The solar cycle

Contents

• Extreme changes and quiet spells in monthly sunspotnumbers (29 April 2011)
  
• Evolution Sunspotnumber since 1610 (18 January 2011)
  
• Overview solar cycles (SC 1 to SC24) (18 January 2011)
  
• The Gnevyshev-Ohl rule (02 February 2011)
  
• Synoptic maps per year for SC23 and SC24 (02 February 2011)
  
• Top 50 of flare-prone sunspotgroups since 1976 (22 January 2011)
  
• Top 50 of biggest sunspotgroups since 1874 (SC12) (20 January 2011)
  
• Predicting SC24-maximum from early SC24-sunspotnumbers (05 April 2010)
  
• Solar flares (more recent version: 28 October 2006)
  
• High Sunspotnumbers early July 2005 (01 August 2005)
  
• The Solar Constant (14 April 2005)
  

Evolution Sunspotnumber since 1610

This graphic shows the evolution of the solar activity since the beginning of telescopic observations. Initially, it was based on the observations of a few sporadic observers. As a consequence, there are quite a number of interruptions in the series. Nonetheless, the low solar activity between 1645 and 1715 is real. It is called the Maunderminimum and is well established by now (see Eddy, Ribes,...). As from 1750, enough observatories contributed observations on a systematic base, and the first official solar cycle started in May 1755. No 2 cycles are alike. Weak solar cycles were present around the turn of the centuries (1800 en 1900). However, during the last decades, the sun has been very active. Data from 1610-1748 from NGDC's ftp-site (monthrg[1].dat - file), the data from 1749-2010 from SIDC. The monthly data were smoothed using the Meeus-formula. Finally, please note Leif Svalgaard's research in calibrating the sunspotnumbers over the last 4 centuries (see his most recent presentations 1, 2 and 3). These indicate that we have not lived in a Grand Maximum of solar activity during the latter half of the 20th century, similar periods having occured in the second half of the 18th century (prior to the Dalton minimum) and between 1830-1880.

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Overview solar cycles (SC 1 to SC24)

This table provides for every official cycle the time of its beginning, its maximum and its end, as well as the minimum and maximum of the monthly Wolfnumber (smoothed according to the Meeus-formula). Also calculated are the duration in months between the minimum and maximum (time of rise), and between the maximum and the subsequent minimum (time of fall). The total length of the solar cycle is the sum of these 2 periods. A solar cycle averages 117 in maximum Sunspotnumber and lasts about 11 years (132 months). Since solar cycle 15, these averages appear to be rather 140 and 10,3 years. However, SC23 peaked at 125,6 and with its 151 months it was one of the longest on record.

The Gnevyshev-Ohl rule states that an unpair solar cycle has a higher intensity (=sum of monthly sunspotnumbers) than its even-numbered predecessor. The "law" is an important help in the prediction of solar cycles, and was used in predicting SC23 (NOAA-panel report) and also SC24 (e.g. Kane, 2008). So far, the only exception was SC05 which was significantly lower and sparked a debate on whether a solar cycle was "missed" in the declining phase of SC04 (see my Jan 2008 article). Assuming there was a cycle missing, the G-O rule would be reestablished and valid for the entire 400-year-span of solar observations.
But with SC23, another exception has been added. Both sunspot number and sunspot area intensity were about 10% lower than SC22-values (see figure below). Some scientists are not convinced and report the rule is still valid in other solar parameters (e.g. Nagovitsyn, 2009). For the prediction of sunspotnumbers, it really does not seem a good idea to rely solely on the G-O rule, or to attach too much weight to it.

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Top 50 of biggest sunspotgroups since 1874

This table provides an overview of the biggest sunspotgroups that have transited the solar disc since 1874 (start Greenwich observations). After the year and month during which the group made its first appearance, there is also the groupnumber (till 1976 Greenwich, then NOAA), the corrected area in MH (millionths of a solar hemisphere; 1000 MH = 3043,7 million km²), the location of the group on the sun, the solar cycle to which the group belonged and the phase during the solar cycle at which it appeared (0,50 means right between the timings of minimum and maximum). The area is corrected for the angle to the center of the solar disc, because groups at the edge always look smaller than when they would be in the middle. The NOAA-areas are determined differently than those of Greenwich. This is why they have to be multiplied by 1,4 in order to be comparable to those of Greenwich. Data and additional information are available at NASA's Marshall Space Flight Center. Data till December 2010.

