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ISSN 0010 9525, Cosmic Research, 2013, Vol. 51, No. 6, pp. 401­412. © Pleiades Publishing, Ltd., 2013. Original Russian Text © N.S. Nikolaeva, Yu.I. Yermolaev, I.G. Lodkina, 2013, published in Kosmicheskie Issledovaniya, 2013, Vol. 51, No. 6, pp. 443­454.

Modeling the Time Behavior of the Dst Index during the Main Phase of Magnetic Storms Generated by Various 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, 117997 Russia
Received December 24, 2012

Abstract--Results of modeling the time behavior of the Dst index at the main phase of 93 geomagnetic storms (­250 < Dst ­50 nT) caused by different types of solar wind (SW) streams: magnetic clouds (MC, 10 storms), corotating interaction regions (CIR, 31 storms), the compression region before interplanetary coronal ejec tions (Sheath before ICME, 21 storms), and "pistons" (Ejecta, 31 storms) are presented. The "Catalog of Large Scale Solar Wind Phenomena during 1976­2000" (ftp://ftp.iki.rssi.ru/pub/omni/) created on the basis of the OMNI database was the initial data for the analysis. The main phase of magnetic storms is approx imated by a linear dependence on the main parameters of the solar wind: integral electric field sumEy, dynamic pressure Pd, and fluctuation level sB in IMF. For all types of SW, the main phase of magnetic storms is better modeled by individual values of the approximation coefficients: the correlation coefficient is high and the standard deviation between the modeled and measured values of Dst is low. The accuracy of the model in question is higher for storms from MC and is lower by a factor of ~2 for the storms from other types of SW. The version of the model with the approximation coefficients averaged over SW type describes worse varia tions of the measured Dst index: the correlation coefficient is the lowest for the storms caused by MC and the highest for the Sheath and CIR induced storms. The model accuracy is the highest for the storms caused by Ejecta and, for the storms caused by Sheath, is a factor of ~1.42 lower. Addition of corrections for the prehis tory of the development of the beginning of the main phase of the magnetic storm improves modeling param eters for all types of interplanetary sources of storms: the correlation coefficient varies within the range from r = 0.81 for the storms caused by Ejecta to r = 0.85 for the storms caused by Sheath. The highest accuracy is for the storms caused by MC. It is, by a factor of ~1.5, lower for the Sheath induced storms. DOI: 10.1134/S0010952513060038

1. INTRODUCTION This paper is dedicated to modeling the time behavior of the Dst index at the main phase of magnetic storms induced by various types of solar wind (SW) streams. It presents a continuation of the series of pub lications [1­7] dedicated to study of the process of generation of magnetic storms by various types of solar wind streams. Based on our results that the Dst index at the main phase of a magnetic storm is well approxi mated by the linear function of the integral of the Bz component of the interplanetary magnetic field (IMF) (substituted at the data processing by summation sumBz) or of the integral of the electric field (sumEy) [1­3], we showed in our previous publica tions [4­6] that the linear character of the Dst depen dence on sumEy on the average is observed for all types of the solar wind, but differs by values of the coeffi cients. For several types of magnetic storms related mainly to the compression regions (CIR, Sheath), the magnetic storm intensity increases strongly (Dst decreases) in the subgroup of points at the main phase with high dynamic pressure. On the background of the Dst dependence on sumEy at the main phase of mag netic storms, a very weak dependence on the fluctua

tion level sB in IMF is observed almost for all types of flows [5, 6]. Note that the linear character of the Dst depen dence of the main phase of a magnetic storm on the integral of Ey (sumEy) follows from [8] in the case of neglecting the term related to the decay of the ring current at the main phase. This result has been con firmed in a series of publications (without any selec tion of magnetic storms by the type of their source in the solar wind) (see, for example, [9­11] and refer ences therein). On the basis of these results, we have earlier per formed a modeling of the Dst index behavior during the main phase of magnetic storms induced by mag netic clouds (MC). It was assumed that the linear rela tion between Dst and the integral of the electric field Ey plays a key role in development of the main phase, whereas the dependencies on pressure Pd and varia tions sB in IMF were believed to be small [7]. The results obtained showed that the proposed approaches make it possible not only to describe satisfactorily the relation of interplanetary parameters of MC to the dynamics of the Dst index but to create forecasting schemes for prediction of Dst values 1­2 hours in advance.

