Tropical Pacific decadal variability and ENSO amplitude modulation in a CGCM

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109,, doi: /2004jc002442, 2004 Tropical Pacific decadal variability and ENSO amplitude modulation in a CGCM Sang-Wook Yeh and Ben P. Kirtman 1 Center for Ocean-Land-Atmosphere Studies, Calverton, Maryland, USA Received 18 April 2004; revised 13 July 2004; accepted 15 September 2004; published 18 November [1] Connections between decadal changes in the tropical Pacific mean state and El Niño Southern Oscillation (ENSO) decadal modulation are examined using three runs of a coupled general circulation model (CGCM). The differences between the three simulations, i.e., a standard coupled model (one AGCM is coupled to a single OGCM) and two interactive ensemble models (six or twelve AGCMs are coupled to a single OGCM), are confined to the amplitude of internal atmospheric variability. All three simulations have the same tropical Pacific basin scale SST mode that dominates the low-frequency variability, which is identified by the first EOF mode. This low-frequency mode is largely independent of the simulated ENSO and is neither a residual of the decadal ENSO modulation nor does it produce any low-frequency modulation of ENSO. The analysis presented here suggests that this low-frequency mode is stochastically driven by atmosphere noise. There are, however, low-frequency changes in the tropical Pacific mean state that are connected to ENSO decadal modulation. The mean state associated with ENSO amplitude has different structures in the SST and wind stress anomalies than does the dominant tropical Pacific mean state identified by the first EOF. The tropical Pacific mean state that is unambiguously associated with ENSO decadal modulation, which is remarkably similar to the second EOF SST mode in two interactive ensemble models, but is difficult to detect in a standard coupled model simulation. These results argue that there is a component of ENSO variability that cannot be explained by a linear, damped and stochastically forced process. INDEX TERMS: 1620 Global Change: Climate dynamics (3309); 3339 Meteorology and Atmospheric Dynamics: Ocean/atmosphere interactions (0312, 4504); 4215 Oceanography: General: Climate and interannual variability (3309); KEYWORDS: ENSO decadal modulation, low-frequency changes, tropical Pacific Citation: Yeh, S.-W., and B. P. Kirtman (2004), Tropical Pacific decadal variability and ENSO amplitude modulation in a CGCM, J. Geophys. Res., 109,, doi: /2004jc Introduction 1 Also at School of Computational Sciences, George Mason University, Fairfax, Virginia, USA. Copyright 2004 by the American Geophysical Union /04/2004JC [2] The amplitude and frequency of the El Niño Southern Oscillation (ENSO) phenomenon exhibits variations on decadal timescales [Gu and Philander, 1995; Wang and Wang, 1996]. There is also considerable evidence that the tropical Pacific decadal variability (TPDV) is an important component of global climate variability [Pan and Oort, 1983; Graham, 1994; Lau and Weng, 1999; Yeh and Kirtman, 2003]. Concurrent changes in the amplitude and frequency of ENSO in the 1980s and 1990s were linked to TPDV [Trenberth and Hurrell, 1994; Wang, 1995; Ji et al., 1996]. However, there is no consensus on the underlying mechanisms of the relationship between TPDV and the decadal modulation of the ENSO amplitude and/or the dominant frequency. Whether the ENSO decadal modulation (EDM) is driven by TPDV [Fedorov and Philander, 2000; McPhaden and Zhang, 2002] or these variations are just sampling issues associated with some sort of random walk process [Thompson and Battisti, 2001; Flügel et al., 2004] has been the subject of some debate. [3] Accordingly, the current literature includes a number of studies proposing mechanisms for TPDV, and, as a counter argument, studies examining the null hypothesis that TPDV is simply related to sampling issues. The potential mechanisms for TPDV can be separated into two broad categories: (1) tropical-extratropical interactions and (2) purely tropical processes. Within these two broad categories there are a number of competing hypotheses. For example, regarding the first category of mechanisms, there have been a number of oceanic studies emphasizing the importance of thermocline ventilation and subduction processes [McCreary and Lu, 1994; Gu and Philander, 1997; Zhang et al., 1998; Chang et al., 2001; Luo and Yamagata, 2001; McPhaden and Zhang, 2002; Bratcher and Giese, 2002]. Similarly, tropical-extratropical interactions associated with shallow subtropical cells [Klinger et al., 2002; Nonaka et al., 2002] have also been shown to 1of19

