Investigating the Potential of Using Radar Echo Reflectivity to Nowcast Cloud-to-Ground Lightning Initiation over Southern Ontario

Y. Helen Yang Ontario Storm Prediction Centre, Environment Canada, Toronto, Ontario, Canada

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Patrick King Meteorological Research Branch, Environment Canada, Toronto, Ontario, Canada

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Abstract

The potential for using radar echo reflectivity to forecast cloud-to-ground (CG) lightning initiation in the 0–1-h time frame was investigated in southern Ontario, Canada. The main purpose of this investigation was to determine a reflectivity threshold at an isothermal altitude and a threshold for echo tops that best predict CG lightning initiation. The study examined lightning, radar, and upper-air sounding data for only airmass-type convection during the summer of 2008. The best predictor of the onset of CG lightning was found to be a 40-dBZ reflectivity level detected at an altitude with an environmental temperature of −10°C, with an average lead time of 17 min. Echo tops reaching or exceeding 7 km were a necessary condition prior to or at the time of the first CG lightning occurrence. Also, certain differences were observed depending on the polarity of the initial lightning flashes. Positive lightning flashes, when compared to negative ones, tended to deliver stronger electric currents and to be farther away from the locations of highest reflectivity on maximum reflectivity (MAXR) radar products. Lead times were observed to be shorter for positive lightning, which might suggest that positive-lightning-producing storm clouds became strongly electrified faster than their negative counterparts. Findings indicate the potential to develop a lightning nowcast algorithm suitable for Canadian forecast operational use.

* Retired

Corresponding author address: Y. Helen Yang, Ontario Storm Prediction Centre, Environment Canada, 4905 Dufferin St., Downsview ON M3H 5T4, Canada. Email: helen.yang3@ec.gc.ca

Abstract

The potential for using radar echo reflectivity to forecast cloud-to-ground (CG) lightning initiation in the 0–1-h time frame was investigated in southern Ontario, Canada. The main purpose of this investigation was to determine a reflectivity threshold at an isothermal altitude and a threshold for echo tops that best predict CG lightning initiation. The study examined lightning, radar, and upper-air sounding data for only airmass-type convection during the summer of 2008. The best predictor of the onset of CG lightning was found to be a 40-dBZ reflectivity level detected at an altitude with an environmental temperature of −10°C, with an average lead time of 17 min. Echo tops reaching or exceeding 7 km were a necessary condition prior to or at the time of the first CG lightning occurrence. Also, certain differences were observed depending on the polarity of the initial lightning flashes. Positive lightning flashes, when compared to negative ones, tended to deliver stronger electric currents and to be farther away from the locations of highest reflectivity on maximum reflectivity (MAXR) radar products. Lead times were observed to be shorter for positive lightning, which might suggest that positive-lightning-producing storm clouds became strongly electrified faster than their negative counterparts. Findings indicate the potential to develop a lightning nowcast algorithm suitable for Canadian forecast operational use.

* Retired

Corresponding author address: Y. Helen Yang, Ontario Storm Prediction Centre, Environment Canada, 4905 Dufferin St., Downsview ON M3H 5T4, Canada. Email: helen.yang3@ec.gc.ca

1. Introduction

Lightning is a high-impact weather phenomenon that causes about 9–10 deaths and 92–164 injuries in Canada each year (Mills et al. 2008). It also causes significant property damage and economic losses. Lightning is particularly important to the aviation industry. Ground operations at airports are sensitive to lightning activity within their aerodromes. Hence, it is of great interest to be able to timely and accurately forecast lightning, as this ability may lead to possible future lightning watch/warning products in Canada.

Numerous studies in the United States and Japan have attempted to utilize radar echoes to nowcast lightning initiation (e.g., Buechler and Goodman 1990; Michimoto 1991, 1993; Hondl and Eilts 1994; Gremillion and Orville 1999; Vincent et al. 2004; Lakshmanan and Stumpf 2005). In Hong Kong, a lightning nowcast algorithm has been undergoing trial operation since 2007 and was incorporated into the Short-Range Warning of Intense Rainstorms in Localized Systems (SWIRLS), a nowcasting system used to track and forecast severe weather (Yeung et al. 2007; L. Yeung 2009, personal communication). In Canada, Larsen and Stansbury (1974) and Marshall and Radhakant (1978) did studies correlating radar reflectivity to lightning flashes in the 1970s, but little has been done since then.

