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This link might also be useful:
http://mintaka.sdsu.edu/GF/explain/atmos_refr/dip.html

-- Richard Langley

On 2013-02-27, at 8:51 PM, Marcel Tschudin wrote:

> Brad,
> 
> The dip results - in addition to the geometric angle - from the refraction 
of the air between observer and horizon which is governed by the temperature 
gradient above the earth's surface. The problem of estimating the dip 
corresponds therefore to the one of estimating the temperature gradient at 
the location of observation. (If I remember right: The calculator on Andy 
Young's site assumes that you know the temperature gradient or calculates it 
from two temperatures at different heights.) If one would measure the 
temperature distribution of the air layers between eyes and horizon with high 
accuracy one would likely also be able to calculate the dip to similar 
accuracy. For the cases where this is not possible the various authors tried 
to find ways how the temperature gradient and its influence on the dip could 
be estimated.
> 
> In Sunset Science II Andy Young and G. Kattawar show that the dip depends 
almost entirely on the difference in temperature between the observer and the 
tops of the waves. Do you have a possibility to obtain copies of this 
publication from a library? You could now measure the dip and compare it e.g. 
with the one resulting from their paper. 
> 
> Regarding 'k': Calculating the dip does not necessarily require knowing or 
calculating beforehand 'k'. (The simple formula provided in Bowditch (and 
N.A.?) for calculating the dip does not mention it.) This parameter is only a 
different mean for expressing the amount of refraction, or - together with 
the earth's radius of curvature - also a mean for expressing the amount of 
dip.
> 
> Marcel
> 
> 
> 
> On Wed, Feb 27, 2013 at 11:15 PM, Brad Morris  wrote:
> Hi Marcel
> 
> For this location we have several National Data Buoy Center buoys.  These 
report air and water temperatures, with a one hour granularity.
> 
> Example: Right now Buoy 44039 (Long island Sound) shows air 40.6 deg F; 
water 36.5 deg F.  Buoy 44017 (nearby Atlantic Ocean) shows air 45.0 deg F; 
water 41.9 deg F
> 
> How do I calculate 'k' from this data, even for a nominal value?
> 
> I've been all over Andrew Young's site and nothing jumps off the page at me. 
 He does have a calculator for determining the lapse rate, but this assumes 
there is a target (like a light house).  My target is the horizon!
> 
> Best Regards
> Brad
> 
> 
> 
> 
> On Feb 27, 2013 1:40 PM, "Marcel Tschudin"  wrote:
> Hi Brad,
> 
> Please find below some further comments inserted into your last 
contribution. I do not know how much this special aspect of navigation is of 
general interest for the other members of NavList. If this should turn out to 
be a pure dialog then it might be preferable to continue with it off list ... 
until obtaining useful results which then would likely be again of interest 
here.
> 
> Marcel
> 
> There is an additional feature of Orient Point (and Montauk Point).  Horizon 
A is the Long Island Sound and Horizon B is the Atlantic Ocean.  The tide 
plays an important role in the sea surface temperature on the Sound.   Tide 
coming in yields the same temp as the Atlantic.  Tide going out yields warmer 
surface temps for the Sound, due to the E/W alignment of the Sound and the 
choke of flow at the western end.  (Of course, the tide also affects the 
height of eye.)
> 
> I would try to find out whether someone measures systematically the water 
temperature at this location. Such data may eventually be collected by and 
available online from some organisations like meteorology, fishery, 
environmental research etc. This water temperature may eventually differ from 
the Sea Surface Temperature (SST) or the temperature of the upper most 
stratum of the waves. The Sea Surface Temperature, generally the temperature 
without diurnal effects, can be obtained on an analysed basis e.g. here 
http://ourocean.jpl.nasa.gov/ by selecting and clicking at the bottom of this 
page on the button "Go To G1SST". Select in the new window the date (with 
available data) and underneath under "Blended SST" also the option 
"Gap-free". Under the global graph you can narrow done your area of interest 
by setting e.g. North 41.3, South 41.0, West -72.5, East -72.0 and click the 
plot button. The temperature of interest to you would probably be an 
estimated mean value.
>  
> The water temperature delta is particularly pronounced in the summer.  So 
anomalous refraction effects on dip will indeed be noted.
> 
> Spring and autumn are generally the seasons with large temperature 
differences, but may be this is different in your area.
>  
> I have noticed, over the years, your expertise on this topic.
> 
> 
> Not really. So far I only collected a lot of data from which I try now to extract some results. 
>  
>   I am just a novice, so please be gentle!  I have seen
> dip = arccos ( (R/(1-k)) / ( h + R/(1-k)) )  
> where R is the radius of the earth
>            k is the refraction factor (?)
>            h is the height of eye
> But in this equation, we are left to guess at k, nominally assigned a value 
of 0.13.  In doing so, the equation agrees within seconds to the 0.02977 
result.
> 
> 
> Yes, personally I also work with this factor k..
>  
> 
> I guess that I should compute each dip separately.  Is there some table of 
air temp to water temp yielding 'k'?
> 
> 
> All the various authors from Andy Young's bibliography tried to improve 
somehow the estimation of the dip, i.e. of the value for k. Try to obtain 
copies of the English publications.
> 
> I hesitate to construct such a table for myself just yet, as there is no 
surety in my measurements.  I need much more practice at 180 degrees.
> 
> 
> Well, you could gain surety in your measurements. You probably would first 
