Reconstruction of Wolf Sunspot Numbers on the Basis of Spectral Characteristics and Estimates of Associated Radio Flux and Solar Wind Parameters for the Last Millennium

A reconstruction of sunspot numbers for the last 1000 years was obtained using a sum of sine waves derived from spectral analysis of the time series of sunspot number R _z for the period 1700–1999. The time series was decomposed in frequency levels using the wavelet transform, and an iterative regression model (ARIST) was used to identify the amplitude and phase of the main periodicities. The 1000-year reconstructed sunspot number reproduces well the great maximums and minimums in solar activity, identified in cosmonuclides variation records, and, specifically, the epochs of the Oort, Wolf, Spörer, Maunder, and Dalton Minimums as well the Medieval and Modern Maximums. The average sunspot number activity in each anomalous period was used in linear equations to obtain estimates of the solar radio flux F _10.7, solar wind velocity, and the southward component of the interplanetary magnetic field.     

Periodicities in solar activity

The techniques of power spectral analysis are used to determine significant periodicities in the annual mean relative sunspot numbers. The main conclusion is that a period of 10.45 yr is very basic and can be associated with an excitation of new solar cycles. When combined with a period of 11.8 yr, associated here with the free-running length of a solar cycle, the mean cycle length of 11.06 yr and a phase variation of 190 yr are explained. Similarly the amplitude variations with periods 88 and 59 yr (previously described as the 80-yr cycle) are due to an amplitude modulation of the solar cycle by a period of 11.9±0.3 yr. The results dispute several associations of planetary position and solar activity.Radiophysics Publication RPP 1647, January, 1973.     

An Analysis of Solar Global Activity

This article proposes a unified observational model of solar activity based on sunspot number and the solar global activity in the rotation of the structures, both per 11-year cycle. The rotation rates show a variation of a half-century period and the same period is also associated to the sunspot amplitude variation. The global solar rotation interweaves with the observed global organisation of solar activity. An important role for this assembly is played by the Grand Cycle formed by the merging of five sunspot cycles: a forgotten discovery by R. Wolf. On the basis of these elements, the nature of the Dalton Minimum, the Maunder Minimum, the Gleissberg Cycle, and the Grand Minima are presented.     

Sunspot groups at high latitude

Data of sunspot groups at high latitude (35°), from the year 1874 to the present (2000 January), are collected to show their evolutional behaviour and to investigate features of the yearly number of sunspot groups at high latitude. Subsequently, an evolutional pattern of sunspot group number at high latitude is given in this paper. Results obtained show that the number of sunspot groups of a solar cycle at high latitude rises to a maximum value about 1 yr earlier than the time of the maximum of sunspot relative numbers of the solar cycle, and then falls to zero more rapidly. The results also show that, at the moment, solar activity described by the sunspot relative numbers has not yet reached its minimum. In general, sunspot groups at high latitude have not appeared on the solar disc during the last 3 yr of a Wolf solar cycle. The asymmetry of the high latitude sunspot group number of a Wolf solar cycle can reflect the asymmetry of solar activity in the Wolf solar cycle, and it is suggested that one could further use the high latitude sunspot group number during the rising time of a Wolf solar cycle, maximum year included, to judge the asymmetry of solar activity over the whole solar cycle.     

Evidence of 6 000-Year Periodicity in Reconstructed Sunspot Numbers

Reconstructed sunspot data are available that extend solar activity back to 11 360 years before the present. We have examined these data using Hurst analysis, a moving average filter, and Fourier analysis. All of the procedures indicate the presence of a long term (≈6 000 year) cycle not previously reported. A number of shorter cycles formerly identified in the literature by using Fourier analysis, Bayes methods, and maximum entropy methods were also detected in the reconstructed sunspot data.     

Thousand-Year Cycle Signals in Solar Activity

Long-term variations of solar activity closely relate to terrestrial phenomena. More and more people attach importance to studies of long-term fluctuations of solar variation. However, because direct observations of solar activity are available only for the past four centuries, such studies are few. In this work, using the wavelet technique, the author investigates long-term fluctuations of reconstructed sunspot number series covering the past 11 400 years, with emphasis on the thousand-year cycle signals of solar variation. The results show a thousand-year cycle in solar activity.     