This paper investigates the potential of using radar echoes to nowcast cloud-to-ground (CG) lightning initiation in the 0–1-h time frame. A total of 143 storm cases were examined within the area covered by the King City radar (WKR) in southern Ontario, Canada (as illustrated in Fig. 1), from June to August of 2008. The primary objective of this study is to determine a threshold value for radar reflectivity that best predicts CG lightning initiation. Any correlation between the radar echo tops and CG lightning was also analyzed. In addition, some radar characteristics associated with negative CG lightning initiation and those associated with positive CG lightning initiation were compared and contrasted.

2. Background information

a. Graupel–ice mechanism for cloud electrification

Scientists commonly view cloud electrification as a complex process involving various factors (e.g., Krehbiel 1986; MacGorman and Rust 1998; Saunders et al. 2006), many of which are still not well understood today. Of all the proposed conceptual models for explaining cloud electrification, the graupel–ice mechanism is most favored by the scientific community, since it is supported by evidence from laboratory studies and in-cloud measurements taken over the past few decades (e.g., Takahashi 1978, 1984; Jayaratne et al. 1983; Maekawa et al. 1992; Takahashi and Miyawaki 2002; MacGorman et al. 2008). The graupel–ice mechanism is discussed in detail by MacGorman and Rust (1998, 65–70).

Basically, this is a noninductive mechanism in which larger riming graupel and smaller ice crystals collide, and consequently electric charges are exchanged by these hydrometeors. The rebounding ice crystals tend to become positively charged, while graupel particles become negatively charged. When such collisions take place in an updraft of a storm, the charged hydrometeors are then separated by gravity; ice crystals, being lighter, are carried by the updraft to the upper storm cloud portion, forming the main positive charge area, and the heavier graupel particles reside in the lower storm cloud portion, which becomes the main negative charge region. Only a simplistic charge distribution of an electrified cloud is presented here [refer to Krehbiel (1986) for a more complete treatment]. Contrary to the above classic dipole structure of a storm cloud, the Severe Thunderstorm Electrification and Precipitation Study (STEPS) conducted in 2000 found that some severe thunderstorms had these polarities reversed, with the main negative charge region above the positive one (Rust et al. 2005).

b. Mixed-phase region

The graupel–ice mechanism occurs in the mixed-phase cloud region where supercooled liquid water and ice coexist. Empirical evidence has shown that strong electrification requires graupel growing by riming and colliding with ice crystals (e.g., Reynolds et al. 1957; Takahashi 1978). It is now recognized that active particle collisions and charge separations occur in the mixed-phase region in or near a storm updraft. MacGorman and Rust (1998) stated that the mixed-phase region is typically located in the cloud layer where the temperature ranges between −10° and −40°C, although most of supercooled liquid water droplets would have frozen by −30°C. According to Wallace and Hobbs (1977, p. 186), there is about a 50% probability of detecting ice in cloud for cloud top temperatures of −10°C, while that probability is better than 95% for cloud top temperatures of −20°C. Knight et al. (1982, p. 188) found that the (adiabatic) liquid water content reaches its maximum in the region of storm clouds corresponding to the temperature range between −15° and −20°C. The significance of finding a temperature range in a mixed-phase cloud region that is optimal for strong electrification will become more apparent in the next section.

c. Main negative charge region

It follows from earlier discussions that the main negative charge region should reside in the mixed-phase layer of a storm cloud, and indeed it has been observed to be so. It is also adjacent to and in a storm updraft (Krehbiel 1986). Furthermore, it remains at fairly constant altitudes as the storm evolves (Krehbiel et al. 1984). Studies throughout the years have offered differing opinions on the exact location of the main negative charge region. Takahashi (1984) found a strong negative charge accumulation near the −10°C level in the mature stage of a storm. Krehbiel et al. (1984) located the main negative charge region at between 6.5 and 8 km MSL, (i.e., between −10° and −20°C). Dye et al. (1986) observed it to be at about −20°C during the early cloud electrical development process. MacGorman et al. (2008) stated that it is between roughly −10° and −25°C.

