Low Dimensional Chaos from the Group Sunspot Numbers

We examine the nonlinear dynamical properties of the monthly smoothed group sunspot number Rg and find that the solar activity underlying the time series of Rg is globally governed by a low-dimensional chaotic attractor. This finding is consistent with the nonlinear study results of the monthly Wolf sunspot numbers. We estimate the maximal Lyaponuv exponent （MLE） for the Rg series to be positive and to equal approximately 0.0187 ± 0.0023 （month^- 1）. Thus, the Lyaponuv time or predictability time of the chaotic motion is obtained to be about 4.46 ± 0.5 years, which is slightly different with the predictability time obtained from Rz. However, they both indicate that solar activity forecast should be done only for a short to medium term due to the intrinsic complexity of the time behavior concerned.

Including Planet 9 in the Solar System Increases the Coherence between the Sunspot Number Record and Solar Inertial Motion

The Sun would be subject to a significant variation of orbital motion about the solar system barycentre if a small planet is orbiting at a very large distance. This paper assesses if the Planet 9 hypothesis, the existence of a ninth planet, is consistent with the planetary hypothesis: the synchronisation of sunspot emergence to solar inertial motion (SIM) induced by the planets. We show that SIM would be profoundly affected if Planet 9 exists and that the hypothesised effect of SIM on sunspot emergence would be radically different from the effect of SIM due to the existing eight planets. We compare the frequency and time variation of Sun to barycentre distance, RB, calculated for both the eight and nine planet systems, with the frequency and time variation of sunspot number (SSN). We show that including Planet 9 improves the coherence between RB and SSN in the decadal, centennial and millennial time range. Additionally, as the variation of RB is sensitive to the longitude and period of Planet 9, it is possible to adjust both parameters to fit the variation of RB to the SSN record and obtain new estimates of the period and present longitude of Planet 9. Finally, we develop the hypothesis that planetary induced solar acceleration reduces meridional flow and consequently sunspot emergence thereby providing an explanation for the observed coincidence of grand solar minima with intervals of extreme solar acceleration.

Predictions of El Nino,La Nina and Record Low Chicago Temperature by Sunspot Number

The El Nino Index, defined as 4 intensities (very strong, strong, moderate, weak) in Oceanic Niño Index (ONI), was positively correlated with the average sunspot number at each intensity. The La Niña Index, defined as 3 intensities (strong, moderate, weak) in ONI, was negatively correlated with the average sunspot number from 1954 to 2017. It appears that very strong El Niño events occur frequently during the maximal sunspot number while strong La Niña events more often occur during the minimal sunspot number. Since greenhouse-gas is continuously increased, it is therefore proposed that the maximal sunspot number is a major parameter for prediction of El Niño while the minimal sunspot number applies in the same way for La Niña. El Nino/La Nina events can be classified as four typical cases depending upon the submarine volcanic activities at seamounts in Antarctica and South America. The Sea Surface Temperature (SST) of the South and Central Americas are warmer than SST of East Australian Current (EAC), due to the strong volcanic eruptions in the Seamounts and the Ridges in South and Central Americas. This results in the Central Pacific Current (CPC) flowing from east to west due to the second law of thermodynamics for thermal flow from hot source to cold sink. In contrast the opposite direction is made if SST in EAC is warmer than SST in the Central/South American Seamounts and Ridges, due to the strong volcanic eruptions in the Antarctic Seamounts and Ridges. Chicago was selected as a case study for the relationship between extreme cold weather conditions and minimal sunspot number. Previous attempts at predicting weather patterns in Chicago have largely failed. The years of the record low temperatures in Chicago were significantly correlated with the years of the minimal sunspot number from 1873 to 2019. It is forecast that there may occur a weak La Niña in 2019 and another record low temperature in Chicago in January of 2020 due to the phase of the minimal sunspot number in 2019. It may be possible to predict very strong El Nino events with the year of maximal sunspot number as El Niño Index (R2 = 0.7363) and the years of strong volcanic eruption in the Galapagos Hot Spot (GHS) (R2 = 0.9939), respectively. An El Niño event is thus expected during the year of strong volcanic eruption in the GHS. Strong La Niña events can be expected during the year of minimal sunspot number with La Niña Index (R2 = 0.9922). Record low temperatures in Chicago can be also predicted (R2 = 0.9995) during the year of the minimal sunspot number, as was recently the case in January, 2019.

