An estimate for the size of cycle 23 based on near minimum conditions

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. A4, PAGES , APRIL 1, 1998 An estimate for the size of cycle 23 based on near minimum conditions Robert M. Wilson, David H. Hathaway, and Edwin J. Reichmann Space Sciences Laboratory, NASA Marshall Space Flight Center, Huntsville, Alabama Abstract. The first occurrence of a high-latitude, new cycle spot group for cycle 23 was in May 1996, in conjunction with a minimum in the smoothed monthly mean sunspot number. Since then, new cycle spot groups have become more predominant, and the smoothed monthly mean sunspot number has slowly risen. Such behavior indicates that new cycle 23 probably had its minimum annual average sunspot number, R(min), equal to 8.7, in Because this value is larger than the average for R(min), cycle 23 is expected to have a maximum amplitude, R(max), that, likewise, will be larger than average, suggesting further that it probably will be both fast rising (i.e., peaking before May 2000) and of shorter than average length (i.e., ending before May 2007). Another parameter well correlated with R(max) is the minimum amplitude of the aa geomagnetic index, aa(min), which usually occurs either in the year of R(min) occurrence or, more often, in the following year. For 1996 the annual average of aa measured Presuming this value to be aa(min) for cycle 23, we calculate cycle 23's R(max) to be about _ (i.e., the 90% prediction interval), based on the stronger (r = 0.98) bivariate fit of R(max) versus both R(min) and aa(min). Comparison of this estimate with others, using various combinations of parameters, yields an overlap in the prediction intervals for R(max) of about 168 _+ 15, a range that is within the consensus recently reported by Joselyn et al. [1997](= 160 _+ 30). Thus this study supports the view that cycle 23 will have an R(max) that will be larger than average but smaller than was seen for cycle 19, the largest cycle on record with R(max) = Introduction employ parametric values found near cycle minimum, we estimate the size of cycle 23 to be about 168 _+ 15, in terms of It has long been recognized that precursor methods (i.e., annual average sunspot number (equivalento about 174 +_ 15, those prediction techniques that are based on the notion of the in terms of smoothed monthly mean sunspot number), a range "extended solar cycle" [e.g., Ohl, 1971; Feynrnan, 1982; that suggests that cycle 23 w.ill be of larger than average size Legrand and Simon, 1991; Simon and Legrand, 1992]) offer (>117.8), faster than average rise (<48 months), and shorter the best chance of reliably predicting the size of an unfolding than average length (<132 months). Our estimate for the size sunspot cycle, especially those based on the aa and Ap geoof cycle 23, in fact, tums out to be very close to the consensus magnetic indices [e.g., Ohl and Ohl, 1979, and references recently reported by Joselyn et al. [1997] (= 160 +_ 30) and to therein; Sargent, 1978; Kane, 1978, 1987, 1989, 1992, 1997; those of Letfus [1994] (based upon a variation of the "even- Brown and Simon, 1986; Gonzalez and Schatten, 1987; odd" effect; compare Wilson [1988c, 1992]; Kopecky Wilson, 1988a, b, 1990b; Thompson, 1988, 1993; Wilson et [1991]), Krernliovsky [1994] (based upon a simple chaotic al., 1996d]. Typically, these methods utilize observed values model), Calvo et al. [1995] (based upon a neural network for particular parameters that are measureduring the declining predictive scheme), and Kane [1997](based on Ohl's precursor portion of a sunspot cycle near (to just following) sunspot method), but slightly higher than those of Schatten et al. minimum for the new cycle. Because onset for new cycle 23 [1996](based upon the "solar dynamo amplitude" index) and Li seems very likely to have already occurred, in 1996 on the [1997] (based upon an inferred variation embedded within the basis of annual averages of sunspot number and in May 1996 Ap index). on the basis of smoothed monthly mean sunspot number (i.e., the 12-month moving average of monthly mean sunspot number, or 13-month running mean, as it is more commonly called [Wilson et a/.,1997]), it now seems appropriate to 2. Sunspot Number and aa Geomagnetic Index Database begin to apply some of these methods to the problem of estimating its size (or maximum amplitude). Using various Table 1 lists selected data for cycles 8-22, those cycles selected single variate and bivariate precursor techniques that considered to be of "fair-to-best" quality sunspot data [Waldrneier, 1961; Eddy, 1977], that are useful for describing sunspot cycles, and, in particular, that have proven useful for This paper is not subject to U.S. copyright. Published in 1998 by the the prediction of maximum amplitude for sunspot cycles American Geophysical Union. [Wilson, 1990b; Wilson et al., 1996a, d]. In the table, SCN refers to the "sunspot cycle number," a sequential numbering Paper number 97JA scheme based on the long-term cyclical behavior of relative /98/97JA sunspot number [Kiepenheuer, 1953; Waldrneier, 1961; 6595

