Size of the coming solar cycle 24 based on Ohl ’ s Precursor Method , final estimate

In Ohl’s Precursor Method (Ohl, 1966, 1976), the geomagnetic activity during the declining phase of a sunspot cycle is shown to be well correlated with the size (maximum sunspot number Rz(max)) of the next cycle. For solar cycle 24, Kane (2007a) used aa(min)=15.5 (12-month running mean), which occurred during March–May of 2006 and made a preliminary estimate Rz(max)=124±26 (12-month running mean). However, in the next few months, the aa index first increased and then decreased to a new low value of 14.8 in July 2007. With this new low value, the prediction wasRz(max)=117±26 (12-month running mean). However, even this proved a false signal. Since then, the aa values have decreased considerably and the last 12-monthly value is 8.7, centered at May 2009. For solar cycle 24, using aa(min)=8.7, the latest prediction is, Rz(max)=58.0±25.0.


Introduction
Prediction of the magnitude of the sunspot maximum Rz(max) is important for planning satellite launching For cycle 23, NOAA's Space Environment Center (SEC) recruited a scientific panel to assess the likely development of cycle 23 and their report entitled "Solar Cycle 23 Project: Summary and Panel Findings," later published as Joselyn et al. (1997), mentioned (i) a range of 160-200 of Rz(max) of cycle 23 as obtained by considering the even/odd behavior and (ii) a range 110-160 of Rz(max) by other methods.The panel gave the greatest weight to precursor methods, since they have proved to be the most successful technique for solar activity predictions in the past.The precursor methods invoke a so-Correspondence to: R. P. Kane (kane@dge.inpe.br)lar dynamo concept, whereby the polar field in the declining phase and at minimum is the seed of future toroidal fields within the Sun that will cause solar activity (e.g., Schatten and Pesnell, 1993).In one of the precursor methods (Ohl's method), geomagnetic aa indices at solar minimum are seen to be well correlated with the succeeding Rz(max) (Ohl, 1966(Ohl, , 1976;;Brown and Williams, 1969;Ohl and Ohl, 1979;Sargent, 1978).Since then, Kane (1978Kane ( , 1987Kane ( , 1992Kane ( , 1997Kane ( , 1998)), Wilson (1988aWilson ( , b, 1992)), and Wilson et al. (1998) have been studying this aspect for the past three decades.For cycle 24, Kane (2007a) evaluated Rz(max) as 124±26 using aa(min)=15.5 which seemed to be a minimum at that time.However, some workers (notably L. Svalgaard, private communication) were apprehensive that since aa(min) usually occurs a few months later than Rz(min), and Rz(min) had not yet occurred in 2006, the aa(min)=15.5 in March 2006 could be a false alarm.A Solar Cycle 24 Prediction Panel composed of international scientists and presided by D. Biesecker, (details given in http://www.sec.noaa.gov/SolarCycle/SC24/index.html),issued on 25 April 2007, a consensus opinion that cycle 24 would commence in March 2008 (±6 months) and two consensus opinions, that the solar maximum would be 140±20 in October 2011 or 90±10 in August 2012.As it happened, the sunspot minimum was nowhere near the range March 2008 (±6 months) mentioned by them, and the old cycle 23 seems to have ended and the new cycle 24 commenced only in the end of 2009.The sunspot numbers seem to have gone through a minimum of zero in August 2009.In this note, the situation of Rz(max) vis-a-vis aa(min) is reexamined to see whether a final estimate can be given for Rz(max) of cycle 24.

Data
The data used are the geomagnetic aa indices (the antipodal amplitudes deduced from the K index of Greenwich, England, and Melbourne, Australia; Mayaud, 1973) available at NOAA ftp://ftp.ngdc.noaa.gov/STP/SOLARDATA/RELATED INDICES/AA INDEX/ and international sunspot numbers Rz (McKinnon, 1987, and further data from NOAA websites ftp and ftp://ftp.ngdc.noaa.gov/STP/SOLAR DATA/SUNSPOT NUMBERS).For aa indices, data are available from 1868 onward only (cycle 11).However, for 1844-1880, Nevanlinna and Kataja (1993) generated an "equivalent" aa index based on the declination data from Helsinki and, for the overlapping period of 13 years 1868-1880, they found a very high correlation (0.99).Hence, we have now aa index data for cycle 9 and 10 also (annual values) and for cycle 11 onward (monthly values).

