abstract: Earth-system models describe the interacting components of the climate system and technological systems that affect society, such as communication infrastructures. Data assimilation addresses the challenge of state specification by incorporating system observations into the model estimates. In this research, a particular data assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is applied to the ionosphere, which is a domain of practical interest due to its effects on infrastructures that depend on satellite communication and remote sensing. This dissertation consists of three main studies that propose strategies to improve space- weather specification during ionospheric extreme events, but are generally applicable to Earth-system models: Topic I applies the LETKF to estimate ion density with an idealized model of the ionosphere, given noisy synthetic observations of varying sparsity. Results show that the LETKF yields accurate estimates of the ion density field and unobserved components of neutral winds even when the observation density is spatially sparse (2% of grid points) and there is large levels (40%) of Gaussian observation noise. Topic II proposes a targeted observing strategy for data assimilation, which uses the influence matrix diagnostic to target errors in chosen state variables. This strategy is applied in observing system experiments, in which synthetic electron density observations are assimilated with the LETKF into the Thermosphere-Ionosphere- Electrodynamics Global Circulation Model (TIEGCM) during a geomagnetic storm. Results show that assimilating targeted electron density observations yields on average about 60%–80% reduction in electron density error within a 600 km radius of the observed location, compared to 15% reduction obtained with randomly placed vertical profiles. Topic III proposes a methodology to account for systematic model bias arising ifrom errors in parametrized solar and magnetospheric inputs. This strategy is ap- plied with the TIEGCM during a geomagnetic storm, and is used to estimate the spatiotemporal variations of bias in electron density predictions during the transitionary phases of the geomagnetic storm. Results show that this strategy reduces error in 1-hour predictions of electron density by about 35% and 30% in polar regions during the main and relaxation phases of the geomagnetic storm, respectively. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2018