Group Sunspot Numbers: A New Solar Activity Reconstruction

In this paper, we construct a time series known as the Group Sunspot Number. The Group Sunspot Number is designed to be more internally self-consistent (i.e., less dependent upon seeing the tiniest spots) and less noisy than the Wolf Sunspot Number. It uses the number of sunspot groups observed, rather than groups and individual sunspots. Daily, monthly, and yearly means are derived from 1610 to the present. The Group Sunspot Numbers use 65941 observations from 117 observers active before 1874 that were not used by Wolf in constructing his time series. Hence, we have calculated daily values of solar activity on 111358 days for 1610–1995, compared to 66168 days for the Wolf Sunspot Numbers. The Group Sunspot Numbers also have estimates of their random and systematic errors tabulated. The generation and preliminary analysis of the Group Sunspot Numbers allow us to make several conclusions: (1) Solar activity before 1882 is lower than generally assumed and consequently solar activity in the last few decades is higher than it has been for several centuries. (2) There was a solar activity peak in 1801 and not 1805 so there is no long anomalous cycle of 17 years as reported in the Wolf Sunspot Numbers. The longest cycle now lasts no more than 15 years. (3) The Wolf Sunspot Numbers have many inhomogeneities in them arising from observer noise and this noise affects the daily, monthly, and yearly means. The Group Sunspot Numbers also have observer noise, but it is considerably less than the noise in the Wolf Sunspot Numbers. The Group Sunspot Number is designed to be similar to the Wolf Sunspot Number, but, even if both indices had perfect inputs, some differences are expected, primarily in the daily values.     

A revised listing of the number of sunspot groups made by Pastorff, 1819 to 1833

J. W. Pastorff of Drossen, Germany, made about 1477 observations of sunspots between 1819 and 1833. These observations were erroneously interpreted by A. C. Ranyard in 1874 and then used by Rudolf Wolf in his calculations of the Wolf Sunspot Numbers. The result is a noisier daily time series and overestimation of the monthly and yearly means for these years. Pastorff was actually a very good observer. In this paper, Pastorff's original observations are reexamined and more nearly correct values for the number of sunspot groups are tabulated. We show some examples of the problems created by Ranyard's interpretation and the consequences for the history of solar activity that a correct interpretation of Pastorff's observations will have. Pastorff's observations provide valuable information on the first strong cycle after the Dalton Minimum (1795–1823).     

A Note on Solar Cycle Length Estimates

Recently, new estimates of the solar cycle length (SCL) have been calculated using the Zurich Sunspot Number (R_Z) and the Regression-Fourier-Calculus (RFC)-method, a mathematically rigorous method involving multiple regression, Fourier approximation, and analytical expressions for the first derivative. In this short contribution, we show estimates of the solar cycle length using the RFC-method and the Group Sunspot Number (R_G) instead the R_Z. Several authors have showed the advantages of R_G for the analysis of sunspot activity before 1850. The use of R_G solves some doubtful solar cycle length estimates obtained around 1800 using R_Z.     

The Sidc: World Data Center for the Sunspot Index

Since January 1981, the Royal Observatory of Belgium (ROB) has operated the Sunspot Index Data Center (SIDC), the World Data Center for the Sunspot Index. From 2000, the SIDC obtained the status of Regional Warning Center (RWC) of the International Space Environment Service (ISES) and became the “Solar Influences Data analysis Center”. As a data analysis service of the Federation of Astronomical and Geophysical data analysis Services (FAGS), the SIDC collects monthly observations from worldwide stations in order to calculate the International Sunspot Number, R _i . The center broadcasts the daily, monthly, yearly sunspot numbers, with middle-range predictions (up to 12 months). Since August 1992, hemispheric sunspot numbers are also provided. Deceased.     

