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NASA NTRS1998

Estimating the Size and Timing of Maximum Amplitude for Cycle 23 from Its Early Cycle Behavior

On the basis of the lowest observed smoothed monthly mean sunspot number, cycle 23 appears to have conventionally begun in May 1996, in conjunction with the first appearance of a new cycle, high-latitude spot-group. Such behavior, however, is considered rather unusual, since, previously (based upon the data- available cycles 12-22), the first appearance of a new cycle, high-latitude spot- group has always preceded conventional onset by at least 3 months. Furthermore, accepting May 1996 as the official start for cycle 23 poses a dilemma regarding its projected size and timing of maximum amplitude. Specifically, from the max-min and amplitude-period relationships we infer that cycle 23 should be above average in size and a fast riser, with maximum amplitude occurring before May 2000 (being in agreement with projections for cycle 23 based on precursor information), yet from its initial languid rate of rise (during the first 6 months of the cycle) we infer that it should be below average in size and a slow riser, with maximum amplitude occurring after May 2000. The dilemma vanishes, however, when we use a slightly later-occurring onset. For example, using August 1996, a date associated with a local secondary minimum prior to the rapid rise that began shortly thereafter (in early 1997), we infer that cycle 23's rate of rise is above that for the mean of cycles 1-22, the mean of cycles 10-22 (the modern era cycles), the mean of the modern era'fast risers,' and the largest of the modern era 'slow risers' (i.e., cycle 20), thereby, suggesting that cycle 23 will be both fast-rising and above average in size, peaking before August 2000. Additionally, presuming cycle 23 to be a well- behaved fast-rising cycle (regardless of whichever onset date is used), we also infer that its maximum amplitude likely will measure about 144.0 q+/- 28.8 (from the general behavior found for the bulk of modern era fast risers; i.e., 5 of 7 have had their maximum amplitude to lie within 20% of the mean curve for modern era fast risers). It is apparent, then, that sunspot number growth during 1998 will prove crucial for correctly establishing the size and shape of cycle 23.

Wilson, Robert M.↗
NASA NTRS1992

On the variation of the Nimbus 7 total solar irradiance

For the interval December 1978 to April 1991, the value of the mean total solar irradiance, as measured by the Nimbus-7 Earth Radiation Budget Experiment channel 10C, was 1,372.02 Wm(exp -2), having a standard deviation of 0.65 Wm(exp -2), a coefficient of variation (mean divided by the standard deviation) of 0.047 percent, and a normal deviate z (a measure of the randomness of the data) of -8.019 (inferring a highly significant non-random variation in the solar irradiance measurements, presumably related to the action of the solar cycle). Comparison of the 12-month moving average (also called the 13-month running mean) of solar irradiance to those of the usual descriptors of the solar cycle (i.e., sunspot number, 10.7-cm solar radio flux, and total corrected sunspot area) suggests possibly significant temporal differences. For example, solar irradiance is found to have been greatest on or before mid 1979 (leading solar maximum for cycle 21), lowest in early 1987 (lagging solar minimum for cycle 22), and was rising again through late 1990 (thus, lagging solar maximum for cycle 22), having last reported values below those that were seen in 1979 (even though cycles 21 and 22 were of comparable strength). Presuming a genuine correlation between solar irradiance and the solar cycle (in particular, sunspot number) one infers that the correlation is weak (having a coefficient of correlation r less than 0.84) and that major excursions (both as 'excesses' and 'deficits') have occurred (about every 2 to 3 years, perhaps suggesting a pulsating Sun).

