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2. - Methodological aspects.

They for the study of the explosive volcanic eruptions (EVE) were used those selected by Newhall and Self, 1982, cited by Handler, 1986. Such selection is based on the values of the VEI, Volcanic Explosivity Index. It is based on several aspects that could be observed or measured, during an eruption, as well as reports on the volcanic eruptions that were take play from 1860 up to 1999. They had been content in the data base BD012, generated by the project 01303012 (Aroche and Antuña 1996), which constituted a partial investigation results (Aroche et al., 1998,2000). The eruptions were divided in two groups, continuing the procedure used by Handler, 1986, according to the geographical latitude of their location. The tropical occurred inside the latitudinal band of the ±30o of latitude, and the extratropical foreign to the tropical band. We used the same criteria referred by saying author, to eliminate the possible mixing of the effects of each individual eruption.

The chronological series of the Annual Frequencies (or total of cases for season), AFTC, AFCF and AFEW, for the study of the behavior of the meteorological interest phenomena; Tropical Cyclones (TC), Cold Fronts (CF) and Easterly Waves (EW), was used. This series were elaborated in the National Forecasts Department of the National Meteorological Center of Cuba, for the periods 1986-1999, 1916-1999, 1967-1997, respectively.

The integral curves of the corrected modulated coefficients were elaborated, for the analysis of the chronological series of each meteorological phenomenon, (Aroche et al., 1999), were obtained. Their principal descriptive statistical parameters were calculated, too. By which we tried to know about the natural variability of the same.

The determination of the influence of the EVE on the frequency of the atmospheric referred atmospherical organisms; it was made starting from considering that the same should expressed through the disturbances in their chronological corresponding series. For this, in each one of the series was calculated not perturbed state and perturbed one. The first would pick up the sum of the components Tendency, Seasonality and Periodicity of the given series in itself, and the last to the disturbed component properly such (Cué et al., 1996).

For the estimate of the two referred states was employed an additive model (Cué et] al., 1996). In this model the not perturbed component was estimated considering that the same would be explained, mainly, for the same component of the representative series of the historical behavior of the energy fundamental source of the process: the sun. In order to obtain an analogy a comparative analysis of the better polinomial adjustment of both series was carried out. The solar activity was characterized by the number of Wolf (Hoyt, 1985), for the interval of years of 1875- 1981. This series was updated with the information derived of the Sunspot Index Dates Center (SIDC, 2000) from Brussels, Belgium. The annual frequency of the given phenomenon was used. The perturbed component was obtained as a difference between the original series of each phenomenon and its corresponding adjusted curve. The obtained disturbances are normalized with regard to the standard deviation of the original series.

The analysis of the series doesn't inform us directly on the causes of the behavior of the given phenomenon. The degree of association between the occurrence of the EVE and the interference in the series of the TC, CF and EW, was stimated for two different methods: that of the disturbances and that of the superposed epoch. The first locates the normalized disturbances of several magnitudes and signs temporarily and is analyzed the degree of correspondence with the moment of occurrence of the EVE. The second, it is a method frequently used on impact of EVE researches, (Sear, et al., 1987; Bradley, 1988, Aroche et al., 1999).