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Paul showed us here
http://fer3.com/arc/m2.aspx/Dip-Temperature-Gradient-Hirose-may-2013-g24035
how the dip depends on differences in height, temperature and pressure
between observer and horizon.

I finally found some time to go through his contribution in detail and
can only now fully appreciate it. Again, thank you Paul. There is not
much to add except that at the end I would go one step further and
show also his eq. 6 in combination of his eq. 5 which results in the
eq. 7 below which calculates the dip at standard nautical conditions
(10°C, 1010hPa) for a given height of eye, h in m, and a "mean lapse
rate" LR (= - dT/dh) between this height and the horizon (sea level):

dip' = 1.926′ * √[ h * (0.7835 + 6.337 * LR) ]    (eq. 7)

Note that the square root blows up when reaching an inversion of LR =
-0.124 K/m. This is about the value where ducting starts, i.e. where
refraction becomes infinite. For more information on this condition
see here
http://mintaka.sdsu.edu/GF/explain/simulations/ducting/duct_intro.html
It should again be mentioned that eq. 7 was derived using a simplified
1-Layer-Model between observer and horizon levels and assuming
temperature T to be linear dependant on height h. This coarse model
has shown to be quite useful for various applications. However, if one
intends to refine it one has to consider that near the earth's surface
the temperature is only linear dependant on the logarithm of the
height. It would therefore be wrong to use in eq. 7 for the "mean
lapse rate" LR a value calculated from the temperature difference
between sea water and air at height of eye.

Marcel

   

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