Meandering Path to Solar Activity Forecast for Cycle 23
H.S. Ahluwalia
Department of Physics and Astronomy, The University of New Mexico, Albuquerque, NM 87131, USA
Abstract. Solar activity affects the shape of the corona as well as the size of the heliosphere. Also, it has a bearing on
the quality of life issues on earth. So it is important that its level be forecast in a reliable manner, well ahead of time, to
allow for proper planning. At Solar Wind Nine, I reported on the discovery of a three-cycle quasi-periodicity in the
magnetized solar wind from the polar coronal holes late in the descending phase of a cycle. This led us to develop a
procedure for forecasting the amplitude and the rise time of solar cycle 23. We predicted a moderate cycle 23 with a
smoothed sunspot number (SSN) at its maximum, in early 2000: 131.5+33/-20. The solar astronomers criticized our
prediction as being overly on the low side and unlikely to come true. So far, our forecast is right on the mark. We
review the solar and geophysical data as of the end of May 2002 and describe the present state of cycle 23 in relation to
those observed over a 400-year period and the lessons learned by us from this exercise.
commonly used as precursors for forecasting the size of
the new cycle [Ahluwalia, 1998]. A new procedure was
devised for computing the annual mean SSNs at the
At Solar Wind Eight conference (Dana Point, CA),
maximum (Rmax) for cycle 23 (119.3 +/-30); we
we questioned an early forecast for the solar cycle 23
predicted
that it would be a moderate cycle (a la cycle
that it would be more active than cycle 22 [Wilson,
17). Our prediction was criticized as being overly on
1992]. Our study of the planetary index Ap data (1932the low side and
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Fig.1. SSN and aa index data (1844-2001).
data (to suppress
the transients),
taking account of the fact that the onset of cycle 23
1994) had led us to conclude that the annual mean
occurred in May rather than in October 1996, assumed
minimum of Ap in 1997 was likely to be like those
in our earlier work [Ahluwalia, 1996]. We reaffirmed
observed in 1934 and 1965 [Ahluwalia, 1995]; the
that cycle 23 will be moderate with a smoothed SSN at
inferred three-cycle quasi-periodicity in the magnetized
solar wind from the coronal holes, seemed to be similar
its maximum (in early 2000): 131.5+33/-20.
to that observed in the frequency of occurrence of
auroras for a period of about four and a half centuries
Cycle 23 Rise Time
and in the SSNs for 1868-1990 period reviewed by
Silverman [1992]. The trend in the galactic cosmic ray
We present a new method for computing the rise time
variations appeared to be similar [Ahluwalia, 1997a].
(Tr) of a solar cycle, using aa index data (1844-2001)
We speculated that one may observe ~ 100 SSNs at the
depicted in the upper half of the Figure 1; also shown
cycle 23 maximum. We reviewed the available data for
are the corresponding SSN data for cycle 9 onwards.
Ap (1932-1997) and aa (1868-1997); these indices are
The aa index was devised by Mayaud [1972] to study
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SSNs
Geomagnetic Index, aa (nT)
INTRODUCTION
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
176
where even cycles of the even-odd pairing are less
active; it disappeared after cycle 21. The physical cause
for this pattern is unknown. One wonders whether this
pattern will manifest itself again in the future.
Figure 2 shows a plot of the annual mean aa index at
the minimum (aamin) of the smoothed SSN cycle
versus the rise time (Tr) of the cycle (defined as the
months between the smoothed SSNs at the minimum
and maximum), beginning with cycle 9 minimum
(1855). The distribution of points indicates a linear
trend. The fit parameters are given by,
Tr (months) = 61.6 — aamin (nT)
(1)
the long term changes in the intensity of magnetic
activity on planet earth. He combined the data from the
two antipodal magnetic observatories to cancel the
observed daily and seasonal variations in the record,
leading to the variations of a planetary character (shown
by points in the figure) from 1868 onwards. Nevanlinna
and Kataja [1993] extended Mayaud''s series back in
time for two additional solar cycles (1844 onwards)
using the magnetic declination observations made at the
Helsinki magnetic observatory in Finland, indicated by
open circles in Figure 1. The two data strings overlap
nicely for the common period. The following
characteristic features may be noted in the time series.
1.After 1901, the aa index seems to be riding on a line
of a positive slope. A question arises whether this rise
will continue indefinitely. Feynman [1982] ascribed
this trend to the increasing phase of the long solar cycle
with an average period of 87 years (Gleissberg cycle).
This interpretation implies that aa indices should have
decreased rapidly after the 1950s. This did not happen,
indicating that the situation may be more complex and
longer periods may be present in the time series. For
example, Silverman [1992] notes that recurring minima
near the turn of a new century are typical of the auroral
occurrence data from 1500 onwards.
2. The three-cycle quasi-periodicity in the annual mean
aa index (near solar cycle minima) are highlighted by
the dashed lines; no such trend is present in SSN time
series. Note that the slope of the dashed line is negative
prior to 1901. A question arises whether the quasiperiodicity will continue after the solar minimum circa
2006 and in what direction. Our forecast for cycle 24
will be greatly influenced by what happens then.
