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C CHANGES TO THE ROUTINES BY A. STOHL
C XI,XI0,ETA,ETA0 ARE DOUBLE PRECISION VARIABLES TO AVOID PROBLEMS
C AT POLES
SUBROUTINE CC2GLL (STRCMP, XLAT,XLONG, UE,VN, UG,VG)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
DOUBLE PRECISION XPOLG,YPOLG,ALONG,SLONG,CLONG,ROT
REAL STRCMP(9)
ALONG = CSPANF( XLONG - STRCMP(2), -180., 180.)
IF (XLAT.GT.89.985) THEN
C* NORTH POLAR METEOROLOGICAL ORIENTATION: "NORTH" ALONG PRIME MERIDIAN
ROT = - STRCMP(1) * ALONG + XLONG - 180.
ELSEIF (XLAT.LT.-89.985) THEN
C* SOUTH POLAR METEOROLOGICAL ORIENTATION: "NORTH" ALONG PRIME MERIDIAN
ROT = - STRCMP(1) * ALONG - XLONG
ELSE
ROT = - STRCMP(1) * ALONG
ENDIF
SLONG = SIN( RADPDG * ROT )
CLONG = COS( RADPDG * ROT )
XPOLG = SLONG * STRCMP(5) + CLONG * STRCMP(6)
YPOLG = CLONG * STRCMP(5) - SLONG * STRCMP(6)
UG = YPOLG * UE + XPOLG * VN
VG = YPOLG * VN - XPOLG * UE
RETURN
END
SUBROUTINE CCRVLL (STRCMP, XLAT,XLONG, GX,GY)
C* WRITTEN ON 9/20/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (REARTH=6 371.2)
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
DOUBLE PRECISION XPOLG,YPOLG,TEMP,ALONG,SLONG,CLONG,CTEMP
REAL STRCMP(9)
ALONG = CSPANF( XLONG - STRCMP(2), -180., 180.)
SLONG = SIN( RADPDG * STRCMP(1) * ALONG)
CLONG = COS( RADPDG * STRCMP(1) * ALONG)
XPOLG = - SLONG * STRCMP(5) + CLONG * STRCMP(6)
YPOLG = CLONG * STRCMP(5) + SLONG * STRCMP(6)
TEMP = SIN(RADPDG * XLAT)
CTEMP = COS(RADPDG * XLAT)
CURV = (STRCMP(1) - TEMP) / CTEMP / REARTH
GX = CURV * XPOLG
GY = CURV * YPOLG
RETURN
END
SUBROUTINE CCRVXY (STRCMP, X,Y, GX,GY)
C* WRITTEN ON 9/20/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (REARTH=6 371.2)
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
REAL STRCMP(9)
DOUBLE PRECISION XPOLG,YPOLG,TEMP,YMERC,EFACT,CURV
TEMP = STRCMP(1) * STRCMP(7) /REARTH
XPOLG = STRCMP(6) + TEMP * (STRCMP(3) - X)
YPOLG = STRCMP(5) + TEMP * (STRCMP(4) - Y)
TEMP = SQRT ( XPOLG ** 2 + YPOLG ** 2 )
IF (TEMP.GT.0.) THEN
YMERC = - LOG( TEMP) /STRCMP(1)
EFACT = EXP(YMERC)
CURV = ( (STRCMP(1) - 1.D0) * EFACT +
A (STRCMP(1) + 1.D0) / EFACT )
B * .5D0 / REARTH
GX = XPOLG * CURV / TEMP
GY = YPOLG * CURV / TEMP
ELSE
IF (ABS(STRCMP(1)) .EQ. 1.) THEN
GX = 0.
GY = 0.
ELSE
GX = 1./REARTH
GY = 1./REARTH
ENDIF
ENDIF
RETURN
END
SUBROUTINE CG2CLL (STRCMP, XLAT,XLONG, UG,VG, UE,VN)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
DOUBLE PRECISION XPOLG,YPOLG,ALONG,SLONG,CLONG,ROT
REAL STRCMP(9)
ALONG = CSPANF( XLONG - STRCMP(2), -180., 180.)
IF (XLAT.GT.89.985) THEN
C* NORTH POLAR METEOROLOGICAL ORIENTATION: "NORTH" ALONG PRIME MERIDIAN
ROT = - STRCMP(1) * ALONG + XLONG - 180.
