JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. A9, PAGES 18,599-18,613, SEPTEMBER 1, 2001

Correlating near-Earth interplanetary magnetic fields: Foreshock effects

Zerefsan Kaymaz Istanbul Technical University, Faculty of Aeronautics and Astronautics, Maslak, Istanbul, Turkey

David G. Sibeck

The Johns Hopkins University, Applied Physics I_•boratory, Laurel, Maryland

Abstract. Interplanetary magnetic field (IMF) observations by ISEE 1 and IMP 8 were correlated to reveal the effects of upstream waves on IMF predictions. Past studies using spacecraft just out- side the Earth's bow shock and far upstream at the L1 libration point attributed frequently poor (_<0.5) correlation coefficients to short IMF scale lengths and difficulties in estimating time delays. We find that the correlation coefficients for two near-Earth spacecraft are actually worse than those for a spacecraft at the L1 point and one just outside the bow shock: 48% of the near-Earth correla- tion coefficients for the IMF magnitude are poor (<0.5), and only 17% are good (>0.8). We at- tribute the poor result to two causes: (1) high-frequency waves and diamagnetic effects in the fore- shock and (2) intervals of low IMF variance. Of these two, high-frequency waves account for 80% of the cases with poor correlation, and the intervals of nearly constant IMF account for the remain- ing 20% of the cases. While correlation coefficients do not increase with solar wind density while both spacecraft are in the solar wind, they do increase when one or both spacecraft lie within the foreshock. We argue that foreshock waves and intervals of low IMF variance must also have re- duced correlation coefficients in previous IMF correlation studies. While the significance of the foreshock waves on the solar wind input into the magnetosphere deserves further study, there is no obstacle to predicting solar wind input into the magnetosphere during intervals with poor correla- tion coefficients but low IMF variance.

1. Introduction

Abrupt variations in solar wind parameters like the interplanetary magnetic field (IMF) orientation or the solar wind dynamic pressure have frequently been invoked as potential triggers for a number of magnetospheric phenomena, including flux transfer events at the dayside magnetopause [e.g., Sibeck, 1990; Lockwood and Wild, 1993] and substorms in the magnetotail [e.g., Schieldge and Siscoe, 1970; Lyons et al., 1997]. To predict such events in advance, it will first be necessary to establish these relationships and then gain access to continuous solar wind observations.

Spacecraft located at the L1 libration point far upstream from Earth can provide near-continual solar wind coverage. However, previous studies have already shown that L1 observations are a poor predictor of conditions nearer to Earth. Russell et al. [ 1980] compared 64 s average of upstream ISEE 3 and near-Earth ISEE 1 IMF observations during a month and a half interval in mid-1978. Less than half of the data set was

usable, primarily because ISEE 1 entered the magnetosheath or magnetosphere, but also because some data were missing. During 20% of the intervals with data from both spacecraft, there was no clear maximum correlation coefficient at a single lag time. In the remaining 80% of the data set (152 three-hour intervals), peak correlation coefficients for the best lag time exceeded 0.85 some 25% of the time but were <0.52 some 25%

Copyright 2001 by the American Geophysical Union

Paper Number 2000JA000283. 0148-0227/01/2000JA000283 $09.00

of the time. Consequently, of the total data set with simultaneous observations by both spacecraft, correlation coefficients exceeded 0.85 some 20% of the time, whereas

meaningful correlation coefficients failed to exceed 0.5 some 40% of the time. Crooker et al. [1982] presented the results of a statistical study employing 400 two-hour intervals of simultaneous ISEE 3 and ISEE 1 64 s IMF observations in the

fall of 1978 and 1979. The correlation coefficients only exceeded 0.8 some 25 % of the time and were <0.5 some 25% of the time. Correlation coefficients increased as the distance

between the two spacecraft in the plane perpendicular to the Earth-Sun line decreased and as the IMF variance increased but

showed no clear dependence upon the solar wind velocity. Similar problems occur when plasma observations from the

L1 point are compared with those from the vicinity of Earth. Paularena et al. [1998] examined 397 six-hour segments of Wind, Interball 1 and IMP 8 solar wind flux observations during late 1995 and mid-1996 to show that correlation coefficients exceeded 0.8 only 43% of the time, but were <0.5 some 19% of the time. Correlation coefficients increased with

increasing solar .wind flux and increasing variability. Richardson et al. [1998] correlated 6-hour stretches of ISEE 3 and IMP 8 solar wind measurements from August 1978 to February 1980, each with a minimum of 50 one-min points, to show that average correlation coefficients are of the order of 0.6 but increase to 0.85 during periods of high solar wind density variations. By contrast, correlation coefficients decrease as the radial distance separating the two spacecraft increase.

Although Crooker et al. [1982] expressly noted that lack of significant variations in solar wind parameters might be a

18,599

18,600 KAYMAZ AND SIBECK: PORESHOCK EFFE•S

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X (Re) Figure 1. Locations of ISEE 1 (squares) and IMP 8 (circles) at the start of each 2-hour trajectory segment in the ecliptic plane. Predicted magnetopause [Roelof and Sibeck, 1993] and bow shock [Fairfield, 1971] locations are also shown for average solar wind parameters. Solid symbols show the times when spacecraft observe high-frequency waves.

cause for cases with poor correlations, past researchers generally interpreted these poor results as evidence for significant small-scale solar wind structure. If so, it might be best to use one or more monitors located just outside the Earth's subsolar bow shock to predict input into the magnetosphere. In this paper, we will correlate IMF observations by two near-Earth spacecraft. We will show that the principle factor reducing correlation is the presence of waves generated within the foreshock. Periods with a low IMF variance play a secondary role. Intervals in which significant variations in the IMF orientation occur on spatial scales comparable to those of the magnetospheric dimensions are very rare. We note a tendency for correlations within the foreshock to increase with increasing solar wind density and suggest that this occurs because periods of high solar wind pressure displace the foreshock earthward and the amplitudes of foreshock waves fall off exponentially with distance from the bow shock. Because all of the previous studies employed at least one spacecraft immediately outside the Earth's bow shock, we argue that waves (and corresponding diamagnetic effects) within the foreshock were a major factor causing poor correlations in these past studies.