Present situation
The origin and development of sunspot numbers are described recently in Clette et al. (2007) and Vaquero (2007).The monthly values of Rz and aa indices vary erratically from month to month.Hence, 12-month running means were evaluated and used.(This is simple average of 12 consecutive monthly values.The centering is half-a-month displaced.To get the centering correct, some workers use 13 consecutive monthly values, with half weight for the first and last values.However, the difference between the two estimates is negligibly small).As shown in Kane (2007a), for cycles 12-23, the Rz(min) occurred earlier than aa(min) by 3, 5, −2, 2, 14,8,16,12,7,7,4,16,9 months.Thus, except for cycle 14 where Rz(max) occurred later by 2 months (−2 italicized), the aa(min) have occurred with delays ranging from 2 to 16 months.Figure 1 shows the plots of the 12-month running means of Rz and aa indices for January 2006 onwards.The following may be noted: 1.The 12-month running mean Rz(min) seems to have occurred only recently.The mean 1.7 occurred in three successive months October, November, December 2008, followed by values 1.9, 1.9, 2.2, 2.3, 2.

Conclusion and discussion
In Ohl's Precursor Method, the geomagnetic activity during the declining phase of a sunspot cycle is shown to be well correlated with the size (maximum sunspot number Rz(max) of the next cycle.Kane (1997, 1998, andreferences therein) and Wilson, Hathaway and Reichmann (1998 and references therein) have been using the aa index during the sunspot minimum year as representative of the geomagnetic activity.For solar cycle 24, using aa(min)=8.7,the latest prediction is Rz(max)=58.0±25.0.Recently, Du et al. (2008Du et al. ( , 2009) ) examined the Ohl method more critically, and pointed out that a higher correlation does not necessarily mean a successful prediction, In their analyses, a higher correlation often yielded a failure prediction.Therefore, they suggest that when a prediction is obtained, its rationality should be analyzed.As one test, they suggest that the prediction could be considered reliable if the prediction lies very near the regression line and the correlation increases.We tried this criterion.For cycles 9-23, the correlation was +0.918.When the value 8.7 for aa(min) in May 2009 was used with predicted Rz(max) as 58, the correlation was slightly higher (+0.931).Thus the predicted value Rz(max)=58±25 for cycle 24 should be fairly reliable, and it is in the low Rz(max) category.
Incidentally, the present author published predictions for cycle 24 by using other methods also and got the results as (i) Kane (2007b) based on solar activity at different solar latitudes, Rz(max)=130, (ii) Kane (2007c) based on extrapolation of spectral components, Rz(max)=92, (iii) Kane (2008a) based on solar cycle lengths, Rz(max)=94, and (iv) Kane (2008b) based on the Ohl-Kopecky rule and the three-cycle periodicity scheme, Rz(max)=106.Almost all these (except 130 in Kane, 2007b) are below the statistical average of ∼115 for the 23 cycles.Thus, cycle 24 is likely to be below average.Recently, a review on this solar minimum has been published by Russell et al. (2010).

1Fig. 1 .
Fig. 1.Plot of the 12-month running means of sunspot number Rz and geomagnetic index aa for January 2006 onwards.Vertical lines mark the month January.Minima are shown by big dots and the corresponding months are indicated.
September 2009.Further, the actual monthly values for July 2009-March indicate that the sunspot activity has started rising.For January-March 2010, monthly values were 13.1, 18.6, 15.4 2. The 12-month running mean aa(min) seemed to have occurred first centered at March 2006 and May 2006 with a value 15.5.In Kane (2007a), this value was used in the regression equation Rz(max)=(−24.9±18.1)+(9.6±0.1.2)aa(min)and yielded the preliminary estimate prediction Rz(max)=124±26.3.However, in retrospect, this seems to have been a false alarm.The aa values increased in the next few months but decreased later considerably, and attained a second minimum centered at July 2007, aa(min)=14.8,smaller in magnitude than the first minimum and 15 months later.This also has proved a false signal and after rising for the next six months, the aa values have decreased considerably.The last 12-monthly running mean for aa index is 8.7, centered on June 2009.If this value 8.7 is used as aa(min), the prediction becomes Rz(max)=58.0±25.0.