On the R z -sunspot relative number variations

The Zürich sunspot relative number R _z series has been analysed by the cyclogram method. The amplitude and the frequency variations of the Fourier 11 yr component between 1700–1983 A.D., were determined in a continuous way.Four distinct time intervals with significantly different characteristics of the periodicities are observed and discussed.Their second harmonics are also considered. The periodicity changes are contemporary to those of the 11 yr cycles.Around the year 1903 it seems that an important event has happened in the Sun. In fact the 11.4 yr cycle periodicity, that was very stable since at least 1825 started to change gradually to smaller values and similarly it happened to the second harmonic which also stopped and abruptly changed of phase of 90°.     

Periodogram analysis of 240 years of sunspot records

We have analyzed the direct records of sunspot number between 1749 and 1990 with the same technique currently used in the study of stellar activity cycles observed with Mount Wilson Observatory's 60-inch telescope. In order to mimic the stellar time series, which span only two decades, we analyzed twenty- and fifty-year intervals of the sunspot data in comparison to the entire record. We also examined the reliability of the oldest (pre-1850) sunspot records. The mean solar cycle period determined from the entire record (1749–1990) is 11.04 yr with a computed precision of ± 0.01 yr, but an overall accuracy of only ±1.1 yr. The large uncertainty is caused by variation of the cycle period with time and not observational uncertainty.The correct sunspot period is found slightly more often (82%) in 50-year intervals compared to 20-year (74%). The cause is twofold: first, a more precise period results from the longer sample length, and second, other periodicities exist in the sunspot record, so that a more accurate determination of the dominant 11.0-year period results from the longer time series. As a guideline for cycle periodicities in other stars, the solar results indicate that the 50-year intervals would produce more precise and accurate periods than the 20-year time series. On the other hand, useful statistics concerning long-term activity could be obtained from a less-frequently sampled group of stars that is substantially larger than the group of 100 lower Main-Sequence stars currently observed at Mount Wilson, although knowledge of short-term variability would be sacrificed.Pre-doctoral fellow, Harvard-Smithsonian Center for Astrophysics.     

Does sunspot activity originate in slow global oscillations of the sun?

We present preliminary results of a spherical-harmonic-Fourier analysis of sunspot activity during the twenty-two years 1933–1954. The results indicate that the sunspot activity might be originating in global solar oscillations with periods of years and decades. However, except for the axisymmetric mode of degree 6, the set of other axisymmetric modes showing ∼ 11 yr periodicities are different from one sunspot cycle to another. A more detailed analysis, preferably with larger data series, will be needed to arrive at a more definite conclusion.     

A nonlinear solar cycle model with potential for forecasting on a decadal time scale

This paper describes a novel non-linear oscillator model of the sunspot cycle which accurately reproduces several of the observed qualitative and quantitative characteristics of the real cycle including the long term amplitude modulation pattern. The model accounts for 96% of cycle peak height variance over the period 1859 to 1980. The aim of this work is to assess the potential of such models for forecasting solar activity on decadal and possibly longer time scales. Longer term forecasts may have practical economic significance because of the growing evidence for relationships between solar cycle variations and terrestrial weather and climatic variations (Bandeen and Moran, 1975; Currie, 1980; Williams, 1981). The model predicts that cycle 22 will have an annual mean peak amplitude in the range 25 to 45, the lowest peak activity for 260 yr.     

Solar cycles during the Maunder minimum

We have obtained new consistent versions of the 400-yr time series of the Wolf sunspot number W, the sunspot group number G, and the total sunspot area S (or the total sunspot magnetic flux Φ). We show that the 11-yr cycle did not cease during the Maunder minimum of solar activity. The characteristics of the extrema of individual 11-yr cycles in 1600–2005 have been determined in terms of the total sunspot area index. We provide arguments for using alternating (“magnetic”) time series of indices in investigating the solar cyclicity.     

