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geopack.f

C
C============================================================================
C============================================================================
C============================================================================
c
c##########################################################################
c#                                                                        #
c#                              GEOPACK                                   #
c#                     (MAIN SET OF FORTRAN CODES)                        #
c#                                                                        #
c##########################################################################
C

c
c    This collection of subroutines is a result of several upgrades of the original
c      package by N. A. Tsyganenko. This release is dated by January 5, 2001.
c
c    Please see the additional file geopack.txt for descriptions of the individual
c    subroutines.
c
c    The following changes were made to the previous release of April 16, 1996:
c
c       (1) The latest set of IGRF expansion coefficients for the epoch 2000.0
c    was added, so that the updated version of the main field model accepts
c    dates through 2005.
c
c       (2) All explicit type statements as well as IMPLICIT NONE were taken
c    out from all subroutines, for the sake of brevity.

c       (3) To avoid potential run-time errors on some types of FORTRAN compilers,
c    the SAVE statements were added in the subroutines IGRF, DIP, RECALC, GEOMAG.
C
C       (4) In the tracing subroutine TRACE, more harmonic terms were allowed
c    to be included in the main field expansion (IGRF) for maintaining a higher
c    accuracy.
c
c       (5) An update and some correction/editing of the documentation file
c    GEOPACK.TXT was made.
c
c
c----------------------------------------------------------------------------------
c
      SUBROUTINE IGRF(IY,NM,R,T,F,BR,BT,BF)
c
C     CALCULATES COMPONENTS OF THE MAIN (INTERNAL) GEOMAGNETIC FIELD IN SPHERICAL
C     GEOGRAPHICAL COORDINATE SYSTEM, USING IAGA INTERNATIONAL GEOMAGNETIC REFERENCE
C     MODEL COEFFICIENTS (e.g., http://www.ngdc.noaa.gov/IAGA/wg8/igrf2000.html)
C
C     UPDATING THE COEFFICIENTS TO A GIVEN EPOCH IS MADE AUTOMATICALLY UPON THE FIRST
C     CALL AND AFTER EVERY CHANGE OF THE PARAMETER IY.
C
C-----INPUT PARAMETERS:
C
C     IY  -  YEAR NUMBER (FOUR-DIGIT; 1965 &LE IY &LE 2005)
C     NM  -  HIGHEST ORDER OF SPHERICAL HARMONICS IN THE SCALAR POTENTIAL (NM &LE 10)
C     R,T,F -  SPHERICAL COORDINATES (RADIUS R IN UNITS RE=6371.2 KM, GEOGRAPHIC
C                COLATITUDE  T  AND LONGITUDE  F  IN RADIANS)
C
C-----OUTPUT PARAMETERS:
C
C     BR,BT,BF - SPHERICAL COMPONENTS OF THE MAIN GEOMAGNETIC FIELD IN NANOTESLA
C
C     LAST MODIFICATION:  JANUARY 5, 2001.
C     THE CODE WAS MODIFIED TO ACCEPT DATES THROUGH 2005.
C     IT HAS ALSO BEEN SLIGHTLY SIMPLIFIED BY TAKING OUT SOME REDUNDANT STATEMENTS,
C     AND A "SAVE" STATEMENT WAS ADDED, TO AVOID POTENTIAL PROBLEMS WITH SOME
C     FORTRAN COMPILERS.
c
C     WRITTEN BY: N. A. TSYGANENKO
C
      SAVE MA,IYR,IPR
C
      DIMENSION A(11),B(11),G(66),H(66),REC(66),G65(66),H65(66),G70(66),
     * H70(66),G75(66),H75(66),G80(66),H80(66),G85(66),H85(66),G90(66),
     * H90(66),G95(66),H95(66),G00(66),H00(66),DG00(45),DH00(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./
      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./
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./
      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./
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./
      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./
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./
      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./
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./
      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./
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./

      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./

      DATA G95/0., -29682.,  -1789.,  -2197.,   3074.,   1685.,   1329.,
     *     -2268.,   1249.,    769.,    941.,    782.,    291.,   -421.,
     *       116.,   -210.,    352.,    237.,   -122.,   -167.,    -26.,
     *        66.,     64.,     65.,   -172.,      2.,     17.,    -94.,
     *        78.,    -67.,      1.,     29.,      4.,      8.,     10.,
     *        -2.,     24.,      4.,     -1.,     -9.,    -14.,      4.,
     *         5.,      0.,     -7.,      4.,      9.,      1.,    -12.,
     *         9.,     -4.,     -2.,      7.,      0.,     -6.,     -3.,
     *        -4.,      2.,     -5.,     -2.,      4.,      3.,      1.,
     *         3.,      3.,      0./

      DATA H95/0.,      0.,   5318.,      0.,  -2356.,   -425.,      0.,
     *      -263.,    302.,   -406.,      0.,    262.,   -232.,     98.,
     *      -301.,      0.,     44.,    157.,   -152.,    -64.,     99.,
     *         0.,    -16.,     77.,     67.,    -57.,      4.,     28.,
     *         0.,    -77.,    -25.,      3.,     22.,     16.,    -23.,
     *        -3.,      0.,     12.,    -20.,      7.,    -21.,     12.,
     *        10.,    -17.,    -10.,      0.,    -19.,     15.,     11.,
     *        -7.,     -7.,      9.,      7.,     -8.,      1.,      0.,
     *         2.,      1.,      3.,      6.,     -4.,      0.,     -2.,
     *         3.,     -1.,     -6./

