Journal of Geophysical Research: Atmospheres

Optical power and energy radiated by natural lightning

Authors

  • Mason G. Quick,

    1. Institute of Atmospheric Physics, University of Arizona, Tucson, Arizona, USA
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  • E. Philip Krider

    Corresponding author
    1. Institute of Atmospheric Physics, University of Arizona, Tucson, Arizona, USA
    • Corresponding author: E. P. Krider, Institute of Atmospheric Physics, University of Arizona, Physics-Atmospheric Sciences Bldg, Rm 542, 1118 E 4th St, PO Box 210081, Tucson, Arizona 85721-0081, USA. (krider@atmo.arizona.edu)

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Abstract

[1] Calibrated measurements of the visible and near-infrared radiation produced by both negative and positive cloud-to-ground (CG) lightning strokes have been made at distances of 5 to 32 km in southern Arizona (AZ) and the central Great Plains using a photodiode sensor with a flat spectral response between 0.4 and 1.0 µm. Time-correlated video images (60 fps) of the channel development provided information about the types of strokes that were detected and reports from the U.S. National Lightning Detection Network indicated their locations, polarities, and estimates of their peak current. In our sample of negative strokes that were suitable for analysis, there were 23 first (or only) strokes (FS), 19 subsequent strokes that created new ground contacts (NGC), and 101 subsequent strokes that re-illuminated a preexisting channel (PEC). We also analyzed 10 positive strokes (in nine flashes), and 73 of the larger impulses that were radiated by intracloud discharges (CPs). Assuming that these events can be approximated as isotropic sources and that the effects of atmospheric extinction are negligible, the peak optical power (Po), total optical energy (Eo), and characteristic widths of the sources (tcw = Eo/Po) have been computed. Median values of Po for negative FS, NGC, and PEC strokes were 1.8 × 1010 W, 1.1 × 1010 W, and 4.4 × 109 W, respectively. Median values of Eo were 3.6 × 106 J, 3.5 × 106 J, and 1.2 × 106 J, respectively. The median characteristic widths of negative FS, NGC, and PEC strokes were 229 µs, 244 µs, and 283 µs, respectively. Positive CG strokes produced a median Po, Eo, and tcw of 1.9 × 1010 W, 9.3 × 106 J, and 497 µs, respectively. Estimates of the space-and-time-average power per unit length (inline image) in the lower portion of negative FS, NGC, and PEC channels had medians of 2.8 × 106 W/m, 3.2 × 106 W/m, and 1.4 × 106 W/m, respectively, and the median inline image for four positive strokes was 8.8 × 106 W/m. Median values for the estimated peak electromagnetic power (PEM) radiated at early times in the strokes are 2.0 × 109 W, 2.5 × 109 W, 1.0 × 109 W, and 9.1 × 109 W for FS, NGC, PEC and positive strokes, respectively. CP events produced a median Po, Eo, and tcw of 2.0 × 109 W, 0.7 × 106 J, and 311 µs, respectively, and are in good agreement with aircraft and satellite measurements. The values of Po, Eo, and inline image for negative CG strokes in AZ are significantly larger than prior measurements in Florida, likely because there is less atmospheric extinction in our dataset, and due to extinction, all the above values of Po, Eo, and inline image are lower limits at the source.

1 Introduction

[2] The amplitudes and energies of lightning optical pulses are currently being used to detect and locate discharges from space [Christian et al., 1989, 2003; Mach et al., 2007; Hamlin et al., 2009; Finke, 2009; Bankert et al., 2011], and optical measurements have been used to estimate the power and energy dissipated by lightning [Krider et al., 1968; Hill, 1979; Guo and Krider, 1982, 1983; Borucki and Chameides, 1984; Sisterson and Liaw, 1990; Paxton et al., 1986; Borovsky, 1998]. Several previous ground-based experiments have measured the irradiance from lightning strokes with fast time resolution [Krider, 1966; Orville, 1968; Mackerras, 1973; Guo and Krider, 1982, 1983; Jordan and Uman, 1983; Ganesh et al., 1984; Orville and Henderson, 1984; Idone and Orville, 1985; Jordan et al., 1995, 1997; Chen et al., 2003; Wang et al., 1970; Lu et al., 2009], and similar experiments have been performed on aircraft [Christian et al., 1983; Brook et al., 1985; Christian and Goodman, 1987; Goodman et al., 1988; Mach et al., 2005] and on satellites [Vorpahl et al., 1970; Turman, 1977, 1978; Orville, 1981; Christian et al., 1989; Christian and Latham, 1998; Suszcynsky et al., 2000, 2001; Kirkland et al., 2001; Davis et al., 2002; Boccippio et al., 2002; Christian et al., 2003; Noble et al., 2004; Koshak, 2010; Jacobson et al., 2011].

