c
c
c ##########################################################################
c # #
c # GEOPACK-2005 #
c # (MAIN SET OF FORTRAN CODES) #
c # #
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. This version is dated May 04, 2005. On that
c date, the IGRF coefficients were updated according to the recently published table of
c IGRF-10 coefficients, so that the main field model now extends through 2010 (a linear
c extrapolation is used for 2005 - 2010, based on the table of secular velocities). For
c more details, see
c http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html (revision of 03/22/2005).
c
c
c Prefatory notes to the version of April 22, 2003:
c
c This package represents an in-depth revision of the previous version, with significant
c changes in the format of calling statements. Users should familiarize themselves with
c the new formats and rules, and accordingly adjust their source codes, as specified
c below. Please consult the documentation file
c
c http://modelweb.gsfc.nasa.gov/magnetos/data-based/Geopack-2005.doc for detailed
c descriptions of individual subroutines.
c
c The following changes were made to the previous release of GEOPACK (of Jan 5, 2001).
c
c (1) Subroutine IGRF, calculating the Earth's main field:
c (a) Two versions of this subroutine are provided here. In the first one (IGRF_GSM)
c both input (position) and output (field components) are in the Geocentric Solar-
c Magnetospheric Cartesian coordinates, while the second one (IGRF_GEO) uses sphe-
c rical geographical (geocentric) coordinates, as in the older releases.
c (b) updating of all expansion coefficients is now made separately in the s/r RECALC,
c which also takes into account the secular change of the coefficients within
c a given year (at the Earth's surface, the rate of the change can reach 7 nT/month).
c (c) the optimal length of spherical harmonic expansions is now automatically set
c inside the code, based on the radial distance, so that the deviation from the
c full-length approximation does not exceed 0.01 nT. (In the previous versions,
c the upper limit NM of the order of harmonics had to be specified by users),
c
c (2) Subroutine DIP, calculating the Earth's field in the dipole approximation:
c (a) no longer accepts the tilt angle via the list of formal parameters. Instead,
c the sine SPS and cosine CPS of that angle are now forwarded into DIP via the
c first common block /GEOPACK1/. Accordingly, there are two options: (i) to
c calculate SPS and CPS by calling RECALC before calling DIP, or (ii) to specify
c them explicitly. In the last case, SPS and CPS should be specified AFTER the
c invocation of RECALC (otherwise they will be overridden by those returned by
c RECALC).
c (b) the Earth's dipole moment is now calculated by RECALC, based on the table of
c the IGRF coefficients and their secular variation rates, for a given year and
c the day of the year, and the obtained value of the moment is forwarded into DIP
c via the second common block /GEOPACK2/. (In the previous versions, only a single
c fixed value was provided for the geodipole moment, corresponding to the most
c recent epoch).
c
c (3) Subroutine RECALC now consolidates in one module all calculations needed to
c initialize and update the values of coefficients and quantities that vary in
c time, either due to secular changes of the main geomagnetic field or as a result
c of Earth's diurnal rotation and orbital motion around Sun. That allowed us to
c simplify the codes and make them more compiler-independent.
c
c (4) Subroutine GEOMAG is now identical in its structure to other coordinate trans-
c formation subroutines. It no longer invokes RECALC from within GEOMAG, but uses
c precalculated values of the rotation matrix elements, obtained by a separate
c external invocation of RECALC. This eliminates possible interference of the
c two subroutines in the old version of the package.
c
c (5) Subroutine TRACE (and the subsidiary modules STEP and RHAND):
c
c (a) no longer needs to specify the highest order of spherical harmonics in the
c main geomagnetic field expansion - it is now calculated automatically inside the
c IGRF_GSM (or IGRF_GEO) subroutine.
c
c (b) the internal field model can now be explicitly chosen by specifying the para-
c meter INNAME (either IGRF_GSM or DIP).
c
c (6) A new subroutine BCARSP was added, providing a conversion of Cartesian field
c components into spherical ones (operation, inverse to that performed by the sub-
c routine BSPCAR).
c
c (7) Two new subroutines were added, SHUETAL_MGNP and T96_MGNP, providing the position
c of the magnetopause, according to the model of Shue et al. [1998] and the one
c used in the T96 magnetospheric magnetic field model.
c
c
c----------------------------------------------------------------------------------
c
SUBROUTINE IGRF_GSM (XGSM,YGSM,ZGSM,HXGSM,HYGSM,HZGSM)
c
C CALCULATES COMPONENTS OF THE MAIN (INTERNAL) GEOMAGNETIC FIELD IN THE GEOCENTRIC SOLAR
C MAGNETOSPHERIC 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
C BEFORE THE FIRST CALL OF THIS SUBROUTINE, OR IF THE DATE/TIME (IYEAR,IDAY,IHOUR,MIN,ISEC)
C WAS CHANGED, THE MODEL COEFFICIENTS AND GEO-GSM ROTATION MATRIX ELEMENTS SHOULD BE UPDATED
c BY CALLING THE SUBROUTINE RECALC
C
C-----INPUT PARAMETERS:
C
C XGSM,YGSM,ZGSM - CARTESIAN GSM COORDINATES (IN UNITS RE=6371.2 KM)
C
C-----OUTPUT PARAMETERS:
C
C HXGSM,HYGSM,HZGSM - CARTESIAN GSM COMPONENTS OF THE MAIN GEOMAGNETIC FIELD IN NANOTESLA
C
C LAST MODIFICATION: MAY 4, 2005.
C THIS VERSION OF THE CODE ACCEPTS DATES FROM 1965 THROUGH 2010.
c
C AUTHOR: N. A. TSYGANENKO
C
C
COMMON /GEOPACK2/ G(105),H(105),REC(105)
DIMENSION A(14),B(14)
CALL GEOGSM (XGEO,YGEO,ZGEO,XGSM,YGSM,ZGSM,-1)
RHO2=XGEO**2+YGEO**2
R=SQRT(RHO2+ZGEO**2)
C=ZGEO/R
RHO=SQRT(RHO2)
S=RHO/R
IF (S.LT.1.E-5) THEN
CF=1.
SF=0.
ELSE
CF=XGEO/RHO
SF=YGEO/RHO
ENDIF
C
PP=1./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.
D=0.
BBR=0.
BBT=0.
BBF=0.
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.
Y=1.
170 Q=P
Z=D
BI=0.
P2=0.
D2=0.
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.E-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
BT=BBT
IF(S.LT.1.E-5) 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
CALL GEOGSM (HXGEO,HYGEO,HZGEO,HXGSM,HYGSM,HZGSM,1)
RETURN
END
C
c==========================================================================================
C
c
SUBROUTINE IGRF_GEO (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
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: MAY 4, 2005.
C THIS VERSION OF THE CODE ACCEPTS DATES FROM 1965 THROUGH 2010.
c
C AUTHOR: N. A. TSYGANENKO
C
C
COMMON /GEOPACK2/ G(105),H(105),REC(105)
DIMENSION A(14),B(14)
C=COS(THETA)
S=SIN(THETA)
CF=COS(PHI)
SF=SIN(PHI)
C
PP=1./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.
D=0.
BBR=0.
BBT=0.
BBF=0.
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.
Y=1.
170 Q=P
Z=D
BI=0.
P2=0.
D2=0.
