Can irregularities of solar proxies help understand quasi-biennial solar variations?

Abstract

Abstract. We define, calculate and analyze irregularity indices λWN and λaa of daily series of sunspot number WN and geomagnetic index aa as a function of increasing smoothing from N = 162 to 648 days. The irregularity indices λ are computed within 4 year sliding windows, with embedding dimensions m = 1 and 2. λWN and λaa display Schwabe cycles with sharp peaks not only at cycle maxima but also at minima: we call the resulting ~5.5 year variations "half Schwabe variations" (HSV). The mean of λWN undergoes a downward step and the amplitude of its variations strongly decreases around 1930. We observe changes in the ratio R of the mean amplitude of λ peaks at solar cycle minima with respect to peaks at solar maxima as a function of date, embedding dimension and importantly smoothing parameter N. We identify two distinct regimes, called Q1 and Q2, defined mainly by the evolution of R as a function of N: Q1, with increasing HSV behavior and R value as N is increased, occurs before 1915–1930 and Q2, with decreasing HSV behavior and R value as N is increased, occurs after ~1975. We attempt to account for these observations with an autoregressive (order 1) model with Poissonian noise and a mean modulated by two sine waves of periods T1 and T2 (T1 = 11 years, and intermediate T2 is tuned to mimic quasi-biennial oscillations QBO). The model can generate both Q1 and Q2 regimes. When m = 1, HSV appears in the absence of T2 variations. When m = 2, Q1 occurs when T2 variations are present, whereas Q2 occurs when T2 variations are suppressed. We propose that the HSV behavior of the irregularity index of WN may be linked to the presence of strong QBO before 1915–1930, a transition and their disappearance around 1975, corresponding to a change in regime of solar activity.