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    Re: Dip uncertainty
    From: Trevor Kenchington
    Date: 2004 Dec 6, 10:16 -0400

    George wrote:
    > What happens to the light which has passed my head, from the horizon 2.8
    > miles away? It still carries on rising, and may be seen from the bridge of
    > a larger vessel, from 24ft high, which is 5.6 miles from that marker on his
    > horizon (because the horizon distance increases with the square root of
    > eye-height) and 2.8 miles to my South.
    > And what dip affects observations from that vessel? The standard dip, from
    > the almanac, is doubled. The anomalous part of the dip will be, initially,
    > the same as affected me at 2.8 miles, but now the light goes on, still
    > close (from 6 to 24 ft) to the sea surface, so there's extra curvature
    > added as a result of that additional 2.8 miles of its path.
    > What Bruce is arguing, it seems to me, is that in the latter part of its
    > path, that light is  sufficiently far (6 to 24 ft) from the sea-surface,
    > that no anomalies of temperature-gradient will occur to affect the dip.
    > This seems to me an unlikely proposition, but even if it were true, the
    > anomalous dip would be no less than it was for me at 6 ft height-of-eye. So
    > I don't accept his argument that anomalous dip will be more of a problem to
    > smaller vessels; it's the other way about, as I see it.
    The light ray which just misses George's head and extends on to the
    sextant held by a navigator on a ship's bridge behind him will, of
    course, have experienced the same anomalous curvature as the ray which
    enters George's sextant. Their vertical displacements, relative to the
    expectation in the standard dip tables, will be identical up to the
    point that one of them is intercepted by George's sextant. However, if
    further anomalous curvature between George's head and the man behind
    were minimal, the angular anomaly corresponding to that vertical
    displacement would be reduced by the greater distance. In practice, of
    course, the anomaly will not all be within the lowest 6 feet of the
    atmosphere. However, the unknown variations there will typically be
    stronger than those between 50 and 60 feet (a more realistic height of
    eye on the bridge of a modern freighter) and hence there should be a
    tendency towards lesser problems with anomalous dip as height of eye
    I would suggest that Bruce has the correct argument.
    Which raises the issue of why Alex can recall a Russian textbook arguing
    for lower heights of eye to address dip. Could that perhaps be for the
    rather special conditions of Arctic navigation?
    With areas of ice causing differential reflection of solar heating, as
    well as local temperature gradients if the ice moves into warmer water,
    plus the possibility of pockets of cold, fresh melt-water lying beside
    warmer, saltier water of similar density, anomalous dip could become a
    nightmare. Under such circumstances, local measurements of water and air
    temperatures might aid estimation of the actual dip but only in the
    immediate vicinity of the ship. Lowering the height of eye would make
    the measurements more representative of the entire light path to the
    navigator's apparent horizon.
    With anything of a sea running, of course, the uncertainties in the
    horizon and in the true height of eye that are produced by wave action
    are likely to overwhelm anomalies in dip for an observer close to the
    sea surface (except perhaps under the most extreme conditions).
    Trevor Kenchington
    Trevor J. Kenchington PhD                         Gadus@iStar.ca
    Gadus Associates,                                 Office(902) 889-9250
    R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
    Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555
                         Science Serving the Fisheries

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