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Currently, there exist a vast number of publications dedicated to the modeling of magnetic storms and their prediction (see, for example, [8, 12­19] and ref erences therein). Various methods are used to predict Dst index, for example the method of filters, when the solar wind­magnetosphere system is considered as a black box, artificial neuron networks, and nonlinear auto regression schemes (see, for example, [20­32]). In the overwhelming majority of papers, the type of SW stream which generated storms is not taken into account. However, there are publications which show that various types of SW streams lead to different dis turbances in the magnetosphere (see, for example, [33­47, 1­6]). In one of the recent publications [32], a compari son is presented of 6 different models [8, 13, 14, 16, 27, 28, 31] by the results of their prediction of 63 strong magnetic storms (minimum Dst ­100 nT) which were split to four groups depending on the type of their source in SW. Twenty seven sMC induced storms (MC with the preceding rapid shock wave), 18 SH events (the compression region Sheath), 8 CIR events (corotating interaction regions), 10 nonMC events (i.e., the ICME type but the field structure dif fers from MC, i.e., Ejecta) were analyzed separately. As a result, it was shown that the TL model [27, 28] is the best for prediction of the Dst index during strong magnetic storms for any type of source in SW, and also for 63 strong storms and all 139 moderate and strong magnetic storms without separation according to the type of sources in SW. We use the traditional description of the storm dynamics by the Dst index for which there are long homogeneous series of data in spite of the fact that var ious current systems of the magnetosphere and iono sphere could contribute to its value (see, for example, [48, 49]). In this paper, a possibility of approximation of the main phase of magnetic storms generated by four types of solar wind streams by linear dependence on the solar wind parameters: the integral electric field sumEy, the dynamic pressure Pd, and the fluctuation level sB in the IMF. The correctness of these assump tions is checked by the comparison of the calculation results to experimental data and results of modeling in other publications. The main aim of this paper is to reveal the differ ences in the development of the main phase of mag netic storms, the source of which are various types of solar wind streams (CIR, Sheath, MC, and Ejecta), by comparison of results of modeling the main phase for various types of storms and by estimation of the con tributions of the main parameters of the SW into the Dst index at the main phase of the storm. 2. INITIAL DATA AND METHOD On the basis of the OMNI database for the period 1976­2000 [50], we identified large scale types of the

solar wind (see "Catalog of Large Scale Solar Wind Phenomena during 1976­2000" at ftp://ftp.iki. rssi.ru/pub/omni/ and in [51]). The method of identi fication of large scale streams of the solar wind com prises a comparison of each point of the OMNI data base [50] to a set of threshold criteria for the key parameters of the solar wind and IMF and is described in detail in [51]. In this paper, magnetic storms for which there were gaps in measurements in the OMNI database making it possible to calculate three parameters (Ey, Pd, and sB) in the period of the main phase of a magnetic storm were excluded from the analysis. Moreover, to reduce the error and improve the approximation, the storms having the approximation coefficients which lie outside two standard deviations from the mean value were also excluded [7]. As a result, 93 magnetic storms (­250 < Dst ­50 nT) induced by 4 types of solar wind streams (CIR (31 storms), Sheath (21 storms), MC (10 storms), and Ejecta (31 storms)) were selected for the analysis. It was shown in several previous publications [52­54] that the strongest (on average) magnetic storms caused by sporadic (i.e., conglomerate Sheath+ICME) streams are related to nonisolated events when the distance between consecutive interplanetary events (between the arrivals of interplanetary shock waves and SSC) was less then 40 hours. In this paper, we did not ana lyze the distance between SW events, but we sorted storms and compared them to the source in SW in the following way. If the time between the Dst minimums was longer than 24 hours, the storms were considered as isolated. If the time between the Dst minimums was less than 24 hours (multistep storm), both minimums were considered as one storm with the intensity equal to the minimum value of Dst. There were a few percent of such single storms with two minimums during 24 hours. Therefore, their contribution to the total dependence is insignificant, whereas the Dst level from the prehistory is accounted for by the coefficient 0) (see below). While modeling the main phase of a magnetic storm, a linear approximation of the Dst index value of the main phase of a magnetic storm is taken into account by three parameters of the solar wind: the integral of the convective electric field of the solar wind sumEy, the dynamic pressure Pd, and interplane tary magnetic field variations sB [7]:
Dst () = 0 + c E s u m E y () + c P Pd () + c B s B() , i i i i i sum E y () =
k =i


k =1

E y (k),

(1)

where i is the current point of the storm phase (varies from i = 1 in the beginning of the phase to i = im at the last point of the phase (in Dst min)) and the summation in sumEy is performed in terms of k (from the begin ning of the storm at the k = 1 point to the current point of the phase k = i). The coefficients 0, E, cP, and cB
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Table 1. The mean and median values of the approximation coefficients at the main phase of a magnetic storm, mean SW parameters to the value of the Dst index for four types of SW streams Type of SW c0, nT median , nT/mV m­1 h median , nT/nPa median , dimensionless median sumEy cE sumEy Pd cp Pd sB cB sB MC 10 storms ­13.77 ± 14.4 ­11 ­2.55 ± 0.75 ­2.4 ­0.92 ± 2.9 1 1.28 ± 3.3 0 16.24 ± 9.78 ­41.41 3.62 ± 2.27 ­3.33 3.07 ± 2.4 3.93 Sheath 21 storms ­13.1 ± 28.8 ­18 ­3.2 ± 1.6 ­3.3 0.97 ± 3.3 1 ­0.8 ± 1.8 ­1 16.4 ± 13.5 ­52.5 5.7 ± 5.7 5.5 5.1 ± 4.1 ­4.08 CIR 31 storms ­28.7 ± 30.5 ­32 ­2.82 ± 1.1 ­2.8 3.3 ± 3.7 2.6 ­0.19 ± 1.96 0 13.3 ± 10.4 ­37.5 5.5 ± 3.1 18.15 5.4 ± 3.3 ­1.03 Ejecta 31 storms ­30.7 ± 23.1 ­32 ­2.3 ± 1.0 ­2.2 2.8 ± 3.9 2.8 ­0.2 ± 2.1 0 15.6 ± 11.8 ­35.9 4.3 ± 2.7 12.04 3.6 ± 2.5 ­0.72

