Nonlinear interdecadal changes of the El Niño-Southern Oscillation

Abstract

Nonlinear interdecadal changes in the El Niño-Southern Oscillation (ENSO) phenomenon are investigated using several tools: a nonlinear canonical correlation analysis (NLCCA) method based on neural networks, a hybrid coupled model, and the delayed oscillator theory. The leading NLCCA mode between the tropical Pacific wind stress (WS) and sea surface temperature (SST) reveals notable interdecadal changes of ENSO behaviour before and after the mid 1970s climate regime shift, with greater nonlinearity found during 1981–99 than during 1961–75. Spatial asymmetry (for both SST and WS anomalies) between warm El Niño and cool La Niña events was significantly enhanced in the later period. During 1981–99, the location of the equatorial easterly anomalies was unchanged from the earlier period, but in the opposite ENSO phase, the westerly anomalies were shifted eastward by up to 25°. According to the delayed oscillator theory, such an eastward shift would lengthen the duration of the warm events by up to 45%, but leave the duration of the cool events unchanged. Supporting evidence was found from a hybrid coupled model built with the Lamont dynamical ocean model coupled to a statistical atmospheric model consisting of either the leading NLCCA or CCA mode.

Appendix 1: Cross-validation for the NLCCA model

Once the weight parameters (in the NN of Fig. 1) have been determined, an NLCCA model is built, the standard deviation std(u) and std(v) are known, and 〈u〉 = 〈v〉 = 0. If new x data become available, then u can be calculated, and v estimated by u · std(v)/std(u), which can then be used to predict y. Similarly, x can be predicted using new y data.

For cross validation, we divided the data for 1961–75 period into three segments of equal length (5 years). Three NLCCA models were to be built. The first was built without the data of the 1st segment, which was to be used as independent validation (or testing) data. Similarly, the 2nd and the 3rd models had the 2nd and 3rd segment of data left out for independent validation, respectively. Independent predictions by the three models were then collected to form a data time series of the whole period from 1961 to 1975, which was then compared with the observed data to alleviate the prediction skill. Same procedures were done on the data for 1981–99. Here we simply focus on the predictions of zero lead time, i.e., predict the WS using the simultaneous SST as predictor, and predict the SST using the simultaneous WS as predictor. Also only the NLCCA or CCA mode 1 is used here.

1.1 A.1 For the WS

Figure 7 shows the time evolution of the zonal WS anomalies along the equator (averaged within 5°S–5°N) predicted by the NLCCA models, where the westerly (easterly) anomalies associated with major El Niño (La Niña) events during the past four decades are successfully reproduced. It is notable that the zonal WS anomalies, especially the westerly anomalies, are intensified during the 1981–99 period. In Fig. 7b, an eastward displacement between the westerly (positive) anomalies and easterly (negative) anomalies can still be seen, although the displacement is much smaller than that shown in Fig. 4f, h. In contrast, there is basically no displacement between the westerly and easterly anomalies in the predictions for 1961–75 (Fig. 7a).

Fig. 7.

Time evolution of the equatorial zonal WS anomalies (averaged between 5°S and 5°N) predicted by the NLCCA models (only mode 1) using SST as predictor. Solid curves denote positive contours, dashed curves, negative contours, and thick curves, zero contours. The contour interval is 5 m²/s². Areas with values greater than 10 are shaded, a and b represent the 1961–75 and 1981–99 period, respectively

Geographical distributions of the prediction skill for the zonal and meridional WS anomalies by the NLCCA models are shown in Fig. 8. For the zonal WS, the higher correlation is located over the central-western equatorial Pacific, and the NLCCA models have higher correlation skill in 1981–99 than in 1961–75 (Fig. 8a, b). Also shown in Fig. 8 are the difference between the skill of NLCCA models and the corresponding CCA models (NLCCA minus CCA), where significant improvement of the correlation (0.3–0.4) occurs in 1981–99 over the central-eastern Pacific and the western Pacific (Fig. 8d), while there is little improvement for 1961–75 (Fig. 8c). For the meridional WS, higher NLCCA skill relative to the CCA skill also occurs in the 1981–99 period over the central equatorial Pacific (Fig. 8h), versus insignificant improvement in the 1961–75 period (Fig. 8g). Similar conclusions are reached when examining the root mean square error (RMSE) (not shown).

Fig. 8.

Distributions of the correlation skill of the WS anomalies predicted by the NLCCA models relative to the observations (a, b, e, f) and the difference between the skill of NLCCA models and that of the corresponding CCA models (NLCCA minus CCA, c, d, g, h). The four panels in the left column represent the period 1961–75, and the right column, the period 1981–99. The upper four panels represent the zonal component, and the lower four panels, the meridional component. The contour interval is 0.1 with positive skill difference shaded

That the NLCCA models exhibit more advantage over the CCA models during the 1981–99 period than during the 1961–75 period indicates that the ENSO mode is more nonlinear after 1980, confirming the results described in Sect. 3.

1.2 A.2 For the SST

Figure 9 shows the time evolution of the equatorial SST anomalies (averaged within 5°S–5°N) predicted by the NLCCA models. Compared to the observations, despite the relative weak amplitudes, the SST anomalies during the past four decades are well predicted even with one NLCCA mode. The asymmetry between El Niño and La Niña, i.e., the eastward shift between the warming and the cooling is also successfully reproduced. This shift is more significant during 1981–99 (Fig. 9b) than during 1961–75 (Fig. 9a), suggesting again that there is more nonlinearity in the ENSO mode after 1980.

Fig. 9.

Time evolution of the equatorial SST anomalies (averaged between 5°S and 5°N) predicted by the NLCCA models (only mode 1) using WS as predictor. Solid curves denote positive contours, dashed curves, negative contours, and thick curves, zero contours. The contour interval is 0.5 °C with values greater than +1.0 °C shaded, a and b represent the 1961–75 and 1981–99 period, respectively

Table 4 lists the correlations and RMSE between the observed and predicted SST anomalies averaged over Niño12 (90°W–80°W, 10°S–0°), Niño3 (150°W–90°W, 5°S–5°N), Niño3.4 (170°W–120°W, 5°S–5°N) and Niño4 (160°E–150°W, 5°S–5°N) areas. During the period 1961–75, the NLCCA and CCA models have comparable prediction skills over all four areas. During 1981–99, despite similar skills over the Niño3.4 and Niño3 areas, significant improvement of prediction skills between the NLCCA and CCA models is achieved over the Niño4 and Niño12 areas. Note that, during 1981–99, the Niño12 area is where strong warming occurred (Fig. 4g), and the Niño4 area, where strong cooling occurred (Fig. 4e). SST anomalies over these two areas cannot be well described by the CCA model. It is natural that the NLCCA models give better prediction skills over these two areas.

Table 4. Cross-validated correlation skill (corr) and RMSE (in °C) of the predicted SST anomalies by the NLCCA models (only the first mode was used) relative to the observations over the Niño12, Niño3, Niño3.4, and Niño4 areas. The difference between the NLCCA and the corresponding CCA model (NLCCA minus CCA) is shown in parenthesis