# Atmospheric refraction approximation

I am studying atmospheric refraction, reading ITU P.834 Effects of tropospheric refraction on radiowave propagation, and I have a question about an approximation. They say that refraction correction, $t$ (degrees), can be evaluated by: $$t=\int_h^{\infty}{\frac{n'(x)}{n(x) \tan{\phi}}dx}.$$ Then they go on to say that $$t = \frac{1}{1.314 + .6437 \theta + .02869 \theta^2 + h(.2305 + .09428 \theta + .01096 \theta^2) + .008583 h^2}$$ has been derived as an approximation for $0 \le h \le 3$ km and $\theta_m \le \theta \le 10$ degrees. Is this just a best fit approximation? Why choose a quadratic in the denominator?

• Well, you've dived into it :-) . If you can, dig up literature related to MODTRAN or other atmospheric propagation models. Practically all such fitting functions are based on best-fit polynomials. – Carl Witthoft Nov 10 '14 at 21:01
• @CarlWitthoft does anyone ever explicitly say that they used data fitting (e.g. "I used least squares..."), or should I just assume that for these types of approximations that appear out of thin air? – Jeff Nov 16 '14 at 19:42