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.help refcoq Jun99 "Slalib Package"
.nf
SUBROUTINE slRFCQ (TDK, PMB, RH, WL, REFA, REFB)
- - - - - - -
R F C Q
- - - - - - -
Determine the constants A and B in the atmospheric refraction
model dZ = A tan Z + B tan**3 Z. This is a fast alternative
to the slRFCO routine - see notes.
Z is the "observed" zenith distance (i.e. affected by refraction)
and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo)
zenith distance.
Given:
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)
Returned:
REFA d tan Z coefficient (radian)
REFB d tan**3 Z coefficient (radian)
The radio refraction is chosen by specifying WL > 100 micrometres.
Notes:
1 The model is an approximation, for moderate zenith distances,
to the predictions of the slRFRO routine. The approximation
is maintained across a range of conditions, and applies to
both optical/IR and radio.
2 The algorithm is a fast alternative to the slRFCO routine.
The latter calls the slRFRO routine itself: this involves
integrations through a model atmosphere, and is costly in
processor time. However, the model which is produced is precisely
correct for two zenith distance (45 degrees and about 76 degrees)
and at other zenith distances is limited in accuracy only by the
A tan Z + B tan**3 Z formulation itself. The present routine
is not as accurate, though it satisfies most practical
requirements.
3 The model omits the effects of (i) height above sea level (apart
from the reduced pressure itself), (ii) latitude (i.e. the
flattening of the Earth) and (iii) variations in tropospheric
lapse rate.
The model was tested using the following range of conditions:
lapse rates 0.0055, 0.0065, 0.0075 deg/metre
latitudes 0, 25, 50, 75 degrees
heights 0, 2500, 5000 metres ASL
pressures mean for height -10% to +5% in steps of 5%
temperatures -10 deg to +20 deg with respect to 280 deg at SL
relative humidity 0, 0.5, 1
wavelengths 0.4, 0.6, ... 2 micron, + radio
zenith distances 15, 45, 75 degrees
The accuracy with respect to direct use of the slRFRO routine
was as follows:
worst RMS
optical/IR 62 mas 8 mas
radio 319 mas 49 mas
For this particular set of conditions:
lapse rate 0.0065 degK/metre
latitude 50 degrees
sea level
pressure 1005 mB
temperature 280.15 degK
humidity 80%
wavelength 5740 Angstroms
the results were as follows:
ZD slRFRO slRFCQ Saastamoinen
10 10.27 10.27 10.27
20 21.19 21.20 21.19
30 33.61 33.61 33.60
40 48.82 48.83 48.81
45 58.16 58.18 58.16
50 69.28 69.30 69.27
55 82.97 82.99 82.95
60 100.51 100.54 100.50
65 124.23 124.26 124.20
70 158.63 158.68 158.61
72 177.32 177.37 177.31
74 200.35 200.38 200.32
76 229.45 229.43 229.42
78 267.44 267.29 267.41
80 319.13 318.55 319.10
deg arcsec arcsec arcsec
The values for Saastamoinen's formula (which includes terms
up to tan^5) are taken from Hohenkerk and Sinclair (1985).
The results from the much slower but more accurate slRFCO
routine have not been included in the tabulation as they are
identical to those in the slRFRO column to the 0.01 arcsec
resolution used.
4 Outlandish input parameters are silently limited to mathematically
safe values. Zero pressure is permissible, and causes zeroes to
be returned.
5 The algorithm draws on several sources, as follows:
a) The formula for the saturation vapour pressure of water as
a function of temperature and temperature is taken from
expressions A4.5-A4.7 of Gill (1982).
b) The formula for the water vapour pressure, given the
saturation pressure and the relative humidity, is from
Crane (1976), expression 2.5.5.
c) The refractivity of air is a function of temperature,
total pressure, water-vapour pressure and, in the case
of optical/IR but not radio, wavelength. The formulae
for the two cases are developed from the Essen and Froome
expressions adopted in Resolution 1 of the 12th International
Geodesy Association General Assembly (1963).
The above three items are as used in the slRFRO routine.
d) The formula for beta, the ratio of the scale height of the
atmosphere to the geocentric distance of the observer, is
an adaption of expression 9 from Stone (1996). The
adaptations, arrived at empirically, consist of (i) a
small adjustment to the coefficient and (ii) a humidity
term for the radio case only.
e) The formulae for the refraction constants as a function of
n-1 and beta are from Green (1987), expression 4.31.
References:
Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral
Atmosphere", Methods of Experimental Physics: Astrophysics 12B,
Academic Press, 1976.
Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press, 1982.
Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63, 1985.
International Geodesy Association General Assembly, Bulletin
Geodesique 70 p390, 1963.
Stone, Ronald C., P.A.S.P. 108 1051-1058, 1996.
Green, R.M., "Spherical Astronomy", Cambridge University Press, 1987.
P.T.Wallace Starlink 4 June 1997
Copyright (C) 1997 Rutherford Appleton Laboratory
Copyright (C) 1995 Association of Universities for Research in Astronomy Inc.
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.endhelp
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