In this paper the Characterization of the convective dust storm that occurred in Tehran on 3 June 2014 with emphasize on the ergodicity hypothesis and using meteorological second generation satellite data is investigated. The results show that during the storm, the size of particles in the top of the convective cloud was small. Also, the base of the convective cloud formed in higher than normal height above surface with no strong updraft inside the cloud. The ambient layer air below the convective cloud, was very deep, warm and slightly humid at the lower levels. As a result, the atmospheric conditions were favorable for organized dry downburst with more and faster evaporation of raindrops below the cloud layer, intensification of the outflow and the strong surface winds.