Douglas V. Hoyt

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 discussion of plausible solar irradiance variations, 1700‐1992

From satellite observations the solar total irradiance is known to vary. Sunspot blocking, facular emission, and network emission are three identified causes for the variations. In this paper we examine several different solar indices measured over the past century that are potential proxy measures for the Suns irradiance. These indices are (1) the equatorial solar rotation rate, (2) the sunspot structure, the decay rate of individual sunspots, and the number of sunspots without umbrae, and (3) the length and decay rate of the sunspot cycle. Each index can be used to develop a model for the Suns total irradiance as seen at the Earth. Three solar indices allow the irradiance to be modeled back to the mid-1700s. The indices are (1) the length of the solar cycle, (2) the normalized decay rate of the solar cycle, and (3) the mean level of solar activity. All the indices are well correlated, and one possible explanation for their nearly simultaneous variations is changes in the Suns convective energy transport. Although changes in the Suns convective energy transport are outside the realm of normal stellar structure theory (e.g., mixing length theory), one can imagine variations arising from even the simplest view of sunspots as vertical tubes of magnetic flux, which would serve as rigid pillars affecting the energy flow patterns by ensuring larger-scale eddies. A composite solar irradiance model, based upon these proxies, is compared to the northern hemisphere temperature departures for 1700-1992. Approximately 71% of the decadal variance in the last century can be modeled with these solar indices, although this analysis does not include anthropogenic or other variations which would affect the results. Over the entire three centuries, ∼50% of the variance is modeled. Both this analysis and previous similar analyses have correlations of model solar irradiances and measured Earth surface temperatures that are significant at better than the 95% confidence level. To understand our present climate variations, we must place the anthropogenic variations in the context of natural variability from solar, volcanic, oceanic, and other sources.

The one hundredth year of Rudolf Wolf's death: Do we have the correct reconstruction of solar activity?

In the one hundred years since Wolf died, little effort has gone into research to see if improved reconstructions of sunspot numbers can be made. We have gathered more than 349,000 observations of daily sunspot group counts from more than 350 observers active from 1610 to 1993. Based upon group counts alone, it is possible to make an objective and homogeneous reconstruction of sunspot numbers. From our study, it appears that the Sun has steadily increased in activity since 1700 with the exception of a brief decrease in the Dalton Minimum (1795–1823). The significant results here are the greater depth of the Dalton Minimum, the generally lower activity throughout the 1700s, and the gradual rise in activity from the Maunder Minimum to the present day. This solar activity reconstruction is quite similar to those Wolf published before 1868 rather than the revised Wolf reconstructions after 1873 which used geomagnetic fluctuations.

How well was the Sun observed during the Maunder Minimum

In this paper we examine how well the Sun and sunspots were observed during the Maunder Minimum from 1645 to 1715. Recent research has given us the dates of observations by Hevelius, Picard, La Hire, Flamsteed, and about 70 other observers. These specific observations allow a ‘lower estimate’ of the fraction of the time the Sun was observed to be deduced. It is found that 52.7% of the days have recorded observations. There are additional 12 observers who provide general statements that no sunspots were observed during specific years or intervals despite diligent efforts. Taking these statements to mean, unrealistically, that every day during these intervals was observed, gives an ‘upper estimate’ of 98% of the days. If the general statements are relaxed by assuming that 100 ± 50 days per year were actually observed by these diligent observers, than our ‘best estimate’ is that 68%±7% of the days during the Maunder Minimum were observed. In short, this supports the view that the Maunder Minimum existed and was not an artifact of few observations. Some sunspots are probably still missed in modern compilations, but the existence of a prolonged sunspot minimum would not be threatened by their discovery in future research. Additional support for intense scrutiny of the Sun comes from a report of a white-light flare in 1705 and from the numerous reports of new sunspots entering the disk of the Sun.

Overlooked sunspot observations by Hevelius in the early Maunder Minimum, 1653–1684

In the bookMachina Coelestis (1679), Johannes Hevelius lists his daily solar observations from 1653 to 1679. He mentions 19 sunspot groups during this interval, of which 14 are unique to Hevelius and five are confirmed by other observers. There are an additional 9 sunspot groups during this interval that were not observed by Hevelius. In five cases he was not observing, but in the other four cases he did observe but failed to comment upon sunspots. The spots he missed or failed to observe tend to occur near the end of his career. This suggests Hevelius occasionally missed sunspots but usually was a reliable observer. These observations are important because they provide us the only known daily listing of solar observations during the early years of the Maunder Minimum. They are also important because they were overlooked by Wolf, Spoerer, Maunder, Eddy, and others in their study of solar activity in the seventeenth century. They provide us the best record of the sunspot maximum of 1660 when one sunspot lasted at least 86 days as it traversed the solar disk four times. The same region was active for seven solar rotations.

Observations of sunspots by Flamsteed during the Maunder Minimum

In the bookHistoria Coelestis Brittannica, John Flamsteed (1725) lists his daily solar observations from 1676 onwards. Coupled with his comments in thePhilosophical Transactions of the Royal Society and his letters to William Derham in the Cambridge University Library, it is possible to reconstruct a daily chronology of his solar and sunspot observations from 1676 to 1700. These observations are important because, coupled with daily logs of observations by Picard, La Hire, Eimmart, and others, a detailed record of the observations during a portion of the Maunder Minimum can be constructed. For example, for 1691, a typical year, the longest gap between observations is only four days. Flamsteeds observations are also important because they add to the data gathered by Wolf, Spoerer, Maunder, Eddy, and others in their study of solar activity in the seventeenth century. Flamsteeds observations are summarized here and a sample of his observations is presented.

New information on solar activity, 1779-1818, from Sir William Herschel's unpublished notebooks

Herschels observations are analyzed in order to determine the level of solar activity for solar cycle 5. It is concluded that solar cycle 5 may have peaked as early as 1801 based upon the average number of groups with a probable secondary maximum in 1804. Depending on the technique adopted, the peak for solar cycle 5 occurred sometime between 1801 and 1804, rather than 1805.2, as commonly assumed. Instead of a solar cycle of 17 yrs, a cycle length of 14 yrs is found. It is also found that the peak yearly mean sunspot number is only about 38 rather than 45, as deduced by Wolf (1855). A technique for making early solar observations homogeneous with modern sunspot observations is proposed.

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 observers 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 Horrebows 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 Earths climate.

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, Pastorffs 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 Ranyards interpretation and the consequences for the history of solar activity that a correct interpretation of Pastorffs observations will have. Pastorffs observations provide valuable information on the first strong cycle after the Dalton Minimum (1795–1823).

A New Reconstruction of Solar Activity, 1610–1993

In the one hundred years since Wolf died, little effort has gone into research to see if improved reconstructions of solar activity can be made. We have gathered more than 348,000 observations of daily sunspot group counts from more than 350 observers active from 1610 to 1993. Based upon group counts alone, it is possible to make an objective and homogeneous reconstruction of solar activity. From our study, it appears that the Sun has steadily increased in activity since 1700 with the exception of a brief decrease in the Dalton Minimum (1795–1823). The significant results here are the greater depth of the Dalton Minimum, the generally lower activity throughout the 1700’s, and the gradual rise in activity from the Maunder Minimum to the present day. This solar activity reconstruction is quite similar to those Wolf published before 1868 rather than the revised Wolf reconstructions after 1873 which used geomagnetic fluctuations.