List of Figures

View Image Figure 1:
Sunspot groups observed each year from 1826 to 1843 by Heinrich Schwabe (1844). These data led Schwabe to his discovery of the sunspot cycle.
View Image Figure 2:
Monthly averages of the daily International Sunspot Number. This illustrates the solar cycle and shows that it varies in amplitude, shape, and length. Months with observations from every day are shown in black. Months with 1 – 10 days of observation missing are shown in green. Months with 11 – 20 days of observation missing are shown in yellow. Months with more than 20 days of observation missing are shown in red. [Missing days from 1818 to the present were obtained from the International daily sunspot numbers. Missing days from 1750 to 1818 were obtained from the Group Sunspot Numbers and probably represent an over estimate.]
View Image Figure 3:
Boulder Sunspot Number vs. the International Sunspot Number at monthly intervals from 1981 to 2007. The average ratio of the two is 1.55 and is represented by the solid line through the data points. The Boulder Sunspot Numbers can be brought into line with the International Sunspot Numbers by using a correction factor k = 0.65 for Boulder.
View Image Figure 4:
American Sunspot Number vs. the International Sunspot Number at monthly intervals from 1944 to 2006. The average ratio of the two is 0.97 and is represented by the solid line through the data points.
View Image Figure 5:
Group Sunspot Number vs. the International Sunspot Number at monthly intervals from 1874 to 1995. The average ratio of the two is 1.01 and is represented by the solid line through the data points.
View Image Figure 6:
RGO Sunspot Area vs. the International Sunspot Number at monthly intervals from 1997 to 2010. The two quantities are correlated at the 99.4% level with a proportionality constant of about 16.7.
View Image Figure 7:
USAF/NOAA Sunspot Area vs. the International Sunspot Number at monthly intervals from 1977 to 2007. The two quantities are correlated at the 98.9% level with a proportionality constant of about 11.3. These sunspot areas have to be multiplied by a factor 1.48 to bring them into line with the RGO sunspot areas.
View Image Figure 8:
Sunspot area as a function of latitude and time. The average daily sunspot area for each solar rotation since May 1874 is plotted as a function of time in the lower panel. The relative area in equal area latitude strips is illustrated with a color code in the upper panel. Sunspots form in two bands, one in each hemisphere, that start at about 25° from the equator at the start of a cycle and migrate toward the equator as the cycle progresses.
View Image Figure 9:
10.7cm Radio Flux vs. International Sunspot Number for the period of August 1947 to March 2009. Data obtained prior to cycle 23 are shown with filled dots while data obtained during cycle 23 are shown with open circles. The Holland and Vaughn formula relating the radio flux to the sunspot number is shown with the solid line. These two quantities are correlated at the 99.7% level.
View Image Figure 10:
Daily measurements of the Total Solar Irradiance (TSI) from instruments on different satellites. The systematic offsets between measurements taken with different instruments complicate determinations of the long-term behavior.
View Image Figure 11:
The PMOD composite TSI vs. International Sunspot Number. The filled circles represent smoothed monthly averages for cycles 21 and 22. The open circles represent the data for cycle 23. While the TSI at the minima preceding cycles 21 and 22 were similar in this composite, the TSI as cycle 23 approaches minimum is significantly lower. The TSI at cycle 23 maximum was similar to that in cycles 21 and 22 in spite of the fact that the sunspot number was significantly lower for cycle 23.
View Image Figure 12:
Hale’s Polarity Laws. A magnetogram from sunspot cycle 22 (1989 August 2) is shown on the left with yellow denoting positive polarity and blue denoting negative polarity. A corresponding magnetogram from sunspot cycle 23 (2000 June 26) is shown on the right. Leading spots in one hemisphere have opposite magnetic polarity to those in the other hemisphere and the polarities flip from one cycle to the next.
Watch/download Movie Figure 13: (avi-Movie; 26984 KB)
Movie: A full-disk magnetogram from NSO/KP used in constructing magnetic synoptic maps over the last two sunspot cycles. Yellows represent magnetic field directed outward. Blues represent magnetic field directed inward.
