The solar cycle



Contents


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.

Solar CycleBegin Max End Rmin Rmax Trise Tfall Ttot
1 May 1755 Jun 1761 Aug 1766 6,8 90,4 73 62 135
2 Aug 1766 Oct 1769 Jun 1775 9,6 125,3 38 68 106
3 Jun 1775 May 1778 May 1784 7,0 161,8 35 72 107
4 May 1784 Nov 1787 Jun 1798 9,1 143,4 42 127 169
5 Jun 1798 Dec 1804 Jul 1810 2,8 52,5 78 67 145
6 Jul 1810 Mar 1816 Apr 1823 0,0 50,8 68 85 153
7 Apr 1823 Jun 1829 Aug 1833 0,1 71,5 74 50 124
8 Aug 1833 Feb 1837 Jul 1843 7,4 152,8 42 77 119
9 Jul 1843 Nov 1847 Jan 1856 10,7 131,3 52 98 150
10 Jan 1856 Jul 1860 Apr 1867 3,3 98,5 54 81 135
11 Apr 1867 Jul 1870 Dec 1878 4,3 144,8 39 101 140
12 Dec 1878 Jan 1884 Feb 1890 2,0 78,1 61 73 134
13 Feb 1890 Aug 1893 Sep 1901 4,0 89,5 42 97 139
14 Sep 1901 Oct 1905 Jun 1913 2,8 63,9 49 92 141
15 Jun 1913 Aug 1917 Apr 1923 1,1 112,1 50 68 118
16 Apr 1923 Jun 1928 Sep 1933 5,6 82,0 62 63 125
17 Sep 1933 May 1937 Apr 1944 2,9 119,8 44 83 127
18 Apr 1944 Jul 1947 Apr 1954 6,5 161,2 39 81 120
19 Apr 1954 Nov 1957 Aug 1964 3,2 208,4 43 81 124
20 Aug 1964 Feb 1969 Mar 1976 8,5 111,6 54 85 139
21 Mar 1976 Nov 1979 Sep 1986 12,4 167,1 44 82 126
22 Sep 1986 Oct 1989 May 1996 12,8 162,1 37 79 116
23 May 1996 Jun 2000 Dec 2008 7,9 125,6 49 102 151
24 Dec 2008 Mar 2014 - 1,7 83,7 63 - -
Mean - - - 5,5 117,6 50,881,5132,3
St.Dev. - - - 3,7 41,6 12,816,515,4


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 28 October 2014. Preliminary data show that NOAA 12192 is by far the biggest group of the last 2 decades, dwarfing all the other big sunspot groups of SC24, such as NOAA 11967 from February 2014 (1580MH). This giant group is even bigger than the Halloween group NOAA 10486 from October 2003 and famous NOAA 9393 from March 2001. On 26 October 2014, NOAA 12192 had a sunspot area of 2750MH according to NOAA (3850MH Greenwich), making it almost in the Top 10 of largest sunspot groups observed since 1874.

