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Solar Cycle 25 Started on November 17, 2019 with 365 Days Smoothing

Abstract and Figures

In our previous article we found a relationship between the adjusted solar flux and the start of sunspot cycles. We used the 13 month smoothed average for it. Building further on this we found a surprising proof that sunspots and the adjusted solar flux are even more related. If we replace the standard smoothing formula with a 365 days smoothed average, some at first sight unbelievable coincidences turn up in the cycle 24-25 transition. The lows from NOAA SN and 2 high resolution SN data series fall on the same day as the low of the adjusted solar flux, while the ISN is quite close.
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Solar Cycle 25 Started on
November 17, 2019 with 365 Days
Smoothing
Abstract
In our previous article we found a relationship between the
adjusted solar flux and the start of sunspot cycles. We used the
13 month smoothed average for it. Building further on this we
found a surprising proof that sunspots and the adjusted solar
flux are even more related. If we replace the standard
smoothing formula with a 365 days smoothed average, some at
first sight unbelievable coincidences turn up in the cycle 24-25
transition. The lows from NOAA SN and 2 high resolution SN
data series fall on the same day as the low of the adjusted solar
flux, while the ISN is quite close.
P. P. A. Geryl email: patrick.geryl@skynet.be
Jan Alvestad (Solar Terrestrial Activity Report)
Keywords
Solar Cycle 25; Sunspot cycles; Low sunspot activity; 13 month smoothed averages;
10.7cm Solar flux;
1.0 Introduction
How do you define the "start" of a solar cycle? It is a rather complicated task, a time
where there are sunspots from both the old and the new cycle. Is the minimum the
time where the number of old cycle spots is equal to the number of new cycle spots?
If we look at each sunspot cycle as independent of other cycles, we could say that a
sunspot cycle physically starts with the first observation of high latitude spots of the
expected polarity orientation. The first observations of spots from a particular
sunspot cycle typically occurs 18-30 months before the statistically determined
minimum that defines the end of one solar cycle and the start of the next. The
minimum would be the time when the combined activity from the ending sunspot
cycle and the beginning sunspot cycle reaches its lowest point. We use objective solar
flux measurements and subjective sunspot observations averaged over 365 days in an
attempt to determine the solar cycle minimum as accurately as possible.
2.0 Problems establishing a minimum
In the early 20th century, the Zürich observatory introduced the smoothing formula,
chosen for its simplicity. Till today it remains the base reference and allows an easy
comparison for multiple scientific analyses. The smoothed sunspot number defines
the maxima and minima for each cycle to which other series can be linked. Currently
many astronomers wonder if it is significant and makes sense to converge the
temporal differences between the minima for the sunspot number and other solar
data series. While the sunspot number http://www.sidc.be/silso/datafiles is a direct measure
of the primary emerged magnetic flux, most other data series will not evolve exactly
in the same way. They are sensitive to different aspects of solar activity as the curve is
very flat around the minimum and lead to a different result when smoothed. You see
hardly any significantly higher values before or after the minimum. Other factors
contribute to the problem like spotless days , the date when the number of new-cycle
groups exceeds the number of old-cycle groups (both 13 month smoothed), and
group sunspot numbers (McKinnon, J. A., 1987). It should be noted that the
minimum in sunspots was originally in May 1996, however, this was moved later to
August 1996 because of the just mentioned factors (Harvey and White, 1999).
The solar flux has a lagged component due to the contribution of decayed/residual
magnetic fields, remaining long after the emergence. A few dispersed active regions,
which leave a signature in the corona and chromosphere, give a slight difference
between data series and may easily shift the date of the lowest values by several
months as can be seen in table 1. Using another smoothing method will give other
values. None of them is better than others, is the current opinion. Podladchikova et
al, 2017, quantified the short term variations in terms of second derivatives to
optimize the sunspot numbers to distinguish if the next Solar Cycle will be stronger or
weaker.
Correlating indicators or measurements of solar activity makes it easier to use each as
a validation of the other one. In case they don't match well, there could be reasons to
look for explanations. Now it gets interesting. Is there a physical reason to prefer one
method over another? With the current method the minimum is an extended interval
of several months. But could it be possible and does it make sense to pick an exact
day as the time of minimum?
Table 1 shows a comparison between the lowest 13 month smoothed solar flux values
from http://www.wdcb.ru/stp/data/solar.act/flux10.7/ World Data Center for Solar-Terrestrial Physics,
Moscow and "Solar Terrestrial Activity Report" or STAR http://www.solen.info/solar/
at cycle transitions in comparison with the lowest 13 month smoothed ISN values.
