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    Re: Refraction at the horizon
    From: Frank Reed
    Date: 2008 Mar 15, 23:42 -0400

    Andres, you posted an image of the atmospheric temperature profile and
    "Temperature stratify the atmosphere in layers of different density, this
    acts diverting the beam of light from celestial bodies."
    It's worth noting that most of the structure that you see in these diagrams
    is actually irrelevant to refraction at ground level, at least at the levels
    of accuracy we deal with in navigation. You can completely ignore the
    temperature above the tropopause --setting the rate of temperature change to
    zero up above that-- and you'll get excellent results.
    You wrote:
    "An approximation to this fact is the well known formula for refraction:
    Ro = 0.0167 / (tan (H + 7.31) / (H + 4.4) )
    But for low angles is more complicated and under abnormal situations
    The formula you quote is nothing more than a "fit" to the standard
    refraction table. There's no reason to prefer the formula except on a device
    with very low available memory, like an old handheld calculator. The
    standard refraction table itself is produced by a numerical integration from
    a specific temperature profile for the atmosphere. We can easily vary the
    profiles and generate as many tables as we desire. This is primarily useful
    for determining the limits on the integration for the standard atmospheric
    model. What you find is that the standard table can be trusted safely above
    three degrees, approximately. You also can figure out the sorts of
    variability that occur at lower altitudes. Now, if you WANT, you can then
    modify the parameters in the refraction formula above to fit the newly
    generated tables. But in today's world of ultra-cheap memory, you might as
    just put the tables directly into whatever application you have in mind (you
    could also run the integration every time, but that would still consume
    noticeable time even on today's fast processors).
    And you concluded:
    "Also the meteorological phenomenon can disturb the standard refraction."
    Yes, anything that varies the density of the air modifies the refraction.
    Primarily, this is the temperature structure of the lower atmosphere
    (temperature inversions, etc.). There are also small effects from humidity.
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