4.1 Observations

The size and shape of the magnetosphere is controlled by the interaction of the interplanetary magnetic field and solar wind flow with the internal geomagnetic field and the magnetospheric plasma environment. The size is largely controlled by the solar wind dynamic pressure, which is balanced by the magnetic pressure inside the magnetosphere. The tail radius and flaring angle (deviation from a cylindrical shape) are to some extent controlled by the interplanetary magnetic field direction, which controls the intensity of reconnection at the nose of the magnetosphere. An empirical model developed by Shue et al. (1997) and tuned for extreme conditions by Shue et al. (1998Jump To The Next Citation Point) gives the standoff distance of the magnetopause (R(ϕ)) as a function of the solar zenith angle (ϕ) as
( ) 2 α R (ϕ) = R0 --------- , (1 ) 1 + cosϕ
where the factors α and R0 depend on the IMF Bz and solar wind dynamic pressure (Psw)
−1∕6.6 R0 = (10.22 + 1.29tanh [0.184 (Bz + 8.14)]) ⋅ Psw α = (0.58 − 0.007Bz)(1 + 0.024 log (Psw)). (2 )
The model assumes the magnetopause to be rotationally symmetric with respect to the Sun-Earth line.

Lacking global measurements of the energy transfer from the interplanetary medium into the magnetosphere, the solar wind energy input is either assumed proportional to the solar wind motional electric field EY = V swBz,IMF or approximated by an empirical parameter

𝜖 = 107VswB2 (7RE )2sin4(𝜃∕2), (3 )
where V sw is the solar wind speed, B the interplanetary magnetic field magnitude, and tan(𝜃) = By∕Bz (in the GSM coordinate system) is the IMF clock angle in a plane perpendicular to the Sun-Earth line (Perreault and Akasofu, 1978Akasofu, 1981). The scale length 7 RE is an empirical scaling parameter originally obtained by comparing the energy input as measured by 𝜖 and the energy dissipation in the known energy sinks, the ionospheric Joule heating, the auroral precipitation, and the ring current. While later analyses have significantly revised the relative roles of the various energy sinks, the original scaling is still used with the understanding that the 𝜖 is more accurate in giving temporal variations than absolute magnitudes of the energy input (Koskinen and Tanskanen, 2002).

The level of geomagnetic activity is often characterized in terms of magnetic indices created using a variety of ground magnetic records. The auroral electrojet indices are derived from the north-south components of 12 northern-hemisphere auroral-latitude (around 70 latitude) magnetic stations as the minimum (AL or auroral lower) or maximum (AU or auroral upper) of the 12 measurements at each time instant at one minute temporal cadence. The auroral electrojet index (AE) is then given as the difference of the two (AE = AU AL). The AL index responds to the enhancement of westward electrojet currents (southward horizontal disturbance field at the Earth’s surface) and is a measure of the intensity of substorm expansion phase activity in the magnetosphere. The AU index responds to the eastward currents, and is a measure of the strength of large-scale convection in the magnetosphere-ionosphere system. While the ionospheric currents are sufficiently close to the ground-based measurement stations so that other magnetospheric current systems do not significantly disturb the measurements, signal arising from ground induction can contribute to the index by as much as 40% during rapidly varying current systems when the induction currents are strongest (Tanskanen et al., 2001). Other geomagnetic indices include the planetary Kp index, which is a quasi-logarithmic scale of geomagnetic activity ranging from 0 to 9, computed from 13 geomagnetic observatories in subauroral latitudes (44 – 60). The A p index ranging from 0 to 32 is derived similarly to the Kp index.

For studies of energy transport through the magnetosphere-ionosphere system, the AE-indices can be used to estimate the amount of energy dissipatedin the ionosphere by frictional Joule heating and by particle precipitation using

8 PJH[W ] = 2 ⋅ 1.9 ⋅ 10∘AE-[nT-] (4 ) PPREC [W ] = 2 ⋅ 109(4.4 AL [nT ] − 7.6), (5 )
(Tanskanen et al., 2002Ahn et al., 1983Jump To The Next Citation PointØstgaard et al., 2002Jump To The Next Citation Point), where the factor 2 accounts for precipitation and Joule heating in both northern and southern hemisphere polar regions.

