A self-consistent semianalytical model of magnetospheric convection including the effect of the latitude and local time variations of ionospheric conductivities is presented. The motions of the inner edge of the magnetospheric ring current, and the associated field-aligned currents, produced by the externally imposed dawn-to-dusk potential drop across the magnetospheric cavity are computed by using a linear approximation. The coupling between the different diurnal harmonics in the local time variations of fields and currents produced by the local time dependence of ionospheric conductivites is described by an appropriate matrix formalism. The calculations show that the enhancement of auroral conductivities by electron precipitation in the auroral zone significantly enhances both the typical duration and the absolute amplitude of the penetration of convection electric fields to midlatitudes. Furthermore, the local time variations of the convection electric field generated at midlatitudes by a sudden increase of the dawn-to-dusk potential drop are in good agreement, both at the initial time and after the steady state is reached, with the available statistical models of the disturbance midlatitude electric field. The amplitude of the steady state field seems sufficient to explain these observations, thus confirming that the concept of the shielding of midlatitudes from the convection electric fields is basically correct but was overestimated in earlier analytical calculations. The large subauroral electric fields observed by several satellites are also reproduced in the model either by a decrease of the subauroral conductivites below the midlatitude values or by the consideration of a very narrow latitudinal extent of the auroral zone. The overall consistency between the results of the model and the electric field obervations thus supports the idea that a large class of phenomena related to magnetospheric convection in the dipole regions of the magnetoshper can be described in a reasonably realistic manner by a linear theory.