Figure 1 shows the TIPP for which the two nearly simultaneous positive
cloud pulses were detected by the NLDN. The duration of these pulses, 10
s, is somewhat longer than the median time of 4 s, but otherwise this
event is typical. On the ground the associated positive pulse was detected
first at station E1 with a rise time of 1.4 microseconds and a fall time of 4
microseconds. At E4, 0.75 milleseconds later, the rise and fall times were 7.0
and 2.2 microseconds respectively. Figure 2 illustrates how
we can use the relative timing of the observed TIPP-associated pulses at our two
stations to triangulate the location of the pulse. The two stations E1 and E4
are 490 km apart (1.63 light-milliseconds). Since the pulse was seen 0.75 ms
later at station E1 than at station E4, one solution is that the stroke occurred
close to a point on the line joining the two stations 1.19 light-ms from E1 and
0.44 light-ms from E4. This source location, 95.7
W and 37.3 N
should produce the largest signal amplitude at both stations, but any source
location on the curved solid isochrons in Figure
2 would produce the same
relative delays at the two stations.
In order to determine where along the isochron the TIPP was initiated we
examine three hypotheses. First, we assume that the signals arrived at the
stations by direct propagation and did not go beyond the optical horizon as seen
by the source discharge high in the cloud. Second, we assume that the signal
was not seen at other stations because it was beyond the horizon for them, and
third we assume that the discharge occurred in an electrically active region, as
is reliably located by NLDN cloud-to-ground records. If the source were in a
cloud at 10 km, consistent with the approximate altitude found for this
event by
Zuelsdorf et al. [1998b], and if
propagation were by direct line of sight,
the source would not be seen beyond a horizon at 360 km from the station. The
solid circles in Figure
2 show the 10 km horizons for each station.
The dashed
circles give the horizons for sources with altitudes between 8 and 12 km.
Clearly for the source to be seen at station E4 by line of sight propagation
from the cloud and to have a delay of 0.75 ms from the detection at E1 there is
only a small possible source region around the point 95.7 W and 37.3
N. This location is over southeastern Kansas if the source lies in the assumed
altitude range.
If the cloud pulse radiated isotropically and if all stations had a 100% detection efficiency we could also "triangulate" on the source region simply by making use of the knowledge of the field of view of the NLDN stations that observed the pulse and of those that did not. The stations ED, F4 and C8, that did not see the pulse, and their 10 km horizons are also shown in Figure 2 with the light circles. There is only a small region, shaded, in which a signal could be seen by E1 and E4 and not by ED, F4 and C8 if the source were strong and isotropic. This region abuts the source region identified from the timing data, lending more support for our identification. However, the radiation may be anisotropic and several factors can cause signals not to be registered by the NLDN detectors [K. Cummins, personal communication, 1997]. In particular, close to the causative pulse, the duration of the pulse may be shorter than that programmed to be recorded by the station and prior activity may have caused a pause in recording of pulses. Thus the time delay results are the more accurate.
Finally, let us examine the constraint provided by the location of other
electrical activity at the time. Figure 3 shows the
triangulated locations of cloud-to-ground strokes identified by the NLDN for
5 minutes around the TIPP we have just studied. At this time a cell of
activity is over the isochron calculated from the relative time delay at E1 and
E4. We assume that the TIPP was caused by a pulse somewhere along this front.
If we now take this storm region as the source location and calculate at what
altitude the source would lie if ground reflection caused the chirp separation
shown for this event in Figure
1, we obtain an altitude of 8 0.7 km, a
value consistent with those of
Zuelsdorf et al. [1998] and
Smith et
al. [1998]. The error reflects the uncertainty of the location of the
causative pulse along the isochron that we assume to occur somewhere within the
active electrical storm.