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ISSN 0010 9525, Cosmic Research, 2015, Vol. 53, No. 2, pp. 119­127. © Pleiades Publishing, Ltd., 2015. Original Russian Text © N.S. Nikolaeva, Yu.I. Yermolaev, I.G. Lodkina, 2015, published in Kosmicheskie Issledovaniya, 2015, Vol. 53, No. 2, pp. 126­135.

* Modeling of the Corrected Dst Index Temporal Profile on the Main Phase of the Magnetic Storms Generated by Different Types of Solar Wind
N. S. Nikolaeva, Yu. I. Yermolaev, and I. G. Lodkina
Space Research Institute, Russian Academy of Sciences, ul. Profsoyuznaya, 84/32, Moscow, 117810 Russia e mail: nnikolae@iki.rsii.ru
Received May 8, 2014

* Abstract--A modeling of the corrected (taking into account the magnetopause currents [9]) D st index during the main phase of magnetic storms generated by four types of the solar wind (SW), namely MC (10 storms), CIR (28 storms), Sheath (21 storms), and Ejecta (31 storms), is performed similarly to our previous work on the simple Dst index [8]. The "Catalog of large scale solar wind phenomena during 1976­2000" ([1], ftp://ftp.iki.rssi.ru/pub/omni/) prepared on the basis of the OMNI database, was used for the identification * of SW types. The time behavior of D st is approximated by a linear dependence on the integral electric field (sumEy), dynamic pressure (Pd), and fluctuation level (sB) of the interplanetary magnetic field (IMF). Three * types of D st modeling are performed: (1) by individual values of the approximation coefficients; (2) by approximation coefficients averaged over SW type, and (3) in the same way as in (2) but with allowance for * the D st index values preceding the beginning of the main phase of the magnetic storm. The results of model * ing the corrected D st index are compared to modeling of the usual Dst index. In the conditions of a strong sta * tistical scatter of the approximation coefficients, the use of Dst instead of D st insignificantly influences the accuracy of the modeling and correlation coefficient. DOI: 10.1134/S0010952515020070

1. INTRODUCTION This work is dedicated to modeling the temporal profile of the correlated (taking into account magne * topause currents) D st index during the main phase of magnetic storms generated by various large scale types of the solar wind (SW) and is the continuation of a series of publications on study of geomagnetic activity dependence on parameters of the interplanetary space [2­7] and of the process of magnetic storm genera tion by various types of SW [8, 9]. Beginning with the publication of Burton et al. [10], it has been shown that Dst is well modeled by the SW and IMF parameters. Currently there exist a large number of papers dedicated to the modeling of mag netic storms and their prediction. Various methods are used to predict the Dst index, wherein the solar wind­ magnetosphere system is considered as a "black box": artificial neuron networks (see, for example, [18­20] and references therein) and nonlinear auto regression schemes (see, for example, [21, 22] and references therein). In the majority of papers dedicated to the model ing of geomagnetic storms and their prediction (see, for example, [10, 12, 13, 15, 16]), the type of the SW

stream that has generates magnetic storms is not taken into account. At the same time, it is known that different types of SW streams interact with the mag netosphere in different ways (see, for example, [2­7, 9, 11, 20, 23­28]). One recent publication [29] could be used as an example of taking into account the type of solar wind into the forecast of space weather. In our previous papers [5­9], we looked for a func tional relation between storm intensity and interplan etary parameters, and we used the usual geomagnetic index Dst for the analysis of development of the mag netic storms main phase and its modeling. However, the Dst index value during magnetic storms is the result of changes in various current systems: the ring current, the current on the magnetopause, and the current of the magnetospheric tail (see, for example, [30­31]). The magnetopause position is governed by an equilibrium between the total pressures in the solar wind and within the magnetosphere. A change in SW dynamic pressure leads to a shift of the magnetopause position to a new equilibrium position. This change is accompanied by both a change in the position of the current sheet on the magnetopause and a change in its value. In order to take into account the contribution of this change in the magnetopause current into the mag

