Atuona case
Figure 4(a) maps the density of the first cohort of strokes, having mostly-sunlit paths to Atuona. The color scale is relative to the maximum-density pixel in this plot , with blue meaning 0.01Xmaximum, and red meaning maximum. The resolution is 1-deg X 1-deg. The white areas are < 0.01Xmaximum. The stroke density is displayed only within the -40 to +40 deg N band. The curves of |dip angle| = 30, 45 deg are shown in heavy black, while the geomagnetic equator is shown as a thinner black curve. Neither the |dip angle| curves, nor the stroke density, are shown within the antipodal cone. Also, the -45 deg dip-angle curve is not shown where (southmost South America) it is outside the latitude band.
Figure 4(b) is like Figure 4(a), except that the density is only for the subset of the day-cohort strokes that are detected by Atuona . Thus comparison of Figure 4(a, b) gives a visual map of the pattern of day-cohort detection/non-detection by Atuona. Note that the eastern two-thirds of South America’s day-cohort lightning is not detected by Atuona, whilst the lightning in SE Asia and Indonesia, though no closer, is largely detected.
Reminder: The color range in the second panel, Figure 4(b), is determined only by the densities in Figure 4(b), and isunrelated to the color range in the first panel, Figure 4(a). Thus for example, the threshold for blue (0.01Xmaximum) is different (and smaller) in Figure 4(b) than in Figure 4(a). This allows blue cells to appear in the second panel, in principle, at a few locations that are white (sub-blue) in the first panel.
Figure 4(c) maps the value of the day logarithmic reference transmission, for all grid points within the selected latitude band, regardless of the incidence of lightning there. The only exception is that the transmission is whited-out in the antipodal cone. The displayed value is lumped into just four ranges of logarithmic reference transmission: > -2 (red), -2 to -3 (yellow), -3 to -4 (green), and < -4 (blue).
Figures (4d-e) are exactly like Figures 4(a-b) except for the second cohort of strokes, having mostly dark paths to Atuona. Figure 4(f) is like Figure 4(c), except for the night logarithmic reference transmission. In night conditions, the asymmetry becomes more dramatic. Atuona detections in South America become insignificant. Comparing Figures 4(c,f), we see that the model prediction is consistent with observations.
Figure 4(g) shows histograms of the actual instantaneouslogarithmic reference transmission, taking account of theinstantaneous solar zenith angle at each point along the path . This is not the contrived ”day” or ”night” prediction of Figures 4 (c,f). The black curve in Figure 4(g) is for all 9.21X108 strokes within the latitude band, while the red curve is for only the 1.09X108 strokes in that band detected by Atuona. By comparing the two curves, it is apparent that Atuona’s detection rate falls off rapidly for logarithmic reference transmission < -2, and is completely insignificant for < -4. These are empirical facts based on the distribution of lightning amplitudes, the proximity of the lightning to Atuona, the performance of the network, and the performance of this particular station. The empirical evidence of Figure 4(g) allows us to interpret the model predictions for contrived pure-day (Figure 4c) and contrived pure-night (Figure 4f). The red-shaded regions correspond to logarithmic reference transmission > -2. We can thus interpret the red regions in Figures 4(c,f) as having unimpeded detectability (at least as far as D-layer effects are concerned.) The yellow-shaded regions are predicted to have relatively lower detection success, though not zero. Green is even lower, and there are predicted to be essentially no detections in the blue-shaded regions, where logarithmic reference transmission is < -4. With that as a guide, we can now appreciate that the behavior of Figure 4(b), relative to Figure 4(a), is roughly consistent with the contrived day model (Figure 4c) and the empirical distribution (Figure 4g). Similarly, the behavior of Figure 4(e), relative to Figure 4(d), is roughly consistent with the contrived night model (Figure 4f) and the empirical distribution (Figure 4g). Notably, Atuona’s complete non-detection of any lightning in South America for mostly-dark paths (Figure 4e) is consistent with the all-blue shading of South America (Figure 4f) in the night model. Likewise, Atuona’s strong detection in the Australasia sector for mostly-dark paths (Figure 4e) is consistent with that region’s being shaded red (Figure 4f) in the night model.
The map-based displays (Figures 4a-f) are useful for illustrating the geographic patterns of detection/non-detection by Atuona for two extreme cases, as well as comparing those patterns with the respective model predictions. However, these map-based displays are extremely complicated to follow, and are patchy in their coverage due to the uneven geographical and temporal occurrence of lightning [Christian et al. , 2003].
Ultimately, the entire quantitative outcome of our data for Atuona can be distilled into the far simpler and clearer Figure 4(g), which usesall the available strokes in the latitude band, without parsing for contrived special cases (mostly-day, mostly-dark). The parent distribution (black curve) shows that > 50% of the network-detected strokes have logarithmic reference transmission (to Atuona) < -3, whilst by contrast, for the subset detected by Atuona (red curve) there are very few detected strokes in that range. Thus the predictive model is consistent with the pattern of Atuona’s detection/non-detection. (We take as axiomatic that large signals tend to be easier to detect than are small signals.)