W3FB10

The W3FB10 routine computes the bearing and great circle distance.
           from point (1) to point (2) assuming a spherical earth.  The
           North and South poles are special cases. If latitude of point
           (1) is within 1e-10 degrees of the North pole, bearing is the
           negative longitude of point (2) by convention.  If latitude of
           point (1) is within 1e-10 degrees of the south pole, bearing is
           the longitude of point (2) by convention.  If point (2) is within
           1e-6 radians of the antipode of point (1), the bearing will be
           set to zero.  If point (1) and point (2) are within 1e-10 radians
           of each other, both bearing and distance will be set to zero.

USAGE:    CALL W3FB10(DLAT1, DLON1, DLAT2, DLON2, BEARD, GCDKM)

   Input argument list:
      DLAT1    - REAL  LATITUDE OF POINT (1) IN DEGREES NORTH.
      DLON1    - REAL  LONGITUDE OF POINT (1) IN DEGREES EAST.
      DLAT2    - REAL  LATITUDE OF POINT (2) IN DEGREES NORTH.
      DLON2    - REAL  LONGITUDE OF POINT (2) IN DEGREES EAST.
 
   Output argument list:
      BEARD    - REAL  BEARING OF POINT (2) FROM POINT (1) IN
                 COMPASS DEGREES WITH NORTH = 0.0, VALUES FROM
                 -180.0 TO +180.0 DEGREES.
      GCDKM    - REAL  GREAT CIRCLE DISTANCE FROM POINT (1) TO
                 POINT (2) IN KILOMETERS.

REMARKS:
        According to the NMC Handbook, the earth's radius is
    6371.2 kilometers.  This is what we use, even though the value
    recommended by the Smithsonian Meteorological Handbook is
    6371.221 KM.  (I wouldn't want you to think that i didn't know
    what the correct value was.)
    METHOD:  The poles are special cases, and handled separately.
    Otherwise, from spherical trigonometry, the law of cosines is used
    to calculate the third side of the spherical triangle having
    sides from the pole to points (1) and (2) (the colatitudes).
    Then the law of sines is used to calculate the angle at point
    (1).  A test is applied to see whether the arcsine result may be
    be used as such, giving an acute angle as the bearing, or whether
    The arcsine result should be subtracted from pi, giving an obtuse
    angle as the bearing.  This test is derived by constructing a
    right spherical triangle using the pole, point (2), and the
    meridian through point(1).  The latitude of the right-angled
    vertex then provides a test--if latitude (1) is greater than this
    latitude, the bearing angle must be obtuse, otherwise acute.
          If the two points are within 1e-6 radians of each other
    a flat earth is assumed, and the four-quadrant arctangent
    function is used to find the bearing.  The y-displacement is
    the difference in latitude and the x-displacement is the
    difference in longitude times cosine latitude, both in radians.
    distance is then the diagonal.
          Fundamental trigonometric identities are used freely, such
    as that cos(x) = sin(pi/2 - x), etc.  See almost any mathematical
    Handbook, such as the C.R.C. standard math tables under 'relations
    in any spherical triangle', or the National Bureau of Standards
    'Handbook of mathematical functions' under section 4.3.149,
    formulas for solution of spherical triangles.
          Double precision is used internally because of the wide
    range of geographic values that may be used.

 


  
W3lib.tar
  
Library contains Fortran 90 decoder/encoder
   routines for GRIB edition 1. (Fortran90) 

   Date posted: 2/22/2007