Wilson, Robert M.↗
NASA NTRS1974

Comparison of activity in solar cycles 18, 19, and 20

Although solar activity cycles are in general remarkably similar, cycles 18, 19, and 20, with maximums in 1947.5, 1958.2, and 1968.9, respectively, differed in the heights of their maximums, in the patterns of their development, and to a certain extent in the character of their manifestations of solar activity. Of the 20 solar cycles since 1755, the maximums in sunspot numbers for cycles 18, 19, and 20 rank as 3, 1, and 10, respectively. Cycle 18, with a maximum smoothed monthly sunspot number of 151.8, was the cycle of 'giant' spots. Cycle 19, with the highest recorded maximum, 201.3, included many large spots but failed to produce spots with areas equal to those of cycle 18. The highest known daily 2800-MHz flux occurred in cycle 18, not in cycle 19. Cycle 20, with a sunspot maximum of only 110.6, appears to have been close to the average cycle of the last 220 years. An attempt is made to compare the general levels of flare production in the three cycles. Cycle 19 is estimated to have been more flare-rich than cycle 18 by a much smaller factor than the original data implied. In cycle 20, general flare production drops conspicuously.

Dodson, H. W.↗
NASA NTRS2018

Effects of Version 2 of the International Sunspot Number on Naive Predictions of Solar Cycle 25

The recalibration of the International Sunspot Number brings new challenges to predictions of Solar Cycle 25. One is that the list of extrema for the original series is no longer usable because the values of all maxima and minima are different for the new version of the sunspot number. Timings of extrema are less sensitive to the recalibration but are a natural result of the calculation. Predictions of Solar Cycle 25 published before 2016 must be converted to the new version of the sunspot number. Any prediction method that looks across the entire time span will have to be reconsidered because values in the nineteenth century were corrected by a larger factor than those in the twentieth century. We report a list of solar maxima and minima values and timings based on the recalibrated sunspot number. Naïve forecasts that depend only on the current values of the time series are common in economic studies. Several naïve predictions of Solar Cycle 25, the climatological average (180 ± 60), two versions of the inertial forecast, and two versions of the even-odd forecast, are derived from that table. The climatological average forecast is the baseline for more accurate predictions and the initial forecast in assimilative models of the Sun. It also provides the error estimate for Monte Carlo techniques that anticipate the long-term effects on the terrestrial environment. The other four predictions are shown to be statistically insignificant.

Pesnell, W. Dean↗
NASA NTRS2004

Application of the Maximum Amplitude-Early Rise Correlation to Cycle 23

On the basis of the maximum amplitude-early rise correlation, cycle 23 could have been predicted to be about the size of the mean cycle as early as 12 mo following cycle minimum. Indeed, estimates for the size of cycle 23 throughout its rise consistently suggested a maximum amplitude that would not differ appreciably from the mean cycle, contrary to predictions based on precursor information. Because cycle 23 s average slope during the rising portion of the solar cycle measured 2.4, computed as the difference between the conventional maximum (120.8) and minimum (8) amplitudes divided by the ascent duration in months (47), statistically speaking, it should be a cycle of shorter period. Hence, conventional sunspot minimum for cycle 24 should occur before December 2006, probably near July 2006 (+/-4 mo). However, if cycle 23 proves to be a statistical outlier, then conventional sunspot minimum for cycle 24 would be delayed until after July 2007, probably near December 2007 (+/-4 mo). In anticipation of cycle 24, a chart and table are provided for easy monitoring of the nearness and size of its maximum amplitude once onset has occurred (with respect to the mean cycle and using the updated maximum amplitude-early rise relationship).

Willson, Robert M.↗
NASA NTRS2015

The Peculiar Behavior of Halo Coronal Mass Ejections in Solar Cycle 24

We report on the remarkable finding that the halo coronal mass ejections (CMEs) in cycle 24 are more abundant than in cycle 23, although the sunspot number in cycle 24 has dropped by approx. 40%. We also find that the distribution of halo-CME source locations is different in cycle 24: the longitude distribution of halos is much flatter with the number of halos originating at a central meridian distance greater than or equal to 60deg twice as large as that in cycle 23. On the other hand, the average speed and associated soft X-ray flare size are the same in both cycles, suggesting that the ambient medium into which the CMEs are ejected is significantly different. We suggest that both the higher abundance and larger central meridian longitudes of halo CMEs can be explained as a consequence of the diminished total pressure in the heliosphere in cycle 24. The reduced total pressure allows CMEs to expand more than usual making them appear as halos.