2 potentially influence TPDV. Atmospheric tropical-extratropical bridge processes could also alter the tropical Pacific mean state on decadal timescales [Kleeman et al., 1999; Barnett et al., 1999; Pierce et al., 2000]. While the physical processes associated with these mechanisms are different, they all ultimately argue for the existence of low-frequency variability in the tropical Pacific mean state. Whether or not this TPDV leads to EDM remains unresolved. [4] There have also been studies identifying purely tropical processes that could lead to TPDV. For instance, Jin [2001] suggests that there are very low frequency modes associated with TPDV due to the ocean-atmosphere interactions in the tropics. Knutson and Manabe [1998] found in their coupled general circulation model (CGCM) that offequatorial Rossby waves could lead to decadal variability of the tropical Pacific [see also Kirtman, 1997]. Again, how TPDV is related to the secular changes in the amplitude and frequency of ENSO is unanswered. On the other hand, An and Wang [2000] argued that the spatial structure of the coupled mode in the tropical Pacific has low-frequency changes that can lead to EDM, although why the structure of the coupled mode changes is unclear. [5] As mentioned above, despite the wealth of potential sources of TPDV, it is still an open question as to whether TPDV drives EDM or whether both variations are merely associated with sampling issues. Are the mean state changes forcing changes in the ENSO statistics as suggested by Fedorov and Philander [2000]? Are the changes in the mean state some nonlinear residual associated with a varying frequency of ENSO events? Are the changes in the mean state actually independent of ENSO as suggested by the null hypothesis of Thompson and Battisti [2001] and Flügel et al. [2004]? Much of the debate hinges on whether ENSO is viewed as fundamentally nonlinear and selfsustained [Zebiak and Cane, 1987; Munnich et al., 1991] or as a damped stochastically driven system [Penland and Sardeshmukh, 1995; Kleeman and Moore, 1997]. For example, in the Kirtman and Schopf [1998] model, which has nonlinear self-sustained ENSO events, relatively low frequency and small amplitude changes in the mean state lead to large changes in the amplitude of ENSO events. Conversely, Flügel and Chang [1999], Yeh et al. [2004], Flügel et al. [2004], and Kleeman et al. [2003] all argue, using damped stochastically driven models, that EDM is entirely noise driven and unrelated to low-frequency changes in the tropical Pacific mean state. [6] There is also considerable disagreement based on observations. For example, Cobb et al. [2003] argued, based on the analysis of the time series of fossil-coral records, that a broad range of ENSO amplitude and period can not be explained by low-frequency changes of the tropical Pacific mean state. However, McPhaden and Zhang [2002] reported that during the past 40 years the tropical Pacific SST has increased and this tends to increase the amplitude and period of ENSO events. There are not many studies on the relationship of these variations using a CGCM. Codron et al. [2001] recently showed that the warmer mean state leads to a doubling of the standard deviation of interannual SSTAs based on comparison of two simulations by a CGCM where small changes in the physical parameterizations were made. [7] In this paper we examine various runs of the Center for Ocean-Land-Studies (COLA) anomaly coupled GCM [Kirtman et al., 2002]. Our goal is to identify connections between decadal changes in the mean state of the tropical Pacific and EDM in a CGCM. It is our purpose to investigate whether decadal mean state changes in the tropical Pacific are associated with decadal variations in ENSO amplitude. [8] We use the data based on three coupled model integrations. The three simulations consist of a standard coupled model, one atmospheric GCM (AGCM) coupled to a single ocean GCM (OGCM), and two interactive ensemble models [Kirtman and Shukla, 2002] which consist of six or twelve AGCMs coupled to a single OGCM. The differences are confined to the amplitude of internal atmospheric variability felt by the ocean component at the air-sea interface. As the interactive ensemble evolves, each AGCM realization experiences the same SST predicted by the OGCM. The OGCM, on the other hand, experiences surface fluxes that are the ensemble average of the six or twelve AGCM realizations. Simply put, the noise variance in two interactive ensemble models has been reduced by a factor of 6 and 12 compared to the standard coupled model. [9] The interactive ensemble approach provides an ideal test bed to examine the processes that maintain TPDV and EDM, and the relationship between them, if it exists. For example, if the null hypothesis of Chang et al. [1996] is correct, that ENSO is a linear, damped, and stochastically forced system, then there should be no statistically significant relationship between TPDV and EDM. Under this condition, when the interactive ensemble is applied, the amplitude of the low-frequency variability should correspondingly decrease, and we can view the low-frequency variability as an extension of the Hasselmann [1976] hypothesis into the tropical Pacific that includes some stable coupled feedbacks [Barsugli and Battisti, 1998]. On the other hand, if we detect an unambiguous relationship between TPDV and EDM irrespective of the number of ensemble members, then we argue that there is some component of ENSO variability that cannot be explained by the null hypothesis. [10] The paper is organized as follows. The description of model and methodology is outlined in the next section. Section 3 describes whether the dominant mode of TPDV impacts EDM using an empirical orthogonal function (EOF) analysis. In section 4, we take the reverse approach by using the decadal modulation of ENSO amplitude to isolate tropical Pacific mean state changes. The specific tropical Pacific mean state, which is associated with EDM, has different structures of SST and wind stress anomalies compared to the dominant mode of TPDV. On the basis of Markov model experiments in section 5, we suggest that this specific tropical Pacific mean state cannot be explained by a damped, linearly stochastically forced system. The conclusion is given in section Model and Methodology [11] The atmospheric component of the standard and interactive ensemble anomaly coupled model is the Center for Ocean-Land-Atmosphere Studies (COLA) AGCM with triangular truncation at zonal wave number 42 and 18 ver- 2of19

