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.     

Comparison of three solar activity indices based on sunspot observations

The following sunspot formation indices are analyzed: the relative sunspot number R _z, the normalized sunspot group number R _g, and the total sunspot area A. Six empirical formulas are derived to describe the relations among these indices after 1908. The earlier data exhibit systematic deviations from these formulas, which can be attributed to systematic errors of the indices. The Greenwich data on the sunspot total area A and the sunspot group number in 1874–1880 are found to be doubtful. Erroneous data at the beginning of the Greenwich series must spoil the values of the index R _g in the XVII–XIX centuries. The Hoyt-Schatten series of R _g may be less reliable than the well-known Wolf number series R _z.     

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.     

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.     

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.     

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.     

Two Unusual Episodes of ≈13-Day Variations II. Implications for the Solar Radio Flux Density, <Emphasis Type="Italic">F</Emphasis><Subscript>10.7 cm</Subscript>

Additional analysis of the behavior of the international sunspot number (R) series and the solar radio flux density (F_{10.7 cm}) series during two long (250–500 days) and distinct episodes of persistent ≈13-day variations (Crane, Solar Phys. 1998, 253, 177) is reported. The conclusion is that while the center-to-limb behavior of R does not change between solar minimum and solar maximum, F_{10.7 cm} exhibits significantly less limb brightening at solar maximum than at solar minimum.     

Sunspot Catalogue of the Valencia Observatory (1920 – 1928)

A sunspot catalogue was maintained by the Astronomical Observatory of Valencia University (Spain) from 1920 to 1928. Here we present a machine-readable version of this catalogue (OV catalogue or OVc), including a quality-control analysis. Sunspot number (total and hemispheric) and sunspot area series are constructed using this catalogue. The OV catalogue data are compared with other available solar data, demonstrating that the present contribution provides the scientific community with a reliable catalogue of sunspot data.     

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.     

Comparison of sunspot area data bases

Sunspot area measurements play an important role in the studies of sunspot groups and variations in solar irradiance. However, the measured areas may be burdened with systematic and random errors, which may affect the results in these fields. Mainly the total solar irradiance models can be improved by using more precise area data. In order to choose the most appropriate area data for a given study or create a homogeneous composite area data base, there is a need to compare the sunspot areas provided by different observatories. In this study we statistically investigated all the available corrected sunspot area data bases for the years 1986 and 1987. We find that the photographic data bases are in good agreement with each other but there are important systematic differences between the photographic and sunspot drawings data bases. We give the characteristic parameters for the systematic and random errors as well as the possible reasons for them.     

Solar Cycle Predictions based on Solar Activity at Different Solar Latitudes

Many methods of predictions of sunspot maximum number use data before or at the preceding sunspot minimum to correlate with the following sunspot maximum of the same cycle, which occurs a few years later. Kane and Trivedi (Solar Phys. 68, 135, 1980) found that correlations of R _z(max) (the maximum in the 12-month running means of sunspot number R _z) with R _z(min) (the minimum in the 12-month running means of sunspot number R _z) in the solar latitude belt 20° – 40°, particularly in the southern hemisphere, exceeded 0.6 and was still higher (0.86) for the narrower belt > 30° S. Recently, Javaraiah (Mon. Not. Roy. Astron. Soc. 377, L34, 2007) studied the relationship of sunspot areas at different solar latitudes and reported correlations 0.95 – 0.97 between minima and maxima of sunspot areas at low latitudes and sunspot maxima of the next cycle, and predictions could be made with an antecedence of more than 11 years. For the present study, we selected another parameter, namely, SGN, the sunspot group number (irrespective of their areas) and found that SGN(min) during a sunspot minimum year at latitudes > 30° S had a correlation +0.78±0.11 with the sunspot number R _z(max) of the same cycle. Also, the SGN during a sunspot minimum year in the latitude belt (10° – 30° N) had a correlation +0.87±0.07 with the sunspot number R _z(max) of the next cycle. We obtain an appropriate regression equation, from which our prediction for the coming cycle 24 is R _z(max )=129.7±16.3.     

