Atmospheric refraction for radio and optical/IR wavelengths palRefro
A suggested value for the TLR argument is 0.0065. 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. The sign of the supplied TLR value is ignored.
A suggested value for the EPS argument is 1E-8. The result is usually at least two orders of magnitude more computationally precise than the supplied EPS value.
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).
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).
. The formula for the water vapour pressure, given the saturation pressure and the relative humidity, is from Crane (1976), expression 2.5.5.
. Provision for radio wavelengths has been added using expressions devised by A.T.Sinclair, RGO
(private communication 1989). The refractivity model currently used is from J.M.Rueger, " Refractive
Index Formulae for Electronic Distance Measurement with Radio and Millimetre Waves" , in Unisurv
Report S-68 (2002), School of Surveying and Spatial Information Systems, University of New South
Wales, Sydney, Australia.
. The optical refractivity for dry air is from Resolution 3 of the International Association of Geodesy adopted at the XXIIth General Assembly in Birmingham, UK, 1999.
. Various small changes have been made to gain speed.
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.
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.
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.
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.
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).
The algorithm is designed for observers in the troposphere. The supplied temperature, pressure and lapse rate are assumed to be for a point in the troposphere and are used to define a model atmosphere with the tropopause at 11km altitude and a constant temperature above that. However, in practice, the refraction values returned for stratospheric observers, at altitudes up to 25km, are quite usable.