A three-dimensional, time-dependent, nonlinear, hydrodynamic model of the plasmasphere has been developed which includes the self-consistent coupling of conjugate hemispheres within the plasmasphere as well as the effects of cross-L drifts due to convection electric fields. The inner region of the plasmasphere was modeled from an L of 1.5 to an L of 3.5 to 4.5, depending on local time. In this first study of the global plasmasphere the model was run for solar minimum conditions until diurnally reproducible results were obtained, indicating that the plasmasphere was fully filled. The results of the model were then compared with applicable measurements of the plasmasphere. It was found that the model tends to overestimate densities somewhat, although it is within a factor of 2 of an average of June and December whistler observations. The model predicts densities within a factor of 2 of most of the satellite observations as well. As anticipated, the diurnal variation of the plasmasphere was found to depend on magnetic latitude. At low latitudes the diurnal variation in density was relatively small, with the largest densities occurring in the afternoon time sector. However, near the plasmapause, the effects of changes in volume of drifting tubes of plasma due to cross-L drifts led to a factor of 3 variation in equatorial density, with the highest densities occurring near local midnight where the volume was lowest. Various limitations of the current model and suggested improvements are also discussed. ¿ Copyright 1990 by the American Geophysical Union