Anomalous increases of the ionization density at middle latitudes (positive ionospheric storms) are often a prominent feature of upper atmospheric storms. One of their possible causes are traveling atmospheric disturbances (TADs) which propagate from polar to equatorial latitudes, carrying along equatorward‐directed meridional winds. At middle latitudes, these winds cause an increase in the height of the F2 layer which in turn will lead to an enhancement of the ionization density. Using a simple description of a TAD and an ionospheric model, we are able to reproduce the basic properties of such perturbations. We also attempt to simulate an actually observed storm period. Rough agreement is obtained when the wind speed is derived from the height of the F2‐layer peak. A more detailed simulation of the initial phase of the storm requires a more refined TAD model with time‐dependent height gradients in the wind field.