The description of the model (PDF, 126K).

Paraboloid model represents the magnetic fields in the Earth's magnetosphere as a superposition of the ring current B_r, of the tail current including the closure currents on the magnetopause B_t, of the Region 1 field-aligned currents B_fac, of the magnetopause currents screening the dipole field B_sd and of the magnetopause currents screening the ring current B_sr:

B_m = B_sd(ψ, R₁) + B_t(ψ, R₁, R₂, Φ_∞) + B_r(ψ, b_r) + B_sr(ψ, R₁, b) + B_fac(I_||) (1)

The mathematical description of the model is published in [Alexeev et al., 2003]. The model is not connected with some database which imposes the limitations on the model’s region of validity, so it can describe the magnetic field during quiet as well as disturbed and extremely disturbed periods. The storm-time dynamics of the magnetosphere is represented as temporal variations of the large-scale current systems.

The model input are key parameters of the magnetospheric current systems, which represent their location and intensity:

• the geomagnetic dipole tilt angle ψ;
• the magnetopause stand-off distance R₁;
• the distance to the inner edge of the tail current sheet R₂;
• the magnetic flux through the tail lobes Φ_pc;
• the ring current magnetic field at the Earth's center b_r;
• the maximum intensity of the field-aligned current I_||

The magnetic field structure in the noon-midnight magnetosphere cross-section on Jan 9, 1997, UT=12:00 and Jan 10, 1997, UT=10:00.

The solar wind driving of the magnetospheric magnetic field is realized through the dependence of the model parameters on empirical data (solar wind plasma parameters, IMF, AL and Dst). The model input parameters can be calculated using so-called submodels (see [Alexeev et al., 1996; Alexeev et al., 2003]). Submodels, can be changed while the magnetic filed calculated by the model remains to be satisfying the boundary conditions. Such three-level structure of the model (data – parameters – magnetic field) allows flexible taking into account the data availability changing the “data-parameters” calculation scheme (changing the submodels).

Example: Quiet Conditions (txt = 100M, Netcdf = 21M)

• 2008-09-10 12h txt Netcdf
• 2010-09-25 01h txt Netcdf

Magnetic storm Nov, 19-21 2003

2003-11-19 23h txt   Netcdf 2003-11-20 12h txt   Netcdf 2003-11-20 17h txt   Netcdf 2003-11-20 21h txt   Netcdf 2003-11-21 00h txt   Netcdf 2003-11-21 21h txt   Netcdf 2003-11 gzipped - 56M, ungzipped 600M

Magnetic storm Aug, 23-25 2005

2005-08-23 18h txt   Netcdf 2005-08-24 06h txt   Netcdf 2005-08-24 10h txt   Netcdf 2005-08-24 11h txt   Netcdf 2005-08-24 19h txt   Netcdf 2005-08-25 15h txt   Netcdf 2005-08 gzipped - 57M, ungzipped 600M

Magnetic storm Mar, 6-11 2012

2012-03-06 10h txt   Netcdf 2012-03-08 11h txt   Netcdf 2012-03-09 03h txt   Netcdf 2012-03-09 08h txt   Netcdf 2012-03-10 12h txt   Netcdf 2012-03-11 12h txt   Netcdf 2012-03 gzipped - 61M, ungzipped 600M

The description of the model (PDF, 126K).

A2000: DYNAMIC PARABOLOID MODEL OF THE EARTH'S MAGNETOSPHERE

(March, 2000; June, 2002)

PREFACE

Dynamic paraboloid model (A2000) allows to calculate the variations of magnetic field of each magnetospheric large scale current systems by empirical data during quite and disturbed periods. Simple submodels are used to calculate the A2000 paraboloid model input parameters via empirical data. Separate sources of the magnetospheric magnetic field can be "switched" on and off. The IMF penetrated into the magnetosphere as well as field-aligned currents magnetic field are included in the total magnetospheric magnetic field.

