THERE has been a growing interest lately in locating cloud

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 2, MAY 2011 407 Remote Measurements of Currents in Cloud Lightning Discharges Amitabh Nag, Member, IEEE, VladimirA.Rakov, Fellow, IEEE, and John A. Cramer, Member, IEEE Abstract Using measured wideband electric field waveforms and the Hertzian dipole (HD) approximation, we estimated peak currents for 48 located compact intracloud lightning discharges (CIDs) in Florida. The HD approximation was used because 1) CID channel lengths are expected to range from about 100 to 1000 m, and in many cases can be considered electrically short and 2) it allows one to considerably simplify the inverse source problem. Horizontal distances to the sources were reported by the U.S. National Lightning Detection Network (NLDN), and source heights were estimated from the horizontal distance and the ratio of electric and magnetic fields. The resultant CID peak currents ranged from 33 to 259 ka with a geometric mean of 74 ka. The majority of NLDN-reported peak currents for the same 48 CIDs are considerably smaller than those predicted by the HD approximation. The discrepancy is primarily because NLDN-reported peak currents are assumed to be proportional to peak fields, while for the HD approximation, the peak current is proportional to the peak of the integral of the electric radiation field. An additional factor is the limited (400 khz) upper frequency response of the NLDN. Index Terms Current, electric fields, electromagnetic propagation, electromagnetic measurements, lightning. I. INTRODUCTION THERE has been a growing interest lately in locating cloud lightning discharges and estimating their peak currents (e.g., Cummins and Murphy [1]; Betz et al. [2]). Estimation of currents from very low frequency/low frequency (VLF/LF) fields requires a field-to-current conversion procedure that can work in the absence of specific information on radiating-channel geometry. In the case of cloud-to-ground discharges, the latter is usually not a problem, since they have grounded channels whose overall lengths typically exceed 5 km, and the field peak is formed when the current wave is within the more or less vertical bottom section (1 km or so) of the channel. In contrast, cloud discharge channels are elevated above ground and can be as short as 100 m or so. As a result, the field-to-current conversion equations that are developed for cloud-to-ground lightning return strokes (for example, those implemented in the U.S. Na- Manuscript received June 6, 2010; revised July 27, 2010; accepted August 30, 2010. Date of publication December 17, 2010; date of current version May 20, 2011. This work was supported in part by the National Science Foundation under Grant ATM-0346164 and Grant ATM-0852869, and by the Defense Advanced Research Projects Agency. A. Nag and V. A. Rakov are with the Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611 USA (e-mail: amitabh@ufl.edu; rakov@ece.ufl.edu). J. A. Cramer is with the Vaisala Inc., Tucson, AZ 85746 USA (e-mail: john.cramer@vaisala.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEMC.2010.2073470 tional Lightning Detection Network (NLDN) and other similar systems) may be not suitable for cloud-discharge processes. Cloud lightning discharges that produce both 1) single, usually solitary bipolar electric field pulses having typical full widths of 10 30 μs and 2) intense high frequency/very high frequency (HF/VHF) radiation bursts (much more intense than those from any other cloud-to-ground or normal cloud discharge process) are referred to as compact intracloud lightning discharges (CIDs). These discharges were first reported by Le Vine [3] and later characterized by Willett et al. [4], Smith et al. [5], Eack [6], Hamlin et al. [7], and Nag et al. [8] among others. Most of the reported electric field signatures of these discharges are produced by distant (tens to hundreds of kilometers) events and hence are essentially radiation. The radiation field pulses produced by CIDs are sometimes referred to as narrow bipolar pulses. CIDs tend to occur at high altitudes (greater than 10 km) and have relatively short channel lengths of 100 1000 m. Many of them are expected to be electrically short radiators (shorter than the shortest significant excitation wavelength). Nag and Rakov [9] proposed a bouncing-wave mechanism to describe electromagnetic radiation produced by CIDs. In this paper, we used the vertical Hertzian dipole (HD) approximation to estimate peak currents of 48 located CIDs from their measured electric fields. The majority of NLDN-reported peak currents for these CIDs are considerably smaller than those predicted