Interaction between equatorially symmetric and asymmetric tropical eastern Pacific SSTs

Transcription

1 Theor Appl Climatol DOI /s y ORIGINAL PAPER Interaction between equatorially symmetric and asymmetric tropical eastern Pacific SSTs Soon-Il An & Jung Choi Received: 23 September 2009 / Accepted: 11 January 2010 # Springer-Verlag 2010 Abstract The third version of the extended reconstructed sea surface temperature (SST) data spanning from 1880 to 2007 was used to investigate the interaction between equatorially symmetric and asymmetric tropical eastern Pacific SSTs. Principal component analysis and wavelet spectrum analysis showed that the asymmetric SST was dominated by an amplitude-modulated annual cycle, while the symmetric SST was a mixture of amplitude-modulated annual cycle and El Niño-Southern Oscillation (ENSO). The symmetric and asymmetric components were significantly correlated, particularly in March and October. In March, when ENSO is usually weak, the interaction between two components is mainly due to the interaction between the amplitude-modulated annual cycles of each component. On the other hand, in October, when ENSO is dominant, the interaction between amplitude-modulated asymmetric annual cycle and ENSO becomes dominant. The interaction in March is partly explained by anomalous southeasterly winds associated with the symmetric SST pattern reducing wind speed over the southeastern Pacific, causing an intensification of the asymmetric SST component. In October, the equatorial asymmetrical development of ENSO causes a significant correlation between the symmetric and asymmetric components. 1 Introduction While a strong semi-annual cycle in the local solar radiation is observed on the equator, the tropical eastern S.-I. An (*) : J. Choi Department of Atmospheric Sciences/Global Environmental Laboratory, Yonsei University, Seoul , South Korea sian@yonsei.ac.kr Pacific sea surface temperature (SST), as well as surface winds, is dominated by the annual cycle (hereafter AC ) with a warm and wet season occurring in boreal spring and a cold and dry season in boreal fall (Mitchell and Wallace 1992). AC in the equatorial eastern Pacific is attributed to mainly the local oceanic process and secondarily to the horizontal advection of temperature rather than direct radiative heating (Hayes et al. 1991; Seageretal. 1988; Koeberle and Philander 1994; Xie1994). Furthermore, asymmetries with respect to the equator in surface wind, ocean currents, and SST, which are driven by seasonal variations in solar radiation in both hemispheres, actually drive AC along the equator, i.e., the symmetric component of AC. Xie (1994), for example, mentioned that the intensification of the northwestward trade over the equator during the boreal summer and its weakening during the boreal winter cause the annual variation of surface evaporative cooling, and hence, of SST. Li and Philander (1996) stressed the importance of the meridional advection of ocean temperature such that the crossequatorial winds induce asymmetric upwelling with respect to the equator and, hence, asymmetric SST, which is maintained throughout the year. The El Niño-Southern Oscillation (ENSO) frequently reaches its peak value during the boreal winter and dies out during the following spring (Rasmusson and Carpenter 1982; An and Wang 2001; Galanti and Tziperman 2000). This seasonal-amplitude locking of ENSO can be understood as either the nonlinear frequency locking of ENSO to an annual period (Jin et al. 1994) or the seasonal change in the linear stability of ENSO (Tziperman et al. 1998). Thus, AC plays the role of phase-setter of ENSO. On the other hand, the AC amplitude in the eastern equatorial Pacific tends to be weaker during El Niño periods and stronger during La Niña periods (Gu and Philander 1995; Xie 1995).

