building a sunspot group number backbone series
DESCRIPTION
Building a Sunspot Group Number Backbone Series. Leif Svalgaard Stanford University 3 rd SSN Workshop, Tucson, Jan. 2013. Why a Backbone? And What is it?. Building a long time series from observations made over time by several observers can be done in two ways:. - PowerPoint PPT PresentationTRANSCRIPT
1
Building a Sunspot Group Number Backbone Series
Leif SvalgaardStanford University
3rd SSN Workshop, Tucson, Jan. 2013
2
Why a Backbone? And What is it?
• Daisy-chaining: successively joining observers to the ‘end’ of the series, based on overlap with the series as it extends so far [accumulates errors]
• Back-boning: find a primary observer for a certain [long] interval and normalize all other observers individually to the primary based on overlap with only the primary [no accumulation of errors]
Building a long time series from observations made over time by several observers can be done in two ways:
Chinese Whispers
When several backbones have been constructed we can join [daisy-chain] the backbones. Each backbone can be improved individually without impacting other backbones
Carbon Backbone
3
The Backbones
• SIDC Backbone [????-2013]
• Japanese Backbone [1921-1995]
• Wolfer Backbone [1841-1945]
• Schwabe Backbone [1794-1883]
• Staudach Backbone [????-????]
• Earlier Backbone(s) [1610-????]
4
Sources of Data
• The primary source is the very valuable tabulations by Hoyt and Schatten of the ‘raw’ count of groups by several hundred observers
• In some cases [especially Wolf and Schwabe] data has been re-entered and re-checked from Wolf’s published lists, as some discrepancies have been found with the H&S list
5
The Wolfer Backbone
1876 1928
Alfred Wolfer observed 1876-1928 with the ‘standard’ 80 mm telescope
80 mm X64 37 mm X20
Rudolf Wolf from 1860 on mainly used smaller 37 mm telescope(s) so those observations are used for the Wolfer Backbone
6
Normalization Procedure, IWhat we do not do:
• Compare only days when both observers actually observed. This is problematic when observations are sparse as during the early years.
• Compare only days when both observers actually recorded at least one group. This is clearly wrong as it will bias towards higher activity.
What we do:• We compute, for each observer, the monthly mean of
actual observations [including days when it was indeed observed that there were no groups].
• We compute, for each observer and for each year, the yearly mean of the average counts for months with at least one observation.
7
Normalization Procedure, II
Wolfer = 1.653±0.047 Wolf
R2 = 0.9868
0
1
2
3
4
5
6
7
8
9
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Yearly Means 1876-1893
Wolf
Wolfer
Number of Groups: Wolfer vs. Wolf
0
2
4
6
8
10
12
1860 1865 1870 1875 1880 1885 1890 1895
Wolf
Wolfer
Wolf*1.653
Number of Groups
For each Backbone we regress each observers group counts for each year against those of the primary observer, and plot the result [left panel]. Experience shows that the regression line almost always very nearly goes through the origin, so we force it to do that and calculate the slope and various statistics, such as 1-σ uncertainty and the F-value. The slope gives us what factor to multiply the observer’s count by to match the primary’s. The right panel shows a result for the Wolfer Backbone: blue is Wolf’s count [with his small telescope], pink is Wolfer’s count [with the larger telescope], and the orange curve is the blue curve multiplied by the slope. It is clear that the harmonization works well [at least for Wolf vs. Wolfer].
