Space Weather

Why Kp is such a good measure of magnetospheric convection

Authors


Abstract

[1] The 3-hour magnetic activity index, Kp, is widely used for measuring the level of magnetospheric activity, and many magnetospheric properties are known to correlate with it. The common denominator for these different properties is the strength of the magnetospheric convection electric field, the large-scale electric field imposed across the magnetosphere by the flow of the magnetized solar wind past the Earth. While the relationship between Kp and the global convection field has long been known, the question of why the relationship exists has apparently not been addressed. In this report, it is proposed that because Kp is derived from magnetic variations obtained at subauroral stations, it is extremely sensitive to the latitudinal distance to the equatorial edge of the auroral region, where the principal causative currents flow. Since the auroral region maps to the plasma sheet in the magnetosphere, motion of the inner edge of the plasma sheet, which is determined by the strength of the convection field, causes significant changes in Kp. Thus, through its dependence on the latitude of the auroral current region, Kp can be viewed as a direct monitor of the strength of magnetospheric convection, explaining the success of previous Kp-dependent models of the global electric field.

1. Introduction

[2] Ever since the variability of the Earth's surface magnetic field has been monitored on a continuous basis, various indices have been developed in an effort to summarize the geomagnetic conditions in a fairly compact form. One such index, the 3-hour range index, K, introduced by Bartels et al. [1939], was the first to be proposed at an international level and was adopted in 1939 by the International Association of Terrestrial Magnetism and Electricity. The K index is a measure of the magnetic variability at each individual observing station, but it was further proposed by Bartels et al. [1939] that the K indices from a network of observatories could be combined to form a planetary index of geomagnetic activity. Subsequent refinements of this idea led finally to the definition of the planetary K index, Kp [Bartels, 1949].

[3] Other magnetic indices have been developed since Kp was proposed, but due in part to its ready availability and its long existence, Kp has been one of the most widely used indices for exploring the causes and consequences of geomagnetic activity. A wide range of magnetospheric properties has been shown to be correlated with Kp, from the latitudinal extent of the auroral oval [e.g., Feldstein and Starkov, 1967] to the average strength of the electric fields measured within the inner magnetosphere [e.g., Rowland and Wygant, 1998]. These relationships have in turn led to its use as a control parameter for a number of practical space weather applications, including global magnetic field models [e.g., Tsyganenko, 1989; Hilmer and Voigt, 1995], modeling the location of the plasmapause [e.g., Gallagher et al., 1995; Moldwin et al., 2002], modeling ring current evolution [e.g., Ebihara and Ejiri, 1998; Jordanova et al., 2001], modeling radiation belt diffusion [e.g., Boscher et al., 1998; Brautigam and Albert, 2000], and modeling geomagnetic activity effects on the ionosphere [e.g., Kutiev and Muhtarov, 2001]. It has also been used in studies assessing geomagnetic hazards to power systems [e.g., Boteler, 2001], in neural network models of geosynchronous relativistic electrons [e.g., Koons and Gorney, 1991], and modeling storm time thermospheric dynamics [e.g., Fesen and Roble, 1991].

[4] For the most part, the studies relating Kp to various magnetospheric properties treated the index as a “measure of magnetospheric activity” and typically concluded that whatever property they were examining also varied with “activity.” It appears that little attention was actually given to what specific aspects of “magnetospheric activity” were actually monitored by Kp. Our own work is a case in point: In 1999 we performed a statistical analysis of the fluxes of ions and electrons observed at geosynchronous orbit [Korth et al., 1999]. In that paper we showed that the local time distribution of average fluxes was very well ordered by Kp, and in fact, the ordering was almost exactly what one would expect if the access of plasma sheet particles to geosynchronous orbit is controlled by a convection electric field with a strength determined by Kp (the concept of magnetospheric “convection” will be discussed more fully below). The Kp-dependent convection that reproduced the observed flux distribution was exactly that derived earlier by other authors from quite different observational bases [e.g., Maynard and Chen, 1975; Gussenhoven et al., 1983].

