The Sun-Earth connect 1: A fractional d-matrix of solar emissions compared to spectral analysis evidence of solar measurements and climate proxies

The possibility that there is a constant ratio underpinning published solar cycles provides an opportunity to explore the harmonics within emission processes. This idea is initially developed by a phenomenological matrix where the elements or emission phases are underpinned by a cyclic fractional dimension d (0.39807) which is shown here to include the fine structure constant (1/137.0356). The Sun's Carrington synodic rotation (27.275d) multiplied by the inverse of the fine structure constant creates elements of this d-matrix which yields possible sequences of self-similar phase periods between harmonic elements of solar emissions. The periodicities of the Carrington rotation is defined by row 1 (R₁) and subsequent rows R₂, R₃, R₄ are the potential phase periods of possible twisting permutations of the tachocline. For solar measurements, the first four rows of the matrix predict at least 98% of the top hundred significant periodicities determined from multi--taper spectral analysis of solar data sets (the satellite ACRIM composite irradiance; the terrestrial 1O.7cm Penticton Adjusted Daily Radio Flux, Series D; and the historical mean monthly International Sunspot Number). At centennial and millennial time scales, the same matrix predicts 'average' significant periodicities (greater than 95%) reported in 23 published climate data sets. This discovery suggests there is strong empirical evidence for a d-cyclic fractional 'solar clock', where the corresponding spectrum of cycles and switching events are embedded into the historical, climatic and geological records of the Earth.