Wavelet power spectra of the anomalies series

Figure 4.2 shows the periodicities in the time of the SOI anomalies series.

It appears that for this series, there are strong periodicities of three to seven years, which are present over most of the length of the time series. There are two exceptions to this behavior, between 1924 and 1937 and between 1962 and 1966, while regions of larger periods have been active in the last three decades.

These intervals have been observed to account for a shift in the correlation lag between SOI and SST and to start the trend of larger El Niño events which has peaked in the last two decades.

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Figure 4.2: Paul wavelet power spectrum of the SOI anomalies series. The con-cave line below is the cone of influence, where finite-size effects underestimate power. The white contours indicate significant regions of different structure than the autocorrelation first-order Markov process.

For periods smaller than two years, the patterns are irregular and of smaller intensity than for the strongest interdecadal periods. Much of these signals represent effectively noise as was observed in the Fourier spectra of the last chapter. Length effects are of importance for this series in periodicities smaller than ten years between 1895 and 1995, as can be seen from the black curve representing the cone of influence. There are some regions, inside the patterns for the largest periodicities, which represent areas with a significant difference to an autocorrelation first-order Markov process simulating the series.

The wavelet power spectrum of figure 4.3, for the SST anomalies series,

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Figure 4.3: Paul wavelet power spectrum of the SST anomalies series. The con-cave line below is the cone of influence, where finite-size effects underestimate power. The white contours indicate significant regions of different structure than the autocorrelation first-order Markov process.

is evidently affected by high-frequency random disturbances. The regions of strong periodicities are found to be larger than for the SOI anomalies series, showing only the interruption around 1960. In the last decades, moreover, strong periodicities of higher frequency have taken place, so that a shift in the frequencies appears to have occured since the begin of the record. This shift enlightens considerably the search for mechanisms which are sought to be responsible for the variability of ENSO in the past half century. The length effects are similar to those of the SOI anomalies, but the significant regions are by far much larger. It is found that these areas occupy more space than

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Figure 4.4: Paul wavelet power spectrum of the MEI anomalies series. The concave line below is the cone of influence, where finite-size effects under-estimate power. The white contours indicate significant regions of different structure than the autocorrelation first-order Markov process.

five percent of the plot, the limit which could have been given by chance, so that this series has been significantly under the action of correlations, espe-cially from 1880 to 1930 and since 1960. Another argument for the positive evaluation of correlations is the localization of the significant areas: these are not likely to have the forms they take by chance.

The wavelet power spectrum of the MEI anomalies series is shown in figure 4.4. This plot appears as a detail of the wavelet power since 1950, and con-sists primarily of three large regions of acting periodicities. It is necessary to considerate only the smallest periods, which reach their maximum of 16 years

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Figure 4.5: Paul wavelet power spectrum of the SOI persistences series. The concave line below is the cone of influence, where finite-size effects under-estimate power. The white contours indicate significant regions of different structure than white noise.

in 1976, for the size of the series allows for large areas of length effects. The largest region of strong influence on ENSO has a periods between 2 to 4 years and is found between 1965 to 2000. Before 1965, a region of larger periods be-tween 4 and 8 years appears. Hence, the MEI series confirms the importance of the shift in the acting frequencies in the evolution of ENSO in the sixties.

The third region of periodicities over the scale of a decade are found mostly below the cone of influence, nevertheless it coincides with the appearence of a similar region for the SOI series.

As for the SST, most of the regions of greater variance in the interdecadal

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Figure 4.6: Paul wavelet power spectrum of the SST persistences series. The concave line below is the cone of influence, where finite-size effects under-estimate power. The white contours indicate significant regions of different structure than white noise.

scale are found to differ from the most similar first-order Markov process. From the MEI series, it appears that practically the last half century presented mid-range correlations.

Many of the apparently non-Markovian areas of the SOI are found to be the events where mid-range correlations take place, which have been found as constant blocks during El Niño or La Niña state. The most prominent of these episodes are found between 1900 and 1920, as in the large episodes between 1965 and 1998. In the case of SST, there are larger continuous areas suggesting non-Markovian behavior. The results of the MEI index support this

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