Yu. P. Maltsev and B. V. Rezhenov
Polar Geophysical Institute, Apatity, Murmansk Region, Russia
The global decrease of the geomagnetic field is the main characteristics of a geomagnetic storm. Dst index which is defined by the disturbance of the geomagnetic field H component averaged over longitudes at a the low-latitudinal observatories is a quantitative measure of this disturbance. The temporal behavior of the Dst variation corrected for solar wind pressure is described by the equation
| (1) |
where Q is the so-called injection function depending on solar wind parameters and t is the characteristic decay time of the currents causing the geomagnetic field decrease during the storm (see the reviews by Feldstein [1992] and Gonzalez et al. [1994]). So far the problem of the contribution of various IMF components to the Q function has no final solution. Some authors relate it only to the IMF southward component and solar wind velocity V, that is, to the interplanetary electric field Ey = -VBz [Burton et al., 1975; Feldstein et al., 1984; Grafe, 1988; Murayama, 1982; Pisarskij et al., 1989; Pudovkin et al., 1985, 1988]. In particular, Burton et al. [1975] derived an empirical expression for Q which relates the injection function to interplanetary electric field Ey = - VBz
 | (2) |
Akasofu [1981, 1996], Gonzalez et al. [1989], and Perreault and Akasofu [1978] suggested a different expression for Q
 | (3) |
where e=aVB2 sin4 q/2, a is a constant, B = (Bx2 + By2 + Bz2)1/2 is the IMF modulus, q = arctan(By/Bz), and By is the IMF dawn-dusk component.
There is some likeness between expressions (2) and (3): they suppose that the magnetosphere behaves as a half-wave rectifier: the IMF southward component affects on the magnetosphere much stronger than the IMF northward component. The main difference is that in (3) there is a dependence on two other IMF components ( Bx and By ), although with lesser weight, whereas these components are absent in (2).
During several decades there existed an opinion that substorms should considerably input to the Dst variation. However the recent study [Iyemori and Rao, 1996] showed convincingly that substorms not only do not enhance the geomagnetic field depression but even reduce it slightly.
In this paper, the influence of all IMF components and also the solar wind velocity and density on the injection function Q and Dst variation is studied. Studying of the relation between storm activity and solar wind parameters is complicated by the fact that these parameters correlate between themselves. One of the goals of this paper is to study relations between various solar wind parameters. In order to eliminate the parameter correlation we will try (if possible) to study the Dst index reaction to each parameter separately.
We used OMNI database of the National Space Data Center (USA) which includes the hourly values of all IMF components, velocity and concentration of solar wind protons, and also hourly Dst indices during 28 years, from 1963 to 1990. In total 112,000 hourly intervals were used. To exclude the influence of the solar wind pressure on the Dst index the formula from Burton et al. [1975] was used
 | (4) |
where the solar wind velocity V is in km s -1 and the proton concentration n is cm -3. The derivative dDst0/dt was replaced by the ratio DDst0/Dt where Dt = 1 h and DDst0 is the difference between Dst0 for two sequent hours
Figure 1a shows the isolines of
DDst0/Dt
= const on
the ( Dst0,
Bz ) plane. The values of
DDst0/Dt
were
averaged in a bin with a size: 40 nT for
Dst0 and 4 nT for
Bz.
The decrease of the bin sizes leads to an appearance of a noise
related to the influence of unknown factors. One can see from
Figure 1a
that the rectifying effect is manifested in a stronger
response of
DDst0/Dt
to the IMF southward component
( Bz < 0 ) than to the IMF northward component ( Bz > 0 ).
Figure 1b shows the isolines of DDst0/Dt = const on the plane of Dst0 and the IMF modulus B = (Bx2 + By2 + Bz2)1/2 under Bz > 0. The bin sizes are the same as in Figure 1a. It follows from Figure 1b that there is no pronounced dependence of DDst0/Dt on the IMF modulus. There is a weak tendency of DDst0/Dt to grow with an increase of B, however this dependence is opposite to the dependence predicted by formula (3).
To compare the influence of various solar wind parameters
on
DDst0/Dt
the isolines of
DDst0/Dt
= const were
drawn in Figure 2
on four planes: (a)
Bz, Bx ; (b)
Bz, By ;
(c)
Bz, V ; and (d)
Bz, N.
The bin sizes are 2 nT for the IMF
components, 100 km s
-1 for the velocity
V, and 4 cm
-3 for the
proton concentration
n.
