A number of tests on have been carried out (e.g., Lockwood, 2001; Clilverd et al., 2002; Cliver and Ling, 2002; Lockwood, 2003; Clilverd et al., 2005; Lockwood et al., 2006b; Lu et al., 2012) which show it to be a reasonable indicator of long-term change. Furthermore, studies of potential factors identified a solar origin of the long-term drift (Clilverd et al., 1998; Stamper et al., 1999; Clilverd et al., 2002). However, there is also evidence of some error in the index, as stored in most data centres at the present time. The first authors to suggest errors in were Svalgaard et al. (2004) who compared against the index: indeed they argued that all centennial change in was erroneous. Comparing with is a valid test of because, as shown in Figure 3, they both correlate best with for near 2. The initial comparisons by Svalgaard et al. (2004) found an almost negligible change in since 1900 which would imply early values were too low: quantitatively they found the mean error in was 8.1 nT over solar cycle 14 (1901 – 1912, inclusive), which considering that the mean over this cycle was lower than the mean for cycles 20, 21, and 22 by the same amount, means that they argued that all the long-term change in was erroneous. However, this early version of was based on just one composite data series from two very nearby stations, Cheltenham and Fredricksburg (intercalibrated using the available 0.75 yr of overlapping data in 1956). Using more stations, Mursula et al. (2004) found there was upward drift in values over the 20th century, but it depended on the station studied; nevertheless they inferred that the drift in was too large. As a result, Svalgaard et al. (2003) revised their estimates, using several stations, such that the cycle-14 mean of was too low by 5.2 nT (this would mean that 64% of the drift in was erroneous). However, Mursula and Martini (2006) showed that about half of this difference was actually in the estimates not and was caused by the use of spot values rather than hourly means in constructing the early data. This was corrected by Svalgaard and Cliver (2007a) who revised their estimate of the difference further downward to 3 nT. These authors also showed that most of the difference arose in a 6-year interval around 1957, which is the time of the move of the northern hemisphere station from Abinger to Hartland. Independently, Lockwood et al. (2006b) carried out tests of using the range index which has been constructed since 1936 from 11 – 13 northern hemisphere stations, and range indices from a number of other stations (thereby ensuring that they were comparing like-with-like). They also found a step-like change around 1957 and estimated it to be about 2 nT in magnitude. Because 1957 was only 11 years before the end of the data series available to Mayaud and because in that time solar cycle 20 was rather unusual, this discontinuity in was not as apparent in the original data as it is now. Other studies also indicate that needs adjusting by about 2 nT at this date (Jarvis, 2004; Martini et al., 2012). The 2 nT discontinuity estimate corresponds to an error in the drift in between cycle 14 and the space age of about 25%. Lockwood et al. (2006b) implemented revised calibrations between stations (the largest change needed being for 1957) and, hence, derived a revised index series . Figure 5 shows that the difference between annual means of and is generally less than 2 nT, which is considerably smaller than the range of the long-term drift in annual means over the last 150 years (approximately 12 nT at sunspot minimum and 16 nT at sunspot maximum).
Many historic datasets exist in the form of hourly mean data (or in the case of some of the earliest data, spot values within the hour) and these have recently also been used to generate indices. Until recently many were in the form of paper records in observatory yearbooks. However, in recent years many have been digitised making a valuable new extra resource for reconstruction work.
Figure 6 shoes the variation of the “median index”, (Lockwood et al., 2006b). The construction of this index recognises that the response to global geomagnetic activity at a given observatory depends upon its magnetic local time (MLT) and, hence, on the Universal Time (UT). However, the station gives information at all UT and so rather than discard data from all but one MLT, the index treats each station-UT as a separate data series. To avoid outliers having a disproportionate effect, is defined as the median of all the normalised annual values for the different station-UT combinations. The black line in the upper panel of Figure 6 is , which also shows a similar long-term variation to the annual means of and shown in Figure 4.
Figure 7 shows the index compiled by Svalgaard and Cliver (2010). These authors take the series back to 1835, just 3 years after the establishment of the first magnetic observatory in Göttingen. This is done using a linear correlation between proper and the index. However, it must be remembered that is not an inter-diurnal variability index before 1872 and Bartels did not regard all the data before this date as reliable. Figure 7 also shows the variation in , the number of stations used to compile .
Note that for both and , the number of stations used decreases as one goes back in time, which contrasts with Mayaud’s philosophy for which was to derive a homogeneously-constructed data series. Given the potential for site-dependent errors and drifts, these indices therefore become increasingly unreliable as one goes further back in time. Svalgaard and Cliver (2010) state that “only a few (good) stations are needed for a robust determination of ”. This is indeed a valid statement: for example, (shown in the bottom panel Figure 4) is based on just one station at any one time, yet for 1880 – 2013 it gives a correlation coefficient of 0.96 with (Lockwood et al., 2013a). However, before 1880 the correlation is considerably lower. Svalgaard and Cliver (2010) note that they had to discard some data because they were more than from the mean. This poses a dilemma if there are too few stations to define the distribution: in such cases these outliers could not be identified and one would have used them, not knowing they were in error. In other words, without sufficient other stations to compare with, one is not able to say which the “good” stations are. It therefore is inevitable that the inhomogeneous data series such as and are less reliable further back in history. Potential causes of additional uncertainty in early data are: (1) there were fewer stations; (2) measurement techniques and equipment improved with time; (3) the realisation of that urban environments were generating magnetic noise problems forced moves to quieter observing sites; and (4) earlier data tend to be spot values rather than hourly means. On the last point, Svalgaard and Cliver (2010) could find no discontinuities in the data series from individual stations (unlike values) when they changed from supplying spot values to hourly means. Nevertheless, it is self-evidently true that hourly means are preferable to spot values, particularly if a site is suffering from any intermittent noise problems and/or if the instrument stability is poorer.
Figures 4, 6, and 7 all show similar long-term variations, despite the fact that the indices presented differ in almost every facet of their compilation. There are, however, important differences that are discussed in Section 6. These data from geomagnetic observatories give an invaluable resource for studying solar-terrestrial physics and solar variability in the 181 years since Gauss’ first observatory was established in Göttingen. In particular, we can study the variations in the solar corona and interplanetary medium that accompany the long-term sunspot variations identified by Gleissberg (1944). Feynman and Crooker (1978) studied the implications of the drift in the index and concluded that either the solar wind speed or the IMF had changed over the past century. The first paper to separate these two influences (using the recurrence index of Sargent, 1986, to quantify solar wind speed), thereby showing that the main change was in the magnetic field, was by Lockwood et al. (1999a). These authors used to reconstruct the unsigned open solar flux, which is the total magnetic flux leaving the top of the solar corona and entering the heliosphere. Other solar terrestrial phenomena, such as lower latitude auroras, were found to reveal the same long term changes as and the derived open solar flux (for example, Pulkkinen et al., 2001).