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    Re: Sextant sights over frozen lake
    From: Frank Reed
    Date: 2019 Nov 24, 10:50 -0800

    Jim Rives, you wrote:
    "Refraction corrections in the Almanac are normally sufficient, I presume.  However, during the winter months on the coast of NH the water temp gets down into the high 30's.  In November it is already down to about 45 and often, especially on "warm days" in the 40s and 50s  there seems to be significant refraction.  Isles of Shoals appear to be floating above the horizon.  I would guess that the horizon is not going to be reliable for shooting in those conditions."

    Yes, whenever you see "floating islands", you can expect anomalous dip. This especially occurs when there is a temperature inversion where the surface air is colder than air a few feet above it. You can get similar effects when there is a more rapid than normal decrease in temperature with altitude. There can be even more complicated temperature structures that produce all of the mirage phenomena that we see (including floating islands, and the Fata Morgana, too). There's no reliable way to correct for this. It's worth noting that these phenomena are generally more pronounced close to land. It's not a major problem offshore. Can you see any of these potentially floating islands from your home? Try setting up your smartphone to take a time-lapse (maybe lined up to look through a small spotting scope at the horizon). During the day as onshore/offshore breezes move the atmospheric layers around, you can see significant changes in these mirages.

    You mentioned the "refraction corrections in the almanac". The refraction tables are for astronomical refraction, generally at angles above the horizontal, which is only slightly affected by these anomalous weather conditions. Dip tables have an implicit refraction correction that is not immediately obvious. Without an atmosphere the dip would be about 1.05·sqrt(ht in feet) but mean refraction reduces the leading factor to 0.97. That's what's tabulated. It's the change in temperature with height above the ground that causes these changes since refraction allows light rays to curve and partially cancel out the Earth's curvature. This built-in correction applies only to mean conditions, and you can expect the horizon to move up or down by half a minute of arc in fairly common circumstances and several minutes of arc in unusual weather conditions. This uncertainty in dip is key among the fundamental limits to the accuracy of manual celestial navigation with a common marine sextant. Manual celestial navigation is barely more accurate today than it was 200 years ago because the horizon is not reliable due to this terrestrial refraction.

    Frank Reed

       
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