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    Re: Measuring (and calculating) Dip
    From: Richard B. Langley
    Date: 2013 Feb 28, 12:42 -0400

    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
    > >
    > >
    > >
    > >
    > >
    > >
    > > View and reply to this message: http://fer3.com/arc/m2.aspx?i=122498
    > 
    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=122499
    > 
    > 
    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=122501
    > 
    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=122505
    > 
    > 
    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=122516
    > 
    
    -----------------------------------------------------------------------------
    | Richard B. Langley                            E-mail: lang@unb.ca         |
    | Geodetic Research Laboratory                  Web: http://www.unb.ca/GGE/ |
    | Dept. of Geodesy and Geomatics Engineering    Phone:    +1 506 453-5142   |
    | University of New Brunswick                   Fax:      +1 506 453-4943   |
    | Fredericton, N.B., Canada  E3B 5A3                                        |
    |        Fredericton?  Where's that?  See: http://www.fredericton.ca/       |
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