[5] This result was in one sense a comforting confirmation of the earlier work on the Kp-dependence of magnetospheric convection, but in another sense it raised for us the puzzling question of why the convection could be so well parameterized by the Kp index, which is after all a summary measure of the magnitude of magnetic field perturbations observed at a set of ground stations. What was the connection? The answer, we now believe, lies in a consideration of the method by which Kp is derived. The purpose of this paper is to review briefly that derivation and to point out what it is about the derivation that makes Kp an excellent measure of the strength of magnetospheric convection. First, however, we briefly review the broad range of magnetospheric properties that have been related to Kp and recapitulate the argument that the common denominator of all of these properties is the convection electric field.

2. Magnetospheric Phenomena Organized by Kp

[6] One of the earliest studies to relate magnetospheric properties to Kp was the demonstration by Feldstein and Starkov [1967] that the magnetic latitude of the equatorward boundary of the auroral oval could be expressed as λm = 65.2–1.04Kp; as Kp increases, the auroral oval moves to lower latitudes. Other authors found a similar dependence [e.g., Lui et al., 1975; Meng et al., 1977; Sheehan and Carovillano, 1978; Slater et al., 1980], and the relationship was very beautifully demonstrated with low-altitude satellite measurements of precipitating auroral particles [Gussenhoven et al., 1981, 1983; Hardy et al., 1981]. From Defense Meteorological Satellite Program (DMSP) observations of the equatorward edge of auroral precipitation, the Air Force Research Laboratory has developed the auroral boundary index (ABI), which represents the estimated latitude of the auroral boundary at the midnight meridian for each pass of a DMSP satellite. Figure 1 [after Gussenhoven et al., 1983] shows the strong statistical correlation between Kp and ABI for an entire year of measurements (both ABI and Kp have been interpolated to 1.2-hour centers before the data were binned by ABI). Figure 2 shows the striking detailed correspondence of ABI and Kp over two months of observations, chosen essentially at random (note that ABI is plotted on an inverted axis).

Figure 1.

Statistical relationship between Kp and the auroral boundary index (ABI) derived from DMSP measurements of auroral precipitation (similar to Gussenhoven et al. [1983]). Values of both indices from the entire year of 1991 have been interpolated to common 1.2-hour centers, then Kp has been binned by ABI and averaged. The 1.2-hour interpolation interval was used in order to minimize the number of redundant contributions from a single measurement of ABI, for which 97% of successive measurements are separated in time by less than this amount. Error bars show the standard deviation in the bin averages.

Figure 2.

Detailed correspondence between Kp and the auroral boundary index (ABI) for 60 days during the year 2000. ABI has been plotted on an inverted scale to emphasize the striking correspondence.

[7] Another magnetospheric property that was related very early to Kp was the size of the plasmasphere, the region of cold, dense plasma confined largely to the region within a few Earth radii of the Earth. From ground-based whistler observations [Carpenter, 1967] and space-based measurements [e.g., Binsack, 1967; Gringauz, 1969; Chappell et al., 1970; Rycroft and Thomas, 1970; Carpenter and Park, 1973], it was found that the distance to the plasmapause decreases as Kp increases.

[8] With high-altitude satellite measurements, the depth of penetration of fresh plasma sheet particles into the near-Earth magnetosphere was also found to be related to Kp [e.g., McIlwain, 1972, 1974; Freeman, 1974; Mauk and McIlwain, 1974; Horwitz et al., 1986; Elphic et al., 1999; Korth et al., 1999; Friedel et al., 2001]. During times of higher Kp, the nightside plasma sheet moves closer to the Earth and covers a wider range of local time at a given radial distance.

[9] Other significant magnetospheric phenomena that have shown a strong relationship to Kp are the cross–polar cap potential drop [e.g., Heppner, 1973; Reiff et al., 1981; Boyle et al., 1997], the strength of ionospheric convection [e.g., Mendillo and Papagiannis, 1971; Evans et al., 1980; Foster et al., 1981; Alcaydé et al., 1986], and the strength of directly measured DC electric fields in the magnetosphere [e.g., Cauffman and Gurnett, 1971; Heppner, 1972; Maynard et al., 1988; Baumjohann et al., 1985; Rowland and Wygant, 1998].

