### SLA_REFRO

Refraction

ACTION:
Atmospheric refraction, for radio or optical/IR wavelengths.
CALL:
CALL sla_REFRO (ZOBS, HM, TDK, PMB, RH, WL, PHI, TLR, EPS, REF)
##### GIVEN:
 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 (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 ($\mu m$) PHI D latitude of the observer (radian, astronomical) TLR D temperature lapse rate in the troposphere (K per metre) EPS D precision required to terminate iteration (radian)

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

NOTES:
(1)
A suggested value for the TLR argument is 0.0065D0 (sign immaterial). 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 $9{0}^{\circ }$ 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).
(4)
The code is based on the AREF optical/IR refraction subroutine (HMNAO, September 1984, RGO: Hohenkerk 1985), with extensions to support the radio case. The modifications to the original HMNAO optical/IR refraction code which affect the results are:
• The angle arguments have been changed to radians, any value of ZOBS is allowed (see Note 6, below) and other argument values have been limited to safe values.
• Revised values for the gas constants are used, from Murray (1983).
• A better model for ${P}_{s}\left(T\right)$ has been adopted, from Gill (1982).
• More accurate expressions for $P{w}_{o}$ 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 (Sinclair 1989). The refractivity model is from Rueger (2002).
• The optical refractivity for dry air is from IAG (1999).
(5)
The radio refraction is chosen by specifying WL $>100$ $\mu m$. 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 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 $9{3}^{\circ }$, a fixed REF value equal to the result for ZOBS $=9{3}^{\circ }$ is returned, appropriately signed.
(7)
As in the original Hohenkerk & 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 ′′01 level is achieved for moderate ZD, worsening to perhaps ′′05 – ′′10 at ZD $8{0}^{\circ }$. 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). 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.
(10)
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.
REFERENCES:
(1)
Coulsen, I. 1995, private communication.
(2)
Crane, R.K., Meeks, M.L. (ed), 1976, “Refraction Effects in the Neutral Atmosphere”, Methods of Experimental Physics: Astrophysics 12B, Academic Press.
(3)
(4)
Hohenkerk, C.Y. 1985, private communication.
(5)
Hohenkerk, C.Y., & Sinclair, A.T. 1985, NAO Technical Note No. 63, Royal Greenwich Observatory.
(6)
International Association of Geodesy, XXIIth General Assembly, Birmingham, UK, 1999, Resolution 3.
(7)
Murray, C.A. 1983, Vectorial Astrometry, Adam Hilger, Bristol.
(8)
Seidelmann, P.K. et al. 1992, Explanatory Supplement to the Astronomical Almanac, Chapter 3, University Science Books.
(9)
Rueger, J.M. 2002, Refractive Index Formulae for Electronic Distance Measurement with Radio and Millimetre Waves, in Unisurv Report S-68, School of Surveying and Spatial Information Systems, University of New South Wales, Sydney, Australia.
(10)
Sinclair, A.T. 1989, private communication.