<HTML> <BODY BGCOLOR=#ccccdd LINK=#0000aa VLINK=#0000ff ALINK=#ff0000 ><BASE TARGET="bottom_target"><PRE>
!
<A NAME='ZEEMAN_UTILITY'><A href='../../html_code/crtm/Zeeman_Utility.f90.html#ZEEMAN_UTILITY' TARGET='top_target'><IMG SRC="../../gif/bar_purple.gif" border=0></A>
MODULE Zeeman_Utility,9
! Description:
! containing routines to load geomagnetic field Lookup table, compute
! geomagnetic field and its angles relative to the wave propagation
! direction.
!
! History:
! ---- -------
! 11/07/2007 created by Y. Han, NOAA/JCSDA
! 11/24/2009 modified for CRTM
!
! -----------------
! Environment setup
! -----------------
! Module use
USE Type_Kinds
, ONLY: fp
USE Message_Handler, ONLY: SUCCESS, FAILURE, Display_Message
USE File_Utility, ONLY: Get_Lun, File_Exists
! Disable implicit typing
IMPLICIT NONE
! ------------
! Visibilities
! ------------
PRIVATE
PUBLIC :: load_bfield_lut ! function to load Geomagnetic field LUT
PUBLIC :: compute_bfield ! subroutine to calculate the Geomagnetic field
! using a LUT and two cosine angles of the field
! relative to the wave propagation direction k.
PUBLIC :: compute_kb_angles ! subroutine to compute two cosine angles of the
! geomagnetic field relative to the wave
! propagation direction k.
<A NAME='COMPUTE_BFIELD'><A href='../../html_code/crtm/Zeeman_Utility.f90.html#COMPUTE_BFIELD' TARGET='top_target'><IMG SRC="../../gif/bar_red.gif" border=0></A>
INTERFACE compute_bfield
MODULE PROCEDURE
MODULE PROCEDURE
MODULE PROCEDURE
END INTERFACE compute_bfield
! Array for Earth's magnetic field
INTEGER, PARAMETER :: n_Lat = 91, n_Lon = 181
INTEGER, SAVE :: BField(3, n_lat, n_lon)
Real(fp), parameter :: DEGREES_TO_RADIANS = 3.141592653589793238462643_fp/180.0_fp
CONTAINS
!--------------------------------------------------------------------------------
!
! NAME:
! load_bfield_lut
!
! PURPOSE:
! Function to the geomagnetic filed LUT
!
! CALLING SEQUENCE:
! Error_Status = load_bfield_lut(filename_LUT)
!
! INPUT ARGUMENT:
!
! filename_LUT: file name for the file containing the LUT of
! the Earth magnetic field.
! UNITS: N/A
! TYPE: character string
! DIMENSION: Scale
! ATTRIBUTES: INTENT(IN)
!----------------------------------------------------------------------------
<A NAME='LOAD_BFIELD_LUT'><A href='../../html_code/crtm/Zeeman_Utility.f90.html#LOAD_BFIELD_LUT' TARGET='top_target'><IMG SRC="../../gif/bar_green.gif" border=0></A>
Function load_bfield_lut(filename_LUT) Result(Error_Status),4
Character(*), Intent(in) :: filename_LUT
Integer :: Error_Status
! local
CHARACTER(*), PARAMETER :: ROUTINE_NAME = 'load_bfield_lut'
Integer :: file_id, io_status
Character (len=80) :: Message
Integer :: i, j, iskip
Error_Status = SUCCESS
IF ( .NOT. File_Exists( TRIM(filename_LUT) ) )THEN
Error_Status = FAILURE
Message = 'File '//TRIM(Filename_LUT)//' not found.'