coronal mass ejections↗
NASA NTRS1999

Comment on "The Predicted Size of Cycle 23 Based on the Inferred three-cycle Quasiperiodicity of the Planetary Index Ap"

Recently, Ahluwalia reviewed the solar and geomagnetic data for the last 6 decades and remarked that these data "indicate the existence of a three-solar-activity-cycle quasiperiodicity in them." Furthermore, on the basis of this inferred quasiperiodicity, he asserted that cycle 23 represents the initial cycle in a new three-cycle string, implying that it "will be more modest (a la cycle 17) with an annual mean sunspot number count of 119.3 +/- 30 at the maximum", a prediction that is considerably below the consensus prediction of 160 +/- 30 by Joselin et al. and of similar predictions by others based on a variety of predictive techniques. Several major sticking points of Ahluwalia's presentation, however, must be readdressed, and these issues form the basis of this comment. First, Ahluwalia appears to have based his analysis on a data set of Ap index values that is erroneous. For example, he depicts for the interval of 1932-1997 the variation of the Ap index in terms of annual averages, contrasting them against annual averages of sunspot number (SSN), and he lists for cycles 17-23 the minimum and maximum value of each, as well as the years in which they occur and a quantity which he calls "Amplitude" (defined as the numeric difference between the maximum and minimum values). In particular, he identifies the minimum Ap index (i.e., the minimum value of the Ap index in the vicinity of sunspot cycle minimum, which usually occurs in the year following sunspot minimum and which will be called hereafter, simply, Ap min) and the year in which it occur for cycles 17 - 23 respectively.

Wilson, Robert M.↗
NASA NTRS2004

Recent Progress in Understanding the Sun's Magnetic Dynamo

100 years ago we thought that the Sun and stars shone as a result of slow gravitational contraction over a few tens of millions of years - putting astronomers at odds with geologists who claimed that the Earth was much, much older. That mystery was solved in the 1920s and 30s with the discovery of nuclear energy (proving that the geologists had it right all along). Other scientific mysteries concerning the Sun have come and gone but three major mysteries remain: 1) How does the Sun produce sunspots with an 11-year cycle? 2) What produces the huge explosions that result in solar flares, prominence eruptions, and coronal mass ejections? and 3) Why is the Sun's outer atmosphere, the corona, so darned hot? Recent progress in solar astronomy reveals a single key to understanding all three of these mysteries.The 11-year time scale for the sunspot cycle indicates the presence of a magnetic dynamo within the Sun. For decades this dynamo was though to operate within the Sun's convection zone - the outmost 30% of the Sun where convective currents transport heat and advect magnetic lines of force. The two leading theories for the dynamo had very different models for the dynamics of the convection zone. Actual measurements of the dynamics using the techniques of helioseismology showed that both of these models had to be wrong some 20 years ago. A thin layer of strongly sheared flow at the base of the convection zone (now called the tachocline) was then taken to be the seat of the dynamo. Over the last 10 years it has become apparent that a weak meridional circulation within the convection zone also plays a key role in the dynamo. This meridional circulation has plasma rising up from the tachocline in the equatorial regions, spreading out toward the poles at a top speed of about 10-20 m/s at the surface, sinking back down to the tachocline in the polar regions, and then flowing back toward the equator at a top speed of about 1-2 m/s in the tachocline itself. Recent dynamo models that include this meridional flow now appear to have some power for predicting the size of future sunspot cycles.

