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# Currents: Dst Case Studies

The purpose of this module is to illustrate how Dst, the disturbance storm time index, may be predicted from a knowledge of solar wind parameters. The formula used is that of Burton et al. (An empirical relationship between interplanetary conditions and Dst, J. Geophys. Res., 80, 4204–4214, 1975). You can change the parameters in the Burton formula and compare the new prediction with the observed values for a specific event.

Dst
A measure of the worldwide deviation of the H component of the Earth’s magnetic field at mid-latitude ground stations from their quiet day values. It is measured in nanoTeslas (nT).
Dst is composed of perturbations due to the ring current (Dst0), the magnetopause currents (bPd½), and the quiet day currents (c).
Dst = Dst0 + bPd½ - c
Dst0
The measure of the perturbation of the H component due to the ring current. Essentially, it is a measure of the strength of the ring current. Dst0 is measured in nanoTeslas (nT).
The ring current changes strength as a result of energy injection and decay.
d(Dst0) / dt = F(E) - aDst0
a
The decay rate of the ring current, 3.6 x 10-5 s-1. 1/a is the decay time of the ring current, 7.7 hours. This parameter can be varied from 1–20 hours using the Ring current decay time, a box.
b
The measure of the response in Dst to changes in the solar wind dynamic pressure (Pd = mnV2, where m is the ion mass, n is the ion density, and V is the solar wind velocity). It is 15.8 nT/nPa½. This parameter can be varied from 5–40 nT/nPa½ using the Response pressure, b box.
c
The measure of the quiet day currents, that is, the currents that exist when the solar wind dynamic pressure is nearly constant and F(E) = 0 (i.e., when Bz is northward). It is 20 nT. This parameter can be varied from 0–50 hours using the Quiet day ring current, c box.
F(E)
Ring current injection parameter F(E) is the rate of ring current injection as a function of a rectified, filtered, and delayed duskward component of the solar wind electric field (Ey). This parameter can be varied from 0–60 minutes using the Ring current injection rate, F(E) box. The only filtering in this module is the 5 minute averaging performed in creating the input data files.
F(E) = d(Ey - 0.5) if Ey > 0.5 mV/m
F(E) = 0 if Ey < 0.5 mV/m
Ey = -VBz, where V is the solar wind velocity and Bz is the north/south component of the interplanetary magnetic field (IMF).
d is the change in injection rate as a function of the rectified and filtered solar wind electric field. It is 1.5 x 10-3 nT/(mV/m)s.
Rectified means that energy is transferred into the magnetosphere only if Ey > 0. This occurs when Bz is southward. Experience (Burton et al., 1975) shows that the magnetosphere acts as a low-pass filter: quickly varying electric fields are not as well rectified as slowly varying electric fields. By averaging to 5 minute resolution we have accounted for some of the effect of the magnetospheric filter but perhaps not all of it. The response in F(E) is delayed with respect to changes in solar wind Ey by the delay time tm. tm is the average time delay between changes in the solar wind electric field observed at the nose of the magnetopause and observed ring current injection (i.e., decreases in Dst).

The values in the graphs may be read by moving the pointer over a graph and clicking the mouse. The readings will appear in the boxes to the left.