Lightning is often initiated in the main negative charge region (e.g., Krehbiel et al. 1984; Yeung et al. 2007). Krehbiel (1986) explained that CG lightning usually occurs between the main negative charge region and the ground by discharging the negative charge to the ground. Though the main negative charge region in cloud cannot be detected without specialized instruments, radar technology can help detect the hydrometeors in this region. In fact, many studies have drawn a strong correlation between lightning initiation and radar echoes at −10° to −20°C levels, where the main negative charge region is typically located (e.g., Krehbiel et al. 1984; Buechler and Goodman 1990; Gremillion and Orville 1999; Vincent et al. 2004).

d. Assumptions

There are five fundamental assumptions made throughout this study: (i) the graupel–ice mechanism is responsible for generating cloud electrification strong enough to initiate lightning, (ii) detectable radar echoes precede the onset of CG lightning, (iii) initial CG lightning activity is originated from the main negative charge region, (iv) the main negative charge region stays at nearly constant altitudes or temperatures as the storm grows (i.e., at levels of −10° to −20°C), and (v) ground conditions are conducive to CG lightning.

3. Data and methods

a. Lightning data

The lightning observation data were supplied by the Canadian Lightning Detection Network (CLDN). The data used for the study were of lightning flashes, as opposed to strokes. A single flash may be composed of multiple strokes. Lightning information is stored in ASCII files, containing data for each lightning flash, such as the date–time of occurrence, its location in latitude and longitude, the polarity and strength of the electric current, and an indicator telling whether it is intracloud (IC) or CG. For the domain studied, the CLDN detection efficiency is 90% or better, and the associated location accuracy is within 0.5 km (Dockendorff and Spring 2009). Only lightning flashes of the CG type were included in the study, partly because the CLDN currently underdetects IC lightning.

b. Radar data

All radar image data were taken from the Unified Radar Processing (URP) software, which is used by the Meteorological Service of Canada for displaying their C-band radar signals (Joe et al. 2002). The URP generates basic conventional and Doppler radar products, as well as ones that assist in tracking and forecasting thunderstorm cells. Maximum reflectivity (MAXR), CAPPI, ECHOTOPS, and (vertical) cross section were the main URP products used in the study, each with a horizontal resolution of 1 km (P. Joe 2009, personal communication). The temporal resolution of the URP at present is 10 min. As the lone radar used for the study, the WKR radar completes the conventional volume scanning in 24 angles from 0.3° to 24.6° and some signal processing in just under 5 min, followed by about 3 min of Doppler scanning, and ends with several more minutes of postsignal processing (D. Hudak 2008, personal communication).

Some radar issues can affect the results of the study. The C-band radars are susceptible to signal attenuation. Common radar problems, such as beam overshooting and the beam volume increasing with range, however cannot be minimized when using only one radar. The relatively lengthy radar time step of 10 min may not accurately capture the evolution of convective storms. Although these issues are acknowledged here, quantifying their impacts is beyond the scope of this study.

c. Dataset and data processing

For all practical purposes in this study, a “case” was defined to be one cell or a cluster of cells on a radar display that may or may not eventually produce lightning. A total of 143 cases taken during days with airmass thunderstorms in the summer of 2008 were chosen and examined. Airmass thunderstorms are associated with warm, humid air, in the absence of any major synoptic forcing. These storms are often triggered by daytime heating and/or lake-breeze convergence in southern Ontario. They tend to develop during the afternoon and dissipate during the evening hours after sunset. Some airmass thunderstorms may be organized by lake breezes and become linked, thus appearing on a radar display as a cluster of cells and making it difficult to differentiate any one cell from the others during their course of evolution. As shown in Table 1, 77 of the 143 cases did produce CG lightning, and the majority (63) had the initial lightning being negative. Only six cases had positive initial lightning, while eight delivered first lightning flashes of both polarities (for a time resolution of 10 min).