The phase variations of the solar cycle

It has previously been shown that the statistics of the phase fluctuation of the sunspot cycle are compatible with the assumption that the solar magnetic field is generated deep in the Sun by a frequency stable oscillator and that the observed substantial phase fluctuation in the sunspot cycle is due to variation in the time required for the magnetic field to move to the solar surface (Dicke, 1978, 1979). It was shown that the observed phase shifts are strongly correlated with the amplitude of the solar cycle. It is shown here that of two empirical models for the transport of magnetic flux to the surface, the best fit to the data is obtained with a model for which the magnetic flux is carried to the surface by convection with the convection velocity proportional to a function of the solar cycle amplitude. The best fit of this model to the data is obtained for a 12-yr transit time. The period obtained for the solar cycle is T = 22.219 ± 0.032 yr. It is shown that the great solar anomaly of 1760–1800 is most likely real and not due to poor data.     

太阳与地磁活动的1.3–1.7 yr振荡关系分析

太阳和地磁活动中的1.3–1.7 yr周期研究对于理解日地空间耦合系统中可能发生的物理过程十分重要.黑子是太阳光球层上最突出的磁场结构, Ap指数则是表征全球地磁活动水平的重要指标.使用同步压缩小波变换得到太阳黑子数和地磁Ap指数的1.3–1.7yr周期,并用互相关方法分析研究它们之间的相位关系.结果如下:(1)太阳黑子数和地磁Ap指数的1.3–1.7 yr周期呈现间歇性的演化特征,且随着时间的变化而不断变化;(2)地磁Ap指数在奇数活动周比相邻的偶数活动周的周期分量更高,表现出上下波动的变化特性;(3)地磁Ap指数和太阳黑子数的相位关系不是一成不变的,在大多数情况下地磁Ap指数滞后太阳黑子数,仅在第18和第22活动周黑子数在相位上滞后.     

Analysis of the 1.3–1.7 yr Oscillation Relationship between Solar and Geomagnetic Activities

The study on the 1.3–1.7 yr period of the solar and geomagnetic activities is very important for understanding the possible physical processes in the solar-terrestrial coupling system. The sunspot is the most prominent magnetic field structure in the solar photosphere, and the Ap index is an important indicator for the global geomagnetic activity level. The 1.3–1.7 yr period for the sunspot number and the geomagnetic Ap index is obtained by the synchro-squeezing wavelet transform, and the phase relationship between them is studied by the cross-correlation analysis. The main results are as follows: (1) The 1.3–1.7 yr period of the geomagnetic Ap index and sunspot number exhibits an intermittent evolutionary characteristics, and changes continuously with the time; (2) the geomagnetic Ap index has a higher periodic component in the odd solar cycles than the neighboring even solar cycles, which is characterized by fluctuations; (3) the phase relationship between the geomagnetic Ap index and the sunspot number is not always invariant, in most cases the geomagnetic Ap index lags behind the sunspot number, except in the 18th and 22th solar cycles.     

Comparison of long-term trend of solar radius with sunspot activity and flare index

Results are presented from a study of solar radius measurements taken with the solar astrolabe at the TUBITAK National Observatory (TUG) over seven years, 2001–2007. The data series with standard deviation of 0.35 arcsec shows the long-term variational trend with 0.04 arcsec/year. On the other hand, the data series of solar radius are compared with the data of sunspot activity and H-α flare index for the same period. Over the seven year trend, we have found significant linear anti-correlations between the solar radius and other indicators such as sunspot numbers, sunspot areas, and H-α flare index. While the solar radius displays the strongest anti-correlation (−0.7676) with sunspot numbers, it shows a significant anti-correlation of −0.6365 with sunspot areas. But, the anti-correlation between the solar radius and H-α flare index is found to be −0.4975, slightly lower than others. In addition, we computed Hurst exponent of the data sets ranging between 0.7214 and 0.7996, exhibiting the persistent behavior for the long term trend. In the light of the strong correlations with high significance, we may suggest that there are a causal relationship between the solar radius and solar time series such as sunspot activity and H-α flare index.     