[3] Here, we will describe ground-based measurements of lightning optical waveforms that were recorded using a calibrated silicon photodiode that had a flat spectral response from about 0.4 to 1.0 µm. These measurements were correlated with digital video recordings of the channel development to determine the types of cloud-to-ground (CG) strokes that were measured and the general viewing conditions between the lightning sources and the sensor. Time-correlated reports from the U.S. National Lightning Detection Network (NLDN) provided the locations of CG strokes, their polarities, and estimates of their peak current [Cummins et al., 1998; Cummins and Murphy, 2009].

[4] We begin by showing examples of the optical waveforms that were produced by negative and positive CG strokes. Then, we describe a method for estimating the peak optical power and total optical energy that was radiated by the source and show how the NLDN estimates of the peak current can be used to compute an estimate of the peak electromagnetic power that was radiated by a stroke. Finally, we summarize all the measurements for three types of negative events: (1) the first strokes (FS) in a flash, i.e., strokes that produced the first (or only) ground termination; (2) strokes that followed the first and that produced a NGC, and (3) the subsequent strokes that re-illuminated a preexisting channel (PEC). We also give the results for 10 positive (POS) CG strokes (in nine flashes) and for a selection of the larger optical impulses (CPs) that were produced by intracloud discharges. Our data and methods of analysis are similar to those described by Guo and Krider [1982, 1983], who analyzed negative CG strokes in Florida, except our measurements were made in southern Arizona (AZ) and the central Great Plains (GP) where the cloud bases are higher and the visibility is usually better than in Florida.

2 Data

[5] Optical waveforms were recorded in AZ and the GP during the summers of 2001, 2003, 2004, and 2005 in experiments that are described by Biagi et al. [2007] and Fleenor et al. [2009]. To make these measurements, the investigators used a calibrated photodiode to trigger a PC-based data recording system that was similar to one described by Parker and Krider [2003]. The system was capable of digitizing two analog signals at a frequency of 500 kHz, and one channel was devoted to the output of the photodiode, a 1.0 cm2 Model PIN 10-DF manufactured by United Detector Technology, Inc. The spectral response of the sensor was measured by the manufacturer in 2005 and again by us in 2012, and it was approximately constant over a wavelength range from about 0.4 to 1.0 µm as shown in Figure 1. For all optical results given below, we have used the calibration that was provided by the manufacturer.

Figure 1.

Spectral responsivity of the PIN 10-DF photodiode provided by the manufacturer in 2005 and measured again by the investigators in 2012.

[6] Orville [1968] and Orville and Henderson [1984] have described time-resolved spectra produced by individual CG strokes over a wavelength interval from about 0.4 to 0.9 µm. These spectra show a number of bright emission lines superimposed on a background continuum, and the characteristics of both the lines and the continuum are strong functions of time and vary from stroke to stroke. Because the spectral response of our photodiode was reasonably flat over a broad range of wavelengths, our measurements should have minimal bias due to the (unknown and time-dependent) lightning spectrum.

[7] The second recording channel was used to measure wideband electric field (E) waveforms that were detected using a flush-plate antenna system with a rise time of about 1 µs and a decay time of 1 s, but the E-field data were not available during all recording sessions. Normally, the digitizing system was run continuously, and the photodiode signal initiated the data capture; therefore, only events that were within the field of view of the optical sensor tended to be recorded. After each trigger, 1.0 s of waveform data were transferred to the PC, 100 ms prior to the trigger and 900 ms after the trigger. A digital video camcorder (Canon GL1) provided images of the lightning channels at a rate of 60 fields per second, and the full field of view of the camera was approximately 45° in both the vertical and horizontal and closely matched that of the optical sensor. The video camera also recorded a blinking LED that was illuminated at 1 s intervals by a GPS clock to ensure that all strokes recorded on video could be accurately correlated with the NLDN stroke reports. Biagi et al. [2007] and Fleenor et al. [2009] have discussed the overall characteristics of the storms that were studied and the performance of the NLDN in the regions of our measurements.

2.1 Analysis Dataset

[8] A sketch of a “typical” optical signal from a negative return stroke is shown in Figure 2. Note that the waveform begins with a small, concave initial portion up to time T1, and then there is a fast, almost linear increase up to time T2. The final rise to peak (at time Tp) is slow, and the peak itself is broad and slowly varying. Guo and Krider [1982] have suggested that the transition from the linear, fast-rising portion to the slower rise (at T2) is caused by the stroke entering the cloud base where the effects of multiple scattering cause the signal to rise more slowly and to broaden in time [Thomason and Krider, 1982; Koshak et al., 1994; Light et al., 2001b. AZ thunderstorms typically have higher cloud bases than storms in Florida; therefore, the transition from the fast-rising portion to the slower rise (at T2) occurs at later times in AZ and is not as well-defined as in Florida storms.

Figure 2.

Sketch of the “typical” optical irradiance produced by a negative GC stroke. A small concave initial onset is followed by a linear increase from time T1 to time T2. The peak irradiance, LP, occurs at time TP (taken from Guo and Krider [1982]).

