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.