Hathaway, David. H.↗
NASA NTRS2016

Solar Activity Studies using Microwave Imaging Observations

We report on the status of solar cycle 24 based on polar prominence eruptions (PEs) and microwave brightness enhancement (MBE) information obtained by the Nobeyama radioheliograph. The north polar region of the Sun had near-zero field strength for more than three years (2012-2015) and ended only in September 2015 as indicated by the presence of polar PEs and the lack of MBE. The zero-polar-field condition in the south started only around 2013, but it ended by June 2014. Thus the asymmetry in the times of polarity reversal switched between cycle 23 and 24. The polar MBE is a good proxy for the polar magnetic field strength as indicated by the high degree of correlation between the two. The cross-correlation between the high- and low-latitude MBEs is significant for a lag of approximately 5.5 to 7.3 years, suggesting that the polar field of one cycle indicates the sunspot number of the next cycle in agreement with the Babcock-Leighton mechanism of solar cycles. The extended period of near-zero field in the north-polar region should result in a weak and delayed sunspot activity in the northern hemisphere in cycle 25.

microwave radio emission↗
NASA NTRS1982

Sunspot time series - Spectrum from square law modulation of the Hale cycle

The spectrum of the sunspot index can be qualitatively accounted for by a very simple time series model which the Hale 22 year cycle dominates; the series is amplitude modulated at the 90 year Gleissberg period with an index of 25%. The square of the modulated Hale cycle reproduces all of the spectral lines of the Zurich sunspot index spectrum, provided that a small offset is included in the Hale carrier. Without this, evidence of the 22 year periodicity disappears. The squaring explains the dominance of the 11 year cycle which is an artifact of the modulation as is the 45 year line. The offset suggests a small relict magnetic field in the sun's core. Lastly Gilliland (1981) finds a radial eigenmode in the sun with period of 76 + or - 8 years suggestive of a physical basis for the Gleissberg modulation.

Sonett, C. P.↗
NASA NTRS1988

On the long-term secular increase in sunspot number

A two-parameter secular fit is extended to the sum of the monthly mean sunspot numbers over the entire cycle, R(sum), and the mean sunspot number for the cycle, R(mean). Both R(sum) and R(mean) are shown to be highly correlated with the maximum amplitude of the sunspot cycle, R(max). Application of the theory to cycle 22 indicates that the present cycle will have an R(max) of 74 + or - 49.0.

Wilson, Robert M.↗
NASA NTRS2006

Examination of the Armagh Observatory Annual Mean Temperature Record, 1844-2004

The long-term annual mean temperature record (1844-2004) of the Armagh Observatory (Armagh, Northern Ireland, United Kingdom) is examined for evidence of systematic variation, in particular, as related to solar/geomagnetic forcing and secular variation. Indeed, both are apparent in the temperature record. Moving averages for 10 years of temperature are found to highly correlate against both 10-year moving averages of the aa-geomagnetic index and sunspot number, having correlation coefficients of approx. 0.7, inferring that nearly half the variance in the 10-year moving average of temperature can be explained by solar/geomagnetic forcing. The residuals appear episodic in nature, with cooling seen in the 1880s and again near 1980. Seven of the last 10 years of the temperature record has exceeded 10 C, unprecedented in the overall record. Variation of sunspot cyclic averages and 2-cycle moving averages of temperature strongly associate with similar averages for the solar/geomagnetic cycle, with the residuals displaying an apparent 9-cycle variation and a steep rise in temperature associated with cycle 23. Hale cycle averages of temperature for even-odd pairs of sunspot cycles correlate against similar averages for the solar/geomagnetic cycle and, especially, against the length of the Hale cycle. Indications are that annual mean temperature will likely exceed 10 C over the next decade.

Wilson, Robert M.↗
NASA NTRS2007

Forecast of the Amplitude of Solar Cycle 24 Based on the Disturbed Days Precursor

