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Peter, you wrote:
"I thought that the "low-precision" refraction formula (which immediately 
follows in the text) was adequate for celestial navigation purposes.  Perhaps 
I was wrong, especially when it comes to lunar and other distances."

The standard formulae for refraction used in most celestial navigation 
software products are certainly adequate for the task most of the time, but 
they can be improved upon.

Of the Saastamoinen formula (and others like it), I think they're clearly 
superior to the Bennett formula (which was always optimized for its brevity). 
But it all depends on one's goal. I can imagine at least two distinct goals: 
reproduce the tables in the Nautical Almanac as exactly as possible (either 
by formula or by incorporating those tables directly), or produce the best 
possible refraction tables even if they do not agree 100% with those tables.

Also, I wouldn't worry about humidity. Humidity has two distinct impacts on 
refraction. Its direct impact, changing the index of refraction of the air, 
is very small and can probably be ignored. Its indirect effect is to change 
the rate at which convective air cools as it rises (dry air cools more 
rapidly than moist air --look up 'adiabatic lapse rate' if you're interested 
in the details) which changes the rate of change of air density with height. 
This only matters for observed altitudes below about 3 degrees, and you could 
just as easily treat lapse rate as a variable which covers more cases.

When you look at the paper by Auer and Standish, bear in mind that this is 
really an article about a technique for performing a numerical integration. 
Their specific density model which they use in a demo of their integration is 
non-physical, and you can safely ignore it. 

Finally, to put some sense of scale on refraction calculations, you may want 
to consider the change in the index of refraction between the blue end and 
the red end of the visible spectrum. This is directly responsible for turning 
very low altitude stars into little stripes that look rather like French 
flags. If the star itself is stretched, measuring its altitude becomes a 
rather ill-defined procedure.

-FER



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