Reflections from an exponential atmosphere

A quantitative explanation of tropospheric radio propagation is derived without the use of arbitrary numerical factors. It is based primarily on the average value and the standard deviation of the index of refraction at the earth's surface, both of which decrease exponentially with height. This method seems to bridge the gap between the internal reflection and scatter hypotheses. The quantitative results are in good agreement with experimental data on distance dependence, frequency dependence, climatic and seasonal variations, and effective antenna gain. One consequence is a new concept of the decrease in effective gain of narrow-beam antennas, which accounts for some hitherto unexplained experimental results.