Artificial neural network model of the dayside magnetopause: Physical consequences

Phys. Chem. Earth (C),

Pergamon

Vol. 25, No. 1-2, pp. 169-172,200O Q 1999 Elsevier Science Ltd All rights reserved 1464-1917/00/$- see front matter

PII: S1464-1917(99)00063-X

Artificial Neural Consequences

Network

Model

of the Dayside

Magnetopause:

Physical

A. V. Dmitriev and A. V. Suvorova Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119899, Moscow, Russia Received

28 August

1998; revised 26 January

1999; accepted

magnetopause position R at the dayside should depend on P’“. Empirical studies showed that B, IMF component is one of more parameters besides P that controls the dayside MP, and influences of the other SW and IMF parameters are negligible or still unclear. The problem of quantitative description of the B, dependence was solved in empirical modeling performed with different approaches. From the other hand, it is well known that the By component influences on some phenomena in the high latitude ionosphere such as the cusp location (e.g., Candidi et al., 1989). In this connection the role of By in the MP problem is studied with ANN modeling. The other question is the real MP shape. Recent investigation of Kuznetsov and Suvorova (1997,1998a) has showed a “dawn-dusk” asymmetry of dayside MP shape under strongly disturbed solar wind conditions: B,<-7 nT (P-4-6 nPa) or P>15 nPa (B>O nT). Origin of this phenomenon is not clear yet. ANN modeling is excellent possibility not only to test this result by alternative method but reconstruct the real MP shape. In the present work we discuss some consequences of the dayside magnetopause ANN model (Dmitriev et al., 1998) that solve the problems described above. The dayside MP distance to the Earth R is presented in the model as a function of five parameters: latitude ;1, longitude Q,in GSE coordinate system, By and B, IMF (GSM) and SW dynamic pressure P. MP shape is modeled in 3D space with mirror symmetry relatively to the equatorial plane through the data deficiency in the southern hemisphere. ANN model code is presented on htto://alDha.nui.msu.su/-alla.

Abstract. Empirical model of the dayside magnetopause developed by means of Artificial Neural Network (ANN) package ‘NeuroShell2’ is discussed. ANN model describes 3D shape of the magnetopause as a function of four external parameters: solar wind velocity, density, B,, and B, components of interplanetary magnetic field. The model shows that the magnetopause shape has the dawn-dusk asymmetry under any solar wind conditions independently on the By direction. The cusp region is modeled. Using ANN model an expression for subsolar point distance is obtained in terms of modified logistic functions. The magnetopause dynamics is interpreted as a transition between two regimes of the magnetopause formation that is controlled by B, component of interplanetary magnetic field. 0 1999 Elsevier Science Ltd. All rights reserved.

1

Introduction

The common characteristics of the magnetopause (MP) models developed last years (Roelof and Sibeck, 1993; Shue et al., 1997; Kunetsov and Suvorova, 1998b) are following: 1) an axial symmetrical magnetopause surface (2D) with apriory defined shape; 2) only two external parameters P and B,; 3) pressure balance equation is used as initial dependence on external parameters. These restrictions are due to regression method applying to the fitting procedure in the models. Recently presented Artificial Neural Network model of the dayside magnetopause (Dmitriev et al., 1998) is free from these restrictions. The model was developed without any aprior assumption about the MP shape and kind of its dependence on external solar wind (SW) and interplanetary magnetic field (IMF) conditions. According to the pressure balance between the SW and the geomagnetic field (Chapman and Ferraro,193 1) the Correspondence

12 April 1999

2

Magnetopause Shape

Results of the dayside MP shape model calculations for the various SW and IMF conditions are presented in Fig. 1, where left panels correspond to meridian cross-sections, and right panels correspond to equatorial cross-sections in the GSE coordinate system. As expected the MP distance R

to: A.V. Dmitriev 169

170

A. V. Dmitriev and A. V. Suvorova: Artificial Neuron Network Model

a

-15jd....~....""' lb

X (RE)

1

C

Fig. 1. Numerical ANN magnetopause surface model in solar-ecliptics coordinate system (GSE). Left panels are magnetopause sections in meridian plane (XT); right panels are magnetopause sections in ecliptic plane (XY).The model is computed for a) Ey=O,&=O, P=l, 2,5, 10,20; b) B,,=O,p=2, &=5,0, -5, 10, -15; c)P=lO, &=lO, 4=20, lO,O, -10, -20.