by the HD approximation. We will show that one reason for this discrepancy is related to the use of different fieldto-current conversion equations, with another reason being the limited upper frequency response of the NLDN. II. DATA Data for the 48 CIDs examined here were acquired in August September of 2008 at the Lightning Observatory in Gainesville (LOG), Florida. The electric field measuring system included an elevated circular flat-plate antenna followed by an integrator and a unity-gain, high-input-impedance amplifier. The system had a useful frequency bandwidth of 16 Hz 10 MHz, the lower and upper limits being determined by the RC time constant (about 10 ms) of the integrator and by the amplifier, respectively. The wideband magnetic field (B), which was used in estimating the source height, was obtained by integrating and combining the two orthogonal components of db/dt.thedb/dt measuring system employed two orthogonal loop antennas, each followed by an amplifier. The upper frequency response of the db/dt measuring system was 15 MHz. All the antennas were installed on the roof of a five-storey building whose electric field enhancement factor (Baba and Rakov [10]) was estimated to be 1.4. Fiberoptic 0018-9375/$26.00 2010 IEEE

408 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 2, MAY 2011 Fig. 1. Electric fields at (a) 2 km and (b) 200 km computed using the HD approximation for a CID with a channel length of 100 m at a height of 15 km, excited by a current pulse whose peak is 34 ka, zero-to-peak risetime is 6 μs, and total duration is 30 μs. The corresponding de/dt signature at 200 km is shown in (c). Electric fields and de/dt computed using the bouncing wave model (with v = 2 10 8 m/s and current reflection coefficients of 0.5 at either end of the channel) are also shown for direct comparison. A good match is evident in each of the three panels. links were used to transmit the field and field-derivative signals from the antennas and associated electronics to an 8-bit digitizing oscilloscope that digitized the signals at 100 MHz. The record length was 500 ms including pre-trigger time of 100 ms. CIDs were identified by their intense VHF radiation signature (also recorded at the LOG) and characteristic wideband field and field derivative waveforms. GPS timestamps were used to identify CIDs recorded at the LOG in the NLDN data. The NLDN includes over 100 stations with an average baseline of about 300 km. NLDN-estimated horizontal distances from the LOG to the 48 CIDs varied from 12 to 89 km. The CIDs were each reported by 4 22 (11 on average) NLDN sensors, although the maximum number of sensors used in the final location calculation was 10 (K. Cummins, personal communication, 2010). The semimajor axis lengths of 50% location error ellipses (Cummins et al. [11]) ranged from 400 m to 4.9 km (mostly 400 m so that the median was as small as 400 m). Simultaneous measurements of electric and magnetic radiation field pulses produced by the 48 CIDs and corresponding NLDN-reported horizontal distances were used to estimate source heights (Nag et al. [8]). The minimum and maximum source heights were 8.8 and 29 km, respectively. The geometric mean (GM) was 16 km and median was 15 km, the latter being similar to the median source height of 13 km reported for the same CID wideband electric field initial polarity by Smith et al. [12]. The overall error in heights was estimated by Nag et al. [8] to range from 4.7% to 95% with a mean of 17%. If nine events with height errors greater than 25% were excluded, the GM height would remain the same as that for the original sample of 48. The height errors appear to be independent of the height value, and the larger height errors have not contributed significantly to the errors in peak currents presented in Section III. III. ESTIMATION OF CID CURRENTS USING THE HD APPROXIMATION A dipole can be viewed as Hertzian or electrically short, if its length Δh is very short compared to the shortest significant excitation wavelength λ. For example, a dipole of length Δh = 500 m can be considered Hertzian, if λ 500 m. This means that the HD approximation is valid for frequencies f 600 khz. Fig. 1 compares, as an example, electric field waveforms produced by a 100-m-long vertical CID channel at 2 and 200 km, as well as de/dt waveform at 200 km, all predicted by the HD approximation (as described in the following) and those based on the bouncing-wave model (see Nag and Rakov [9]). A good agreement is seen at both near (2 km) and far (200 km) distances. Nag [13] showed that the HD approximation is consistent with