      DATA G00/0., -29615.,  -1728.,  -2267.,   3072.,   1672.,   1341.,
     *     -2290.,   1253.,    715.,    935.,    787.,    251.,   -405.,
     *       110.,   -217.,    351.,    222.,   -131.,   -169.,    -12.,
     *        72.,     68.,     74.,   -161.,     -5.,     17.,    -91.,
     *        79.,    -74.,      0.,     33.,      9.,      7.,      8.,
     *        -2.,     25.,      6.,     -9.,     -8.,    -17.,      9.,
     *         7.,     -8.,     -7.,      5.,      9.,      3.,    - 8.,
     *         6.,     -9.,     -2.,      9.,     -4.,     -8.,     -2.,
     *        -6.,      2.,     -3.,      0.,      4.,      1.,      2.,
     *         4.,      0.,     -1./


      DATA H00/0.,      0.,   5186.,      0.,  -2478.,   -458.,      0.,
     *      -227.,    296.,   -492.,      0.,    272.,   -232.,    119.,
     *      -304.,      0.,     44.,    172.,   -134.,    -40.,    107.,
     *         0.,    -17.,     64.,     65.,    -61.,      1.,     44.,
     *         0.,    -65.,    -24.,      6.,     24.,     15.,    -25.,
     *        -6.,      0.,     12.,    -22.,      8.,    -21.,     15.,
     *         9.,    -16.,     -3.,      0.,    -20.,     13.,     12.,
     *        -6.,     -8.,      9.,      4.,     -8.,      5.,      0.,
     *         1.,      0.,      4.,      5.,     -6.,     -1.,     -3.,
     *         0.,     -2.,     -8./


      DATA DG00/0.0,  14.6,    10.7,   -12.4,     1.1,    -1.1,     0.7,
     *         -5.4,   0.9,    -7.7,    -1.3,     1.6,    -7.3,     2.9,
     *         -3.2,   0.0,    -0.7,    -2.1,    -2.8,    -0.8,     2.5,
     *          1.0,  -0.4,     0.9,     2.0,    -0.6,    -0.3,     1.2,
     *         -0.4,  -0.4,    -0.3,     1.1,     1.1,    -0.2,     0.6,
     *         -0.9,  -0.3,     0.2,    -0.3,     0.4,    -1.0,     0.3,
     *         -0.5,  -0.7,    -0.4/

      DATA DH00/0.0,   0.0,   -22.5,     0.0,   -20.6,    -9.6,     0.0,
     *          6.0,  -0.1,   -14.2,     0.0,     2.1,     1.3,     5.0,
     *          0.3,   0.0,    -0.1,     0.6,     1.7,     1.9,     0.1,
     *          0.0,  -0.2,    -1.4,     0.0,    -0.8,     0.0,     0.9,
     *          0.0,   1.1,     0.0,     0.3,    -0.1,    -0.6,    -0.7,
     *          0.2,   0.0,     0.1,     0.0,     0.0,     0.3,     0.6,
     *         -0.4,   0.3,     0.7/
c
c
      DATA MA,IYR,IPR/0,0,0/

      IF(MA.NE.1) GOTO 10
      IF(IY.NE.IYR) GOTO 30
      GOTO 130
10    MA=1
C
      DO 20 N=1,11
         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
30    IYR=IY
      IF (IYR.LT.1965) IYR=1965
      IF (IYR.GT.2005) IYR=2005
      IF (IY.NE.IYR.AND.IPR.EQ.0) WRITE (*,999)IY,IYR
      IF (IYR.NE.IY) IPR=1
      IF (IYR.LT.1970) GOTO 50            !INTERPOLATE BETWEEN 1965 - 1970
      IF (IYR.LT.1975) GOTO 60            !INTERPOLATE BETWEEN 1970 - 1975
      IF (IYR.LT.1980) GOTO 70            !INTERPOLATE BETWEEN 1975 - 1980
      IF (IYR.LT.1985) GOTO 80            !INTERPOLATE BETWEEN 1980 - 1985
      IF (IYR.LT.1990) GOTO 90            !INTERPOLATE BETWEEN 1985 - 1990
      IF (IYR.LT.1995) GOTO 100           !INTERPOLATE BETWEEN 1990 - 1995
      IF (IYR.LT.2000) GOTO 110         !INTERPOLATE BETWEEN 1995 - 2000
C
C       EXTRAPOLATE BEYOND 2000:
C
      DT=FLOAT(IYR)-2000.
      DO 40 N=1,66
         G(N)=G00(N)
         H(N)=H00(N)
         IF (N.GT.45) GOTO 40
         G(N)=G(N)+DG00(N)*DT
         H(N)=H(N)+DH00(N)*DT
40    CONTINUE
      GOTO 300
C
C       INTERPOLATE BETWEEEN 1965 - 1970:
C
50    F2=(IYR-1965)/5.
      F1=1.-F2
      DO 55 N=1,66
         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=(IYR-1970)/5.
      F1=1.-F2
      DO 65 N=1,66
         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=(IYR-1975)/5.
      F1=1.-F2
      DO 75 N=1,66
         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=(IYR-1980)/5.
      F1=1.-F2
      DO 85 N=1,66
         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=(IYR-1985)/5.
      F1=1.-F2
      DO 95 N=1,66
         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=(IYR-1990)/5.
      F1=1.-F2
      DO 105 N=1,66
         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=(IYR-1995)/5.
      F1=1.-F2
      DO 115 N=1,66
         G(N)=G95(N)*F1+G00(N)*F2
115      H(N)=H95(N)*F1+H00(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 120 N=2,11
         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 120 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
120         H(MNN)=H(MNN)*P
C
C     NOW CALCULATE THE FIELD COMPONENTS
C     (IN CASE OF MULTIPLE INVOCATIONS WITH THE SAME VALUES OF IY AND NM,
C      CALCULATIONS START RIGHT HERE):
C
130   PP=1./R
      P=PP