1. PROGRAM USAGE

call a2000(ut,iy,mo,id,ro,v,bimf,dst,al,x,bm,bb)

INPUT PARAMETERS:
x0(3) - point where the magnetic field is being calculated, in GSM coordinates, Re;
ut - Universal Time (hours);
iy - year;
mo - month;
id - day in month;
ro, V - solar wind density and velocity, cm^-3, km/s.
bimf - IMF's GSM-components, nT.
dst - Dst index, nT;
al - AL index, nT.

OUTPUT PARAMETERS:
bm(3) - magnetic field components in GSM coordinates, nT;
bb(7,3) - magnetospheric current system contributions to bm(3).
bb(1,i) - geomagnetic dipole magnetic field;
bb(2,i) - ring current magnetic field;
bb(3,i) - geomagnetic tail currents magnetic field;
bb(4,i) - magnetic field of CF currents shielding dipole;
bb(5,i) - magnetic field of CF currents shielding ring current;
bb(6,i) - magnetic field of Region 1 FAC;
bb(7,i) - IMF penetrated into the magnetosphere.

2. DESCRIPTION OF SOME PROGRAMS

There are a set of the model input parameters controlling the large scale current systems geometry and intensities. They may be defined by empirical data via submodels (subroutine SUBMOD). Subroutine a_field allows to calculate the magnetic field in the magnetosphere by the model input parameters.

2.1. a_field
Calculation of the magnetic field in the magnetosphere by the model input parameters.

call a_field(x0,par,bm,bb)

INPUT PARAMETERS:
x0(3) - point where the magnetic field is being calculated, in GSM coordinates, Re;
par(1-10) - model input parameters:
par(1) - geomagnetic dipole tilt angle, degrees;
par(2) - dipole magnetic field at equator, nT;
par(3) - magnetic flux through the tail lobes, Wb;
par(4) - maximum ring current intensity, nT;
par(5) - the total current of Region 1 FAC, MA;
par(6) - magnetopause stand-off distance, Re;
par(7) - distance to the inner edge of geotail current sheet, Re;
par(8-10) - IMF components in GSM coord., nT.

OUTPUT PARAMETERS:
magnetic field components at the point x0(3) in GSM coordinates:
bm(3), bb(7,3) are the same as in a2000.

WARNING: Because of the paraboloid coordinates singularity, avoid magnetic field calculations at the Ox axis.

2.2. trans
Program calculating the geomagnetic dipole tilt angle and the transition matrix between GSM and geographic coordinates.

call trans(UT,iday,PSI,BD)

INPUT PARAMETERS:
UT - universal time, hours;
iday - day of year.

OUTPUT PARAMETERS:
PSI is the geomagnetic dipole tilt angle, degrees;
BD is the geomagnetic dipole magnetic field at the Earth's equator.

NOTE: The transition matrix G2GSM(3,3) is stored in CONNON BLOCK /TRAN/.

2.3. IDD
Calculation of the day index in a year.

x=IDD(iy,mo,id)

INPUT PARAMETERS:
iy - year;
mo - month;
id - day of month.

OUTPUT PARAMETER:
day of year.

2.4. PERE2
Transition of vector A into vector B by T for k>0 (B=T*A) or T^{-1} matices for k<=0 (B=T^{-1}*A).

pere2(A,B,T,k)

2.5. SUBMOD(ut,iy,mo,id,ro,v,bimf,dst,al,par)
Calculation of the paraboloid model input parameters by empiric data.

call submod(ut,iy,mo,id,ro,v,bimf,dst,al,par)

INPUT PARAMETERS:
Model input parameters are described in Sec.1.

OUTPUT PARAMETERS:
Model output parameters are described in Sec. 2.1.

2.6. SMtoGSM
Calculates the transition matrix from SM coordinates to GSM ones.

call SMtoGSM(CPSI,SPSI,SM2GSM)

INPUT PARAMETERS:
CPSI - cosine of the dipole tilt angle;
SPSI - sine of the dipole tilt angle.

OUTPUT PARAMETERS:
SM2GSM(3,3) - transition matrix from SM coordinates to GSM one: VectGSM=(SM2GSM)*VectSM.