NAG et al.: REMOTE MEASUREMENTS OF CURRENTS IN CLOUD LIGHTNING DISCHARGES 409 Fig. 2. Geometrical parameters needed in calculating the vertical electric field at observation point P on perfectly conducting ground at horizontal distance r from a vertical HD (source) representing the CID channel. Also given are equations used in estimating source heights (Nag et al. [8]). the bouncing-wave model for a reasonably large subset of allowed combinations of propagation speed and channel length. Let us consider a vertical HD of length Δh at height h above perfectly conducting ground carrying a uniform current i(t) (see Fig. 2). The total electric field at the observation point P on the ground at a horizontal distance r is given by: E z (r, t) = 1 [ (2h 2 r 2 )Δh t 2πε 0 R 5 i(τ R/c)dτ 0 + (2h2 r 2 )Δh cr 4 i(t R/c) r2 Δh di(t R/c) c 2 R 3 dt where ε 0 is the electric permittivity of free space, c is the free-space speed of light, and R is the inclined distance from the dipole to the observation point, which is given by R = h 2 + r 2. Note that current i in (1) varies only as a function of time, with all the geometrical parameters being fixed. Equation (1) can be rewritten as a second-order differential equation de z = Δh [ (2h 2 r 2 ) dt 2πε 0 R 5 i + (2h2 r 2 ) di cr 4 dt r2 d 2 ] i c 2 R 3 dt 2 (2) where arguments of E z and i have been dropped to simplify notation. For known E z and the geometrical parameters (Δh, h, and r), this equation can be numerically solved for i. We employed the Runge Kutta method of order three (with four stages and an embedded second-order method, also known as the Bogacki Shampine method (Bogacki and Shampine [14]) to solve (2) for i using measured electric fields E z of the 48 CIDs with known h and r. Channel lengths Δh for 9 of the 48 CIDs were estimated from reflections in electric field derivative (de/dt) waveforms (also measured at the LOG) and assumed propagation speed of 2.5 10 8 m/s. For the remaining 39 CIDs, ] (1) there were no reflection signatures observed, and a reasonable value of Δh = 350 m was assumed. This value is consistent with the HD approximations for speeds in the range of 2 3 10 8 m/s (Nag [13]). The initial and final values of current were required to be zero, and the error tolerance of the numerical solution was set to 10 6. For E z measured at far distances, the peak current can also be estimated using the radiation field approximation, given by the third term of (2) de z dt = Δhr2 2πε 0 c 2 R 3 d 2 i dt 2 (3) from which it follows that E z is proportional to di/dt E z = Δhr2 di 2πε 0 c 2 R 3 dt. (4) In contrast, for distant lightning return strokes represented by the transmission line (TL) model (Uman and McLain [15]), E z is proportional to i E z = v 2πε 0 c 2 r i (5) where v is the return-stroke propagation speed. Equation (5) is valid when 1) the height above ground of the upward-moving return stroke front is much smaller than the distance r between the observation point on ground and channel base so that all contributing channel points are essentially equidistant from the observer; 2) v = const; 3) the return-stroke front has not reached the top of the channel; and 4) the ground conductivity is high enough so that field propagation effects are negligible. The corresponding magnetic radiation field can be found from B φ = E z /c. The apparent disparity between (4) [E z (di/dt)] and (5) (E z i) is because of 1) integration over height z (over many electrically short dipoles) that is involved in derivation of (5) and 2) direct proportionality between the time and spatial derivatives of current ( i/ t = v( i/ z)) predicted by the TL model, on which (5) is based. The CID currents based on the HD approximation are affected by errors in heights and in NLDN-estimated horizontal distances. Nag [13] estimated that the errors in currents due to errors in heights and horizontal distances were less than 15% for 47 of the 48 CIDs (including those with height errors greater than 25%) and for one CID (which had an unusually large horizontal distance error of 21%) the error in current was 23%. Perhaps the largest uncertainty in our current estimates based on the HD approximation is due to the uncertainty in Δh. For nine events with channel lengths estimated from channel traversal times (reflection signatures in de/dt waveforms) for the assumed v = 2.5 10 8 m/s, the uncertainty in current does not exceed 25% (Nag [13]). For the remaining 39 events, which did not exhibit reflection signatures and for which the channel length was assumed to be 350 m, we cannot assign any specific uncertainty (which is expected to be larger than that for the nine events discussed above) to the estimated currents. However, we will see in Section V that the 9- and 39-event data subsets generally exhibit similar trends.

