The magnetic field at a point is the summed effect of all moving charges particles in the cosmos on that point. Because the Biot–Savart law contains an inverse-square dependence on the distance between the moving charges and the point in question, the effects of closer currents tend to dominate over more distant ones but all contribute. As a result, although the deflections seen by a ground based magnetometer usually reflect changes in the closer large-scale currents in the magnetosphere-ionosphere system, there will also always be some effects of other currents flowing elsewhere. The following subsections briefly outline indices that will be employed in this review. In some relatively clear-cut cases, such as , , and , there is discussion of the currents in near-Earth space which contribute most to the detected variations in the index. However, for other cases the combination of currents that the index is monitoring is not so straightforward, as will be discussed in Section 6. Section 2.1 lists standard indices in widespread use whereas Section 2.2 discusses some research indices, designed for reconstruction work using historic datasets. Section 2.3 presents an initial study of how these various indices vary with parameters describing near-Earth interplanetary space.
The (Disturbed Storm Time) index is constructed using hourly means of the horizontal component measured at four equatorial magnetometer stations: Honolulu, San Juan, Hermanus, and Kakioka. The index was first constructed for the International Geophysical Year and is available for 1957 onwards. The derivation and station selection is described by Sugiura and Kamei (1991). Because of the low latitudes of the stations, the index chiefly monitors the disturbances produced by changes in the ring current, which flows westward around the magnetosphere at geocentric distances of about (where is a mean Earth radius), as shown in part (b) of Figure 2. Negative perturbations in Dst correspond to storm time enhancements in the ring current. However there are also small contributions from the cross-tail sheet current in the magnetotail and some contamination from auroral ionospheric currents. In addition, positive variations in are caused by the compression of the magnetosphere due to solar wind dynamic pressure increases, showing that it also responds to changes in the magnetopause (Chapman–Ferraro) currents.
The Auroral Electrojet indices (, , , and ) were first introduced by Davis and Sugiura (1966) to a measure the auroral electrojet currents that flow in the high-latitude ionosphere. In order to achieve this, the stations contributing to the index lie within the band of the auroral oval. A ring of 12 longitudinally-spaced magnetometers ensures that one station is always close to the peak of the westward auroral electrojet whilst another station is always close to the peak of the eastward electrojet (Tomita et al., 2011). The stations are all in the northern hemisphere and a corresponding southern hemisphere ring is precluded by the southern oceans which do not allow sufficiently even and full longitudinal coverage of the southern auroral oval. The exact number of stations has varied somewhat over time, data prior to 1964 coming from a somewhat different distribution of stations including contributions from the southern hemisphere. The indices can be generated using a great many stations, but the standard indices employ 12 and are referred to as . They are recorded at high time resolution (usually 2.5 minutes) and quiet time diurnal variations are first removed from the component. The maximum and minimum values of the background-subtracted at any one time seen by the ring stations are the and values, respectively. (Also often quoted are , the difference between and , and , which is their mean, but neither are used in this review). The auroral currents causing geomagnetic activity are divided into the “DP1” and “DP2” systems (e.g., Clauer and Kamide, 1985). Studies of the station contributing the maximum deflection (e.g., Tomita et al., 2011) reveal that large (negative) perturbations to are caused by the nightside westward electrojet (the DP1 or substorm current wedge system, see Section 6) which responds to magnetic energy that is stored in the magnetotail and then explosively released into the westward auroral electrojet during events called “substorm expansion phases”, whereas is set by the eastward part of the dayside DP2 currents that are directly driven by the solar wind (e.g., Clauer and Kamide, 1985; Consolini and De Michelis, 2005). Under quiet conditions reflects the westward electrojet of the DP2 system in the morning sector (DP2 currents are generally detected on the dayside where ionospheric conductivities are higher). The eastward, quiet westward and disturbed westward auroral electrojets are all labelled in part (c) of Figure 2. There is some contamination of and from the ring current. Data are available for 1957 onwards.
