Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1643–1647www.elsevier.com/locate/jastp

Comparison of the solar wind energy input to themagnetosphere measured by Wind and Interball-1

A.A. Petrukovicha ; ∗, S.I. Klimova, A. Lazarusb, R.P. LeppingcaSpace Research Institute, 84=32 Profsoyuznaya St., 117810, Moscow, Russia

bCenter for Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USAcLaboratory for Extraterrestrial Physics, NASA GSFC, Greenbelt, MD 20771, USA

Received 19 October 2000; received in revised form 14 March 2001; accepted 20 March 2001

Abstract

Timely solar wind measurements are indispensable for space weather forecasts and magnetospheric studies, but solar windvariations detected by a distant spacecraft might be di6erent from those actually hitting Earth’s magnetosphere. To determinehow important these di6erences can be for geophysical applications, we compared energy input to the magnetosphere whichwas simultaneously measured by the Wind and Interball-1 spacecraft at various distances from the Earth. The percentageof equal (with di6erences less than 15%) measurements was found to increase from 30% at energies associated with smallsubstorms to 100% for storm-level energies. The degree of the spacecraft separation along the X GSE coordinate and in theYZ GSE plane appeared to be of minor importance within the limits of Wind and Interball-1 orbits. c© 2001 Elsevier ScienceLtd. All rights reserved.

Keywords: Solar wind; Interplanetary magnetic =eld; Magnetospheric storms; Magnetospheric substorms

1. Introduction

Reliable solar wind measurements are crucial for e6ec-tive space weather forecasts and proper understanding ofthe magnetospheric processes. The L1 libration point be-tween Sun and Earth is a convenient place for such monitor-ing spacecraft. However, because of the inherent temporaland spatial variability of the solar wind, structures actuallyhitting the Earth might be di6erent from those detected bya distant spacecraft. Among the solar wind characteristicsa6ecting the state of the Earth’s magnetosphere, the inter-planetary magnetic =eld (IMF) is the most important oneand very variable. In the several statistical investigations,cross-correlation of magnetic =eld pro=les measured by twospacecraft was used as a quantitative measure of these dif-ferences (Russell et al., 1980; Crooker et al., 1982; Collieret al., 1998). The average correlation was rather high, but

∗ Corresponding author.E-mail address: apetruko@iki.rssi.ru (A.A. Petrukovich).

low coeBcients were often reported. Signi=cant di6erencesbetween IMF pro=les at two locations were also observedin a number of case studies (Perreault and Kamide, 1976;Sergeev et al., 1998), demonstrating that the problem isimportant for the magnetospheric dynamics.

Correlation analysis of IMF time sequences is quite jus-ti=ed if heliospheric aspects of solar wind variability (suchas scale sizes, etc) are the focus of the studies. However, ifgeomagnetic activity is the primary interest, it is also nec-essary to understand how important these di6erences arefor magnetospheric dynamics. For example, IMF variationswith average northward Bz are less important for the magne-tosphere than the same IMF variations with average south-ward Bz , even if correlation characteristics are equal. Tomake solar wind analysis more geophysically meaningful, itis convenient to compare quantities combining several so-lar wind characteristics (possibly with time integration) in asingle number. These so-called coupling functions quantifyvarious aspects of the solar wind and IMF interaction withthe magnetosphere and can serve as proxies of geomagnetic

1364-6826/01/$ - see front matter c© 2001 Elsevier Science Ltd. All rights reserved.PII: S1364 -6826(01)00039 -6

1644 A.A. Petrukovich et al. / Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1643–1647

activity (e.g. Gonzalez et al., 1994). For this study we se-lected the time integral of the epsilon-parameter, which isthe measure of the electromagnetic energy input into themagnetosphere (Perreault and Akasofu, 1978). With such anapproach both the di6erence between parameters measuredat two spatially separated locations and the value of the pa-rameter itself can be interpreted in terms of their importancefor the dynamics of the magnetosphere.

