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    Re: Measuring (and calculating) Dip
    From: Marcel Tschudin
    Date: 2013 Feb 27, 13:32 +0200
    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:


    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 Höhe über Wasseroberflächen,” Deutsche Hydrographische Zeitschrift 4, 29–44 (1951).

    with a correction by Brocks:

    K. Brocks “Bemerkungen zu H. C. Freiesleben, Die Strahlenbrechung in geringer Höhe über Wasseroberflächen,” 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, “Über den Zusammenhang der Kimmtiefe mit meteorologischen Größen,” 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. Prüfer “Das Kimmtiefenproblem,” Ann. Hydrog. Maritim. Met. 71, 171–174 (1943).


    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?


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