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3 The Long-Term Variability of Geomagnetic Activity

The first homogeneous, long-term record of geomagnetic activity was the aa index compiled by Mayaud, who analysed 100 years’ data (1868 – 1968) from observatories in southern England and near their antipodal locations in Australia (Mayaud, 1971, 1972, 1980). In each hemisphere, three different stations were required to make a continuous record and, as for all such composites, inter-calibration problems between the different stations arise. Means over calendar years and over 27-day Bartels solar rotation intervals are plotted in the top panel of Figure 4View Image. When aa was first used to reconstruct the solar magnetic fields, there were several vociferous objections that, despite Mayaud’s careful calibration work, the drift seen in Figure 4View Image was merely an instrumental artefact. There are, indeed, a great many problems that can cause long-term changes in the record from a magnetometer station: in addition to instrument changes, drifts and re-adjustments, a change in the local water table can have an influence, as can the construction of power or railway lines nearby and, on very long timescales, the secular drift in the magnetic poles of the Earth causes the geomagnetic coordinates of a station to drift. The argument that the aa values could not be as low as derived around 1900 by Mayaud has been proved to be wrong by the recent long and low solar minimum between solar cycles 23 and 24 (Russell et al., 2010Jump To The Next Citation Point; Lockwood, 2010Jump To The Next Citation Point). During this minimum (around 2008), comparably low annual mean aa was observed, as is shown by Figure 4View Image. Analyses suggesting calibration problems were often based on comparisons with hourly mean data (Svalgaard et al., 2004Jump To The Next Citation Point; Svalgaard and Cliver, 2005Jump To The Next Citation Point; Mursula and Martini, 2007). However, it has become clear that hourly mean data are not observing the same mix of currents and phenomena as the range indices (see Section 6) and, hence, many of the differences are real rather than instrumental. This is underlined by the bottom panel of Figure 4View Image, which shows the corresponding means for another homogeneously-constructed long-term index, IDV (1d). Although many features can be seen in both indices, there are many differences, particularly in the 27-day means. The long-term change is seen in both indices despite 3 major differences between them: (1) they are constructed using data from entirely different observatories, (2) one uses hourly means and the other range data, and (3) the compilation algorithms (including the removal of quite day variations and secular change in station latitudes) are entirely different. The correlation coefficients between aa and IDV (1d) for 27-data and annual means (for 1868 – 2013) are 0.68 and 0.76, respectively. These correlations should be compared with those over the same interval between the independent aa indices for the northern and southern hemispheres, aaN and aaS, which are 0.94 for the 27-day means and 0.98 for the annual means.
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Figure 4: Averages over Bartels 27-day solar rotation intervals (coloured) and calendar years (in black) of (top) the aa geomagnetic index and (bottom) the IDV (1d ) index. The colours give the station(s) contributing the data to the indices at any one time. This version of the aa index is as stored in the World Data Centres. The data labelled Niemegk are a composite from the three nearby stations, Niemegk, Potsdam, and Seddin.
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Figure 5: Comparison of annual means of the standard aa index (in red) and the modified version aaC derived by Lockwood et al. (2006bJump To The Next Citation Point) (in blue). The estimated maximum uncertainty, relative to modern values, is shown by the grey band. The green dots are annual means of the Ap index.

A number of tests on aa have been carried out (e.g., Lockwood, 2001Jump To The Next Citation Point; Clilverd et al., 2002Jump To The Next Citation Point; Cliver and Ling, 2002; Lockwood, 2003Jump To The Next Citation Point; Clilverd et al., 2005Jump To The Next Citation Point; Lockwood et al., 2006bJump To The Next Citation Point; 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., 1999Jump To The Next Citation Point; Clilverd et al., 2002). However, there is also evidence of some error in the aa index, as stored in most data centres at the present time. The first authors to suggest errors in aa were Svalgaard et al. (2004Jump To The Next Citation Point) who compared aa against the IHV index: indeed they argued that all centennial change in aa was erroneous. Comparing with IHV is a valid test of aa because, as shown in Figure 3View Image, they both correlate best with BV n SW for n near 2. The initial comparisons by Svalgaard et al. (2004) found an almost negligible change in IHV since 1900 which would imply early aa values were too low: quantitatively they found the mean error in aa was 8.1 nT over solar cycle 14 (1901 – 1912, inclusive), which considering that the mean aa 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 aa was erroneous. However, this early version of IHV 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. (2004Jump To The Next Citation Point) found there was upward drift in IHV values over the 20th century, but it depended on the station studied; nevertheless they inferred that the drift in aa was too large. As a result, Svalgaard et al. (2003Jump To The Next Citation Point) revised their estimates, using several stations, such that the cycle-14 mean of aa was too low by 5.2 nT (this would mean that 64% of the drift in aa was erroneous). However, Mursula and Martini (2006) showed that about half of this difference was actually in the IHV estimates not aa and was caused by the use of spot values rather than hourly means in constructing the early IHV data. This was corrected by Svalgaard and Cliver (2007aJump To The Next Citation Point) 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 aa station from Abinger to Hartland. Independently, Lockwood et al. (2006bJump To The Next Citation Point) carried out tests of aa using the range Ap index which has been constructed since 1936 from 11 – 13 northern hemisphere stations, and range k 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 aa was not as apparent in the original aa data as it is now. Other studies also indicate that aa 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 aa between cycle 14 and the space age of about 25%. Lockwood et al. (2006bJump To The Next Citation Point) implemented revised calibrations between stations (the largest change needed being for 1957) and, hence, derived a revised index series aaC. Figure 5View Image shows that the difference between annual means of aa and aaC is generally less than 2 nT, which is considerably smaller than the range of the long-term drift in aa annual means over the last 150 years (approximately 12 nT at sunspot minimum and 16 nT at sunspot maximum).

