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diff --git a/math/slalib/doc/refcoq.hlp b/math/slalib/doc/refcoq.hlp new file mode 100644 index 00000000..153ed66e --- /dev/null +++ b/math/slalib/doc/refcoq.hlp @@ -0,0 +1,167 @@ +.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. + +.fi +.endhelp |