410 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 2, MAY 2011 Fig. 3. Arithmetic mean horizontal distances (diamonds) and ranges of horizontal distances (vertical bars) from CIDs to all contributing NLDN sensors as a function of NLDN-reported peak current. Note that the mean distance tends to increase with increasing peak current. The number of contributing sensors ranged from 4 to 22 (11 on average). IV. ESTIMATION OF PEAK CURRENTS BY THE NLDN The NLDN outputs a peak current estimate for each stroke using the measured magnetic radiation field peaks and distances to the ground strike point reported by multiple sensors. The following empirical field-to-current conversion equation is used: i p = 0.185 Mean(RNSS) (6) where i p is the peak current in ka and Mean(RNSS) is the arithmetic mean of range normalized (to 100 km) magnetic field signal strengths, in so-called LLP units, from all sensors allowed by the central analyzer to participate in the peak current estimate. Generally, contributions from sensors at distances up to several hundreds of kilometers are included (see Fig. 3). Equation (6) implies that the magnetic (as well as electric) radiation field is proportional to the current, similar to (5) based on the TL model. Normalization of measured magnetic field signal strength SS to 100 km is performed taking into account signal attenuation due to its propagation over lossy ground. The following empirical formula has been used since 2004 to compensate for the field propagation effects (Cummins et al. [16]): ( r ) ( ) r 100 RNSS = SS exp (7) 100 1000 where r is in kilometers and SS is in LLP units. This equation assumes that the distance dependence of signal strength is r 1 exp( r/1000), where r 1 corresponds to the propagation over perfectly conducting ground and exp( r/1000) represents additional attenuation due to ground being lossy. The exponential function in (7) should increase the RNSS in order to compensate for propagation effects. For r = 625 km, for example, this function is equal to 1.7, although no compensation is provided for r = 100 km and for r ranging from 0 to 100 km, it varies from about 0.9 to 1. The median value of absolute current estimation error by the NLDN for negative subsequent strokes was found, using rocket- Fig. 4. Histogram of peak currents estimated for 48 CIDs using the HD approximation (2). For nine events (shaded histogram columns) with reflection signatures, channel lengths were inferred using channel traversal times measured in de/dt waveforms and assumed propagation speed of 2.5 10 8 m/s. For the other 39 events (blank histogram columns), an assumed channel length of 350 m (implied v 2 10 8 m/s) was used. Statistics given are the arithmetic mean (AM), GM, minimum value (Min), and maximum value (Max) for the 9 and 39 events individually and for all data combined. triggered lightning data, to be about 20% (Jerauld et al. [17]; Nag et al. [18]). No current error estimates are available for first strokes or for cloud discharges. V. ANALYSIS AND DISCUSSION Histogram of peak currents estimated using the HD approximation for the 48 CIDs is shown in Fig. 4. The peak currents range from 33 to 259 ka with the GM value being 74 ka. Histogram of NLDN-reported peak currents for the same 48 CIDs is shown in Fig. 5. The peak currents range from 18 to 67 ka with the GM value being 35 ka. The latter is about a factor of 2.1 smaller than the GM peak current based on the HD approximation. Fig. 6 shows a scatter plot of the NLDNreported peak current versus peak current estimated using the HD approximation. As seen in Fig. 6, the majority of NLDN-reported peak currents are considerably smaller than those predicted by the HD approximation. Some discrepancy is expected because NLDN-reported peak currents are assumed to be proportional to peak fields, which is a reasonable approximation for return strokes, but not for electrically short radiators, while for the HD