The index was devised and compiled by Mayaud (1971, 1972, 1980). It is a “range” index, meaning it is based on the range of variation seen during three-hour intervals, as introduced by Bartels et al. (1939). At each station contributing to the index, a semi-logarithmic index is derived by first removing the quiet-time variation and then using the larger of the differences between the maximum and minimum values of either the horizontal or vertical field in the 3-hourly intervals (the range), giving eight values per day. Data are taken from just two mid-latitude stations selected to be close to antipodal, with the northern hemisphere station in southern England and the southern in Australia. In both hemispheres, three different stations were needed to give a continuous index: in the north they are Greenwich (1868 – 1925), Abinger (1926 – 1956), and Hartland (1957 – present) and in the south they are Melbourne (1868 – 1919), Toolangi (1920 – 1979), and Canberra (1980 – present). The indices are generated using a site-dependent scale to normalise them to the values seen at the Niemegk station, giving and for the north and south hemispheres and is defined as the arithmetic mean of the two.
The , , and indices are range indices constructed in the same way as but use a greater number of stations. Mid-latitude stations (around a target geomagnetic latitude of 50°), spread across geomagnetic longitudes in both the northern and southern hemispheres, are used. The exact mix of stations has varied somewhat over time, as have the longitudinal sectors into which they have been divided, but typically number 16 in the north and 9 in the south. The values are averaged over the longitudinal sectors (5 in the north, 4 in the south) before being normalised and then averaged over the northern hemisphere, southern hemisphere and globally to give , , and , respectively. Data are available from 1959.
The index is another range index, which is available for 1932 onwards. It is a 3-hourly planetary index compiled using the indices from 11 – 13 longitudinally-spaced mid-latitude stations in the northern hemisphere.
The , , , , , , and indices are all well-established, in widespread use and formally recognised by international organisations such as IAGA (the International Association of Geomagnetism and Aeronomy). However there are other valuable indices that have been compiled by individual researchers to meet specific purposes. These generally employ hourly mean or hourly “spot values” (samples).
The index was developed by Bartels (1932). It was based on the absolute value of the difference between the mean values of for a day and for the preceding day. Taking this difference is a simple but effective way of removing quiet time variation. The index is the weighted mean of data from a collection of stations. Prior to averaging the data from the various stations, each was normalised to the magnetic latitude () of Niemegk using an empirical dependence. Bartels used data from Seddin (1905 – 1928), Potsdam (1891 – 1904), Greenwich (1872 – 1890), Bombay (1872 – 1920), Batavia (1884 – 1899 and 1902 – 1926), Honolulu (1902 – 1930), Puerto Rico (1902 – 1916), Tucson (1917 – 1930), and Watheroo (1919 – 1930). He notes stability problems with the Greenwich data in deriving interdiurnal variation data (from one day to the next) and ascribes half weighting to it as a result. (Recently, Lockwood et al., 2013a have studied all the hourly data from Greenwich and confirmed these problems). In addition Bartels notes many data gaps in the Bombay data. The index is based on 2 stations for 1872 – 1891 (Greenwich and Bombay and Bartels expresses reservations about the quality of both), rising to 6 by 1919 before falling to 3 again by 1930. Data for 1835 – 1872 was compiled by Bartels and is called the index but is not the same as the index after 1872. Bartels notes that before 1872, no proper data to generate an interdiurnal index was available to him and so other correlated measures of the diurnal variation are used as proxies. Bartels himself stresses that the values before 1872 are “more for illustration than for actual use”. The index was criticised at the time for failing to register the recurrent geomagnetic storms and, as a result, he himself developed the range indices as an alternative (Bartels et al., 1939). However, as pointed out by Svalgaard and Cliver (2005), this feature is a positive advantage of as it means that it is not complicated by a response to solar wind speed variations. The index data cease in 1930.
