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Diffstat (limited to 'ast/erfa/refco.c')
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diff --git a/ast/erfa/refco.c b/ast/erfa/refco.c new file mode 100644 index 0000000..918d990 --- /dev/null +++ b/ast/erfa/refco.c @@ -0,0 +1,262 @@ +#include "erfa.h" + +void eraRefco(double phpa, double tc, double rh, double wl, + double *refa, double *refb) +/* +** - - - - - - - - - +** e r a 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. +** +** Given: +** phpa double pressure at the observer (hPa = millibar) +** tc double ambient temperature at the observer (deg C) +** rh double relative humidity at the observer (range 0-1) +** wl double wavelength (micrometers) +** +** Returned: +** refa double* tan Z coefficient (radians) +** refb double* 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 eraRefco 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). +** +** 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. +** +** 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. +** +** Copyright (C) 2013-2016, NumFOCUS Foundation. +** Derived, with permission, from the SOFA library. See notes at end of file. +*/ +{ + int optic; + double p, t, r, w, ps, pw, tk, wlsq, gamma, beta; + + +/* Decide whether optical/IR or radio case: switch at 100 microns. */ + optic = ( wl <= 100.0 ); + +/* Restrict parameters to safe values. */ + t = ERFA_GMAX ( tc, -150.0 ); + t = ERFA_GMIN ( t, 200.0 ); + p = ERFA_GMAX ( phpa, 0.0 ); + p = ERFA_GMIN ( p, 10000.0 ); + r = ERFA_GMAX ( rh, 0.0 ); + r = ERFA_GMIN ( r, 1.0 ); + w = ERFA_GMAX ( wl, 0.1 ); + w = ERFA_GMIN ( w, 1e6 ); + +/* Water vapour pressure at the observer. */ + if ( p > 0.0 ) { + ps = pow ( 10.0, ( 0.7859 + 0.03477*t ) / + ( 1.0 + 0.00412*t ) ) * + ( 1.0 + p * ( 4.5e-6 + 6e-10*t*t ) ); + pw = r * ps / ( 1.0 - (1.0-r)*ps/p ); + } else { + pw = 0.0; + } + +/* Refractive index minus 1 at the observer. */ + tk = t + 273.15; + if ( optic ) { + wlsq = w * w; + gamma = ( ( 77.53484e-6 + + ( 4.39108e-7 + 3.666e-9/wlsq ) / wlsq ) * p + - 11.2684e-6*pw ) / tk; + } else { + gamma = ( 77.6890e-6*p - ( 6.3938e-6 - 0.375463/tk ) * pw ) / tk; + } + +/* Formula for beta from Stone, with empirical adjustments. */ + beta = 4.4474e-6 * tk; + if ( ! optic ) beta -= 0.0074 * pw * beta; + +/* Refraction constants from Green. */ + *refa = gamma * ( 1.0 - beta ); + *refb = - gamma * ( beta - gamma / 2.0 ); + +/* Finished. */ + +} +/*---------------------------------------------------------------------- +** +** +** Copyright (C) 2013-2016, NumFOCUS Foundation. +** All rights reserved. +** +** This library is derived, with permission, from the International +** Astronomical Union's "Standards of Fundamental Astronomy" library, +** available from http://www.iausofa.org. +** +** The ERFA version is intended to retain identical functionality to +** the SOFA library, but made distinct through different function and +** file names, as set out in the SOFA license conditions. The SOFA +** original has a role as a reference standard for the IAU and IERS, +** and consequently redistribution is permitted only in its unaltered +** state. The ERFA version is not subject to this restriction and +** therefore can be included in distributions which do not support the +** concept of "read only" software. +** +** Although the intent is to replicate the SOFA API (other than +** replacement of prefix names) and results (with the exception of +** bugs; any that are discovered will be fixed), SOFA is not +** responsible for any errors found in this version of the library. +** +** If you wish to acknowledge the SOFA heritage, please acknowledge +** that you are using a library derived from SOFA, rather than SOFA +** itself. +** +** +** TERMS AND CONDITIONS +** +** Redistribution and use in source and binary forms, with or without +** modification, are permitted provided that the following conditions +** are met: +** +** 1 Redistributions of source code must retain the above copyright +** notice, this list of conditions and the following disclaimer. +** +** 2 Redistributions in binary form must reproduce the above copyright +** notice, this list of conditions and the following disclaimer in +** the documentation and/or other materials provided with the +** distribution. +** +** 3 Neither the name of the Standards Of Fundamental Astronomy Board, +** the International Astronomical Union nor the names of its +** contributors may be used to endorse or promote products derived +** from this software without specific prior written permission. +** +** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +** POSSIBILITY OF SUCH DAMAGE. +** +*/ |