3 Figure 1. First EOF mode for the 10-year running mean SSTA in the SC. The first EOF mode explains 46.4% of the filtered variance. Shading is positive. Contour interval is Unit is nondimensional. See color version of this figure in the HTML. tical levels. The ocean model is adapted from the Geophysical Fluid Dynamical Laboratory (GFDL) modular ocean model [Rosati and Miyakoda, 1988; Pacanowski et al., 1993] version 3 (MOM3). The component models are anomaly coupled in terms of heat, momentum, and fresh water [Kirtman et al., 2002]. With this coupling strategy, the component model monthly climatologies must be specified at the sea surface. In the case of the ocean, the model climatology is determined from an uncoupled extended integration forced by observed momentum flux, with surface relaxation of temperature and salinity to their observed values. In the case of atmosphere, the model climatology is determined from a multidecadal simulation with specified observed SST. The coupling frequency of the model is once a day with daily mean values being exchanged between the ocean and the atmosphere. The purpose of the anomaly coupling strategy is to prevent or significantly reduce climate drift. In this sense, it can be interpreted as being analogous to flux corrections. The procedure, however, does not prevent the model from developing anomalies on decadal or longer timescales. [12] The results from interactive ensemble model with the six (IE-6) and twelve (IE-12) AGCM realizations are compared to those of the standard anomaly coupled model (SC). All of the analysis shown here is based on the data for 300 years (SC), 500 years (IE-6), and 250 years (IE-12). Note that the SST anomaly (SSTA) is defined as the deviation from the 100-year running mean annual cycle calculated over the entire record of each model. [13] The time series of the 10 year running mean of the monthly NINO3.4 (5 N 5 S, 170 E 240 E) amplitude (NINO3.4 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (5 N 5 S, 170 E 240 E) amplitude is defined as ðnino3:4þ ðnino3:4þ) is used as an index of EDM. An EOF analysis is applied to the low-pass (period >10 years) filtered SSTA in order to isolate the decadal variability in the tropical Pacific. We identify the dominant mode of TPDV as an SSTA pattern having a broad meridional structure with a triangular shape in the tropical Pacific basin. Decadal changes between relatively warm and cold states in the tropical Pacific are described by the basin scale pattern of variability. A similar pattern of variability has been noted in the observations with a broad meridional structure in the eastern Pacific extending along much of the North and South American coasts in the eastern part of the tropical basin with a triangular shape [Zhang et al., 1997; Knutson and Manabe, 1998; Yeh and Kirtman, 2003]. 3. Mean State Changes and ENSO Amplitude [14] Kirtman and Shukla [2002] describe some characteristics of the tropical Pacific SST interannual variability of a 150-year run in the SC and IE-6. Yeh and Kirtman [2004] also analyzed the characteristic SST variability of the Pacific Ocean of a 200-year run in the SC, IE-6, and IE-12. We will not repeat their analysis here although the analyzed period is much longer. Power spectral analysis of three simulations yields a broad peak between 2 and 4 years. The IE-6 and IE-12 has more power than the SC near biennial timescales. The dominant timescales in these three simulations are shorter than in observations [Kirtman and Shukla, 2002; Yeh and Kirtman, 2004]. The ENSO events in all three model simulations are irregular Standard Coupled Model [15] We begin by showing the dominant mode of TPDV in the SC. Figure 1 shows the first EOF for the 10-year running mean SSTA. The first EOF of the decadal SSTA explains 46.4% of the filtered variance. The spatial pattern of the leading mode represents the structure of the dominant mode of tropical Pacific decadal SSTA variability with a broad triangular shape in the tropical Pacific basin. [16] In order to examine whether this dominant mode of TPDV is associated with EDM, we plotted a 10-year running mean of the NINO3.4 amplitude (dashed line in Figure 2) with the PC time series (solid line in Figure 2) of the first EOF for a period of 300 years. Note that the magnitude of the NINO3.4 amplitude is indicated on the left of the panel. The 10-year averaging period was chosen for convenient comparison with the PCs. Modifying the averaging period has little qualitative impact on the results. 3of19

4 Figure 2. Time series of a 10-year running mean of the NINO3.4 (5 N 5 S, 170 E 240 E) amplitude (dashed line) and the PC time series of EOF1 for a period of 300 years (solid line). Unit is C. [17] The decadal variations are readily apparent in both time series of PCs and NINO3.4 amplitude. There are periods when the PCs are in phase with NINO3.4 amplitude and periods when the PCs are out of phase with NINO3.4 amplitude. This simply suggests that there is little or no relationship between the dominant mode of decadal SST variability in the tropical Pacific and EDM. The simultaneous correlation between the two time series in Figure 2 is 0.08, which does not exceed the 95% confidence level. Moreover, the lead-lag correlations of NINO3.4 amplitude with the PCs of the first EOF mode for the lagged period of ±20 years also do not show any significant relationship (not shown). [18] To further examine the potential relationship between this dominant decadal mode and EDM, we computed composites based on the PC time series of the first EOF. Relatively warm states in the tropical Pacific are based on periods when the PC time series exceeds 1 standard deviation. Similarly, cold states are based on periods when the PC time series are less than 1 standard deviation below normal. Figures 3a and 3b are the anomalous mean SSTAs and wind stress anomalies for the tropical warm and cold state, respectively. [19] The spatial patterns for both tropical Pacific warm and cold SST state (Figures 3a and 3b) resemble the first EOF mode shown in Figure 1. The tropical Pacific warm state (Figure 3a) is marked by anomalous westerlies across the basin from the western equatorial Pacific. There are also significant mean westerlies over the central and eastern subtropical Pacific corresponding to the subtropical warm state. Conversely, the tropical Pacific cold state (Figure 3b) is marked by anomalous easterlies in the equatorial Pacific basin with strong easterlies in the eastern and central subtropical Pacific. These westerly or easterly anomalies in the subtropics are associated with the subtropical SSTA variability. Because the climatological winds are easterly in the subtropics, anomalous westerlies mean weak trade-wind variations and anomalous easterlies mean strong trade-wind variations. Westerly wind anomalies reduce the total trade wind speed, warming the mixed layer by reducing the fluxes of sensible and latent heat. The reverse holds in the case of easterly wind anomalies [Cayan, 1992; Lau and Nath, 1994]. [20] Even though there are substantial mean state differences, there is no detectable impact on ENSO amplitude. Figure 3c shows the difference in the SSTA standard deviation calculated separately for the warm and the cold periods using the unfiltered SSTA. Note that there are no regions in which the differences exceed the 95% significance based on a chi-square test. This indicates that decadal mean state changes identified by the first EOF have no relationship with low-frequency changes in ENSO amplitude. [21] On the basis of this brief analysis we conclude that (1) decadal changes in the mean state of the tropical Pacific (identified by the first EOF) are not related to EDM and (2) these decadal mean states, which have a broad meridional structure with a triangular shape in the tropical Pacific basin, are not a residual associated with periods of either more or less active ENSO. This result appears to agree with the so-called null hypothesis : There are robust large scale decadal mean state changes that are entirely independent of EDM. However, it will be shown in section 4 that there are low-frequency changes in the tropical Pacific mean state that are connected with EDM Interactive Ensemble Model [22] As mentioned in section 1, previous simple model results indicate that the relationship between TPDV and EDM depends on whether ENSO is self-sustained or damped and stochastically forced (i.e., Kirtman and Schopf [1998] versus Thompson and Battisti [2001]). In the previous sections, we found that the dominant mode of TPDV in the standard coupled model did not modulate the amplitude or frequency (not shown) of ENSO. This is largely consistent with the null hypothesis (i.e., damped coupled feedbacks), and we conjecture that in applying the interactive ensemble the relative amplitude of this mode should be reduced. If the amplitude is reduced by a factor of 6 in the case of the six-member interactive ensemble or 12 in the case of the twelve-member interactive ensemble, then coupled feedbacks are unimportant and the variability can be viewed as agreeing with Hasselmann s [1976] theory. However, if the reduction in the amplitude is somewhat less, then we argue that damped coupled feedbacks or internal variability due to oceanic dynamics [Yeh and Kirtman, 2004] may be enhancing the low-frequency variability, but the stochastic forcing is still required. [23] We first show the TPDV identified by the first EOF in the IE-6 and IE-12 (Figures 4a and 4b). Note that a 10-year running mean is applied to the SST data for a period of 500 years (IE-6) and 250 years (IE-12). The first EOF of 4of19