Cycle
transition
Lowest 13month
smoothed
ISN
Lowest 13month
smoothed adjusted
flux
Date ISN
Date sfu
18-19
1954/04 5.1
1954/04 69.7
19-20
1964/10 14.3
1964/10 72.5
20-21
1976/03 17.8
1976/06 73.3
21-22
1986/09 13.5
1986/09 72.9
22-23
1996/08 11.2
1996/05 71.4
23-24
2008/12 2.2
2008/10 68.2
24-25
2019/12 1.9
2019/12 69.3
We see a difference of 3 months during the cycle transitions 20-21 and 22-23 and one
of 2 months in cycle transition 23-24.
3.0 Potential problems with the 13 month smoothing formula
We see two potential problems with using the 13 month smoothing formula and
where the formula can introduce noise.
1. The effective smoothing window is not constant. When leap year February is
involved in the calculation, the effective smoothing window becomes 365.5 or 366
days compared to the normal 365 days.
2. The contribution from the flanking months is variable. If you are calculating the
smoothed sunspot number for February, the previous August and the next August are
the flanking months and each contribute with activity for 15.5 days. Conversely if the
center month is August, the flanking months is the previous and the next February.
The number of days contributed from each flanking month will then be 14 or 14.5 (if a
leap year is involved) days.
3. Because the Sun rotates about once every 27 days, some monthly averages could
have twice an active region (Hathaway, 2015).
4.0 The 365 days smoothing formula
Could the previous problems be related to the inexact 13 months smoothing formula?
We think it is. Therefore we disagree with the previous arguments as we have found a
new method where sunspot and solar flux minimum are converging. This is also to be
expected as they are measurements related to the same phenomenon. Most of the
problems previously seen using smoothing on these measurements appears to be
related to the smoothing formula. Always using 365d smoothing removes those
problems and also the unwanted influence of the extra half month on each side of the
month being smoothed. 13 months smoothing gives inexact minima, 365 days lets
you determine the minimum as accurately as possible. It all depends on what you are
after. Based on what you study, as in our first article A Formula for the Start of
Sunspot Cycles, only a subset of reference data series are relevant, the same like for
this study: the sunspot number and the solar flux. The formula for the 13 month
smoothed sunspot number can be found in our previous article The Adjusted Solar
Flux & the Start of Solar Cycle 25 or at the site of the Royal Observatory of Belgium.
How does the 365 day formula look like? This is quite easy to understand. Take a
center value (dc) plus the sum of the values till 182 days before (-d182) and after
(+d182), while making the mean.
Example formula:
[ (-d182) + (-d181)…. + (dc) + (d1)… + (d182) ]/365
(where dc = value for November 22, 2017, -d182 = value for May 24, 2017 and d182 =
value for May 23, 2018). Any missing daily values for the smoothing interval will
reduce the data set available for calculation.
5.0 The 365 days smoothing formula and the Solar Cycle 24-25 transition
As for the transition from cycle24-25, 4 out of 5 data series using 365d averages have
the minimum on the same day - November 17, 2019 (F10.7, NOAA SN, STAR 1K,
STAR 2K), and one on November 28 for the ISN (see table 2 and figure 1). As can be
seen using 365d averages is significantly more accurate than using 13 months
smoothing. It gives a lower minimum, in the case of cycle 24-25 ISN 13 months
smoothed minimum is 1.9, while the 365d average has the ISN minimum at 1.65
(again logical as there will be one month less to increase the minimum).
Table 2 shows the lowest 365 day smoothed adjusted solar flux in relation with the
lowest 365 day smoothed sunspot number for the Solar Cycle 24-25 transition:
Cycle
transition
Lowest 365 day
smoothed SSN
Date ISN
24-25
2019/11/28 1.65
Date NOAA
2019/11/17 1.67
Date STAR 2K
2019/11/17 11.49
Date STAR 1K
2019/11/17 4.62
Figure 1. Illustration of the transition from solar cycle 24 to 25. Chart used with
permission from co-author Jan Alvestad.
Black = F10.7 (1AU) 365d average
Blue = STAR 2K SN 365d average
Red = STAR 1K SN 365d average
Cyan = ISN 365d average
Green= NOAA SN 365d average
6.0 The 365 days smoothing formula and 7 transition cycles
We researched the other cycles since the start of flux measurements (see table 3). We
found that for those 7 transitions the calculated minimum 365 day smoothed ISN and
adjusted solar flux occurred within days of each other. In 4 cases there were 3 or less
days between the flux and sunspot minima. The notable deviation from this rule was
the transition between solar cycles 23 and 24 when the minima where spaced by 44
days.
