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c
c
c ##########################################################################
c # #
c # GEOPACK-2008_dp #
c # (MAIN SET OF FORTRAN CODES) #
c # (double-precision version of 03/21/08) #
C # #
c ##########################################################################
C
c------- Licensing information: ------------------------------------------------------------
c
c Copyright 1979, 1986, 1996, 2003, 2005, 2008 Nikolai Tsyganenko
c
c This package containing 20 Fortran subroutines is free software: you can redistribute it
c and/or modify it under the terms of the GNU General Public License as published by the Free
c Software Foundation, either version 3 of the License, or any later version.
c
c This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
c without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
c See GNU General Public License for more details.
c
c A copy of the GNU General Public License can be found at .
c
c Copyright 1979, 1986, 1996, 2005, 2008, Nikolai Tsyganenko
c This program is free software: you can redistribute it and/or modify it under the terms of
c the GNU General Public License as published by the Free Software Foundation, either version 3
c of the License, or any later version. This program is distributed in the hope that it will
c be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
c FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
c
c A copy of the GNU General Public License can be found as a separate file on this website and/or
c at .
c
c---------------------------------------------------------------------------------------------
c
c This collection of subroutines is a result of several upgrades of the original package
c written by N. A. Tsyganenko in 1978-1979.
c
c PREFATORY NOTE TO THE VERSION OF FEBRUARY 4, 2008:
c
c To avoid inappropriate use of obsolete subroutines from earlier versions, a suffix 08 was
c added to the name of each subroutine in this release.
c
c A possibility has been added in this version to calculate vector components in the
c "Geocentric Solar Wind" (GSW) coordinate system, which, to our knowledge, was first
c introduced by Hones et al., Planet. Space Sci., v.34, p.889, 1986 (aka GSWM, see Appendix,
c Tsyganenko et al., JGRA, v.103(A4), p.6827, 1998). The GSW system is analogous to the
c standard GSM, except that its X-axis is antiparallel to the currently observed solar wind
c flow vector, rather than aligned with the Earth-Sun line. The orientation of axes in the
c GSW system can be uniquely defined by specifying three components (VGSEX,VGSEY,VGSEZ) of
c the solar wind velocity, and in the case of a strictly radial anti-sunward flow (VGSEY=
c VGSEZ=0) the GSW system becomes identical to the standard GSM, which fact was used here
c to minimize the number of subroutines in the package. To that end, instead of the special
c case of the GSM coordinates, this version uses a more general GSW system, and three more
c input parameters are added in the subroutine RECALC_08, the observed values (VGSEX,VGSEY,
c VGSEZ) of the solar wind velocity. Invoking RECALC_08 with VGSEY=VGSEZ=0 restores the
c standard (sunward) orientation of the X axis, which allows one to easily convert vectors
c between GSW and GSM, as well as to/from other standard and commonly used systems. For more
c details, see the documentation file GEOPACK-2008.DOC.
c
c Another modification allows users to have more control over the procedure of field line
c mapping using the subroutine TRACE_08. To that end, three new input parameters were added
c in that subroutine, allowing one to set (i) an upper limit, DSMAX, on the automatically
c adjusted step size, (ii) a permissible step error, ERR, and (iii) maximal length, LMAX,
c of arrays where field line point coordinates are stored. Minor changes were also made in
c the tracing subroutine, to make it more compact and easier for understanding, and to
c prevent the algorithm from making uncontrollable large number of multiple loops in some
c cases with plasmoid-like field structures.
c
C One more subroutine, named GEODGEO_08, was added to the package, allowing one to convert
c geodetic coordinates of a point in space (altitude above the Earth's WGS84 ellipsoid and
c geodetic latitude) to geocentric radial distance and colatitude, and vice versa.
c
C For a complete list of modifications made earlier in previous versions, see the
c documentation file GEOPACK-2008.DOC.
c
c----------------------------------------------------------------------------------
c
SUBROUTINE IGRF_GSW_08 (XGSW,YGSW,ZGSW,HXGSW,HYGSW,HZGSW)
c
C CALCULATES COMPONENTS OF THE MAIN (INTERNAL) GEOMAGNETIC FIELD IN THE GEOCENTRIC SOLAR-WIND
C (GSW) COORDINATE SYSTEM, USING IAGA INTERNATIONAL GEOMAGNETIC REFERENCE MODEL COEFFICIENTS
C (e.g., http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html, revised 22 March, 2005)
c
C THE GSW SYSTEM IS ESSENTIALLY SIMILAR TO THE STANDARD GSM (THE TWO SYSTEMS BECOME IDENTICAL
C TO EACH OTHER IN THE CASE OF STRICTLY ANTI-SUNWARD SOLAR WIND FLOW). FOR A DETAILED
C DEFINITION, SEE INTRODUCTORY COMMENTS FOR THE SUBROUTINE GSWGSE_08 .
C
C BEFORE THE FIRST CALL OF THIS SUBROUTINE, OR, IF THE DATE/TIME (IYEAR,IDAY,IHOUR,MIN,ISEC),
C OR THE SOLAR WIND VELOCITY COMPONENTS (VGSEX,VGSEY,VGSEZ) HAVE CHANGED, THE MODEL COEFFICIENTS
c AND GEO-GSW ROTATION MATRIX ELEMENTS SHOULD BE UPDATED BY CALLING THE SUBROUTINE RECALC_08.
C
C-----INPUT PARAMETERS:
C
C XGSW,YGSW,ZGSW - CARTESIAN GEOCENTRIC SOLAR-WIND COORDINATES (IN UNITS RE=6371.2 KM)
C
C-----OUTPUT PARAMETERS:
C
C HXGSW,HYGSW,HZGSW - CARTESIAN GEOCENTRIC SOLAR-WIND COMPONENTS OF THE MAIN GEOMAGNETIC
C FIELD IN NANOTESLA
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C THIS VERSION OF THE CODE ACCEPTS DATES FROM 1965 THROUGH 2010.
c
C AUTHOR: N. A. TSYGANENKO
C
C
IMPLICIT REAL*8 (A-H,O-Z)
COMMON /GEOPACK2/ G(105),H(105),REC(105)
DIMENSION A(14),B(14)
CALL GEOGSW_08 (XGEO,YGEO,ZGEO,XGSW,YGSW,ZGSW,-1)
RHO2=XGEO**2+YGEO**2
R=DSQRT(RHO2+ZGEO**2)
C=ZGEO/R
RHO=DSQRT(RHO2)
S=RHO/R
IF (S.LT.1.D-10) THEN
CF=1.D0
SF=0.D0
ELSE
CF=XGEO/RHO
SF=YGEO/RHO
ENDIF
C
PP=1.D0/R
P=PP
C
C IN THIS VERSION, THE OPTIMAL VALUE OF THE PARAMETER NM (MAXIMAL ORDER OF THE SPHERICAL
C HARMONIC EXPANSION) IS NOT USER-PRESCRIBED, BUT CALCULATED INSIDE THE SUBROUTINE, BASED
C ON THE VALUE OF THE RADIAL DISTANCE R:
C
IRP3=R+2
NM=3+30/IRP3
IF (NM.GT.13) NM=13
K=NM+1
DO 150 N=1,K
P=P*PP
A(N)=P
150 B(N)=P*N
P=1.D0
D=0.D0
BBR=0.D0
BBT=0.D0
BBF=0.D0
DO 200 M=1,K
IF(M.EQ.1) GOTO 160
MM=M-1
W=X
X=W*CF+Y*SF
Y=Y*CF-W*SF
GOTO 170
160 X=0.D0
Y=1.D0
170 Q=P
Z=D
BI=0.D0
P2=0.D0
D2=0.D0
DO 190 N=M,K
AN=A(N)
MN=N*(N-1)/2+M
E=G(MN)
HH=H(MN)
W=E*Y+HH*X
BBR=BBR+B(N)*W*Q
BBT=BBT-AN*W*Z
IF(M.EQ.1) GOTO 180
QQ=Q
IF(S.LT.1.D-10) QQ=Z
BI=BI+AN*(E*X-HH*Y)*QQ
180 XK=REC(MN)
DP=C*Z-S*Q-XK*D2
PM=C*Q-XK*P2
D2=Z
P2=Q
Z=DP
190 Q=PM
D=S*D+C*P
P=S*P
IF(M.EQ.1) GOTO 200
BI=BI*MM
BBF=BBF+BI
200 CONTINUE
C
BR=BBR
BT=BBT
IF(S.LT.1.D-10) GOTO 210
BF=BBF/S
GOTO 211
210 IF(C.LT.0.) BBF=-BBF
BF=BBF
211 HE=BR*S+BT*C
HXGEO=HE*CF-BF*SF
HYGEO=HE*SF+BF*CF
HZGEO=BR*C-BT*S
C
CALL GEOGSW_08 (HXGEO,HYGEO,HZGEO,HXGSW,HYGSW,HZGSW,1)
C
RETURN
END
C
c==========================================================================================
C
c
SUBROUTINE IGRF_GEO_08 (R,THETA,PHI,BR,BTHETA,BPHI)
c
C CALCULATES COMPONENTS OF THE MAIN (INTERNAL) GEOMAGNETIC FIELD IN THE SPHERICAL GEOGRAPHIC
C (GEOCENTRIC) COORDINATE SYSTEM, USING IAGA INTERNATIONAL GEOMAGNETIC REFERENCE MODEL
C COEFFICIENTS (e.g., http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html, revised: 22 March, 2005)
C
C BEFORE THE FIRST CALL OF THIS SUBROUTINE, OR IF THE DATE (IYEAR AND IDAY) WAS CHANGED,
C THE MODEL COEFFICIENTS SHOULD BE UPDATED BY CALLING THE SUBROUTINE RECALC_08
C
C-----INPUT PARAMETERS:
C
C R, THETA, PHI - SPHERICAL GEOGRAPHIC (GEOCENTRIC) COORDINATES:
C RADIAL DISTANCE R IN UNITS RE=6371.2 KM, COLATITUDE THETA AND LONGITUDE PHI IN RADIANS
C
C-----OUTPUT PARAMETERS:
C
C BR, BTHETA, BPHI - SPHERICAL COMPONENTS OF THE MAIN GEOMAGNETIC FIELD IN NANOTESLA
C (POSITIVE BR OUTWARD, BTHETA SOUTHWARD, BPHI EASTWARD)
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C THIS VERSION OF THE CODE ACCEPTS DATES FROM 1965 THROUGH 2010.
c
C AUTHOR: N. A. TSYGANENKO
C
C
IMPLICIT REAL*8 (A-H,O-Z)
COMMON /GEOPACK2/ G(105),H(105),REC(105)
DIMENSION A(14),B(14)
C=DCOS(THETA)
S=DSIN(THETA)
CF=DCOS(PHI)
SF=DSIN(PHI)
C
PP=1.D0/R
P=PP
C
C IN THIS NEW VERSION, THE OPTIMAL VALUE OF THE PARAMETER NM (MAXIMAL ORDER OF THE SPHERICAL
C HARMONIC EXPANSION) IS NOT USER-PRESCRIBED, BUT CALCULATED INSIDE THE SUBROUTINE, BASED
C ON THE VALUE OF THE RADIAL DISTANCE R:
C
IRP3=R+2
NM=3+30/IRP3
IF (NM.GT.13) NM=13
K=NM+1
DO 150 N=1,K
P=P*PP
A(N)=P
150 B(N)=P*N
P=1.D0
D=0.D0
BBR=0.D0
BBT=0.D0
BBF=0.D0
DO 200 M=1,K
IF(M.EQ.1) GOTO 160
MM=M-1
W=X
X=W*CF+Y*SF
Y=Y*CF-W*SF
GOTO 170
160 X=0.D0
Y=1.D0
170 Q=P
Z=D
BI=0.D0
P2=0.D0
D2=0.D0
DO 190 N=M,K
AN=A(N)
MN=N*(N-1)/2+M
E=G(MN)
HH=H(MN)
W=E*Y+HH*X
BBR=BBR+B(N)*W*Q
BBT=BBT-AN*W*Z
IF(M.EQ.1) GOTO 180
QQ=Q
IF(S.LT.1.D-5) QQ=Z
BI=BI+AN*(E*X-HH*Y)*QQ
180 XK=REC(MN)
DP=C*Z-S*Q-XK*D2
PM=C*Q-XK*P2
D2=Z
P2=Q
Z=DP
190 Q=PM
D=S*D+C*P
P=S*P
IF(M.EQ.1) GOTO 200
BI=BI*MM
BBF=BBF+BI
200 CONTINUE
C
BR=BBR
BTHETA=BBT
IF(S.LT.1.D-10) GOTO 210
BPHI=BBF/S
RETURN
210 IF(C.LT.0.D0) BBF=-BBF
BPHI=BBF
RETURN
END
C
c==========================================================================================
c
SUBROUTINE DIP_08 (XGSW,YGSW,ZGSW,BXGSW,BYGSW,BZGSW)
C
C CALCULATES GSW (GEOCENTRIC SOLAR-WIND) COMPONENTS OF GEODIPOLE FIELD WITH THE DIPOLE MOMENT
C CORRESPONDING TO THE EPOCH, SPECIFIED BY CALLING SUBROUTINE RECALC_08 (SHOULD BE
C INVOKED BEFORE THE FIRST USE OF THIS ONE, OR IF THE DATE/TIME, AND/OR THE OBSERVED
C SOLAR WIND DIRECTION, HAVE CHANGED.
C
C THE GSW COORDINATE SYSTEM IS ESSENTIALLY SIMILAR TO THE STANDARD GSM (THE TWO SYSTEMS BECOME
C IDENTICAL TO EACH OTHER IN THE CASE OF STRICTLY RADIAL ANTI-SUNWARD SOLAR WIND FLOW). ITS
C DETAILED DEFINITION IS GIVEN IN INTRODUCTORY COMMENTS FOR THE SUBROUTINE GSWGSE_08 .
C--INPUT PARAMETERS: XGSW,YGSW,ZGSW - GSW COORDINATES IN RE (1 RE = 6371.2 km)
C
C--OUTPUT PARAMETERS: BXGSW,BYGSW,BZGSW - FIELD COMPONENTS IN GSW SYSTEM, IN NANOTESLA.
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION).
