太阳黑子数月平均变化的长期行为的可预报性

本文用非线性动力系统理论探讨了现代太阳周（１８５０年１月─１９９２年５月）黑子相对数月平均变化过程的可预报性。用时间延迟方法重构吸引子，计算它的最大Ｌｙａｐｕｎｏｖ指数（λ_１＝０．０２３±０．００４ｂｉｔｓ／月），估算了用这些黑子数进行确定性预报的理论时限（ｔ＝３．６±０．６年）．结果表明，动力系统的可预报性与它的最大Ｌｙａｐｕｎｏｖ指数有直接关系，黑子数月平均变化过程的演化不是周期的，也不是拟周期的，而是混沌的。即使今后找到了描述该过程的确定性方程，它的长期行为也不可能准确地预报，只能作短期预报，这是黑子数本身的混沌特性决定的。用于黑子数预报的纯粹数值统计方法仅对短期预报才有效。     

太阳黑子周极小年的统计性质——兼论第22周起始极小是否已经出现

探讨太阳周极小年的性质关系到确定极小值的位置及太阳周的长度,从而与太阳活动周的研究、太阳活动预报及水文、气象等地球物理现象的研究密切相关.当前对第22黑子周特征值的预报相当弥散,第22周起始极小是否已经出现的问题受到普遍关注.不同的太阳活动指标达到极值的时间不同,一般以太阳黑子数月均平滑最低值的位置来定义极小年.     

第22周太阳活动上升期黑子群的一些特点

本文对22太阳周上升段期间的太阳黑子及质子耀斑进行了统计分析,结果表明此期间太阳活动确实存在一些明显的特点。并确定了上升期的活动经度:L220°—300°和L70°—130°。此外对四个强的活动区进行了介绍。     

大行星运动对太阳黑子活动的可能影响

本文计算了由太阳系大行星轨道运动引起的日心相对于太阳系质心的轨道运动角动量变化率j_⊙,在理论上对j_⊙作展开,表明它存在多项短周期变化,与太阳黑子资料的分析结果相比较,两者结果是符合的,它们具有一致的谱结构。因此,行星的轨道运动对太阳黑子活动存在动力作用的可能性又进一步得到了验证。     

太阳活动周期的起源——纪念巴布科克模型提出50周年

2011年的春节刚刚过去,零星的鞭炮声还不时响起,人们还在回味着旧历年的欢乐与温馨,太阳突然间活跃起来,表面最多有5群太阳黑子。正月初十（2月12日）太阳表面南半球新浮现出编号为Noaal158的黑子群。这个黑子群迅速发展,只2—3天的时间东西跨度就增大为约10个地球直径。     

冕洞演化与太阳活动周的关系及在日地预报中的应用

冕洞的研究在近二十多年里取得了丰硕的成果。本文回顾了冕洞的发现及观测历史，系统阐述了冕洞的结果特征，形成及演化规律，讨论了冕洞对日地空间产生的影响，冕洞与超级活动区的关系以及冕洞在太阳活动预报中所起的作用，在此基础上利用１９７０－１９９５年的晚洞资料听时空分 布和磁极性演化规律与太阳活动区的关系以及冕洞的时空分布和磁极性演化 规律与太阳活性周的得出以下结论：（１）冕洞在南北半球的分布在形态上基本是     

用自激励门限自回归分析方法模拟和预报太阳黑子数的长期变化

本文用一种新方法——自激励门限自回归分析方法对太阳黑子相对数年平均值进行拟合和预报检验,并对未来第22周逐年年均值作出预报。 目激励门限自回归分析模型的形式如下: 在对1956至1985年逐年太阳黑子相对数年均值的预报检验中,最大拟会误差为40.6,最小拟合误差为0.3,平均拟合误差为±12.5。 对1986至1997年逐年太阳黑子相对数年均值的预报见表(4)。定出第21周极小在1986年或1987年,极大在1990或1991年,极大值R_M=81.2±16.2。     

太阳活动周期及其数学描述

概述和分析了太阳活动周期的研究进展,太阳活动呈现非常复杂的周期性,其周期性范围从几天至上百年,11年周期意义比较大,也比较明显;几天至几个月的周期性可能发生在太阳活动高峰期,155天或更短的周期存在,对中期预报有帮助;几年左右的周期对气象学的研究有作用;"蒙德极小期"是否存在至今还没有定论.对太阳活动11年周期的数学描述虽然很多,从效果上看,一般情况下,参数较多的函数计算量很大,误差相对较小;参数少的函数相比参数多的函数误差大,但计算量小;目前还没有一个非常理想的函数.能够对每个活动周都能很好的描述且误差很小.     

冕洞边界区磁结构的探讨──Ⅱ．太阳活动20、21周的冕洞及其边界区磁结构的变化

本文分析讨论了太阳活动２０、２１周的冕洞及其边界区磁结构的变化。它包括：冕洞区光球磁场强度、磁极性的变化；冕洞面积与高速太阳风风速的关系；冕洞边界周围的环境。重点探讨太阳活动下降、极小相低纬、赤道冕洞区与其边界区磁结构的变化。     

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.     

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.     

A Stochastic Prediction Model for the Sunspot Cycles

A stochastic prediction model for the sunspot cycle is proposed. The prediction model is based on a modified binary mixture of Laplace distribution functions and a moving-average model over the estimated model parameters. A six-parameter modified binary mixture of Laplace distribution functions is used for the modeling of the shape of a generic sunspot cycle. The model parameters are estimated for 23 sunspot cycles independently, and the primary prediction-model parameters are derived from these estimated model parameters using a moving-average stochastic model. A correction factor (hump factor) is introduced to make an initial prediction. The hump factor is computed for a given sunspot cycle as the ratio of the model estimated after the completion of a sunspot cycle (post-facto model) and the prediction of the moving-average model. The hump factors can be applied one at a time over the moving-average prediction model to get a final prediction of a sunspot cycle. The present model is used to predict the characteristics of Sunspot Cycle 24. The methodology is validated using the previous Sunspot Cycles 21, 22, and 23, which shows the adequacy and the applicability of the prediction model. The statistics of the variations of sunspot numbers at high solar activity are used to provide the lower and upper bound for the predictions using the present model.     