3. Kp-Dependent Convection

[10] It was actually realized quite early that these various relationships could be explained if the global magnetospheric convection depends on Kp [e.g., Vasyliunas, 1968; McIlwain, 1972; Kivelson, 1976], and several Kp-dependent models of magnetospheric convection were proposed [e.g., Grebowsky, 1970; McIlwain, 1972, 1986; Volland, 1973, 1975, 1978; Chen and Grebowsky, 1974; Chen et al., 1975; Stern, 1977; Sojka et al., 1986]. The discussion of Kivelson [1976] was a particularly nice summary of the convection as the common denominator of these relationships.

[11] The key is the important role played by global electric and magnetic fields in the transport of magnetospheric plasma. This picture is based on the expression for the gyroaveraged drift of a charged particle in a macroscopic electric and magnetic field [e.g., Kavanagh et al., 1968; see Lyons and Williams, 1984, and references therein]:

equation image

The first term on the right-hand side of equation (1) represents the so-called “convective” drift experienced by all charged particles, independent of their mass, charge, or energy. Thus magnetospheric “convection” is associated with a global electric field. The second term on the right-hand side represents the combined “gradient and curvature” drift experienced by charged particles in an inhomogeneous magnetic field like that of the Earth's dipole. Unlike the electric drift term, the size and direction of the magnetic drift depend on the charge, q, of the particle and its energy, mv2/2 (the subscripts ⊥ and ∥ indicate the components of the velocity parallel and perpendicular, respectively, to the local magnetic field, B). The net transport of the particle is a combination of the E × B drift and the gradient and curvature drift.

[12] There are two principal contributions to the global magnetospheric electric field: The first contribution is from the corotation electric field (Ecorot), produced by the collisional coupling between the ionospheric plasma and the Earth's corotating neutral atmosphere. This electric field maps out along the electrically conducting dipole magnetic field lines; in the absence of other influences, the effect of the corotation electric field is to force the plasma in the magnetosphere to corotate with the Earth. However, superposed on the corotation electric field is a global electric field oriented roughly from dawn to dusk across the entire magnetosphere. This “convection” electric field (Econv) is produced by coupling between the magnetosphere and the magnetized solar wind blowing past the Earth.

[13] Because the strength of the corotation field varies inversely with the square of the distance from the Earth, near the Earth corotation dominates the total electric field, while far from the Earth the solar wind driven convection field dominates. As a consequence, there are two classes of equipotentials (and hence cold plasma drift paths): A class that is closed around the Earth, representing drift orbits that close on themselves such that particles can repeatedly circle the Earth at nearly corotational velocity; and a class that is open, coming in from the tail, skirting the near-Earth region, and exiting through the dayside magnetopause. This separation between closed and open cold plasma drift paths forms the basis of the explanation for the existence of the plasmasphere [e.g., Nishida, 1966], and the separatrix between open and closed drift trajectories for cold plasma can in steady state be identified as the plasmapause.

[14] The location of the open-closed separatrix depends on the relative strength of the two contributing electric fields: As the convection field strength increases, the region dominated by corotation (i.e., the closed drift path region) shrinks. This, on a very basic level, illustrates how the location of the plasmapause is determined by the strength of the convection electric field.

[15] If the particle energy is nonzero, the magnetic drift term in equation (1) comes into play. The net drift paths of electrons in the total (corotation + convection) electric field, combined with the gradient and curvature drifts, are shown in Figure 3 [after Lyons and Williams, 1984]. The four panels correspond to electrons with different energies, and the patterns differ from panel to panel because the magnetic drift term in equation (1) is energy dependent. However, all four panels illustrate the fact that, even for nonzero energy, charged-particle drift paths separate into a region of closed trajectories close to the Earth and a region of open drift trajectories (from the tail through to the dayside magnetopause) at larger distances. While the picture is somewhat more complicated for ions, the basic separation into open and closed drift regions remains.

Figure 3.

Net drift paths of electrons in the total (corotation plus convection) electric field, combined with energy-dependent gradient and curvature drift. Each panel corresponds to a different electron energy specified at L = 10. Electrons on open drift trajectories enter from the tail plasma sheet and drift sunward toward the dayside magnetopause [after Lyons and Williams, 1984].