Table 3 shows the minimum 365 day smoothed sunspot number and the minimum
365 day smoothed adjusted solar flux
Cycle
transition
Minimum 365 day
smoothed ISN
Minimum 365 day
smoothed adjusted
solar flux
Date ISN
Date sfu
18-19
1954/04/16 4.85
1954/03/27 69.70
19-20
1964/10/11 13.93
1964/10/09 72.41
20-21
1976/06/08 16.98
1976/06/09 73.11
21-22
1986/09/12 13.28
1986/09/13 72.60
22-23
1996/05/22 10.45
1996/05/19 71.04
23-24
2008/11/19 2.12
2008/10/06 68.15
24-25
2019/11/28 1.65
2019/11/17 69.13
Remark: during the 18-19 cycle transition around 56 days were recorded without flux
measurements. This suggests we should interpret this transition carefully.
We can conclude that there is a tighter than expected relationship between the 365
days smoothed adjusted flux and 365 day smoothed ISN.
7.0 The 365 days smoothing formula and the Solar Cycle 24 high
Our formula gives relatively similar results for the high of cycle 24. Both NOAA
ftp://ftp.swpc.noaa.gov/pub/warehouse and ISN peak on the same day, April 7, 2014 (see
table 4 and figure 2). 2K peaks on April 9 with a slightly smaller peak on June 1. 1K
has two similar peaks, the first on April 9 and the next one June 2 (slightly larger
than the first peak). F10.7 peaks on June 28. The sunspot data series are pretty close
as we see it, even at solar maximum.
Table 4 shows the highest 365 day smoothed sunspot number from cycle 24
Cycle
Highest 365 day
smoothed SSN
Highest 365 day
smoothed adjusted
solar flux
Date ISN
Date sfu
24
2014/04/07 118.0
2014/6/28 145.5
Date NOAA
2014/04/07 126.9
Date 2K
2014/04/09 249.6
2014/06/01 248.7
Date 1K
2014/04/09 170.2
2014/06/02 170.8
Figure 2. Cycle 24 solar maximum to solar minimum using 365 days smoothing.
Chart used with permission from co-author Jan Alvestad.
Black = F10.7 (1AU) 365d average
Blue = STAR 2K SN 365d average
Red = STAR 1K SN 365d average
Cyan = ISN 365d average
Green= NOAA SN 365d average
8.0 Higher highs and the 365 days smoothing formula
Using 365d averages gives a higher maximum (logical with one less month with lower
values to drag the average down). For instance ISN 13 months smoothed maximum
for cycle 19 is 285.0 (see table 5), while the 365d average has the ISN maximum at
287.8 (see table 6). The same can be said for the solar flux. For instance the solar flux
13 months smoothed maximum for cycle 24 is 145.1 (table 5), while the 365d average
has the sfu maximum at 145.9 (table 6). Wilson et al, 1987, found that the maximum
solar flux from cycles 20 and 21 lagged around 1.5 years from the smoothed sunspot
high. This is still the case - even a bit more for cycle 20 - with the revised sunspot
series, Clette et al, 2016. The 365 days method gives a slight improvement for cycle
20.
Table 5 shows the highest 365 day smoothed sunspot number for cycles 19-24
Cycle
13 month
smoothed ISN
13 month
smoothed sfu
Date ISN
Date sfu
19
1958/03 285.0
1958/03 245.2
20
1968/11 156.6
1970/07 156.3
21
1979/12 232.9
1981/05 204.4
22
1989/11 212.5
1989/06 213.0
23
2001/11 180.3
2002/02 196.8
24
2014/04 116.4
2014/06 145.1
Table 6 shows the highest 365 day smoothed solar flux for cycles 19-24
Cycle
Highest 365 day
smoothed ISN
Highest 365 day
smoothed sfu
Date ISN
Date sfu
19
1958/03/09 288.2
1958/02/28 246.7
20
1969/01/09 158.8
1970/06/21 156.8
21
1979/12/29 233.6
1981/06/13 206.2
22
1989/10/27 213.4
1989/06/11 213.8
23
2001/12/06 182.8
2002/02/23 198.1
24
2014/04/07 118.0
2014/06/28 145.5
9.0 Discussion & conclusion
If we look at the 13 month smoothed average for cycle transitions 20-21 and 22-23,
we see that there is a 3 month difference between the low of the ISN and the 10.7
solar flux. In stark contrast they have respectively a 2 day and 1 day difference using
the 365 day smoothing method. At first sight, we couldn’t believe our results, but
after checking multiple times, we had to conclude they are irrefutable. The difference
of future cycle transitions like 23-24 (44 days) can be strongly improved by using
high resolution sunspot calculations. For instance the ISN had an 11 day difference
with the solar flux for cycle transition 24-25, while the high resolution had none.