C
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
COMMON /GEOPACK1/ AA(10),SPS,CPS,BB(22)
COMMON /GEOPACK2/ G(105),H(105),REC(105)
C
DIPMOM=DSQRT(G(2)**2+G(3)**2+H(3)**2)
C
P=XGSW**2
U=ZGSW**2
V=3.D0*ZGSW*XGSW
T=YGSW**2
Q=DIPMOM/DSQRT(P+T+U)**5
BXGSW=Q*((T+U-2.D0*P)*SPS-V*CPS)
BYGSW=-3.D0*YGSW*Q*(XGSW*SPS+ZGSW*CPS)
BZGSW=Q*((P+T-2.D0*U)*CPS-V*SPS)
RETURN
END
C*******************************************************************
c
SUBROUTINE SUN_08 (IYEAR,IDAY,IHOUR,MIN,ISEC,GST,SLONG,SRASN,SDEC)
C
C CALCULATES FOUR QUANTITIES NECESSARY FOR COORDINATE TRANSFORMATIONS
C WHICH DEPEND ON SUN POSITION (AND, HENCE, ON UNIVERSAL TIME AND SEASON)
C
C------- INPUT PARAMETERS:
C IYR,IDAY,IHOUR,MIN,ISEC - YEAR, DAY, AND UNIVERSAL TIME IN HOURS, MINUTES,
C AND SECONDS (IDAY=1 CORRESPONDS TO JANUARY 1).
C
C------- OUTPUT PARAMETERS:
C GST - GREENWICH MEAN SIDEREAL TIME, SLONG - LONGITUDE ALONG ECLIPTIC
C SRASN - RIGHT ASCENSION, SDEC - DECLINATION OF THE SUN (RADIANS)
C ORIGINAL VERSION OF THIS SUBROUTINE HAS BEEN COMPILED FROM:
C RUSSELL, C.T., COSMIC ELECTRODYNAMICS, 1971, V.2, PP.184-196.
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
C ORIGINAL VERSION WRITTEN BY: Gilbert D. Mead
C
IMPLICIT REAL*8 (A-H,O-Z)
DATA RAD/57.295779513D0/
C
IF(IYEAR.LT.1901.OR.IYEAR.GT.2099) RETURN
FDAY=DFLOAT(IHOUR*3600+MIN*60+ISEC)/86400.D0
DJ=365*(IYEAR-1900)+(IYEAR-1901)/4+IDAY-0.5D0+FDAY
T=DJ/36525.D0
VL=DMOD(279.696678D0+0.9856473354D0*DJ,360.D0)
GST=DMOD(279.690983D0+.9856473354D0*DJ+360.D0*FDAY+180.D0,360.D0)/
* RAD
G=DMOD(358.475845D0+0.985600267D0*DJ,360.D0)/RAD
SLONG=(VL+(1.91946D0-0.004789D0*T)*DSIN(G)+0.020094D0
* *DSIN(2.D0*G))/RAD
IF(SLONG.GT.6.2831853D0) SLONG=SLONG-6.283185307D0
IF (SLONG.LT.0.D0) SLONG=SLONG+6.283185307D0
OBLIQ=(23.45229D0-0.0130125D0*T)/RAD
SOB=DSIN(OBLIQ)
SLP=SLONG-9.924D-5
C
C THE LAST CONSTANT IS A CORRECTION FOR THE ANGULAR ABERRATION DUE TO
C EARTH'S ORBITAL MOTION
C
SIND=SOB*DSIN(SLP)
COSD=DSQRT(1.D0-SIND**2)
SC=SIND/COSD
SDEC=DATAN(SC)
SRASN=3.141592654D0-DATAN2(DCOS(OBLIQ)/SOB*SC,-DCOS(SLP)/COSD)
RETURN
END
C
C================================================================================
c
SUBROUTINE SPHCAR_08 (R,THETA,PHI,X,Y,Z,J)
C
C CONVERTS SPHERICAL COORDS INTO CARTESIAN ONES AND VICE VERSA
C (THETA AND PHI IN RADIANS).
C
C J>0 J<0
C-----INPUT: J,R,THETA,PHI J,X,Y,Z
C----OUTPUT: X,Y,Z R,THETA,PHI
C
C NOTE: AT THE POLES (X=0 AND Y=0) WE ASSUME PHI=0 WHEN CONVERTING
C FROM CARTESIAN TO SPHERICAL COORDS (I.E., FOR J<0)
C
C LAST MOFIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
IF(J.GT.0) GOTO 3
SQ=X**2+Y**2
R=DSQRT(SQ+Z**2)
IF (SQ.NE.0.D0) GOTO 2
PHI=0.D0
IF (Z.LT.0.D0) GOTO 1
THETA=0.D0
RETURN
1 THETA=3.141592654D0
RETURN
2 SQ=DSQRT(SQ)
PHI=DATAN2(Y,X)
THETA=DATAN2(SQ,Z)
IF (PHI.LT.0.D0) PHI=PHI+6.283185307D0
RETURN
3 SQ=R*DSIN(THETA)
X=SQ*DCOS(PHI)
Y=SQ*DSIN(PHI)
Z=R*DCOS(THETA)
RETURN
END
C
C===========================================================================
c
SUBROUTINE BSPCAR_08 (THETA,PHI,BR,BTHETA,BPHI,BX,BY,BZ)
C
C CALCULATES CARTESIAN FIELD COMPONENTS FROM LOCAL SPHERICAL ONES
C
C-----INPUT: THETA,PHI - SPHERICAL ANGLES OF THE POINT IN RADIANS
C BR,BTHETA,BPHI - LOCAL SPHERICAL COMPONENTS OF THE FIELD
C-----OUTPUT: BX,BY,BZ - CARTESIAN COMPONENTS OF THE FIELD
C
C LAST MOFIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
C WRITTEN BY: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
S=DSIN(THETA)
C=DCOS(THETA)
SF=DSIN(PHI)
CF=DCOS(PHI)
BE=BR*S+BTHETA*C
BX=BE*CF-BPHI*SF
BY=BE*SF+BPHI*CF
BZ=BR*C-BTHETA*S
RETURN
END
c
C==============================================================================
C
SUBROUTINE BCARSP_08 (X,Y,Z,BX,BY,BZ,BR,BTHETA,BPHI)
C
CALCULATES LOCAL SPHERICAL FIELD COMPONENTS FROM THOSE IN CARTESIAN SYSTEM
C
C-----INPUT: X,Y,Z - CARTESIAN COMPONENTS OF THE POSITION VECTOR
C BX,BY,BZ - CARTESIAN COMPONENTS OF THE FIELD VECTOR
C-----OUTPUT: BR,BTHETA,BPHI - LOCAL SPHERICAL COMPONENTS OF THE FIELD VECTOR
C
C NOTE: AT THE POLES (THETA=0 OR THETA=PI) WE ASSUME PHI=0,
C AND HENCE BTHETA=BX, BPHI=BY
C
C WRITTEN AND ADDED TO THIS PACKAGE: APRIL 1, 2003
c LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
RHO2=X**2+Y**2
R=DSQRT(RHO2+Z**2)
RHO=DSQRT(RHO2)
IF (RHO.NE.0.D0) THEN
CPHI=X/RHO
SPHI=Y/RHO
ELSE
CPHI=1.D0
SPHI=0.D0
ENDIF
CT=Z/R
ST=RHO/R
BR=(X*BX+Y*BY+Z*BZ)/R
BTHETA=(BX*CPHI+BY*SPHI)*CT-BZ*ST
BPHI=BY*CPHI-BX*SPHI
RETURN
END
C
c=====================================================================================
C
SUBROUTINE RECALC_08 (IYEAR,IDAY,IHOUR,MIN,ISEC,VGSEX,VGSEY,VGSEZ)
C
C 1. PREPARES ELEMENTS OF ROTATION MATRICES FOR TRANSFORMATIONS OF VECTORS BETWEEN
C SEVERAL COORDINATE SYSTEMS, MOST FREQUENTLY USED IN SPACE PHYSICS.
C
C 2. PREPARES COEFFICIENTS USED IN THE CALCULATION OF THE MAIN GEOMAGNETIC FIELD
C (IGRF MODEL)
C
C THIS SUBROUTINE SHOULD BE INVOKED BEFORE USING THE FOLLOWING SUBROUTINES:
C IGRF_GEO_08, IGRF_GSW_08, DIP_08, GEOMAG_08, GEOGSW_08, MAGSW_08, SMGSW_08, GSWGSE_08,
c GEIGEO_08, TRACE_08, STEP_08, RHAND_08.
C
C THERE IS NO NEED TO REPEATEDLY INVOKE RECALC_08, IF MULTIPLE CALCULATIONS ARE MADE
C FOR THE SAME DATE/TIME AND SOLAR WIND FLOW DIRECTION.
C
C-----INPUT PARAMETERS:
C
C IYEAR - YEAR NUMBER (FOUR DIGITS)
C IDAY - DAY OF YEAR (DAY 1 = JAN 1)
C IHOUR - HOUR OF DAY (00 TO 23)
C MIN - MINUTE OF HOUR (00 TO 59)
C ISEC - SECONDS OF MINUTE (00 TO 59)
C VGSEX,VGSEY,VGSEZ - GSE (GEOCENTRIC SOLAR-ECLIPTIC) COMPONENTS OF THE OBSERVED
C SOLAR WIND FLOW VELOCITY (IN KM/S)
C
C IMPORTANT: IF ONLY QUESTIONABLE INFORMATION (OR NO INFORMATION AT ALL) IS AVAILABLE
C ON THE SOLAR WIND SPEED, OR, IF THE STANDARD GSM AND/OR SM COORDINATES ARE
C INTENDED TO BE USED, THEN SET VGSEX=-400.0 AND VGSEY=VGSEZ=0. IN THIS CASE,
C THE GSW COORDINATE SYSTEM BECOMES IDENTICAL TO THE STANDARD GSM.
C
C IF ONLY SCALAR SPEED V OF THE SOLAR WIND IS KNOWN, THEN SETTING
C VGSEX=-V, VGSEY=29.78, VGSEZ=0.0 WILL TAKE INTO ACCOUNT THE ~4 degs
C ABERRATION OF THE MAGNETOSPHERE DUE TO EARTH'S ORBITAL MOTION
C
C IF ALL THREE GSE COMPONENTS OF THE SOLAR WIND VELOCITY ARE AVAILABLE,
C PLEASE NOTE THAT IN SOME SOLAR WIND DATABASES THE ABERRATION EFFECT
C HAS ALREADY BEEN TAKEN INTO ACCOUNT BY SUBTRACTING 29.78 KM/S FROM VYGSE;
C IN THAT CASE, THE UNABERRATED (OBSERVED) VYGSE VALUES SHOULD BE RESTORED
C BY ADDING BACK THE 29.78 KM/S CORRECTION. WHETHER OR NOT TO DO THAT, MUST
C BE EITHER VERIFIED WITH THE DATA ORIGINATOR OR DETERMINED BY AVERAGING
C VGSEY OVER A SUFFICIENTLY LONG TIME INTERVAL.
C
C-----OUTPUT PARAMETERS: NONE (ALL OUTPUT QUANTITIES ARE PLACED
C INTO THE COMMON BLOCKS /GEOPACK1/ AND /GEOPACK2/)
C
C OTHER SUBROUTINES CALLED BY THIS ONE: SUN_08
C
C AUTHOR: N.A. TSYGANENKO
C DATE: DEC.1, 1991
C
C REVISION OF NOVEMBER 15, 2007: ADDED THE POSSIBILITY TO TAKE INTO ACCOUNT THE OBSERVED
C DEFLECTION OF THE SOLAR WIND FLOW FROM STRICTLY RADIAL DIRECTION. TO THAT END, THREE
C GSE COMPONENTS OF THE SOLAR WIND VELOCITY WERE ADDED TO THE INPUT PARAMETERS.
C
c CORRECTION OF MAY 9, 2006: INTERPOLATION OF THE COEFFICIENTS (BETWEEN
C LABELS 50 AND 105) IS NOW MADE THROUGH THE LAST ELEMENT OF THE ARRAYS
C G(105) AND H(105) (PREVIOUSLY MADE ONLY THROUGH N=66, WHICH IN SOME
C CASES CAUSED RUNTIME ERRORS)
c
C REVISION OF MAY 3, 2005:
C The table of IGRF coefficients was extended to include those for the epoch 2005
c the maximal order of spherical harmonics was also increased up to 13
c (for details, see http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html)
c
C REVISION OF APRIL 3, 2003:
c The code now includes preparation of the model coefficients for the subroutines
c IGRF_08 and GEOMAG_08. This eliminates the need for the SAVE statements, used
c in the old versions, making the codes easier and more compiler-independent.
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
IMPLICIT REAL*8 (A-H,O-Z)
SAVE ISW
C
COMMON /GEOPACK1/ ST0,CT0,SL0,CL0,CTCL,STCL,CTSL,STSL,SFI,CFI,
* SPS,CPS,DS3,CGST,SGST,PSI,A11,A21,A31,A12,A22,A32,A13,A23,A33,
* E11,E21,E31,E12,E22,E32,E13,E23,E33
C
C THE COMMON BLOCK /GEOPACK1/ CONTAINS ELEMENTS OF THE ROTATION MATRICES AND OTHER
C PARAMETERS RELATED TO THE COORDINATE TRANSFORMATIONS PERFORMED BY THIS PACKAGE
C
COMMON /GEOPACK2/ G(105),H(105),REC(105)
C
C THE COMMON BLOCK /GEOPACK2/ CONTAINS COEFFICIENTS OF THE IGRF FIELD MODEL, CALCULATED
C FOR A GIVEN YEAR AND DAY FROM THEIR STANDARD EPOCH VALUES. THE ARRAY REC CONTAINS
C COEFFICIENTS USED IN THE RECURSION RELATIONS FOR LEGENDRE ASSOCIATE POLYNOMIALS.
