Kennedy Space Center, 1997

At the Kennedy Space Center (KSC) in 1997, the slow antenna instrument was placed on top of a building. The antenna's location was near the corner of the building, where the electric field was probably enhanced. The calibrator, however, was placed in an open level field away from the building. Thus, the local electric field calibration (Appendix B.6.1), which is based on calibrated electric field readings from the calibrator, should have been unaffected by the placement of the slow antenna. Unfortunately, the calibrator's calibration data for KSC was lost, making it impossible to reliably determine the electric field amplitude of sferics recorded by the calibrator.

The op-amp for the calibrator was temporarily replaced at KSC since the previous op-amp had burned out. The replacement op-amp was obtained on short notice and was not identical to the type of op-amp normally used. Thus, the data obtained at other sites (with other op-amps) for the calibrator's V/m range could not be used for the KSC data. The net effect is that the local electric field calibration could not be performed on the KSC data. An independent means of determining the electric field was necessary.

The time, location, and peak-current of CG strokes is recorded by the National Lightning Detection Network, which is operated by Global Atmospherics Inc. (Cummins et al., 1998). If the ground can be assumed to be a perfect conductor at the dominant frequency of the return stroke ($\sim$10 kHz), then the peak-current, $I_p$, is related to the peak electric field, $E_p$, by (Orville, 1991; Uman et al., 1975):

$$E_p = \frac{I_p\,V_{rs}}{2\,\pi\,r\,\epsilon_o\,c^2}\$$ (B.3)

where $V_{rs}$ is the velocity of the return stroke ($\sim\,$1.2$\times$10$^8$ m/s (Idone and Orville, 1982)), $r$ is the distance between the return stroke and the electric field meter, $\epsilon_o$ is the permittivity of free space, and $c$ is the velocity of light.

The range-normalized signal strength ($S_{RN}$) which is reported by the NLDN in ``LLP units'' is related to the raw signal strength ($S$) recorded at the sensor by the following signal propagation model (Cummins et al., 1998):

$$S_{RN} = C\,S\,\Big(\frac{r}{l}\Big)^p\,{e^{(\frac{r-l}{A})}}$$ (B.4)

where $r$ is the range in kilometers, $l$ is the normalization range (100 km), $p$ is an attenuation exponent, $A$ is the e-folding length for attenuation, and $C$ is a constant. Currently, the NLDN signal strengths are based on $p=1.13$ and $A=10^5$ km (Cummins et al., 1998).

The peak current is determined from NLDN data by the following relationship:

$$I_p = \frac{S_{RN}}{5.4}$$ (B.5)

Substituting Equation B.5 into Equation B.3 for $r=100$ km (the normalization range) yields the result that one LLP unit of signal strength would produce a field change of 0.045 V/m at 100 km range. Assuming that $S=E_p$, then $C=1/0.045$ in Equation B.4. Solving for $E_p$:

$$E_p = 0.045\,S_{RN}\,\Big(\frac{100}{r}\Big)^{1.13}\,e^{\big(\frac{100 - r}{1\times10^5}\big)}$$ (B.6)

where $r$ is in units of kilometers.

The values of $p$ and $A$ used to derive Equation B.6 are based on data collected in Florida and may not be valid for other regions. Furthermore, Equation B.6 should only be used to predict $E_p$ between about 50 and 200 km range (K. Cummins, private communication, 1999). The attenuation factors at other ranges may be different.

Table B.2 shows the electric field calibration which was used for the KSC data. Several strokes near the optimum 100 km normalization range occurred around the time of the 1:42:57 UT sprite-producing dicharge which was analyzed in Section 3.6. The LLP signal strengths reported by the NLDN were used to calculate a peak electric field, $E_p$, at the range of the electric field meter from the stroke. A change in the fast antenna electric field data, recorded as 12-bit values (0-4095), was produced by each stroke. The average ratio of the changes in digital units to the $E_p$ values showed that a field change of 1 V/m produced a change of 182$\pm$10 digital units in the fast antenna data. Thus, the full-scale range of the recorded fast-antenna data was $4096/(182\pm10)=22.5\pm1.3$ V/m.

Table B.2: Several ``CG'' strokes recorded by the NLDN on June 22, 1997 were used to calibrate the fast antenna data. For each stroke, the LLP signal strength ($S_{RN}$) and range ($r$) were used to calculate a predicted peak electric field ($E_p$). The change in digital units of recorded data (12-bit: 0-4095) produced by the electric field change of amplitude $E_p$ was used to calculate the number of digital units which corresponded to a 1 V/m field change.

Fast Antenna Calibration on June 22, 1997 at KSC
Time	$S_{RN}$	Range	$E_p$	Digital	Number of digital
[UT]	[LLP]	[km]	[V/m]	units	units per V/m
1:39:55.845158	$-$120.0	83	$-$6.64	$-$1221	183.9
1:41:19.120782	$-$145.9	83	$-$8.07	$-$1556	194.1
1:41:33.758866	$-$105.5	74	$-$6.68	$-$1206	180.5
1:41:49.389430	$-$65.6	81	$-$3.77	$-$620	164.4
1:42:21.406597	$-$81.6	83	$-$4.54	$-$775	170.7
1:42:40.669062	$-$116.5	87	$-$6.13	$-$1191	194.3
1:44:33.520315	$-$99.3	119	$-$3.67	$-$671	182.8
1:44:59.627920	$+$55.0	93	$+$2.68	$+$500	186.6
Average: 182$\pm$10 units/V/m

On June 22, 1997, the fast antenna was operated in a 10x mode of amplification relative to the slow antenna. The slow antenna data was also digitally sampled with 12-bit resolution. Since the 12-bit analog-to-digital converters for the slow and fast antenna data have nearly identical full-scale input voltage ranges, a $22.5\pm1.3$ V/m range on the fast antenna translated into a $225\pm13$ V/m full-scale range on the slow antenna.