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.E-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.E-5) GOTO 210
BPHI=BBF/S
RETURN
210 IF(C.LT.0.) BBF=-BBF
BPHI=BBF
RETURN
END
C
c==========================================================================================
c
SUBROUTINE DIP (XGSM,YGSM,ZGSM,BXGSM,BYGSM,BZGSM)
C
C CALCULATES GSM COMPONENTS OF A GEODIPOLE FIELD WITH THE DIPOLE MOMENT
C CORRESPONDING TO THE EPOCH, SPECIFIED BY CALLING SUBROUTINE RECALC (SHOULD BE
C INVOKED BEFORE THE FIRST USE OF THIS ONE AND IN CASE THE DATE/TIME WAS CHANGED).
C
C--INPUT PARAMETERS: XGSM,YGSM,ZGSM - GSM COORDINATES IN RE (1 RE = 6371.2 km)
C
C--OUTPUT PARAMETERS: BXGSM,BYGSM,BZGSM - FIELD COMPONENTS IN GSM SYSTEM, IN NANOTESLA.
C
C LAST MODIFICATION: MAY 4, 2005
C
C AUTHOR: N. A. TSYGANENKO
C
COMMON /GEOPACK1/ AAA(10),SPS,CPS,BBB(23)
COMMON /GEOPACK2/ G(105),H(105),REC(105)
DIPMOM=SQRT(G(2)**2+G(3)**2+H(3)**2)
P=XGSM**2
U=ZGSM**2
V=3.*ZGSM*XGSM
T=YGSM**2
Q=DIPMOM/SQRT(P+T+U)**5
BXGSM=Q*((T+U-2.*P)*SPS-V*CPS)
BYGSM=-3.*YGSM*Q*(XGSM*SPS+ZGSM*CPS)
BZGSM=Q*((P+T-2.*U)*CPS-V*SPS)
RETURN
END
C*******************************************************************
c
SUBROUTINE SUN (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 31, 2003 (ONLY SOME NOTATION CHANGES)
C
C ORIGINAL VERSION WRITTEN BY: Gilbert D. Mead
C
DOUBLE PRECISION DJ,FDAY
DATA RAD/57.295779513/
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.
VL=DMOD(279.696678+0.9856473354*DJ,360.D0)
GST=DMOD(279.690983+.9856473354*DJ+360.*FDAY+180.,360.D0)/RAD
G=DMOD(358.475845+0.985600267*DJ,360.D0)/RAD
SLONG=(VL+(1.91946-0.004789*T)*SIN(G)+0.020094*SIN(2.*G))/RAD
IF(SLONG.GT.6.2831853) SLONG=SLONG-6.2831853
IF (SLONG.LT.0.) SLONG=SLONG+6.2831853
OBLIQ=(23.45229-0.0130125*T)/RAD
SOB=SIN(OBLIQ)
SLP=SLONG-9.924E-5
C
C THE LAST CONSTANT IS A CORRECTION FOR THE ANGULAR ABERRATION DUE TO
C THE ORBITAL MOTION OF THE EARTH
C
SIND=SOB*SIN(SLP)
COSD=SQRT(1.-SIND**2)
SC=SIND/COSD
SDEC=ATAN(SC)
SRASN=3.141592654-ATAN2(COS(OBLIQ)/SOB*SC,-COS(SLP)/COSD)
RETURN
END
C
C================================================================================
c
SUBROUTINE SPHCAR (R,THETA,PHI,X,Y,Z,J)
C
C CONVERTS SPHERICAL COORDS INTO CARTESIAN ONES AND VICA 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: APRIL 1, 2003 (ONLY SOME NOTATION CHANGES AND MORE
C COMMENTS ADDED)
C
C AUTHOR: N. A. TSYGANENKO
C
IF(J.GT.0) GOTO 3
SQ=X**2+Y**2
R=SQRT(SQ+Z**2)
IF (SQ.NE.0.) GOTO 2
PHI=0.
IF (Z.LT.0.) GOTO 1
THETA=0.
RETURN
1 THETA=3.141592654
RETURN
2 SQ=SQRT(SQ)
PHI=ATAN2(Y,X)
THETA=ATAN2(SQ,Z)
IF (PHI.LT.0.) PHI=PHI+6.28318531
RETURN
3 SQ=R*SIN(THETA)
X=SQ*COS(PHI)
Y=SQ*SIN(PHI)
Z=R*COS(THETA)
RETURN
END
C
C===========================================================================
c
SUBROUTINE BSPCAR (THETA,PHI,BR,BTHETA,BPHI,BX,BY,BZ)
C
C CALCULATES CARTESIAN FIELD COMPONENTS FROM SPHERICAL ONES
C-----INPUT: THETA,PHI - SPHERICAL ANGLES OF THE POINT IN RADIANS
C BR,BTHETA,BPHI - SPHERICAL COMPONENTS OF THE FIELD
C-----OUTPUT: BX,BY,BZ - CARTESIAN COMPONENTS OF THE FIELD
C
C LAST MOFIFICATION: APRIL 1, 2003 (ONLY SOME NOTATION CHANGES)
C
C WRITTEN BY: N. A. TSYGANENKO
C
S=SIN(THETA)
C=COS(THETA)
SF=SIN(PHI)
CF=COS(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 (X,Y,Z,BX,BY,BZ,BR,BTHETA,BPHI)
C
CALCULATES 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 - 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 AUTHOR: N. A. TSYGANENKO
C
RHO2=X**2+Y**2
R=SQRT(RHO2+Z**2)
RHO=SQRT(RHO2)
IF (RHO.NE.0.) THEN
CPHI=X/RHO
SPHI=Y/RHO
ELSE
CPHI=1.
SPHI=0.
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 (IYEAR,IDAY,IHOUR,MIN,ISEC)
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, IGRF_GSM, DIP, GEOMAG, GEOGSM, MAGSM, SMGSM, GSMGSE, GEIGEO.
C
C THERE IS NO NEED TO REPEATEDLY INVOKE RECALC, IF MULTIPLE CALCULATIONS ARE MADE
C FOR THE SAME DATE AND TIME.
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
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
C
C AUTHOR: N.A. TSYGANENKO
C DATE: DEC.1, 1991
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 and GEOMAG. This eliminates the need for the SAVE statements, used in the
c old versions, making the codes easier and more compiler-independent.