Relationship between the Sunspot Number and Solar Polar Field by Wavelet-Based Multifractal Analysis

There is increasing interest in finding the relation between the sunspot number (SSN) and solar polar field. In general, fractal properties may be observed in the time series of the dynamics of complex systems, such as solar activity and climate. This study investigated the relations between the SSN and solar polar field by performing a multifractal analysis. To investigate the change in multifractality, we applied a wavelet transform to time series. When the SSN was maximum and minimum, the SSN showed monofractality or weak multifractality. The solar polar field showed weak multifractality when that was maximum and minimum. When the SSN became maximum, the fractality of the SSN changed from multifractality to monofractality. The multifractality of SSN became large before two years of SSN maximum, then that of the solar polar field became large and changed largely. It was found that the change in SSN triggered the change in the solar polar field. Hence, the SSN and solar polar field were closely correlated from the view point of fractals. When the maximum solar polar field before the maximum SSN was larger, the maximum SSN of the next cycle was larger. The formation of the magnetic field of the sunspots was correlated with the solar polar field.

Predictions of Galapagos Volcanic Eruption, El Niño, Ecuadorian Earthquake, Global Volcanic Eruption and Forest Fire by Sunspot Number

The earthquake number was correlated (R2 = 0.8781) with the volcano number in the East Pacific and Central American countries. The year of volcanic eruptions in the Galapagos Hot Spot (GHS) was proportional to the year of El Ni&#241o events (R2 = 0.9939) as well as to the year of earthquake events (R2 = 0.9943) in Ecuador, Colombia, and Peru from 1977 to 2016. Therefore, there can be El Ni&#241o and earthquake events in Ecuador, Colombia and Peru if there are strong volcanic eruptions either from aboveground volcanoes or undersea seamounts in the GHS during the maximal sunspot number’s period. Global volcanic eruptions were occurred during the maximal temperature departure, the latter being reversely proportional (R2 = 0.4512) to the sunspot number from 1980 to 2019. Forest fires occurred in middle latitude countries (South Korea, California, western Russia, Australia) around 35 degree from Pacific Equator during La Ni&#241a events at the time of the minimal sunspot number. Since there were intense forest fires in South Korea, Australia and California in 2019, more are expected in 2030 due to the 11 year cyclical variation in the sunspot number. The sequence of forest fires can be schematically summarized as below. 1) La Ni&#241a event in Equator causes the low vapor pressure of water due to the low sea surface temperature (SST);2) There is the pumping of freshwater from the warm Pacific Ocean to cold Equator with simultaneous transfer of heat (warm Pacific Ocean to cold Equator) and mass (water enriched Pacific Ocean to water lean Equator);3) Strong winds from dry zone pass Mountains to cause the forest fires in the residential land with bushes and trees. 4) According to the Bernoulli’s principle, the pressure gradient between the high Mountains and the low Ocean, induces the decrease of static velocity gradient for vigorously upwards flares in the Mountains and the residential land during the forest fires, which may be why it is difficult to extinguish the forest fires until burnt up bushes and trees in the Mountains and residential land with serious damages. Most effective solution to forest fires is to change the events from La Ni&#241a to El Ni&#241o for reductions of temperature and pressure gradients by Gay-Lussac’s law. Such a transition may be induced by artificial submarine volcanic eruptions among volcanoes of Fernandina, Sierra Negra and Wolf in the GHS for Korea and California. As for Australia, artificial volcanic eruptions can be caused in huge underwater volcano chain in Tasmania. The strong damages of forest fires in South Korea, Australia and California were observed in the period of the minimal sunspot number, as were in October of 2019 to February of 2020. Simultaneous transfers of momentum (velocity), heat (temperature) and mass (freshwater) were occurred from the dry zone or the hot Deserts via the Mountains and the residential land with bushes and trees to the cold Sea or Ocean. It is expected the lowest SST during the year of the minimal sunspot number to induce the strong damages of forest fires, as was in South Korea, Australia and California during the years from 2019 to 2020. CO2 emissions in Australia showed 34.5% increase, 70% coal power and no nuclear power to induce bushfires because of increases of ozone hole area and UV radiation for the hot land in the period of La Ni&#241a. Fossil fuel operation should be cut down to decrease the ozone hole area and UV radiation for weak bushfires in Australia. A few coming years may still have bushfires in Australia although their damages may not be as terrible as was in 2020. A simple remedy can be the reduction of CO2 emissions as low as possible. It was proposed that the maximal sunspot number induced El Ni&#241o event, GHS volcanic eruption and Ecuadorian earthquakes, while the minimal sunspot number induced La Ni&#241a events in Ecuador, Colombia, Peru and intense forest fires in middle latitude countries of South Korea (forest fires), Australia (bushfires) and California (wildfires).