NAG et al.: REMOTE MEASUREMENTS OF CURRENTS IN CLOUD LIGHTNING DISCHARGES 411 Fig. 6. NLDN-reported peak current versus peak current estimated using the HD approximation for 48 CIDs. For nine events (solid circles), channel lengths were inferred using channel traversal times measured in de/dt waveforms and assumed propagation speed of 2.5 10 8 m/s. For the other 39 events (hollow circles) an assumed channel length of 350 m (with implied v 2 10 8 m/s) was used. Fig. 5. Histogram of NLDN-estimated [see (6) and (7)] peak currents for 48 CIDs. Statistics given are the arithmetic mean (AM), GM, minimum value (Min), and maximum value (Max) for the 9 (with reflection signatures, shaded histogram columns) and 39 (without reflection signatures, blank histogram columns) events individually and for all data combined. approximation, the peak of electric (as well as magnetic) radiation field component is proportional to the peak of the time derivative of current (di/dt), as seen in (4). It follows that for the HD approximation, the CID current peak is proportional to the peak of the integral of electric (or magnetic) radiation field, which occurs at the time of field zero-crossing. In order to examine this discrepancy further, we computed CID peak currents using our measured electric field peaks and (5) with v = 1.8 10 8 m/s. This value of speed was used because it had provided a good match between NLDN-reported peak currents and those estimated using the TL model for negative first and subsequent return strokes recorded at the LOG (Nag [13]). Thus, these calculations, assuming direct proportionality between i and E z, simulate, to some extent, NLDN peak current estimates. The results are shown in Fig. 7. Clearly, the discrepancy between the predictions of (5) and NLDN-reported values is appreciably smaller than that between the predictions of (2) and NLDN estimates (the ratio of GM values in the former case is 1.2 versus 2.1 in the latter). However, there seem to be additional factors that make NLDN-reported currents smaller than their counterparts based on (5). One of these factors is the limited (400 khz) upper frequency response of the NLDN. We digitally low-pass filtered our 48 electric field waveforms using a 4-pole Bessel filter having 6 db frequency of 400 khz. The result of filtering for one Fig. 7. NLDN-reported peak current versus peak current estimated using peaks of electric fields measured at LOG and (5), based on the TL model with v = 1.8 10 8 m/s for 48 CIDs. CID is illustrated in Fig. 8, which shows that the waveform after filtering becomes smoother and the peak value significantly decreases (from 68 to 47 V/m). Histogram of the ratio of peaks in measured and filtered waveforms for the 48 CIDs is shown in Fig. 9. The GM ratio is 1.3. Clearly, the limited upper frequency response of the NLDN results in an appreciable

412 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 2, MAY 2011 Fig. 10. NLDN-reported peak current versus peak current estimated using peaks of filtered electric field waveforms and (5), based on the TL model with v = 1.8 10 8 m/s for 48 CIDs. Fig. 8. CID electric field waveforms (a) before and (b) after 400-kHz low-pass filtering. The filtering simulates the 400-kHz upper frequency response of the NLDN. Note that after filtering, the electric field peak E p reduces from 68 to 47 V/m. underestimation of CID field peaks, which in turn leads to underestimation of CID peak currents reported by the NLDN. The use of peaks from filtered waveforms in (5) results in a better match with the HD estimates (compare Figs. 7 and 10). The ratio of GM values of two current estimates in this case is 0.9. It appears that, due to the use of inapplicable field-to-current conversion equation and limited upper frequency response, the NLDN underestimates CID peak currents by about a factor of 2 on average (compare Figs. 4 and 5). However, it is worth noting that most of the peak current estimates based on the HD approximation cannot be viewed as real ground-truth data due to uncertainties in the model input parameters (primarily Δh). While for the nine events with channel lengths estimated from channel traversal times those uncertainties do not exceed 25%, they are much larger for the other 39 events (see Section III). On the other hand, the two data subsets generally exhibit similar trends (see Figs. 6, 7, and 10), which suggests that our conclusions would hold, if the less reliable data for the 39 events were excluded from the analysis. Fig. 9. Histogram of the ratio of CID electric field peaks before and after filtering. The GMs for the 9- and 39-event subsets are 1.45 and 1.24, respectively. VI. SUMMARY CIDs tend to occur at high altitudes (greater than 10 km) and have relatively short channel lengths of 100 1000 m. Many of them are expected to be electrically short radiators (shorter than the shortest significant excitation wavelength). We estimated peak currents for 48 located CIDs using measured wideband electric field waveforms and the HD (electrically short dipole) approximation. The majority of NLDN-reported peak currents for these CIDs are considerably smaller than those predicted by the HD approximation. Some discrepancy is expected because NLDN-reported peak currents are assumed to be proportional to peak fields, which is a reasonable approximation for return