C
COMMON /GEOPACK1/ ST0,CT0,SL0,CL0,CTCL,STCL,CTSL,STSL,SFI,CFI,SPS,
* CPS,SHI,CHI,HI,PSI,XMUT,A11,A21,A31,A12,A22,A32,A13,A23,A33,DS3,
* CGST,SGST,BA(6)
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 G65/0.,-30334.,-2119.,-1662.,2997.,1594.,1297.,-2038.,1292.,
*856.,957.,804.,479.,-390.,252.,-219.,358.,254.,-31.,-157.,-62.,
*45.,61.,8.,-228.,4.,1.,-111.,75.,-57.,4.,13.,-26.,-6.,13.,1.,13.,
*5.,-4.,-14.,0.,8.,-1.,11.,4.,8.,10.,2.,-13.,10.,-1.,-1.,5.,1.,-2.,
*-2.,-3.,2.,-5.,-2.,4.,4.,0.,2.,2.,0.,39*0./
DATA H65/0.,0.,5776.,0.,-2016.,114.,0.,-404.,240.,-165.,0.,148.,
*-269.,13.,-269.,0.,19.,128.,-126.,-97.,81.,0.,-11.,100.,68.,-32.,
*-8.,-7.,0.,-61.,-27.,-2.,6.,26.,-23.,-12.,0.,7.,-12.,9.,-16.,4.,
*24.,-3.,-17.,0.,-22.,15.,7.,-4.,-5.,10.,10.,-4.,1.,0.,2.,1.,2.,
*6.,-4.,0.,-2.,3.,0.,-6.,39*0./
c
DATA G70/0.,-30220.,-2068.,-1781.,3000.,1611.,1287.,-2091.,1278.,
*838.,952.,800.,461.,-395.,234.,-216.,359.,262.,-42.,-160.,-56.,
*43.,64.,15.,-212.,2.,3.,-112.,72.,-57.,1.,14.,-22.,-2.,13.,-2.,
*14.,6.,-2.,-13.,-3.,5.,0.,11.,3.,8.,10.,2.,-12.,10.,-1.,0.,3.,
*1.,-1.,-3.,-3.,2.,-5.,-1.,6.,4.,1.,0.,3.,-1.,39*0./
DATA H70/0.,0.,5737.,0.,-2047.,25.,0.,-366.,251.,-196.,0.,167.,
*-266.,26.,-279.,0.,26.,139.,-139.,-91.,83.,0.,-12.,100.,72.,-37.,
*-6.,1.,0.,-70.,-27.,-4.,8.,23.,-23.,-11.,0.,7.,-15.,6.,-17.,6.,
*21.,-6.,-16.,0.,-21.,16.,6.,-4.,-5.,10.,11.,-2.,1.,0.,1.,1.,3.,
*4.,-4.,0.,-1.,3.,1.,-4.,39*0./
c
DATA G75/0.,-30100.,-2013.,-1902.,3010.,1632.,1276.,-2144.,1260.,
*830.,946.,791.,438.,-405.,216.,-218.,356.,264.,-59.,-159.,-49.,
*45.,66.,28.,-198.,1.,6.,-111.,71.,-56.,1.,16.,-14.,0.,12.,-5.,
*14.,6.,-1.,-12.,-8.,4.,0.,10.,1.,7.,10.,2.,-12.,10.,-1.,-1.,4.,
*1.,-2.,-3.,-3.,2.,-5.,-2.,5.,4.,1.,0.,3.,-1.,39*0./
DATA H75/0.,0.,5675.,0.,-2067.,-68.,0.,-333.,262.,-223.,0.,191.,
*-265.,39.,-288.,0.,31.,148.,-152.,-83.,88.,0.,-13.,99.,75.,-41.,
*-4.,11.,0.,-77.,-26.,-5.,10.,22.,-23.,-12.,0.,6.,-16.,4.,-19.,6.,
*18.,-10.,-17.,0.,-21.,16.,7.,-4.,-5.,10.,11.,-3.,1.,0.,1.,1.,3.,
*4.,-4.,-1.,-1.,3.,1.,-5.,39*0./
c
DATA G80/0.,-29992.,-1956.,-1997.,3027.,1663.,1281.,-2180.,1251.,
*833.,938.,782.,398.,-419.,199.,-218.,357.,261.,-74.,-162.,-48.,
*48.,66.,42.,-192.,4.,14.,-108.,72.,-59.,2.,21.,-12.,1.,11.,-2.,
*18.,6.,0.,-11.,-7.,4.,3.,6.,-1.,5.,10.,1.,-12.,9.,-3.,-1.,7.,2.,
*-5.,-4.,-4.,2.,-5.,-2.,5.,3.,1.,2.,3.,0.,39*0./
DATA H80/0.,0.,5604.,0.,-2129.,-200.,0.,-336.,271.,-252.,0.,212.,
*-257.,53.,-297.,0.,46.,150.,-151.,-78.,92.,0.,-15.,93.,71.,-43.,
*-2.,17.,0.,-82.,-27.,-5.,16.,18.,-23.,-10.,0.,7.,-18.,4.,-22.,9.,
*16.,-13.,-15.,0.,-21.,16.,9.,-5.,-6.,9.,10.,-6.,2.,0.,1.,0.,3.,
*6.,-4.,0.,-1.,4.,0.,-6.,39*0./
c
DATA G85/0.,-29873.,-1905.,-2072.,3044.,1687.,1296.,-2208.,1247.,
*829.,936.,780.,361.,-424.,170.,-214.,355.,253.,-93.,-164.,-46.,
*53.,65.,51.,-185.,4.,16.,-102.,74.,-62.,3.,24.,-6.,4.,10.,0.,21.,
*6.,0.,-11.,-9.,4.,4.,4.,-4.,5.,10.,1.,-12.,9.,-3.,-1.,7.,1.,-5.,
*-4.,-4.,3.,-5.,-2.,5.,3.,1.,2.,3.,0.,39*0./
DATA H85/0.,0.,5500.,0.,-2197.,-306.,0.,-310.,284.,-297.,0.,232.,
*-249.,69.,-297.,0.,47.,150.,-154.,-75.,95.,0.,-16.,88.,69.,-48.,
*-1.,21.,0.,-83.,-27.,-2.,20.,17.,-23.,-7.,0.,8.,-19.,5.,-23.,11.,
*14.,-15.,-11.,0.,-21.,15.,9.,-6.,-6.,9.,9.,-7.,2.,0.,1.,0.,3.,
*6.,-4.,0.,-1.,4.,0.,-6.,39*0./
c
DATA G90/0., -29775., -1848., -2131., 3059., 1686., 1314.,
* -2239., 1248., 802., 939., 780., 325., -423.,
* 141., -214., 353., 245., -109., -165., -36.,
* 61., 65., 59., -178., 3., 18., -96.,
* 77., -64., 2., 26., -1., 5., 9.,
* 0., 23., 5., -1., -10., -12., 3.,
* 4., 2., -6., 4., 9., 1., -12.,
* 9., -4., -2., 7., 1., -6., -3.,
* -4., 2., -5., -2., 4., 3., 1.,
* 3., 3., 0., 39*0./
DATA H90/0., 0., 5406., 0., -2279., -373., 0.,
* -284., 293., -352., 0., 247., -240., 84.,
* -299., 0., 46., 154., -153., -69., 97.,
* 0., -16., 82., 69., -52., 1., 24.,
* 0., -80., -26., 0., 21., 17., -23.,
* -4., 0., 10., -19., 6., -22., 12.,
* 12., -16., -10., 0., -20., 15., 11.,
* -7., -7., 9., 8., -7., 2., 0.,
* 2., 1., 3., 6., -4., 0., -2.,
* 3., -1., -6., 39*0./
DATA G95/0., -29692., -1784., -2200., 3070., 1681., 1335.,
