1. Introduction
El Niño–Southern Oscillation (ENSO) is the dominant mode of climate variability on interannual timescales, with effects that extend from the tropical Pacific to the entire globe (Philander 1990). While not perfectly periodic, ENSO variability is sufficiently regular to suggest that the underlying dynamics are characterized by a relatively small number of degrees of freedom, perhaps subject to fluctuating atmospheric forcing. In particular, Penland and Sardeshmukh (1995) found empirically that increasing beyond 15 the number of sea surface temperature (SST) principal components retained in their linear inverse forecast model did not improve the model's forecast skill, suggesting that ENSO may be characterized by a relatively low-dimensional attractor that can be embedded in this 15-dimensional Cartesian space. The characterization of this presumed ENSO attractor is important both for guiding the theoretical understanding of ENSO and for assessing the ability of coupled general circulation models (GCMs) to represent this phenomenon.
While considerable progress in understanding the dynamics of ENSO has been made with linearized models of the tropical Pacific (e.g., Penland and Sardeshmukh 1995; Kleeman and Moore 1997; Thompson and Battisti 2000), the distribution of SSTs is manifestly non-Gaussian. In particular, the Niño-3 index is positively skewed, so that strong El Niño events are associated with larger SST anomalies than strong La Niña events (Hannachi et al. 2003; An and Jin 2004), although the statistical significance of this skewness has been questioned (Ewald et al. 2004); the tropical Pacific SST field displays significant skewness (Burgers and Stephenson 1999); and the composite SST anomaly patterns for El Niño and La Niña are not mirror images (Hoerling et al. 1997; Rodgers et al. 2004). Furthermore, Monahan (2001) demonstrated that the leading two principal component analysis (PCA) time series of tropical Pacific SST for the period 1950–98 are not statistically independent, despite being linearly uncorrelated by construction. This nonlinear coupling of the PCA modes manifests itself in the difference in spatial structure between El Niño and La Niña composite maps: the pattern that changes sign between El Niño and La Niña, characteristic of the linear component of the dynamics, is essentially identical to the spatial structure of PCA mode 1, while the pattern that does not change sign, reflecting nonlinearities in the dynamics, is essentially identical to PCA mode 2.
The tropical Pacific is a tremendously important component of the climate system, but has been poorly observed. Consequently, long-term gridded SST datasets can only be obtained as historical reconstructions in which statistical algorithms are used to interpolate between sparsely sampled observations. The present study extends Monahan (2001), considering El Niño–La Niña asymmetry in several different historical SST and surface air temperature (SAT) reconstructions. In an earlier analysis of historical SST reconstructions, Hurrell and Trenberth (1999) demonstrated significant differences between the first- and second-order statistics of these datasets, as well as differences in large-scale trends. Similarities and differences in nonlinear structure, which are the focus of the present study, were not considered by Hurrell and Trenberth (1999).
Finally, the accurate simulation of ENSO by coupled GCMs is an important measure of their ability to represent the earth's climate system. Intercomparison studies have investigated the ability of different GCMs to simulate the mean and variance of the tropical Pacific system (Latif et al. 2001; AchutaRao and Sperber 2002; Davey et al. 2002), as well as their ability to simulate the skewness of the Niño-3 index (Burgers and Stephenson 1999; Hannachi et al. 2003; Rodgers et al. 2004). This study will consider the extent to which four state-of-the-art coupled GCMs can simulate the spatial structure of ENSO nonlinearity, as characterized in Monahan (2001).
The datasets considered in this study are described in section 2. The analysis of historical SST and SAT reconstructions is detailed in section 3, and that of the coupled GCMs is detailed in section 4. A discussion of the results is presented in section 5, and a summary and conclusions are given in section 6.