View Image Figure 14:
A Magnetic Butterfly Diagram constructed from the longitudinally averaged radial magnetic field obtained from instruments on Kitt Peak and SOHO. This illustrates Hale’s Polarity Laws, Joy’s Law, polar field reversals, and the transport of higher latitude magnetic field elements toward the poles.
View Image Figure 15:
Monthly M- and X-class flares vs. International Sunspot Number for the period of March 1976 to January 2010. These two quantities are correlated at the 94.8% level but show significant scatter when the sunspot number is high (greater than 100).
View Image Figure 16:
Monthly X-class flares and International Sunspot Number. X-class flares can occur at any phase of the sunspot cycle – including cycle minimum.
View Image Figure 17:
Geomagnetic activity and the sunspot cycle. The geomagnetic activity index aa is plotted in red. The sunspot number (divided by five) is plotted in black.
View Image Figure 18:
Geomagnetic activity index aa vs. Sunspot Number. As Sunspot Number increases the baseline level of geomagnetic activity increases as well.
View Image Figure 19:
The smoothed R- and I-components of the geomagnetic index aa.
View Image Figure 20:
Cosmic Ray flux from the Climax Neutron Monitor and rescaled Sunspot Number. The monthly averaged neutron counts from the Climax Neutron Monitor are shown by the solid line. The monthly averaged sunspot numbers (multiplied by five and offset by 4500) are shown by the dotted line. Cosmic ray variations are anti-correlated with solar activity but with differences depending upon the Sun’s global magnetic field polarity (A+ indicates periods with positive polarity north pole while A– indicates periods with negative polarity).
View Image Figure 21:
Signal transmission for filters used to smooth monthly sunspot numbers. The 13-month running mean and the 12-month average pass significant fractions (as much as 20%) of signals with frequencies higher than 1/year. The 24-month FWHM Gaussian passes less than 0.3% of those frequencies and passes less than about 1% of the signal with frequencies of 1/2-years or higher.
View Image Figure 22:
The left panel shows cycle periods as functions of Cycle Number. Filled circles give periods determined from minima in the 13-month mean while open circles give periods determined from the 24-month Gaussian smoothing. Both measurements give a mean period of about 131 months with a standard deviation of about 14 months. The “Wilson Gap” in periods between 125 and 134 months from the 13-month mean is shown with the dashed lines. The right panel shows histograms of cycle periods centered on the mean period with bin widths of one standard deviation. The solid lines show the distribution from the 13-month mean while the dashed lines show the distribution for the 24-month Gaussian. The periods appear normally distributed and the “Wilson Gap” is well populated with the 24-month Gaussian smoothed data.
View Image Figure 23:
The left panel shows cycle amplitudes as functions of cycle number. The filled circles show the 13-month mean maxima with the Group Sunspot Numbers while the open circles show the maxima with the International Sunspot Numbers. The right panel shows the cycle amplitude distributions (solid lines for the Group values, dotted lines for the International values). The Group amplitudes are systematically lower than the International amplitudes for cycles prior to cycle 12 and have a nearly normal distribution. The amplitudes for the International Sunspot Number are skewed toward higher values.
View Image Figure 24:
The average of cycles 1 to 22 (thick line) normalized to the average amplitude and period. The average cycle is asymmetric in time with a rise to maximum over 4 years and a fall back to minimum over 7 years. The 22 individual, normalized cycles are shown with the thin lines.
View Image Figure 25:
The average cycle (solid line) and the Hathaway et al. (1994) functional fit to it (dotted line) from Equation (6View Equation). This fit has the average cycle starting 4 months prior to minimum, rising to maximum over the next 54 months, and continuing about 18 months into the next cycle.
View Image Figure 26:
The Waldmeier Effect. The cycle rise time (from minimum to maximum) plotted versus cycle amplitude for International Sunspot Number data from cycles 1 to 23 (filled dots) and for 10.7 cm Radio Flux data from cycles 19 to 23 (open circles). This gives an inverse relationship between amplitude and rise time shown by the solid line for the Sunspot Number data and with the dashed line for the Radio Flux data. The Radio Flux maxima are systematically later than the Sunspot number data as also seen in Table 4.
View Image Figure 27:
The Amplitude–Period Effect. The period of a cycle (from minimum to minimum) plotted versus following cycle amplitude for International Sunspot Number data from cycles 1 to 22. This gives an inverse relationship between amplitude and period shown by the solid with Amplitude(n+1) = 380 – 2 × Period(n).
