NavList:

Marcel, you wrote:
"I encourage you to continue with your direct measurements of the dip, hopefully arriving at a data set covering all seasons, with dips resulting from positive and negative temperature differences between air and sea."

And you two can have roasted wild goose for dinner next New Year's Eve.

You also worte
"This would unfortunately not help much because one would use for this
verification the (astronomical) refraction which itself is not exact."

What? The astronomical refraction is most certainly "exact", as far as sextant observations are concerned, except for altitudes below two or three degrees. Your personal, specific choice of a problem to analyze --sunsets-- is indeed subject to this problem combining the worst case scenario of astronomical refraction with the uncertainty of dip. But this problem does not affect normal sextant observations at sea.

Bruce had asked if celestial fixes might benefit from using "smaller dip" values. I've said it before, but I will say it again: this is a wild good chase. Even so, setting that aside, you can always treat dip as an unknown if you have more than four (better yet dozens of) observations from the same height of eye. Just count it as a systematic error. Then you adjust that common offset to all observations until the scatter in the plot of LOPs is minimized. Naturally any other systematic error, for example a small error in IC, will be included in the result. There is no way to separate this from a systematic error in dip.

But is this news?? Of course not. The basic principle has been known for decades. Nautical astronomers have been making experimental observations to better understand dip for over two hundred years --since the very beginning of modern scientific celestial navigation. The idea that there is some large, obvious correction to be made to the dip tables borders on the absurd. There are variations in dip on the order of half a minute of arc or more that arise from well-known causes, but which cannot be corrected in any practical way.

You concluded that:
"The "Nautical Almanac"-model (1) is not the best one."

This statement is so minimalist that it cannot literally be false. Unfortunately, it "suggests" that there is something wrong in practical terms with the normal dip tables. And that is not true. It IS true that the uncertainty of the horizon has always been the principal uncertainty in altitude observations. But "fixing up" the dip tables or adding more independent variables is not going to remove that principal uncertainty.

Also, there is a small technical error here. You've put the number "(1)" in this description referring back to your original list "Model 1: Refraction with Bennett formula and Dip [etc. ...]" That could easily be misleading. The refraction tables are not computed from some variation of the so-called "Bennett formula". It is the other way around. The refraction tables have been derived from a combination of modelling of atmospheric physics and astronomical observations. They are generally computer by numerical integration. This was a difficult task as little as thirty years ago, but today it is simple. The editors threw the Bennett formula into the explanatory pages in the Nautical Almanac decades ago as a token offering to amateur calculation enthusiasts. The Bennett formula and its cousins have value when you need a quick, computationally cheap way of generating refraction values (for example, it's easy to type in a spreadsheet cell), but it is not a "fundamental" equation.

Marcel, you concluded:
"A noticeable improved estimation can be attained by considering additional environmental parameters."

You've spent several years collecting a mountain of data on sunsets. From your perspective, there damn well better be some improvement in estimation that results from all that hard work. Or... maybe... it's a wild goose chase.

I have so far seen nothing with respect to dip variability that could be of any practical value to anyone attempting practical celestial navigation under any circumstances that I can imagine, whether manually or in automation. Dip IS variable, especially approaching land, at a level of some fraction of a minute of arc. Occasionally, under extreme environmental conditions, the dip is MUCH MORE variable. It is important to know that it's variable. It's potentially useful to understand how simple variations in the temperature structure of the lowest level of the atmosphere can influence the dip. It's certainly useful to be aware of other "signs" that may promote extraordinary dip. But unfortunately, the only observable measure of that temperature structure over the distance scale we require, is the terrestrial refraction itself: the dip or some equivalent. You can observe the dip to estimate the terrestrial refraction. And from the terrestrial refraction you can calculate the dip.

-FER

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