* -2267., 1249., 759., 940., 780., 290., -418.,
* 122., -214., 352., 235., -118., -166., -17.,
* 68., 67., 68., -170., -1., 19., -93.,
* 77., -72., 1., 28., 5., 4., 8.,
* -2., 25., 6., -6., -9., -14., 9.,
* 6., -5., -7., 4., 9., 3., -10.,
* 8., -8., -1., 10., -2., -8., -3.,
* -6., 2., -4., -1., 4., 2., 2.,
* 5., 1., 0., 39*0./
DATA H95/0., 0., 5306., 0., -2366., -413., 0.,
* -262., 302., -427., 0., 262., -236., 97.,
* -306., 0., 46., 165., -143., -55., 107.,
* 0., -17., 72., 67., -58., 1., 36.,
* 0., -69., -25., 4., 24., 17., -24.,
* -6., 0., 11., -21., 8., -23., 15.,
* 11., -16., -4., 0., -20., 15., 12.,
* -6., -8., 8., 5., -8., 3., 0.,
* 1., 0., 4., 5., -5., -1., -2.,
* 1., -2., -7., 39*0./
DATA G00/0.,-29619.4, -1728.2, -2267.7, 3068.4, 1670.9, 1339.6,
* -2288., 1252.1, 714.5, 932.3, 786.8, 250., -403.,
* 111.3, -218.8, 351.4, 222.3, -130.4, -168.6, -12.9,
* 72.3, 68.2, 74.2, -160.9, -5.9, 16.9, -90.4,
* 79.0, -74.0, 0., 33.3, 9.1, 6.9, 7.3,
* -1.2, 24.4, 6.6, -9.2, -7.9, -16.6, 9.1,
* 7.0, -7.9, -7., 5., 9.4, 3., - 8.4,
* 6.3, -8.9, -1.5, 9.3, -4.3, -8.2, -2.6,
* -6., 1.7, -3.1, -0.5, 3.7, 1., 2.,
* 4.2, 0.3, -1.1, 2.7, -1.7, -1.9, 1.5,
* -0.1, 0.1, -0.7, 0.7, 1.7, 0.1, 1.2,
* 4.0, -2.2, -0.3, 0.2, 0.9, -0.2, 0.9,
* -0.5, 0.3, -0.3, -0.4, -0.1, -0.2, -0.4,
* -0.2, -0.9, 0.3, 0.1, -0.4, 1.3, -0.4,
* 0.7, -0.4, 0.3, -0.1, 0.4, 0., 0.1/
DATA H00/0., 0., 5186.1, 0., -2481.6, -458.0, 0.,
* -227.6, 293.4, -491.1, 0., 272.6, -231.9, 119.8,
* -303.8, 0., 43.8, 171.9, -133.1, -39.3, 106.3,
* 0., -17.4, 63.7, 65.1, -61.2, 0.7, 43.8,
* 0., -64.6, -24.2, 6.2, 24., 14.8, -25.4,
* -5.8, 0.0, 11.9, -21.5, 8.5, -21.5, 15.5,
* 8.9, -14.9, -2.1, 0.0, -19.7, 13.4, 12.5,
* -6.2, -8.4, 8.4, 3.8, -8.2, 4.8, 0.0,
* 1.7, 0.0, 4.0, 4.9, -5.9, -1.2, -2.9,
* 0.2, -2.2, -7.4, 0.0, 0.1, 1.3, -0.9,
* -2.6, 0.9, -0.7, -2.8, -0.9, -1.2, -1.9,
* -0.9, 0.0, -0.4, 0.3, 2.5, -2.6, 0.7,
* 0.3, 0.0, 0.0, 0.3, -0.9, -0.4, 0.8,
* 0.0, -0.9, 0.2, 1.8, -0.4, -1.0, -0.1,
* 0.7, 0.3, 0.6, 0.3, -0.2, -0.5, -0.9/
*
DATA G05/0.,-29556.8, -1671.8, -2340.5, 3047., 1656.9, 1335.7,
* -2305.3, 1246.8, 674.4, 919.8, 798.2, 211.5, -379.5,
* 100.2, -227.6, 354.4, 208.8, -136.6, -168.3, -14.1,
* 72.9, 69.6, 76.6, -151.1, -15.0, 14.7, -86.4,
* 79.8, -74.4, -1.4, 38.6, 12.3, 9.4, 5.5,
* 2.0, 24.8, 7.7, -11.4, -6.8, -18.0, 10.0,
* 9.4, -11.4, -5.0, 5.6, 9.8, 3.6, -7.0,
* 5.0, -10.8, -1.3, 8.7, -6.7, -9.2, -2.2,
* -6.3, 1.6, -2.5, -0.1, 3.0, 0.3, 2.1,
* 3.9, -0.1, -2.2, 2.9, -1.6, -1.7, 1.5,
* -0.2, 0.2, -0.7, 0.5, 1.8, 0.1, 1.0,
* 4.1, -2.2, -0.3, 0.3, 0.9, -0.4, 1.0,
* -0.4, 0.5, -0.3, -0.4, 0.0, -0.4, 0.0,
* -0.2, -0.9, 0.3, 0.3, -0.4, 1.2, -0.4,
* 0.7, -0.3, 0.4, -0.1, 0.4, -0.1, -0.3/
DATA H05/0., 0.0, 5080.0, 0.0, -2594.9, -516.7, 0.0,
* -200.4, 269.3, -524.5, 0.0, 281.4, -225.8, 145.7,
* -304.7, 0.0, 42.7, 179.8, -123.0, -19.5, 103.6,
* 0.0, -20.2, 54.7, 63.7, -63.4, 0.0, 50.3,
* 0.0, -61.4, -22.5, 6.9, 25.4, 10.9, -26.4,
* -4.8, 0.0, 11.2, -21.0, 9.7, -19.8, 16.1,
* 7.7, -12.8, -0.1, 0.0, -20.1, 12.9, 12.7,
* -6.7, -8.1, 8.1, 2.9, -7.9, 5.9, 0.0,
* 2.4, 0.2, 4.4, 4.7, -6.5, -1.0, -3.4,
* -0.9, -2.3, -8.0, 0.0, 0.3, 1.4, -0.7,
* -2.4, 0.9, -0.6, -2.7, -1.0, -1.5, -2.0,
* -1.4, 0.0, -0.5, 0.3, 2.3, -2.7, 0.6,
* 0.4, 0.0, 0.0, 0.3, -0.8, -0.4, 1.0,
* 0.0, -0.7, 0.3, 1.7, -0.5, -1.0, 0.0,
* 0.7, 0.2, 0.6, 0.4, -0.2, -0.5, -1.0/
DATA DG05/0.0, 8.8, 10.8, -15.0, -6.9, -1.0, -0.3,
* -3.1, -0.9, -6.8, -2.5, 2.8, -7.1, 5.9,
* -3.2, -2.6, 0.4, -3.0, -1.2, 0.2, -0.6,
* -0.8, 0.2, -0.2, 2.1, -2.1, -0.4, 1.3,
* -0.4, 0.0, -0.2, 1.1, 0.6, 0.4, -0.5,
* 0.9, -0.2, 0.2, -0.2, 0.2, -0.2, 0.2,
* 0.5, -0.7, 0.5/
DATA DH05/0.0, 0.0, -21.3, 0.0, -23.3, -14.0, 0.0,
* 5.4, -6.5, -2.0, 0.0, 2.0, 1.8, 5.6,
* 0.0, 0.0, 0.1, 1.8, 2.0, 4.5, -1.0,
* 0.0, -0.4, -1.9, -0.4, -0.4, -0.2, 0.9,
* 0.0, 0.8, 0.4, 0.1, 0.2, -0.9, -0.3,
* 0.3, 0.0, -0.2, 0.2, 0.2, 0.4, 0.2,
* -0.3, 0.5, 0.4/
C
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)=FLOAT((N-M)*(N+M-2))/FLOAT(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=FLOAT(IY)+FLOAT(IDAY-1)/365.25-2005.
