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For bubble observations I would omit refraction corrections for
nonstandard pressure and temperature, and just apply a correction for
altitude above sea level (if significant). For that, assume a standard
atmosphere. Putting "standard atmosphere" in a search engine will
reveal many online calculators to give you the air density if altitude
is known.

This one is convenient because you can select "sigma" for the density
units. Sigma is density relative to sea level.
http://www.digitaldutch.com/atmoscalc/

If you input 5000 feet for altitude, you'll see that sigma = .86, so
the refraction correction would be 86% of the value listed in the
Nautical Almanac.

That assumes the temperature vs. altitude relationship is standard.
According to the calculator, standard temperature at 5000 feet is 41
F. But suppose the actual temperature is 90 F. The increased
temperature reduces the air density (and refraction), the correction
factor being equal to the ratio of the absolute temperatures. In my
example they are 41 F and 90 F, so the temperature correction factor
is (460 + 41) / (460 + 90) = .91. (The number 460 converts from
Fahrenheit to degrees above absolute zero.)

Finally, suppose the barometric pressure is 29.7 inches Hg instead of
the standard 29.9. To correct for that, the multiplier is 29.7 / 29.9
= .99.

To apply all the corrections, multiply the Almanac refraction by .86 *
.91 * .99, for an overall correction factor of .77. If the tabulated
refraction is 6', the adjusted refraction becomes 4.6'. If we had
neglected the corrections for nonstandard temperature and pressure, it
would be 5.2'. That's not much different, even though my example had
large deviations from standard conditions and the corrections were in
the same direction.


If you want to get anal-retentive, this person has a site with
formulas for determining air density in several different ways:

http://www.wahiduddin.net/calc/density_altitude.htm

It has links to authoritative references for such things as exactly
how the "raw" station pressure is converted to barometric pressure
corrected to sea level, or altimeter setting.

   

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