2 Geomagnetic Indices

A large number of indices have been developed and deployed to quantify the geomagnetic activity detected by the global network of magnetic observatories. These indices vary in which observatories are used, which data from those observatories are used, how those data are processed, and how the data from different observatories are combined together. As a result, the different indices monitor different parts of the system of coupled currents that flow in near-Earth space in response to the flow of the magnetised solar wind plasma around the magnetosphere. Figure 2View Image is a schematic showing the currents that flow in the magnetosphere-ionosphere system and how they are connected.
View Image

Figure 2: Simplified schematic of the currents flowing in the magnetosphere-ionosphere system in the northern hemisphere (southern hemisphere currents are omitted for clarity). Part (a) shows (in orange) segments of the Chapman–Ferraro currents that flow in the magnetopause and separate the geomagnetic and (shocked) interplanetary fields: the relevant segments are at the sunward edge of the magnetospheric tail and flow from dusk to dawn (see also Figure 14View Image). These connect to the high-latitude ionosphere via the Region 1 field-aligned (Birkeland) currents (shown in blue). The Region 2 field-aligned currents are needed to maintain ionospheric current continuity and because of the incompressibility of the ionosphere (in the sense that the magnetic field there is essentially constant). As shown in red in (b), these Region 2 currents close via the ring current that flows westward around the Earth in the inner magnetosphere (in cyan), caused by the gradient and curvature drifts of trapped energetic particles. Part (c) shows the Region 1 and 2 currents entering and leaving the polar E-region ionosphere and how they connect to the Pedersen currents there (in green), which flow in the direction of the electric field. The paired up and down field-aligned currents transfer solar wind energy, momentum, and electric field down into the ionosphere as well as current (see review by Lockwood, 1997). The Hall currents (shown by black lines) flow perpendicular to the electric field (and so cause no energy dissipation) and are antiparallel to associated ionospheric flow (convection) in the over-lying F-region ionosphere. For a uniform spatial distribution of conductivities, the effects of field-aligned and Pederson currents cancel beneath the ionosphere and only the Hall currents are detected by high-latitude magnetometers on the ground. The formation of the westward electrojet in the substorm current wedge (shown here in mauve) is described later by Figure 14View Image. In this electrojet, a highly conducting channel is formed by ionisation generated by the associated particle precipitation and the Cowling conductivity is relevant.

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 Dst, AU, and AL, 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.

2.1 Standard geomagnetic indices

2.1.1 The Dst index

The Dst (Disturbed Storm Time) index is constructed using hourly means of the horizontal component H 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 Dst index chiefly monitors the disturbances produced by changes in the ring current, which flows westward around the magnetosphere at geocentric distances of about 3– 6R E (where 1R E is a mean Earth radius), as shown in part (b) of Figure 2View Image. 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 Dst 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.

2.1.2 The AU and AL indices

The Auroral Electrojet indices (AE, AL, AU, and AO) 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., 2011Jump To The Next Citation Point). 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 AE (12). They are recorded at high time resolution (usually 2.5 minutes) and quiet time diurnal variations are first removed from the H component. The maximum and minimum values of the background-subtracted H at any one time seen by the ring stations are the AU and AL values, respectively. (Also often quoted are AE, the difference between AU and AL, and AO, 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, 1985Jump To The Next Citation Point). Studies of the station contributing the maximum deflection (e.g., Tomita et al., 2011Jump To The Next Citation Point) reveal that large (negative) perturbations to AL 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 AU 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 AL 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 2View Image. There is some contamination of AU and AL from the ring current. Data are available for 1957 onwards.

2.1.3 The aa index

The aa index was devised and compiled by Mayaud (1971Jump To The Next Citation Point, 1972Jump To The Next Citation Point, 1980Jump To The Next Citation Point). 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. (1939Jump To The Next Citation Point). At each station contributing to the index, a semi-logarithmic k 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 k indices are generated using a site-dependent scale to normalise them to the values seen at the Niemegk station, giving aaN and aaS for the north and south hemispheres and aa is defined as the arithmetic mean of the two.

2.1.4 The Am, An, and As indices

The Am, An, and As indices are range indices constructed in the same way as aa 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 k 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 An, As, and Am, respectively. Data are available from 1959.

2.1.5 The Ap index

The Ap index is another range index, which is available for 1932 onwards. It is a 3-hourly planetary index compiled using the k indices from 11 – 13 longitudinally-spaced mid-latitude stations in the northern hemisphere.

2.2 Specialist geomagnetic indices

The Dst, AU, AL, Am, An, As, and Ap 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).

2.2.1 The u index

The u index was developed by Bartels (1932Jump To The Next Citation Point). It was based on the absolute value of the difference between the mean values of H for a day and for the preceding day. Taking this difference is a simple but effective way of removing quiet time variation. The u 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 (Λ) of Niemegk using an empirical 1∕cos(Λ ) 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., 2013aJump To The Next Citation Point have studied all the hourly data from Greenwich and confirmed these problems). In addition Bartels notes many data gaps in the Bombay data. The u 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 u 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 u values before 1872 are “more for illustration than for actual use”. The u 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 (2005Jump To The Next Citation Point), this feature is a positive advantage of u as it means that it is not complicated by a response to solar wind speed variations. The u index data cease in 1930.