have to calibrate your Reflecting Circle and would then have to gain practice 
to measure the dip to noticeably better than one min of arc; may be to about 
a quater of it? You then start collecting your measurements and the 
corresponding meteorological data. A few years later, when you arrived at 
several hundred or thousand observations you analyse them. Your result will 
then tell others how, according to your observations, the value for k is best 
estimated. This is a long term project. But may be you are sufficiently 
interested in it to give it a try.
>  
> Regards
> Brad
> 
> On Feb 27, 2013 6:39 AM, "Marcel Tschudin"  wrote:
> >
> > ________________________________
> 
> 
> > Brad, you wrote:
> >>
> >> ________________________________
> >>
> >> I had to begin somewhere! I will try again soon.
> >
> >
> > Congratulation for having given it a try! And yes, please continue! You 
might eventually end up with a valuable data set.
> >
> > The value 0.02977 for calculating the dip may give a wrong impression on 
the attainable accuracy. One can find different values for estimating the 
dip. My guess is that these simplified estimations agree with those observed 
under "any condition" to not better than about +/- 1 to 2 min of arc 
(Std.Dev.). This can possibly be reduced by avoiding recognisable "bad 
conditions" or/and by considering more relevant parameters in the estimation.
> >
> > The dip can indeed vary considerably. This remains mostly unnoticed 
because one generally observes the horizon without an object serving as a 
fixed angle reference. One way to make these variations visible consists in 
observing the horizon from a place (same eye position) where the horizon is 
seen close to a nearby construction feature like a roof or a fence. 
Unfortunately I did not have such a feature for my sunset photos for 
measuring refraction. However, there are numerous photos where the apparent 
sea horizon is in front of some skyline protruding from behind the horizon, 
and at some days the height of the same skyline feature above the sea horizon 
differs by up to about 5 min of arc. Note that the dip depends on temperature 
differences near the earth's surface and that the temperature difference 
between ambient air and sea changes during the day. Ambient air is generally 
coldest at sun rise and warmest during afternoon whereas the sea (surface) 
temperature remains almost constant. 
> >
> > In the context of the analysis of my photos which provide a measurement of 
dip AND refraction (I try to separate the two contributions) I received 
recently from Andrew T. Young from SDSU (known for his Web-pages on 
refraction and in particular on green-flashs) the following extensive 
bibliography on dip (in German: Kimmtiefe) which I think is appropriate to 
mention here:
> >
> > quote
> >
> > Regarding dip: remember that George Kattawar and I found that the dip 
depends almost entirely on the difference in temperature between the observer 
and the tops of the waves:
> >
> > A. T. Young, G. W. Kattawar, Sunset Science.  II. A Useful Diagram, Appl. Opt. 37, 3785-3792 (1998)
> >
> > -- so the details of the temperature profile in between are not 
significant.  But the problem is to determine the effective wave height, 
which sets the level at which the "surface" that forms the apparent horizon 
actually occurs.  See the very useful discussions of these matters by H. C. 
Freiesleben:
> >
> > H. C. Freiesleben, �Die Berechnung der Kimmtiefe,� Deutsche 
Hydrographische Zeitschrift 1, 26�29 (1948). 
> >
> > H. C. Freiesleben, �Geophysikalische Folgerungen aus 
Kimmtiefenbeobachtungen,� Deutsche Hydrographische Zeitschrift 2, 78�82 
(1949). 
> >
> > H. C. Freiesleben, �Investigations into the dip of the horizon,� J.. Inst. 
Navigation (London) 3, 270�279 (1950).
> 
> >  
> > H. C. Freiesleben, �Die Strahlenbrechung in geringer H�he �ber 
Wasseroberfl�chen,� Deutsche Hydrographische Zeitschrift 4, 29�44 (1951).
> >
> > with a correction by Brocks:
> >
> > K. Brocks �Bemerkungen zu H. C. Freiesleben, Die Strahlenbrechung in 
geringer H�he �ber Wasseroberfl�chen,� Deutsche Hydrographische Zeitschrift 
4, 121�122 (1951). 
> >
> > and finally
> >
> > H. C. Freiesleben �The dip of the horizon,� J. Inst. Navigation 4, 8�9 (March, 1954). 
> >
> > and the closely related work by Lutz Hasse:
> >
> > L. Hasse, ��ber den Zusammenhang der Kimmtiefe mit meteorologischen 
Gr��en,� Deutsche Hydrographische Zeitschrift 13, 181�197 (1960).
> >
> > summarized in English in
> >
> > L. Hasse �Temperature-difference corrections for the dip of the horizon,� 
J. Inst. Nav. (London) 17, 50�56 (1964)
> >
> > These are the essential papers for understanding the dip, I think. They 
are all in my on-line bibliography, where I have some comments about their 
content.  You might also be interested in the historical discussion:
> >
> > C. Pr�fer �Das Kimmtiefenproblem,� Ann. Hydrog. Maritim. Met. 71, 171�174 (1943).
> >
> > unquote
> >
> >
> > I do not yet have most of these references, but hope to obtain them in the near future.
> >
> > The noticeable correlation I observe in my data with the temperature 
difference between Sea Surface and ambient air are consistent with his 
findings that the dip depends on the difference in temperature between the 
observer and the tops of the waves.
> >
> > So, Brad, how about trying to improve the understanding and estimation of 
the dip by performing your own measurements?
> >
> > Marcel
> >
> >
> >
> >
> >
> >
> > : http://fer3.com/arc/m2.aspx?i=122498
> 
> : http://fer3.com/arc/m2.aspx?i=122499
> 
> 
> : http://fer3.com/arc/m2.aspx?i=122501
> 
> : http://fer3.com/arc/m2.aspx?i=122505
> 
> 
> : http://fer3.com/arc/m2.aspx?i=122516
> 

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| Richard B. Langley                            E-mail: lang@unb.ca         |
| Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/ |
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