It should be noted, however, that discussion of physicalprocesses behind the epsilon parameter and other couplingfunctions is beyond the scope of this report. For our study itis suBcient that these coupling functions correlate well withstorm and substorm activity. Our approach is detailed in thenext section. Besides the primary goal of comparing twosets of solar wind measurements, it illustrates also a variantof describing the solar wind input into the magnetosphere.Hereafter all magnetic =eld values are in GSM coordinates,and all spacecraft coordinates are in GSE.

2. Method of calculations and data set

We use the epsilon parameter (�) in the form

E=∑

2× 107VswB2IMF sin

4(�=2)Ht=∑

�Ht J; (1)

where Vsw is the solar wind bulk velocity in km=s, BIMF theIMF magnitude in nT, �= − arcsin(Bz=

√B2y + B2

z ) is theIMF clock angle, and

∑Ht denotes integration over the

time interval in seconds. This parameter is applicable both tostorm-size and substorm-size magnetospheric disturbancesand it accounts for the inJuence of the IMF By component,which is important for smaller substorms (Petrukovich et al.,2000). The use of � as a measure of solar wind energy in-put into the magnetosphere during geomagnetic storms wassubstantiated in the original paper by Perreault and Akasofu(1978). A geomagnetic storm usually starts after at least 3 hof IMF Bz = −10 nT or less (Gonzalez et al., 1994). Forsuch IMF conditions and solar wind velocity of 400 km=s;the corresponding value of E is∼1016 J. Kallio et al. (2000)have shown that the solar wind input, measured in terms of �correlates well with the ionospheric dissipation during sub-storms. For a substorm commencing after 90 min of IMFBz = − 5 nT; E ∼ 1015 J. Smaller (contracted-oval) sub-storms can occur after accumulating somewhat more than1014 J (Petrukovich et al., 2000).For computation of E we have used key parameter data

of Wind Magnetic Field Instrument (Lepping et al., 1995),Wind Solar Wind Experiment (Ogilvie et al., 1995) andInterball-1 magnetic =eld experiment (Klimov et al., 1997)for the period of 1995–1999. The solar wind velocity mea-surements aboard Interball-1 are available only for limitedperiods of time. Fortunately, the solar wind bulk velocityis a substantially less variable parameter compared with theIMF and is of secondary importance for geomagnetic ac-tivity. Therefore, we used solar wind velocity measured byWind both for Wind and Interball-1 data sets.

Fig. 1. Interball-1 and Wind orbital positions during 1995–1999.Interball points form a dark ring around the origin. All wind posi-tions are at X ¿ 30RE.

Wind measurements were shifted in time to adjust for thesolar wind propagation to the Interball position with the useof values of Vx solar wind velocity and X GSE spacecraftseparation without accounting for possible non-radial sym-metric structures. Then, the data sets were averaged (merelyfor convenience purposes) to obtain the 10-min sampling.In some investigations, this 10-min scale was reported as thecharacteristic time of the magnetosphere response to IMFchanges (Ruohoniemi and Greenwald, 1998). It is notewor-thy, that as we =nally analyze integral characteristics of 1.5-hlong intervals (see below), the degree of the initial averag-ing (here, 10 min) should not be important.

The full data set totalled about 31,440 points or 5; 240 h.Wind orbits covered a wide range of positions from the L1libration point to close vicinity of the Earth, while Interball-1was in the elliptic orbit with apogee 30RE (Fig. 1). For mostdata points, the transverse separation (in the YZ GSE plane)was within 50RE.

We calculated E for each point in our data set by twomethods. The E1 parameter is the energy input de=ned byEq. (1) and integrated over the preceding time interval forwhich the power input was greater than 5× 109 W. When adata gap or lower input were detected for more the 30 min;the E1 value was reset to zero. This parameter is useful asan estimate of the total energy deposition during an event.The E2 parameter was integrated over the preceding 1:5 h.Such a length of accumulation interval is of the order of theduration of a substorm growth phase. In the following wedescribe di6erences between Wind Ew and Interball-1 Ei interms of the ratio

R= |Ei − Ew|=Ei: (2)

We binned R values in the ranges 0–0.15, 0.15–0.3, 0.3–0.5, and more than 0.5 for each of the parameters E1 andE2. Measurements at two spacecraft were considered equalwhen R¡ 0:15.