3. Since the slope of the line marking the longer-term
trend must turn negative eventually, the data suggest
the presence of a cyclic variation of greater than 100
years in aa index.
4. Beginning with cycle 10, one observes a pattern
aa (min) index (nT)
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Cycle Rise Time (months)
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Fig.2. A linear correlation between aa and Tr.
with a correlation coefficient (cc) = - 0.76 at a
confidence level (cl) > 99% [see Appendix C in Taylor,
1985]. For 1996, aamin = 18.6 nT, so Tr = 43 mos; with
the observed scatter of the points within +/-6 mos off
of the fit, giving a forecast for cycle 23 rise time Tr =
43 +/-6 mos. Cycle 23 reached maximum in April 2000
(47 months after onset), well within the limits set by
(1).
Cycle 23 Timeline
Smoothed SSN
In Figure 3, the timeline for cycle 23 is compared to
those for 6 prior cycles (17 to 22) for 66 months after
onset;
cycles
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months.
Months From Cycle Onset
The
Fig. 3. timeline of cycle 23 is compared to those of 6 prior cycles for 66 months.
177
Figure 5 shows a 300-year record (1700-2000) of the
annual mean SSNs. The following points may be noted.
1. There is a tendency for the solar cycles to be less
active at the start of a new century. About six cycles in
each century are moderate (Rmax ~ 100 or less). Four
most active cycles (18, 19, 21, 22) all occurred towards
the later half of the 20th century. One wonders whether
this fact has a bearing on the cycles to come in the 21st
century. No clear answer is available yet.
2. For the 18th and 19th centuries the average cycle
length is about 11 years, since there are nine cycles per
century present. However, for the 20th century more
than nine cycles are present, including the rising phase
of the cycle 23. This may be indicative of the presence
of a cyclic variation of greater than 100 years in SSNs .
following features may be noted.
1. The timelines may be classified into 2 groups. Cycles
18, 19, 21, 22 exhibit above average activity; 19 was
the most active cycle ever observed in nearly 400 years
of SSN observing period. Cycles 17 and 20 exhibit
moderate activity. A clear separation occurs between
the two groups 30 months after their onsets; cycle 17
starts out less active than 20 but its timeline settles at a
higher level after 39 months. On the other hand, cycle
22 starts out more active than 19 but became less so
after 18 months.
2. Cycle 23 starts out mimicking cycle 20 for 21
months, drifting closer to cycle 17 timeline settling
below it after 33 months, rising above cycle 20 timeline
after 42 months and that for cycle 17 after 45 months
and lingering at the higher level afterwards, reaching a
broad maximum 47 months (April 2000) after onset. It
is at its second maximum as of the end of May 2002; all
solar and geophysical phenomena exhibit two maxima,
known as the Gnevyshev gap [Ahluwalia, 2000b].
3. The only suspense left for cycle 23 is whether it
would again mimic cycle 20 in its declining phase and
end up being a long cycle with a length of 12 years or
be a short cycle (~10 years) like others in recent times.
Sunspot Number
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Smoothed Sunspot Numbers
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According to Waldmeier [1955], the rise time of a cycle
is determined by a single parameter, namely the SSN at
its maximum (Rmax). He showed that active cycles
have a steeper rise and moderate ones rise more slowly.
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Months From Cycle Onset
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Sunspot Number
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Fig. 5 Annual mean SSNs (1700-2000)
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YEAR
Historic Record
90 1900
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Fig. 4 Average active and moderate cycles
Figure 4 shows an average of the monthly smoothed
SSNs for the recent active (18, 19, 21, 22) and
moderate (17, 20, 23) cycles, plotted for 66 months
after onset; all cycles are normalized at the origin, as in
Fig.3. So the Waldmeier effect is alive and well but its
physical cause is unknown. The moderate cycles attain
their maximum an average of 5 months later and have a
tendency to linger near the maximum. We have to wait
another 6 years or so to learn how the fall time (Tf)
compares to the rise time (Tr) for the two groups.
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90 2000
solar message may get embedded on the planetary
indices, several details need to be worked out before we
understand the physical link between the observations
and the workings of the solar dynamo. Even so, our
simplified operational procedure for forecasting the rise
time and the amplitude for a new cycle appears to have
been vindicated for cycle 23. For the first time, in the
long history of observations of the sunspots, a forecast
was made for a solar cycle; it was defended against peer
criticism and has turned out to be right on the mark.
2. The only mystery left is whether cycle 23 will follow
the timeline for cycle 20 in its declining phase and be a
long cycle or end up with a duration ~ 10 years like
other more recent cycles.
3. Waldmeier effect is alive and well but its physical
cause is not known; it may be used as a confirming tool
for a forecast ~ 30 months after the new cycle onset.
4. No explanation is available at present for the
disappearance of the pattern observed from cycle 10 to
21 where even cycles of the even-odd pairings were
observed to be less active. It is not clear whether the
pattern will reappear in the future.
