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Ann. Geophys., 26, 231-241, 2008
www.ann-geophys.net/26/231/2008/
© European Geosciences Union 2008
Nonlinear solar cycle forecasting: theory and perspectives
A. L. Baranovski1,*, F. Clette1, and V. Nollau2
1Royal Observatory of Belgium, Brussels, Belgium
2Dresden University of Technology, Institute for Mathematical Stochastics Dresden, Germany
*now at: Center for Information Services and High Performance Computing, Dresden University of Technology, Dresden, Germany
Abstract. 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, 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, 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.
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