CALL Display_Message( ROUTINE_NAME, &
TRIM( Message ), &
Error_Status)
END IF
! Find a free logical unit number for file access
file_id = Get_Lun()
OPEN( file_id, FILE = filename_LUT, &
& STATUS = 'OLD', &
& IOSTAT = io_status )
IF ( io_status /= 0 ) THEN
Error_Status = FAILURE
WRITE( Message, '( "Error opening ", a, ". IOSTAT = ", i5 )' ) &
& TRIM(filename_LUT), io_status
CALL Display_Message( ROUTINE_NAME, &
TRIM( Message ), &
Error_Status)
RETURN
END IF
READ(file_id, *, iostat = io_status)iskip, iskip, &
((BField(:, i, j), j=1,n_Lon), i=1,n_Lat)
If(io_status /= 0) Then
Error_Status = FAILURE
Write( Message, '( "Error reading data from ", a, ". IOSTAT = ", i5 )' ) &
& TRIM(filename_LUT), io_status
CALL Display_Message( ROUTINE_NAME, &
TRIM( Message ), &
Error_Status)
Return
Endif
Close( unit = file_id )
End Function load_bfield_lut
!--------------------------------------------------------------------------------
!
! NAME:
! compute_bfield
!
! PURPOSE:
! Subroutine to calculate the Geomagnetic field using a LUT and
! two cosine angles of the field relative to the wave propagation
! direction k.
!
! CALLING SEQUENCE:
!
! CALL compute_bfield(latitude, longitude, & ! Inputs
! Bx, By, Bz, Be) ! Outputs
!
! OR
!
! CALL compute_bfield(latitude, & ! input
! longitude, & ! input
! sensor_zenang, & ! input
! sensor_aziang, & ! input
! Be, & ! output
! cos_bkang, & ! output
! cos_baziang) ! output
!
! OR
!
! CALL compute_bfield(latitude, & ! input
! longitude, & ! input
! sensor_zenang, & ! input
! sensor_relative_aziang, & ! input
! Julian_day, & ! input
! utc_time, & ! input
! Be, & ! output
! cos_bkang, & ! output
! cos_baziang) ! output
!
!
! INPUT ARGUMENTS:
!
!
! latitude : Latitude, 0 - 180 (0 North Pole; 180 - South Pole
! UNITS: Degree
! TYPE: real(fp)
! DIMENSION: Scale
! ATTRIBUTES: INTENT(IN)
!
! longitude: longitude, 0 - 360 East
! UNITS: Degree
! TYPE: real(fp)
! DIMENSION: Scale
! ATTRIBUTES: INTENT(IN)
!
! sensor_zenang: sensor zenith angle
! UNITS: Degree
! TYPE: real(fp)
! DIMENSION: Scale
! ATTRIBUTES: INTENT(IN)
!
! sensor_aziang: sensor azimuth angle (starts from East,
! positive counterclockwise)
! UNITS: Degree
! TYPE: real(fp)
! DIMENSION: Scale
! ATTRIBUTES: INTENT(IN)
!
! sensor_relative_aziang: sensor azimuth angle relative to the sun azimuth
! angle.
! Sun_azimuth_angle - from north, East positive
! sensor_relative_aziang = 90 - (sun_azimuth_angle + Sensor_aziang)
! UNITS: degree
! TYPE: real(fp)
! DIMENSION: Scale
! ATTRIBUTES: INTENT(IN)
!
! Julian_day: Julian_Day 1=Jan 1, 365=Dec31 (366 leap year)
! UNITS: day
! TYPE: integer(JPIM)
! DIMENSION: Scale
! ATTRIBUTES: INTENT(IN)
!
! utc_time: Universal_Time 0.00-23.999,(GMT,Z time)
! UNITS: hour
! TYPE: real(fp)
! DIMENSION: Scale
! ATTRIBUTES: INTENT(IN)
!
! OUTPUT ARGUMENTS:
! Bx: Magetic field East component
! UNITS: Gauss
! TYPE: real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! By: Magetic field North component
! UNITS: Gauss
! TYPE: real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! Bz: Magetic field zenith component (positive upward)
! UNITS: Gauss
! TYPE: real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! Be: Magetic field strength (sqrt(BxBx + ByBy + BzBz))
! UNITS: Gauss
! TYPE: real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! cos_bkang: cosine of the angle between the magnetic field Be
! vector and the wave propagation direction k.
