Solar variability: Evolution of correlation properties

Abstract

The solar activity, with its conspicuous 11 year cycle, has been studied for long by geophysicists and solar physicists. The question of a possible relationship between the solar activity and the climate—in fact the so-called global temperature of the Earth—has received recently a strong renewal of interest. And it is well known that the magnetic activity, i.e. the time variations of the ionospheric and magnetospheric fields in a large domain of frequencies, estimated through various magnetic indices, is closely linked to the solar activity. Long series of the daily sunspot numbers (more than 150 years long), of the three-hourly global aa index (more than 130 years long), and of the daily means of the three components of the geomagnetic field in a number of observatories (up to 100 years long) exist. Of course they have been studied extensively, principally using linear techniques. We propose here an original nonlinear approach. It is mainly based on the concept of Markov correlation. We establish a relationship between the high-frequency and the low-frequency components of the considered signal, and are able to discriminate a modulated noise from an additive one. We estimate the Markov autocorrelation (MA) of the high-frequency component and study its long-term evolution when the signal is well organized. We apply our technics to the daily data series mentioned above: sunspot numbers, aa-index and geomagnetic field data from a local station. We demonstrate that all these series can be considered as a modulated noise signal, the low-frequency component being the same for all of them. On the contrary, the high-frequency components of the considered series have different characteristics. The MA of the noise component of the sunspot numbers reflects general features of the solar activity, unlike that of aa index. The mean lifetime of sunspots is roughly estimated from the analysis of the Wolf number series. Ignoring obvious solar cycle related variations, we obtain rather constant life times for two long periods: 1848–1925, and again after 1950. The mean lifetime of sunspots grows by a factor 1.7 in the period 1925–1950, which would reveal an overall growth of solar activity.