Spanish Flu, SARS, MERS-CoV by CO₂Emission and Maximal Sunspot Number

The 1918 Spanish flu, 2002 severe acute respiratory syndrome (SARS), and 2012 Middle East respiratory syndrome coronavirus (MERS-CoV) were investigated to reveal their causes and routes of transmission. They have the common features such as 1) the induction by viruses (Spanish flu;avian influenza virus (AIV), SARS and MERS-CoV;coronavirus), 2) the outbreak during the maximal sunspot number, 3) the aeolian desert dust region (Spanish flu;Saharan, SARS;Asian, MERS-CoV;Arabian), and 4) similar incubation period (AIV;5, SARS;2 - 7, MERS-CoV;5 days), 5) different transmission reservoir (Spanish flu;aquatic bird/swine, SARS;bat, MERS-CoV;bat/dromedary camel). When carbon dioxide (CO2) combustion emissions were simultaneously high at the maximal sunspot number, UV radiation in the Poles was so extensive to mutate the aquatic virus through the food web to be the fundamental reason for these pandemic. Guangdong Province and Hong Kong in China are the source of 2002-2003 SARS. The stranded dead whales and dolphins along the coast of the Persian Gulf might be fed on by coastal animals in the Arabian Desert to transmit MERS-CoV. Mutations in the hot temperature in the Arabian Desert and Persian Gulf, and the maximal sunspot numbers were observed in Saudi Arabia. Saudi crude burn in power plants since 2009 with coincidental outbreaks of MERS-CoV in Saudi Arabia since 2012 peaking in 2014. The reduction of CO2 emissions by nuclear power plants is a unique solution to decrease MERS-CoV outbreaks.

Cross wavelet analysis of the relationship between total solar irradiance and sunspot number

Using the observational data of total solar irradiance(TSI)from 1976 to 2006,the evolution of total solar irradiance and the rela-tionship between TSI and sunspot number(SSN)have been analyzed with the wavelet technique.The results of the continuous wavelet transform(CWT)indicate that the TSI has multi-scale evolutionary characteristics.In the low frequency band,the TSI and SSN show similar variation with a significant and steady oscillation period from 8 to 11.4 a.While in the high frequency band,only around the maximum time of solar cycles,both the TSI and SSN present a significant intermittent oscillation period from 2 to 6 months.The results of the cross wavelet transform indicate that there is significant in-phase resonance oscillation between the TSI and SSN in 8-11.4 a band,where the variation of the SSN is 2 months ahead of that of TSI.Those results confirm the SSN as the primary cause for TSI's periodic variation in the time scale of 8-11.4 a.However for the 2-6 month band,significant resonance periodicity is observed only within the maximum time of solar cycle,but the phase relationship between the TSI and SSN is unsteady.Finally,a reliable TSI monthly series from 1878 to 1975 is reconstructed and tested.

Phase relationship between the relative sunspot number and solar 10.7 cm flux

A range of analysis approaches,namely continuous wavelet,cross wavelet,and wavelet coherence analyses,are employed to clarify the phase relationship between the smoothed monthly mean sunspot number and solar 10.7 cm flux(F10.7).Analysis shows that there is a region of high spectral power sitting across the Schwabe cycle belt,where the two time series are in phase.However,analysis of the cross-wavelet transform and wavelet coherence unveils asynchronous behavior featured with phase mixing in the high-frequency components of sunspot activity and solar F10.7,which may explain the different activity properties of the photosphere and corona on a short time scale.

A method to predict amplitude and date of maximum sunspot number

A method to predict the amplitude and date of the maximum sunspot number is introduced. The regression analysis of the relationship between the variation rate of monthly sunspot numbers in the initial stage of solar cycles and both of the maximum and the time-length of ascending period of the cycle showed that they are closely correlative. In general, the maximum will be larger and the ascending period will be shorter when the rate is larger. The rate of sunspot numbers in the initial 2 years of the 23rd cycle is thus analyzed based on these grounds and the maximum of the cycle is predicted. For the smoothed monthly sunspot numbers, the maximum will be about 139.2 ±18.8 and the time-length of ascending period will be about 3.31 ±0.42 years, that is to say, the maximum will appear around the spring of the year 2000. For the mean monthly ones, the maximum will be near 170.1±22.9 and the time-length of ascending period will be about 3.42 ±0.46 years, that is to say, the appearing date of the maximum

Prediction of the smoothed monthly mean sunspot numbers for solar cycle 24

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 as- suming 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. Consid- ering the latest observed sunspot number so far available for cycle 23 and the pre- dictions for the minimum SMSN of cycle 24, a date calibration is done for the ob- tained time profiles, and thus, SMSNs for 127 months of cycle 24, from October 2007 to April 2018, are predicted.

