The results of field measurements taken in the near–Caspian (2002, 2003, 2007, 2009, 2010, 2011, 2013, 2014, 2016 years) and near–Aral sea (1998) deserts under the conditions of weak winds (almost in the absence of saltation processes) and strong heating of the land surface are given. The data contain the daytime mean distributions of aerosol–particle concentrations, the deviations of the aerosol mass concentrations at 0.5 m from the 2-m values for particles 0.15–1.5 µm in size, the daytime (from 9 a.m. to 7 p.m.) friction velocity values. The simplest distribution approximations are given based on the Kolmogorov direct differential equation which usually used in considering the Poisson distributions in equations for queuing systems. The measurement results show that the fine long–lived aerosol in the region under consideration constitutes a significant fraction of the total aerosol content in the atmospheric near surface layer. The small dust aerosol fractions (with a diameter of less than 2 µm), which have a significant lifetime in the atmosphere, are especially important for the atmospheric radiation budget, since such fractions interact most efficiently with the shortwave solar radiation.