From 40e5a5811c6ffce9b0974e93cdd927cbcf60c157 Mon Sep 17 00:00:00 2001
From: Joe Hunkeler <jhunkeler@gmail.com>
Date: Tue, 11 Aug 2015 16:51:37 -0400
Subject: Repatch (from linux) of OSX IRAF

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+.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
-- 
cgit 