Short-Term Correlation of Solar Activity and Sunspot: Evidence of Lifetime Increase

We perform a nonlinear study of the short-term correlation properties of the solar activity (daily range) in order to reveal their long-life variations. We estimate the lifetime of the high-frequency component of a Markov-type signal when the high-frequency component is modulated by a slowly varying multiplicative factor. This treatment is applied to different series of solar activity: Wolf Sunspot numbers (WSN), Sunspot Group numbers (SGN), and Royal Greenwich Observatory (RGO) sunspot group series. We obtain that all the lifetime estimates exhibit similar temporal variations that agree with the variations of the sunspot lifetimes directly measured from the RGO data and those of the sunspot areas. An increase of lifetimes by a factor 1.4 is observed from 1915 to 1940. At the same time, a stable ratio is observed between the sunspot group’s maximal area and the lifetime, confirming the Gnevyshev–Waldmeier-type relationship. The analysis identifies also time intervals where the homogeneity of the different time series may be questioned.     

A new look at wolf sunspot numbers in the late 1700's

Long-term homogeneous observations of solar activity or many solar cycles are essential for investigating many problems in solar physics and climatology. The one key parameter used in most long-term studies is the Wolf sunspot number, which is susceptible to observer bias, particularly because it is highly sensitive to the observer's ability to see the smallest sunspots. In this paper we show how the Wolf sunspot number can be derived from the number of sunspot groups alone. We utilize this approach to obtain a Group Wolf number. This technique has advantages over the classical method of determining the Wolf number because corrections for observer differences are reduced and long-term self-consistent time series can be developed. The level of activity can be calculated to an accuracy of ± 5% using this method. Applying the technique to Christian Horrebow's observations of solar cycles 1, 2, and 3 (1761–1777), we find that the standard Wolf numbers are nearly homogeneous with sunspot numbers measured from 1875 to 1976 except the peak of solar cycle 2 is too low by 30%. This result suggests that further analyses of early sunspot observations could lead to significant improvements in the uniformity of the measurements of solar activity. Such improvements could have important impacts upon our understanding of long-term variations in solar activity, such as the Gleissberg cycle, or secular variations in the Earth's climate.     

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.     

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.     

Observations of hysteresis in solar cycle variations among seven solar activity indicators

We show that smoothed time series of 7 indices of solar activity exhibit significant solar cycle dependent differences in their relative variations during the past 20 years. In some cases these observed hysteresis patterns start to repeat over more than one solar cycle, giving evidence that this is a normal feature of solar variability. Among the indices we study, we find that the hysteresis effects are approximately simple phase shifts, and we quantify these phase shifts in terms of lag times behind the leading index, the International Sunspot Number. Our measured lag times range from less than one month to greater than four months and can be much larger than lag times estimated from short-term variations of these same activity indices during the emergence and decay of major active regions. We argue that hysteresis represents a real delay in the onset and decline of solar activity and is an important clue in the search for physical processes responsible for changing solar emission at various wavelengths. The High Altitude Observatory is sponsored by the National Science Foundation.     

A comparison of the spectral characteristics of the Wolf Sunspot Number (RZ) and Group Sunspot Number (RG)

The objective of this paper is to compare the spectral features of the recently derived Group Sunspot Numbers (R _G) and the traditional Wolf Sunspot Numbers (R _Z) for the 1700–1995 period. In order to study the spectral features of both time series, two methods were used, including: (a) the multitaper analysis and (b) the wavelet analysis. Well-known features of the solar variability, such as the 98.6-yr (Gleissberg cycle), 10–11-yr (Schwabe cycle) and 5-yr (second solar harmonic) periodicities were identified with high confidence using the multitaper analysis. Also observed was a larger amount of power spread in high frequencies for R _Z than for R _G spectra. Furthermore, a multitaper analysis of two subsets, A (1700–1850) and B (1851–1995), has indicated that the main differences occurred in the first subset and seem to be due to uncertainties in the early observations. The wavelet transform, which allows observing the spectra evolution of both series, showed a strong and persistent 10–11-yr signal that remained during the whole period. The Meyer Wavelet Transform was applied to both R _Z and R _G. This study indicates that the main spectral characteristics of both series are similar and that their long-term variability has the same behavior.     