[16] For electron energies in the range of 100 eV to a few tens of keV, the primary source is solar wind (and perhaps ionospheric) entry into the tail plasma sheet. Thus “fresh” plasma sheet particles convect in to the near-Earth region on open drift trajectories. Once in the near-Earth vicinity, these particles are subject to very significant losses (primarily by precipitation into the atmosphere, forming the aurorae), so their fluxes are strikingly reduced by the time they arrive on the dayside [e.g., Thomsen et al., 1998]. Any such plasma that manages to get into the closed-trajectory region suffers similarly strong losses, so effectively the region of closed drift paths is empty of particles in this energy range. The result is that upon crossing the drift separatrix, especially on the night side of the magnetosphere, an outbound spacecraft would observe a dramatic increase in flux: This has been termed the earthward edge of the plasma sheet, and the energy-dependent drift separatrix is also known as the “Alfvén” boundary [Kavanagh et al., 1968].

[17] The equatorial region we have been discussing maps to low altitudes along the magnetic field lines. Thus the earthward edge of the plasma sheet maps directly to its equatorward edge at low altitudes. This is the boundary that the low-altitude DMSP satellites identify as the equatorward edge of auroral precipitation, on which the auroral boundary index (ABI) is based. Since the location of the drift separatrix (between open and closed drift trajectories) is determined by the strength of the convection electric field, a Kp-dependent convection electric field could explain the observations of a Kp association with the inner edge of the plasma sheet, either at high altitudes near the equatorial plane or at low altitudes in DMSP orbit.

[18] Returning to the other magnetospheric phenomena listed above, the fact that directly measured magnetospheric (and ionospheric) electric fields correlate well with Kp argues quite directly for the Kp dependence of magnetospheric convection. Such a dependence also explains the relationship between Kp and the cross–polar cap potential. This potential drop is essentially produced by the electric field in the solar wind (see equation (1)), mapped to the Earth along those magnetic field lines that have, through magnetopause reconnection, become interconnected with solar wind field lines. The potential drop also maps along the outermost dipolar field lines to the equatorial plane and represents the potential difference that is applied across the magnetosphere, producing the global convection electric field. Thus the strength of the electric field scales as this applied potential, divided by the diameter of the magnetosphere. The latter does not vary strongly with solar wind variability, so there exists a direct relationship between the cross–polar cap potential difference and the strength of the convection electric field.

[19] Figure 4 summarizes these various relationships. Figure 4a shows a dawn-dusk cut through the magnetosphere, illustrating that the cross–polar cap potential drop maps to the flanks of the equatorial projection in Figure 4b, resulting in the electric field imposed across the inner magnetosphere of ΔΦpc/Dmsp, where Dmsp is the diameter of the magnetosphere at the terminator. Figure 4c is a noon-midnight cut through the magnetosphere, illustrating the mapping between the equatorward edge of the auroral precipitation (and primary auroral current region) at low altitudes to the earthward edge of the plasma sheet at high altitudes in the equatorial projection of Figure 4d. This boundary, the flow separatrix for plasma sheet electrons, is also coincident with the plasmapause, the flow separatrix for cold plasmaspheric plasma.

Figure 4.

Schematic illustration of the relationship between various convection-dependent parameters: (a and b) basic mapping between the cross–polar cap potential drop and the convection electric field and (c and d) mapping between the low-altitude equatorward edge of the auroral electron precipitation (where the main auroral currents flow) and the equatorward edge of the plasma sheet in the equatorial plane. The drift separatrix forming this boundary also forms the plasmapause.

4. Construction of Kp

[20] The discussion above presents the evidence that Kp is somehow a good measure of magnetospheric convection, but it doesn't address the question of why. For that we need to look more closely at how Kp is actually determined. The following brief summary follows the extensive discussion of this topic by Mayaud [1980] as well as the later very helpful review by Menvielle and Berthelier [1991]. In the interest of brevity, a number of details will be omitted, but the general outline of the process suffices to reveal the relationship between Kp and magnetospheric convection. For a more accurate discussion of the full process by which Kp is obtained, readers are referred to Mayaud [1980].

