Statistical Characterization of PDD- Observed Lightning

Statistical Effects of Signal Discrimination

Prior to our discussion of the statistical nature of the PDD data it should be noted that our filtered data set does contain those events that were likely triggered by lightning but for which the compensation rate may have been too slow or too fast. In cases where the background intensity is increasing but the compensation rate is too slow, the peak signal amplitudes will be artificially elevated. In a rigorous treatment of the data these effects would be identified and removed. Unfortunately, it is not possible to discriminate against events for which the compensation rate was not ideal due to the possibility of misidentifying those events that result from rapid, sequential retriggering of the PDD on long-duration, structured optical signals, such as is shown in Figure 6.

Figure 6 shows a sequence of events, on a common time axis, that were recorded east of Hawaii at 0837:55 UT on October 8, 1997. Each of the six curves shows structure. Since we expect CG strokes to be separated by tens of milliseconds, the timescale of the interpulse interval in Figure 6 is suggestive of intracloud lightning. However, in the more general case, Brook et al. [1985] also noted structure in observations of transcloud optical lightning signals taken at an altitude of 20 km. They interpreted the structure that they observed as due to dart or stepped leader processes, or branching of the lightning channel. Goodman et al. [1988] have made similar interpretations of their above-cloud observations of lightning.

In the case of events shown in Figure 6 the signal level offsets at the beginning or end of a PDD event record are due to the finite PDD record length, not to the signal compensation. We expect signals of this variety to affect the peak amplitude and energy distributions (see sections 5.2 and 5.3). However, a review of 680,000 internal trigger mode, night/slow lightning events revealed only 4000 (<0.6%) such events. Thus we disregard the impact that these types of signals have on the statistical nature of the data set.

Peak Irradiance Distribution

Figure 7 shows two curves that represent the distribution of peak amplitudes for unfiltered events (solid line) and for filtered events (dashed line) (refer to section 3.3 for a description of the down-selection process). The low-amplitude edge of the filtered event distribution shows a hard cutoff at 3.3 10 ^-5 W m ^-2. This cutoff is artificial and arises primarily from the imposition of the noise rejection criterion, although the events at the lowest amplitudes in the unfiltered distribution are typically removed by the imposition of the particle rejection criterion. We note that the low-amplitude edge of the unfiltered distribution differs from the artificial cutoff by only a small amount in terms of absolute irradiance.

The VELA and DMSP optical data reported by Turman [1977, 1978] are the only comparable (pulse time history) data from satellite-based observations of lightning emissions that are known to these authors to have been previously reported. The median peak optical irradiance observed by the PDD is 1.3 10 ^-5 W m ^-2 as measured at the sensor. To compare with the observation reported by Turman, we assume that the signal is produced by an isotropic light source that is located at nadir and crudely range correct the signal amplitude by the satellite altitude R. We can thus estimate the peak power for the signal at the source by taking the product of the irradiance and 4R ². Doing so, we estimate the median peak optical power at the source to be 8.5 10 ⁸ W. This median value of peak power nearly corresponds with DMSP observations which gave the median peak power to be 1 10 ⁹ W [Turman, 1977, 1978]. We note that we have assumed that all events occur at nadir so that off-nadir range errors likely do exist. We also have not accounted for atmospheric extinction. The removal of these range and extinction errors would elevate the median value of peak power.

Optical Energy Distribution

Figure 8 shows the distribution of source optical energy for optical lightning events observed by the PDD. The source energy was estimated by assuming that all pulses had durations less than 2 ms. Recall that in section 3.5 we estimated that truncated signals account for <1% of the data set, so that our assumption does not introduce gross errors. The source energy was derived by computing the time-integrated irradiance for all filtered events (section 3.3) and then range corrected by assuming all events occurred at nadir (as in section 5.2).

Again, this method of estimating the source optical energy actually provides a lower bound on the optical energy of the sources. This statement follows from three assumptions. The first assumption was that there was no extinction of the optical signal due to cloud reflection or absorption. The second assumption was that all events were located at nadir rather than at off-nadir angles where the range increases by as much as 30% for a given altitude. The last assumption is that no part of the lightning optical signal was weaker than the subtracted background signal.

Nevertheless, we find that the pseudo-range-corrected optical energies observed by the PDD do lie in the same range as independent observations made above and below clouds. Goodman et al. [1988] report source optical energies as measured by a U-2 flying at an altitude of 20 km to be between 100 kJ and 1 MJ. Guo and Krider [1982] report on ground-based measurements of events near and within this energy range (77-370 kJ). The median estimated optical source energy is 450 kJ.

Observed Effective Pulse Widths

Definition of effective pulse width. The durations of optical pulses detected by the PDD are dependent on the source duration and the light-scattering effects of intervening clouds. In this paper, we compare the PDD-observed pulse widths with those from optical lightning pulses observed from aircraft and ground-based instrumentation. However, problems arise when the signal is not a single, clean pulse, which is amenable to simple measures of pulse width. Additional problems arise when the signal is not entirely captured within a PDD record. Figure 6 illustrates both of these types of problems. Of all six waveforms shown in Figure 6, none were completely captured. Further, if the first and second waveforms (counted from the left) had been completely captured, the complex signal shapes do not lend themselves to simple, direct measures of a characteristic width. Instead, we employ an indirect measure used by MacKerras [1973] called an "effective pulse width," which is based on the energy and peak irradiance of the observed signal. This indirect measure of pulse width is valid when the actual signal durations are smaller than the PDD record length. To calculate the effective pulse width, we integrate an observed signal through the 1.9-ms data window to arrive at event energy. We then multiply this representation of pulse energy by the reciprocal of the pulse's peak irradiance. The resulting moment-of-energy parameter has units of time (seconds) and serves as our effective pulse width [see MacKerras, 1973]. It is the width of a rectangular pulse having as much energy as the observed signal but with an amplitude corresponding only with the peak irradiance. This measure of characteristic pulse duration has been employed by other investigators [e.g., Guo and Krider, 1982; Suszcynsky et al., 2000]. The use of this indirect measure of pulse width mitigates the problems imposed by completely captured, complex signals. However, we are still faced with the problem posed by incompletely captured, or truncated, signals. In section 3.4 we noted that truncated signals account for <1% of the 680,000 events in our down-selected, filtered data set. Thus we do not expect truncated signals, such as those shown in Figure 6, to dramatically affect the effective pulse width statistics.

