Updating the Historical Sunspot Record

The Sunspot Record goes back 400 years and is the basis for many reconstructions of solar parameters (e.g. TSI), but, how good is it? And can we agree on which one (Wolf Number, International Number, ‘Boulder’ Number, Group Number, …)? Are the old values good? Are the new ones? And what is a ‘good’ or ‘correct’ Sunspot Number anyway?

Johann Rudolf Wolf (1859) defined his Relative Sunspot Number, taking into account both individual spots and their appearance in distinct groups (what we today call ‘active regions’), as R W = 10 Groups + Spots. Wolf started his own observations in 1849 and assembled observations from earlier observers back to 1749 and beyond (Figure 1). As is clear, the earlier values were subsequently adjusted (upwards) as Wolf were struggling with the difficulty of bringing different observers onto the same 2 Svalgaard ‘scale’, compensating for telescope size, counting method, acuity, seeing, and personal bias.

Wolf published several versions of his celebrated Relative Sunspot Numbers based on data gathered from many observers from both before and during Wolf’s own lifetime (Figure 2). How to ‘harmonize’ data from different observers?

A current system in the ionospheric E-layer is created and maintained by solar UV radiation (Figure 3). The current has a magnetic field of its own which is readily observed on the ground even with 18th Century technology. This variation was, in fact, discovered in 1722 by George Graham (1724) as a regular variation of typically 10 arc minutes during each day of the angle (called the Declination today) a compass needle makes with true North. The amplitude (rD) of this variation is an excellent proxy for solar UV. Stations rotate into and out of the magnetic field of this system, recording it (right). Wolf (1859) discovered that this amplitude has a strong linear relationship with his newly defined Relative Number, R W : rD = a + b R W and used the relationship to calibrate the sunspot number on a yearly basis (Figure 4). By comparing sunspot numbers (SSN) reported by other observers with his own, Wolf introduced a scale factor to compensate for the differences: SSN = k W (10 Groups + Spots).

Hoyt & Schatten (1998) proposed basing the Sunspot number solely on the number of groups reported by the observers: GSN = 12 Groups. The calibration constant was used to make the value of the GSN comparable to the modern Sunspot Number. However, the number of sunspot groups is also observer dependent (Figure 5), by up to a factor of two or more, so an observerdependent adjustment factor is also needed: GSN = 12 k G Groups. So, the conceptually cleaner GSN also needs adjustment and ‘bridges’ from one observer to the next, and the next, etc, lacking the ‘absolute’ calibration afforded by another physical observable. This may lead to a possibly spurious secular change (Figure 6).

Extensive datasets exist (Schmidt (1909)) from the ‘Magnetic Crusade’ in the 1840s and for times after the First Polar Year 1882 (Figure 7). As the current flows along meridians on the morning and evening sides, the magnetic deflection is along latitude circles and the magnitude in force units (nT) is largely constant from station to station over a wide latitude range (20 • -60 • ). From the observed values of rD and of the Horizontal component, H, the range in force units, rY, is readily calculated as shown. Wolf didn’t know that the important parameter is rY and not rD, so he had to contend with regression coefficients that varied from station to station and with time. While not a serious problem once you know why, this variation nevertheless weakened other researchers’ confidence in Wolf’s procedure.

As shown in Figure 8, after ∼1882 the GSN (pink) and the SSN (blue) have the same relation with the range of geomagnetic variation and cluster neatly along a common regression line, also found for SSN for stations regardless of time interval. If we add the GSN averages (red diamonds) for stations before 1850, we find that they all fall well below the regression line for stations after 1880 (Figure 9).

If the diurnal range, rY, is a satisfactory measure of the kind of solar activity we believe the sunspot should be a proxy for, then the above analysis would suggest that the Group Sunspot Number should be increased by a factor of 1.4 sometime before ∼1880, removing most of the discrepancy between the two sunspot number series.

It is instructive to plot the ratio of the Wolf number and the Group number (omitting years where either is close to zero). Figure 10 shows that with the above adjustment by a factor of 1.4 before ∼1880, the ratio seems to be near unity, with an expected large noise component early on. A discontinuity in 1945 when Max Waldmeier took over production of the Zürich Sunspot Number is apparent. Alfred Wolfer became Wolf’s assistant around 1880 and began to influence the ‘Wolf’ number from then on. Wolf did not count pores and the smallest spots. His a