5 Figure 3. Anomalous mean SSTAs and wind stress anomalies for the tropical (a) warm and (b) cold state. (c) Difference of standard deviation of SSTA between Figures 3a and 3b. Shading is positive. Contour interval is 0.05 C for Figures 3a and 3b and 0.1 C for Figure 3c. See color version of this figure in the HTML. the decadal SST for the IE-6 explains 41.6% of the filtered variance and 28.1% for the IE-12. The spatial patterns of the leading mode for the IE-6 and IE-12 resemble the first EOF of the SC. All three of these simulations, i.e., SC, IE-6, and IE-12, have similar dominant TPDV with a broad meridional structure in the tropical Pacific basin. The distinction is in the percentage of explained variance. As the number of ensemble member increases, the relative amplitude for the dominant TPDV decreases from 46.4% (SC), 41.6% (IE-6), to 28.1% (IE-12). Since the EOF calculation for each 5of19

6 Figure 4. (a) Same as in Figure 1 except for the IE-6. (b) Same as in Figure 1 except for the IE-12. The first EOF mode for the IE-6 (IE-12) explains 41.6% (28.1%) of the filtered variance. See color version of this figure in the HTML. simulation is done independently, it is possible that the difference in explained variance is due to EOFs from a particular simulation projecting onto higher-order EOFs from different simulation. We have eliminated this possibility by confirming that the first EOF from a particular simulation is independent of higher-order EOFs from the other simulations. This result suggests that in all simulations this dominant mode of TPDV, which is independent of EDM (shown below), is noise forced, but damped coupled feedbacks or internal ocean dynamics enhance this variability. [24] The subject of the remainder of this section is to identify the relationship between decadal mean state changes associated with the first EOF in the tropical Pacific and EDM in the IE6 and IE-12. A 10-year running mean of the NINO3.4 amplitude (dashed line) in the IE-6 for a period of 500 years has been plotted with PC time series of the first EOF (solid line) in Figure 5a. Figure 5b is the same as Figure 5a except for the IE-12 for a period of 250 years. As with the results from the SC simulation, there are periods when the PC time series are in phase with NINO3.4 amplitude and periods when they are out of phase. The simultaneous correlation between the two time series in Figure 5a is 0.03 and that in Figure 5b is The lead-lag correlations for the lagged period of ±20 years between the two time series in Figure 5a (5b) do not exceed ±0.2 (±0.4). Note that the 95% significant confidence levels should be above ±0.6. Again, this suggests that there is little or no relationship between the dominant mode of TPDV and EDM in the IE-6 and IE-12 simulation. [25] We repeat the composite analysis based on the PC time series of the first EOF mode to show the potential relationship between the dominant tropical Pacific mean state and EDM. Figures 6a 6c are the same as Figures 3a 3c except for the IE-6 simulation. The tropical Pacific warm and cold SST state in the IE-6 have spatial structures similar to the dominant mode of TPDV shown in Figures 4a and 4b. The tropical Pacific warm state is characterized by anomalous mean westerlies across the basin from the western equatorial Pacific and vice versa in the tropical Pacific cold state. 6of19

7 Figure 5. (a) Same as in Figure 2 except for the IE-6 for a period of 500 years. (b) Same as in Figure 5a except for the IE-12 for a period of 250 years. 7of19

8 Figure 6. Same as in Figure 3 except for the IE-6. See color version of this figure in the HTML. [26] As shown in the low-frequency variability of the first EOF PC time series for the IE-6 (Figure 5a), there are decadal changes in the dominant mean state of the tropical Pacific basin with a triangular shape (Figures 6a and 6b). However, these changes in the dominant tropical Pacific mean state on decadal timescales have little effect on EDM. There is no significant difference in the SSTA standard deviation between the tropical Pacific warm and cold states (Figure 6c). The decadal mean state identified by the first EOF has no significant connection with the decadal variability in ENSO amplitude. We found the same results when these analyses were applied to the results in the IE-12 (not shown). [27] On the basis of this analysis our results suggest that in the presence of reduced noise (1) the amplitude of tropical SSTA variability is uncorrelated to this dominant mode of decadal changes in the tropical Pacific, (2) decadal mean states having a broad meridional structure in the 8of19