The index is a variant of the index that was devised by Svalgaard and Cliver (2005). The main difference in its derivation is that instead of using daily mean values of , the hourly mean (or spot value) closest to solar local midnight is employed. As for , the difference between values on successive days is taken. The latitude normalisation is also slightly different, using an empirically-derived dependence. is found to not depend on solar wind speed, and depends on just the IMF field strength in annual means. One of the great advantages of is that it’s compilation is much simpler than the range-based indices and this has allowed the use of historic hourly mean (or spot) values to produce a meaningful index that extends back many years. Svalgaard and Cliver (2005) adopt a different philosophy in compiling to that adopted by Mayaud (1971) in compiling . Mayaud’s philosophy was to use as homogeneous a data series as possible. The philosophy of Svalgaard and Cliver (2005) (and of Lockwood et al., 2006b in the derivation of the index, see below) was to use all available data that are of sufficient quality. Inevitably this means that fewer data are available at earlier times and the construction of means that (like ) it is not homogeneous. Svalgaard and Cliver (2010) added more stations and also extended the sequence back to 1835 using a linear correlation with the Bartels index. In this context, note Bartels’ reservations about the early data discussed in Section 2.2.1.
The index has recently been introduced by Lockwood et al. (2013a). This is very similar to with two differences. The first is that it employs daily means rather than the near-midnight hourly mean or spot values: in other words, Lockwood et al. (2013a) returned to the formulation used by Bartels (1932) to generate . This means that 24 times the volume of data are used than in generating because data from the 23 UT-hours away from local midnight are not discarded. This has advantages in noise suppression by averaging. Lockwood et al. (2013a) adopted the name (rather than reverting to the name ) because of the other major difference, namely that the composite is homogeneous in its construction (i.e., it uses the philosophy of and not that of and ), using data from three intercalibrated stations sequentially to form a composite. Data from Helsinki were used for 1846 – 1890 (inclusive) and 1893 – 1897 and from Eskdalemuir from 1911 to the present day. The gaps are filled using data from the Potsdam (1891 – 1892 and 1898 – 1907) and the nearby Seddin observatories (1908 – 1910) and intercalibration achieved using the Potsdam/Seddin/Niemegk data sequence for 1890 – 1931. To remove site effects and the effects of secular drifts in geomagnetic latitudes, the dependence found by Svalgaard and Cliver (2005) was shown to apply and was used to make a small ( 5% between 1846 and 2013) correction to the data based on model predictions of the magnetic latitude of the stations, . The index extends back to the start of the Helsinki data in mid 1845. One key justification of is that it correlates with the IMF as well as (in fact very slightly better than) , despite the fact that it is based on data from just one station (which is Eskdalemuir throughout the space age) rather than the approximately 50 stations contributing to at that time (see Figure 3). One concern, however, is the use of the historic data from Helsinki which is at a higher corrected magnetic latitude and so more subject to auroral current contamination of the kind noted by Svalgaard and Cliver (2010) and Finch et al. (2008), and which could introduce a dependence on solar wind speed, . Models of the geomagnetic field give corrected magnetic latitudes of Helsinki varying between 55.5° and 56.5° over the interval that data are used from this station. The survey by Finch et al found that the correlation with IMF began to drop above 60° (and that with began to rise). Hence, Helsinki is close to being at too high magnetic latitude. To investigate if this was a problem, Lockwood et al. (2013a) used modern data from the Nurmijärvi station (close to Helsinki) and compared IDV(1d) derived from them to that from Eskdalemuir. The correlation is 0.931 in 27-day means and 0.982 in annual means. Furthermore, the dependence of from Nurmijärvi on was investigated and the peak correlation found near , very close to the value for Eskdalemuir (see Figure 3). The same tests were applied to modern data from the Niemegk station.
The homogeneous nature of is a major advantage when making historic reconstructions of interplanetary parameters because one can have greater confidence that it will have responded to changes in the solar wind before the space age in the same way that it was observed to do during the space age. If an index is not constructed in a homogeneous manner then one cannot have that confidence to the same extent. Hence, for reconstructions of interplanetary parameters, homogeneously constructed indices such as and are preferable to inhomogeneous ones such as and .
