Atmospheric noise resulting from lightning discharges is modeled as a Poisson-related process that depends on two major physical factors: (a) the world distribution of thunderstorms and (b) the prevailing propagation conditions. In this work theoretical models of atmospheric noise have been developed by postulating physically motivated combinations of source distributions and propagation conditions. Then the noise statistics at the output of a narrow-band receiver for each combination are calculated. Particular noise statistics that are computed for several cases include the amplitude-probability distribution, the average envelope-level crossing rate, and the pulse-spacing distribution. The models postulated are found to be consistent with both experimental and prior theoretical results.