      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.
      U=T
      CF=COS(F)
      SF=SIN(F)
      C=COS(U)
      S=SIN(U)
      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
      RETURN
210   IF(C.LT.0.) BBF=-BBF
      BF=BBF

      RETURN
C
999   FORMAT(//1X,
     * 'IGRF WARNS:**** YEAR IS OUT OF INTERVAL 1965-2005: IY =',I5,/,
     *',        CALCULATIONS WILL BE DONE FOR IYR =',I5,' ****'//)
      END
C

c
       SUBROUTINE DIP(PS,X,Y,Z,BX,BY,BZ)
C
C
C  CALCULATES GSM COMPONENTS OF A GEODIPOLE FIELD WITH THE DIPOLE MOMENT
C  CORRESPONDING TO THE EPOCH OF 2000.
C
C----INPUT PARAMETERS:
C     PS - GEODIPOLE TILT ANGLE IN RADIANS,
C     X,Y,Z - GSM COORDINATES IN RE (1 RE = 6371.2 km)
C
C----OUTPUT PARAMETERS:
C     BX,BY,BZ - FIELD COMPONENTS IN GSM SYSTEM, IN NANOTESLA.
C
C  LAST MODIFICATION: JAN. 5, 2001. THE VALUE OF THE DIPOLE MOMENT WAS UPDATED TO 2000.
C    AND A "SAVE" STATEMENT HAS BEEN ADDED, TO AVOID POTENTIAL PROBLEMS WITH SOME
C    FORTRAN COMPILERS
C
C  WRITTEN BY: N. A. TSYGANENKO
C
      SAVE M,PSI
      DATA M,PSI/0,5./
      IF(M.EQ.1.AND.ABS(PS-PSI).LT.1.E-5) GOTO 1
      SPS=SIN(PS)
      CPS=COS(PS)
      PSI=PS
      M=1
  1   P=X**2
      U=Z**2
      V=3.*Z*X
      T=Y**2
      Q=30115./SQRT(P+T+U)**5
      BX=Q*((T+U-2.*P)*SPS-V*CPS)
      BY=-3.*Y*Q*(X*SPS+Z*CPS)
      BZ=Q*((P+T-2.*U)*CPS-V*SPS)
      RETURN
      END


c
      SUBROUTINE SUN(IYR,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:  JAN 5, 2001 (NO ESSENTIAL CHANGES, BUT
C     SOME REDUNDANT STATEMENTS TAKEN OUT FROM THE PREVIOUS VERSION)
C
C     ORIGINAL VERSION WRITTEN BY:    Gilbert D. Mead
C
      DOUBLE PRECISION DJ,FDAY
      DATA RAD/57.295779513/
C
      IF(IYR.LT.1901.OR.IYR.GT.2099) RETURN
      FDAY=DFLOAT(IHOUR*3600+MIN*60+ISEC)/86400.D0
      DJ=365*(IYR-1900)+(IYR-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
      SUBROUTINE SPHCAR(R,TETA,PHI,X,Y,Z,J)
C
C   CONVERTS SPHERICAL COORDS INTO CARTESIAN ONES AND VICA VERSA
C    (TETA AND PHI IN RADIANS).
C
C                  J &Gt 0            J &Lt 0
C-----INPUT:   J,R,TETA,PHI     J,X,Y,Z
C----OUTPUT:      X,Y,Z        R,TETA,PHI
C
C   LAST MOFIFICATION:  JAN 5, 2001 (NO ESSENTIAL CHANGES, BUT
C                        SOME REDUNDANT STATEMENTS TAKEN OUT)
C
C   WRITTEN BY:  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
      TETA=0.
      RETURN
  1   TETA=3.141592654
      RETURN
  2   SQ=SQRT(SQ)
      PHI=ATAN2(Y,X)
      TETA=ATAN2(SQ,Z)
      IF (PHI.LT.0.) PHI=PHI+6.28318531
      RETURN
  3   SQ=R*SIN(TETA)
      X=SQ*COS(PHI)
      Y=SQ*SIN(PHI)
      Z=R*COS(TETA)
      RETURN
      END




c
      SUBROUTINE BSPCAR(TETA,PHI,BR,BTET,BPHI,BX,BY,BZ)
C
C   CALCULATES CARTESIAN FIELD COMPONENTS FROM SPHERICAL ONES
C-----INPUT:   TETA,PHI - SPHERICAL ANGLES OF THE POINT IN RADIANS
C              BR,BTET,BPHI -  SPHERICAL COMPONENTS OF THE FIELD
C-----OUTPUT:  BX,BY,BZ - CARTESIAN COMPONENTS OF THE FIELD
C
C   LAST MOFIFICATION:  JAN 5 2001 (NO ESSENTIAL CHANGES, BUT
C                        SOME REDUNDANT STATEMENTS TAKEN OUT)
C
C   WRITTEN BY:  N. A. TSYGANENKO
C
      S=SIN(TETA)
      C=COS(TETA)
      SF=SIN(PHI)
      CF=COS(PHI)
      BE=BR*S+BTET*C
      BX=BE*CF-BPHI*SF
      BY=BE*SF+BPHI*CF
      BZ=BR*C-BTET*S
      RETURN
      END
c


