Approximate Method for Estimating Gaseous Loss at Very Low Angles Along Paths of Finite Length and Earth-Space Paths

摘要

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.