The observed ACF peaks cannot be modeled or described to a reasonable level by using the conventional analyses of frequency domain and time domain analyses: a time filtering method, the auto regression model, moving average model, auto regression and moving average model, and others. For a reasonable explanation, we come to use the concept of spread spectrum technique popular in communications, which gives a best explanation for the observed features. Based on the fundamental assumption of the spread spectrum technique, we presumed the following relationship for a simple model of rainfall and sunspot variations,

In the above, *SR* represents the observed rainfall time series, *S* represents the annual sunspot numbers, and *R* means the prior modulation rainfalls, and the last term denotes noises from observation and other origins. *SR* and *S* are given and *R* and the delta component are not. For the variables not given to us, we assume that they resemble the sequences of random noise numbers. The character *l* signifies phase difference between the sunspot variations and the other variables such as the observed rainfalls and the prior modulation rainfalls.

The obvious differences of the assumed spread spectrum technique compared with the conventional one are that we only have a one signal and analogue carrier codes rather than many signals and the predefined digital carrier codes in the original technique. In the approach, we do not know the carrier codes at all, which is quite different from the predefined random noise time series in the conventional spread spectrum technique. In general the carrier codes, here the prior modulation rainfalls, are remarkably close to random noise sequence. Since we cannot exploit the original de-spreading scheme used in the conventional spread spectrum technology, we devised a direct de-spreading method by dividing *SR* with *S* in order to estimate *R* values. The direct de-spreading of the rainfalls by using the sunspot numbers removes the above two autocorrelation peaks simultaneously, which has never been expected before actual calculation. The spectrum-spreading obscures the 11-year frequency component in the spectrum function of the rainfalls. Our discovery suggests that we may need to reexamine some of the geophysical fluid motions with periods of three to six years in their origin and in the validity of established explanations.

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