Geomagnetic Calibration of Sunspot Numbers Leif Svalgaard Stanford University 2 nd SSN Workshop, Brussels, May 212 1
Wolf s Several Lists of SSNs During his life Wolf published several lists of his Relative Sunspot Number : 1857 Using Sunspot Drawings by Staudacher 1749-1799 as early SSNs 1861 Doubling Staudacher s Numbers to align with the large variation of the Magnetic Needle in the 178s 1874 Adding newer data and published list 188 Increasing all values before his own series [beginning 1849] by ~25% based on Milan Declination 192 [Wolfer] reassessment of cycle 5 reducing it significantly, obtaining the Definitive List in use today 2
Geomagnetic Regimes 1) Solar FUV maintains the ionosphere and influences the daytime field. 2) Solar Wind creates the magnetospheric tail and influences the nighttime field 3
Justification of the Adjustments rests on Wolf s Discovery: rd = a + b R W. ry North X H Morning rd D Evening East Y Y = H sin(d) dy = H cos(d) dd For small D, dd and dh A current system in the ionosphere [E-layer] is created and maintained by solar FUV radiation. Its magnetic effect is measured on the ground. 4
1 Days of geomagnetic variations ry 5
Disturbance Current Systems are East-West, thus their Magnetic Effects are North-South Equatorial Electrojet Ring Current Auroral Electrojets Disturbances are mainly a Nighttime phenomenon 6
The Diurnal Variation of the Declination for Low, Medium, and High Solar Activity 8 6 4 2-2 -4-6 -8-1 8 6 4 2-2 -4-6 -8-1 dd' 1957-1959 1964-1965 dd' 184-1849 Diurnal Variation of Declination at Praha (Pruhonice) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year Diurnal Variation of Declination at Praha Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year 9 1 rd 7
3 F1.7 25 y = 5.4187x - 129.93 2 R 2 =.9815 15 1 y =.4385x 2.642 5 R 2 =.975948 ry 3 35 4 45 5 55 6 65 7 Using ry from nine chains of stations we find that the correlation between F1.7 and ry is extremely good (more than 98% of the variation is accounted for) 25 2 F1.7 sfu F1.7 calc = 5.42 ry - 13 Solar Activity From Diurnal Variation of Geomagnetic East Component Nine Station Chains 15 1 12 13 14 15 16 17 18 19 2 21 22 23 5 25+Residuals 188 189 19 191 192 193 194 195 196 197 198 199 2 21 22 This establishes that Wolf s procedure and calibration are physically sound 8
Wolf got Declination Ranges for Milan from Schiaparelli and it became clear that the pre-1849 SSNs were too low 16 Justification for Adjustment to 1874 List 14 12 1 8 6 4 R Wolf Wolf = 1.23 Schwabe '1861 List' 1849-186 Wolf '1874 List' 1836-1873 '1861 List' 1836-1848 Schwabe 2 rd' Milan 4 5 6 7 8 9 1 11 12 13 The 1874 list included the 25% [Wolf said 1/4] increase of the pre-1849 SSN 9
Wolf s SSN was thus now consistent with his many-station compilation of the diurnal variation of Declination 1781-188 First cycle of Dalton Minimum It is important to note that the relationship is linear for calculating averages 1
Wolfer s Revision of Solar Cycle 5 Based on Observations at Kremsmünster 9 Rudolf Wolf's Sunspot Numbers for Solar Cycle 5 8 7 6 Wolf 1882 Wolfer 192 GSN 1996 SC 5 5 4 3 2 1 1798 1799 18 181 182 183 184 185 186 187 188 189 181 1811 11
Comparing Diurnal Ranges A vast amount of hourly [or fixed-hours] measurements from the mid-19 th century exists, but is not yet digitized We often have to do with second-hand accounts of the data, e.g. the monthly or yearly averages as given by Wolf, so it is difficult to judge quality and stability Just measuring the daily range [e.g. as given by Ellis for Greenwich] is not sufficient as it mixes the regular day-side variation in with night-time solar wind generated disturbances 12
Adolf Schmidt s (199) Analysis Schmidt collected raw hourly observations and computed the first four Fourier components [to 3-hr resolution] of the observed Declination in his ambitious attempt to present what was then known in an einheitlicher Darstellung [uniform description] Observatory Years Lat Long Washington DC 184-1842 38.9 282. Dublin 184-1843 53.4 353.7 Philadelphia 184-1845 4. 284.8 Praha 184-1849 5.1 14.4 Muenschen 1841-1842 48.2 11.6 St. Petersburg 1841-1845 6. 3.3 Greenwich 1841-1847 51.5. Hobarton 1841-1848 -42.9 147.5 Toronto 1842-1848 43.7 28.6 Makerstoun 1843-1846 55.6 357.5 6 4 2-2 -4-6 Potsdam 189-1899 dd' Local time 3 6 9 12 15 18 21 24 Greenwich 1883-1889 51.4. P. Saint-Maur 1883-1899 48.8.2 Potsdam 189-1899 52.4 13.1 København 1892-1898 55.7 12.6 Utrecht 1893-1898 52.1 5.1 Odessa 1897-1897 46.4 3.8 Tokyo 1897-1897 35.7 139.8 Bucarest 1899-1899 44.4 26.1 Irkutsk 1899-1899 52.3 194.3 Zi-ka-wei 1899-1899 31.2 121.2-8 Engelenburg and Schmidt calculated the average variation over the interval for each month and determined the amplitude and phase for each month. From this we can reconstruct the diurnal variation and the yearly average amplitude, dd [red curve]. 13