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Top 50 of flare-prone sunspotgroups since 1976 (SC21, 22 & 23)

This table provides an overview of those sunspotgroups that have been particularily flare-active since the start of the satellite-observations (GOES, 1976). After the year and the month the group produced its first flare, there's the groupnumber (NOAA), its location (average latitude and longitude) and its area as determined by NOAA, the number of C-, M- and X-flares that were produced during its transit, the total number of flares, the fluence (the sum of the peakvalue of each flare; an M-flare is 10x stronger than a C-flare, and a X-flare is 10x stronger than a M-flare). Finally, also the number of high-energetic flares is mentioned, as well as the number that reached a peak > X10. The last column mentions to which solar cycle the group belonged. Data and additional information can be obtained at NGDC. Data till December 2010.

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Synoptic maps per year for SC23 and SC24

Synoptic maps give an idea on how the activity is spread over the solar surface. This can be done by dividing the solar surface in areas of 10° longitude by 10° latitude. Then, over the course of a year, the total number of groups that appeared in each of these sectors is determined.
The following maps deal with SC23 and SC24 activity. As from 1996 onwards, they provide a yearly overview of the activity-spread concerning the number of groups, the activity areas (according to Waldmeier-classification), the sunspotarea, the number of M- and X-flares, and the flare-fluence.

• 1996
• 1997
• 1998
• 1999
• 2000
• 2001
• 2002
• 2003
• 2004
• 2005
• 2006
• 2007
• 2008
• 2009
• 2010

In the course of a solar cycle, the evolution of the number of groups per latitude-band can be represented in a contourmap. For any given year and per 10° latitude, one can determine which band was the most active, and follow the changes throughout a solar cycle. A similar procedure can be applied on the number of a certain group-type (Waldmeier). By using % one can also study the internal evolutions (between resp. the latitude-bands and the group-types).

Based on the NOAA-data, all necessary information was deduced for SC23 and SC24 and transformed into contourmaps. Aside the butterfly-diagram, the evolution of the number of groups also reveal that the latest solar maximum was dominated by the northern solar hemisphere. Also very obvious is the high (percentual) activity since 2003 between the latitudes -5° and -15°. The southern hemisphere clearly remained more active for a longer time than the northern one. It can also be well seen how the two SC overlap each other (2008), and that at the beginning of SC24 the northern hemisphere is the dominant one (2009).

The evolution of the Waldmeiergroups clearly shows the transition from the inactive A- and B-groups (minimum) to the much more active D-groups. The number of E- and F-groups seems to be relatively low, but this is due to the fact that the McIntosh groups E/F . o (big open groups) are classified under Waldmeier's type G. Only a few H-groups have appeared during SC23, but it must be noted that Waldmeier type C also contains a large number of McIntosh C h/k . groups. It is curious that the stand-still in activity on the northern solar hemisphere, which started in 2006, persisted throughout SC23-24 transit. The growing proportion of inactive A- and J-groups heralded the end of SC23 which took place in December 2008. Similar to the beginning of SC23, the small inactive A and B-groups are dominating.

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The Solar Constant

The solar constant is defined as the total amount of solar energy (irradiance) falling per second perpendicular on a surface of 1 m² above earth's atmosphere, with the distance earth-sun 1 A.U. (Astronomical Unit, 149.597.870 km).

Satellite	Name	Radiometer	Period
Nimbus-7	Nimbus-7	Hickey-Frieden (HF)	16 Nov 1978 - 13 Dec 1993
SMM	Solar Maximum Mission	ACRIM-I	16 Feb 1980 - 01 Jun 1989
ERBS	Energy Radiation Budget Satellite	Active Cavity Radiometer (ACR)	25 Oct 1984 - Present
NOAA-9	National Oceanic and Atmospheric Administration	-	23 Jan 1985 - 20 Dec 1989
NOAA-10	National Oceanic and Atmospheric Administration	-	22 Oct 1986 - 01 Apr 1987
UARS	Upper Atmospheric Research Satellite	ACRIM-II	05 Oct 1991 - May 2001
SOHO	Solar and Heliospheric Observatory	VIRGO/Diarad	18 Jan 1996 - Present
AcrimSat	ACR Irradiance Monitor Satellite	ACRIM-III	04 Apr 2000 - Present
SORCE	Solar Radiation and Climate Experiment	ACR	25 Feb 2003 - Present

