. As a result, there is always some noise left in the system that can excite ENSO, making it hard to determine whether the model ENSO resides in a damped regime or a self-sustained regime. One thing that appears certain is that our model ENSO does not reside in a strongly nonlinear regime, because its characteristics are strongly influenced by the noise. Therefore, our best estimate is that the model ENSO resides in a regime close to the bifurcation boundary between a damped and self-sustained oscillatory regimes and the role of the atmospheric noise is to enhance the variance of the ENSO and cause irregularity in the ENSO cycle.
Perhaps the most striking difference between the two runs lies in the change in seasonal phase locking of ENSO. Figure 6 compares the standard deviation of the Niño-3 SST anomalies in the two cases as a function of calendar month. As can been seen, the seasonal phase locking is substantially altered in the absence of internal atmospheric variability. The ENSO cycle is no longer phase locked to the boreal winter. Instead, the filtered ENSO cycle does not show any strong seasonal preference (blue bar in Fig. 6). This suggests that atmospheric internal variability has a dramatic effect on the seasonal phase locking of ENSO.
Figure 7 illustrates the El Niño evolution in the fully filtered (left panel) and control (right panel) runs. Because the ENSO in the filtered experiment is no longer phase locked to the annual cycle, a composite of the events was made by simply lining up the maximum value amplitude of each identified El Niño event, instead of using calendar months for the control run. However, the same criterion is being used as in the control run to identify El Niño events: the SST anomalies averaged over the Niño-3 region exceed one standard deviation for at least three consecutive months. Over the 100-yr record of the fully filtered run, there are a total number of 22 El Niño events. The warm SST anomalies develop in the west-central Pacific 9 months before the peak of the event, which corresponds to March–May [MAM(0)] in the control run. Here, 0 and +1 in parentheses refer to the developing and decaying years of ENSO, respectively. Overall, the canonical evolution of the El Niño in this case behaves very similarly to the ENSO-only El Niño in the control simulation, which is independent of the MM (shown in the right panel). This implies that after filtering internal atmospheric variability, the number of El Niño events preceded by MM drops significantly so that the canonical El Niño behaves like the ENSO-only events in the control simulation.
b. Meridional mode and its relationship to ENSO
Does the Pacific meridional mode still exist in this filtered experiment? If the MM is a coupled mode, it should remain, but its variance should be reduced substantially because internal atmospheric variability acts as a major source of external forcing for the MM. To test this idea, we used the approach of Chiang and Vimont (2004), where the maximum covariance analysis (MCA) is performed on the monthly residual data after linearly removing the ENSO signal, to identify the MM in the filtered run. To directly compare with the results from the control simulation, the same MCA is also applied to the first 100-yr monthly data of the control run.
Figure 8 illustrates the spatial pattern of the leading MCA, along with the seasonal dependence of the corresponding wind stress expansion coefficient, respectively, for the filtered experiment (Figs. 8a,b) and the control run (Figs. 8c,d). The analysis shows that MM’s temporal characteristics in the two experiments are very similar with maximum variance in boreal spring [February–May (FMAM)]. There is, however, a substantial reduction (about 30%) in amplitude of the MM of the filtered run, particularly during later winter and early spring [January–April (JFMA)]. The spatial patterns of the MM from both experiments also share some similarities, but again the MM in the filtered case is much weaker than in the control case. The associated positive SST anomaly north of the mean ITCZ is much weaker and narrower in the filtered run than in the control run (not shown). Consequently, the gradient between the positive and negative SST anomaly is weaker, as is the corresponding wind stress anomaly associated with this MM. Though weakened, this result does suggest that the MM can exist in the absence of, or with very little influence from, internal atmospheric variability. To confirm this claim, we correlated the SST expansion coefficient associated with the MM in the fully filtered run to the sea level pressure anomaly at different lags (not shown) and found no significant correlation (correlation less than 0.15), which is in sharp contrast to the control run. This further supports the idea that the meridional mode is indeed a coupled mode and that atmospheric internal variability plays a major role in exciting it and enhancing its variability.