2. Data Sets and Method

We present the results of a statistical study correlating IMP 8 and ISEE 1 IMF magnetic field observations from 1978 to 1981, a period which includes the time interval selected by

Crooker et al. [1982] for comparison of ISEE 3 and ISEE 1 and ISEE 2 observations. For this purpose, 4 years of ISEE 1 and IMP 8 magnetic field traces were scanned for solar wind intervals excluding magnetospheric and magnetosheath data. The 4 s time resolution ISEE 1 data and 15.36 s time resolution

IMP 8 data were then averaged/interpolated to 15 s for comparison. Using observations with 15 s time resolution should suffice to catch the effects of waves within the

foreshock, which typically have periods ranging from 20 to 100 s [Fairfield, 1969], as well as the more protracted diamagnetic effects' associated with entries into the foreshock [e.g., Wibberenz et al., 1985]. ISEE 2 observations were used to fill in the ISEE 1 data gaps. Because of its orbit, ISEE 1 only enters the solar wind from July to December each year, while IMP 8 makes solar wind observations throughout the year. We identified a total of 265 two-hour intervals of simultaneous IMF observations by both spacecraft from 1978 to 1981.

Figure 1 shows projections of the ISEE 1 (squares) and IMP 8 (circles) positions at the start of each 2-hour trajectory segment together with the locations of the magnetopause and bow shock for average solar wind parameters in geocentric solar ecliptic (GSE) coordinates, in which x points to the Sun, z points perpendicular to the ecliptic plane, and y completes the fight-handed coordinate system. Note that by comparison with the spacecraft employed in past studies, neither IMP 8 nor ISEE 1 ever moves far upstream, and consequently the results of this study will essentially pertain to spacecraft separations in

KAYMAZ AND SIBECK: I::OR•HOCK EI-,YF.,CTS 18,601

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Figure 2. Percentage distributions of IMP 8 and ISEE 1 correlation coefficients for (a) Bx, (b) By, (c) Bz, (d) total magnetic field strength, (e) hybrid, and (f) average correlation coefficients. Average correlation coefficient is given on the left of each panel.

18,602 KAYMAZ AND SIBECK: I:;O•H•K EFFECTS

the plane perpendicular to the Earth-Sun line. As such, they can serve as a baseline for studies that include the effect of

large separations along the Earth-Sun line. We calculated the cross-correlation coefficients for each of

the 265 cases using standard linear cross-correlation techniques. We shifted the data sets relative to each other to determine correlation coefficients for the full range of lag times and the full field values. Because them are data gaps, we required a minimum of 320 valid points (two-thirds coverage) to calculate a correlation coefficient at each lag time. We then determined the lag time at which the peak coefficients for each 2-hour interval occurred.

Since the magnitude and lag for the peak correlation coefficient vary by component, Crooker et al. [1982] devised a hybrid correlation coefficient representing the square root of the average of the squares of the correlation coefficients for each component. In addition to computing Crooker et al.'s

hybrid coefficient (rhyb=[(rx 2 + ry 2 + rz2)/411/2), Collier et al. [1998b] also calculated the average of the coefficients for each component. Here for easy comparison with the work of Crooker et al. [1982] and Collier et al. [1998b] we computed both the hybrid and. average correlation coefficients for each of the 265 intervals.

3. Correlation Results

3.1. Foreshock Effects

Figure 2 presents distributions of IMP 8 and ISEE 1 correlation coefficients for the total magnetic field strength and each component of the magnetic field. It also illustrates distributions for the hybrid and average correlation coefficients used in previous studies. The distributions indicate that there is a better chance of predicting variations in the B z component than the By component and a better chance of predicting the By component than the B x component. Since B z is the principle factor determining geomagnetic activity, this conclusion has considerable significance for substorm studies.

Table 1 compares results for our total field magnitude, hybrid, and average correlation coefficients (Figures 2d and 2e) with those obtained. by Craaker et al. [1982] and Collier et al. [1998b]. Despite the fact that we have employed two spacecraft separated by distances much less than those in previous studies, the fraction of our cases with good (_>0.8) hybrid correlation coefficients is even lower (12%) than that found in those previous studies. Similarly, the fraction of cases with poor (_<0.5) hybrid correlation coefficients (35%) in our study exceeds that of previous studies. Because this contradicts expectations, we will investigate the origin of the poor correlation cases in detail.

Perhaps the poor correlation cases occur during intervals of great separation between IMP 8 and ISEE 1. There has been much discussion in the literature concerning the significance of spacecraft separation distances perpendicular to the Earth- Sun line as a factor reducing IMF correlation coefficients. Lanzerotti [1989] reported an example in which two spacecraft separated by only 30 R E observed completely different IMF orientations. Borodkova et al. [1995], Sibeck and Korotova [1996], and Lyons et al. [1997] all argued that solar wind triggers for magnetospheric events can only be reliably detected by spacecraft within several tens of R E from the Earth- Sun line. Collier et al. [1998a] and Crooker et al. [1982] reported that the effects of spacecraft separation perpendicular to the Earth-Sun line become important beyond distances of 41 or 90 R E respectively.

Figure 3 presents our results for correlation coefficients as a function of the distance separating ISEE 1 and IMP 8 in the plane perpendicular to the Earth-Sun line. The solid line shows the linear least squares fit. The slope of the line and the goodness of fit (R) are given on the top right of each panel. In Figure 3, poor correlation coefficients occur even for short spacecraft separation distances, and there is only a very small tendency for the correlation coefficients to decrease with increasing distance. Clearly, separation distances in the y-z plane are not the main factor determining correlation coefficients, at least for the separation distances up to 50 R E considered here. We need to find some factor more specific to the near-Earth environment that can explain the poor correlation coefficients in our study.

We can learn much by inspecting several examples. At 2130 UT on August 21, 1979, ISEE 1 and IMP 8 were located at GSE (x, y, z ) = (14.5, 16.0, 1.9) and (-1.4, 36.5, 1.7) R E as indicated by the circles in Figure 4. The hourly averaged IMF

in GSE was (B x, By, Bz) = (-3.1, -0.6, -0.3) nT. The solar wind speed was 564 km/s and the density was 11.5 cm '3. Figure 5a presents the total magnitude of the magnetic field observed by ISEE 1 (top trace) and IMP 8 (bottom trace) for this interval. To avoid overlapping the two traces, the ISEE 1 total magnetic field strength has been displaced by 7 nT. Large amplitude high-frequency magnetic field fluctuations dominate both traces throughout the interval, indicating that both spacecraft were in the foreshock. The fluctuations were greater at ISEE 1, located nearer the bow shock. The correlation coefficient for

this 2-hour interval was poor, only 0.27. As already noted by Le and Russell [1990], correlation coefficients for low- frequency waves in the foreshock fall to 0.5 for separation distances as small as 1 R E.

