Supplementary material
Time-varying spectral characteristics of ENSO indices over the Last Millennium
Quantile-quantile analysis
Further assessment of the Nino3.4 distributions can be gained by comparing the observed and modelled SOI using quantile-quantile (QQ) plots (Figure S1). Of the models assessed here, the statistical distribution of the observed Nino3.4 is best characterised by the CCSM4 model, with the best fit to the 1:1 line on the QQ plots. However, the variance of CCSM4Nino3.4 is higher than observed, and it simulates El Niños that are stronger than observed. All the other models have variance lower than observed, and the intensity of both their El Niños and La Niñas are too weak relative to observations.
Two non-parametric tests are used here to compare the location and dispersion of the modelled and observed statistical distributions of theNino3.4. The Wilcoxon rank-sum (RS) test (equivalent to a Mann-Whitney U-test) operates with the null hypothesis that data in the two samples are from continuous distributions with equal medians, against the alternative that they are not. The Anasari-Bradley (AB) test operates with the null hypothesis that the two samples are from the same distribution and the alternative hypothesis that the samples come from distributions with the same median and shape but different dispersion (e.g. variances). Note that the AB test was performed on observed and modelled Nino3.4 data with the median first subtracted. All models pass the RS test, indicating no statistically significant difference between the observed and modelled Nino3.4 medians at the 5% significance level. However, the CCSM4 model is the only model to pass the Anasari-Bradley test, indicating that this model best characterises the dispersion of the observed Nino3.4 data.
Figure S1. Quantile-quantile plots for modelled Nino3.4 in historical CMIP5-PMIP3 experiments against observed annual Nino3.4 (1871–2005); dashed red line is the 1:1 line; blue crosses are quantiles for cumulative probabilities on the interval [0.01, 0.99] at 0.01 spacing; Wilcoxon rank sum (RS) test and Anasari-Bradley (AB) test results between modelled and observed Nino3.4 distributions shown (H=null hypothesis at 5% significance level; p=p-value).
Z-scores of bandpower
To assess the whether peaks in the bandpower series are significant, the Z scores for each series are shown in Figures S2 to S5.
Figure S2. Z scores of the timeseries of bandpower in a range of frequency bands in 50-year moving windows for observed Nino3.4 (top panel) and SOI (lower panel). The 2-3 (yellow), 3-8 (red) and 8-25 (blue) year bands are shown, with the total spectral power in purple.
Figure S3. As Figure S2, but for Nino3.4from the Historical climate model simulations.
Figure S4. As Figure S2, but for Nino3.4from the Last Millennium climate model simulations. Vertical lines indicate the timing of major volcanic eruptions.
Figure S5. As Figure S2, but for the palaeo-ENSO reconstructions. Vertical lines indicate the timing of major volcanic eruptions.