9 Figure 7. Simultaneous linear regression coefficients between the 10-year running mean time series of NINO3.4 amplitude and the tropical Pacific SSTAs (contour) and wind stress anomalies (arrows). The contour interval is 0.2. The contours are nondimensional, and the scale of the arrows is shown dyne/cm 2. See color version of this figure in the HTML. tropical Pacific basin are not a residual associated with high and low ENSO amplitude, and (3) the variability is consistent with the null hypothesis, i.e., a linear, damped and stochastically forced system. 4. Modulation of ENSO Amplitude [28] The dominant mode of TPDV identified with the EOF analysis above is uncorrelated to modulation of ENSO amplitude on decadal timescales. This result raises the question of whether there are any mean state changes associated with low-frequency modulation of ENSO amplitude. Moreover, if there are mean state changes, are they forcing the ENSO changes or are they a nonlinear residual associated with stronger or weaker ENSO events? Here we take a different approach than was used in the previous section by using changes in NINO3.4 amplitude to isolate mean state changes in the tropical Pacific Standard Coupled Model [29] To isolate the tropical Pacific mean state associated with EDM, we compute the simultaneous linear regression coefficients between the 10-year running mean time series of NINO3.4 amplitude and both the tropical Pacific SSTAs and wind stress anomalies in the SC simulation (Figure 7). [30] The spatial structure of tropical Pacific mean state, which is associated with EDM, has some similarities and differences from the dominant mode of TPDV identified by the first EOF mode (Figure 1). The tropical Pacific mean SSTAs associated with EDM have a center of action in the central equatorial Pacific as well as the band in the northeastern tropical Pacific, which is a common feature with the dominant mode of TPDV. However, Figure 7 shows somewhat asymmetric structures with sign alternating around 140 E and the date line with large variability in the western and central tropical Pacific, which has some marked differences from the first EOF shown in Figure 1. The regressed wind stress anomalies (Figure 7) are characterized by westerlies in the central tropical Pacific (10 N 10 S, 160 E 160 W) and easterlies in the far western and eastern equatorial Pacific. The regressed SSTAs and wind stress anomalies noted in Figure 7 stand in contrast to those of the tropical Pacific mean state uncorrelated to EDM (i.e., Figure 1). Note that the dominant tropical Pacific warm (cold) states identified by the first EOF, which have a broad meridional structure with a triangular shape in the tropical Pacific basin, are marked by anomalous westerlies (easterlies) across the basin from the western equatorial Pacific (Figures 3a and 3b). [31] Figure 8a shows the anomalous mean SSTAs and wind stress anomalies obtained by subtracting periods of low ENSO amplitude from periods of high ENSO amplitude. The high ENSO amplitude is based on periods when the 10-year running mean time series of the NINO3.4 amplitude (dashed line in Figure 2) exceed 1 standard deviation. Similarly, the low ENSO amplitude is based on periods when the same time series exceed 1 standard deviation below normal. Note that the standard deviation is calculated from the 10-year running mean time series of NINO3.4 amplitude in which the grand mean for the entire period has been subtracted. The spatial structure of SSTAs and wind stress anomalies is similar to the regressed pattern (Figure 7). The westerlies in the central equatorial Pacific and easterlies in the far western equatorial Pacific are also similar to characteristics of regressed wind stress anomalies shown in Figure 7, which is in contrast to the basin scale westerlies or easterlies of decadal mean states uncorrelated to EDM. [32] Figure 8b shows the difference in the SSTA standard deviation between the high and low ENSO amplitude periods. The shading is the regions exceeding 90% significance based on a chi-square test. Maximum differences in the SSTA standard deviation are located in around 150 W along the equator with order of C. The standard 9of19

10 Figure 8. (a) Difference of anomalous mean SSTAs and wind stress anomalies between periods of high ENSO variance and periods of low ENSO variance. Shading is positive, and contour interval is 0.1 C. The unit for wind stress anomaly is dyne/cm 2. (b) Difference of standard deviation of SSTA between the high and low ENSO amplitude periods. Contour interval is 0.1 C. The shading in Figure 8b indicates regions exceeding 90% significance based on a chi-square test. See color version of this figure in the HTML. deviation of tropical Pacific SSTA variability during a period of 300 years in the SC has a maximum order of C around 160 W along the equator (not shown). [33] Our result suggests that the specific tropical Pacific mean state, which is associated with the variability in ENSO amplitude, has different structures of SSTAs and wind stress anomalies compared to the dominant mode of TPDV. However, we do not know that the tropical Pacific mean state shown in Figure 7 is truly associated with EDM even though there are significant differences of the amplitude of SSTA variability in composite analysis (Figure 8b). The large amplitude of TPDV in the SC, which is unrelated to EDM, can be smeared into composites of tropical Pacific mean state based on the variability of ENSO amplitude. In the next subsection we present the tropical Pacific mean states associated with EDM based on the interactive ensemble model. Here the noise forcing is small enough so that detecting the mean state changes that are associated with EDM is facilitated Interactive Ensemble Model: IE-6 and IE-12 [34] In order to isolate the tropical Pacific mean state associated with EDM in the IE-6 and the IE-12 simulation, we follow the same procedure as in the previous section. Figure 9a is the same as in Figure 7 except for the IE-6 based on a period of 500 years. Figure 9b is the same as in Figure 9a except for the IE-12 based on a period of 250 years. Both the regressed SSTAs and wind stress anomalies are quite similar in the IE-6 and IE-12. The tropical Pacific mean state associated with EDM shows somewhat asymmetric structures with alternating sign in the western and central tropical Pacific. The regressed wind stress anomalies have maximum variability in the far western and central equatorial Pacific with opposite sign, which is consistent with large zonal gradient of SSTA. These characteristic are intensified in the tropical Pacific mean state associated with EDM for the IE-12 (Figure 9b) compared to the IE-6 (Figure 9a). [35] The structure of tropical Pacific mean state associated with EDM has some similarities in the western and central tropical Pacific and differences in the eastern tropical Pacific between the SC (Figure 7) and the IE-6 (Figure 9a). This is not the case for the comparison between the IE-6 (Figure 9a) and the IE-12 (Figure 9b). The overall noise level is reduced in the IE-12 compared to the IE-6. However, the tropical Pacific mean state associated with EDM is 10 of 19