Despite its name, the solar constant is not constant. Since satellites started measuring its value late November 1978, it averages 1366,0 W/m². Big sunspotgroups can decrease its value with a few W/m², but bright faculae fields can push it above 1368 W/m². This is why the solar constant is highest during a sunspotmaximum, and lowest during the minimum. In the course of a solar cycle, its average value changes only very little, from 1365,5 W/m² to 1366,7 W/m², or hardly 0,09%. This change is believed to be too small to have any influence on the earth's climate. Still, drastic climate changes like the Little Ice Age during the 17th century are being linked to a decreased solar activity, and there exists actually a monthly index for the solar constant (Reconstructed Solar Constant Monthly Index, Hoyt & Schatten).

Top 10 Daily minima Solar Constant (W/m2) - Nov 1978-Feb 2005 Day Value Cycle 29 Oct 2003 1361,953 SC23 29 Jan 1984 1363,113 SC21 28 Apr 1984 1363,267 SC21 15 Jan 2005 1363,679 SC23 01 Jul 1988 1363,768 SC22 25 Jul 1981 1363,822 SC21 27 Oct 1991 1363,862 SC22 20 Nov 1990 1363,998 SC22 22 Sep 2000 1364,007 SC23 16 Jun 1989 1364,096 SC22 Top 10 Daily maxima Solar Constant (W/m2) - Nov 1978-Feb 2005 Day Value Cycle 12 May 1989 1368,227 SC22 12 Apr 1989 1367,949 SC22 26 Jul 1980 1367,757 SC21 10 Apr 1991 1367,737 SC22 13 Mar 1979 1367,668 SC21 06 Mar 1991 1367,618 SC22 02 Apr 1981 1367,613 SC21 01 Jan 1982 1367,578 SC21 31 Dec 2001 1367,574 SC23 27 Jan 2002 1367,573 SC23

The table above depicts days during which the solar constant was significantly higher or lower than average. In fact, every day belongs to a period of a few days during which the solar constant was significantly higher or lower than average, but the other days of these periods have been omitted to avoid confusion. As an example, the solar constant during the period from 27 till 30 October 2003 was lower than e.g. on 29 January 1984. This period coincides with the appearance of the famous Halloweengroups (NOAA 10484, 10486 and 10488). It's also not a surprise that the highest daily values are in April and May 1989. That is resp. 1 and 2 solar rotations after the transit of spectacular NOAA 5395, the biggest and one of the most flare-active sunsporgroups in the 22nd solar cycle (SC22). The depth of the dip is not only determined by the area of the sunspotgroup, but also by its compactness, its location on the solar surface, and the presence of hot faculae fields during its transit.

The daily values of the solar constant can also be put into time-graphics. The values can be averaged over 1 solar rotation (27 days), or e.g. over 1 year (351 days or 13 solar rotations). The graph underneath shows the evolution over the last 27 years (since the start of satellite measurements). It shows the day-to-day variation, the much smoother evolution of the yearly average. The table gives minima and maxima of the respective solar cycles. Though the 3 solar cycles each have a double sunspotmaximum, for the solar constant this can be well seen in the 23rd solar cycle only (SC23). It's also interesting to note that the cycle maximum (yearly average) of SC23 is higher than that of SC22, though the average Wolfnumber is not.

	Solar Constant (W/m2)				Wolfnumber
SC	Minimum	Date	Maximum	Date	Rmax	Date
21	-	-	1366,688	31 Dec 1980	167,1	Nov 1979
22	1365,567	29 Aug 1985	1366,489	30 Jul 1989	162,1	Oct 1989
23	1365,482	08 Jun 1996	1366,526	17 Jan 2002	125,6	Jun 2000

One can also take a look at the groups being responsible for the dips in the solar constant during SC23. The table underneath shows they were all caused by the biggest sunspotgroups that have been visible during the ongoing solar cycle. The area (in MH; 1 MH = 3,0437 . 10⁶ km²) is not corrected for the angular distance ρ, such that the group's area is represented as it was seen in reality.

