Solar cycle forecasting: A nonlinear dynamics approach

The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activities, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a successful quantitative theoretical model of the Sun's magnetic cycle. Starting from a recent previous work, we checked the reliability and accuracy of a forecasting model based on concepts of nonlinear dynamical systems applied to experimental time series, such as embedding phase space, Lyapunov spectrum, chaotic behaviour. The model is based on a local hypothesis of the behaviour on embedding space, utilising an optimal number of neighbour vectors to predict the future evolution. The performances of this method for the current 23rd solar cycle suggest its valuable insertion in the set of the so-called non-precursor statistical-numerical prediction techniques. The main task is to set up and to compare a promising numerical nonlinear prediction technique, essentially based on an inverse problem, with the most accurate prediction methods, like the so-called precursor methods which appear now reasonably accurate in predicting long-term Sun activity, with particular reference to solar and geomagnetic precursor methods based on a solar dynamo theory.