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The work reported herein empirically derived the coefficients of the power-law relation between the specific attenuation Y and each of two other quantities: the radar reflectivity factor Z and the rainfall rate R. The derivation was accomplished using raindrop size distributions (DSDs) measured in Montreal and Toronto using the precipitation occurrence sensor system (POSS) and a Joss-Waldvogel disdrometer (JWD). The specific attenuation was calculated for both spherical and oblate spheroidal raindrops. Prior to doing so, the effects of inaccuracies in small drop detection by the two systems on the resulting Y-Z and Y-R relations were examined. In computing the relations, the influence of grouping the DSDs according to the corresponding values of Z was assessed. The results from the two sites were then combined in a regression analysis to determine the coefficients of the power-law expressions. The final expressions were used to calculate the probability distribution of rain attenuation over several path lengths at 30 GHz. Conclusions that can be drawn from this work include that (i) the uncertainties in the measurements of small drops do not appear to be critical to the derived relations for some frequencies considered in this work, (ii) in computing rain attenuation estimates from radar reflectivity factors, different criteria for grouping the reflectivity factor measurements can be adopted without changing the statistics of the corresponding attenuation estimates, (iii) differences, which are the smallest for frequencies around 20-30 GHz, are observed in the coefficients derived from the measured DSDs compared with those recommended by the ITU-R, and (iv) the attenuation statistics at 30 GHz computed by applying the Y-Z power-law expression are resistant to spatial averaging.