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    Re: U.S. Standard Atmosphere Supplements
    From: Frank Reed CT
    Date: 2005 Aug 27, 00:34 EDT

    Marcel, you wrote:
    "The U.S. Standard  Atmosphere Supplements, 1966 (possibly also in a newer
    edition) includes  tables of temperature, pressure, density etc. for five
    northern latitudes  (15, 30, 45, 60, 75), for summer (July?) and winter
    (January?) conditions as  a function of height."
    I think you'll find that the US Standard  Atmosphere is mostly relevant to
    very high altitude issues like  supersonic/hypersonic flight and spacecraft
    re-entries (and in fact if you  search for this title on google image search
    you'll discover photos of its cover  art which shows a satellite orbiting the
    Earth). For refraction near the  horizon, you need details on the lower troposphere
    which is really a weather  issue. And as such you can find data on it from
    weather resources. Today, I did  a sample calculation based on today's and
    yesterday's weather balloon data from  Chatham, Massachusetts USA. You can access
    plots of this data here:  http://weather.unisys.com/upper_air/skew/.
    I converted these data into  lapse rate models as follows:
    Mean Lrate on both days: -6.0 deg C per km from  0 to 13km, 0 above that.
    For August 26:
    Lapse Rate,  Upper Limit  (m)
    0, 200
    -6.5, 2050
    -2.6, 4375
    -6.7, 6625
    -8, 11000
    -5,  13000
    0, >13000
    For August 27:
    Lapse Rate,  Upper Limit  (m)
    25, 200
    -6.5, 2050
    -5.3, 5100
    -8, 8450
    -7.4, 10750
    -4.9,  13000
    0, >13000
    Next taking the profiles, I can generate the  atmospheric density as a
    function of altitude and from that the refraction  table. As usual, all of this
    structure has no impact above about 3 degrees of  altitude. Below 3 degrees
    altitude, there are significant differences in  refraction as follows:
    Alt(deg), mean ref, ref on 8/26, ref on  8/27:
    0,  35.02, 42.23, 36.32
    0.5, 29.07, 30.57, 29.43
    1, 24.57,  25.08, 24.74
    1.5, 21.11, 21.33, 21.2
    2, 18.39, 18.49, 18.44
    2.5, 16.21,  16.27, 16.24
    3, 14.44, 14.47, 14.46
    3.5, 12.99, 13.01, 13.00
    4, 11.77,  11.79, 11.78
    4.5, 10.75, 10.76, 10.75
    5, 9.88, 9.88, 9.88
    The "mean  ref" column is the refraction in minutes of arc calculated from a
    simple  constant lapse rate of -6.0 degrees from sea level up to 13km. The
    other columns  are the calculated refraction in minutes of arc for yesterday and
    today based on  the lapse rate profiles described above. At the time of the
    balloon flights (0h  GMT), these refraction tables very likely would have
    corresponded closely to  actual observations. But the real point is simply to
    demonstrate the sort of  daily variability that we should expect and to indicate
    where this variability  arises and the fact that we can calculate it if desired.
    Atmospheric refraction  is no mystery, but the atmosphere is a messy place,
    even on a sunny  day.
    42.0N 87.7W, or 41.4N  72.1W.

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