! UNITS: N/A
! TYPE: real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! cos_baziang: cosine of the azimuth angle of the Be vector in the
! (v, h, k) coordinates system, where v, h and k comprise
! a right-hand orthogonal system, similar to the (x, y, z)
! Catesian coordinates. The h vector is normal to the
! plane containing the k and z vectors, where k points
! to the wave propagation direction and z points
! to the zenith. h = (z cross k)/|z cross k|. The
! azimuth angle is the angle on the (v, h) plane
! from the positive v axis to the projected line of the
! Be vector on this plane, positive counterclockwise.
! UNITS: N/A
! TYPE: real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
!--------------------------------------------------------------------------------
<A NAME='COMPUTE_BFIELD_F1'><A href='../../html_code/crtm/Zeeman_Utility.f90.html#COMPUTE_BFIELD_F1' TARGET='top_target'><IMG SRC="../../gif/bar_red.gif" border=0></A>
SUBROUTINE compute_bfield_F1(latitude, longitude, & ! Inputs 3,3
Bx, By, Bz, Be) ! Outputs
REAL(fp), INTENT(IN) :: latitude, longitude
REAL(fp), INTENT(OUT) :: Bx, By, Bz, Be
! Local
REAL(fp) :: x2, w1_lat, w1_lon
INTEGER :: idx_lat, idx_lon
REAL(fp), PARAMETER :: dlat = 2.0_fp, dlon = 2.0_fp
idx_lat = INT(latitude/dlat)+1
IF(idx_lat >= n_Lat)idx_lat = n_lat-1
idx_lon = INT(longitude/dlat)+1
IF(idx_lon >= n_Lon)idx_lon = n_lon-1
x2 = REAL(idx_lat, fp)*dlat
w1_lat = (x2 - latitude)/dlat
x2 = REAL(idx_lon, fp)*dlat
w1_lon = (x2 - longitude)/dlat
Bx = BField_Component(1, Bfield, w1_lat, w1_lon, idx_lat, idx_lon)
By = BField_Component(2, Bfield, w1_lat, w1_lon, idx_lat, idx_lon)
Bz = BField_Component(3, Bfield, w1_lat, w1_lon, idx_lat, idx_lon)
Be = SQRT(Bx*Bx+By*By+Bz*Bz)
CONTAINS
<A NAME='BFIELD_COMPONENT'><A href='../../html_code/crtm/Zeeman_Utility.f90.html#BFIELD_COMPONENT' TARGET='top_target'><IMG SRC="../../gif/bar_green.gif" border=0></A>
FUNCTION BField_Component(comp, Bfield, w1_lat, w1_lon, & 3
idx_lat, idx_lon) Result(B)
INTEGER, INTENT(IN) :: comp
INTEGER, INTENT(IN) :: BField(:,:,:)
REAL(fp), INTENT(IN) :: w1_lat, w1_lon
INTEGER, INTENT(IN) :: idx_lat, idx_lon
REAL(fp) :: B
REAL(fp), PARAMETER :: Scale = 0.001_fp
REAL(fp) :: w2_lat, w2_lon
w2_lat = 1.0_fp - w1_lat
w2_lon = 1.0_fp - w1_lon
B = (w1_lon*(w1_lat*REAL(BField(comp,idx_lat, idx_lon), fp) + &
w2_lat*REAL(BField(comp,idx_lat+1, idx_lon), fp)) &
+ w2_lon*(w1_lat*REAL(BField(comp,idx_lat, idx_lon+1),fp) + &
w2_lat*REAL(BField(comp,idx_lat+1, idx_lon+1),fp)))*Scale
END FUNCTION BField_Component
END SUBROUTINE compute_bfield_F1
<A NAME='COMPUTE_BFIELD_F2'><A href='../../html_code/crtm/Zeeman_Utility.f90.html#COMPUTE_BFIELD_F2' TARGET='top_target'><IMG SRC="../../gif/bar_red.gif" border=0></A>
Subroutine compute_bfield_F2(latitude, longitude, sensor_zenang, sensor_aziang, & 1,2
Be, cos_bkang, cos_baziang)
!subroutine arguments:
Real(fp), Intent(in) :: latitude
Real(fp), Intent(in) :: longitude
Real(fp), Intent(in) :: sensor_zenang
Real(fp), Intent(in) :: sensor_aziang
Real(fp), Intent(out) :: Be
Real(fp), Intent(out) :: cos_bkang
Real(fp), Intent(out) :: cos_baziang
! local variable
Real(fp) :: Bx, By, Bz
