We should not expect these two classes of indices to behave in the same way. Consider a “steady convection event” (see, for example, Lockwood et al., 2009a, and references therein) lasting, for example, 24 hours in which DP2 is enhanced but DP1 is not because of the lack of substorms. There has been debate about whether or not the ring current is enhanced during such events (Pulkkinen, 2007), the outcome of which appears to be that although ring current enhancements are weaker because of the lack of substorms, they are still present (for example Zhou et al., 2003). Given that interdiurnal variability indices appear to be particularly sensitive to the ring current and/or the DP2 system, steady convection events will influence these indices much more than range indices (which respond most strongly to the DP1 currents). On the other hand, because the substorm cycle of energy storage in the magnetospheric tail (associated with DP2) and its explosive release (associated with DP1) generally takes place within 3-hour intervals, we would expect to see strong signatures of substorms in the range indices, but weaker ones in interdiurnal range indices. This line of argument suggests that the ratio of sensitivities to DP1 and DP2/ may be greater for range indices than for interdiurnal variability indices. In this section, we will discuss evidence that this is the case and show that it causes them to have different responses to variations in the interplanetary medium, such that the optimum coupling functions are not the same.
The paper by Finch et al. (2008) provides a very important insight. These authors devised the “sigma-H” indices for each station, based on hourly mean data (see Section 2.2.6). The series of values for each station were correlated with three interplanetary parameters: , , and . The zero-lag correlation coefficients are plotted in Figure 12 as a function of the modulus of the station’s invariant geomagnetic latitude, . The top panel of Figure 12 shows that the correlation coefficient for is very high (, significant at the level) except at auroral latitudes (between the two vertical dashed lines) where it falls to a minimum of about 0.6. On the other hand, the correlation with (middle panel) is low outside the auroral oval (generally below about ), but rises to a peak of about 0.85 within the oval. The bottom panel shows that is high and outside the oval and within it. Thus the influence of arises in the auroral oval, making correlate best there but elsewhere alone provides the highest correlation.
Figure 13 shows the MLT at which the peak correlations within the auroral oval occur. The primary source of the correlation with occurs in the midnight MLT sector. This is when and where westward electrojet of the DP1 system is most likely to be detected (Tomita et al., 2011). The maximum correlation with can occur at any time except in the midnight sector. Therefore, it is clear that the correlation with the solar wind velocity at yearly time scales is linked to the storage-release system of the magnetotail and the westward auroral electrojet of the DP1 current system. At all other locations the correlation is better with and appears to be more associated with the directly-driven DP2 currents and/or with the ring current.
This finding makes good sense, physically. The westward auroral electrojet of the DP1 current system is part of the “substorm current wedge” (see Figure 14), in which the dawn-to-dusk current in the near-Earth edge of the magnetospheric cross-tail current sheet is diverted during substorm expansion through the midnight-sector auroral oval (McPherron et al., 1973). In this schematic, (a) and (b) are for a substorm growth phase, (c) and (d) are for a substorm expansion phase. The undisturbed IMF, is draped over the nose of the magnetosphere by the slowing effect of the bow shock (currents ). The IMF in this schematic points due south in the GSM frame which favours magnetic reconnection at , driven by the large magnetic shear across the dayside magnetopause current sheet. This generates open magnetospheric flux that is appended to the tail by the solar wind flow, causing rises in the tail lobe field and in the current in the near-Earth cross-tail current sheet () during the growth phase. This rise comes to an end at the onset of the expansion phase, when the Earthward edge of the cross-tail current is disrupted in the area shown in grey in (c) and (d). This current is diverted down post-midnight field lines, along the westward electrojet in the ionosphere and back up pre-midnight field lines. This path is shown in mauve in (c) and is called the “substorm current wedge” which gives the magnetic disturbances classed as DP1. Within the wedge the field dipolarises as shown in (d) (the dashed line being the stretched field line before onset and the white arrow the sunward convection surge of the frozen-in plasma). Part (d) also shows open flux now being destroyed by reconnection at a “near-Earth neutral line”, . The DP2 currents that dominate during the growth phase are driven by the reconnection in the dayside magnetopause and so depend strongly on the southward IMF. In comparison, the cross-tail current diverted into the auroral electrojet (to give the DP1 disturbances) is set by which depends on both the total open magnetospheric flux, (and, hence, also on the IMF) and the solar wind dynamic pressure () which squeezes the tail where the current disruption takes place. This is because the cross-tail current disruption occurs close to the Earth where the magnetotail is still flaring (i.e., its radius is increasing with distance away from Earth) which means that enhanced dynamic pressure caused by enhanced solar wind velocity can squeeze the tail at this location and so increase the field in both tail lobes, giving a higher magnetic shear across the cross-tail current sheet for a given amount of open magnetospheric flux in the tail lobes. Indeed, that there must be this dependence in substorm-related phenomena can be seen by considering what happens further down the tail, at greater negative coordinates. Here the tail reaches its maximum, asymptotic radius so is no longer flaring, so the magnetopause becomes parallel to the solar wind flow and has no influence. The magnetopause location is here set by pressure balance between the magnetic pressure that dominates in the tail lobes, , and the static pressure of the solar wind, dominated by the thermal pressure of the particles, (, where is the solar wind temperature). Substorms occur because of the growth of open flux in the tail. Because in the far tail, is set by pressure balance with the static pressure in the interplanetary medium, adding more open flux causes the far tail radius to increase, but and remain constant. Only closer to the Earth, where the tail is flaring, does the solar wind dynamic pressure act to constrain the tail radius so that the accumulation of open magnetospheric flux there causes a rise in and . Hence, substorm phenomena such as the current disruption and the formation of the near-Earth neutral line must occur relatively close to the Earth and must have a dependence on solar wind dynamic pressure (as inferred from observations by Karlsson et al., 2000).
The conclusion from the above considerations is that the current available to be diverted when the current wedge forms is higher when is high. The net result is that the DP1 currents have a dependence on . Recalling the conclusion, discussed earlier in this section, that range indices are likely to be influenced by the DP1 currents to a much greater extent than interdiurnal variation indices, we would expect the optimum coupling function to have a dependence on for range indices (and for ) that is not seen for interdiurnal variation indices such as and .
That this is indeed the case for and was first noted and exploited by Svalgaard et al. (2003) and has subsequently been used by Svalgaard and Cliver (2007a), Rouillard et al. (2007), and Lockwood et al. (2009d). The difference for and is demonstrated by Figure 15. Lockwood et al. (2009d) investigated the correlations of both and with the general form and the exponents and giving peak correlation were quantified using the Nelder–Mead simplex search method (Nelder and Mead, 1965). Results were almost identical if the minimum r.m.s. fit residual was searched for. In both cases, was extremely close to unity (as used in Figure 3) and was found to be 2 for and 0.3 for . Thus, as predicted above, is more dependent on than . Figure 16 underlines that the difference in the exponent for the two cases is significant. If the exponent were to be the same in the two cases its optimum value would be about for which the combined significance of peaks at 13%, so the difference between the exponents in the two cases is significant at the 87% level. Plots equivalent to Figure 15 and Figure 16 reveal this difference is even more significant for the combinations and , and , and and .
This difference between the dependence of the two geomagnetic indices on is extremely useful. Using the best-fit regressions such as those shown in Figure 15, the variations of both and can be derived and, hence, the variations of both and can be obtained.