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We identify several pairs of 'equivalent' observers defined as observers with equal or nearly equal 'observational threshold' areas of sunspots on the solar disk as determined by the 'Active Days Fraction' method [e.g. Willamo et al., 2017]. For such pairs of observers, the ADF-method would be expected to map the actually observed sunspot group numbers for the individual observers to two reconstructed series that are very nearly equal and (it is claimed) represent 'real' solar activity without arbitrary choices and deleterious, error-accumulating 'daisy-chaining'. We show that this goal has not been achieved (for the critical period at the end of the 19th century and the beginning of the 20th), rendering the ADF-methodology suspect and not reliable nor useful for studying the long-term variation of solar activity., Comment: 13 pages; 14 Figures. arXiv admin note: substantial text overlap with arXiv:1704.07061

Recent work on improving and revising estimates of solar activity [Clette et al., 2014] has resulted in renewed interest in what has been called the longest running 'Science Experiment'. We compare four reconstructions of solar activity as reflected in the number of sunspot groups ('active regions') constructed by different authors using very different methods. We concentrate on the period since AD 1900 where the underlying solar and geomagnetic data are plentiful and of sufficient quality and find that all four methods yield essentially the same Sunspot Group Number series. We take that as indicating that protracted and pernicious criticisms of the individual methods are neither fruitful nor helpful and we suggest that future efforts be directed towards understanding the specific reasons why the methods give discordant results for centuries prior to the 20th. The main area of disagreement occurs during the last 25 years of the 19th century and feeds back into the time prior to that. The solar Extreme Ultraviolet flux can be reconstructed since the 1740s [Svalgaard, 2016] and with suitable scaling fits the Svalgaard & Schatten [2016] Sunspot Group Number series since 1865 very well, so we argue that the discordant group series have problems once we move out of the 20th century, and that the community should concentrate on finding out what those are, so a true and useful consensus can emerge., Comment: 13 pages, 11 figures

We discuss recent papers very critical of our Group Sunspot Number Series (Svalgaard & Schatten [2016]). Unfortunately, we cannot support any of the concerns they raise. We first show that almost always there is simple proportionality between the group counts by different observers and that taking the small, occasional, non-linearities into account makes very little difference. Among other examples: we verify that the RGO group count was drifting the first twenty years of observations. We then show that our group count matches the diurnal variation of the geomagnetic field with high fidelity, and that the heliospheric magnetic field derived from geomagnetic data is consistent with our group number series. We evaluate the 'correction matrix' approach [Usoskin et al. 2016] and show that it fails to reproduce the observational data. We clarify the notion of daisy-chaining and point out that our group number series has no daisy-chaining for the period 1794-1996 and therefore no accumulation of errors over that span. We compare with the cosmic ray record for the last 400+ years and find good agreement. We note that the Active Day Fraction method (of Usoskin et al.) has the fundamental problem that at sunspot maximum, every day is an 'active day' so ADF is nearly always unity and thus does not carry information about the statistics of high solar activity. This 'information shadow' occurs for even moderate group numbers and thus need to be extrapolated to higher activity. The ADF method also fails for 'equivalent observers' who should register the same group counts, but do not. We conclude that the criticism of Svalgaard & Schatten [2016] is invalid and detrimental to progress in the important field of long-term variation of solar activity., Comment: 53 pages, 59 figures

A “Solar Dynamo” (SODA) Index prediction of the amplitude of Solar Cycle 25 is described. The SODA Index combines values of the solar polar magnetic field and the solar spectral irradiance at 10.7 cm to create a precursor of future solar activity. The result is an envelope of solar activity that minimizes the 11-year period of the sunspot cycle. We show that the variation in time of the SODA Index is similar to several wavelet transforms of the solar spectral irradiance at 10.7 cm. Polar field predictions for Solar Cycles 21 – 24 are used to show the success of the polar field precursor in previous sunspot cycles. Using the present value of the SODA index, we estimate that the next cycle’s smoothed peak activity will be about 140 ± 30 solar flux units for the 10.7 cm radio flux and a Version 2 sunspot number of 135 ± 25. This suggests that Solar Cycle 25 will be comparable to Solar Cycle 24. The estimated peak is expected to occur near 2025.2 ± 1.5 year. Because the current approach uses data prior to solar minimum, these estimates may improve as the upcoming solar minimum draws closer.

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 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.

It has recently been reported that the total radiative emission variations from solar type stars exceeds the currently solar constant variations (from spacecraft over the last decade) by a factor near 4. Aside from other remote alternatives, this suggests three clear possibilities: (1) the Sun may undergo irradiance variations several times larger than any we have seen; (2) our Sun is highly unusual with regard to its radiative output; or (3) our terrestrial position in the heliosphere provides a special vantage point which reduces the observed solar irradiance variations. We investigate the last possibility by considering the influence of observer latitude upon calculated irradiance variations using a simple model for emission from solar contrast features. We consider modeled sunspots, faculae, and network structures. As the latitude angle of the observer rises relative to the heliographic equator, sunspot deficit contributions diminish and facular plus network contributions escalate. We find that the observing latitude can influence the irradiance variations by a factor near 6. When we integrate the irradiance variations, over the celestial sphere, they average to 3 times the terrestrial effect, suggesting that the solar cycle luminosity variations are proportionally, 3 times larger than the solar constant variations. Thus we suggest the Sun's luminosity output varies even more strongly with the solar cycle than is apparent in the solar constant variations. The influence of the observer viewing angle relative to stellar spin axis, studied here, may be possible to investigate with a thorough statistical examination of other type stars. Additionally, the rotational modulation due to active regions (as a function of observer viewing angle) may also be a valuable are for future investigation.

