The theoretical data assimilative model of the ionosphere (TDAMI) was created to answer the most challenging problem in ionospheric physics: modeling the ionospheric disturbances (in particular, parameters related to the peak of the F layer: f0F2 and hmF2) during geomagnetic storms. It is an analytical model that calculates maximum electron density (Nm) distribution and the height of this maximum (hm) as a function of time, latitude, longitude, season and solar activity. Tested as a climatological, i.e., monthly average, model over the worldwide midlatitude ionospheric data set for different seasons and solar activity conditions, TDAMI yields results comparable with the well-known empirical models of the International Radio Consultative Committee (CCIR) and the Union Radio Scientifique Internationale (URSI). The mean annual relative error in f0F2 is <8% for all levels of solar activity, while the mean seasonal errors do not exceed 12%. A comparison between the model simulations and all existing vertical incidence (VI) data for the geomagnetically disturbed period October 10--11, 1988, shows that TDAMI adequately simulates the UT-latitudinal-longitudinal dependence of the ionospheric reaction to the geomagnetic disturbance. During the hours of maximum depletion in the electron density, the improvement achieved by the model is more than 70--80% compared to international reference ionosphere (IRI) global distributions (by CCIR and URSI coefficients sets). The maximum TDAMI model error is 20--25%. ¿ 2001 American Geophysical Union