View Image Figure 28:
Latitude positions of the sunspot area centroid in each hemisphere for each Carrington Rotation as functions of time from cycle minimum. Three symbol sizes are used to differentiate data according to the daily average of the sunspot area for each hemisphere and rotation. The centroids of the centroids in 6-month intervals are shown with the red line for large amplitude cycles, with the green line for medium amplitude cycles, and with the blue line for the small amplitude cycles.
View Image Figure 29:
Latitudinal widths of the sunspot area centroid in each hemisphere for each Carrington Rotation as functions of time from cycle minimum. Three symbol sizes are used to differentiate data according to the daily average of the sunspot area for each hemisphere and rotation. The centroids of the centroids in 6-month intervals are shown with the red line for large amplitude cycles, with the green line for medium amplitude cycles, and with the blue line for the small amplitude cycles.
View Image Figure 30:
Absolute north–south asymmetry (North – South) in four different activity indicators. Sunspot area is plotted in black. The Flare Index scaled by 146 is shown in red. The number of sunspot groups scaled by 443 is shown in green. The Magnetic Index scaled by 234 is plotted in blue.
View Image Figure 31:
Smoothed north–south asymmetry in sunspot area. The hemispheric difference is shown with the solid line while the total area scaled by 1/10 is shown with the dotted line.
View Image Figure 32:
Active longitudes in sunspot area. The normalized sunspot area in 5° longitude bins is plotted in the upper panel (a) for the years 1878 – 2009. The dotted lines represent two standard errors in the normalized values. The sunspot area in several longitude bins meets or exceeds these limits. The individual cycles (12 through 23) are shown in the lower panel (b) with the normalized values offset in the vertical by the cycle number. Some active longitudes appear to persist from cycle to cycle.
View Image Figure 33:
The Maunder Minimum. The yearly averages of the daily Group Sunspot Numbers are plotted as a function of time. The Maunder Minimum (1645 – 1715) is well observed in this dataset.
View Image Figure 34:
The Gleissberg Cycle. The best fit of cycle amplitudes to a simple sinusoidal function of cycle number is shown by the solid line (which includes the secular trend).
View Image Figure 35:
Gnevyshev–Ohl Rule. The ratio of the odd cycle sunspot sum to the preceding even cycle sunspot sum is shown with the filled circles. The ratio of the odd cycle amplitude to the preceding even cycle amplitude is shown with the open circles.
View Image Figure 36:
Short-term variations. The lower panel shows the daily International Sunspot Number (SSN) smoothed with a 24-rotation FWHM Gaussian. The upper panel shows the residual SSN signal smoothed with a 54-day Gaussian and sampled at 27-day intervals.
View Image Figure 37:
Morlet wavelet transform spectrum of the bandpass-limited daily International Sunspot Number. Increasing wavelet power is represented by colors from black through blue, green, and yellow to red. The Cone-Of-Influence is shown with the white curves. Periods of 154-days are indicated by the horizontal red line.
View Image Figure 38:
Predictions for cycles 22 and 23 using the Modified McNish–Lincoln (M-M-L) auto-regression technique and the Hathaway, Wilson, and Reichmann (H-W-R) curve-fitting technique 24 months after the minima for each cycle.
View Image Figure 39:
Ohl’s method for predicting cycle amplitudes using the minima in the smoothed aa index (panel a) as precursors for the maximum sunspot numbers of the following sunspot number maxima (panel b).
View Image Figure 40:
A modification of Feynman’s method for separating geomagnetic activity into a sunspot number related component and an “Interplanetary” component (panels a and b). The maxima in aaI prior to minimum are well correlated with the following sunspot number maxima (panel c).
View Image Figure 41:
Thompson method for predicting sunspot number maxima. The number of geomagnetically disturbed days in a cycle is proportional to the sum of the maxima of that cycle and the next.
View Image Figure 42:
Polar magnetic fields as measured at the Wilcox Solar Observatory. The average of the north and south field strengths near the time of sunspot cycle minimum is expected to be an indicator for the amplitude of the next sunspot cycle.