2 WILSON ET AL.: ESTIMATE FOR THE SIZE OF CYCLE 23 Table 1. Listing of Selected Data for Cycles 8-22 E E R R aa aa ASC PER SCN (min) (max) (min) (max) (min) (E(min)) class class w w F S (<14.1) S L (10.3) (10.3) S L (16.0) (16.0) F L * 7.3 S L ! 10.7' 12.6 F L S L S S ' 10.3 S S ' 16.4 F S ' 17.8 F S F S ' 17.2 S L * 22.3 F S ' 20.9 F S? Mean s.d Sunspot data are considered reliable only from The aa index begins in Values prior to 1868 are aa-equivalents, computed from Helsinki declination data that began in The aa(min) value for cycle 9 is the lowest observed value following E(min), observed in This value has been ignored in all computations. Cycle 21's actual aa(min) was 18.1, occurring in The value listed as aa(min) for cycle 21 was the observed "minimum" value in the vicinityof E(min). For ASC class, F, fast riser; S, slow riser. For PER class, s, short period; L, long period. Values of aa listed above are for the year following E(min). Schove, 1983; McKinnon, 1987]. As an example, SCN 22 refers to cycle 22 which had its onset (i.e., the epoch of minimum amplitude occurrence, E(min)) in 1986, based on annual averages of sunspot number, and its maximum (i.e., the epoch of maximum amplitude occurrence, E(max)) in The values of annual average sunspot number associated with the epochs of minimum and maximum amplitudes for cycle 22 were R(min) = 13.4 and R(max) = 157.6, respectively. In comparison to other sunspot cycles in the span of cycles 8-22, we see that cycle 22's R(max) ranks as the second largest, being slightly larger than that of cycle 21's (= 155.4) and below that of cycle 19's (= 190.2). (In terms of smoothed monthly mean sunspot number, cycle 22's maximum amplitude was slightly smaller than cycle 21's: versus ) Continuing, in the table the terms aa(min) and aa(e(min)) refer to the minimum amplitude value of the aa geomagnetic index in the vicinity of cycle minimum and to the value of the aa index for the cycle minimum year (i.e., E(min)), respectively, both expressed as annual averages. In actuality, values of the aa geomagnetic index are known only since 1868, compiled from hand-scaled K values from two, almost antipodal, observatories in England and Australia by Mayaud [1973] and Mayaud and Romana [1977]; however, recently, Nevanlinna and Kataja [1993] have generated an "aa-equivalent" index, based upon an incomplete listing of hourly declination readings of the Helsinki magnetic-meteorological observatory, that can be used to extend the record back to These aa- equivalent values are easily recognizable in Table 1 as those that are enclosed in parentheses. The purpose of the asterisks is to remind the reader that the aa(min) value usually occurs i n the year following E(min), true for 8 of 11 cycles based solely on the actual values of the aa index and for 8 of 13 cycles based on the combined record of aa and "aa-equivalent index values. In our example of cycle 22, aa(min) and aa(e(min)) measured 19.0 and 20.9, respectively, and aa(min)is observed to have occurred in the year following E(min). Also given in Table 1 are "bimodal" classes [from Wilson et al., 1996c] for each cycle, based upon a simple classification scheme that subdivide sunspot cycles, separately, according to their ascent durations (ASC) and periods (PER), as determined using smoothed monthly mean sunspot numbers. Here for the ASC class, F means that the cycle was a "fast" riser (ASC <48 months; i.e., the length of time from minimum amplitude to maximum amplitude, as determined using smoothed monthly mean sunspot numbers, was <48 months) and S means that the cycle was a "slow" riser (ASC >_48 months), and, for the PER class, S means that the cycle was of "short" period (PER <132 months; i.e., the length of time between two successive sunspot minima, as determined using smoothed monthly mean sunspot numbers, was <132 months) and L means that the cycle was of "10ng" period (PER >132 months). For our example of cycle 22 we note that its ASC (= 34 months) was shorter than 48 months; thus it is classified as a fast riser (F). Also, because the minimum smoothed monthly mean sunspot number for cycle 23 appears to have occurred in May 1996 (implying that, in the conventional sense, cycle 22 has end.ed [cf. Wilson et al., 1997]), we note that cycle 22's PER (= 116 months) is shorter than 132 months; thus it is classified as a short-period cycle (S). (Please note that, because cycle 22 can now be classified as a short-period cycle, this provides further evidence that cycle 23's R(max) will be larger than average size, from the amplitude-period effect. For example, Hathaway et al. [1994] and Wilson et al. [1996a] have found that a cycle of larger than average size usually follows a cycle of shorter than average period, while a cycle of smaller-than-average size usually follows a cycle of longerthan-average period.) Finally, the mean and standar deviation, s.d. for R(min), R(max), aa(min), and aa(e(min)) are tabulated across the bottom. Based on the sample of cycles 8-22, we note that R(min) averages about 7.1, having a range of ; R(max) averages about 117.8, having a range of ; aa(min) averages about 13.0, having a range of ; and aa(e(min)) averages about 14.1, having a range of Single Variate and Bivariate Fits for R(max) Table 1 suggests a number of statistically valid schemes for estimating the maximum amplitude, R(max), of a sunspot cycle 2-3 years (or more) in advance. For example, presuming that R(max) is distributed normally and that cycle 23 will be "well behaved" (i.e., the values of its parameters, like R(min), R(max), etc., will not be statistical outliers), we expect its R(max) to lie within the range of (based on the sample of cycles 8-22 and employing the 90% prediction interval which equals times 37.5, the standardeviation associated with R(max); is the value of t a in the Student distribution for "n minus 1" degrees of freedom (dof)(or,! 5-1 = 14 dof), where n is the sample size [Lapin, 1978, p. A-25]).