were estimated by the standard least squares method (at the same time, the number of points during the main phase should be larger than the number of unknowns, i.e., im > 4). The coefficients E, cP, and cB determine the value of the linear relation of the Dst index to the integral of convective electric field of the solar wind sumEy, dynamic pressure Pd, and variations in the interplanetary magnetic field sB. The 0 coeffi cient is related mainly to the prehistory of the Dst index prior to the magnetic storm commencement, because the storm can "start" from any initial value of the index both due to the beginning of a new storm during the recovery phase of the previous storm (a decrease in the level relative to "zero") and due to the presence of the storm sudden commencement (SSC) related to the arrival of the shock wave prior to the storm com mencement (an increase in the level). For each type of magnetic storm, the modeling of the main phase was performed in three steps. First, the individual approximation coefficients (0, , , ) are determined for the main phase of a particular storm of each type. Then the approximation coeffi cients of the main phase of a storm are averaged according to the type of SW (0, , , ) and for the version of the model, the contribution to Dst during the main phase from particular SW parameters entering equation (1) is estimated. On the basis of the analysis of these versions of the model, for each type of SW, third version of the model is created due to the corrections taking into account the prehistory of the development of the main phase of a magnetic storm by the calculation of a linear function relating the average value of the Dst index over three points (the first point of the main phase and two previous points) and the value of 0 [7].
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Each version of the model was estimated by two parameters (for example, [12]): 1) the linear correla tion coefficient (r) between the measured Dst and modeled Dst mod values (how correctly the model describes the real variations in the Dst index) and 2) the standard deviation () between the measured value of Dst and the value calculated using the model Dst mod (how strong are the differences between the measured Dst and Dst mod values calculated in the model, i.e., the modeling accuracy). 3. RESULTS 3.1. Estimation of Contribution of Various SW Parameters to the Approximation of the Main Phase of a Magnetic Storm Induced by Various Streams of SW Table 1 shows the mean and median values of the approximation coefficients of the main phase of a magnetic storm (0, , , ), mean SW parameters (sumEy, Pd, sB) and contributions of these parameters (cE sumEy, cP Pd, cB sB) to the value of the Dst index for four types of SW streams (MC, Sheath, CIR, and Ejecta). Although the scatter of individual coefficients is sufficiently high (which one can see in the standard deviations of the values) their mean values are close to the median ones, that is, the scatter of the individual values is fairly sym metrical relative to the mean values. In all cases, when the standard deviation exceeds the mean (median) value, the statistical significance of the corresponding coefficient is not high enough to draw a reliable con clusion on the basis of this coefficient, so we show such results as a possible hypothesis which requires further checks.


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The 0 coefficient is negative for all types of SW (that is, it always "reduces" Dst which is natural due to the definition of the magnetic storm beginning and its main phase). The 0 coefficient varies by a factor of ~2.4 from the maximum value for MC and Sheath (high level of Dst from which the storm begins possibly due to SSC prior to the storm beginning) to the mini mum value for CIR and Ejecta. However, the scatter in values of 0 (for particular storms) is high and compa rable to the value of the mean value 0 itself and even exceeds it (for the storms caused by Sheath). The coefficient is determined by how strong the electric field (the sumEy parameter) changes the Dst index at the main phase of storms. The coeffi cient is negative and reduces the Dst value for all four types of storms. The strongest and weakest reduction in Dst from the integral electric field is observed for the storms caused by Sheath and Ejecta, respectively (it varies by a factor of ~1.4). The strongest decrease in Dst is observed for the Sheath induced storms and it leads under the same value of the field to more rapid decrease in Dst than for other types of SW. The contribution of into Dst (i.e., the value of cE sumEy) is the largest and the smallest for the storms caused by Sheath and Ejecta, respectively. The maximum difference in the contribution of this term reaches a factor of ~1.4 and is determined mainly by the coefficient but not by the sumEy value. The coefficient determines the contribution of the dynamic pressure into the value of Dst at the main phase. On average, the value varies from the mini mum value for the MC induced storms (i.e., slight inten sification of the storm or a decrease in Dst) to the maxi mum value for the CIR induced storms (i.e., weakening of the storm or increase in Dst). However, the strong scat ter in the values within each type is comparable and sometimes exceeds the mean value of for the given type of storm. One can say only that there is a tendency of Dst increase (weakening of the storm) with an increase in Pd for three types of storm (except MC). The contribution of Pd to Dst (i.e., the value of c Pd is maximum for the CIR and Ejecta induced storms (a strong weakening of the storm) and minimum for the Sheath induced storms (weaker by a factor of ~2.5­3.5). An inverse effect (a very weak decrease in Dst, i.e., an intensification of the storm) is observed for the MC induced storms. The large positive contribu tion of Pd to Dst for the CIR and Ejecta induced storms leads to a weakening (by 30­50%) of the con tribution of the main parameter sumEy. Higher pres sure Pd within these types of SW is a possible cause of this effect. The cB coefficient determines the efficiency of the contribution of the magnetic fluctuations s in IMF into Dst at the main phase. On average, the value of cB varies insignificantly for all types of SW, reduc ing slightly Dst and increasing the strength of a Sheath induced storm and increasing slightly Dst and reducing the strength of a MC induced storm.