C
DIMENSION G65(105),H65(105),G70(105),H70(105),G75(105),H75(105),
+ G80(105),H80(105),G85(105),H85(105),G90(105),H90(105),G95(105),
+ H95(105),G00(105),H00(105),G05(105),H05(105),DG05(45),DH05(45)
C
DATA ISW /0/
c
DATA G65/0.D0,-30334.D0,-2119.D0,-1662.D0,2997.D0,1594.D0,1297.D0,
*-2038.D0,1292.D0,856.D0,957.D0,804.D0,479.D0,-390.D0,252.D0,
*-219.D0,358.D0,254.D0,-31.D0,-157.D0,-62.D0,45.D0,61.D0,8.D0,
*-228.D0,4.D0,1.D0,-111.D0,75.D0,-57.D0,4.D0,13.D0,-26.D0,-6.D0,
*13.D0,1.D0,13.D0,5.D0,-4.D0,-14.D0,0.D0,8.D0,-1.D0,11.D0,4.D0,
*8.D0,10.D0,2.D0,-13.D0,10.D0,-1.D0,-1.D0,5.D0,1.D0,-2.D0,-2.D0,
*-3.D0,2.D0,-5.D0,-2.D0,4.D0,4.D0,0.D0,2.D0,2.D0,0.D0,39*0.D0/
DATA H65/0.D0,0.D0,5776.D0,0.D0,-2016.D0,114.D0,0.D0,-404.D0,
*240.D0,-165.D0,0.D0,148.D0,-269.D0,13.D0,-269.D0,0.D0,19.D0,
*128.D0,-126.D0,-97.D0,81.D0,0.D0,-11.D0,100.D0,68.D0,-32.D0,-8.D0,
*-7.D0,0.D0,-61.D0,-27.D0,-2.D0,6.D0,26.D0,-23.D0,-12.D0,0.D0,7.D0,
*-12.D0,9.D0,-16.D0,4.D0,24.D0,-3.D0,-17.D0,0.D0,-22.D0,15.D0,7.D0,
*-4.D0,-5.D0,10.D0,10.D0,-4.D0,1.D0,0.D0,2.D0,1.D0,2.D0,6.D0,-4.D0,
*0.D0,-2.D0,3.D0,0.D0,-6.D0,39*0.D0/
c
DATA G70/0.D0,-30220.D0,-2068.D0,-1781.D0,3000.D0,1611.D0,1287.D0,
*-2091.D0,1278.D0,838.D0,952.D0,800.D0,461.D0,-395.D0,234.D0,
*-216.D0,359.D0,262.D0,-42.D0,-160.D0,-56.D0,43.D0,64.D0,15.D0,
*-212.D0,2.D0,3.D0,-112.D0,72.D0,-57.D0,1.D0,14.D0,-22.D0,-2.D0,
*13.D0,-2.D0,14.D0,6.D0,-2.D0,-13.D0,-3.D0,5.D0,0.D0,11.D0,3.D0,
*8.D0,10.D0,2.D0,-12.D0,10.D0,-1.D0,0.D0,3.D0,1.D0,-1.D0,-3.D0,
*-3.D0,2.D0,-5.D0,-1.D0,6.D0,4.D0,1.D0,0.D0,3.D0,-1.D0,39*0.D0/
DATA H70/0.D0,0.D0,5737.D0,0.D0,-2047.D0,25.D0,0.D0,-366.D0,
*251.D0,-196.D0,0.D0,167.D0,-266.D0,26.D0,-279.D0,0.D0,26.D0,
*139.D0,-139.D0,-91.D0,83.D0,0.D0,-12.D0,100.D0,72.D0,-37.D0,-6.D0,
*1.D0,0.D0,-70.D0,-27.D0,-4.D0,8.D0,23.D0,-23.D0,-11.D0,0.D0,7.D0,
*-15.D0,6.D0,-17.D0,6.D0,21.D0,-6.D0,-16.D0,0.D0,-21.D0,16.D0,6.D0,
*-4.D0,-5.D0,10.D0,11.D0,-2.D0,1.D0,0.D0,1.D0,1.D0,3.D0,4.D0,-4.D0,
*0.D0,-1.D0,3.D0,1.D0,-4.D0,39*0.D0/
c
DATA G75/0.D0,-30100.D0,-2013.D0,-1902.D0,3010.D0,1632.D0,1276.D0,
*-2144.D0,1260.D0,830.D0,946.D0,791.D0,438.D0,-405.D0,216.D0,
*-218.D0,356.D0,264.D0,-59.D0,-159.D0,-49.D0,45.D0,66.D0,28.D0,
*-198.D0,1.D0,6.D0,-111.D0,71.D0,-56.D0,1.D0,16.D0,-14.D0,0.D0,
*12.D0,-5.D0,14.D0,6.D0,-1.D0,-12.D0,-8.D0,4.D0,0.D0,10.D0,1.D0,
*7.D0,10.D0,2.D0,-12.D0,10.D0,-1.D0,-1.D0,4.D0,1.D0,-2.D0,-3.D0,
*-3.D0,2.D0,-5.D0,-2.D0,5.D0,4.D0,1.D0,0.D0,3.D0,-1.D0,39*0.D0/
C
DATA H75/0.D0,0.D0,5675.D0,0.D0,-2067.D0,-68.D0,0.D0,-333.D0,
*262.D0,-223.D0,0.D0,191.D0,-265.D0,39.D0,-288.D0,0.D0,31.D0,
*148.D0,-152.D0,-83.D0,88.D0,0.D0,-13.D0,99.D0,75.D0,-41.D0,-4.D0,
*11.D0,0.D0,-77.D0,-26.D0,-5.D0,10.D0,22.D0,-23.D0,-12.D0,0.D0,
*6.D0,-16.D0,4.D0,-19.D0,6.D0,18.D0,-10.D0,-17.D0,0.D0,-21.D0,
*16.D0,7.D0,-4.D0,-5.D0,10.D0,11.D0,-3.D0,1.D0,0.D0,1.D0,1.D0,3.D0,
*4.D0,-4.D0,-1.D0,-1.D0,3.D0,1.D0,-5.D0,39*0.D0/
c
DATA G80/0.D0,-29992.D0,-1956.D0,-1997.D0,3027.D0,1663.D0,1281.D0,
*-2180.D0,1251.D0,833.D0,938.D0,782.D0,398.D0,-419.D0,199.D0,
*-218.D0,357.D0,261.D0,-74.D0,-162.D0,-48.D0,48.D0,66.D0,42.D0,
*-192.D0,4.D0,14.D0,-108.D0,72.D0,-59.D0,2.D0,21.D0,-12.D0,1.D0,
*11.D0,-2.D0,18.D0,6.D0,0.D0,-11.D0,-7.D0,4.D0,3.D0,6.D0,-1.D0,
*5.D0,10.D0,1.D0,-12.D0,9.D0,-3.D0,-1.D0,7.D0,2.D0,-5.D0,-4.D0,
*-4.D0,2.D0,-5.D0,-2.D0,5.D0,3.D0,1.D0,2.D0,3.D0,0.D0,39*0.D0/
C
DATA H80/0.D0,0.D0,5604.D0,0.D0,-2129.D0,-200.D0,0.D0,-336.D0,
*271.D0,-252.D0,0.D0,212.D0,-257.D0,53.D0,-297.D0,0.D0,46.D0,
*150.D0,-151.D0,-78.D0,92.D0,0.D0,-15.D0,93.D0,71.D0,-43.D0,-2.D0,
*17.D0,0.D0,-82.D0,-27.D0,-5.D0,16.D0,18.D0,-23.D0,-10.D0,0.D0,
*7.D0,-18.D0,4.D0,-22.D0,9.D0,16.D0,-13.D0,-15.D0,0.D0,-21.D0,
*16.D0,9.D0,-5.D0,-6.D0,9.D0,10.D0,-6.D0,2.D0,0.D0,1.D0,0.D0,3.D0,
*6.D0,-4.D0,0.D0,-1.D0,4.D0,0.D0,-6.D0,39*0.D0/
c
DATA G85/0.D0,-29873.D0,-1905.D0,-2072.D0,3044.D0,1687.D0,1296.D0,
*-2208.D0,1247.D0,829.D0,936.D0,780.D0,361.D0,-424.D0,170.D0,
*-214.D0,355.D0,253.D0,-93.D0,-164.D0,-46.D0,53.D0,65.D0,51.D0,
*-185.D0,4.D0,16.D0,-102.D0,74.D0,-62.D0,3.D0,24.D0,-6.D0,4.D0,
*10.D0,0.D0,21.D0,6.D0,0.D0,-11.D0,-9.D0,4.D0,4.D0,4.D0,-4.D0,5.D0,
*10.D0,1.D0,-12.D0,9.D0,-3.D0,-1.D0,7.D0,1.D0,-5.D0,-4.D0,-4.D0,
*3.D0,-5.D0,-2.D0,5.D0,3.D0,1.D0,2.D0,3.D0,0.D0,39*0.D0/
C
DATA H85/0.D0,0.D0,5500.D0,0.D0,-2197.D0,-306.D0,0.D0,-310.D0,
*284.D0,-297.D0,0.D0,232.D0,-249.D0,69.D0,-297.D0,0.D0,47.D0,
*150.D0,-154.D0,-75.D0,95.D0,0.D0,-16.D0,88.D0,69.D0,-48.D0,-1.D0,
*21.D0,0.D0,-83.D0,-27.D0,-2.D0,20.D0,17.D0,-23.D0,-7.D0,0.D0,8.D0,
*-19.D0,5.D0,-23.D0,11.D0,14.D0,-15.D0,-11.D0,0.D0,-21.D0,15.D0,
*9.D0,-6.D0,-6.D0,9.D0,9.D0,-7.D0,2.D0,0.D0,1.D0,0.D0,3.D0,6.D0,
*-4.D0,0.D0,-1.D0,4.D0,0.D0,-6.D0,39*0.D0/
c
DATA G90/0.D0,-29775.D0,-1848.D0,-2131.D0,3059.D0,1686.D0,1314.D0,
* -2239.D0, 1248.D0, 802.D0, 939.D0, 780.D0, 325.D0,-423.D0,
* 141.D0, -214.D0, 353.D0, 245.D0,-109.D0,-165.D0, -36.D0,
* 61.D0, 65.D0, 59.D0, -178.D0, 3.D0, 18.D0, -96.D0,
* 77.D0, -64.D0, 2.D0, 26.D0, -1.D0, 5.D0, 9.D0,
* 0.D0, 23.D0, 5.D0, -1.D0, -10.D0, -12.D0, 3.D0,
* 4.D0, 2.D0, -6.D0, 4.D0, 9.D0, 1.D0, -12.D0,
* 9.D0, -4.D0, -2.D0, 7.D0, 1.D0, -6.D0, -3.D0,
* -4.D0, 2.D0, -5.D0, -2.D0, 4.D0, 3.D0, 1.D0,
* 3.D0, 3.D0, 0.D0,39*0.D0/
DATA H90/0.D0, 0.D0,5406.D0, 0.D0,-2279.D0,-373.D0, 0.D0,
* -284.D0,293.D0,-352.D0, 0.D0, 247.D0,-240.D0, 84.D0,
* -299.D0, 0.D0, 46.D0, 154.D0, -153.D0, -69.D0, 97.D0,
* 0.D0,-16.D0, 82.D0, 69.D0, -52.D0, 1.D0, 24.D0,
* 0.D0,-80.D0, -26.D0, 0.D0, 21.D0, 17.D0,-23.D0,
* -4.D0, 0.D0, 10.D0, -19.D0, 6.D0, -22.D0, 12.D0,
* 12.D0,-16.D0, -10.D0, 0.D0, -20.D0, 15.D0, 11.D0,
* -7.D0, -7.D0, 9.D0, 8.D0, -7.D0, 2.D0, 0.D0,
* 2.D0, 1.D0, 3.D0, 6.D0, -4.D0, 0.D0, -2.D0,
* 3.D0, -1.D0, -6.D0,39*0.D0/
DATA G95/0.D0,-29692.D0,-1784.D0,-2200.D0,3070.D0,1681.D0,1335.D0,
* -2267.D0, 1249.D0, 759.D0, 940.D0, 780.D0, 290.D0,-418.D0,
* 122.D0, -214.D0, 352.D0, 235.D0,-118.D0,-166.D0, -17.D0,
* 68.D0, 67.D0, 68.D0, -170.D0, -1.D0, 19.D0, -93.D0,
* 77.D0, -72.D0, 1.D0, 28.D0, 5.D0, 4.D0, 8.D0,
* -2.D0, 25.D0, 6.D0, -6.D0, -9.D0, -14.D0, 9.D0,
* 6.D0, -5.D0, -7.D0, 4.D0, 9.D0, 3.D0, -10.D0,
* 8.D0, -8.D0, -1.D0, 10.D0, -2.D0, -8.D0, -3.D0,
* -6.D0, 2.D0, -4.D0, -1.D0, 4.D0, 2.D0, 2.D0,
* 5.D0, 1.D0, 0.D0, 39*0.D0/
DATA H95/0.D0, 0.D0,5306.D0, 0.D0,-2366.D0,-413.D0, 0.D0,
* -262.D0,302.D0,-427.D0, 0.D0, 262.D0,-236.D0, 97.D0,
* -306.D0, 0.D0, 46.D0,165.D0, -143.D0, -55.D0,107.D0,
* 0.D0,-17.D0, 72.D0, 67.D0, -58.D0, 1.D0, 36.D0,
* 0.D0,-69.D0, -25.D0, 4.D0, 24.D0, 17.D0,-24.D0,
* -6.D0, 0.D0, 11.D0,-21.D0, 8.D0, -23.D0, 15.D0,
* 11.D0,-16.D0, -4.D0, 0.D0, -20.D0, 15.D0, 12.D0,
* -6.D0, -8.D0, 8.D0, 5.D0, -8.D0, 3.D0, 0.D0,
* 1.D0, 0.D0, 4.D0, 5.D0, -5.D0, -1.D0, -2.D0,
* 1.D0, -2.D0, -7.D0,39*0.D0/
DATA G00/0.D0,-29619.4D0,-1728.2D0,-2267.7D0,3068.4D0,1670.9D0,
* 1339.6D0, -2288.D0, 1252.1D0, 714.5D0, 932.3D0, 786.8D0,
* 250.D0, -403.D0, 111.3D0, -218.8D0, 351.4D0, 222.3D0,
* -130.4D0, -168.6D0, -12.9D0, 72.3D0, 68.2D0, 74.2D0,
* -160.9D0, -5.9D0, 16.9D0, -90.4D0, 79.0D0, -74.0D0,
* 0.D0, 33.3D0, 9.1D0, 6.9D0, 7.3D0, -1.2D0,
* 24.4D0, 6.6D0, -9.2D0, -7.9D0, -16.6D0, 9.1D0,
* 7.0D0, -7.9D0, -7.D0, 5.D0, 9.4D0, 3.D0,
* - 8.4D0, 6.3D0, -8.9D0, -1.5D0, 9.3D0, -4.3D0,
* -8.2D0, -2.6D0, -6.D0, 1.7D0, -3.1D0, -0.5D0,
* 3.7D0, 1.D0, 2.D0, 4.2D0, 0.3D0, -1.1D0,
* 2.7D0, -1.7D0, -1.9D0, 1.5D0, -0.1D0, 0.1D0,
* -0.7D0, 0.7D0, 1.7D0, 0.1D0, 1.2D0, 4.0D0,
* -2.2D0, -0.3D0, 0.2D0, 0.9D0, -0.2D0, 0.9D0,
* -0.5D0, 0.3D0, -0.3D0, -0.4D0, -0.1D0, -0.2D0,
* -0.4D0, -0.2D0, -0.9D0, 0.3D0, 0.1D0, -0.4D0,
* 1.3D0, -0.4D0, 0.7D0, -0.4D0, 0.3D0, -0.1D0,
* 0.4D0, 0.D0, 0.1D0/
DATA H00/0.D0, 0.D0,5186.1D0, 0.D0,-2481.6D0,-458.0D0, 0.D0,
* -227.6D0,293.4D0,-491.1D0, 0.D0, 272.6D0,-231.9D0,119.8D0,