Since E1 and E2 were calculated for every 10-min point,one should associate with caution these E values with par-ticular storms or substorms. For example, during storms, the

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Fig. 2. Wind (light curve) and Interball-1 (dark curve) data fordays 193–196 of 1997. In a case when measurements are similar,curves nearly coincide. (a) IMF Bz; (b) E1; and (c) E2.

energy input often continues after the minimalDst is reached,and the additional energy does not contribute to the stormstrength as measured by Dst . For a particular substorm, thesolar wind input should be integrated over the interval ofgrowth and expansion phases (Kallio et al., 2000).

3. Results of comparison

In Fig. 2 we present an example of IMF Bz; E1; andE2. Note that the curves coincide when both spacecraft de-tect similar magnetic =eld. Intervals of enhanced energy in-puts can be discerned as maxima in E1 plot. The largest E1

maximum at 195th day of the year (DOY) corresponds tothe period of large southward IMF Bz and the geomagneticstorm with the minimal Dst =− 51 nT. Smaller E1 maximawith amplitudes 1014–1015 J should cause geomagnetic sub-storms. At ∼193:75 DOY, 1997, several resets of E1 to zerooccurred in the data sequence from one spacecraft, while inthe other it continued to grow. There was no drastic di6er-ence in the magnetic =eld data at these moments. In fact,such an arti=cial discrepancy can occur if both data sets areclose to the reset criterion (described in the previous sec-tion) and even small absolute di6erences can cause a resetin one data set. E2 parameter (Fig. 2c) did not exhibit sucharti=cial di6erences because it is not reset. However, con-trary to E1; E2 did not reJect adequately the total energydeposited during the storm period (195–196 DOY) due tothe short summation interval.

Fig. 3. (a) Fraction of equal (within 15%) energy inputs with re-spect to amplitude of input. Solid curve—E2, dashed curve—E1.(b) Fraction of di6erent E2 at the two spacecraft: 15–30% di6er-ence (diamonds), 30–50% (triangles), ¿ 50% (squares).

The percentage of observations with equal (R¡ 15%) E1

(dashed curve) and E2 (solid curve) is presented in Fig. 3awith respect to E values. At the substorm-level energies inthe range 1014–5 × 1015 J; the fraction of equal observa-tions grew from 30% to 80%, respectively. For E1 it wasof the order of 20% lower than for E2 and this di6erenceis statistically signi=cant. Resets in accumulation causedby arti=cially introduced threshold (see relevant discussionabove) are responsible for this depletion. When such resetswere forced to occur simultaneously for both spacecraft, thisdi6erence between E1 and E2 vanished (not shown here).Therefore, at energies below 6 × 1015 J we analyzed onlyE2 statistics.

At the storm-level energies higher than 3 × 1016 J, al-most all measurements were equal. The E2 parameter wasnot plotted at energies higher than 6 × 1015 J because toosmall number of points were available. At such high ener-gies the E1 parameter is quite accurate because intense solarwind input is far beyond the reset threshold. The E1 is alsomore adequate parameter to estimate the total storm energybecause it is not limited by a prede=ned integration time.

In Fig. 3b, fractions of R values for the E2 parameterin several ranges are presented for substorm-scale events.Fractions of large R diminish with the growing amplitudes ofE2. At the energy of 1015 J, which is typical for a substorm,the probability of large di6erence (R¿ 0:5) is still about5% and at 25% of cases moderate error of 15–30% shouldbe expected.

