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    Re: Refraction at the horizon.
    From: George Huxtable
    Date: 2008 Mar 20, 10:02 -0000

    This is getting a bit off the topic of navigation. But it's giving Marcel
    and me a bit of fun, so I hope we'll be given some latitude.
    I had written, in an effort to help Marcel uncover the curious behaviour of
    his refraction simulation-
    | ... It's going to be hard to explain the
    | very different amount of refraction change in response to a 10% increase
    | absolute temperature, and to a 10% reduction in pressure, either of which
    | should have exactly the same effect on air density.
    which was OK, I think. But continued-
    | ...If you made both those
    | changes together, the air density should remain constant, and so the
    | refraction should be unchanged.
    What I should have said, of course, was to make those changes in opposing
    directions (10% increased temperature with 10% increased pressure, say) to
    keep the density constant. It seems that Marcel understood my meaning.
    Anyway, to continue, setting that glitch aside-
    Somewhat naively, I had presumed that if you increased the absolute
    temperature by 10% at all heights, and increased the pressure by 10% at all
    heights, then the air density would be unchanged everywhere, so the
    refraction path of light would be quite unaltered.
    If you could, then it would. Trouble is, on second thoughts, I think I have
    naively proposed a physical impossibility.
    Yes, you can freely specify a temperature distribution in an air column, and
    you can specify a pressure at a particular height, but you are then bound by
    the laws of hydrostatics, which define the pressures at other heights.
    If we took two air columns A and B, each with constant air temperature, in
    which the temperature in B was 10% greater, and the air pressure at ground
    level was also 10% greater, then the air densities at ground level would
    match exactly. And then, if you looked a bit higher up the column (a metre
    up, say) both pressures would be correspondingly reduced, and by exactly the
    same amount, because the pressure gradient depends only on the density, the
    same in both cases. But this is the same pressure difference numerically, in
    amount, between those heights, so not the same as a percentage change.
    Because the ground-level pressure at B was 10% greater, that pressure change
    at B is a smaller percentage, than the corresponding pressure change in A.
    What I am saying, then, is at other heights than the one where pressure in B
    was specified to be 10% greater, the pressure ratio must inevitably diverge
    from that 10% difference, and so the air densities can not remain the same
    everywhere, for A and B.. Therefore, the refracted light paths must
    inevitably differ somewhat between the two cases.
    I should add that it seems Marcel has understood all this (when I didn't),
    writing in [4733]-
    "For clarification I should have added here also that the 10% changes of
    temperature and pressure were made at the observer; the rest of the
    atmospheric model was adjusted according the given lapse rate profile (and
    layer heights)."
    Nevertheless, there remains much explaining to do, about the very different
    senstivity Marcel's model shows, to pressure changes and to temperature
    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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