An empirical model is developed to describe the variations of midlatitude F region ionization along all longitudes within the dip latitude band (30¿--55 ¿N), induced by geomagnetic activity, by using the relative deviations (&PHgr;) of the F region critical frequency f0F2 from its monthly median. The geomagnetic activity is represented by the Kp index. The main statistical relationship between &PHgr; and Kp is obtained by using 11 years of data from 26 midlatitude ionosondes. The statistical analysis reveals that the average dependence of &PHgr; on Kp is quadratic, the average response of the ionosphere to geomagnetic forcing is delayed with a time constant T of about 18 hours, and the instantaneous distribution of &PHgr; along local times can be assumed sinusoidal. A continuity equation is written for &PHgr; with the production term being a function of Kp modulated by a sinusoidal function of local time and the loss term proportional to &PHgr; with a loss coefficient &bgr;=1/T. A new, modified function of geomagnetic activity (Kf) is introduced, being proportional to &PHgr; averaged over all longitudes. The model &PHgr; is defined by two standing sinusoidal waves with periods of 24 and 12 hours, rotating synchronously with the Sun, modulated by the modified function Kf. The wave amplitudes and phases, as well as their average offset, are obtained by fitting to the data. A new error estimate called prediction efficiency (Peff) is used, which assigns equal weights to the model errors at all deviations of data from medians. The prediction efficiency estimate gives a gain of accuracy of 29%. ¿ 2001 American Geophysical Union