3 WILSON ET AL.: ESTIMATE FOR THE SIZE OF CYCLE Thus based on normal statistics, for cycle 23 we estimate only a 5% chance that its R(max) will be either >183.8 or <51.8. On the other hand, because four of the past five cycles are the largest cycles for the whole interval of cycles 8-22, and, as a group, cycles seem to be statistically distinct from cycles 8-14 [Wilson, 1995], we perceive that an increase in the value of R(max) against SCN may have taken place [cf. Wilson et al., 1996d]. Representing this increase as a linear trend, we infer that cycle 23's R(max) should lie within the range of (again, based on the sample of cycles 8-22 and employing the 90% prediction interval, but now using t = for 13 d.o.f. (i.e., "n- 2" dot') and the standard error of estimate se = 35.9); hence presuming the validity of the inferred linear fit, it follows that for cycle 23 there is only a 5% chance that its R(max) will be either >207.4 or <80.2. Instead of viewing each sunspot cycle separately, we can pair them into Hale cycles consisting of two consecutivelynumbered sunspot cycles. Recall that during even-numbered cycles, the preceding spots of the Sun's northern hemisphere are predominantly of southward (negative) polarity, while they are predominantly of northward (positive) polarity during oddnumbered cycles. The behavior is opposite this for the Sun's southern hemisphere. This alternating pattern of solar activity has become known as the "Law of Sunspot Polarity" or, more simply, the Hale (or double sunspot) cycle, named in honor of George Ellery Hale who first discovered it [Hale, 1924]. According to Gnevyshev and Ohl [1948] (compare de Jager [1959, p. 328], Vitinskii [1965], Kopecky [1991], and Wilson [1992]), the inferred pairing for any given Hale cycle is even-leading and odd-following. The basis for this decision rule is the strength of the inferred correlation when comparing separately cycle-related parameters, like R(max), for evenleading to odd-following cycles, as contrasted against oddleading to even-following cycles (i.e., when cycles are grouped as even-odd pairs, in that order, the inferred correlation is very strong, while it is weak when cycles are grouped as odd-even pairs). For the seven complete Hale cycle pairs contained in the table, we find that the odd-following cycle usually has the larger R(max), true for six of the seven observed Hale cycle pairs, with only cycles 8-9 behaving differently (it must be noted, however, that, in the statistical sense, cycles 8 and 9 are of comparable size [compare Wilson, 1992]). Based on a linear fit of R(max)oaa.fo.owing versus R(max)... eaaing, having a coefficient of correlation r = 0.81 (or equal to 0.97 if we ignore cycles 8-9), we infer that cycle 23's R(max) should be about (based on cycle 22's observed maximum amplitude, equal to 157.6, and employing the 90% prediction interval, having t = for 5 dof, based on the sample of seven Hale cycle pairs (i.e., cycles 8-9, ) and se = 22.3); hence we infer only a 5% chance that cycle 23's R(max) will be either >222.4 or < Table 2. Summary of Important Fits for Predicting R(max) Comparing this estimate with those gleaned above (i.e., assuming a normal distribution for R(max) and a linear increase in R(max) against SCN), we find that the most probable range for cycle 23's R(max) should be (or ), based on the overlap. So, based solely on the observed statistics for cycles 8-22, we easily deduce that cycle 23's R(max) probably will be larger than average (117.8), although not of record size (190.2). Continuing, from Table 1 we also find that statistically significant correlations exist between R(max) and R(min), R(max) and aa(min), and R(max) and aa(e(min)), each being described as a single variate fit. Furthermore, both aa(min) and aa(e(min)) can be combined with R(min) to generate even more statistically significant correlations between R(max) and the combined parameters, than exists singly for the individual parameters, each of these fits being described as a bivariate fit. Table 2 collectively summarizes important aspects of these single vatlate and bivariate fits. In the table, r refers to the coefficient of correlation, r 2 to the coefficient of determination (which is a measure of the amount of variance from the mean fit that the inferred regression can explain), and se to the standard error of estimate (in units of annual sunspot number). The column marked "cycles" identifies those individual sunspot cycles that were used in the regression analyses. Clearly, R(max) is strongly associated with the size of the aa index near cycle minimum. Based on the single variate method that relates R(max) to aa(min) (method 5), we find that the value of aa(min) alone can account for about 82% of the observed variance in R(max). Perhaps, even more astonishing is the finding that, together, both R(min) and aa(min) (method 7) can account for about 95% of the variance in R(max). Even if we are not sure that the value for the aa index is the minimum value (i.e., aa(min)), but are relatively sure that E(min) has, indeed, been observed, we can still estimate R(max) to a fairly high degree (method 8, having r = 0.92, r = 0.84, and se = 17.4 units of annual sunspot number). 