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EOF analysis and characterization of extreme La Niña events.

EOF analysis was applied to observed SST anomalies, referenced to the long-term mean since 1979, in an equatorial domain (15° S–15° N, 140° E–80° W). The extreme La Niña events were diagnosed using a suite of distinct process-based indicators associated with the two EOFs, such as low temperature, low rainfall and wind anomalies. In particular, the SST anomalies are centred at the central Pacific during extreme La Niña, as opposed to the eastern equatorial Pacific during extreme El Niño. The difference in spatial patterns is captured by a different combination of two principal variability patterns. EOF1 reflects a canonical La Niña pattern embedded in the commonly used Niño3 index, featuring cool and dry anomalies extending from the eastern equatorial Pacific to the central Pacific. EOF2 resembles the La Niña Modoki pattern²⁶, featuring cool and dry anomalies in the central Pacific, but warm and wet anomalies in the far western equatorial Pacific. Thus, an extreme La Niña is an appropriately weighted superposition of the two patterns, giving rise to an anomaly centred in the central Pacific. As such, a depiction of extreme La Niña must use a different index from that for extreme El Niño, and we show that an average of SST anomalies over the Niño4 region is an appropriate index.

Model selection and analysis.

We used 21 CMIP5 coupled global climate models (CGCMs; Supplementary Table 1) forced with historical anthropogenic and natural forcings, and future greenhouse gases under the Representative Concentration Pathway 8.5 (ref. 13) emission scenario, covering a 200-year period. These were chosen from a total of 32 models, on the basis of their ability to simulate extreme La Niña events (Supplementary Table 1). As extreme La Niña tends to occur after extreme El Niño, we select models that are also able to simulate extreme El Niño. These were selected in terms of two features¹⁰: the positive skewness of rainfall anomalies, and the ability to generate rainfall greater than 5 mm d⁻¹ over the eastern equatorial Pacific. Only a subgroup of CGCMs simulate the observed nonlinear ocean–atmosphere coupling that characterizes extreme El Niño, as depicted by the positive skewness of rainfall anomalies over the eastern equatorial Pacific during austral summer (December–February), which is 2.7 in observations since 1979. The level of nonlinearity varies vastly among CGCMs, and we considered positive skewness of 1 as our threshold. Out of the 32 CGCMs, 21 models satisfy the rainfall skewness criterion. The selected CGCMs yield a mean skewness of 2.6, close to the observed value of 2.7 (Supplementary Table 1).

All 21 selected CGCMs reproduce the observed extreme La Niña pattern. Before the analysis, data were interpolated onto a common grid of 1.5° latitude by 1.5° longitude. As for the observations, EOF analysis was carried out for each individual model using SST anomalies referenced to the mean over the Control period. All 21 models produce the nonlinear relationship between the two leading EOFs, indicating their ability to generate the nonlinear equatorial positive feedback associated with extreme La Niña events. On the basis of analysis of observed SSTs, we used a quadratically detrended Niño4 index over the full 200-year period to describe La Niña events. Applying quadratical detrending over each of the periods separately yields almost identical results.

We tested the sensitivity of our results to varying threshold values for Niño4 (Supplementary Table 1). We also tested our results using a negative Niño4 SST skewness (Supplementary Text and Table 2), as observations show a negative skewness of −0.44 (using data since 1979). In all cases, including using all available models (Supplementary Text), there is an increase in the occurrences of extreme La Niña events from the Control to the Climate Change period, with a strong inter-model consensus.

Statistical significance test.

We used a bootstrap method to examine whether the increased frequency is statistically significant. The 2,100 samples from the 21 models in the Control period were re-sampled randomly to construct 10,000 realizations of 2,100-year records. In the random re-sampling process, any extreme La Niña event is allowed to be selected again. The standard deviation of the extreme La Niña frequency using a threshold value of Niño4 amplitude greater than 1.75 s.d. in the inter-realization is 9.4 events per 2,100 years, far smaller than the difference of 67 events per 2,100 years between the Climate Change and the Control periods. Using a threshold value of Niño4 amplitude greater than 1.5 s.d. in the inter-realization yields 12 events per 2,100 years, also far smaller than the difference of 65 events per 2,100 years between the Climate Change and the Control periods (Fig. 3a, b), indicating strong statistical significance. Using a threshold value of Niño4 amplitude greater than 2.0 s.d. again shows a strong significance. Increasing the realizations to 20,000 or 30,000 in the bootstrapping methodology yields essentially identical results.