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=(FLOAT(IY)+FLOAT(IDAY-1)/365.25-1965)/5.
F1=1.-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=(FLOAT(IY)+FLOAT(IDAY-1)/365.25-1970)/5.
F1=1.-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=(FLOAT(IY)+FLOAT(IDAY-1)/365.25-1975)/5.
F1=1.-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=(FLOAT(IY)+FLOAT(IDAY-1)/365.25-1980)/5.
F1=1.-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=(FLOAT(IY)+FLOAT(IDAY-1)/365.25-1985)/5.
F1=1.-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=(FLOAT(IY)+FLOAT(IDAY-1)/365.25-1990)/5.
F1=1.-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=(FLOAT(IY)+FLOAT(IDAY-1)/365.25-1995)/5.
F1=1.-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=(FLOAT(IY)+FLOAT(IDAY-1)/365.25-2000)/5.
F1=1.-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.
DO 130 N=2,14
MN=N*(N-1)/2+1
S=S*FLOAT(2*N-3)/FLOAT(N-1)
G(MN)=G(MN)*S
H(MN)=H(MN)*S
P=S
DO 130 M=2,N
AA=1.
IF (M.EQ.2) AA=2.
P=P*SQRT(AA*FLOAT(N-M+1)/FLOAT(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 THE COMPONENTS OF THE UNIT VECTOR EzMAG IN GEO COORD.SYSTEM:
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=SQRT(SQ)
SQR=SQRT(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
CALL SUN (IY,IDAY,IHOUR,MIN,ISEC,GST,SLONG,SRASN,SDEC)
C
C S1,S2, AND S3 ARE THE COMPONENTS OF THE UNIT VECTOR EXGSM=EXGSE IN THE
C SYSTEM GEI POINTING FROM THE EARTH'S CENTER TO THE SUN:
C
S1=COS(SRASN)*COS(SDEC)
S2=SIN(SRASN)*COS(SDEC)
S3=SIN(SDEC)
CGST=COS(GST)
SGST=SIN(GST)
C
C DIP1, DIP2, AND DIP3 ARE THE COMPONENTS OF THE UNIT VECTOR EZSM=EZMAG
C IN THE SYSTEM GEI:
C
DIP1=STCL*CGST-STSL*SGST
DIP2=STCL*SGST+STSL*CGST
DIP3=CT0
C
C NOW CALCULATE THE COMPONENTS OF THE UNIT VECTOR EYGSM IN THE SYSTEM GEI
C BY TAKING THE VECTOR PRODUCT D x S AND NORMALIZING IT TO UNIT LENGTH:
C
Y1=DIP2*S3-DIP3*S2
Y2=DIP3*S1-DIP1*S3
Y3=DIP1*S2-DIP2*S1
Y=SQRT(Y1*Y1+Y2*Y2+Y3*Y3)
Y1=Y1/Y
Y2=Y2/Y
Y3=Y3/Y
C
C THEN IN THE GEI SYSTEM THE UNIT VECTOR Z = EZGSM = EXGSM x EYGSM = S x Y
C HAS THE COMPONENTS:
C
Z1=S2*Y3-S3*Y2
Z2=S3*Y1-S1*Y3
Z3=S1*Y2-S2*Y1
C
C THE VECTOR EZGSE (HERE DZ) IN GEI HAS THE COMPONENTS (0,-SIN(DELTA),
C COS(DELTA)) = (0.,-0.397823,0.917462); HERE DELTA = 23.44214 DEG FOR
C THE EPOCH 1978 (SEE THE BOOK BY GUREVICH OR OTHER ASTRONOMICAL HANDBOOKS).
C HERE THE MOST ACCURATE TIME-DEPENDENT FORMULA IS USED:
C
DJ=FLOAT(365*(IY-1900)+(IY-1901)/4 +IDAY)
* -0.5+FLOAT(IHOUR*3600+MIN*60+ISEC)/86400.
T=DJ/36525.
OBLIQ=(23.45229-0.0130125*T)/57.2957795
DZ1=0.
DZ2=-SIN(OBLIQ)
DZ3=COS(OBLIQ)
C
C THEN THE UNIT VECTOR EYGSE IN GEI SYSTEM IS THE VECTOR PRODUCT DZ x S :
C
DY1=DZ2*S3-DZ3*S2
DY2=DZ3*S1-DZ1*S3
DY3=DZ1*S2-DZ2*S1
C
C THE ELEMENTS OF THE MATRIX GSE TO GSM ARE THE SCALAR PRODUCTS:
C CHI=EM22=(EYGSM,EYGSE), SHI=EM23=(EYGSM,EZGSE), EM32=(EZGSM,EYGSE)=-EM23,
C AND EM33=(EZGSM,EZGSE)=EM22
C
CHI=Y1*DY1+Y2*DY2+Y3*DY3
SHI=Y1*DZ1+Y2*DZ2+Y3*DZ3
HI=ASIN(SHI)
C
C TILT ANGLE: PSI=ARCSIN(DIP,EXGSM)
C
SPS=DIP1*S1+DIP2*S2+DIP3*S3
CPS=SQRT(1.-SPS**2)
PSI=ASIN(SPS)
C
C THE ELEMENTS OF THE MATRIX MAG TO SM ARE THE SCALAR PRODUCTS:
C CFI=GM22=(EYSM,EYMAG), SFI=GM23=(EYSM,EXMAG); THEY CAN BE 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 THE 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 THE COMPONENTS OF EYSM IN GEI WERE FOUND ABOVE AS Y1, Y2, AND Y3;
C NOW WE ONLY HAVE TO COMBINE THE 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
XMUT=(ATAN2(SFI,CFI)+3.1415926536)*3.8197186342
C
C THE ELEMENTS OF THE MATRIX GEO TO GSM ARE THE SCALAR PRODUCTS:
C
C A11=(EXGEO,EXGSM), A12=(EYGEO,EXGSM), A13=(EZGEO,EXGSM),
C A21=(EXGEO,EYGSM), A22=(EYGEO,EYGSM), A23=(EZGEO,EYGSM),
C A31=(EXGEO,EZGSM), A32=(EYGEO,EZGSM), A33=(EZGEO,EZGSM),
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 EXGSM=(S1,S2,S3), EYGSM=(Y1,Y2,Y3), EZGSM=(Z1,Z2,Z3)
C AND THEREFORE:
C
A11=S1*CGST+S2*SGST
A12=-S1*SGST+S2*CGST
A13=S3
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
10 FORMAT(//1X,
*'**** RECALC WARNS: YEAR IS OUT OF INTERVAL 1965-2010: IYEAR=',I4,
* /,6X,'CALCULATIONS WILL BE DONE FOR IYEAR=',I4,/)
RETURN
END
c
c====================================================================
C
SUBROUTINE GEOMAG (XGEO,YGEO,ZGEO,XMAG,YMAG,ZMAG,J)
C
C CONVERTS GEOGRAPHIC (GEO) TO DIPOLE (MAG) COORDINATES OR VICA 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
C ATTENTION: SUBROUTINE RECALC MUST BE INVOKED BEFORE GEOMAG 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
C LAST MOFIFICATION: MARCH 30, 2003 (INVOCATION OF RECALC INSIDE THIS S/R WAS REMOVED)
C
C AUTHOR: N. A. TSYGANENKO
C
COMMON /GEOPACK1/ ST0,CT0,SL0,CL0,CTCL,STCL,CTSL,STSL,AB(19),BB(8)
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 (XGEI,YGEI,ZGEI,XGEO,YGEO,ZGEO,J)
C
C CONVERTS EQUATORIAL INERTIAL (GEI) TO GEOGRAPHICAL (GEO) COORDS
C OR VICA 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 MUST BE INVOKED BEFORE GEIGEO 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 LAST MODIFICATION: MARCH 31, 2003
C AUTHOR: N. A. TSYGANENKO
C
COMMON /GEOPACK1/ A(27),CGST,SGST,B(6)
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 (XMAG,YMAG,ZMAG,XSM,YSM,ZSM,J)
C
C CONVERTS DIPOLE (MAG) TO SOLAR MAGNETIC (SM) COORDINATES OR VICA 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 MUST BE INVOKED BEFORE MAGSM IN TWO 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 LAST MODIFICATION: MARCH 31, 2003
C
C AUTHOR: N. A. TSYGANENKO
C
COMMON /GEOPACK1/ A(8),SFI,CFI,B(7),AB(10),BA(8)
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 GSMGSE (XGSM,YGSM,ZGSM,XGSE,YGSE,ZGSE,J)
C
C CONVERTS GEOCENTRIC SOLAR MAGNETOSPHERIC (GSM) COORDS TO SOLAR ECLIPTIC (GSE) ONES
C OR VICA VERSA.
