| 1 | #include "sofa.h"
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| 2 |
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| 3 | void iauRefco(double phpa, double tc, double rh, double wl,
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| 4 | double *refa, double *refb)
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| 5 | /*
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| 6 | ** - - - - - - - - -
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| 7 | ** i a u R e f c o
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| 8 | ** - - - - - - - - -
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| 9 | **
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| 10 | ** Determine the constants A and B in the atmospheric refraction model
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| 11 | ** dZ = A tan Z + B tan^3 Z.
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| 12 | **
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| 13 | ** Z is the "observed" zenith distance (i.e. affected by refraction)
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| 14 | ** and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo)
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| 15 | ** zenith distance.
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| 16 | **
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| 17 | ** This function is part of the International Astronomical Union's
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| 18 | ** SOFA (Standards of Fundamental Astronomy) software collection.
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| 19 | **
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| 20 | ** Status: support function.
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| 21 | **
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| 22 | ** Given:
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| 23 | ** phpa double pressure at the observer (hPa = millibar)
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| 24 | ** tc double ambient temperature at the observer (deg C)
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| 25 | ** rh double relative humidity at the observer (range 0-1)
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| 26 | ** wl double wavelength (micrometers)
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| 27 | **
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| 28 | ** Returned:
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| 29 | ** refa double* tan Z coefficient (radians)
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| 30 | ** refb double* tan^3 Z coefficient (radians)
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| 31 | **
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| 32 | ** Notes:
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| 33 | **
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| 34 | ** 1) The model balances speed and accuracy to give good results in
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| 35 | ** applications where performance at low altitudes is not paramount.
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| 36 | ** Performance is maintained across a range of conditions, and
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| 37 | ** applies to both optical/IR and radio.
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| 38 | **
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| 39 | ** 2) The model omits the effects of (i) height above sea level (apart
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| 40 | ** from the reduced pressure itself), (ii) latitude (i.e. the
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| 41 | ** flattening of the Earth), (iii) variations in tropospheric lapse
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| 42 | ** rate and (iv) dispersive effects in the radio.
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| 43 | **
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| 44 | ** The model was tested using the following range of conditions:
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| 45 | **
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| 46 | ** lapse rates 0.0055, 0.0065, 0.0075 deg/meter
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| 47 | ** latitudes 0, 25, 50, 75 degrees
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| 48 | ** heights 0, 2500, 5000 meters ASL
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| 49 | ** pressures mean for height -10% to +5% in steps of 5%
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| 50 | ** temperatures -10 deg to +20 deg with respect to 280 deg at SL
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| 51 | ** relative humidity 0, 0.5, 1
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| 52 | ** wavelengths 0.4, 0.6, ... 2 micron, + radio
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| 53 | ** zenith distances 15, 45, 75 degrees
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| 54 | **
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| 55 | ** The accuracy with respect to raytracing through a model
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| 56 | ** atmosphere was as follows:
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| 57 | **
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| 58 | ** worst RMS
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| 59 | **
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| 60 | ** optical/IR 62 mas 8 mas
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| 61 | ** radio 319 mas 49 mas
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| 62 | **
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| 63 | ** For this particular set of conditions:
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| 64 | **
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| 65 | ** lapse rate 0.0065 K/meter
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| 66 | ** latitude 50 degrees
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| 67 | ** sea level
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| 68 | ** pressure 1005 mb
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| 69 | ** temperature 280.15 K
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| 70 | ** humidity 80%
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| 71 | ** wavelength 5740 Angstroms
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| 72 | **
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| 73 | ** the results were as follows:
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| 74 | **
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| 75 | ** ZD raytrace iauRefco Saastamoinen
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| 76 | **
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| 77 | ** 10 10.27 10.27 10.27
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| 78 | ** 20 21.19 21.20 21.19
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| 79 | ** 30 33.61 33.61 33.60
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| 80 | ** 40 48.82 48.83 48.81
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| 81 | ** 45 58.16 58.18 58.16
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| 82 | ** 50 69.28 69.30 69.27
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| 83 | ** 55 82.97 82.99 82.95
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| 84 | ** 60 100.51 100.54 100.50
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| 85 | ** 65 124.23 124.26 124.20
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| 86 | ** 70 158.63 158.68 158.61
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| 87 | ** 72 177.32 177.37 177.31
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| 88 | ** 74 200.35 200.38 200.32
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| 89 | ** 76 229.45 229.43 229.42
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| 90 | ** 78 267.44 267.29 267.41
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| 91 | ** 80 319.13 318.55 319.10
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| 92 | **
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| 93 | ** deg arcsec arcsec arcsec
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| 94 | **
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| 95 | ** The values for Saastamoinen's formula (which includes terms
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| 96 | ** up to tan^5) are taken from Hohenkerk and Sinclair (1985).
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| 97 | **
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| 98 | ** 3) A wl value in the range 0-100 selects the optical/IR case and is
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| 99 | ** wavelength in micrometers. Any value outside this range selects
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| 100 | ** the radio case.