The influence of Bz on DDst0/Dt is well seen on all four planes, whereas Bx and By do not demonstrate any visual influence. The absence of a linear relation between DDst0/Dt and V, predicted by (2) and (3) is an unexpected result. Some dependence of DDst0/Dt on V appears in the region of large velocities ( V > 500 km s -1 ) and southward IMF ( Bz < -7 nT). However this dependence is not reliable because of insufficient number of measurements in this region. Thus the result obtained does not allow stating with confidence that there is a dependence of DDst0/Dt on V and hence that the dawn-dusk electric field Ey = -VBz is more preferable than the southward IMF component for studying the DDst0/Dt response.
Practically absent is also a dependence of DDst0/Dt on the proton concentration n. This is seen especially well in the range -3 nT < Bz < 3 nT.
We consider now the behavior of
DDst0/Dt
and
Dst0 on
the plane of the proton concentration ( n ) and solar wind velocity
( V ) in three ranges of the IMF
Bz component variation (Figure 3).
One can see in Figure 3a that the dependence of
DDst0/Dt
on both the concentration and velocity appears under
Bz > 0. It
is worth noting at once that the data with
n > 14 cm
-3 are
absent under
V > 550 km s
-1 (this problem will be considered in
detail in 3.2) and under these
n and
V the
DDst0/Dt
and
Dst0 counters in all diagrams in Figure 3 are a result of the
extrapolation by the "surfer" program of the data under
V < 550 km s
-1.
The strongest relation of DDst0/Dt to the proton concentration n and velocity V is seen for n < 12 cm -3 and n > 12 cm -3, respectively. The DDst0/Dt value increases with a growth of the velocity or concentration. Probably, this increase is due to an inaccuracy of formula (4).
Figure 3c shows the isolines of DDst0/Dt = const for Bz < -1 nT. Unlike in Figure 3a, the isolines have a more smooth form. Moreover under the velocity increase from 300 to 600 km s -1 and the concentration increase (for V < 550 km s -1 ), DDst0/Dt decreases. Thus the influence of the proton concentration n and solar wind velocity V on DDst0/Dt is opposite under positive and negative values of Bz.
Consider now the
DDst0/Dt
relation to
n and
V under
-1 < Bz < 1 nT, that is, under the average
Bz 
0 (Figure 3b).
One can see from Figure 3b that no visible relation is observed.
Evidently it indicates that in reality neither the proton
concentration nor the solar wind velocity influence
DDst0/Dt
in a significant way.
Figures 3d, e, f show the isolines of Dst0 = const on the n,V plane in three ranges of the IMF Bz component values. On the whole the behavior of Dst0 is identical in all three diagrams: the value of Dst0 decreases with a decrease of Bz. Under n > 12-14 cm -3 and V < 550 km s -1 the dependence of Dst0 on the proton concentration disappears. The dependence of Dst0 on the solar wind velocity is stronger under high concentrations n > 12-14 cm -3 than under low concentrations (for V < 550 km s -1 ).
Figure 4a shows the dependence of
Dst0 on the IMF
Bx and
By components under
-1 < Bz < 1 nT
and the dependence on
Bz > 0 and
Bz < 0. The approximating formulae are also shown.
The strongest dependence of Dst0 is on the IMF southward component (Figure 4a). It is unexpected that the storm activity is also intensified under an increase of the IMF northward component. The value of Dst0 reaches -40 nT under Bz = 16 nT. The well pronounced dependence of Dst0 on both Bx and By is even a more unexpected result, the influence of Bx being stronger than that of By. One can see from Figure 4a that positive and negative Bx and By values influence Dst0 in the same way.
Figure 4b shows the relation between Dst0, Dst, and the solar wind velocity under -1 < Bz < 1 nT, -6 < (Bx, By) < 6 nT and -7 < Bz < -3 nT, -6 < (Bx, By) < 6 nT. Both Dst0 and Dst depend linearly on V and their dependencies coincide within the accuracy limit, though, according to formula (4), the values of Dst0 lie below the values of Dst. It is worth noting that the limitations on Bx and By were introduced to eliminate the influence of these IMF components on Dst0 and Dst (see Figure 4a).
To estimate the importance of the injection function
Q and decay
time of the currents responsible for the
Dst variation, the
dependence of
DDst0 on
Dst0 under three
Bz was drawn
(Figure 5a).
The dependence has approximately a linear character
with the same slope of the lines for all three
Bz values
(1/t =0.08 h
-1 which gives
t = 12.5 h).
