A long-term investigation of the attenuation in non-rainy conditions has been carried out, for a tropical and a temperate location, using meteorological data and NWP (Numerical Weather Prediction) products during the period 2011-2015. The results show that ERA-5 full profiles are appropriate to estimate non-rainy attenuation in lieu of radiometric or radiosonde observations. Simpler regression-based methods are established. A new formulation for oxygen attenuation is introduced, which only requires surface temperature and pressure. Mass absorption coefficients are used for water vapour and cloud attenuation. Simpler regression-based approaches are then validated. The non-rainy attenuation at K, Ka and Q bands has been found noticeably higher in the tropics than in the temperate region. This study would facilitate the planning of global mobile satellite communication systems.