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    Re: Refraction at the horizon.
    From: George Huxtable
    Date: 2008 Mar 15, 17:01 -0000

    Marcel Tschudin made-
    | An additional comment regarding the sunset observations made by
    | Schaefer and Liller:
    | Unfortunately they don't mention in their paper the meteorological
    | conditions (temperature, pressure) at the time of the observations.
    | The variations of the published refraction values contain therefore
    | also the variations in meteorological conditions.
    That information has no relevance to a study of refraction which is based on
    the timing of sunsets. If refraction had been measured as a deflection from
    the true horizontal, with a theodolite, then local atmospheric conditions
    would have mattered. But it wasn't, so they didn't. The only atmospheric
    conditions that were relevant , to Cerro Tololo sunset times, were those
    that existed more than 50 miles out into the Pacific Ocean. Unless I've
    completely misunderstood something.
    I ask Marcel to re-read what I wrote in a previous mailing, as follows-
    "It worried me, initially, that these observations were being made from such
    great heights, so far from the ocean. Cerro Tololo observatory is quoted as
    being at 2215 metres, which is why the Pacific can be seen from such a great
    distance. Its horizon is about 100 miles away, or about 50 miles out from
    the coast, into the Pacific.
    But on second thoughts, does that matter a jot?. No, it isn't a coastal
    site, it's an ocean site, as far as sunset timings are concerned. Those are
    only affected by what's going on in the atmosphere, further out than that
    distant horizon. Atmospheric effects, between that horizon point and the
    observation point, have no effect at all, inversions or not, because they
    bend light from the Sun upper-limb and light from the horizon in EXACTLY the
    same way. If I've got that right, the only relevant temperature profiles
    would be those taken from 50 to say 150 miles out to sea. If Marcel knows of
    such information, it could be of interest."
    In an earlier posting, Navlist 4684, Marcel wrote-
    I missed to reply on one important item:
    George wrote:
    >  refraction depends on temperature gradients at FAR greater heights.[than
    > the observer near sea level]
    The word far (even written in upper case) may lead here to a
    misunderstanding. The air layers near the observer (below his eyes and
    above them) contribute most to the total refraction. Air layers high
    above him contribute only an epsilon to the total. In case of
    inversions, only those in layers close to the observer may cause
    ducting (infinite refraction); an inversion at a layer having a great
    distance (in height) to the observer can't produce ducting because the
    angle of incidence is too large.
    Both Marcel and I are guilty, to some extent, of using imprecise speech, in
    using words such as near and far, without making it clear what actual range
    of heights in the atmosphere we are talking about. (In my case, that
    covers-up, in part, my unfamiliarity with this topic of atmospherics.)
    I will do my best to explain how I see it.
    We were discussing surface effects, and Marcel was recommending the
    measuring of sea/air temperature differences, writing-
    | In
    | spring the water is still cold from winter and the air may already be
    | warm; this leads at the surface to inversions with ducting...
    And I had replied-
    "Well, measuring the temperature of the surface seawater (by dipping a
    bucket) and seeing how it differed from air temperature above it was once a
    recommended way of assessing what the horizon dip would be, because dip was
    so dependent on temperature gradients just above the surface. But it was
    found to have little predictive value, and was abandoned. Horizontal
    refraction depends on temperature gradients at FAR greater heights.""
    If we go to a dip table, that gives the total correction, geometrical +
    mean-refraction, for for different heights of eye. Mean refraction is about
    one-twelfth of that total. So for 3 metres height, mean refraction is about
    0.25', for 48m., it's about 1'. That's the same as the mean refraction of
    horizontal light, which is travelling from that height to reach the surface.
    Only a small fraction, you will notice, of total mean refraction, all the
    way in from outer space, which sums up to about 34'.
    I find it hard to reconcile that with Marcel's claim that "The air layers
    near the observer (below his eyes and above them) contribute most to the
    total refraction." It's clear that his notion of "near the observer" differs
    from mine. Yes, of course, it's true, if by "near ...above them" he includes
    several kilometres of the atmosphere.
    I suggest, then, that in the context, it's Marcel's words rather than mine
    that are likely to lead to misunderstanding.
    So far, I've been referring to MEAN refraction, its average value, whereas
    our previous discussions have centred on its fluctuations. It's probably
    true to say that most of the fluctuation in the horizontal refraction occurs
    in the lowest kilometre or so of the atmosphere. I base that on Schaefer's
    statement, on the temperature profiles he studied, that "all of the
    temperature profiles had steadied down before the altitude had reached 2000
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Navigation List archive: www.fer3.com/arc
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