Burton et al. [1975]
obtained
t = 7.7 h. We think that
t = 12.5 h
is a more realistic value, since it is based on much larger
quantity of the data. Figure 5b shows the dependence of
DDst0/Dt
on
Bz under four
Dst0 values. One can obtain from
Figure 5b
the following dependence:
 | (5) |
where Bs is the IMF southward component ( Bs = Bz under Bz < 0 and Bs = 0 under Bz > 0 ). Comparing (5) and (1), we obtain
 | (6) |
For a typical velocity of V = 400 km s -1 (6) gives Q by approximately a factor of two lower than is predicted by formula (2).
Figure 6 shows the relation between the solar wind parameters:
Bx, By,
Bz,
n, and
V.
The standard deviation of a series of
measurements is shown by vertical lines (the absence of vertical
lines means that the deviation is small because of a large amount
of data.) The deviation was calculated by the formula
[Kassandrova and Lebedev, 1970]
 | (7) |
The error of an individual measurement is by a factor of N1/2 higher than the one given by (7).
One can see from Figures 6a, b, d, e, f that there is a good linear relationship between the concentration n and IMF Bz component (6a), between Bx, By and Bz (6b), between the IMF module B and n (6d), between Bx and By (6e), and between n and V (6f). It follows from Figure 6c that the high-velocity solar wind has lower density than the low-velocity one. With V increasing by a factor of four, the concentration decreases almost by a factor of four.
Figure 6d shows the dependence of B = (Bx2 + By2)1/2 on the concentration. One can see that this dependence is weak enough. Under an increase of n by a factor of five, B increases only by 1.5 nT. The relationship between the IMF Bx, By, and Bz components and solar wind velocity is almost absent. Rezhenov and Maltsev [1998] presented some other relationships between the solar wind parameters.
Formulae (1) and (5) are useful not only to predict Dst0 values but also to understand better the physical processes during a storm.
One can see from Figures 1b and 2 that the Akasofu parameter e has no advantage as compared to function (6) which depends on the IMF southward component. For several storms Feldstein [1992] and Murayama [1982] have shown earlier that the DDst0/Dt behavior correlates better to the injection function Q which depends on Bs than to e. Wu and Lundstedt [1997] obtained the same result with the help of the neutron network. They did not use equation (1), that is, their approach, being useful to predict storm activity, is hardly suitable to understand the geomagnetic storm physics.
There exist two magnetic storm theories. The traditional theory considers the magnetic storm depression during a storm as the ring current effect. The ground-based disturbance induced by the ring current is proportional to the total energy of the particles captured into the magnetosphere [Dessler and Parker, 1959; Sckopke, 1966]. The parameter e fits completely this concept since it is proportional to the magnetic energy flux in the solar wind.
The new storm theory proposed by Maltsev [1991] relates the magnetic field decrease mainly to the magnetic flux in the magnetosphere tail. During a storm the magnetic flux in the magnetotail increases due to its transport from the daytime side to the night-time side because of the reconnection of the geomagnetic field with the IMF southward component [Dungey, 1961], the process rate being independent of the energy flux in the solar wind. From the magnetic flux conservation condition one can obtain the following expression for a low-latitude magnetic disturbance [Maltsev et al., 1996]:
 | (8) |
where Bm is the magnetic field in the subsolar point at the magnetopause, DR is the ring current effect, S is the equatorial section area of the inner magnetosphere limited by the counter B =Bm, and F is the magnetic flux outside the inner magnetosphere, that is, the flux going out into the tail. Differencing (8) in respect to time we obtain
 | (9) |
where k is the coefficient varying from 0.5 to 1.5 and depending on the magnetosphere state and solar wind pressure [Arykov and Maltsev, 1996].
One can present the magnetic flux variation in the following form
 | (10) |
where U is the potential difference between the dawn and dusk sides of the inner magnetosphere, tF is the magnetic flux decay time in the magnetosphere tail, and F(0) is the magnetic flux in the tail under U = 0. Substituting (10) in (9) we obtain
 | (11) |
During magnetic storms Bm usually grows due to the increase of the solar wind pressure. The negative DR modulus also increases. On the basis of the data available, Maltsev et al. [1996] found that two last terms in the right-hand part of (11) compensate each other to a considerable degree. Comparing (11) with (1) one can reveal the part of the injection function which depends on the magnetic flux growth in the magnetotail
 | (12) |
The counter B = Bm is close to the circle with radius R = (Rd +Rn)/2 where Rd and Rn are the geocentric distances to the B =Bm counter at the daytime and night-time sides of the magnetosphere, respectively, Rd being the distance to the subsolar point of the magnetopause and Rn being equal to 0.7 Rd [Feshchenko and Maltsev, 1997]. The potential difference between the dawn and dusk sides of the inner magnetosphere is
 | (13) |
where Eym is the electric field in the equatorial plane. If the field is homogeneous then
 | (14) |
where Upc is the potential difference between the dawn and dusk sides of the magnetosphere which is equal to the potential difference between the dawn and dusk sides of the polar cap, and Rf is the distance to the magnetosphere flank.
