Application to Sunspot Numbers and Total Solar Irradiance

Abstract

Time series of sunspots and total solar irradiance are studied here at monthly and annual sampling intervals as samples of scalar and bivariate (at $\Delta t = 1$ month) stationary random processes with the goal to understand their statistical predictability. Because of the high autoregressive orders, the scalar time series have to be analyzed for their properties mostly within the frequency domain. Their statistical predictability within the Kolmogorov–Wiener theory of linear extrapolation is shown to be rather strong especially for the annual data. Examples of predictions are not successful at a monthly sampling interval, probably because of the asymmetry of the solar cycle and due to our linear approach. Both SSN and TSI have probability densities that strongly differ from Gaussian, and their extrapolation through nonlinear methods may provide better results. Predicting the height of SSN peaks seems to be impossible within the KWT frame. The bivariate TSI/SSN model shows that SSN drives TSI variations; the model provides a quantitative description of the interdependences within the system. At frequencies corresponding to the solar cycle, a change of SSN by ten units causes a TSI change by about 0.05 W/m² and TSI is shown to lag behind SSN by about two months.