A comparison of the spectral characteristics of the Wolf Sunspot Number (R Z) and Group Sunspot Number (R G)

The objective of this paper is to compare the spectral features of the recently derived Group Sunspot Numbers (R _G) and the traditional Wolf Sunspot Numbers (R _Z) for the 1700–1995 period. In order to study the spectral features of both time series, two methods were used, including: (a) the multitaper analysis and (b) the wavelet analysis. Well-known features of the solar variability, such as the 98.6-yr (Gleissberg cycle), 10–11-yr (Schwabe cycle) and 5-yr (second solar harmonic) periodicities were identified with high confidence using the multitaper analysis. Also observed was a larger amount of power spread in high frequencies for R _Z than for R _G spectra. Furthermore, a multitaper analysis of two subsets, A (1700–1850) and B (1851–1995), has indicated that the main differences occurred in the first subset and seem to be due to uncertainties in the early observations. The wavelet transform, which allows observing the spectra evolution of both series, showed a strong and persistent 10–11-yr signal that remained during the whole period. The Meyer Wavelet Transform was applied to both R _Z and R _G. This study indicates that the main spectral characteristics of both series are similar and that their long-term variability has the same behavior.     

A Comparison of the 10.7-cm Radio Flux Values and the International Sunspot Numbers for Solar Activity Cycles 19, 20, and 21

A nonlinear analysis of the daily 10.7-cm radio flux values for each of Solar Cycles 19, 20, and 21 is used to determine if the results match those of the International Sunspot Numbers for each of these cycles. Fractals and chaos are described and a brief review of utilizing fractals and chaos is given. The origin of the 10.7-cm radio flux is discussed and a short review of recent work discussing its measurement and its relation to the international sunspot number and other proxies for solar activity cycles given. The parameters used to describe chaos for the 10.7-cm radio flux are discussed. The length of the data sets for either statistical analysis or nonlinear analysis of the 10.7-cm radio flux values is considered. These results indicate that the 10.7-cm radio flux values appear to be stochastic for Cycle 19 and chaotic for Cycles 20 and 21. The International Sunspot Numbers show similar behavior for these three cycles. A day-by-day comparison of the dimensionless 10.7-cm radio flux values and the dimensionless International Sunspot Numbers differences shows a linear trend. The results remain consistent in that the 10.7-cm radio flux values indicate, as did the International Sunspot Numbers, that there is a transition from stochastic behavior for Cycle 19 to chaotic behavior in Cycles 20 and 21. The day-by-day comparison of the 10.7-cm radio flux values and the International Sunspot Numbers emphasizes that the 10.7?cm radio flux values are responding to the magnetic field associated with the sunspots.     

To the description of long-term variations in the solar magnetic flux: The sunspot area index

We show that the Wolf sunspot numbers W and the group sunspot numbers GSN are physically different indices of solar activity and that it is improper to compare them. Based on the approach of the so-called “primary” indices from the observational series of W(t) and GSN(t), we suggest series of yearly mean sunspot areas beginning in 1610 and monthly mean sunspot areas beginning in 1749.     

Lowering of Asymmetry

Asymmetry, a well established fact, can be extracted from various solar atmospheric activity indices. Although asymmetry is being localized within short time scale, it also persists at different time scales. In the present study we examine the character and nature of asymmetry at various time scales by optimizing the data set, in units of Carrington Rotations (CRs), for Sunspot Area (SA) and soft X-ray flare index (FI _SXR). We find from three solar cycles (21-23) that at a small time scale (viz., daily, CRs and monthly) activity appears to be asymmetric with less significance. At larger time scales (≥01 CRs) strength of asymmetry enhances. Number of significant asymmetry points probably depends upon the solar heights. For different combination of data, asymmetry strength appears to be lowered at certain periods ～06, ～12, ～18 CRs (164, 327 and 492 days i.e., harmonics of ～1.3 years. Owing to similar behavior of emergence of magnetic flux, it is conjectured that emergence of flux on the surface probably contributes to the asymmetry of the solar activity.     

