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SOME COMMENTS ON THE PROBLEM OF SOLAR CYCLE PREDICTION V. N. OBRIDKO
IZMIRAN, Troitsk, Moscow Region 142092, Russia (Received 26 November, 1993; in revised form 8 September, 1994)

Abstract. The paper provides a number of regression equations that can be used to calculate the height of the odd Wolf number cycle. The feasibility of the rule of Gnevyshev-Ohl is analyzed as applied to the geomagnetic aa-index. A modified rule of Gnevyshev-Ohl has been formulated to describe the behaviour of aa-indices. A new method is suggested for early prediction of the next solar cycle. In this method, the angular coefficient (straightline slope) of linear dependence of aa-indices on the Wolf number at the descending branch of the cycle has been used as a prediction index. It is shown to a high degree of certainty that the new prediction index is related to the height of the forthcoming cycle. While the methods based on the ratio of the even-odd cycles in a pair give very high values of cycle 23 maximum (203.2 4- 10.7), our new index, on the contrary, gives very low values (74.7 4- 6.9). There are some contradictory symptoms indicating that the forthcoming cycle 23 is likely to violate the regularities established for the past 125 years.

1. The Rule of Gnevyshev-Ohl Gnevyshev and Ohl (1948) showed that the annual mean Wolf numbers summed up over 11-year cycles display an important regularity: if the Wolf number cycles are arranged in pairs in the sequence even-odd cycle, the second cycle in the pair is always higher than the first one. The correlation coefficient is 0.91. The only exception is the pair of cycles 4-5. The pairs of cycles arranged in the opposite way (odd-even cycle) do not display any sensible regularity. In such a pair the second cycle can be both higher and lower than the first one, with the correlation coefficient as small as 0.50. This means that the true physical cycle of solar activity lasts for 22 years (as it should do in accordance with the Hale law of alternating magnetic polarities), and begins with an even solar cycle. Kopeck~ (1950) established that the rule of Gnevyshev-Ohl is valid also for the relation between corresponding Wolf numbers in the same phase of different cycles. With this addition, it can be called the rule of Gnevyshev-Ohl-Kopeck~ (GOK rule), and has already two exceptions - pairs 4-5 and 8-9 (for details see Vitinsky, KopeckS, and Kuklin, 1986). The GOK-rule can be used directly for prediction purposes because the relationship between the heights of the solar cycles in a pair is rather close and satisfies the regression equation

RM2k+I = 34.7411 + 0.94054 RMzk,
n=10, r=0.837, se=21.9, ci>99.5.

(1)

Solar Physics 156: 179-190, 1995. (E) 1995 Kluwer Academic Publishers. Printed in Belgium.


180

v.N. OBRIDKO

240.

200" 160
120

°s°'~ў-

+...,,..,V""

80.

404

0

Fig. 1. The maximum Wolf number in the odd cycle, RM2k+t, as a function of the maximum Wolf number in the preceding cycle, RM2k.The pairs of cycles 0-9 are marked with asterisks (except pair 4-5) and those of 10-21 with crosses. The values predicted for cycle 23 are triangles. Equation (1) is represented by a solid line, Equation (2) by a dashed line. Note the coincidence between pairs 23 and 20-21 (arrow). Here n is the number of points, r is the correlation coefficient, se is the standard observation error, and el is the confidence level. Equation (1) is valid for cycles from number 0 (k = 0) to number 21 (k = 10), except for the pair of cycles 4-5. The regression equation calculated for the last six pairs, beginning with cycle 10 (k > 5), has the form

RMzk+I
n=6,

= 27.674+ r=0.974,

1.114 RM2k , se=9.60, ci>99.5.

(2)

We introduce an index, a(RM), that is the ratio of the maximum annual mean Wolf numbers in the odd-following and the even cycles in a pair. Its average value is

a(RM)

= 1.356 4- 0.233

(3)

for all cycles from 0 to 21 (except cycles 4-5) and

a(RM)

= 1.437 4- 0.148

(4)

for cycles 10 to 21. Figure 1 illustrates dependences for Equations (1) and (2), as well as the predicted values for cycle 23.


