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    Re: Measuring (and Calculating) Dip
    From: Brad Morris
    Date: 2013 Mar 5, 16:25 -0800

    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.

    Kind Regards

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