A merged lightning and radar dataset was produced to enable the identification of cases that produced lightning and those that did not. All CG lightning flashes located within the area defined by the WKR radar range were extracted and grouped every 10 min, matching the radar time step. A lightning map (e.g., Fig. 2a) for each 10-min period was then plotted using R.1 Finally, a composite map (Fig. 2c) was created by overlaying the lightning data onto the corresponding radar MAXR–CAPPI image using ImageMagick.2 The temporal resolution of the lightning data plotted on a composite map was therefore considered to be 10 min, the same as the radar data, and shall be treated as so in the rest of this paper.

To avoid ambiguity, we attempted to choose isolated cases. Also, a lightning flash was assigned to a particular case only if the distance between the flash and that case was the shortest as compared to other cases. Specifically, the distance was measured between the flash and the location of highest reflectivity of the case on MAXR. The longest distance observed was 11.2 km from Fig. 3. Apparently, lightning can occur as far as 16 km away from the storm (Cooper et al. 2007, p. 67).

As discussed earlier, the storm updraft layer between about −10° and −20°C plays a significant role in initiating lightning. The main goal of this study is to determine what radar reflectivity threshold value at which temperature level can best predict the onset of CG lightning. Table 2 lists the various radar reflectivity threshold values studied at the −10°, −15°, and −20°C levels. To simplify this process, these isotherms within a storm updraft were approximated with ambient environment isotherms in this study. This approximation should be adequate since the studied storms were estimated to mostly have low CAPE values (90% with CAPE < 1200 J kg−1, 10% between 1200 and 2400 J kg−1). Also, entrainment would further bridge the gap between the updraft and environment isotherms. The altitudes corresponding to the isotherms in each case were estimated from the archived upper-air sounding data from the following stations: Maniwaki, Quebec (CWMW); Albany, New York (KALB); Gaylord, Michigan (KAPX); Buffalo, New York (KBUF); and White Lake, Michigan (KDTX). Linear extrapolation was applied whenever a desired temperature lay between two observational values. Data from only one upper-air station was used directly if the station was in close proximity to a given case. In a situation where a case was located at some distance from each station, the altitude of a desired temperature was calculated as the weighted average of data from multiple stations, with closer stations weighted more heavily than farther ones. The mean values of the altitudes for the time periods studied are shown in Fig. 4. It can be seen that the isothermal altitudes (MSL) were lower in June when days were relatively cooler than during the other months.

When a case was identified and selected on a composite map, a vertical cross section was made at each 10-min radar time step throughout its evolution and possibly leading up to the occurrence of its first CG lightning. Then, the reflectivity value at each of the three isothermal altitudes was read off the cross-section plot to see if any threshold value as specified in Table 2 was reached or exceeded. It would be considered a “hit” for a particular threshold at a certain temperature level when this threshold was reached–exceeded prior to or at the time of first lightning. On the other hand, it would be regarded as a “miss” if the threshold was not reached by the time of first lightning. A third option would be a “false alarm,” where the threshold was met but there was no lightning detected at all. Two things are worth noting here. First, reflectivity values at a given height were read subjectively from contoured values on a video display. Second, cross-sectional views of a case could appear to be different depending on the cuts. Consequently, the cross-sectional view that gave the greatest reflectivity at an altitude of interest was used. An example of cross sections and threshold assessments is illustrated in Fig. 5. In this example, the threshold of 40 dBZ at the −10°C level (−10°C–40 dBZ) was first reached at 2140 UTC. The first lightning appeared at 2200 UTC. Therefore, −10°C–40 dBZ had a lead time of 20 min. Lead time is defined as the difference between the time when a threshold is first met and the time of first lightning occurrence.

4. Results and discussions

a. Radar echo reflectivity threshold and lead time

Given the hits, misses, and false alarms for the predictors mentioned in Table 2, some statistical methods were applied to evaluate the forecast skill associated with the various reflectivity thresholds at different temperature levels. They are the probability of detection (POD), false alarm ratio (FAR), and critical success index (CSI), all of which are defined in the appendix. Table 3 contains these statistical quantities calculated for all cases.

