A comparison of low-frequency radio noise amplitude probability distribution models

One of the most commonly modeled statistics in atmospheric radio noise studies is the noise envelope voltage amplitude probability distribution (APD). Although a number of models have been introduced to characterize atmospheric noise envelope APDs, the quantity of real data that exist to verify their accuracy is somewhat limited, especially in the ELF and VLF bands. This paper presents the results of a statistical analysis in which thousands of hours of ELF/VLF noise are processed to derive APDs, which are then compared with various APD models to determine which of the models is most accurate. The error criterion used to find the optimal parameters of each APD model, as well as to compare the models against each other, is the expected value of the log error squared (where the log error is the difference in decibels between the data histogram and the model histogram). This criterion provides a means by which the models may be evaluated and compared numerically. The most accurate model is found to depend on geographic location, time of year and day, bandwidth, and center frequency, but two of the simplest models (i.e., each with only two parameters) are found to give extremely good performance in general. These are the Hall and alpha-stable (or a-stable) models, both of which approximate the Rayleigh distribution for low-amplitude values but decay with an inverse power law for high-amplitude values. This paper concludes that the Hall model is the optimal choice in terms of accuracy and simplicity for locations exposed to heavy sferic activity (e.g., lower latitudes) and the alpha-stable model is best for locations relatively distant from heavy sferic activity (e.g., the polar regions).