2.2.2 The IDV index

The IDV index is a variant of the u index that was devised by Svalgaard and Cliver (2005Jump To The Next Citation Point). The main difference in its derivation is that instead of using daily mean values of H, the hourly mean (or spot value) closest to solar local midnight is employed. As for u, the difference between values on successive days is taken. The latitude normalisation is also slightly different, using an empirically-derived 0.7 1∕ cos (Λ) dependence. IDV is found to not depend on solar wind speed, VSW and depends on just the IMF field strength B in annual means. One of the great advantages of IDV 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 (2005Jump To The Next Citation Point) adopt a different philosophy in compiling IDV to that adopted by Mayaud (1971Jump To The Next Citation Point) in compiling aa. Mayaud’s philosophy was to use as homogeneous a data series as possible. The philosophy of Svalgaard and Cliver (2005Jump To The Next Citation Point) (and of Lockwood et al., 2006bJump To The Next Citation Point in the derivation of the m 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 IDV means that (like m) it is not homogeneous. Svalgaard and Cliver (2010Jump To The Next Citation Point) added more stations and also extended the sequence back to 1835 using a linear correlation with the Bartels u index. In this context, note Bartels’ reservations about the early u data discussed in Section 2.2.1.

2.2.3 The IDV(1d) index

The IDV (1d) index has recently been introduced by Lockwood et al. (2013aJump To The Next Citation Point). This is very similar to IDV 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. (2013aJump To The Next Citation Point) returned to the formulation used by Bartels (1932) to generate u. This means that 24 times the volume of data are used than in generating IDV 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. (2013aJump To The Next Citation Point) adopted the name IDV (1d ) (rather than reverting to the name u) because of the other major difference, namely that the IDV (1d) composite is homogeneous in its construction (i.e., it uses the philosophy of aa and not that of u and IDV), 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 1∕cos0.7(Λ ) dependence found by Svalgaard and Cliver (2005Jump To The Next Citation Point) 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, Λ. The IDV (1d) index extends back to the start of the Helsinki data in mid 1845. One key justification of IDV (1d) is that it correlates with the IMF B as well as (in fact very slightly better than) IDV, 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 IDV at that time (see Figure 3View Image). 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 (2010Jump To The Next Citation Point) and Finch et al. (2008Jump To The Next Citation Point), and which could introduce a dependence on solar wind speed, VSW. 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 B began to drop above 60° (and that with VSW began to rise). Hence, Helsinki is close to being at too high magnetic latitude. To investigate if this was a problem, Lockwood et al. (2013aJump To The Next Citation Point) 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 IDV (1d) from Nurmijärvi on n BV SW was investigated and the peak correlation found near n = 0, very close to the value for Eskdalemuir (see Figure 3View Image). The same tests were applied to modern data from the Niemegk station.

The homogeneous nature of IDV (1d) 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 IDV (1d ) and aa are preferable to inhomogeneous ones such as IDV and m.

2.2.4 The m index

The m index was introduced by Lockwood et al. (2006bJump To The Next Citation Point) and used by Rouillard et al. (2007Jump To The Next Citation Point) and Lockwood et al. (2009dJump To The Next Citation Point). 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, H σ1yr. These are then correlated with, and linearly regressed against, the annual means of aaC shown in Figure 5View Image to yield σ′ = s × σH1yr + c. These normalisations are needed because both the sensitivity s and offset c 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, 2008Jump To The Next Citation Point). 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 > 0.5) with those of aa C. In addition, m 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 m over IDV is that data from all 24 UT-hours are employed, as opposed to just the one (near midnight) value used by IDV. The disadvantage is that its compilation is much more complex and time-consuming than that of IDV and so new data cannot be as readily added. Furthermore, m does not correlate as highly with interplanetary parameters as does IDV (see Figure 3View Image). Lockwood et al. (2006bJump To The Next Citation Point) consider that the m index is less reliable before 1902 because then it is based on data from just one station (Potsdam).

2.2.5 The IHV index

The IHV index was devised and introduced by Svalgaard et al. (2003Jump To The Next Citation Point) and Svalgaard and Cliver (2007aJump To The Next Citation Point) and uses only nightside data to minimise the effect of the diurnal variation. IHV 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 AL. 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 (2007aJump To The Next Citation Point).

2.2.6 “sigma-H” indices

Finch et al. (2008Jump To The Next Citation Point) devised the σH n indices for each station, which – like IDV, IDV (1d) and m – is based on hourly mean data. H σn at a given station is defined as the value of the standard deviation of the hourly-averaged H values at a given UT over a period of n days, each single UT-hour being treated separately, as for m. There will therefore be 24 values for each period of n days at each station. (Note that the m index is, using this notation, the median for all available station-UTs of the σH 366 values for leap years and σH 365 for all other years). Finch et al. (2008Jump To The Next Citation Point) used n = 28 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 u, IDV, IDV (1d) indices, but because it applies to each station individually it is, in some respects, equivalent to the k values used in the derivation of range indices.

