Total sunspot area as a solar activity index

Observational time series of the total sunspot area A in the visible solar hemisphere are analyzed. A technique that allows the instability of the scale of these series to be found and corrected has been developed. An internally homogeneous series of the index A on the Greenwich scale can be obtained from 1875 to the present. A method for the approximate calculation of the yearly mean A from the Wolf sunspot numbers known since 1700 is suggested to extend this series into the past. The resulting series of the index A characterizes the solar activity variations over a period of ～300 years. These data are used to study processes in the Solar System related to the variability of the central star.     

Evolution of Solar and Geomagnetic Activity Indices, and Their Relationship: 1960?�C?2001

We employ annually averaged solar and geomagnetic activity indices for the period 1960??C?2001 to analyze the relationship between different measures of solar activity as well as the relationship between solar activity and various aspects of geomagnetic activity. In particular, to quantify the solar activity we use the sunspot number R _s, group sunspot number R _g, cumulative sunspot area Cum, solar radio flux F10.7, and interplanetary magnetic field strength IMF. For the geomagnetic activity we employ global indices Ap, Dst and Dcx, as well as the regional geomagnetic index RES, specifically estimated for the European region. In the paper we present the relative evolution of these indices and quantify the correlations between them. Variations have been found in: i) time lag between the solar and geomagnetic indices; ii) relative amplitude of the geomagnetic and solar activity peaks; iii) dual-peak distribution in some of solar and geomagnetic indices. The behavior of geomagnetic indices is correlated the best with IMF variations. Interestingly, among geomagnetic indices, RES shows the highest degree of correlation with solar indices.     

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.     

Wavelet Analysis on Solar Wind Parameters and Geomagnetic Indices

The geomagnetic activity is the result of the solar wind–magnetosphere interaction. It varies following the basic 11-year solar cycle; yet shorter time-scale variations appear intermittently. We study the quasi-periodic behavior of the characteristics of solar wind (speed, temperature, pressure, density) and the interplanetary magnetic field (B _x , B _y , B _z , β, Alfvén Mach number) and the variations of the geomagnetic activity indices (D _ST, AE, A _p and K _p). In the analysis of the corresponding 14 time series, which span four solar cycles (1966?–?2010), we use both a wavelet expansion and the Lomb/Scargle periodograms. Our results verify intermittent periodicities in our time-series data, which correspond to already known solar activity variations on timescales shorter than the sunspot cycle; some of these are shared between the solar wind parameters and geomagnetic indices.     

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)     

Reconstruction of a Monthly Homogeneous Sunspot Area Series Since 1832

In this work, a procedure to elaborate a homogeneous sunspot area series using the Royal Greenwich Observatory/USAF/NOAA data (from 1874 to the present) and the De la Rue and co-workers data (from 1832 to 1868) is presented. These two data series correspond to time intervals that do not overlap and a direct comparison between them could not be carried out. We used the International Sunspot Number (R_i) and the Group Sunspot Number (R_G) as a link between the two original series. Thus, two homogeneous sunspot area series have been built using a simple mathematic procedure based on linear relations.     

Total sunspot area before 1875 (reconstruction)

Empirical functions approximating the dependences of total sunspot area A on relative sunspot number W and group sunspot number GN have been found. In the function A(W), allowance for its dependence on the secular activity cycle has been made; it is shown that this allowance is not needed for the function A(GN). The yearly mean A for 1700–1874 have been reconstructed using these functions and the available W and GN time series. Having supplemented the original data with archival observations, we have been able to reconstruct the monthly mean A _W since 1821. We discuss the causes of the systematic difference between the reconstructions using W and GN.     

Series of classical solar activity indices: Kislovodsk data

We present data on the series of solar activity indices, Wolf sunspot numbers W and total sunspot areas S, obtained at the Kislovodsk high-altitude station of the Pulkovo Observatory. The problem of properly extending the 133-year-long Zürich series of W and the 102-year-long Greenwich series of S, which were discontinued in 1980 and 1976, respectively, is emphasized. We stress that the Kislovodsk data have retained mutual homogeneity with the classical series until now and that they are preferred for extension. The question under consideration is of fundamental importance in studying the solar activity variations on long time scales and related processes in the Sun-Earth system.     