Bimodality and the Hale cycle

Because of the bimodal distribution of sunspot cycle periods, the Hale cycle (or double sunspot cycle) should show evidence of modulation between 20 and 24 yr, with the Hale cycle having an average length of about 22 yr. Indeed, such a modulation is observed. Comparison of consecutive pairs of cycles strongly suggests that even-numbered cycles are preferentially paired with odd-numbered following cycles. Systematic variations are hinted in both the Hale cycle period and R _sum (the sum of monthly mean sunspot numbers over consecutively paired sunspot cycles). The preferred even-odd cycle pairing suggests that cycles 22 and 23 form a new Hale cycle pair (Hale cycle 12), that cycle 23 will be larger than cycle 22 (in terms of R _M, the maximum smoothed sunspot number, and of the individual cycle value of R _sum), and that the length of Hale cycle 12 will be longer than 22 yr. Because of the strong correlation (r = 0.95) between individual sunspot cycle values of R _sum and R _M, having a good estimate of R _Mfor the present sunspot cycle (22) allows one to predict its R _sum, which further allows an estimation of both R _Mand R _sum for cycle 23 and an estimation of R _sum for Hale cycle 12. Based on Wilson's bivariate fit (r = 0.98), sunspot cycle 22 should have an R _Mequal to 144.4 ± 27.3 (at the 3- level), implying that its R _sum should be about 8600 ± 2200; such values imply that sunspot cycle 23 should have an R _sum of about 10500 ± 2000 and an R _Mof about 175 ± 40, and that Hale cycle 12 should have an R _sum of about 19100 ± 3000.     

Relationship between group sunspot numbers and Wolf sunspot numbers

Continuous wavelet transform and cross‐wavelet transform have been used to investigate the phase periodicity and synchrony of the monthly mean Wolf (R_z) and group (R_g) sunspot numbers during the period of June 1795 to December 1995. The Schwabe cycle is the only one common period in R_g and R_z, but it is not well‐defined in case of cycles 5–7 of R_g and in case of cycles 5 and 6 of R_z. In fact, the Schwabe period is slightly different in R_g and R_z before cycle 12, but from cycle 12 onwards it is almost the same for the two time series. Asynchrony of the two time series is more obviously seen in cycles 5 and 6 than in the following cycles, and usually more obviously seen around the maximum time of a cycle than during the rest of the cycle. R_g is found to fit R_z better in both amplitudes and peak epoch during the minimum time time of a solar cycle than during the maximum time of the cycle, which should be caused by their different definition, and around the maximum time of a cycle, R_g is usually less than R_z. Asynchrony of R_g and R_z should somewhat agree with different sunspot cycle characteristics exhibited by themselves (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Can the Solar Cycle Amplitude Be Predicted Using the Preceding Solar Cycle Length?

In this work, the evolution of the relationship between Solar Cycle Length of solar cycle n (SCL _n ) and Solar Cycle Amplitude of the solar cycle n+1 (SCA _n+1) is studied by using the R _Z and R _G sunspot numbers. We conclude that this relationship is only strongly significant in a statistical sense during the first half of the historical record of R _Z sunspot number whereas it is considerably less significant for the R _G sunspot number. In this sense we assert that these simple lagged relationships should be avoided as a valid method to predict the following solar activity amplitude.     

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.     

A sunspot analysis: 1943–1977

Sunspot data from the Catania Astrophysical Observatory, covering cycles 18, 19, and 20 (1943–1977) have been analyzed, taking into account, besides the usual parameters, the number n of zones, namely latitude belts 5° wide, showing sunspot activity and the area covered by spots for each of these zones. A comparison between our conclusions and those drawn from other authors on the same subject is made.     

The Relationship between Prediction Accuracy and Correlation Coefficient

The correlation coefficient (r) between the maximum amplitude (R _m) of a sunspot cycle and the preceding minimum aa geomagnetic index (aa _min), in terms of geomagnetic cycle, can be fitted by a sinusoidal function with a four-cycle periodicity superimposed on a declining trend. The prediction index (χ) of the prediction error relative to its estimated uncertainty based on a geomagnetic precursor method can be fitted by a sinusoidal function with a four-and-half-cycle periodicity. A revised prediction relationship is found between the two quantities: χ<1.2 if r varies in a rising trend, and χ>1.2 if r varies in a declining trend. The prediction accuracy of R _m depends on the long-term variation in the correlation. These results indicate that the prediction for the next cycle inferred from this method, R _m(24)=87±23 regarding the 75% level of confidence (1.2-σ), is likely to fail. When using another predictor of sunspot area instead of the geomagnetic index, similar results can be also obtained. Dynamo models will have better predictive powers when having considered the long-term periodicities.