Revising a less-reliable prediction for the solar cycle based on the variation in correlation

The geomagnetic precursor method has been widely used to predict the maximum amplitude (S) of the sunspot cycle using the preceding minimum aa geomagnetic index (aa). The prediction error of this method was sometimes larger than expected. In the present study, a revision method is proposed to correct a less-reliable prediction in advance according to the variation in the correlation coefficient (R) between S and aa. For the last ten cycles n= 15 –24, R was found to vary with n in a period of approximately 2 solar cycles, and most (90%) predictions (S) met the prediction condition: when R became stronger (weaker), the prediction error (| S- S|) was likely to be smaller (larger) than the standard deviation of the regression (σ), and the MSE (Mean Square Error) skill score was about 0.86 (- 0.71). For the case R became weaker (n= 15 , 16, 18, 20, 22, and 23), the prediction was less reliable and a revision method is proposed to correct it by analyzing the values that differ by ± 2 σ from the original prediction to search for the one that meets the decreasing trend in R (at a faster rate). The revised predictions have a much smaller mean absolute (relative) error [10.5 (5.8%)] and a much higher MSE skill score (0.87) than the original ones have, 38.8 (22.6%) and - 0.71 , respectively. For the current cycle (n= 25), R(25) should be smaller than R(24) inferring from its recent past behavior, and the maximum amplitude is predicted to be 111.2 ± 27.6 by the above method.