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NASA NTRS2011

An Estimate of the Size and Shape of Sunspot Cycle 24 Based on its Early Cycle Behavior using the Hathaway-Wilson-Reichmann Shape-Fitting Function

On the basis of 12-month moving averages (12-mma) of monthly mean sunspot number (R), sunspot cycle 24 had its minimum amplitude (Rm = 1.7) in December 2008. At 12 mo past minimum, R measured 8.3, and at 18 mo past minimum, it measured 16.4. Thus far, the maximum month-to-month rate of rise in 12-mma values of monthly mean sunspot number (AR(t) max) has been 1.7, having occurred at elapsed times past minimum amplitude (t) of 14 and 15 mo. Compared to other sunspot cycles of the modern era, cycle 24?s Rm and AR(t) max (as observed so far) are the smallest on record, suggesting that it likely will be a slow-rising, long-period sunspot cycle of below average maximum amplitude (RM). Supporting this view is the now observed relative strength of cycle 24?s geomagnetic minimum amplitude as measured using the 12-mma value of the aa-geomagnetic index (aam = 8.4), which also is the smallest on record, having occurred at t equals 8 and 9 mo. From the method of Ohl (the inferred preferential association between RM and aam), one predicts RM = 55 +/- 17 (the ?1 se prediction interval) for cycle 24. Furthermore, from the Waldmeier effect (the inferred preferential association between the ascent duration (ASC) and RM) one predicts an ASC longer than 48 mo for cycle 24; hence, maximum amplitude occurrence should be after December 2012. Application of the Hathaway-Wilson-Reichmann shape-fitting function, using an RM = 70 and ASC = 56 mo, is found to adequately fit the early sunspot number growth of cycle 24.

Wilson, Robert M.↗
NASA NTRS1984

Description of sunspot cycles by orthogonal functions

Based on the principal component analysis technique and evidence for a 22-yr double-sunspot cycle periodicity. The time series of sunspot numbers is represented as a sum of mutually orthogonal eigenvectors in the time domain. It is shown that the first two eigenvectors account for about 90 percent of the cumulative 'signal power,' and that this is sufficient for reconstruction of the raw data curve. It is also noted that the second eigenvector behaves as the time derivative of the first, and that a phase-plane plot of these eigenvectors (i.e. a plot of a variable vs. its rate of change) suggests that the sun's sunspot cycle is driven by an oscillator; the implication is that, embedded within the sun, a chronometer is at work (e.g. Dicke, 1979).

Teuber, D. L.↗
NASA NTRS2002

Group Sunspot Numbers: Sunspot Cycle Characteristics

We examine the "Group" sunspot numbers constructed by Hoyt and Schatten to determine their utility in characterizing the solar activity cycle. We compare smoothed monthly Group Sunspot Numbers to Zurich (International) Sunspot Numbers, 10.7-cm radio flux, and total sunspot area. We find that the Zurich numbers follow the 10.7-cm radio flux and total sunspot area measurements slightly better than the Group numbers. We examine several significant characteristics of the sunspot cycle using both Group numbers and Zurich numbers. We find that the "Waldmeier Effect" - the anti-correlation between cycle amplitude and the elapsed time between minimum and maximum of a cycle - is much more apparent in the Zurich numbers. The "Amplitude-Period Effect" the anti-correlation between cycle amplitude and the length of the previous cycle from minimum to minimum - is also much more apparent in the Zurich numbers. The "Amplitude-Minimum Effect" - the correlation between cycle amplitude and the activity level at the previous (onset) minimum is equally apparent in both the Zurich numbers and the Group numbers. The "Even-Odd Effect" - in which odd-numbered cycles are larger than their even-numbered precursors - is somewhat stronger in the Group numbers but with a tighter relationship in the Zurich numbers. The "Secular Trend" - the increase in cycle amplitudes since the Maunder Minimum - is much stronger in Group numbers. After removing this trend we find little evidence for multi-cycle periodicities like the 80 year Gleissberg cycle or the two- and three-cycle periodicities. We also find little evidence for a correlation between the amplitude of a cycle and its period or for a bimodal distribution of cycle periods. We conclude that the Group numbers are most useful for extending the sunspot cycle data further back in time and thereby adding more cycles and improving the statistics. However, the Zurich numbers are more useful for characterizing the on-going levels of solar activity.