* -303.8D0, 0.D0, 43.8D0,171.9D0, -133.1D0, -39.3D0,106.3D0,
* 0.D0,-17.4D0, 63.7D0, 65.1D0, -61.2D0, 0.7D0, 43.8D0,
* 0.D0,-64.6D0, -24.2D0, 6.2D0, 24.D0, 14.8D0,-25.4D0,
* -5.8D0, 0.0D0, 11.9D0,-21.5D0, 8.5D0, -21.5D0, 15.5D0,
* 8.9D0,-14.9D0, -2.1D0, 0.0D0, -19.7D0, 13.4D0, 12.5D0,
* -6.2D0, -8.4D0, 8.4D0, 3.8D0, -8.2D0, 4.8D0, 0.0D0,
* 1.7D0, 0.0D0, 4.0D0, 4.9D0, -5.9D0, -1.2D0, -2.9D0,
* 0.2D0, -2.2D0, -7.4D0, 0.0D0, 0.1D0, 1.3D0, -0.9D0,
* -2.6D0, 0.9D0, -0.7D0, -2.8D0, -0.9D0, -1.2D0, -1.9D0,
* -0.9D0, 0.0D0, -0.4D0, 0.3D0, 2.5D0, -2.6D0, 0.7D0,
* 0.3D0, 0.0D0, 0.0D0, 0.3D0, -0.9D0, -0.4D0, 0.8D0,
* 0.0D0, -0.9D0, 0.2D0, 1.8D0, -0.4D0, -1.0D0, -0.1D0,
* 0.7D0, 0.3D0, 0.6D0, 0.3D0, -0.2D0, -0.5D0, -0.9D0/
*
DATA G05/0.D0,-29556.8D0,-1671.8D0,-2340.5D0, 3047.D0,1656.9D0,
* 1335.7D0, -2305.3D0, 1246.8D0, 674.4D0, 919.8D0, 798.2D0,
* 211.5D0, -379.5D0, 100.2D0, -227.6D0, 354.4D0, 208.8D0,
* -136.6D0, -168.3D0, -14.1D0, 72.9D0, 69.6D0, 76.6D0,
* -151.1D0, -15.0D0, 14.7D0, -86.4D0, 79.8D0, -74.4D0,
* -1.4D0, 38.6D0, 12.3D0, 9.4D0, 5.5D0, 2.0D0,
* 24.8D0, 7.7D0, -11.4D0, -6.8D0, -18.0D0, 10.0D0,
* 9.4D0, -11.4D0, -5.0D0, 5.6D0, 9.8D0, 3.6D0,
* -7.0D0, 5.0D0, -10.8D0, -1.3D0, 8.7D0, -6.7D0,
* -9.2D0, -2.2D0, -6.3D0, 1.6D0, -2.5D0, -0.1D0,
* 3.0D0, 0.3D0, 2.1D0, 3.9D0, -0.1D0, -2.2D0,
* 2.9D0, -1.6D0, -1.7D0, 1.5D0, -0.2D0, 0.2D0,
* -0.7D0, 0.5D0, 1.8D0, 0.1D0, 1.0D0, 4.1D0,
* -2.2D0, -0.3D0, 0.3D0, 0.9D0, -0.4D0, 1.0D0,
* -0.4D0, 0.5D0, -0.3D0, -0.4D0, 0.0D0, -0.4D0,
* 0.0D0, -0.2D0, -0.9D0, 0.3D0, 0.3D0, -0.4D0,
* 1.2D0, -0.4D0, 0.7D0, -0.3D0, 0.4D0, -0.1D0,
* 0.4D0, -0.1D0, -0.3D0/
DATA H05/0.D0, 0.0D0,5080.0D0, 0.0D0,-2594.9D0,-516.7D0, 0.0D0,
* -200.4D0,269.3D0,-524.5D0, 0.0D0, 281.4D0,-225.8D0,145.7D0,
* -304.7D0, 0.0D0, 42.7D0,179.8D0, -123.0D0, -19.5D0,103.6D0,
* 0.0D0,-20.2D0, 54.7D0, 63.7D0, -63.4D0, 0.0D0, 50.3D0,
* 0.0D0,-61.4D0, -22.5D0, 6.9D0, 25.4D0, 10.9D0,-26.4D0,
* -4.8D0, 0.0D0, 11.2D0,-21.0D0, 9.7D0, -19.8D0, 16.1D0,
* 7.7D0,-12.8D0, -0.1D0, 0.0D0, -20.1D0, 12.9D0, 12.7D0,
* -6.7D0, -8.1D0, 8.1D0, 2.9D0, -7.9D0, 5.9D0, 0.0D0,
* 2.4D0, 0.2D0, 4.4D0, 4.7D0, -6.5D0, -1.0D0, -3.4D0,
* -0.9D0, -2.3D0, -8.0D0, 0.0D0, 0.3D0, 1.4D0, -0.7D0,
* -2.4D0, 0.9D0, -0.6D0, -2.7D0, -1.0D0, -1.5D0, -2.0D0,
* -1.4D0, 0.0D0, -0.5D0, 0.3D0, 2.3D0, -2.7D0, 0.6D0,
* 0.4D0, 0.0D0, 0.0D0, 0.3D0, -0.8D0, -0.4D0, 1.0D0,
* 0.0D0, -0.7D0, 0.3D0, 1.7D0, -0.5D0, -1.0D0, 0.0D0,
* 0.7D0, 0.2D0, 0.6D0, 0.4D0, -0.2D0, -0.5D0, -1.0D0/
DATA DG05/0.0D0, 8.8D0,10.8D0,-15.0D0,-6.9D0,-1.0D0,-0.3D0,
* -3.1D0,-0.9D0,-6.8D0, -2.5D0, 2.8D0,-7.1D0, 5.9D0,
* -3.2D0,-2.6D0, 0.4D0, -3.0D0,-1.2D0, 0.2D0,-0.6D0,
* -0.8D0, 0.2D0,-0.2D0, 2.1D0,-2.1D0,-0.4D0, 1.3D0,
* -0.4D0, 0.0D0,-0.2D0, 1.1D0, 0.6D0, 0.4D0,-0.5D0,
* 0.9D0,-0.2D0, 0.2D0, -0.2D0, 0.2D0,-0.2D0, 0.2D0,
* 0.5D0,-0.7D0, 0.5D0/
DATA DH05/0.0D0, 0.0D0,-21.3D0, 0.0D0,-23.3D0,-14.0D0, 0.0D0,
* 5.4D0,-6.5D0, -2.0D0, 0.0D0, 2.0D0, 1.8D0, 5.6D0,
* 0.0D0, 0.0D0, 0.1D0, 1.8D0, 2.0D0, 4.5D0,-1.0D0,
* 0.0D0,-0.4D0, -1.9D0,-0.4D0, -0.4D0, -0.2D0, 0.9D0,
* 0.0D0, 0.8D0, 0.4D0, 0.1D0, 0.2D0, -0.9D0,-0.3D0,
* 0.3D0, 0.0D0, -0.2D0, 0.2D0, 0.2D0, 0.4D0, 0.2D0,
* -0.3D0, 0.5D0, 0.4D0/
C
IF (VGSEY.EQ.0..AND.VGSEZ.EQ.0..AND.ISW.NE.1) THEN
PRINT *, ''
PRINT *,
*' RECALC_08: RADIAL SOLAR WIND --> GSW SYSTEM IDENTICAL HERE'
PRINT *,
*' TO STANDARD GSM (I.E., XGSW AXIS COINCIDES WITH EARTH-SUN LINE)'
PRINT *, ''
ISW=1
ENDIF
IF ((VGSEY.NE.0.D0.OR.VGSEZ.NE.0.D0).AND.ISW.NE.2) THEN ! CORRECTED NOV 27, 2009
PRINT *, ''
PRINT *,
*' WARNING: NON-RADIAL SOLAR WIND FLOW SPECIFIED IN RECALC_08;'
PRINT *,
*' HENCE XGSW AXIS IS ASSUMED ORIENTED ANTIPARALLEL TO V_SW VECTOR'
PRINT *, ''
ISW=2
ENDIF
C
IY=IYEAR
C
C WE ARE RESTRICTED BY THE INTERVAL 1965-2010, FOR WHICH THE IGRF COEFFICIENTS
c ARE KNOWN; IF IYEAR IS OUTSIDE THIS INTERVAL, THEN THE SUBROUTINE USES THE
C NEAREST LIMITING VALUE AND PRINTS A WARNING:
C
IF(IY.LT.1965) THEN
IY=1965
WRITE (*,10) IYEAR,IY
ENDIF
IF(IY.GT.2010) THEN
IY=2010
WRITE (*,10) IYEAR,IY
ENDIF
C
C CALCULATE THE ARRAY REC, CONTAINING COEFFICIENTS FOR THE RECURSION RELATIONS,
C USED IN THE IGRF SUBROUTINE FOR CALCULATING THE ASSOCIATE LEGENDRE POLYNOMIALS
C AND THEIR DERIVATIVES:
c
DO 20 N=1,14
N2=2*N-1
N2=N2*(N2-2)
DO 20 M=1,N
MN=N*(N-1)/2+M
20 REC(MN)=DFLOAT((N-M)*(N+M-2))/DFLOAT(N2)
C
IF (IY.LT.1970) GOTO 50 !INTERPOLATE BETWEEN 1965 - 1970
IF (IY.LT.1975) GOTO 60 !INTERPOLATE BETWEEN 1970 - 1975
IF (IY.LT.1980) GOTO 70 !INTERPOLATE BETWEEN 1975 - 1980
IF (IY.LT.1985) GOTO 80 !INTERPOLATE BETWEEN 1980 - 1985
IF (IY.LT.1990) GOTO 90 !INTERPOLATE BETWEEN 1985 - 1990
IF (IY.LT.1995) GOTO 100 !INTERPOLATE BETWEEN 1990 - 1995
IF (IY.LT.2000) GOTO 110 !INTERPOLATE BETWEEN 1995 - 2000
IF (IY.LT.2005) GOTO 120 !INTERPOLATE BETWEEN 2000 - 2005
C
C EXTRAPOLATE BEYOND 2005:
C
DT=DFLOAT(IY)+DFLOAT(IDAY-1)/365.25D0-2005.D0
DO 40 N=1,105
G(N)=G05(N)
H(N)=H05(N)
IF (N.GT.45) GOTO 40
G(N)=G(N)+DG05(N)*DT
H(N)=H(N)+DH05(N)*DT
40 CONTINUE
GOTO 300
C
C INTERPOLATE BETWEEEN 1965 - 1970:
C
50 F2=(DFLOAT(IY)+DFLOAT(IDAY-1)/365.25D0-1965)/5.D0
F1=1.D0-F2
DO 55 N=1,105
G(N)=G65(N)*F1+G70(N)*F2
55 H(N)=H65(N)*F1+H70(N)*F2
GOTO 300
C
C INTERPOLATE BETWEEN 1970 - 1975:
C
60 F2=(DFLOAT(IY)+DFLOAT(IDAY-1)/365.25D0-1970)/5.D0
F1=1.D0-F2
DO 65 N=1,105
G(N)=G70(N)*F1+G75(N)*F2
65 H(N)=H70(N)*F1+H75(N)*F2
GOTO 300
C
C INTERPOLATE BETWEEN 1975 - 1980:
C
70 F2=(DFLOAT(IY)+DFLOAT(IDAY-1)/365.25D0-1975)/5.D0
F1=1.D0-F2
DO 75 N=1,105
G(N)=G75(N)*F1+G80(N)*F2
75 H(N)=H75(N)*F1+H80(N)*F2
GOTO 300
C
C INTERPOLATE BETWEEN 1980 - 1985:
C
80 F2=(DFLOAT(IY)+DFLOAT(IDAY-1)/365.25D0-1980)/5.D0
F1=1.D0-F2
DO 85 N=1,105
G(N)=G80(N)*F1+G85(N)*F2
85 H(N)=H80(N)*F1+H85(N)*F2
GOTO 300
C
C INTERPOLATE BETWEEN 1985 - 1990:
C
90 F2=(DFLOAT(IY)+DFLOAT(IDAY-1)/365.25D0-1985)/5.D0
F1=1.D0-F2
DO 95 N=1,105
G(N)=G85(N)*F1+G90(N)*F2
95 H(N)=H85(N)*F1+H90(N)*F2
GOTO 300
C
C INTERPOLATE BETWEEN 1990 - 1995:
C
100 F2=(DFLOAT(IY)+DFLOAT(IDAY-1)/365.25D0-1990)/5.D0
F1=1.D0-F2
DO 105 N=1,105
G(N)=G90(N)*F1+G95(N)*F2
105 H(N)=H90(N)*F1+H95(N)*F2
GOTO 300
C
C INTERPOLATE BETWEEN 1995 - 2000:
C
110 F2=(DFLOAT(IY)+DFLOAT(IDAY-1)/365.25D0-1995)/5.D0
F1=1.D0-F2
DO 115 N=1,105 ! THE 2000 COEFFICIENTS (G00) GO THROUGH THE ORDER 13, NOT 10
G(N)=G95(N)*F1+G00(N)*F2
115 H(N)=H95(N)*F1+H00(N)*F2
GOTO 300
C
C INTERPOLATE BETWEEN 2000 - 2005:
C
120 F2=(DFLOAT(IY)+DFLOAT(IDAY-1)/365.25D0-2000)/5.D0
F1=1.D0-F2
DO 125 N=1,105
G(N)=G00(N)*F1+G05(N)*F2
125 H(N)=H00(N)*F1+H05(N)*F2
GOTO 300
C
C COEFFICIENTS FOR A GIVEN YEAR HAVE BEEN CALCULATED; NOW MULTIPLY
C THEM BY SCHMIDT NORMALIZATION FACTORS:
C
300 S=1.D0
DO 130 N=2,14
MN=N*(N-1)/2+1
S=S*DFLOAT(2*N-3)/DFLOAT(N-1)
G(MN)=G(MN)*S
H(MN)=H(MN)*S
P=S
DO 130 M=2,N
AA=1.D0
IF (M.EQ.2) AA=2.D0
P=P*DSQRT(AA*DFLOAT(N-M+1)/DFLOAT(N+M-2))
MNN=MN+M-1
G(MNN)=G(MNN)*P
130 H(MNN)=H(MNN)*P
G10=-G(2)
G11= G(3)
H11= H(3)
C
C NOW CALCULATE GEO COMPONENTS OF THE UNIT VECTOR EzMAG, PARALLEL TO GEODIPOLE AXIS:
C SIN(TETA0)*COS(LAMBDA0), SIN(TETA0)*SIN(LAMBDA0), AND COS(TETA0)
C ST0 * CL0 ST0 * SL0 CT0
C
SQ=G11**2+H11**2
SQQ=DSQRT(SQ)
SQR=DSQRT(G10**2+SQ)
SL0=-H11/SQQ
CL0=-G11/SQQ
ST0=SQQ/SQR
CT0=G10/SQR
STCL=ST0*CL0
STSL=ST0*SL0
CTSL=CT0*SL0
CTCL=CT0*CL0
C
C NOW CALCULATE GEI COMPONENTS (S1,S2,S3) OF THE UNIT VECTOR S = EX_GSE
C POINTING FROM THE EARTH'S CENTER TO SUN
C
CALL SUN_08 (IY,IDAY,IHOUR,MIN,ISEC,GST,SLONG,SRASN,SDEC)
C
S1=DCOS(SRASN)*DCOS(SDEC)
S2=DSIN(SRASN)*DCOS(SDEC)
S3=DSIN(SDEC)
C
C NOW CALCULATE GEI COMPONENTS (DZ1,DZ2,DZ3) OF THE UNIT VECTOR EZGSE
C POINTING NORTHWARD AND ORTHOGONAL TO THE ECLIPTIC PLANE, AS
C (0,-SIN(OBLIQ),COS(OBLIQ)). FOR THE EPOCH 1978, OBLIQ = 23.44214 DEGS.
