Abstract
In this work we describe a technique developed to improve medium-term prediction methods of monthly smoothed sunspot numbers. Each month, the predictions are updated using the last available observations (see the monthly output in real time at http://sidc.oma.be/products/kalfil ). The improvement of the predictions is provided by applying an adaptive Kalman filter to the medium-term predictions obtained by any other method, using the six-monthly mean values of sunspot numbers covering the six months between the last available value of the 13-month running mean (the starting point for the predictions) and the “current time” (i.e. now). Our technique provides an effective estimate of the sunspot index at the current time. This estimate becomes the new starting point for the updated prediction that is shifted six months ahead in comparison with the last available 13-month running mean, and it provides an increase of prediction accuracy. Our technique has been tested on three medium-term prediction methods that are currently in real-time operation: The McNish–Lincoln method (NGDC), the standard method (SIDC), and the combined method (SIDC). With our technique, the prediction accuracy for the McNish–Lincoln method is increased by 17 – 30%, for the standard method by 5 – 21% and for the combined method by 6 – 57%.
Similar content being viewed by others
References
Brown, R.G.: 1963, Smoothing Forecasting and Prediction in Discrete Time Series, Prentice Hall, New York, 468.
Conway, A.J.: 1998, Time series, neural networks and the future of the Sun. New Astron. Rev. 42, 343.
Denkmayr, K., Cugnon, P.: 1997, About sunspot number medium-term predictions. In: Heckman, G., Maruboshi, K., Shea, M.A., Smart, D.F., Thompson, R. (eds.) Proceedings of the 5th Solar–Terrestrial Predictions Workshop, Hiraiso Solar Terrestrial Research Center, Japan, 103.
Fessant, F., Pierret, C., Lantos, P.: 1996, Comparison of neural network and McNish and Lincoln methods for the prediction of the smoothed sunspot index. Solar Phys. 168, 423.
Hanslmeier, A., Denkmayr, K., Weiss: 1999, Longterm prediction of solar activity using the combined method. Solar Phys. 184, 213.
Hathaway, D.H., Wilson, R.M., Reichmann, E.J.: 1994, The shape of the sunspot cycle. Solar Phys. 151, 177.
Kalman, R.E.: 1960, A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng. 82, 35.
Koeckelenbergh, A.: 1986, Comments on medium-term prediction of solar activity. In: Simon, P.A., Heckman, G., Shea, M.A. (eds.) Solar–Terrestrial Predictions, US Department of Commerce, NOAA, ERL, Boulder, 113.
Lantos, P.: 2006, Solar cycle prediction: Combining precursor methods with McNish and Lincoln technique. Solar Phys. 236, 399.
Macpherson, K.P., Conway, A.J., Brown, J.C.: 1995, Prediction of solar and geomagnetic activity data using neural networks. J. Geophys. Res. 100, 21735.
McNish, A.G., Lincoln, J.V.: 1949, Prediction of sunspot numbers. EOS 30, 673.
Pankratova, N.D., Podladchikova, T.V.: 2008, Estimation and prediction of difficult formalized processes of different physical nature. J. Autom. Inf. Sci. 40, 23.
Podladchikova, T.: 2006, Identification of unknown noise statistics for non-stationary state space systems. In: Bobtsov, A.A., Nikiforov, V.O. (eds.) Preprints of the 11th International Student Olympiad on Automatic Control (Baltic Olympiad), State University of Information Technologies, Mechanics and Optics, Saint-Petersburg, 103.
Sello, S.: 2001, Solar cycle forecasting: A nonlinear dynamics approach. Astron. Astrophys. 377, 312.
Steward, F.G., Ostrow, S.M.: 1970, Improved version of the McNish–Lincoln method for prediction of solar activity. Telecommun. J. 37, 228.
Waldmeier, M.: 1968, Sonnenfleckenkurven und die Methode der Sonnenaktivitätsprognose. Astron. Mitt. Eidgenöss. Sternwarte Zürich 286, 13.
Zhang, Q.: 1996, A nonlinear prediction of the smoothed monthly sunspot numbers. Astron. Astrophys. 310, 646.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Podladchikova, T., Van der Linden, R. A Kalman Filter Technique for Improving Medium-Term Predictions of the Sunspot Number. Sol Phys 277, 397–416 (2012). https://doi.org/10.1007/s11207-011-9899-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11207-011-9899-y