2. Data
This study focuses on the tropical Pacific, defined as 20°N–20°S, 125°E–65°W. Five monthly average SST reconstructions are considered: the United Kingdom Met Office (UKMO) Hadley Centre Sea Ice and SST dataset (HadISST; Rayner et al. 2003); the Lamont-Doherty Earth Observatory reconstruction by Kaplan et al. [1998; data available from the National Oceanic and Atmospheric Administration–Cooperative Institute for Research in Environmental Sciences (NOAA–CIRES) Climate Diagnostics Center online at http://www.cdc.noaa.gov/;] and the National Climatic Data Center (NCDC) Extended Reconstruction SST versions 1 (ERSST.v1; Smith and Reynolds 2003) and 2 (ERSST.v2; Smith and Reynolds 2004; data available online at http://www1.ncdc.noaa.gov/pub/data/ersst) and Optimum Interpolation (OI) SST datasets [Smith et al. (1996); data available online from the NCAR Data Support Section (DSS) at http://dss.ucar.ed/datasets/ds277.0/data/recon/;]. Also, two monthly averaged SAT reconstructions are considered from the reanalysis projects of the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR; Kalnay et al. 1996; data available online at http://www.cdc.noaa.gov/;) and the European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40; Simmons and Gibson 2000; data available online at http://data.ecmwf.int/data/d/era40/;).
These historical reconstructions differ considerably in the periods covered and in the algorithms used to produce gridded estimates of sparsely sampled fields. The SST reconstructions use multivariate statistical schemes to objectively interpolate observed SSTs onto regular latitude–longitude grids; no explicit dynamical information is used in these reconstructions. Conversely, the reanalysis SAT fields are produced using dynamical– statistical models so as to be optimally consistent with both observations and atmospheric dynamics, as represented by the atmospheric GCMs used in the reanalyses. These GCMs are themselves driven by reconstructed SST fields: a combination of the NCDC OI SST reconstruction and UKMO Global Sea Ice and SST dataset (GISST; an earlier version of HadISST) for the NCEP–NCAR reanalysis, and a combination of HadISST and Reynolds OI SST for the ERA-40 reanalysis. While the raw observations entering these reconstructions are similar, there are significant differences among the reconstruction algorithms (e.g., Hurrell and Trenberth 1999; Smith and Reynolds 2004).
Sea surface temperature datasets from four coupled GCM control simulations are considered. These models are the Geophysical Fluid Dynamics Laboratory (GFDL) R30 coupled climate model (Delworth et al. 2002; data available online at http://nomads.gfdl.noaa.gov/;), the Hadley Centre HadCM3 model (Collins et al. 2001), the Department of Energy (DOE) Parallel Climate Model (PCM; Washington et al. 2000; Dai et al. 2001), and the NCAR Community Climate System Model (CCSM; Blackmon et al. 2001).
For each dataset, anomaly fields were produced by subtracting the long-term average seasonal cycle at each grid point. No other preprocessing of the data was carried out prior to the statistical analyses described in the subsequent sections. Table 1 summarizes the resolutions and durations of the reconstructed and simulated datasets considered in this study.
3. El Niño–La Niña asymmetry in historical reconstructions
The statistical model (1) was designed to be a minimal nonlinear model of the dependence of the field X on the index λ; it is not physically motivated, but rather corresponds to the two leading terms of a Taylor series expansion. In the absence of any a priori assumptions about the distributions of X and λ, nothing can be said about the distribution of the residuals ϵ except that, by construction of the estimators (2) and (3), 〈ϵ〉− = 〈ϵ〉+ = 0. Because this study is an exploratory analysis of non-Gaussian structure in X and λ, it is not appropriate to make any a priori assumptions about their distributions. It is worth noting that the estimators (2) and (3) behave reasonably in simple limiting cases: in particular, if a(2) = 0, then by (1), 〈X〉− and 〈X〉+ are proportional to 〈λ〉− and 〈λ〉+, respectively, and the right-hand side of (3) is identically zero, regardless of the distribution of λ. Furthermore, if the distribution of λ is symmetric about its mean, then 〈λ〉− = 〈λ〉+ and 〈λ2〉− = 〈λ2〉+ , so a(1) and a(2) reduce to the difference and sum maps defined in Hoerling et al. (1997) (up to constant scaling factors).
Identical analyses to those performed on the HadISST SST reconstruction were carried out on the ERSST.v1, ERSST.v2, Kaplan, and OI SST reconstructions, and on the NCEP–NCAR and ERA-40 SAT reanalyses; the results are presented in Table 2. The spatial structures of the leading two PCA modes for each of these historical reconstructions were in good agreement with those shown in Fig. 1. Because the anomaly pattern of a PCA mode is only determined up to a sign, in these and all subsequent PC analyses this ambiguity was eliminated by ensuring that the anomaly patterns of the leading two PCA modes agree in sign with those displayed in Fig. 1. The strong spatial correlation between the symmetric component of the composite and EOF2 is evident in all reconstructions except ERSST.v1. Furthermore, the ratio of the root-mean-squared amplitudes of a(1) and a(2), which measures the amplitude of the ENSO asymmetry rather than its pattern, is also indicated in Table 2. The amplitude of the symmetric component of the composite relative to the antisymmetric component for the ERSST.v1 is considerably less than that of all other reconstructions. The relatively high value of the ratio ‖a(2)‖/‖a(1)‖ for the Kaplan SST reconstruction arises because a long-term trend in this dataset projects strongly onto EOF2.