[21] Kp, the planetary K index, is a measure of the range of magnetic variability at 13 representative ground magnetometer stations (listed in Table 1) over a 3-hour interval. It is computed by averaging the standardized K index that is derived at each of those stations. As can be seen from Table 1, the Kp stations are all largely subauroral. This choice was deliberate: At subauroral latitudes magnetic variations are observed that are attributable both to large-scale ring current variations, which dominate the variability at low latitudes, and to auroral current systems, which at higher latitudes produce large field perturbations that vary strongly with local time. The subauroral response to auroral activity is less drastically dependent on local time. Thus it was expected that indices derived from subauroral measurements would give a global measure of magnetospheric response to solar wind energy input, with a minimum of confusion due to local time dependences.

Table 1. Kp Network Stationsa
ObservatoryGeomagnetic LocationbCGL,c deg
Station NumberNameCodeIntervalLatitude, degLongitude, deg
1LerwickLER1932 to current62.089.257.93
2MeanookMEA1932 to current61.7305.761.99
3SitkaSIT1932 to current60.4279.859.68
4EskdalemuirESK1932 to current57.983.952.59
5LovöLOV1954 to current57.9106.555.94
6AgincourtAGN1932 to 196954.1350.554.44
 OttawaOTT1969 to current55.8355.055.69
7Rude SkovRSV1932 to 198455.599.452.28
 BrorfeldeBFE1984 to current55.498.652.05
8AbingerABN1932 to 195753.484.547.40
 HartlandHAD1957 to current54.080.247.44
9WingstWNG1938 to current54.195.150.00
10WitteveenWIT1932 to 198853.792.349.01
 NiemegkNGK1988 to current51.997.747.95
11CheltenhamCLH1932 to 195749.1353.849.32
 FredericksburgFRD1957 to current48.6353.148.89
12ToolangiTOO1972 to 1981−45.6223.0−48.28
 CanberraCNB1981 to current−42.9226.8−45.41
13AmberleyAML1932 to 1978−46.9254.1−49.82
 EyrewellEYR1978 to current−47.2253.8−50.17

[22] The foundation of the Kp index is the K index computed at each of the network ground stations. The K index, designed by Bartels et al. [1939], is determined by the largest range (i.e., difference between the highest and lowest values) of variation, during each 3-hour interval, in either of the horizontal components of the magnetic field, relative to a smoothed curve that approximates the “regular” variation, SR, of that component for the day. SR is primarily due to atmospheric dynamo contributions. The measurement, illustrated in Figure 5, is conducted for each 3-hour interval of the day. The measured range (indicated by a in Figure 5) then determines the assigned value of the index K, according to a quasi-logarithmic scale that is different at each station, but is designed such that the long-term frequency distribution of assigned K values is approximately the same at all stations. The values of a that bracket the a range assigned to each value of K at a given station are proportional to the bracketing a values for the same K value as measured at the reference station of Niemegk. The constant of proportionality is determined entirely by the latitude of the station, in corrected geomagnetic coordinates [Hakura, 1965]. This scaling of the bracketing values of a at each location is the way the K assignment is typically described [e.g., Mayaud, 1980; Menvielle and Berthelier, 1991], but it is approximately equivalent and perhaps somewhat simpler to view the process as a scaling of the individual values of a for comparison with a standard K table, that is, that of Niemegk. The scaling process thus can be written as

equation image

where a is the locally measured range at a station with corrected geomagnetic latitude l, and as is the scaled value. The numbers A(NGK) and A(l) are determined from a fit to the observed l dependence of the average a measured at a chain of European observatories over a 9-year interval. This fit and the corresponding averages are shown in Figure 6 [after Mayaud, 1980].

Figure 5.

Illustration of the determination of the 3-hour range, a, of the horizontal surface field measured at a particular ground station [after Mayaud, 1980].

Figure 6.

Nine-year averaged 3-hour range, a, at a chain of European observatories used to determine the dependence of a on corrected geomagnetic latitude. Also shown is the resulting fit to a(l) obtained by Mayaud [1980] and used to scale range measurements at other observatories, including those contributing to the determination of Kp. The short vertical lines crossing the fit curve identify the approximate latitude range of the subauroral and midlatitude bands that are targeted by the Kp index [after Mayaud, 1980].