Doyle and Burke [1983] obtained several empirical expressions for potential difference between the dawn and dusk sides of the polar cap. One of them has the form
 | (15) |
where Upc is in kilovolts and Bz is in nanoteslas. Substituting (13)-(15) into (12) and assuming Rd = 10 RE, Rn = 7 RE, R =8.5 RE, Rf = 20 RE, and k = 0.75 we obtain
 | (16) |
Expression (16) is similar to expression (6) which has been obtained empirically. The difference in the constant terms is possibly caused by the datum level of the Dst variation which can not be obtained from ground-based data.
Thus expression (6) agrees well with the new magnetic storm theory. It should be noted that Arykov and Maltsev [1996] demonstrated that expression (2) is also in a good agreement with the theory. The theory explains the magnetic field decrease during a storm by the growth of the magnetic flux in the magnetotail, the growth being caused by the dawn-dusk magnetospheric electric field. It is not clear which solar wind parameter affects the magnetospheric field: the dawn-dusk electric field or IMF southward component. Doyle and Burke [1983] did not answer this question since they presented two sets of empirical equations relating the potential difference in the polar cap to both the electric and magnetic fields in the solar wind. Our results show that the magnetic convection is related to the IMF southward component rather than to the electric field of the solar wind.
Recently views on the problem of the relation between storms and substorms underwent significant variations. It has been thought for decades that a magnetic storm is a superposition of intense substorms [Akasofu, 1968]. However it should be noted at once that there exists no convincing experimental proof of this hypothesis. Instead, investigators have been trying to find a physical basis for that relation. For example, Gonzalez et al. [1994] wrote that there are good physical reasons to assume that a magnetic storm consists of intense substorms. During substorm activity intervals, the energy may be stored in the inner magnetosphere thus leading to a formation of the co-called partial ring current (which is connected to the auroral electrojets via field-aligned currents.)
In recent years more and more authors doubt the existence of such a relationship. Kamide et al. [1998] noted that currently the relationship between substorms and storms is badly understood and, therefore the main question is still open: whether the magnetic storm is a superposition of intense substorms. Rostoker et al. [1997] agrees that now it is impossible to answer the question: whether there is any relationship between storms and substorms.
Doubts arise because the Dst-index variations correlate better to solar wind parameters than to substorm activity. McPherron [1997] indicates that the relation of the Dst index variations to the solar wind is strikingly exact and does not require attracting any data on substorm activity, for example, AL index. Moreover Dst reacts too fast to the solar wind, therefore the injection during the substorm development phase can not be a cause of the Dst variations. If the substorms were a direct cause of the energy injection into the ring current, then one should expect that the relation to the AL index would be better than to VBz. Actually, the opposite picture takes place.
Using minute but not hourly values of the Dst index Iyemori and Rao [1996] obtained very important result on the relationship between storms and substorms. Analyzing approximately 100 substorms by the superposition epoch method, they found that after a beginning of the substorm expansion phase the storm depression does not increase but, on the contrary, slightly decreases (the Dst index grows).
This discovery requires essential reconsideration of the problem of the relationship between storms and substorms. However many investigators still believe that the magnetic field decrease during a storm is caused by the ring current, and the fact that during the substorm development phase the ring current decreases instead of increasing astonishes them very much [Kamide et al., 1997]. These authors believe that if a substorm is considered in a more general sense including preliminary phase as an injection source into the ring current, then substorms would be a cause of storms. However this new hypothesis also needs experimental evidence.
It should be reminded that the magnetic storm theory developed by Arykov and Maltsev [1996], Maltsev [1991], and Maltsev et al. [1996] does not require a presence of substorms for the storm development. According to this theory the magnetic field decrease during a storm is due to an accumulation of the magnetic flux transported from the daytime side into the magnetotail. The transported flux is proportional to the IMF southward component and does not depend on substorm activity. The small attenuation of the storm depression observed during the substorm expansion phase, also finds its explanation in the scope of the new theory. According to Arykov and Maltsev [1996], Maltsev [1991], and Maltsev et al. [1996] the storm depression is proportional to the magnetic flux in the magnetosphere tail. It is known that during the substorm expansion phase the magnetic flux in the tail decreases. Therefore the storm depression is attenuated.