Rank Year Month Group Corr. Area Grw. Area Latitude Longitude Solar Cycle Phase
1 1947 3 1488603 6132 6132 -24 84 18 0,29
2 1946 1 1441702 5202 5202 26 298 18 0,17
3 1989 3 5395 3600 5040 17 254 22 0,26
4 1951 5 1676304 4865 4865 13 87 18 0,71
5 1946 7 1458503 4720 4720 22 196 18 0,22
6 1947 3 1485104 4554 4554 -23 91 18 0,29
7 1982 6 3776 3100 4340 13 314 21 0,60
8 1989 8 5669 3080 4312 -12 82 22 0,30
9 1990 11 6368 3080 4312 18 26 22 0,43
10 1988 6 5060 2900 4060 -19 5 22 0,18
11 1982 7 3804 2870 4018 15 321 21 0,60
12 2014 10 12192 2750 3850 -12 248 24 ---
13 1926 1 986103 3716 3716 21 35 16 0,26
14 1982 2 3594 2640 3696 -10 207 21 0,56
15 2003 10 10486 2610 3654 -16 284 23 0,59
16 1938 1 1267304 3627 3627 17 225 17 0,41
17 1984 4 4474 2590 3626 -13 343 21 0,77
18 1917 2 797700 3590 3590 -16 9 15 0,37
19 1988 10 5175 2540 3556 -15 154 22 0,22
20 1991 3 6555 2530 3542 -23 188 22 0,47
21 1991 8 6891 2440 3416 -10 195 22 0,51
22 2001 3 9393 2440 3416 17 153 23 0,38
23 1938 7 1290203 3379 3379 -12 40 17 0,46
24 1937 9 1255304 3340 3340 9 265 17 0,38
25 1905 1 544100 3339 3339 -15 328 14 0,28
26 1991 6 6659 2360 3304 31 247 22 0,49
27 1937 7 1245502 3303 3303 32 354 17 0,36
28 1989 6 5528 2340 3276 21 94 22 0,28
29 1981 10 340300 2301 3221 -11 281 21 0,53
30 1980 11 277900 2300 3220 -11 105 21 0,44
31 1968 1 2148200 3202 3202 13 165 20 0,29
32 1917 8 818100 3178 3178 16 129 15 0,42
33 1982 9 3902 2240 3136 -19 258 21 0,62
34 1984 1 4398 2210 3094 15 109 21 0,75
35 1991 1 6471 2210 3094 -12 142 22 0,45
36 1941 9 1393703 3088 3088 12 210 17 0,76
37 1939 8 1339402 3054 3054 -14 348 17 0,56
38 1892 2 242100 3038 3038 -28 256 13 0,17
39 1938 10 1302402 3003 3003 17 305 17 0,48
40 2000 9 9169 2140 2996 11 77 23 0,34
41 1905 10 568200 2995 2995 14 162 14 0,35
42 1939 9 1340503 2993 2993 -14 224 17 0,57
43 1981 7 323400 2120 2968 -12 294 21 0,51
44 1983 5 4173 2110 2954 -11 348 21 0,68
45 1947 2 1481303 2944 2944 -21 85 18 0,28
46 1925 12 983004 2934 2934 23 30 16 0,26
47 1940 1 1350202 2860 2860 10 120 17 0,60
48 1950 2 1641003 2856 2856 10 264 18 0,58
49 2004 7 10652 2010 2814 7 346 23 0,65
50 1959 1 1910900 2805 2805 12 249 19 0,46
51 2002 8 10069 1990 2786 -6 299 23 0,50

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Top 50 of flare-prone sunspot groups since 1976 (SC21-24)

This table provides an overview of those sunspot groups that have been particularly 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 group number (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 peak value 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 (>M5) 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 2014.