The index was introduced by Lockwood et al. (2006b) and used by Rouillard et al. (2007) and Lockwood et al. (2009d). 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, . These are then correlated with, and linearly regressed against, the annual means of shown in Figure 5 to yield . These normalisations are needed because both the sensitivity and offset for a station were 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 median of these data series is used as it is less influenced by extreme outliers than the arithmetic mean. Somewhat conservative criteria are used for the inclusion of data, in that annual means of the station-UT time series must correlate reasonably well (correlation coefficient ) with those of . In addition, does not employ any isolated fragments of data from stations that ceased operating before the start of the space age and only used data from stations that continued to take data into the space age (or there was a nearby station, with which one could make a composite, that did). The advantage of over is that data from all 24 UT-hours are employed, as opposed to just the one (near midnight) value used by . The disadvantage is that its compilation is much more complex and time-consuming than that of and so new data cannot be as readily added. Furthermore, does not correlate as highly with interplanetary parameters as does (see Figure 3). Lockwood et al. (2006b) consider that the index is less reliable before 1902 because then it is based on data from just one station (Potsdam).
The index was devised and introduced by Svalgaard et al. (2003) and Svalgaard and Cliver (2007a) and uses only nightside data to minimise the effect of the diurnal variation. for a given station is defined as the sum of the absolute values of the difference between hourly means (or spot values) for a specified geomagnetic component from one hour to the next over the 7-hour interval around local midnight. The variation with the corrected magnetic latitude shows strong peaks in the auroral oval, indicating it responds most to the variability in the nightside westward auroral electrojet and so it behaves rather like . Because the variation with corrected geomagnetic latitude is flat equatorward of 55° only stations equatorward of this were employed in the global IHV index. The normalisation, grouping and averaging of data from different stations to obtain a global index is described in Svalgaard and Cliver (2007a).
Finch et al. (2008) devised the indices for each station, which – like , and – is based on hourly mean data. at a given station is defined as the value of the standard deviation of the hourly-averaged values at a given UT over a period of days, each single UT-hour being treated separately, as for . There will therefore be 24 values for each period of days at each station. (Note that the index is, using this notation, the median for all available station-UTs of the values for leap years and for all other years). Finch et al. (2008) used days (close to the solar rotation period, as seen from Earth, which is the Carrington rotation period of 27.2753 days), which gives thirteen 28-day periods per year (with any excess days assigned to the final such period in the year). It is a different measure of the inter-diurnal variation quantified by the , , indices, but because it applies to each station individually it is, in some respects, equivalent to the values used in the derivation of range indices.
In-situ spacecraft data on the near-Earth interplanetary medium became increasingly available from 1963, at the start of the space age. Early studies comparing geomagnetic activity to the near-Earth interplanetary parameters (e.g., Arnoldy, 1971) showed that geomagnetic activity was enhanced when the interplanetary magnetic field (IMF) pointed southward in a reference frame aligned by Earth’s magnetic axis: Geocentric Solar Magnetospheric, GSM, is widely used (Russell, 1971; Hapgood, 1992). This had been predicted in the seminal paper by Dungey (1961), who proposed that for this IMF orientation, magnetic reconnection in the dayside magnetopause current sheet would allow the solar wind to drive stronger F-region ionospheric flows (convection) and hence the associated E-region ionospheric currents and geomagnetic activity seen at Earth’s surface would also be stronger. The southward IMF orientation in GSM occurs for 50% of the time (Hapgood et al., 1991). The DP2 or “directly driven” currents respond to IMF variations with a lag of a few minutes (Nishida, 1968), whereas the larger DP1 or “storage-release system” currents are enhanced during substorm expansion phases following a lag of typically one hour (e.g., Baker et al., 1981). The high latitude auroral currents link to the magnetospheric ring current via the Region-2 field-aligned currents, as shown in Figure 2. The ring current has long been understood in terms of injection and decay of the trapped particles that carry it (Burton et al., 1975) and the injection is more efficient when the interplanetary magnetic field points southward (see, e.g., Shi et al., 2012). The response is complicated by the fact that the interplanetary electric field also influences the decay of the ring current and there are other, internal magnetospheric factors which influence both the injection and the decay (see reviews by Kozyra and Liemohn, 2003; Pulkkinen, 2007). Enhancements of the ring current cause negative depressions in the index but will also influence other geomagnetic indices.