The highs of the cycles are not as consistent as the lows. If the cycle is weak, as cycle
24, then the values are close to each other. When they are stronger, the values can
differ by several months, approximately the same as for the 13 month smoothed
method. We need to caution here that we used solar flaring compensation for cycle
24 since January 2012. This wasn’t always the case in the past and could be a
contributing factor for the good results seen in cycle 24. However, we are convinced
that the high resolution sunspot method can reduce the differences substantially.
We strongly suggest to abolish the use of the 13 month smoothing method where
possible, especially for calculating the start of sunspot cycles. This would also apply to
sunspot observations prior to the start of the solar flux data series. Furthermore we
see that the high resolution sunspot data series is more similar to the 10.7 solar flux
series than any other sunspot method, especially at the maximum of cycle 24. The 2K
and 1K method give a small bump close to the F10.7 peak, while the ISN and NOAA
decline further. Such a close relationship between the high resolution sunspot
number and the solar flux seems too good to ignore. What if both are in fact the
same? What if the solar flux is the magnetic equivalent of the sunspot formation in
some way? That the 10.7 flux is a mirror of the axial dipole field, which governs the
sunspot formation as found by Robert Cameron and Manfred Schüssler, 2015? That
could bring the study of the Sun’s dynamics to a new dimension. We don’t have the
hemispheric sunspot fluxes, but we can study the hemispheric sunspot numbers. Will
we be able to find more with the 365 days smoothing method and the hemispheric
sunspot numbers? They don’t have the same lows and highs and possible unexpected
results remain to be discovered.
As early as on June 3, 2020 smoothing of several data series strongly suggested that
Solar Cycle 25 had started on November 17, 2019. This was 5 months earlier than the
NASA prediction panel, which predicted April 2020 in December 2019. Above that,
we were already confident in November 2019 that the latest starting month for Solar
Cycle 25 would be January 2020. All the other used methods were still at least 7
months away from a final conclusion.
Sources and data files
Source: WDC-SILSO, Royal Observatory of Belgium, Brussels"..
SILSO, World Data Center - Sunspot Number and Long-term Solar Observations, Royal Observatory
of Belgium, on-line Sunspot Number catalogue: http://www.sidc.be/SILSO/, ‘year(s)-of-data 1947-
2020’
Source 10.7cm radio flux values (sfu): World Data Center for Solar-Terrestrial Physics, Moscow
Source 10.7cm radio flux values (sfu): spaceweather.gc.ca.
Source 10.7cm radio flux values (sfu): "Solar Terrestrial Activity Report" (STAR) from 2012.01.01
Source NOAA: swpc.nooa.gov.
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Article
Full-text available
Forecasting the strength of the sunspot cycle is highly important for many space weather applications. Our previous studies have shown the importance of sunspot number variability in the declining phase of the current 11-year sunspot cycle to predict the strength of the next cycle when the minimum of the current cycle has been observed. In this study we continue this approach and show that we can remove the limitation of having to know the minimum epoch of the current cycle, and that we can already provide a forecast of the following cycle strength in the early stage of the declining phase of the current cycle. We introduce a method to reliably calculate sunspot number second differences (SNSD) in order to quantify the short-term variations of sunspot activity. We demonstrate a steady relationship between the SNSD dynamics in the early stage of the declining phase of a given cycle and the strength of the following sunspot cycle. This finding may bear physical implications on the underlying dynamo at work. From this relation, a relevant indicator is constructed that distinguishes whether the next cycle will be stronger or weaker compared to the current one. We demonstrate that within 24–31 months after reaching the maximum of the cycle, it can be decided with high probability (0.96) whether the next cycle will be weaker or stronger. We predict that sunspot cycle 25 will be weaker than the current cycle 24.
