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    Re: Refraction at the horizon. was: Re: Celestial Navigation without a sextant.
    From: Marcel Tschudin
    Date: 2008 Mar 14, 22:23 +0200

    Here some further comments to George's reply:
    
    >  | 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.
    
    As higher the observer as larger becomes the zenith distance to the
    apparent horizon and as consequence also larger refractions. An
    increased mass of air below the observer increases also the variation
    in refraction. What I wanted to indicate is that near sea level
    refraction at the horizon and the scatter of such data are less than
    somewhere high up.
    
    >
    >
    >  |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.
    
    As mentioned above, "here" means a latitude of about 40 deg North. The
    angle between a vertical line and the trajectory line of the setting
    sun corresponds quite well to the latitude of the observer. At the
    equator the sun sets along the vertical line and at the poles the sun
    turns along an almost horizontal line. At a given latitude the time
    difference between lower and the upper limbs touch the horizon is
    fairly constant.
    
    >  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?
    
    There are differences between our observations:
    1) the hight(!) Terro Cololo 2215m, Vina del Mar 120m and mine at 3 to 4m
    2) the body of water over which the sunsets are observed: at the east
    coast of Chile they observed over the cold Pacific and I observe at my
    present domicile over a sea corresponding rather to a big lake, the
    Marmara sea, which - at least in summer - is very likely warmer than
    the Pacific. These differences are also visible in statistically
    derived typical monthly temperature profiles taken from a large number
    of balloon soundings at "representative" coastal locations.
    
    >
    >  =======================
    >
    >
    >  | 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.
    
    I agree that my suggestion is very likely not applicable. I guess the
    temperature measurements would have to be done to a quite high
    accuracy.
    
    >
    >  ========================
    >
    > |
    >  | 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.
    
    George answers:
    >  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.
    
    My answer to George's thoughts is: may be.
    First: "coastal" means for me in this context where the diurnal
    temperature range (DTR) is between the low value at sea and the high
    value at continental locations. Looking at a lot of such data indicate
    that locations being about 10km from the coast tend to have already
    continental DTR values.
    Second: Your thoughts are probably correct for an observer directly at
    the coast. The influence on refraction of the sea-coast-transition
    (different height of atmospheric boundary layers and different diurnal
    temperature cycles) seems to be minimal. However, from my own
    observations the sea-coast-transition seems in certain cases to play
    an important role. In particular I do not know what effect it has for
    an observer being 70 km behind such a transition. Things may again
    look different for an observer at an altitude above 2000m.
    
    >
    >  | ... 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.
    
    I don't know, I didn't do a literature search on it. The graph which
    Victor Reijs presents on his Web-page here
    http://www.iol.ie/~geniet/eng/refract.htm
    shows these differences nicely.
    
    For those who are more interested in this:
    
    (1) the following Web-page contains some interesting information on
    the boundary layer and the diurnal changes of lapse rates in it:
    http://www.windwisdom.net/
    
    (2) A. Lapworth, The Morning Transition of The Nocturnal Boundary
    Layer, Boundary-Layer Meteorology (2006) 119: 501-526
    Lapworth describes the results of a field study performed at Cardington, UK.
    
    Marcel
    
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