Hathaway, D. H.↗
NASA NTRS1989

The sunspot cycle variations of the neutral line on the source surface

The earlier presentation method of the sunspot cycle variations of the neutral line on the source surface by introducing the view longitude is defined. It is shown that the neutral line seen from the view longitude and the equivalent dipole (determined by Hoeksema, 1984) showed a trend of rotation throughout the sunspot cycle. However, the surface bounded by the neutral line is generally far from a circle. In fact, our combined presentation of both the equivalnet dipole and the nuetral line indicates graphically that such a simple description of the rotating (equivalent) dipole may be misleading. The concept of an inclined dipole with respect to the rotation axis may also be misleading.

Saito, T.↗
NASA NTRS2009

Predicting the Size of Sunspot Cycle 24 on the Basis of Single- and Bi-Variate Geomagnetic Precursor Methods

Examined are single- and bi-variate geomagnetic precursors for predicting the maximum amplitude (RM) of a sunspot cycle several years in advance. The best single-variate fit is one based on the average of the ap index 36 mo prior to cycle minimum occurrence (E(Rm)), having a coefficient of correlation (r) equal to 0.97 and a standard error of estimate (se) equal to 9.3. Presuming cycle 24 not to be a statistical outlier and its minimum in March 2008, the fit suggests cycle 24 s RM to be about 69 +/- 20 (the 90% prediction interval). The weighted mean prediction of 11 statistically important single-variate fits is 116 +/- 34. The best bi-variate fit is one based on the maximum and minimum values of the 12-mma of the ap index; i.e., APM# and APm*, where # means the value post-E(RM) for the preceding cycle and * means the value in the vicinity of cycle minimum, having r = 0.98 and se = 8.2. It predicts cycle 24 s RM to be about 92 +/- 27. The weighted mean prediction of 22 statistically important bi-variate fits is 112 32. Thus, cycle 24's RM is expected to lie somewhere within the range of about 82 to 144. Also examined are the late-cycle 23 behaviors of geomagnetic indices and solar wind velocity in comparison to the mean behaviors of cycles 2023 and the geomagnetic indices of cycle 14 (RM = 64.2), the weakest sunspot cycle of the modern era.

Wilson, Robert M.↗
NASA NTRS1979

Very large geomagnetic disturbance during sunspot cycle 21: A prediction

Evidence is presented which suggests that very large geomagnetic disturbances (350 gammas or greater at an invariant magnetic latitude of 50 degrees) occur once or twice per sunspot cycle, on the average. There is also some tendency for these disturbances to group in large odd numbered sunspot cycles similar to the current cycle, cycle 21. No such disturbance was noted during the past cycle although a series of major solar flares was observed in August 1972. At least one very large geomagnetic disturbance is expected during the current cycle; a prediction with perhaps serious consequences for electric power companies.

Sargent, H. H., III↗
NASA NTRS2006

An Examination of Sunspot Number Rates of Growth and Decay in Relation to the Sunspot Cycle

On the basis of annual sunspot number averages, sunspot number rates of growth and decay are examined relative to both minimum and maximum amplitudes and the time of their occurrences using cycles 12 through present, the most reliably determined sunspot cycles. Indeed, strong correlations are found for predicting the minimum and maximum amplitudes and the time of their occurrences years in advance. As applied to predicting sunspot minimum for cycle 24, the next cycle, its minimum appears likely to occur in 2006, especially if it is a robust cycle similar in nature to cycles 17-23.