The mean values of the fluctuations level sB cor respond to physical conditions in SW types and vary from a minimum value for the MC induced storms to a maximum value for the storms caused by the com pression regions of the CIR and Sheath induced storms (that is, almost by a factor of 2 higher in the compression region, corresponding to the definition of the given type of streams). The contribution of the fluctuation level sB into Dst is small (as compared to the contribution of sumEy for all types of storms and depends on the type of SW. For the Sheath induced storms, it reduces Dst intensifying the storm, whereas for the MC induced storms, on the contrary, it increases Dst weakening the storm. The magnetic fluctuations intensify the storm slightly for the CIR and Ejecta induced storms. Because of insufficiently high accuracy, the data shown in Table 1 by non bold type could be interpreted in the following way: (1) for cP the mean cP 0 for MC and Sheath and (2) for the mean 0 for all types of SW. For these data the statistics should be increased and an additional analysis should be performed. Thus the largest contributions to Dst of the main phase are provided by the 0 parameters (by a factor of 2.4 higher for MC than for Ejecta) and the integral electric field sumEy (by a factor of 1.4 higher for Sheath than for Ejecta), the value of which depends on the SW type. The contribution of the pressure Pd is the largest for CIR induced and by a factor of 1.5 lower for the Ejecta induced storms. For the Sheath induced storms, the contribution of Pd is by a factor of 3.3 weaker than for the CIR induced storms. For Ejecta the con tribution of Pd weakens the storm (a positive coeffi cient), whereas for MC the contribution of pressure intensifies the storm (a negative coefficient). For all types of SW, the contribution of magnetic fluctuation level sB in IMF to Dst at the main phase is insignificant as compared to the main contribution from the sumEy and its value presumably depends on the SW type. For the MC induced storms, the fluctuations in IMF lead to a small increase in Dst of the phase (a weakening of the storm) which is almost compensated by a slight decrease in Dst (an intensification of the storm) due to the contribution of the pressure Pd. On the contrary, for the Sheath induced storms, the fluctuations sB in IMF lead to a slight decrease in Dst (an intensification of the storm) which is almost compensated by a slight increase in Dst (a weakening of the storm) due to the contribution of the pressure Pd. 3.2. Comparison of Three Versions of Models of the Main Phase of Magnetic Storms Induced by Four Types of SW Streams The dependence of the Dst index measured during the main phase on the model value Dst mod calculated using individual approximation coefficients for each storm and four types of SW is shown in Fig. 1: (a) CIR, (b) Sheath, (c) MC, and (d) Ejecta. The correlation
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MODELING THE TIME BEHAVIOR OF THE Dst INDEX DURING THE MAIN PHASE 31 ­ storms caused by CIR (279 points) 21 ­ storms caused by Sheath (166 points)

405

0

­100 Dst () ­200 (b)

­300 10 ­ storms caused by (77 points) 0 31 ­ storms caused by Ejecta (324 points)

­100 Dst (c) ­200 (d)

­300

­200 Dst
mod

­100

0

­300

­200 D

­100
st mod

0

Fig. 1. The dependence of the Dst index measured during the main phase on the model value Dst mod calculated using individual approximation coefficients for each storm: (a) 31 CIR induced storms; (b) 21 Sheath induced storms; (c) 10 MC induced storms; (d) 31 Ejecta induced storms.

