A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Marcel Tschudin
Date: 2013 Mar 7, 13:33 +0200
These dip equations may have given you the impression that they would allow you to calculate the dip "exactly" by considering some additional parameters than the height of eye only. However, the large uncertainties in the measurement of such additional parameters like e.g. the large relative errors of small temperature differences and the differences in atmospheric properties between assumed model and real condition, suggest, that the calculated values will scatter with considerable spread around the real ones. It could therefore well be that the NA did not consider such additional parameters because the error from their measurement (or their estimation) did not really lead to an improved accuracy of the calculated dip. Or, in other words, in the presence of the existing noise the signals of the additional parameters were too weak to be of real use. It is only by comparing with measurements that one can recognise how accurate a certain estimation procedure is. The publications from Freiesleben and Hasse do unfortunately not show how the proposed dip formulae compare with the measurements which they used for deriving them; i.e. they did not show by how much the calculated values scatter around the measured ones. May be you understand now why I suggested to produce a systematically collected data set of measured Dips. Such a data set could serve as a reference for comparing the accuracy of different formulae.
Thank you for your measurements which is a valuable drop in the bucket. The differences to calculated values may possibly only belong to the "natural" scatter. May I ask you the date, approx. time and approx. location of these observations? I ask you this just in case your measurements should become one day part of a substantial data set.
I have been having an off line conversation with Dr. Andrew Young at SDSU about calculating dip. As you may recall, Dr. Young's website at SDSU has a wealth of information about calculating dip and also about the green flash at sunset.
Andy, as he prefers to be called, has pointed out that I should be using Friesenleben's paper from 1954. This article appears in the Institute of Navigation release of 2007. I have attached it herein. (linked? a fine test of the new system!)
Andy was careful to point out that there was a typographical error in the paper, but then wanted me to find it. Sneaky way to see if I'm comprehending the paper or just mindlessly copying an equation. So after I found the typo, I confirmed it with Andy. He indicated that indeed the correct typo had been located. The equation in question should say
The typo is the last operator, correct is a minus sign, incorrect as published is the plus sign.
Why so much fuss? Because Dr. Young has stated that this is the best dip equation to use, assuming you don't fall into the typo trap! Andy specifically indicated that I should not be using Friesenleben's earlier (1948&1951) linearized equations (which I was, to wit Dip=1.74sqrt(h)-tsubh+tsub0 ) The delta temperature belongs in the square root.
Next, Andy was quite emphatic that I not use the water temp for tsub0. Tsub0 is the temperature (degrees C) layer of air right next to the water, not the water itself. Tsubh is the temperature of the air at eye level, degrees C.
When I asked him about how to calculate tsub0 as a function of the air temp, wind velocity and water temp temp; he responded as follows:
This has been very extensively studied by the boundary-layer meteorologists. I user the "Dyer-Businger" formulation of Monin-Obukhov similarity theory to calculate the temperature profile under unstable (i.e., inferior-mirage) conditions. The main problem is knowing what value to assign to the aerodynamic roughness length, as well as the Obukhov length itself (for which I rather arbitrarily adopted a value of -10 meters, as I don't usually have wind speeds or heating rates to do a proper calculation). R.B.Stull's "An Introduction to Boundary Layer Meteorology" (Kluwer, Dordrecht, 1988) is a very readable introduction to the subject; but you will need to consult journal articles to get into the necessary details.
Here's a quickie shortcut for you:
I just wanted to set the record straight on the calculation of dip. The more I understand, the less I understand.
One thing is becoming crystal clear to me. The dip corr'n, as provided by NA Table, contains major uncertainty. The effect of waves on the horizon, un-accounted for. The bob (heave) of the ship on the surface, un-accounted for. Any anomally in refraction, as it would affect dip, un-accounted for.
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Friesenleben.pdf (no preview available)