[9] Many negative strokes also produce more complex optical waveforms due to branching, M-components, and/or other variations in the channel luminosity [Mach et al., 2005]. For example, Figure 3 shows the waveforms that were radiated by a five-stroke negative CG flash in the GP that produced two ground terminations at ranges of 25 and 26 km from our measuring site. Note that the vertical scales in the figure vary in each panel. The first return stroke in Figure 3 begins at time zero, the data acquisition trigger time, and the overall waveform closely resembles the sketch shown in Figure 2. The second (or first subsequent) stroke in Figure 3 created a NGC 86.5 ms after the FS. This waveform has a small secondary optical peak around 0.15 ms after the initial peak and a slow, nearly linear decay in luminosity for approximately 0.4 ms that is followed by an M-component [Schonland, 1956; Jordan et al., 1995; Campos et al., 2007, 2009]. A secondary peak like the one exhibited here is quite common in the data set. The onset of the third return stroke occurred 38 ms following the previous stroke and was superimposed on the light from the leader or a cloud discharge. Onsets of the fourth and fifth return strokes follow the previous stroke by 43 ms and 41 ms, respectively, and are both preceded by large dart leader signatures that are similar to those described by Guo and Krider [1985] and Jordan et al. [1997]. The optical waveform of the fourth stroke has more structure, perhaps three peaks superimposed on each other, and is followed by a weak M-component approx 0.9 ms after the initial rise in luminosity. The fifth stroke in Figure 3 contains many features of the previous strokes including an M-component about 0.9 ms after the initial peak that is more luminous than the initial optical peak.

Figure 3.

Optical waveforms from a five-stroke CG flash that occurred at 21:16:10 Z on 7/06/2005 in the central Great Plains (GP). The top panel shows the waveform of the first return stroke, and the second panel was produced by a subsequent stroke that established a NGC. The lower three panels show the waveforms of subsequent strokes that reilluminated a PEC. Note that the amplitude and time scales vary between panels. The horizontal axis shows the time in milliseconds after the trigger at zero in the top panel. The electric field was not recorded during this event.

[10] Figure 4 shows four additional examples of optical waveforms that were produced by negative CG strokes in AZ plus one cloud pulse together with the associated E-signatures. Note how the peaks of the optical waveforms always occur tens to hundreds of microseconds after the peak E-field, a feature noted previously by Guo and Krider [1982]. It can also be seen in Figure 4 that the secondary peaks and M-components in the optical waveform are preceded by rapid changes in the E-field waveform with a similar time delay between peaks. The peak E-field is produced at early times when most of the return stroke current is still close to the ground. The delay of the peak optical signal is caused primarily by the geometrical growth of the channel and any branches that are in the sensor field of view, and this is superimposed on any time variations that occur in the channel current and the effects of optical scattering in the atmosphere. Because all CP events were produced by sources that were inside optically thick clouds, the effects of multiple scattering cause those waveforms to rise more slowly and have less high frequency structure than the waveforms produced by ground strokes [Thomason and Krider, 1982; Christian and Goodman, 1987; Koshak et al., 1994; Light et al., 2001a, 2001b; Davis and Marshak, 2002].

Figure 4.

Examples of time-correlated optical (black) and electric field (red) produced by four negative CG strokes (in different flashes) and one cloud pulse or CP. The electric field has been plotted with an inverted polarity so that a positive excursion shows a negative field change with the normal physics convention. The strokes have been labeled with their type, estimated peak current, Ip, and range, R. The signal strength is in relative units, and the amplitude and time scales vary between the plots.

[11] Figure 5 shows examples of optical waveforms that were produced by five positive CG strokes in the GP. Positive optical waveforms exhibit similar features to the negative waveforms, but tend to be larger in both amplitude and duration than the negative strokes shown in Figures 3 and 4.

Figure 5.

Examples of optical waveforms produced by positive CG strokes. Note that both the horizontal and vertical scales vary between panels. The top panel features the return stroke with the largest estimated peak current in our dataset.

2.2 Methods of Analysis

[12] Following Guo and Krider [1982], we can make a rough estimate of the peak optical power (Po) that is radiated at time TP (see Figure 2) by assuming that the source is localized in space at that time (a point source) and that it radiates uniformly in all directions. In that case,

display math(1)

where R is the distance from the sensor to the source, and LP is the measured irradiance at time TP. After the peak, the stroke luminosity usually decreases slowly due to a reduction and eventual termination of the channel current; sometimes, however, there are additional optical pulses (like those shown in Figures 3, 4, and 5) that are due to M-components, branches, and a variety of other factors [Schonland, 1956; Guo and Krider, 1982; Jordan et al., 1995, 1997; Wang et al., 2000, 2004; Mach et al., 2005].

[13] An estimate of the total optical energy (Eo) that is radiated by the source can be obtained by integrating the optical waveform over the duration of the pulse where the signal amplitude is more than a few standard deviations above the baseline of the noise. An effective duration or “characteristic width” (tcw) can be obtained simply by dividing Eo by Po or tcw = Eo/Po.