C HERE WE USE A MORE ACCURATE TIME-DEPENDENT VALUE, DETERMINED AS:
C
DJ=DFLOAT(365*(IY-1900)+(IY-1901)/4 +IDAY)
* -0.5+DFLOAT(IHOUR*3600+MIN*60+ISEC)/86400.D0
T=DJ/36525.D0
OBLIQ=(23.45229D0-0.0130125D0*T)/57.2957795D0
DZ1=0.D0
DZ2=-DSIN(OBLIQ)
DZ3=DCOS(OBLIQ)
C
C NOW WE OBTAIN GEI COMPONENTS OF THE UNIT VECTOR EYGSE=(DY1,DY2,DY3),
C COMPLETING THE RIGHT-HANDED SYSTEM. THEY CAN BE FOUND FROM THE VECTOR
C PRODUCT EZGSE x EXGSE = (DZ1,DZ2,DZ3) x (S1,S2,S3):
C
DY1=DZ2*S3-DZ3*S2
DY2=DZ3*S1-DZ1*S3
DY3=DZ1*S2-DZ2*S1
C
C NOW LET'S CALCULATE GEI COMPONENTS OF THE UNIT VECTOR X = EXGSW, DIRECTED ANTIPARALLEL
C TO THE OBSERVED SOLAR WIND FLOW. FIRST, CALCULATE ITS COMPONENTS IN GSE:
C
V=DSQRT(VGSEX**2+VGSEY**2+VGSEZ**2)
DX1=-VGSEX/V
DX2=-VGSEY/V
DX3=-VGSEZ/V
C
C THEN IN GEI:
C
X1=DX1*S1+DX2*DY1+DX3*DZ1
X2=DX1*S2+DX2*DY2+DX3*DZ2
X3=DX1*S3+DX2*DY3+DX3*DZ3
C
C NOW CALCULATE GEI COMPONENTS (DIP1,DIP2,DIP3) OF THE UNIT VECTOR DIP = EZ_SM = EZ_MAG,
C ALIGNED WITH THE GEODIPOLE AND POINTING NORTHWARD FROM ECLIPTIC PLANE:
C
CGST=DCOS(GST)
SGST=DSIN(GST)
C
DIP1=STCL*CGST-STSL*SGST
DIP2=STCL*SGST+STSL*CGST
DIP3=CT0
C
C THIS ALLOWS US TO CALCULATE GEI COMPONENTS OF THE UNIT VECTOR Y = EYGSW
C BY TAKING THE VECTOR PRODUCT DIP x X AND NORMALIZING IT TO UNIT LENGTH:
C
Y1=DIP2*X3-DIP3*X2
Y2=DIP3*X1-DIP1*X3
Y3=DIP1*X2-DIP2*X1
Y=DSQRT(Y1*Y1+Y2*Y2+Y3*Y3)
Y1=Y1/Y
Y2=Y2/Y
Y3=Y3/Y
C
C AND GEI COMPONENTS OF THE UNIT VECTOR Z = EZGSW = EXGSW x EYGSW = X x Y:
C
Z1=X2*Y3-X3*Y2
Z2=X3*Y1-X1*Y3
Z3=X1*Y2-X2*Y1
C
C ELEMENTS OF THE MATRIX GSE TO GSW ARE THE SCALAR PRODUCTS:
C
C E11=(EXGSE,EXGSW) E12=(EXGSE,EYGSW) E13=(EXGSE,EZGSW)
C E21=(EYGSE,EXGSW) E22=(EYGSE,EYGSW) E23=(EYGSE,EZGSW)
C E31=(EZGSE,EXGSW) E32=(EZGSE,EYGSW) E33=(EZGSE,EZGSW)
C
E11= S1*X1 +S2*X2 +S3*X3
E12= S1*Y1 +S2*Y2 +S3*Y3
E13= S1*Z1 +S2*Z2 +S3*Z3
E21=DY1*X1+DY2*X2+DY3*X3
E22=DY1*Y1+DY2*Y2+DY3*Y3
E23=DY1*Z1+DY2*Z2+DY3*Z3
E31=DZ1*X1+DZ2*X2+DZ3*X3
E32=DZ1*Y1+DZ2*Y2+DZ3*Y3
E33=DZ1*Z1+DZ2*Z2+DZ3*Z3
C
C GEODIPOLE TILT ANGLE IN THE GSW SYSTEM: PSI=ARCSIN(DIP,EXGSW)
C
SPS=DIP1*X1+DIP2*X2+DIP3*X3
CPS=DSQRT(1.D0-SPS**2)
PSI=DASIN(SPS)
C
C ELEMENTS OF THE MATRIX GEO TO GSW ARE THE SCALAR PRODUCTS:
C
C A11=(EXGEO,EXGSW), A12=(EYGEO,EXGSW), A13=(EZGEO,EXGSW),
C A21=(EXGEO,EYGSW), A22=(EYGEO,EYGSW), A23=(EZGEO,EYGSW),
C A31=(EXGEO,EZGSW), A32=(EYGEO,EZGSW), A33=(EZGEO,EZGSW),
C
C ALL THE UNIT VECTORS IN BRACKETS ARE ALREADY DEFINED IN GEI:
C
C EXGEO=(CGST,SGST,0), EYGEO=(-SGST,CGST,0), EZGEO=(0,0,1)
C EXGSW=(X1,X2,X3), EYGSW=(Y1,Y2,Y3), EZGSW=(Z1,Z2,Z3)
C AND THEREFORE:
C
A11=X1*CGST+X2*SGST
A12=-X1*SGST+X2*CGST
A13=X3
A21=Y1*CGST+Y2*SGST
A22=-Y1*SGST+Y2*CGST
A23=Y3
A31=Z1*CGST+Z2*SGST
A32=-Z1*SGST+Z2*CGST
A33=Z3
C
C NOW CALCULATE ELEMENTS OF THE MATRIX MAG TO SM (ONE ROTATION ABOUT THE GEODIPOLE AXIS);
C THEY ARE FOUND AS THE SCALAR PRODUCTS: CFI=GM22=(EYSM,EYMAG)=(EYGSW,EYMAG),
C SFI=GM23=(EYSM,EXMAG)=(EYGSW,EXMAG),
C DERIVED AS FOLLOWS:
C
C IN GEO, THE VECTORS EXMAG AND EYMAG HAVE THE COMPONENTS (CT0*CL0,CT0*SL0,-ST0)
C AND (-SL0,CL0,0), RESPECTIVELY. HENCE, IN GEI THEIR COMPONENTS ARE:
C EXMAG: CT0*CL0*COS(GST)-CT0*SL0*SIN(GST)
C CT0*CL0*SIN(GST)+CT0*SL0*COS(GST)
C -ST0
C EYMAG: -SL0*COS(GST)-CL0*SIN(GST)
C -SL0*SIN(GST)+CL0*COS(GST)
C 0
C NOW, NOTE THAT GEI COMPONENTS OF EYSM=EYGSW WERE FOUND ABOVE AS Y1, Y2, AND Y3,
C AND WE ONLY HAVE TO COMBINE THESE QUANTITIES INTO SCALAR PRODUCTS:
C
EXMAGX=CT0*(CL0*CGST-SL0*SGST)
EXMAGY=CT0*(CL0*SGST+SL0*CGST)
EXMAGZ=-ST0
EYMAGX=-(SL0*CGST+CL0*SGST)
EYMAGY=-(SL0*SGST-CL0*CGST)
CFI=Y1*EYMAGX+Y2*EYMAGY
SFI=Y1*EXMAGX+Y2*EXMAGY+Y3*EXMAGZ
C
10 FORMAT(//1X,
*'**** RECALC_08 WARNS: YEAR IS OUT OF INTERVAL 1965-2010: IYEAR=',
*I4,/,6X,'CALCULATIONS WILL BE DONE FOR IYEAR=',I4,/)
RETURN
END
c
c==================================================================================
SUBROUTINE GSWGSE_08 (XGSW,YGSW,ZGSW,XGSE,YGSE,ZGSE,J)
C
C THIS SUBROUTINE TRANSFORMS COMPONENTS OF ANY VECTOR BETWEEN THE STANDARD GSE
C COORDINATE SYSTEM AND THE GEOCENTRIC SOLAR-WIND (GSW, aka GSWM), DEFINED AS FOLLOWS
C (HONES ET AL., PLANET.SPACE SCI., V.34, P.889, 1986; TSYGANENKO ET AL., JGRA,
C V.103(A4), P.6827, 1998):
C
C IN THE GSW SYSTEM, X AXIS IS ANTIPARALLEL TO THE OBSERVED DIRECTION OF THE SOLAR WIND FLOW.
C TWO OTHER AXES, Y AND Z, ARE DEFINED IN THE SAME WAY AS FOR THE STANDARD GSM, THAT IS,
C Z AXIS ORTHOGONAL TO X AXIS, POINTS NORTHWARD, AND LIES IN THE PLANE DEFINED BY THE X-
C AND GEODIPOLE AXIS. THE Y AXIS COMPLETES THE RIGHT-HANDED SYSTEM.
C
C THE GSW SYSTEM BECOMES IDENTICAL TO THE STANDARD GSM IN THE CASE OF
C A STRICTLY RADIAL SOLAR WIND FLOW.
C
C AUTHOR: N. A. TSYGANENKO
C ADDED TO 2008 VERSION OF GEOPACK: JAN 27, 2008.
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C J>0 J<0
C-----INPUT: J,XGSW,YGSW,ZGSW J,XGSE,YGSE,ZGSE
C-----OUTPUT: XGSE,YGSE,ZGSE XGSW,YGSW,ZGSW
C
C IMPORTANT THINGS TO REMEMBER:
C
C (1) BEFORE CALLING GSWGSE_08, BE SURE TO INVOKE SUBROUTINE RECALC_08, IN ORDER
C TO DEFINE ALL NECESSARY ELEMENTS OF TRANSFORMATION MATRICES
C
C (2) IN THE ABSENCE OF INFORMATION ON THE SOLAR WIND DIRECTION, E.G., WITH ONLY SCALAR
C SPEED V KNOWN, THIS SUBROUTINE CAN BE USED TO CONVERT VECTORS TO ABERRATED
C COORDINATE SYSTEM, TAKING INTO ACCOUNT EARTH'S ORBITAL SPEED OF 29 KM/S.
C TO DO THAT, SPECIFY THE LAST 3 PARAMETERS IN RECALC_08 AS FOLLOWS:
C VGSEX=-V, VGSEY=29.0, VGSEZ=0.0.
C
C IT SHOULD ALSO BE KEPT IN MIND THAT IN SOME SOLAR WIND DATABASES THE ABERRATION
C EFFECT HAS ALREADY BEEN TAKEN INTO ACCOUNT BY SUBTRACTING 29 KM/S FROM VYGSE;
C IN THAT CASE, THE ORIGINAL VYGSE VALUES SHOULD BE RESTORED BY ADDING BACK THE
C 29 KM/S CORRECTION. WHETHER OR NOT TO DO THAT, MUST BE VERIFIED WITH THE DATA
C ORIGINATOR (OR CAN BE DETERMINED BY CALCULATING THE AVERAGE VGSEY OVER
C A SUFFICIENTLY LONG TIME INTERVAL)
C
C (3) IF NO INFORMATION IS AVAILABLE ON THE SOLAR WIND SPEED, THEN SET VGSEX=-400.0
c AND VGSEY=VGSEZ=0. IN THAT CASE, THE GSW COORDINATE SYSTEM BECOMES
c IDENTICAL TO THE STANDARD ONE.
C
IMPLICIT REAL*8 (A-H,O-Z)
COMMON /GEOPACK1/ AAA(25),E11,E21,E31,E12,E22,E32,E13,E23,E33
C
C DIRECT TRANSFORMATION:
C
IF (J.GT.0) THEN
XGSE=XGSW*E11+YGSW*E12+ZGSW*E13
YGSE=XGSW*E21+YGSW*E22+ZGSW*E23
ZGSE=XGSW*E31+YGSW*E32+ZGSW*E33
ENDIF
C
C INVERSE TRANSFORMATION: CARRIED OUT USING THE TRANSPOSED MATRIX:
C
IF (J.LT.0) THEN
XGSW=XGSE*E11+YGSE*E21+ZGSE*E31
YGSW=XGSE*E12+YGSE*E22+ZGSE*E32
ZGSW=XGSE*E13+YGSE*E23+ZGSE*E33
ENDIF
C
RETURN
END
C
C========================================================================================
C
SUBROUTINE GEOMAG_08 (XGEO,YGEO,ZGEO,XMAG,YMAG,ZMAG,J)
C
C CONVERTS GEOGRAPHIC (GEO) TO DIPOLE (MAG) COORDINATES OR VICE VERSA.