2 S.-I. An, J. Choi Therefore, the two systems strongly interact with one another. In fact, the generation of deterministic chaos, that is, the irregularity of the ENSO, has been understood in terms of this two-way interaction (Jin et al. 1994; Chang et al. 1994, 1996; Tziperman et al. 1994, 1995; Wang and Fang 1996; Jin 1996; Wang et al. 1999). On the whole, the mechanisms driving the AC of the equatorial eastern Pacific and the interaction between AC and ENSO are very important topics in the climate study society. So far, AC has been studied without reference to its origins. Here, we separated the equatorial eastern Pacific SST into its symmetric and asymmetric components with respect to the equator. Although this is a simple statistical separation, it is highly applicable as a classification for the causes of these phenomena because the symmetric components of AC and ENSO are mainly (dynamically) driven by the air sea interaction, while its asymmetric component is mainly driven by solar forcing. This study may be considered as an extension of Wang (1994b, hereafter, W94 ). W94 found that the asymmetric AC does not directly interact with ENSO but symmetric AC does with ENSO. However, W94 applied a modedecomposition into only AC, while we further analyze the relationship between the equatorially symmetric and asymmetric components of the eastern Pacific SST including both AC and ENSO. The data and method are introduced in the following section. The general features of the symmetric and asymmetric tropical eastern Pacific SST are documented in Section 3. In Section 4, the relationship between the symmetric and asymmetric components is described. A summary and remarks are given in the last section. 2 Data and method In this study, the third version of the extended reconstructed sea surface temperature (ERSST.v3) on a 2 grid (Xue et al. 2003; Smith et al. 2008) was utilized. This monthly mean data started in January 1854, but we analyzed the data from 1880 to 2007 to avoid errors due to the sparseness of data prior to ERSST.v3 is an improved and extended reconstruction over version 2; details are available at lwf.ncdc.noaa.gov/oa/climate/research/sst/sst.php. We also obtained the monthly mean surface wind speed data and the net of outgoing longwave radiation (OLR) data from the NCEP/NCAR global reanalysis (Kalnay et al. 1996) for The net of OLR is defined by the difference in upward longwaves between the surface and the top of the atmosphere. Therefore, a positive (negative) value indicates more (fewer) clouds. The data are divided into symmetric (denoted by SYM) and asymmetric (denoted by ASY) components. An SST field T (x, y, and t) was partitioned into symmetric and asymmetric components as Tx; ð y; tþ ¼ Tx; ð yþþt 0 SYM ð x; y; t ÞþT 0 ASY ð x; y; t Þ; where T 0 SYM ð x; y; t Þ ¼ T 0 ðx; y; tþþt 0 ðx; y; tþ 2 T 0 ASY ð x; y; t Þ ¼ T 0 ðx; y; tþ T 0 ðx; y; tþ 2 T 0 ðx; y; t Þ ¼ Tx; ð y; tþ Tx; ð yþ and where x and y are the longitudinal and latitudinal distance (y=0 at equator), respectively. T indicates the SST anomaly, the perturbation from the total mean (T), showing that both of the components are independent of one another, i.e., no intersection between them. In contrast with the present study, W94 considered symmetric and asymmetric components only for the mean seasonal cycle (see Eqs. 3 and 4 in W94). The symmetric (asymmetric) component is composed of the SST anomalies (departure from conventional climatology) and the symmetric (asymmetric) part of mean seasonal cycle. Therefore, W94's symmetric and asymmetric components contain the same SST anomalies. 3 Equatorially symmetric and asymmetric eastern Pacific SSTs To determine the dominant pattern and its temporal evolution, empirical orthogonal function analysis (EOF; a. k.a. principal component (PC) analysis) was applied to the T 0 SYM and T 0 ASY. The first EOF mode (EOF1) of the symmetric SST anomaly explains 47.4% of the total variance (Fig. 1a). The maximum loading was confined to the equatorial eastern Pacific. As in the corresponding time series of the PC (Fig. 1c, hereafter SYM PC1 ), and also in the wavelet power spectrum (see Fig. 2), this mode represented the symmetric AC and ENSO signals (also W94; Wang 1994a). The large peaks of PC mostly corresponded to ENSO and partly to amplitude-modulated symmetric AC. Here, amplitude-modulated AC refers to signals that fluctuated with an annual period but whose amplitudes varied interannually, and ENSO refers to the signals that fluctuated with an interannual period. Nonetheless, the two signals cannot be separated easily because of the seasonal locking nature of ENSO. In some senses, ENSO can be interpreted as an interannually modulated AC (e.g., W94). This modulation is not symmetrical: the fall season is affected most strongly because of the seasonally