Biggest dips in Solar Constant during SC23
Date	NOAA	Non-Corr. Area (MH)	NOAA	Non-Corr. Area (MH)	Total Non-Corr. Area (MH)	Solar Constant (W/m2)
29 Oct 03	10486	2401	10488	1395	4306	1361,953
15 Jan 05	10720	1541	-	-	1877	1363,679
22 Sep 00	9169	1777	9166	498	2521	1364,007
28 Mar 01	9393	2109	-	-	3162	1364,098
17 Aug 02	10069	1891	-	-	2499	1364,145
22 Jul 04	10652	1719	-	-	1924	1364,191

These dips can also easily be found in the graph underneath of the solar constant during SC23. The drawings originate from the archives of Kanzelhöhe Solar Observatory. These drawings are for the dates of the table above.

Especially the daily evolution of the solar constant during the deepest "valley" of SC23 is worth follwing. The graph (15 Oct 03 till 10 Nov 03) shows that the beginning of the period is marked by a increase in the solar constant, though the (uncorrected) area is continuously decreasing. This is possibly being caused by bright faculae fields accompanying NOAA 10484. A similar phenomenon occurs at the end of the period, this time with the groups NOAA 10486 and 10488.
The decreasing branch of the curve is asymmetric compared to the ascending branch for two reasons. NOAA 10484 appears on 18 October and leaves the solar surface on 31 October, NOAA 10486 appears on 22 October and rounds the western solar edge on 04 November. However, NOAA 10488 appears on 27 October and grows at a spectacular speed, to leave the solar surface together with NOAAA 10486 on 04 November. These differences in growth and visibility-criteria are the first cause of the asymmetry. The second cause is in the fact that as from 27 October, numerous small inactive groups appear. These contribute a few hundred MH in sunspot area, but do not decrease further the solar constant. This also explains why the minimum of the total non-corrected area of the sunspotgroups happens on 30 October, while the minimum of the solar constant arrived one day earlier (29 October), which is the day the 3 big sunspotgroups reached a maximum in sunspotarea.

Links and Literature

1. Janssens J., De "variabele" zonneconstante, Heelal, September 1993, pp. 228-233. (in Dutch)
2. Janssens J., Bourgeois J. en Zimmerman L., Mesure de la constante solaire avec un calorimètre d'amateur, Ciel et Terre, September-October 2001, pp. 114-118. (in French)
3. Sert J., Measuring the solar constant
4. NOAA/Space Environment Center, Measuring the solar constant
5. World Radiation Center / PMO Davos, Solar Constant
6. SOHO / Virgo / Diarad, Welcome to the DIARAD homepage
7. Lee R.B., Wilson R.S. and Thomas S., Long-term Total Solar Irradiance (TSI) Variability Trends: 1984-2004, AMS 13th Conference, 20-24 September 2004.

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High Sunspotnumbers early July 2005

Early July 2005, there was some significant solar activity, reminding a lot of observers to the past solar maximum! However, energetic solar eruptions were lacking.

Activity seemed to be very high: On July 4^th, NOAA's Wolfnumber reached 192, Catania 163, and Kanzelhöhe 187. Yet, one has to take into account that official values can be about 25 to 50% lower. This is because these observations, mostly performed with large telescopes, need to be reduced as if they were done with an 8-cm-refractor (Wolf's telescope). Only that way, old and recent observations can reliably be compared with each other. From this, one can expect the official R-values to be between 100 and 150, which of course is still very high at this stage of the solar cycle.

I've been checking the SIDC's daily Wolfnumbers, continuously available since 1849. In particular, for each solar cycle I determined the last day for which R was 100 or more prior to the (Meeus) smoothed cycle minimum. This resulted in table underneath:

Cycle	Last day with R > 100	   R	   Cycle minimum    Delta in months
 09	     29 Dec 1852	  111         Jan 1856	          37
 10          20 Feb 1866	  118         Apr 1867	          14
 11          20 Aug 1874	  100	      Dec 1878	          52
 12          07 Mar 1886	  114	      Feb 1890		  47
 13	     20 Sep 1896	  103	      Sep 1901		  60
 14	     02 Dec 1909	  108	      Jun 1913		  42
 15	     07 Mar 1922	  108	      Apr 1923		  13
 16	     23 Feb 1931          100	      Sep 1933		  31
 17	     20 Apr 1942	  105	      Apr 1944		  24
 18	     23 Dec 1951	  106	      Apr 1954		  28
 19          27 Feb 1962	  108	      Aug 1964		  30
 20	     07 Aug 1975          102	      Mar 1976		   7
 21	     14 Mei 1984	  111	      Sep 1986		  28
 22	     06 Jan 1994	  101	      Mei 1996	          28