ELSEIF (XLAT.LT.-89.985) THEN
C* SOUTH POLAR METEOROLOGICAL ORIENTATION: "NORTH" ALONG PRIME MERIDIAN
ROT = - STRCMP(1) * ALONG - XLONG
ELSE
ROT = - STRCMP(1) * ALONG
ENDIF
SLONG = SIN( RADPDG * ROT )
CLONG = COS( RADPDG * ROT )
XPOLG = SLONG * STRCMP(5) + CLONG * STRCMP(6)
YPOLG = CLONG * STRCMP(5) - SLONG * STRCMP(6)
UE = YPOLG * UG - XPOLG * VG
VN = YPOLG * VG + XPOLG * UG
RETURN
END
SUBROUTINE CG2CXY (STRCMP, X,Y, UG,VG, UE,VN)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (REARTH=6 371.2)
REAL STRCMP(9)
DOUBLE PRECISION XPOLG,YPOLG,TEMP,XI0,ETA0,XI,ETA
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
XI0 = ( X - STRCMP(3) ) * STRCMP(7) / REARTH
ETA0 = ( Y - STRCMP(4) ) * STRCMP(7) /REARTH
XI = XI0 * STRCMP(5) - ETA0 * STRCMP(6)
ETA = ETA0 * STRCMP(5) + XI0 * STRCMP(6)
RADIAL = 2. * ETA - STRCMP(1) * (XI*XI + ETA*ETA)
IF (RADIAL.GT.STRCMP(8)) THEN
C* CASE NORTH OF 89 DEGREES. METEOROLOGICAL WIND DIRECTION DEFINITION
C* CHANGES.
CALL CNXYLL(STRCMP, XI,ETA, XLAT,XLONG)
C* NORTH POLAR METEOROLOGICAL ORIENTATION: "NORTH" ALONG PRIME MERIDIAN
ROT = STRCMP(1) * (XLONG - STRCMP(2)) - XLONG - 180.
SLONG = - SIN( RADPDG * ROT )
CLONG = COS( RADPDG * ROT )
XPOLG = SLONG * STRCMP(5) + CLONG * STRCMP(6)
YPOLG = CLONG * STRCMP(5) - SLONG * STRCMP(6)
ELSE IF (RADIAL.LT.STRCMP(9)) THEN
C* CASE SOUTH OF -89 DEGREES. METEOROLOGICAL WIND DIRECTION DEFINITION
C* CHANGES.
CALL CNXYLL(STRCMP, XI,ETA, XLAT,XLONG)
C* SOUTH POLAR METEOROLOGICAL ORIENTATION: "NORTH" ALONG PRIME MERIDIAN
ROT = STRCMP(1) * (XLONG - STRCMP(2)) + XLONG
SLONG = - SIN( RADPDG * ROT )
CLONG = COS( RADPDG * ROT )
XPOLG = SLONG * STRCMP(5) + CLONG * STRCMP(6)
YPOLG = CLONG * STRCMP(5) - SLONG * STRCMP(6)
ELSE
C* NORMAL CASE. METEOROLOGICAL DIRECTION OF WIND RELATED TO TRUE NORTH.
XPOLG = STRCMP(6) - STRCMP(1) * XI0
YPOLG = STRCMP(5) - STRCMP(1) * ETA0
TEMP = SQRT ( XPOLG ** 2 + YPOLG ** 2 )
XPOLG = XPOLG / TEMP
YPOLG = YPOLG / TEMP
END IF
UE = ( YPOLG * UG - XPOLG * VG )
VN = ( YPOLG * VG + XPOLG * UG )
RETURN
END
REAL FUNCTION CGSZLL (STRCMP, XLAT,XLONG)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180D0/PI)
REAL STRCMP(9)
DOUBLE PRECISION SLAT,YMERC,EFACT
IF (XLAT .GT. 89.985) THEN
C* CLOSE TO NORTH POLE
IF (STRCMP(1) .GT. 0.9999) THEN
C* AND TO GAMMA == 1.
CGSZLL = 2. * STRCMP(7)
RETURN
ENDIF
EFACT = COS(RADPDG * XLAT)
IF (EFACT .LE. 0.) THEN
CGSZLL = 0.
RETURN
ELSE
YMERC = - LOG( EFACT /(1. + SIN(RADPDG * XLAT)))
ENDIF
ELSE IF (XLAT .LT. -89.985) THEN
C* CLOSE TO SOUTH POLE
IF (STRCMP(1) .LT. -0.9999) THEN
C* AND TO GAMMA == -1.0
CGSZLL = 2. * STRCMP(7)
RETURN
ENDIF
EFACT = COS(RADPDG * XLAT)
IF (EFACT .LE. 0.) THEN
CGSZLL = 0.
RETURN
ELSE
YMERC = LOG( EFACT /(1. - SIN(RADPDG * XLAT)))
ENDIF
ELSE
SLAT = SIN(RADPDG * XLAT)
YMERC = LOG((1. + SLAT) / (1. - SLAT))/2.
C EFACT = EXP(YMERC)
C CGSZLL = 2. * STRCMP(7) * EXP (STRCMP(1) * YMERC)
C C / (EFACT + 1./EFACT)
ENDIF
CGSZLL = STRCMP(7) * COS(RADPDG * XLAT) * EXP(STRCMP(1) *YMERC)
RETURN
END
REAL FUNCTION CGSZXY (STRCMP, X,Y)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (REARTH=6 371.2,ALMST1=.9999999)
REAL STRCMP(9)
DOUBLE PRECISION YMERC,EFACT
DOUBLE PRECISION XI0,ETA0,XI,ETA
XI0 = ( X - STRCMP(3) ) * STRCMP(7) / REARTH
ETA0 = ( Y - STRCMP(4) ) * STRCMP(7) /REARTH
XI = XI0 * STRCMP(5) - ETA0 * STRCMP(6)
ETA = ETA0 * STRCMP(5) + XI0 * STRCMP(6)
RADIAL = 2. * ETA - STRCMP(1) * (XI*XI + ETA*ETA)
EFACT = STRCMP(1) * RADIAL
IF (EFACT .GT. ALMST1) THEN
IF (STRCMP(1).GT.ALMST1) THEN
CGSZXY = 2. * STRCMP(7)
ELSE
CGSZXY = 0.