coefficients (r) and standard deviations () as well as the lines of regression of Dst on Dst mod for three versions of models are shown in Table 2. Three bottom lines in the first column show the model versions: (1v) model with individual coefficients, (2v) model with averaged coefficients, and (3v) third model. For the model with individual approximation coefficients (1v) the corre lation coefficient between Dst and Dst mod for all four types of SW is very high (r = 0.98 for the CIR and Ejecta induced storms and r = 0.99 for the MC and Sheath induced storms). The standard deviation is the lowest for the MC induced storms, by a factor of two higher for the CIR and Ejecta induced storms, and is the highest for the Sheath induced storms (the difference is a factor of 2.3). As expected, the individual coefficients obtained from an approximation for a particular storm
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provide the best result for modeling the main phase of a storm with any type of source in SW. Various storm types differ only by values of the correlation coefficients and . The current version of the model describes the main phase of the MC induced storms [7] most accurately, but its accuracy is lower for the storms caused by Ejecta and Sheath by a factor of 2­2.3. Figure 2 shows the same as in Fig. 1, but the model calculations of Dst mod are performed using the values of the approximation coefficients 0, , , , averaged over SW type (see Table 1). For this version of the model (2v), the correlation coefficient between the Dst values measured during the main phase and the modeled Dst mod and also the model accuracy decrease substantially for all types of SW. The highest correla tion coefficient is for the storms caused by Sheath and


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NIKOLAEVA et al. for 3 versions of models Ejecta 31 storms 324 points Y = 0.4 X ­ 0.292 Y = 0.7 X ­ 16.5 0.810 Y = 0.7 X ­ 18.4 0.758 = 1 X ­ 4.5 5.2 0.978 24.5 12.6

Table 2. The dependence of approximation coefficient c0 on (aveDst) and measured Dst on Dst and for 4 types of SW streams Type of SW Values of parameters c0 on (aveDst) r (3v) Dst on (Dst_mod) r (2v) Dst on (Dst_mod) r (1v) Dst on (Dst_mod) r MC 10 storms 77 points Y = 0.69 X­ 6.51 0.730 Y = 0.9 X + 0.84 15.64 0.832 Y = 0.68 X ­ 9.96 21.74 0.648 Y = 1.0 X + 2.445 2.6 0.994 Sheath 21 storms 116 points Y = 0.26 X ­ 9.8 0.239 Y = 0.8 X ­ 2.55 23.4 0.837 Y = 0.8 X ­ 3.5 26.2 0.804 Y = 1 X ­ 4 â 10­8 6.06 0.988 CIR 31 storms 279 points

mod

Y = 0.33 X ­ 26.15 0.233 Y = 0.9 X ­ 6.5 17.8 0.846 Y = 0.9 X ­ 6.6 20.1 0.803 Y = 1.0 X ­ 5 â 10­7 Y 5.5 0.984

12.6

â 10­6

CIR, whereas the lower correlation coefficient is for the storms caused by MC (the difference is a factor of ~1.23). The Ejecta induced storms have an interme diate value. The highest accuracy of the model (low ) is for the Ejecta induced storms. The lowest accuracy is for the storms caused by Sheath and MC (that is, a decrease in the accuracy by a factor of 1.4­1.2 as com pared to Ejecta). In comparison to the previous ver sion of the model (using individual coefficients), the reduction of the accuracy for the given types of SW is by a factor of ~4­8. In order to increase the accuracy of the main phase modeling, we introduced corrections taking into account the prehistory of development of the begin ning of the main phase of a magnetic storm [7]. Instead of a constant mean value of the 0 coeffi cient, for each storm j (within the given type of SW) we took values of c0(j) calculated on the basis of the dependence of the 0(j) coefficient on the average value aveDst(j). This improved version of the model has the form: Dst
mod(i)

these parameters 0 = 0.69 aveDst ­ 6.51 is observed with a correlation coefficient of 0.73. Figure 3 shows the Dst dependence on Dst mod for four types of storms for the third version of the Dst mod model when instead of a constant average value 0 for each storm j values of c0(j) calculated using the above mentioned linear dependence of the 0(j) coefficient on aveDst(j) are taken. One can see that this version of the model (3v) describes the experimental data better than the version with averaged coefficients (2v). The highest correlation coefficient is for the CIR induced storms; it is slightly lower for the storms caused by Sheath and MC. The lowest correlation coefficient is for the storms caused by Ejecta (the difference in the r values is only ~1.05). The lowest value of the standard deviation is for the storms caused by MC and the high est standard deviation is for the storms caused by Sheath (they differ almost by a factor of 1.5). The storms caused by MC and Ejecta have similar values of . 4. DISCUSSION Thus, we proposed and tested a model for descrip tion of the main phase of magnetic storms induced by four types of SW (10 MC induced storms, 31 CIR induced storms, 21 Sheath induced storms, and 31 Ejecta induced storms). The model is based on the assumption of linear dependence of Dst at the main phase on the integral electric field sumEy, dynamic pressure Pd, and fluctuation level sB in IMF. The analysis of results shows that the main contri bution into the Dst index at the main phase is provided by the integral electric field sumEy, which for all types of SW reduces the Dst value (intensifies the storm), the value of the reduction depending on the type of the storm source in SW. The strongest dependence of the Dst index on the integral electric field is observed for the Sheath induced storms, this fact manifesting their
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= c0(j) + cE sumEy(i)