[14] After a return stroke begins at or just above the ground, the luminosity front propagates rapidly up the leader channel at a speed close to the speed of light [Schonland, 1956; Rakov and Uman, 2003, Chapter 4]. Assuming that at these early times, the linear, fast-rising portion of the optical waveform is dominated by the rapid geometric growth of the channel and that on average the channel is straight and vertical, then an estimate of the average luminous power per unit length (inline image) that is emitted can be obtained from the following expression,

display math(2)

where R is the distance to the stroke, v is the speed of propagation, and dL/dt is the measured slope of the irradiance, L, between T1 and T2 [Guo and Krider, 1982]. In nature, each small segment of channel will actually radiate a luminosity that depends on how the current in that segment varies with time [Jordan and Uman, 1983; Jordan et al., 1997; Wang et al., 2000, 2004, 1970; Chen et al., 2003; Lu et al., 2008, 2009]; therefore, the values of inline image actually represent a coarse spatial- and temporal-average of the luminous power per unit length of channel at early times [Guo and Krider, 1983]. The assumption that the channel is straight is likely to be valid only at the beginning of a return stroke when the bulk of the current is close to the ground, and at these early times, CG strokes will not usually have large branches.

[15] Broadband electric field or E-waveforms have been discussed by Weidman and Krider [1978] and many others [see, for example, Chapters 4 and 12 in Rakov and Uman, 2003]. Since the NLDN uses range-normalized values of the peak E-field to compute estimates of the peak current, assuming that EP is proportional to Ip as in the simple transmission line model [Cummins and Murphy, 2009; Nag et al., 2011], we can use the NLDN estimates of Ip to compute estimates of the peak electromagnetic power, PEM, that strokes radiate into the upper half-space. Following the discussions in Krider and Guo [1983] and Krider [1992], the peak electromagnetic power that a straight and vertical stroke radiates upward is,

display math(3)

[16] Here, it has been assumed that the simple transmission line model is valid at early times, Zo is the impedance of free space, Ip is the peak current, and β is the ratio of the return stroke speed to the speed of light. In the limit of small β, equation (3) becomes

display math(4)

[17] The algorithm that the NLDN uses to estimate Ip from the measured peak E-fields and distances effectively assumes a return stroke velocity v of 1.2 × 108 m/s [Idone et al., 1998]; therefore, for our estimates of PEM, we have assumed β = 0.4.

2.3 Selection Criteria

[18] Strokes were included in our analysis dataset only if they passed several selection criteria. For example, any channel that was partially blocked by obstructions or propagated outside the sensor field of view, or was severely attenuated by precipitation, was not included in the analysis. Also, the photodiode electronics had several possible gain settings, and on occasion, very bright strokes would saturate the electronics. In these cases, it was not possible to measure accurate waveform parameters, so those events were not included in the analysis. The total number of saturated waveforms that were removed from our original dataset included 18 negative FS, five subsequent NGC, six subsequent PEC events, and two positive strokes; the removal of these events has biased our sample toward fainter sources.

[19] Equation (1) assumes that at the time of the peak optical emission, the channel radiates isotropically. This approximation works well at large distances, but calculations show that when a CG stroke is closer than about 10 km, the effects of the finite and tilted geometry can cause the values of Po computed using equation (1) to deviate from the true values by as much as a factor of 2. Also, the effects of atmospheric extinction due to scattering and absorption will reduce the optical signal as it propagates from the source to the sensor, particularly at large distances. Calculations of Rayleigh scattering discussed in section 4.1 indicate that only about 60% of the optical power, assuming a blackbody source, emitted within our sensor bandwidth is transmitted to 32 km (see Figure 10 to follow). For these reasons, we have restricted estimates of Po and Eo to only those strokes that were within a range interval of 10 to 32 km. There were 23 negative FS, 19 NGC, and 101 PEC strokes to ground, 10 positive CG strokes and 73 CP events that were in this range interval.

[20] Because of the assumptions that are inherent in equation (2), a clear view of the lowest portion of the channel is needed in order to get a good measure of dL/dt, and in order to monitor low altitudes, the strokes must be reasonably close to the sensor. Therefore, only strokes that were between 5 and 20 km were used to compute inline image. For negative strokes, there were 15 FS, 11 NGC, and 42 PEC events that were between 5 and 20 km, and there were four positive strokes in that range interval. In general, about half of the strokes were tilted in the video imagery and had only a small amount of tortuosity in the lowest channel section. Such geometrical effects will typically bias our estimates of inline image to lower values.

[21] Finally, the NLDN has a finite detection threshold that corresponded to an estimated peak current of 5 to 7 kA in AZ [Biagi et al., 2007] and 4 to 6 kA in the GP [Fleenor et al., 2009] at the times our data were collected. These thresholds will bias our sample toward strokes that have large values of Ip, particularly in the case of subsequent strokes that re-illuminate a PEC. However, if any flash detected on video had at least one stroke reported by the NLDN, the distance to any other unreported strokes in the same channel can be assumed to be at the same range as the reported stroke. Therefore, by combining our video records with the NLDN reports, we were able to increase our sample of subsequent strokes that remained in a PEC by 49 events. The addition of these strokes to the PEC dataset partially offsets the bias introduced by the finite NLDN detection thresholds.