Rank Year Month Group Lat. Long. NOAA Area C M X Total Fluence HEF X10+ SC
1 1991 6 6659 31 247 2360 38 28 6 72 7843 11 6 22
2 2003 10 10486 -16 284 2610 16 20 7 43 7679 12 3 23
3 1989 3 5395 17 254 3600 48 48 11 107 5314 18 1 22
4 2005 9 10808 -11 229 1430 47 20 10 77 4513 13 1 23
5 1982 6 3763 -9 84 1250 37 52 6 95 4387 15 1 21
6 1982 7 3804 15 321 2870 34 68 5 107 3862 13 - 21
7 1989 8 5629 -17 75 1320 32 17 5 54 3305 7 1 22
8 1991 3 6555 -23 188 2530 44 28 7 79 3177 13 - 22
9 1978 7 1203 18 175 1370 47 27 4 78 3131 8 1 21
10 1989 10 5747 -27 210 1160 27 21 5 53 2819 9 1 22
11 2001 3 9393 17 153 2440 28 24 3 55 2768 3 1 23
12 1980 11 2779 -11 105 2300 28 49 4 81 2754 8 - 21
13 2001 4 9415 -22 359 880 16 6 5 27 2631 7 1 23
14 1982 12 4026 -11 78 640 22 12 4 38 2420 7 1 21
15 1984 4 4474 -13 343 2590 67 30 3 100 2339 6 1 21
16 2006 12 10930 -5 9 680 42 5 4 51 2115 5 - 23
17 1990 5 6063 34 318 940 10 8 5 23 2114 6 - 22
18 2005 1 10720 13 179 1630 66 17 5 88 2054 8 - 23
19 2014 10 12192 -13 248 2750 49 36 6 91 2032 10 - 24
20 1991 8 6891 -10 195 2440 50 26 5 81 2022 7 - 22
21 1984 5 4492 -10 358 670 44 11 3 58 1984 5 1 21
22 1982 6 3776 13 314 3100 36 32 5 73 1954 8 - 21
23 1989 1 5312 -31 306 1800 12 33 6 51 1877 14 - 22
24 1991 3 6538 -23 342 910 38 17 5 60 1581 7 - 22
25 1981 4 3049 15 - - 16 9 5 30 1569 6 - 21
26 1991 1 6471 -12 142 2210 19 12 2 33 1501 4 1 22
27 1980 10 2776 12 174 1440 20 24 3 47 1475 7 - 21
28 1979 8 1943 5 198 1340 25 3 3 31 1456 3 - 21
29 1978 4 1092 23 81 1280 37 10 3 50 1412 5 - 21
30 1982 12 4025 -7 88 580 6 2 3 11 1392 4 1 21
31 1981 7 3234 -12 294 2120 55 26 3 84 1366 6 - 21
32 1989 8 5669 -12 82 3080 41 38 3 82 1342 7 - 22
33 1991 3 6545 -8 287 830 35 16 6 57 1312 9 - 22
34 1979 9 1994 6 198 1180 27 12 3 42 1264 4 - 21
35 1997 10 8100 -20 351 1000 24 4 2 30 1247 2 - 23
36 1989 6 5533 -19 73 920 24 16 2 42 1202 5 - 22
37 1992 10 7321 -24 70 1650 24 9 2 35 1191 2 - 22
38 1982 6 3781 16 278 1080 28 29 3 60 1175 4 - 21
39 1982 1 3576 -14 322 1360 32 14 6 52 1174 7 - 21
40 1988 6 5047 -16 153 900 28 6 4 38 1173 6 - 22
41 2000 11 9236 20 354 630 20 3 5 28 1110 5 - 23
42 2004 7 10649 -10 46 530 46 10 6 62 1089 6 - 23
43 1989 9 5698 -22 223 1250 23 7 1 31 1074 1 - 22
44 2003 6 10375 12 22 1250 49 29 3 81 1062 6 - 23
45 1981 10 3390 -18 339 1570 47 11 2 60 1062 3 - 21
46 2012 3 11429 18 301 1270 32 14 2 48 1062 5 - 24
47 2012 6 11515 -16 205 900 74 30 1 105 1062 5 - 24
48 2004 8 10656 -13 82 1360 98 25 2 125 1044 5 - 23
49 2000 7 9077 18 310 1010 15 12 3 30 1040 5 - 23
50 2002 8 10069 -6 299 1990 55 17 2 74 1005 5 - 23

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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.

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).

SatelliteNameRadiometerPeriod
Nimbus-7Nimbus-7Hickey-Frieden (HF)16 Nov 1978 - 13 Dec 1993
SMMSolar Maximum MissionACRIM-I16 Feb 1980 - 01 Jun 1989
ERBSEnergy Radiation Budget SatelliteActive Cavity Radiometer (ACR)25 Oct 1984 - Present
NOAA-9National Oceanic and Atmospheric Administration-23 Jan 1985 - 20 Dec 1989
NOAA-10National Oceanic and Atmospheric Administration-22 Oct 1986 - 01 Apr 1987
UARSUpper Atmospheric Research SatelliteACRIM-II05 Oct 1991 - May 2001
SOHOSolar and Heliospheric ObservatoryVIRGO/Diarad18 Jan 1996 - Present
AcrimSatACR Irradiance Monitor SatelliteACRIM-III04 Apr 2000 - Present
SORCESolar Radiation and Climate ExperimentACR25 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
DayValueCycle
29 Oct 20031361,953SC23
29 Jan 19841363,113SC21
28 Apr 19841363,267SC21
15 Jan 20051363,679SC23
01 Jul 19881363,768SC22
25 Jul 19811363,822SC21
27 Oct 19911363,862SC22
20 Nov 19901363,998SC22
22 Sep 20001364,007SC23
16 Jun 19891364,096SC22
Top 10 Daily maxima Solar Constant (W/m2) - Nov 1978-Feb 2005
DayValueCycle
12 May 19891368,227SC22
12 Apr 19891367,949SC22
26 Jul 19801367,757SC21
10 Apr 19911367,737SC22
13 Mar 19791367,668SC21
06 Mar 19911367,618SC22
02 Apr 19811367,613SC21
01 Jan 19821367,578SC21
31 Dec 20011367,574SC23
27 Jan 20021367,573SC23



