.help refz Jun99 "Slalib Package"
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      SUBROUTINE slREFZ (ZU, REFA, REFB, ZR)

     - - - - -
      R E F Z
     - - - - -

  Adjust an unrefracted zenith distance to include the effect of
  atmospheric refraction, using the simple A tan Z + B tan**3 Z
  model (plus special handling for large ZDs).

  Given:
    ZU    dp    unrefracted zenith distance of the source (radian)
    REFA  dp    tan Z coefficient (radian)
    REFB  dp    tan**3 Z coefficient (radian)

  Returned:
    ZR    dp    refracted zenith distance (radian)

  Notes:

  1  This routine applies the adjustment for refraction in the
     opposite sense to the usual one - it takes an unrefracted
     (in vacuo) position and produces an observed (refracted)
     position, whereas the A tan Z + B tan**3 Z model strictly
     applies to the case where an observed position is to have the
     refraction removed.  The unrefracted to refracted case is
     harder, and requires an inverted form of the text-book
     refraction models;  the formula used here is based on the
     Newton-Raphson method.  For the utmost numerical consistency
     with the refracted to unrefracted model, two iterations are
     carried out, achieving agreement at the 1D-11 arcseconds level
     for a ZD of 80 degrees.  The inherent accuracy of the model
     is, of course, far worse than this - see the documentation for
     slRFCO for more information.

  2  At ZD 83 degrees, the rapidly-worsening A tan Z + B tan**3 Z
     model is abandoned and an empirical formula takes over.  Over a
     wide range of observer heights and corresponding temperatures and
     pressures, the following levels of accuracy (arcsec) are
     typically achieved, relative to numerical integration through a
     model atmosphere:

              ZR    error

              80      0.4
              81      0.8
              82      1.5
              83      3.2
              84      4.9
              85      5.8
              86      6.1
              87      7.1
              88     10
              89     20
              90     40
              91    100         } relevant only to
              92    200         } high-elevation sites

     The high-ZD model is scaled to match the normal model at the
     transition point;  there is no glitch.

  3  Beyond 93 deg zenith distance, the refraction is held at its
     93 deg value.

  4  See also the routine slREFV, which performs the adjustment in
     Cartesian Az/El coordinates, and with the emphasis on speed
     rather than numerical accuracy.

  P.T.Wallace   Starlink   19 September 1995

  Copyright (C) 1995 Rutherford Appleton Laboratory
  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.

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