By contrast, Figure 5b presents an interval in which the total magnetic field strengths exhibit good correlation. At 1330 UT on October 7, 1979, ISEE 1 and IMP 8 were located

near GSE (x, y, z) = (10.6, -5, 3.9) and (35.0, 7.4, 14.2) RE, as

Table 1. Comparison to Craaker et al. [1982] and Collier et al. [1998b] Correlation Coefficient Results

Study Total Cases Good(>0.8) Poor (<0.5)

Crooker et al. [1982] (rhyb) 800 189 (23.6%) 173 (21.6%) Collier et al. [1998b] (rhyb) 543 67 (12.3%) 127 (23.4%) This study (rhyb) 265 33 (12%) 93 (35%) This study (ray o) 265 26 (10%) 121 (46%) This study (rBm•g) 265 45 (17%) 128 (48%)

KAYMAZ AND SIBECK: FiORESHOCK EIq•'ECTS 18,603

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indicated by the squares in Figure 5. For this example, enhanced solar wind dynamic pressure moved the boundaries earthward of the nominal positions, thereby enabling both spacecraft to remain within the solar wind. ISEE 1 observed IMF features some 6 min later than IMP 8, and neither spacecraft observed high-frequency waves. The resulting peak correlation coefficient was 0.85. A comparison of Figures 5a and 5b suggests that correlation coefficients diminish greatly when one or both spacecraft enter the foreshock to observe high-frequency waves with amplitudes greater than those of any intrinsic solar wind variations.

By identifying intervals when high-frequency magnetic field fluctuations and/or energetic ion populations were observed at either spacecraft, we separated the 265 two-hour intervals into foreshock and nonforeshock categories. Solid symbols in Figure 1 indicate foreshock intervals. For an interval to be identified as foreshock, the spacecraft must have observed magnetic field fluctuations >0.5 nT lasting over 30 min during the 2-hour interval. ISEE 1 entered the foreshock during 143 of the 265 two-hour intervals (54%). IMP 8 entered the foreshock during 89 of the 265 two-hour intervals (34%). In general, ISEE 1 observed significantly greater wave amplitudes than

18,604 KAYMAZ AND SIBECK: FORF_,SHOCK EFFECTS

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Figure 4. Locations of ISEE 1 (open symbols) and IMP 8 (solid symbols) for the magnetic field traces in Figure 5 for August 21, 1979 (circles), October 7, 1979 (squares) and in Figure 8 for August 16, 1979 (triangles).

IMP 8. This is consistent with the fact that IMP 8 was generally further from the bow shock than ISEE 1/ISEE 2 and with past work indicating that energetic ion fluxes (and therefore wave amplitudes) fall off exponentially with distance from the bow shock [e.g., Lee, 1983; Trattner et al., 1994].

Figure 6a compares histograms of the correlation coefficients for each component of the IMF. Left panels in Figure 6a present histograms for foreshock events, while right panels show histograms for nonforeshock events. Consistent with our expectations, poor correlations are more likely in the foreshock than in the undisturbed solar wind. Once again, IMF B z is better correlated than IMF B,,, and IMF B,, is better correlated than IMF Bx, both inside al•d outside the f•reshock.

Both Figure 6b, which compares correlation coefficients for total field magnitudes, and Figure 6c, which presents histograms for hybrid and average correlation coefficients, provide clear evidence for a substantial foreshock effect. Table 2 summarizes the results for this comparison. Foreshock effects increase the fraction of cases with poor (_•0.5) correlation coefficients for all components, total field, and the hybrid and average correlation coefficients. The foreshock effects are particularly notable for the total field strength and average correlation coefficients.

The results in Figure 6 confirm our hypothesis that the presence or absence of foreshock waves is a major factor determining the IMF correlation coefficients in our study. If so, it should prove possible to retrieve the previously reported dependence of the correlation coefficient upon separation distance, but only for the cases outside the foreshock. Figures

7a and 7b compare the correlation coefficients for various magnetic field components versus the separation distance for the foreshock (Figure 7a) and nonforeshock cases (Figure 7b). Again the line gives the best fit to the data and the goodness of fit (R) is given on the top right of each panel. Both slopes and goodness of fit are greater for the nonforeshock cases than the foreshock cases. Both good and poor correlations occur at all distances in both categories.

Not all the cases with poor correlation coefficients occur within the foreshock. About 25% of the correlation

coefficients (25 cases) for the total magnetic field strengths in the nonforeshock cases (see Table 2) are <0.5. A reexamination of these intervals indicates that all of these

cases exhibited nearly constant magnetic field strengths and orientations at both spacecraft. Figure 8 presents an example of one of these cases in a format similar to that of Figure 5. The location of the spacecraft for this interval is given by triangles in Figure 4. The field strength shows no significant variation at either spacecraft for this interval and the correlation coefficient is low, 0.27. The average and the standard deviation Of the field at ISEE 1 are 5.6 nT and 0.09 nT

and are 5.5 nT and 0.15 nT for IMP 8. We suggest that sometimes the IMF remains so steady that only variations are noise-related, in which case it becomes impossible to establish any correlation between the observations at two spacecraft.

Crooker et al. [1982] noted that correlation coefficients increase with increasing IMF variability. To check whether it really is the case that a substantial fraction of our poor

KAYMAZ AND SIBECK: FORF3HOCK EFFECTS 18,605

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13.5 14 14.5 15 15.5 16

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Figure 5. (a) A 2-hour example of the trace of the total magnetic field strength on August 21, 1979, when high-frequency waves observed by both ISEE 1 and IMP 8 caused the correlation coefficients to be poor (r = 0.27). (b) A 2-hour example of trace of the total magnetic field strength on October 7, 1979, when the correlation coefficient was good (r = 0.85). During this interval, neither spacecraft observed high-frequency waves.

