A global assimilative ionospheric model (GAIM) has been developed to improve the modeling of ionospheric weather. GAIM adopts a fixed three-dimensional Eulerian grid following a geomagnetic dipole configuration. A four-dimensional variational approach (4DVAR) with the adjoint technique is presented, which attempts to minimize the difference between modeled and measured line-of-sight total electron content (TEC) using nonlinear least squares minimization. The minimization is achieved by solving for corrections to the initial (climatological) model drivers so that the density state becomes consistent with the observations. The 4DVAR approach is exercised with GAIM in an observation system simulation experiment (OSSE) conducted for estimating the weather behavior of E × B drift at low latitudes. The OSSE takes the constellation of global positioning system (GPS) satellites and an existing global GPS receiver network as the observation system. The effectiveness of the 4DVAR technique with such an observation system is assessed in the experiment, which indicates that one can solve for the low-latitude E × B drift and improve the density modeling using ground-based, integrated line-of-sight (TEC) measurements from a relatively small number of stations.