4. Application to Cycle 23 Wilson et al. [1996b] have shown that the behavior of cycle 22 is consistent with it being described as a short-period cycle (i.e., PER <132 months) [cf. Wilson, 1993, 1995]. In fact, the first high-latitude (>25 ø ) spot group for new cycle 23 appeared in May 1996, in conjunction with the occurrence of the lowest value of smoothed monthly mean sunspot number that has been observed thus far (= 8.1), and high-latitude, new cycle spot groups have been seen in every month since, although they have only recently (April 1997) begun to predominate (in terms of spot group area). Figure 1 updates the distribution of spot group latitudes for the interval of January 1995 through July 1997, using the "modified" butterfly Method Fit r r2 SE Cycles R(max) = m R(max) = SCN 0.39 R(max) = R(min) 0.54 R(max)o_f = R(max)e-I 0.81 R(max) = aa(min) 0.91 R(max) = aa(e(min)) 0.84 R(max) = R(min) aa (min) 0.98 R(max) = R(min) aa (E(min)) For method 4, the subscripts "o-f' and "e-l" refer to "odd-following" and "even-leading" cycles, respectively

4 6598 WILSON ET AL.' ESTIMATE FOR THE SIZE OF CYCLE lo I I I I I I I I I I I I I I I I I I 5 f I f_l *] * I * I ] f..i. I,.L.L * I J I I ] ] I lltl I I I I ] I i ] I J 1995 J 1996 J 1997 J Calendar Date (Year-Month) Figure 1. The distribution of spot group latitudes (combining both north and southeliolatitudes) for January 1995 to July Spot groups at latitude _25 ø are considered high-latitude spot groups; the first high-latitude spot group for cycle 23 occurred in May The monthly mean-latitude, weighted according to spot group area, is shown by the thin, jagged line, while the smoothed monthly mean-latitude, again weighted according to spot group area, is shown as the thick, smoothed line. Notice the sharp transition to latitude >20 ø in April 1997, inferring that higher-latitude, new cycle spot groups are now beginning to predominate lower-latitude, old cycle spot groups (in terms of spot group area). Based on the smoothed monthly mean-latitude, the rise to higher value began in December diagram [Wilson et al., 1996b]. Recall that in an ordinary size of the weighted mean latitude, at least, through March butterfly diagram, spot group latitude (in degrees) versus time In April 1997, however, the weighted mean latitude is plotted separately by hemispheric location (northern and shifted strongly upward to a value >20 ø, indicating that, now, southern hemispheres); here we modify the usual diagram by the higher-latitude, new cycle spot groups are finally ignoring the hemispheric location of the individual spot beginning to be more predominant. For cycles 15-22, when groups and simply plot spot group latitude versus time (for the this sharp transition occurred (i.e., from one that is dominated combined hemispheric grouping). The thin, jagged line by lower-latitude, old cycle spot groups to one dominated by running through the distribution of spot group latitudes is the higher-latitude, new cycle spot groups), onset for the new monthly value of the "weighted mean latitude" [Wilson et al., cycle (based on the occurrence of the lowest value of smoothed 1996b], so called because it weights latitude according to the monthly mean sunspot number) had either already taken place area of the individual spot groups. The thick, smoother line (five of eight cycles) or was just abouto take place (within the running through the distribution is the 12-month moving next 6 months; three of eight cycles). By constraining the average of the weighted mean latitude. The distribution shows value of the weighted mean latitude to remain >10 ø for the next that both old cycle 22 (lower latitude) and new cycle 23 (higher several months following the strong transition to >20 ø, we latitude) spot groups are clearly discernible, with the old cycle find that nearly all (seven of eight) of cycles meet these spot groups appearing to exert the greatest influence on the conditions and that minimum amplitude for the new cycle very