NAG et al.: REMOTE MEASUREMENTS OF CURRENTS IN CLOUD LIGHTNING DISCHARGES 413 strokes, while for the HD approximation, the peak of electric radiation field is proportional to the peak of the time derivative of current (di/dt). It follows that the CID current peak is proportional to the peak of the integral of electric (or magnetic) radiation field, which occurs at the time of field zero-crossing. Additionally, the limited (400 khz) upper frequency response of the NLDN apparently contributed to the discrepancy. It is worth noting that most of the peak current estimates based on the HD approximation cannot be viewed as real ground-truth data due to uncertainties in the model input parameters. While for the nine events with channel lengths estimated from channel traversal times, those uncertainties do not exceed 25%, they are much larger for the other 39 events (see Section III). However, these two data subsets generally exhibit similar trends. The results of this study have important implications for estimation of peak currents for cloud discharges (e.g., Cummins and Murphy [1] and Betz et al. [2]). If the radiator is short, as in the case of CIDs, the field-to-current conversion procedure designed for return strokes, in which the current is directly proportional to the field, may yield incorrect results. ACKNOWLEDGMENT The authors would like to thank K. Cummins for his helpful comments on the paper. REFERENCES [1] K. L. Cummins and M. J. Murphy, An overview of lightning locating systems: history, techniques, and data uses, with an in-depth look at the U.S. NLDN, IEEE Trans. Electromagn. Compat.,vol.51,no.3,pp.499 518, Aug. 2009. DOI: 10.1109/TEMC.2009.2023450. [2] H.-D. Betz, K. Schmidt, and W.P. Oettinger, LINET An international VLF/LF lightning detection network in Europe, in Lightning: Principles, Instruments and Applications, H.-D. Betz, U. Schumann, and P. Laroche, Eds. New York: Springer-Verlag, 2009, pp. 115 140. [3] D. M. Le Vine, Sources of the strongest RF radiation from lightning, J. Geophys. Res., vol. 85, pp. 4091 4095, 1980. [4] J. C. Willett, J. C. Bailey, and E. P. Krider, A class of unusual lightning electric field waveforms with very strong high-frequency radiation, J. Geophys. Res., vol. 94, pp. 16255 16267, 1989. [5] D. A. Smith, X. M. Shao, D. N. Holden, C. T. Rhodes, M. Brook, P. R. Krehbiel, M. Stanley, W. Rison, and R. J. Thomas, A distinct class of isolated intracloud discharges and their associated radio emissions, J. Geophys. Res., vol. 104, pp. 4189 4212, 1999. [6] K. B. Eack, Electrical characteristics of narrow bipolar events, Geophys. Res. Lett., vol. 31, p. L20102, 2004. DOI:10.1029/2004GL021117. [7] T. Hamlin, K. C. Wiens, A. R. Jacobson, T. E. L. Light, and K. B. Eack, Space- and ground-based studies of lightning signatures, in Lightning: Principles, Instruments and Applications, H.-D. Betz, U. Schumann, and P. Laroche, Eds. New York: Springer-Verlag, 2009, pp. 287 307. [8] A. Nag, V. A. Rakov, D. Tsalikis, and J. A. Cramer, On phenomenology of compact intracloud lightning discharges, J. Geophys. Res., vol. 115, p. D14115, 2010. DOI: 10.1029/2009JD012957. [9] A. Nag and V. A. Rakov, Electromagnetic pulses produced by bouncing-wave-type lightning discharges, IEEE Trans. Electromagn. Compat., vol. 51, no. 3, pp. 466 470, Aug. 2009. DOI: 10.1109/TEMC.2009.2025495. [10] Y. Baba and V. A. Rakov, Electromagnetic fields at the top of a tall building associated with nearby lightning return strokes, IEEE Trans. Electromagn. Compat., vol. 49, no. 3, pp. 632 643, Aug. 2007. DOI: 10.1109/TEMC.2007.902402. [11] K. L. Cummins, M. J. Murphy, E. A. Bardo, W. L. Hiscox, R. B. Pyle, and A. E. Pifer, A Combined TOA/MDF Technology Upgrade of the U.S. National Lightning