3 Results

3.1 Negative Strokes to Ground

[22] Our final dataset contained 143 negative CG strokes that were suitable for analysis; 104 were recorded in AZ and 39 in the GP. Table 1 lists the numbers and types of strokes that were analyzed in each region together with the medians, means, and standard deviations of Ip, PEM, Po, Eo, tcw,, and inline image. Note in Table 1 that the mean Ip for FS events was −21 kA in both AZ and the GP and that the mean values Po, Eo, and inline image for these events were 50 to 100% larger in AZ than in the GP. The possible reasons for these geographical differences will be considered further in section 4.2.

Table 1. Median and Mean Values With Standard Deviations of the Parameters of Negative CG Strokes in the Specified Geographic Regions. The Number of Events Used in the Computations Are Given in Parentheses. Events Were Selected Using Criterea Described in Section 2.3
TypeaRegionbIp (kA)Pem (109 W)Po (109 W)Eo (106 J)tcw (µs)o (106 W/m)
  1. a

    FS is for first strokes, NGC is for the subsequent strokes that create a new ground contact, and PEC is for the subsequent strokes that reilluminated a preexisting channel.

  2. b

    AZ represents southern Arizona and GP the central Great Plains.

FS       
 AZ−21 ± 12 (18)3.9 ± 5.6 (18)21 ± 15 (18)4.9 ± 3.2 (18)258 ± 82 (18)6.4 ± 6.9 (13)
 GP−21 ± 11 (5)3.6 ± 3.7 (5)14 ± 16 (5)2.5 ± 2.0 (5)267 ± 176 (5)1.7 ± 0.5 (2)
 FS Mean−21 ± 12 (23)3.9 ± 5.2 (23)19 ± 15 (23)4.4 ± 3.1 (23)260 ± 104 (23)5.7 ± 6.6 (15)
 FS Median−17 (23)2.0 (23)18 (23)3.6 (23)229 (23)2.8 (15)
NGC       
 AZ−16 ± 5.8 (7)1.9 ±1.5 (7)9.2 ± 4.6 (7)3.4 ± 2.6 (7)351 ± 163 (7)2.6 ± 2.0 (6)
 GP−24 ± 12 (12)4.9 ± 4.5 (12)15 ± 12 (12)4.0 ± 2.7 (12)341 ± 239 (12)4.8 ± 2.9 (5)
 NGC Mean−21 ± 11 (19)3.8 ± 3.9 (19)13 ± 10 (19)3.8 ± 2.6 (19)344 ± 209 (19)3.6 ± 2.6 (11)
 NGC Median−19 (19)2.5 (19)11 (19)3.5 (19)244 (19)3.2 (11)
PEC       
 AZ−13 ± 7.3 (52)1.5 ± 1.9 (52)6.3 ± 7.0 (79)2.1 ± 2.3 (79)309 ± 149 (79)2.3 ± 3.6 (38)
 GP−24 ± 15 (15)5.3 ± 6.8 (15)7.8 ± 8.4 (22)2.4 ± 2.4 (22)310 ± 131 (22)2.7 ± 0.7 (4)
 PEC Mean−15 ± 10 (67)2.4 ± 3.9 (67)6.7 ± 7.3 (101)2.2 ± 2.3 (101)309 ± 145 (101)2.3 ± 3.4 (42)
 PEC Median−12 (67)1.0 (67)4.4 (101)1.2 (101)283 (101)1.4 (42)

[23] Cumulative distributions of Po, Eo, and tcw for all negative strokes are shown in Figures 6, 7, and 8, respectively. The medians of Po for the FS, NGC, and PEC events were 1.8 × 1010 W, 1.1 × 1010 W, and 4.4 × 109 W, respectively; the medians of Eo were 3.6 × 106 J, 3.5 × 106 J, and 1.2 × 106 J, respectively; and the medians of tcw were 229 µs, 244 µs, and 283 µs, respectively.

Figure 6.

Cumulative distributions of the peak optical power, Po, for 23 negative FS, 19 NGC, and 101 PEC events; 10 positive strokes; and 72 CPs.

Figure 7.

Cumulative distributions of the optical energy, Eo, produced by 23 negative FS, 19 NGC, and 101 PEC events; 10 positive strokes; and 72 CP.

Figure 8.

Cumulative distributions of the characteristic widths, tcw, of 23 negative FS, 19 NGC, and 101 PEC events; 10 positive strokes, and 72 CP. Horizontal axis has been truncated to emphasize the bulk of the distribution. One CP even lies beyond the axis limits at 6.2 ms.

[24] Figure 9 shows distributions of inline image for the negative FS, NGC, and PEC events that were suitable for analysis. Note here that the shapes of the distributions are similar for FS and NGC strokes and that the corresponding medians (see Table 1) were 2.8 × 106 W/m and 3.2 × 106 W/m, respectively. The median inline image for subsequent strokes that re-illuminated a PEC was 1.4 × 106 W/m.

Figure 9.

Cumulative distributions of the average optical power per unit length, inline image, for the lower portion of 15 negative FS, 11 NGC, and 42 PEC events together with four positive strokes.