SOME COMMENTS ON THE PROBLEM OF SOLAR CYCLE PREDICTION

181

2. The Rule of Gnevyshev-Ohl for the Geomagnetic aa-Index
Ohl (1966) was the first to show that the recurrent geomagnetic activity at the decay of the solar cycle can be used as an efficient predictor of the intensity of the following cycle. Before proceeding to modification of this method, let us discuss the applicability of the rule of Gnevyshev-Ohl (G-O rule) to geomagnetic activity. In other words, let us check the validity of the statement: if the cycles ofaa-indices

are arranged in even-odd pairs, the second cycle in the pair is always higher than thefirst one. This question is not so simple, because the maxima and the minima of
geomagnetic activity do not coincide with those of the Wolf numbers. Therefore, the beginnings and the ends of the geomagnetic cycles are not as unambiguous, as in the case of the Wolf number cycle. So, we have chosen the following variants of the sums and of the monthly means of aa-index values: (1) s(1) is the sum of monthly mean aa-indices over an interval between two consecutive Wolf number minima, and q(1) is the mean value over the same interval; (2) s(2) is the sum of the monthly mean aa-indices over an interval between two consecutive aa-index minima, and q(2) is the mean value over the same interval; (3) s(3) is the sum of the monthly mean aa-indices over an interval between two consecutive Wolf number maxima, and q(3) is the mean value over the same interval; (4) s(4) is the sum of the monthly mean aa-indices over an interval between two consecutive aa maxima, and q(4) is the mean value over the same interval. The data of aa(M)-index are taken from Mayaud (1973) and then from subsequent annual IAGA reports. The epochs of the aa(M)-cycle minima and maxima are derived from the smoothed monthly data of the aa(M)-index, obtained in the same way as the smoothed monthly sunspot numbers. Unfortunately, the data series we have got at our disposal begin at 1868, i.e., cover only 5 pairs of solar cycles. The results of calculations are presented in Table I, which gives for all four variants: i - the number of the cycle; to - the first month in each summation interval; the sums (s) and the mean values (q); as and aq - the second to the first cycle ratios of s and q in a pair. The Wolf number cycle 22 was assumed to begin in September 1986, and it reached a maximum in July 1989; the minimum of the aa-index occurred in January 1987, and the maximum in September 1991. It should be noted that the dates of extrema of the aa-index are rather tentative. However, in fact, our further conclusions are independent of a certain small inaccuracy that might arise in determining the calendar dates. One comment should be made about the numbers of cycles in column 1. For variants 1 and 2, the conventional numbering is used. For variants 3 and 4, we use the number of the cycle in which the cycle defined by epochs of the maxima of Wolf number or aa-index starts. Thus, the descending branch of the current cycle is joined with the ascending branch of the following cycle.


182

v.N. OBRIDKO TABLE I Sums (s) and means (q) of monthly aa-indices in cycles 11-21

i 12 13 14 15 16 17 18 19 20 21 i 11 12 13 14 15 16 17 18 19 20 21

to Dec. 1878 Feb. 1890 Jan. 1902 Aug. 1913 Aug. 1923 Sep. 1933 Feb. 1944 Ap~ 1954 Oct. 1964 June 1976 to

s(1) 2022 2142 1853 2039 2100 2536 2792 3027 2966 3008 s(3)

q(1) 15.09 15.19 13.43 17.13 17.50 20.45 23.07 24.22 21.34 24.66 q(3)

as
1.06 0.87 1.10 1.03 1.21 1.10 1.08 0.98 1.01

aq
1.01 0.88 1.28 1.02 1.17 1.13 1.05 0.88 1.16

to
Jan. 1879 July 1890 Sep. 1901 Aug. 1913 Oct. 1924 June 1934 Ape 1945 Ap~ 1955 June 1965 Dec. 1976 to Feb. 1873 Sep. 1882 July 1892 Jan. 1911 Dec. 1918 May1930 Oct. 1943 Dec. 1951 July 1960 Sep. 1974 Dec. 1982

s(2) 2060 2074 1878 1272 2986 2662 2755 2933 2979 2956 s(4) 1394 1911 3163 1387 2301 3202 2211 2513 3600 2348 2671

q(2) 15.04 15.59 13.22 17.42 17.06 20.63 23.15 24.24 21.75 24.64 q(4) 12.12 16.33 14.31 14.75 16.92 20.01 22.79 24.88 21.18 23.96 25.69