+ cP Pd(i) + cB sB(i), where i is the point in the phase; c0(j) = aveDst(j) + b (here aveDst(j) for the j storm of the given SW type is the average value over three points including two points prior to the storm commence ment and the first point of the main phase of the storm, a and b are coefficients of approximation of the 0(j) dependence on aveDst(j), and the other coeffi cients cE, cP, cB as earlier are taken from the aver aging over all storms of the given SW type). Estimates of a possible relation of the 0(j) coefficients to the value of Dst, aveDst(j) averaged over three points (that is, the coef ficients of correlation between them) and the approxima tion coefficients "a, b" are shown in the top line of Table 2. For 10 MC induced storms, a linear dependence between


MODELING THE TIME BEHAVIOR OF THE Dst INDEX DURING THE MAIN PHASE 31 ­ storms caused by CIR (279 points) 0 21 ­ storms caused by Sheath (166 points)

407

­100 Dst () ­200 (b)

­300 10 ­ storms caused by (77 points) 0 31 ­ storms caused by Ejecta (324 points)

­100 Dst
(c)

(d)

­200

­300

­200 Dst

­100
mod

0

­300

­200 D

­100
st mod

0

Fig. 2. The same as in Fig.1, but for model calculations of Dst mod the averaged by SW type values of the approximation coeffi cients were used.

higher efficiency (that is, ability to lead to stronger intensity of magnetic storms, Dst min) as compared to other types of storms. This statement is confirmed by the sam pling of storms caused by Sheath for which the intensity of a magnetic storm at its minimum reaches Dstmin ~ ­250 nT (super strong storms), whereas for other type of SW the value of Dst min during magnetic storms varies within more narrow range (from ­50 to ­150 nT). The higher intensity of the storms generated by Sheath was earlier noted qualitatively in [3, 35, 36, 39, 41, 47, 55­58]. However, in this paper, we, for the first time, present a numerical comparison of contributions (the cE coefficients) for various interplanetary sources of storms. The contribution of the dynamic pressure to Dst of the main phase also depends on the storm type. In par ticular, for two types of storms caused by MC and Sheath, the contribution of Pd is almost an order of magnitude less than the main contribution to Dst from
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sumEy, and so it influences weakly Dst at the main phase (about 10%). At the same time, for two types of storms caused by CIR and Ejecta, the pressure Pd weakens the main phase of the storm by 30­50%. The contribution of the fluctuation level s in IMF to Dst at the main phase is small as compared to the contribution of sumEy and also depends on the type of storm source. For example, for storms caused by CIR and Ejecta, it is a minimum and hardly influences Dst at the main phase (an intensification of the storm by 3%). For the storms caused by Sheath, it is a maximum (a factor of ~4 higher than for the CIR and Ejecta induced storms) and leads to (~10%) decrease in Dst at the phase (an intensification of the storm). The third version of the model with the 0 coeffi cient obtained from the 0 dependence on Dst values in the preceding times prior to the storm beginning is characterized by higher values of the correlation coef ficient between the measured Dst and Dst mod for Ejecta


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NIKOLAEVA et al. 31 ­ storms caused by CIR (279 points) 0 21 ­storms caused by Sheath (166 points)

­100 Dst () ­200 (b)

­300 10 ­ storms caused by (77 points) 0 31 ­ storms caused by Ejecta (324 points)

­100 Dst
(c)

(d)

­200

­300

­200 Dst

­100
mod

0

­300

­200 Dst

­100
mod

0

Fig. 3. The same as in Fig.1 and 2, but for model calculations of Dst mod the corrections taking into account the prehistory of development of the beginning of the main phase of a magnetic storm were used.

and CIR, and lower standard deviations for MC and Sheath, which is substantially better than for the model version with averaged approximation coefficients. It is worth comparing our results obtained with the third model to the results of modeling the Dst index of magnetic storms separated by the SW type presented in other publications. Note that testing of various models should be performed using an independent set of data different from the data set used for the optimi zation of these models. Table 3 shows the correlation coefficients (r) and standard deviations for four types of SW and seven models including six models from [32] (which have been tested using a data set different from ours, see Introduction) and our third model (3v) taking into account the prehistory of Dst development prior to the beginning of the main phase. Our third version of the model (3v) describes fairly well the main phase of storms for all types of SW. The