Table 2. Peak Correlation Coefficients for Foreshock and Nonforeshock Events

N=265 Foreshock Events, N=164, 62% Nonforeshock Events, N=101, 38%

Good (>-0.8) Poor (<0.5) Good (>-0.8) Poor (<0.5)

r•; x 21 (13%) 80 (49%) 27 (27%) 33 (33%) r•; 37 (23%) 51 (31%) 31 (31%) 21 (21%) r•, 18 (22%) 48 (29%) 42 (42%) 14 (14%) r•;mag 18 (11%) 103 (63%) '27 (27%) 25 (25%) rhy b 10 (6%) 74 (45%) 23 (23%) 19 (19%) ray • 10 (6%) 92 (56%) 20 (20%) 29 (29%)

18,606 KAYMAZ AND SIBECK: FE)RF•HOCK EFFECTS

3O

28

26

24

22

2O

18

16

14

12

10

8

6

30, 28

26- ,

24 ,

22 ,

20 ,

18

16 ,

14 ,

12 ß

lO ß

8 ß

6 ß

4 ß

2 ß

o -0.2

3o

28

26

24

22

2o

18

16

14

12

lO

8

6

4

2

o -0.2

' I ' I ' I ' I ' I '

Bx fshock (a) Mean = 0.52

0.0 0.2 0.4 0.6 0.8 1.0

rsx

' I ' I ' I ' I ' I ' ß

By fshock (b) ß

Mean = 0.60

0.2 0.4 0.6 0.8 1.0

rBy

' I ' I ' I ' I ' [ ' t Bz fshock (c) •

Mean = 0.60

_

0.0 0.2 0.4 0.6 0.8 1.0

rBz

3O

28

26

24

22

2O

18

16

14 ß

12 ß

lO ß

8 ß

6 ß

4 ß

2 ,

o -0.2

30

28

26

24

22

20

18

16

14

12

lO

8

6

4

2

o -0.2

' I

Bx '- Mean = 0.63 '_

'_

_

_

_

_

i I

nfshock

! ß I

(d)

0.2 0.4 0.6 0.8 1.0

rBx

' I ' I ' I ' I ' I '

- By nfshock (e) - - Mean = 0.66 - -- -

- -

- _

- , -

- -

- _

- _

-

- -

- _

-

0.0 0.2 0.4 0.6 0.8 1.0

rBy 3O

28

26

24

22

2O

18

16

14

12

10

8

6

4

2

0 -0.2

. ' I ' i ' I ' I ' I Bz nfshock f) - - Mean = 0.72 -

-- _

,- ,

.

-

.

-- _

ß

_ _

_ _

_ _

_ _

_

_

_

0.0 0.2 0.4 0.6 0.8 1.0

rbz

Figure 6a. Percentage distributions of IMP 8 and ISEE 1 correlation coefficients for components of the magnetic field (a and d) Bx, (b and e) By, and (c and f) B z when foreshock waves were present (left panels) and when foreshock waves were absent (right panels). The average correlation coefficient is given on the left of each panel.

30

• 28 • 26 i• 24 .-.q 22

: 20 o

& 18 • 16

ß 1

,_ 1 o

ß I ' I ' I ' I ' I

- Bmug fshock (a) - - Mean = 0.47 -

4 --

2 - -

0-

8-

6-

4 - -

2- [__q - 0 , -0.2 0.0 0.2 0.4 0.6 0.8 1.0

rBmag

28 Bmug 26 Mean = 0.65 24

22

20

18 - 16 - 14 - 12 - 10 - 8- 6- 4 -

I

I ' I ' I '

nfshock (b)

0.2 0.4 0.6 0.8 1

rBmag

Figure 6b. Percentage distributions of IMP 8 and ISEE 1 correlation coefficients for total magnetic field strength (a) when foreshock waves were present and (b) when foreshock waves were absent. Average correlation coefficient is given on the left of each panel..

o

i

o

o

30

28

26

24

22

2O .

18 .

16 ,

14 ß

12 ß

lO ß

8 ß

6 ß

4 =

2 ß

o -0.2

3o

28

26

24

22

2o

18

16

14

12

lO

8

6

4

' I ' I ' I ' I ' I '

rhyb fshock (a) Mean = 0.53

,

, I

0.0 0.2 0.4 0.6 0.8 1.0

rhyb -- ' I ' I ' I ' I ' I '

- rhyb nfshock (c) - - Mean = 0.65 -

_

_ -

_ -

_ -

_

_ -

ß

_

.

.

_

.

_

.

, I , 2

o -o.2

3o

28

26

24

22

2o

18

16

14 ß

12 .

lO ß

8 .

6 ß

4

0 -0.2

' I '

rave ,

Mean = 0.47

'_

'_

o.o 0.2

•o

,.8

,.6

,.4

•2

!o-

8

6

4

2

o

8

6

4

2

o -0.2

' I '

rave Mean = 0.61

I ' ! '

fshock (b) -

ß

ß

ß

0.4 0.6 0.8 1.0

rave

I

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6

rhyb rave

ß I ' I ' I

nfshock (d)

0.8 1.0

Figure 6c. Percentage distributions of IMP 8 and ISEE 1 correlation coefficients for (a and c) hybrid and (b and d) average correlation coefficients when foreshock waves were present (top panels) and when foreshock

1 waves were absent (bottom panels). Average corre,atien coefficient is given on the left of each panel.

18,608 KAYMAZ AND SIBECK: I::;O•H•K F_,I-'Y•S

60

rr50

•40

N

•-30

.9 20

e10

slope•=,-5,.6.5,, R=O. 10 ' ' ' I ' ' ' I ' ' ' I ..... ß

! ol Oo . ß

.............. ............. ½ .............. ..... o...i ...... o ....... .......... ' 0 0 o o• /o o• oo io% io øø iøøc• o o ø • 0 : : .

............................. ? .... 6 --a ..... ? ...... o ...... : ............... 4:• ...... •"-

o o o:. OOoiOOoo o • o • i •. i •o o:

o Ooo : : : : 0 ß .• o a•:o• o : o

.............. ; ........... •'•' .... •'S'":"'•"•'•' •g" ¾•;" • i -o ,• :- oo "7o ..... i o .: o : ci o• i • •oo ? o io o o

":":- ..... F ............ '.= ............. T"; .......... •'"; .... ?' ............... IsnocK • i o i o

:

ø-o''' .2 . rO.4 0.6 0.8 Bx

s, lope•=,-6,.2,5, R= 0.10 60 ...,'''•'''l ....