3.2 Positive Strokes to Ground

[25] Table 2 lists the parameters of 10 positive CG strokes that were recorded in the GP. Even though the number of strokes is limited, distributions of the parameters have been included in Figures 6 to 9 to facilitate a comparison with negative strokes. As expected from previous studies, positive strokes produced larger values of Ip on average than negative strokes (43 ± 21 kA vs. 21 ± 12 kA), and the average PEM was 1.5 ± 1.9 × 1010 W vs. 3.9 ± 5.2 × 109. The median Po for positive strokes was 1.9 × 1010 W; the median Eo was 9.3 × 106 J; and the average tcw was 497 µs. Note that the average Eo for positive strokes is nearly a factor of 2 larger than negative FS, primarily because the widths of positive optical waveforms are about a factor of 2 larger than the negative FS. A positive stroke produced the largest Ip, PEM, Po, and Eo in our dataset with values of 99 kA, 6.7 × 1010 W, 7.3 × 1010 W, and 2.6 × 107 J, respectively.

Table 2. Optical Characteristics of 10 Positive CG Strokes (in Nine Flashes) in the GP
Trigger DateStroke TimeTypeRange (km)IP (kA)Pem (109 W)Po (109 W)Eo (106 J)tcw (µs)o a (106 W/m)
  1. a

    Only strokes between 5 and 20 km were used to estimate inline image.

7/5/200522:49:18.231FS2845142920675-
7/5/200522:55:19.935FS315520105521-
7/5/200523:03:11.832FS2799677327363-
7/5/200523:03:11.961NGC26369106653-
7/6/200501:10:01.088FS18317221147511.6
7/6/200523:08:44.502FS313793311319-
7/10/200523:11:29.701FS1629610.54310.2
7/10/200523:48:53.439FS202961087355.9
7/10/200523:50:29.483FS1830618845413.4
7/10/200523:56:33.153FS233792111518-
 Mean 24 ± 5.543 ± 2115 ± 1916 ± 207.4 ± 7.5514 ± 1367.8 ± 6.0
 Median 25369199.34979

3.3 Cloud Pulses

[26] The waveforms of 73 of the larger optical impulses radiated by intracloud discharges were analyzed, and distributions of those parameters have been included in Figures 6, 7, and 8. Since in most cases, the NLDN did not report a CP event, there were no reliable estimates of Ip or measurements of the distances to those sources. In cases where a CP was detected during a flash that had one or more ground strokes reported by the NLDN, the range to the CP was assumed to be the same as the average distance to all the reported strokes in that flash. If the CP was not accompanied by a NLDN report, then the range was assumed to be the average distance to all strokes that were reported in the same storm cell.

[27] Figures 6, 7, and 8 show that the CP events usually produced values of Po and Eo that were about a factor of 2 smaller than those of negative subsequent strokes that re-illuminated a PEC, and tcw was about a factor of 3 larger. The means and standard deviations of Po and Eo for CP events were 3.0 ± 2.9 × 109 W and 1.5 ± 2.2 × 106 J, respectively, and the mean tcw was 711 ± 1100 µs. The median values of Po, Eo, and tcw were 1.9 × 109 W, 7.3 × 105 J, and 311 µs, respectively.

4 Discussion

[28] Tables 1 and 2 list the median and average values of PEM for negative and positive strokes, respectively, that were computed using equation (3) and the ranges and values of Ip that were reported by the NLDN. It should be noted that the numerical values of Po for negative strokes are significantly larger than the values of PEM. For example, the median Po is 1.8 × 1010 W for negative FS which is about a factor of 9 larger than the median PEM of 2.0 × 109 W. Subsequent strokes producing a NGC have a median Po of 1.1 × 1010 W which is about a factor of 4 larger than the median PEM of 2.5 × 109 W. In our discussion of Figure 4, we noted that the optical waveforms reach a peak tens to hundreds of microseconds after the peak E-field, so the same time delay will be present between PEM and Po. It is certainly reasonable that Po (which occurs at a time the entire channel is illuminated) is larger than PEM (which is produced early when the current is a maximum near the ground). What is intriguing is that the values of PEM and Po for positive strokes (see Table 2) are often of similar magnitude and occasionally PEM is larger than Po. For example, in Table 2 the 99 kA positive stroke had a PEM of 6.7 × 1010 W and the corresponding Po was 7.3 × 1010 W; the 55 kA positive stroke had a PEM of 2.0 × 1010 W and a Po of only 1.0 × 1010 W. At this time, we offer no explanation for this observation.