171

A. V. Dmitriev and A. V. Suvorova: Artificial Neuron Network Model

decreases with increasing of SW dynamic pressure P (Fig. la) and with decreasing of B, IMF component (Fig. lb). One can see that MP size in the equatorial plane is larger than in the meridian plane under the same external conditions. This result agrees with previous studies (Sibeck et al., 1991; Kuznetsov et al., 1992). On the meridian sections (the left panels in Fig.1) it is clearly seen “dimples” at latitudes ht45”, that may be associated with magnetic cusp regions. Near equator plane Z=O the MP became some concave at B,<-10 nT (left panel in Fig. lb). We interpret this feature as magnetospheric magnetic field erosion in subsolar region under the strong negative B, (Rufenach et al., 1989). The strong deformations of the MP shape are clearly seen in the equatorial section (the right panels in Fig.1): the shape is asymmetrical relatively X-axis under any SW and IMF conditions. The bow point is shifted relatively X-axis toward the negative Y direction (prenoon sector) at about 5”

that is in order of aberration angle. Under any SW conditions the magnetopause size at X=0 for DO is larger than for Y
SW and IMF parameters. Using ANN model we have calculated the dependencies R,,(p) for different values of B, in the range -20+20 nT and for two values of B,, (0 and 20 nT), that has a good agreement with the power law (Eq.(2)) under any conditions. The coefficients a and b for each value of B, and By are determined by simple power fitting and presented in Fig.2. Model dependencies a(B,) and b(B,) can be approximated by modified logistic function: (3), y(x)= r,+l+exp{;(x-y)j where variables Y0and c1 were estimated as asymptotic of the functions a(B,) and b(B,). The coefficients l3 and y in Eq. (3) are determined by fitting procedure. The results of approximations of ANN model calculations for By=0 nT and By=20 nT are also shown in Fig.2. As result we have obtained the following representations of the Eq.(2) for By=0 and By=20 nT respectively: 4.7 R $8 = i 12.2-

1+

,0.32(&+5.4)

- 0.17 .P

5.2

3

B, IMF Component Influence

R,, = 124-

allows firstly estimate the role of the By IMF component in the MP dynamics. As we can see in Fig. lc the MP distance R decreases slightly with increasing absolute value of the By IMF component. We present the direct dependence on By extracted from the model code: ANN modeling

~(~JJyJz,~)

= F(;1,~,Bz,P).exP{f(jZ,q,By,P)}

f(lE,~,&,P)=45.1~&(1-q~*/4050)(1.55P”~-2.37)+

(1)

+2.3~By2~(l-~2/4O5O)(1.55P”4-2.37)-By3~(/22/311-7.5)/1O. where F(A, (0, Bz, P) is a complex nonlinear function of ,l, # Bz, P only.

Note, only square values of the angle coordinates d and Q, are in Eq.(l). Therefore B,, direction can not be a cause of the MP ‘dawn-dusk’ asymmetry. The influence of B,, IMF component is increased with the SW dynamic pressure P. Thus, the results of the ANN modeling agree with and complete the previous investigations (Kuznetsov and Suvorova, 1998a,b): the degree of the asymmetry increases with P increasing or B, decreasing and it does not relate with sign of By

1

+,0.32@+5.0)

0.12 I+e03’(8T+‘.l)

- 0.19 .P

@a) 0.12 ,+ea32.@z+49)

(4b)

It is clearly seen in Fig. 2 that three regimes correspond to Rss dependence on B,: the first one is a regime of positive B,O nT, the second one is an intermediate (-lO
4

Pressure Balance at Subsolar Point

Let us consider the pressure balance equation at the subsolar point in the common form: R,,(P)

= a. P-’

m

where it is assumed that the magnetic field value B,, at the subsolar point has a power dependence on the MP distance &,, and coefficients a and b are considered as functions of

second regime R,, depends both on P and BP In the third regime the dependence R,(BJ has a tendency of disappearing, and then R, = 7.5. p-W, i.e. the dependence of R,, on the SW dynamic pressure becomes weaker. Therefore we obtain more strong Bss(Rss) dependence: B S-R,:, lo. Such dependence is connected probably with formation of additional magnetic field sources on the MP surface.

