# NavList:

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

**Re: Refraction at the horizon**

**From:**Frank Reed

**Date:**2008 Mar 17, 18:42 -0400

A few things about the Auer-Standish paper... First, so there's no misunderstanding, this is not a "new" way to determine refraction. It's an integration procedure that makes the standard way of calculating refraction easier to implement. The underlying physics is long-established. It's Snell's Law applied to a continuous medium with the assumption that the index of refraction is given by n = 1+alpha(f,c)*rho(x,y,z) where alpha(f,c) is a small number, near 0.000292 (the value in the article is missing a zero), which depends on frequency and atmospheric composition (including humidity), and rho(x,y,z) is the density of the atmosphere at point x,y,z (normalized to 1 for standard temperature and pressure at sea level). Next, this standard approach to refraction still assumes a very limited set of variations in the atmosphere, specifically the atmosphere is in hydrostatic equilibrium with the only variations determined by the vertical temperature structure. This is where most of the action happens, and it's more than enough to explain some very exotic refraction phenomena, but this approach cannot handle horizontal variations. Finally, in the original paper, a non-physical model of the atmosphere is used that should really just be ignored (I think they use it because it allows for comparisons with earlier published papers). They have all sorts of details here that really do not belong in this article. For example, they list the "altitude of troposphere" (should be tropopause) as 11,019 meters, which is very strange. If you want to model an atmosphere that reproduces their "polytropic" atmosphere, use a constant lapse rate of -5.692 degrees per km up to 11km altitude (zero lapse rate above that). Also set the sea level temperature to 0 Celsius. When I used these values, I was able to reproduce their sample refraction tables to the nearest tenth of a second of arc for a sea level observer and the nearest half-second of arc for an observer at 15km altitude. Of course, for a proper refraction table, you want to use a realistic set of lapse rates based on real meteorology. There are a number of possibilities here. You can use data from soundings. You could use a standard model atmosphere (there are several of these). Or you could use a theoretical meteorological atmosphere based on variable adiabatic lapse rates. Incidentally, based on these integrations, I concocted some short formulas that cover a broader range of refraction possibilities but consistent with the Nautical Almanac's (implicit) atmosphere model. Posted here: http://www.fer3.com/arc/m2.aspx?i=025346&y=200508. Also while re-reading messages from August 2005, I discovered that I made GIF images of the Auer-Standish article available on my web site (forgot about that!), so if you want to read the article and can't get the PDF or you want a faster download, go here: http://www.HistoricalAtlas.com/lunars/ref.html. And I posted a simple coding of this algorithm here: http://www.fer3.com/arc/m2.aspx?i=025268&y=200508. One more thing that I think is worth mentioning. For a navigational context, there's no use worrying about differences in refraction smaller than 1 or 2% (of the refraction for that altitude above/below the horizon) since at that level even different colors of light will be refracted by different amounts turning a low altitude image of a star into a little "French flag". -FER --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---