R. J. Thompson (1993, Solar Physics 148, 383) exhibited a significant linear relationship between the number of geomagnetically disturbed days (those that exceed some threshold value of the Ap or nu index) in a solar cycle and the sum of the peak sunspot number in that cycle and the next cycle. Thus, the number of disturbed days during a full cycle, together with the peak sunspot number in that cycle, is a predictor of the amplitude of the next cycle. The work reported here applies Thompson's method to the current cycle. Linear relationships as described above are derived both for the pure aa record (1868-2006) and for a composite of aa (1868-1931) and Ap (1932-2006). For the composite record, the relationship between aa and Ap is determined cycle-by-cycle during the period of overlap. The method is tested for sensitivity to the adopted Ap (or equivalent aa) threshold. The highest smoothed monthly sunspot number for Cycle 24 is forecasted to be R(sub z) = 115 plus or minus 30, where the uncertainty is conservatively based on the full spread of the data around the fitted line in the sunspot number direction. In terms of smoothed monthly 10.7-cm radio flux, the forecast is F10.7 = 164 plus or minus 28.

Rabin, Douglas M.↗
NASA NTRS1988

Quasiperiodicity in cataclysmic variable stars caused by solar-type magnetic cycles

Cyclical variations of orbital periods, quiescent magnitudes and outburst intervals in the activity of cataclysmic variable binary stars are inter-related and are ascribed to variations in radii of the secondaries, caused by solar-type (sunspot) magnetic cycles. In the nova remnant DQ Herculis the observed variations in orbital period and quiescent magnitude are consistent with this mechanism. But accretion onto the white dwarf, from an accretion disk acquired from its companion, cannot explain the observed variation of the 71-second oscillations.

Warner, Brian↗
NASA NTRS1978

Updating of ADAPT predictions of sunspot activity

An eigenvector analysis procedure was used to analyze and develop algorithms for predicting sunspot numbers. The predictors in these algorithms consist of sunspot numbers from the preceding two solar cycles and magnetic index data from the preceding cycle. Predictions are presented for cycles 21 and 22. The sunspot activity for cycle 21 is predicted to remain below 100 until early 1980 when it will rapidly reach a peak of approximately 120. The two sigma accuracy on these estimates is approximately 20 sunspot numbers in the region of the peak and 10 sunspot numbers early and late in the cycle. Algorithms were also developed for predicting the period of future sunspot cycles using the same predictor vector.

Hunter, H. C.↗
NASA NTRS2007

Role of Coronal Mass Ejections in the Heliospheric Hale Cycle

The 11-year solar cycle variation in the heliospheric magnetic field strength can be explained by the temporary buildup of closed flux released by coronal mass ejections (CMEs). If this explanation is correct, and the total open magnetic flux is conserved, then the interplanetary-CME closed flux must eventually open via reconnection with open flux close to the Sun. In this case each CME will move the reconnected open flux by at least the CME footpoint separation distance. Since the polarity of CME footpoints tends to follow a pattern similar to the Hale cycle of sunspot polarity, repeated CME eruption and subsequent reconnection will naturally result in latitudinal transport of open solar flux. We demonstrate how this process can reverse the coronal and heliospheric fields, and we calculate that the amount of flux involved is sufficient to accomplish the reversal within the 11 years of the solar cycle.

Owens, M. J.↗
NASA NTRS1993

On the variation of the sun's X ray background flux and its relation to the sun's flaring rate, energetic event rate, and the solar cycle

Daily averages of the sun's X-ray background flux as measured by the GOES satellite are combined to yield monthly means and 'smoothed' monthly means (12-month moving averages) for the interval January 1986 through May 1992 (minimum rise, maximum, and initial decline of solar cycle 22). These averages are then compared directly to the sun's optical flaring rate, energetic event rate, and the usual markers of the solar cycle (e.g., sunspot number, total corrected sunspot area, and 10.7-cm solar radio flux, number of groups, and number of spots). The results of this analysis support previous findings that there exists a remarkably close positive relationship between the optical flaring rate and the X-ray background flux rate (the independent variable), and that the X-ray background flux rate can be used as a proxy for the solar cycle. Additionally, this study has found that a strong positive relationship exists between the energetic event rate and the X-ray background flux rate (the independent variable), and that the lag between the maxima of the rates of optical flaring and X-ray background flux reported for cycle 21 did not recur for cycle 22.

Wilson, Robert M.↗