The Diurnal Range ry is a very good proxy for the Solar Flux at 1.7 cm 25 2 15 1 5 Relationship F1.7 and Diurnal Range ry F1.7 1947-25 y = 5.9839x - 129.25 R 2 =.9736 ry 1 2 3 4 5 6 7 Which itself is a good proxy for solar Ultraviolet radiation and solar activity in general [what the sunspot number is trying to capture]. 25 Comparison Observed and Calculated F1.7 2 15 1 5 F1.7 obs. F1.7 calc from ry 194 1945 195 1955 196 1965 197 1975 198 1985 199 1995 2 25 21 14
Compare with F1.7 Flux and Ca II Emission 1 9 8 7 6 5 ry nt Diurnal variation of the East Component and the F1.7 flux 4 3 2 1 Northern Hemisphere Southern Hemisphere Dots, Average Ca-II scaled to ry, Ca-II = 5549*rY+36.66 F1.7 scaled to ry, F1.7* =.185*rY+39.7 188 189 19 191 192 193 194 195 196 197 198 199 2 21 15
Diurnal Variation as a Function of Latitude 6 ry nt 5 4 3 2 1 Latitude 15 2 25 3 35 4 45 5 55 6 65 Only slight dependence 16
Hemispheric Variation 1 9 8 7 6 5 4 12 3 2 1 ry nt ry nt Northern Hemisphere Southern Hemisphere 8 191 192 193 194 195 196 197 198 199 2 21 6 4 2 191 192 193 194 195 196 197 198 199 2 21 17
The Amplitude of the Diurnal Variation, ry, [from many stations] shows a Change in Rz ~1945 18
7 Scaling to 9-station chain ry '9-station Chain' 65 6 55 y = 1.1254x + 4.5545 R 2 =.9669 5 45 4 35 1884-198 1953-28 Helsinki, Nurmijärvi 3 25 3 35 4 45 5 55 Helsinki-Nurmijärvi Diurnal Variation Helsinki and its replacement station Numijärvi scales the same way towards our composite of nine long-running observatories and can therefore be used to check the calibration of the sunspot number (or more correctly to reconstruct the F1.7 radio flux see next slide) Range of Diurnal Variation of East Component 7 65 ry nt 6 9-station Chain 55 5 45 4 35 3 Helsinki Nurmijärvi 184 185 186 187 188 189 19 191 192 193 194 195 196 197 198 199 2 21 19
The HLS-NUR data show that the Group Sunspot Number before 188 must be Increased by a factor 1.64±.15 to match ry (F1.7) This conclusion is independent of the calibration of the Zürich SSN, Rz 2
Group SSN, Zurich SSN, and Diurnal Variation Comparison Group SSN, Zurich SSN, and Geomagnetic ry 7 2 65 nt SSN 18 16 6 14 55 12 1 5 8 45 6 4 4 2 35 184 186 188 19 192 194 196 198 2 21
Wolf s Geomagnetic Data Wolf found a very strong correlation between his Wolf number and the daily range of the Declination. Today we know that the relevant parameter is the East Component, Y, rather than the Declination, D. Converting D to Y restores the stable correlation without any significant long-term drift of the base values Wolfer found the original correlation was not stable, but was drifting with time and gave up on it in 1923. 22
Using the East Component We Recover Wolf s Tight Relationship Relationship Between Rz SSN and ry East component Range 16 14 12 1 8 6 4 2 Rz Rz = 4.54±.15 (ry - 32.6±1.5) R 2 =.9121 1883-1922 Rz = 4.26±.23 (ry - 32.5) R 2 =.8989 1836-1882 Rz = 4.61±.21 (ry - 32.5) R 2 =.9138 ry 3 35 4 45 5 55 6 65 Relationship Between Rg SSN and ry East component Range 14 12 1 8 6 4 2 Rg 1883-1922 Rg = 4.4±.27 (ry - 32.4) R 2 =.8765 1836-1882 Rg = 3.54±.18 (ry - 32.2) R 2 =.8994 ry 3 35 4 45 5 55 6 65 The regression lines are identical within their errors before and after 1883.. This means that likely most of the discordance with Rg ~1882 is not due to change of guard or method at Zürich. It is also clear that Rg before 1883 is too low. 23
New paper on Eastward Component JGR, 212 24
Where do we go from here? Find and Digitize as many 19 th century geomagnetic hourly values as possible Determine improved adjustment factors based on the above and on model of the ionosphere Co-operate with agencies producing sunspot numbers to harmonize their efforts in order to produce an adjusted and accepted sunspot record that can form a firm basis for solar-terrestrial relations, e.g. reconstructions of solar activity important for climate and environmental changes Follow-up Workshop in Tucson, January 213 25