Quantifying the residual effects of ENSO on low-frequency variability in the tropical Pacific



The asymmetry of El Niño-La Niña, one of the well-known characteristics of the El Niño-Southern Oscillation (ENSO), is suggested to produce a non-zero residual effect that could rectify the background state, and thereby generates the low-frequency variability in the tropical Pacific. So far, this rectification effect has been hardly quantified apart from the low-frequency variability because the low-frequency variability captured via conventional methods represents the mixture of both the residual effects of ENSO and the no-ENSO-related natural decadal variability. Here we separate the residual effects of ENSO from the natural decadal variability that appears in four historical sea surface temperature datasets during the last century by applying a long-term moving average. A significant correlation between the computed residual effect and the decadal change in the ENSO skewness (i.e. the measure of the El Niño-La Niña asymmetry) confirmed the applicability of our computational method. Quantitatively, the residual effects of ENSO consistently account for at least 15% of the total low-frequency variability in four datasets, especially over the eastern and central tropical Pacific. This implies that the asymmetry of ENSO enhances the tropical Pacific decadal variability for the last century. Copyright © 2012 Royal Meteorological Society

1. Introduction

El Niño events are often stronger than La Niña events (Burgers and Stephenson, 1999; An and Jin, 2004). Such asymmetry in the behaviour of El Niño versus La Niña is prominent not only during the mature phases of the phenomena (Choi et al., 2009), but also during the developing or transition phases (Okumura and Deser, 2010). Interestingly, the nonlinearity of the El Niño-Southern Oscillation (ENSO), as measured by a higher-order momentum metric such as ‘skewness’, fluctuates over interdecadal timescales (An, 2004). Furthermore, the decadal changes in El Niño-La Niña asymmetry are probably linked to decadal changes in the mean climate states (An, 2009). Such a correlation may be attributed to the strong dependency of ENSO characteristics on the background climate state (An and Jin, 2000; Fedorov and Philander, 2001; Timmermann 2003; Choi et al. 2011) or the non-zero residual effect of the asymmetric ENSO cycle on the slowly varying background state (Choi et al., 2009). Rodgers et al. (2004) argued that the pattern of the decadal sea surface temperature (SST) anomaly resembles the residuals induced by ENSO asymmetry. Schopf and Burgman (2006) showed the existence of non-zero residual forcing generated by the spatial asymmetry between El Niño and La Niña. Recently, Sun and Yu (2009) used observation data to analyse the residuals induced by two different types of ENSO, while Choi et al. (published online) analysed the relationship between the residuals of ENSO and decadal variability using a long-term coupled general circulation model output. In these studies, it was suggested that ENSO residuals have qualitative effects on the tropical Pacific decadal variability (TPDV). However, a quantitative examination of the rectification effects of ENSO is hardly pursued so far, because the low-frequency variability captured by conventional methods (e.g. low-pass filtering, sliding average) involves both the residual effects of ENSO and the natural decadal variability. In this work, thus we attempt to separate the residual effects of ENSO from the low-frequency variability that appears in historical SST datasets and examine their quantitative effects on the natural decadal variability.

This paper is organized as follows. The historical datasets are outlined in Section 2. In Section 3, the methodology and residual effects of ENSO are described. Finally, a summary of the research is given in Section 4.

2. Data

In this study, the four historical SST datasets are used; (1) the Extended Reconstructed Sea Surface Temperature (hereafter, ERSST) dataset, version 3 (Smith and Reynolds, 2004), (2) the Hadley Centre Sea Ice and Sea Surface Temperature (hereafter, HadISST) dataset, version 1 (Rayner et al., 2003), (3) the extended Kaplan SST (hereafter, Kaplan SST), version 2 (Kaplan et al., 1998), and (4) the Simple Ocean Data Assimilation (hereafter, SODA) reanalysis dataset, version 2.2.4 (Carton et al., 2005; Carton and Giese, 2008; Giese and Ray, 2011). The SODA reanalysis project was to reconstruct historical ocean climate variability over space and time scales similar to atmospheric reanalysis projects. Each datasets covers the periods of January 1854–October 2011 (ERSST), January 1871–October 2011 (HadISST), January 1856–September 2011 (Kaplan SST), and January 1871–December 2008 (SODA). Their horizontal grids are interpolated onto a uniform 2° × 2° grid. Anomalies are defined as the departure from the 1951–1980 climatological values for each month. All data are linearly detrended which might be associated with global warming trend before statistics are calculated.