A trend can be readily detected upon examining the POD values. For each temperature level, POD is diminished as the reflectivity threshold increases. Also, with increasing altitude, POD decreases with higher thresholds. This is not surprising, since lightning-producing storms could reach weaker thresholds (i.e., lower dBZ values) more easily than stronger ones (i.e., higher dBZ values). Hence, the lower a threshold was, the greater its POD was. A similar trend is also seen in FAR, but, of course, opposite the desired effect. The stronger a threshold was, the smaller its FAR was. This suggests that a stronger convection pattern likely promotes more graupel production and ultimately leads to greater chances of cloud electrification, thus reducing the number of false alarms.

In fact, the trend above is also noted in the average lead times given in Table 3d. With increasing height, the lead time decreases with stronger reflectivity thresholds. It takes time for thunderstorms to develop in terms of both strength and height. The lead time varied from case to case for different thresholds at different altitudes, ranging from 0 to 70 (±5) min. An airmass thunderstorm cell has a lifetime of about 30 min (Wallace and Hobbs 1977, p. 238). Hence, a case with a relatively long lead time likely consisted of two or more cells clustered together at different stages of their life cycles, and perhaps organized by lake breezes, which might have encouraged longer lifetimes. The box-and-whisker plots in Fig. 6 depict lead time distributions associated with the different temperature–reflectivity predictors. The median lead time shown in general was either 10 or 20 (±5) min. Obviously, the lead time can be improved by lowering the threshold, but doing so would worsen the FAR. The best predictor chosen has to strike a balance between the two in an operational forecast settings; it should give forecasters enough warning time with reasonable accuracy to be useful.

The threshold of 40 dBZ at the −10°C level scored the best in the study, with the highest CSI value of 76% and an average lead time of 17 ±5 min. These results are comparable to those obtained in previous studies, despite many differences in the settings between this study and the others, such as in time, geography, radar instrumentation, etc. Some of the studies from the past few decades are listed in Table 4 for comparison. A radar reflectivity of near 40 dBZ had already been identified as significant in lightning initiation as early as the 1970s by Larsen and Stansbury (1974) and Marshall and Radhakant (1978). However, their temperature levels associated with 40 dBZ were cooler–higher than the −10°C level found in this study. Michimoto (1991, 1993) suggested that a threshold of 30 dBZ at the −20°C level was a necessary but not sufficient criterion for the onset of lightning, for both warm and cold seasons. This was not found to be so in this study; some cases did produce lightning without ever reaching 30 dBZ at the −20°C level. Dye et al. (1989) found that strong electrification could not happen until about 40 dBZ had been reached at a height representing approximately −10°C. Buechler and Goodman (1990), Gremillion and Orville (1999), and Vincent et al. (2004) concluded that 40 dBZ at −10°C could best predict lightning initiation, a result in agreement with this study. Their associated lead times also corroborated with the ones obtained from this study. The POD, FAR, and CSI values for −10°C–40 dBZ derived here all lay within the ranges among those given in their studies. Unlike all other works in Table 4, Wolf (2007) suggested that the temperature level within a storm updraft should be used rather than the environment temperature level. According to Wolf, the −6°C isotherm within an updraft is often at about the same altitude as the environment’s −10°C isotherm in moderately unstable environments. He found that −6°C–40 dBZ (within an updraft) produced a higher POD (and FAR) than did −10°C–40 dBZ (within an updraft), as indicated in Table 4. His results further validate the reflectivity threshold of 40 dBZ at the environment −10°C level as a good predictor for the onset of CG lightning.

b. Radar-echo-top threshold

The potential of using radar echo tops to help predict lightning initiation was explored in this study as well. First, the discussions here focus on echo tops in relation to only warm season lightning. Second, echo tops of convection on warmer days are expected to be higher than those during colder days (e.g., Michimoto 1991). Indeed, the echo-top heights in cases selected from the relatively cooler month of June were up to only about 8–9 km, as compared to a maximum height of 12–13 km from the warmer months of July and August. Third, higher echo tops generally indicate stronger updrafts and lower echo tops for weaker updrafts (e.g., Doswell 1985, section III E). Empirical evidence has shown that weak updrafts cannot produce the intense electrification needed to generate lightning (e.g., Michimoto 1993; Zipser and Lutz 1994).

