The power spectra were plotted as cumulative percentage contribution to total variance versus the normalized standard deviation t given as (Equation 9).

where L is the period in years and T₅₀ the period up to which the cumulative percentage contribution to total variance is equal to 50. The phase spectra were plotted as cumulative(%) normalized (normalized to total rotation) phase .The variance and phase spectra alongwith statistical normal distribution for the data sets (Table 2) are shown in Figures 7 - 9.

    The cumulative percentage contribution to total variance and the cumulative (%) normalized phase (normalized w. r. t. the total rotation) for each dominant waveband is computed for two representative data sets and shown in Figure 10 to illustrate Berry's phase, namely the progressive increase in phase with increase in period and also the close association between phase and variance (see Item d, Section 4.2).

    Table 3 gives the following results of continuous periodogram analyses for the data sets: (1) The period T₅₀ upto which the cumulative percentage contribution to total variance is equal to 50 . (2) The dominant peak periodicities in wavebands 2 - 3, 3 - 4, 4 - 6, 6 - 12, 12 - 20, 20 - 30, 30 - 50, 50 - 80. These wavebands include the model predicted (Equation 5) dominant peak periodicities 2.2, 3.6, 5.8, 9.5, 15.3, 24.8, 40.1, and 64.9 years for values of n ranging from -1 to 6 .

T₅₀ is the period up to which the cumulative % contribution to total variance is equal to 50.

Dominant peak periodicities significant at or less than 5% level are given in bold letters.
 
 

The following analyses was done to illustrate the two important results: (a) superimposition of dominant peak peridicities contribute to the observed departure from mean for the time series, (b) projection into the future for times of occurrences of dominant peaks helps predict near future trend in departure from mean. Two representative data sets used for the study were taken from All India monsoon (JJAS) rainfall for the 19-years periods 1952-1971 and 1967-1986. Periodogram estimates of number of positive and negative dominant peaks for half-year preceding each year was computed for all the years in the two series and also the projected values for the following two major rainfall deficit years 1972 and 1987 and shown in Figure 11.

There is a close association between the observed departures and frequency of occurrence of dominant peaks for the two data sets and the projected values indicate the observed negative departures.