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
SCMinimumDateMaximumDateRmaxDate
21--1366,68831 Dec 1980167,1Nov 1979
221365,56729 Aug 19851366,48930 Jul 1989162,1Oct 1989
231365,48208 Jun 19961366,52617 Jan 2002125,6Jun 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
DateNOAANon-Corr. Area (MH)NOAANon-Corr. Area (MH)Total Non-Corr. Area (MH)Solar Constant (W/m2)
29 Oct 0310486240110488139543061361,953
15 Jan 05107201541--18771363,679
22 Sep 0091691777916649825211364,007
28 Mar 0193932109--31621364,098
17 Aug 02100691891--24991364,145
22 Jul 04106521719--19241364,191

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

The data for the graphics come from the World Radiation Center (Solar Constant), the MSFC (sunspot area) and the NGDC (satellites). The drawings from the sunspotgroups ara adaptations from the daily drawings made at Kanzelhöhe Solar Observatory.
  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 4th, 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:

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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Satellites monitoring the solar-terrestrial relationships

There are quite a few satellites out there observing the sun and its influence on the earth and its surroundings. Table underneath summarizes the ongoing missions and provides some links to the home- and data pages. It is an update from the overview in my book "Zon en Aarde: Een unieke relatie" (Table F.4.) and from the late John A. Eddy's outstanding work "The Sun, The Earth, and Near-Earth Space" (pp. 251-253). Both books date back from resp. 2003 and 2009, so an update seemed entirely appropriate.
In compiling this overview, I verified the operational status of all missions mentioned in the books, and added all relevant missions launched since 2008 based on the Spacecraft Encyclopedia, Scholarpedia and NASA Science Missions. Yellow bars indicate spacecraft with specific solar and heliospheric objectives, and green bars indicate magnetospheric and terrestrial monitoring.