Detection Network, J. Geophys. Res., vol.103, no. D8, pp. 9035 9044, 1998. [12] D. A. Smith, M. J. Heavner, A. R. Jacobson, X. M. Shao, R. S. Massey, R. J. Sheldon, and K. C. Weins, A method for determining intracloud lightning and ionospheric heights from VLF/LF electric field records, Radio Sci., vol. 39, p. RS1010, 2004. DOI: 10.1029/2002RS002790. [13] A. Nag, Characterization and modeling of lightning processes with emphasis on compact intracloud discharges, Ph.D. dissertation, Univ. of Florida, Gainesville, May 2010. [14] P. Bogacki and L. F. Shampine, A 3(2) pair of Runge Kutta formulas, Appl. Math. Lett., vol. 2, no. 4, pp. 321 325, 1989. DOI: 10.1016/0893 9659(89)90079 7. [15] M. A. Uman and D. K. McLain, Magnetic field of the lightning return stroke, J. Geophys. Res., vol. 74, pp. 6899 6910, 1969. [16] K. L. Cummins, J. A. Cramer, C. J. Biagi, E.P. Krider, J. Jerauld, M. A. Uman, and V. A. Rakov, The U.S. National Lightning Detection Network: Post-upgrade status, in Proc. 2nd Conf. Meteorol. Appl. Lightning Data, Atlanta, GA, 2006. Paper 6.1. [17] J. Jerauld, V. A. Rakov, M. A. Uman, K. J. Rambo, D. M. Jordan, K. L. Cummins, and J. A. Cramer, An evaluation of the performance characteristics of the U.S. National Lightning Detection Network in Florida using rocket-triggered lightning, J. Geophys. Res., vol. 110, p. D19106, 2005. DOI: 10.1029/2005JD005924. [18] A. Nag, J. Jerauld, V. A. Rakov, M. A. Uman, K. J. Rambo, D. M. Jordan, B. A. DeCarlo, J. Howard, K. L. Cummins, and J. A. Cramer, NLDN responses to rocket-triggered lightning at Camp Blanding, Florida, in 2004 and 2005, in Proc. 29th Int. Conf. Lightning Protection, Uppsala, Sweden, 2008. Paper 2 05. Amitabh Nag (M 04) received the M.S. and Ph.D. degrees in electrical and computer engineering in 2007 and 2010, respectively, from the University of Florida, Gainesville. He is currently employed as a Postdoctoral Research Associate in the University of Florida. Since 2005, he has been in-charge of the Lightning Observatory in Gainesville at the International Center for Lightning Research and Testing (ICLRT), University of Florida. He is the author or coauthor of over 40 papers and technical reports on various aspects of lightning, with eleven papers being published in reviewed journals. His current research interests include electromagnetic wave propagation and detection, measurement, analysis, and modeling of electromagnetic fields, sensors and systems, and lightning protection. Dr. Nag is a member of the American Meteorological Society (AMS) and the American Geophysical Union (AGU). Vladimir A. Rakov (SM 96 F 03) received the M.S. and Ph.D. degrees in electrical engineering from the Tomsk Polytechnical University (Tomsk Polytechnic), Tomsk, Russia, in 1977 and 1983, respectively. From 1977 to 1979, he worked as an Assistant Professor of electrical engineering at Tomsk Polytechnic. In 1978, he became involved in lightning research at the High Voltage Research Institute (a division of Tomsk Polytechnic), where from 1984 to 1994, he held the position of the Director of the Lightning Research Laboratory. He is currently a Professor at the Department of Electrical and Computer Engineering, University of Florida, Gainesville, and Co-Director of the International Center for Lightning Research and Testing (ICLRT). He is the lead author of one book, Lightning: Physics and Effects, and author or coauthor of over 500 other publications on various aspects of lightning, with over 180 papers being published in reviewed journals. Dr. Rakov is Editor or Associate Editor of three technical journals, Life Member of the Advisory Committee of the Center of Excellence on Lightning Protection (CELP), Co-Chairman of URSI WG E.4 Lightning Discharges and Related Phenomena, and Convener of CIGRE WG C4.407 Lightning Parameters for Engineering Applications. Besides IEEE, he is a Fellow of the American Meteorological Society and the Institution of Engineering and Technology (formerly IEE). John A. Cramer (M 00) received the B.S. and M.S. degrees in electrical and computer engineering in 1990 and 2001, respectively, from the University of Arizona, Tucson. He is currently employed with Vaisala Inc. and has held the role of Network Engineering Manager since 2007. He is the author or co-author of several papers and technical reports on lightning detection.