F = 1202
8
Schmidt, Winkler
Wolfer = 1.313±029 Schmidt
R2 = 0.9971
0
1
2
3
4
5
6
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Number of Groups: Wolfer vs. Schmidt
Wolfer
Schmidt
Yearly Means 1876-1883
0
2
4
6
8
10
12
1840 1850 1860 1870 1880 1890 1900
Wolfer
Schmidt
Schmidt*1.313
Number of Groups
Wolfer = 1.311±0.035 Winkler
R2 = 0.9753
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7
Yearly Means 1882-1910Wolfer
Winkler
Number of Groups: Wolfer vs. Winkler
0
1
2
3
4
5
6
7
8
9
1880 1885 1890 1895 1900 1905 1910
Winkler*1.311
Wolfer
Winkler
Number of Groups
F = 2062
F = 1241
9
Weber, Spörer
F = 2062
F = 1241
Wolfer = 1.510±0.145 Weber
R2 = 0.9476
0
1
2
3
4
5
6
0 0.5 1 1.5 2 2.5 3 3.5 4
Number of Groups: Wolfer vs. Weber
Yearly Means 1876-1883Wolfer
Weber
0
2
4
6
8
10
12
14
16
1855 1860 1865 1870 1875 1880 1885 1890 1895
Wolfer
Weber
Weber*1.510
Number of Groups
F = 109
Wolfer = 1.416±0.145 Spörer
R2 = 0.9504
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7
Number of Groups: Wolfer vs. Spörer
Yearly Means 1876-1893Wolfer
SpörerF = 347
0
2
4
6
8
10
12
14
1860 1865 1870 1875 1880 1885 1890 1895 1900 1905
Wolfer
Spörer
Spörer*1.416
Number of Groups
10
Tacchini, Quimby
F = 2062
Wolfer = 1.130±0.030 Tacchini
R2 = 0.9835
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8
Number of Groups: Wolfer vs. Tacchini
Yearly Means 1876-1900Wolfer
TacchiniF = 13790
1
2
3
4
5
6
7
8
9
10
1865 1870 1875 1880 1885 1890 1895 1900 1905
Tacchini*1.130
Tacchini
Wolfer
Number of Groups
Wolfer = 1.284±0.034 Quimby
R2 = 0.9771
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7
Wolfer
Quimby
Yearly Means 1889-1921
Number of Groups: Wolfer vs. Quimby
F = 1352
0
1
2
3
4
5
6
7
8
9
1885 1890 1895 1900 1905 1910 1915 1920 1925
Number of Groups
Quimby
Wolfer
Quimby*1.284
11
Wolfer = 1.264±0.041 Leppig
R2 = 0.9956
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 0.5 1 1.5 2 2.5 3 3.5 4
Number of Groups: Wolfer vs. Leppig
Wolfer
Leppig
Yearly Means 1876-1881
Wolfer = 1.016±0.018 Broger
R2 = 0.99
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7 8 9
Number of Groups: Wolfer vs. Broger
Wolfer
Broger
Yearly Means 1897-1928
Broger, Leppig
F = 3003
F = 953
0
1
2
3
4
5
6
7
8
9
1895 1900 1905 1910 1915 1920 1925 1930 1935 1940
Wolfer
Broger
Broger*1.016
Number of Groups
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1895 1900 1905 1910 1915 1920 1925 1930
Broger*/Wolfer Groups
0
1
2
3
4
5
6
7
8
9
1865 1870 1875 1880 1885 1890
Wolfer
Leppig*1.264
Leppig
Number of Groups
12
Wolfer = 1.295± Mt.Holyoke
R2 = 0.9784
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6 7
Number of Groups: Wolfer vs. Mt. Holyoke
Wolfer
Mt. Holyoke
Yearly Means 1907-1925
Wolfer = 1.562±0.034 Konkoly
R2 = 0.9916
0
1
2
3
4
5
6
7
8
9
0 1 2 3 4 5 6
Number of Groups: Wolfer vs. Konkoly
Yearly Means 1885-1905
Konkoly, Mt. Holyoke
F = 2225
F = 953
0
1
2
3
4
5
6
7
8
9
1880 1885 1890 1895 1900 1905 1910
Wolfer
Konkoly
Konkoly*1.561
Number of Groups
0
1
2
3
4
5
6
7
8
9
1905 1910 1915 1920 1925 1930
Wolfer
Mt. Holyoke
Mt. Holyoke*1.295
Number of Groups
Etc… Dawson, Guillaume, Bernaerts, Woinoff, Merino, Ricco, Moncalieri, Sykora, Brunner,…
13
The Wolfer Group Backbone
0
2
4
6
8
10
12
14
1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940
0
2
4
6
8
10
12
14Wolfer Group Backbone
Number of ObserversStandard Deviation
Wolfer Backbone Groups Weighted by F-value
If we average without weighting by the F-value we get very nearly the same result as the overlay at the left shows
14
Hoyt & Schatten used the Group Count from RGO [Royal Greenwich Observatory] as their Normalization Backbone. Why don’t we?
José Vaquero found a similar result which he reported at the 2nd Workshop in Brussels.
Because there are strong indications that the RGO data is drifting before ~1900
Could this be caused by Wolfer’s count drifting? His k-factor for RZ was, in fact, declining slightly the first several years as assistant (seeing fewer spots early on – wrong direction). The group count is less sensitive than the Spot count and there are also the other observers…
Sarychev & Roshchina report in Solar Sys. Res. 2009, 43: “There is evidence that the Greenwich values obtained before 1880 and the Hoyt–Schatten series of Rg before 1908 are incorrect”.
15
The Schwabe BackboneSchwabe received a 50 mm telescope from Fraunhofer in 1826 Jan 22. This telescope was used for the vast majority of full-disk drawings made 1826–1867.
For this backbone we use Wolf’s observations with the large 80mm standard telescope
Schwabe’s House?
16
Wolf, Shea
Schwabe = 0.990±0.008 Wolf
R2 = 0.9992
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6
Yearly Means 1849-1860Schwabe
Wolf
Too good?
