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A Bayesian Approach to Forecasting Solar Cycles Using a Fokker-Planck Equation
Noble, P. L.; Wheatland, M. S.
AA(Sydney Institute for Astronomy, School of Physics, The University of Sydney), AB(Sydney Institute for Astronomy, School of Physics, The University of Sydney)
Solar Physics, Volume 276, Issue 1-2, pp. 363-381 (SoPh Homepage)
Publication Date:
Solar cycle, models, Sunspots, statistics
Abstract Copyright:
(c) 2012: Springer Science+Business Media B.V.
Bibliographic Code:


A Bayesian method for forecasting solar cycles is presented. The approach combines a Fokker-Planck description of short-timescale (daily) fluctuations in sunspot number (Noble and Wheatland, Astrophys. J. 732, 5, 2011) with information from other sources, such as precursor and/or dynamo models. The forecasting is illustrated in application to two historical cycles (cycles 19 and 20), and then to the current solar cycle (cycle 24). The new method allows the prediction of quantiles, i.e. the probability that the sunspot number falls outside large or small bounds at a given future time. It also permits Monte Carlo simulations to identify the expected size and timing of the peak daily sunspot number, as well as the smoothed sunspot number for a cycle. These simulations show how the large variance in daily sunspot number determines the actual reliability of any forecast of the smoothed maximum of a cycle. For cycle 24 we forecast a maximum daily sunspot number of 166±24, to occur in March 2013, and a maximum value of the smoothed sunspot number of 66±5, indicating a very small solar cycle.
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