SUBROUTINE iau_REFCO ( PHPA, TC, RH, WL, REFA, REFB ) *+ * - - - - - - - - - - * i a u _ R E F C O * - - - - - - - - - - * * Determine the constants A and B in the atmospheric refraction model * dZ = A tan Z + B tan^3 Z. * * 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. * * This routine is part of the International Astronomical Union's * SOFA (Standards of Fundamental Astronomy) software collection. * * Status: support routine. * * Given: * PHPA d pressure at the observer (hPa = millibar) * TC d ambient temperature at the observer (deg C) * RH d relative humidity at the observer (range 0-1) * WL d wavelength (micrometers) * * Returned: * REFA d tan Z coefficient (radians) * REFB d tan^3 Z coefficient (radians) * * Notes: * * 1) The model balances speed and accuracy to give good results in * applications where performance at low altitudes is not paramount. * Performance is maintained across a range of conditions, and * applies to both optical/IR and radio. * * 2) 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), (iii) variations in tropospheric lapse * rate and (iv) dispersive effects in the radio. * * The model was tested using the following range of conditions: * * lapse rates 0.0055, 0.0065, 0.0075 deg/meter * latitudes 0, 25, 50, 75 degrees * heights 0, 2500, 5000 meters 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 raytracing through a model * atmosphere 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 K/meter * latitude 50 degrees * sea level * pressure 1005 mb * temperature 280.15 K * humidity 80% * wavelength 5740 Angstroms * * the results were as follows: * * ZD raytrace iau_REFCO 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). * * 3) A WL value in the range 0-100 selects the optical/IR case and is * wavelength in micrometers. Any value outside this range selects * the radio case. * * 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 * Equations (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), Equation (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, wavelength. The formulae for the two cases are * developed from Hohenkerk & Sinclair (1985) and Rueger (2002). * The IAG (1999) optical refractivity for dry air is used. * * 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 Equation (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), Equation (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. * * Green, R.M., "Spherical Astronomy", Cambridge University Press, * 1987. * * Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63, * 1985. * * IAG Resolutions adopted at the XXIIth General Assembly in * Birmingham, 1999, Resolution 3. * * Rueger, J.M., "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, 2002. * * Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996. * * This revision: 2020 August 17 * * SOFA release 2023-10-11 * * Copyright (C) 2023 IAU SOFA Board. See notes at end. * *----------------------------------------------------------------------- IMPLICIT NONE DOUBLE PRECISION PHPA, TC, RH, WL, REFA, REFB LOGICAL OPTIC DOUBLE PRECISION P, T, R, W, PS, PW, TK, WLSQ, GAMMA, BETA * - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - * Decide whether optical/IR or radio case: switch at 100 microns. OPTIC = WL.LE.100D0 * Restrict parameters to safe values. T = MIN(MAX(TC,-150D0),200D0) P = MIN(MAX(PHPA,0D0),10000D0) R = MIN(MAX(RH,0D0),1D0) W = MIN(MAX(WL,0.1D0),1D6) * Water vapour pressure at the observer. IF (P.GT.0D0) THEN PS = 10D0**((0.7859D0+0.03477D0*T)/(1D0+0.00412D0*T))* : (1D0+P*(4.5D-6+6D-10*T*T)) PW = R*PS/(1D0-(1D0-R)*PS/P) ELSE PW = 0D0 END IF * Refractive index minus 1 at the observer. TK = T + 273.15D0 IF (OPTIC) THEN WLSQ = W*W GAMMA = ((77.53484D-6+(4.39108D-7+3.666D-9/WLSQ)/WLSQ)*P : -11.2684D-6*PW)/TK ELSE GAMMA = (77.6890D-6*P-(6.3938D-6-0.375463D0/TK)*PW)/TK END IF * Formula for beta adapted from Stone, with empirical adjustments. BETA=4.4474D-6*TK IF (.NOT.OPTIC) BETA=BETA-0.0074D0*PW*BETA * Refraction constants from Green. REFA = GAMMA*(1D0-BETA) REFB = -GAMMA*(BETA-GAMMA/2D0) * Finished. *+---------------------------------------------------------------------- * * Copyright (C) 2023 * Standards of Fundamental Astronomy Board * of the International Astronomical Union. * * ===================== * SOFA Software License * ===================== * * NOTICE TO USER: * * BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND * CONDITIONS WHICH APPLY TO ITS USE. * * 1. The Software is owned by the IAU SOFA Board ("SOFA"). * * 2. Permission is granted to anyone to use the SOFA software for any * purpose, including commercial applications, free of charge and * without payment of royalties, subject to the conditions and * restrictions listed below. * * 3. You (the user) may copy and distribute SOFA source code to others, * and use and adapt its code and algorithms in your own software, * on a world-wide, royalty-free basis. That portion of your * distribution that does not consist of intact and unchanged copies * of SOFA source code files is a "derived work" that must comply * with the following requirements: * * a) Your work shall be marked or carry a statement that it * (i) uses routines and computations derived by you from * software provided by SOFA under license to you; and * (ii) does not itself constitute software provided by and/or * endorsed by SOFA. * * b) The source code of your derived work must contain descriptions * of how the derived work is based upon, contains and/or differs * from the original SOFA software. * * c) The names of all routines in your derived work shall not * include the prefix "iau" or "sofa" or trivial modifications * thereof such as changes of case. * * d) The origin of the SOFA components of your derived work must * not be misrepresented; you must not claim that you wrote the * original software, nor file a patent application for SOFA * software or algorithms embedded in the SOFA software. * * e) These requirements must be reproduced intact in any source * distribution and shall apply to anyone to whom you have * granted a further right to modify the source code of your * derived work. * * Note that, as originally distributed, the SOFA software is * intended to be a definitive implementation of the IAU standards, * and consequently third-party modifications are discouraged. 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The provision of any version of the SOFA software under the terms * and conditions specified herein does not imply that future * versions will also be made available under the same terms and * conditions. * * In any published work or commercial product which uses the SOFA * software directly, acknowledgement (see www.iausofa.org) is * appreciated. * * Correspondence concerning SOFA software should be addressed as * follows: * * By email: sofa@ukho.gov.uk * By post: IAU SOFA Center * HM Nautical Almanac Office * UK Hydrographic Office * Admiralty Way, Taunton * Somerset, TA1 2DN * United Kingdom * *----------------------------------------------------------------------- END