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Bill Noyce wrote-

| I think the refraction between the observer and his horizon *does*
| make a bit of difference in how sunsets are timed.  Specifically, it
| affects how distant that horizon actually is, and therefore affects
| the direction of the light-ray that just grazes the ocean surface.
| How big is this effect?

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Response from George.

Bill Noyce has put his finger on the weakness in my argument. I had claimed
that measurements of refraction, made by timing sunsets, were immune from
the effects of local refraction between along the path between horizon and
observer, because light-rays from the horizon were refracted over that path
by exactly the same amount as were the corresponding rays from the setting
Sun.

I am sorry that my first response to Bill's posting was somehat dismissive.
Now I have slept on the problem, and given it a rethink, and concluded that
Bill is correct, and my argument was wrong. Refraction over that part of the
light-path shifts the distance to the horizon accordingly, so it has to be
taken fully into account, especially when the observations are made from
high up a mountain.

As far as I can tell, the Schaefer paper corrects the sunset times ONLY for
the geometrical dip, according to the observer's height, and makes no
attempt to correct data for any predicted refraction, between horizon and
observer. That is a reasonable approach, given that details of the
refraction in that part of the path are unknown, and because refraction is
what the paper is trying to assess. But as I now see it, the result of
taking that line is that the difference, between observed and calculated
sunset times, becomes a measure of TOTAL refraction along the whole path,
from the Sun limb to the horizon, then up to the height of the observer.
From up a mountain, it is then likely to be significantly greater that the
horizontal refraction, from space down to the horizon and no further, which
has an average book-value of 34 arc-minutes.

Which would mean that a collection of observations, made from different
heights, would show a scatter in total refraction simply because of that
fact, and it is therefore invalid to analyse that data for scatter as though
all are measurements of the same quantity.

What's more, from high on a mountain, back from the sea (as many of these
observations were) a significant part of the light-path would be over land.
Even though the air density would be lower, one would expect higher
temperature gradients and therefore more fluctuation over that section than
over the part of the path, more relevant to the mariner's interests, that
passes over the ocean.

And indeed, when you look at the scatter-diagram of the 27 computed
refractions from Cerro Tololo, at 2215 metres, the mean refraction comes out
as 41.5 arc-minutes, quite significantly greater than from other
observations from lower levels, which come out close to the book-value of
34' for a standard atmosphere. And that, alone, is enough to account for a
significant part of overall scatter presented in the paper.

Indeed, most of the observations recorded are at two Chilean Pacific sites,
the other being at 120 metres, and showing much less scatter than at Cerro
Tololo. Schaefer says "we can think of no reason that explains why these
virtually identical sites apparently have a different R0 [horizontal
refraction]". Perhaps, after Bill Noyce's help, we are starting to
understand why.

However, two of the observations were from Mauna Kea, Hawaii, at the great
height of 4205 metres, at which height much of the atmosphere has been left
behind. Based on the arguments above, one might expect to see the total
refraction significantly increased, with the extra refraction on the way up
being quite a large fraction of what it was on the way down. However, the
results show total refractions of 16' and 30'. Not good statistics, but
giving no support at all to the notion of a highly augmented total
refraction.

In the case of Mauna Kea, the sea horizon is over 120 miles away, and less
than 30 miles of that path is over land, and that at significantly reduced
pressure. Would sunset times at that location therefore be expected to show
little fluctuation?

I would be pleased if Bill or Marcel were to take a look at these arguments,
and assess whether they think I have it right, now, or not. If so, next step
may be to try them out on Brad Schaefer, to see what he has to say.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


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