ENDIF
RETURN
ENDIF
IF (ABS(EFACT) .LT. 1.E-2) THEN
TEMP = (EFACT / (2. - EFACT) )**2
YMERC = RADIAL / (2. - EFACT) * (1. + TEMP *
C (1./3. + TEMP *
C (1./5. + TEMP *
C (1./7. ))))
ELSE
YMERC = - LOG( 1. - EFACT ) /2. /STRCMP(1)
ENDIF
IF (YMERC .GT. 6.) THEN
IF (STRCMP(1) .GT. ALMST1) THEN
CGSZXY = 2. * STRCMP(7)
ELSE
CGSZXY = 0.
ENDIF
ELSE IF (YMERC .LT. -6.) THEN
IF (STRCMP(1) .LT. -ALMST1) THEN
CGSZXY = 2. * STRCMP(7)
ELSE
CGSZXY = 0.
ENDIF
ELSE
EFACT = EXP(YMERC)
CGSZXY = 2. * STRCMP(7) * EXP (STRCMP(1) * YMERC)
C / (EFACT + 1./EFACT)
ENDIF
RETURN
END
SUBROUTINE CLL2XY (STRCMP, XLAT,XLONG, X,Y)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (REARTH=6 371.2)
REAL STRCMP(9)
CALL CNLLXY(STRCMP, XLAT,XLONG, XI,ETA)
X = STRCMP(3) + REARTH/STRCMP(7) *
C (XI * STRCMP(5) + ETA * STRCMP(6) )
Y = STRCMP(4) + REARTH/STRCMP(7) *
C (ETA * STRCMP(5) - XI * STRCMP(6) )
RETURN
END
SUBROUTINE CNLLXY (STRCMP, XLAT,XLONG, XI,ETA)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
C MAIN TRANSFORMATION ROUTINE FROM LATITUDE-LONGITUDE TO
C CANONICAL (EQUATOR-CENTERED, RADIAN UNIT) COORDINATES
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
PARAMETER (ALMST1=.9999999)
REAL STRCMP(9)
DOUBLE PRECISION GAMMA
DOUBLE PRECISION DLONG,DLAT,SLAT,MERCY,GMERCY
GAMMA = STRCMP(1)
DLAT = XLAT
DLONG = CSPANF(XLONG - STRCMP(2), -180., 180.)
DLONG = DLONG * RADPDG
GDLONG = GAMMA * DLONG
IF (ABS(GDLONG) .LT. .01) THEN
C CODE FOR GAMMA SMALL OR ZERO. THIS AVOIDS ROUND-OFF ERROR OR DIVIDE-
C BY ZERO IN THE CASE OF MERCATOR OR NEAR-MERCATOR PROJECTIONS.
GDLONG = GDLONG * GDLONG
SNDGAM = DLONG * (1. - 1./6. * GDLONG *
C (1. - 1./20. * GDLONG *
C (1. - 1./42. * GDLONG )))
CSDGAM = DLONG * DLONG * .5 *
C (1. - 1./12. * GDLONG *
C (1. - 1./30. * GDLONG *
C (1. - 1./56. * GDLONG )))
ELSE
C CODE FOR MODERATE VALUES OF GAMMA
SNDGAM = SIN (GDLONG) /GAMMA
CSDGAM = (1. - COS(GDLONG) )/GAMMA /GAMMA
ENDIF
SLAT = SIN(RADPDG * DLAT)
IF ((SLAT .GE. ALMST1) .OR. (SLAT .LE. -ALMST1)) THEN
ETA = 1./STRCMP(1)
XI = 0.
RETURN
ENDIF
MERCY = .5 * LOG( (1. + SLAT) / (1. - SLAT) )
GMERCY = GAMMA * MERCY
IF (ABS(GMERCY) .LT. .001) THEN
C CODE FOR GAMMA SMALL OR ZERO. THIS AVOIDS ROUND-OFF ERROR OR DIVIDE-
C BY ZERO IN THE CASE OF MERCATOR OR NEAR-MERCATOR PROJECTIONS.
