The most important characteristic of the Southern Oscillation are its ir-regular periodicities. They determine in which year a phenomenon of El Niño or La Niña will take place, or if the tropical Pacific behavior will be neutral.
Since none of the time series of SST, MEI or SOI anomalies or persistences correspond to a linear and deterministic process, the Fourier power spectra in the time of these variables show many peaks, where the highest of them represent the most recurrent periodicity to be expected for every variable.
As figure 3.4 reveals, the anomalies of the Hadley Centre’s SST data show their strongest periodicities in a time interval between three and four years, with a third large peak around six years. There are two other peaks of smaller extent around five years and another around three years, which together should account for most of the variability of the time series in its extreme episodes.
There exists, however, variability of SST on longer time scales. This cannot be found for larger periods, since the Fourier transform is strongly affected by the length of the series. This will be the case in the study of the MEI anomalies below.
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Power spectrum of the SST anomalies
1 2 3 4 5 6 7 8
Power spectrum of the MEI anomalies
Fourier
Power spectrum of the SOI anomalies
Fourier power spectrum
years
Figure 3.4: Power spectra vs. time in years for the SST, MEI and SOI anoma-lies series.
Conversely, the MEI anomalies show only two high peaks, around five and three and half years. This is not fully in concordance with the spectrum of the foregoing series, even though SST is definitely an important component of MEI. Part of the answer to this discrepancy lies in the fact that, as a much shorter time series, MEI does not allow for the same resolution as SST, leaving a broad band of time in which the peaks of MEI can really be sharply located or distributed between the depicted points. A consequence of the shortness of the MEI series is thus that the spectrum cannot be extended with any desirable
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Power spectrum of the SST Persistences
Fourier
Power spectrum of the MEI anomalies
Fourier
Power spectrum of the SOI persistences
Fourier power spectrum
years
Figure 3.5: Power spectra vs. time in years for the SST, MEI and SOI persis-tences series.
reliability beyond a periodicity of eight years.
The anomalies of the SOI present a somewhat more similar structure to the SST than those of MEI. This is a remarkable result though the difference in the series is evidence for the importance of interactions between the ocean and atmosphere in El Niño and La Niña phases, which perceived as a superposition of high anomalies in the climatological variables are responsible for most of the interannual variability. Again, periods of three to four years and around six years are the most pronounced. It is notable that the last of these periods has
Figure 3.6: Correlations between the SST anomalies, MEI and SOI series.
been responsible for the strong El Niño events of the last decade.
The spectra of the fluctuations are much more complex than that of the anomalies. This is shown in the figure 3.5, where no definite periods in the persistences of any of the time series is found. There is a prohibitive amount of noise in them originated in the plot of the spectrum as a function of the period in a linear scale, since it is the inverse of the frequency found in the pe-riodogram. This effect is included to illustrate more complex noise frequencies of the following chapter. The SST persistence data presents the periodicities at the higest time scales, up to four years, but like for the other variables, with no more influence than periodicities even under one year. As an extrem case, the SOI series consists almost only of very rapid fluctuations.
It is also interesting to observe the redundancy in the information given by the different time series. For this purpose the cross-correlations between the
time series have been found, as given for the time series X =x1, ..., xmax and Y =y1, ..., ymax as
C(t) = < xnyn+v >−< x >< y >
σxσy (3.1)
and is depicted in the figure 3.6. It is found that there is certain redundancy in the information given by the SST anomalies and the SOI, which takes the form of an anticorrelation, related to the different signs of the series at El Niño and La Niña events. This correlation has the magnitude of 0.6 of the product of the standard deviations of both series and decreases as a damped sinusoid, reaching the first zero correlation after thirteen months. A similar case is found between the SST and MEI series, which higher correlations than the former ones. Here, the correlation reaches the value of the product of the standard deviations and is highest until the time lag of MEI is larger than four months, and becoming zero again after thiteen months. In this both cases is the behaviour of the correlation oscillatory, though not periodic or related to the yearly trend. Conversely, the correlation between the SOI and MEI indexes is negligible and independent of the time lag. Hence, it appears that there is a certain redundancy specially in the data of SST and MEI, an understandable result, since SST is one of the variables used in computing MEI. Nevertheless, it should be remembered that this correlation analysis only accounts for lin-ear relationships between the variable and hence nonlinlin-ear quantifiers as the transinformation lead to complementary results.