An Early Prediction of the Amplitude of Solar Cycle 25

A “Solar Dynamo” (SODA) Index prediction of the amplitude of Solar Cycle 25 is described. The SODA Index combines values of the solar polar magnetic field and the solar spectral irradiance at 10.7 cm to create a precursor of future solar activity. The result is an envelope of solar activity that minimizes the 11-year period of the sunspot cycle. We show that the variation in time of the SODA Index is similar to several wavelet transforms of the solar spectral irradiance at 10.7 cm. Polar field predictions for Solar Cycles 21?–?24 are used to show the success of the polar field precursor in previous sunspot cycles. Using the present value of the SODA index, we estimate that the next cycle’s smoothed peak activity will be about \(140 \pm30\) solar flux units for the 10.7 cm radio flux and a Version 2 sunspot number of \(135 \pm25\). This suggests that Solar Cycle 25 will be comparable to Solar Cycle 24. The estimated peak is expected to occur near \(2025.2 \pm1.5\) year. Because the current approach uses data prior to solar minimum, these estimates may improve as the upcoming solar minimum draws closer.     

Prediction of Solar Cycle Maximum Using Solar Cycle Lengths

If the rise time RT, fall time FT, and total time TT (i.e., RT+FT) of a solar cycle are compared against the maximum amplitude Rz(max ) for the following cycle, then only the association between TT and Rz(max ) is inferred to be well anticorrelated, inferring that the larger (smaller) the value of Rz(max ) for the following cycle, the shorter (longer) the TT of the preceding cycle. Although the inferred correlation (−0.68) is statistically significant, the inferred standard error of estimate is quite large, so predictions using the inferred correlation are not very precise. Removal of cycle pairs 15/16, 19/20, and 20/21 (statistical outliers) yields a regression that is highly statistically significant (−0.85) and reduces the standard error of estimate by 18%. On the basis of the adjusted regression and presuming TT=140 months for cycle 23, the present ongoing cycle, cycle 24’s 90% prediction interval for Rz(max ) is estimated to be about 94±44, inferring only a 5% probability that its Rz(max ) will be larger than about 140, unless of course cycle pair 23/24 is a statistical outlier.     

第22和23太阳周太阳活动预测

本文首先分析指出第22太阳周前半周的太阳活动所具有的特点:(1)有最高的起始极小值;(2)上升速度快;(3)升段时间最短;(4)峰期长,可能有双峰;(5)个别时段活动水平极高.然后对第22周后半周的活动情况做了预计:在后半周将可能观测到大约2800个活动区,28000个耀斑,210个X级X射线爆发和大约80次太阳质子事件.最后,应用本文给出的太阳周参量关系式.预报第23周太阳黑子数月均平滑值的峰值为119,位于2001.6年.     

第23太阳活动周发展趋势预测

利用压强改正莫斯科中子监测值,对第２３太阳活动周的未来发展趋势作了预测,推测第 ２３周太阳活动和第 ２２周相当,约在 ２００１年达到 １５１± １６的极大月平均黑子相对数．     

Prediction of Solar Cycle 24 Using Sunspot Number near the Cycle Minimum

Correlations between monthly smoothed sunspot numbers at the solar-cycle maximum [R _max] and duration of the ascending phase of the cycle [T _rise], on the one hand, and sunspot-number parameters (values, differences and sums) near the cycle minimum, on the other hand, are studied. It is found that sunspot numbers two?–?three years around minimum correlate with R _max or T _rise better than those exactly at the minimum. The strongest correlation (Pearson’s r=0.93 with P<0.001 and Spearman’s rank correlation coefficient r _S=0.95 with P=9×10^?12) proved to be between R _max and the sum of the increase of activity over 30 months after the cycle minimum and the drop of activity over 30 or 36 months before the minimum. Several predictions of maximal amplitude and duration of the ascending phase for Solar Cycle 24 are given using sunspot-number parameters as precursors. All of the predictions indicate that Solar Cycle 24 is expected to reach a maximal smoothed monthly sunspot number (SSN) of 70?–?100. The prediction based on the best correlation yields the maximal amplitude of 90±12. The maximum of Solar Cycle 24 is expected to be in December 2013?–?January 2014. The rising and declining phases of Solar Cycle 24 are estimated to be about 5.0 and 6.3 years, respectively. The minimum epoch between Solar Cycles 24 and 25 is predicted to be at 2020.3 with minimal SSN of 5.1?–?5.4. We predict also that Solar Cycle 25 will be slightly stronger than Solar Cycle 24; its maximal SSN will be of 105?–?110.     