RHOG1 = MERCY * (1. - .5 * GMERCY *
C (1. - 1./3. * GMERCY *
C (1. - 1./4. * GMERCY ) ) )
ELSE
C CODE FOR MODERATE VALUES OF GAMMA
RHOG1 = (1. - EXP(-GMERCY)) / GAMMA
ENDIF
ETA = RHOG1 + (1. - GAMMA * RHOG1) * GAMMA * CSDGAM
XI = (1. - GAMMA * RHOG1 ) * SNDGAM
END
SUBROUTINE CNXYLL (STRCMP, XI,ETA, XLAT,XLONG)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
C MAIN TRANSFORMATION ROUTINE FROM CANONICAL (EQUATOR-CENTERED,
C RADIAN UNIT) COORDINATES
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
PARAMETER (ALMST1=.9999999)
REAL STRCMP(9)
DOUBLE PRECISION GAMMA,TEMP,ARG1,ARG2,YMERC,ALONG,GXI,CGETA
DOUBLE PRECISION XI,ETA
GAMMA = STRCMP(1)
C CALCULATE EQUIVALENT MERCATOR COORDINATE
ODIST = XI*XI + ETA*ETA
ARG2 = 2. * ETA - GAMMA * (XI*XI + ETA*ETA)
ARG1 = GAMMA * ARG2
C Change by A. Stohl to avoid problems close to the poles
C IF (ARG1 .GE. ALMST1) THEN
C DISTANCE TO NORTH (OR SOUTH) POLE IS ZERO (OR IMAGINARY ;) )
C XLAT = SIGN(90.,STRCMP(1))
C XLONG = STRCMP(2)
C RETURN
C ENDIF
IF (ABS(ARG1) .LT. .01) THEN
C CODE FOR GAMMA SMALL OR ZERO. THIS AVOIDS ROUND-OFF ERROR OR DIVIDE-
C BY ZERO IN THE CASE OF MERCATOR OR NEAR-MERCATOR PROJECTIONS.
TEMP = (ARG1 / (2. - ARG1) )**2
YMERC = ARG2 / (2. - ARG1) * (1. + TEMP *
C (1./3. + TEMP *
C (1./5. + TEMP *
C (1./7. ))))
ELSE
C CODE FOR MODERATE VALUES OF GAMMA
YMERC = - LOG ( 1. - ARG1 ) /2. / GAMMA
ENDIF
C CONVERT YMERC TO LATITUDE
TEMP = EXP( - ABS(YMERC) )
XLAT = SIGN(ATAN2((1. - TEMP) * (1. + TEMP), 2. * TEMP), YMERC)
C FIND LONGITUDES
GXI = GAMMA*XI
CGETA = 1. - GAMMA * ETA
IF ( ABS(GXI) .LT. .01*CGETA ) THEN
C CODE FOR GAMMA SMALL OR ZERO. THIS AVOIDS ROUND-OFF ERROR OR DIVIDE-
C BY ZERO IN THE CASE OF MERCATOR OR NEAR-MERCATOR PROJECTIONS.
TEMP = ( GXI /CGETA )**2
ALONG = XI / CGETA * (1. - TEMP *
C (1./3. - TEMP *
C (1./5. - TEMP *
C (1./7. ))))
ELSE
C CODE FOR MODERATE VALUES OF GAMMA
ALONG = ATAN2( GXI, CGETA) / GAMMA
ENDIF
XLONG = SNGL(STRCMP(2) + DGPRAD * ALONG)
XLAT = XLAT * DGPRAD
RETURN
END
SUBROUTINE CPOLLL (STRCMP, XLAT,XLONG, ENX,ENY,ENZ)
C* WRITTEN ON 11/23/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (PI=3.14159265358979,RADPDG=PI/180.,DGPRAD=180./PI)
DOUBLE PRECISION XPOLG,YPOLG,ALONG,SLONG,CLONG,ROT
REAL STRCMP(9)
ALONG = CSPANF( XLONG - STRCMP(2), -180., 180.)
ROT = - STRCMP(1) * ALONG
SLONG = SIN( RADPDG * ROT )
CLONG = COS( RADPDG * ROT )
XPOLG = SLONG * STRCMP(5) + CLONG * STRCMP(6)
YPOLG = CLONG * STRCMP(5) - SLONG * STRCMP(6)
CLAT = COS(RADPDG * XLAT)
ENX = CLAT * XPOLG
ENY = CLAT * YPOLG
ENZ = SIN(RADPDG * XLAT)
RETURN
END
SUBROUTINE CPOLXY (STRCMP, X,Y, ENX,ENY,ENZ)
C* WRITTEN ON 11/26/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (REARTH=6 371.2)
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
REAL STRCMP(9)
DOUBLE PRECISION XPOL,YPOL,TEMP,XI0,ETA0,XI,ETA,RADIAL
DOUBLE PRECISION TEMP2,YMERC,ARG,OARG,CLAT
XI0 = ( X - STRCMP(3) ) * STRCMP(7) / REARTH
ETA0 = ( Y - STRCMP(4) ) * STRCMP(7) /REARTH
XI = XI0 * STRCMP(5) - ETA0 * STRCMP(6)
ETA = ETA0 * STRCMP(5) + XI0 * STRCMP(6)
RADIAL = 2. * ETA - STRCMP(1) * (XI*XI + ETA*ETA)
TEMP = STRCMP(1) * RADIAL
IF (TEMP .GE. 1.) THEN
ENX = 0.