as 1.01 0.91 0.68 2.35 0.89 1.04 1.06 1.02 0.99

aq 1.04 0.85 1.32 0.98 1.21 1.12 1.05 0.90 1.13

as

aq

as 1.37 1.66 0.44 1.66 1.39 0.69 1.14 1.43 0.65 1.14

aq 1.35 0.88 1.03 1.15 1.18 1.14 1.09 0.85 1.13 1.07

Aug. 1870 2346 14.76 0.84 1.11 Dec. 1883 1968 16.40 0.95 0.79 Jan. 1894 1865 12.95 1.08 1.14 Feb. 1906 2022 14.76 1.05 1.13 Aug. 1917 2113 16.64 0.92 1.09 Ap~ 1928 1946 18.19 1.37 1.22 Ap~ 1937 2670 22.25 1.15 1.07 May1947 3066 23.76 0.92 0.93 Ma~ 1958 2822 22.22 1.07 1.03 No~ 1968 3018 22.86 0.94 1.09 Dec. 1979 2842 24.93

lower in the interval from the Wolf number maximum or aa-index maximum in the odd cycle to that in the even cycle, than in the same interval from the even to the odd cycle.
(d) From Table I (as well as from Figure 2) one can see a strong long-term variation of aa(M)-index. Our a-index in Table I is greater than 1.0 not only for the even-odd cycle pairs, as required by the G-O rule, but also for some odd-

In spite of limited data, the calculations have shown that: (a) The G-O rule in its original form applied to the sums only for variant 1, i.e., when the beginning and the end of the in the traditional way. (b) The G-O rule in a modified form applied to the mean is valid for variants 1 and 2. (c) For variants 3 and 4, a new rule similar to that of G-O as follows: the monthly mean geomagnetic activity is always

of aa-indices is valid cycle are determined values of aa-indices should be formulated


SOME COMMENTS ON THE PROBLEM OF SOLAR CYCLE PREDICTION

183

3200 ,...., 2800.

I

26
22' 18: 14"

1

2400
2000' 1600

l

z/
1'2 1'4

/
1'6'1'8'2'0'22

/

/

1 200110 ,

lO.

)" 1'2 ' 1'4 ' 1'6 ' 1'8' ' 2'0 ' 2

Fig. 2. S(1) and q(1) as functions of the cycle number.

even pairs. This may be a consequence of a rapid secular increase of geomagnetic activity, in addition to the effect of the G-O rule. As a result of secular variation combined with the effect of the G-O rule, the values of our a-index of the even-odd cycle pairs can be greater than those of the following odd-even cycle pairs (regardless of whether they are greater than 1.0 or not). In fact, this is true for both the sums and the means in variant 1, only for the means in variant 2, and is not true at all in variants 3 and 4. (e) Moreover, a combined effect of the secular variation and the G-O rule results in a strong regression coupling between the cycles. We can calculate regression relations of odd-following cycle data versus even cycle ones, as well as evenfollowing cycle data vs odd cycle ones for all four variants. Five of 8 regression relations for the sums (except for the even-odd pair in variant 4 and the oddeven pair in variants 2 and 4) and all 8 relations for the means reach confidence levels greater than 90%. However, if the selection criteria are more rigorous (the confidence level greater than 97.5% and the correlation coefficient greater than 0.925) then we deal only with the cases described in items (a), (b), and (c), i.e., the even-odd pair in variant 1 for the sums, the even-odd pair in variants 1 and 2 for the means, and the odd-even pair in variants 3 and 4 for the means. (f) The G-O rule for the aa-index is most clearly pronounced in variant 1, i.e., when the beginning and the end of the cycle are determined in a traditional way. Only in this case are the additional rigorous criteria, stated in items (d) and (e), satisfied both for the sums and for the means. Figure 2 illustrates s(1) and q(1) as functions of the cycle number. The regression equations have the form
S(1)2k+l = 456.832 + 0.892155 S(1)2k, (5)

n=5,

r=0.955,

se= 160.1,

c1>99.0 ,


184
q(1)2k+ 1 -~

V. N. OBRIDKO

2.9847 + 0.9590q(1)2k,

n=5,

r=0.931,

se=1.776,

cl>97.5.

(6)

The average ratio of s (1) in the following and the preceding cycles in an evenodd pair is 1.092 ± 0.074, and the average ratio of q(1) is 1.1342-4- 0.107 in an even -odd pair. This agrees with the results obtained by Hedeman and Dodson-Prince (1986). Taking into account the high correlation coefficient, we give also the regression equation for the odd-even pair in variant 3:
q(3)2k+ 2 = 2.822 + 0.9216 q(3)2k+l ,

n=5,

r=0.997,

8e=0.357,

c1>99.5.