3. Methodology and results

We used the NIÑO3.4 SST anomaly index (SST anomaly averaged over the region 170°W–120°W, 5°S–5°N), which is a representative ENSO index. The standard deviation and skewness of the NIÑO3.4 SST anomaly index in each datasets are listed in Table I, where the skewness indicates the normalized third statistical moment (An, 2004). A positive skewness means that the amplitude of warm event (El Niño) is larger than that of cold event (La Niña) (An, 2004) or can be resulted from the spatial asymmetry between warm and cold events (Schopf and Burgman, 2006). The standard deviation and skewness of NIÑO3.4 index in SODA data are larger than those of other datasets. To separate the NIÑO3.4 SST anomaly index into low- and high-frequency variability, we first performed the 10-year sliding average to the NIÑO3.4 SST anomaly index. This average was defined as the Low-Frequency Variability (hereafter, LFV); it is shown in Figure 1 (thick-grey lines). The High-Frequency Variability (hereafter, HFV) was then defined by subtracting the LFV index from the original anomaly index. Thus,

equation image(1)


equation image(2)

Both the standard deviation and skewness of the HFV index are nearly identical to those of the original anomaly index (Table I), indicating that the asymmetry of El Niño and La Niña events remains in the HFV index. This means that statistical measurements of ENSO asymmetry do not originate from the anomaly of decadal variability.

Figure 1.

The thick-grey and thin-black lines indicate the LFV and LFV without high-frequency residuals (i.e. tropical Pacific decadal variability) of the NIÑO3.4 sea surface temperature (SST) anomaly index, respectively. All indices are calculated by 10-year sliding window from (a) ERSST, (b) HadISST, (c) Kaplan SST, and (d) SODA

Table I. The standard deviation and skewness of the NIÑO3.4 SST anomaly index from original anomaly (X) and the high-frequency variability (HFV, X′)
Original anomaly (X)Standard deviation0.750.770.750.88
HFV (X′)Standard deviation0.730.740.720.86

To quantify the dominant time scale of each index, the wavelet analysis was applied to the original anomaly index, the LFV index, and the HFV index. The original index is dominated by interannual-to-interdecadal variations. As expected, the LFV and HFV indices have a strong spectrum power over interdecadal and interannual time scales, respectively (not shown). Therefore, it seems that the 10-year sliding average properly separates the decadal variability from the original anomaly index. The dominant interannual variability in the HFV index is obviously related to ENSO and its main period is similar to that of the original anomaly index. Such similarities between the original anomaly and HFV indices imply that the HFV index involves the intrinsic characteristics of ENSO. We also examined the characteristics of ENSO using the HFV of equatorial SST anomalies. In the analysis, the composites of El Niño and La Niña events were compared separately with respect to the original anomaly and HFV. No significant difference was found between the composite of the original anomaly and that of the HFV (not shown).

The LFV of the NIÑO3.4 index involves both the natural decadal variability and high-frequency variability (i.e. ENSO) residual effects. The natural decadal variability, or the LFV without high-frequency residual effects, is called the TPDV in this study. Thus,

equation image(3)

where the LFV is simply defined by the 10-year sliding average. By computing high-frequency residual effects in LFV, we performed the 10-year sliding average to the HFV index. As shown in Table I, the main inherent features of ENSO remain in the HFV index and thus the 10-year sliding average of the HFV can be considered as the asymmetric ENSO-induced residuals. Thus,

equation image(4)

In this regard, the TPDV could be defined as the difference between the LFV and the 10-year sliding averaged HFV (i.e. TPDV is (A) in Equation (4)). Also (B) is considered as newly calculated ENSO signals. The black lines shown in Figure 1 indicate the calculated TPDV index. Regardless of the datasets, the TPDV fluctuated more smoothly than the LFV. This indicates that the high-frequency residual effects are effectively removed from LFV in all datasets.

To show the HFV residual effects from the ENSO asymmetry, we compared the time series of HFV residual effects and 10-year sliding skewness of newly computed ENSO signals such as (B) in Equation (4). Figure 2 shows those time series and temporal correlation. Both the HFV residual effects and the sliding skewness are highly correlated by 99% confidence level. Interestingly, after 1960, all SST datasets represent the similar temporal variation in the HFV residual effects and sliding skewness. These results refer that the HFV residual effects in LFV is originated from the asymmetric feature of ENSO.

Figure 2.

The thick-grey and thin-black lines indicate the high-frequency residuals and 10-year sliding skewness of El Niño-Southern Oscillation in the Equation (4) from (a) ERSST, (b) HadISST, (c) Kaplan SST, and (d) SODA. Their temporal correlations are statistically significant at 99% confidence level

To examine the validity of the above method, we applied the technique to the same set of data, but used different sliding window sizes of 15 and 20 years. Regardless of the window sizes, the time series of TPDV fluctuated more smoothly than that of LFV (not shown). The 10-year averaged LFV is highly correlated to both the 15- and 20-year averaged LFVs. In addition, the correlation coefficients between the TPDVs are larger than those between the LFVs. In other words, both the LFV and TPDV are less sensitive to the selected window size. However, the 10-year sliding-averaged HFV residuals are poorly correlated with both the 15- and 20-year sliding-averaged HFV residuals, indicating that the time series of HFV residual effects are sensitive to the selected window size. Such sensitivity arises because the involved ENSO events for defining HFV residual effects change with respect to the selected window size. Nevertheless, the 15-year window HFV residual effects are highly correlated with the 15-year sliding skewness of ENSO. The result for 20-year window is also same as that of 10- or 15-year window. This indicates that the HFV residual effects are generated from the asymmetric feature of ENSO, and the HFV residual effects are efficiently removed from the LFV, regardless of window size. Therefore, while the signals of the ENSO residuals are dependent on the window size, the results do not significantly change with respect to different sliding window sizes.

