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    Re: Refraction at the horizon.
    From: George Huxtable
    Date: 2008 Mar 19, 19:52 -0000

    We have been discussing  "Refraction near the horizon", Publ. astron.
    society of the Pacific, vol 102, pages 796 - 805 (July 1990), by Schaefer
    and Liller. I have now made contact with an author of that paper, Brad
    Schaefer. He acknowledges that the quantity being measured, by the sunset
    timings, is indeed total refraction, in the path from the Sun, then tangent
    to the ocean surface, then up to the observer. So that refraction is greater
    than the horizontal refraction observed at the sea-surface, and if the
    observer is on a mountain, significantly so.
    It then seems wrong, to me, to put together all that data, some from high
    altitudes, and some from near sea level, into a common data set, and analyse
    it for scatter, without attempting some sort of correction for observer's
    altitude. Schaefer defends it in these terms- "The effect is there but small
    and largely swamped by the variations." I do not go along with that, and
    have had a go at extracting better information from his data.
    Schaefer and Liller quote an average horizontal refraction for 144
    observations as 33.1' +/- 9.6', where the quoted error corresponds to 1
    standard deviation, so about two-thirds of observations should lie within
    that range. I have translated their values, given in degrees, to minutes.
    This accords pretty well with Meeus' quoted result from that paper, that
    "the refraction at the horizon fluctuates fluctuates by 0.3 degrees around a
    mean value normally, and in some cases apparently much more".
    What I have done next is to include only those sunset timings that have been
    taken from altitudes of 120m. and below, thus excluding all the
    high-mountain observations. And then, those remaining 83 observations give a
    mean value of horizontal refraction of 31.0' +/- 4.9'. This is a
    considerable reduction in scatter, which I surmise comes about for two
    reasons. First, because there's now much less variation in the additional
    length of light path, after skimming the horizon. And second, because nearly
    all the light path is now over ocean, with little of its length over land,
    with its more turbulent atmosphere.
    There is an additional point to be made, for what it's worth, though I don't
    wish to overstate it. A large part of that scatter is the result of a single
    discordant observation, at 40m. altitude on Hawaii, which produced a
    refraction of 67'. It's a dangerous business excluding data for no other
    reason than that it seems out of line, especially when investigating
    scatter. If we chose to exclude it, then the remaining 82 observations would
    provide a mean refraction of 30.5' +/- 2.9', a big reduction in the scatter.
    Not that I am suggesting we should do that. But it shows what an uncertain
    business it is, trying to estimate scatter. And interestingly enough, it
    corresponds rather well with what Greg Rudzinski wrote, back in [4628], as
    follows- "Perform normal sight reduction and expect 6 minutes of arc
    accuracy under normal weather conditions." (and to which I objected).
    So, in the end, and with Bill Noyce's help, we seem to have got some useful
    information from our scrutiny of that paper, in exposing some serious flaws,
    and in correcting our (well, my) overestimate of refraction errors at the
    horizon, at sea. Where did it all start?  "40South" asked- "Supposing one
    was in a small boat with an accurate timepiece and the necessary tables, how
    accurate could you determine your longitude by observing the rising or
    setting of the sun or any other celestial body? " We seem to have progressed
    well past that point, but thanks to 40South for triggering us off.
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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