One Possible Reason for Double-Peaked Maxima in Solar Cycles: Is a Second Maximum of Solar Cycle 24 Expected?

We investigate solar activity by focusing on double maxima in solar cycles and try to estimate the shape of the current solar cycle (Cycle 24) during its maximum. We analyzed data for Solar Cycle 24 by using Learmonth Solar Observatory sunspot-group data collected since 2008. All sunspot groups (SGs) recorded during this time interval were separated into two groups: The first group includes small SGs [A, B, C, and H classes according to the Zurich classification], the second group consists of large SGs [D, E, and F]. We then calculated how many small and large sunspot groups occurred, their sunspot numbers [SSN], and the Zurich numbers [Rz] from their daily mean numbers as observed on the solar disk during a given month. We found that the temporal variations for these three different separations behave similarly. We also analyzed the general shape of solar cycles from Cycle 1 to 23 by using monthly International Sunspot Number [ISSN] data and found that the durations of maxima were about 2.9 years. Finally, we used the ascending time and SSN relationship and found that the maximum of Solar Cycle 24 is expected to occur later than 2011. Thus, we conclude that i) one possible reason for a double maximum in solar cycles is the different behavior of large and small sunspot groups, and ii) a double maximum is expected for Solar Cycle 24.     

Is the Suess cycle present in historical naked-eye observations of sunspots?

Sunspot numbers are available for the past four centuries. However, solar activity indices with a longer time span are required by geophysicists and solar physicists. The yearly naked-eye sunspot number in the past is reconstructed using observations recorded in historical documents. Some studies from different solar proxies (including radiocarbon and aurora records) show the presence of the so-called Suess cycle (around 200 years) in solar variability. In this work, a modified Lomb–Scargle periodogram analysis is used to investigate the Suess cycle in naked-eye observations of sunspots during 200 BC–1918 AD. The most relevant characteristic of the periodogram is a cycle with a frequency very close to the Suess cycle, though this cycle is not significant statistically.     

On the solar activity during the year 1784

The solar observations performed by the Mexican astronomer J. A. Alzate during the year 1784 are analysed in this work. These observations are very valuable for the reconstruction of solar activity because Hoyt and Schatten (1998), who defined the Group Sunspot Number (R _G), only found five observations during this year — all performed by J. C. Staudacher. Using conjointly the data provided by Alzate and Staudacher for 1784, one can determine a value of R _G equal to 0.3±0.1 with eighty records for that year.     

Prediction for the amplitude of solar cycle 24 from the pattern of activity near the cycle minimum

Correlations are investigated between the pattern of solar activity described by the smoothed monthly relative sunspot numbers (Wolf numbers) near the minimum of a solar cycle and the cycle amplitude. The closest correlation is found between the amplitude of a solar cycle and the sum of the decrease in activity over two years prior to the cycle minimum and the increase in activity over two years after the minimum; the correlation coefficient between these parameters is 0.92. This parameter is used as a precursor to predict the amplitude of solar cycle 24, which is expected to reach its maximum amplitude (85 ± 12) in February 2014. Based on the correlations between the mean parameters of solar cycles, cycle 24 is expected to last for approximately 11.3 years and the minimum of the next cycle 25 is predicted for May 2020.     

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 periodicity of solar activity cycles

On the basis of published Wolf Numbers and Schove Row, solar activity cycles in the interval of 11 to hundreds of years have been investigated. In this case the method of investigation of pulsating stars showing the Blazhko effect was applied. The elements of cycles and O-C were calculated and compared with results of solar activity parameters determined by classical methods.