5 WILSON ET AL.' ESTIMATE FOR THE SIZE OF CYCLE probably has already occurred (only cycle 20 fails, in that its sharp transition is found to precede its minimum amplitude occurrence by a few months). Using the smoothed monthly weighted mean latitude, we see that the upturn actually began about December 1995 and that values are continuing to rise. In cycles 21 and 22, this rapid increase in the smoothed monthly weighted mean latitude preceded sunspot minimum by 7 and 6 months, respectively. Presuming sunspot minimum for cycle 23 in May 1996, we calculate that its rapid rise preceded sunspot minimum by 5 months. For all data-available cycles (12 to present), we find that once the strong upward progression of the smoothed monthly weighted mean latitude is manifest the lowest observed value of smoothed monthly mean sunspot number that follows has always been the marker of sunspot minimum (without fail). Thus it seems highly likely that minimum amplitude occurrence for cycle 23 has, indeed, already occurred (i.e., in May 1996). (Howard[1977] has noted that the length of overlap for old and new cycles is about 1-3 years; accepting May 1996 as the official start for cycle 23, in the conventional sunspot number sense, the length of the overlap for cycles 22 and 23 has already persisted for more than 1 year.) Figure 2 displays the history of (left) annual and monthly mean sunspot number and (fight) annual and monthly mean aa index value for the interval of January 1995 through July 1997 (through April 1997 for the aa index, the last available entry). For sunspot number, an annual average of 8.7 was attained in 1996 which compares favorably with that which is expected if it is, indeed, R(min) (i.e., < 13.4; based on the statistics of cycles 8-22, them is only a 5% chance that R(min) would be expected to exceed 13.4). The value of monthly mean sunspot number was at its lowest (= 1.6) in September 1996, and provisional values of monthly mean sunspot number have been increasing through mid Because seven of the last nine monthly mean sunspot number values exceed the 1996 annual average of 8.7, we infer that 1996 will, in all likelihood, be the year of E(min) for cycle 23. (As previously mentioned, the lowest value of smoothed monthly mean sunspot number that has been seen thus far occurred in May 1996, measuring 8.1; values have since risen above 10. So, this, too, suggests that onset for cycle 23, indeed, has already taken place.) For the aa index, an annual average of 18.6 was attained in Because E(min) for cycle 23 appears to be 1996, we infer that this value is, consequently, aa(e(min)). In 1996 the lowest monthly mean value of the aa index occurred in June (= 11.1) and the familiar double-peaked pattern, associated with the semiannual variation of geomagnetic indices [e.g., Patel, 1977], is quite noticeable (i.e., a weaker "spring" peak in March, measuring 22.3, and a stronger "fall" peak in September, measuring 26.2). Presently, on the basis of the published aa index values (Solar Geophysical Data, No. 634, Part I, p. 109, June 1997) we cannot strictly determine if the annual average of the aa index for 1996 may also be aa(min) for cycle 23, as was the case for cycle 19 (see Table 1) when its aa(min) and aa(e(min)) values occurred congruently. We do note, however, that the 7-month average of the Ap index (not shown) for January through July 1997 (= 8.7) is slightly higher than its corresponding 7-month average for 1 year earlier (-- 8.6) and that the 12-month moving average of Ap seems to be getting larger (having a minimum of 9.1 in late 1996), suggesting that 1996 may well turn out to be the year of Ap(min). Because of the strong behavioral similarity between Ap and aa, we infer that 1996 may be the year of occurrence for aa(min), as well. Accepting 8.7 as R(min) (i.e., taking 1996 to be E(min)) and 18.6 as both aa(min) and aa(e(min)) allows us to apply the previously described regressions to cycle 23, thereby obtaining a number of estimates for its size (i.e., R(max)). Figure 3 depicts these estimates. The mean fit (based on the statistics of cycles 8-22) is shown as fit 1, the secular fit (R(max) versus $CN)is shown as fit 2, and so forth. For the eight fits, the range of overlap for the estimates of R(max) is about Thus, presuming that 1996 was, indeed, cycle 23's E(min), we infer that cycle 23 should have an expected R(max) of about 168 _+ 15 (based on the overlap), suggesting that cycle 23 will be stronger than average in size, perhaps, 3O - Provisional 3O ø I,I = 20 E "10 IIl,11 1 I I I i,, i I I I I I I I I I 1111 III J 1995 J 1996 J 1997 J Calendar Date (Year-Month) J 1995 J 1996 J 1997 J Calendar Date (Year-Month) Figure 2. (left) Monthly mean sunspot number and (fight) aa geomagnetic index between January 1995 and July 1997 (sunspot data after December 1996 are considered provisional). Annual averages are shown as horizontal lines, and the value of each is given. The lowest monthly mean sunspot number (1.6) occurred in September 1996; the lowest monthly mean aa index (11.1), so far, occurred in June 1996.

