4.3 Determination of flash location using high-resolution timing

Figure 4.13: Location of luminosity in elves. Quadrangles show the deduced source locations of the first elves luminosity in each photometer. Constrained lower altitudes are also shown for some photometers.

The time-resolved optical features of elves as measured in the Fly's Eye not only discriminate elves from other flashes, but also provide quantitative information regarding the location of each elve with respect to its causative CG lightning stroke. The field-of-view of each Fly's Eye photometer was measured precisely (Figure 3.11 on page ), and the pointing elevation and azimuth at any time during observations were recorded by an electronic clinometer and a compass-adjusted, graduated mount. This knowledge, coupled with the lightning locations given by the NLDN and the delay in each photometer between the sferic and the flash onset, constrain in three dimensions the source of the first light seen in each photometer [Inan et al., 1997].

Figure 4.1 shows how this is possible for the case of a photometer pointed directly over the causative CG. The VLF radio pulse from the CG return stroke constitutes a ground wave propagating at very nearly the speed of light ($c$). It reaches points on the surface of the Earth a time $t$$=$$s/c$ after the return stroke occurs; here, $s$ is the great circle path length from the lightning location.

The onset of an optical flash in a photometer which is colocated with the VLF receiver is due to a VLF pulse propagating to an ionospheric point, and the resulting optical wavelengths propagating from that point to the photometer, both at the speed of light. The segment length $l$ between a point near the ground (observer or lightning) and one in the ionosphere for a spherical Earth is

$$l=(R_{\rm E}+h) \frac{\sin\left(\displaystyle{\frac{s}{R_{\rm E}}}\right) }{ \cos\left(\theta+\displaystyle{\frac{s}{R_{\rm E}}}\right)}$$

where $R_{\rm E}$ is the Earth radius, $h$ is the observer's altitude, and $\theta$ is the observer's viewing elevation angle above horizontal. Because the source of the photon production is constrained to be along the line of sight of the observer, the time difference between arrival of the sferic and an optical pulse in a photometer constrains the optical source location.

The onset delays in each photometer for all the events ranged from 97 $\mu$s to 620 $\mu$s, where the longer times correspond to parts of the elves located behind the source lightning or far to the side of it. However, the first appearance of each event in any photometer occurred almost exclusively between 100 $\mu$s and 200 $\mu$s after reception of the associated sferic.

Figure 4.13 shows a top-down view of source locations determined in this way for a bright flash. The uncertainty due to the extent of the fields-of-view is shown by the dotted quadrilaterals. We performed this analysis for all identified elves associated with an NLDN flash, and in a majority of cases, flashes were localized at a distance of over 100 to 200 km from the source lightning. In several cases this distance was well over 300 km, as predicted for strong discharges [Inan et al., 1997].

While both the altitude and the geographic location of the initial observed point of each flash are determined in this way, the altitude is not as tightly constrained for very low elevation angles (about 4$^\circ$ on the 27th of August). Nevertheless, the deduced lower altitudes of each flash source remained roughly consistent with the predicted 85-95 km [Inan et al., 1996c] and served as a sanity check for the discrimination of elves from Rayleigh-scattered light, which, due to its short onset delay, would have a deduced altitude near zero (see page ).