ENY = 0.
ENZ = SIGN(1.,STRCMP(1))
RETURN
ENDIF
IF (ABS(TEMP).LT.1.E-2) THEN
TEMP2 = (TEMP / (2. - TEMP))**2
YMERC = RADIAL / (2. - TEMP) * (1. + TEMP2 *
C (1./3. + TEMP2 *
C (1./5. + TEMP2 *
C (1./7.))))
ELSE
YMERC = -.5 * LOG(1. - TEMP) / STRCMP(1)
ENDIF
ARG = EXP( YMERC )
OARG = 1./ARG
CLAT = 2./(ARG + OARG)
ENZ = (ARG - OARG) * CLAT /2.
TEMP = CLAT / SQRT(1. - TEMP)
XPOL = - XI * STRCMP(1) * TEMP
YPOL = (1. - ETA * STRCMP(1) ) * TEMP
ENX = XPOL * STRCMP(5) + YPOL * STRCMP(6)
ENY = YPOL * STRCMP(5) - XPOL * STRCMP(6)
RETURN
END
REAL FUNCTION CSPANF (VALUE, BEGIN, END)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
C* REAL FUNCTION CSPANF RETURNS A VALUE IN THE INTERVAL (BEGIN,END]
C* WHICH IS EQUIVALENT TO VALUE, MOD (END - BEGIN). IT IS USED TO
C* REDUCE PERIODIC VARIABLES TO A STANDARD RANGE. IT ADJUSTS FOR THE
C* BEHAVIOR OF THE MOD FUNCTION WHICH PROVIDES POSITIVE RESULTS FOR
c* POSITIVE INPUT, AND NEGATIVE RESULTS FOR NEGATIVE INPUT
C* INPUT:
C* VALUE - REAL NUMBER TO BE REDUCED TO THE SPAN
C* BEGIN - FIRST VALUE OF THE SPAN
C* END - LAST VALUE OF THE SPAN
C* RETURNS:
C* THE REDUCED VALUE
C* EXAMPLES:
C* ALONG = CSPANF(XLONG, -180., +180.)
C* DIR = CSPANF(ANGLE, 0., 360.)
REAL FIRST,LAST
FIRST = MIN(BEGIN,END)
LAST = MAX(BEGIN,END)
VAL = MOD( VALUE - FIRST , LAST - FIRST)
IF ( VAL . LE. 0.) THEN
CSPANF = VAL + LAST
ELSE
CSPANF = VAL + FIRST
ENDIF
RETURN
END
SUBROUTINE CXY2LL (STRCMP, X,Y, XLAT,XLONG)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (REARTH=6 371.2)
DOUBLE PRECISION XI0,ETA0,XI,ETA
REAL STRCMP(9)
XI0 = ( X - STRCMP(3) ) * STRCMP(7) / REARTH
ETA0 = ( Y - STRCMP(4) ) * STRCMP(7) /REARTH
XI = XI0 * STRCMP(5) - ETA0 * STRCMP(6)
ETA = ETA0 * STRCMP(5) + XI0 * STRCMP(6)
CALL CNXYLL(STRCMP, XI,ETA, XLAT,XLONG)
XLONG = CSPANF(XLONG, -180., 180.)
RETURN
END
REAL FUNCTION EQVLAT (XLAT1,XLAT2)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
SIND(X) = SIN (RADPDG*X)
SINL1 = SIND (XLAT1)
SINL2 = SIND (XLAT2)
IF (ABS(SINL1 - SINL2) .GT. .001) THEN
AL1 = LOG((1. - SINL1)/(1. - SINL2))
AL2 = LOG((1. + SINL1)/(1. + SINL2))
ELSE
C CASE LAT1 NEAR OR EQUAL TO LAT2
TAU = - (SINL1 - SINL2)/(2. - SINL1 - SINL2)
TAU = TAU*TAU
AL1 = 2. / (2. - SINL1 - SINL2) * (1. + TAU *
C (1./3. + TAU *
C (1./5. + TAU *
C (1./7.))))
TAU = (SINL1 - SINL2)/(2. + SINL1 + SINL2)
TAU = TAU*TAU
AL2 = -2. / (2. + SINL1 + SINL2) * (1. + TAU *
C (1./3. + TAU *
C (1./5. + TAU *
C (1./7.))))
ENDIF
EQVLAT = ASIN((AL1 + AL2) / (AL1 - AL2))/RADPDG
RETURN
END
SUBROUTINE STCM1P(STRCMP, X1,Y1, XLAT1,XLONG1,
C XLATG,XLONGG, GRIDSZ, ORIENT)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
REAL STRCMP(9)
DO K=3,4
STRCMP (K) = 0.
ENDDO
TURN = RADPDG * (ORIENT - STRCMP(1) *
C CSPANF(XLONGG - STRCMP(2), -180., 180.) )
STRCMP (5) = COS (TURN)
STRCMP (6) = - SIN (TURN)
STRCMP (7) = 1.
