.help refro Jun99 "Slalib Package"
.nf

      SUBROUTINE slRFRO (ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR,
     :                      EPS, REF)

     - - - - - -
      R F R O
     - - - - - -

  Atmospheric refraction for radio and optical/IR wavelengths.

  Given:
    ZOBS    d  observed zenith distance of the source (radian)
    HM      d  height of the observer above sea level (metre)
    TDK     d  ambient temperature at the observer (deg K)
    PMB     d  pressure at the observer (millibar)
    RH      d  relative humidity at the observer (range 0-1)
    WL      d  effective wavelength of the source (micrometre)
    PHI     d  latitude of the observer (radian, astronomical)
    TLR     d  temperature lapse rate in the troposphere (degK/metre)
    EPS     d  precision required to terminate iteration (radian)

  Returned:
    REF     d  refraction: in vacuo ZD minus observed ZD (radian)

  Notes:

  1  A suggested value for the TLR argument is 0.0065D0.  The
     refraction is significantly affected by TLR, and if studies
     of the local atmosphere have been carried out a better TLR
     value may be available.

  2  A suggested value for the EPS argument is 1D-8.  The result is
     usually at least two orders of magnitude more computationally
     precise than the supplied EPS value.

  3  The routine computes the refraction for zenith distances up
     to and a little beyond 90 deg using the method of Hohenkerk
     and Sinclair (NAO Technical Notes 59 and 63, subsequently adopted
     in the Explanatory Supplement, 1992 edition - see section 3.281).

  4  The code is a development of the optical/IR refraction subroutine
     AREF of C.Hohenkerk (HMNAO, September 1984), with extensions to
     support the radio case.  Apart from merely cosmetic changes, the
     following modifications to the original HMNAO optical/IR refraction
     code have been made:

     .  The angle arguments have been changed to radians.

     .  Any value of ZOBS is allowed (see note 6, below).

     .  Other argument values have been limited to safe values.

     .  Murray's values for the gas constants have been used
        (Vectorial Astrometry, Adam Hilger, 1983).

     .  The numerical integration phase has been rearranged for
        extra clarity.

     .  A better model for Ps(T) has been adopted (taken from
        Gill, Atmosphere-Ocean Dynamics, Academic Press, 1982).

     .  More accurate expressions for Pwo have been adopted
        (again from Gill 1982).

     .  Provision for radio wavelengths has been added using
        expressions devised by A.T.Sinclair, RGO (private
        communication 1989), based on the Essen & Froome
        refractivity formula adopted in Resolution 1 of the
        13th International Geodesy Association General Assembly
        (Bulletin Geodesique 70 p390, 1963).

     .  Various small changes have been made to gain speed.

     None of the changes significantly affects the optical/IR results
     with respect to the algorithm given in the 1992 Explanatory
     Supplement.  For example, at 70 deg zenith distance the present
     routine agrees with the ES algorithm to better than 0.05 arcsec
     for any reasonable combination of parameters.  However, the
     improved water-vapour expressions do make a significant difference
     in the radio band, at 70 deg zenith distance reaching almost
     4 arcsec for a hot, humid, low-altitude site during a period of
     low pressure.

  5  The radio refraction is chosen by specifying WL > 100 micrometres.
     Because the algorithm takes no account of the ionosphere, the
     accuracy deteriorates at low frequencies, below about 30 MHz.

  6  Before use, the value of ZOBS is expressed in the range +/- pi.
     If this ranged ZOBS is -ve, the result REF is computed from its
     absolute value before being made -ve to match.  In addition, if
     it has an absolute value greater than 93 deg, a fixed REF value
     equal to the result for ZOBS = 93 deg is returned, appropriately
     signed.

  7  As in the original Hohenkerk and Sinclair algorithm, fixed values
     of the water vapour polytrope exponent, the height of the
     tropopause, and the height at which refraction is negligible are
     used.

  8  The radio refraction has been tested against work done by
     Iain Coulson, JACH, (private communication 1995) for the
     James Clerk Maxwell Telescope, Mauna Kea.  For typical conditions,
     agreement at the 0.1 arcsec level is achieved for moderate ZD,
     worsening to perhaps 0.5-1.0 arcsec at ZD 80 deg.  At hot and
     humid sea-level sites the accuracy will not be as good.

  9  It should be noted that the relative humidity RH is formally
     defined in terms of "mixing ratio" rather than pressures or
     densities as is often stated.  It is the mass of water per unit
     mass of dry air divided by that for saturated air at the same
     temperature and pressure (see Gill 1982).

  Called:  slDA1P, slATMT, slATMS

  P.T.Wallace   Starlink   3 June 1997

  Copyright (C) 1997 Rutherford Appleton Laboratory
  Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.

.fi
.endhelp