What the Sunspot Record Tells Us About Space Climate

The records concerning the number, sizes, and positions of sunspots provide a direct means of characterizing solar activity over nearly 400 years. Sunspot numbers are strongly correlated with modern measures of solar activity including: 10.7-cm radio flux, total irradiance, X-ray flares, sunspot area, the baseline level of geomagnetic activity, and the flux of galactic cosmic rays. The Group Sunspot Number provides information on 27 sunspot cycles, far more than any of the modern measures of solar activity, and enough to provide important details about long-term variations in solar activity or “Space Climate.” The sunspot record shows: 1) sunspot cycles have periods of 131± 14 months with a normal distribution; 2) sunspot cycles are asymmetric with a fast rise and slow decline; 3) the rise time from minimum to maximum decreases with cycle amplitude; 4) large amplitude cycles are preceded by short period cycles; 5) large amplitude cycles are preceded by high minima; 6) although the two hemispheres remain linked in phase, there are significant asymmetries in the activity in each hemisphere; 7) the rate at which the active latitudes drift toward the equator is anti-correlated with the cycle period; 8) the rate at which the active latitudes drift toward the equator is positively correlated with the amplitude of the cycle after the next; 9) there has been a significant secular increase in the amplitudes of the sunspot cycles since the end of the Maunder Minimum (1715); and 10) there is weak evidence for a quasi-periodic variation in the sunspot cycle amplitudes with a period of about 90 years. These characteristics indicate that the next solar cycle should have a maximum smoothed sunspot number of about 145 ± 30 in 2010 while the following cycle should have a maximum of about 70 ± 30 in 2023.     

Flattening Index of the Solar Corona and the Solar Cycle

The photometrical flattening index of the solar corona a+b is defined according to Ludendorff. In this paper we have investigated how the flattening index varies with respect to the phase of solar activity and the sunspot number. We have compiled 170 values of the flattening index using the data on 60 total solar eclipses from 1851 to 2010. We have found that the flattening index takes values from 0 to 0.4, and is anticorrelated with solar activity. The value of the flattening index at the beginning of solar cycle 24 was used as a precursor to forecast the amplitude of the cycle. It was found that the amplitude of solar cycle 24 will be about 95 in terms of the smoothed monthly sunspot numbers.     

Predicting maximum sunspot number in solar cycle 24

A few prediction methods have been developed based on the precursor technique which is found to be successful for forecasting the solar activity. Considering the geomagnetic activity aa indices during the descending phase of the preceding solar cycle as the precursor, we predict the maximum amplitude of annual mean sunspot number in cycle 24 to be 111 ± 21. This suggests that the maximum amplitude of the upcoming cycle 24 will be less than cycles 21–22. Further, we have estimated the annual mean geomagnetic activity aa index for the solar maximum year in cycle 24 to be 20.6 ± 4.7 and the average of the annual mean sunspot number during the descending phase of cycle 24 is estimated to be 48 ± 16.8.     

Activity cycle of solar filaments

Long-term variation in the distribution of the solar filaments observed at the Observatorie de Paris, Section de Meudon from March 1919 to December 1989 is presented to compare with sunspot cycle and to study the periodicity in the filament activity, namely the periods of the coronal activity with the Morlet wavelet used. It is inferred that the activity cycle of solar filaments should have the same cycle length as sunspot cycle, but the cycle behavior of solar filaments is globally similar in profile with, but different in detail from, that of sunspot cycles. The amplitude of solar magnetic activity should not keep in phase with the complexity of solar magnetic activity. The possible periods in the filament activity are about 10.44 and 19.20 years. The wavelet local power spectrum of the period 10.44 years is statistically significant during the whole consideration time. The wavelet local power spectrum of the period 19.20 years is under the 95% confidence spectrum during the whole consideration time, but over the mean red-noise spectrum of α = 0.72 before approximate Carrington rotation number 1500, and after that the filament activity does not statistically show the period. Wavelet reconstruction indicates that the early data of the filament archive (in and before cycle 16) are more noiseful than the later (in and after cycle 17).     

New Evidence for Long-Term Persistence in the Sun's Activity

Possible persistence of sunspot activity was studied using rescaled range and detrended fluctuation analyses. In addition to actual Wolf numbers (1700–2000 A.D.), two solar proxies were used in this research, viz., an annual sunspot proxy obtained for 1090–1700 A.D. and sunspot numbers reconstructed from the decadal radiocarbon series (8005 B.C. – 1895 A.D). The reconstruction was made using a five-box carbon exchange model. Analyses showed that in all cases the scaling exponent is significantly higher than 0.5 in the range of scales from 25 yr up to 3000 yr. This indicates the existence of a long-term memory in solar activity, in agreement with results obtained for other solar indices.