value of the correlation coefficient (r) and the accu racy of the model () depend on the SW type. For par ticular types of SW, our model could be better than many others, for some types it is, on the contrary, worse than other models. For example, the value of the correlation coefficient in our third model depends on the type of SW: (1) for the Sheath induced storms it is better than all models except the TL model [27, 28], (2) for the MC and Ejecta models it coincides with the FL model [13] specially aimed at the MC induced storms, but is worse than all other models including the B model [8]; (3) for the CIR induced storms it is better than the B and FL models [8, 13] but worse than the other four models [14, 16, 31, 27, 28]. Similarly, concerning the accuracy ( in nT) our third model: (1) for the MC induced storms it is better than all models (including the TL model [27, 28]) and by a fac tor of three more accurate than the B and FL models [8, 13], (2) for the Sheath induced storms it is better than
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MODELING THE TIME BEHAVIOR OF THE Dst INDEX DURING THE MAIN PHASE Table 3. The correlation coefficients and standard deviations for four types of SW streams and seven models MC Models r 3v B model FL model OM model W model TL model NM model 0.83 0.89 0.83 0.9 0.91 0.94 0.88 15.6 51.4 51.7 26.5 22.4 18.5 24.1 r 0.84 0.71 0.66 0.8 0.81 0.92 0.82 Sheath 23.4 56.1 50.0 27.6 25.4 12.5 26.4 r 0.85 0.77 0.66 0.87 0.87 0.95 0.87 CIR 17.8 48.2 39.9 19.0 16.2 11.8 19.5 r 0.81 0.88 0.81 0.9 0.92 0.94 0.89 Ejecta 16.5 39.2 34.2 20.2 15.3 11.8 19.6 [8] [13] [14] [16]

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References

[27, 28] [31]

all models except the TL model (which is a factor of two more accurate than our model) [27, 28] and is by a factor of 2­2.5 more accurate than the B and FL models [8, 13], (3) for the CIR induced storms it is better than all models except the TL model [27, 28] and by a factor of 2.2­2.7 more accurate than the B and FL models [8, 13], but a factor of 1.5 worse than the TL model [27, 28], (4) for the Ejecta induced storms our model is better than four models but worse than the W and TL models [16, 27, 28] (which is a fac tor of 1.4 more accurate than our model) and by a factor of 2­2.4 more accurate than the B and FL models [8, 13]. Thus, the results of calculations using the third ver sion of the model (with a correction for the storm beginning) agree with the experimental data and by their quality are no worse than the results of modeling by other authors. 5. CONCLUSIONS The modeling of the main phase of 93 magnetic storms (­250 < Dst < ­50 nT) for four types of SW, assuming a linear dependence of Dst on the parameters sumEy, Pd, and sB in IMF, showed that the contribu tion of each parameter of the SW to Dst, as well as the correlation coefficient and accuracy of the model on average depend on the type of storm source in SW. However, the statistical significance of the coefficients for Pd and sB in IMF for some types of SW requires further investigations. The modeling of the main phase is performed in three versions: (1) using individual approximation coefficients, (2) using the averaged approximation coefficients, and (3) using the averaged approximation coefficients as in case (2) but taking into account the prehistory of the development of the beginning of the main phase. The results of the analysis show that: 1) For all types of SW, the model version with indi vidual approximation coefficients is the most accurate and describes in the best way the Dst variations during
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the main phase as compared to other models. Its accu racy depends on the SW type: the highest accuracy is for the storms caused by MC, the accuracy for the storms caused by Ejecta and CIR is lower by a factor of two, and the lowest accuracy (a factor of 2.3 lower) is for the storms caused by Sheath. 2) The largest contribution into Dst at the main phase of storms caused by various types of SW is pro vided by the integral electric field sumEy. For the storms caused by Sheath, the contribution is higher (by a factor of 1.4), this fact being caused by higher efficiency of these interplanetary sources of storms rel ative to other types of SW. 3) The contribution of the dynamic pressure Pd to Dst at the main phase also depends on the SW type: the low est contribution is for the MC and Sheath induced storms and it is higher for the CIR and Ejecta induced storms (it weakens Dst of storms by 30­50%). 4) The contribution of the fluctuations s in IMF is small for all types of SW, but its value also depends on the SW type. 5) The third version of the model (with the correc tion for the storm beginning) is the best for a descrip tion of the development of the main phase of a storm for all types of SW, both for a description of variations in Dst and in accuracy. The correlation coefficient var ies within the range from r = 0.81 for the storms caused by Ejecta to r = 0.85 for the storms caused by CIR. The highest and lowest accuracy is for the MC induced storms (15.6 nT) and Sheath induced storms (worse by a factor of 1.5), respectively. 6) The comparison to six models [8, 13, 14, 16, 27, 28, 31] from [32] shows that our third version of the model for the storms caused by MC and Ejecta is as good (by the correlation coefficient) as the FL model [13] (but worse than the other models [8, 14, 16, 27, 28, 31]). For the Sheath induced storms it is better than almost all models except models [27, 28] and for the storms caused by CIR its efficiency is higher than that of the FL and B models [8, 13]. In accuracy our


