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    Re: Refraction at the horizon
    From: Frank Reed
    Date: 2008 Mar 17, 18:42 -0400

    A few things about the Auer-Standish paper...
    
    First, so there's no misunderstanding, this is not a "new" way to determine
    refraction. It's an integration procedure that makes the standard way of
    calculating refraction easier to implement. The underlying physics is
    long-established. It's Snell's Law applied to a continuous medium with the
    assumption that the index of refraction is given by
     n = 1+alpha(f,c)*rho(x,y,z)
    where alpha(f,c) is a small number, near 0.000292 (the value in the article
    is missing a zero), which depends on frequency and atmospheric composition
    (including humidity), and rho(x,y,z) is the density of the atmosphere at
    point x,y,z (normalized to 1 for standard temperature and pressure at sea
    level).
    
    Next, this standard approach to refraction still assumes a very limited set
    of variations in the atmosphere, specifically the atmosphere is in
    hydrostatic equilibrium with the only variations determined by the vertical
    temperature structure. This is where most of the action happens, and it's
    more than enough to explain some very exotic refraction phenomena, but this
    approach cannot handle horizontal variations.
    
    Finally, in the original paper, a non-physical model of the atmosphere is
    used that should really just be ignored (I think they use it because it
    allows for comparisons with earlier published papers). They have all sorts
    of details here that really do not belong in this article. For example, they
    list the "altitude of troposphere" (should be tropopause) as 11,019 meters,
    which is very strange. If you want to model an atmosphere that reproduces
    their "polytropic" atmosphere, use a constant lapse rate of -5.692 degrees
    per km up to 11km altitude (zero lapse rate above that). Also set the sea
    level temperature to 0 Celsius. When I used these values, I was able to
    reproduce their sample refraction tables to the nearest tenth of a second of
    arc for a sea level observer and the nearest half-second of arc for an
    observer at 15km altitude.
    
    Of course, for a proper refraction table, you want to use a realistic set of
    lapse rates based on real meteorology. There are a number of possibilities
    here. You can use data from soundings. You could use a standard model
    atmosphere (there are several of these). Or you could use a theoretical
    meteorological atmosphere based on variable adiabatic lapse rates.
    
    Incidentally, based on these integrations, I concocted some short formulas
    that cover a broader range of refraction possibilities but consistent with
    the Nautical Almanac's (implicit) atmosphere model. Posted here:
    http://www.fer3.com/arc/m2.aspx?i=025346&y=200508. Also while re-reading
    messages from August 2005, I discovered that I made GIF images of the
    Auer-Standish article available on my web site (forgot about that!), so if
    you want to read the article and can't get the PDF or you want a faster
    download, go here: http://www.HistoricalAtlas.com/lunars/ref.html. And I
    posted a simple coding of this algorithm here:
    http://www.fer3.com/arc/m2.aspx?i=025268&y=200508.
    
    One more thing that I think is worth mentioning. For a navigational context,
    there's no use worrying about differences in refraction smaller than 1 or 2%
    (of the refraction for that altitude above/below the horizon) since at that
    level even different colors of light will be refracted by different amounts
    turning a low altitude image of a star into a little "French flag".
    
     -FER
    
    
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