Prediction of the Beginning of Solar Activity Cycle 24 by the Similar Cycle Method

In this paper, the method of similar cycles is applied to predict the start time of the 24th cycle of solar activity and the sunspot numbers in the later part of the descending phase of cycle 23. According to the characteristic parameters and the morphological characters of the descending phase of cycle 23 and of cycles 9, 10, 11, 15, 17 and 20 (cycles selected as the similar cycles for the descending phase of cycle 23), the start time of cycle 24 is predicted to be in 2007 yr 5 ± 1m, the smoothed monthly mean spot number, 7.1 ± 2.6 and the length of the 23rd cycle, 11.1 yr. These results agree rather well with those stated in Refs.[11] & [12] as well as those of MSFC. Our work shows that the method of similar cycles can well be applied to the long-term prediction of solar activity.     

An Early Prediction of Maximum Sunspot Number in Solar Cycle 24

A non-linear coupling function between sunspot maxima and aa minima modulations has been found as a result of a wavelet analysis of geomagnetic index aa and Wolf sunspot number yearly means since 1844. It has been demonstrated that the increase of these modulations for the past 158 years has not been steady, instead, it has occurred in less than 30 years starting around 1923. Otherwise sunspot maxima have oscillated about a constant level of 90 and 141, prior to 1923 and after 1949, respectively. The relevance of these findings regarding the forecasting of solar activity is analyzed here. It is found that if sunspot cycle maxima were still oscillating around the 141 constant value, then the Gnevyshev–Ohl rule would be violated for two consecutive even–odd sunspot pairs (22–23 and 24–25) for the first time in 1700 years. Instead, we present evidence that solar activity is in a declining episode that started about 1993. A value for maximum sunspot number in solar cycle 24 (87.5±23.5) is estimated from our results.     

A Prediction of the Peak Sunspot Number for Solar Cycle 23

We use a precursor technique based on the geomagneticaa index during the decline (last 30%) of solar cycle 22 to predict a peak sunspot number of 158 (± 18) for cycle 23, under the assumption that solar minimum occurred in May 1996. This method appears to be as reliable as those that require a year of data surrounding the geomagnetic minimum, which typically follows the smoothed sunspot minimum by about six months.     

A Prediction of Solar Cycle 24 Using a Modified Precursor Method

Based on cycles 17 – 23, linear correlations are obtained between 12-month moving averages of the number of disturbed days when Ap is greater than or equal to 25, called the Disturbance Index (DI), at thirteen selected times (called variate blocks 1, 2,… , each of six-month duration) during the declining portion of the ongoing sunspot cycle and the maximum amplitude of the following sunspot cycle. In particular, variate block 9, which occurs just prior to subsequent cycle minimum, gives the best correlation (0.94) with a minimum standard error of estimation of ± 13, and hindcasting shows agreement between predicted and observed maximum amplitudes to about 10%. As applied to cycle 24, the modified precursor technique yields maximum amplitude of about 124±23 occurring about 45±4 months after its minimum amplitude occurrence, probably in mid to late 2011.     

Verification of a Similar Cycle Prediction for the Ascending and Peak Phases of Solar Cycle 23

Reviews of long-term predictions of solar cycles have shown that a precise prediction with a lead time of 2 years or more of a solar cycle remains an unsolved problem. We used a simple method, the method of similar cycles, to make long-term predictions of not only the maximum amplitude but also the smoothed monthly mean sunspot number for every month of Solar Cycle 23. We verify and compare our prediction with the latest available observational results.     

The Prediction of Maximum Amplitudes of Solar Cycles and the Maximum Amplitude of Solar Cycle 24

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.     

Prediction of Solar Cycle 24 Using Geomagnetic Precursors: Validation and Update

In the previous study (Dabas et al. in Solar Phys. 250, 171, 2008), to predict the maximum sunspot number of the current solar cycle 24 based on the geomagnetic activity of the preceding sunspot minimum, the Ap index was used which is available from the last six to seven solar cycles. Since a longer series of the aa index is available for more than the last 10 – 12 cycles, the present study utilizes aa to validate the earlier prediction. Based on the same methodology, the disturbance index (DI), which is the 12-month moving average of the number of disturbed days (aa≥50), is computed at thirteen selected times (called variate blocks 1,2,…,13; each of them in six-month duration) during the declining portion of the ongoing sunspot cycle. Then its correlation with the maximum sunspot number of the following cycle is evaluated. As in the case of Ap, variate block 9, which occurs exactly 48 months after the current cycle maximum, gives the best correlation (R=0.96) with a minimum standard error of estimation (SEE) of ± 9. As applied to cycle 24, the aa index as precursor yields the maximum sunspot number of about 120±16 (the 90% prediction interval), which is within the 90% prediction interval of the earlier prediction (124±23 using Ap). Furthermore, the same method is applied to an expanded range of cycles 11 – 23, and once again variate block 9 gives the best correlation (R=0.95) with a minimum SEE of ± 13. The relation yields the modified maximum amplitude for cycle 24 of about 131±20, which is also close to our earlier prediction and is likely to occur at about 43±4 months after its minimum (December 2008), probably in July 2012 (± 4 months).     