119


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* netospheric Dst index, a corrected Dst index has been * proposed which is determined by the formula: D st = 1/2 Dst ­ b(Pd) + c, where the coefficients are the fol lowing: b is the measure of the response to changes in the SW dynamic pressure (with an increase in the dynamic pressure Pd, the magnetopause approaches the Earth and the contribution of the current related to * it is taken into account in D st ) and c is the measure of the currents on quiet days (see, for example, [10, 12, 13]). Initially the b and c coefficients were taken to be constant and were obtained in [10] for the quiet time using a limited set of SW data. Later the authors [12, 13] obtained new values of these coefficients, to esti mate which they used SW data of the OMNI base for a 30 year time period, assuming a possible dependence of the coefficients on interplanetary electric field value (y = VBs). For example, the authors showed in [32] that the coefficient b depends on the value of the inter planetary electric field and with its increase (up to y = 18 mV/m) the value of b decreases by a factor of 5 as compared to the quiet time (y = 0). However the difference in the values of the coefficient b obtained by various authors using different datasets falls into the 50% scatter of its value in [10, 12, 13, 32].
* Using for modeling the corrected D st index, we actually take into account the physical process described above and its influence on value of the sim ple Dst index. In previous publications [8, 9], we took into account the contribution of the SW pressure in the form of the additive term cPPd, and it was assumed that the contribution of this term is small (that is, the influence of the SW dynamic pressure on Dst is small) and can be approximated by a linear term. The results of [9] showed that for CIR and Ejecta, this term should not be considered small, and the above assumption could be a source of an error. That is why in this paper we process the temporal profile of the corrected (taking * into account the magnetopause currents) D st index, similar to the correction performed in [9]. The main task of this paper is to obtain an answer to the question: * "For which index (Dst or D st ) does our method of modeling the temporal profile of magnetic storm development work better?" 2. INITIAL DATA AND METHOD In this work we perform a modeling of the temporal * profile of the corrected D st during the main phase of 90 magnetic storms (­250 < Dst 50 nT) induced by four types of solar wind flows: CIR (28 storms), Sheath (21 storms), MC (10 storms), and EjectÞ (31 storms). Because of the absence of data on the cor * rected D st , the number of magnetic storms induced by

CIR was slightly reduced as compared to the previous paper [9], but it did not influence the results (see table). While modeling the main phase of a magnetic * storm, a linear approximation of the D st index of the main phase of a magnetic storm by three solar wind parameters is used: by the integral of the convective electric field of the solar wind sum, dynamic pres sure Pd, and variations in the interplanetary magnetic field sB [9]:
Dst ()* = c* + c* s u m E y () + c* Pd () + c* s B() , i i i i 0 E i su m E y () =
k =i


k =1

(1)
E y (k),

where i is the current point of the storm phase which varies from i = 1 in the beginning of the phase to i = im at the last point of the storm (in Dst min), and in sumEy the summation is performed in terms of k (from the beginning of the storm at point k = 1 to the current point of the phase k = i). For each type of magnetic storm, the modeling of the main phase is performed in three stages. At first, the individual approximation coef ficients (c*, c*, c*, c*) are determined for the main 0P phase of the particular storm of each type. Then the approximation coefficients of the main phase of the storm are averaged over the SW type

(

c* , c * , c* , c* . At this stage, contributions to 0

)

* the D st index of the main phase of particular SW param
eters c* s u m E y , c* Pd , c* s B mated [9]. At the third account the prehistory beginning of the main are inserted. Instead of the c* 0

(

stage, corrections taking into * of the D st index prior to the phase of the magnetic storm the constant average value of

)

are esti

coefficient, for each storm j (within the

given type of SW), the values of c * ( j ) calculated 0 from the linear dependence of the c*( j) coefficient 0 on the values of the aveDst*(j) index, averaged over three points (the point of storm beginning and two preceding points), were taken. The processing method was described in detail in [8, 9]. In order to evaluate the quality of the modeling, we use the linear correlation coefficient (r) and root mean square (standard) deviation () between the corrected * * D st and model Dst mod indices [9]. 3. RESULTS For four types of SW stream (MC, Sheath, CIR, and Ejecta), the table shows the average and median values * of the approximation coefficients of the corrected D st
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* MODELING OF THE CORRECTED D st INDEX