5. It is too early to make a forecast for cycle 24 in view
of the uncertainties discussed in this paper. We have to
wait for about 4 years more for cycle 23 to have run its
course.
3. As noted earlier, one observes a pattern where an
even cycle of the even-odd pairing is less active,
beginning with cycle 10 and ending with cycle 21. It is
not clear how this is linked to the workings of the solar
dynamo.
DISCUSSION
Ohl [1971] was the first to realize that sun advertises
in advance what to expect by way of its activity (SSNs)
in a new cycle. He posited that sun's subliminal
message is conveyed to earth via geomagnetic indices;
he used sum Kp data. However, he could not explain
how this incretion of sun s message actually occurs. At
first sight it sounds incredible that planetary indices (aa,
Ap, Kp) should be such good solar activity
development indicators. We suspected that solar wind
must be the carrier of the weak solar signal. So, we
carried out a detailed analysis of the available solar
wind data (1963-1998) to understand the sunmagnetosphere relationships and Ap's role in it
[Ahluwalia, 2000b]. We discovered that the three-cycle
quasi-periodicity in the annual mean Ap minima in a
solar cycle may be ascribed to the corresponding time
variations of the flux of the open field lines of the solar
magnetic field carried by the high speed solar wind
streams (HSSWS) from the coronal holes (measured in
situ at earth 's orbit), late in the declining phase of a
cycle. We suggested that the pertinent information from
the sun is transferred to the magnetosphere via temporal
fluctuations of the induced interplanetary electric field,
leading to the appropriate temporal variations of the
planetary indices. These results appear to be in
qualitative agreement with Babcock 's Solar Dynamo
model [1961] which outlines a scheme whereby high
latitude solar poloidal fields near solar minimum appear
as toroidal fields on the opposite sides of the solar
equator in the new cycle. We speculate that the
precursor solar poloidal fields are entrained in HSSWS
and brought to earth 's orbit. It is not clear whether the
three-cycle quasi-periodicity is generated on the surface
of the sun at high latitudes where Babcock' s dynamo
operates or whether it has to do with an intrinsic
property of the circulation pattern in the convection
zone under the solar surface. Some light may be shed
on these issues if the solar modelers attempt to solve the
MHD equations, applied self-consistently to the sun.
ACKNOWLEDGEMENTS
This research is supported by NSF Grant: ATM9904989. Smoothed SSN data are from the Sunspot
Index Data Center (SDIC), at Brussels, Belgium.
REFERENCES
Ahluwalia, H.S., Solar Wind Eight Conf. Paper, p. 469. AIP
Conf. Proc. Eds. D. Winterhalter, J.T. Gosling, W.S. Kurth, and
M. Neugebauer, Woodbury, NY, (1995).
Ahluwalia, H.S., Int. Cosmic Ray Conf. 28th, 2, 109 (1997a).
Ahluwalia, H.S., J. Geophys. Res., 102, 24229 (1997b).
Ahluwalia, H.S., J. Geophys. Res., 103, 12103 (1998).
Ahluwalia, H.S., J. Geophys. Res., 104, 2559 (1999a).
Ahluwalia, H.S., Solar Wind Nine Conf. Paper, p. 415. AIP Conf
Proc. Eds. S. Habbal, R. Risser, J. Hollweg, and P. Isenberg,
Woodbury, NY, (1999b)
Ahluwalia, H.S., Adv. Space Res., 26, 187 (2000a)
Ahluwalia, H.S., J. Geophys. Res., 105, 27481 (2000b).
Babcock, H.W., Astrophys. J., 133, 572 (1961).
Feynman, J., J. Geophys. Res., 87, 6153 (1982).
Mayaud, P.N., J. Geophys. Res., 77, 6870 (1972).
Nevanlinna, H., and E. Kataja, Geophys. Res. Lett., 20, 2703 (1993).
Ohl, A.I., Geomag. Aeron., 11, 549 (1971).
Schatten, K.H., P. Scherrer, L. Svalgaard, and J.M. Wilcox,
Geophys. Res. Lett., 5, 411 (1978).
Silverman, S.M., Rev. Geophys., 30, 333 (1992).
Taylor, J.P., An Introduction to Error Analysis, Univ. Sci. Books,
Mill Valley, Calif., (1985).
Waldmeier, M., Ergebnisse und Probleme der Sonnenforschung,
p. 154, 2nd Ed., Leipzig, (1955).
Wilson, R.M., Solar Phys., 140, 181 (1992).
Wilson, R.M., and D. Hathaway, J. Geophys. Res., 105, 2555 (2000).
CONCLUSIONS
1. Ohl' s hunch is correct; the sun advertises in advance
what to expect by way of activity in a new cycle. The
suggestion by Schatten et al [1978] that Ohl' s hunch
may be understood on the basis of Babcock 's model of
a solar dynamo appears to be plausible. While we have
made considerable progress in understanding how the
179