50 .............. : ............... : .......... •': .............. ? ............ • .... o ....... i i• o•io% o•io .% _ i øiøø i o •do o "P o'•

40 .............. :' ............... ; .............. * .......... •'"*'•-u "ø .... ,.-o, ......... [ i oi i •,o I -• •: o :1 I. : : o : :o Oo : o -I

! ! i•, •, !o o o 30[ .............. • ........... ."'-"'"'";:-- :•'"Y._+;:• ...... •?;: ........ I: i • øi o - o j • : ool

20F ............. i ........... o..::•.• .... <•.;•..•.o•.•.•:..•;.•.•...•

. . o .:o.o.:ooo.oO -I 10 ............. .• ............... ..:---* ........ .f .......... a--.f;; ............ ..'- ......... •fshock io i ø i o o i o ]

nr, , , i , , , i , , , i , , , i , , , i , , ,i :0.2 0 0.2 0.4 0.6 0.8 1

r By

slope= -9.96, R=0.19 60 ......... !,,-!,,,!,,,•

o o i • o i 50 ..... .o. ........................ • ............. • ............... .• .......... o...• ...... o.._]

• o i o oo' Oo o o i %.o _? o. • ' 0 0 ß 0•. 0 -- ,• ß v ! ! ! o _• e •!o o -I

40 ...... o ...... • ......... o .... ! ............... • ............... .•...W..• .... -.'... ........ -I ----.•_ e o i o i' • o•.oøo o]

i --•__: io o i, O?o"1 30 ......................... •"•'•_ ..... * ..... • .........

! o: . : o • o

2 0 .............. i ............. oO? o r o: i : ! o io o .- o -I

.............. i ............... i .... o ......... i .... .o..o. ..... •i ...... .o....o...o....: ..... .o..._1 10 _•_A. i i c•.o ø ø o ø od o.,f•"uu• i i i ,,,,, ,:• -0.2 0 0.2 rO.4 0.6 0.8 1

Bz

slope= -2.01, R= 0.03

i oo • • ø • :1 ............. : ............... : ............... • ..... o .... .• ............. .:. ...... .e.,-,- 1

i o_•, o•o •,,•o • : o :1 i o:oo ,5oo e _: : o : ::o_. o, :o o": : -I

............. : ............... .• ......... ':'• ......... •'"'.:'• ........... •"u ........

o :.o o•i oo '..,,•, ø.i, ø ............. , ............... i ......... .½.i..;,.o. ...... .,4...ø .......... ...-...o..O...=..

............ 7o o ;;-- !-•- o---:.--c"--'.•-- : o •o.: .o o j• o io o

............. • ............... i½,%<--%,-•.--.•:---•-,•,,---.•-; .... .-- i : o yoOo : : ! o o : o';, g :

............. i ......... o .... :...?..ø..ø...."...i ....... .o. ..... .•. ............. .:,,..o. .......... : % o .ø o

fshoc.i< oo i ø ! i o , ,,j,,, •.,. i,.. i.,, i,,.

0 O.E 1,0.4 0.• 0.8 1 Brnag

sIop•= -7.66)R= 0.11 • ø i i ' :0 : : '

50 ............................. : ............... • ...... • ..... '- ........ ø .... +• .......... i• o øo--i Ooo ! o • : oo •% _øo ! o _q .

: 'b o',' :o U• . 40 ............. i ............... i .............. • ...... • .... ".""•"'*'•+ .............

I: : o: oeo_ • •.oO i ' I" i ! ooi-o !o -• o io '

30 F- ............ ! ............. .-.;•....ø.•øo..•..... o. ......... .: .... •. ..... I: • io o ,• o - :..•-•'•• - r : : • o • _.'=' " :__oo .

a0 t. ............ i ............ •.•.,..._.,o..•.%.o...•.• ...... o.,...•.". .......... - I. i : 'ø'•'oi • o-•.oao• '• : o o -

: : o• o • ! - ' ' : 0 O' ' : : ß ß 0 0 O* '10 : : o_ oo: % •o :o ............. • ............... • ..... • ........ '• .............. •1•' ............. ': ..............

0 •' 0 f•hocl< Oo o i

00 , , , i , , , I , , , I , , , i , , . i , . , .• 0 0.2 0.4 0.• 0.8 1

slope=-103g, R= 0.17 ." " " I ' ' " I ' ' • I " " " I ' ' " I ' ' ' .

.....

: : !o : i 0 : 0 , : •0 ! : : *

............. • .............. • ........... •.• ..... o ....... • ....... o ..... •.e ..........

• •øøLø fi)%o øi øø oO • o ,,! .............. • ............... .:, ...... ø ....... .':o'•--o- .... ;--? ........ •,"6':.- .............

i oi o ooi_ i ,,o,,O ; 0 : 0 0 :u O--oV :0

............. •-----------•--.•-o, ..... •- ................ • .... • ....... • o • o -• o! i o i •o•- .•-•..• : •/•: 0 : : : O: 0 : v-- :

............. :: ............ : .............. • ....... ; .... • .......... -;;: ............. fshock !o o o i o ,,,i,,,i,,,•,,,i,,,i,,,

-t).2 0 0.2 0.4 0.6 0.8 r

ave

Figure 7a. Correlation coefficients for the components of the magnetic field as a function of spacecraft separation distance in the plane perpendicular to the Earth-Sun line when foreshock waves were presenL Slope and the goodness of the fit (R) are given on the top right of each panel.

correlation cases result from small fluctuations about nearly identical fields at both spacecraft, we divided our nonforeshock cases into two categories: those with correlation coefficients for the total magnitude of the field <0.5 and those >0.8. Figures 9a and 9b compare plots of the standard deviation versus correlation coefficient for nonforeshock cases with

good and bad correlation coefficients. The standard deviations for the cases with good correlation coefficients considerably exceed those for the cases with poor correlation coefficients.

Although the small perturbations about nearly constant field strengths may reduce correlation coefficients, the key parameter for predicting solar wind input into the

magnetosphere is the magnetic field orientation. We have therefore tested the nonforeshock poor correlation events for constant magnetic field direction by calculating the normalized sum of the dot products between the two time sequences of magnetic field vectors. The results shown in Figure 9c suggest that field orientations at the two spacecraft were generally similar. We therefore conclude that the poor correlation coefficients for these nonforeshock intervals result from very small measurement errors or fluctuations superimposed upon nearly identical magnetic fields. For completeness, Figure 9d illustrates the total product for nonforeshock good cases. Not surprisingly, most of the total dot products are again above

KAYMAZ AND SIBECK: PORF•HOCK E•'FECTS 18,609

slope= -10.26• R=0.20 60 ...... • ...... i,,,• ,,, .