C
      SUBROUTINE RECALC(IYR,IDAY,IHOUR,MIN,ISEC)
C
C  PREPARES ELEMENTS OF ROTATION MATRICES FOR TRANSFORMATIONS OF VECTORS BETWEEN
C  SEVERAL COORDINATE SYSTEMS, MOST FREQUENTLY USED IN SPACE PHYSICS.
C
C  THIS SUBROUTINE SHOULD BE INVOKED BEFORE USING THE FOLLOWING SUBROUTINES:
C         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     IYR   -  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 BLOCK /GEOPACK/)
C
C    OTHER SUBROUTINES CALLED BY THIS ONE: SUN
C
C   ################################################
C   #  WRITTEN BY  N.A. TSYGANENKO ON DEC.1, 1991  #
C   ################################################
c
c    Last modification:  January 5, 2001.
c    The code has been modified to accept dates through 2005.
c    Also, a "save" statement was added, to avoid potential problems
c    with some Fortran compilers.
C
      COMMON /GEOPACK/ 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,
     * K,IY,CGST,SGST,BA(6)
c
      SAVE IYE,IDE,IPR
      DATA IYE,IDE,IPR/3*0/
C
      IF (IYR.EQ.IYE.AND.IDAY.EQ.IDE) GOTO 5
C
C   IYE AND IDE ARE THE CURRENT VALUES OF YEAR AND DAY NUMBER
C
      IY=IYR
      IDE=IDAY
      IF(IY.LT.1965) IY=1965
      IF(IY.GT.2005) IY=2005
C
C  WE ARE RESTRICTED BY THE INTERVAL 1965-2005,
C  FOR WHICH THE IGRF COEFFICIENTS ARE KNOWN; IF IYR IS OUTSIDE THIS INTERVAL
C  THE SUBROUTINE PRINTS A WARNING (BUT DOES NOT REPEAT IT AT NEXT INVOCATIONS)
C
      IF(IY.NE.IYR.AND.IPR.EQ.0) WRITE (*,10) IYR,IY
      IF(IY.NE.IYR) IPR=1
      IYE=IY
C
C  LINEAR INTERPOLATION OF THE GEODIPOLE MOMENT COMPONENTS BETWEEN THE
C  VALUES FOR THE NEAREST EPOCHS:
C
      IF (IY.LT.1970) THEN                            !1965-1970
         F2=(FLOAT(IY)+FLOAT(IDAY)/365.-1965.)/5.
         F1=1.D0-F2
           G10=30334.*F1+30220.*F2 ! HERE G10 HAS OPPOSITE SIGN TO THAT IN IGRF TABLES
         G11=-2119.*F1-2068.*F2
         H11=5776.*F1+5737.*F2
      ELSEIF (IY.LT.1975) THEN                        !1970-1975
         F2=(FLOAT(IY)+FLOAT(IDAY)/365.-1970.)/5.
         F1=1.D0-F2
           G10=30220.*F1+30100.*F2 ! HERE G10 HAS OPPOSITE SIGN TO THAT IN IGRF TABLES
         G11=-2068.*F1-2013.*F2
         H11=5737.*F1+5675.*F2
      ELSEIF (IY.LT.1980) THEN                        !1975-1980
         F2=(DFLOAT(IY)+DFLOAT(IDAY)/365.-1975.)/5.
         F1=1.D0-F2
           G10=30100.*F1+29992.*F2 ! HERE G10 HAS OPPOSITE SIGN TO THAT IN IGRF TABLES
         G11=-2013.*F1-1956.*F2
         H11=5675.*F1+5604.*F2
      ELSEIF (IY.LT.1985) THEN                        !1980-1985
         F2=(FLOAT(IY)+FLOAT(IDAY)/365.-1980.)/5.
         F1=1.D0-F2
           G10=29992.*F1+29873.*F2 ! HERE G10 HAS OPPOSITE SIGN TO THAT IN IGRF TABLES
         G11=-1956.*F1-1905.*F2
         H11=5604.*F1+5500.*F2
      ELSEIF (IY.LT.1990) THEN                  !1985-1990
         F2=(FLOAT(IY)+FLOAT(IDAY)/365.-1985.)/5.
         F1=1.D0-F2
           G10=29873.*F1+29775.*F2 ! HERE G10 HAS OPPOSITE SIGN TO THAT IN IGRF TABLES
         G11=-1905.*F1-1848.*F2
         H11=5500.*F1+5406.*F2
      ELSEIF (IY.LT.1995) THEN                  !1990-1995
         F2=(FLOAT(IY)+FLOAT(IDAY)/365.-1990.)/5.
         F1=1.D0-F2
           G10=29775.*F1+29682.*F2 ! HERE G10 HAS OPPOSITE SIGN TO THAT IN IGRF TABLES
         G11=-1848.*F1-1789.*F2
         H11=5406.*F1+5318.*F2
        ELSEIF (IY.LT.2000) THEN                        !1995-2000
       F2=(FLOAT(IY)+FLOAT(IDAY)/365.-1995.)/5.
         F1=1.D0-F2
           G10=29682.*F1+29615.*F2 ! HERE G10 HAS OPPOSITE SIGN TO THAT IN IGRF TABLES
           G11=-1789.*F1-1728.*F2
           H11=5318.*F1+5186.*F2
        ELSE                                            !2000-2005
C
C   LINEAR EXTRAPOLATION BEYOND 2000 BY USING SECULAR VELOCITY COEFFICIENTS:
C
           DT=FLOAT(IY)+FLOAT(IDAY)/366.-2000.
           G10=29615.-14.6*DT      ! HERE G10 HAS OPPOSITE SIGN TO THAT IN IGRF TABLES
           G11=-1728.+10.7*DT
           H11=5186.-22.5*DT
      ENDIF
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
C      THE CALCULATIONS ARE TERMINATED IF ONLY GEO-MAG TRANSFORMATION
C       IS TO BE DONE  (IHOUR>24 IS THE AGREED INDICATOR FOR THIS CASE):
C
   5   IF (IHOUR.GT.24) RETURN
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)CC  DIP1, DIP2, AND DIP3 ARE THE COMPONENTS OF THE UNIT VECTOR EZSM=EZMAGC   IN THE SYSTEM GEI:C      DIP1=STCL*CGST-STSL*SGST      DIP2=STCL*SGST+STSL*CGST      DIP3=CT0CC  NOW CALCULATE THE COMPONENTS OF THE UNIT VECTOR EYGSM IN THE SYSTEM GEIC   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/YCC   THEN IN THE GEI SYSTEM THE UNIT VECTOR Z = EZGSM = EXGSM x EYGSM = S x YC    HAS THE COMPONENTS:C      Z1=S2*Y3-S3*Y2      Z2=S3*Y1-S1*Y3      Z3=S1*Y2-S2*Y1CC    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 FORC   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)CC  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*S1CC   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)=EM22C      CHI=Y1*DY1+Y2*DY2+Y3*DY3      SHI=Y1*DZ1+Y2*DZ2+Y3*DZ3      HI=ASIN(SHI)CC    TILT ANGLE: PSI=ARCSIN(DIP,EXGSM)C      SPS=DIP1*S1+DIP2*S2+DIP3*S3      CPS=SQRT(1.-SPS**2)      PSI=ASIN(SPS)CC    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:CC 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            -ST0C  EYMAG:    -SL0*COS(GST)-CL0*SIN(GST)C            -SL0*SIN(GST)+CL0*COS(GST)C             0C  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*EXMAGZC      XMUT=(ATAN2(SFI,CFI)+3.1415926536)*3.8197186342CC  THE ELEMENTS OF THE MATRIX GEO TO GSM ARE THE SCALAR PRODUCTS:CC   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),CC   ALL THE UNIT VECTORS IN BRACKETS ARE ALREADY DEFINED IN GEI:CC  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=Z3C 10   FORMAT(//1X,     * '****RECALC WARNS:  YEAR IS OUT OF INTERVAL 1965-2005: IYR=
',I4,     * /,6X,'CALCULATIONS WILL BE DONE FOR IYR=




































































































































































































































































































