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    Re: formula for refraction
    From: Marcel Tschudin
    Date: 2007 May 3, 13:53 +0300

    On 5/2/07, dw  wrote:
    > The following short FORTRAN program reproduces the critical table for
    > refraction from the NA.  It is NOT based on fitted equations.  It uses
    > the canonical multilayer-ray-following method of Biot-Auber-Standish
    > (Astronomical Journal,119,2472-2474,2000 May).  It calls the slREFRO
    > program of Wallace based on the work of Hohenkerk (HMNAO. Sept 1984).
    > http://stsdas.stsci.edu/cgi-bin/gethelp.cgi?refro.hlp
    > You can change pressue, temp, humidity, etc to generate your own
    > table.
    > .....
    It should be noted that this program calculates the refraction
    integral exact; however, this doesn't mean that the results would be
    more exact than what one can read out of published tables. The
    limitation is the simple atmospheric model used in these calculations
    which corresponds to the standard atmosphere, i.e. a temperature
    gradient of -6.5K/km in the troposphere (0km to 11km height) and 0K/km
    between in the stratosphere (11km to 80km height). In order to improve
    the accuracy of the calculated refractions near the horizon one would
    have to adjust the atmospheric model to one which represents it more
    realistic at the time of observation. Such a realistic model will most
    likely have more than just the two layers  for the troposphere and the
    stratosphere. This means that those programs would have to be
    completely re-adapted. The mentioned papers are very helpful for
    understanding the procedures and for writing your own program. If I
    remember right, I still should have these papers as pdf-files
    somewhere on my computer. I can send them e.g. by email to those who
    are interest in them.
    Conclusion: Whether one uses refraction values from tables or from
    programs like the one mentioned above, the limitation remains the
    underlying atmospheric model. The standard model used is a sort of
    average for mid-latitude, mid-season and mid-day. It is for this
    reason that the limitations which Frank mentioned already in an
    earlier posting, i.e. that refraction values near the horizon (below
    e.g. 5 deg altitude) should not be used, is also true in the case of
    calculating the refraction value "precise".
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