refco.c

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#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) 2013-2015, 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) 2013-2015, 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.
**  
**  
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