太阳活动23周上升阶段质子事件的 预报分析

以２２周太阳活动低年（１９９３－１９９５）质子事件及其对应活动区的综合分析结果为判据,预报２３周太阳活动上升阶段的质子事件．从１９９７年１１月开始到１９９８年１２月,用该方法预报的质子事件共６个,报准３个,不确定一个,虚报１个,漏报１个（太阳背面产生的事件）．本文对用该方法预报的结果进行了分析讨论,并与世界警报中心的预报结果进行了比对,结果表明,该方法对于质子事件的短期预报是有效的．     

Solar Cycle Workshop

The presentations and discussions which took place during the second meeting of the Solar Cycle Workshop are summarized under the headings: sunspot minimum, the extended cycle, the large-scale photospheric motions, the large-scale magnetic fields and the polar reversal, the small-scale fields, global cyclic phenomena and the fundamental processes. The progress achieved so far is assessed and the directions for future observational and theoretical work are suggested.     

Solar Cycle Prediction: Combining Precursor Methods with McNish and Lincoln Technique

Medium-term and long-term prediction of the magnitude of the maximum of smoothed sunspot numbers, and thus of the solar cycle time profile, is a basic input for many space environment predictions. The widely used statistical technique of McNish and Lincoln is systematically compared to predictions based on precursors, either related to the cycle time profile characteristics or to geomagnetic indices. It is shown that when cycles 13 – 23 are considered, all prediction methods give, at least for one of the cycles, an error much larger than 20%, an inadequate result. None of the methods is fully reliable. Thus, it is proposed to combine the predictions based on precursors and to improve McNish and Lincoln results with them in order to limit such rare but large errors and to improve significantly the reliability of the predictions performed in the course of the solar cycle ascending phase.     

Solar Cycle Workshop

Conclusion Clearly there is no concensus or agreement at present about the nature and mechanism of the solar cycle or, indeed, about many of its observed features. However, by highlighting these areas of agreement and disagreement through the presentations and discussions during this meeting, it is hoped that the work of the Workshop Groups will be directed to resolving at least some of these questions at or before the next meeting (planned for August, 1987). In particular, it is hoped that Group V (The Sun as a Star) will be able to contribute through studies of the sun in relation to stellar cycles and activity.     

太阳黑子的世纪周期及对24、25活动周的预报

太阳活动除了具有公认的11 a周期以外,还存在着一个80～120 a变化的世纪周期,也称为Gleissberg周期.使用傅里叶变换和小波分析的方法,分析了1700～2008年的年均黑子数世纪周期的变化规律.得到结果:在太阳活动世纪周期的低谷期,所对应11 a太阳周的极大年和极小年的黑子数目都比其他太阳周的低.在这300多年里,世纪周期的周期长度也有变化.由世纪周期的变化趋势,预测第24、25太阳活动周将处于世纪周期的低谷期.通过对以前3个世纪周期的谷期黑子数求平均的方法,得到第24,25太阳周极大年年均黑子数为63.6±21.1,极小年的为2.2±2.1.这些结果有助于理解当前太阳活动反常宁静这一现象.     

On Prediction of the Strength of the 11-Year Solar Cycle No. 24

Various forecast techniques have been analyzed with reference to solar activity cycle 24. Three prediction indices have been proposed: the intensity of the polar field, the mean field at the source surface, and a recurrence index of geomagnetic disturbances. As a rule, the forecast based on the polar field and extrapolation of local fields gives a height for cycle 24 that is smaller than that of cycle 23. The use of the recurrence index and the global field value leads us to the conclusion that cycle 24 will be medium high: the same as or somewhat higher than cycle 23.     

The Solar Cycle Workshop

The contributions to the third meeting of the Solar Cycle Workshop are briefly summarized. The topics discussed at the meeting included (i) predictions and precursors, (ii) large and small-scale magnetic fields, (iii) photospheric velocity fields, (iv) coronal phenomena, (v) the Sun as a star, (vi) limb temperature measurements and helioseismic data, (vii) theoretical modelling of the cycle, (viii) cyclic activity in stars, and (ix) the interpretation of the Elatina Sandstone Layers.This paper was presented at the third meeting of the Solar Cycle Workshop, held in Sydney, Australia, January 9–13, 1989.     

Predictions of Solar Cycle 24

A summary and analysis of more than 50 predictions of the amplitude of the upcoming Solar Cycle 24 is presented. All of the predictions were published before solar minimum and represent our efforts to anticipate solar maximum at ever-earlier epochs. The consistency of the predictions within their assigned categories is discussed. Estimates of the significance of the predictions, compared to the climatological average, are presented.