6 Differences Between Range and Hourly Mean Geomagnetic Data and the Effect of Solar Wind Speed

Figure 3View Image shows that there is a consistent difference between interdiurnal variation indices and the range indices. The interdiurnal variation indices, such as IDV, IDV (1d), and m all correlate best with the IMF field strength B on annual averaging timescales whereas mid-latitude range indices (aa, Ap, Kp, Am – and its northern and southern hemisphere components An and As) all correlate best with a coupling function close to 2 BV.

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/Dst 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. (2008Jump To The Next Citation Point) provides a very important insight. These authors devised the “sigma-H” H σ n indices for each station, based on hourly mean data (see Section 2.2.6). The series of ⟨σH28⟩1yr values for each station were correlated with three interplanetary parameters: B, VSW, and V 2SWB. The zero-lag correlation coefficients are plotted in Figure 12View Image as a function of the modulus of the station’s invariant geomagnetic latitude, |Λ |. The top panel of Figure 12View Image shows that the correlation coefficient for B is very high (∼ 0.9, significant at the 2σ 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 VSW (middle panel) is low outside the auroral oval (generally below about 0.4), but rises to a peak of about 0.85 within the oval. The bottom panel shows that V 2SWB is high and ≈ 0.8 outside the oval and ≈ 0.9 within it. Thus the influence of VSW arises in the auroral oval, making 2 VSWB correlate best there but elsewhere B alone provides the highest correlation.

View Image

Figure 12: Correlation coefficients of the annual means of the coupling functions (top) IMF magnitude B, (middle) VSW, and (bottom) V 2 B SW with σH 28 indices from a variety of magnetic observatories, shown as a function of the modulus of their invariant magnetic latitude |Λ |. Solid diamonds are for northern hemisphere stations and open circles for southern. Black and grey symbols are for correlations that are significant at the 2σ and 1σ levels, respectively. The vertical dashed lines show the auroral oval between absolute invariant latitudes of 60° and 82°. Image reproduced by permission from Finch et al. (2008Jump To The Next Citation Point), copyright by AGU.

Figure 13View Image shows the MLT at which the peak correlations within the auroral oval occur. The primary source of the correlation with VSW 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 B 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 B and appears to be more associated with the directly-driven DP2 currents and/or with the ring current.

View Image

Figure 13: MLT dependence of maximum correlations of H ⟨σ28⟩1yr for stations shown in Figure 12View Image with ∘ ∘ 60 < |Λ | < 82. In the top panel, filled circles and open diamonds show the MLT (magnetic local time) – Geographic longitude coordinates of the maximum correlation of ⟨σH28⟩1yr with |VSW | and B, respectively. The bottom two panels show the histograms of the MLT of the maxima in the correlations for |V | SW (in black) and B (in white). Image reproduced by permission from Finch et al. (2008), copyright by AGU.
View Image

Figure 14: Schematic of Earth’s magnetospheric current systems. Parts (b) and (d) are views of the noon-midnight cross-section of the magnetosphere, ABDC, from the ecliptic on dusk side of the Earth and show current sheets in orange, interplanetary field lines in green, open geomagnetic field lines (that thread the magnetopause) in red and closed field lines (that do not) in blue. Parts (a) and (c) are views of the northern-hemisphere currents in the tail and dayside magnetopause from high northern latitudes in the pre-midnight sector. In all panels X, Y, and Z are the axes of the GSM reference frame. Parts (a) and (b) are for a substorm growth phase, whereas (c) and (d) are for a substorm expansion phase. B is the undisturbed IMF and JBS is the current in the Bow Shock. In all panels magnetic reconnection is taking place at XMP in the dayside magnetopause. The tail lobe field is B TL and the current in the cross-tail current sheet (J CT) is disrupted in the grey areas in (c) and (d). The mauve currents in (c) are the “substorm current wedge” within which the magnetospheric field lines “dipolarise” at onset (the dashed line in (d) shows the stretched field line before onset and the arrow the associated sunward convection surge of the frozen-in plasma). The “near-Earth neutral line”, X TL, is also shown in (d).