Results of an analysis of the HadISST, Kaplan, ERSST.v1, and ERSST.v2 SST reconstructions for the 1950–2000 period, corresponding roughly to the period covered by the OI reconstruction and the NCEP–NCAR and ERA-40 reanalyses, are presented in parentheses in Table 2. For each of these three reconstructions, the connection between a(2) and EOF2 is stronger in this last 50-yr period than it is over the complete 130-yr record; the increase in pattern correlation is marginal for the HadISST, ERSST.v2, and Kaplan reconstructions, but considerable for the ERSST.v1 reconstruction. The magnitude of a(2) relative to a(1) over this period is somewhat smaller for the Kaplan reconstruction, because the trend in PC2 is weaker in the last 50 yr than it is over the entire record, and the ratio is considerably stronger for the HadISST and ERSST.v2 reconstructions. A small increase in the ratio of magnitudes of the symmetric and antisymmetric components of the composite is evident for the ERSST.v1 reconstruction, but the ratio is still small relative to other reconstructions of this period.
To examine temporal variations in the strength of the El Niño–La Niña asymmetry and its projection on EOF2, each of the HadISST, ERSST.v1, ERSST.v2, and Kaplan SST reconstructions were split into a series of nine overlapping 50-yr subsets, with the central year increasing in 10-yr increments. For each of these data subsets, the annual cycles, principal components, and ENSO composites were calculated independently. Figure 3 plots the subset pattern correlations between EOF1 and a(1) and between EOF2 and a(2), as well as the subset ratios of the magnitude of a(2) to that of a(1), for each of the SST reconstructions. Clearly, for each of the SST reconstructions, the relationship between EOF1 and the antisymmetric component of the ENSO composite is robust to the subsampling of the dataset. The relationship between EOF2 and the symmetric component of the composite is more variable. The Kaplan, HadISST, and ERSST.v2 reconstructions display consistently strong projections characterized by distinct interdecadal variability. However, the projection is only strongly positive for the ERSST.v1 reconstruction at the end of the record; for most of the period of the reconstruction, the projection is weak or, for the period 1871–1920, strongly negative. For the HadISST, ERSST.v2, and Kaplan reconstructions, the amplitude of the symmetric (i.e., nonlinear) component of the ENSO component relative to the antisymmetric (i.e., linear) component also displays interdecadal variability. This ratio is weak for the ERSST.v1, and displays considerably less interdecadal variability than the other reconstructions.
Interdecadal variations in the strength and structure of the El Niño–La Niña asymmetry in the HadISST, ERSST.v2, and Kaplan SST reconstructions appear to be connected to interdecadal variations in the strength of ENSO, as measured by the standard deviation of PC1. This relationship is illustrated in Fig. 4. Note that in general both the strength of the asymmetry and the spatial correlation of a(2) with EOF2 increase with increases in std(PC1). During periods in which ENSO variability is relatively weak (strong), the spatial structure of SST is relatively symmetric (asymmetric) between warm and cool events. Not surprisingly, such a clear relationship between the strength of ENSO and the character of its nonlinearity is absent in the ERSST.v1 SST reconstruction.
Thus, there is evidence in historical reconstructions of tropical Pacific SST and SAT for a coupling between PCA modes 1 and 2, such that the average “linear” component of ENSO variability is captured by EOF1, while the average “nonlinear” component is strongly associated with EOF2. This coupling of PCA modes is a nontrivial result, as they are by construction uncorrelated. In fact, this asymmetry between average El Niño and La Niña events is the most prominent feature of the description of the ENSO attractor beyond single indices such as Niño-3 or Niño-3.4. While there is considerable scatter in the El Niño–La Niña asymmetry between the different SST and SAT reconstructions, the qualitative similarities are strong, with the notable exception of the ERSST.v1 reconstruction; we will return to this point in section 5. Having diagnosed this relationship in historical datasets, we proceed to address the question of how will the El Niño–La Niña asymmetry is captured in coupled GCMs.
