The quasi-decadal modulation of running correlations involving the QBO

Abstract

Running correlations between "ideal" periodic sine series, u(t) and y(t) ,are analyzed in the present work, which, in this case, results in a kind of beating of the two waves. u(t) is considered as a quasi-biennial periodic function standing for an idealized quasi-biennial oscillation (QBO). The beat frequency in the running correlation coefficient series will correspond to a decadal oscillation if periodicities in y(t) are around 0.6-0.8 years greater or 0.4-0.5 years smaller than u(t) period. The periodicities required by y(t) to generate a decadal variation in the running correlation with u(t), may appear in series associated to the 11-year solar activity cycle due to its asymmetry: solar activity rises to maximum levels faster than it falls to minimum levels. Therefore, running correlations between the stratosphere QBO and time series with a biennial or triennial oscillation, associated or not to the solar cycle, could present a decadal oscillation due merely to the statistics involved. Taking into account the idealization of the series considered, without any relationship or interaction between them, neither a decadal modulation in u(t), we obtain a quasi-decadal oscillation in running correlations, as that obtained when certain empirical data series are correlated with the QBO in the stratosphere.