3 Interaction between symmetric and asymmetric eastern Pacific SSTs Fig. 1 The spatial pattern of the first empirical orthogonal function mode of (a) the symmetric sea surface temperature (SST) component and (b) the asymmetric SST component. The corresponding time series for (c) the symmetric SST component (SYM PC1) and (d) the asymmetric SST component (ASY PC1) dependent ENSO evolution. The first EOF mode of the asymmetric SST anomaly explained 93.2% of the total variance (Fig. 1b), indicating that the asymmetric component of SST is mainly driven by a single factor, i.e., the seasonal variation in solar radiation (also see Fig. 2d). The AC component of the asymmetric mode was dominant, and the amplitude modulation of this mode appearing in the corresponding PC (Fig. 1d, hereafter ASY PC1 ) was relatively weak. In order to examine the AC and interannual components in the PC time series separately, we applied wavelet analysis to each PC time series, as shown in Fig. 2. The wavelet analysis decomposed the time series into time- and frequency-space data simultaneously, giving both the amplitude of any periodic signals within the series and how this amplitude varied with time (Torrence and Compo 1998). Note again that it did not totally separate AC and ENSO because of the seasonal dependency of ENSO and the nonlinear interaction between two components; here, we were merely attempting to separate them on a timescale basis alone. As shown in Fig. 2, SYM PC1 included various time scales, from an annual period to a period of nearly a decade. For example, before the 1960s, longerperiod variability of 5 to 7 years occurred occasionally. After the 1960s and through the late 1970s, a shorter-period variability of about 3 years was dominant, and afterwards, the loading shifted to a relatively longer-period variability of 4 to 5 years. A mechanism regarding the decadal change in the interannual variability, especially for the last 50 years, has been documented in An and Jin (2001), Wang and An Fig. 2 The real part of the wavelet analysis of (a) SYM PC1 and (c) ASY PC1. The scale-averaged power from 0.5 to 1.5 years of (c) SYM PC1 and (d) ASY PC1

4 S.-I. An, J. Choi Fig. 3 Seasonal climatology of SYM PC1 and ASY PC1 (2001). and many others. In order to isolate the symmetric AC from the interannual variability, we calculated the scaleaveraged wavelet power for the annual band of years, which represented the slowly varying amplitude modulation of the symmetric AC. Figure 2b shows that the maximum amplitude of the symmetric AC was almost double its minimum amplitude. Large amplitudes were recorded around the 1890s, 1910s, s, and 1990s, and small amplitudes around the 1900s and s. Decadal modulation of the symmetric AC amplitude was clearly visible, but the association with the interannual variability was either more (mostly before 1980s; Gu and Philander 1995) or less (after 1980s; Wang and Wang 1996) recognizable depending on the decadal period (e.g., Setoh et al. 1999). The scale-averaged wavelet power of the counterpart associated with ASY PC1 was also calculated (Fig. 2d). The fluctuation range in the amplitude of the asymmetric AC was relatively smaller than that of the symmetric AC, but the absolute value was larger. Interestingly, the increasing trend since 1920s was dominant, which was not shown in the symmetric AC. This trend is possibly due to the global warming effect, because the warming trend in the northern hemisphere (NH) was larger than that in the southern hemisphere (SH) (Cavalieri et al. 1997; Flato and Boer 2001), increasing the north south temperature contrast. So far, we have documented the dominant patterns of equatorial symmetric and asymmetric SSTs and the characteristics of their temporal evolutions. Hereafter, we focus on the seasonality of these two