4.1 Atmospheric Extinction

[29] None of the optical parameters reported here have been corrected for the effects of atmospheric extinction (i.e., scattering and absorption) between the lightning sources and the optical sensor. Because the Rayleigh scattering cross section of an air molecule varies as the inverse fourth power of wavelength, λ (i.e., 1/λ4), the shorter (blue) wavelengths will be scattered substantially more than the longer (red) wavelengths. Unfortunately, to our knowledge the time-resolved spectrum of a lightning source has never been measured on an absolute scale, but we can make a rough estimate of the effects of molecular scattering by assuming that ground strokes radiate like a perfect blackbody. The temperature of a return stroke channel rises very quickly to a peak near 30,000 K [Orville, 1968], and most of the optical radiation is produced at about the time of peak temperature [Uman, 1964]. We can compute the fraction of the radiation emitted by a 30,000 K source between 0.4 and 1.0 µm that would be detected at various distances in a standard molecular atmosphere. For this estimate, we have used the Beer–Lambert law with the extinction coefficients as tabulated by Bucholtz [1995]. The results are shown in Figure 10.

Figure 10.

The percentage of the optical radiation between 0.4 and 1.0 µm from a blackbody source at 30,000 °K that would be transmitted to different ranges in a standard Rayleigh atmosphere.

[30] We can also estimate how the effects of molecular scattering will change the spectrum of a 30,000 °K source that would be transmitted to various distances, and those results are shown in Figure 11. Note in Figure 10 that at a horizontal range of only 15 km, molecular scattering will reduce the total blackbody irradiance in our sensor bandwidth by about 25%, and at larger distances, the effects will be even greater. The changes in the spectra shown in Figure 11 are largest at short wavelengths, and even though our sensor had a flat spectral response (see Figure 1), molecular scattering will introduce a spectral dependence into our measurements of the broadband irradiance. Of course, lightning channels do not actually radiate like a perfect blackbody [Orville and Henderson, 1984], but we can expect that the effects of molecular scattering will be generally similar to those shown in Figures 10 and 11.

Figure 11.

The effects of Rayleigh scattering on the spectrum of the radiation from a blackbody source at 30,000 °K, at different distances in a standard molecular atmosphere.

[31] In our analyses of the optical waveforms, we have also neglected any effects of the intervening aerosol, including cloud and precipitation particles [Atlas and Bartnoff, 1953; Charlson, 1969; Twomey, 1977; Ulbrich and Atlas, 1985], and those effects can be very significant in a thunderstorm environment. There will also be some molecular absorption due to water vapor, ozone, and other trace gases, particularly in the near-infrared (IR) spectral region. The aerosol extinction (or turbidity) of humid air, such as in a Florida seacoast environment (or the central GP), will usually reduce the visibility much more than the clear, dry air in southern AZ [Malm et al., 1994]. Table 1 shows that although the average Ip in our sample of negative FS in AZ is nearly the same as in the GP, the values of Po and Eo are 50 to 100% larger in AZ, while the tcw is only about 3% smaller. This behavior is consistent with less turbidity in AZ relative to the GP. Since atmospheric visibility will vary from storm-to-storm as well as region-to-region, and is usually not known within or near thunderstorms, we will not consider the effects of extinction further except to note that because of such effects, all values of the optical parameters given in this paper represent lower limits at the source.

4.2 Comparison With Other Ground-Based Measurements

[32] The values of Po that we have obtained for negative ground strokes in AZ are significantly larger than prior measurements in Florida. For example, the mean Po for negative FS in AZ is 2.1 ± 1.5 × 1010 W (see Table 1), and this is almost an order of magnitude larger than the mean obtained by Guo and Krider [1982] in Florida (2.3 ± 1.8 × 109 W). The mean Po for subsequent strokes that re-illuminated a PEC was 6.3 ± 7.0 × 109 W in AZ, and this too is substantially larger than the 4.8 ± 3.6 × 108 W reported by Guo and Krider for “normal subsequent strokes” in Florida. The values of inline image produced by negative ground strokes in AZ are a factor of 2 to 5 larger than comparable measurements in Florida [Guo and Krider, 1982, 1983]. As suggested by Guo and Krider [1982], we expect that the primary reasons for the larger values in AZ are higher cloud bases and generally better visibility in AZ (and the GP) than in Florida.

4.3 Comparison With Aircraft and Satellite Measurements

[33] When we compare our results with aircraft and satellite measurements, we must keep in mind that there are significant differences not only in the sensing technology, the viewing geometry, and the effects of clouds, but also in the extinction of light propagating horizontally and vertically in the atmosphere. Clearly, when observations are made from a high-altitude aircraft or satellite platform, any luminosity from CG strokes will usually be reduced or even eliminated by the effects of geometry and intervening clouds. Also, sensors aloft will preferentially detect the luminosity produced by cloud discharges and/or the in-cloud portion of CG flashes [Thomason and Krider, 1982; Christian and Goodman, 1987; Koshak et al., 1994; Light et al., 2001a, 2001b].

[34] Aircraft measurements of lightning optical emissions have been described by Christian and Goodman [1987], Goodman et al. [1988], and Mach et al. [2005]. Goodman et al. have estimated that the broadband peak optical power that was produced by their (predominantly intracloud) sources was on the order of a few times 108 W and that the optical energy was of the order of 105 J. These results are generally consistent with the results of Guo and Krider [1982] and somewhat smaller than our measurements of the larger CP sources in AZ and the GP.