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| 101 | **
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| 102 | ** 4) Outlandish input parameters are silently limited to
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| 103 | ** mathematically safe values. Zero pressure is permissible, and
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| 104 | ** causes zeroes to be returned.
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| 105 | **
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| 106 | ** 5) The algorithm draws on several sources, as follows:
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| 107 | **
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| 108 | ** a) The formula for the saturation vapour pressure of water as
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| 109 | ** a function of temperature and temperature is taken from
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| 110 | ** Equations (A4.5-A4.7) of Gill (1982).
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| 111 | **
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| 112 | ** b) The formula for the water vapour pressure, given the
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| 113 | ** saturation pressure and the relative humidity, is from
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| 114 | ** Crane (1976), Equation (2.5.5).
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| 115 | **
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| 116 | ** c) The refractivity of air is a function of temperature,
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| 117 | ** total pressure, water-vapour pressure and, in the case
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| 118 | ** of optical/IR, wavelength. The formulae for the two cases are
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| 119 | ** developed from Hohenkerk & Sinclair (1985) and Rueger (2002).
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| 120 | **
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| 121 | ** d) The formula for beta, the ratio of the scale height of the
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| 122 | ** atmosphere to the geocentric distance of the observer, is
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| 123 | ** an adaption of Equation (9) from Stone (1996). The
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| 124 | ** adaptations, arrived at empirically, consist of (i) a small
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| 125 | ** adjustment to the coefficient and (ii) a humidity term for the
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| 126 | ** radio case only.
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| 127 | **
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| 128 | ** e) The formulae for the refraction constants as a function of
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| 129 | ** n-1 and beta are from Green (1987), Equation (4.31).
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| 130 | **
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| 131 | ** References:
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| 132 | **
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| 133 | ** Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral
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| 134 | ** Atmosphere", Methods of Experimental Physics: Astrophysics 12B,
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| 135 | ** Academic Press, 1976.
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| 136 | **
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| 137 | ** Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press,
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| 138 | ** 1982.
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| 139 | **
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| 140 | ** Green, R.M., "Spherical Astronomy", Cambridge University Press,
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| 141 | ** 1987.
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| 142 | **
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| 143 | ** Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63,
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| 144 | ** 1985.
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| 145 | **
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| 146 | ** Rueger, J.M., "Refractive Index Formulae for Electronic Distance
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| 147 | ** Measurement with Radio and Millimetre Waves", in Unisurv Report
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| 148 | ** S-68, School of Surveying and Spatial Information Systems,
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| 149 | ** University of New South Wales, Sydney, Australia, 2002.
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| 150 | **
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| 151 | ** Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996.
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| 152 | **
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| 153 | ** This revision: 2013 October 9
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| 154 | **
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| 155 | ** SOFA release 2015-02-09
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| 156 | **
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| 157 | ** Copyright (C) 2015 IAU SOFA Board. See notes at end.
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| 158 | */
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| 159 | {
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| 160 | int optic;
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| 161 | double p, t, r, w, ps, pw, tk, wlsq, gamma, beta;
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| 162 |
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| 163 | /* Decide whether optical/IR or radio case: switch at 100 microns. */
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| 164 | optic = ( wl <= 100.0 );
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| 165 |
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| 166 | /* Restrict parameters to safe values. */
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| 167 | t = gmax ( tc, -150.0 );
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| 168 | t = gmin ( t, 200.0 );
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| 169 | p = gmax ( phpa, 0.0 );
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| 170 | p = gmin ( p, 10000.0 );
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| 171 | r = gmax ( rh, 0.0 );
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| 172 | r = gmin ( r, 1.0 );
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| 173 | w = gmax ( wl, 0.1 );
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| 174 | w = gmin ( w, 1e6 );
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| 175 |
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| 176 | /* Water vapour pressure at the observer. */
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| 177 | if ( p > 0.0 ) {
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| 178 | ps = pow ( 10.0, ( 0.7859 + 0.03477*t ) /
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| 179 | ( 1.0 + 0.00412*t ) ) *
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| 180 | ( 1.0 + p * ( 4.5e-6 + 6e-10*t*t ) );
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| 181 | pw = r * ps / ( 1.0 - (1.0-r)*ps/p );
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| 182 | } else {
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| 183 | pw = 0.0;
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| 184 | }
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| 185 |
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| 186 | /* Refractive index minus 1 at the observer. */
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| 187 | tk = t + 273.15;
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| 188 | if ( optic ) {
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| 189 | wlsq = w * w;
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| 190 | gamma = ( ( 77.53484e-6 +
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| 191 | ( 4.39108e-7 + 3.666e-9/wlsq ) / wlsq ) * p
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| 192 | - 11.2684e-6*pw ) / tk;
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| 193 | } else {
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| 194 | gamma = ( 77.6890e-6*p - ( 6.3938e-6 - 0.375463/tk ) * pw ) / tk;
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| 195 | }
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| 196 |
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| 197 | /* Formula for beta from Stone, with empirical adjustments. */
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| 198 | beta = 4.4474e-6 * tk;
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| 199 | if ( ! optic ) beta -= 0.0074 * pw * beta;
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| 200 |
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| 201 | /* Refraction constants from Green. */
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| 202 | *refa = gamma * ( 1.0 - beta );
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| 203 | *refb = - gamma * ( beta - gamma / 2.0 );
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| 204 |
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| 205 | /* Finished. */
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| 206 |
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| 207 | /*----------------------------------------------------------------------
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| 208 | **
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| 209 | ** Copyright (C) 2015
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| 210 | ** Standards Of Fundamental Astronomy Board
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| 211 | ** of the International Astronomical Union.