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NIKOLAEVA et al. storms on the solar wind parameters for different types of streams, Geomagn. Aeron., 2011, vol. 51, no. 1, pp. 49­65. Nikolaeva, N.S., Yermolaev, Yu.I., and Lodkina, I.G., Dependence of geomagnetic activity during magnetic storms on the solar wind parameters for different types of streams: 2. Main phase of storm, Geomagn. Aeron., 2012, vol. 52, no. 1, pp. 28­36. Nikolaeva, N.S., Yermolaev, Yu.I., and Lodkina, I.G., Geomagnetic activity during magnetic storms as a function of solar wind parameters for different types of flows: 3. Development of storm, Geomagn. Aeron., 2012, vol. 52, no. 1, pp. 37­48. Nikolaeva, N.S., Yermolaev, Yu.I., and Lodkina, I.G., Geomagnetic activity during magnetic storms as a function of solar wind parameters for different types of flows: 4. Modeling for magnetic clouds, Geomagn. Aeron., 2013, no. 6. (in press). Burton, R.K., McPherron, R.L., and Russell, C.T., An empirical relationship between interplanetary condi tions and Dst, J. Geophys. Res., 1975, vol. 80, pp. 4204­ 4214. Kane, R.P., Severe geomagnetic storms and Forbush decreases: interplanetary relationships reexamined, Ann. Geophys., 2010, vol. 28, pp. 479­489. Ontiveros, V., Geomagnetic storms caused by shocks and ICMEs, J. Geophys. Res., 2010, vol. 115, A10244. doi: 10.1029/2010JA015471. Weigel, R.S., Solar wind density influence on geomag netic storm intensity, J. Geophys. Res., 2010, vol. 115, A09201. doi: 10.1029/2009JA015062. Feldstein, Y.I., Modelling of the magnetic field of mag netospheric ring current as a function of interplanetary parameters, Space Sci. Rev., 1992, vol. 59, pp. 83­165. Fenrich, F.R. and Luhmann, J.G., Geomagnetic response to magnetic clouds of different polarity, Geo phys. Res. Lett., 1998, vol. 25, pp. 2999­3002. O'Brien, T.P. and McPherron, R.L., An empirical phase space analysis of ring current dynamics: Solar wind control of injection and decay, J. Geophys. Res., 2000, vol. 105, pp. 7707­7720. O'Brien, T.P. and McPherron, R.L., Forecasting the ring current index Dst in real time, J. of Atmosph. and Sol. Terrestr. Phys., 2000, vol. 62, pp. 1295­1299. Wang, C.B., Chao, J.K., and Lin, C. H., Influence of the solar wind dynamic pressure on the decay and injec tion of the ring current, J. Geophys. Res., 2003, vol. 108, no. A9, p. 1341. doi: 10.1029/2003JA009851. Maltsev, Y.P., Points of controversy in the study of mag netic storms, Space Sci. Rev., 2004, vol. 110, pp. 227­ 267. Siscoe, G., McPherron, R.L., Liemohn, M.W., Ridley, A.J., and Lu, G., Reconciling prediction algo rithms for Dst, J. Geophys. Res., 2005, vol. 110, A02215. doi: 10.1029/2004JA010465. Podladchikova, T.V. and Petrukovich, A.A., Extended geomagnetic storm forecast ahead of available solar wind measurements, Space Weather, 2012, vol. 10, S07001. doi: 10.1029/2012SW000786. Vassiliadis, D., Klimas, A.J., Baker, D.N., and Roberts, D.A., A description of solar wind­magneto
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third model is better for the MC induced storms than almost all models including the TL model [27, 28], for the Sheath induced storms is only worse than the TL model [27, 28], but is more accurate than five other models [8, 13, 14, 16, 31], and for the Ejecta and CIR induced storms is only worse than the TL and W models [16, 27, 28] but better than four other models [8, 13, 14, 31]. Thus it is shown that the contributions of the main parameters of SW into Dst at the main phase, the cor relation coefficient between the measured Dst and modeled Dst mod values, and the accuracy of various versions of models depend on the SW type. The results agree with the earlier conclusions and confirm them quantitatively (for example, [3, 47]). We selected each of the SW types on the basis of certain physical criteria with various values of the SW parameters [51]. More over, in our sampling of storms with different type of SW, very strong storms (­250 < Dst min < ­150 nT) are present only in the sampling for the storms caused by Sheath. Nevertheless, the model (third version of the model) of the main phase for various types of SW rivals successfully other models both in the description of real variations in Dst and in accuracy (see [32] and references therein). Different coefficients of the model obtained for different interplanetary sources make it possible to forecast magnetic storms more accurately, analyzing in real time parameters of the interplanetary environment measured on board space vehicles of the type Wind or ACE [7]. ACKNOWLEDGMENTS The authors are grateful for the use of the OMNI database. The OMNI data were taken from GSFC/SPDF OMNIWeb at the site http://omni web.gsfc.nasa.gov. The work was supported by the Russian Foundation for Basic Research (projects Nos. 10 02 00277a and 13 02 00158a) and also by the Pro gram No. P 22 of the Presidium of the Russian Acad emy of Sciences. REFERENCES
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