172

A. V. Dmitriev and A. V. Suvorova: Artificial Neuron Network Model

0.20

5

3D dayside magnetopause ANN model well describes the following main features of the MP: the cusp region, errosion “dimple” near equator plane at B,<-10 nT, ‘dawndusk’ asymmetry under any SW and IMF condition. The asymmetry does not associate with IMF component along Y-axis. The contribution of By IMF influence on the magnetopause dynamics increases with SW dynamic pressure. The common pressure balance equation is obtained with coefficients in the form of modified logistic functions of B,. Three regimes of magnetopause dynamics are controlled by B, IMF component.

E 0.15 a

Conclusions

1 I0.10 t I-

,ppr. By=

nT

Acknowledgements. We thank Dr. J.King and others of Goddard Space Flight Center for maintaining the OMNI on line database of solar wind parameters. We thank Prof. LG. Persiantsev, S.A. Dolenko, Yu.V. Grlov and Ju.S. Shugai for helpful comments and suggestions in practical aspects of ANN usage.

;y=O nT

D nl n-r

-20

-15

-10

-5

0 5 Bz (nT)

10

15

20

Fig. 2. Coefftcients a (lower panel) and b (upper panel) of Eq.(2) versus & for By=0 nT (circles) and 8,=20 nT (triangles). Approximation of the dependences a(BJ and b(BJ by modified logistic fimction for By=0 nT (solid line) and for 8,=20 nT (dashed line).

References Candidi,M., Mastrantonio,G., Men&C.-I., et al., Evidence of the influence of the azimuthal component on polar cusp configuration, J. Geophys. Res., 94, AlO, 13585-13598,1989.

Chapman&

and Ferraro,V.C.A., A new theory of magnetic storms,

Terrest. Mug. Atmosph. Elec., 36,77-97,

1931. Dmitriev,A.V., Orlov,Yu.V., Persiantsev,I.G., and Suvorova_A.V., Artificial neural network 3D model of the dayside magnetopause, accepted for publ. in Geomagnetizm i Aeronomia, 1998. Kuznetsov,S.N., Zastenker,G.N., and Suvorova,A.V., Correlation between interplanetary conditions and the dayside magnetopause, Cosm.Res. (USA) 30, N6,466-471,1992.

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and

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shape

near

geosynchronous orbit, Geomagnetizm i Aeronomia, 37, N3, l-l 1,1997. Kunetsov,S.N. and Suvorova,A.V., Solar wind magnetic field and plasma during magnetopause crossings at geosynchronous orbit, Adv. Space Rex, 22, Nol, 63-66, 1998a.

Kuznetsov,S.N.

and Suvorova,A.V.,

An empirical

model of the

magnetopause for broad ranges of solar wind pressure and Bz IMF, In: Polar

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by J.Moen, A.Egeland,

M.Lockwood, Khtwer Academic Publishers, Dordrecht, 51-61,1998b. Roe.lof,E.C. and Sibeck,D.G., The magnetopause shape as a bivariate function of IMF Bz and solar wind dynamic pressure, J. Geophys. Res., 98,21421-21450, 1993. Rufenach,C.L., Martin,R.F.,Jr., and Sauer,H.H., A study of geosynchronous magnetopause crossings, J.Geoplys. Res. 94, 15125, 1989. Shue,J.-H., Chao,J.K., Fu,H.C., et al., A new functional form to study the solar wind control of the magnetopause size and shape, J.Geoplys. Rex, IO2,9497-9511,1997.

Fig. 3. The calculations of subsolar point distance (in the Earth’s radii) as a function of P and & component by using Eq (4a) for By=0nT (solid lines) and Eq(4b) for 8,=20 nT (dashed lines).

Sibeck,D.G., Lopez,R.E., and Roelof,E.C., Solar wind control of the magnetopause shape, location, and motion, J.Geophys.Res., 96, 54895495,199l.