121

Table. Mean and median values of the approximation coefficients and SW parameters (with standard deviations) and also * the contributions of these parameters into the D st (marked by asterisks *) and Dst indices during the main phase of magnetic storms for four SW types SW type MC 10 storm ­32.32 ± 25.6 ­20 ­13.77 ± 14.4 ­11 ­2.04 ± 1.1 2 ­2.55 ± 0.75 ­2.4 ­0.8 ± 3.5 0 ­0.92 ± 2.9 1 1.29 ± 3.95 0 1.28 ± 3.3 0 16.24 ± 9.78 Sheath 21 storms ­28.88 ± 45.1 ­20 ­13.1 ± 28.8 ­18 ­3.4 ± 1.9 ­3 ­3.2 ± 1.6 ­3.3 0.38 ± 3.4 ­0.5 0.97 ± 3.3 1 ­0.57 ± 2.3 ­1.3 ­0.8 ± 1.8 ­1 16.4 ± 13.5 CIR 28/31 storms ­38.6 ± 33.7 ­35.5 ­28.7 ± 30.5 ­32 ­2.98 ± 1.5 ­2.9 ­2.82 ± 1.1 ­2.8 2.72 ± 3.65 2.5 3.3 ± 3.7 2.6 ­0.53 ± 2.3 ­0.6 ­0.19 ± 1.96 0 13.7 ± 10.7 13.3 ± 10.4 ­33.12 ­41.41 3.62 ± 2.27 ­55.8 ­52.5 5.7 ± 5.7 ­40.8 ­37.5 5.4 ± 3.1 5.5 ± 3.1 ­2.89 ­3.33 3.07 ± 2.4 2.16 5.5 5.1 ± 4.1 14.7 18.15 5.3 ± 3.3 5.4 ± 3.3 3.96 3.93
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Ejecta 31 storms ­40 ± 28 ­35 ­30.7 ± 23.1 ­32 ­2.1 ± 1.1 ­1.7 ­2.3 ± 1.0 ­2.2 1.9 ± 4.5 1.6 2.8 ± 3.9 2.8 ­0.4 ± 2.7 0 ­0.2 ± 2.1 0 15.6 ± 11.8

c* , nT 0
median*

c

0

median

c* , nT V­1 m h­1 E
median*

c

E

median

c* , nT/nPa
median*

c



median

c* , dimensionless
median*





median

* su m E y
sum E
y

* c* s u m E y
c


­32.8 ­35.9 4.3 ± 2.7

sumE

y

Pd*
Pd

c* Pd*
c


8.2 12.04 3.6 ± 2.5

Pd

sB * sB
c* s B * B c
B

­2.9 ­4.08

­2.8 ­1.03

­1.44 ­0.72

sB

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NIKOLAEVA et al.

index of the main phase of magnetic storms ( c* , c* , c* , c* with standard deviations), the 0 E P B

For all types of storms, the integral electric field provides the largest contribution into development of

* average parameters of SW ( su m E y , Pd* , s B *
and their standard deviations), and also the contribu tions of these parameters

* * Dst of the main phase ( c* s u m E y in table) with E
the maximum change (approximately by a factor of 1.7) between the storms induced by Sheath and Ejecta. The contribution of the dynamic pressure c* Pd* is small for various types of SW (varies between ~3% for Sheath and ~36% for CIR): it changes from a mod erate contribution for storms induced by CIR and Ejecta (it weakens the storms) to a small one for storms induced by MC and Sheath (it intensifies the storm by ~10%). The contribution of magnetic fluctuations

c* Pd* , c* s B * P B
are the Dst [9].

marked by asterisks *). For the sake of comparison, table shows also similar parameters for the measured index (without asterisks) obtained by us earlier in For both indices, the mean values of the integral
y

)

(

* c* s u m E y , E

* to the D st index value (these

electric field su m E

, dynamic pressure Pd , and

* c* s B * into development of Dst is small. For all
types of storms it is opposite by sign to the contribution of the dynamic pressure and that leads to their partial compensation for the MC and Sheath induced storms (by ~74%) and for CIR and Ejecta induced storms (within ~19%). Figure 1 shows the results of the first stage of model * ing of the corrected Dst index using individual coeffi cients of approximation of the storm main phase. The correlation coefficients (r) and standard deviations () characterizing the modeling quality are shown in Figs. 4a and 4b. The modeling with individual approxi * mation coefficients (stage one) describes very well Dst of the main phase for all types of SW. The highest and * lowest accuracy of the Dst modeling is for the MC induced storms and Sheath induced storms, respectively (the difference is by a factor of 1.3). For all types of SW, the correlation coefficients are very high (within r ~ 0.97­0.99). Figure 2 shows the results of the second stage of the * Dst modeling, using approximation coefficients aver aged over the SW type, so this model can be easily used for real time forecasting of the storm value, because the coefficients are known in advance [8]. One can see * in Figs. 4c and 4d that the accuracy of the Dst model ing varies approximately by a factor of 1.5 between the highest one for the MC and Ejecta induced storms and the lowest one for the Sheath induced storms, whereas the correlation coefficient is the lowest and highest for the MC and Shaeth induced storms, respectively (within r ~0.63­0.77). Figures 3, 4e, and 4f show the results of the third * stage of the modeling of the main phase Dst when the * model values of Dst mod are calculated using the approx imation coefficients averaged over the SW type (in the same way as at the previous stage 2), taking into * account the values of the Dst index preceding the begin ning of the magnetic storm main phase (see [8, 9]). The * accuracy of the third stage of the Dst modeling varies by a factor of ~1.7 from the highest one for the MC
COSMIC RESEARCH Vol. 53 No. 2 2015

