Extended version. Occurrence of solar flares viewed with GPS: statistics and fractal nature

Abstract

In this paper we describe the statistical properties of the EUV solar flux sudden variation. The solar flux variation is modeled as a time series characterized by the subsolar VTEC (Vertical Total Electron Content) double-difference in time, computed with dual frequency GNSS (Global Navigation Satellite System) measurements in the daylight hemisphere. By assuming a sudden overionization pattern of solar origin, during the last solar cycle, we propose a model that explains it's characteristics, and the forecasting limitations. The two defining characteristics of this time series, is an extreme variability (i.e.\ in a solar cycle one can find events at $400 \sigma$ from the mean value) and a temporal correlation that is independent of the time scale. We give a characterization of a model that explains the empirical results, and properties such as, a) the persistence and presence of bursts of solar flares, b) their long tail peak values of the solar flux variation. We show that the solar flux variation time series can be characterized by a fractional Brownian model for the long term dependence, and a powerlaw distribution for the extreme values that appear in the time series.