components. First, in Fig. 3, we plotted the average value of the PCs (SYM PC1, ASY PC1) for each calendar month, which describes the climatology of each PC. The climatology of SYM PC1 (hereafter CLIM_SYM_PC1) showed a seasonal curve, reaching its positive peak around April and its negative peak around September, and the spring peak was larger than the fall peak. Here, the positive and negative values indicated the warm and cold SST anomaly patterns, respectively, over the equatorial eastern Pacific. Similarly, early spring (positive; NH cold and SH warm) peaks in the climatology of ASY PC1 (hereafter CLIM_ASY_PC1) and early fall (negative; NH warm and SH cold) peaks were observed. The positive peak appeared around February to March, and the negative around August to September. It thus appears that the CLIM_ASY_PC1 peak led that of the CLIM_SYS_PC1 by about 1 month. The detailed analysis of the relationship between SYM PC1 and ASY PC1 are presented in the following section. 4 Relationship between equatorially symmetric and asymmetric eastern Pacific SSTs The correlation between SYM PC1 and ASY PC1 at each calendar month was calculated (Fig. 4a). For example, the January correlation coefficient quantified the correlation between the January PC values, and Fig. 4a depicts the seasonality of the relationship between the symmetric and asymmetric components of the tropical eastern Pacific SST p ffiffiffiffi anomaly. pffiffiffiffiffiffiffiffiffiffiffiffi Based on the fact that the statistic t ¼ r d f = 1 r 2 (where r is a correlation coefficient, and d f is a degree of freedom) has student's distribution, the Student t test (Spiegel 1990) was performed for the significant test. The degree of freedom was determined by using S-method proposed by Wang and Shen (1999). Significant correlations were clearly visible during the Fig. 4 a Correlation between the original SYM PC1 and ASY PC1 for each calendar month. b Same as (a), except for the AC band (open square) and the interannual band (closed circle). Dotted line in (a) indicates the 95% significant level a b

5 Interaction between symmetric and asymmetric eastern Pacific SSTs spring and fall, but with opposite values. The positive correlation during spring, especially in March, was supposed to be due to the dynamic interaction between the symmetric the and asymmetric ACs: the large thermal contrast between NH cooling and SH warming during the spring (i.e., the positive phase of EOF1 of the asymmetric component) leads to the weakening of the southeast trade wind and, consequently, the warming of the symmetric AC via the reduction of surface heat flux to the atmosphere and weakening upwelling (i.e., positive phase of EOF1 of symmetric component) (Xie 1994; Li and Philander 1996). On the other hand, this thermodynamic coupling effect between the asymmetric component (i.e., north south thermal contrast) and the symmetric component weakens during the fall because of strong dynamical atmosphere ocean coupling processes such as Bjerknes feedback (Bjerknes 1966, 1969). The fall is usually an El Niñodeveloping season. Thus, the correlation between the symmetric and asymmetric components during the fall must be strongly influenced by El Niño activity. To confirm our argument further, we repeated the computations for Fig. 4a but applied a band-pass filter of years to the PCs and then calculated the correlation (hereafter AC band). The same calculation for the low-pass filter data (actually original data minus year bandpass filter data; hereafter, the interannual band) was performed for a cross-checking purpose (no significant correlations were observed over the whole year). As seen in Fig. 4b, the positive correlation for March was also observed in the AC band case, but the negative correlation during fall season was not observed except during October. This implies again that the negative correlation between the symmetric and asymmetric components may not be due to the interaction between the symmetric and asymmetric ACs but rather to the interaction between the symmetric ENSO and the asymmetric AC. As evidence, the correlation between symmetric ENSO and asymmetric AC on October is Dynamically, both the deep thermocline and the deep mixed layer during the El Niño fall suppressed the interaction between the symmetric and asymmetric