(1) i o •5o ............................. -': ........................................................ C]) ' Oo øoø o'• ooi o " c- ............................. i ................. 8- oø $ i o o o. c•40

' '0 OC• 0 0 • ,i ,• o o.Jo cP •Oo•o__ .o • ..-'""-,Ea,.;•; o _'i •'" i o

.............. , .............. 1 ....... ! '•- • o io ! • o: ø 0 c- : : o • o Ooøi:' .o_ 2 0 .............. • ............... .'., ...... '6 ...... '..'.•"o'6'"oi ..... • ..... •'! ...... •-e-

ß . ,

c• ! i ! i ø !%o c). 1 0 .............. ! .............. -... ............................. .....•; ........... i ............. co nfshobk • :

0 ,,,i,,,i,,,i,,, i,,,i,,, -0.2 0 0.2 rO.4 0.6 0.8

Bx

6 0 slope= - 11.1 O, R=0.22 ' ' .... I ' ' ' I ' ' ' I ' ' ' I ' ' '

ß 50 .............................. i ........ • .... -" .............. ::-o ............ ..'- ............. • o i ø ø io ø o•iOoeo (-' ß : oo: • 40 .............................. • ............................. -- .............. : ..............

' i '"o-'"""' :-,,,.,g.E,..,•Oo o":• • .

>' 30 ............................ ½ ........................ : o "',•".." ......... ..•"'.-..:•- c- , :o ß :

ß - : . • oi% oøf : 0 ' ø

.9 20 .............. • ............... ... .............. -.. ....... .•. .... :: ........ .,•,•.•o

0.. • , : o oi o © 10 .............. i ............... i ............................. ..'- ...... ;; ...... T ............. c• nfshobk i i i o

ß .

0 ,,, I , , , i .... , , I ,, , I , ,, -0.2 0 0.2 rO.4 0.6 0.8 1

By

60 ...... •''' • ,slo, p,e•-!2;2,0, R?,O.!9

. . .............. ............... i ............... i ............... ............. .......... • i i io ooot o t) •40 .............. i ............... i ............... i ........ .o. ..... .... .............. .•.s. ....... ._q • - i • ••oOOi,•o oo_•ø_& o-I-• ,a. i ! - .-'?'"'-•L_•_ izcPe •o: ,,o 4 :•30 .............. : ............... , ....... o .... •: ............... !..• ...... ••! •-

._ o i _ • ol o

a i • :o •* :•o -1õ 0 : ! o-

a,,., ! • i • o •ooO ___j •

o• nfshoi:k i i ! i o • 0 , , , i , , , i , ,., i , , , i , , , i , , ,] -0.2 0 0.2 0.4 0.6 0.8 1

r Bz

60 . .• 5O

40

30

20

-1:).2 0 0.2 0.4 0.6 0.8 1

6.0

5.0

4.0

2,0

20

10

.Oo

o

o

o

o

o

o

D -0.2 0

i i i i i i

..................................................... •. ..... •. .............. • .............

• o•o iS o o :o ........................................................... ..•.....ø...o ..... 'Z .............

i'-o o•.' o

_ o.• o cl.'•o OSe O; :

................................................... •. .......... •..•.,•...•, ..... 0 • 0 0

............. , ............... : ............... • .......... .ø..4 ......... .ø..o..,.'..ø. ........... nfsho•k i o!

i " , , , I , ..... • • t I • t a I • •

.2 0 0.2 0.4 0.6 0.8 r hyb

slope=•-17.05, tR= 0.29 ' ' ' I ' ' ' I ' ' ' I ' ' ' ' ' ' ' ' '

............. i .............. i .................. • ..... ø'+ . : o : o o ø • i•o

.............. i ............. i ............... ........ .o. ..... ...... i; ............ i o

............. $ .............. $ .......... Z.$ .... :...o.. _,.'w•...,,,,,,,..9..: . : : ø :• o T '•.'"'• ..... • ! ! o i o :•'"'""-- i i io,, ø oøi o •%o

............. -.: .............. ? ................ • ....... •,...*..,• .... •..v..•...•, ..... : : 0 :0 0 : : : : : :

............. •, ............... • ............... .• ........ .o. .... , .... .o. .... .o.....:..o. ........... : : 0 :

ntshobk i i øi • , , i , , , i , , , ,,, i,,,I,,,

0.2 rO.4 0.6 0.8 ave

r Bmag

slope= -18.99, R= 0.27

Figure 7b. Total magnetic field strength, hybrid and average correlation coefficients as a function of spacecraft separation distance in the plane perpendicular to the Earth-Sun line when foreshock waves were absent. Slope and the goodness of the fit (R) are given on the top right of each panel.

0.8. We conclude that even though correlation coefficients coefficients depend upon solar wind densities or velocities may be low for some nonforeshock cases, the field [e.g., Chang and Nishida, 1973; Crookeret al., 1982]. orientations and strengths for these cases are very stable, As illustrated in Figure 1, the ISEE 1 apogee lies a short enabling easy prediction of the solar wind input into the distance outside the nominal position of the Earth's bow magnetosphere. shock. During periods of reduced solar wind dynamic pressure

the bow shock moves outward and the spacecraft may be 3.2. Solar Wind' Plasma Effects located immediately outside the bow shock and deep within in

We have already seen that the presence of the foreshock can the foreshock. Conversely, during periods of high solar wind greatly diminish correlation coefficients. In this section, we pressure the bow shock moves earthward and the ISEE 1 consider the possibility that the foreshock is at least partially spacecraft lies in the outer foreshock. Since suprathermal ion responsible for past reports indicating that correlation populations diminish exponentially with distance from the

18,610 KAYMAZ AND SIBECK: FE)RESHOCK EFFF•-TS

25

August il 6, 1979i . ß ß

20 ' ß ß

r •- 0.27 Bmag i

,•, .

I-- 1 5 ................................................................... • ........................................... c• •------.,,L'.•a._____;_"',--'-':----' ' _•-.-- •'-_:--• ¾_•

E • 10 .................................................................................................................. • .....................

