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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2019 May 27, 11:06 -0700
The refraction is proportional to air density. Air density decreases exponentially with altitude. Multiply the standard refraction by exp(-h/h0) to correct for the decreased atmospheric density at higher altitudes above sea level. The scale height, h0, is around 9km depending on details, equivalent to about 10% decrease in density per kilometer.
I wouldn't say it's merely "academic" for lunars. If the refraction correction at sea level is, let's say 3.0', and if you're 2.5km above sea level, then the refraction is reduced to 2.3' which is a substantial difference for lunars and even worth considering for ordinary altitude sights.
We can take the normal meteoroligical barometric pressure and correct for it with an altitude factor, as above. There's another approach that's actually superior in some ways: skip the altitude factor and get the actual air pressure. The meteorological reporting pressure is usually adjusted for altitude so that sites at different altitudes in a region can make useful comparisons of their individual, altitude-dependent pressures. I normally recommend this approach.
Frank Reed