[35] Suszcynsky et al. [2000, 2001], Light et al. 2001b], and Davis et al. [2002] have analyzed the optical waveforms that were detected by a broadband photodiode on the FORTE spacecraft. Cloud pulses clearly dominate in the dataset of Suszcynsky et al., and because of the natural variability in of lightning and the effects of clouds, they suggest that a broadband, satellite-based measurement covering the visible and near-IR spectral regions can only determine the source optical energy of a source to an order of magnitude; however, if we compare their median peak power, 8.5 × 108 W, with our median for the larger CP events, 2.0 × 109 W, there is rather good agreement. The effective widths of the impulsive CP events detected by FORTE average 630 µs [Davis et al., 2002], and this too is in good agreement with our mean width of 711 ± 1100 µs. Of course, both datasets were affected by multiple scattering and other factors, but we think the overall agreement is rather good.

4.4 Relationships Between Po, inline image, and Ip

[36] In 1984, Ganesh et al. reported that both the peak luminosity and the logarithm of the peak luminosity emitted by lightning channels were correlated with the peak electric field produced by natural return strokes. Idone and Orville [1985] and more recently Wang et al. [1970] have reported significant correlations between the luminosity emitted by the lower portion of rocket-triggered strokes and the peak current measured directly at the channel base. All these studies suggest that early in a stroke, there may be a relationship between Po and Ip, particularly in the case of subsequent strokes that re-illuminate a PEC because those strokes are likely similar to rocket-triggered strokes [Rakov and Uman, Chapter 7].

[37] Figures 12 and 13 show plots of Po vs. Ip and inline image vs. Ip together with the best linear and quadratic fits to the data for PEC strokes in several different storms. Our sample is limited, but these figures show that Po and inline image both increase with increasing Ip. Linear and quadratic curves fit the data with about equal significance, so we cannot say which relationship is more compelling. Wang et al. [1970] have noted that the light produced in the lowest 3.6 m of a rocket-triggered channel is proportional to the current measured at the channel base, at least during its initial, fast-rising onset. This proportionality breaks down after the current peak, but Wang et al. also suggest that there may be a proportionality for the entire channel. The fact that Figures 12 and 13 do show that Po (measured at a time the entire channel is illuminated) and inline image (measured at early times) both increase with Ip (measured at the time of the peak E-field) supports the hypothesis of Wang et al.

Figure 12.

Plots of Po vs. Ip for negative subsequent strokes in 3 storm intervals that reilluminated a PEC and were at ranges of 10 to 32 km. The R2 values are for linear and quadratic fits to Ip. Note that there were two different cells of electrical activity on 23 August 2003 (bottom panel); Cell A (solid dots) was enhanced by back-scattering from cloud and precipitation but cell B (open circles) was not.

Figure 13.

Plots of inline image vs. Ip for negative subsequent strokes that reilluminated a PEC and were at ranges of 5 to 20 km. The R2 values are for linear and quadratic fits to Ip.

4.5 Enhancement of Lightning Optical Signals by Scattering

[38] It should be noted in Figures 12 and 13 that the proportional behavior of Po and Ip and inline image and Ip is not the same for all convective cells of lightning activity, even in the same storm interval (see, for example, the lower plot in Figure 12). The video imagery on 23 August 2003 shows that two different cells of electrical activity were producing ground strokes in the same interval and that there was cloud and precipitation directly behind one of the cells (cell A) but not the other (cell B). The strokes in cell A produced larger values of Po relative to Ip than strokes in cell B as shown in the bottom panel of Figure 12. Additionally, the strokes in cell A had larger Eo, inline image and tcw on average, while the average Ip and PEM values were lower than cell B. Means and standard deviations of the parameters for each of the two cells are shown in Table 3 for comparison. Our interpretation is that the cloud and rain were back-scattering a substantial fraction of the light emanating from cell A but not from cell B; therefore, the effects of clouds and rain can both enhance as well as reduce the optical signal from a lightning source.

Table 3. Mean and Standard Deviations of Stroke Parameters in Two Cells of Lightning Activity on 23 August 2003. Strokes in Cell A Were in Front of Cloud and Precipitation While Strokes in Cell B Were Not
 Cell ACell B
Strokes1711
Ip (kA)12 ± 615 ± 10
Po (GW)6.2 ± 4.22.7 ± 2.2
Eo (MJ)2.0 ± 1.30.8 ± 0.7
tcw (µs)320 ± 120260 ± 80
lo (MW/m)1.7 ± 1.21.1 ± 1.2
PEM (GW)1.3 ± 1.22.2 ± 3.3

Acknowledgments

[39] The authors are grateful to C. J. Biagi, K. L. Cummins, and C. D. Weidman for assistance with the data acquisition and analysis and to Michael Lesser and Roy Tucker in the UA Imaging Technology Laboratory for assistance with the sensor calibration. The lead author (MGQ) has submitted this research in partial fulfillment of the requirements for a M.S. degree in atmospheric sciences at the University of Arizona. This work has been supported in part by the NASA Kennedy Space Center, Grant NNK06 EB55G, and by the DARPA NIMBUS program through the University of Florida.

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