Our laboratory has been conducting a global survey of extremely low frequency (ELF) and very low frequency (VLF) radio noise since February 1985. Eight measurement stations around the world record the instantaneous noise amplitude in each of sixteen narrow‐frequency bands in the 10‐Hz to 32‐kHz frequency range, and we have calculated the monthly averages of these amplitudes for the four stations with the longest times of operation. The period, amplitude, and phase of temporal variations in the averages are important indicators of the sources and propagation characteristics of the noise in the various frequency bands. Furthermore, since the principal source of ELF/VLF radio noise is lightning, long‐term variations of the noise must relate to changes in global thunderstorm activity. We find that the noise amplitudes vary seasonally by up to a factor of 4 in some of the sixteen frequency bands; in addition, many of the variations correlate quite well with global lightning flash rates.

that greatly improved the results of Chapter 4 and for a variety of worthwhile interactions during my time at Stanford; and Professor Howard Zebker, for serving as the fourth member of my defense panel. efforts to enhance my education and quality of life; and to all my family and friends (especially Kim) who were supportive along the way.

Abstract. 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 a-stable model is best for locations relatively distant from heavy sferic activity (e.g., the polar regions). IntroductionNaturally occurring radio noise above approximately 100 MHz is well modeled for most applications as a Gaussian random process; however, radio noise below 100 MHz (denoted atmospheric noise) is impulsive in nature and is not well modeled as Gaussian. Individual atmospheric events (mainly sferics, the electromagnetic emissions from lightning) produce large impulses in the noise waveform, so atmospheric noise consists of high-amplitude impulses superimposed on a background of low-level

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[1] The noise waveform of atmospheric radio noise below 100 MHz is typically impulsive in nature. The impulses are caused by atmospheric events, mainly lightning strokes, that create electromagnetic emissions known as sferics. Sferic impulses in the noise waveform are seen to cluster in groups, indicating an underlying clustering process related to the physical characteristics of the lightning mechanism. The objective of this work is the statistical modeling of the clustering of noise impulses in atmospheric radio noise in the range 10 Hz to 60 kHz (denoted low-frequency noise). Based on hundreds of hours of impulse interarrival time measurements made by the Stanford Radio Noise Survey System on such noise, a new Clustering Poisson atmospheric noise model is developed to describe the clustering process. This new statistical model is based on several previously known statistical-physical models of atmospheric radio noise, but in addition to these models it takes into account the clustering of sferic impulses. It is shown that the clustering model accurately characterizes the impulse interarrival time distributions found in low-frequency radio noise data.