C J>0 J<0
C-----INPUT: J,XGSM,YGSM,ZGSM J,XGSE,YGSE,ZGSE
C----OUTPUT: XGSE,YGSE,ZGSE XGSM,YGSM,ZGSM
C
C ATTENTION: SUBROUTINE RECALC MUST BE INVOKED BEFORE GSMGSE IN TWO 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 LAST MODIFICATION: MARCH 31, 2003
C
C AUTHOR: N. A. TSYGANENKO
C
COMMON /GEOPACK1/ A(12),SHI,CHI,AB(13),BA(8)
C
IF (J.GT.0) THEN
XGSE=XGSM
YGSE=YGSM*CHI-ZGSM*SHI
ZGSE=YGSM*SHI+ZGSM*CHI
ELSE
XGSM=XGSE
YGSM=YGSE*CHI+ZGSE*SHI
ZGSM=ZGSE*CHI-YGSE*SHI
ENDIF
RETURN
END
C
C=====================================================================================
C
SUBROUTINE SMGSM (XSM,YSM,ZSM,XGSM,YGSM,ZGSM,J)
C
C CONVERTS SOLAR MAGNETIC (SM) TO GEOCENTRIC SOLAR MAGNETOSPHERIC
C (GSM) COORDINATES OR VICA VERSA.
C J>0 J<0
C-----INPUT: J,XSM,YSM,ZSM J,XGSM,YGSM,ZGSM
C----OUTPUT: XGSM,YGSM,ZGSM XSM,YSM,ZSM
C
C ATTENTION: SUBROUTINE RECALC MUST BE INVOKED BEFORE SMGSM IN TWO 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 LAST MODIFICATION: MARCH 31, 2003
C
C AUTHOR: N. A. TSYGANENKO
C
COMMON /GEOPACK1/ A(10),SPS,CPS,B(15),AB(8)
IF (J.GT.0) THEN
XGSM=XSM*CPS+ZSM*SPS
YGSM=YSM
ZGSM=ZSM*CPS-XSM*SPS
ELSE
XSM=XGSM*CPS-ZGSM*SPS
YSM=YGSM
ZSM=XGSM*SPS+ZGSM*CPS
ENDIF
RETURN
END
C
C==========================================================================================
C
SUBROUTINE GEOGSM (XGEO,YGEO,ZGEO,XGSM,YGSM,ZGSM,J)
C
C CONVERTS GEOGRAPHIC (GEO) TO GEOCENTRIC SOLAR MAGNETOSPHERIC (GSM) COORDINATES
C OR VICA VERSA.
C
C J>0 J<0
C----- INPUT: J,XGEO,YGEO,ZGEO J,XGSM,YGSM,ZGSM
C---- OUTPUT: XGSM,YGSM,ZGSM XGEO,YGEO,ZGEO
C
C ATTENTION: SUBROUTINE RECALC MUST BE INVOKED BEFORE GEOGSM IN TWO 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 LAST MODIFICATION: MARCH 31, 2003
C
C AUTHOR: N. A. TSYGANENKO
C
COMMON /GEOPACK1/AA(17),A11,A21,A31,A12,A22,A32,A13,A23,A33,D,B(8)
C
IF (J.GT.0) THEN
XGSM=A11*XGEO+A12*YGEO+A13*ZGEO
YGSM=A21*XGEO+A22*YGEO+A23*ZGEO
ZGSM=A31*XGEO+A32*YGEO+A33*ZGEO
ELSE
XGEO=A11*XGSM+A21*YGSM+A31*ZGSM
YGEO=A12*XGSM+A22*YGSM+A32*ZGSM
ZGEO=A13*XGSM+A23*YGSM+A33*ZGSM
ENDIF
RETURN
END
C
C=====================================================================================
C
SUBROUTINE RHAND (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)
C
C LAST MODIFICATION: MARCH 31, 2003
C
C AUTHOR: N. A. TSYGANENKO
C
DIMENSION PARMOD(10)
C
C EXNAME AND INNAME ARE NAMES OF SUBROUTINES FOR THE EXTERNAL AND INTERNAL
C PARTS OF THE TOTAL FIELD
C
COMMON /GEOPACK1/ A(15),PSI,AA(10),DS3,BB(8)
CALL EXNAME (IOPT,PARMOD,PSI,X,Y,Z,BXGSM,BYGSM,BZGSM)
CALL INNAME (X,Y,Z,HXGSM,HYGSM,HZGSM)
BX=BXGSM+HXGSM
BY=BYGSM+HYGSM
BZ=BZGSM+HZGSM
B=DS3/SQRT(BX**2+BY**2+BZ**2)
R1=BX*B
R2=BY*B
R3=BZ*B
RETURN
END
C
C===================================================================================
C
SUBROUTINE STEP (X,Y,Z,DS,ERRIN,IOPT,PARMOD,EXNAME,INNAME)
C
C RE-CALCULATES {X,Y,Z}, MAKING A STEP ALONG A FIELD LINE.