An initial comparison of above and below cloud effective pulse widths. The solid curve in Figure 9 illustrates the observed effective duration of down-selected optical pulses. A comparison of PDD effective pulse widths with other observations taken from above clouds [e.g., Brook et al., 1980, 1985; Goodman et al., 1988] shows relatively good agreement, with a slight bias in the median PDD-observed effective pulse widths toward larger values. However, when we compare our median effective pulse duration with those obtained below clouds [e.g., Guo and Krider, 1982; MacKerras, 1973], one may infer an estimate of the amount of additional path length incurred by cloud scattering. The additional path length is inferred by assuming that the photons propagate at the speed of light from the source to the sensor but that the propagation path is lengthened by Mie scattering so that some photons arrive much later than would be expected from transport through a cloud-free atmosphere. For comparison, MacKerras [1973] observed a median pulse width of 200 s below clouds in Australia. Guo and Krider [1982] inferred a median effective pulse width of 157 s below thunderclouds in Florida. The median value of the down-selected PDD event distribution shown in Figure 9 (solid curve) is 592 s. We infer some amount of photon scattering by cloud droplets, a subject also addressed in detail by Suszcynsky et al. [2000].

Effective pulse widths for cloud-to-ground strokes. One outstanding question is whether or not CG and IC events can be discriminated by satellite optical sensors on the basis of pulse width. In order to address this question, we compare the PDD pulse width distribution to the distribution of pulse widths observed by the PDD for signals that correlate with NLDN-reported events. In this section we compare the effective pulse width distribution for the PDD event population down selected in section 3.3 to the pulse width distribution for a subpopulation of PDD events that also correlate with NLDN-reported events. This comparison will show the distributions to be similar, a fact that apparently contradicts an earlier analysis given by Suszcynsky et al. [2000]. However, we will also show that the apparent contradiction does not exist and that our comparison is sound, and we will draw our conclusions from these facts. On the basis of the comparison with NLDN data in section 4 we believe that the population of PDD-observed lightning contains intracloud events. This poses a problem in any comparison with a population of cloud-to-ground (CG) events, such as those observed by MacKerras [1973] and Guo and Krider [1982]. We cannot conclusively determine that any given PDD event originated from a cloud-to-ground stroke using the PDD data alone. Thus, to make the comparison with the median effective pulse widths for CG strokes reported by MacKerras [1973] or Guo and Krider [1982] more appropriate, we endeavor to identify those PDD pulses associated with CG strokes reported by the National Lightning Detection Network (NLDN). To select for relevant NLDN-detected CG events, we impose the requirement that the NLDN-reported CG stroke location occur within the PDD field of view within 5 ms of a PDD-detected event. The imposition of this requirement provides 2552 PDD events coincident with 2842 NLDN events so that some PDD events are associated with multiple NLDN events. The dashed curve shown in Figure 9 gives the observed occurrence frequency of PDD pulse widths for the down-selected NLDN-reported CG population. The shape of the PDD/NLDN distribution in Figure 9 is grossly similar to the parent distribution derived in section 5.4.2, and the median pulse width of PDD events associated with NLDN-reported CG strokes is 604 s. However, Suszcynsky et al. [2000] report a median effective pulse width of 338 s for 237 PDD events that are correlated with VHF emissions that were determined via comparison with NLDN data to originate from CG strokes. So there is an appearance of an inconsistency that interferes with the development of a conclusion regarding the discrimination of CG and IC events by space-based optical sensors. Figure 10 shows the relationship between the estimated PDD source peak power and the effective pulse width for the 2552 down-selected PDD events associated with NLDN-reported CG strokes. There is a slight, but clear inverse relationship between the estimated peak optical power at the source and the effective pulse width. The median peak optical power at the source is 35 GW for pulses having effective widths of 210 s. For those pulses having effective widths of 600 s the median peak power is only 2 GW, nearly the median value of the source peak power shown in Figure 7. In order to determine the cause of the apparent inconsistency between these results and those reported by Suszcynsky et al. [2000], we reexamined the operational history of FORTE. We determined that the operators had unwittingly introduced a bias into the data set employed by Suszcynsky et al. [2000] by collecting 75% of the joint VHF/PDD records discussed by Suszcynsky et al. [2000] under daytime conditions. This artificially filtered the PDD data set used by Suszcynsky et al. [2000], allowing only bright lightning events to be detected by the PDD. When we consider Figure 10, it is clear that this also biased the pulse widths observed by Suszcynsky et al. [2000] to smaller values (i.e., 338 s). The apparent inconsistency is resolved. What this exercise that revealed to us is that given the PDD detection efficiency of NLDN CG events and given the similarities of the pulse width distributions, the identification of IC and CG events cannot be made on the basis of pulse width. This conclusion was also made by Goodman et al. [1988].

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