| Description |
The finite-difference time-domain (FDTD) method is a robust numerical modeling approach that has been widely utilized over the past couple decades to solve for electro- magnetic (EM) wave propagation in the Earth-ionosphere waveguide. There are two main approaches to modeling EM wave propagation in the ionosphere: (1) treating the ionosphere as an isotropic medium; or (2) treating the ionosphere as an anisotropic medium (i.e., magnetized ionospheric plasma). The first approach simply utilizes an electrical conductivity profile to represent the ionosphere and ignores the influence of the geomagnetic field. The second approach accounts for the Earth's magnetic field as well as the density and collision frequencies of the electrons. All of the existing FDTD-based Earth-ionosphere models to date account for only the average composition values of the ionosphere and then solve for only the expected average EM fields without considering uncertainties. Not accounting for the variability of the ionosphere content limits the utility and capability of EM modeling for applications such as communications, surveillance, navigation, and geophysical applications. The primary objective of this dissertation is to improve the versatility and computational efficiency of FDTD models by treating the ionosphere as a random medium. Specifically, stochastic methods are applied to FDTD models in order to better assess how ionosphere variability affects the characteristics of EM wave propagation in the Earth-ionosphere waveguide. Two different stochastic algorithms are implemented into FDTD models: the Galerkin-based polynomial chaos expansion, namely PCE-FDTD, and the delta method, namely S-FDTD. The former is applied to both isotropic and anisotropic ionosphere models. While its accuracy and efficiency show potential advantages compared with the conventional Monte Carlo method, its efficiency is declined when applying to anisotropic model due to the complexity nature of the anisotropic magnetized plasma algorithm. Therefore, the latter is applied to anisotropic model in order to search a more effective model in term of computational cost. |