C
C J>0 J<0
C-----INPUT: J,XGEO,YGEO,ZGEO J,XMAG,YMAG,ZMAG
C-----OUTPUT: XMAG,YMAG,ZMAG XGEO,YGEO,ZGEO
C
C ATTENTION: SUBROUTINE RECALC_08 MUST BE INVOKED BEFORE GEOMAG_08 IN TWO CASES:
C /A/ BEFORE THE FIRST TRANSFORMATION OF COORDINATES
C /B/ IF THE VALUES OF IYEAR AND/OR IDAY HAVE BEEN CHANGED
C
C NO INFORMATION IS REQUIRED HERE ON THE SOLAR WIND VELOCITY, SO ONE
C CAN SET VGSEX=-400.0, VGSEY=0.0, VGSEZ=0.0 IN RECALC_08.
C
C LAST MOFIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
COMMON /GEOPACK1/ ST0,CT0,SL0,CL0,CTCL,STCL,CTSL,STSL,AB(26)
IF(J.GT.0) THEN
XMAG=XGEO*CTCL+YGEO*CTSL-ZGEO*ST0
YMAG=YGEO*CL0-XGEO*SL0
ZMAG=XGEO*STCL+YGEO*STSL+ZGEO*CT0
ELSE
XGEO=XMAG*CTCL-YMAG*SL0+ZMAG*STCL
YGEO=XMAG*CTSL+YMAG*CL0+ZMAG*STSL
ZGEO=ZMAG*CT0-XMAG*ST0
ENDIF
RETURN
END
c
c=========================================================================================
c
SUBROUTINE GEIGEO_08 (XGEI,YGEI,ZGEI,XGEO,YGEO,ZGEO,J)
C
C CONVERTS EQUATORIAL INERTIAL (GEI) TO GEOGRAPHICAL (GEO) COORDS
C OR VICE VERSA.
C J>0 J<0
C----INPUT: J,XGEI,YGEI,ZGEI J,XGEO,YGEO,ZGEO
C----OUTPUT: XGEO,YGEO,ZGEO XGEI,YGEI,ZGEI
C
C ATTENTION: SUBROUTINE RECALC_08 MUST BE INVOKED BEFORE GEIGEO_08 IN TWO CASES:
C /A/ BEFORE THE FIRST TRANSFORMATION OF COORDINATES
C /B/ IF THE CURRENT VALUES OF IYEAR,IDAY,IHOUR,MIN,ISEC HAVE BEEN CHANGED
C
C NO INFORMATION IS REQUIRED HERE ON THE SOLAR WIND VELOCITY, SO ONE
C CAN SET VGSEX=-400.0, VGSEY=0.0, VGSEZ=0.0 IN RECALC_08.
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
COMMON /GEOPACK1/ A(13),CGST,SGST,B(19)
C
IF(J.GT.0) THEN
XGEO=XGEI*CGST+YGEI*SGST
YGEO=YGEI*CGST-XGEI*SGST
ZGEO=ZGEI
ELSE
XGEI=XGEO*CGST-YGEO*SGST
YGEI=YGEO*CGST+XGEO*SGST
ZGEI=ZGEO
ENDIF
RETURN
END
C
C=======================================================================================
C
SUBROUTINE MAGSM_08 (XMAG,YMAG,ZMAG,XSM,YSM,ZSM,J)
C
C CONVERTS DIPOLE (MAG) TO SOLAR MAGNETIC (SM) COORDINATES OR VICE VERSA
C
C J>0 J<0
C----INPUT: J,XMAG,YMAG,ZMAG J,XSM,YSM,ZSM
C----OUTPUT: XSM,YSM,ZSM XMAG,YMAG,ZMAG
C
C ATTENTION: SUBROUTINE RECALC_08 MUST BE INVOKED BEFORE MAGSM_08 IN THREE CASES:
C /A/ BEFORE THE FIRST TRANSFORMATION OF COORDINATES, OR
C /B/ IF THE VALUES OF IYEAR,IDAY,IHOUR,MIN,ISEC HAVE CHANGED, AND/OR
C /C/ IF THE VALUES OF COMPONENTS OF THE SOLAR WIND FLOW VELOCITY HAVE CHANGED
C
C IMPORTANT NOTE:
C
C A NON-STANDARD DEFINITION IS IMPLIED HERE FOR THE SOLAR MAGNETIC COORDINATE
C SYSTEM: IT IS ASSUMED THAT THE XSM AXIS LIES IN THE PLANE DEFINED BY THE
C GEODIPOLE AXIS AND THE OBSERVED VECTOR OF THE SOLAR WIND FLOW (RATHER THAN
C THE EARTH-SUN LINE). IN ORDER TO CONVERT MAG COORDINATES TO AND FROM THE
C STANDARD SM COORDINATES, INVOKE RECALC_08 WITH VGSEX=-400.0, VGSEY=0.0, VGSEZ=0.0
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
COMMON /GEOPACK1/ A(8),SFI,CFI,B(24)
C
IF (J.GT.0) THEN
XSM=XMAG*CFI-YMAG*SFI
YSM=XMAG*SFI+YMAG*CFI
ZSM=ZMAG
ELSE
XMAG=XSM*CFI+YSM*SFI
YMAG=YSM*CFI-XSM*SFI
ZMAG=ZSM
ENDIF
RETURN
END
C
C=====================================================================================
C
SUBROUTINE SMGSW_08 (XSM,YSM,ZSM,XGSW,YGSW,ZGSW,J)
C
C CONVERTS SOLAR MAGNETIC (SM) TO GEOCENTRIC SOLAR-WIND (GSW) COORDINATES OR VICE VERSA.
C
C J>0 J<0
C-----INPUT: J,XSM,YSM,ZSM J,XGSW,YGSW,ZGSW
C----OUTPUT: XGSW,YGSW,ZGSW XSM,YSM,ZSM
C
C ATTENTION: SUBROUTINE RECALC_08 MUST BE INVOKED BEFORE SMGSW_08 IN THREE CASES:
C /A/ BEFORE THE FIRST TRANSFORMATION OF COORDINATES
C /B/ IF THE VALUES OF IYEAR,IDAY,IHOUR,MIN,ISEC HAVE BEEN CHANGED
C /C/ IF THE VALUES OF COMPONENTS OF THE SOLAR WIND FLOW VELOCITY HAVE CHANGED
C
C IMPORTANT NOTE:
C
C A NON-STANDARD DEFINITION IS IMPLIED HERE FOR THE SOLAR MAGNETIC (SM) COORDINATE
C SYSTEM: IT IS ASSUMED THAT THE XSM AXIS LIES IN THE PLANE DEFINED BY THE
C GEODIPOLE AXIS AND THE OBSERVED VECTOR OF THE SOLAR WIND FLOW (RATHER THAN
C THE EARTH-SUN LINE). IN ORDER TO CONVERT MAG COORDINATES TO AND FROM THE
C STANDARD SM COORDINATES, INVOKE RECALC_08 WITH VGSEX=-400.0, VGSEY=0.0, VGSEZ=0.0
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
COMMON /GEOPACK1/ A(10),SPS,CPS,B(22)
IF (J.GT.0) THEN
XGSW=XSM*CPS+ZSM*SPS
YGSW=YSM
ZGSW=ZSM*CPS-XSM*SPS
ELSE
XSM=XGSW*CPS-ZGSW*SPS
YSM=YGSW
ZSM=XGSW*SPS+ZGSW*CPS
ENDIF
RETURN
END
C
C==========================================================================================
C
SUBROUTINE GEOGSW_08 (XGEO,YGEO,ZGEO,XGSW,YGSW,ZGSW,J)
C
C CONVERTS GEOGRAPHIC (GEO) TO GEOCENTRIC SOLAR-WIND (GSW) COORDINATES OR VICE VERSA.
C
C J>0 J<0
C----- INPUT: J,XGEO,YGEO,ZGEO J,XGSW,YGSW,ZGSW
C---- OUTPUT: XGSW,YGSW,ZGSW XGEO,YGEO,ZGEO
C
C ATTENTION: SUBROUTINE RECALC_08 MUST BE INVOKED BEFORE GEOGSW_08 IN THREE CASES:
C /A/ BEFORE THE FIRST TRANSFORMATION OF COORDINATES, OR
C /B/ IF THE VALUES OF IYEAR,IDAY,IHOUR,MIN,ISEC HAVE CHANGED, AND/OR
C /C/ IF THE VALUES OF COMPONENTS OF THE SOLAR WIND FLOW VELOCITY HAVE CHANGED
C
C NOTE: THIS SUBROUTINE CONVERTS GEO VECTORS TO AND FROM THE SOLAR-WIND GSW COORDINATE
C SYSTEM, TAKING INTO ACCOUNT POSSIBLE DEFLECTIONS OF THE SOLAR WIND DIRECTION FROM
C STRICTLY RADIAL. BEFORE CONVERTING TO/FROM STANDARD GSM COORDINATES, INVOKE RECALC_08
C WITH VGSEX=-400.0 and VGSEY=0.0, VGSEZ=0.0
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
COMMON /GEOPACK1/ AA(16),A11,A21,A31,A12,A22,A32,A13,A23,A33,B(9)
C
IF (J.GT.0) THEN
XGSW=A11*XGEO+A12*YGEO+A13*ZGEO
YGSW=A21*XGEO+A22*YGEO+A23*ZGEO
ZGSW=A31*XGEO+A32*YGEO+A33*ZGEO
ELSE
XGEO=A11*XGSW+A21*YGSW+A31*ZGSW
YGEO=A12*XGSW+A22*YGSW+A32*ZGSW
ZGEO=A13*XGSW+A23*YGSW+A33*ZGSW
ENDIF
RETURN
END
C
C=====================================================================================
C
SUBROUTINE GEODGEO_08 (H,XMU,R,THETA,J)
C
C THIS SUBROUTINE (1) CONVERTS VERTICAL LOCAL HEIGHT (ALTITUDE) H AND GEODETIC
C LATITUDE XMU INTO GEOCENTRIC COORDINATES R AND THETA (GEOCENTRIC RADIAL
C DISTANCE AND COLATITUDE, RESPECTIVELY; ALSO KNOWN AS ECEF COORDINATES),
C AS WELL AS (2) PERFORMS THE INVERSE TRANSFORMATION FROM {R,THETA} TO {H,XMU}.
C
C THE SUBROUTINE USES WORLD GEODETIC SYSTEM WGS84 PARAMETERS FOR THE EARTH'S
C ELLIPSOID. THE ANGULAR QUANTITIES (GEO COLATITUDE THETA AND GEODETIC LATITUDE
C XMU) ARE IN RADIANS, AND THE DISTANCES (GEOCENTRIC RADIUS R AND ALTITUDE H
C ABOVE THE EARTH'S ELLIPSOID) ARE IN KILOMETERS.
C
C IF J>0, THE TRANSFORMATION IS MADE FROM GEODETIC TO GEOCENTRIC COORDINATES
C USING SIMPLE DIRECT EQUATIONS.
C IF J<0, THE INVERSE TRANSFORMATION FROM GEOCENTRIC TO GEODETIC COORDINATES
C IS MADE BY MEANS OF A FAST ITERATIVE ALGORITHM.
C
c-------------------------------------------------------------------------------
C J>0 | J<0
c-------------------------------------------|-----------------------------------
C--INPUT: J H XMU | J R THETA
c flag altitude (km) geodetic | flag geocentric spherical
c latitude | distance (km) colatitude
c (radians) | (radians)
c-------------------------------------------|-----------------------------------
c |
C----OUTPUT: R THETA | H XMU
C geocentric spherical | altitude (km) geodetic
C distance (km) colatitude | latitude
C (radians) | (radians)
C-------------------------------------------------------------------------------
C
C AUTHOR: N. A. TSYGANENKO
c DATE: DEC 5, 2007
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
IMPLICIT REAL*8 (A-H,O-Z)
DATA R_EQ, BETA /6378.137D0, 6.73949674228D-3/
c
c R_EQ is the semi-major axis of the Earth's ellipsoid, and BETA is its
c second eccentricity squared
c
DATA TOL /1.D-6/
c
c Direct transformation (GEOD=>GEO):
c
IF (J.GT.0) THEN
COSXMU=DCOS(XMU)
SINXMU=DSIN(XMU)
DEN=DSQRT(COSXMU**2+(SINXMU/(1.0D0+BETA))**2)
COSLAM=COSXMU/DEN
SINLAM=SINXMU/(DEN*(1.0D0+BETA))
RS=R_EQ/DSQRT(1.0D0+BETA*SINLAM**2)
X=RS*COSLAM+H*COSXMU
Z=RS*SINLAM+H*SINXMU
R=DSQRT(X**2+Z**2)
THETA=DACOS(Z/R)
ENDIF
c
c Inverse transformation (GEO=>GEOD):
c
IF (J.LT.0) THEN
N=0
PHI=1.570796327D0-THETA
PHI1=PHI
1 SP=DSIN(PHI1)
ARG=SP*(1.0D0+BETA)/DSQRT(1.0D0+BETA*(2.0D0+BETA)*SP**2)
XMUS=DASIN(ARG)
RS=R_EQ/DSQRT(1.0D0+BETA*DSIN(PHI1)**2)
COSFIMS=DCOS(PHI1-XMUS)
H=DSQRT((RS*COSFIMS)**2+R**2-RS**2)-RS*COSFIMS
Z=RS*DSIN(PHI1)+H*DSIN(XMUS)
X=RS*DCOS(PHI1)+H*DCOS(XMUS)
RR=DSQRT(X**2+Z**2)
DPHI=DASIN(Z/RR)-PHI
PHI1=PHI1-DPHI
N=N+1
IF (DABS(DPHI).GT.TOL.AND.N.LT.100) GOTO 1
XMU=XMUS
ENDIF
RETURN
END
C
C=====================================================================================
C
SUBROUTINE RHAND_08 (X,Y,Z,R1,R2,R3,IOPT,PARMOD,EXNAME,INNAME)
C
C CALCULATES THE COMPONENTS OF THE RIGHT HAND SIDE VECTOR IN THE GEOMAGNETIC FIELD
C LINE EQUATION (a subsidiary subroutine for the subroutine STEP_08)
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION PARMOD(10)
C
C EXNAME AND INNAME ARE NAMES OF SUBROUTINES FOR THE EXTERNAL AND INTERNAL
C PARTS OF THE TOTAL FIELD, E.G., T96_01 AND IGRF_GSW_08
C
COMMON /GEOPACK1/ A(12),DS3,BB(2),PSI,CC(18)
CALL EXNAME (IOPT,PARMOD,PSI,X,Y,Z,BXGSW,BYGSW,BZGSW)
CALL INNAME (X,Y,Z,HXGSW,HYGSW,HZGSW)
BX=BXGSW+HXGSW
BY=BYGSW+HYGSW
BZ=BZGSW+HZGSW
B=DS3/DSQRT(BX**2+BY**2+BZ**2)
R1=BX*B
R2=BY*B
R3=BZ*B
RETURN
END
C
C===================================================================================
C
SUBROUTINE STEP_08(X,Y,Z,DS,DSMAX,ERRIN,IOPT,PARMOD,EXNAME,INNAME)
C
C RE-CALCULATES THE INPUT VALUES {X,Y,Z} (IN GSW COORDINATES) FOR ANY POINT ON A FIELD LINE,
C BY MAKING A STEP ALONG THAT LINE USING RUNGE-KUTTA-MERSON ALGORITHM (G.N. Lance, Numerical
C methods for high-speed computers, Iliffe & Sons, London 1960.)