Studies, including the one here, have attempted to find the minimal echo-top threshold required for the onset of lightning. As shown in Fig. 7, echo tops of all lightning-producing cases reached or exceeded 7 km. Cases that did not produce lightning had lower echo tops in general, but nearly 79% of them also reached or exceeded 7 km. Therefore, echo tops reaching at least 7 km seemed to be a necessary condition but obviously not a sufficient one. This result is supported by Krehbiel (1986), who gave the minimal echo-top threshold of 7–8 km in the summer. Buechler and Goodman (1990), however, proposed that it should exceed 9 km. Gremillion and Orville (1999) found that all storms that produced CG lightning had echo tops higher than 9.5 km, and over half of the no-lightning storms also had echo tops higher than 9.5 km. The higher threshold of 9–9.5 km may be explained by the fact that their storms occurred over the southern United States where the air mass tends to be warmer than that over southern Ontario, which was the domain of this study.

In terms of temperature levels, an altitude of 7 km was equivalent to somewhere between −13° and −29°C levels for all cases examined. This temperature range seems wide when compared to −15° to −20°C, which corresponds to 7–8 km as given by Krehbiel (1986). This reflects the large fluctuations in airmass temperatures over Ontario. Because of the limited resolution of URP echo-top products, it is impossible to associate echo-top heights with exact temperature values—only temperature ranges can be derived. At least 73 (and at most 75) of all 77 of the lightning-producing cases obtained echo-top temperatures of −20°C or colder, and all 77 had echo-top temperatures lower than −10°C. Incidentally, at least 44 (and at most 57) of all 66 of the no-lightning cases showed echo-top temperatures of −20°C or colder. Tomine et al. (1986, in Michimoto 1991) also saw a similar phenomenon in their study of winter convections in Japan, where lightning-producing storms showed echo-top temperatures of −20°C or colder, and yet echo tops for some storms without lightning were just as cold.

The minimum echo-top threshold of 7 km could be used in conjunction with reflectivity thresholds to enhance the accuracy of predicting lightning initiation. For instance, the combined predictor of −10°C–40 dBZ with echo tops of at least 7 km would improve the FAR and CSI (in Table 3), each by 1%. Nevertheless, the associated POD would remain the same because all lightning-producing cases showed echo tops reaching at least 7 km.

c. Negative versus positive CG lightning

Some characteristics of negative initial CG lightning flashes were found to be perceivably different from those belonging to positive ones. It is cautioned that any difference discussed here was drawn from only a small sample size of positive flashes included in the study. For the sake of simplicity, cases that produced both polarities upon lightning initiation were handled such that they were counted toward both negative and positive cases during statistical computations.

The magnitudes of the electric current associated with positive flashes were found to be generally larger than those of negative flashes (see Fig. 8); this result agrees with past studies (e.g., Orville et al. 2002). Positive flashes tend to be more damaging and lethal than negative ones in nature. Also, as shown in Fig. 3, negative flashes seemed to be closer to storm locations of maximum reflectivity on MAXR than positive ones. This suggests that negative CG lightning likely occurred closer to the main negative charge cloud region where the highly reflective graupel particles were more concentrated. In other words, positive CG lightning likely happened farther away from the main negative charge cloud region. This result seems reasonable; in the graupel–ice electrification mechanism, graupel particles become negatively charged. As for echo-top heights, there was no significant difference between the negative and positive lightning; that is, the polarity of the initial lightning could not be distinguished based on the updraft strength, which is implied by the echo-top height.

When the predictors as specified in Table 2 were used to forecast lightning with the polarity taken into account, two conclusions were drawn. (i) POD, FAR, and CSI showed inconclusive results. Negative lightning was no better or worse at forecasting than was positive lightning by most of these thresholds, based on POD alone. For some unknown reason, −10°C–40 dBZ, −15°C–40 dBZ, and −20°C–40 dBZ did score higher PODs in predicting positive than negative lightning, however. Also, since false alarm cases had no lightning polarity, it was pointless to calculate FAR and CSI. (ii) All predictors had significantly shorter lead times for positive lightning. For instance, as stated in Table 5, −10°C–40 dBZ, which was deemed the best predictor, had an average lead time of 18 min for forecasting negative lightning, but it was halved (9 min) for positive lightning. The shorter lead times likely indicate that strong cloud electrification happened much faster in cases that produced first lightning of positive polarity.

