Prediction of unspots using reconstructed chaotic system equations

Modeling of sunspots is important since they indicate the relative activity of the Sun which in turn influence different terrestrial properties. To predict the nonlinear and chaotic behavior of sunspot time series, the problem of reconstructing underlying system equations is studied. The proposed procedure for this is (1) based on the behavior of observed time series and dimension of strange attractor, find reference system equations (in our case the modified Rössler equations) that show similar basic features as the time series (e.g., appearance of attractor, amplitude and pseudoperiod), (2) assume a general structure of the governing system equations by Taylor series expansion, (3) use the reference equation systems as initial state in an updating procedure (extended Kalman filtering) to estimate the structure of the governing system equations. Using this procedure, results show that predictions on an average up to eight months ahead can be made with good agreement for sunspot time series after identifying the governing system equations. The extended Kalman filter was shown to be an efficient tool to identify parameter values and to make updated predictions of the chaotic system.