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Marcel Tschudin provided a thoughtful posting, but I am going to argue back
about some of his comments.

But not about this one, in response to my statement-

| >  Half of Schaefer's events we are considering were sunrises, so
presumably
| >  were in the early morning, and all were close to shore, in that

to which Marcel replied

| Liller's observations at Vina del Mar and Schaefer's observation at
| Cerro Tololo were made at sunset (around 22h/23h UT). As far I
| remember from looking up these places in Google Earth they wouldn't
| have been able to observe sunrises over the sea from their locations.
| In addition to sunsets Schaefer mentions a few set events of Moon and
| Venus.

Yes, Marcel is correct, and I was quite wrong. They were indeed all sunsets.

I had written-

| >  ... I suggest that Greg Rudzinski missed the important difference
| >  between refraction at and near the horizon, and that at much higher
angles,
| >  when he wrote, in Navlist 4649- .
| >
| >  " I base my 6 minutes of arc figure on the refration variables as
| >  seen in the A4 table of the Nautical Almanac. The temperature and
| >  pressure extremes are -7.3' to +6.9' from the mean."
| >
|
| I think that's not really Greg's fault. It's the fault that over
| several decades refraction tables have been published providing
| refraction values for large zenith distances which are (only) based on
| the standard atmosphere.

Yes, that's true. The Nautical Almanac (my 2005 edition) doesn't provide an
adequate warning. To quote (page 259) "An additional correction, given on
page 4, is required for the change in the refraction due to variations of
pressure and temperature from  the adopted standard conditions; it may
generally be ignored for altitudes greaterbthan 10 degrees, except in exreme
conditions." and under "Accuracy", (page 261) is added- "But the actual
values of the dip and of the refraction at low altitudes may, in extreme
atmospheric conditions, differ considerably from the mean values used in
these tables."

Certainly, the Almanac leaves the impression that as long as such conditions
are not "extreme", and the corrections for local temperature/pressure have
been made, the standard of accuracy will be maintaned. We can see from
Schaefer that for light AT the horizon, the refraction can vary very
significantly from the book value, much more frequently that could be
attributable to "extreme atmospheric conditions". I do not blame Greg
Rudzinski for taking the information in the Almanac at face value, but all
of us would do better to take it with a large pinch of salt, where
horizontal and near-horizontal light is concerned.

==========================
|
| George wrote:
| >  Yes, Greg can correct that 34 arc-minute figure for local air density
if he
| >  wishes, but that is no more than a tiny fraction of the overall
fluctuation
| >  in refraction at the horizon.
|
| This really depends on the height and latitude of the observer. Most
| of my observations are done at about 3 to 4m height and at about 40N.
| The height is probably not much different to navigational
| observations.

I fail to see how the observer's height comes into the question. I will
consider that matter later in discussing the observing locations.

|The above mentioned 34 arc minutes are only marginally
| larger than the sun's diameter. The duration of the sunset, i.e. the
| time between the lower and the upper limbs touch the horizon is here a
| bit less than 3 minutes.

Where is "here"? Presumably, that time interval varies somewhat with the
season.

Delayed sunsets by half a minute, a full
| minute or so are quite common; larger delays are rather rare. These
| observations don't confirm your above comment related to the 34 arc
| min "...but that is no more than a tiny fraction". Things start to be
| different when observing from higher up.

What I was trying to say (but failed to express my meaning clearly enough)
was not that the 34 arc-minutes was a tiny fraction of the overall
fluctuation in refraction at the horizon, but that Greg's proposed
correction for local air density was no more than a tiny fraction of it.
Having made that clear, does there then remain a large discrepancy between
Schaefer's findings and Marcel's observations?

=======================

| George wrote:
| >
| >  I ask on what evidence Frank bases his assertion that-
| >
| >  | "under
| >  | certain very common circumstances, e.g. at sea in temperate climates,
the
| >  | day-to-day variability in the refraction at the horizon is relatively
| >  small
| >  | (a few minutes of arc), "
| >
| >  And even if that assertion is valid, how on Earth does a navigator
know,
| >  when trying to use a sunset time to ascertain his position, whether
Frank's
| >  restrictions apply or not, within the "variation within the
variability"
| >  that he conjures up?
|
| My suggestion would be that one measures the temperature of the water
| and of the air. If this temperature difference is "considerable",
| extreme refractions may be likely. Unfortunately I'm not in a position
| to quantify the "considerable". From my own experience at my present
| location these effects are more likely during spring and autumn. 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. In autumn
| the sea is still warm from summer and the air already cold; this leads
| to "Omega" sunsets or inferior mirages.

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
Marcel could predict whether a particular temperature difference at the
surface would increase, or decrease, that 34-minute refraction, that might
be of value. But otherwise, I don't see how a mariner could use the
statements he makes.

========================
|
| George wrote:
| >   If we are talking about use of timing a sunset for real navigation,
| >  requirements for position knowledge can be very relaxed in mid ocean.
It is
| >  only when a land mass is being approached that navigation becomes
critical.
| >  So observations made at coastal sites, with a view over the ocean, will
be
| >  particularly relevant in assessing the navigator's problem. And those
are
| >  exactly the sites from which Schaefer and Liller have timed sunsets, at
sea,
| >  in temperate climes.
|
| Cerro Tololo is not what I would call a coastal site; it's about 70km
| from the coast.
|
| Side note: Looking at temperature profiles derived statistically from
| a lot of sounding profiles in this area suggest that the sunset
| observations over the Pacific from Vina del Mar and Cerro Tololo tend
| to have inversions (water of the Pacific colder than the air) and thus
| may be prone to delayed sunsets by ducting.

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.

| ... Its these
| differences which are responsible for the refraction differences
| between sunrise and sunset.

I agree that one might well expect there to be significant differences
between refraction at sunrise and sunset. Has any information on that
subject been published? The Almanac is silent about it. Schaefer includes
one set of sunrise/sunset observations, made by a US Naval Observatory team,
with Seidelmann, who were at the time studying, not refraction, but
irradiation, for the Almanac.

They observed two successive sunrises and sunsets from the outer banks from
North Carolina; the sunsets looking westwards from Kitty Hawk, the sunrises
from Nag's head, which is presumably somewhere close by on the ocean-facing
shore. Several  altitudes of both limbs were observed with respect to the
horizon, close to (but not at) the moments of rise and set, measured from
land by a sextant on a stand. Significant differences between the rising and
setting refractions, of the order of 6 arc-minutes, were noted. In that
case, however, there were significant differences between the two
environments, the sunsets being seen across the sheltered waters of
Albemarle Sound, the sunrises out to the ocean.

What was particularly interesting was the short-term scatter, from minute to
minute, in the measured altitudes of the limbs of the low Sun, which
presumably indicated turbulence in the atmosphere.

These are observations that could be repeated by small-boat sailors in the
right conditions, from well off-shore, in which case the local environment
would be the same at rising and setting. Navlist members could contribute to
the body of knowledge, quite simply.

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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