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.     

Sunspot Catalogue of the Observatory of the University of Coimbra (1929 – 1941)

A sunspot catalogue was published by the Coimbra Astronomical Observatory (Portugal), which is now called the Geophysical and Astronomical Observatory of the University of Coimbra, for the period 1929?–?1941. We digitalised data included in that catalogue and provide a machine-readable version. We show the reconstructions for the (total and hemispheric) sunspot number index and sunspot area according to this catalogue and compare it with the sunspot number index (version 2) and the Balmaceda sunspot area series (Balmaceda et al. in J. Geophys. Res.114, A07104, 2009). Moreover, we also compared the Coimbra catalogue with records made at the Royal Greenwich Observatory. The results demonstrate that the historical catalogue compiled by the Coimbra Astronomical Observatory contains reliable sunspot data and can therefore be considered for studies about solar activity.     

Recurrent magnetic activity,sunspot number and its rate of decline

Power spectral densities computed from low-latitude horizontal intensity of the Earth's magnetic field over two-year periods of declining phases of solar cycles 16 to 19 show a close relationship with the maximum relative sunspot number of the following solar cycles. The maximum sunspot number shows an exponential rise with the power density near 1/27 cd^?1; maximum R _z,however, increases linearly with power density near 1/14 cd^?1. It is also shown that the rate of decline of sunspot number in a solar cycle is almost exactly related, linearly, to power spectral density for the preceding solar cycle. Power densities near 1/27 and 1/14 cd^?1 in declining phase of solar cycle appear to be satisfactory indices for the maximum relative sunspot number of the following cycle and its rate of decline thereafter.     

The G–O Rule and Waldmeier Effect in the Variations of the Numbers of Large and Small Sunspot Groups

We have analyzed the combined Greenwich and Solar Optical Observing Network (SOON) sunspot group data during the period of 1874??C?2011 and determined variations in the annual numbers (counts) of the small (maximum area A _M<100 millionth of solar hemisphere, msh), large (100??A _M<300?msh), and big (A _M??300?msh) spot groups. We found that the amplitude of an even-numbered cycle of the number of large groups is smaller than that of its immediately following odd-numbered cycle. This is consistent with the well known Gnevyshev and Ohl rule (G?CO rule) of solar cycles, generally described by using the Zurich sunspot number (R _Z). During cycles 12??C?21 the G?CO rule holds good for the variation in the number of small groups also, but it is violated by cycle pair (22, 23) as in the case of R _Z. This behavior of the variations in the small groups is largely responsible for the anomalous behavior of R _Z in cycle pair (22, 23). It is also found that the amplitude of an odd-numbered cycle of the number of small groups is larger than that of its immediately following even-numbered cycle. This might be called the ??reverse G?CO rule??. In the case of the number of the big groups, both cycle pairs (12, 13) and (22, 23) violated the G?CO rule. In many cycles the positions of the peaks of the small, large, and big groups are different, and considerably differ with respect to the corresponding positions of the R _Z peaks. In the case of cycle?23, the corresponding cycles of the small and large groups are largely symmetric/less asymmetric (the Waldmeier effect is weak/absent) with their maxima taking place two years later than that of R _Z. The corresponding cycle of the big groups is more asymmetric (strong Waldmeier effect) with its maximum epoch taking place at the same time as that of R _Z.     

Solar indices and solar u.v.-irradiances

Solar radio fluxes, Zurich relative sunspot number R_z, and Solar Call plage indexes daily values for the period 1957–1980 are analyzed in order to test the stability of the series with respect to time and solar activity. It is found that between the series of the 3,8 and 10 cm radio fluxes and the series of R_z no significant trend with time, solar activity or solar cycle exists when mean values for periods of the order of one year are considered.Then, the daily solar u.v.-irradiances measured since 1969 for H-Lyman-alpha and-beta, the Hel-resonance line and HeII-Lyman-alpha are compared with the 10.7 cm radio fluxes and adjusted. After adjustment, the behaviour of the four series of irradiances with respect to the 10.7 cm flux shows a similar structure as the behaviour typical for the series of the 3 cm or the 8 cm fluxes.This adjustment allows the determination of the slope of the mean variation of the u.v.-irradiances with solar activity. The increases from solar minimum to solar maximum related to the minimum values are respectively : 60% for H-Lyman-alpha, 80% for H-Lyman-beta and 90% for Hel and Hell.     