C DS IS A PRESCRIBED VALUE OF THE CURRENT STEP SIZE, DSMAX IS ITS UPPER LIMIT.
C ERRIN IS A PERMISSIBLE ERROR (ITS OPTIMAL VALUE SPECIFIED IN THE S/R TRACE_08)
C IF THE ACTUAL ERROR (ERRCUR) AT THE CURRENT STEP IS LARGER THAN ERRIN, THE STEP IS REJECTED,
C AND THE CALCULATION IS REPEATED ANEW WITH HALVED STEPSIZE DS.
C IF ERRCUR IS SMALLER THAN ERRIN, THE STEP IS ACCEPTED, AND THE CURRENT VALUE OF DS IS RETAINED
C FOR THE NEXT STEP.
C IF ERRCUR IS SMALLER THAN 0.04*ERRIN, THE STEP IS ACCEPTED, AND THE VALUE OF DS FOR THE NEXT STEP
C IS INCREASED BY THE FACTOR 1.5, BUT NOT LARGER THAN DSMAX.
C IOPT IS A FLAG, RESERVED FOR SPECIFYNG A VERSION OF THE EXTERNAL FIELD MODEL EXNAME.
C ARRAY PARMOD(10) CONTAINS INPUT PARAMETERS FOR THE MODEL EXNAME.
C EXNAME IS THE NAME OF THE SUBROUTINE FOR THE EXTERNAL FIELD MODEL.
C INNAME IS THE NAME OF THE SUBROUTINE FOR THE INTERNAL FIELD MODEL (EITHER DIP_08 OR IGRF_GSW_08)
C
C ALL THE ABOVE PARAMETERS ARE INPUT ONES; OUTPUT IS THE RECALCULATED VALUES OF X,Y,Z
C
C LAST MODIFICATION: APRIL 21, 2008 (SEE ERRATA AS OF THAT DATE)
C
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION PARMOD(10)
COMMON /GEOPACK1/ A(12),DS3,B(21)
EXTERNAL EXNAME,INNAME
1 DS3=-DS/3.D0
CALL RHAND_08 (X,Y,Z,R11,R12,R13,IOPT,PARMOD,EXNAME,INNAME)
CALL RHAND_08 (X+R11,Y+R12,Z+R13,R21,R22,R23,IOPT,PARMOD,EXNAME,
* INNAME)
CALL RHAND_08 (X+.5D0*(R11+R21),Y+.5D0*(R12+R22),Z+.5D0*
*(R13+R23),R31,R32,R33,IOPT,PARMOD,EXNAME,INNAME)
CALL RHAND_08 (X+.375D0*(R11+3.D0*R31),Y+.375D0*(R12+3.D0*R32
*),Z+.375D0*(R13+3.D0*R33),R41,R42,R43,IOPT,PARMOD,EXNAME,INNAME)
CALL RHAND_08 (X+1.5D0*(R11-3.D0*R31+4.D0*R41),Y+1.5D0*(R12-
*3.D0*R32+4.D0*R42),Z+1.5D0*(R13-3.D0*R33+4.D0*R43),
*R51,R52,R53,IOPT,PARMOD,EXNAME,INNAME)
ERRCUR=DABS(R11-4.5D0*R31+4.D0*R41-.5D0*R51)+DABS(R12-4.5D0*R32
*+4.D0*R42-.5D0*R52)+DABS(R13-4.5D0*R33+4.D0*R43-.5D0*R53)
C
C READY FOR MAKING THE STEP, BUT CHECK THE ACCURACY; IF INSUFFICIENT,
C REPEAT THE STEP WITH HALVED STEPSIZE:
C
IF (ERRCUR.GT.ERRIN) THEN
DS=DS*.5D0
GOTO 1
ENDIF
C
C ACCURACY IS ACCEPTABLE, BUT CHECK IF THE STEPSIZE IS NOT TOO LARGE;
C OTHERWISE REPEAT THE STEP WITH DS=DSMAX
C
IF (DABS(DS).GT.DSMAX) THEN
DS=DSIGN(DSMAX,DS)
GOTO 1
ENDIF
C
C MAKING THE STEP:
C
2 X=X+.5D0*(R11+4.D0*R41+R51)
Y=Y+.5D0*(R12+4.D0*R42+R52)
Z=Z+.5D0*(R13+4.D0*R43+R53)
C
C IF THE ACTUAL ERROR IS TOO SMALL (LESS THAN 4% OF ERRIN) AND DS SMALLER
C THAN DSMAX/1.5, THEN WE INCREASE THE STEPSIZE FOR THE NEXT STEP BY 50%
C
IF(ERRCUR.LT.ERRIN*.04D0.AND.DS.LT.DSMAX/1.5D0) DS=DS*1.5D0
RETURN
END
C
C==============================================================================
C
SUBROUTINE TRACE_08 (XI,YI,ZI,DIR,DSMAX,ERR,RLIM,R0,IOPT,PARMOD,
* EXNAME,INNAME,XF,YF,ZF,XX,YY,ZZ,L,LMAX)
C
C TRACES A FIELD LINE FROM AN ARBITRARY POINT OF SPACE TO THE EARTH'S
C SURFACE OR TO A MODEL LIMITING BOUNDARY.
C
C THIS SUBROUTINE ALLOWS TWO OPTIONS:
C
C (1) IF INNAME=IGRF_GSW_08, THEN THE IGRF MODEL WILL BE USED FOR CALCULATING
C CONTRIBUTION FROM EARTH'S INTERNAL SOURCES. IN THIS CASE, SUBROUTINE
C RECALC_08 MUST BE CALLED BEFORE USING TRACE_08, WITH PROPERLY SPECIFIED DATE,
C UNIVERSAL TIME, AND SOLAR WIND VELOCITY COMPONENTS, TO CALCULATE IN ADVANCE
C ALL QUANTITIES NEEDED FOR THE MAIN FIELD MODEL AND FOR TRANSFORMATIONS
C BETWEEN INVOLVED COORDINATE SYSTEMS.
C
C (2) IF INNAME=DIP_08, THEN A PURE DIPOLE FIELD WILL BE USED INSTEAD OF THE IGRF MODEL.
C IN THIS CASE, THE SUBROUTINE RECALC_08 MUST ALSO BE CALLED BEFORE TRACE_08.
C HERE ONE CAN CHOOSE EITHER TO
C (a) CALCULATE DIPOLE TILT ANGLE BASED ON DATE, TIME, AND SOLAR WIND DIRECTION,
C OR (b) EXPLICITLY SPECIFY THAT ANGLE, WITHOUT ANY REFERENCE TO DATE/UT/SOLAR WIND.
C IN THE LAST CASE (b), THE SINE (SPS) AND COSINE (CPS) OF THE DIPOLE TILT
C ANGLE MUST BE SPECIFIED IN ADVANCE (BUT AFTER HAVING CALLED RECALC_08) AND FORWARDED
C IN THE COMMON BLOCK /GEOPACK1/ (IN ITS 11th AND 12th ELEMENTS, RESPECTIVELY).
C IN THIS CASE THE ROLE OF THE SUBROUTINE RECALC_08 IS REDUCED TO ONLY CALCULATING
C THE COMPONENTS OF THE EARTH'S DIPOLE MOMENT.
C
C------------- INPUT PARAMETERS:
C
C XI,YI,ZI - GSW COORDS OF THE FIELD LINE STARTING POINT (IN EARTH RADII, 1 RE = 6371.2 km),
C
C DIR - SIGN OF THE TRACING DIRECTION: IF DIR=1.0 THEN THE TRACING IS MADE ANTIPARALLEL
C TO THE TOTAL FIELD VECTOR (E.G., FROM NORTHERN TO SOUTHERN CONJUGATE POINT);
C IF DIR=-1.0 THEN THE TRACING PROCEEDS IN THE OPPOSITE DIRECTION, THAT IS, PARALLEL TO
C THE TOTAL FIELD VECTOR.
C
C DSMAX - UPPER LIMIT ON THE STEPSIZE (SETS A DESIRED MAXIMAL SPACING BETWEEN
C THE FIELD LINE POINTS)
C
C ERR - PERMISSIBLE STEP ERROR. A REASONABLE ESTIMATE PROVIDING A SUFFICIENT ACCURACY FOR MOST
C APPLICATIONS IS ERR=0.0001. SMALLER/LARGER VALUES WILL RESULT IN LARGER/SMALLER NUMBER
C OF STEPS AND, HENCE, OF OUTPUT FIELD LINE POINTS. NOTE THAT USING MUCH SMALLER VALUES
C OF ERR MAY REQUIRE USING A DOUBLE PRECISION VERSION OF THE ENTIRE PACKAGE.
C
C R0 - RADIUS OF A SPHERE (IN RE), DEFINING THE INNER BOUNDARY OF THE TRACING REGION
C (USUALLY, EARTH'S SURFACE OR THE IONOSPHERE, WHERE R0~1.0)
C IF THE FIELD LINE REACHES THAT SPHERE FROM OUTSIDE, ITS INBOUND TRACING IS
C TERMINATED AND THE CROSSING POINT COORDINATES XF,YF,ZF ARE CALCULATED.
C
C RLIM - RADIUS OF A SPHERE (IN RE), DEFINING THE OUTER BOUNDARY OF THE TRACING REGION;
C IF THE FIELD LINE REACHES THAT BOUNDARY FROM INSIDE, ITS OUTBOUND TRACING IS
C TERMINATED AND THE CROSSING POINT COORDINATES XF,YF,ZF ARE CALCULATED.
C
C IOPT - A MODEL INDEX; CAN BE USED FOR SPECIFYING A VERSION OF THE EXTERNAL FIELD
C MODEL (E.G., A NUMBER OF THE KP-INDEX INTERVAL). ALTERNATIVELY, ONE CAN USE THE ARRAY
C PARMOD FOR THAT PURPOSE (SEE BELOW); IN THAT CASE IOPT IS JUST A DUMMY PARAMETER.
C
C PARMOD - A 10-ELEMENT ARRAY CONTAINING INPUT PARAMETERS NEEDED FOR A UNIQUE
C SPECIFICATION OF THE EXTERNAL FIELD MODEL. THE CONCRETE MEANING OF THE COMPONENTS
C OF PARMOD DEPENDS ON A SPECIFIC VERSION OF THAT MODEL.
C
C EXNAME - NAME OF A SUBROUTINE PROVIDING COMPONENTS OF THE EXTERNAL MAGNETIC FIELD
C (E.G., T89, OR T96_01, ETC.).
C INNAME - NAME OF A SUBROUTINE PROVIDING COMPONENTS OF THE INTERNAL MAGNETIC FIELD
C (EITHER DIP_08 OR IGRF_GSW_08).
C
C LMAX - MAXIMAL LENGTH OF THE ARRAYS XX,YY,ZZ, IN WHICH COORDINATES OF THE FIELD
C LINE POINTS ARE STORED. LMAX SHOULD BE SET EQUAL TO THE ACTUAL LENGTH OF
C THE ARRAYS, DEFINED IN THE MAIN PROGRAM AS ACTUAL ARGUMENTS OF THIS SUBROUTINE.
C
C-------------- OUTPUT PARAMETERS:
C
C XF,YF,ZF - GSW COORDINATES OF THE ENDPOINT OF THE TRACED FIELD LINE.
C XX,YY,ZZ - ARRAYS OF LENGTH LMAX, CONTAINING COORDINATES OF THE FIELD LINE POINTS.
C L - ACTUAL NUMBER OF FIELD LINE POINTS, GENERATED BY THIS SUBROUTINE.
