This paper describes a computerized physical model that predicts both horizontally and vertically polarized noise in the ELF to LF band (10 Hz to 60 kHz). Since naturally occurring radio noise in this band is produced by lightning and propagates to the receiver via the Earth‐ionosphere waveguide, the model starts with average lightning flash density data from which it calculates radiated power for horizontal and vertical noise. Adjustments are made to the radiated power to account for seasonal and latitudinal differences in the lightning processes. The noise power is then integrated over fairly large geographic areas to formulate horizontal and vertical equivalent noise transmitters. The power radiated from each of these transmitters is propagated to the receiver location using standard anisotropic long wave propagation algorithms and well‐known models of the Earth‐ionosphere waveguide. From the received power the model predicts RMS noise, standard deviation, voltage deviation VD, and the amplitude probability distribution of the noise for both polarizations. Since the model is based on theory, it can also predict these parameters under disturbed ionospheric conditions. The model's generally good agreement with RMS noise data is demonstrated.

Nearly all ionospheric heaters operate at vertical incidence. Oblique waves cannot satisfy frequency‐matching conditions necessary to excite the parametric decay instability, and they are weakened by geometric spreading below the ionosphere. Those spreading losses are mitigated, however, by focussing near caustics. This paper calculates fields near the caustics of oblique waves and estimates the corresponding increases in electron temperature. It finds that a transmitter having a power‐gain product of 5 MW can raise the temperature of F‐layer electrons by a hundred degrees or more. Those temperature increases are initially concentrated in narrow regions near caustics, but spread by heat conduction over tens of kilometers.

This paper presents a practical method for computing radio fields in regions of strong focusing, using ray intercept data provided by a standard ray-tracing program. The procedure extends the usefulness of the ray trace by allowing fields to be computed near caustics and cusps where ray density calculations fail. Using a plane wave decomposition of the field components, phase integrals are computed by curvefitting intercepts of rays traced through ionospheric or tropospheric media whose refractive indices vary arbitrarily with altitude. A numerical algorithm is described for performing the plane wave angular spectral integrations. This procedure avoids the complications associated with higher-order asymptotic techniques, allowing a broad range of refractive-index profiles to be analyzed by a single method. It is applied to two sample profiles, and the results agree very closely with higher-order stationary-phase estimates in caustic regions. Moreover, the computer code runs efficiently, despite the presence of highly oscillatory integrands. The method is capable of including the effects of weak collisions, the spherical earth, and azimuthally dependent transmitter configurations. INTRODUCTIONThis paper presents a method for using ray tracing to calculate radio field strengths in strong-focusing regions of the ionosphere or troposphere. Because of its versatility and numerical efficiency, ray tracing is an established technique for predicting radio field strengths in regions without strong focusing. It is desirable to extend the applicability of ray trace results to strong-focusing regions as well. This paper describes a practical numerical method for doing so using state-of-the-art ray-tracing programs [e.g., Jones and Stephenson, 1975].The procedure for computing radio fields in stratified media from ray tracing outside caustic regions uses the well-known correspondence, developed by Booker [ 1939], Budden [ 1961 ], and others, between ray trajectories and the first-order asymptotic approximation to the angular spectral representation of the field components. Budden [1976] and others show how the phase and amplitude of fields are directly related to the path-integrated refractive-index variation and the ray curvature, both easily computed with a ray-tracing program in regions where neighboring rays do not cross. That correspondence solves the radio field problem for stratified media outside caustic areas. 514 Breakdown of the first-order stationary-phase result near caustics has led to the development of higherorder asymptotic formulas that uniformly interpolate the field through caustic regions and can extend field strength calculations based on ray density into strong focusing regions [Maslin, 1976b;Budden, 1976]. Unfortunately, asymptotic methods have two drawbacks that make them inconvenient for use in conjunction with a ray tracing program:1. Different closed-form expressions involving special functions are needed for different degrees of focusing, e.g., Airy functions for caustics and Pearcey's [1946] ...

Phase velocity transitions in the earth-ionosphere waveguide can focus or shadow ELF signals and give rise to anomalies less than a megameter in extent. This paper develops a hybrid method to calculate those effects: it uses full-wave theory to determine local TEM mode parameters, but traces rays to describe the signal's lateral structure. The method is applied to models of the terminator and disturbed polar cap boundary, including one based on the November 22, 1982 solar proton event (SPE). During that event a receiver in the Gulf of Alaska measured a severe signal fade. That fade probably was caused by refraction of the signal away from the polar cap boundary and into the disturbed cap, where the TEM-mode phase velocity is slowest. Focusing and shadowing, lasting about an hour, are predicted for signals whose great-circle path grazes the terminator.

Abstract. In this paper we discuss an investigation into the feasibility of using current and forecasted weather data to forecast lightning occurrence. These lightning occurrence forecasts are intended to be used to improve the accuracy of near-term long wave communication systems coverage predictions. Various weather information sources were reviewed to determine which data and parameters could be used to predict lightning and which techniques were best suited for selected forecast periods. Review of atmospheric and lightning physics resulted in several methods for establishing relationships between weather data parameters and lightning flash rates for selected forecasting periods. We review these methods and show results of tests which were conducted to compare the forecasted lightning occurrence with measured data. These tests were limited to the continental United States where empirical data on lightning occurrence from the National Lightning Detection Network are available. The results of the techniques developed for several example days are shown, as is the impact that using the techniques might have on the coverage prediction for an example long wave transmitter.