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.     

The Greenwich Photo-heliographic Results (1874 – 1976): Procedures for Checking and Correcting the Sunspot Digital Datasets

Attention is drawn to the existence of errors in the original digital dataset containing sunspot data extracted from certain sections of the printed Greenwich Photo-heliographic Results (GPR) 1874?–?1976. Calculating the polar coordinates from the heliographic coordinates and comparing them with the recorded polar coordinates reveals that there are both isolated and systematic errors in the original sunspot digital dataset, particularly during the early years (1874?–?1914). It should be noted that most of these errors are present in the compiled sunspot digital dataset and not in the original printed copies of the Greenwich Photo-heliographic Results. Surprisingly, many of the errors in the digitised positions of sunspot groups are apparently in the measured polar coordinates, not the derived heliographic coordinates. The mathematical equations that are used to convert between heliographic and polar coordinate systems are formulated and then used to calculate revised (digitised) polar coordinates for sunspot groups, on the assumption that the heliographic coordinates of every sunspot group are correct. The additional complication of requiring accurate solar ephemerides in order to solve the mathematical equations is discussed in detail. It is shown that the isolated and systematic errors, which are prevalent in the sunspot digital dataset during the early years, disappear if revised polar coordinates are used instead. A comprehensive procedure for checking the original sunspot digital dataset is formulated in an Appendix.     

The Greenwich Photo-heliographic Results (1874 – 1976): Summary of the Observations, Applications, Datasets, Definitions and Errors

The measurements of sunspot positions and areas that were published initially by the Royal Observatory, Greenwich, and subsequently by the Royal Greenwich Observatory (RGO), as the Greenwich Photo-heliographic Results (GPR), 1874?–?1976, exist in both printed and digital forms. These printed and digital sunspot datasets have been archived in various libraries and data centres. Unfortunately, however, typographic, systematic and isolated errors can be found in the various datasets. The purpose of the present paper is to begin the task of identifying and correcting these errors. In particular, the intention is to provide in one foundational paper all the necessary background information on the original solar observations, their various applications in scientific research, the format of the different digital datasets, the necessary definitions of the quantities measured, and the initial identification of errors in both the printed publications and the digital datasets. Two companion papers address the question of specific identifiable errors; namely, typographic errors in the printed publications, and both isolated and systematic errors in the digital datasets. The existence of two independently prepared digital datasets, which both contain information on sunspot positions and areas, makes it possible to outline a preliminary strategy for the development of an even more accurate digital dataset. Further work is in progress to generate an extremely reliable sunspot digital dataset, based on the programme of solar observations supported for more than a century by the Royal Observatory, Greenwich, and the Royal Greenwich Observatory. This improved dataset should be of value in many future scientific investigations.     

Wavelet Analysis of solar,solar wind and geomagnetic parameters

The sunspot number, solar wind plasma, interplanetary magnetic field, and geomagnetic activity index A _p have been analyzed using a wavelet technique to look for the presence of periods and the temporal evolution of these periods. The global wavelet spectra of these parameters, which provide information about the temporal average strength of quasi periods, exhibit the presence of a variety of prominent quasi periods around 16 years, 10.6 years, 9.6 years, 5.5 years, 1.3 years, 180 days, 154 days, 27 days, and 14 days. The wavelet spectra of sunspot number during 1873–2000, geomagnetic activity index A _p during 1932–2000, and solar wind velocity and interplanetary magnetic field during 1964–2000 indicate that their spectral power evolves with time. In general, the power of the oscillations with a period of less than one year evolves rapidly with the phase of the solar cycle with their peak values changing from one cycle to the next. The temporal evolution of wavelet power in R _z, v _sw, n, B _y, B _z, |B|, and A _p for each of the prominent quasi periods is studied in detail.     