C DS IS THE STEP SIZE, ERRIN IS PERMISSIBLE ERROR VALUE, IOPT SPECIFIES THE EXTERNAL
C MODEL VERSION, THE ARRAY PARMOD CONTAINS INPUT PARAMETERS FOR THAT MODEL
C EXNAME IS THE NAME OF THE EXTERNAL FIELD SUBROUTINE
C INNAME IS THE NAME OF THE INTERNAL FIELD SUBROUTINE (EITHER DIP OR IGRF)
C
C ALL THE PARAMETERS ARE INPUT ONES; OUTPUT IS THE RENEWED TRIPLET X,Y,Z
C
C LAST MODIFICATION: MARCH 31, 2003
C
C AUTHOR: N. A. TSYGANENKO
C
DIMENSION PARMOD(10)
COMMON /GEOPACK1/ A(26),DS3,B(8)
EXTERNAL EXNAME,INNAME
1 DS3=-DS/3.
CALL RHAND (X,Y,Z,R11,R12,R13,IOPT,PARMOD,EXNAME,INNAME)
CALL RHAND (X+R11,Y+R12,Z+R13,R21,R22,R23,IOPT,PARMOD,EXNAME,
* INNAME)
CALL RHAND (X+.5*(R11+R21),Y+.5*(R12+R22),Z+.5*
*(R13+R23),R31,R32,R33,IOPT,PARMOD,EXNAME,INNAME)
CALL RHAND (X+.375*(R11+3.*R31),Y+.375*(R12+3.*R32
*),Z+.375*(R13+3.*R33),R41,R42,R43,IOPT,PARMOD,EXNAME,INNAME)
CALL RHAND (X+1.5*(R11-3.*R31+4.*R41),Y+1.5*(R12-
*3.*R32+4.*R42),Z+1.5*(R13-3.*R33+4.*R43),
*R51,R52,R53,IOPT,PARMOD,EXNAME,INNAME)
ERRCUR=ABS(R11-4.5*R31+4.*R41-.5*R51)+ABS(R12-4.5*R32+4.*R42-.5*
*R52)+ABS(R13-4.5*R33+4.*R43-.5*R53)
IF (ERRCUR.LT.ERRIN) GOTO 2
DS=DS*.5
GOTO 1
2 X=X+.5*(R11+4.*R41+R51)
Y=Y+.5*(R12+4.*R42+R52)
Z=Z+.5*(R13+4.*R43+R53)
IF(ERRCUR.LT.ERRIN*.04.AND.ABS(DS).LT.1.33) DS=DS*1.5
RETURN
END
C
C==============================================================================
C
SUBROUTINE TRACE (XI,YI,ZI,DIR,RLIM,R0,IOPT,PARMOD,EXNAME,INNAME,
*XF,YF,ZF,XX,YY,ZZ,L)
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 THE HIGHEST ORDER OF SPHERICAL HARMONICS IN THE MAIN FIELD EXPANSION USED
C IN THE MAPPING IS CALCULATED AUTOMATICALLY. IF INNAME=IGRF_GSM, THEN AN IGRF MODEL
C FIELD WILL BE USED, AND IF INNAME=DIP, A PURE DIPOLE FIELD WILL BE USED.
C IN ANY CASE, BEFORE CALLING TRACE, ONE SHOULD INVOKE RECALC, TO CALCULATE CORRECT
C VALUES OF THE IGRF COEFFICIENTS AND ALL QUANTITIES NEEDED FOR TRANSFORMATIONS
C BETWEEN COORDINATE SYSTEMS INVOLVED IN THIS CALCULATIONS.
C
C ALTERNATIVELY, THE SUBROUTINE RECALC CAN BE INVOKED WITH THE DESIRED VALUES OF
C IYEAR AND IDAY (TO SPECIFY THE DIPOLE MOMENT), WHILE THE VALUES OF THE DIPOLE
C TILT ANGLE PSI (IN RADIANS) AND ITS SINE (SPS) AND COSINE (CPS) CAN BE EXPLICITLY
C SPECIFIED AND FORWARDED TO THE COMMON BLOCK GEOPACK1 (11th, 12th, AND 16th ELEMENTS, RESP.)
C
C------------- INPUT PARAMETERS:
C
C XI,YI,ZI - GSM COORDS OF INITIAL POINT (IN EARTH RADII, 1 RE = 6371.2 km),
C
C DIR - SIGN OF THE TRACING DIRECTION: IF DIR=1.0 THEN WE MOVE ANTIPARALLEL TO THE
C FIELD VECTOR (E.G. FROM NORTHERN TO SOUTHERN CONJUGATE POINT),
C AND IF DIR=-1.0 THEN THE TRACING GOES IN THE OPPOSITE DIRECTION.
C
C R0 - RADIUS OF A SPHERE (IN RE) FOR WHICH THE FIELD LINE ENDPOINT COORDINATES
C XF,YF,ZF SHOULD BE CALCULATED.
C
C RLIM - UPPER LIMIT OF THE GEOCENTRIC DISTANCE, WHERE THE TRACING IS TERMINATED.
C
C IOPT - A MODEL INDEX; CAN BE USED FOR SPECIFYING AN OPTION OF THE EXTERNAL FIELD
C MODEL (E.G., INTERVAL OF THE KP-INDEX). 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 MODEL PARAMETERS, NEEDED FOR A UNIQUE
C SPECIFICATION OF THE EXTERNAL FIELD. THE CONCRETE MEANING OF THE COMPONENTS
C OF PARMOD DEPENDS ON A SPECIFIC VERSION OF THE EXTERNAL FIELD MODEL.
C
C EXNAME - NAME OF A SUBROUTINE PROVIDING COMPONENTS OF THE EXTERNAL MAGNETIC FIELD
C (E.G., T96_01).
C INNAME - NAME OF A SUBROUTINE PROVIDING COMPONENTS OF THE INTERNAL MAGNETIC FIELD
C (EITHER DIP OR IGRF_GSM).
C
C-------------- OUTPUT PARAMETERS:
C
C XF,YF,ZF - GSM COORDS OF THE LAST CALCULATED POINT OF A FIELD LINE
C XX,YY,ZZ - ARRAYS, CONTAINING COORDS OF FIELD LINE POINTS. HERE THEIR MAXIMAL LENGTH WAS
C ASSUMED EQUAL TO 999.
C L - ACTUAL NUMBER OF THE CALCULATED FIELD LINE POINTS. IF L EXCEEDS 999, TRACING
C TERMINATES, AND A WARNING IS DISPLAYED.
C
C
C LAST MODIFICATION: MARCH 31, 2003.
C
C AUTHOR: N. A. TSYGANENKO
C
DIMENSION XX(1000),YY(1000),ZZ(1000), PARMOD(10)
COMMON /GEOPACK1/ AA(26),DD,BB(8)
EXTERNAL EXNAME,INNAME
C
ERR=0.0001
L=0
DS=0.5*DIR
X=XI
Y=YI
Z=ZI
DD=DIR
AL=0.
