GROUP SUNSPOT NUMBERS: SUNSPOT CYCLE …

1 GROUP SUNSPOT NUMBERS: SUNSPOT CYCLE CHARACTERISTICSDAVID H. HATHAWAY, ROBERT M. WILSON and EDWIN J. REICHMANNNASA/Marshall Space Flight Center, Huntsville, AL 35812, (Received 26 February 2002; accepted 17 April 2002) examine the GROUP SUNSPOT numbers constructed by Hoyt and Schatten to determinetheir utility in characterizing the solar activity CYCLE . We compare smoothed monthly GROUP sunspotnumbers to Z rich (International) SUNSPOT numbers, radio flux, and total SUNSPOT area. Wefind that the Z rich numbers follow the radio flux and total SUNSPOT area measurements onlyslightly better than the GROUP numbers. We examine several significant characteristics of the sunspotcycle using both GROUP numbers and Z rich 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 Z rich numbers. The Amplitude Period Effect the anti-correlationbetween CYCLE amplitude and the length of the previous CYCLE from minimum to minimum is alsomuch more apparent in the Z rich numbers.

2 The Amplitude Minimum Effect the correlationbetween CYCLE amplitude and the activity level at the previous (onset) minimum is equally apparent inboth the Z rich numbers and the GROUP numbers. The Even Odd Effect in which odd-numberedcycles are larger than their even-numbered precursors is somewhat stronger in the GROUP numbersbut with a tighter relationship in the Z rich numbers. The Secular Trend the increase in cycleamplitudes since the Maunder Minimum is much stronger in GROUP numbers. After removing thistrend 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 ofa CYCLE and its period or for a bimodal distribution of CYCLE periods. We conclude that the Groupnumbers are most useful for extending the SUNSPOT CYCLE data further back in time and thereby addingmore cycles and improving the statistics.

3 However, the Z rich numbers are slightly more useful forcharacterizing the on-going levels of solar IntroductionThe single most important index of solar activity has been the Z rich or Wolfsunspot number (now referred to as the International SUNSPOT number ). Thisindex, first introduced in 1848 by Rudolf Wolf, provides the longest continuousmeasure of solar activity over time (Kiepenheuer, 1953; Waldmeier, 1961;McKinnon, 1987). Initially it was provided and maintained by the Swiss FederalObservatory in Z rich, Switzerland. Today the index is provided and maintainedby the SUNSPOT Index Data Center in Brussels, Belgium, where monthly updatesare available Z rich number has proven invaluable in studies of long-term changes insolar activity, especially as related to terrestrial climate ( , Eddy, 1980; Hoyt andSchatten, 1997; Wilson, 1998a). However, certain deficiencies have been recog-nized in the record for specific intervals of time.

4 For example, during the earliestSolar Physics211:357 370, 2002. 2002 Kluwer Academic Publishers. Printed in the H. HATHAWAY, R. M. WILSON AND E. J. REICHMANN portion of the record the shapes and amplitudes of some of the cycles appear highlyquestionable ( , Baiada and Merighi, 1982; Hoyt, Schatten, and Nesmes-Ribes,1994; Hoyt and Schatten, 1995a d; Wilson, 1998b).In a recent series of papers Hoyt and Schatten (1995a d, 1998a, b) describe theirfruitful efforts at uncovering early historical records of SUNSPOT observations. Fromthis work they construct a GROUP SUNSPOT number (Hoyt and Schatten, 1998a)that is designed to be a consistent replacement or alternative to the Z rich sunspotnumber. As the name implies, this index is based purely on the number of sunspotgroups identified on the Sun. The number is normalized with a multiplicative factorto produce an activity index that closely mimics the Z rich number . By using thisindex coupled with the early solar observations they uncovered, Hoyt and Schat-ten provide a more complete record of SUNSPOT numbers dating back to Galileo sobservations in we examine the GROUP SUNSPOT number and its characteristics relative toother datasets to assess its value as an indicator of solar activity and as a tool forunderstanding the solar activity CYCLE .

5 Because the GROUP SUNSPOT number is basedupon a much larger set of observations than the Z rich SUNSPOT number , especiallyduring the early years, it is expected to provide a better description of overall Datasets and Data PreparationIn producing the Z rich SUNSPOT number index Wolf recognized the difficulty inidentifying individual spots and the importance of SUNSPOT groups. His relative SUNSPOT number index,RZ,isgivenbyRz=k(10g+n),(1)whereki s a correction factor for the observer,gis the number of identified sunspotgroups, andnis the number of individual sunspots . In spite of the apparent arbitrarynature of this formula, it has been found to correlate extremely well with other,more physical measures of solar activity such as SUNSPOT area, radio flux,X-ray flare frequency, and magnetic flux. Monthly values forRZare available from1749 onward but many of the values prior to 1849 are based on incomplete ormissing and Schatten (1998a) introduced the GROUP SUNSPOT number ,RG,asanalternative to the Z rich SUNSPOT number .