(7)

3. New Method for Prediction of Future Solar Cycle from Geomagnetic Data As mentioned above, Ohl (1966, 1968) was the first to suggest that characteristics of recurrent geomagnetic activity be used for predicting the height of the following solar cycle. Afterwards the method was repeatedly modified and improved by different authors (e.g., see Ohl, 1976; Ohl and Ohl, 1979; Thomson, 1990; Brown, 1990, and references therein). In fact, all modifications of the method are based on a positive correlation between the geophysical activity at the descending branch of the sunspot cycle and the height of the following cycle. It is not critical what geophysical index is chosen as a predictor. On the other hand, the level of geophysical activity, and especially its deviation from the statistical level corresponding to the current value of Wolf numbers, is of great importance. All modifications of the method use as a predictor the difference between the normalized geophysical parameter and the Wolf number. Unfortunately, in spite of reliability and other advantages of the method, it is inapplicable for early prediction because it is based on the data series extending up to the first year after the minimum, i.e., it practically predicts the cycle that has already started. In this paper, we suggest as a predictor the degree of dependence of the geophysical index on the Wolf numbers, i.e., p = Oaa/OR. To be more precise, we are going to use as a predictor the angular regression coefficient (straight line slope), p, between the aa-index and the Wolf number derived for a relatively small interval at the descending branch of the cycle. Since the Wolf numbers at the descending branch decrease much faster than the aa-index (which even grows at the beginning of the branch), extremely high geophysical activity will obviously correspond to great negative values of the p-index, so that high correlation can be expected between p and the height of the following cycle.


SOME COMMENTS ON THE PROBLEM OF SOLAR CYCLE PREDICTION

185

200

RI+1 x\
160

%

\x*
x
N % \

120
%

80 " Pi

~°oh'0'-b:0'5'
Fig. 3.

'--b:0b' 'd.dg ' '6J6 ' 'd.

The maximum Wolf number in the forthcoming cycle, Ri+l, as function of the p~ index.

For convenience of application of the method and for early prediction, we have used unsmoothed monthly mean values of aa-index and Wolf numbers, and tried to reduce to a minimum the selection interval over which the p-index was calculated. As the first month of the selection interval, we have used either the exact calendar date of maximum of the unsmoothed Wolf number (month 0), or the date a year and a half later (month 18). The latter was chosen proceeding from the consideration that the global magnetic field reversal in the Sun usually occurs 1-2 years after the Wolf number maximum (Makarov, Fatianov, and Sivaraman, 1983; Makarov and Sivaraman, 1983). The end of the selection interval was initially fixed at month 50 (i.e., the overall length of the selection interval was 51 or 33 months in the first and the second case, respectively). Then we tried shorter intervals (18-47 and 18-41) to enable earlier prediction. The selection interval beginning 18 months and ending 50 months after the maximum of the Wolf number cycle, i.e., lasting for 33 months, proved to be most suitable, if we do not discriminate between the even and the odd cycles and do not eliminate the pair of cycles 4-5. Figure 3 illustrates Ri+l as a function of Pi. The regression equation has the form

Ri+l = -743.5pi + 152.4,
n=ll, r=-0.924,

se=18.1,

cl > 99.5.

(7)

Note that correlation with the height of the current maximum is practically absent, r = -0.170. Taking into account all said above about the rule of Gnevyshev-Ohl, it is interesting to see how the proposed method works when separately applied to odd and even cycles. Table II presents the correlation coefficients of correlations


186

v.N. OBRIDKO TABLE II Correlation coefficientsbetween RM and p-index 0-50 18-50 18-47 18-41

Odd-even pair Correlation of p2k+l and RMzk+2 P2k+l and RMz~+I -0.962 -0.400 -0.816 -0.0056 -0.855 -0.100 -0.563 -0.362

Even-odd pair Correlation of p2k and RM2k+I p2k and RM2k -0.190 -0.364 -0.992 -0.941 -0.964 -0.960 -0.927 -0.977

between p-index and RM of the following and the current cycle for different combinations of cycles and for different lengths of the selection interval for which the p-index was determined. As seen from Table II, there is a difference in application of our method to even and odd cycles. In the odd cycle, the best correlation between the p-index and the RM of the following cycle is achieved when a very long selection interval (51 months) is used. This dependence is illustrated in Figure 4(a). The regression equation has the form R2k+2 = -661.76pak+l + 127.45, n=6, r=-0.962, se=12.42, cl > 99.5.