c
c here we call RHAND 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 (X,Y,Z,R1,R2,R3,IOPT,PARMOD,EXNAME,INNAME)
AD=0.01
IF (X*R1+Y*R2+Z*R3.LT.0.) AD=-0.01
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=SQRT(X**2+Y**2+Z**2)+AD
1 L=L+1
IF(L.GT.999) GOTO 7
XX(L)=X
YY(L)=Y
ZZ(L)=Z
RYZ=Y**2+Z**2
R2=X**2+RYZ
R=SQRT(R2)
c check if the line hit the outer tracing boundary; if yes, then terminate
c the tracing (label 8):
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 (i) we are moving outward, or (ii) we are still sufficiently
c far from Earth (beyond R=5Re); if yes, proceed further:
c
IF (R.GE.RR.OR.R.GT.5.) GOTO 5
c now we moved closer inward (between R=3 and R=5); go to 3 and begin logging
c previous values of X,Y,Z, to be used in the interpolation (after having
c crossed the inner tracing boundary):
IF (R.GE.3.) GOTO 3
c
c we entered inside the sphere R=3: to avoid too large steps (and hence inaccurate
c interpolated position of the footpoint), enforce the progressively smaller
c stepsize values as we approach the inner boundary R=R0:
c
FC=0.2
IF(R-R0.LT.0.05) FC=0.05
AL=FC*(R-R0+0.2)
DS=DIR*AL
GOTO 4
3 DS=DIR
4 XR=X
YR=Y
ZR=Z
5 RR=R
CALL STEP (X,Y,Z,DS,ERR,IOPT,PARMOD,EXNAME,INNAME)
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=999
8 XF=X
YF=Y
ZF=Z
RETURN
10 FORMAT(//,1X,'**** COMPUTATIONS IN THE SUBROUTINE TRACE ARE',
*' TERMINATED: THE CURRENT NUMBER OF POINTS EXCEEDED 1000 ****'//)
END
c
C====================================================================================
C
SUBROUTINE SHUETAL_MGNP(XN_PD,VEL,BZIMF,XGSM,YGSM,ZGSM,
* XMGNP,YMGNP,ZMGNP,DIST,ID)
C
C FOR ANY POINT OF SPACE WITH COORDINATES (XGSM,YGSM,ZGSM) AND SPECIFIED CONDITIONS
C IN THE INCOMING SOLAR WIND, THIS SUBROUTINE:
C
C (1) DETERMINES IF THE POINT (XGSM,YGSM,ZGSM) LIES INSIDE OR OUTSIDE THE
C MODEL MAGNETOPAUSE OF SHUE ET AL. (JGR-A, V.103, P. 17691, 1998).
C
C (2) CALCULATES THE GSM 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 {XGSM,YGSM,ZGSM}, 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 XGSM,YGSM,ZGSM - GSM POSITION OF THE OBSERVATION POINT IN EARTH RADII
C
C OUTPUT: XMGNP,YMGNP,ZMGNP - GSM POSITION OF THE BOUNDARY POINT
C DIST - DISTANCE (IN RE) BETWEEN THE OBSERVATION POINT (XGSM,YGSM,ZGSM)
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
C
c AUTHOR: N.A. TSYGANENKO,
C DATE: APRIL 4, 2003.
C
IF (VEL.LT.0.) THEN
PD=XN_PD
ELSE
PD=1.94E-6*XN_PD*VEL**2 ! PD 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 (YGSM.NE.0..OR.ZGSM.NE.0.) THEN
PHI=ATAN2(YGSM,ZGSM)
ELSE
PHI=0.
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=(10.22+1.29*TANH(0.184*(BZIMF+8.14)))*PD**(-.15151515)
ALPHA=(0.58-0.007*BZIMF)*(1.+0.024*ALOG(PD))
R=SQRT(XGSM**2+YGSM**2+ZGSM**2)
RM=R0*(2./(1.+XGSM/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 (PD,-1.,XGSM,YGSM,ZGSM,XMT96,YMT96,ZMT96,DIST,ID96)
C
RHO2=YMT96**2+ZMT96**2
R=SQRT(RHO2+XMT96**2)
ST=SQRT(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=ATAN2(ST,CT)
RM=R0*(2./(1.+CT))**ALPHA
F=R-RM
GRADF_R=1.
GRADF_T=-ALPHA/R*RM*ST/(1.+CT)
GRADF=SQRT(GRADF_R**2+GRADF_T**2)
DR=-F/GRADF**2
DT= DR/R*GRADF_T
R=R+DR
T=T+DT
ST=SIN(T)
CT=COS(T)
DS=SQRT(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.E-4) GOTO 1
XMGNP=R*COS(T)
RHO= R*SIN(T)
YMGNP=RHO*SIN(PHI)
ZMGNP=RHO*COS(PHI)
DIST=SQRT((XGSM-XMGNP)**2+(YGSM-YMGNP)**2+(ZGSM-ZMGNP)**2)
RETURN
END
C
C=======================================================================================
C
SUBROUTINE T96_MGNP (XN_PD,VEL,XGSM,YGSM,ZGSM,XMGNP,YMGNP,ZMGNP,
* DIST,ID)
C
C FOR ANY POINT OF SPACE WITH GIVEN COORDINATES (XGSM,YGSM,ZGSM), THIS SUBROUTINE DEFINES
C THE POSITION OF A POINT (XMGNP,YMGNP,ZMGNP) AT THE T96 MODEL MAGNETOPAUSE, HAVING 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 XGSM,YGSM,ZGSM - COORDINATES OF THE OBSERVATION POINT IN EARTH RADII
C
C OUTPUT: XMGNP,YMGNP,ZMGNP - GSM POSITION OF THE BOUNDARY POINT, HAVING THE SAME
C VALUE OF TAU-COORDINATE AS THE OBSERVATION POINT (XGSM,YGSM,ZGSM)
C DIST - THE DISTANCE BETWEEN THE TWO POINTS, IN RE,
C ID - POSITION FLAG; ID=+1 (-1) MEANS THAT THE POINT (XGSM,YGSM,ZGSM)
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
C
C DEFINE SOLAR WIND DYNAMIC PRESSURE (NANOPASCALS, ASSUMING 4% OF ALPHA-PARTICLES),
C IF NOT EXPLICITLY SPECIFIED IN THE INPUT:
IF (VEL.LT.0.) THEN
PD=XN_PD
ELSE
PD=1.94E-6*XN_PD*VEL**2
C
ENDIF
C
C RATIO OF PD TO THE AVERAGE PRESSURE, ASSUMED EQUAL TO 2 nPa:
RAT=PD/2.0
RAT16=RAT**0.14
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.
S00=1.08
X00=5.48
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 ON 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 (YGSM.NE.0..OR.ZGSM.NE.0.) THEN
PHI=ATAN2(YGSM,ZGSM)
ELSE
PHI=0.
ENDIF
C
RHO=SQRT(YGSM**2+ZGSM**2)
C
IF (XGSM.LT.XM) THEN
XMGNP=XGSM
RHOMGNP=A*SQRT(S0**2-1)
YMGNP=RHOMGNP*SIN(PHI)
ZMGNP=RHOMGNP*COS(PHI)
DIST=SQRT((XGSM-XMGNP)**2+(YGSM-YMGNP)**2+(ZGSM-ZMGNP)**2)
IF (RHOMGNP.GT.RHO) ID=+1
IF (RHOMGNP.LE.RHO) ID=-1
RETURN
ENDIF
C
XKSI=(XGSM-X0)/A+1.
XDZT=RHO/A
SQ1=SQRT((1.+XKSI)**2+XDZT**2)
SQ2=SQRT((1.-XKSI)**2+XDZT**2)
SIGMA=0.5*(SQ1+SQ2)
TAU=0.5*(SQ1-SQ2)
C
C NOW CALCULATE (X,Y,Z) FOR THE CLOSEST POINT AT THE MAGNETOPAUSE
C
XMGNP=X0-A*(1.-S0*TAU)
ARG=(S0**2-1.)*(1.-TAU**2)
IF (ARG.LT.0.) ARG=0.
RHOMGNP=A*SQRT(ARG)
YMGNP=RHOMGNP*SIN(PHI)
ZMGNP=RHOMGNP*COS(PHI)
C
C NOW CALCULATE THE DISTANCE BETWEEN THE POINTS {XGSM,YGSM,ZGSM} 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=SQRT((XGSM-XMGNP)**2+(YGSM-YMGNP)**2+(ZGSM-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