Ionosphere ray tracing of radio-frequency signals and solution sensitivities to model parameters

Methods are developed to determine the refracted propagation paths of high-frequency radio signals in the ionosphere and to determine the sensitivities of these paths to changes of the input model parameters. These techniques are being developed to support the assimilation of data from monostatic and multistatic ionosondes with the goal of improving parameterized estimates of ionosphere electron density profiles. An additional application area is that of navigation using signals from a ground-based network of high-frequency beacons. A nonlinear two-point boundary value problem solver is developed using the shooting method with Newton updates. Robust convergence is achieved by seeding the algorithm with carefully designed first guesses of the wave vector's initial aiming angles and terminal group delay. Partial derivative sensitivities of the raypath solution are calculated using the adjoint of the two-point boundary value problem. This approach speeds the calculations when the partial derivatives of many ionosphere model parameters need to be computed. The new algorithm has been applied successfully to determine the paths of O-mode and X-mode radio waves between known transmitter and receiver locations and to spitze reflection points. Spitze singularities pose no difficulties for the new algorithm because it uses a Hamiltonian raypath formulation that remains nonsingular at a spitze.