',I4,/)      RETURN      ENDC      SUBROUTINE GEOMAG(XGEO,YGEO,ZGEO,XMAG,YMAG,ZMAG,J,IYR)CC    CONVERTS GEOGRAPHIC (GEO) TO DIPOLE (MAG) COORDINATES OR VICA VERSA.C    IYR IS YEAR NUMBER (FOUR DIGITS).CC                           J &Gt  0                J &Lt 0C-----INPUT:  J,XGEO,YGEO,ZGEO,IYR   J,XMAG,YMAG,ZMAG,IYRC-----OUTPUT:    XMAG,YMAG,ZMAG        XGEO,YGEO,ZGEOCC   OTHER SUBROUTINES CALLED BY THIS ONE:  RECALCCC   LAST MOFIFICATION:  JAN 5, 2001 (NO ESSENTIAL CHANGES, BUTC                         SOME REDUNDANT STATEMENTS TAKEN OUT)CC   WRITTEN BY:  N. A. TSYGANENKOC      COMMON /GEOPACK/ ST0,CT0,SL0,CL0,CTCL,STCL,CTSL,STSL,AB(19),     * K,IY,BB(8)      SAVE II      DATA II/1/C      IF(IYR.EQ.II) GOTO 1      II=IYR      CALL RECALC(II,0,25,0,0)  1   CONTINUE      IF(J.LT.0) GOTO 2      XMAG=XGEO*CTCL+YGEO*CTSL-ZGEO*ST0      YMAG=YGEO*CL0-XGEO*SL0      ZMAG=XGEO*STCL+YGEO*STSL+ZGEO*CT0      RETURN  2   XGEO=XMAG*CTCL-YMAG*SL0+ZMAG*STCL      YGEO=XMAG*CTSL+YMAG*CL0+ZMAG*STSL      ZGEO=ZMAG*CT0-XMAG*ST0      RETURN      ENDcc      SUBROUTINE GEIGEO(XGEI,YGEI,ZGEI,XGEO,YGEO,ZGEO,J)CC   CONVERTS EQUATORIAL INERTIAL (GEI) TO GEOGRAPHICAL (GEO) COORDSC   OR VICA VERSA.C                    J &Gt 0                J &Lt 0C----INPUT:  J,XGEI,YGEI,ZGEI    J,XGEO,YGEO,ZGEOC----OUTPUT:   XGEO,YGEO,ZGEO      XGEI,YGEI,ZGEICC  ATTENTION:  SUBROUTINE  RECALC  MUST BE INVOKED BEFORE GEIGEO IN TWO CASES:C     /A/  BEFORE THE FIRST INVOCATION OF GEIGEOC     /B/  IF THE CURRENT VALUES OF IYEAR,IDAY,IHOUR,MIN,ISEC HAVE BEEN CHANGEDCC     LAST MODIFICATION:  JAN 5, 2001 (NO ESSENTIAL CHANGES, BUTC                         SOME REDUNDANT STATEMENTS TAKEN OUT)C     WRITTEN BY:  N. A. TSYGANENKOC      COMMON /GEOPACK/ A(27),KKKK(2),CGST,SGST,B(6)C      IF(J.LT.0) GOTO 1      XGEO=XGEI*CGST+YGEI*SGST      YGEO=YGEI*CGST-XGEI*SGST      ZGEO=ZGEI      RETURN  1   XGEI=XGEO*CGST-YGEO*SGST      YGEI=YGEO*CGST+XGEO*SGST      ZGEI=ZGEO      RETURN      ENDCC      SUBROUTINE MAGSM(XMAG,YMAG,ZMAG,XSM,YSM,ZSM,J)CC  CONVERTS DIPOLE (MAG) TO SOLAR MAGNETIC (SM) COORDINATES OR VICA VERSACC                    J &Gt 0              J &Lt 0C----INPUT: J,XMAG,YMAG,ZMAG     J,XSM,YSM,ZSMC----OUTPUT:    XSM,YSM,ZSM       XMAG,YMAG,ZMAGCC  ATTENTION:  SUBROUTINE  RECALC  MUST BE INVOKED BEFORE MAGSM IN TWO CASES:C     /A/  BEFORE THE FIRST INVOCATION OF MAGSMC     /B/  IF THE VALUES OF IYEAR,IDAY,IHOUR,MIN,ISEC HAVE BEEN CHANGEDCC     LAST MODIFICATION:  JAN 5, 2001 (NO ESSENTIAL CHANGES, BUTC                            SOME REDUNDANT STATEMENTS TAKEN OUT)CC     WRITTEN BY:  N. A. TSYGANENKOC      COMMON /GEOPACK/ A(8),SFI,CFI,B(7),AB(10),K,IY,BA(8)C      IF (J.LT.0) GOTO 1      XSM=XMAG*CFI-YMAG*SFI      YSM=XMAG*SFI+YMAG*CFI      ZSM=ZMAG      RETURN  1   XMAG=XSM*CFI+YSM*SFI      YMAG=YSM*CFI-XSM*SFI      ZMAG=ZSM      RETURN      ENDC       SUBROUTINE GSMGSE(XGSM,YGSM,ZGSM,XGSE,YGSE,ZGSE,J)CC CONVERTS GEOCENTRIC SOLAR MAGNETOSPHERIC (GSM) COORDS TO SOLAR ECLIPTIC (GSE) ONESC   OR VICA VERSA.C                    J &Gt 0                J &Lt 0C-----INPUT: J,XGSM,YGSM,ZGSM    J,XGSE,YGSE,ZGSEC----OUTPUT:   XGSE,YGSE,ZGSE      XGSM,YGSM,ZGSMCC  ATTENTION:  SUBROUTINE  RECALC  MUST BE