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    Re: Astronomical Refraction: Computational Method for All Zenith Angles
    From: Marcel Tschudin
    Date: 2005 Aug 20, 04:05 +0300

    Frank, just before closing down here (it's already 4am):
    you wrote
    > Oh, by the way, I'm Frank, not Fred. There's a Fred on the list,  too.
    Sorry, Frank; I really hope that this type of mistake, does not happen
    > In another message you wrote:
    > " I only realised then,
    > that the  integration needs also to be splited into two parts, one for the
    > troposphere  and one for the stratosphere. "
    > I don't think the integration itself  needs to be split unless there's a
    > problem with the model atmosphere. The model  atmosphere in the
    > Auer-Standish
    > article does have two pieces though: polytropic  in the troposphere and
    > exponential in the stratosphere and above (structure  in levels of the
    > atmosphere above
    > the stratosphere are not relevant to  astronomical refraction unless the
    > observer is in those levels).
    My above remark refered to the following paragraph in the paper from Auer
    and Standish:
    In the case of a piecewise atmosphere, the integrand of equation (3) is not,
    in general, a continuous function across the boundaries of each region. It
    is therefore necessary to integrate each region separately and then sum the
    parts. The limits on the integrals are then the corresponding values of psi
    at each boundary. These may be found directly by solving equation (2) as a
    function of r.
    Does this not apply for the transition from troposphere to stratosphere? Or,
    could it be that my mind was to much focused on temperature?
    Refering the proposed model and the denisity data:
    Thank you for sending it. I will have a closer look at it later on today,
    hopefully then with a fresher mind.
    Good night for now.

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