It is also useful to analyze the inJuence of several factorswhich potentially might worsen the statistics. In a fore-shock

1646 A.A. Petrukovich et al. / Journal of Atmospheric and Solar-Terrestrial Physics 63 (2001) 1643–1647

Fig. 4. (a) Fraction of equal inputs E2 for all data (solid curve)and for data subset without fore-shock (dashed curve). (b) Frac-tion of equal energy inputs for the subsets with closer than 120REof separation along X GSE (solid curve) and farther than 120RE(dashed curve). (c) Fraction of equal energy inputs for the sub-sets with closer than 25RE transverse separation (solid curve) andfarther than 25RE (dashed curve).

region (on a =eld line connected to the bow shock), themagnetic =eld can be modi=ed relative to the undisturbedIMF, introducing additional di6erences in the data set. Weused the Fair=eld (1971) shock model and the local mag-netic =eld to determine whether such a magnetic connectionexist for each point in the data set. The fraction of equalE2 in the reduced data set with excluded fore-shock points(Fig. 4a, dashed curve) increased only marginally in com-parison with that in the full data set (solid curve).

Amount of di6erences practically did not depend on thespacecraft separation along GSE X axis (Fig. 4b). Here,we used HX =120RE as the threshold dividing our dataset in two equal subsets. Two spacecraft separated by asigni=cant distance not only along the Sun–Earth line, butalso across it (in YZ GSE plane) will detect di6erent so-lar wind structures more often if such distance is largerthan some characteristic scale. In the extensive investiga-tion of Crooker et al. (1982) this scale was determined tobe about 50RE. In our data set such spacecraft separation

was less than 50RE for almost all points. Therefore, we ana-lyzed our data in two subsets with transverse distances closer(Fig. 4c, solid curve) and larger (dashed curve) than 25RE.The fraction of points with equal energy input for closelyspaced (in YZ plane) spacecraft was higher by less than10%. The results also proved to be insensitive to reasonablechanges in the duration of accumulation intervals, thresh-olds and other parameters in algorithms of E1 and E2 com-putation (not shown here).

4. Discussion and conclusions

We compared simultaneous distant and near-Earth solarwind measurements by the Wind and Interball-1 spacecraftduring 1995–1999. Di6erences between the two data setscaused by inherent temporal and spatial variability of thesolar wind might be interpreted as an error in the forecast bythe distant solar wind monitor. In an attempt to understandhow important such di6erences might be for the dynamicsof the magnetosphere we used time-integrals of epsilon pa-rameter (Perreault and Akasofu, 1978) for the comparison.

Our statistical analysis con=rmed conclusions of the casestudies showing that solar wind variability might signi=-cantly a6ect accuracy of the solar wind input estimates dur-ing substorm studies. The fraction of equal (within 15%)measurements grew with increasing magnitude of the solarwind input. For larger substorms the fraction of expectedequal measurements was quite comfortable (∼ 70%), withthe probability to make large errors ∼ 5%. However, forsmaller substorms (e.g., of contracted-oval type) reliable so-lar wind input determination would be rather diBcult due toonly ∼30% of expected coincidence.

The storm-level solar wind inputs, which are of primeinterest for the space weather applications, were almostidentical. This particular result is not unexpected sincegeomagnetic storms are associated with very large-scaleSun-generated disturbances such as magnetic clouds(Burlaga, 1995), while IMF changes causing substorms aresmaller-scale Alfvenic variations of the solar wind plasma.

The main results of our comparison should be applicablenot only to the epsilon parameter measurements but also tothat of the other coupling functions (at least qualitatively),because all these expressions are combinations of the samesolar wind and IMF characteristics. Furthermore, as thelevel of di6erences between two spacecraft was found to bepractically insensitive to the spacecraft separation (withinthe limits of Wind and Interball-1 orbits), we consider thatour conclusions are valid not only for the speci=c Wind–Interball-1 pair, but could also describe the general accuracyof the solar wind monitoring at the L1 orbit.

Acknowledgements

The authors would like to thank NASA GSFC for theproduction of Wind key parameters. The work of A.A.P.was partially supported by the RFBR Grant 98-02-16279.

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