Wilson, Robert M.↗
NASA NTRS1990

On the average rate of growth in sunspot number and the size of the sunspot cycle

The average rate of growth in sunspot number over selected time intervals and the maximum average value as they both relate to the size of the cycle are examined, in order to predict the size of cycle 22. The predictions are compared with those of Wilson (1990) to determine whether a consensus is apparent. The average rate of growth during the ascending portion of the sunspot cycle, defined as the difference in smoothed sunspot number values between elapsed time t and sunspot minimum divided by t, is shown to correlate with the size of the sunspot cycle, especially for t greater or equal to 18 months. The maximum value of the average rate of growth is also shown to highly correlate (r = 0.98) with the size of the cycle. Using 4.5 as the maximum value of the average rate of growth, a lower limit for R(M) is estimated. The results show that the findings are consistent with the previous single variate predictions for R(M) for cycle 22.

Wilson, Robert M.↗
NASA NTRS1988

A prediction for the maximum phase and duration of sunspot cycle 22

A projected value of the maximum amplitude of sunspot cycle 22 is used to predict the ascent, maximum phase, and length of the cycle. It is suggested that cycle 22 will have a lower maximum amplitude than cycle 21. This would make cycle 22 a 'negative-valued' maximum amplitude first-difference cycle with an ascent with a median value of 4 years. Cycle 22 is predicted to be a long-period cycle with a length in the range of 138 + or - 8 months. It is concluded that cycle 22 will probably peak sometime in the latter half of 1990 or the first half of 1991 and that it will not end until early to mid 1998.

Wilson, Robert M.↗
NASA NTRS1985

A simulation study of two major events in the heliosphere during the present sunspot cycle

The two major disturbances in the heliosphere during the present sunspot cycle, the event of June to August, 1982, and the event of April to June, 1978, are simulated by the method developed by Hakamada and Akasofu (1982). Specifically, an attempt was made to simulate the effects of six major flares from three active regions in June and July, 1982, and April and May, 1978. A comparison of the results with the solar wind observations at Pioneer 12 (approximately 0.8 au), ISEE-3 (approximately 1 au), Pioneer 11 (approximately 7 to 13 au) and Pioneer 10 (approximately 16 to 28 au) suggests that some major flares occurred behind the disk of the sun during the two periods. The method provides qualitatively some information as to how such a series of intense solar flares can greatly disturb both the inner and outer heliospheres. A long lasting effect on cosmic rays is discussed in conjunction with the disturbed heliosphere.

Akasofu, S. I.↗
NASA NTRS1987

On the distribution of sunspot cycle periods

A comparison is made between the observed distribution of sunspot cycle periods and distributions based on uniform, normal, and bimodal distributions. The bimodal distribution, composed of short-period and long-period cycles, is found to best describe the observed distribution. Compared to the normal distribution for the most reliably determined cycles (cycles 8-20), the bimodal distribution has a residual (sum of squares of differences) that is about 86 percent smaller. Means for short-period and long-period cycles are estimated to be 122 + or - 4 months and 140 + or - 5 months, respectively.

Wilson, Robert M.↗
NASA NTRS1990

Solar rotation and the sunspot cycle

Reexamination of the published sunspot rotation rates from Mount Wilson for the period from 1921 to 1982 suggests that the sun rotates more rapidly when there are fewer sunspots. This behavior is seen over the course of each cycle with the most rapid rotation usually observed at sunspot minimum. It is also seen in hemispheric differences with the southern hemisphere, having fewer spots, rotating more rapidly than the northern hemisphere. Furthermore, the rotation rate averaged over each cycle also shows that the sun rotates more rapidly during cycles with fewer sunspots and less sunspots area. This inverse correlation between sunspot area and rotation rate suggests that during the Maunder minimum the sun may have rotated slightly faster than is observed today.

Hathaway, David H.↗
NASA NTRS1976

Three-dimensional structure of the extended solar magnetic field and the sunspot cycle variation in cosmic ray intensity

A principal cause for the eleven-year sunspot cycle variation in the primary cosmic ray intensity observed at earth may be a variation in the solid angle of the heliosphere occupied by the extended solar polar magnetic field. Galactic cosmic rays have relatively easy access to the inner solar system through the regular extended solar polar fields, and relatively difficult access through the irregular extended solar sector structure fields.

Svalgaard, L.↗