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    Re: Refraction
    From: Clive Sutherland
    Date: 2005 Aug 9, 00:09 +0100
    The original message you have quoted below contains an error for which I apologise.
    I should have said that the first formula given as Ref =... is for use with Standard Temperatures and Pressures, the values of which are quoted in the Nautical Almanac as '10 deg C ' and '1010mbs.' These are clearly at sea level.
    Where  any Abnormal atmospheric conditions are suspected by the observer,   Abn = ...  should be used.  i.e. it is intended to correct for temperatures and pressures different from the above.
    The 'Abn' formula is quoted by GGBennet as correct within 0.2 min between -20 < Air Temp < +40, and  970 <air pressure mbs < 1050.
    I have now retrieved the reference above  The full title  is ''The Calculation of astronomical Refraction in Marine Navigation. G.G.Bennet.  J.Inst.Nav.(35,255).May 1982.'
    However I do not know the complete source of the correction formula, It may originate with Bennet. But I am of the opinion that both formulae are applicable only when the observer is close to sea level.
    The following references may also be of use to you, although they are not explicitly for negative observed altitudes or for large observatory elevations.
    1. 'THE COMPUTATION OF ANGULAR ATMOSPHERIC REFRACTION AT LARGE ZENITH ANGLES'.  by C.Y.Hohenkirk and A.T.Sinclair. H.M.Nautical Almanac Office Technical Note No 63.Apr 1985.
    2. 'ASTRONOMICAL REFRACTION'. by M.E.Thomas and R.I.Joseph. John Hopkins APL Technical Digest. Vol 17 No 3.(1996). This is quite good for Sunset observations as also is 
    3. REFRACTION NEAR THE HORIZON'. by B.E.Schaefer and W Liller. Pub in 'The Astronomical Society of the Pacific'  102. 796-805, July 1990.
    If I can help more directly my email is  clive@jcsutherland.wanadoo.co.uk
    ----- Original Message -----
    Sent: Monday, August 08, 2005 6:28 PM
    Subject: Re: Refraction

    Clive wrote
    The following  is one I use,
    Ref = Tan  (90-Altitude - 0.999139 * Altitude - (7.31 / (Altitude + 4.4)))
    between -20 < Air Temp < +40, and  970 <air pressure mbs < 1050
    or else use the correction below for abnormal temperature and Pressure
    Abn = (( Baro Pressure - 80 ) / 930) * (1 / ( 1 + 0.00008 * (Refraction + 39) * (Temperature - 10))), 
    using mbs,deg celsius and deg Altitude.
    Refraction = Ref  * Abn and  True Altitude  = Observed Altitude - Refraction
    Does anyone of you know where this correction for abnormal condition comes from?
    What is actually ment with "abnormal"? As an example, the standard atmosphere also has temperatures below -20°C and air pressures below 970 mBar above a certain height, but this I would consider rather "normal". Could it be that the abnormal conditions refer to sea level conditions?
    Thanks Marcel
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