F = 16352
Number of Groups: Schwabe vs. Wolf
0
1
2
3
4
5
6
7
1840 1845 1850 1855 1860 1865 1870
Number of Groups
Groups
Wolf
Schwabe
Wolf*0.990
Schwabe = 1.284±0.052 Shea
R2 = 0.937
0
1
2
3
4
5
6
7
8
0 1 2 3 4 5 6
Yearly Means 1847-1865
Number of Groups: Schwabe vs. Shea
Schwabe
Shea0
1
2
3
4
5
6
7
8
1840 1845 1850 1855 1860 1865 1870
Number of Groups
Groups
Schwabe
Shea
Shea*1.284
F = 493
Mixing records!
17
Schwabe = 0.830±0.059 Schmidt
R2 = 0.8789
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10
Number of Groups: Schwabe vs. Schmidt
Yearly Means 1841-1866Schwabe
Schmidt
Schmidt, Carrington
0
1
2
3
4
5
6
7
8
9
10
1835 1840 1845 1850 1855 1860 1865 1870 1875 1880 1885
Number of Groups
Groups
SchmidtSchwabe
Schmidt*0.830
F = 161
Schwabe = 1.017±0.048 Carrington
R2 = 0.988
0
1
2
3
4
5
6
7
8
0 1 2 3 4 5 6 7 8
Number of Groups: Schwabe vs. Carrington
Schwabe
Carrington
Yearly Means 1854-1860
F = 4310
1
2
3
4
5
6
7
8
1850 1852 1854 1856 1858 1860 1862 1864
Number of Groups
Schwabe
Carrington
Carrington*1.017
Groups
18
Schwabe = 0.659±0.079 Peters
R2 = 0.9411
0
1
2
3
4
5
6
7
0 2 4 6 8 10
Number of Groups: Schwabe vs. Peters
Yearly Means 1845-1867Schwabe
Peters
Schwabe = 0.867±0.075 Spörer
R2 = 0.9619
0
1
2
3
4
5
6
0 1 2 3 4 5 6
Yearly Means 1861-1867Schwabe
Spörer
Number of Groups: Schwabe vs. Spörer
Spörer, Peters
F = 159
F = 73
0
1
2
3
4
5
6
7
8
9
10
1850 1855 1860 1865 1870 1875
Number of Groups
Spörer
Schwabe
Spörer*0.867
Groups
0
1
2
3
4
5
6
7
8
9
10
1840 1845 1850 1855 1860 1865 1870 1875
Number of Groups
Schwabe
Peters
Peters*0.679
Groups
19
Schwabe = 0.844±0.054 Weber
R2 = 0.9746
0
1
2
3
4
5
6
7
0 2 4 6 8
Number of Groups: Schwabe vs. Weber
Schwabe
Weber
Yearly Means 1860-1867
Schwabe = 0.816±0.064 Pastorff
R2 = 0.9635
0
1
2
3
4
5
6
0 1 2 3 4 5 6
Number of Groups: Schwabe vs. Pastorff
Yearly Means 1825-1833Schwabe
Pastorff
Pastorff, Weber
F = 158
F = 234
0
1
2
3
4
5
6
7
1824 1826 1828 1830 1832 1834 1836 1838
Number of Groups
Schwabe
Pastorff
Pastorff*0.816
Groups
0
1
2
3
4
5
6
7
8
9
10
1855 1860 1865 1870 1875 1880 1885
Number of Groups
Schwabe
Weber
Weber*0.844
Groups
20
Schwabe = 0.862±0.044 Stark'
R2 = 0.9324
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10
Number of Groups: Schwabe vs. Stark'
Schwabe
Stark'
Yearly Means 1826-1836
Schabe = 0.970±0.083 Hussey
R2 = 0.9114
0
1
2
3
4
5
6
7
8
9
0 2 4 6 8 10
Number of Groups: Schwabe vs. Hussey
Hussey
Schwabe Yearly Means 1826-1837
Hussey, Stark’
F = 116
F = 289
0
1
2
3
4
5
6
7
8
9
1824 1826 1828 1830 1832 1834 1836 1838 1840 1842
Number of Groups
Groups
Schwabe
Hussey
Hussey*0.970
0
1
2
3
4
5
6
7
8
9
1820 1825 1830 1835 1840
Groups
Number of Groups
Schwabe
Stark
Stark*0.862
21
Tevel, Arago
0
2
4
6
8
10
12
1810 1815 1820 1825 1830 1835 1840 1845
Number of Groups
Schwabe
Groups
Tevel
Tevel*1.02
Tevel OutlierSchwabe = 1.029±0.3 Tevel
R2 = 0.4807
0
1
2
3
4
5
6
7
8
0 1 2 3 4 5 6
<Schwabe>/<Tevel> = 1.007
Number of Groups: Schwabe vs. Tevel
Schwabe
Tevel
Yearly Means 1816-1836
F = 2.3
Schwabe = 1.56 Arago
R2 = 0.5427
0
1
2
3
4
5
6
0 0.5 1 1.5 2 2.5 3 3.5
Number of Groups: Schwabe vs. Arago
Schwabe
Arago
0
1
2
3
4
5
6
1815 1820 1825 1830 1835 1840
Number of Groups
Arago
SchwabeArago*1.560
F = 8.3
22