INVOKED BEFORE GSMGSE IN TWO CASES:C     /A/  BEFORE THE FIRST INVOCATION OF GSMGSEC     /B/  IF THE VALUES OF IYEAR,IDAY,IHOUR,MIN,ISEC HAVE BEEN CHANGEDCC     LAST MODIFICATION:  JAN 5, 2001  (NO ESSENTIAL CHANGES, BUTC                             SOME REDUNDANT STATEMENTS TAKEN OUT)CC     WRITTEN BY:  N. A. TSYGANENKOC      COMMON /GEOPACK/ A(12),SHI,CHI,AB(13),K,IY,BA(8)C      IF (J.LT.0) GOTO 1      XGSE=XGSM      YGSE=YGSM*CHI-ZGSM*SHI      ZGSE=YGSM*SHI+ZGSM*CHI      RETURN1     XGSM=XGSE      YGSM=YGSE*CHI+ZGSE*SHI      ZGSM=ZGSE*CHI-YGSE*SHI      RETURN      ENDC       SUBROUTINE SMGSM(XSM,YSM,ZSM,XGSM,YGSM,ZGSM,J)CC CONVERTS SOLAR MAGNETIC (SM) TO GEOCENTRIC SOLAR MAGNETOSPHERICC   (GSM) COORDINATES OR VICA VERSA.C                  J &Gt 0                 J &Lt 0C-----INPUT: J,XSM,YSM,ZSM        J,XGSM,YGSM,ZGSMC----OUTPUT:  XGSM,YGSM,ZGSM       XSM,YSM,ZSMCC  ATTENTION:  SUBROUTINE  RECALC  MUST BE INVOKED BEFORE SMGSM IN TWO CASES:C     /A/  BEFORE THE FIRST INVOCATION OF SMGSMC     /B/  IF THE VALUES OF IYEAR,IDAY,IHOUR,MIN,ISEC HAVE BEEN CHANGEDCC     LAST MODIFICATION:  JAN 5, 2001  (NO ESSENTIAL CHANGES, BUTC                             SOME REDUNDANT STATEMENTS TAKEN OUT)CC     WRITTEN BY:  N. A. TSYGANENKOC      COMMON /GEOPACK/ A(10),SPS,CPS,B(15),K,IY,AB(8)      IF (J.LT.0) GOTO 1      XGSM=XSM*CPS+ZSM*SPS      YGSM=YSM      ZGSM=ZSM*CPS-XSM*SPS      RETURN  1   XSM=XGSM*CPS-ZGSM*SPS      YSM=YGSM      ZSM=XGSM*SPS+ZGSM*CPS      RETURN      ENDC      SUBROUTINE GEOGSM(XGEO,YGEO,ZGEO,XGSM,YGSM,ZGSM,J)CC CONVERTS GEOGRAPHIC (GEO) TO SOLAR MAGNETOSPHERIC (SM) COORDINATES OR VICA VERSA.CC                   J &Gt 0                   J &Lt 0C----- INPUT:  J,XGEO,YGEO,ZGEO    J,XGSM,YGSM,ZGSMC---- OUTPUT:    XGSM,YGSM,ZGSM      XGEO,YGEO,ZGEOCC  ATTENTION:  SUBROUTINE  RECALC  MUST BE INVOKED BEFORE GEOGSM IN TWO CASES:C     /A/  BEFORE THE FIRST INVOCATION OF GEOGSMC     /B/  IF THE VALUES OF IYEAR,IDAY,IHOUR,MIN,ISEC  HAVE BEEN CHANGEDCC     LAST MODIFICATION:  JAN 5, 2001 (NO ESSENTIAL CHANGES, BUTC                            SOME REDUNDANT STATEMENTS TAKEN OUT)CC     WRITTEN BY:  N. A. TSYGANENKOC      COMMON /GEOPACK/ AA(17),A11,A21,A31,A12,A22,A32,A13,A23,A33,     *  D,K,IY,B(8)C      IF (J.LT.0) GOTO 1      XGSM=A11*XGEO+A12*YGEO+A13*ZGEO      YGSM=A21*XGEO+A22*YGEO+A23*ZGEO      ZGSM=A31*XGEO+A32*YGEO+A33*ZGEO      RETURN  1   XGEO=A11*XGSM+A21*YGSM+A31*ZGSM      YGEO=A12*XGSM+A22*YGSM+A32*ZGSM      ZGEO=A13*XGSM+A23*YGSM+A33*ZGSM      RETURN      ENDC      SUBROUTINE RHAND(X,Y,Z,R1,R2,R3,IOPT,PARMOD,EXNAME)CC  COMPUTES RIGHT HAND EXPRESSIONS IN THE GEOMAGNETIC FIELD LINE EQUATIONC      (a subsidiary subroutine for the subr. STEP)CC     LAST MODIFICATION:  JAN 5, 2001 (NO ESSENTIAL CHANGES, BUTC                            SOME REDUNDANT STATEMENTS TAKEN OUT)CC     WRITTEN BY:  N. A. TSYGANENKOC      DIMENSION PARMOD(10)      EXTERNAL EXNAMEC      COMMON /GEOPACK/ A(15),PSI,AA(10),DS3,K,IY,BB(8)      CALL EXNAME(IOPT,PARMOD,PSI,X,Y,Z,BX,BY,BZ)      IF (K.EQ.0) GOTO 1      CALL GEOGSM(XG,YG,ZG,X,Y,Z,-1)      CALL SPHCAR(R,T,F,XG,YG,ZG,-1)      CALL IGRF(IY,K,R,T,F,BR,BT,BF)      CALL BSPCAR(T,F,BR,BT,BF,FX,FY,FZ)      CALL