Lightning Sferics: Analysis of the Instantaneous Phase and Frequency Inferred From Complex Waveforms

Abstract

Analysis of very low frequency lightning waveforms, or radio sferics, can contribute to research into lower ionosphere perturbations and the corresponding atmospheric chemistry. Lightning waveforms can also be characterized on the basis of their propagation distance from receivers in order to study radio wave propagation. A bank of average waveforms, that is, the waveform bank, <1,000 km with a spatial resolution of 10 km has been produced, based on the lightning waveforms recorded in Europe on 8 August 2014. These average lightning waveforms at different distances exhibit a sequence of consecutive maxima resulting from ionospheric reflections, named sky waves. The spectral waveform bank shows a sequence of consecutive modal maxima at different frequencies depending on distance. The Hilbert transform is applied to produce complex lightning waveforms, which provide additional information to the original real waveforms alone, that is, the instantaneous phase and frequency. The time differences calculated from the instantaneous phases of complex lightning waveforms give the minimum arrival time difference error when compared to other analyzed signal processing methods. The derivative of the instantaneous phase, that is, the instantaneous frequency, represents the amplitude‐weighted average of frequency components at maximum amplitude according to theory and numerical simulation. In real experiments, the instantaneous frequency can be understood as the median value of the real frequency distribution calculated at maximum amplitude. It is found that the instantaneous frequencies at maximum amplitudes are distance dependent. This finding might enable the development of a novel method to determine lightning distances in the future.

First Map of Coherent Low‐Frequency Continuum Radiation in the Sky

“…It is currently not known with certainty whether this phase stability is a property of the causative lightning discharge or a consequence of the electromagnetic wave propagation within the Earth‐ionosphere cavity. However, it is speculated that the distance between the lightning discharge and the array contributes significantly to the observed instantaneous frequencies (Liu et al, ).…”

“…It was recently reported that the instantaneous frequency of lightning pulses implicitly depends on the instantaneous amplitude because the phase is better defined during relative maximum amplitudes when compared to relative minimum amplitudes (Liu et al, ). We extend this analysis here by comparing the instantaneous frequencies of all the measured relative amplitude maxima and minima of the amplitude envelope.…”

“…The difference between the peaks of the observed instantaneous frequency distributions at 11 and 10 kHz therefore indicates that the observed instantaneous frequencies of lightning pulses are physically meaningful. These instantaneous frequencies of lightning pulses possibly depend on the average distance between the array and the lightning discharges (Liu et al, ). In summary, the phase stability of lightning pulses is determined by the instantaneous frequencies that exhibit a significant offset from the center frequency chosen for the signal processing.…”

“…The main reason why phase measurements are less common is that the associated signal processing has a larger degree of complexity (e.g., Gross et al, ; Koh et al, , and references therein). More recently, phase measurements of lightning discharges have become of increasing interest, partly to determine the impact of lightning on the lower ionosphere (McCormick et al, ) or for their use in lightning detection networks (Liu et al, ; see also Dowden et al, ; Liu et al, ). In particular, three‐dimensional lightning detection networks, commonly referred to as lightning interferometers, have made extensive use of the cross‐correlation function, which implicitly includes phase information (e.g., Shao et al, ; see also Abbasi et al, ; Lyu et al, ; Rison et al, ; Stock et al, ; Wu et al, , and references therein).…”

Detection of Low‐Frequency Continuum Radiation

“…On the other hand, lightning researchers often describe radio transmissions as noise (e.g., Füllekrug et al, ; Jacobson et al, ; Smith et al, , and references therein) because anthropogenic radio transmissions limit the detection threshold for natural weak lightning processes such that the influence of disturbing radio transmitters needs to be mitigated. For example, in long‐range lightning detection networks spectral filter techniques are applied to increase the detection efficiency (Dowden et al, ; Liu et al, , , and references therein). When electromagnetic signatures from intermittent lightning discharges and radio transmissions in specific frequency ranges are absent, or removed, small radio signals originating from wave particle interactions in near‐Earth space can be observed at high latitudes and from satellites in space (e.g., LaBelle & Anderson, ; Manninen et al, ; Parrot et al, ; Titova et al, , and references therein).…”