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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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