2.3 Dependencies of the various indices on interplanetary parameters

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 2View Image. 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, 2007Jump To The Next Citation Point). Enhancements of the ring current cause negative depressions in the Dst index but will also influence other geomagnetic indices.

View Image

Figure 3: Linear correlation coefficients of annual means of various geomagnetic indices with BV n SW, as a function of n, the exponent of the solar wind speed, V SW (B is the IMF field strength). The primes denote the fact that data have been omitted in calculating either set of annual means if any of VSW, B or the geomagnetic index are missing because of data gaps exceeding 1 hour duration. Values of BV nSW are computed hourly and then averaged. Correlograms are shown for: (red line) AL; (green line) AU; (blue solid line) − Dst; (blue dashed line) the negative part of Dst, − Dst 1 (where Dst 1 is the same as Dst but intervals when Dst > 0 are treated as data gaps); (cyan) aa; (orange) Ap; (black dashed) IDV; (black solid line) IDV (1d); (mauve) Am; (yellow) m and (red dashed) IHV. For indices which are increasingly negative for increasing activity (Dst, Dst1 and AL) the index has been multiplied by − 1. Image reproduced from Lockwood et al. (2013aJump To The Next Citation Point).

Figure 3View Image explores the dependence, on annual averaging timescales, of the geomagnetic indices described on Sections 2.1 and 2.2 on the solar wind speed, VSW. The correlation between each index and n BV SW is presented where B is the IMF field strength and n 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 B, VSW or the geomagnetic index are missing due to a data gap. In the case of the 3-hour range indices aa, Am and Ap, the procedure adopted by Finch and Lockwood (2007Jump To The Next Citation Point) is followed to ensure only simultaneous geomagnetic and IMF data are included in the annual means. In the case of IDV (1d), each daily value contains information on H 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 (2007Jump To The Next Citation Point): 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 3View Image, all the correlations are somewhat improved by taking these steps and, importantly, the n of peak correlation is sometimes also affected. Note that only annual mean data for IDV and IHV have been published and the way m 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 IDV, IHV, or m in Figure 3View Image).

The coupling functions n BV SW have been calculated in hourly data and then averaged, so that ⟨BV SnW ⟩1yr is used rather than ⟨B⟩1yr(⟨VSW ⟩1yr)n. The AL auroral electrojet index (red line) shows peak correlation n = 2, i.e., it has a BV S2W dependence. The AU index (green line) gives a peak at n = 1.1 (i.e., it has close to a BV SW dependence and, hence, varies with the interplanetary electric field). The Dst index shows a peak at n = 0.4 (blue line) but some of this dependence on VSW arises from the compression of the equatorial field by enhanced solar wind dynamic pressure: if we use only the negative part of Dst (Dst1, which is the same as Dst but treats all intervals where Dst > 0 as data gaps and so only contains intervals when Dst is dominated by ring current effects), we get the dashed blue line with a higher correlation coefficient peak at n = 0.1. This peak is flat and, hence, the peak n is not significantly different from zero (i.e., the dependence is on B alone). The cyan line is for the aa index and peaks at n = 1.9 (very close to the BV 2SW dependence of AL), the mauve line is for Am and peaks at n = 1.8 and the orange line is for Ap and peaks at n = 1.6. The black line is for the IDV (1d) index, which peaks at n near − 0.1. Hence IDV (1d), like IDV and Dst1, is not significantly different from having a dependence on B only. Thus, as concluded by Svalgaard and Cliver (2010Jump To The Next Citation Point), the negative part of Dst (i.e., ring current enhancement) is closest to explaining the behaviour of the interdiurnal variability indices on these annual timescales. The range indices, aa and Ap respond in a manner similar to the auroral indices and, in particular, the influence of the westward auroral electrojet on aa (as monitored by AL) can be inferred from the fact that both have a dependence that is not significantly different from 2 BV SW. The correlation for Ap peaks at a slightly lower n than for AL, Am, or aa, which may be a greater influence of the directly-driven currents or may be the effect of the ring current (as both AU and Dst give peaks at lower n). The IHV index correlation peaks at n = 1.9 and so, as pointed out by Svalgaard et al. (2003Jump To The Next Citation Point) and Svalgaard and Cliver (2007aJump To The Next Citation Point), behaves very much like AL and all the range indices with a 2 BV SW dependence, as expected because it is a monitor of the nightside auroral electrojet.

The m index (yellow line) correlation peaks at n = 0.3 and there are a number of possible reasons why this value of n exceeds zero. It could be that the response of m is set by a mixture of the ring current (with its n = 0 dependence) and the DP2 auroral currents (with their n = 1 dependence). An alternative explanation is that the normalisation against the aa index in the derivation of m has introduced a small dependence on VSW. We also note that m employed data from some auroral stations such as Sodankylä, which, as discussed in Section 6, introduces a V2SW dependence into σH values.

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