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Andres, you posted an image of the atmospheric temperature profile and
wrote:
"Temperature stratify the atmosphere in layers of different density, this
acts diverting the beam of light from celestial bodies."

It's worth noting that most of the structure that you see in these diagrams
is actually irrelevant to refraction at ground level, at least at the levels
of accuracy we deal with in navigation. You can completely ignore the
temperature above the tropopause --setting the rate of temperature change to
zero up above that-- and you'll get excellent results.


You wrote:
"An approximation to this fact is the well known formula for refraction:
Ro = 0.0167 / (tan (H + 7.31) / (H + 4.4) )
[...]
But for low angles is more complicated and under abnormal situations
unpredictable."

The formula you quote is nothing more than a "fit" to the standard
refraction table. There's no reason to prefer the formula except on a device
with very low available memory, like an old handheld calculator. The
standard refraction table itself is produced by a numerical integration from
a specific temperature profile for the atmosphere. We can easily vary the
profiles and generate as many tables as we desire. This is primarily useful
for determining the limits on the integration for the standard atmospheric
model. What you find is that the standard table can be trusted safely above
three degrees, approximately. You also can figure out the sorts of
variability that occur at lower altitudes. Now, if you WANT, you can then
modify the parameters in the refraction formula above to fit the newly
generated tables. But in today's world of ultra-cheap memory, you might as
just put the tables directly into whatever application you have in mind (you
could also run the integration every time, but that would still consume
noticeable time even on today's fast processors).

And you concluded:
"Also the meteorological phenomenon can disturb the standard refraction."

Yes, anything that varies the density of the air modifies the refraction.
Primarily, this is the temperature structure of the lower atmosphere
(temperature inversions, etc.). There are also small effects from humidity.

 -FER



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