For sites located in different climatic regions, we estimated the relationship between the annual average probability distributionof exceeding a fixed rain attenuation, and the carrier frequency in the range 16 to 100 GHz, in the zenith paths of GeoSurf satellite constellations. In these constellations rain attenuation is independent of the altitude and number of satellites. Rain attenuation iss calculated with the Synthetic Storm Technique, a reliable prediction method, by using on-site measured rain-rate time series. A suitably defined outage probability factor shows that the outage probability, for fixed power margin, tends to saturate as frequency increases. In wideband radio-links, such as in spread spectrum design, there is very likely a long-term distortion due to the in-band outage probability. The results are oriented to design systems faded by rain attenuation whose value is also the total power margin available due to a mixture of coding and hardware technology, whose combination is not of concern here.