11 Figure 9. (a) Same as in Figure 7 except for the IE-6 based on a period of 500 years. (b) Same as in Figure 7 except for the IE-12 based on a period of 250 years. See color version of this figure in the HTML. the same in both the IE-6 and IE-12. This result suggests that the tropical Pacific mean state shown in Figures 9a and 9b is nearly independent of the amplitude of atmospheric noise. When the overall noise level is reduced in the IE-6 and IE-12 simulation, the tropical Pacific mean state associated with EDM, which is independent of changes of noise amplitude, is detected. [36] To clarify the tropical Pacific mean state associated with EDM, we performed a composite analysis. The analysis presented here is based on the results of IE-6 simulation; however, similar results are obtained when the same analysis is applied to the IE-12. Figure 10a is the same as in Figure 8a except for the IE-6 simulation. The spatial pattern of the composite tropical Pacific mean state associated with EDM is similar to the regressed SSTAs shown in Figure 9a. Most of the central and eastern tropical Pacific is warmer and the most of the western equatorial Pacific is colder during periods of high ENSO amplitude. The pattern correlation between the regressed SSTAs (Figure 9a) and composite SSTAs (Figure 10a) is The tropical Pacific mean SSTAs change sign around 140 E and the date line with a large zonal temperature gradient (Figure 10a). The warm SSTA is characterized by anomalous mean westerlies in the central equatorial Pacific, and the cold SSTA in the western Pacific is marked by easterlies in the far western equatorial Pacific, similar to the regressed wind stress anomalies shown in Figure 9a. Figure 10b shows the difference in the SSTA standard deviation between the high and low ENSO amplitude periods. As expected, there are significant differences in the SSTA standard deviation between the two periods. Shading indicates the regions exceeding 90% confidence level. [37] On the basis of the above results we suggest that there are tropical Pacific mean state changes associated with low-frequency modulation of ENSO amplitude in the SC, IE-6, and IE-12. Moreover, the tropical Pacific mean state associated with EDM in the IE-6 and IE-12 is unrelated to changes of noise amplitude. This tropical Pacific mean state 11 of 19

12 Figure 10. Difference of anomalous mean SSTAs and wind stress anomalies between the high and low ENSO variance periods. Shading is positive, and contour interval is 0.05 C. The unit for wind stress anomaly is dyne/cm 2. (b) Difference for standard deviation of SSTA between the high and low ENSO amplitude periods. Contour interval is 0.1 C. The shading in Figure 10b indicates regions exceeding 90% significance based on a chi-square test. See color version of this figure in the HTML. is distinct from the dominant tropical Pacific mean state identified by the first EOF in both the spatial pattern of SSTAs and the structure of wind stress anomalies. In the next subsection we will show that this tropical Pacific mean state associated with EDM looks surprisingly similar to the structure and variability of the second EOF SST mode in two interactive ensemble models, but is difficult to detect in a standard coupled model EOF2 in the SC, IE-6, and IE-12 [38] As a check on the robustness of the mean state association with the modulation of ENSO amplitude, we examined the higher-order EOFs. Here the relative amplitude of the second EOF mode in the three simulations is more than 10% of the filtered variance. Note that EOFs three and greater explain only a few percent of the filtered variance in three simulations. Figures 11a 11c show the second EOF modes for the 10-year running mean SSTA in the SC, IE-6, and IE-12, respectively. The second EOF mode of the decadal SST explains 11.6% (SC), 10.6% (IE-6), and 22.9% (IE-12). [39] The structure of the second EOF mode for the SC is different from the IE-6, but the spatial structure is similar between the IE-6 and the IE-12. If we compare to the second EOFs in the IE-6 and IE-12 (Figures 11b and 11c), it is interesting to note that when the noise is reduced the explained variance for the second EOF increases with similar spatial structures. When the noise variance decreases from the IE-6 to the IE-12, the relative amplitude for the second EOF mode increases from 10.6% to 22.8%. This is in contrast to the relative amplitude for the dominant TPDV forced by uncoupled atmospheric noise, which is identified by the first EOF mode, which decreases from 41.6% (IE-6) to 28.1% (IE-12). Simply put, this suggests that the variability of the second EOF is not a damped and stochastically forced mode. However, this second EOF, which was derived from low-pass filtered SSTA, explains 45% of total SST variability in the IE-6 and IE-12. For more detail we calculated the spatially averaged SST variance explained by the second EOF mode in the tropical Pacific basin (30 N 30 S, 120 E 90 W) for the entire period of the simulation. This variance is obtained by the projection of the principal components (PCs) into the second EOF. We found that the ratio of decadal SST variance explained by the second EOF and the total SST variance is less than 10% in the IE-6 and IE-12. While this percentage of total 12 of 19

13 Figure 11. Second EOF mode for the 10-year running mean SSTA in the (a) SC, (b) IE-6, and (c) IE-12. Shading is positive. Contour interval is 0.01 and unit is nondimensional. See color version of this figure in the HTML. explained variance is small, it is consistent with observed decadal SST explained variance. The spatial pattern of the second EOF mode (Figures 11b and 11c) is remarkably similar to that of the regressed SSTA based on the 10-year running mean time series of NINO3.4 amplitude (Figures 9a and 9b) in both the IE-6 and IE-12, but this is not the case with the SC. The pattern correlation between the second EOF mode and the regressed SSTA based on the 10-year running mean time series of NINO3.4 amplitude is 0.94 in the IE-6 and 0.98 in the IE-12. In the SC, the regressed 13 of 19

