Modeling the multi-peak structure of the solar cycle

We develop a data-oriented methodology to model and accommodate a potential multi-peak structure in the solar cycle. The method incorporates and extends the multi-level Bayesian model for a single-peaked solar cycle developed by Yu et al. (2012). Yu et al. (2012) considered only monthly mean sunspot numbers as a proxy for solar activity; we instead include polar flux data as an additional proxy and use Gaussian Process regression to model complex features of the solar cycle that are missed by the single-peaked, single-proxy model. The result is an augmented model that we fit via a two-stage approach. In the first stage, the Yu et al. (2012) model is fit to the monthly mean sunspot numbers using standard Bayesian techniques. In the second stage, the residuals resulting from the first stage are modeled with a Gaussian Process that incorporates the polar flux data as input. We demonstrate through hindcasts that the augmented model is able to make predictions that are more consistent with the observed monthly mean sunspot numbers, and therefore the underlying solar cycle, by capturing multi-peak structure. We also make a prediction for timing and morphology of the upcoming solar cycle maximum, under both the Yu et al. (2012) model and our augmented model.