4. Asymmetry in coupled GCMs
The analyses of the SST and SAT reconstructions described in the previous section were carried out on each of the GCM datasets described in section 2. Plots of SST EOF1 and EOF2 for each of the model datasets are given in Fig. 5, of the spatial structure of SST standard deviation and skewness are given in Fig. 6, and of the antisymmetric and symmetric components of the ENSO composites are given in Fig. 7. For each of the model datasets, the ENSO index was defined, as in section 3, as the leading principal component time series (normalized to unit variance), rather than as an “area based” index such as Niño-3.4. This is because the geographical distribution of SST variance in the model climates differs from that of observations; in particular, the GFDL SST variance maximum is located near the date line, far to the west of the observed maximum (Fig. 6). As the standard area-based indices are tuned to the observed variance distribution, by using an internally defined ENSO index, we are able to more directly study the asymmetries of the models' ENSO variabilities. It is clear from Figs. 5 and 7 that for each of the coupled GCMs, EOF1 is essentially identical to the antisymmetric component of the ENSO composite; the pattern correlations were above 0.99 in all cases. On the other hand, the strong connection between EOF2 and the symmetric component of the ENSO composite manifest in most of the historical reconstructions is captured only in the GFDL model although the maximum of the pattern is shifted to the central Pacific. From Fig. 7 and Table 2, it is clear that in the HadCM3, DOE PCM, and NCAR CCSM models, the symmetric components of the ENSO composites are weak and disorganized in comparison to those of the historical reconstructions and the GFDL simulation. Similarly, in each model there is a manifest similarity between SST EOF1 and the SST standard deviation field (Fig. 6), but only the GFDL SST simulation is characterized by an organized skewness field that projects strongly onto EOF2. For the other three models, the SST skewness fields are weak and spatially disorganized. It is worth noting that these results further reinforce the connection between the nonlinear coupling of EOF1 and EOF2, ENSO asymmetry, and SST skewness: only in the model with a strong asymmetry between average El Niño and La Niña SST patterns is the SST skewness strong and are the leading two EOF modes coupled. It should be noted that of the four coupled GCMs analyzed in this study, only the GFDL model uses surface flux adjustments to maintain a realistic climate. Interestingly, Rodgers et al. (2004) report an asymmetry between composite El Niño and La Niña fields in the flux-adjusted ECHO-G coupled GCM.
Figure 4 displays plots of the pattern correlation of EOF2 with a(2), and of the relative magnitude of the symmetric and antisymmetric components of the composite, for each 50-yr subset of the simulations. As was the case with the HadISST, ERSST.v2, and Kaplan historical SST reconstructions, the pattern correlation between EOF2 and the antisymmetric component of the ENSO composite for the GFDL simulation is generally large and increases as the standard deviation of PC1 increases. This behavior is not evident in the HadCM3, DOE PCM, or NCAR CCSM simulations. Furthermore, the increase in the magnitude of the nonlinear component of ENSO with the standard deviation of the ENSO index observed in the HadISST, ERSST.v2, and Kaplan reconstructions is captured only in the GFDL simulation, and does not appear in the HadCM3, PCM, or CCSM models. Thus, of the four coupled GCM simulations considered, only that of the GFDL model reproduces the nonlinear coupling between EOF modes 1 and 2 evident in the historical SST and SAT reconstructions, despite its unrealistic covariance structure.
5. Discussion
The seven historical SST and SAT reconstructions considered in this study are in broad agreement that ENSO variability in the second half of the twentieth century was asymmetric between El Niño and La Niña events, with a linear structure of variability that projects strongly onto EOF1 and a nonlinear structure that projects strongly onto EOF2, consistent with the results of Monahan (2001). Furthermore, while the interdecadal variability of this nonlinear structure over the period 1871–2000 is broadly the same in the HadISST, Kaplan, and ERSST.v2 reconstructions, it is significantly different in the ERSST.v1 reconstruction, in which the magnitude of the symmetric component of the ENSO composite is too small and there is no clear relationship between a(2) and EOF2. In fact, the differences between ERSST.v1 and the other long-term SST reconstructions are not surprising given that ERSST.v1 has been shown to have a number of shortcomings, in particular in the tropical Pacific (Smith and Reynolds 2004). The ERSST.v2 reconstruction was developed to supersede ERSST.v1, and the present analysis demonstrates that the later reconstruction's characterisation of the nonlinear variability of the tropical Pacific SST is in good agreement with the HadISST and Kaplan reconstructions. The relatively small differences between the temporal and spatial structure of El Niño and La Niña as represented by the ERSST.v2, Kaplan, and HadISST reconstructions evident in Fig. 3 reflect differences in raw input data and reconstruction algorithms.