ACs that occurs mostly on the ocean surface (e.g., Gu and Philander 1995; Xie 1995); thus, the correlation between the symmetric and asymmetric ACs becomes insignificant during the fall. The separation between the AC and the ENSO using the digital filtering technique was somewhat problematic, because of the possibility that part of the ENSO signal was buried in AC. Therefore, it was necessary to use a separate method to confirm our hypothesis. To do that, we calculated the regression map of the SST anomaly with respect to the SYM PC1 and ASY PC1 only for March (Fig. 5a, b) and October (Fig. 5c, d). The regression map of the SST anomaly to SYM PC1 for March exhibited an El Niño-like pattern, whose maximum poles were located in the equatorial eastern Pacific around 150 W and the coastal zone of South America (Fig. 5a). Thus, this regression map was similar to the EOF1 pattern of the symmetric component. On the other hand, the regression map of the SST anomaly to ASY PC1 for March exhibited a large positive anomaly in SH (the negative anomaly in NH was very weak) and a small positive anomaly along the equator (Fig. 5b). The symmetric positive anomaly in the equatorial region associated with the asymmetric component may contribute to the intensification of the symmetric component. Since the two regression maps were similar to the EOF patterns, a positive correlation between the two PCs for March was expected. The regression maps for October were also calculated. As shown in Fig. 5c, the October SST pattern associated with SYM PC1 resembled an El Niño pattern. Overall, this pattern was symmetric, but the negative anomaly in the off-equatorial SH was also dominant and may have fed into the asymmetric component. The October SST pattern associated with the Fig. 5 Map of the regression coefficients of the sea surface temperature anomaly with respect to (a, c) SYM PC1 and (b, d) ASY PC1 in March (left panels) and October (right panels). The statistically significant regions are shaded. Units are [K]. Light-gray, gray, and dark-gray shadings indicate 90%, 95%, and 99% significant levels, respectively a b c d

6 S.-I. An, J. Choi Fig. 6 Map of the regression coefficients of the wind speed with respect to (a, c) SYM PC1 and (b, d) ASY PC1 in March (left panels) and October (right panels). The statistically significant regions are shaded. Units are [m/s]. Light-gray, gray, and dark-gray shadings indicate 90%, 95%, and 99% significant levels, respectively a b c d asymmetric mode exhibited the negative anomaly over the equatorial and off-equatorial NH and a positive anomaly in the off-equatorial SH (Fig. 5d). Thus, two regression patterns were more likely opposite to each other, resulting in a negative correlation between the two PCs. To understand the intrinsic mechanism buried in the interaction between the asymmetric and symmetric components, we calculated the regression map of the surface wind speed anomaly with respect to SYM PC1 and ASY PC1 for either March (Fig. 6a, b) or October (Fig. 6c, d). The wind speed is directly linked to the surface heat flux: an intensified (weakened) wind speed causes intensified (weakened) cooling. As shown in Fig. 6a, the regression map to SYM PC1 for March exhibited a reduced wind speed over the southeastern Pacific, which resulted in surface warming through the reduction of evaporative cooling, and the surface warming matches to the positive regression coefficient of SST anomaly that appears in Fig. 5a. These results suggest that an intensified symmetric component (or El Niño-like pattern) drives the anomalous surface wind convergence toward the equatorial warm center (considered as a simple Gill-type response). In particular, the anomalous surface wind in the SH, i.e., the southeasterly, blows opposite to the seasonal cycle component of wind associated with the asymmetric SST component, a northwesterly. Thus, the wind speed is reduced, consequently warming the southeastern Pacific. The regression map of wind speed to ASY PC1 was not significant overall. The regression map of wind speed for October was also calculated. As Fig. 6c shows, reduced wind speed over the tropical central Pacific was observed. This reduced wind speed was attributed to the reduction of trade winds associated with an El Niño pattern appearing in the a c b d Fig. 7 Map of the regression coefficients of the net outgoing longwave radiation with respect to (a, c) SYM PC1 and (b, d) ASY PC1 in March (left panels) and October (right panels). The statistically significant regions are shaded. Units are [W m 2 ]. Lightgray, gray, and dark-gray shadings indicate 90%, 95%, and 99% significant levels, respectively