GEOGSM(FX,FY,FZ,HX,HY,HZ,1)      GOTO 2  1   CALL DIP(PSI,X,Y,Z,HX,HY,HZ)  2   BX=BX+HX      BY=BY+HY      BZ=BZ+HZ      B=DS3/SQRT(BX**2+BY**2+BZ**2)      R1=BX*B      R2=BY*B      R3=BZ*B      RETURN      ENDC      SUBROUTINE STEP(N,X,Y,Z,DS,ERRIN,IOPT,PARMOD,EXNAME)CC RE-CALCULATES COORDS X,Y,Z FOR ONE STEP ALONG FIELD LINE. N IS MAXIMUMC ORDER OF HARMONICS IN MAIN FIELD EXPANSION, DS IS STEP SIZE, ERRIN ISC PERMISSIBLE ERROR VALUE, IOPT AND EXNAME - SEE COMMENTS TO SUBROUTINE TRACEC  ALL THE PARAMETERS ARE INPUT ONES; OUTPUT IS THE RENEWED TRIPLET X,Y,ZCC     LAST MODIFICATION:  JAN 5, 2001 (NO ESSENTIAL CHANGES, BUTC                            SOME REDUNDANT STATEMENTS TAKEN OUT)CC     WRITTEN BY:  N. A. TSYGANENKOCC      DIMENSION PARMOD(10)      COMMON /GEOPACK/ A(26),DS3,K,IY,B(8)      EXTERNAL EXNAME      K=N  1   DS3=-DS/3.      CALL RHAND(X,Y,Z,R11,R12,R13,IOPT,PARMOD,EXNAME)      CALL RHAND(X+R11,Y+R12,Z+R13,R21,R22,R23,IOPT,PARMOD,EXNAME)      CALL RHAND(X+.5*(R11+R21),Y+.5*(R12+R22),Z+.5*     *(R13+R23),R31,R32,R33,IOPT,PARMOD,EXNAME)      CALL RHAND(X+.375*(R11+3.*R31),Y+.375*(R12+3.*R32     *),Z+.375*(R13+3.*R33),R41,R42,R43,IOPT,PARMOD,EXNAME)      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)      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      ENDC      SUBROUTINE TRACE(XI,YI,ZI,DIR,RLIM,R0,IHARM,NP,IOPT,PARMOD,EXNAME,     *XF,YF,ZF,XX,YY,ZZ,L)CC   TRACES A FIELD LINE FROM AN ARBITRARY POINT OF SPACE TO THE EARTH'S
C   SURFACE OR TO A MODEL LIMITING BOUNDARY.
C
C------------- INPUT PARAMETERS:
C
C   XI,YI,ZI - GSM COORDS OF INITIAL POINT (IN EARTH RADII),
C
C   DIR - SIGN OF TRACING DIRECTION: IF DIR=1. THEN ANTIPARALLEL TO
C     B VECTOR (E.G. FROM NORTHERN TO SOUTHERN CONJUGATE POINT),
C     AND IF DIR=-1. THEN PARALLEL TO B.
C
C   R0 -  RADIUS OF A SPHERE (IN RE) FOR WHICH FOOTPOINT POINT COORDINATES
C     XF,YF,ZF  ARE TO BE CALCULATED.
C
C   RLIM - UPPER LIMIT OF THE GEOCENTRIC DISTANCE, WHERE THE TRACING IS TERMINATED.
C
C   IHARM - THE HIGHEST ORDER OF SPHERICAL HARMONICS IN THE MAIN FIELD EXPANSION,
C     THIS PARAMETER DEPENDS ON A VERSION OF THE MAIN GEOMAGNETIC FIELD MODEL.
C     THE SUBROUTINE IGRF INCLUDED IN THIS PACKAGE HAS IHARM=10.
C     IF THE MAIN FIELD CAN BE ASSUMED PURELY DIPOLAR, THEN TAKE IHARM=0
C     AND SPECIFY A VALUE OF THE GEODIPOLE TILT ANGLE PSI (IN RADIANS)
C     IN THE 16-TH ELEMENT OF THE COMMON BLOCK /GEOPACK/ BEFORE INVOKING TRACE.
C     OTHERWISE INVOKE  RECALC  BEFORE USING  TRACE.
C
C   NP - UPPER ESTIMATE OF THE NUMBER OF STEPS ALONG A FIELD LINE
C     (IN MOST CASES, NP=500 IS SUFFICIENT).
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 CAN BE JUST IGNORED.
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
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. THEIR SIZE SHOULD BE
C      NOT LESS THAN  NP.
C   L - ACTUAL NUMBER OF THE CALCULATED FIELD LINE POINTS. IF L EXCEEDS NP, THE TRACING
C     TERMINATES, AND A WARNING IS DISPLAYED.
C
C
C     LAST MODIFICATION:  JAN 5, 2001 (NO ESSENTIAL CHANGES)
C
C     WRITTEN BY:  N. A. TSYGANENKO
C
      DIMENSION XX(NP),YY(NP),ZZ(NP), PARMOD(10)
      COMMON /GEOPACK/ AA(26),DD,K1,K2,BB(8)
      EXTERNAL EXNAME