6 6600 WILSON ET AL.' ESTIMATE FOR THE SIZE OF CYCLE 23 R (max) [231 o o I I I I I I I I I I I I I I I I I I I [ Mean Fit 8-22 I Max-Min Fit 8-22 Secular Fit 8-22 I I R(max)- aa(min) Fit I I R(max)- aa(e(min) )Fit Odd-Even Fit 8-21 I I R(max)- R(min), aa(min) Fit I R(max)- R(min), aa(e(min)) Fit Overlap t t ttt ttt t Relative Maxima Cycles (Cycles of 20th Century) I I Fast Riser (ASC <48 months) I Slow Riser (ASC >48 months) I Short-Period Cycle (PER <132 months) I Long-Period Cycle (PER >132 months) Figure 3. Predictions of R(max) for cycle 23. Fits 1-8 are described in Table 2. The overlap of the 90% prediction intervals is identified. The relative sizes of R(max) for cycles (cycles of the 20th century) are shown. Ninety percent prediction intervals of R(max) for specific bimodal classes are also given. Here a fast riser is a sunspot cycle that has an ascent duration from minimum-to-maximum amplitude (based on smoothed monthly mean sunspot number) ASC <48 months; a slow riser has an ASC >48 months. Likewise, a short-period cycle is a sunspot cycle whose minimum-to-minimum amplitude period (based on smoothed monthly mean sunspot number) PER <132 months; a long-period cycle has a PER >132 months. becoming the new second-largest cycle on record; certainly, it 5. Discussion and Summary appears very likely to be among the top five strongest cycles of the 20th century. According to Thompson [1988, 1993], the only prediction Also, shown in Figure 3 (to the right) are estimates for the methods which meet with approval from the majority of the size of cycle 23, presuming it to be either a fast- or slow-rising scientific community are the "precursor" techniques, which cycle or to be either a short- or long-period cycle, where each operate on the notion of the "extended solar cycle" [Ohl, of the intervals is the 90% prediction interval of R(max) based 1971; Feynman, 1982; Legrand and Simon, 1991; Simon and on the statistics of cycles 8-22, following subdivision by Legrand, 1992], wherein the size of the following sunspot bimodal classes. A comparison of these intervals with the cycle (here, cycle 23) is directly related to conditions that overlap (from the single variate and bivariate methods) exist during the decline of the preceding cycle (here, cycle 22), strongly suggests that, in addition to being a cycle of larger especially near the onset of the new cycle. Recall that it has than average size, cycle 23 should be a fast riser of shorter been known for some time that the level of geomagnetic than average period, as well. Thus, presuming May 1996 as the activity (in particular, the occurrence of geomagnetic storms, official start for cycle 23, we infer that its ascent duration the number of disturbed days, etc.) is determined by changes should be <48 months (in the range of months) and that (of solar origin) in the solar wind and that there exists some its maximum amplitude (in terms of smoothed monthly mean statistical relation to the sunspot cycle [Maunder, 1904; sunspot number) should occur after February 1999, but before Greaves and Newton, 1928, 1929; Allen, 1944; Saemundsson, May Similarly, we infer that its period should be < ; Gonzalez and Schatten, 1987; Thompson, 1988, 1993; months in length (in the range of months) and that Wilson, 1990b]. Geomagnetic storms consist of two general cycle 23 should end (and cycle 24 begin) before May 2007, types: recurrent and nonrecurrent (or sporadic), with recurrent probably between January and October storms tending to recur every 27 days and appearing to be

7 , WILSON ET AL.: ESTIMATE FOR THE SIZE OF CYCLE associated with long-lived, open field line structures on the Sun (like coronal holes) and nonrecurrent storms appearing to be associated with specific event-related features on the Sun (like flares and disappearing filaments and their associated coronal mass ejections that give rise to magnetic clouds [e.g., Wilson and Hildner, 1984, 1986; Wilson, 1987, 1990a, 1996]).. Ohl [1971] found that both types of storms vary with the solar cycle but in different phase. For example, he noticed that the frequency of nonrecurrent storms was maximal when sunspot number was maximal and that the frequency of recurrent storms was maximal just before sunspot minimum. Additionally, he found that the size of the recurrent maximum appeared to relate strongly with the size of the following sunspot number maximum. Hence he concluded that there exists a close connection between the development of unipolar magnetic regions on the Sun at the end of a given cycle and the subsequent development of bipolar magnetic regions in the following cycle and that the true beginning of the solar cycle takes place several years before the epoch of sunspot minimum (which connotes the conventional start of a sunspot cycle). Later, Feynrnan [1982] showed that one can easily track the recurrent and nonrecurrent components of the solar wind, on the basis of annual averages of the aa index, using sunspot number as the independent variable. For example, she decomposed the aa index into two components: (aa)r