A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2021 May 21, 19:02 -0700
Well, I'm still not entirely clear what it was that you were asking, Doug, so I'll just continue in two directions. :)
What happens to a reflecting puddle of fluid, an artificial horizon as you climb up a mountain? Nothing at all. It works just the same as it does at sea level, apart from some small changes in fluid properties like Greg Herdt mentioned. Well, up to a point. There is a point where the fluid's properties change quite dramatically, and while this is more likely to occur at high altitude, it can even happen at sea level. Your reflective puddle can turn into an un-reflective, non-leveling rock. It can freeze solid. Your A.H. can be "bricked". Even Mercury horizons freeze up just above -40° F/C (the scales cross at this temp), and that was a real problem for polar expeditions.
And this isn't just "first-order" as John suggested. The vertical is the vertical. There are some very small changes in the deflection of the vertical at extremely high altitudes (local details in the gravitational field average out as you leave the planet), but the oblateness is no more consquential for puddle horizons (artificial horizons) than for a sea horizon or a bubble horizon. Latitude on the Earth defines away that concern.
As for refraction at altitude in the context or early explorers' observations, a lot depended on the purpose of the observations. If you're just shooting Noon Sun for latitude for "navigation" in the sense of getting from one place to another as you explore, then the nearest minute of arc is a reasonable level of accuracy, and you don't need to worry much about refraction changes within the usual ranges of possible altitude changes. But if you're shooting lunars or trying for survey-quality latitudes and other lines of position, then you would be concerned by altitude corrections as small as a few seconds of arc. And explorers often took observations of temperature and pressure in situ along with all their astronomical observations. They recorded everything that they could manage to observe so that they could do as much analysis as possible when they got home.
For a modern observer, as I mentioned in my earlier post, you can just take standard sea level refraction values and divide by two for every 6600 meters of altitude above sea level, or for the lowest altitudes just subtract 1% for every 100 meters above sea level (same thing). OR if you have proper temperature and barometric data (which has not been adjusted to sea level, as is normal with meteorological data), then you can apply that as normal with no explicit height correction. Either approach works.