What about the relationship between the MM and El Niño events when atmospheric internal variability is suppressed? To answer this question, the FMAM wind expansion coefficient (blue) and December–February (DJF) Niño-3 index (red) are plotted against each other in Fig. 9 for both the fully filtered (Fig. 9a) and control (Fig. 9b) runs. Each time series has been normalized by its standard deviation. The correlation between these two is 0.36 for the filtered case, which is substantially lower than the value of the control run (0.56). Using the same criterion as for the control run to classify all of the El Niño and MM events in the filtered run, we found that 33% of the El Niño events (7 out of 21), indicated as red dots, are led by MM events (MM–ENSO); 67% of the El Niño events (14 out of 21), indicated as green dots, are independent of MM events (ENSO only); and 59% of the MMs events (10 out of 17) do not lead to El Niño (MM only), denoted as blue dots. In comparison, the populations of El Niño events and MMs in each of these categories, based on the first 100 yr of the control simulation, are that 73% of the El Niño events (19 out of 26) are tied to the MMs, 27% of the El Niño events (7 out of 26) are independent of the MMs, and 30% of the MMs events (8 out of 27) do not lead to El Niño. Therefore, there is a significant difference in population distribution among the three groups of El Niño and MM events in the two experiments. The population in MM–ENSO drops dramatically in the filtered case, compared with the control run, while the populations in ENSO only and MM only increase markedly. There is also a decrease in the total number of the MM events and El Niño events in the filtered run.
These statistics confirm that atmospheric internal variability does play an important role in determining the strength and occurrence of the MM events, consequently having an impact on the relationship between the MM and El Niño. When atmospheric internal variability is present, the MM events are strong and frequent. Therefore, the MMs are very effective in affecting El Niño, and the correlation between the two is high. One sees that the majority of El Niño events follows an MM event. On the other hand, when atmospheric internal variability is suppressed, the MM variability is weakened, making it more difficult to affect El Niño. Therefore, the correlation between the two is relatively low. A majority of El Niño events become independent of the MMs, which results in an increase in the population of ENSO only. As a result of this change, the seasonal phase locking of ENSO is altered.
4. Relative importance of dynamic and thermodynamic noise forcing
Internal atmospheric variability can affect coupled feedbacks in the tropics via its impact on surface wind stress and surface heat flux exchanges. However, which of these exchanges is more important in terms of affecting ENSO in the coupled model? To address this question, two additional filtered experiments are carried out. 1) Only surface heat flux is filtered, so that only the signal of the surface heat flux is passed to the ocean during the coupling. The result of this experiment will indicate the extent to which internal atmospheric variability in wind stress only can affect ENSO. 2) Only wind stress is filtered, so that only the signal of the wind stress is passed to the ocean during the coupling. The result of this experiment will shed light on to the extent to which internal atmospheric variability in the heat flux can influence ENSO. Like the fully filtered experiment, each of these experiments has 100-yr integration. Hereafter, we will refer to these experiments as the filtered-flux and filtered-wind experiments.
a. ENSO variance
The variance of the SST anomaly from the filtered-flux experiment in the Pacific region is shown in Fig. 10a and the variance from the filtered-wind experiment is shown in Fig. 10b. For the filtered-flux experiment, the SST variance outside the deep tropics is reduced markedly, while the reduction within the deep tropics is small. For the filtered-wind experiment, the reduction in the deep tropics is more severe than that outside of the tropics and the overall structure remains more similar to that of the control run (Fig. 4b). This suggests that filtering the noise in the surface heat flux has a stronger impact on the SST variance in the extratropics, while filtering the noise in the wind stress has a stronger impact on the SST variance in the deep tropics. This is consistent with the ENSO dynamics: SST variability within the deep tropics is more controlled by the ocean dynamics, which is closely related to wind stress fluctuations. Outside the deep tropics, SST changes are controlled more by mixed layer dynamics, which is predominantly driven by surface heat flux.
Let us now take a further look at the model ENSO variability in each of these experiments. Figures 11 and 12 show the time series, power spectra, and phase locking of the Niño-3 index for the filtered-flux and the filtered-wind experiments, respectively. A marked change is observed for the phase locking of ENSO, which in the filtered-flux run shows no seasonal preference, as in the fully filtered run (Fig. 4). Another change is that the period of the ENSO cycle is somewhat longer, around 4–5 yr, compared with the control run. In the experiment where only wind stress is filtered, the phase locking of ENSO does not change substantially (Fig. 12c), compared to the control run. The ENSO cycle seems to occur more frequently, every 2–3 yr, than in the filtered-flux experiment. This indicates that noise in wind stress plays a role in shifting the frequency of ENSO toward the lower-frequency end of the spectrum. A comparison of the Niño-3 spectra of the two cases also indicates that the noise in the wind stress also tends to broaden the spectral peak while shifting it toward the lower frequency. This effect of noise in the wind stress has been noted previously by Blanke et al. (1997) and others.