and (aa), where the first component is in phase and directly related to the current value of the annual average sunspot number R, expressed as a linear relationship that has been called the "line of extremeslocus" [Li, 1997], and the second component is the difference (or remainder) of (aa)- (aa)r. She showed that a minimum in the latter component occurs close to the time of maximum amplitude (E(max)) for each of the sunspot maxima in the 20th century and, conversely, that the largest value of the latter component tends to occur shortly before sunspot minimum (E(min)). Subsequently, Legrand and Simon [ 1991 ] and Simon and Legrand [1992] came to the conclusion that the solar cycle consists of two distinct components, dipole and toroidal, with the toroidal component being strongly linked (with a 5- to 6-year delay) to the preceding dipole component. It has also been established that there exists a strong correlation between the size of polar coronal holes (that are larger near solar minimum) and the size (maximum amplitude) of the following cycle [e.g., Schatten et al., 1978, 1996; Bravo and Otaola, 1989' Layden et al., 1991' Schatten and Pesnell, 1993; Bravo and Stewart, 1994; Dorotovic, 1996], where the level of minimum geomagnetic activity (using either the aa or Ap index) is taken to be indicative of the strength of the Sun's polar magnetic fields, since the strength of the equatorial magnetic fields should be minimal near sunspot minimum. Thus a relatively large geomagnetic minimum suggests a larger area of polar coronal holes (and stronger polar fields), thereby indicating a larger relative maximum ampi!rude for the following cycle, as compared to a relatively small geomagnetic minimum which suggests a smaller area of polar coronal holes (and weaker polar fields), thereby indicating a smaller relative maximum amplitude. In this paper, on the basis of annual averages of selected parameters (R(min), aa(min), and aa(e(min))for cycles 8-22, the cycles of fair-to-best quality sunspot data, and on the presumption that 1996 marks the year of onset (E(min)) for cycle 23, we have generated a number of estimates for its size (i.e., maximum amplitude R(max)), based on a variety of single variate and bivariate precursor techniques. The overlapping range of the 90% prediction intervals for these various estimates is about (in terms of annual averages of sunspot number). Such a range for R(max) precludes cycle 23 from being a cycle of "below" average size and even one considered to be of "average" size (= , the 90% prediction interval of the expected value for the mean of the population of R(max), given the sample of R(max) values for cycles 8-22). In fact, the inferred range of R(max) for cycle 23 strongly suggests that its size will rank among the five strongest cycles of the 20th century,' although probably not the strongest (i.e., cycle 19 which had an R(max) = 190.2). Furthermore, its inferred range of R(max) strongly suggests that cycle 23 will be both fast rising and of short period, having an ascent duration <48 months and a period <132 months. Presuming that cycle 23, indeed, had its official onset (i.e., minimum amplitude in terms of smoothed monthly mean sunspot number) in May 1996, we expect its maximum amplitude to occur before May 2000, probably sometime during the interval of March 1999 to April 2000, and we expect onset for cycle 24 to occur before May 2007, probably sometime during.the interval of January'to October Statistically speaking, it has been known since the epoch of maximum amplitude for cycle 22 (1989) that cycle 23 should have a maximum amplitude that probably will be larger than average size. The statistics of cycles 8-22 (as shown here) strongly suggesthat cycle 23's maximum amplitude should be about _+ 25.6, based on the overlap of the prediction intervals presuming a normal distribution, a linear secula rise, and the existence of the even-odd effect. Likewise, supporting this estimate, is the now well-established number of disturbed days (i.e., the number of days when Ap _>25) for cycle 22 (some 610 between cycle 22 minimum and cycle 23 minimum, presuming May 1996 to be cycle 23 minimum). Recall that Thompson [1993] has previously shown that there exists a simple linear relation between the sum of R c + Rn, where R c refers to the maximum amplitude for the current cycle and R n refers to the maximum amplitude of the next cycle, and Nc is the number of disturbe days observeduring t.he current cycle. The relation is strongly linear (r = 0.97) and suggests that R(max) for cycle 23 will be about _ On the basis of the observed 2 x 2 contingency.table of R c + R versus No we find that the median value of N c is 399, based on the data-available cycles (11-21); hence when this value is exceeded this can be taken as indicating that the next cycle will be of larger than average size. Cycle 22's cumulative count of number of disturbed days exceeded the median value in January Thus, as early as 1993, we had additional evidence that cycle 23 should be larger than average size. Thompson [1993] also