Usually intense substorms appear under the southward IMF therefore
the substorms and storms are independent phenomena but having a
common cause. The substorm intensity depends on
Bs. A mean
substorm appears under
Bs 
-2 nT
[Caan et al., 1978]
and requires by a factor of two-three stronger
Bs [Maltsev et al., 1996;
Yokoyama and Kamide, 1997].
Hence a natural
conclusion follows that substorms occurring during storms are more
intense than substorms occurring in the absence of storms.
Figures 3d, e, f show that Dst0 (unlike DDst0/Dt) depends strongly on the velocity V and in a lesser degree on the proton concentration within all variation ranges of the IMF Bz component. The density given, the velocity growth by a factor of two leads to the Dst0 increase approximately by a factor of four, while the velocity given, the concentration growth by a factor of four increases Dst0 by a factor of 1.5. We note that in all the diagrams of Figure 3 the right top angle presents the extrapolation results, since according to Figure 6c high-velocity fluxes have low density. It is worth mentioning here that DDst/Dt (t, t+1) where t is the current hour, manifests the process dynamics related to the magnetic field transport and its accumulation in the tail lobes (function Q ), and Dst manifests the magnetosphere state (for example, its configuration) under the given parameters of the solar wind. So we believe that an increase of V and n leads to a pressure increase in the magnetotail lobes and therefore to a current increase across the tail. Evidently the process of pressure equilibrium establishment is rather slow and almost is not manifested in the DDst0/Dt value.
The Dst0 dependence on the IMF Bx and By components has possibly a statistic nature rather than a physical one and is caused by the relationship between these components and other solar wind parameters (Figure 6).
Here we will not consider causes of the interrelation between solar wind parameters, noting only that some of the relationships are well known, for example, the one between the solar wind velocity and concentration. It is natural that the correlation between solar wind parameters makes difficult studying their influence on DDst0/Dt and Dst0.
Studying the hourly values of the Dst variations and solar wind parameters during 28 years (112,000 measurements), we obtained that DDst0/Dt depends strongly on the IMF southward component whereas the dependence of the IMF modulus (under Bz > 0 ), proton concentration, and solar wind velocity on Bx and By is negligible. Hence one can conclude that the storm activity is controlled by the magnetic flux transport from the daytime side to the magnetosphere tail rather than by the magnetic energy flux value in the solar wind (the Akasofu parameter e ).
At the same time, Dst demonstrates a significant statistical dependence on solar wind velocity. In a lesser degree Dst depends on the proton concentration and also on the IMF Bx and By components. The dependence is evidently due to the fact that these solar wind parameters cause a pressure increase in the tail lobes and therefore an increase of the current across the tail. Most of the solar wind parameters are also related statistically between themselves.
Akasofu, S.-I., Polar and Magnetospheric Substorms, 198 pp., D. Reidel, Norwell, Mass., 1968.
Akasofu, S.-I., Energy coupling between the solar wind and the magnetosphere, Space Sci. Rev., 28, 121, 1981.
Akasofu, S.-I., Search for the "unknown" quantity in the solar wind: A personal account, J. Geophys. Res., 101, 10,531, 1996.
Arykov, A. A., and Yu. P. Maltsev, Direct-driven mechanism for geomagnetic storms, Geophys. Res. Lett., 23, 1689, 1996.
Burton, R. K., R. L. McPherron, and C. T. Russell, An empirical relationship between interplanetary conditions and Dst, J. Geophys. Res., 80, 4204, 1975.
Caan, M. N., R. L. McPherron, and C. T. Russell, The statistical magnetic signature of magnetospheric substorms, Planet. Space Sci., 26, 269, 1978.
Dessler, A. J., and E. N. Parker, Hydromagnetic theory of geomagnetic storms, J. Geophys. Res., 64, 2239, 1959.
Doyle, M. A., and W. I. Burke, S3-2 measurements of the polar cap potential, J. Geophys. Res., 88, 9125, 1983.
Dungey, J. W., Interplanetary magnetic field and the auroral zones, Phys. Rev. Lett., 6, 47, 1961.
Feldstein, Y. I., Modelling of the magnetic field of magnetospheric ring current as a function of interplanetary parameters, 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, 1984.