STRCMP (7) = GRIDSZ * STRCMP(7)
C / CGSZLL(STRCMP, XLATG, STRCMP(2))
CALL CLL2XY (STRCMP, XLAT1,XLONG1, X1A,Y1A)
STRCMP(3) = STRCMP(3) + X1 - X1A
STRCMP(4) = STRCMP(4) + Y1 - Y1A
RETURN
END
SUBROUTINE STCM2P(STRCMP, X1,Y1, XLAT1,XLONG1,
C X2,Y2, XLAT2,XLONG2)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
REAL STRCMP(9)
DO K=3,6
STRCMP (K) = 0.
ENDDO
STRCMP (5) = 1.
STRCMP (7) = 1.
CALL CLL2XY (STRCMP, XLAT1,XLONG1, X1A,Y1A)
CALL CLL2XY (STRCMP, XLAT2,XLONG2, X2A,Y2A)
DEN = SQRT( (X1 - X2)**2 + (Y1 - Y2)**2 )
DENA = SQRT( (X1A - X2A)**2 + (Y1A - Y2A)**2 )
STRCMP(5) = ((X1A - X2A)*(X1 - X2) + (Y1A - Y2A) * (Y1 - Y2))
C /DEN /DENA
STRCMP(6) = ((Y1A - Y2A)*(X1 - X2) - (X1A - X2A) * (Y1 - Y2))
C /DEN /DENA
STRCMP (7) = STRCMP(7) * DENA / DEN
CALL CLL2XY (STRCMP, XLAT1,XLONG1, X1A,Y1A)
STRCMP(3) = STRCMP(3) + X1 - X1A
STRCMP(4) = STRCMP(4) + Y1 - Y1A
RETURN
END
C* GENERAL CONFORMAL MAP ROUTINES FOR METEOROLOGICAL MODELERS
C* WRITTEN ON 3/31/94 BY
C* Dr. Albion Taylor
C* NOAA / OAR / ARL Phone: (301) 713-0295 x 132
C* Rm. 3151, 1315 East-West Highway Fax: (301) 713-0119
C* Silver Spring, MD 20910 E-mail: ADTaylor@arlrisc.ssmc.noaa.gov
C* SUBROUTINE STLMBR (STRCMP, TNGLAT, CLONG)
C* THIS ROUTINE INITIALIZES THE MAP STRUCTURE ARRAY STRCMP TO
C* THE FORM OF A SPECIFIC MAP PROJECTION
C* INPUTS:
C* TNGLAT - THE LATITUDE AT WHICH THE PROJECTION WILL BE TANGENT
C* TO THE EARTH. +90. FOR NORTH POLAR STEREOGRAPHIC,
C* -90. FOR SOUTH POLAR STEREOGRAPHIC, 0. FOR MERCATOR,
C* AND OTHER VALUES FOR LAMBERT CONFORMAL.
C* -90 <= TNGLAT <= 90.
C* CLONG - A LONGITUDE IN THE REGION UNDER CONSIDERATION. LONGITUDES
C* BETWEEN CLONG-180. AND CLONG+180. WILL BE MAPPED IN ONE
C* CONNECTED REGION
C* OUTPUTS:
C* STRCMP - A 9-VALUE MAP STRUCTURE ARRAY FOR USE WITH SUBSEQUENT
C* CALLS TO THE COORDINATE TRANSFORM ROUTINES.
C*
C* REAL FUNCTION EQVLAT (XLAT1,XLAT2)
C* THIS FUNCTION IS PROVIDED TO ASSIST IN FINDING THE TANGENT LATITUDE
C* EQUIVALENT TO THE 2-REFERENCE LATITUDE SPECIFICATION IN THE LEGEND
C* OF MOST LAMBERT CONFORMAL MAPS. IF THE MAP SPECIFIES "SCALE
C* 1:XXXXX TRUE AT 40N AND 60N", THEN EQVLAT(40.,60.) WILL RETURN THE
C* EQUIVALENT TANGENT LATITUDE.
C* INPUTS:
C* XLAT1,XLAT2: THE TWO LATITUDES SPECIFIED IN THE MAP LEGEND
C* RETURNS:
C* THE EQUIVALENT TANGENT LATITUDE
C* EXAMPLE: CALL STLMBR(STRCMP, EQVLAT(40.,60.), 90.)
C* SUBROUTINE STCM2P (STRCMP, X1,Y1, XLAT1,XLONG1,
C* X2,Y2, XLAT2,XLONG2)
C* SUBROUTINE STCM1P (STRCMP, X1,Y1, XLAT1,XLONG1,
C* XLATG,XLONGG, GRIDSZ, ORIENT)
C* THESE ROUTINES COMPLETE THE SPECIFICATION OF THE MAP STRUCTURE
C* ARRAY BY CONFORMING THE MAP COORDINATES TO THE SPECIFICATIONS
C* OF A PARTICULAR GRID. EITHER STCM1P OR STCM2P MUST BE CALLED,
C* BUT NOT BOTH
C* INPUTS:
C* STRCMP - A 9-VALUE MAP STRUCTURE ARRAY, SET TO A PARTICULAR MAP
C* FORM BY A PREVIOUS CALL TO STLMBR
C* FOR STCM2P:
C* X1,Y1, X2,Y2 - THE MAP COORDINATES OF TWO POINTS ON THE GRID
C* XLAT1,XLONG1, XLAT2,XLONG2 - THE GEOGRAPHIC COORDINATES OF THE
C* SAME TWO POINTS
C* FOR STCM1P:
C* X1,Y1 - THE MAP COORDINATES OF ONE POINT ON THE GRID
C* XLAT1,XLONG1 - THE GEOGRAPHIC COORDINATES OF THE SAME POINT
C* XLATG,XLONGG - LATITUDE AND LONGITUDE OF REFERENCE POINT FOR
C* GRIDSZ AND ORIENTATION SPECIFICATION.