determined a bix3ariate fit, comparin g n against Rc and N c. Based on this fit (r = 0.91), we deduce that R(max) for cycle 23 will be about _ Following Feynman's approach [Feynman, 1982] and using a line of extreme locus for (aa) R = R, we deduce that the maximum (aa)j for cycle 22 was 21.2, having occurred in On the basis of the inferred regression (r = 0.90) between R(max) of the next cycle and the maximum value of (aa) l hat occurs during the decline of the current cycle (the one that is in closest proximity and prior to cycle minimum for the current cycle which often, but not always, is the maximum (aa) for the cycle), we deduce cycle 23's R(max) to be Combining these latter estimates with the others still results in our best estimate of R(max) for cycle 23 being about

8 6602 WILSON ET AL.: ESTIMATE FOR THE SIZE OF CYCLE 23 In summary, then, it appears highly likely, based on several Kane, R. P., A preliminary estimate of the size of the coming Solar varied precursor methods, that cycle 23 will be a large-ampli- Cycle 23, based on Ohl's precursor method, Geophys. Res. Lett., 24, tude cycle, having R(max) = , thus supporting the , consensus recently reported by Joselyn et al. [1997] that cycle Kiepenheuer, K. O., Solar activity, in The Sun, edited by G. P. Kuiper, pp , Univ. of Chicago Press, Chicago, II1., should have a maximum amplitude of about 160 _+ 30. Kopecky, M., Forecast of the maximum of the next I 1-year cycle of Because large-amplitude cycles tend to be fast-rising cycles of sunspots no. 23, Bull. Astron. Inst. Czech., 42, , shorter than average period, we also infer that the epoch of Kremliovsky, M. N., Can we understand time scales of solar activity?, maximum amplitude (E(max)) for cycle 23 should occur before Sol. Phys., 151, , May 2000 and that the epoch of minimum amplitude (E(min)) Lapin, L., Statistics for Modern Business Decisions, 2nd ed., Harcourt for cycle 24 should occur before May Brace Jovanovich, New York, Layden, A. C., P. A. Fox, J. M. Howard, A. Sarajedini, K. H. Schatten, and S. Sofia, Dynamo-based scheme for forecasting the magnitude Acknowledgment. The authors acknowledge partial support for this of solar activity cycles, Sol. Phys., 132, 1-40, study through NASA's Space Environments & Effects program. Legrand, J.P., and P. A. Simon, A two-component solar. cycle, Sol. Phys., 131, , 199 I. Letfus, V., Prediction of the height of solar cycle 23 Sol. Phys., 149, References Li, Y., Predictions of the features for sunspot cycle 23, Sol. Phys., 170, , Allen, C. W., Relation between magnetic storms and solar activity, Mon. Maunder, E. W., Magnetic disturbances, 1882 to 1903, as recorded at Not. R. Astron. 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9 WILSON ET AL.: ESTIMATE FOR THE SIZE OF CYCLE Wilson, R. M., Geomagnetic response to magneti clouds, Planet. Space Sci., 35(3), , Wilson, R. M., A prediction for the size of sunspot cycle 22, Geophys. Res. Lett., 15, , 1988a. Wilson, R. M., An alternative view of the size of solar cycle 22, Nature, 335, 773, 1988b. Wilson, R. M., Bimodality and the Hale cycle, Sol. Phys., 117, , 1988c. Wilson, R. M., On the behavior of the Dst geomagnetic index in the vicinity of magnetic cloud passages at Earth, J. Geophys. Res., 95, 2!5-219, 1990a. Wilson, R. M., On the level of skill in predicting maximum sunspot number: A comparative study of single variate and bivariate precursor techniques, Sol. Phys., 125, , 1990b. Wilson, R. M., An early estimate for the size of cycle 23, Sol. Phys., 140, , Wilson, R. M., A prediction for the onset of cycle 23, J. Geophys. Res., 98, , Wilson, R. M., On the "first spotless day" as a predictor for sunspot minimum, Sol. Phys., 158, , Wilson, R. M., On the relationship between transient velocity of interplanetary shocks and solar active processes, Planet. Space Sci., 44(5), , Wilson, R. M., and E. Hildner, Are interplanetary magnetic clouds 1-AU manifestations of coronal transients? Sol. Phys., 91, , Wilson, R. M., and E. Hildner, On the association of magnetic clouds with disappearing filaments, J. Geophys. Res., 91, , Wilson, R. M., D. H. Hathaway, and E. J. Reichmann, On the Importance of Cycle Minimum in Sunspot Cycle Prediction, NASA Tech. Paper 3648, 1996a. Wilson, R. M., D. H. Hathaway, and E. J. Reichmann, On the behavior of the sunspot cycle near minimum, J. Geophys. Res., 101, 19,967-19,972, 1996b. Wilson, R. M., D. H. Hathaway, and E. J. Reichmann, On Determining the Rise, Size, and Duration Classes of t Sunspot Cycle, NASA Tech. Paper 3652, 1996c. Wilson, R. M., D. H. Hathaway, and E. J. Reichmann, Prelude to Cycle 23: The Case for a Fast-Rising, Large-Ampl#ude Cycle, NASA Tech. Paper 3654, 1996d. Wilson, R. M., D. H. Hathaway, and E. J. Reichmann, Gauging the Nearness and Size of Cycle Minimum, NASA Tech. Paper 3674, D. H. Hathaway, E. J. Reichmann and R.M. Wilson, Space Sciences Laboratory, Solar Physics Branch, ES82 (96-025), NASA Marshall Space Flight Center, Huntsville, AL ( ; wilsorm@ssl.msfc.nasa.gov) (Received May 13, 1997; revised September 15, 1997; accepted September 23, 1997.)