Wavelet multiresolution based multifractal analysis of electric fields by lightning return strokes

Abstract

Lightning can be seen as a large-scale cooperative phenomenon, which may evolve in self-similar cascaded way. Using the electric field waveforms recorded by the slow antenna system, the mono-and multifractal behaviors of 115 first return strokes in negative cloud-to-ground discharges have been investigated with wavelet multi-resolution based multifractal method. The results show that the return stroke process, in term of its electric field waveform, has apparent fractality and strong degree of multifractality. The multifractal spectrums obtained for the 115 cases are all well fitted to a modified version of the binomial cascade multifractal model. The width of the multifractal spectrums, which measure the strength of multifractality, is 1.6 in average. The fractal dimension of the electric field waveforms ranges from 1.2 to 1.5 with an average of 1.3, a similar value to the fractal dimension of the lightning channel obtained by others. This suggests that the lightning-produced electric fields may appear the same fractal dimension as its channel. The relationship between the peak current of a return stroke and the charge deposition in its channel was also discussed. The results suggest that the wavelet and scaling analysis may be a powerful tool in interpretation of the lightning-produced electric fields and therefore in understanding of the lightning.

Tree Topology Estimation

“…Fortunately, good theoretical and empirical models have been developed in several domains to describe the expected morphology or growth pattern of a particular type of tree. Well-studied trees include blood vessels [31], [33], plant roots [2], [20], neurons [24], [28], leafy trees [3], [34], and lightning [15], [29]. …”

Uso de la Transformada de Ondeletas (Wavelet Transform) en la Reducción de Ruidos en las Señales de Campo Eléctrico producidas por Rayos

“…En diferentes lugares del mundo se han llevado a cabo en las últimas décadas múltiples mediciones de las señales de los campos eléctricos de los rayos, las cuales han permitido avanzar en el conocimiento de sus principales características (Fernando y Cooray, 2007;Nag, 2009;Ahmad et al, 2010). Sin embargo, la obtención de estos parámetros a partir de las formas de onda del campo eléctrico o la corriente de la descarga de retorno no es una tarea sencilla debido a la existencia de diferentes tipos de ruido en las señales registradas (Baba et al, 2004;Gou et al, 2009;Nedjah et al, 2010). En algunos casos si se conoce la frecuencia del ruido éste puede reducirse empleando filtros análogos o mediante el procesamiento de las señales medidas.…”

“…Miranda (2008) y Sharma et al (2010) utilizaron la Transformada Wavelet para evaluar el espectro de potencia de los diferentes eventos de los rayos a partir de mediciones del campo eléctrico. Gou et al (2009) estudiaron el comportamiento fractal de las formas de onda del campo eléctrico producidas por la primera descarga de retorno empleando una técnica Wavelet multiresolución.…”

Local polynomial approximation and intersection of confidence intervals for removing noise of lightning electric field measurements

“…However, the extraction of lightning parameters from LEF or current measurements is not a simple task due to the presence of noise in the recorded signals, mainly caused by the measuring system itself and other undesired components present in the electromagnetic environment [7][8][9].…”

“…To develop and evaluate models of the lightning return stroke and determine the lightning current features, it is necessary to determine, in a reliable way, various temporal features of the electric field waveforms such as: the peak value, rise-time, zero-crossing time, slow-front and fast-front duration, and peak value of the electric field derivative [6][7][8] [ [6][7][8]. However, the extraction of lightning parameters from LEF or current measurements is not a simple task due to the presence of noise in the recorded signals, mainly caused by the measuring system itself and other undesired components present in the electromagnetic environment [7][8][9].…”