To further investigate the rectification effects of ENSO residuals on the low-frequency variability, we compared the amplitudes of the LFV and TPDV using the following equation:

equation image(5)

where σ represents the standard deviation at each grid point. The ENSO residual effects on the LFV of the tropical Pacific SST obtained using the ERSST, HadISST, Kaplan SST, and SODA datasets are shown in Figure 3(a)–(d) respectively. Shading indicates the regions above 15% level in each figure. In the four datasets, the residuals of ENSO account for at least 15% of the LFV in the tropical Pacific SST. The effective region of ENSO residuals tends to be broadened towards the eastern Pacific. Note that the number of percentage is suitable for the 10-year window size. Because of the changes in number of involving ENSO events, the accounts of ENSO residual effect on LFV are slightly different according to the selected window size. However, the patterns do not change significantly with different window sizes. The pattern correlation between ENSO residual effects (Figure 3) for different sliding window sizes (15 and 20-year) is shown in Table II. The pattern correlation was computed with respect to the results obtained with a 10-year sliding window. All pattern correlations are statistically significant by a 99% confidence level. The effects of ENSO residuals are more dominant over the equatorial eastern Pacific than over the western Pacific, regardless of the sliding window size. Thus, the amplitude of ENSO residuals is confined to a region over the equatorial Pacific. However, the large amplitude of LFV is not confined solely to a region over the equator, but rather expands towards the off-equatorial region. Therefore, a larger ratio of ENSO residuals is found over the tropical Pacific, especially in the region confined along the equatorial eastern Pacific.

Figure 3.

The percentage of El Niño-Southern Oscillation residual effects in the low-frequency variability of the sea surface temperature (SST) for (a) ERSST, (b) HadISST, (c) Kaplan SST, and (d) SODA. The regions are shaded above 15%. The contour interval is 5%

Table II. Spatial correlation between the percentage of ENSO residual effects in 10-year window (Figure 3) and that in different window sizes (15 or 20 years)
  1. ENSO, El Niño-Southern Oscillation; ERSST, extended reconstructed SST; HadISST, Hadley centre sea ice and SST; SODA, simple ocean data assimilation; SST, sea surface temperature.

15 years0.920.940.920.92
20 years0.840.870.840.78

4. Summary

In this study, we quantified the effects of ENSO residuals reflected in the low-frequency variability over the tropical Pacific. For the computations, we first separated the low- and high-frequency variability using a conventional sliding average method. The characteristics of the high-frequency variability reveal the asymmetric features of ENSO. From the high-frequency variability, we calculated the ENSO residuals using same sliding window size as defined for low-frequency variability. By doing so, we separated the natural TPDV and the rectified effect of ENSO residuals in the low-frequency variability. The fluctuations in the low-frequency variability without ENSO residuals were smoother than those of the original low-frequency variability. The results obtained with the employed method were consistent regardless of the sliding window size or datasets.

To examine the spatial structure of ENSO residual effects, we performed identical analyses of equatorial SST anomaly datasets obtained from ERSST, HadISST, Kaplan SST, and SODA. Consequently, we found that the residuals induced by asymmetric ENSO could amplify the magnitude of the natural TPDV. A quantitative examination of the residual effects revealed that the ENSO residuals account for at least 15% of the low-frequency variability in the SST over the tropical Pacific when we used the 10-year sliding window. In addition, the effective region is broadened towards the eastern Pacific.

These results indicate that the ENSO residuals could intensify the amplitude of TPDV. However, this rectification effect of ENSO tends to enhance on the specific spatial pattern of decadal variability. According to the previous studies, there exist at least two types of TPDV. One is the ENSO-like decadal variability, which has a spatial structure resembling the ENSO but wider meridional expansion (i.e. triangular structure in SST anomaly). This decadal variability is the most dominant mode in observation (Zhang et al., 1997); however, there is no or weak relationship between the ENSO's decadal modulation (Yeh and Kirman, 2004). The other TPDV is related to the decadal ENSO modulation, which has an east–west dipole structure in the tropical Pacific (Rodgers et al., 2004). The decadal ENSO modulation could lead to the changes in residual effects of ENSO. Therefore, the residual effects of ENSO are more related to the dipole-like decadal variability rather than the triangular structure decadal variability. However, such calculations in this study do not sufficiently describe the origins of specific TPDV and their mechanisms. Therefore, more studies on the physical mechanism of TPDV should be conducted.


This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2009-C1AAA001-2009-0093042).