C
C ----------------------------------------------------------
C
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
C AUTHOR: N. A. TSYGANENKO
C
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION XX(LMAX),YY(LMAX),ZZ(LMAX), PARMOD(10)
COMMON /GEOPACK1/ AA(12),DD,BB(21)
EXTERNAL EXNAME,INNAME
C
L=0
NREV=0
DD=DIR
C
C INITIALIZE THE STEP SIZE AND STARTING PONT:
C
DS=0.5D0*DIR
X=XI
Y=YI
Z=ZI
c
c here we call RHAND_08 just to find out the sign of the radial component of the field
c vector, and to determine the initial direction of the tracing (i.e., either away
c or towards Earth):
c
CALL RHAND_08 (X,Y,Z,R1,R2,R3,IOPT,PARMOD,EXNAME,INNAME)
AD=0.01D0
IF (X*R1+Y*R2+Z*R3.LT.0.D0) AD=-0.01D0
C
c |AD|=0.01 and its sign follows the rule:
c (1) if DIR=1 (tracing antiparallel to B vector) then the sign of AD is the same as of Br
c (2) if DIR=-1 (tracing parallel to B vector) then the sign of AD is opposite to that of Br
c AD is defined in order to initialize the value of RR (radial distance at previous step):
RR=DSQRT(X**2+Y**2+Z**2)+AD
c
1 L=L+1
IF(L.GT.LMAX) GOTO 7
XX(L)=X
YY(L)=Y
ZZ(L)=Z
RYZ=Y**2+Z**2
R2=X**2+RYZ
R=DSQRT(R2)
C
c check if the line hit the outer tracing boundary; if yes, then terminate
c the tracing (label 8). The outer boundary is assumed reached, when the line
c crosses any of the 3 surfaces: (1) a sphere R=RLIM, (2) a cylinder of radius 40Re,
c coaxial with the XGSW axis, (3) the plane X=20Re:
IF (R.GT.RLIM.OR.RYZ.GT.1600.D0.OR.X.GT.20.D0) GOTO 8
c
c check whether or not the inner tracing boundary was crossed from outside,
c if yes, then calculate the footpoint position by interpolation (go to label 6):
c
IF (R.LT.R0.AND.RR.GT.R) GOTO 6
c check if we are moving outward, or R is still larger than 3Re; if yes, proceed further:
c
IF (R.GE.RR.OR.R.GE.3.D0) GOTO 4
c
c now we entered inside the sphere R=3: to avoid too large steps (and hence
c inaccurate interpolated position of the footpoint), enforce the progressively
c smaller stepsize values as we approach the inner boundary R=R0:
c
FC=0.2D0
IF(R-R0.LT.0.05D0) FC=0.05D0
AL=FC*(R-R0+0.2D0)
DS=DIR*AL
c
4 XR=X
YR=Y
ZR=Z
c
DRP=R-RR
RR=R
c
CALL STEP_08 (X,Y,Z,DS,DSMAX,ERR,IOPT,PARMOD,EXNAME,INNAME)
c
C check the total number NREV of changes in the tracing radial direction; (NREV.GT.2) means
c that the line started making multiple loops, in which case we stop the process:
C
R=DSQRT(X**2+Y**2+Z**2)
DR=R-RR
IF (DRP*DR.LT.0.D0) NREV=NREV+1
IF (NREV.GT.2) GOTO 8
C
GOTO 1
c
c find the footpoint position by interpolating between the current and previous
c field line points:
c
6 R1=(R0-R)/(RR-R)
X=X-(X-XR)*R1
Y=Y-(Y-YR)*R1
Z=Z-(Z-ZR)*R1
GOTO 8
7 WRITE (*,10)
L=LMAX
8 XF=X
YF=Y
ZF=Z
RETURN
10 FORMAT(//,1X,'**** COMPUTATIONS IN THE SUBROUTINE TRACE_08 ARE',
*' TERMINATED: THE NUMBER OF POINTS EXCEEDED LMAX ****'//)
END
c
C====================================================================================
C
SUBROUTINE SHUETAL_MGNP_08(XN_PD,VEL,BZIMF,XGSW,YGSW,ZGSW,
* XMGNP,YMGNP,ZMGNP,DIST,ID)
C
C FOR ANY POINT OF SPACE WITH COORDINATES (XGSW,YGSW,ZGSW) AND SPECIFIED CONDITIONS
C IN THE INCOMING SOLAR WIND, THIS SUBROUTINE:
C
C (1) DETERMINES IF THE POINT (XGSW,YGSW,ZGSW) LIES INSIDE OR OUTSIDE THE
C MODEL MAGNETOPAUSE OF SHUE ET AL. (JGR-A, V.103, P. 17691, 1998).
C
C (2) CALCULATES THE GSW POSITION OF A POINT {XMGNP,YMGNP,ZMGNP}, LYING AT THE MODEL
C MAGNETOPAUSE AND ASYMPTOTICALLY TENDING TO THE NEAREST BOUNDARY POINT WITH
C RESPECT TO THE OBSERVATION POINT {XGSW,YGSW,ZGSW}, AS IT APPROACHES THE MAGNETO-
C PAUSE.
C
C INPUT: XN_PD - EITHER SOLAR WIND PROTON NUMBER DENSITY (PER C.C.) (IF VEL>0)
C OR THE SOLAR WIND RAM PRESSURE IN NANOPASCALS (IF VEL<0)
C BZIMF - IMF BZ IN NANOTESLAS
C
C VEL - EITHER SOLAR WIND VELOCITY (KM/SEC)
C OR ANY NEGATIVE NUMBER, WHICH INDICATES THAT XN_PD STANDS
C FOR THE SOLAR WIND PRESSURE, RATHER THAN FOR THE DENSITY
C
C XGSW,YGSW,ZGSW - GSW POSITION OF THE OBSERVATION POINT IN EARTH RADII
C
C OUTPUT: XMGNP,YMGNP,ZMGNP - GSW POSITION OF THE BOUNDARY POINT
C DIST - DISTANCE (IN RE) BETWEEN THE OBSERVATION POINT (XGSW,YGSW,ZGSW)
C AND THE MODEL NAGNETOPAUSE
C ID - POSITION FLAG: ID=+1 (-1) MEANS THAT THE OBSERVATION POINT
C LIES INSIDE (OUTSIDE) OF THE MODEL MAGNETOPAUSE, RESPECTIVELY.
C
C OTHER SUBROUTINES USED: T96_MGNP_08
C
c AUTHOR: N.A. TSYGANENKO,
C DATE: APRIL 4, 2003.
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
IMPLICIT REAL*8 (A-H,O-Z)
C
IF (VEL.LT.0.) THEN
P=XN_PD
ELSE
P=1.94D-6*XN_PD*VEL**2 ! P IS THE SOLAR WIND DYNAMIC PRESSURE (IN nPa)
ENDIF
c
c DEFINE THE ANGLE PHI, MEASURED DUSKWARD FROM THE NOON-MIDNIGHT MERIDIAN PLANE;
C IF THE OBSERVATION POINT LIES ON THE X AXIS, THE ANGLE PHI CANNOT BE UNIQUELY
C DEFINED, AND WE SET IT AT ZERO:
c
IF (YGSW.NE.0.D0.OR.ZGSW.NE.0.D0) THEN
PHI=DATAN2(YGSW,ZGSW)
ELSE
PHI=0.D0
ENDIF
C
C FIRST, FIND OUT IF THE OBSERVATION POINT LIES INSIDE THE SHUE ET AL BDRY
C AND SET THE VALUE OF THE ID FLAG:
C
ID=-1
R0=(10.22D0+1.29D0*DTANH(.184D0*(BZIMF+8.14D0)))*P**(-.15151515D0)
ALPHA=(0.58D0-0.007D0*BZIMF)*(1.D0+0.024*DLOG(P))
R=DSQRT(XGSW**2+YGSW**2+ZGSW**2)
RM=R0*(2.D0/(1.D0+XGSW/R))**ALPHA
IF (R.LE.RM) ID=+1
C
C NOW, FIND THE CORRESPONDING T96 MAGNETOPAUSE POSITION, TO BE USED AS
C A STARTING APPROXIMATION IN THE SEARCH OF A CORRESPONDING SHUE ET AL.
C BOUNDARY POINT:
C
CALL T96_MGNP_08(P,-1.D0,XGSW,YGSW,ZGSW,XMT96,YMT96,ZMT96,DIST,
* ID96)
C
RHO2=YMT96**2+ZMT96**2
R=DSQRT(RHO2+XMT96**2)
ST=DSQRT(RHO2)/R
CT=XMT96/R
C
C NOW, USE NEWTON'S ITERATIVE METHOD TO FIND THE NEAREST POINT AT THE
C SHUE ET AL.'S BOUNDARY:
C
NIT=0
1 T=DATAN2(ST,CT)
RM=R0*(2.D0/(1.D0+CT))**ALPHA
F=R-RM
GRADF_R=1.D0
GRADF_T=-ALPHA/R*RM*ST/(1.D0+CT)
GRADF=DSQRT(GRADF_R**2+GRADF_T**2)
DR=-F/GRADF**2
DT= DR/R*GRADF_T
R=R+DR
T=T+DT
ST=DSIN(T)
CT=DCOS(T)
DS=DSQRT(DR**2+(R*DT)**2)
NIT=NIT+1
IF (NIT.GT.1000) THEN
PRINT *,
*' BOUNDARY POINT COULD NOT BE FOUND; ITERATIONS DO NOT CONVERGE'
ENDIF
IF (DS.GT.1.D-4) GOTO 1
XMGNP=R*DCOS(T)
RHO= R*DSIN(T)
YMGNP=RHO*DSIN(PHI)
ZMGNP=RHO*DCOS(PHI)
DIST=DSQRT((XGSW-XMGNP)**2+(YGSW-YMGNP)**2+(ZGSW-ZMGNP)**2)
RETURN
END
C
C=======================================================================================
C
SUBROUTINE T96_MGNP_08(XN_PD,VEL,XGSW,YGSW,ZGSW,XMGNP,YMGNP,ZMGNP,
* DIST,ID)
C
C FOR ANY POINT OF SPACE WITH GIVEN COORDINATES (XGSW,YGSW,ZGSW), THIS SUBROUTINE DEFINES
C THE POSITION OF A POINT (XMGNP,YMGNP,ZMGNP) AT THE T96 MODEL MAGNETOPAUSE WITH THE
C SAME VALUE OF THE ELLIPSOIDAL TAU-COORDINATE, AND THE DISTANCE BETWEEN THEM. THIS IS
C NOT THE SHORTEST DISTANCE D_MIN TO THE BOUNDARY, BUT DIST ASYMPTOTICALLY TENDS TO D_MIN,
C AS THE OBSERVATION POINT GETS CLOSER TO THE MAGNETOPAUSE.
C
C INPUT: XN_PD - EITHER SOLAR WIND PROTON NUMBER DENSITY (PER C.C.) (IF VEL>0)
C OR THE SOLAR WIND RAM PRESSURE IN NANOPASCALS (IF VEL<0)
C VEL - EITHER SOLAR WIND VELOCITY (KM/SEC)
C OR ANY NEGATIVE NUMBER, WHICH INDICATES THAT XN_PD STANDS
C FOR THE SOLAR WIND PRESSURE, RATHER THAN FOR THE DENSITY
C
C XGSW,YGSW,ZGSW - COORDINATES OF THE OBSERVATION POINT IN EARTH RADII
C
C OUTPUT: XMGNP,YMGNP,ZMGNP - GSW POSITION OF THE BOUNDARY POINT, HAVING THE SAME
C VALUE OF TAU-COORDINATE AS THE OBSERVATION POINT (XGSW,YGSW,ZGSW)
C DIST - THE DISTANCE BETWEEN THE TWO POINTS, IN RE,
C ID - POSITION FLAG; ID=+1 (-1) MEANS THAT THE POINT (XGSW,YGSW,ZGSW)
C LIES INSIDE (OUTSIDE) THE MODEL MAGNETOPAUSE, RESPECTIVELY.
C
C THE PRESSURE-DEPENDENT MAGNETOPAUSE IS THAT USED IN THE T96_01 MODEL
C (TSYGANENKO, JGR, V.100, P.5599, 1995; ESA SP-389, P.181, OCT. 1996)
C
c AUTHOR: N.A. TSYGANENKO
C DATE: AUG.1, 1995, REVISED APRIL 3, 2003.
C LAST MODIFICATION: MARCH 21, 2008 (DOUBLE-PRECISION VERSION)
C
C DEFINE SOLAR WIND DYNAMIC PRESSURE (NANOPASCALS, ASSUMING 4% OF ALPHA-PARTICLES),
C IF NOT EXPLICITLY SPECIFIED IN THE INPUT:
C
IMPLICIT REAL*8 (A-H,O-Z)
C
IF (VEL.LT.0.D0) THEN
PD=XN_PD
ELSE
PD=1.94D-6*XN_PD*VEL**2
C
ENDIF
C
C RATIO OF PD TO THE AVERAGE PRESSURE, ASSUMED EQUAL TO 2 nPa:
RAT=PD/2.0D0
RAT16=RAT**0.14D0
C (THE POWER INDEX 0.14 IN THE SCALING FACTOR IS THE BEST-FIT VALUE OBTAINED FROM DATA
C AND USED IN THE T96_01 VERSION)
C
C VALUES OF THE MAGNETOPAUSE PARAMETERS FOR PD = 2 nPa:
C
A0=70.D0
S00=1.08D0
X00=5.48D0
C
C VALUES OF THE MAGNETOPAUSE PARAMETERS, SCALED BY THE ACTUAL PRESSURE:
C
A=A0/RAT16
S0=S00
X0=X00/RAT16
XM=X0-A
C
C (XM IS THE X-COORDINATE OF THE "SEAM" BETWEEN THE ELLIPSOID AND THE CYLINDER)
C
C (FOR DETAILS OF THE ELLIPSOIDAL COORDINATES, SEE THE PAPER:
C N.A.TSYGANENKO, SOLUTION OF CHAPMAN-FERRARO PROBLEM FOR AN
C ELLIPSOIDAL MAGNETOPAUSE, PLANET.SPACE SCI., V.37, P.1037, 1989).
C
IF (YGSW.NE.0.D0.OR.ZGSW.NE.0.D0) THEN
PHI=DATAN2(YGSW,ZGSW)
ELSE
PHI=0.D0
ENDIF
C
RHO=DSQRT(YGSW**2+ZGSW**2)
C
IF (XGSW.LT.XM) THEN
XMGNP=XGSW
RHOMGNP=A*DSQRT(S0**2-1.D0)
YMGNP=RHOMGNP*DSIN(PHI)
ZMGNP=RHOMGNP*DCOS(PHI)
DIST=DSQRT((XGSW-XMGNP)**2+(YGSW-YMGNP)**2+(ZGSW-ZMGNP)**2)
IF (RHOMGNP.GT.RHO) ID=+1
IF (RHOMGNP.LE.RHO) ID=-1
RETURN
ENDIF
C
XKSI=(XGSW-X0)/A+1.D0
XDZT=RHO/A
SQ1=DSQRT((1.D0+XKSI)**2+XDZT**2)
SQ2=DSQRT((1.D0-XKSI)**2+XDZT**2)
SIGMA=0.5D0*(SQ1+SQ2)
TAU=0.5D0*(SQ1-SQ2)
C
C NOW CALCULATE (X,Y,Z) FOR THE CLOSEST POINT AT THE MAGNETOPAUSE
C
XMGNP=X0-A*(1.D0-S0*TAU)
ARG=(S0**2-1.D0)*(1.D0-TAU**2)
IF (ARG.LT.0.D0) ARG=0.D0
RHOMGNP=A*DSQRT(ARG)
YMGNP=RHOMGNP*DSIN(PHI)
ZMGNP=RHOMGNP*DCOS(PHI)
C
C NOW CALCULATE THE DISTANCE BETWEEN THE POINTS {XGSW,YGSW,ZGSW} AND {XMGNP,YMGNP,ZMGNP}:
C (IN GENERAL, THIS IS NOT THE SHORTEST DISTANCE D_MIN, BUT DIST ASYMPTOTICALLY TENDS
C TO D_MIN, AS WE ARE GETTING CLOSER TO THE MAGNETOPAUSE):
C
DIST=DSQRT((XGSW-XMGNP)**2+(YGSW-YMGNP)**2+(ZGSW-ZMGNP)**2)
C
IF (SIGMA.GT.S0) ID=-1 ! ID=-1 MEANS THAT THE POINT LIES OUTSIDE
IF (SIGMA.LE.S0) ID=+1 ! ID=+1 MEANS THAT THE POINT LIES INSIDE
C THE MAGNETOSPHERE
RETURN
END
C
C===================================================================================
C
c