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The solar cycle is reviewed. The 11-year cycle of solar activity is characterized by the rise and fall in the numbers and surface area of sunspots. A number of other solar activity indicators also vary in association with the sunspots including; the 10.7 cm radio flux, the total solar irradiance, the magnetic field, flares and coronal mass ejections, geomagnetic activity, galactic cosmic ray fluxes, and radioisotopes in tree rings and ice cores. Individual solar cycles are characterized by their maxima and minima, cycle periods and amplitudes, cycle shape, the equatorward drift of the active latitudes, hemispheric asymmetries, and active longitudes. Cycle-to-cycle variability includes the Maunder Minimum, the Gleissberg Cycle, and the Gnevyshev-Ohl (even-odd) Rule. Short-term variability includes the 154-day periodicity, quasi-biennial variations, and double-peaked maxima. We conclude with an examination of prediction techniques for the solar cycle and a closer look at cycles 23 and 24. Electronic Supplementary Material Supplementary material is available for this article at 10.1007/lrsp-2015-4.
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Sunspots and the plethora of other phenomena occurring in the course of the 11-year cycle of solar activity are a consequence of the emergence of magnetic flux at the solar surface. The observed orientations of bipolar sunspot groups imply that they originate from toroidal (azimuthally orientated) magnetic flux in the convective envelope of the Sun. We show that the net toroidal magnetic flux generated by differential rotation within a hemisphere of the convection zone is determined by the emerged magnetic flux at the solar surface and thus can be calculated from the observed magnetic field distribution. The main source of the toroidal flux is the roughly dipolar surface magnetic field at the polar caps, which peaks around the minima of the activity cycle. Copyright © 2015, American Association for the Advancement of Science.
Article
Establishing the time of minimum between cycles 22 and 23 is complicated because there are two periods of low solar activity during 1996. To resolve this controversy, we studied the time of minimum in terms of the historical basis for defining this fiducial point in the solar cycle using several measures of solar activity, as well as the cycle membership of active regions observed during the minimum phase between these two cycles. Our conclusion is that cycle minimum is not defined solely on the basis of the occurrence of the minimum in the smoothed sunspot number, but rather by several additional parameters, including the monthly (or rotationally) averaged sunspot number, the number of regions (total, new- and old-cycle), and the number of spotless days. Using these specific measures of solar activity, we recommend that the minimum between cycles 22 and 23 occurred in September 1996 (1996.7) and not in May 1996 (1996.4).
Article
During sunspot cycles 20 and 21, the maximum in smoothed 10.7-cm solar radio flux occurred about 1.5 yr after the maximum smoothed sunspot number, whereas during cycles 18 and 19 no lag was observed. Thus, although 10.7-cm radio flux and Zurich sunspot number are highly correlated, they are not interchangeable, especially near solar maximum. The 10.7-cm flux more closely follows the number of sunspots visible on the solar disk, while the Zurich sunspot number more closely follows the number of sunspot groups. The number of sunspots in an active region is one measure of the complexity of the magnetic structure of the region, and the coincidence in the maxima of radio flux and number of sunspots apparently reflects higher radio emission from active regions of greater magnetic complexity. The presence of a lag between sunspot-number maximum and radio-flux maximum in some cycles but not in others argues that some aspect of the average magnetic complexity near solar maximum must vary from cycle to cycle. A speculative possibility is that the radio-flux lag discriminates between long-period and short-period cycles, being another indicator that the solar cycle switches between long-period and short-period modes.
Sol Phys (2016) 291: 2733. The Revised Brussels-Locarno Sunspot Number
  • F Clette
  • L Lefèvre
  • M Cagnotti
Clette, F., Lefèvre, L., Cagnotti, M. et al. Sol Phys (2016) 291: 2733. The Revised Brussels-Locarno Sunspot Number (1981 - 2015), DOI: https://doi.org/10.1007/s11207-016-0875-4
A Formula for the Start of a New Sunspot Cycle
  • P P A Geryl
  • J Alvestad
Geryl P.P.A., Alvestad J., A Formula for the Start of a New Sunspot Cycle (2020) DOI: 10.1007/s10509-020-03800-x https://www.researchgate.net/publication/340477337_A_Formula_for_the_Start_of_a_New_Sunspot_Cycle
The Adjusted Solar Flux & the Start of Solar Cycle
  • P P A Geryl
  • J Alvestad
Geryl P.P.A., Alvestad J., The Adjusted Solar Flux & the Start of Solar Cycle 25 (2020)
  • J A Mckinnon
McKinnon, J. A., 1987, Sunspot Numbers: 1610-1985 (based on The Sunspot-Activity in the Years 1610-1960, by Prof. M. Waldmeier, Copyright 1961, Swiss Federal Observatory, Zurich, Switzerland), UAG Reports, UAG-95, National Geophysical Data Center, NOAA, Boulder, CO.