C* GRIDSZ - THE DESIRED GRID SIZE IN KILOMETERS, AT XLATG,XLONGG
C* ORIENT - THE ANGLE, WITH RESPECT TO NORTH, OF A Y-GRID LINE, AT
C* THE POINT XLATG,XLONGG
C* OUTPUTS:
C* STRCMP - A 9-VALUE MAP STRUCTURE ARRAY, FULLY SET FOR USE BY
C* OTHER SUBROUTINES IN THIS SYSTEM
C* SUBROUTINE CLL2XY (STRCMP, XLAT,XLONG, X,Y)
C* SUBROUTINE CXY2LL (STRCMP, X,Y, XLAT,XLONG)
C* THESE ROUTINES CONVERT BETWEEN MAP COORDINATES X,Y
C* AND GEOGRAPHIC COORDINATES XLAT,XLONG
C* INPUTS:
C* STRCMP(9) - 9-VALUE MAP STRUCTURE ARRAY
C* FOR CLL2XY: XLAT,XLONG - GEOGRAPHIC COORDINATES
C* FOR CXY2LL: X,Y - MAP COORDINATES
C* OUTPUTS:
C* FOR CLL2XY: X,Y - MAP COORDINATES
C* FOR CXY2LL: XLAT,XLONG - GEOGRAPHIC COORDINATES
C* SUBROUTINE CC2GXY (STRCMP, X,Y, UE,VN, UG,VG)
C* SUBROUTINE CG2CXY (STRCMP, X,Y, UG,VG, UE,VN)
C* SUBROUTINE CC2GLL (STRCMP, XLAT,XLONG, UE,VN, UG,VG)
C* SUBROUTINE CG2CLL (STRCMP, XLAT,XLONG, UG,VG, UE,VN)
C* THESE SUBROUTINES CONVERT VECTOR WIND COMPONENTS FROM
C* GEOGRAPHIC, OR COMPASS, COORDINATES, TO MAP OR
C* GRID COORDINATES. THE SITE OF THE WIND TO BE
C* CONVERTED MAY BE GIVEN EITHER IN GEOGRAPHIC OR
C* MAP COORDINATES. WIND COMPONENTS ARE ALL IN KILOMETERS
C* PER HOUR, WHETHER GEOGRAPHIC OR MAP COORDINATES.
C* INPUTS:
C* STRCMP(9) - 9-VALUE MAP STRUCTURE ARRAY
C* FOR CC2GXY AND CG2CXY: X,Y - MAP COORDINATES OF SITE
C* FOR CC2GLL AND CG2CLL: XLAT,XLONG - GEOGRAPHIC COORDINATES OF SITE
C* FOR CC2GXY AND CC2GLL: UE,VN - EAST AND NORTH WIND COMPONENTS
C* FOR CG2CXY AND CG2CLL: UG,VG - X- AND Y- DIRECTION WIND COMPONENTS
C* OUTPUTS:
C* FOR CC2GXY AND CC2GLL: UG,VG - X- AND Y- DIRECTION WIND COMPONENTS
C* FOR CG2CXY AND CG2CLL: UE,VN - EAST AND NORTH WIND COMPONENTS
C* SUBROUTINE CCRVXY (STRCMP, X, Y, GX,GY)
C* SUBROUTINE CCRVLL (STRCMP, XLAT,XLONG, GX,GY)
C* THESE SUBROUTINES RETURN THE CURVATURE VECTOR (GX,GY), AS REFERENCED
C* TO MAP COORDINATES, INDUCED BY THE MAP TRANSFORMATION. WHEN
C* NON-LINEAR TERMS IN WIND SPEED ARE IMPORTANT, A "GEODESIC" FORCE
C* SHOULD BE INCLUDED IN THE VECTOR FORM [ (U,U) G - (U,G) U ] WHERE THE
C* INNER PRODUCT (U,G) IS DEFINED AS UX*GX + UY*GY.
