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The performance of the satellite communication systems employing polarisation diversity or frequency-reuse schemes to improve the spectral efficiency is degraded due to the depolarisation-induced interference originated by raindrops and ice particles present along the Earth-Space propagation path. Two models account for both rain and ice contributions. One predicts the long-term cumulative distribution function (CDF) of cross-polarisation discrimination (XPD). The other predicts the relationship between XPD and co-polar attenuation (CPA) and it was derived considering exclusively data at the V-band. In this study, the former model is improved by considering the individual ice and rain contributions and their combined effects, while the latter is validated against new measurements at the Ka band. New models are then proposed for the XPD-CPA relationships at the Ka-band taking into account both rain and ice contributions and also their combined effects. Finally, the predictions provided by the first model are usually converted to the corresponding XPD-CPA relationship using the long-term first-order statistics of rain attenuation, (incorrectly) considering that the equiprobability hypothesis applies. A new approach for the conversion of the XPD CDF into the corresponding XPD-CPA relationship is presented. [ABSTRACT FROM AUTHOR]