Satellite / Module # probes Date Launch Orbit Organisation Mission Links
IRIS 1 17 Jun 2013 620-670 km / 97,89° NASA Chromosphere and Transition region Homepage NASA; Homepage LMSAL; Wiki
RBSP 2 30 Aug 2012 500-30600 km / <18° NASA Van Allen radiation belts Homepage
RAX 2 1 28 Oct 2011 641-652 km / 72° NASA Ionospheric turbulence Homepage; Wiki; RAX-2
ISS / AMS-02 1 16 May 2011 350 km NASA, Europe, Asia Cosmic Rays Homepage; Wiki
Elektro-L1 1 20 Jan 2011 Geost. at 76°E Russia Solar radiation; weather imaging Homepage
Falconsat-5 1 20 Nov 2010 637-661 km / 72° NASA Ionosphere and influence on radio-signals Wiki
PICARD 1 15 Jun 2010 726-728 km / 98,3° ESA Solar irradiance, solar diameter, helioseismology Homepage; Wiki
GOES-15 1 04 Mar 2010 35800 km NASA Solar X-ray, EPS; Magnetometers; Weather Press Kit; SXI; SWPC
SDO 1 11 Feb 2010 36000 km / 28,5° NASA Small-scale multi-wavelength obs. of solar magnetic field; solar wind, energetic particles,... Homepage (& data); Wiki
PROBA-2 1 02 Nov 2009 700-800 km / 98,3° ESA Solar flares (wide UV); EUV Corona; Magnetospheric plasma Homepage; LYRA-curves; SWAP-movies; Science Center
IBEX 1 19 Oct 2008 16000-325000 km NASA Mapping the heliosphere and the edge of our solar system NASA; Homepage
FERMI 1 11 Jun 2008 550 km / 28,5° NASA; Europe Solar gamma flares (sec. mission) Homepage; NASA; Wiki; Solar flares
C/NOFS / CINDI 1 16 Apr 2008 400-700 km / 13° NASA Study of elements that influence space weather around earth's equator Homepage; UT Dallas
TWINS 2 28 Jun 2006 & 13 Mar 2008 1138-39210 km / 63,2°; 1652-38702 km / 63,4° NASA 3D mapping of the earth's ring current Homepage; NASA; Wiki
AIM 1 25 Apr 2007 600 km / 97,8° NASA Noctilucent clouds Homepage
THEMIS & ARTEMIS 5 17 Feb 2007 Various NASA THEMIS: Substorms (3); ARTEMIS (2): solar wind influence on Moon Homepage; Wiki; ARTEMIS
STEREO 2 25 Oct 2006 Solar; +/-1 AU NASA CME; Energetic particles; Solar Wind Homepage; APL; Data; Wiki
Hinode 1 22 Sep 2006 sun-synchronous 600 km JAXA/ISAS, NASA, ESA Solar Magnetic field & corona Homepage; Wiki; DARTS
Resurs-DK1 / PAMELA 1 15 Jun 2006 350-610 km / 70° Russia; Europe Cosmic Rays, SEP, Radiation belts Homepage; Universe Today
GOES-13 1 24 May 2006 35800 km NASA EPS; Magnetometers; Weather Press Kit; SXI; SWPC
SORCE 1 25 Jan 2003 645 km / 40° NASA Solar irradiance (TSI); ozone; UV-B; NIR; X-ray Homepage; Scholarpedia
RHESSI 1 05 Feb 2002 600 km / 38° NASA Solar flares Homepage; Wiki
TIMED 1 07 Dec 2001 625 km / 74° NASA Solar and human influences on the lower atmosphere (60-180 km) Homepage
PROBA-1 1 22 Oct 2001 553-677 km / 97,9° ESA Earth radiation belts; Earth imaging Homepage
Cluster-II 4 16 Jul & 09 Aug 2000 19000-119000 km ESA 3D-mapping magnetosphere Homepage; Wiki
ACRIMSAT 1 20 Dec 1999 700 km NASA Measuring solar irradiance (TSI) Homepage; NASA; Wiki; Science Page
ACE 1 25 Aug 1997 L1 NASA Solar Wind Homepage; Real Time Data
SOHO 1 02 Dec 1995 L1 ESA, NASA Solar interior; Corona; CME Homepage; MDI archive
Wind 1 01 Nov 1994 L1 NASA Solar wind Homepage; Wiki
Geotail 1 24 Jul 1992 8-200 Re JAXA/ISAS, NASA Earth's magnetotail; magnetosphere Homepage; Wiki
Voyager 2 05 Sep & 20 Aug 1977 Heliopause NASA Boundaries Heliosphere Homepage
Major missions from the past
Hi-C 1 11 Jul 2012 End: 11 Jul 2012 NASA, MSFC, UAH, SAO, Russia, UK High-Resolution EUV images of corona Results page; Wiki
RAX 1 1 20 Nov 2010 End: 2011 NASA Ionospheric turbulence Homepage; Wiki
KORONAS-Foton 1 30 Jan 2009 End: 01 Dec 2009 Russia Solar Corona Homepage
Double Star 2 29 Dec 2003 & 25 Jul 2004 End: TC1: Oct 2007; TC2: data?? ESA, CNSA Magnetosphere Homepage; Data; ESA
Genesis 1 08 Aug 2001 End: 08 Sep 2004 NASA Sample return solar wind from L1 Homepage; Wiki
Image 1 25 Mar 2000 End: 18 Dec 2005 NASA Inner magnetosphere Homepage; Wiki
TRACE 1 02 Apr 1998 End: 21 Jun 2010 NASA Solar corona & transition region Homepage; Wiki
FAST 1 21 Aug 1996 End: 01 May 2009 NASA Aurorae Homepage; Berkeley; Wiki
Polar 1 24 Feb 1996 End: 28 Apr 2008 NASA Aurorae & magnetosphere Homepage; Wiki
Yohkoh 1 30 Aug 1991 End: 14 Dec 2001 JAXA/ISAS Solar observations in X-ray bands & gamma Homepage; DARTS; Science Nuggets
Compton GRO 1 05 Apr 1991 End: 04 Jun 2000 NASA Solar flares in X-ray & gamma Homepage; Scholarpedia; SDAC/BATSE
Ulysses 1 06 Oct 1990 End: 30 Jun 2009 NASA, ESA Solar poles, solar wind; heliosphere; cosmic rays; ... NASA Homepage; ESA Homepage; Wiki
Hinotori 1 21 Feb 1981 End: 11 Jul 1991 JAXA/ISAS Solar hard X-ray imaging Homepage; Scholarpedia
Solar Maximum Mission 1 14 Feb 1980 End: 02 Dec 1989 NASA Solar flares; TSI History; Scholarpedia; Wiki
P78-1 1 24 Feb 1979 End: 13 Sep 1985 NASA Corona & CME GSFC; Scholarpedia; Wiki
Skylab / ATM 1 14 May 1973 End: 11 Jul 1979 NASA ATM: Multi-spectral solar observatory History; Scholarpedia; Wiki
OSO 1-8 1 07 Mar 1962 End: 01 Oct 1978 NASA (E)UV imaging and (E)UV, X-ray, gamma spectroscopy GSFC; Scholarpedia; Wiki

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