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+.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