# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Measuring (and calculating) Dip**

**From:**Brad Morris

**Date:**2013 Feb 27, 14:34 -0500

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

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

BradOn Feb 27, 2013 6:39 AM, "Marcel Tschudin" <marcel.e.tschudin---com> wrote:

>

> ________________________________> H. C. Freiesleben, “Investigations into the dip of the horizon,” J. Inst. Navigation (London) 3, 270–279 (1950).

> 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, “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).

>

> 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

>

>

>

>

>

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