•p 8 ,

,

......................................... :•..•2•;Z:• .................. ' .•[ ..................... 5 • • -•---- -••••-•

01 .... • .... I .... • ........ • , • • , 8 18.5 19 19.5 20 20.5 21

Time (hours) Figure 8. A 2-hou• example of the trace of the to•l magnetic field on August 16, 1979, when the co.elation wm poor (r = 0.27) and the magnetic fic]d traces at both spaccc•t wcm nc•ly consent.

nfshock, r _< 0.5 4 .... I''''1''''1 .... I''''1''''1''''

• mi Imp •j Mead = 0.•3 (a) o• ei Isee • Meari = 0.3,"1 •3 ß

E 3 ........................ i ................................................................

O :

ß

o 2 ........................ i .......................... • ......................... -..- ...........

1:1 ........................ ' ........... .. i ß ' ß ,

...,.. i i 8 i • i i i i , i i i i I i i

r Bmag

nfshock, r > 0.8

ß Ise• 1 Mear• = 0.79 ................. i ................. i .................. '• ................. f .......... •---

................ i ................. i .................. i ................. .'"', .............

................ .... : .... -""!'"; .... ' .... ........... '"' 0.75 0.8 0.85 0.9 0.95 1

r Bmag

1 nfshock, r_< 0.5

• ....... ' ........ ' .... ' .... "•'" 1 f .... ;• "•'.i ;' ........... ': ' ".d : 0.9

........................ 0.9i ............... -. ..... • ......... i.. s : - i ' • ";'i .......... ;;i ....... *'-- ! - ! "';i'"'""• ..... ? ................ • .

-o ß ."...'.:. .'.;- ........ • 0.8 ............... ,?_oo.8 ........................ i ....................... ,. .................. • ............ ....! ........... .. .... i .......... o .... • ................

QO.7 - 0.7 ............... -:' ................. i .................. • ................. •- ................

• Mean = 0j89 i i •- Mean = 0.91

........................ -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.75 0.8 0.85r r 0.9 0.95

Bmag Bmag

nfshock, r _> 0.8 .

Figure 9. (a and b) Standard deviations when there are no foreshock waves but the correlation coefficients were poor due to a stable IMF (nonforeshock poor cases, r <_ 0.5, left panels) and for the cases when both effects are not seen (nonforeshock good cases, r _> 0.8, right panels). Standard deviations of the magnetic field, ISEE i (solid symbols), and IMP 8 (open symbols), show the field variations at both spacecraft are small for nonforeshock poor cases as expected from the nearly constant fields. The average correlation coefficient is given on the left of each panel. (c and d) Total dot product results for nonforeshock poor and good cases. A dot product close to 1 means that the field orientation is nearly identical at both spacecraft. Again, the average correlation coefficient is given in each panel.

KAYMAZ AND SIBECK: FO•H• EFFF•q'S 18,611

60 ............... ,slo, p•,= ,7.0,4,,R•0:29 610

.-. 50 ß (a • 5;0 • 40 .• 4.0 '•3o • • 3;0 =: .... • 20•- ' ß ß ' '1 2:0

r- ß ß ß ß am m_ '1

...'.'.,.......' ,1 L ...... .4..---•.• {•1•. mqml _ a-"•'.m •'j•-• ß ß .I P ....... ..'._?•.•'•. "1•- ß ."• ß -I

0 ' ' 0

[] nfshock ß fshock ß ß ß i . . ß i ß ß ß i . ß . i ß ß ß i ß ß '

-0.2 0 0.2 0.4 0.6 0.8 1 r Bmag

slope = -46.75, R=O. 12

800 . . . , . . . , . . . , . . . , . . . , .(•). 80(: •700 •'700

• ß ,,' ß ß = E •'600 ß . ß _ • 600 •' _am ß ß ß m

0 ß ß m m lmm ß _ ß • 500 .. ß •. ß . .. •. 500

oo[- . _ I: ... .'%. dr• I. -. ;, .• :[• 0 I. mm.q•m nm• ß I1 -m •1 •-_• ß ß ß •- .! •o•b "'".;' •%." ß ..-.."..m% .."..{

out.,[ -. ß . ,r.'l, q, .m ] u3300 200m,.. i,.. m.,, m,,, I,,, , ,,, m 200

-0.2 0 0.2 0.4 0.6 0.8 I -0.2 .r

Bmag

-0.2 0 0.2 0.4 0.6 0.8 1 r Bmag

[] nfshock ß fshock ,

' ' ' i ß ß , i , ß ß i , , , i ß ß ß i ß , .

(d)

mm ß

ß "'m m ß ..,, .ø o , "• .

ß 13

ß ß m m •o ß ß ß ß ß ß mm m

• fro, .o .-

,..%.-.. ."" "•t '• %=",, -" •<. u c] jmm

mm •m•m m

I , ! m I , , , m , , , m , , ,

0.2 0.4 0.6 0.8 r Brnag

Figure 10. Correlation coefficients for all cases versus (a) the solar wind density, and (b) the solar wind velocity. Solid lines show linear fits in the variation. Slope and the goodness of fit (R) are given on the top right of both panels. Correlation coefficients for foreshock (solid squares), and nonforeshock (open squares) cases versus (c) the solar wind density, and (d) solar wind speed. It is clear that low correlation coefficients are associated with the low-speed, high-density solar wind, while the opposite is true for high correlations.

bow shock over scale lengths of ~3.3 R E [Trattner et al., 1994], even small changes in the solar wind dynamic pressure can substantially modulate foreshock wave amplitudes. Consequently, one. might expect correlation coefficients to diminish during periods of low solar wind density and increase during periods of high solar wind density. To test this hypothesis, Figures 10a and lob present the dependence of the correlation coefficients for the magnetic field magnitude upon the solar wind density and speed for all the cases in this study. The least squares fit shown as solid lines in Figures 10a and lob indicates that correlation coefficients increase slightly for the higher solar wind densities. As in previous figures, the goodness of fit (R) is given at the top right along with the slope of the linear fit. Although very weak, a slight increase in solar wind velocity at poor correlations is also evident in Figure 10e.

Figures 10c and 10d illustrate the dependence of the correlation coefficients for the total magnetic field strength upon the solar wind density and velocity separately for solar wind (open squares) and foreshock (solid squares) intervals. Foreshock cases predominate at low densities and low correlations and (to a lesser degree) at high solar wind velocities and low correlations. Figures 10e and 10d confh'm that entry into the foreshock is an important reason why

correlation coefficients diminish during periods of low solar wind density.

