Solar activity, Earth’s rotation rate and climate variations in the secular and semi-secular time scales

By applying the wavelet formalism to sudden storm commencements and aa geomagnetic indices and solar total irradiation, as a proxy data for solar sources of climate-forcing, we have searched the signatures of those variables on the Northern Hemisphere surface temperature. We have found that cyclical behaviour in surface temperature is not clearly related to none of these variables, so we have suggested that besides them surface temperature might be related to Earth’s rotation rate variations. Also it has been suggested that in the long-term Earth’s rotation rate variations might be excited by geomagnetic storm time variations which, in turn, depends on solar activity.The study of these phenomena and its relationships is addressed in the present paper. With this purpose we perform an analysis of the evolution during the last 350 years of the signals that conform the 11-year sunspot cycle maxima envelope for different time scales. The result is applied to analyze the relationship between long-term variations in sunspot number and excess of length of day; and to unearth the signature in surface temperature of this last from that of sudden storm commencement and aa geomagnetic indices and total solar irradiation.As solar dynamo experiments transient processes in all the time scales from seconds to centuries, Fourier analysis and its requirement for the process to be stationary is likely to produce spurious periodicities. We resort instead to wavelet formalism. By this representation we found that sunspot maxima envelope for the last 350 years may be described by means of the superposition of two cycles – a decadal and a semi-secular one – and a secular trend. And that the changing amplitude and phase of the cycles are well reconstructed using the superposition of two wavelets with nearby periods. The strong temporal changes in amplitude of the cycles facilitate to detect its phase in a given time series. It is found that a strong semi-secular cycle in the sunspot maxima envelope that started during the 1705 chaotic transition having its maximum amplitude at the Dalton minimum, was mapped 94 years later in Earth’s rotation rate and simultaneously in surface temperature. Also, there was a decrease (increase) of 0.022 °C for each millisecond of decrease (increase) in the Earth’s rotation period for the semi-secular cycle as well as the secular trend.