(8)

Note that correlation with the maximum of the current cycle is very small (-0.400). A somewhat different situation arises in the even cycles. Here, the correlation between the p-index and the maximum of the following cycle is the largest at a selection interval of 18-50 months, as in the case where the type of the cycle (even or odd) is not taken into account (see Equation (7)). This relation is illustrated in Figure 4(b). The regression equation has the form Rzk+l = --735.12pzk + 152.17, (9) n=5, r=--0.992, se=6.93, cl > 99.5.

Here, some remarks should be made: (a) In the even cycles, the correlation of the p-index with the maximum Wolf number in the current cycle is also high, which naturally results from the rule of Gnevyshev-Ohl.


SOME COMMENTS ON THE PROBLEM OF SOLAR CYCLE PREDICTION

] 87

210

10,,
4
%

,,

170

Ri+l
% % % % % % % %

70"1 R;+I
1

"~
% % %. %

130

30-~
d

%

go

% %

90-I
'I I

P|

5-°0.1b ' '-ob,~'
a)

'-o:o6''

6.6s' '" 6.

'-'o:ob ' "6.65'
b)

' " 6. o

Fig. 4. The maximum Wolf number in the forthcoming cycle, P~+~, as a function of p{ for the odd (4a, i = 2k + 1) and the even (4b, i = 2k) cycles.

(b) Though the data series for the aa-index are shorter (only cycles 11 to 22) than for the Wolf numbers, the statistics are at least not worse than in the case of the rule of Gnevyshev-Ohl for the Wolf numbers. (c) The length of the descending branch in the odd cycles 11-21 ranges from 72 to 100 months with an average of 85.0 4- 9.8 months, and in the even cycles 12 -20 - from 65 to 91 months with an average of 80.8 4- 9.8 months. A prediction based on our new method can be made well before the cycle minimum. (d) There is a fundamental difference between the prediction methods based only on the sunspot number and those using geomagnetic activity data. As mentioned in Section 1, from the rule of Gnevyshev-Ohl it follows that the forecast can only be obtained for the odd-following cycles. In other words, the G-O rule says that the pairs of even and odd-following cycles are mutually dependent and the pairs of odd and even-following cycles are independent. Both Ohl's and our new method are based on geomagnetic activity. Therefore they can provide a relatively early forecast of the height not only for the odd, but also for the even cycles.

4. Prediction of Cycle 23 The unexpectedly high cycle 22 brought many scientists to believe that the next cycle 23 would be very high, or even higher than ever. This point of view was also supported by the author (see Obridko and Kuklin, 1994; Obridko et al., 1994; Obridko, Oraevsky, and Allen, 1994). Some forecasts of cycle 23 are summarized in Table III, taken from Obridko et al. (1994) with some minor changes. The same paper gives a detailed analy-


188

v.N. OBRIDKO

TABLE III Forecasts of the maximum Wolf numbers for cycle 23 Author Wilson (1988) Wilson (1992) Kopeck3~ (1991) Makarov and Mikhailutsa (1992) Makarova (1991) Vitinsky (1992) Rivin (1992) Obridko, Orajevsky, and Allen (1994) Tritakis (1986) Shove (1983) Chistyakov (1983) Kontor et al. (1983) Kuklin (1993) Monthly mean value 175.0 4- 40 213.9 4- 37.5 198.8 4- 36.5 214.7 Annual mean value

208.3 210 -4- 10 > 160 189 225 4- 8 200 4- 25 140 4- l0 85-120 75 110

41 or 206

sis of the applied prediction methods. Without repeating here the whole analysis, we should note that the methods based on the relationship of the cycles in a pair (Wilson, 1988, 1992; KopeckS, 1991; Vitinsky, 1992; Rivin, 1992; Obridko et al., 1994; Obridko, Oraevsky, and Allen, 1994) yield high values of the forthcoming cycle. To this group belongs the prediction of Tritakis (1986). High values are also obtained when the phenomena observed in the preceding cycle are taken into account, in particular the behaviour of high-latitude filaments and faculae (Makarova, 1991; Makarov and Mikhailutsa, 1992). The predictions based on secular and super-secular variations of the 11-year cycle show rather low values (Shove, 1983; Chistyakov, 1983; Kontor et al., 1983). Kuklin (1993) regarded the relation between the neighbouring odd cycles as a one-dimensional logistic mapping of the process with intermittence, and obtained two versions of the forecast: abnormally high and abnormally low cycle 23 (see also Obridko et aI., 1994). In fact, it is easy to obtain from (1)-(4) the following values (consecutively):

RM23 = 184.14 :t: 21.9,
RM23 =

(la) (2a) (3a) (4a)

203.2 4- 10.7,

RM23 = 213.7 -I- 36.7, RM23 = 226.5 4- 23.3.