Flaugergues, Herschel
Schwabe = 1.958±0.9 Flaugergues
0
1
2
3
4
5
6
0 0.5 1 1.5 2 2.5 3
Number of Groups: Schwabe vs. Flaugergues
Schwabe
Flaugergues
0
1
2
3
4
5
6
1790 1800 1810 1820 1830 1840
Number of Groups
Schwabe
Flaugergues
Flaugergues*1.958
Schwabe = 0.79 Herschel
R2 = 0.47
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10
Number of Groups: Schwabe vs. Herschel
Herschel
Schwabe
0
1
2
3
4
5
6
7
8
9
1790 1800 1810 1820 1830 1840
Number of Groups
Schwabe
Herschel
Herschel*0.790
F = 2.3
F = 0.1
Etc… Lindener, Schwarzenbrunner, Derfflinger…
23
0
1
2
3
4
5
6
7
8
1790 1795 1800 1805 1810 1815 1820 1825 1830 1835 1840 1845 1850 1855 1860 1865 1870 1875 1880 1885
0
1
2
3
4
5
6
7
8
9
10Schwabe Group Backbone
Schwabe Backbone Groups
Standard Deviation
Number of Observers
The Schwabe Group Backbone
Weighted by F-value
0
1
2
3
4
5
6
7
8
9
1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890
0
1
2
3
4
5
6
7
8
9
10Comparing Schwabe Backbone with Hoyt & Schatten Group Number
Groups
Schwabe Backbone
H&S Groups
24
Joining two Backbones
0
2
4
6
8
10
12
1860 1865 1870 1875 1880 1885 1890 1895 1900
Comparing Overlapping Backbones
WolferSchwabe
Wolfer = 1.55±0.05 Schwabe
R2 = 0.9771
0
2
4
6
8
10
12
0 1 2 3 4 5 6 7 8
1860-1883Wolfer
Schwabe
Reducing Schwabe Backbone to Wolfer Backbone
1.55
Comparing Schwabe with Wolfer backbones over 1860-1883 we find a normalizing factor of 1.55
25
Comparison Backbone with GSN and WSN
4
6
8
10
12
14
16
18
1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940
Heliospheric Magnetic Field at Earth
IDV
B nT
0
2
4
6
8
10
12
14
1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940
Backbone
Sunspot Group Numbers 1790-1945
Groups = GSN/13.149Groups = WSN/12.174
26
How do we Know HMF B?
0123456789
10
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
012345678910
B std.dev
Coverage100% =>
B obs
B calc from IDV
B obs median
nT
0
2
4
6
8
10
12
14
16
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
B = 1.333 IDV 0.7 B obs.
Heliospheric Magnetic Field Magnitude B from Geomagnetic Activity IDV (27-Day Bartels Rotations)
13-rotation running means
The IDV-index is the unsigned difference from one day to the next of the Horizontal Component of the geomagnetic field averaged over stations and a suitable time window. The index correlates strongly with HMF B [and not with solar wind speed]
27
Staudach Observations
0
1
2
3
4
5
6
7
8
1740 1750 1760 1770 1780 1790 1800 1810
Number of Groups: Staudach
Monthly Means 1749-1799Groups
28
Zucconi, Horrebow
Staudach = 1.070 Zucconi
R2 = 0.7509
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5
Number of Groups: Staudach vs. Zucconi
Yearly Means 1754-1760 Staudach
Zucconi
0
0.5
1
1.5
2
2.5
3
3.5
1745 1750 1755 1760 1765 1770
Staudach
Zucconi
Zucconi*1.05
Number of Groups
Groups
Staudach = 0.551 Horrebow
R2 = 0.7365
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 1 2 3 4 5 6 7
Number of Groups: Staudach vs.Horrebow
Staudach Yearly Means 1761-1776
Horrebow
0
1
2
3
4
5
6
7
1750 1755 1760 1765 1770 1775 1780 1785
Number of Groups
Groups
Staudach
Horrebow
Horrebow*0.585
29
Staudach Backbone
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1740 1750 1760 1770 1780 1790 1800
Staudach Backbone
Groups