Estimating positive narrow bipolar event channel characteristics from current pulse reflection signatures

We examine a set of fast electric field change records from lightning events located by the Los Alamos Sferic Array in June and July of 2005. From that large set, approximately 0.35% were classified as being intra-cloud events of type `Narrow Bipolar' and 84% of these were positive in polarity (a phenomenological definition: polarity referenced to the physics sign convention of the initial field change in the bipolar waveform and narrow meaning a primary pulse width time (rise + fall) of < 10 μs). When a current pulse traveling along a wire encounters a discontinuity in impedance it will reflect some fraction of its amplitude, depending on the magnitude of the mismatch. In the case of an unterminated transmission line, the load impedance is much less than that of air and the reflected pulse retains the same polarity as the incident. We believe that we see evidence of a similar phenomenon in the fast electric field change records for approximately 12% of the positive narrow bipolar events in our dataset (the negative polarity events have not yet been examined). By measuring the time difference between the primary field change peak, and the peak of the signature presumed to be the intra-channel current pulse reflection, a simple estimate can be made on the possible values of channel length range (bound by the speed of light as maximum propagation speed, and a reasonable lower-limit). By taking the ratio of the primary and reflected amplitudes, and assuming a reflection coefficient near unity, approximation of spatial decay length-scale can be made. With the bounds of assumed propagation speed, the decay length-scale translates into a temporal decay rate. Preliminary results show an average peak to reflected peak time of approximately 7 μs and a mean amplitude ratio of 6. Assuming current propagation at the speed of light, this estimates the upper bound for typical positive narrow bipolar event channel length to be 2.1 km, and a `1/e' decay scale-length of 1.2 km (1/e decay rate of 4 μs). Assuming a lower bound propagation speed of one-tenth the speed of light, the lower bounds become 210 m and 120 m (4 μs) respectively.