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SLA_REFRO - Refraction   

Atmospheric refraction, for radio or optical/IR wavelengths.


ZOBS D observed zenith distance of the source (radians)
HM D height of the observer above sea level (metre)
TDK D ambient temperature at the observer (degrees K)
PMB D pressure at the observer (mB)
RH D relative humidity at the observer (range 0-1)
WL D effective wavelength of the source ($\mu{\rm m}$)
PHI D latitude of the observer (radian, astronomical)
TLR D temperature lapse rate in the troposphere (degrees K per metre)
EPS D precision required to terminate iteration (radian)


REF D refraction: in vacuo ZD minus observed ZD (radians)

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.
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.
The routine computes the refraction for zenith distances up to and a little beyond $90^{\circ}$ using the method of Hohenkerk & Sinclair (NAO Technical Notes 59 and 63, subsequently adopted in the Explanatory Supplement to the Astronomical Almanac, 1992 - see section 3.281).
The code is based on the AREF optical/IR refraction subroutine of C.Hohenkerk (HMNAO, September 1984), with extensions to support the radio case. The modifications to the original HMNAO optical/IR refraction code which affect the results are:
  • Murray's values for the gas constants have been used (Vectorial Astrometry, Adam Hilger, 1983).
  • 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 12th International Geodesy Association General Assembly (Bulletin Géodésique 70 p390, 1963).
None of the changes significantly affects the optical/IR results with respect to the algorithm given in the 1992 Explanatory Supplement. For example, at $70^\circ$ zenith distance the present routine agrees with the ES algorithm to better than $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.05$

for any reasonable combination of parameters. However, the improved water-vapour expressions do make a significant difference in the radio band, at $70^\circ$ zenith distance reaching almost $4\hspace{-0.05em}^{'\hspace{-0.1em}'}$ for a hot, humid, low-altitude site during a period of low pressure.

The radio refraction is chosen by specifying WL >100 $\mu{\rm m}$. Because the algorithm takes no account of the ionosphere, the accuracy deteriorates at low frequencies, below about 30MHz.
Before use, the value of ZOBS is expressed in the range $\pm \pi$. If this ranged ZOBS is negative, the result REF is computed from its absolute value before being made negative to match. In addition, if it has an absolute value greater than $93^\circ$, a fixed REF value equal to the result for ZOBS $=93^\circ$ 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 $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$ level is achieved for moderate ZD, worsening to perhaps $0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$ - $1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0$ at ZD $80^\circ$. 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 familiar $\nu=p_w/p_s$ or $\nu=\rho_w/\rho_s$ expressions can differ from the formal definition by several percent, significant in the radio case.

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SLALIB --- Positional Astronomy Library
Starlink User Note 67
P. T. Wallace
12 October 1999