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| 212 | **
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| 213 | ** =====================
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| 214 | ** SOFA Software License
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| 215 | ** =====================
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| 216 | **
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| 217 | ** NOTICE TO USER:
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| 218 | **
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| 219 | ** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
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| 220 | ** CONDITIONS WHICH APPLY TO ITS USE.
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| 221 | **
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| 222 | ** 1. The Software is owned by the IAU SOFA Board ("SOFA").
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| 223 | **
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| 224 | ** 2. Permission is granted to anyone to use the SOFA software for any
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| 225 | ** purpose, including commercial applications, free of charge and
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| 226 | ** without payment of royalties, subject to the conditions and
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| 227 | ** restrictions listed below.
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| 228 | **
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| 229 | ** 3. You (the user) may copy and distribute SOFA source code to others,
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| 230 | ** and use and adapt its code and algorithms in your own software,
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| 231 | ** on a world-wide, royalty-free basis. That portion of your
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| 232 | ** distribution that does not consist of intact and unchanged copies
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| 233 | ** of SOFA source code files is a "derived work" that must comply
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| 234 | ** with the following requirements:
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| 235 | **
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| 236 | ** a) Your work shall be marked or carry a statement that it
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| 237 | ** (i) uses routines and computations derived by you from
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| 238 | ** software provided by SOFA under license to you; and
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| 239 | ** (ii) does not itself constitute software provided by and/or
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| 240 | ** endorsed by SOFA.
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| 241 | **
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| 242 | ** b) The source code of your derived work must contain descriptions
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| 243 | ** of how the derived work is based upon, contains and/or differs
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| 244 | ** from the original SOFA software.
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| 245 | **
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| 246 | ** c) The names of all routines in your derived work shall not
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| 247 | ** include the prefix "iau" or "sofa" or trivial modifications
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| 248 | ** thereof such as changes of case.
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| 249 | **
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| 250 | ** d) The origin of the SOFA components of your derived work must
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| 251 | ** not be misrepresented; you must not claim that you wrote the
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| 252 | ** original software, nor file a patent application for SOFA
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| 253 | ** software or algorithms embedded in the SOFA software.
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| 254 | **
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| 255 | ** e) These requirements must be reproduced intact in any source
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| 256 | ** distribution and shall apply to anyone to whom you have
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| 257 | ** granted a further right to modify the source code of your
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| 258 | ** derived work.
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| 259 | **
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| 260 | ** Note that, as originally distributed, the SOFA software is
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| 261 | ** intended to be a definitive implementation of the IAU standards,
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| 262 | ** and consequently third-party modifications are discouraged. All
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| 263 | ** variations, no matter how minor, must be explicitly marked as
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| 264 | ** such, as explained above.
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| 265 | **
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| 266 | ** 4. You shall not cause the SOFA software to be brought into
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| 267 | ** disrepute, either by misuse, or use for inappropriate tasks, or
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| 268 | ** by inappropriate modification.
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| 269 | **
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| 270 | ** 5. The SOFA software is provided "as is" and SOFA makes no warranty
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| 271 | ** as to its use or performance. SOFA does not and cannot warrant
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| 272 | ** the performance or results which the user may obtain by using the
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| 273 | ** SOFA software. SOFA makes no warranties, express or implied, as
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| 274 | ** to non-infringement of third party rights, merchantability, or
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| 275 | ** fitness for any particular purpose. In no event will SOFA be
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| 276 | ** liable to the user for any consequential, incidental, or special
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| 277 | ** damages, including any lost profits or lost savings, even if a
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| 278 | ** SOFA representative has been advised of such damages, or for any
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| 279 | ** claim by any third party.
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| 280 | **
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| 281 | ** 6. The provision of any version of the SOFA software under the terms
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| 282 | ** and conditions specified herein does not imply that future
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| 283 | ** versions will also be made available under the same terms and
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| 284 | ** conditions.
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| 285 | *
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| 286 | ** In any published work or commercial product which uses the SOFA
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| 287 | ** software directly, acknowledgement (see www.iausofa.org) is
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| 288 | ** appreciated.
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| 289 | **
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| 290 | ** Correspondence concerning SOFA software should be addressed as
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| 291 | ** follows:
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| 292 | **
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| 293 | ** By email: sofa@ukho.gov.uk
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| 294 | ** By post: IAU SOFA Center
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| 295 | ** HM Nautical Almanac Office
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| 296 | ** UK Hydrographic Office
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| 297 | ** Admiralty Way, Taunton
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| 298 | ** Somerset, TA1 2DN
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| 299 | ** United Kingdom
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| 300 | **
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| 301 | **--------------------------------------------------------------------*/
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| 302 |
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| 303 | }
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