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

Abstract. We define, calculate and analyze irregularity indices λ_ISSN of daily series of the International Sunspot Number ISSN 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. λ_ISSN displays Schwabe cycles with ~5.5-year variations ("half Schwabe variations" HSV). The mean of λ_ISSN 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 ISSN 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.