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.     

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.     

The Schwabe and Gleissberg Periods in the Wolf Sunspot Numbers and the Group Sunspot Numbers

Three wavelet functions: the Morlet wavelet, the Paul wavelet, and the DOG wavelet have been respectively performed on both the monthly Wolf sunspot numbers (R_z) from January 1749 to May 2004 and the monthly group sunspot numbers (R_g) from June 1795 to December 1995 to study the evolution of the Gleissberg and Schwabe periods of solar activity. The main results obtained are (1) the two most obvious periods in both the R_z and R_g are the Schwabe and Gleissberg periods. The Schwabe period oscillated during the second half of the eighteenth century and was steady from the 1850s onward. No obvious drifting trend of the Schwabe period exists. (2) The Gleissberg period obviously drifts to longer periods the whole consideration time, and the drifting speed of the Gleissberg period is larger for R_z than for R_g. (3) Although the Schwabe-period values for R_z and R_g are about 10.7 years, the value for R_z seems slightly larger than that for R_g. The Schwabe period of R_z is highly significant after the 1820s, and the Schwabe period of R_g is highly significant over almost the whole consideration time except for about 20 years around the 1800s. The evolution of the Schwabe period for both R_z and R_g in time is similar to each other. (4) The Gleissberg period in R_z and R_g is highly significant during the whole consideration time, but this result is unreliable at the two ends of each of the time series of the data. The evolution of the Gleissberg period in R_z is similar to that in R_g.     

Identification of Gleissberg Cycles and a Rising Trend in a 315-Year-Long Series of Sunspot Numbers

We show in this short note that the method of singular spectrum analysis (SSA) is able to clearly extract a strong, clean, and clear component from the longest available sunspot (International Sunspot Number, ISN) time series (1700?–?2015) that cannot be an artifact of the method and that can be safely identified as the Gleissberg cycle. This is not a small component, as it accounts for 13% of the total variance of the total original signal. Almost three and a half clear Gleissberg cycles are identified in the sunspot number series. Four extended solar minima (XSM) are determined by SSA, the latest around 2000 (Cycle 23/24 minimum). Several authors have argued in favor of a double-peaked structure for the Gleissberg cycle, with one peak between 55 and 59 years and another between 88 and 97 years. We find no evidence of the former: solar activity contains an important component that has undergone clear oscillations of \(\approx90\) years over the past three centuries, with some small but systematic longer-term evolution of “instantaneous” period and amplitude. Half of the variance of solar activity on these time scales can be satisfactorily reproduced as the sum of a monotonous multi-secular increase, a \(\approx90\)-year Gleissberg cycle, and a double-peaked (\(\approx10.0\) and 11.0 years) Schwabe cycle (the sum amounts to 46% of the total variance of the signal). The Gleissberg-cycle component definitely needs to be addressed when attempting to build dynamo models of solar activity. The first SSA component offers evidence of an increasing long-term trend in sunspot numbers, which is compatible with the existence of the modern grand maximum.     

The Gleissberg Cycle of Minima

In this short article we show that the sunspot cycle minima exhibit a long cycle (Gleissberg) in addition to the 11-yr cycle. From 1750 onwards, three periods of the Gleissberg cycle can be detected.     

A New Method for Prediction of Peak Sunspot Number and Ascent Time of the Solar Cycle

The purpose of the present study is to develop an empirical model based on precursors in the preceding solar cycle that can be used to forecast the peak sunspot number and ascent time of the next solar cycle. Statistical parameters are derived for each solar cycle using “Monthly” and “Monthly smoothed” (SSN) data of international sunspot number (R _i). Primarily the variability in monthly sunspot number during different phases of the solar cycle is considered along with other statistical parameters that are computed using solar cycle characteristics, like ascent time, peak sunspot number and the length of the solar cycle. Using these statistical parameters, two mathematical formulae are developed to compute the quantities [Q _C] _n and [L] _n for each nth solar cycle. It is found that the peak sunspot number and ascent time of the n+1th solar cycle correlates well with the parameters [Q _C] _n and [L] _n /[S _Max] _n+1 and gives a correlation coefficient of 0.97 and 0.92, respectively. Empirical relations are obtained using least square fitting, which relates [S _Max] _n+1 with [Q _C] _n and [T _a] _n+1 with [L] _n /[S _Max] _n+1. These relations predict a peak of 74±10 in monthly smoothed sunspot number and an ascent time of 4.9±0.4 years for Solar Cycle 24, when November 2008 is considered as the start time for this cycle. Three different methods, which are commonly used to define solar cycle characteristics are used and mathematical relations developed for forecasting peak sunspot number and ascent time of the upcoming solar cycle, are examined separately.     

Prediction of the Amplitude of Sunspot Cycle 23

A few prediction methods have been developed using the precursor techniques and are found to be successful. On the basis of geomagnetic activity aa indices during the descending phase of the preceding cycle, we have established an expression which predicts the maximum annual mean sunspot number in cycle 23 to be 166.2. This indicates that cycle 23 would be a highly active and historic cycle. The average geomagnetic activity aa index during the ascending phase of cycle 23 would be about 24.9, comparable to 22.2 and 24.8 in cycles 21 and 22, respectively. This further indicates that during the ascending phase of cycle 23 energetic two-ribbon flares will be produced so as to give rise to strong proton events.