The curious case of the greenwich faculae

We analyze the record of facular areas compiled by the Royal Greenwich Observatory (RGO) from daily white-light observations between 1874 and 1976. Curiously, the relative amplitudes of the three largest sunspot cycles 17, 18, and 19 in this record are reversed when they are ranked by facular area. We show that this negative correlation arises from a general decrease of the ratioA _F/A _S, of facular to sunspot area, with increasingA _S. Within a given cycle,A _F/A _Sdecreases in active regions of largeA _S, butA _F/A _Sis also lower at allA _S, in cycles of higher peak amplitude inA _S. This decrease ofA _F/A _Sin large spot groups is consistent with its decrease in younger, more active solar-mass stars, and it may explain why stars only slightly more magnetically active than the Sun tend to exhibit much greater variability in broad-band photometry. We suggest that the physical explanation is an increased spatial filling factor of magnetic flux, favoring formation of sunspots over faculae. We also explain why the decrease inA _F/A_Sis not seen in the disc-integrated Ca K plage areas, nor in theF10.7 microwave index, both of which exhibit remarkable linearity when plotted against smoothed sunspot area. This explanation suggests how complementary data on faculae and plages from RGO and Mt. Wilson could be used to improve empirical models of total irradiance variation, extending back to 1874.     

The Greenwich Photo-heliographic Results (1874 – 1976): Initial Corrections to the Printed Publications

A new sunspot and faculae digital dataset for the interval 1874?–?1955 has been prepared under the auspices of the NOAA National Geophysical Data Center (NGDC). This digital dataset contains measurements of the positions and areas of both sunspots and faculae published initially by the Royal Observatory, Greenwich, and subsequently by the Royal Greenwich Observatory (RGO), under the title Greenwich Photo-heliographic Results (GPR), 1874?–?1976. Quality control (QC) procedures based on logical consistency have been used to identify the more obvious errors in the RGO publications. Typical examples of identifiable errors are North versus South errors in specifying heliographic latitude, errors in specifying heliographic (Carrington) longitude, errors in the dates and times, errors in sunspot group numbers, arithmetic errors in the summation process, and the occasional omission of solar ephemerides. Although the number of errors in the RGO publications is remarkably small, an initial table of necessary corrections is provided for the interval 1874?–?1917. Moreover, as noted in the preceding companion papers, the existence of two independently prepared digital datasets, which both contain information on sunspot positions and areas, makes it possible to outline a preliminary strategy for the development of an even more accurate digital dataset. Further work is in progress to generate an extremely reliable sunspot digital dataset, based on the long programme of solar observations supported first by the Royal Observatory, Greenwich, and then by the Royal Greenwich Observatory.     

The Relative Umbral Area in Spot Groups as an Index of Cyclic Variation of Solar Activity

The Greenwich series of data was used to study the ratio [q] of the total umbra area to the total area of the sunspot group (for brevity “relative umbral area”) for the period 1874?–?1976. It was revealed that the annual mean value of q varied in time from 0.15 to 0.28 and reached its maximum in the early 1930s. The dependence of q on the sunspot group area [S] was considered to show that the smallest groups, of area less than 100 m.v.h. (millionths of the visible hemisphere), contributed most significantly to the temporal variation of q. In contrast to the earlier results, the dependence obtained proved to be rather complicated. The coefficients of the linear expansion q(S) are themselves dependent on the sunspot-group area and time [t]; i.e. the relation of q to both S and t is nonlinear. Only in sunspot groups with a large area does dependence disappear, and q becomes constant, equal to 0.18. This is the value given in textbooks. The relations obtained show that the relive umbral area and the relative number of small groups are important parameters of the secular variation of solar activity. In particular, they may account for variations in the mean magnetic field in active regions, the complexity of a group according to the magnetic classification, the flare activity of a sunspot group, and its geophysical impact. It is conjectured that the parameter q describes the time-varying relative contribution from the interior and subsurface dynamo mechanisms.