Principal component analysis of the solar magnetic field I: the axisymmetric field at the photosphere

A principal component analysis, or proper orthogonal decomposition, of the axisymmetric magnetic field at the photosphere is carried out to find an optimal representation of the observed solar cycle. The 22-year periodic field requires just two modes. NSO Kitt Peak synoptic maps for Carrington rotations 1664-2007 were reduced by taking both the mean and the median field over longitude to produce two sequences of functions of sine latitude spanning 25.7 years. The lowest modes of each are determined by the polar fields. The mean field is most efficient at representing the periodic field, but the median field is more efficient at representing the evolution of the diffuse field patterns.