! get Earth magnetic filed from LUT
Call compute_bfield_F1(latitude, longitude, & ! inputs
Bx, By, Bz, Be) ! outputs
! compute the cosines of the angle between the magnetic field Be and
! propagation direction and Be's azimuth angle
Call Compute_kb_Angles(Bx, By, Bz, sensor_zenang, sensor_aziang, & ! Input
cos_bkang, cos_baziang) ! Output
End Subroutine compute_bfield_F2
<A NAME='COMPUTE_BFIELD_F3'><A href='../../html_code/crtm/Zeeman_Utility.f90.html#COMPUTE_BFIELD_F3' TARGET='top_target'><IMG SRC="../../gif/bar_red.gif" border=0></A>
Subroutine compute_bfield_F3(latitude, longitude, sensor_zenang, & 1,3
sensor_relative_aziang, julian_day, utc_time, &
Be, cos_bkang, cos_baziang)
!subroutine arguments:
Real(fp), Intent(in) :: latitude
Real(fp), Intent(in) :: longitude
Real(fp), Intent(in) :: sensor_zenang
Real(fp), Intent(in) :: sensor_relative_aziang
Integer, Intent(in) :: julian_day
Real(fp), Intent(in) :: utc_time
Real(fp), Intent(out) :: Be
Real(fp), Intent(out) :: cos_bkang
Real(fp), Intent(out) :: cos_baziang
! Local
Real(fp) :: Bx, By, Bz, Solar_ZA, Solar_AZ, lat, lon, sensor_aziang
! compute the cosines of the angle between the magnetic field Be and
! propagation direction and Be's azimuth angle
Call compute_bfield_F1(latitude, longitude, & ! inputs
Bx, By, Bz, Be) ! outputs
lat = 90.0_fp - latitude
lon = Longitude
If(lon > 180.0_fp)lon = lon - 360.0_fp
! Compute Solar azimuth angle
Call Solar_ZA_AZ(lat,lon, Real(julian_day, fp), utc_time, &
Solar_ZA, Solar_AZ)
! Compute satellite azimuth angle (starts from East, positive counterclockwise)
sensor_aziang = sensor_relative_aziang + solar_AZ
sensor_aziang = 90.0_fp - sensor_aziang
! compute for cos_bkangle, cos_baziangle
Call Compute_kb_Angles(Bx, By, Bz, sensor_zenang, sensor_aziang, & ! Input
cos_bkang, cos_baziang) ! Output
End Subroutine compute_bfield_F3
!--------------------------------------------------------------------------------
!
! NAME:
! Compute_kb_Angles
!
! PURPOSE:
! Subroutine to calculate the cosine of the angle between the Geomagnetic
! field (Be) and wave propagation direction (k) and the cosine of the
! azimuth angle of the Be vector in the (v, h, k) coordinates system (see
! more detailed description below)
!
!
! CALLING SEQUENCE:
! CALL Compute_kb_Angles(Bx, By, Bz, & ! Input
! sensor_zenang, sensor_aziang, & ! Input
! cos_bk_Angle, cos_baziang) ! Output
! INPUT ARGUMENTS:
!
! Bx: Magetic field East component
! UNITS: Gauss
! TYPE: Real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! By: Magetic field North component
! UNITS: Gauss
! TYPE: Real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! Bz: Magetic field zenith component (positive upward)
! UNITS: Gauss
! TYPE: Real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! sensor_zenang : sensor zenith angle
! UNITS: Degree
! TYPE: Real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! sensor_aziang : sensor zenith angle defined as the
! angle from the East towards North.
! UNITS: Degree
! TYPE: Real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! OUTPUT ARGUMENTS:
! cos_bkang: cosine of the angle between the magnetic field Be
! vector and the wave propagation direction k.
