Full text of DOI:10.1007/BF02900615

number and a fluctuation of 13 associated monthly mean
sunspot numbers to the smoothed number as a new index,
indicating the solar activity level. Then, we study the pos-
sible trace of the index of a certain cycle around its
maximum, and give an estimation of the peak appearance
time of the cycle. An application of this method to Cycle
23 shows that the maximum of Cycle 23 should have ap-
peared in the period from April to August 2000. Namely,
the maximum of Cycle 23 has appeared, and it is in the
descending phase of the cycle even if there might be a
sub-peak in the phase.
Has the maximum of Solar
Cycle 23 appeared?
WANG Jialong1, GONG Jiancun2, TONG Jizhou2,
SUN Jinglan1 & ZHU Cuilan1
1. Beijing Astronomical Observatory, Chinese Academy of Sciences,
National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100012, China;
2. Center for Space Science and Applied Research, Chinese Academy of
Sciences, Beijing 100080, China
Correspondence should be addressed to Wang Jialong (e-mail: wjl@
class1.bao.ac.cn)
1 The trace of the level of solar activity near a
maximum
Abstract
In this note, we define firstly a compositive
The definition of a smoothed monthly mean sunspot
parameter as an index describing the level of solar activity in
a solar cycle. The parameter is derived from a combination
of the smoothed monthly mean sunspot number with the
fluctuation of the associated monthly mean sunspot numbers
to the smoothed one. Then, a method is developed for
estimating the time of the appearance of a solar maximum
based on the conception of similar cycles. An application of
number, R(M, n), for the month n and cycle M and the
fluctuation D(M, n) of the associated 13 monthly mean
sunspot numbers to R(M, n) are given in eqs. (1) and (2),
respectively. The former is an indicator of the mean level
of solar activity, while the latter can be used to reflect the
possible deviation of the observed activity level to the
mean one.
the method to the 23rd solar cycle shows that the maximum
of the cycle should have appeared in the period from April to
August 2000, and the descending phase of Cycle 23 has come.
-
1
1
°
12 2
R(M , n)
[r(M , n ꢁ 6) ꢀ r(M , n ꢀ 6)]
®
°
Keywords: solar cycle, sunspot number, estimate of peak time, 23rd
solar cycle.
¯
(1)
nꢀ5
½
°
ꢀ
r(M , j) ,
¾
¦
Smoothed monthly mean sunspot numbers
(smoothed numbers hereafter) are widely used to describe
levels of solar activity and decide characteristics such as
phases and extrema of a solar cycle. However, we cannot
decide the peak value and peak time of a solar cycle from
observational data until at least the eighth month after the
appearance of the maximum, due to the need of 13
°
j nꢁ5
¿
-
-
1
1
2
°°
®®
D(M , n)2
[r(M , n ꢁ 6) ꢀ r(M , n ꢀ 6)]
12
°°
¯
¯
2
nꢀ5
½
½
°
°
monthly mean sunspot numbers for calculating
a
ꢁ R(M , n)
ꢀ
[r(M , j) ꢁ R(M , n)]2
j nꢁ5
,
¾
¾
¦
smoothed number (see eq. (1)). Now, it is not far to or
from the maximum of Cycle 23, but we are still not able
to know the precise time of the cycle’s maximum. On the
other hand, predictions of the time of the 23rd cycle’s
maximum published before or during the minimum of the
cycle at the beginning show a large dispersion to each
other: the time range of the appearance of the cycle’s
maximum covers a long period from June 2000 to June
2006[1]. While predictions published recently show a
common tendency: the peak time of the cycle is in A.D.
°
°
¿
¿
(2)
where r(M, n) is the monthly mean sunspot number
of the month n, cycle M. The relation of R(M, n) with
D(M, n) near the maximum of cycle M can then be studied
if r(M, n)s is taken around the maximum of cycle M.
For a month by month comparison of the level of
solar activity, a compositive parameter, A(M, n), is derived
from R(M, n) and D(M, n) given in eq. (3). One may see
from eq. (3) that A(M, n) not only represents a combina-
tion of R(M, n) and D(M, n) but also makes R(M, n) the
dominant component in the index. Meanwhile, A(M, n) is
of the same magnitude as a sunspot number which is
traditionally known in many fields.
ü
2000— 2001[2 5],1). Thus, whether the maximum of Cycle
23 has appeared is still an open question at present.
In this note, we try to develop a method for estimat-
ing the appearance time of a cycle’s maximum when it is
not far to or from the maximum. Firstly, we define a
compositive parameter derived from a smoothed sunspot
1) Space Environment Center NOAA U.S., Dept. of Commerce, Predicted sunspot number and radio flux.
Gopher://sec.noaa.gov/00/weekly/predict.txt, 2000, October.
