4e. Closing the observational case that the model is consistent
with the data
We have presented observations of the geographical patterns of
detection/non-detection for ten selected stations around the globe, at
low and low-middle latitudes. The geographical patterns are shown for
separately for mostly-day, and then mostly-night transmission paths. The
observed patterns of detection/non-detection are consistent with the
patterns of predicted logarithmic reference transmission, for the
respective day or night cases. More quantitatively, the distributions of
actual logarithmic reference transmission to each selected station, both
for the parent distribution and for the subset of strokes in whose
location the selected station is a participant (i.e. detected by the
selected station), show that the paths for detected strokes are
clustered at the high-transmission end of the parent distribution. Thus
the model predicts which cases are more likely to be detected, and which
are not.
As mentioned earlier, this logic rests on an axiom: All other things
being equal, a strong pulse is more likely to be detected than is a weak
pulse. And we assume, all other things being equal, that paths involving
relatively weaker transmission will cause weaker detected pulses than
will paths involving relatively stronger transmission.
We now perform a ”sanity check” on this key assumption. Figure 14 shows
distributions of the detected, raw ADC amplitudes for pulses detected by
the Tel Aviv station. The ADC is 16-bits deep (0 to 65535), but we show
the distributions out to only ADC level 5000. The two panels in Figure
14 are for two adjacent tranches of modeled logarithmic reference
transmission: (a) > -2, and (b) in the range -2 down to
-2.5. The shoulder at about ADC level 100 - 200 corresponds to the
local-time servo adjustments of the station’s software trigger
threshold. The higher-transmission distribution (a) contains
1.8X108 detections, while the lower-transmission
distribution (b) contains only ~12% as many detections.
Moreover, in (a) the high-transmission distribution’s tail, relative to
the distribution’s peak, is much more relatively populated than in (b).
Finally, whereas in (a) the peak occurs at ADC level ~
800, in (b) it has retracted to ~ 500.
Thus Figure 14 supports the picture that the high-transmission
population’s extended tail (to higher values of detected ADC level)
becomes depleted at lower transmission, with those tail members being
swept to the left end of the distribution. Most of those then are swept
to sub-threhold ADC level, but some remain above the threshold and
constitute the peak in (b). Let us see if this picture makes
quantitative sense. The change in logarithmic reference transmission
between these two tranches is in the range 0.5 to 0.75, depending on
where, within a tranche, it is figured. The first part of this study
demonstrated that the ”r” parameter, which multiplies the logarithmic
reference transmission to give the actual physical transmission, was
fitted by the data of JHB1 to lie in the range from 2 to 3 Nepers (see
Figures 6 and 9, and discussion thereof, in JHB1). Let us choose 2.5
Nepers. Then the change in logarithmic reference transmission between
these two tranches in the range 0.5 to 0.75 Nepers corresponds to a
change in physical logarithmic transmission in the range 1.25 to
1.88 Nepers. In linear amplitudes, the range is a multiplicative factor
from ~3.5 to ~6.5. This implies that the
transition from Figure 14(a) to 14(b) can be understood as taking tail
members in (a) and moving them leftward (to lower ADC level) in (b) down
to ADC levels only 1/3.5 to 1/6.5 as big. Fortunately, we see that the
tail in (a) contains sufficient population to permit this simple occur.
Thus the relative distributions of detected raw ADC levels are
consistent with the predicted transmissions of adjacent tranches of the
transmission distribution.