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STATEMENT OF THE PROBLEM



How can the Digital Signal Processing (DSP) features in an ordinary home computer be applied to analysis of dispersed, remote, lightning strike events?



HYPOTHESIS



It is possible to obtain information from a single lightning strike event to estimate approximate location of a distant lightning strike, due to the fact that:

The electromagnetic signal generated by a distant lightning strike is dispersed in time as it travels the long waveguide path from the point of origin to the point of reception
Analysis of such a pulse can be made using Fourier Transform equations
o This will yield information regarding the length of the path of the dispersed signal
The use of Fourier Transforms is cumbersome, but Fast Fourier Transform (FFT) algorithms streamline this process, and such FFTs can be found in basic home computer sound cards
FFTs change amplitude versus time parameters into frequency versus time displays and make possible graphical display, printout, and analysis of such transformed signals.



MATERIALS



20 sferic .WAV files obtained from the internet (some containing tweeks and whistlers)
one (1) computer system
Computer Program "SPECTRAN"
Computer Program "Excel"
Calculator
Pencil
Paper



PROCEDURES



1. Obtain 23 data records of lightning strike events by download from the internet, in a .WAV format.

2. Using available home computer program, SPECTRAN, which incorporates the necessary DSP algorithms, isolate the data of interest.

3. Using the .WAV files in SPECTRAN, identify at least two frequency versus time of arrival cross points for the lightning event captured. Attempt to have maximum frequency separation (highest to lowest) between the cross points for the captured event.

4. Enter data into an Excel data collection spreadsheet, containing all necessary formulas for automatic calculation. Alternatively, use the collected data and manually calculate the length of path.

5. Having obtained length of path either by the Excel spreadsheet or manually, use this information to calculate the distance along a Great Circle path to determine the approximate location of the lightning strike.

6. Repeat steps three through five for the remaining 22 captured events.




RESULTS



Information regarding the speed of a wave generated by a lightning strike and the distance of that lightning strike from where the sferic data sample was captured were determined by this experiment. In conducting the experiment, two important points must be made with respect to the procedures outlined. First, the need for manually calculating the distance of lightning strikes was not necessary as the formulas embedded in the Excel spreadsheet were found to be accurate and reliable. Second, despite the statement in the paper that tweeks would be the only sferics analyzed, this did not prove to be the case. In most cases, the sferic captured in the .wav file turned out to be a whistler rather than a tweek.
As mentioned in the paper, the propogation of a tweek follows a path that is bounded by the earth's surface and the underside of the ionosphere. Whistlers, on the other hand, propogate along a magnetic line of force which results in a far longer path. Despite this fact, the mathematical equation for determining the distance of the lightning strike from where the sferic was captured applies equally to both tweeks and whistlers. The constant of the equation, called the Frequency of cutoff in the tweek case, is different than for the whistler, which is called the cyclonic frequency. These two constants are known to be of a similar range, although the cyclonic frequency is more difficult to calculate and was not analyzed for this paper. The important point here is that the use of the mathematical formula very clearly demonstrates the vast difference between the length of a tweek path and that of a whistler path. To determine the length of the path, the velocity of progogation (V) had to be determined. The velocity of propogation is the speed of the wave generated by the lightning strike and approaches the speed of light at the higher frequencies. As seen in Table 1 below, the velocity of propogation varied from a low of just over 35 million meters per second to a high of over 206 million meters per second for the samples captured. The higher velocity of 206 million meters per second means that the frequency was very high compared to the velocity of 35 million meters per second.
TABLE 1: CALCULATED VELOCITY OF PROPOGATION (ms)
and DISTANCE OF LIGHTNING STRIKE (km)
DATA Velocity of Propogation (ms) Distance (km)
Sample 1 121,312,275 53,998
Sample 2 73,596,193 37,066
Sample 3 86,289,788 7,270
Sample 4 86,289,788 50,889
Sample 5 121,312,275 65,206
Sample 6 121,312,275 89,658
Sample 7 163,229,353 136,166
Sample 8 170,153,190 70,827
Sample 9 186,207,739 98,294
Sample 10 154,736,519 89,544
Sample 11 73,596,193 35,115
Sample 12 35,027,985 3,173
Sample 13 105,863,769 78,554
Sample 14 58,381,369 7,250
Sample 15 113,802,976 77,043
Sample 16 35,027,985 19,831
Sample 17 113,802,976 58,700
Sample 18 86,289,788 7,270
Sample 19 165,251,275 36,822
Sample 20 73,596,193 1,951
Sample 21 35,027,985 1,586
Sample 22 206,185,006 462,238
Sample 23 105,863,769 6,546
ms = meters per second km = kilometers


The calculation for determining the velocity of propogation was the speed of light multiplied by the square root of (one minus the frequency of cutoff divided by the low frequency point (of the captured data sample) squared. As mentioned in the footnotes of the data table, the frequency of cutoff is the point below which a radio wave fails to penetrate a layer of the ionosphere. As such, each sample captured used a high frequency point on the tweek or whistler sample and a low frequency point that was above the frequency of cutoff.
To determine the approximate distance of the lightning strike, the formula required that the speed of light be multiplied by the velocity of propogation by the difference in time between high and low frequency points, divided by the speed of light less the velocity of propogation. The calculated distance for each sample is reflected in Table 1 above and Figure 1 below. The average velocity for all of the samples was 108,354,638 meters per second and the average distance was 65,000 kilometers. As seen in the Conclusions section that follows, the hypothesis was partially supported in this experiment.



CONCLUSIONS



The purpose of this project was to use data which had been previously collected, along with a simple home computer program, to attempt to determine the approximate location of a lightning strike, by analyzing the sferics, such as tweeks and whistlers, caused by the strike. The data files of the sferics were analyzed to find their high and low frequencies of each sample (with the low frequency at least above the frequency of cutoff level), and the amount of time that elapsed from the high frequency point to the low frequency point. Once this data was collected, using the DSP formulas embedded in SPRECTRAN, the distance of a lightning strike from the point of capture of the tweek or whistler was able to be determined. After conducting the experiment, the hypothesis was found to be partially supported. With the information collected, a circle on the surface of the earth was determinable, the circumference of which identified all of the possible points on which the strike could have occurred. Because this particular project does not use variables the only possible sources of error would have been in recording the data, which has been analyzed again and is correct. Absent real time information, which could have provided specific meteorological data about storms occurring along the defined circumference, the location of the strike was not able to be determined. As such, the hypothesis was supported in that the distance of the strike was determined but was not supported as the location of the strike was not found.
It is of interest to note that, although the formula used in this experiment was intended for use with analyzing tweeks, it showed very clear differences in path lengths between tweeks and whistlers. This is because the whistler path length is not restricted to ionospheric paths, but is instead determined by the length of a magnetic line of force. This was information that was not expected to be discovered when setting out to perform this experiment.
As this experiment used simple home computer software, the results provided limited information about specific meteorological phenomena. However, the internet sources reviewed showed that NASA and other government organizations are also looking at similar events. As these organizations have much more sophisticated tools at their disposal, the positive impact to society that these experiments could have can only be imagined. By the fact that experiments are being done by these government bodies, the experiment conducted in this paper can most definitely be improved upon and would, in all likelihood, rely on much more powerful computer programs and real time meteorological data, which could, and most likely would, provide very important information to society.


















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