7 Interaction between symmetric and asymmetric eastern Pacific SSTs SST regression map (Fig. 5c). The regression map of wind speed to ASY PC1 showed an increase of wind speed over the equatorial central Pacific near the dateline and a small reduction over the equatorial eastern Pacific (Fig. 6d), which was not matched to the associated SST regression map. However, the intensified wind speed over the northeastern Pacific was somehow matched to the negative regression of the SST. Finally, we calculated the regression map of the net OLR with respect to PCs only for either March (Fig. 7a, b) or October (Fig. 7c, d). In the tropical region, the positive (negative) net OLR indicated more (fewer) clouds. As Fig. 7a shows, the positive regression of net OLR (i.e., more clouds) over the equatorial eastern Pacific matched overall the positive regression of SST, and the negative regression of the OLR over the off-equatorial western Pacific was matched to the negative regression of the SST. Since warm SSTs promote more convection, the net OLR and SST patterns were dynamically consistent. Similarly, the positive regression of the net OLR in Fig. 7b over the southeastern Pacific was collocated with the positive regression of the SST in Fig. 5b. Actually, greater cloud cover also causes surface cooling by blocking solar radiation, so the positive regression of OLR in this region was presumably a result of surface warming in turn due to weakening wind speed. A similar relationship was also found between the OLR and the SST in the October case (Fig. 7c, d), such that the positive (negative) regression of the net OLR was associated with a positive (negative) regression of the SST. The overall relationship was more pronounced in the regression map of the symmetric component. 5 Summary The ERSST.v3 data spanning from 1880 to 2007 were analyzed to investigate the interaction between the symmetric and asymmetric tropical Pacific SSTs with respect to the equator. The dominant spatial and temporal (PC) patterns were obtained by applying the EOF method to the symmetric and asymmetric components of the SST. The wavelet spectrum of the PCs revealed that the asymmetric SST was dominated by an amplitude-modulated AC, and that the symmetric SST was a mixture of an amplitudemodulated AC and the ENSO. The correlation between the PCs of the symmetric and asymmetric components for each calendar month was significant in both March (positive) and October (negative). The positive correlation of the March data was mainly due to the interaction between the amplitude-modulated ACs of each component. On the other hand, the negative correlation of the October data was due to the interaction between the amplitude-modulated asymmetric AC and the ENSO. In March, the symmetric SST pattern drove an anomalous southeasterly over the southeastern Pacific, which was actually opposite to the anomalous northwesterly associated with the asymmetric SST pattern, lowering the wind speed and increasing the surface temperature and, hence, intensifying the asymmetric SST component. In October, the ENSO was developed not simply symmetrically but asymmetrically; the equatorial SST shared its sign with the NH SST but had the opposite sign as that of the SH SST. The negative correlation in October was mainly due to the asymmetric development of the ENSO. Acknowledgements This work was supported by the National Comprehensive Measures against Climate Change Program by the Ministry of Environment, Korea (Grant No ) and by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund, KRF C00784). References An S-I, Jin F-F (2001) Collective role of thermocline and zonal advective feedbacks in ENSO mode. J Climate 14: An S-I, Wang B (2001) Mechanisms of locking the El Niño and La Niña mature phases to boreal winter. J Climate 27: Bjerknes J (1966) A possible response of the atmospheric Hadley circulation to equatorial anomalies of ocean temperature. Tellus 18: Bjerknes J (1969) Atmospheric teleconnections