the level of IMF fluctuations s B coincide and are not shown in table except for the storms induced by CIR the statistics of which decreased, but the corresponding to them values presented in table are close to each other. * It follows from the table that for Dst the average value of the c* coefficient is strongly negative and 0 depends weakly on the type of SW driver of the mag netic storm (the difference is ~38% between the high (negative) value for the Ejecta induced storms and lower value for the Sheath induced storms). Depend ing on the storm type, the value of the c* coefficient varies within 65% (between the highest (negative) value for the Sheath induced storms and low value for the storms induced by MC). Taking into account the large scatter of each coefficient for all four SW types, one can see that the c* coefficients differ substan tially depending on the SW type (they are higher for the compression regions CIR and Sheath and lower for MC and Ejecta). The c* coefficient value is slightly negative for the MC induced storms, but slightly positive for the other types: Sheath , CIR , and Ejecta induced storms (depending on the SW type, the difference between the positive coefficients

c* reaches a factor of 7 with the minimum and max imum values for the Sheath induced storms and CIR induced storms, respectively). One can assume
that the c* coefficient is ~0 for the MC and Sheath induced storms, but is high for the CIR and Ejecta induced storms (2.7 and 1.9, respectively), but additional studies are needed to increase the signifi cance the result for these types of storms. The value of the c* coefficient is close to the c* value, but opposite by sign.


* MODELING OF THE CORRECTED D st INDEX

123 (b)

() * Dst 28 ­ storms induced by CIR (246 points) 0

21 ­ storms induced by Sheath (166 points)

­100

­200

­300 (c) 10 ­ storms induced by (77 points) 0 (d) 31 ­ storms induced by Ejecta (324 points)

­100

­200 ­300

­200

­100

0

­200 D st *

­100
mod

0

* * Fig. 1. Dependence of the corrected Dst index on the model value Dst storms induced by different SW type (stage 1).

mod

with individual approximation coefficients for magnetic

and Ejecta induced storms to the lowest for the Sheath induced storms. The correlation coefficient r is high and varies within r ~ 0.79­0.82. 4. DISCUSSION AND CONCLUSIONS The mean values of the approximation coefficients * for both the corrected D st and measured Dst indices vary depending on the SW type in a similar way, but insignificantly differ from each other by their value, within the scatter of these coefficients. For all types of SW, the c* value (as compared to the c 0
0

Ejecta induced storms, respectively). For each SW type, the c* coefficients differ slightly (within E 25%) from the c
E

coefficients. For the Ejecta and

Sheath induced storms, the c* coefficient decreased strongly in comparison with c


(by a factor of 1.5­2,

still staying positive). The c* coefficient increased in comparison with c tor but less the


coeffi

(became more negative by a fac

cient) increases ( c* is more negative by a factor of 0 2.3 and 2.4 for the MC and Sheath induced storms, respectively, and by 35 and 33% for the CIR and
COSMIC RESEARCH Vol. 53 No. 2 2015

of 2­2.5) for the Ejecta and CIR induced storms, decreases for the Sheath induced storms (became negative by a factor of 1.4), and did not change for MC induced storms.


124

NIKOLAEVA et al. () * Dst 28 ­ storms induced by CIR (246 points) 0 (b) 21 ­ storms induced by Sheath (166 points)

­100

­200

­300 (c) 10 ­ storms induced by (77 points) 0 (d) 31 ­ storms induced by Ejecta (324 points)

­100

­200 ­300 ­200 ­100 0 ­300 ­200 D st mod * ­100 0

* Fig. 2. The same as in Fig. 1, but for Dst

mod

with the approximation coefficients averaged over SW types (stage 2).

In comparison with the for the Dst index, the contri butions of particular parameters into the temporal pro * file of the corrected D st index vary in the following way: (1) The contribution of the integral electric field * c* s u m E y changed insignificantly (within 6­ 32%) for all SW types (staying the largest as compared to other terms of the approximation equilibrium); (2) The contribution of the dynamic pressure c* Pd* decreased slightly for the MC and CIR induced storms (within 15­23%), but became stronger for the Ejecta and Sheath induced storms (by a factor of 1.5­2.5); (3) The contribution of the fluctuations c* s B * increased (in negative value) for the storms induced by Ejecta and CIR by factors of 2 and 2.7, respectively, however a decrease of the contribution from the Sheath induced storms by 41% (more negative value) is observed. The contributions are the same for the MC induced storms.