14 Figure 12. Time series of a 10-year running mean of the NINO3.4 amplitude (dashed line) with PC time series of the second EOF mode (solid line) in the (a) SC, (b) IE-6, and (c) IE-12. SSTA based on the 10-year running mean time series of NINO3.4 amplitude (Figure 7) does not resemble either the spatial pattern of the first EOF nor the second EOF. [40] The variability of the second EOF mode is coincident with that of a 10-year running mean of the NINO3.4 amplitude in the IE-6 and IE-12, but this is not detected in the SC. Figures 12a 12c show the time series of a 10-year running mean of the NINO3.4 amplitude (dashed line) with PC time series of the second EOF (solid line) in the SC, IE-6, and IE-12, respectively. In contrast to a fluctuating in-phase/ out-of-phase relationship of two time series in the SC, the variability between the NINO3.4 amplitude and the PC time series of the second EOF mode has an in-phase relationship in both IE-6 and IE-12. The simultaneous correlation between the two time series is significantly high, 0.76 in the IE-6 and 0.92 in the IE-12. [41] These results indicate that the tropical Pacific mean state associated with EDM (i.e., the second EOF) becomes more dominant when the overall noise level decreases from the IE-6 to the IE-12. However, the identification of tropical Pacific mean state associated with EDM using an EOF analysis is difficult in the case of the SC. We are not arguing that there is no specific tropical Pacific mean state associated with EDM in the SC. We are arguing that the large amplitude of atmospheric noise makes it difficult to detect the decadal mean state changes associated with EDM. When the overall noise is reduced from the SC to the IE-6, the variability of the second EOF mode associated with EDM is easier to detect. With more reduction in the amplitude of the noise in the IE-12, this mode of variability explains a larger fraction of the low-frequency variability. However, we do not know whether the variability of the second EOF mode associated with EDM forces the ENSO changes or is a nonlinear residual mode associated with stronger and weaker ENSO events. 5. Markov Model Experiment [42] In order to demonstrate that this second EOF mode argues against the null hypothesis, we develop a simple Markov model based on the output of IE-6. We show that the Markov model is unable to capture the correlation between EDM and the tropical Pacific mean state changes described by EOF2. In order to construct the Markov model we use the first 10 EOF modes and each PC time series of the IE-6 simulation for the tropical SSTA in which no running mean has been applied. The first three EOFs of SST (not shown) account for 38%, 7%, and 6% of the total variance, and each of the higher-order EOFs accounts for less than 5%. The 10 combined EOFs explain more than 70% of the total variance. The Markov model is T nþ1 ¼ AT n þ N n ; where T n is the vector of PCs for the first 10 EOFs, A is the transition matrix, and N n is Gaussian white noise. Multi- ð1þ 14 of 19

15 Figure 13. (a) First EOF mode for the 10-year running mean SSTA in the Markov model. The first EOF mode explains 64.4% of the filtered variance. Shading is positive, and contour interval is (b) Same as in Figure 2 except for the Markov model for a period of 500 years. See color version of this figure in the HTML. 15 of 19

16 Figure 14. Simultaneous linear regression coefficients between the 10-year running mean time series of NINO3.4 amplitude and tropical Pacific SSTAs for a period of 500 years in Markov model. The shading is positive, and contour interval is 0.2. Unit is nondimensional. See color version of this figure in the HTML. plying by the transpose of vector T n on both sides of (1) gives ht nþ1 ðt n Þ T i¼aht n ðt n Þ T iþhn n ðt n Þ T i; ð2þ where h...i means the average over a period of 500 years. Because the N n does not correlate with T n, A ¼hT nþ1 ðt n Þ T iht n ðt n Þ T i 1 ¼ C n ðd n Þ 1 : ð3þ Here C n is the lag-1 covariance matrix, while D n is the autocovariance matrix. The amplitude of the noise is chosen to reproduce the variance of the model PCs. On the basis of the Markov model, we produce a synthetic tropical SSTA for a period of 1500 years. The following results are based on the data for the last 500 years. [43] In order to separate the decadal variability, a 10-year running mean is applied to the reconstructed SST data for a period of 500 years. Figure 13a shows the first EOF mode for the 10-year running mean SSTA. The spatial pattern of the leading mode is similar to the first EOF mode of the IE-6 (Figure 4a). The first EOF mode of the decadal SST explains 64.4% of the filtered variance, indicating that the Markov model has dominant decadal variability with a broad meridional structure in the tropical Pacific basin similar to the IE-6. The relationship between the dominant tropical decadal mode and EDM in the Markov model is shown in Figure 13b. A 10-year running mean of the NINO3.4 amplitude (dashed line) in the Markov model for a period of 500 years has been plotted with PC time series of the first EOF (solid line). Similar to the IE-6, the two time series show a fluctuating in-phase/out-of-phase relationship on decadal timescales. With the high explained variance of the first EOF mode in the Markov model, these results support our previous conclusion that the stochastic noise forcing explains this mode of decadal variability, which is uncorrelated to changes in ENSO amplitude. [44] Here we take the same approach that was used in the previous section by using change in NINO3.4 amplitude to isolate tropical Pacific mean state in the Markov model. Figure 14 is the simultaneous linear regression coefficients between the 10-year running mean time series of NINO3.4 amplitude (dashed line in Figure 13b) and tropical Pacific SSTAs for a period of 500 years in the Markov model. This figure should be compared to Figure 9a based on the same approach in the IE-6. There is no significant relationship between the tropical Pacific SSTA and changes of ENSO amplitude in the Markov model. Moreover, the structure of regressed SSTAs shown in Figure 14 is different from that in Figure 9a. [45] In the previous section we showed that the variability of the second EOF mode has an in-phase relationship with changes of ENSO amplitude in the IE-6. The spatial pattern of the second EOF mode is also similar to that of the tropical Pacific mean state associated with EDM. We find that the third EOF in the Markov model looks like the second EOF in the IE-6; however, this mode of variability is not related to the variability of ENSO amplitude. Figure 15 is the same as Figure 13 except for the third EOF mode in Markov model. The spatial pattern of the third EOF mode (Figure 15a) is quite similar to that of the second EOF mode in the IE-6 (Figure 11b), but the PC time series of this mode shows an in-phase/out-of-phase relationship with changes of ENSO amplitude (Figure 15b). The simultaneous correlation coefficient between the two time series (0.01) is not significant. This is in contrast to the variability of the second EOF mode in the IE-6, which has significantly high correlation (0.76) with the 10-year running mean of the NINO3.4 amplitude. The Markov model is unable to reproduce this relationship. These results suggest that (1) the variability of the second EOF mode, which is associated with EDM in the IE-6 and IE-12, is not forced by atmospheric noise and (2) important dynamics, i.e., nonlinearity or external forcing is needed to explain this mode of decadal variability. In particular, we mean to 16 of 19

