Nonlinear solar cycle forecasting: theory and perspectives

Nonlinear solar cycle forecasting: theory and perspectives

Blog Article

In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics.We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle.The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum.In a second step, beer button down shirts for men we extract a chaotic mapping for the successive values of one of the key model parameters – the rate of the exponential growth-decrease of the solar activity during the n-th cycle.We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function.

We find analytical relationships for the sunspot maxima and minima, viqua-f4 as well as their occurrence times, as functions of chaotic values of the above parameter.Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.