! UNITS: N/A
! TYPE: real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! cos_baziang: cosine of the azimuth angle of the Be vector in the
! (v, h, k) coordinates system, where v, h and k comprise
! a right-hand orthogonal system, similar to the (x, y, z)
! Catesian coordinates. The h vector is normal to the
! plane containing the k and z vectors, where k points
! to the wave propagation direction and z points
! to the zenith. h = (z cross k)/|z cross k|. The
! azimuth angle is the angle on the (v, h) plane
! from the positive v axis to the projected line of the
! Be vector on this plane, positive counterclockwise.
! UNITS: N/A
! TYPE: Real(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
!--------------------------------------------------------------------------------
<A NAME='COMPUTE_KB_ANGLES'><A href='../../html_code/crtm/Zeeman_Utility.f90.html#COMPUTE_KB_ANGLES' TARGET='top_target'><IMG SRC="../../gif/bar_red.gif" border=0></A>
SUBROUTINE Compute_kb_Angles(Bx, By, Bz, & ! Input 2
sensor_zenang, sensor_aziang, & ! Input
cos_bkang, cos_baziang) ! Output
REAL(fp), INTENT(IN) :: Bx, By, Bz
REAL(fp), INTENT(IN) :: sensor_zenang, sensor_aziang
REAL(fp), INTENT(OUT) :: cos_bkang, cos_baziang
! Local
REAL(fp) :: B, B_v, B_h, B_p, kx, ky, kz, &
SIN_SenZA, COS_SenAZ, SIN_SenAZ, COS_SenZA
SIN_SenZA = SIN(sensor_zenang*DEGREES_TO_RADIANS)
COS_SenZA = COS(sensor_zenang*DEGREES_TO_RADIANS)
SIN_SenAZ = SIN(sensor_aziang*DEGREES_TO_RADIANS)
COS_SenAZ = COS(sensor_aziang*DEGREES_TO_RADIANS)
! compute k directional vector from satellite's zenith and azimuth angles
kx = SIN_SenZA*COS_SenAZ
ky = SIN_SenZA*SIN_SenAZ
kz = COS_SenZA
! compute consine of the angle between the magnetic field B and k
B = SQRT(bx*bx+by*by+bz*bz)
cos_bkang = (kx*bx + ky*by + kz*bz)/B
! Project the B vector on the V and H plane: B_v - B component on the V
! axis; B_h - B component on the H axis.
B_v = bx*kx*kz + by*ky*kz - bz*(ky*ky + kx*kx) ;
B_h = -bx*ky + by*kx
! compute the cosine of the azimuth angle
B_p = SQRT(B_v*B_v + B_h*B_h)
If(B_p /= 0.0_fp)Then
cos_baziang = B_v / B_p
Else
cos_baziang = 0.0 ! not defined (take an arbitrary value)
Endif
END SUBROUTINE Compute_kb_Angles
<A NAME='SOLAR_ZA_AZ'><A href='../../html_code/crtm/Zeeman_Utility.f90.html#SOLAR_ZA_AZ' TARGET='top_target'><IMG SRC="../../gif/bar_red.gif" border=0></A>
Subroutine Solar_ZA_Az(latitude, & 1
longitude, &
julian_day, &
universal_time, &
ZA, &
Az)
!
!************************************************************************
!* *
!* Module Name: Solar_Az_Za *
!* *
!* Language: Fortran Library: *
!* Version.Rev: 1.0 22 Feb 91 Programmer: Kleespies *
!* 1.1 28 Feb 91 Kleespies *
!* Put equation of time into hour angle. *
!*
!* updated to f95, 4, September 2007, Y. Han *
!* *
!* Calling Seq: Call Solar_Az_ZA( *
!* & latitude, *
!* & longitude, *
!* & julian_day, *
!* & universal_time, *
!* & ZA, *
!* & Az) *
!* *
!* *
!* Description: Computes solar azimuth and zenith angle for a *
!* given place and time. Solar azimuth is the angle *
!* positive east of north form a point to the center of *
!* the solar disc. Solar zenith angle is the angle *
!* in degrees from zenith to the center of the solar disk. *
!* The algorithms are taken from "Introduction to Solar *
!* Radiation" by Muhamad Iqbal, Academic Press, 1983. *
!* Note that lat=0,lon=0, 21Mar 12z will not give sun *
!* overhead, because that is not the way things work. *
!* *
!* Input Args: R*4 Latitude, +NH, -SH degrees *
!* R*4 Longitude,-W, +E *
!* R*4 Julian_Day 1=Jan 1, 365=Dec31 (366 leap yr)*
!* R*4 Universal_Time 0.00-23.99,(GMT,Z time) *
!* *
!* Output Args: R*4 ZA Solar Zenith Angle *
!* R*4 AZ Solar Azmuth Angle *
!* *
!* Common Blks: none *
!* Include: none *
!* Externals: none *
!* Data Files: none *
!* *
!* Restrictions: Accurate to within .1 deg. *
!* No checking made to the validity of input *
!* parameters. *
!* Since solar zenith angle is a conic angle, *
!* it has no sign. *
!* No correction made for refraction. *
!* *
!* Error Codes: none *
!* *
!* Error Messages: *
!* *
!************************************************************************
!
