NavList:

Brian Villmoare you wrote:  Formulas for calculating the effects of refraction on the angle of observation often include temperature and air pressure. For aeronautical celestial navitation, is there a formula that directly employs altitude? 

Brian.
There undoubtedly is one hidden somewhere inside and used by the various official national observatories, but you might have difficulty finding it.  Celestial air navigation tended to favour speed and practicality in completion over decimal place accuracy especially as aircraft sextants were only accurate to one minute of arc at their very best (often closer to 3’).  Therefore, you’re more likely to find ready use tables in your air almanac such as the one on Page A167 (908) of the 2025 Air Almanac link https://aa.usno.navy.mil/publications/aira .  This page is explained in the instructions at pages A15/756 and A16/757, but they're careful not to reveal the formula they use (or used, the same table has been around for decades).  You’ll note that the table starts to get tricky at very low height sextants, which is why air navigators got a slap on the wrist if they didn’t select stars with a decent altitude.  Obviously, if you only had the Sun, Moon, or Venus available, some very low Hs sights were sometimes necessary.  DaveP