b. Meridional mode and its relationship to ENSO
To examine the Pacific meridional mode, an MCA analysis was performed on the monthly data of the two filtered experiments after linearly removing ENSO. Figure 13 depicts the spatial pattern of the first MCA analysis, and the seasonal dependence of the corresponding wind expansion coefficient, respectively, for the filtered-flux experiment (Figs. 13a,b) and the filtered-wind experiment (Figs. 13c,d). The expansion coefficients display similar seasonality, except that the filtered-wind case has a noticeable boreal spring phase locking. The spatial patterns also share some similarities, but the MM in the filtered-flux case is clearly weaker than in the filtered-wind case, especially for the positive SST anomaly north of the mean ITCZ region and the associated southwesterly wind anomaly. Overall, the MM in the filtered-wind experiment resembles more closely that of the control run (Fig. 8c), while the one in the filtered-flux run resembles the fully filtered run (Fig. 8a). This suggests that it is the noise in heat flux that plays a more important role in maintaining the MM, which in turn affects the onset of ENSO.
Consequently, one would expect that the relationship between the MM and El Niño events in the filtered-flux experiment would be less tightly correlated than in the filtered-wind experiment. The FMAM wind expansion coefficient (blue) and DJF Niño-3 index (red) from the two experiments are plotted in Fig. 14, with the upper panel showing the filtered-flux experiment and lower panel showing the filtered-wind experiment. Each time series has been normalized by its standard deviation. The correlation between the wind expansion coefficient and the Niño-3 index is 0.20 and 0.75, respectively, for the filtered-flux experiment and for the filtered-wind experiment. Using the same classification criteria for the control run, we found 20% of El Niño events (3 out of 15), indicated as red dots, in the filtered-flux experiment are led by the MMs; 80% of El Niño events (12 out of 15), indicated as green dots, are independent of the MMs; and 85% of the MMs (17 out of 20) do not lead to ENSO events, denoted as blue dots. Therefore, the majority of El Niño events in the filtered-flux experiment are independent of the MMs.
In the filtered-wind experiment, 62% of El Niño events (18 out of 29) are tied to the MMs, 38% of El Niño events (11 out of 29) are independent of the MMs, and 25% of the MMs (6 out of 24) do not lead to ENSO events. Therefore, the populations of the El Niño events for MM–ENSO and ENSO only are very similar to those for the control run, suggesting again that the noise in the wind stress does not have a strong impact on the MM and its relationship to ENSO.
This finding is further supported by a composite of the wind expansions coefficient of the first MCA for the filtered-flux experiment and for the filtered-wind experiment, shown in Fig. 15. This is done by averaging all of the MM events as a function of calendar month within the years that these events occur in the filtered-flux experiment (left-hand side) and the filtered-wind experiment (right-hand side), respectively. The major difference between the two experiments is the persistence of the wind anomaly. In the filtered-wind experiment, the winds appear to persist much longer, from late winter to summer, without reversing sign, while the winds in the filtered-flux experiment appear to be short lived, lose strength dramatically, and even reverse sign starting in June. This further demonstrates that the noise in heat flux has a very important role in maintaining the MM, whose persistence is crucial for determining whether a MM event can excite ENSO.
5. Summary and discussion
In this study, we have demonstrated the use of a specially designed noise filter to remove internal atmospheric variability in our coupled CCM3–RGO model. We showed that the noise filter can effectively reduce the internal atmospheric variability in the air–sea fluxes, and therefore can be used as an effective tool to study the role of internal atmospheric variability in ENSO.