6 It uses only the number of SUNSPOT groupsbut is normalized to make it agree with the Z rich numbers during the years from1874 to 1976 when the Royal Greenwich Observatory provided daily reports on thenumber and characteristics of SUNSPOT groups. With this normalization the Groupsunspot number is given byRG=1NN i= ,(2) GROUP SUNSPOT NUMBERS: SUNSPOT CYCLE CHARACTERISTICS359whereNis the number of observers,kiis the correction factor for observeri,andgiis the number of SUNSPOT groups reported by observeri. Through the diligentefforts of Hoyt and Schatten this dataset is more complete than the Z rich values ofRGare available from 1610 albeit with missing values up to1795. Their dataset ends in 1995 but for this study we extend it to 2002 using thenumber of groups reported daily by the US National Oceanic and addition to the Z rich and GROUP SUNSPOT numbers we also consider the radio flux and SUNSPOT area measurements as alternative solar activity indicatorsthat cover several cycles.

7 The radio flux has been measured on a nearlydaily basis since early 1947. Monthly values are available from February 1947 tothe present covering nearly 5 cycles. Although the radio receivers were movedfrom Ottawa, Ontario to Penticton, British Columbia in 1990, this dataset remainsvery uniform and is often preferred as an indicator of solar activity. SUNSPOT areameasurements are available from the Royal Greenwich Observatory from 1874 to1976. We augment these data with data from the NOAA/USAF SOON networkas reported in theRegion Reportsat the NOAA web site. An inter-comparison be-tween the Greenwich, NOAA, and overlapping Mt. Wilson data (Howard, Gilman,and Gilman, 1984) indicates that the NOAA SUNSPOT areas need to be increasedby 40% to match the earlier Greenwich data. Including this correction gives areasonably uniform dataset extending from 1874 to the records of solar activity all display the inherent noisiness of the solarcycle.

8 Daily and even monthly values vary widely. The underlying characteristicsof the solar CYCLE are more evident when the data is smoothed by more than justmonthly averages. The usual smoothing is the 13-month running mean which iscentered on a given month and averages over that month and the six months beforeand after with half weights given to the monthly values on either end. Unfortunatelythis temporal filter allows many high frequencies to pass which in turn can influ-ence the statistics related to the solar CYCLE . For example, high-frequency peaksoccurring near solar minimum or maximum can give ambiguous results for thetimes and values of these extrema. Gaussian shaped filters are well known to havecleaner frequency responses. In order to smooth monthly values to see the solarcycle behavior we prefer a 24-month Gaussian average with relative weights givenbyW( t)=exp[ 2 t2/b2] exp[ 2](3 2 t2/b2),(3)where tis the number of months from the center andb(=24 months) is thefull width at half maximum.

9 Both the filter weight and its first derivative vanishat bmonths. In Figure 1 we compare the frequency response of this 24-monthGaussian to that of the 13-month running mean. The 13-month running meanpasses significant signal at frequencies much greater than a CYCLE -per-year whilethe 24-month Gaussian suppresses all of these higher frequencies as well as thosewith frequencies as low as one CYCLE in two H. HATHAWAY, R. M. WILSON AND E. J. REICHMANNF igure transmission factors for the 13-month running mean (solid line) and the 24-monthGaussian average (dashed line) as functions of signal frequency. The 13-month running mean passes20% of the signal with frequencies near cycles per year and about 4% of the signal with fre-quencies near cycles per year. The 24-month Gaussian passes less than of all signals withfrequencies greater than 1 CYCLE per rich SUNSPOT numbers (solid line), GROUP SUNSPOT numbers (dashed line), total sunspotarea (dotted line), and flux (dash-dotted line) smoothed with the 24-month Gaussian filterfor the last century.

10 A strong correlation between these indices is evident in how closely they followeach other. The utility of the 24-month Gaussian filter for solar CYCLE studies can be seen by the lackof high-frequency oscillations and the production single-peaked CYCLE maxima and monthly values forRZ,RG, SUNSPOT area, and radio flux (smoothedwith the 24-month Gaussian) are shown in Figure 2 for the last century. This figureshows how this temporal filter retains the basic CYCLE shape with uniquely definedmaxima and minima. A 12-month Gaussian (while attractive because of its shorterlength) passes enough signal with periods near 18 to 24-months to produce doublepeaked cycles with non-unique SUNSPOT NUMBERS: SUNSPOT CYCLE CHARACTERISTICS361 Figure relationship betweenRZand SUNSPOT area is shown in (a). The relationship betweenRGand SUNSPOT area is shown in (b).RZhas a slightly stronger correlation with SUNSPOT area thandoesRGand a slightly tighter fit to a linear relationship between the Comparison of SUNSPOT CYCLE CharacteristicsThe four indices plotted in Figure 2 track each other quite closely through timebut nonetheless display some differences.