The possibility should be noted that the nonlinear structure in the HadISST, ERSST.v2, and Kaplan datasets is spurious, and is an artifact of the reconstruction algorithms. This is unlikely, because the algorithms used to reconstruct historical SST values over data-sparse regions assume stationarity of the covariance structure, but make no use of third- or higher-order moments. These algorithms would therefore be expected to bias the reconstructed data toward multivariate Gaussianity, and in fact for the Kaplan and HadISST reconstructions the magnitude of the symmetric composite is generally lower in the early part of the record than in the later. Therefore, it would not be expected that the robust connection between the spatial structure of the symmetric component of the ENSO composite and EOF2 in the HadISST, ERSST.v2, and Kaplan reconstructions would arise as an artifact of the reconstruction algorithm.
Recent studies by Timmermann (2003) and Rodgers et al. (2004) have found evidence in long integrations of coupled GCMs (ECHAM4/OPYC3 and ECHO-G, respectively) that decadal modulations of the amplitude of ENSO are associated with decadal changes in the zonal tilt of the equatorial thermocline, such that large-amplitude ENSO events occur when the tilt is anomalously low. Furthermore, Rodgers et al. (2004) demonstrate that the El Niño and La Niña composites of the tropical Pacific SST and 20°C isotherm depth (Z20) fields from the flux-corrected ECHO-G GCM are characterized by asymmetries similar to those highlighted in the present study, and that the spatial patterns of these asymmetries strongly resemble those of the regression patterns of an index characterizing decadal variability in the equatorial thermocline tilt on SST and Z20. Rodgers et al. (2004) interpret these results as following from a hypothesized (but not explicitly demonstrated) proportionality of the magnitude of the ENSO asymmetry to the ENSO amplitude: during periods of large ENSO events, the asymmetry is presumed to be strong, so the asymmetry pattern should correlate well with an index of ENSO amplitude. The results of the present study provide evidence for this proposed proportionality, and for the suggestion that a portion of decadal variability in the tropical Pacific may result from nonlinear dynamics acting on ENSO time scales.
The historical SST and SAT reconstructions indicate that the dominant nonlinearity in ENSO variability can be associated with the nonlinear coupling of EOF modes 1 and 2, as manifest in the strong projection of the symmetric component of the ENSO composite onto EOF2. The full spatial characterization of this nonlinearity therefore requires more than just a single index of ENSO variability, such as the Niño-3 or Niño-3.4 index (as in Hannachi et al. 2003). The importance of multiple indices for characterizing the ENSO attractor was stressed by Trenberth and Stepaniak (2001), who introduced the Trans-Niño Index (TNI) as a measure of the SST gradient between the eastern and the central Pacific. The correlation coefficient between the TNI and PC2 for the HadISST SST reconstruction is 0.83; they describe similar variability. Trenberth and Stepaniak (2001) demonstrated the existence of significant lagged correlations between the Niño-3.4 and TNI indices (at least in the period before 1977). The present analysis demonstrates that the TNI is nonlinearly coupled to the Niño-3.4 index at zero month lag, and that the associated spatial pattern reflects the asymmetry in spatial structure of average El Niño and La Niña events. It should be emphasized here that this nonlinear coupling does not imply that the Niño-3.4 and TNI indices are redundant; the TNI time series contains information that is not present in the square of Niño-3.4. In particular, there are no strong lagged correlations between Niño-3.4 and its square. Nevertheless, EOF2 (the TNI index, equivalently) is seen to play an important role in both the spatial and temporal structure of the ENSO attractor.