C* INPUTS:
C* STRCMP(9) - 9-VALUE MAP STRUCTURE ARRAY
C* FOR CCRVXY: X,Y - MAP COORDINATES OF SITE
C* FOR CCRVLL: XLAT,XLONG - GEOGRAPHIC COORDINATES OF SITE
C* OUTPUTS:
C* GX,GY - VECTOR COEFFICIENTS OF CURVATURE, IN UNITS RADIANS
C* PER KILOMETER
C* REAL FUNCTION CGSZLL (STRCMP, XLAT,XLONG)
C* REAL FUNCTION CGSZXY (STRCMP, X,Y)
C* THESE FUNCTIONS RETURN THE SIZE, IN KILOMETERS, OF EACH UNIT OF
C* MOTION IN MAP COORDINATES (GRID SIZE). THE GRID SIZE AT ANY
C* LOCATION DEPENDS ON THAT LOCATION; THE POSITION MAY BE GIVEN IN
C* EITHER MAP OR GEOGRAPHIC COORDINATES.
C* INPUTS:
C* STRCMP(9) - 9-VALUE MAP STRUCTURE ARRAY
C* FOR CGSZXY: X,Y - MAP COORDINATES OF SITE
C* FOR CGSZLL: XLAT,XLONG - GEOGRAPHIC COORDINATES OF SITE
C* RETURNS:
C* GRIDSIZE IN KILOMETERS AT GIVEN SITE.
C* SUBROUTINE CPOLXY (STRCMP, X,Y, ENX,ENY,ENZ)
C* SUBROUTINE CPOLLL (STRCMP, XLAT,XLONG, ENX,ENY,ENZ)
C* THESE SUBROUTINES PROVIDE 3-D VECTOR COMPONENTS OF A UNIT VECTOR
C* IN THE DIRECTION OF THE NORTH POLAR AXIS. WHEN MULTIPLIED
C* BY TWICE THE ROTATION RATE OF THE EARTH (2 * PI/24 HR), THE
C* VERTICAL COMPONENT YIELDS THE CORIOLIS FACTOR.
C* INPUTS:
C* STRCMP(9) - 9-VALUE MAP STRUCTURE ARRAY
C* FOR CPOLXY: X,Y - MAP COORDINATES OF SITE
C* FOR CPOLLL: XLAT,XLONG - GEOGRAPHIC COORDINATES OF SITE
C* RETURNS:
C* ENX,ENY,ENZ THE DIRECTION COSINES OF A UNIT VECTOR IN THE
C* DIRECTION OF THE ROTATION AXIS OF THE EARTH
C* SUBROUTINE CNLLXY (STRCMP, XLAT,XLONG, XI,ETA)
C* SUBROUTINE CNXYLL (STRCMP, XI,ETA, XLAT,XLONG)
C* THESE SUBROUTINES PERFORM THE UNDERLYING TRANSFORMATIONS FROM
C* GEOGRAPHIC COORDINATES TO AND FROM CANONICAL (EQUATOR CENTERED)
C* COORDINATES. THEY ARE CALLED BY CXY2LL AND CLL2XY, BUT ARE NOT
C* INTENDED TO BE CALLED DIRECTLY
C* REAL FUNCTION CSPANF (VALUE, BEGIN, END)
C* THIS FUNCTION ASSISTS OTHER ROUTINES IN PROVIDING A LONGITUDE IN
C* THE PROPER RANGE. IT ADDS TO VALUE WHATEVER MULTIPLE OF
C* (END - BEGIN) IS NEEDED TO RETURN A NUMBER BEGIN < CSPANF <= END
SUBROUTINE STLMBR(STRCMP, TNGLAT, XLONG)
C* WRITTEN ON 3/31/94 BY Dr. Albion Taylor NOAA / OAR / ARL
PARAMETER (PI=3.14159265358979,RADPDG=PI/180,DGPRAD=180/PI)
PARAMETER (REARTH=6 371.2)
REAL STRCMP(9)
STRCMP(1) = SIN(RADPDG * TNGLAT)
C* GAMMA = SINE OF THE TANGENT LATITUDE
STRCMP(2) = CSPANF( XLONG, -180., +180.)
C* LAMBDA_0 = REFERENCE LONGITUDE
STRCMP(3) = 0.
C* X_0 = X- GRID COORDINATE OF ORIGIN (XI,ETA) = (0.,0.)
STRCMP(4) = 0.
C* y_0 = Y-GRID COORDINATE OF ORIGIN (XI,ETA) = (0.,0.)
STRCMP(5) = 1.
C* COSINE OF ROTATION ANGLE FROM XI,ETA TO X,Y
STRCMP(6) = 0.
C* SINE OF ROTATION ANGLE FROM XI,ETA TO X,Y
STRCMP(7) = REARTH
C* GRIDSIZE IN KILOMETERS AT THE EQUATOR
CALL CNLLXY(STRCMP, 89.,XLONG, XI,ETA)
STRCMP(8) = 2. * ETA - STRCMP(1) * ETA * ETA
C* RADIAL COORDINATE FOR 1 DEGREE FROM NORTH POLE
CALL CNLLXY(STRCMP, -89.,XLONG, XI,ETA)
STRCMP(9) = 2. * ETA - STRCMP(1) * ETA * ETA
C* RADIAL COORDINATE FOR 1 DEGREE FROM SOUTH POLE
RETURN
END
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