On solar cycle predictions and reconstructions

Context. Generally, there are two procedures for solar cycle predictions: the empirical methods - statistical methods based on extrapolations and precursor methods - and methods based on dynamo models. Aims. The goal of the present analysis is to forecast the strength and epochs of the next solar cycle, to investigate proxies for grand solar minima and to reconstruct the relative sunspot number in the Maunder minimum. Methods. We calculate the asymmetry of the ascending and descending solar cycle phases (Method 1) and use this parameter as a proxy for solar activity on longer time scales. Further, we correlate the relative sunspot numbers in the epochs of solar activity minima and maxima (Method 2) and estimate the parameters of an autoregressive moving average model (ARMA, Method 3). Finally, the power spectrum of data obtained with the Method 1 is analysed and the Methods 1 and 3 are combined. Results. Signatures of the Maunder, Dalton and Gleissberg minima were found with Method 1. A period of about 70 years, somewhat shorter than the Gleissberg period was identified in the asymmetry data. The maximal smoothed monthly sunspot number during the Maunder minimum was reconstructed and found to be in the range 0-35 (Method 1). The estimated Wolf number (also called the relative sunspot number) of the next solar maximum is in the range 88-102 (Method 2). Method 3 predicts the next solar maximum between 2011 and 2012 and the next solar minimum for 2017. Also, it forecasts the relative sunspot number in the next maximum to be 90 +/- 27. A combination of the Methods 1 and 3 gives for the next solar maximum relative sunspot numbers between 78 and 99. Conclusions. The asymmetry parameter provided by Method 1 is a good proxy for solar activity in the past, also in the periods for which no relative sunspot numbers are available. Our prediction for the next solar cycle No. 24 is that it will be weaker than the last cycle, No. 23. This prediction is based on various independent methods.