• transionospheric;
  • ray tracing;
  • time delay;
  • Doppler shifts;
  • lookup tables

[1] Lookup tables have been constructed that address group delay and RF carrier phase advance for transionospheric signal propagation referenced to a ground-based transmitter. The tables are based on parameterizations of ray-tracing results using the Reilly ray trace/ICED, Bent, Gallagher (RIBG) model with the magnetic field turned off. The quantities of interest are incremental group and phase path lengths referenced to straight-line distance between transmitter and receiver and are designated by Δlg and Δlp (as defined, both quantities are positive). Equations are presented that relate these quantities to group delay and ionospheric Doppler shifts. Tables currently in use are three-dimensional, expressed in terms of frequency (f), elevation angle (θ), and straight-line total electron content (TECSL). At high frequencies, Δlg and Δlp can be accurately expressed by a straight-line propagation formula that is proportional to TECSL. With decreasing frequency, these quantities become greater than their straight-line counterparts due to additional refraction effects, including ray bending. Extensive ray-tracing runs have been performed under a variety of ionospheric conditions to produce scatterplots of Δlg and Δlp versus TECSL for given pairs of [f, θ] values. The current ranges in these variables are from 20 to 100 MHz and 5° to 90°, respectively. The tables contain coefficients from fourth-degree polynomial fits to the distributions of points within the scatterplots. Where scatter is problematic, the introduction of a fourth parameter, slab thickness, is shown to significantly reduce this scatter. Magnetic field effects are discussed and are shown to have a small effect on table coefficients. Discussion is also included on the use of the tables with a model ionosphere.