Three experiments, each a century in length, are examined, where the filter is utilized to suppress internal atmospheric variability in surface wind stresses and surface heat fluxes either simultaneously or separately. These experiments indicate that reducing the effect of internal atmospheric variability or “noise” can alter the characteristics of ENSO in a number of ways, including its regularity, frequency, and seasonal phase-locking characteristics. In the first experiment, in which both surface wind stresses and surface heat fluxes are suppressed, the MM becomes weaker and less effective in triggering ENSO. However, it does not completely suppress the ENSO cycle in the model, suggesting that the model ENSO may reside in the self-sustained regime. Not only is the simulated ENSO substantially weakened, but it is no longer phase locked to the boreal winter. Interestingly, the periodicity of the ENSO is not affected by the weakened noise. Hence, ENSO’s time scale seems to be intrinsic to the dynamical couple system of the tropical Pacific, but its phasing may be dictated by extratropical atmospheric variability via the MM.
In the second experiment, only the surface heat fluxes are suppressed, while in the third experiment, only surface wind stresses are suppressed. The results of these experiments reveal different effects of the noise in the wind stress and heat flux on ENSO. The noise in the wind stress does not have a significant impact on the MM and its relationship to ENSO. Therefore, filtering wind stress noise yields a similar seasonal phase locking of ENSO. This type of noise, however, does have an influence on ENSO’s frequency and regularity; it tends to broaden the spectral peak, while shifting it toward lower frequencies. The noise in the heat flux, on the other hand, has a direct impact on the strength of the MM, and consequently its ability to influence ENSO. Reducing the effect of heat flux noise yields substantially weakened MM activity and its relationship to ENSO, which leads to altered seasonal phase-locking characteristics. The latter is perhaps the most provocative discovery of this study, suggesting that ENSO’s seasonal phase locking is tied to the internal atmospheric variability.
This finding is at odds with previous studies that attribute the seasonal phase locking to interactions between the tropical annual cycle and ENSO (Jin et al. 1996; Chang et al. 1996; Blanke et al. 1997; Tziperman et al. 1998). In fact, many of these studies (Jin et al. 1996; Chang et al. 1996; Blanke et al. 1997) show that the inclusion of atmospheric noise does not strongly alter ENSO’s phase locking. A more recent study by Roulston and Neelin (2000), while still attributing the seasonal phase locking to the nonlinear interaction between the ENSO cycle and annual cycle, finds that the phase-locking dynamics are more complex than what is indicated in previous studies, and that there is considerable variation in ENSO’s phase-locking behavior. This variation can be caused by deterministic dynamics resulting from competition between the inherent ENSO frequency, and the tendency to phase lock to a preferred season and/or stochastic dynamics resulting from internal atmospheric variability. Therefore, these previous studies indicate that the atmospheric noise has either little or a negative effect on ENSO’s phase-locking behavior. What causes the results of this study to be different?
A key dynamic difference between this study and previous studies is that thermodynamic coupling via feedback between surface heat flux and SST, which has been either ignored or oversimplified in the previous studies, is treated rigorously in this study. The added coupled dynamics allow for the existence of the Pacific MM. The MM’s strength is strongly affected by surface heat flux fluctuations induced by boreal winter internal atmospheric variability. The stochastic heat flux forcing causes stronger MM activities during boreal spring, and thus triggers stronger thermodynamic coupling, which makes the events last longer, so that they can play a role in forcing the onset of ENSO. Therefore, it is through the MM that internal atmospheric variability and ENSO are connected. This result is confirmed by the comparison between the fully filtered and filtered-flux experiments.
Our study is consistent with the previous studies in finding that the noise in the surface wind stress has an effect on ENSO irregularity and its frequency, but not so much on its seasonal phase-locking characteristics. This result is seen clearly in the filtered-wind experiment. In the absence of noise in the winds, the ENSO cycle tends to be more regular and have a shorter period compared to those in the CCM3–RGO control run, but its seasonal phase-locking characteristics remains unchanged. The latter is consistent with the argument that the MM is a thermodynamically coupled mode and is not directly affected by the noise in surface wind stress. Therefore, the relationship between the MM and ENSO is not changed substantially by suppressing the noise in the wind stress. The result, that the noise in surface wind stress can enhance the irregularity of ENSO, is easily understood and shown in the previous study. However, the result that the noise in surface wind stresses can lead to a longer periodicity of ENSO cycle is not well understood. Blanke et al. (1997) attribute this result to nonlinear effects in the system. Chang et al. (2004) shows that maximum spectral peaks of a linear dynamic system forced stochastically by white noise generally tend to occur at lower frequencies than the frequencies of the leading eigenmode. It remains to be explored which of these two arguments is more effective in explaining the low-frequency shift in the ENSO spectral peak.