[23] With the local amplitudes scaled for the magnetic latitude dependence, the K values are then assigned according to Table 2. These K values, however, contain daily and annual variations that are site specific, and to remove those effects, statistically based conversion tables are applied, resulting in a standardized index, Ks, from each station. The standardized index is expressed in the familiar Kp scale of thirds (0, 0+, 1−, 1, 1+, etc.), and the Kp value is then simply the average of the Ks values from the 13 Kp stations.

Table 2. K Assignment Table
Scaled Amplitude, aS, nTK Index Value
0–50
5–101
10–202
20–403
40–704
70–1205
120–2006
200–3307
330–5008
500+9

5. Kp and Convection

[24] The key to understanding the relationship between Kp and the strength of magnetospheric convection is contained in Figure 6. What Figure 6 shows is that the size of the magnetic perturbation detectable at a ground station depends very strongly on magnetic latitude. More correctly, it depends very strongly on the station's proximity to the auroral zone, where the dominating currents are flowing. If the auroral zone expands equatorward, one can imagine that the entire curve in Figure 6 would shift to the right, and subauroral stations would see a very substantial increase in the magnitude of the perturbations. This is illustrated in Figure 7, which shows the original curve shifted 3° and 5° toward lower latitudes. The vertical lines in Figure 7 indicate the corrected geomagnetic latitudes of the 13 Kp stations, calculated for the epoch 2004. At these stations, a 3° equatorward shift of the auroral current region would cause a 30–100% increase in the perturbation magnitude, even if the strength of the currents stayed steady.

Figure 7.

Schematic illustration of the expected effect on the magnetic variability range of an equatorward shift in the location of the auroral currents. Dashed curves are offset from the average curve by 3° and 5° of corrected geomagnetic latitude. Vertical lines show the locations of the 13 Kp observatories. Even a small shift in the location of the auroral currents can profoundly increase the magnetic range measured at the Kp stations.

[25] The auroral current region essentially coincides with the electron plasma sheet [e.g., Paschmann et al., 2002] (we use the qualifier “electron” because in the near-Earth region, gradient and curvature drifts cause a species-dependent displacement of the inner edge of the region accessible to plasma sheet ions and plasma sheet electrons). Thus an equatorward displacement of the auroral currents corresponds directly to an equatorward motion of the low-latitude edge of the auroral electron precipitation, which, as described above, is monitored by DMSP as the ABI. Therefore both Kp and ABI are monitoring rather directly the location of the inner edge of the plasma sheet, which we have seen is determined by the strength of the magnetospheric convection.

[26] From Figure 1 it can be seen that a 3° equatorward shift in ABI would result in an increase of 1.2 in Kp if it were a continuous variable. From Table 2, one can show that a step up in K of one level would require roughly a doubling of the scaled field perturbation range. The schematic in Figure 7 does suggest that such a shift would cause increased perturbations approaching this magnitude. This shows that the latitude effect can plausibly explain the dependence of Kp on magnetospheric convection. However, other effects, such as an intensification of the currents themselves, might make a similarly significant contribution, and it would be valuable to explore quantitatively whether Kp variations simply record the strength of the convection or whether they contain information about other significant changes in the magnetospheric currents. It is a subject for future research to determine whether a shift in latitude of the auroral zone is quantitatively sufficient to account for the changes in Kp or whether other effects may also be contributing.

6. Conclusion

[27] From the days of its inception, Kp has been considered to be a measure of “geomagnetic activity.” The above discussion suggests that we should more appropriately consider it a measure of the strength of magnetospheric convection and justifies its use as such a measure. For example, this realization gives a firmer foundation to the use of Kp as a risk indicator for the electric power industry, which is primarily vulnerable to ground currents induced by strong auroral currents flowing overhead. Moreover, recognition of the first-order dependence of Kp on the latitude of the auroral currents could lead to the development of refined indices to extract the influence of other factors on the size of geomagnetic perturbations.

Acknowledgments

[28] I am grateful to Haje Korth, whose work first led me to this puzzle, and to my colleagues at Los Alamos for their advice and consent. This work was performed under the auspices of the U.S. Department of Energy, with partial support from NASA through the LWS program.

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