Tuesday

Applying Principal Components Analysis (PCA) to the full-disk synoptic maps of solar magnetic field variations obtained by Wilcox Solar Observatory in solar cycles 21-24 we derive 4 pairs of eigen values and eigen vectors (Zharkova et al, 2015) and analytical expressions as the sums of periodic cosine functions for the first pair (principal components). The analytical expression for the summary curve of the pair is applied for prediction of solar magnetic field variations in the two layers of the solar interior in the past three millennia. Extrapolation of the summary curve of PCs in the past 3000 years confirms the eight grand cycles of ~350-400-years superimposed on 22 year-cycles caused by beating effect of the two dynamo waves generated by dipole magnetic sources in the two (deep and shallow) layers of the solar interior. The grand cycles in different periods comprise a different number of individual 22-year cycles. Furthermore, the summary curve reproduces a remarkable resemblance to the sunspot and terrestrial activity reported in the past: Maunder Minimum, Wolf minimum, Homeric minimum, Medieval warmth period and Roman Warmth Period. Temporal variations of the dynamo waves are modelled for dipole sources with the two-layer mean dynamo model with meridional circulation revealing a remarkable resemblance of temporal variations and butterfly diagrams to those derived with PCA and predicting the upcoming modern grand minimum in 2020-2055. Addition of quadruple magnetic waves in the inner layer allowed us to recover Dalton minimum and the other minima of Glessberg’s cycle.