Figure 3 explores the dependence, on annual averaging timescales, of the geomagnetic indices described on Sections 2.1 and 2.2 on the solar wind speed, . The correlation between each index and is presented where is the IMF field strength and is an exponent that is here varied between –2 and 4. The correlations are for annual means between 1966 and 2012, inclusive. Parameters marked with a prime denote that data have been omitted in computing both sets of annual means if any of the simultaneous (allowing for the predicted satellite-to-Earth solar wind propagation lag) hourly means of , or the geomagnetic index are missing due to a data gap. In the case of the 3-hour range indices , and , the procedure adopted by Finch and Lockwood (2007) is followed to ensure only simultaneous geomagnetic and IMF data are included in the annual means. In the case of , each daily value contains information on from two whole days: in order to be included in the annual means, we here require that there be 75% coverage of the IMF observations over those two days. The value of 75% is chosen as a compromise between not eliminating too much of the data and removing data for which the interplanetary means could be misleading because the data coverage is low. The effects of not carrying out this piecewise removal of data from both sets during datagaps were studied by Finch and Lockwood (2007): effectively one is assuming that annual means are representative, even when large fractions of the data are missing (as they are in some years for the interplanetary data). Even with the piecewise removal of data during data gaps, we here only employ annual means that have data availability exceeding 50% to avoid years of reduced data having undue weight. In the study presented in Figure 3, all the correlations are somewhat improved by taking these steps and, importantly, the of peak correlation is sometimes also affected. Note that only annual mean data for and have been published and the way is generated only yields annual values: as a result, no allowance for gaps in the interplanetary data can be made in these three cases (hence there is no prime symbol attached to , , or in Figure 3).
The coupling functions have been calculated in hourly data and then averaged, so that is used rather than . The auroral electrojet index (red line) shows peak correlation , i.e., it has a dependence. The index (green line) gives a peak at (i.e., it has close to a dependence and, hence, varies with the interplanetary electric field). The index shows a peak at (blue line) but some of this dependence on arises from the compression of the equatorial field by enhanced solar wind dynamic pressure: if we use only the negative part of (, which is the same as but treats all intervals where as data gaps and so only contains intervals when is dominated by ring current effects), we get the dashed blue line with a higher correlation coefficient peak at . This peak is flat and, hence, the peak is not significantly different from zero (i.e., the dependence is on alone). The cyan line is for the index and peaks at (very close to the dependence of ), the mauve line is for and peaks at and the orange line is for and peaks at . The black line is for the index, which peaks at near . Hence , like and , is not significantly different from having a dependence on only. Thus, as concluded by Svalgaard and Cliver (2010), the negative part of (i.e., ring current enhancement) is closest to explaining the behaviour of the interdiurnal variability indices on these annual timescales. The range indices, and respond in a manner similar to the auroral indices and, in particular, the influence of the westward auroral electrojet on (as monitored by ) can be inferred from the fact that both have a dependence that is not significantly different from . The correlation for peaks at a slightly lower than for , , or , which may be a greater influence of the directly-driven currents or may be the effect of the ring current (as both and give peaks at lower ). The index correlation peaks at and so, as pointed out by Svalgaard et al. (2003) and Svalgaard and Cliver (2007a), behaves very much like and all the range indices with a dependence, as expected because it is a monitor of the nightside auroral electrojet.
The index (yellow line) correlation peaks at and there are a number of possible reasons why this value of exceeds zero. It could be that the response of is set by a mixture of the ring current (with its dependence) and the DP2 auroral currents (with their dependence). An alternative explanation is that the normalisation against the index in the derivation of has introduced a small dependence on . We also note that employed data from some auroral stations such as Sodankylä, which, as discussed in Section 6, introduces a dependence into values.