from the equatorial Pacific. Mon Weather Rev 97: Cavalieri DJ, Gloersen P, Parkinson CL, Comiso JC, Zwally JJ (1997) Observed hemispheric asymmetry in global sea ice changes. Science 278: Chang P, Wang B, Li T, Ji L (1994) Interactions between the seasonal cycle and the Southern Oscillation: frequency entrainment and chaos in a coupled ocean-atmosphere model. Geophys Res Lett 21: Chang P, Ji L, Li H, Flugel M (1996) Chaotic dynamics versus stochastic processes in El Niño-Southern Oscillation in coupled ocean-atmosphere models. Physica D 98: Flato GM, Boer GJ (2001) Warming asymmetry in climate change simulations. Geophys Res Lett 28: Galanti E, Tziperman E (2000) ENSO's phase locking to the seasonal cycle in the far-sst, far-wave, and mixed-mode regimes. J Atmos Sci 57: Gu D, Philander SGH (1995) Secular changes of annual and interannual variability in the tropics during the past century. J Climate 8: Hayes SP, Chang P, McPhaden MJ (1991) Variability of the sea surface temperature in the eastern equatorial Pacific during J Geophys Res 96:10,553 10,566 Jin FF (1996) Tropical ocean-atmosphere interaction, the Pacific cold tongue, and the El Nino-Southern Oscillation. Science 274:76 78 Jin FF, Neelin JD, Ghil M (1994) El Niño on the devil's staircase: annual subharmonic steps to chaos. Science 264:70 72 Kalnay E et al (1996) The NCEP/NCAR 40-year reanalysis project. Bull Am Meteorol Soc 77: Koeberle C, Philander SGH (1994) On the processes that control seasonal variations of sea surface temperatures in the tropical ocean. Tellus 46A:

8 S.-I. An, J. Choi Li T, Philander SGH (1996) On the annual cycle of the eastern equatorial Pacific. J Climate 9: Mitchell TP, Wallace JM (1992) On the annual cycle in equatorial convection and sea-surface temperature. J Climate 5: Rasmusson EM, Carpenter TH (1982) Variations in tropical sea surface temperature and surface wind fields associated with the Southern Oscillation/El Niño. Mon Weather Rev 110: Seager R, Zebiak SE, Cane M (1988) A model of the tropical Pacific sea surface temperature climatology. J Geophys Res 93: Setoh T, Imawaki S, Ostrovskii A, Umatani S-I (1999) Interdecadal variations of ENSO signals and annual cycles revealed by wavelet analysis. J Oceanogr 55: Smith TM, Reynolds RW, Peterson TC, Lawrimore J (2008) Improvements to NOAA's historical merged land-ocean surface temperature analysis ( ). J Climate 21: Spiegel MR (1990) Schaum's outline of theory and problems of statistics. McGraw-Hill, New York, p 504 Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79:61 78 Tziperman E, Stone L, Cane MA, Jarosh H (1994) El Niño chaos: overlapping of resonances between the seasonal cycle and the Pacific ocean-atmosphere oscillator. Science 264:72 74 Tziperman E, Cane MA, Zebiak SE (1995) Irregularity and locking to the seasonal cycle in an ENSO prediction model as explained by the quasi-periodicity route to chaos. J Atmos Sci 52: Tziperman E, Cane MA, Zebiak SE, Xue Y, Blumenthal B (1998) Locking of El Niño's peak time to the end of the calendar year in the delayed oscillator picture of ENSO. J Climate 11: Wang B (1994a) On the annual cycle in the tropical eastern central Pacific. J Climate 7: Wang XL (1994b) The coupling of the annual cycle and ENSO over the tropical Pacific. J Atmos Sci 51: Wang B, An S-I (2001) Why the properties of El Niño changed during the late 1970s. Geophys Res Lett 28: Wang B, Fang Z (1996) Chaotic oscillations of tropical climate: a dynamic system theory for ENSO. J Atmos Sci 53: Wang C, Picaut J (2004) Understanding ENSO physics a review. In: Wang C, Xie S-P, Carton JA (eds) Earth's climate: the ocean atmosphere interaction. Geophysical Monograph Series. AGU, Washington, pp Wang X, Shen SS (1999) Estimation of spatial degrees of freedom of a climate field. J Climate 12: Wang B, Wang Y (1996) Temporal structure of the Southern Oscillation as revealed by waveform and wavelet analysis. J Climate 9: Wang B, Barcilon A, Fang Z (1999) Stochastic dynamics of El Niño- Southern Oscillation. J Atmos Sci 56:5 23 Xie S-P (1994) On the genesis of the equatorial annual cycle. J Climate 7: Xie S-P (1995) Interaction between the annual and interannual variations in the equatorial Pacific. J Phys Oceanogr 25: Xue Y, Smith TM, Reynolds RW (2003) Interdecadal changes of 20-yr SST normals during J Climate 16: