Attenuation due to the propagation of radio waves through the Earth's atmosphere plays a major role in satellite link attenuation at frequencies beyond 20 GHz. This paper presents the development of an artificial neural network (ANN) to separate out the respective roles played by the three types of contributor, namely, gases (oxygen and water vapor), clouds, and rain, to the overall attenuation of radio waves. Whereas the inputs to the ANN are the total attenuation measured at either one, two, or three frequencies, the ANN outputs provide the three atmospheric attenuation components at a single frequency. Several neural networks were trained by using a simulated statistically significant data set, derived from absorption and diffusion models applied to atmospheric profiles. Good overall performance was observed, and a particularly good fit was achieved in the case where attenuation inputs were provided at two frequencies. From the estimated values of atmospheric attenuation for the three contributors, corresponding frequency scaling models were applied on each to estimate the three contributions at a new frequency. Total atmospheric attenuation at this new frequency can then be estimated. The method works using measured data at either one, two, or three frequencies and allows the total attenuation to be predicted at any other frequency in the range 20--50 GHz. Validation was successfully performed on real data.