Chinese Science Bulletin Vol. 46 No. 19 October 2001
1603

NOTES
Fig. 1. Retation of R(M, n) with D(M, n)
near the maximum for 7 cycles, respectively.
1
2
A(M , n)
>
R(M , n)2 ꢀ D(M , n)2
@
.
(3)
relation of the R(M, n) with D(M, n) is morphologically
similar to that of Cycle 23. We have 6 cycles which satisfy
conditions (ν) and (ξ), and relations of R(M, n) with
D(M, n) for these cycles and for Cycle 23 are respectively
shown in fig. 1. It is easy to find that Cycle 20 does not
satisfy condition (ο). Finally, we have Cycles 8, 9, 11, 15
and 17, which satisfy all of the three conditions.
Obviously for a certain cycle, e.g. cycle M, the rela-
tion of A(M, n) with n should show the variation of A(M, n)
with time, namely the trace of A(M, n).
2
Decision of the 23rd cycle’s maximum
We will decide the time of the 23rd cycle’s maxi-
mum by means of finding the possible limits of the trace
of A(M, n) near the maximum. According to the observa-
tional data and predictions we have already had for Cycle
23, among the past 15 cycles (from the 8th to the 22nd
cycle), several cycles satisfying the following three condi-
tions are selected to be similar cycles to Cycle 23. The
three conditions are: (ν) its maximum of the smoothed
number is in the range of 100—150, (ξ) its ascending
phase is not less than 3 years, and (ο) the shape of the
In eqs. (4) and (5), an average of A(M, n), written as
, and the standard error of
, written as
A(M , n)
A(M , n)
, can be deduced for the selected 5 cycles, using
'A(M , n)
observational data and taking ns around the five maxima.
1
A(n)
A(M , n),
¦
5
M
(4)
M 8, 9,11,15,17,
1604
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3
Discussion
-
°
½
°
1
4
2
'A(n)
>
A(M , n) ꢁ A(n)
@
,
®
¾
¦
The time estimation of the maximum of a certain
°
°
¿
M
¯
cycle given by the method developed in this note is
strongly related to the selection of similar cycles. The
more strictly the similar conditions are used in the method,
the less errors may be obtained but the larger risk must be
faced and vice versa. Although the time span of our result
is 5 months, from April to August 2000, we may definitely
state that the maximum of Cycle 23 has appeared.
M 8, 9,11,15,17.
(5)
Results obtained in this way mentioned above are
shown in fig. 2, where black points and pairs of short bars
represent respectively
and
for
A(M , n)s
'A(M , n)s
the 5 cycles. One can see that
and
A(M , n)s
'A(M , n)s
in fig. 2 unitedly and clearly describe the range of the
23rd cycle’s trace. Then, using 15 groups of observational
data taken from the latest 15 months (Feburary
1999—April 2000) of Cycle 23, we get 15 values of A(23,
n), labeled by circles in fig. 2. By moving these circles in
the way parallel to axis n and considering the error bars,
we may find two extreme cases outlining the most possi-
ble limits of the trace of Cycle 23 by two lines of circles
(fig. 2), and can conclude that the maximum of Cycle 23
would have appeared in the period from April to August
2000, and it is now in the descending phase of the cycle.
A similar idea was successfully proposed to forecast
the beginning minimum of the 23rd cycle in 1996[6].
Comparably, in this note, we not only use the widely ac-
cepted smoothed numbers instead of the one used in 1996,
but also extend the forecasting object of our study from
minima to maxima of solar cycles.
Acknowledgements This work was supported by the National Natural
Science Foundation of China (Grant Nos. 4999-0451 and 10073013) and
Space Environment Forecast Center.
References
1. Wang Jialong, On solar activity prediction and disaster prediction,
Progress in Geophysics,1999, 14(suppl.): 117.
2. Wang Jialong, Han Yanben, Forecast of smoothed monthly mean
sunspot numbers and non-smoothed monthly mean sunspot num-
bers for Solar Cycle 23, Astrophysics Reports, Publ. of the Beijing
Astron. Obs., 1997, 1(Supplement series): 76.
3. Kane, R. P., Prediction of the sunspot maximum of Solar Cycle 23
by extrapolation of spectral components, Solar Phys., 1999, 189:
217.
4. Landscheidt, T., Extrema in sunspot cycle linked to sun’s motion,
Solar Phys., 1999, 189: 415.
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sunspot number, Chinese Science Bulletin, 2000, 45(14): 1287.
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lar-Terrestrial Prediction-V(eds. Heckman, G., Marubashi, K.,
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Fig. 2. Average path around the maximum for 5 cycles similar to Cycle
23 and decision of the time of maximum of Cycle 23.
(Received April 13, 2001)
Chinese Science Bulletin Vol. 46 No. 19 October 2001
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