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A new approach to characterizing the rain profile for applications involving attenuation beyond 10 GHz is presented. It is based on the use of three functionals of the rain intensity profile (referred to as "intrinsic profile parameters" because of their peculiarity of being independent of frequency) which encompasses all the relevant information contained in the profile itself with respect to the attenuation. The attenuation can then be evaluated without the need for any profile model, as happens when starting from the more usual "average rain intensity" or other similar meteorological parameters. The intrinsic parameters therefore allow for the separate accounting of the profile and the other factors affecting attenuation such as frequency, raindrop size distribution, etc. Moreover, they can be easily related to the various kinds of "effective rain intensity" and "rainy path length" defined in the literature, thus offering a tool to clean out the inherent dependence of these latter on frequency and to obtain results that are comparable among each other even though they are collected under different circumstances.