THE FRACTAL RESEARCH AND PREDICATING ON THE TIME SERIES OF SUNSPOT RELATIVE NUMBER

In this paper, with the theory of nonlinear dynamic systems, It is analyzed that the dynamic behavior and the predictability for the monthly mean variations of the sunspot relative number recorded from January 1891 to December 1996. In the progress, the fractal dimension (D = 3.3 +/- 0.2) for the variation process rt as computed. This helped us to determine the embedded dimension [2 x D + 1] = 7. By computing the Lyapunov index (lambda(1) = 0.863), it was indicated that the variation process is a chaotic system. The Kolmogorov entropy (K = 0.0260) was also computed, which provides, theoretically, the predicable time scale. And at the end, according to the result of the analysis above, an experimental predication is made, whose data was a part cut from the sample data.

钱塘江径流丰枯演变规律的天文成因研究

天文因子是流域来水的影响因素之一,不同的天文因子对流域来水的影响程度和影响规律不同。为探究影响钱塘江流域来水最主要的天文因子及其对流域来水的影响规律,采用线性相关系数法、互信息法和灰色关联度法等相关性分析方法,对太阳黑子相对数、月球赤纬角、24节气阴历日期等26个天文因子进行分析识别,并统计分析主要天文因子与流域来水之间的变化规律。结果如下:①线性相关系数法、互信息法和灰色关联度法的结果显示月球赤纬角与钱塘江流域来水的相关性最大,表明月球赤纬角是对钱塘江流域来水影响最大的天文因子;②月球赤纬角由大变小时流域来水偏丰,丰水年概率为46.4%,而由小变大时来水偏枯,枯水年概率为54.5%,且容易发生极端来水;③在月球赤纬角峰年期来水偏枯,枯水年概率为66.7%,且特枯水年频发,而在谷年期极端来水频发,50%的年份为极端来水。研究结果可为钱塘江流域未来长期径流演变分析以及洪水预报等提供依据和支撑。

用径向基函数神经网络方法预报太阳黑子数平滑月均值

简单介绍了径向基函数神经网络方法的原理和应用,发展了用径向基函数(RBF)对平滑月平均黑子数进行预报的方法.用不同的数据序列对网络进行训练,对未来8个月的平滑月平均黑子数进行预报.用该方法对第23周开始后的平滑月平均黑子数进行逐月预报,并与实测值进行比较,结果表明随着预报实效的延长预报误差被逐渐放大,该方法可以较准确地做出未来4个月的预报,绝对误差可以控制在20以内,标准差为4.8,相对误差控制在38%以内,大部分相对误差不超过15%(占总预报数的89%),具有较好的应用价值.用于网络训练的样本数量对预报结果会产生一定的影响.

地磁Ap指数与太阳黑子数的交叉小波分析及R/S分析

利用1932～2009年间的地磁Ap指数和太阳黑子数资料,用交叉小波方法和R/S方法分析了地磁Ap指数和太阳黑子数的关系。分析结果表明,①地磁Ap指数和太阳黑子数在高频段上显著带的形状有一定程度的相似性,具有显著和稳定的8.02～11.35 a的振荡周期;在低频部分,地磁Ap指数和太阳黑子数4～6月的周期变化不连续,仅在部分年份通过了95%的红噪声检验。②地磁Ap指数和太阳黑子数在8.02～11.35 a的频段上具有显著的共振周期,且在此频段上地磁Ap指数落后太阳黑子数1.5 a左右稳定的相位变化。地磁Ap指数和太阳黑子数在低频部分存在4～6月共振周期,但二者的位相关系不稳定。③地磁Ap指数和太阳黑子数时间序列的Hurst指数分别为0.79和0.81,表明地磁Ap指数和太阳黑子数都是持续的时间序列,且未来的变化将持续过去的变化趋势,具有长期记忆性和混沌特征。

太阳10.7cm射电辐射流量预报方法初探

引进“相似周”方法,通过两种方式对第23周太阳10.7cm辐射流量(E10.7)月均值进行预报和预报试验.由“相似周”方法得到的第23周太阳黑子数月均平滑预测值来预测F10.7月均值和直接采用“相似周”方法对F10.7月均平滑值进行预测.通过对两种预报试验结果分析,得到以下结论. (1)两种预测结果与实际都比较吻合,都得到双峰结构. (2)直接通过相似胤预测的F10.7的月均值结果较间接通过太阳黑子数的预测结果所推断的F10.7预测结果更接近实际观测结果. (3)使用“相似周”预报方法,可以给出F10.7比较精细的剖面结构,这是其他普通预报方法很难做到的.