implicit none
real(fp), intent(in) :: latitude,longitude,julian_day,universal_time
real(fp), intent(out) :: ZA, Az
real(fp) :: local_sun_time,solar_elevation,equation_of_time
real(fp) :: cosza,cosaz
real(fp) :: hour_angle,day_angle
real(fp) :: solar_declination
real(fp) :: rlatitude, rlongitude
real(fp), parameter :: DEGREES_TO_RADIANS = 3.141592653589793238462643_fp/180.0_fp
real(fp), parameter :: one_eighty_over_pi = 1.0/DEGREES_TO_RADIANS
real(fp), parameter :: threesixty_over_24 = 15.0
real(fp), parameter :: threesixty_over_365 = 0.98630137
real(fp), parameter :: min_declination = -23.433
real(fp), parameter :: day_offset = 10.0 ! original equation had this nine
!* Compute day angle
day_angle = threesixty_over_365*(julian_day-1.0)*DEGREES_TO_RADIANS
rlatitude = latitude * DEGREES_TO_RADIANS
rlongitude = longitude * DEGREES_TO_RADIANS
!* Compute equation of Time
Equation_of_Time = &
( 0.000075 &
+ 0.001868*Cos(Day_Angle) &
- 0.032077*Sin(Day_Angle) &
- 0.014615*Cos(2.*Day_Angle) &
- 0.040890*Sin(2.*Day_Angle) )*229.18/60 ! in hours
!* Compute local sun time
local_sun_time = universal_time &
+ Equation_of_Time &
+ longitude/threesixty_over_24
!* Compute solar declination
solar_declination = &
( 0.006918 &
- 0.399912 * cos(day_angle) &
+ 0.070257 * sin(day_angle) &
- 0.006758 * cos(2*day_angle) &
+ 0.000907 * sin(2*day_angle) &
- 0.002697 * cos(3*day_angle) &
+ 0.001480 * sin(3*day_angle) )
!* Compute hour angle
hour_angle = threesixty_over_24*mod(local_sun_time+12.0_fp , 24.0_fp)
!* Compute solar zenith angle
cosza = sin(rlatitude)*sin(solar_declination) &
+ cos(rlatitude)*cos(solar_declination)*cos(hour_angle*DEGREES_TO_RADIANS)
ZA = acos(cosza)*one_eighty_over_pi
!* Compute solar azimuth angle
solar_elevation = 90.0 - ZA
If(Solar_Elevation .eq. 90.0) Then
Az = 180.0 ! handle arbitrary case
Else
cosaz = (sin(solar_elevation*DEGREES_TO_RADIANS)*sin(rlatitude) - &
sin(solar_declination)) / &
(cos(solar_elevation*DEGREES_TO_RADIANS)*cos(rlatitude))
If(cosaz .lt. -1.0) cosaz = -1.0
If(cosaz .gt. 1.0) cosaz = 1.0
Az = acos(cosaz)*one_eighty_over_pi
! The above formula produces azimuth positive east, zero south.
! We want positive east, zero north.
!
If (Az .ge. 0.0) Then
Az = 180.0 - Az
Else
Az = -180.0 + Az
EndIf
If(hour_angle .lt. 180.0) Az = - Az
If(Az .lt. 0) Az = 360.0 + Az
EndIf
end Subroutine Solar_ZA_Az
End MODULE Zeeman_Utility