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>
>  Marcel Tschudin made-
>
>  | An additional comment regarding the sunset observations made by
>  | Schaefer and Liller:
>  |
>  | Unfortunately they don't mention in their paper the meteorological
>  | conditions (temperature, pressure) at the time of the observations.
>  | The variations of the published refraction values contain therefore
>  | also the variations in meteorological conditions.

George's comment:
>  That information has no relevance to a study of refraction which is based on
>  the timing of sunsets. ....

I agree, but what I mentioned above are the VARIATIONS of observed
refractions. Normalising the measured refractions to one set of
temperature and pressure would allow to look at the variations of
observed refractions without the influence of different climatic
conditions; it also would allow to see how well one of those different
functions used for calculating refraction could predict these
observations. I needed this information to scale the atmospheric model
for calculating these cases.

George continues:
>  I ask Marcel to re-read what I wrote in a previous mailing, as follows-
>
>  "It worried me, initially, that these observations were being made from such
>  great heights, so far from the ocean. Cerro Tololo observatory is quoted as
>  being at 2215 metres, which is why the Pacific can be seen from such a great
>  distance. Its horizon is about 100 miles away, or about 50 miles out from
>  the coast, into the Pacific.
>
>  But on second thoughts, does that matter a jot?. No, it isn't a coastal
>  site, it's an ocean site, as far as sunset timings are concerned. Those are
>  only affected by what's going on in the atmosphere, further out than that
>  distant horizon. Atmospheric effects, between that horizon point and the
>  observation point, have no effect at all, inversions or not, because they
>  bend light from the Sun upper-limb and light from the horizon in EXACTLY the
>  same way. If I've got that right, the only relevant temperature profiles
>  would be those taken from 50 to say 150 miles out to sea. If Marcel knows of
>  such information, it could be of interest."

I already made a reply to this in NavList 4663. Let me add the following:
The practical problem is very likely that you don't have the
atmospheric data from 50 to 150 miles out of to sea.
When calculating refraction numerically one deals "generally" with an
atmospheric model assuming that the atmosphere is horizontally
homogeneous, i.e. an air layer at a certain height has everywhere the
same temperature and pressure independent of the distance from the
observer. If this condition doesn't apply, one may - in case of small
differences - try to use a "mean condition" as you suggested; larger
differences probably require a completely different approach. May be
one could try to split up the refraction calculation in two parts.

George's next comment:
>  In an earlier posting, Navlist 4684, Marcel wrote-
>
>  I missed to reply on one important item:
>
>  George wrote:
>  >  refraction depends on temperature gradients at FAR greater heights.[than
>  > the observer near sea level]
>
>  The word far (even written in upper case) may lead here to a
>  misunderstanding. The air layers near the observer (below his eyes and
>  above them) contribute most to the total refraction. Air layers high
>  above him contribute only an epsilon to the total. In case of
>  inversions, only those in layers close to the observer may cause
>  ducting (infinite refraction); an inversion at a layer having a great
>  distance (in height) to the observer can't produce ducting because the
>  angle of incidence is too large.
>
>  ==============================
>
>  Both Marcel and I are guilty, to some extent, of using imprecise speech, in
>  using words such as near and far, without making it clear what actual range
>  of heights in the atmosphere we are talking about. (In my case, that
>  covers-up, in part, my unfamiliarity with this topic of atmospherics.)
>
>  I will do my best to explain how I see it.
>
>  We were discussing surface effects, and Marcel was recommending the
>  measuring of sea/air temperature differences, writing-
>
>  | In
>  | spring the water is still cold from winter and the air may already be
>  | warm; this leads at the surface to inversions with ducting...
>
>  And I had replied-
>
>  "Well, measuring the temperature of the surface seawater (by dipping a
>  bucket) and seeing how it differed from air temperature above it was once a
>  recommended way of assessing what the horizon dip would be, because dip was
>  so dependent on temperature gradients just above the surface. But it was
>  found to have little predictive value, and was abandoned. Horizontal
>  refraction depends on temperature gradients at FAR greater heights.""
>
>  If we go to a dip table, that gives the total correction, geometrical +
>  mean-refraction, for for different heights of eye. Mean refraction is about
>  one-twelfth of that total. So for 3 metres height, mean refraction is about
>  0.25', for 48m., it's about 1'. That's the same as the mean refraction of
>  horizontal light, which is travelling from that height to reach the surface.
>  Only a small fraction, you will notice, of total mean refraction, all the
>  way in from outer space, which sums up to about 34'.
>
>  I find it hard to reconcile that with Marcel's claim that "The air layers
>  near the observer (below his eyes and above them) contribute most to the
>  total refraction." It's clear that his notion of "near the observer" differs
>  from mine. Yes, of course, it's true, if by "near ...above them" he includes
>  several kilometres of the atmosphere.
>
>  I suggest, then, that in the context, it's Marcel's words rather than mine
>  that are likely to lead to misunderstanding.
>
>  So far, I've been referring to MEAN refraction, its average value, whereas
>  our previous discussions have centred on its fluctuations. It's probably
>  true to say that most of the fluctuation in the horizontal refraction occurs
>  in the lowest kilometre or so of the atmosphere. I base that on Schaefer's
>  statement, on the temperature profiles he studied, that "all of the
>  temperature profiles had steadied down before the altitude had reached 2000
>  metres".

I agree that "far" and "near" don't really have a meaning in the
context we were talking. The same is also true for "most" in my
comment "The air layers near the observer (below his eyes and above
them) contribute most to the total refraction." The models of the
atmosphere may go to heights up to about 80 to 100km. All the
atmosphere above the troposphere (around 10km height) contributes to
the total refraction only with a lot of epsilons; in many cases this
part can completely be omitted. If I remember right when dealing with
normal temperature profiles: the upper part of the troposphere (5 to
10 km) contributed less to the total refraction than the lower part (0
to 5km). That's about all what I remember. It would be interesting to
see once by how much each layer of the model contributes to the total
(something similar to a  probability density function). I might
actually do that once I'm working again with that program; this will
be after my present occupation.

Marcel

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