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 Sun's 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 Sun's 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 Sun's convective energy transport. Although changes in the Sun's 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 pillas 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 depatures 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, approx. 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.

In this paper, we briefly review the 'dynamo' and 'geomagnetic precursor' methods of long-term solar activity forecasting. These methods depend upon the most basic aspect of dynamo theory to predict future activity, future magnetic field arises directly from the magnification of pre-existing magnetic field. We then generalize the dynamo technique, allowing the method to be used at any phase of the solar cycle, through the development of the 'Solar Dynamo Amplitude' (SODA) index. This index is sensitive to the magnetic flux trapped within the Sun's convection zone but insensitive to the phase of the solar cycle. Since magnetic fields inside the Sun can become buoyant, one may think of the acronym SODA as describing the amount of buoyant flux. Using the present value of the SODA index, we estimate that the next cycle's smoothed peak activity will be about 210 +/- 30 solar flux units for the 10.7 cm radio flux and a sunspot number of 170 +/- 25. This suggests that solar cycle #23 will be large, comparable to cycle #22. The estimated peak is expected to occur near 1999.7 +/- 1 year. Since the current approach is novel (using data prior to solar minimum), these estimates may improve when the upcoming solar minimum is reached.

Herschel's 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.

An introduction to the background of Sir William Herschel's notebooks and the historical context within which his observations were made are provided. The observations have relevance in reconstructing solar behavior, as discussed in a separate analysis paper by Hoyt and Schatten (1992), and in understanding active features on the sun such as faculae. The text of Herschel's notebooks with modern terms used throughout forms the body of this paper. The complete text has not previously been published and is not easily accessible to scholars. Herschel used different words for solar features than are used today, and thus, for clarity, his terminology is changed on two occasions. A glossary explains the terminology changed. In the text of the notebooks, several contemporaries are mentioned; a brief description of Herschel's colleagues is provided.

Faculae appear increasingly bright toward the limb of the sun. Recent observations also have shown that, in the infrared, these features appear dark at disk center. It is demonstrated that the hillock model of Schatten et al. (1986) can describe the essential features of these observations. In light of this model, a simple explanation is given for the contrast behavior of faculae. The observations are discussed in the context of the alternative well model.

Sunspots and faculae were modeled using a modified stellar envelope code. Downflow velocities of 50 m/sec can achieve a 1,000 K drop in the surface temperature of the photosphere and reduce the surface irradiance to half its value. Concurrently, a 600 km Wilson depression forms that is associated with the enhanced density of the cooler gases. Similar upflow velocities provide for slightly enhanced temperatures and 150 km uplifted surfaces for faculae. The calculations show that, to first approximation, sunspot and facular structures (in density, temperature and pressure) can be obtained by simply vertically shifting the undisturbed photospheric materials to form wells and hillock geometries, respectively. However, the chromospheric manifestations of these features can be quite different owing to the influence of the magnetic field and flow.

Discussed here is the solar constant model published recently (Schatten, 1988), but with a modified phasing and amplitude. This model enables the known solar constant variations to be calculated from known active region and quiet region solar parameters. The features which can be modelled are sunspots and faculae, the only two features which mark the photospheric continuum with their unusual contrast behavior. They include both the active region features (sunspots and faculae) and the quiet region features (global faculae). Although the direct influences of sunspots upon the solar constant leads to short term decreases, an opposite, nearly in phase, 11 year variation in the solar constant is modelled, thereby agreeing with the Active Cavity Radiometer Irradiance Monitor (ACRIM) and Earth Radiation Budget (ERB) secular trends observed. This opposite behavior results primarily from global faculae (polar, network, and active region). The main contributors to the global behavior are the network faculae. The model attributes the observed variations in the solar constant entirely to magnetic features in the solar atmosphere. The present model serves purely to model the secular (long term) trend in the solar constant. The model suggests a change of approx. 0.5 W/sq m for the differences between the late twentieth century solar constant and the 17th century solar constant. This supports Eddy's view that this difference could give rise to the glacial increase during the little ice age of the 17th century. Important for present day climate studies, is that it shows the recent peak activity (peaking in 1958) is associated with an atypically high value of the solar constant, with respect to the past few hundred years.

The conference on The Climate Impact of Solar Variability, was held at Goddard Space Flight Center from April 24 to 27, 1990. In recent years they developed a renewed interest in the potential effects of increasing greenhouse gases on climate. Carbon dioxide, methane, nitrous oxide, and the chlorofluorocarbons have been increasing at rates that could significantly change climate. There is considerable uncertainty over the magnitude of this anthropogenic change. The climate system is very complex, with feedback processes that are not fully understood. Moreover, there are two sources of natural climate variability (volcanic aerosols and solar variability) added to the anthropogenic changes which may confuse our interpretation of the observed temperature record. Thus, if we could understand the climatic impact of the natural variability, it would aid our interpretation and understanding of man-made climate changes.