This finding makes good sense, physically. The westward auroral electrojet of the DP1 current system is part of the “substorm current wedge” (see Figure 14View Image), 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, B is draped over the nose of the magnetosphere by the slowing effect of the bow shock (currents JBS). The IMF in this schematic points due south in the GSM frame which favours magnetic reconnection at XMP, 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 BTL and in the current in the near-Earth cross-tail current sheet (JCT) 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”, X TL. 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 BTL which depends on both the total open magnetospheric flux, (and, hence, also on the IMF) and the solar wind dynamic pressure (∝ V 2SW) 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 PSW caused by enhanced solar wind velocity VSW 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 V 2 SW dependence in substorm-related phenomena can be seen by considering what happens further down the tail, at greater negative X 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 PSW has no influence. The magnetopause location is here set by pressure balance between the magnetic pressure that dominates in the tail lobes, 2 B TL∕(2μo ), and the static pressure of the solar wind, dominated by the thermal pressure of the particles, (NSWkTSW, where TSW is the solar wind temperature). Substorms occur because of the growth of open flux in the tail. Because in the far tail, BTL 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 BTL and JCT 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 B TL and J CT. 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 VSW is high. The net result is that the DP1 currents have a dependence on 2 V SW. 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 VS2W for range indices (and for IHV) that is not seen for interdiurnal variation indices such as IDV and IDV (1d).

That this is indeed the case for IHV and IDV was first noted and exploited by Svalgaard et al. (2003Jump To The Next Citation Point) and has subsequently been used by Svalgaard and Cliver (2007aJump To The Next Citation Point), Rouillard et al. (2007Jump To The Next Citation Point), and Lockwood et al. (2009dJump To The Next Citation Point). The difference for aaC and m is demonstrated by Figure 15View Image. Lockwood et al. (2009dJump To The Next Citation Point) investigated the correlations of both aa C and m with the general form BpV n SW and the exponents p and n giving peak correlation were quantified using the Nelder–Mead simplex search method (Nelder and Mead, 1965Jump To The Next Citation Point). Results were almost identical if the minimum r.m.s. fit residual was searched for. In both cases, p was extremely close to unity (as used in Figure 3View Image) and n was found to be 2 for aaC and 0.3 for m. Thus, as predicted above, aaC is more dependent on V SW than m. Figure 16View Image underlines that the difference in the exponent n for the two cases is significant. If the exponent were to be the same in the two cases its optimum value would be about n = 1.6 for which the combined significance of (1 − Saac) × (1 − Sm ) peaks at 13%, so the difference between the exponents n in the two cases is significant at the 87% level. Plots equivalent to Figure 15View Image and Figure 16View Image reveal this difference is even more significant for the combinations IDV and IHV, IDV and aa C, and IDV (1d) and aaC.

This difference between the dependence of the two geomagnetic indices on VSW is extremely useful. Using the best-fit regressions such as those shown in Figure 15View Image, the variations of both BV 2 SW and BV 0.3 SW can be derived and, hence, the variations of both B and VSW can be obtained.

View Image

Figure 15: Scatter plots and best fit regressions of annual means of (left) aaC against 2 BV SW and (right) m against BV 0S.3W. The best-fit regression lines are derived using the Bayesian least-squares regression fit procedure described by Rouillard et al. (2007Jump To The Next Citation Point). The correlation for aaC with BV 2 SW is r = 0.97 aac and using the autoregressive AR-1 red noise model this correlation is found to be significant at greater than the −5 10 level. The correlation of m with 0.3 BV SW is rm = 0.89 with significance exceeding the 5×10 −5 level. Image reproduced by permission from Lockwood et al. (2009dJump To The Next Citation Point), copyright by AAS.
View Image

Figure 16: Top: Correlograms showing the correlation coefficients raac (between aaC and BV SnW, dashed line) and rm (between m and BV SnW, solid line) as a function of the exponent n. The vertical dashed lines mark the peaks at n = 2 and n = 0.3, respectively. Middle: the significances Saac and Sm (dashed and solid lines, respectively) of the differences between the correlations at general n and the peak values, as evaluated using the Fischer-Z transform and (bottom) the joint probability (1 − Saac) × (1 − Sm ). Image reproduced by permission from Lockwood et al. (2009dJump To The Next Citation Point), copyright by AAS.

  Go to previous page Scroll to top Go to next page