## 1. Introduction

[2] The Raytrace/Ionospheric Conductivity and Electron Density–Bent-Gallagher (RIBG) ionospheric propagation model [*Reilly*, 1993] adapts a ray trace propagation model [*Reilly*, 1991] to a global climatological ionospheric model, whose components are the Ionospheric Conductivity and Electron Density (ICED) model and the Bent and Gallagher ionospheric models. RIBG starts with the ICED model [*Tascione et al.*, 1988] for heights 0–1000 km. ICED is based on monthly median global maps of the *F*_{2} layer maximum plasma frequency *f*_{o}*F*_{2} [*Rush et al.*, 1989] and the maximum usable frequency factor *M*(3000)*F*_{2}, which is used to determine the height at maximum density *h*_{m}*F*_{2}. The notation used here is the same as that of *Davies* [1990], who describes the use of these maps. For heights 1000–3000 km, the fourth and fifth exponential layers of the Bent model [*Bent et al.*, 1975] are joined continuously with the ICED model at 1000 km. At height 3000 km, the Gallagher plasmaspheric model [*Gallagher et al.*, 1988], the update of which [*Gallagher and Craven*, 2000] we have not yet incorporated, is joined continuously onto the Bent model and is extended upward to a cutoff height, defined by the condition ln(*n*_{e}) = 1 for electron density *n*_{e} (cm^{–3}).

[3] We have modified RIBG since the 1993 paper by (1) adapting it to the WGS-84 oblate Earth geometry; (2) incorporating updates of the geomagnetic reference field; (3) changing the bottomside (below *h*_{m}*F*_{2}) model of ICED so that superposition of Chapman height profiles for *E*, *F*_{1}, and *F*_{2} layers does not alter the values determined for the critical densities and heights of these layers, (4) improving the method by which the Chapman topside *F*_{2} Chapman profile in ICED joins with the Elkins-Rush topside profile, and (5) joining the Gallagher plasmaspheric model continuously to the top of the Bent profile at height 3000 km. The Elkins-Rush profile has the form exp[−*A* tan^{−1} (α*h*)], where *h* is the height and *A *and α are constants that depend on latitude and longitude (but not height). The height derivative of the exponent defines a scale height, and joining with the *F*_{2} topside Chapman layer occurs where the two scale heights match. Otherwise, height profile segment joining is made continuous by adjusting the amplitude factor for the upper segment.

[4] The RIBG electron density height profile is driven by effective sunspot numbers “SF2” for *f*_{o}*F*_{2}, “SM3” for *M*(3000)*F*_{2}, and “SWDTH” for the width parameter of the *F*_{2} layer. The other driving parameters are “CFAC,” a constant in the denominator of the expression for parameter *A* in RIBG, and the usual planetary 3-hour geomagnetic activity index *Kp*, which primarily affects the high-latitude model in ICED. The quoted driving parameters are the parameter names we use in the RIBG program. Ideally, they can be determined from external ionospheric data in the space-time vicinity of the region of interest, whereas the index *Kp* is obtained from the Internet (e.g., see www.sec.noaa.gov/ftpmenu/indices/old_indices.html). For simulations of ionospheric penetration in this paper, however, we select typical driving parameters.

[5] RIBG obtains results for propagation parameters in either point-to-point or area coverage calculations. In the latter, rays are sent out from a point in a fan of azimuth and elevation angles to a specified height. Rays are traced through a user-specified grid of latitude-longitude points. Each grid point is associated with a set of parameters that specify the height versus electron density profile, which consists of a series of analytic height profile segments. As the ray path calculation traverses the ionospheric model grid, the electron density variation is continuous. The ray path necessarily crosses boundaries between adjacent height profile segments, but care is taken to ensure that the ray is not in any way scattered by these artificial model boundaries. Details are found in work by *Reilly* [1991]. The program works well for frequencies at HF or above, but we are applying it now to the low-frequency regime 0.5–4.0 MHz and ionospheric penetration from a radio source on the ground to an elevated receiver. In the process, numerical procedures are strained, and the need for modifications becomes apparent. We find we need to include the effect of collisions in the index of refraction in the low-frequency regime. Otherwise, ionospheric penetration is limited to frequencies in excess of the maximum plasma frequency along the ray path (assuming this is larger than the electron gyrofrequency). However, ionospheric penetration of low-frequency whistler modes of radio propagation is a well-known phenomenon, and we find that inclusion of the electron collision frequency gives them to us.

[6] Section 2 shows the derivation of the ray trace equations for the complex index of refraction. We include the derivation because it is unusual and elegant and leads directly to the results of interest. The derivation in Appendix A of *Reilly* [1991] is similar to, but falls short of, the present derivation. Also included is the expression for the electron collision frequency versus height, which fits graphs given by *Budden* [1985] and *Davies* [1990]. Section 3 discusses what the Appleton index tells us about low-frequency ionospheric penetration and then gives results of the calculations of ionospheric penetration. Section 4 discusses modifications of numerical procedures that were necessary for the calculations and will be necessary for future work. Section 5 discusses results and gives conclusions and suggestions for future work.