These values are so large that it seems reasonable to expect a very high cycle.


SOMECOMMENTSON THE PROBLEMOF SOLARCYCLEPREDICTION

189

However, the situation becomes quite different if our new method is applied. To predict the height of cycle 23, we can use Equations (7) and (9). Over the interval of months 18 to 50 after the maximum of cycle 22, p = 0.1054. Substitute this into (7) and (9) to give, respectively,
RM23 = 73.8 4- 18.1,

(7a) (9a)

RM23 = 74.7 4- 6.9,

which disagrees with the values inferred from the rule of Gnevyshev-Ohl. Somewhat larger values (87.9 4- 20.0 and 92.8 + 14.2, respectively) are obtained if the selection intervals 18-47 are used. Thus, the following conclusions can be made: (1) Two methods of similar statistical reliability yield basically different results. Today, we do not know which of them is preferable. (2) Both methods were correct in the past, but now we are facing an anomaly of the type of cycles 4-5 and 8-9. It may be either a break-down of regularities, or a mere fluctuation. In any case, the next cycle is expected to be absolutely abnormal.

Acknowledgements
The work was fulfilled thanks to the financial support obtained from the Russian Foundation for Fundamental Investigation (Project 93-02-2866) and, partly, thanks to the International Science Foundation Grant awarded by the American Physical Society. Also, I would like to thank the unknown referee who pointed out some inaccuracies and whose valuable advice helped me formulate more exactly the basic statements of the paper.

References
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v.N. OBRIDKO

Makarova, V. V.: 1991, private communication. Mayaud, E N.: 1973, 1AGA Bull. No. 33. Obridko, V. N. and Kuklin, G. V.: 1994, in J. Hru~ka, M. A. Shea, D. E Smart, and G. Heckman (eds.), Solar Terrestrial Predictions Proc., Ottawa, Canada, Vol. 2, p. 273. Obridko, V. N., Oraevsky, V. N., and Allen, J. H.: 1994, in D. N. Baker, V. O. Papitashvili, and M. J. Teague (eds.), Proc. of the 1992 STEP Symposium/5th COSPAR Colloquium, held in Laurel, Maryland, U.S.A., 24-28 August, 1992, p. 557. Obridko, V, Belov, A., Ishkov, V., Rivin, Yu., Kuklin, G., and Vitinsky, Yu.: 1994, in J. Hru~ka, M. A. Shea, D. E Smart, and G. Heckman (eds.), Solar Terrestrial Predictions Proc., Ottawa, Canada, Vol. 2, p. 261. Ohl, A. I.: 1966, Soln. Dann. No. 12, 84. Ohl, A. I.: 1968, Probl. ofArctic and Antarctic, No. 28, p. 137. Ohl, A. I." 1976, Soln. Dann. No. 9, 73. Ohl, A. I. and Ohl, G. I.: 1979, in R. E Donnelly (ed.), Solar-Terrestrial Predictions Proc., Boulder, U.S.A., Vol. 2, p. 246. Rivin, Yu. R.: 1992, 'The Forecast of Unusually High Values of Solar Activity at the End of the Current Century and Its Discussion', in Cycles of Natural Processes, Dangerous Phenomena, and Ecological Forecasting, MNTK 'Geos', Moscow, 1992, p. 144. Schove, D. J.: 1983, Ann. Geophys. 1, 391. Thomson, T.: 1990, in R. J. Thompson, D. G. Cole, P. J. Wilkinson, M. A. Shea, D. Smart, and G. Heckman (eds.), Solar-Terrestrial Predictions Proc., 1989, Leura, Australia, Vol. 1, p. 598. Tritakis, V. P.: 1986, Solar-Terrestrial Predictions Proc., in E A. Simon, G. Hedeman, and M. A. Shea (eds.), Meudon, France, p. 106. Vitinsky, Yu. I.: 1992, private communication. Vitinsky, Yu. I., KopeckS, M., and Kuklin, G. V.: 1986, Statistika pyatnoobrazovatelnoi deyatelnosti Solntsa, Moscow, Nauka. Wilson, R. N.: 1988, Solar Phys. 117, 269. Wilson, R. N., 1992, SolarPhys. 140, 181.