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    Re: Refraction and dip
    From: Frank Reed CT
    Date: 2005 Oct 12, 19:18 EDT

    Marcel you wrote:
    "After downloading millions  of balloon data of stations at different
    latitudes, I calculated in a first  test run refraction and dip for latitude
    May I ask, who's your  intended "market" or "user base" for your
    calculations? I know you mentioned at  one point that you were trying to calculate the
    positions of stars etc. as  accurately as possible. If this is strictly for
    astronomical use, an interesting  issue arises. Shouldn't you limit your balloon
    data to days/nights when the sky  was clear or mostly so? It's important because
    certain types of temperature  inversions arise because clouds are forming or
    have formed at the altitude of  the inversion. Also, there are big day/night
    variations which may be much more  important astronomically than some of the
    latitudinal variation which has been  the traditional "averaging" bin for these
    sorts of data.
    " The  results showed that the refraction and the dip vary with the
    seasons and that  the values are generally higher than the published values
    which seem to have  been calculated on the basis of a standard atmosphere.
    The lowest  (unrealistic?) values are those new ones published by USNO. The
    results  showed also that the Bowditch formula for calculating the dip (the
    factor  1.76 in the metric version) should be at 60N during January around
    1.65 and  during July around 1.73 (the other months can be interpolated using
    a cosine  function). This might also be (one of) the reason(s) why Bill
    encounters  these differences with the Chicago buildings or for Asbjorn's
    differences who  is living somewhere around 60N. "
    I don't think very much of it would  come from differences in the *average*
    lapse rate. It's really a very small  difference. You have to be a hundred feet
    above the ground before a 10%  difference in the dip constant yields even a 1
    minute of arc difference in the  calculated dip. That said, we can expect
    very large differences in the dip when  there is a really large variance from the
    standard atmospheric lapse rate (even  at low observer heights above sea
    level). For example, if the atmospheric lapse  rate is -34.1deg Celsius per km (as
    opposed to the average rates of -6.5 for  moist air and -9.75 for dry air),
    there is no refraction at all. That is, a pure  geometric calculation of dip
    will work and the equation sqrt(2*height/R_Earth)  will match observations of
    actual dip. One can go beyond this and calculate dip  as a function of lapse
    rate and temperature (dip DOES depend on temperature but  only weakly).
    By the way, when considering the refraction tables and dip  tables published
    in the Nautical Almanac, it's worth remembering that these are  specifically
    designed to be useful for observers AT SEA. If you look at weather  balloon
    sounding data from places like Bermuda, Jamaica, Pago Pago, etc, the  patterns
    are different from inland sites at similar latitudes. So a direct  comparison
    between the Nautical Almanac tables and your intended use may not  work out very
    "A main problem arose by realising that  the
    lapse rate distributions within a height layer are  distributed
    asymmetrically, meaning that taking the average or the median of  these
    values is not good enough. At the moment I try to derive a  calculation
    procedure in order to find an estimate for the most likely value  (mode) of
    lapse rate within a height layer. "
    Why would you want that  mode value? What I mean is, what purpose would that
    serve (it doesn't  necessarily have to serve any purpose at all --I'm just
    curious to know how you  would use this mode result)?
    42.0N 87.7W, or 41.4N  72.1W.

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