6. Summary and conclusions
The fact that tropical Pacific variability is not Gaussian, so that average El Niño and La Niña events are not mirror images, has been noted in several studies (Hoerling et al. 1997; Burgers and Stephenson 1999; Timmermann and Jin 2002; Hannachi et al. 2003; An and Jin 2004; Rodgers et al. 2004). It was suggested in Monahan (2001) that a basic feature of the ENSO attractor is that the asymmetry in SST anomaly spatial patterns between average El Niño and La Niña events is characterized by a nonlinear coupling of SST PCA modes 1 and 2, such that the “nonlinear” component of the anomaly patterns that does not change sign between warm and cold events projects strongly on the spatial pattern of PCA mode 2.
The present study has extended Monahan (2001) to consider this asymmetry in seven different historical SST and SAT reconstructions, and in coupled GCM simulations. It was found that there is broad agreement among the historical reconstructions for this coupling of PCA modes in the 1950–2000 period. For three of the four SST reconstructions that extend back to 1871 (HadISST, Kaplan, and ERSST.v2), the connection between the nonlinear pattern and EOF2 is apparent over the entire record. This connection is not evident in earlier parts of the ERSST.v1 reconstruction, but this reconstruction is known to be problematic in the tropical Pacific (Smith and Reynolds 2004); in fact, ERSST.v2 was developed as a replacement for ERSST.v1. Furthermore, subsampling the historical reconstructions into overlapping 50-yr intervals indicates in the HadISST, ERSST.v2, and Kaplan reconstructions that the strength of the nonlinearity and its identification with EOF2 depend on the strength of ENSO. Finally, it is found that of four state-of-the-art coupled GCMs, only one (the GFDL R30 model) accurately simulates the nonlinear structure in ENSO, despite simulating the geographical distribution of variance relatively poorly. Simulated SSTs from HadCM3, CCSM, and PCM coupled models display skewness fields that are weak and disorganized compared to historical SST reconstructions and the GFDL simulations, and El Niño–La Niña composite patterns that are essentially mirror images. The divergence between the nonlinearity of ENSO as simulated in different coupled models is not surprising considering the continuing difficulties in representing the mean state and variance of the tropical Pacific (Latif et al. 2001; AchutaRao and Sperber 2002; Davey et al. 2002), and the fact that Burgers and Stephenson (1999) and Hannachi et al. (2003) found that most coupled GCMs do not accurately simulate the skewness of the Niño-3 index. It is worth noting that of the four coupled GCMs only the GFDL model uses surface flux adjustments to maintain a realistic climate. Recently, Rodgers et al. (2004) have reported an asymmetry in composite El Niño and La Niña SST patterns similar to that of the observations in the (flux adjusted) ECHO-G GCM. It would be interesting to see if this asymmetry is associated with a nonlinear coupling of PCA modes 1 and 2.
Historical SST reconstructions interpolate sparsely sampled observations using algorithms that make a number of highly questionable assumptions, such as stationarity of the covariance structure over the reconstruction period. Consequently, they are not ideally suited for analyses of climate variability, as Rayner et al. (2003) caution. Nevertheless, these are the only datasets presently available for the analysis of basin-scale variability in the tropical Pacific on multidecadal time scales. The possibility that the results of this analysis are to some extent spurious artifacts of the reconstruction algorithms must be admitted. However, given the agreement between all datasets for the 1950–2000 period; between the Kaplan, HadISST, and ERSST.v2 reconstructions for the 1871–2000 period; and the fact that all of the HadISST, Kaplan, and ERSST.v2 reconstructions make no use of statistical moments above the second and should therefore bias SST reconstructions toward Gaussianity, we believe it is unlikely that the results presented in section 3 are merely artifacts of the reconstruction.
The physical mechanisms responsible for the asymmetry between El Niño and La Niña are still unclear. Suggested mechanisms include nonlinearities in oceanic vertical temperature advection in the cold tongue region (Hannachi et al. 2003; An and Jin 2004), nonlinear rectification of the Madden–Julian oscillation (Kessler and Kleeman 2000), nonlinearities in the dependence of tropical deep convection on the underlying SST (Hoerling et al. 1997), and the action of phytoplankton as a “biological thermostat” (Timmermann and Jin 2002). Yet another possibility is that the positive skewness of SST in the eastern tropical Pacific reflects the positive skewness of the surface zonal wind in the western tropical Pacific (Monahan 2004). The winds in the western tropical Pacific are characterized by westerly bursts, and not easterly ones; the standard stochastic oscillator conception of ENSO (e.g., Penland and Sardeshmukh 1995; Burgers 1999) would then predict stronger El Niños than La Niñas, on average. Of course, all of these mechanisms may play a role in generating the nonlinear structure of ENSO, the understanding of which is an important step in improving our understanding of the ENSO attractor.