One caveat in our noise-filtering approach is its implied linearity. Our approach assumes that the noise is additive. Some recent studies have pointed to the multiplicative nature of the noise (Sura and Penland 2002) and argued that the nonlinear nature of the noise can be a quite important factor for stochastic ENSO theory. The result of Blanke et al. (1997), on the other hand, suggests that accurate treatment of the multiplicative noise is a less burning issue in ENSO study. Also our noise-filtering approach is based on ergodic assumption. Some noise may still exist after noise-filtering procedure. One way to test our noise-filtering approach is to compare it with the interactive ensemble approach of Kirtman and Shukla (2002) and Kirtman et al. (2005), which does not depend on the linearity assumption, but is computationally more expensive. We plan to carry out a comparison study of these two different approaches in the future.
Acknowledgments
Some work in this paper is from LZ’s dissertation at Texas A&M University. LZ is supported by the National Oceanographic and Atmospheric Administration (NA06OAR4310067). PC is supported by the NOAA CLIVAR Program and Frontier Research System for Global Change. We thank referees for their valuable criticism of the manuscript.
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(a), (c), (e) Spatial and (b), (d), (f) temporal patterns, respectively, of the leading EOF of zonal wind stress in the tropical Pacific for the signal derived from a 10-member ensemble mean, for an arbitrarily chosen ensemble member, and for the signal estimate from the same individual ensemble member.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
The time series of the first EOFs of zonal wind stress for (a) the 10 individual ensemble members (gray lines) and (b) the corresponding noise-filtered ones (gray lines), and the signal estimate [black line in both (a) and (b)].
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
The time series associated with the first EOFs of zonal wind stress for January (a) before and (b) after applying the noise filter. Variance maps of the January zonal wind stress anomalies of one (c) unfiltered and (d) filtered individual ensemble member.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
SST anomaly variance in the tropical Pacific region (a) from the fully filtered run and (b) from the CCM3–RGO control run.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
The time series of the Niño-3 index (a) for the 100-yr fully filtered run and (b) for the first 100-yr control run. (c) Power spectra and (d) autocorrelation of the Niño-3 index for the control run (red line) and the fully filtered run (blue line).
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
Standard deviation of the Niño-3 SST anomalies as a function of calendar month, for the first 100-yr control run (red) and for the 100-yr fully filtered run (blue).
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
El Niño evolutions in the (left) fully filtered run are averaged from (a) −12 to −10 months, (b) from −9 to −7 months, (c) from −6 to −4 months, (d) from−3 to −1 months, and (e) from 0 to 2 months, which correspond to (f) DJF(0), (g) MAM(0), (h) JJA(0), (i) SON(0), and (j) DJF(+1) in (right) the control simulation. This evolution behaves very similar to ENSO only in the control simulation.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
(a), (c) Spatial properties of the leading MCA mode between the residual wind stress and residual SST anomaly for the (top) fully filtered run and (bottom) 100-yr control run, after linearly removing the ENSO signal. (b), (d) The seasonal dependence of the wind expansion coefficient.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
Normalized FMAM wind expansion coefficient (blue line) and normalized DJF Niño-3 index (red line) from the (a) fully filtered run and (b) control run. Red dots indicate MM–ENSO, green dots indicate ENSO only, and blue dots indicate MM only.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
SST anomaly variance in the tropical Pacific region from the (a) filtered-flux run and (b) filtered-wind run.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
The (a) time series, (b) power spectra, and (c) seasonal dependence of standard deviation of the Niño-3 index for the filtered-flux run.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
Same as in Fig. 11, but for the filtered-wind run.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
(a), (c) Spatial properties of the leading MCA mode between the residual wind stress and residual SST anomaly for the (top) filtered-flux run and (bottom) filtered-wind run, after linearly removing the ENSO signal. (b), (d) The seasonal dependence of the wind expansion coefficient.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
Normalized FMAM wind expansion coefficient (blue line) and normalized DJF Niño-3 index (red line) from the (a) filtered-flux run and (b) filtered-wind run. Red dots indicate MM–ENSO, green dots indicate ENSO only, and blue dots indicate MM only.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
Composites of the wind expansion coefficient for the (left) filtered-flux run and (right) filtered-wind run.
Citation: Journal of Climate 22, 4; 10.1175/2008JCLI2474.1
