Modeling of Earth's ionosphere and variational approach for data assimilation

The Earth's ionosphere plays an important role in wireless communication. One of the primary goals of this research is to improve the techniques for monitoring and forecasting of the conditions of the Earth's ionosphere. The work in this thesis focuses on modeling of the ion and electron density changes in the Earth's ionosphere and the assimilation of remote sensing measurements into the numerical model. The governing equations of the ionosphere consist of equations of fluid for chemically active plasma in the ionosphere. These equations form a system of coupled nonlinear convection-diffusion equations. In this thesis, we establish the well-posedness of the equations in some special cases. We also establish the numerical stability and consistency of the approximation. The resulting numerical model of the ionosphere produces stable and physically meaningful predictions of densities for all major ion species in the ionosphere. The numerical method is used in this research as a basis for the development of a 4-dimensional variational (4DVAR) data assimilation approach to help in the estimation of the driving forces in the ionosphere. The 4DVAR technique uses the adjoint approach in the computation of the gradient of performance functional.;In addition to theoretical discussions on the mathematical properties of the basic ionospheric model and its numerical implementation, extensive work has been devoted to the validation of both the basic ionospheric model and 4DVAR implementation. In this work we demonstrate that the new model can accurately reproduce all major characteristics of the ionosphere and the 4DVAR approach can be effective in determining the crucial drivers of the Earth's ionosphere.