It appears that solar cycles 10, 15 and 20 all had high Wolfnumbers one year or less prior to the subsequent cycle minimum. However, half of the cycles (7 out of 14 solar cycles) have high R-values about 2 to 3 years prior to this minimum. Cycles 10, 15 and 20 do have higher R-values, but they are farther away from the Wolfminimum:

Cycle	   Day with R > 100	   R	   Cycle minimum  Delta in months
 10	     13 Aug 1864	  134	      Apr 1867	          32
 15	     02 Mar 1922	  127	      Apr 1923		  13
 20	     03 Sep 1973	  130	      Mar 1976		  30

So, though not unusual, current activity can be interpreted as a sign that the coming solar minimum will take place in 2007 rather than end 2006. That also seems to be more in agreement with the hitherto very low number of spotless days (only a handful since January 2004), the very slowly rising of polar faculae number, and predictions by a couple of professional astronomers.

It's going to be very interesting what the official Wolfnumbers will be, and also how solar activity will evolve. Once again, big sunspotgroups (area bigger than 720 MH) can occur till about a half year prior to the solar minimum. No doubt the sun still has some surprizes for us!

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Predicting SC24-maximum from early SC24-sunspotnumbers

Bendel and Staps (1980) deviced two statistical methods to predict a solar cycle maximum from early, smoothed sunspotnumbers (SSN) using the P-17 method (pp. 327-328 of the Handbook of Practical Astronomy). In the first method, they use the time of rise in SSN between months 17 and 18 after the solar minimum. In the second method, they use the SSN 25 months after solar minimum. The correlations with the subsequent cycle maximum (resp. r² = 0.76 and .92) are much better than that from e.g. time of rise (r² = 0.59) or other prediction methods, presumably because the methods operate much closer to cycle maximum.

Using all solar cycle data, including 3 new datapoints (SC21, 22 and 23), and applying the Meeus-formula, correlations and formulas were calculated again.

Graph underneath shows the correlations between resp. the monthly rise of SSN (blue) and the monthly SSN (red) versus the final solar cycle maximum. For the rise in SSN, best correlation is obtained during month 20 (v₂₀); r²=.78), well in agreement with Bendel and Staps.
For the monthly SSN, r² rises fast till about month 23, then to continue increasing but much more slowly. Which month to choose, i.e. what is still a timely prediction without losing too much in correlation?

Graph underneath shows that the amount of increase reaches a maximum (v > 4/month) for the months 22-25. This indicates an inflection point (faster => slower increase in SSN) in the increase in monthly SSN. Thus, it seems a reasonable compromise to take month 25 as the key-month for the second method, as it gives the highest correlation for the 4 inflection points. Note the obtained correlation (r² = 0.82) is a lot lower than the one obtaines by Bendel and Staps, but they did not include data from SC 9 and 13, which deviate significantly from the relationship.

The relation between v₂₀ and SSN₂₅, and the subsequent cycle maximum is as follows:

• R_max = 14,810 . v₂₀ + 62,299; (+20; r² = 0.78)
• R_max = 1,156 . SSN₂₅ + 48,690; (+18; r² = 0.82)

In order to make predictions using these methods, one has to wait resp. 26 and 31 months after solar cycle minimum. For SC24, predictions can be done in resp. February and July 2011. So, by the summer of 2011, we would have a reasonable estimate of the next solar cycle maximum. A word of caution though: Despite the good correlations, both methods had a handful of predicted cycle maxima that deviated significantly (> 1,5 st.dev.) from the real ones...

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Extreme changes and quiet spells in monthly sunspotnumbers

Early April 2011, on a thread at the WUWT-site, one wondered how unusual the increase in sunspotnumber was as observed in March (from 29,4 in February to 56,2 in March - preliminary numbers by the SIDC). This is not a question which is easily answered, because how to objectively quantify if a change in sunspotnumber from 10 to 30 is more (or less) important than a change e.g. from 70 to 100?