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Figure 6: The median index, m. For each station at a given UT, the standard deviation of the hourly means of the horizontal component of the geomagnetic field is computed over a full year, σH 1yr. These are then correlated with, and linearly regressed against, the annual means of aa shown in Figure 4View Image to yield ′ H σ = s × σ 1yr + c. These normalisations are needed because both the sensitivity s and offset c for a station have been shown to depend on its location and on the UT hour (which, for example, alters the location of the station relative to the midnight-sector auroral oval) (Finch, 2008). Each station-UT is treated as an independent data series. The grey lines show the variations of the σ ′ values for all station-UTs for which the correlation coefficient exceeds 0.5 and is significant at the 2σ level. The number of station-UTs meeting this criterion is shown as a function of time by the black histogram in the lower panel. The black line in the upper panel is the median of all the available data for each year and is called the “median index”, m. Image reproduced from Lockwood et al. (2006bJump To The Next Citation Point).

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 6View Image shoes the variation of the “median index”, m (Lockwood et al., 2006bJump To The Next Citation Point). 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 m index treats each station-UT as a separate data series. To avoid outliers having a disproportionate effect, m 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 6View Image is m, which also shows a similar long-term variation to the annual means of aa and IDV (1d) shown in Figure 4View Image.

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Figure 7: Annual means of the IDV index compiled by Svalgaard and Cliver (2010Jump To The Next Citation Point). The grey curves are the variations for individual stations. The red curve is the index, defined as the arithmetic mean of the median and average values of the individual station values. A few station values were very large outliers of the distribution at any one time and those that were more than five standard deviations from the average were omitted in calculating the IDV value for that year. The number of contributing stations, N, is shown by the thin blue curve. The dashed blue line is the corresponding number of stations used by Svalgaard and Cliver (2005Jump To The Next Citation Point). Bartels’ u index is considered a single station and gives the dotted line extension to before 1871 using a linear regression of 1871 – 1930 data with the IDV index proper. Image reproduced by permission from Svalgaard and Cliver (2010Jump To The Next Citation Point), copyright by AGU.

Figure 7View Image shows the IDV index compiled by Svalgaard and Cliver (2010Jump To The Next Citation Point). 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 IDV proper and the u index. However, it must be remembered that u is not an inter-diurnal variability index before 1872 and Bartels did not regard all the data before this date as reliable. Figure 7View Image also shows the variation in N, the number of stations used to compile IDV.

Note that for both IDV and m, the number of stations used decreases as one goes back in time, which contrasts with Mayaud’s philosophy for aa 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 (2010Jump To The Next Citation Point) state that “only a few (good) stations are needed for a robust determination of IDV”. This is indeed a valid statement: for example, IDV (1d) (shown in the bottom panel Figure 4View Image) is based on just one station at any one time, yet for 1880 – 2013 it gives a correlation coefficient of 0.96 with IDV (Lockwood et al., 2013aJump To The Next Citation Point). However, before 1880 the correlation is considerably lower. Svalgaard and Cliver (2010Jump To The Next Citation Point) note that they had to discard some data because they were more than 5 σ 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 m and IDV 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 (2010Jump To The Next Citation Point) could find no discontinuities in the IDV data series from individual stations (unlike IHV 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 4View Image, 6View Image, and 7View Image 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 aa 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, 1986Jump To The Next Citation Point, to quantify solar wind speed), thereby showing that the main change was in the magnetic field, was by Lockwood et al. (1999aJump To The Next Citation Point). These authors used aa 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 aa and the derived open solar flux (for example, Pulkkinen et al., 2001).


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