Abstract
This paper presents an approximate method for estimating gaseous absorption at very low elevation angles along paths of finite length or Earth-space paths, taking into account both the effects of the Earth curvature and refraction. An exponential atmosphere is assumed. Gaseous absorption is evaluated by breaking its integral representation into a number of smaller pieces that are evaluated in closed form by the leading term of their asymptotic expansions; there is no need for numerical integration. The new method extends the validity of Annex 2 of Recommendation ITU-R P.676-10 to path elevation angles below 5°. Comparisons with the line-by-line method of the same Recommendation, using radiosonde data as input, show good to very good agreement at 20, 30, and 350 GHz for an Arctic location, a tropical area in Australia, and two midlatitude locations-one in the Rocky Mountains and the other closer to sea level. Some limitations of the approximate method over very high mountains, where surface pressure is lower than the 780-hPa reference of the water vapor attenuation model of Annex 2, are also discussed.
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