We present a brief review of predictions of solar cycle maximum amplitude with a lead time of 2 years or more. It is pointed out that a precise prediction of the maximum amplitude with such a lead-time is still an open question despite progress made since the 1960s. A method of prediction using statistical characteristics of solar cycles is developed: the solar cycles are divided into two groups, a high rising velocity (HRV) group and a low rising velocity (LRV) group, depending on the rising velocity in the ascending phase for a given duration of the ascending phase. The amplitude of Solar Cycle 24 can be predicted after the start of the cycle using the formula derived in this paper. Now, about 5 years before the start of the cycle, we can make a preliminary prediction of 83.2-119.4 for its maximum amplitude.

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We find that the solar cycles 9, 11, and 20 are similar to cycle 23 in their respective descending phases. Using this similarity and the observed data of smoothed monthly mean sunspot numbers (SMSNs) available for the descending phase of cycle 23, we make a date calibration for the average time sequence made of the three descending phases of the three cycles, and predict the start of March or April 2008 for cycle 24. For the three cycles, we also find a linear correlation of the length of the descending phase of a cycle with the difference between the maximum epoch of this cycle and that of its next cycle. Using this relationship along with the known relationship between the rise-time and the maximum amplitude of a slowly rising solar cycle, we predict the maximum SMSN of cycle 24 of 100.2±7.5 to appear during the period from May to October 2012.

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The prediction for the smoothed monthly mean sunspot numbers (hereafter SMSNs) of solar cycle 23, which was given with a similar cycle method proposed by us at the beginning time of cycle 23, is analyzed and verified in this paper. Using our predicted maximum SMSN and the ascending length for solar cycle 24, and assuming their relative errors to be respectively 20% and ± 7 months, solar cycles 2, 4, 8, 11, 17, 20 and 23 are selected to be the similar cycles to cycle 24. The selected solar cycles are divided into two groups. The first group consists of all the selected cycles; while the second group consists of only cycles 11, 17, 20 and 23. Two SMSN time profiles then may be obtained, respectively, for the two similar cycle groups. No significant difference is found between the two predicted time profiles. Considering the latest observed sunspot number so far available for cycle 23 and the predictions for the minimum SMSN of cycle 24, a date calibration is done for the obtained time profiles, and thus, SMSNs for 127 months of cycle 24, from October 2007 to April 2018, are predicted. solar cycle, sunspot numbers, prediction of cycle 24A Wolf sunspot number, or the so-called relative sunspot number, is usually used as one of the solar indices describing solar activity, which is made of the number of sunspots and the number of sunspot groups [1] . The number is obviously lack of physical meanings compared, for examples, with the solar flux at 2800 MHz, the total area of sunspots [2] , and the group sunspot number [3] . The relative sunspot number has a historical record longer than 200 years, its time sequence reflects clearly the periodicities of solar activity [4] , and the number has close relations with the productivities of solar activities such as solar flares [5] and coronal mass ejections [6,7] . So, the number is used in the fields of solar physics, geophysics and space weather more frequently than other indices. The Wolf number is often simply called sunspot number. However, in studies and predictions of long-term variations of solar activities, the smoothed monthly mean sunspot number (hereafter