2.7. PSTATUS
Determination of the parameters providing the model tuning (Large-scale magnetospheric magnetic field sources switch on/off).

call PSTATUS(X1,X2,X3,X4,X5,X6,X7)

INPUT PARAMETERS:
x1=0/1 - dipole field on/off;
x2=0/1 - RC field on/off;
x3=0/1 - tail current field on/off;
x4=0/1 - dipole shielding field on/off;
x5=0/1 - RC shielding field IMF on/off;
x6=0/1 - Region 1 FAC field on/off;
x7=0/1 - IMF on/off.

2.8. DIPGARM
Calculation of the first three Gaussian coefficients of the internal magnetic field for the given year (year>=1900). Last values are for 1995.

call dipgarm(iyear, gauss)

INPUT PARAMETERS:
iyear - year.

OUTPUT PARAMETERS:
gauss(3) - the first three Gaussian coefficients of internal magnetic field.

3. MODEL LIMITATIONS AND PECULARITIES

1. Because of the paraboloid coordinates singularity, avoid magnetic field calculations at the Ox axis and magnetic field line calculations on the y=0 plane.
2. The magnetic fields of Region 2 field-aligned currents and partial ring current are not yet taken into account.
3. Despite taking into account the IMF penetrated inside the magnetosphere, the magnetosheath magnetic field is not considered.
4. You can change submodels in A2000 to calculate input parameters on your own manner.

4. HOW TO CHANGE SUBMODELS?

The magnetospheric model parameters are calculated from a set of data measured in the Earth's environment. The necessary set of data should include data on the solar wind and IMF, as well as the values characterizing a disturbed magnetosphere. The relationships between the model parameters and experimental data are described by submodels. Calculation techniques for the model parameters are presented in the subroutine SUBMOD. The submodels presented enable calculation of the parameters of the magnetospheric current systems and, consequently, the magnetospheric dynamics with known parameters of the solar wind, the total energy of ring current particles, the polar oval dimensions and AL-index of auroral perturbation.

1. Take the subroutine SUBMOD. You can find the commented blocks for all the model input parameters.
2. Replace the needed block.
3. Relace SUBMOD in the model with the new SUBMOD.
4. ATTENTION: YOU CAN DO IT ONLY ON YOUR OWN RISK!

5. FIXED BUGS and SMALL PROGRAM CORRECTIONS

1. 19 June 2002. The error in Fortran codes arising during calculations in the near vicinity of OX axis was found and fixed.
2. 27 June 2002. The default value for the ring current maximum location was chosen to be equal to 4 Re.
3. 8 July 2002. Inaccurate description of PAR(5) parameter was corrected in program comments and in this file as well.

6. BIBLIOGRAPHY

1. Alexeev I.I. Regular magnetic field in the Earth's magnetosphere // Geom. and aeron. 1978. V.18. P.656.(in Russian).
2. Alexeev I.I., Kalegaev V.V., Feldstein Ya. I. Modelling the magnetic field in strongly excited magnetosphere // Geom. and aeron. 1992. V.32. P.8.(in Russian).
3. Alexeev I. I., Belenkaya E. S., Kalegaev V. V., Feldstein Ya. I, Grafe A. Magnetic Storms and Magnetospheric Currents // J. Geophys. Res. 1996. V.101. P.7737.
4. Alexeev, I. I. and V. V. Kalegaev, Magnetic field and the plasma flow structure near the magnetopause // J. Geophys. Res. 1995. V. 100. P.19267.
5. Alexeev I.I., Kalegaev V.V., Belenkaya E.S., Bobrovnikov S.Yu., Feldstein Ya.I., Gromova L.I. // J. Geophys. Res., 2001, V.106, No A11, P. 25,683-25,694.

7. GENERAL INFORMATION

If you have some questions and comments on the dynamic paraboloid model or related software, please address

I.I.Alexeev (Paraboloid model of the magnetosphere)
Tel.: (095) 939-1036, E-mail: alexeev@dec1.npi.msu.su

V.V.Kalegaev (Software support)
Tel.: (095) 939-1915, E-mail: klg@dec1.npi.msu.su

Address:
Institute of Nuclear Physics,
Moscow State University,
Moscow 119992,
Russian Federation

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