It is important to notice that the formal transition * from the Dst index to the D st index presents an attempt to take into account the contribution into the index of the solar wind pressure via the b(Pd)1/2 term, however at approximation by our model, there still remains the * dependence of the D st index on the pressure Pd: for two types of storms (induced by CIR and Ejecta), the

c* coefficient does not vanish and the contribution of
the pressure c* Pd* still remains substantial (though it decreases). Thus, our results show that in the corrected * Dst index, a dependence on the pressure, possibly, for all SW types (especially for CIR and Ejecta) is present. This fact agrees with the results of other publications [11, 14, 26, 33, 34] demonstrating a rather complicated relation of the Dst index to other SW parameters. At the first stage of the modeling of the corrected * index in comparison with the modeling of the Dst, Dst a reduction of modeling accuracy (increase in the standard deviation ) is typical for all SW types, but is strongest for MC induced storms (by a factor of ~2).
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* MODELING OF THE CORRECTED D st INDEX

125 (b)

() * Dst 28 ­ storms induced by CIR (246 points) 0

21 ­ storms induced by Sheath (166 points)

­100

­200

­300 (c) 10 ­ storms induced by (77 points) 0 (d) 31 ­ storms induced by Ejecta (324 points)

­100

­200 ­300 ­200 ­100 0 ­300 ­200 D st *
* Fig. 3. The same as in Figs. 1 and 2, but for Dst phase of a magnetic storm (stage 3).
mod

­100

0

mod

* taking into account the Dst index values preceding the beginning of the main

The correlation coefficient values change slightly (within ~1%). In comparison with the Dst index, the second stage * of modeling of the corrected Dst is characterized by a reduction in the accuracy almost for all SW types (within 17­19%) except for the MC induced storms (an increase by ~3%) and by a decrease in the correla tion coefficient for all SW types (within 3­15%), most strongly for Ejecta. In comparison with the modeling of the Dst index, * the accuracy of the third stage of modeling of D st also decreases for all four SW types (~5­25%), but is stron ger for the compression regions CIR and Sheath (19­ 25%) than for Ejecta and MC (5­9%). The correlation coefficient decreased for all SW types (within ~2­6%), but more strongly for the CIR and Sheath induced storms (4­6%) than for the MC and Ejecta induced storms (~2%). It is necessary to emphasize once more that the scatters of the mean approximation coefficients are
COSMIC RESEARCH Vol. 53 No. 2 2015

large enough and, except for c* , exceed substan tially their difference between SW types. That is why one can state only tendencies in the differences. The main conclusions: (1) Under our method of modeling, the measured Dst index describes the dynamics of the main phases of magnetic storms of all SW types at all stages of the modeling more effectively than the corrected * D st index. It is manifested by higher correlation coef ficient r and lower value of . (2) At the second stage of the modeling, the mea sured Dst index describes variations in the main phase of the Ejecta induced storms better than the corrected * D st index (that is, provides higher correlation coeffi cient), but provides a stronger increase in the accuracy (a decrease in the standard deviation ) of Dst (as com * pared to D st ) for the Sheath induced storms. (3) At the third stage of the modeling (taking into account the index values preceding the beginning of


126 () 40 ­ (stage 1)

NIKOLAEVA et al. (b) 1.0 r ­ (stage 1) (c) ­ (stage 2) 30 20 10 0 (e) 30 20 10 0 MC Sheath CIR Ejecta 0.9 0.8 0.7 0.6 MC Sheath CIR Ejecta 0.9 0.8 0.7 0.6 (f) Dst * Dst 0.9 0.8 0.7 0.6 (d)

30 20 10 0

­ (stage 3)

Fig. 4. The standard deviations () and correlation coefficients (r) as a function of the SW type at three stages of modeling of main phase: (a, b) by individual coefficients (stage 1), (c, d) by approximation coefficients averaged over SW type (stage 2), and (e, f) taking

* into account the Dst index values preceding beginning of main phase of magnetic storm (stage 3).

the main phase of a magnetic storm), both the Dst and * D st indices describe variations in the main phases of magnetic storms induced by MC and Ejecta almost identically as well (close correlation coefficients and accuracies). At the same time, the CIR and Sheath induced storms are better described by the * simple Dst index than by the corrected D st index. ACKNOWLEDGMENTS The authors thank for the possibility to use the OMNI database. The OMNI data are obtained from GSFC/SPDF OMNIWeb at the site http://omni web.gsfc.nasa.gov. The work was supported by Russian Foundation for Basic Research (project no. 13 02 00158a) and also by the Program of the Presidium of RAS (no. P22).

r ­ (stage 3)

r ­ (stage 2)

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Translated by A. Danilov