# NavList:

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

**Re: Refraction and dip**

**From:**Frank Reed CT

**Date:**2005 Oct 12, 19:18 EDT

Marcel you wrote: "After downloading millions of balloon data of stations at different latitudes, I calculated in a first test run refraction and dip for latitude 60N." May I ask, who's your intended "market" or "user base" for your calculations? I know you mentioned at one point that you were trying to calculate the positions of stars etc. as accurately as possible. If this is strictly for astronomical use, an interesting issue arises. Shouldn't you limit your balloon data to days/nights when the sky was clear or mostly so? It's important because certain types of temperature inversions arise because clouds are forming or have formed at the altitude of the inversion. Also, there are big day/night variations which may be much more important astronomically than some of the latitudinal variation which has been the traditional "averaging" bin for these sorts of data. And: " The results showed that the refraction and the dip vary with the seasons and that the values are generally higher than the published values which seem to have been calculated on the basis of a standard atmosphere. The lowest (unrealistic?) values are those new ones published by USNO. The results showed also that the Bowditch formula for calculating the dip (the factor 1.76 in the metric version) should be at 60N during January around 1.65 and during July around 1.73 (the other months can be interpolated using a cosine function). This might also be (one of) the reason(s) why Bill encounters these differences with the Chicago buildings or for Asbjorn's differences who is living somewhere around 60N. " I don't think very much of it would come from differences in the *average* lapse rate. It's really a very small difference. You have to be a hundred feet above the ground before a 10% difference in the dip constant yields even a 1 minute of arc difference in the calculated dip. That said, we can expect very large differences in the dip when there is a really large variance from the standard atmospheric lapse rate (even at low observer heights above sea level). For example, if the atmospheric lapse rate is -34.1deg Celsius per km (as opposed to the average rates of -6.5 for moist air and -9.75 for dry air), there is no refraction at all. That is, a pure geometric calculation of dip will work and the equation sqrt(2*height/R_Earth) will match observations of actual dip. One can go beyond this and calculate dip as a function of lapse rate and temperature (dip DOES depend on temperature but only weakly). By the way, when considering the refraction tables and dip tables published in the Nautical Almanac, it's worth remembering that these are specifically designed to be useful for observers AT SEA. If you look at weather balloon sounding data from places like Bermuda, Jamaica, Pago Pago, etc, the patterns are different from inland sites at similar latitudes. So a direct comparison between the Nautical Almanac tables and your intended use may not work out very well. And: "A main problem arose by realising that the lapse rate distributions within a height layer are distributed asymmetrically, meaning that taking the average or the median of these values is not good enough. At the moment I try to derive a calculation procedure in order to find an estimate for the most likely value (mode) of lapse rate within a height layer. " Why would you want that mode value? What I mean is, what purpose would that serve (it doesn't necessarily have to serve any purpose at all --I'm just curious to know how you would use this mode result)? -FER 42.0N 87.7W, or 41.4N 72.1W. www.HistoricalAtlas.com/lunars