We consider a mathematical model of the atmosphere and of the process of consideration of water vapor and formation of water droplets and ice cristals; we use the equations of a compressible heat-conducting visicous gas to describe the atmosphere's motion and use the density of water droplets and that of the ice cristals in the air to formulate the equations of microphysical processes. Under some hypotheses we prove the local existence and uniqueness of the solution of a general system, while for the equations of falling droplets with coagulation process, we
obtain the existence of a stationary solution and the convergence to it of the evolution solution. Concerning the relations between the atmosphere and the radiation, we study the problem of their heating effect. Moreover, we show some numerical results about the air flow in which the water vapor can be condensated.