Acknowledgments
The authors would like to thank Jonathan Gregory for providing access to the HadCM3 data and Ron Stouffer for the GFDL model data. The HadISST data were provided by the Met Office Hadley Centre. John Fyfe and Bill Merryfield provided helpful comments on an earlier draft of the manuscript. The authors would like to thank two anonymous referees, whose thoughtful comments considerably improved this manuscript. A. Monahan is supported by the Natural Sciences and Engineering Research Council of Canada, by the Canadian Foundation for Climate and Atmospheric Sciences, and by the Canadian Institute for Advanced Research.
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Maps of HadISST SST EOF1 (contours …−0.1°, 0.1°, 0.3°C, …), SST EOF2 (contours …−0.05°, 0.05°, 0.15°C, …), the antisymmetric component of the ENSO composite a(1) (contours …−0.1°, 0.1°, 0.3°C, …), the symmetric component of the ENSO composite a(2) (contours −0.02°, 0.02°, 0.06°C, …), the SST std dev (contours 0.1°, 0.3°C, …), and the SST skewness (contours …−0.1, 0.1, 0.3, …)
Citation: Journal of Climate 17, 15; 10.1175/1520-0442(2004)017<3026:TSATSO>2.0.CO;2
Scatterplot of HadISST SST PC1 with PC2. For consistency with Fig. 1, both time series have been normalized to unit std dev
Citation: Journal of Climate 17, 15; 10.1175/1520-0442(2004)017<3026:TSATSO>2.0.CO;2
Plots of the pattern correlation of EOF1 with a(1), the antisymmetric component of the ENSO composite (thick line); of the pattern correlation of EOF2 with a(2), the symmetric component of the ENSO composite (thin line); and of the ratio of the amplitude of a(2) to that of a(1) (dashed line), for each of the 50-yr subintervals. The circles correspond to the center of each subinterval
Citation: Journal of Climate 17, 15; 10.1175/1520-0442(2004)017<3026:TSATSO>2.0.CO;2
Scatterplots of the std dev of SST PC1 (normalized by the std dev of PC1 for the entire record) vs (upper panels) the pattern correlation of SST EOF2 with a(2), the symmetric component of the ENSO composite, and vs (lower panels) the ratio of the magnitude of the symmetric component of the composite to the magnitude of the antisymmetric component of the composite, a(1), for each of the 50-yr data subsets
Citation: Journal of Climate 17, 15; 10.1175/1520-0442(2004)017<3026:TSATSO>2.0.CO;2
Maps of EOF1 (contours …−0.1°, 0.1°, 0.3°C, …) and EOF2 (contours …−0.05°, 0.05°, 0.15°C, …) for modeled SST datasets. Thick (thin) lines denote positive (negative) contours
Citation: Journal of Climate 17, 15; 10.1175/1520-0442(2004)017<3026:TSATSO>2.0.CO;2
Maps of std dev (contours 0.1°, 0.3°C, …) and skewness (contours …−0.1, 0.1, 0.3, …) for modeled SST datasets. Thick (thin) lines denote positive (negative) contours
Citation: Journal of Climate 17, 15; 10.1175/1520-0442(2004)017<3026:TSATSO>2.0.CO;2
Maps of the antisymmetric component of the ENSO composite [a(1); contours …−0.1°, 0.1°, 0.3°C, …] and of the symmetric component [a(2); contours …−0.02°, 0.02°, 0.06°C, …] for modeled SST datasets. Thick (thin) lines denote positive (negative) contours
Citation: Journal of Climate 17, 15; 10.1175/1520-0442(2004)017<3026:TSATSO>2.0.CO;2
Details of the datasets considered in this study
Pattern correlation between EOF2 and a(2) (the symmetric component of the ENSO composite), and the relative magnitude of the symmetric and antisymmetric components of the composite, for the SST and SAT reconstructions and simulations considered in this study. Values in parentheses correspond to estimates of these quan tities over the period from 1950 to 2000
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