17 Figure 15. Same as in Figure 13 except for the third EOF mode in Markov model. See color version of this figure in the HTML. 17 of 19

18 suggest processes that are external to the deep tropics. These processes may include, for example, variations in the subtropical cells or midlatitude thermocline ventilation. 6. Conclusion and Discussion [46] Despite recent advances in our understanding of ENSO, many aspects of its physics remain unknown. One of the largest uncertainties concerns the relationship between TPDV and EDM. There is no consensus whether decadal variations in the amplitude and frequency of ENSO are entirely noise driven and unrelated to low-frequency changes in the mean state or there is an unambiguous relationship between TPDV and EDM. Using the interactive ensemble model approach, we examine the processes that maintain TPDV and EDM, and the relationship between them. [47] We first identify the dominant mode of TPDV as an SSTA pattern having a broad meridional structure with a triangular shape in the tropical Pacific basin. In the observations a similar pattern has been noted by Zhang et al. [1997] and Yeh and Kirtman [2003]. The Pacific Ocean climate during the 1980s and early 1990s shows the distinctive triangular-shaped warming anomaly pattern [Knutson and Manabe, 1998]. The triangular region of recent warming extends along much of the North and South American coasts in the eastern part of the basin. On the basis of an EOF analysis, we examine whether this dominant mode of TPDV impacts EDM. We obtain the following conclusions: [48]. Decadal changes in the tropical Pacific mean state having a broad meridional structure with a triangular shape (identified by the first EOF) are not related to ENSO decadal modulation, and these decadal mean states are not a residual associated with periods of either more or less active ENSO. [49]. This mode is consistent with linear, damped, and stochastically forced coupled system. [50] The above results raise questions of whether there are any mean state changes associated with low-frequency modulation of ENSO amplitude. In order to isolate tropical Pacific mean state associated with EDM, we use the variability of ENSO amplitude in the three simulations. Here we conclude as follows: [51]. The tropical Pacific mean state associated with EDM has structures of SST and wind stress anomalies, which are different than the dominant tropical Pacific mean state identified by the first EOF. [52]. The amplitude of atmospheric noise can make it difficult to detect decadal mean state changes associated with EDM. When the overall noise level is reduced, the tropical Pacific mean state variability associated with EDM, similar to the structure and variability of the second EOF SST mode, is detected in the two interactive ensemble models. [53]. On the basis of a Markov model experiment, the variability of the second EOF mode, associated with changes of ENSO amplitude in the interactive ensemble models, is not forced by atmospheric noise. Important dynamics, i.e., nonlinearity or external forcing, is needed to explain this mode of decadal variability. [54] On the basis of all of the above results, we suggest that there are two important modes of TPDV. The first has a basin-wide scale, is unconnected to the variability of ENSO amplitude, and appears to be stochastically forced. The second mode of TPDV is unambiguously connected to the modulation of ENSO amplitude. If the second mode of TPDV exists in nature, there may be some potential for predicting the predictability of ENSO since higheramplitude ENSO may imply higher predictability and vice versa. This would allow for a somewhat more optimistic view than the null hypothesis in being able to predict whether ENSO will reside in a quiet or active period. [55] However, detecting the second mode of TPDV by an EOF analysis can be inhibited by strong atmospheric noise, i.e., the standard coupled model. Although not shown here, we applied the same analysis to the low-pass filtered observed SSTA [Kaplan et al., 1998]. Using observed SSTA during we investigated connections between Pacific decadal variability and low-frequency amplitude modulation of ENSO. We did not find a significant tropical Pacific mode associated with EDM in the observations, whereas the stochastically forced first EOF described here is detected (S.-W. Yeh and B. P. Kirtman, Pacific decadal variability and ENSO amplitude modulation, submitted to Journal of Climatology, 2004). This supports our conjecture that the second EOF in the SC model is masked by uncoupled atmospheric stochastic forcing. Additional details can be found in a COLA technical note ( grads.iges.org/pub/ctr/ctr_168.pdf). [56] The interactive ensemble models help to detect this mode, here identified by the second EOF. Important dynamics, i.e., nonlinearity or external forcing, is needed to explain the variability of the second mode of TPDV, which is part of our ongoing research activities. [57] Acknowledgments. The authors are grateful to Ragu Murtugudde and two anonymous reviewers, who provided many suggestions that have improved this manuscript. The authors are indebted to B. Huang and D. Straus for their careful reading. This research was supported by grants from the National Science Foundation (ATM and ATM ), the National Oceanic and Atmospheric Administration (NA16-GP2248), and National Aeronautics and Space Administration (NAG ). References An, S.-I., and B. Wang (2000), Interdecadal change of the structure of the ENSO mode and its impact on the ENSO frequency, J. Clim., 13, Barnett, T. P., D. W. Pierce, M. Latif, D. Dommenget, and R. Saravanan (1999), Interdecadal interactions between the tropics and midlatitudes in the Pacific basin, Geophys. Res. Lett., 26, Barsugli, J., and D. S. 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