      J=IHARM
      ERR=0.0005
      L=0
      DS=0.5*DIR
      X=XI
      Y=YI
      Z=ZI
      DD=DIR
      K1=IHARM
      AL=0.
      CALL RHAND(X,Y,Z,R1,R2,R3,IOPT,PARMOD,EXNAME)
      AD=SIGN(0.01,X*R1+Y*R2+Z*R3)
      RR=SQRT(X**2+Y**2+Z**2)+AD
  1   L=L+1
      IF(L.GT.NP) GOTO 7
      XX(L)=X
      YY(L)=Y
      ZZ(L)=Z
      RYZ=Y**2+Z**2
      R2=X**2+RYZ
      R=SQRT(R2)
      IF(R.GT.RLIM.OR.RYZ.GT.1600..OR.X.GT.20.) GOTO 8
      IF(R.LT.R0.AND.RR.GT.R) GOTO 6
      IF(R.GE.RR) GOTO 5
      IF(R.GT.5.) GOTO 5
      IF(R.GE.3.) GOTO 3
      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
      AL=1.
  4   XR=X
      YR=Y
      ZR=Z
  5   RR=R
      IF(IHARM.NE.0) J=1+20./(R-AL)
      IF(J.GT.IHARM) J=IHARM
      CALL STEP(J,X,Y,Z,DS,ERR,IOPT,PARMOD,EXNAME)
      GOTO 1
  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=NP
      RETURN
  8   XF=X
      YF=Y
      ZF=Z
      DO 9 I=L,NP
      XX(I)=XF
      YY(I)=YF
  9   ZZ(I)=ZF
      RETURN
 10   FORMAT(//,1X,'**** COMPUTATIONS IN THE SUBROUTINE TRACE',
     *' ARE TERMINATED: NP IS TOO SMALL ****'//)
      END

c----------------------------------------------------------------------------------
c
c<b>Author and curator:</b><p>
c<i> Nikolai Tsyganenko  - USRA/GSFC (ys2nt@lepvax.gsfc.nasa.gov)</i><p>
c<br>
c<address>
c<p>
c<b> Last updated: August 7, 2001 </b><p>

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