The histograms in Figure 11 and f illustrate more clearly the relationships between correlation coefficients, densities, velocities and dynamic pressures, inside and outside the foreshock. While histograms give the averaged values for the solar wind parameters in each correlation bin, the vertical bars show the standard errors. The clearest relationship is the one between density and correlation coefficient within the foreshock (Figure 1 la). The next clearest is the relationship between solar wind dynamic pressure and correlation coefficient in the foreshock (Figure 11c). In both cases the distributions are different and statistically significant at 71% for density and 98% for dynamic pressure. Both parameters increase with increasing correlation coefficient. Any relationship between density (or pressure) and correlation coefficient outside the foreshock is much less clear (Figures lid and 11f), and there are no clear relationships between velocity and correlation coefficient either inside or outside the foreshock. The observations are consistent with our

expectations for the foreshock's effect upon the correlation coefficients, namely that high densities/pressures move the bow shock and foreshock inward, away from the observing spacecraft, and thereby diminish effect on the correlations.

18,612 KAYMAZ AND SIBECK: FORESHOCK EFFECTS

26

24

22

•' 20

o 18

•>, 16 .m

• •4

c3 12

._c 10

'- 8

o o3 6

4

2

0 -0.2

ß I '

Foreshock .

.

_

- - _

I

i

0.0 0.2 0.4 0.6 0.8 1.0

Correlation Bins For Bmag

26

24

22

•" 20

o E 18

•16 • 14 C312

lO

4

2

0 -0.2

' I ' I

Nonforeshock

I

(d)

0.2 0.4 0.6 0.8

Correlation Bins For Bmag

550

525

.• 500

'• 475 v

•>, 450

o 425

'o 400

'- 375

o

O3 350

325

Foreshock (b)

300 I -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.0

Correlation Bins For Bmag

55O

525

,•, 500

'•475 v

•>,450 o

,425 • 400

• 375 o

O3 350

325

300 '• -0.2

ß I ' I

Nonforeshock

0.2

' I ' I ' I '

(e)

0.4 0.6 0.8 1.0

Correlation Bins For Bmag

6 6 • , , , , , , , , , , , 5 •' 5 nforeshock (f)

3 .e 3 g

• 2 • 2

0 O• • • -0.2 0.0 0.2 0.4 0.6 0.8 1.0 -0.2 0.0 0.2 0.4 0.6 0ø8 1.0

Correlation Bins For Bmag Correlation Bins For Bmag

Figure 11. Histograms of average (a and d) solar wind density, (b and e) velocity and (e and f) solar wind dynamic pressure binned over correlation coefficients for foreshock (left panels) and nonforeshock (right panels) cases. Bars show standard errors at each bin.

KAYMAZ AND SIBECK: FORESHOCK EI•YECFS 18,613

4. Conclusions

We correlated IMF observations by two near Earth spacecraft to provide a baseline for past and future studies that correlated observations by a spacecraft far upstream with those by a spacecraft located immediately outside the Earth's bow shock. To our surprise, we obtained a lower occurrence rate for good correlation coefficients (17%) and a higher occurrence rate for poor correlation coefficients (48%) than in previous studies.

Of the 128 cases exhibiting poor correlation coefficients for the total magnetic field strength, high-frequency foreshock waves were present in 103 cases and the IMF strength and direction were nearly constant in 25 cases. The foreshock waves introduce strong local variations that cannot be observed by both .solar wind monitors and greatly reduce correlation coefficients. By contrast, during periods of nearly constant solar wind magnitude and orientation, only noise variations are present, and these also greatly reduce correlation coefficients. We suggested that similar phenomena account for the poor correlation coefficients obtained by past studies that employed observations by spacecraft in near-Earth orbits.

Because the foreshock perturbations may greatly modify solar wind parameters shortly before their encounter with the Earth's magnetosphere, they may pose a serious problem for studies that seek to relate transient magnetospheric phenomena to solar wind features. By contrast, although correlation coefficients are frequently very low for intervals of nearly constant IMF strength and orientation, the fact that the IMF parameters are nearly constant means the input into the magnetosphere can be accurately predicted.

As in past studies, we noted that correlation coefficients decrease during periods of diminished solar wind density and enhanced solar wind velocity. The bow shock waves move outward during periods of low solar wind density, enhancing the likelihood that one or both near-Earth solar wind monitors

will enter the foreshock and correlation coefficients will decrease.

Finally, we noted a tendency for correlation coefficients for the B z component to exceed those for either of the other two components. At least in the case of the events seen within or near the foreshock we suppose that this is because significant fluctuations in the B z component preferentially cause near- Earth equatorial monitors to exit the foreshock by disconnecting them from the bow shock. Consider the case of an equatorial spacecraft located outside the dawn or dusk bow shock. Almost all ecliptic IMF orientations connect the spacecraft to the bow shock, whose dimensions extend from x=+15 R E to _oo. By contrast, not all meridional IMF orientations connect the spacecraft to the bow shock, whose dimensions only extend from z=-25 to +25 R E As a result, large B z variations more effectively disconnect equatorial spacecraft from the bow shock, thereby removing wave interference and enhancing correlations.

Acknowledgments. This research was supported by NASA grants NAG5-4679, NAG5-7920 and NSF grant ATM-98190707. IMP 8 and ISEE 1 interplanetary magnetic field data were obtained from the NSSDC and IGPP-UCLA respective web sites. We thank the PIs of both magnetometers (R. P. Lepping and C. T. Russell) for making their data public. Z. Kaymaz would like to acknowledge her university for granting her leave of absence at JI-IU APL to perform the study.

Janet G. Luhmann thanks Charles W. Smith and another referee for

their assistance in evaluating this paper.

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Z. Kaymaz, Faculty of Aeronautics and Astronautics, Istanbul Technical University, Ayazaga Kampiisii, Maslak, 80626, Istanbul, Turkey. (zerefsan@itu.edu.tr)

D.G. Sibeck, Applied Physics Laboratory, Johns Hopkins University, 11100 Johns Hopkins Road, Laurel, MD 20723. (david.sibeck@j huapl. edu)

(Received July 17, 2000; revised February 27, 2001; accepted February 27, 2001.)