利用EMD方法提取太阳活动周期成分

EMD(经验模态分解)方法在处理非线性及非平稳时间序列时表现出了很大的优势和应用潜力．利用EMD方法研究太阳活动周期,对110年(1894—2003)和55年(1949—2003)的太阳黑子数月均值进行分解,分别得到一系列模式和一个趋势项,其中都可能包含有1．3至1．4年周期分量,25至30个月QBO(准双年振荡)分量,11年太阳周分量和22年Hale周分量．其中11年周期分量幅度最大,变化特征与太阳黑子数原始数据具有很高的相似性．不同于传统方法,EMD方法给出了太阳活动在不同时间尺度上各自分离的变化特征．

太阳黑子数与电离层TEC的相关性分析

为了研究电离层TEC与太阳黑子数在短周期上的相关关系,采用1997～2004年的太阳黑子数资料与同期厦门站的电离层TEC数据,利用小波功率谱分析的方法提取3个尺度的短周期,并利用小波相干谱的方法重点研究了两者在27.8d周期上的相关性。研究表明:太阳黑子数和电离层TEC主要存在准27d、准半年周期以及年周期等短周期,而且电离层TEC和太阳黑子在准27d周期上有良好的相关性。位相计算表明,电离层TEC的变化滞后于太阳黑子数2～3d。厦门地区TEC与太阳活动的相关性在夏季比其他季节更强,这对提高该地区电离层TEC预报精度有很大意义。

用太阳活动拟合近2000年的温度变化

利用两个反映太阳活动的指标—太阳黑子相对数及太阳黑子周期长度—来拟合近 2 0 0 0年我国的温度变化 ,其结果与近 2 0 0 0年 ,特别是近 70 0年来温度变化的总趋势基本一致。同时拟合了 12 0年来北半球温度的演变 ,结果表明 :太阳活动是引起 10 1年以上气温变化的基本因素 ,近十多年来温室气体的作用似乎不可忽略。

太阳黑子数及Ap指数周期变化特征的小波分析

应用Morlet小波变换方法从多个变化尺度上对1932-2000年的太阳黑子数及Ap指数的变化特征进行分析. (1)太阳黑子数存在准11年、准32年的周期变化特征及Ap指数存在准32年、准11年、准6个月、准27天和准13.9天的周期变化特征;(2)太阳黑子数及Ap指数有着相似的准11年周期变化,但Ap指数极值的出现要比太阳黑子数极值出现滞后1-2年; (3)AP指数准27天的周期变化在太阳黑子活动高、低年不同,在太阳活动低年,Ap指数有着较稳定的准27天周期变化,但在太阳活动高年, 27天的周期变化几乎消失,这种周期变化的消失和出现时间可在Morlet小波变换图中体现出来.

辽宁省旱涝灾害与太阳黑子活动的相关性

应用辽宁省1956—2011年22个气象台站的逐月降水资料，通过z指数确定了该地区的旱涝等级及发生年份；采用频率分析法分析了太阳黑子极值年附近的旱涝特征；运用Morlet小波分析技术，对辽宁省近56a来降水z指数与太阳黑子的小波系数变化进行了分析。结果表明：（1）该地区近56a中旱涝发生频率基本相等，旱涝情况整体趋势为由涝转旱，尤其是进入21世纪后，旱灾发生次数明显增多，呈现干旱化现象。（2）各年太阳黑子数与该地区的z指数整体上呈负相关关系；该地区在太阳黑子峰值年或峰值年附近易出现旱年，在太阳黑子谷值年或谷值年附近易出现涝年。（3）太阳黑子与z指数在7～11a有较好的对应关系，太阳黑子的活跃期对应降水偏少期，太阳黑子的低谷期对应降水丰沛期，说明太阳黑子的变化对辽宁省降水有较大的影响，未来几年处于太阳黑子的活跃期附近，为降水偏少期。