The computation of radiowave attenuation in the atmosphere is a series of radio propagation models and methods to estimate the path loss due to attenuation of the signal passing through the atmosphere by the absorption of its different components. There are many well-known facts on the phenomenon and qualitative treatments in textbooks. A document published by the International Telecommunication Union (ITU) provides some basis for a quantitative assessment of the attenuation. That document describes a simplified model along with semi-empirical formulas based on data fitting. It also recommended an algorithm to compute the attenuation of radiowave propagation in the atmosphere. NASA also published a study on a related subject. Free software from CNES based on ITU-R recommendations is available for download and is available to the public. The model and the ITU recommendation The document ITU-R pp. 676–78 of the ITU-R section considers the atmosphere as being divided into spherical homogeneous layers; each layer has a constant refraction index. By the use of trigonometry, a couple of formulas and an algorithm were derived. Through the use of an invariant, the same results can be directly derived: An incident ray at A under the angle Φ hits the layer B at the angle θ. From basic Euclidean geometry: By Snell's law: so that Notes: One proof starts from the Fermat's principle. As a result, one gets proof of the Snell's law along with this invariance. This invariant is valid in a more general situation; the spherical radius is then replaced by the radius of curvature at points along the ray. It is also used in equation (4) of the 2005 NASA's report in an application of satellite tracking. The assumption of the refraction index varying with the latitude is not strictly compatible with the notion of layers. However the variation of the index is very small, this point is usually ignored in practice. The ITU recommended algorithm consists of launching a ray from a radio source, then at each step, a layer is chosen and a new incidence angle is then computed. The process is iterated until the altitude of the target is reached. At each step, the covered distance dL is multiplied by a specific attenuation coefficient g expressed in dB/km. All the increments g dL are added to provide the total attenuation. Note that the algorithm does not guaranty that the target is actually reached. For this, a much