Sunspot random walk and 22‐year variation

We examine two stochastic models for consistency with observed long‐term secular trends in sunspot number and a faint, but semi‐persistent, 22‐yr signal: (1) a null hypothesis, a simple one‐parameter log‐normal random‐walk model of sunspot‐number cycle‐to‐cycle change, and, (2) an alternative hypothesis, a two‐parameter random‐walk model with an imposed 22‐yr alternating amplitude. The observed secular trend in sunspots, seen from solar cycle 5 to 23, would not be an unlikely result of the accumulation of multiple random‐walk steps. Statistical tests show that a 22‐yr signal can be resolved in historical sunspot data; that is, the probability is low that it would be realized from random data. On the other hand, the 22‐yr signal has a small amplitude compared to random variation, and so it has a relatively small effect on sunspot predictions. Many published predictions for cycle 24 sunspots fall within the dispersion of previous cycle‐to‐cycle sunspot differences. The probability is low that the Sun will, with the accumulation of random steps over the next few cycles, walk down to a Dalton‐like minimum. Our models support published interpretations of sunspot secular variation and 22‐yr variation resulting from cycle‐to‐cycle accumulation of dynamo‐generated magnetic energy.