I actually did a similar study in 1999 because also at that time sunspotnumbers behaved quite peculiary. The results were published in the October Newsletter of the Belgian Solar Section (article available upon request). At the time, I used change rates (%) but it certainly was not the best approach, e.g. I had to leave out all 0 sunspotnumbers (e.g. (10-0)/0 gives an error...), and I limited myself at Sunspotnumbers above 50 (so e.g. a drop from 80 to 30 would not show up...). This time I had to do a better job!

Let's skip the 2 weeks of trial-and-error and proceed immediately to the technique that was eventually applied. Since May 1755, which is the the start of the official series of solar cycles, there are now 3071 (monthly) datapoints, including the 3 preliminary numbers for 2011. Monthly change was calculated, and the group was split up in months with positive changes (Incr, 1542 data points) and negative changes (Decr, 1529 data points). The months with a zero change were all included in the Incr-group.

In each group, the data were then ranked in increasing sunspotnumber. They were binned in groups of about equal data points, in this case 140 (about 10% of total). Only the last bin then contained a slightly different number, but acceptable. For each bin the average delta Davg en standard deviation Dsd was calculated. For each datapoint within the bin, the value t1 = (delta-Davg)/(2.Dsd) was calculated. Assuming normal distribution, a value t1 > 1 means there's only a 2,5% chance such a value would be attained within this bin. This was repeated for all bins.

Because a value close to one of the limits of the bin (e.g. datapoint 139 of the first bin) is treated differently than a datapoint in the neighbouring bin (e.g. datapoint 3 of the second bin - remember: datapoints are ranked according to increasing sunspotnumber, so they are quite close) because of the different Davg en Dsd used, a new binning was done by shifting the bin over all of the datapoints by half a bin. A similar procedure as above was then applied, resulting in a value t2 for all datapoints except for the first 70 and last +/- 70 datapoints of the series. The average t was then determined, and the t1 value was taken for the other data.

Data were then ranked according to their t-value, and all data with t > 1 (for Incr; 51 points) or t < -1 (for Decr; 66 points) were taken as significant (> 2.Dsd) changes. These are the values indicated in resp. blue and red in the graph underneath. The green dot indicates the March 2011-value (56,2; up 26,8 from February), ranking 110th of all-time monthly increases in sunspotnumbers. That's pretty high (a significant change), but certainly not extreme.

A similar method was applied to quantify quiet periods, these are extended periods of time during which the monthly sunspotnumber hardly changes. In stead of the change from the previous month, the standard deviation was calculated over the last 4 months (i.e. from Ri to Ri-3). Binning was done over 310 datapoints, and final ranking from most negative to positive, hence giving the largest quiet spell compared to the average standard deviation for that bin. The top 2,5% data were taken, resulting in 77 "quiet" periods. Note some of these months clit together, so there are actually only 44 quiet periods, the longest being from September 1792 to July 1793 during which the sunspotnumber varied all the time between 50 and 60! Another noteworthy period is that from January 1859 till July 1859 (R between 95,2 and 83,7), just one month prior to the famous Carrington White Light Flare! A notable absent is the period from October 1809 till June 1811, during which the monthly sunspotnumber was zero for the entire period. With the 229th place it is ranked high, but not high enough to make it into the table with most significant quiet periods.

All significant changes and quiet periods were then put into a graph of the sunspotnumber since 1755. The top graph shows all solar cycles together, the next 4 show 80 years of data, with an overlap of 20 years.

On the average, one can expect 7 significant events per solar cycle: 2 quiet periods, 3 decreases and 2 increases. However, as shown in tables underneath, it may be clear that there exist large differences between the individual solar cycles, some having almost no peculiar event, while other have many. SC24 so far has no significant events (yet), the last one dating back to 2001 when the sunspotnumber decreased from 134 in June to 81,8 in July.

Defining Minimum of a solar cycle as the period during which the Meeus smoothed sunspotnumber is below 20, and Maximum as the period during which this smoothed sunspotnumber is above 80% of the SC-amplitude, then the definition for the ascending and descending phase are deduced logically from these. Decreases and in particular increases are characteristic for both the Minimum and ascending phase of a solar cycle, whereas quiet periods and decreases occur most often during Maximum and the descending phase. More than one third of all the significant events occur during the descending phase of a solar cycle.

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