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# Atmospheric Refraction Fundamentals
Title Atmospheric Refraction
Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Level Basic
Year of Publication 2011

The electromagnetic signals experience changes in velocity (speed and direction) when passing through the atmosphere due to the refraction.

According to the Fermat's principle, the measured range $\displaystyle{ l }$ is given by the integral of the refractive index $\displaystyle{ n }$ along the ray path from the satellite to receiver:

$\displaystyle{ l= \int_{_{\mbox{ray path}}}{n\,dl}\qquad\mbox{(1)} }$

Thence, the signal delay can be written as:

$\displaystyle{ \Delta= \int_{_{\mbox{ray path}}}{n\,dl}-\int_{_{\mbox{straight line}}}{dl}\qquad\mbox{(2)} }$

where the second term integral is the Euclidean distance between the satellite and receiver.

Notice that the previous definition includes both the signal bending and propagation delay. A simplification of previous expression is to approximate the first integral along the straight line between the satellite and receiver:

$\displaystyle{ \Delta= \int_{_{\mbox{straight line}}}{(n-1)\,dl}\qquad\mbox{(3)} }$

From the point of view of signal delay, the atmosphere can be divided in two main components: the neutral atmosphere (i.e., the non ionised part), which is a non dispersive media, and the ionosphere, where the delay experienced by the signals depends on their frequency.

It must be pointed out that the neutral ionosphere includes the troposphere and stratosphere, but the dominant component is the troposphere, and thence, usually the name of the delay refers only to the troposphere (as tropospheric delay).