Since the oscillating pattern of the Southern Oscillation has been found as a consequence of the intrinsic dynamics of the coupled system of the ocean and the atmosphere, most of the attention in the understanding of this phenomenon has been directed to study its irregularity. There are several models which capture different modes, [10, 106, 135] , which are however periodic, so that random noise is necessary to make the oscillations irregular. It is also possible to obtain different frequencies by tuning the coupling parameters [74], and introducing nonlinearity in the interaction [119]. This assumption has been very productive, especially by modifying the equation (2.50) for the coupling of the sea surface temperature with the thermocline anomaly [70], since it has allowed the investigation of the Southern Oscillation as a chaotic time series [118], [126]. This could signify that the irregularity of the Southern Oscillation is, as its oscillating character, a consequence of the coupled dynamics.
Another interesting problem is the effect of the seasonal cycle on the South-ern Oscillation. Most studies specify the values of the cycle in the dynamical equations, for it is extremely difficult to approach this problem in an attempt to illuminate quantitatively in detail the origin of the seasonal cycle itself.
This problem has been tried only with coupled general circulation models [67].
Hence, the annual variability is examined primarily parametrizing the inter-action between the ocean and the atmosphere. Chaos is also possible in this scenario, which however does not explain some well-defined temporal corre-lations of El Niño and the seasonal cycle [18]. The procedure of a seasonal depending parametrization has simulated correctly the phase locking of the Southern Oscillation to the seasonal cycle so that the heat anomaly in the eastern Pacific peaks in a standard composite El Niño towards the end of the year, principally as a consequence of a dynamical balance between the Kelvin and Rossby waves [32].
The introduction of stochastic forcing has been a fruitful step in examining the origin of the irregularity of the Southern Oscillation [83], since it accounts for "weather"phenomena of high frequency and very short memory, which have an effect in the dynamics that depends on the coupling of the ocean and atmosphere, which is in turn a function of the month of the year. Hence, it appears that the Southern Oscillation is more appropriately described as a stochastic process than as a result of chaotic dynamics [19]. Moreover, Wang [125] argues that the introduction of noise allows to consider El Niño as a phenomenon caused by stochastic resonance [2]. In the light of this results and the characteristic regular Oscillation of the ocean-atmosphere dynamics, it is possible to pose the problem of the irregularity of El Niño in terms of the role of stochastic forcing over modes which can be stable or unstable without forcing. There are consequently four possible scenarios for the dynamics of the El Niño and the Southern Oscillation (ENSO):
• ENSO is an unstable chaotic mode where stochastic forcing plays no important role,
• ENSO is an unstable, saturated mode, where external noise causes tran-sient growth that either cancels or reinforces the warm and cold events so that they take on their irregular appearance,
• ENSO is a neutral or slightly damped mode where noise alters the phase and amplitude of the peaks so that they take on their irregular appear-ance, and
• ENSO is a highly damped mode where noise and transient growth create all warm and cold events.
Philander and coworkers [29] claim that the two extreme cases cannot describe appropriately the Southern Oscillation. The two latter possibilities are studied in detail in the work of Thompson and Battisti [111], [112].
The predictability of El Niño is a problem which is studied with dynamical and statistical methods. While the dynamical methods depend on the perfor-mane of the models, statistical methods have been affected by the scarcity of oceanographical data. Nevertheless, early studies such as [31], [36] and [37]
have tried put some limits to the time in advance a correct forecasting can be made. Dynamical predictions [58], [134], [5] have shown that there is a so-called "spring barrier", which makes the prediction of events during the northern spring more difficult than during other times of the year. It has been tried to explain this effect as a consequence of the smallness of the signal to be forecasted [134]. The most addressed topics in the study of the predictability of the Southern Oscillation are the time in advance of a succesful prediction and the variability of the predictability along the months of the year. There is nevertheless much more to investigate about the predictability of the South-ern Oscillation. The relationship of the predictability and time correlations of indices of El Niño has been analyzed by Ausloos and Ivanova [3] and Ortiz-Tanchez, Ebeling and Lanius [76]. In the latter of the works, the fact that the predictability of La Niña is significantly higher than that of El Niño has been detected and quantified. The study of the predictabilities of the South-ern Oscillation in the present work is devoted to its relationship to mid-range correlations and a detail of the predictability of specific sequences obtained with three significative indices of the Southern Oscillation.
The El Niño of 1997-98 has shown that there is still much effort is nec-essary to understand and predict the Southern Oscillation reasonably. Many prediction methods [47], [105], [50] performed badly [80] and the search for an explanation for this circumstance is still on the run [120]. It is a possibil-ity that during the past two decades the Southern Oscillation has changed, as investigations on the spring barrier reveal [6]. The effect that the global warming has on El Niño is studied at the present [28], [113], especially with modifications of the seasonal cycle. It remains to be seen to which extent the
overall changing dynamics of the earth affect the Southern Oscillation.