Forecast of the Decadal Average Sunspot Number

摘要

The forecast of the decadal average sunspot number (SN) becomes possible with an extension of telescopic observations based on proxy reconstructions using the tree ring radiocarbon data during the Holocene. These decadal numbers (SN_RC) provide a powerful statistic to verify the forecasting methods. Complicated dynamics of long-term solar activity and noise of proxy-based reconstruction make the one-step-ahead forecast challenging for any forecasting method. Here we construct a continuous data set of SN_RC which extends the group sunspot number and the international sunspot number. The known technique of nonlinear forecast, the local linear approximation, is adapted to estimate the coming SN. Both the method and the continuous data set were tested and tuned to obtain the minimum of a normalized average prediction error (E) during the last millennium using several past millennia as a training data set. E=0.58σ _D is achieved to forecast the SN successive differences whose standard deviation is σ _D=7.39 for the period of training. This corresponds to the correlation (r=0.97) between true and forecasted SN. This error is significantly smaller than the prediction error when the surrogate data were used for the training data set, and proves the nonlinearity in the decadal SN. The estimated coming SN is smaller than the previous one.