The real time Dst estimates presented are made using a modified version of the formula derived by Burton et al. [1975]. Burton et al. found that the Dst could be predicted quite successfully using the following formula.

d(Dst*)/dt = F(E) - aDst*

where

Dst* = Dst - b sqrt(Pdyn) + c

and

F(E) = 0		Ey < 0.5 mV/m
F(E) = d(Ey - 0.5)		Ey > 0.5 mV/m>

with

a = 3.6x10^-5 /s
b = .20 nT/sqrt(eV/cm^3)
c = 20 nT
d = -1.5x10^-3 nT/(s mV/m)

In this equation Dst* is the change to Dst from only the injected ring current.

The constant b is a measure of the Dst response to solar wind dynamic pressure (Pdyn=solar wind mass density*square of solar wind flow) while c is a measure of the quiet time ring current. F(E) is the ring current injection rate and only depends upon the dawn to dusk solar wind electric field, Ey, which is just the negative product of the solar wind speed, Vp, and the southward component ofthe interplanetary magnetic field, Bz. The constant d is a measure of the response of the injection rate to Ey which is assumed to be linear, and the parameter "a" is a measure of ring current decay, the value of which corresponds to an e folding time of 7.7 hours.

For the Dst estimates presented here two modifications to the above formula aremade. First, the injection function F(E) is modified to be dependent upon the solar wind dynamic pressure as well as Ey. This modification is based upon th study done by Murayama [1982] which found better correlations between estimate and measured Dst when the injection function was of the form Ey*(Pdyn)^1/3. Thus the injection function used here is

F(E) = d'(Pdyn)^1/3(Ey-0.5), d'=-1.2x10^-3 nT/(s mV/m)

where d' is chosen such that d'(Pdyn)^1/3 is consistent with Burton et al's d value for the case where Pdyn is a typical 2 nPa.

The second modification is in the ring current decay parameter "a". Feldstein [1992] presented a summary of numerous studies of ring current decay and found that variations in "a" during a single storm must be taken into account. The value of "a" depends upon geocentric distance, ion composition and ion energy of the ring current which can vary substantially between the main phase and therecovery phase of a storm. Numerous authors [eg. Feldstein et al., 1984] foundimproved Dst estimates by using faster decay rates during the main phase of storms. Thus in the real time estimates presented here we use a decay rate corresponding to an e folding time of 3 hours during the main phase of a storm when Ey is greater than 4 mV/m and an e folding time of 7.7 hours during all other times.

Thus the input parameters required to estimate the Dst index are Bz, the southward component of the IMF; Vx, the radial solar wind speed; and n, the solar wind plasma density. For the Dst estimates presented in this web page these parameters are aquired from the Advanced Composition Explorer (ACE) which is positioned at the Earth-sun libration point (L1) and provides continuous real time solar wind conditions. For more information about ACE see the ACE Home Page at http://www.gsfc.nasa.gov/ace/ace.html .


References

Burton, R.K., R.L. McPherron, and C.T. Russell, An empirical relationship between interplanetary conditions and Dst, J. Geophys. Res., 80, 4204-4214, 1975.

Feldstein, Y.I., Modelling of the magnetic field, Space Sci. Rev., 59, 83, 1992.

Feldstein, Y.I., V. Y. Pisarsky, N.M. Rudneva, and A. Grafe, Ring current simulation in connection with interplanetary space conditions, Planet. Space Sci., 32, 975-984, 1984.

Murayama, T., Coupling function between solar wind parameters and geomagnetic indices, Rev. Geophys. Space Phys., 20, 623-629, 1982.




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