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Abstract The dayside equatorial ionospheric electrodynamics exhibit strong variability driven simultaneously by highly changeable external forcings that originate from the solar extreme ultraviolet (EUV), magnetosphere, and lower atmosphere. We investigate this variability by carrying out comprehensive data‐driven ensemble modeling using a coupled model of the thermosphere and ionosphere, with the focus on the verticalE×Bdrift variability during a solar minimum and minor storm period. The variability of verticalE×Bdrift in response to the changes and uncertainty of primary forcings (i.e., solar EUV, high‐latitude plasma convection and auroral particle precipitation, and lower‐atmospheric tide and wave forcing) is investigated by ensemble forcing sensitivity experiments that incorporate data‐driven stochastic perturbations of these forcings into the model. Second, the impact of assimilating FORMOsa SATellite‐3/Constellation Observing System for Meteorology, Ionosphere, and Climate (FORMOSAT‐3/COSMIC) electron density profiles (EDPs) on the reduction of uncertainty of the modeled verticalE×Bdrift variability resulting from inadequately specified external forcing is revealed. The Communication and Navigation Outage Forecasting System (C/NOFS) ion drift velocity observations are used for validation. The validation results support the importance of the use of a data‐driven forcing perturbation methods in ensemble modeling and data assimilation. In conclusion, the solar EUV dominates the global‐scale day‐to‐day variability, while the lower atmosphere tide and wave forcing is critical to determining the regional variability. The modeled verticalE×Bdrift is also sensitive to the magnetospheric forcing. The ensemble data assimilation of FORMOSAT‐3/COSMIC EDPs helps to reduce the uncertainty and improves agreement of the modeled verticalE×Bdrifts with C/NOFS observations.