The north-south components of four midlatitude (around 20 – 40 latitude) stations are used to create the Dst index, which gives a proxy for the intensity of the ring current encircling the Earth. As the amount of ring current intensification is a key parameter in the magnetic storm evolution, this index is used to characterize magnetic storm intensity. The Dst index is computed as an average of the station measurements weighted by the cosines of the station colatitudes (Dst = ΣnΔHnΣn cos 𝜃n) to compensate for the effects of the varying latitudes of the stations. The Dst index is given as hourly values. A high-resolution SYM-H index is computed in an almost similar way but with 1-min temporal cadence.

The ring current consists of two parts, a symmetric ring current encircling the Earth and an asymmetric part carried by particles on open drift paths drifting from the magnetotail to the dayside magnetopause. This partial ring current is closed by field-aligned currents to and from the ionosphere. The ASY-H index is a measure of the asymmetric ring current and is given as the difference between the maximum and minimum disturbances (weighted similarly to Dst) as measured at the six stations distributed around the globe.

As the magnetometers integrate over all current systems, the SYM-H and ASY-H as well as the Dst indices are sensitive not only to the ring current, but as well to the cross-tail current, the field-aligned currents, the magnetopause currents, and currents induced within the conducting Earth. While during quiet times the contributions from the other current systems can be assumed to be small, during magnetic storms (exactly when the indices are most needed) all currents intensify and move closer to the Earth such that the contributions from the other systems can be as large as 50% (Turner et al., 2000Ohtani et al., 2001Häkkinen et al., 2002).

The energy input to the ring current trapped particle population has been modeled by Burton et al. (1975Jump To The Next Citation Point), who give the temporal evolution of the Dst index as a function of the driving solar wind electric field and magnetospheric losses. However, as the magnetopause currents can significantly contribute to the Dst index at times when the magnetic pressure is high, the Dst index is first pressure-corrected to the form

∘ ---- Dst ∗ = Dst − 7.26 P + 11.0, (6 ) sw
where Psw is the solar wind dynamic pressure and the correction factors have been recently re-defined by O’Brien and McPherron (2000). For the pressure-corrected Dst one can then write
dDst ∗ Dst∗ ------ = Q (t) − ----- dt τ Q(t) = − 4.4 (VswBs −(Ec),VswBs ≥ E)c -----9.74----- τ = 2.40 exp 4.69 + VswBs , (7 )
where Bs is the southward component of the IMF, critical value for the solar wind electric field is Ec = 0.49 mVm below which the driver function Q(t) = 0, and τ is the ring current decay time in hours.
View Image

Figure 7: Magnetic storm on April 6 – 7, 2000. Left, from top to bottom: interplanetary magnetic field Bx and By, Bz, solar wind density and pressure, speed, and motional electric field. Right, from top to bottom: 𝜖-parameter giving a measure of the energy input to the system; AU and AL indices giving a proxy of the ionospheric electrojet current activity; AL-index-based proxies for ionospheric Joule heating and particle precipitation power; Dst index and its pressure-corrected variant Dst, Dst and its prediction using Equation 7View Equation that provide an estimate of the ring current intensity.

Figure 7View Image shows an example of a large storm that occurred on April 6 – 7, 2000. The storm was driven by a strongly negative IMF Bz within the sheath region of an interplanetary CME, and caused significant ring current enhancement, strong auroral activity (Huttunen et al., 2002Jump To The Next Citation Point), and space weather effects both in space and on ground (Pulkkinen et al., 2003). A specific feature of this storm was that the solar wind density and dynamic pressure were high, which created much more intense ring current activity than that predicted by the Burton et al. formulation. The left panel shows the driving solar wind and IMF parameters, while the ionospheric dissipation parameters as well as the ring current dissipation (both observed and predicted) are shown in the right panels.

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