Feshchenko, E. Yu., and Yu. P. Maltsev, Erosion of the inner magnetosphere during geomagnetic storms, Ann. Geophys., 15, 1532, 1997.
Gonzalez, W. D., J. A. Joselyn, Y. Kamide, H. W. Kroehl, G. Rostoker, B. T. Tsurutani, and V. M. Vasyliunas, What is a geomagnetic storm?, J. Geophys. Res., 99, 5771, 1994.
Gonzalez, W. D., B. T. Tsurutani, A. L. C. Gonzalez, E. J. Smith, F. Tang, and S.-I. Akasofu, Solar wind-magnetosphere coupling during intense magnetic storms (1978-1979), J. Geophys. Res., 94, 8835, 1989.
Grafe, A., The influence of the recovery phase injection on the decay of the ring current, Planet. Space Sci., 36, 765, 1988.
Iyemori, T., and D. R. K. Rao, Decay of the Dst field of geomagnetic disturbance after substorm onset and its implication to storm-substorm relation, Ann. Geophys., 14, 608, 1996.
Kamide, Y., et al., Magnetic storms: Current understanding of outstanding questions, in Magnetic Storms, Geophys. Monogr. Ser., vol. 98, edited by B. T. Tsurutani, W. D. Gonzalez, Y. Kamide, and J. K. Arballo, pp. 1-19, AGU, Washington, D.C., 1997.
Kamide, Y., et al., Current understanding of magnetic storms: Storm-substorm relationships, J. Geophys. Res., 103, 17,705, 1998.
Kassandrova, O. N., and V. V. Lebedev, Processing of Observation Results, 104 pp., Nauka, Moscow, 1970 (in Russian).
Maltsev, Yu. P., Relation of the Dst variation to the magnetospheric geometry, Geomagn. Aeron., 31, 567, 1991 (in Russian).
Maltsev, Y. P., A. A. Arykov, E. G. Belova, B. B. Gvozdevsky, and V. V. Safargaleev, Magnetic flux redistribution in the storm time magnetosphere, J. Geophys. Res., 101, 7697, 1996.
McPherron, R. L., The role of substorms in the generation of magnetic storms, in Magnetic Storms, Geophys. Monogr. Ser., vol. 98, edited by B. T. Tsurutani, W. D. Gonzalez, Y. Kamide, and J. K. Arballo, pp. 131-147, AGU, Washington, D.C., 1997.
Murayama, T., Coupling function between solar wind parameters and geomagnetic indices, Rev. Geophys. Space Phys., 20, 623, 1982.
Perreault, P., and S.-I. Akasofu, A study of geomagnetic storms, Geophys. J. Roy. Astron. Soc., 54, 547, 1978.
Pisarskij, V. Yu., Ya. A. Feldstein, N. M. Rudenova, and A. Prigancova, Ring current and interplanetary medium parameters, Studia Geophys. Geodet., 33, 61, 1989.
Pudovkin, M. I., S. A. Zaitseva, and L. Z. Sizova, Growth rate and decay of magnetospheric ring current, Planet. Space Sci., 33, 1097, 1985.
Pudovkin, M. I., A. Grafe, S. A. Zaitseva, L. Z. Sizova, and A. V. Usmanov, Calculating the Dst variation field on the basic of solar wind parameters, Gerlands Beitr. Geophys., 97, 525, 1988.
Rezhenov, B. V., and Yu. P. Maltsev, Comparison of effects of different solar wind parameters on the Dst variation, in Physics of Auroral Phenomena, Proceedings of the 21st Annual Seminar, March 24-27, 1998, pp. 99-102, Apatity, 1998.
Rostoker, G., W. Baumjohann, W. Gonzalez, Y. Kamide, S. Kokubun, R. L. McPherron, and B. T. Tsurutani, Comment on "Decay the Dst field of geomagnetic disturbance after substorm onset and its implication to storm-substorm relation" by Iyemori and Rao, Ann. Geophys., 15, 848, 1997.
Sckopke, N., A general relation between the energy of trapped particles and the disturbance field near the Earth, J. Geophys. Res., 71, 3125, 1966.
Wu, J.-G., and H. Lundstedt, Geomagnetic storm predictions from solar wind data with the use of dynamic neutral networks, J. Geophys. Res., 102, 14,225, 1997.
Yokoyama, N., and Y. Kamide, Statistical nature of geomagnetic storms, J. Geophys. Res., 102, 14,215, 1997.