5. Conclusions and remarks

With the graupel–ice mechanism in cloud electrification as the basis for this study, relevant data from the CLDN, URP system, and upper-air soundings were scrutinized for airmass storms that occurred in southern Ontario during the summer of 2008, for the purpose of assessing the potential for nowcasting CG lightning initiation using radar information. The study found that a radar reflectivity threshold of 40 dBZ at an altitude where the environmental temperature was −10°C could best predict the onset of CG lightning. The associated POD, FAR, CSI, and average lead time were 88%, 16%, 76%, and 17 ±5 min, respectively. Because there was a trade-off between the lead time and number of false alarms, the reflectivity threshold could be lowered to gain more lead time, if required by forecast operational needs. Having echo tops that reached or exceeded 7 km was deemed a necessary but not a sufficient condition prior to or at the beginning of CG lightning activity. These results agree fairly well with those from previous studies; some disagreements may be attributed to seasonal, geographical, and radar technological variations. In addition, certain differences were observed depending on the polarity of the initial lightning flashes. Positive lightning flashes tended to deliver stronger electric currents and to be located farther away from the storm area of maximum reflectivity on MAXR. This means that positive lightning was likely more energetic and that negative lightning occurred closer to the main negative charge region in the storm. Our results showed no definitive difference in skill when forecasting lightning of different polarities. Nevertheless, lead times were found to be shorter in positive cases, which suggests that positive-lightning-producing storm clouds became strongly electrified faster than negative-lightning-producing storm clouds.

Exploring other radar characteristics as potential lightning predictors using URP, and studying more and different cases, are recommended for future work. For example, vertically integrated liquid (VIL) may be used as a predictor (e.g., Lakshmanan and Stumpf 2005; Yeung et al. 2007). The charging of riming graupel depends on the liquid water content (e.g., Takahashi 1978; Jayaratne et al. 1983; Saunders et al. 2006; Pereyra et al. 2008), which can be inferred from the VIL. The growth–lapse rate of radar echo reflectivity has been suggested in some studies as being important for lightning production (e.g., Michimoto 1991, 1993; Hondl and Eilts 1994; Vincent et al. 2004). Also, one can take advantage of the dual-polarimetric aspect of the WKR radar to distinguish hydrometeors (e.g., distinguish graupel particles from liquid water droplets) at different temperature levels. Rather than using only one radar, is as done in this study, multiple radars are recommended to compensate for radar geometry imperfections, in order to get data that better represent the three-dimensional nature of storms. Moreover, our knowledge of lightning initiation can be furthered by studying other types of convection, such as mesoscale convective complexes (MCCs), squall lines, frontal types, etc., during different seasons.

It is hoped that the findings of this study and of any future work may help in eventually developing a lightning nowcast algorithm to be used as part of a future URP nowcasting application tool for forecast operations within Environment Canada. It would be difficult to accurately warn the public and other clients against lightning in a timely way without such a tool.

Acknowledgments

We thank the Ontario Storm Prediction Centre and the National Laboratory for Nowcasting and Remote Sensing Meteorology for the opportunity of conducting this study. We much appreciate the encouragement and support from Ed Becker and Glenn Robinson. We are very grateful to Paul Joe for providing the essential archived URP radar data and his expertise. Special thanks go to David Hudak, Norman Donaldson, and Jim Young at the King City radar facility for their help. We thank the following people for their helpful suggestions: Mark Alliksaar, William Burrows, Zuohao Cao, Victor Chung, Mike Leduc, Syd Peel, and David Sills.

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  • Joe, P., Falla M. , Van Rijn P. , Stamadianos L. , Falla T. , Magosse D. , Ing L. , and Dobson J. , 2002: Radar data processing for severe weather in the National Radar Project of Canada. Preprints, 21st Conf. on Severe Local Storms, San Antonio, TX, Amer. Meteor. Soc., P4.13. [Available online at http://ams.confex.com/ams/pdfpapers/47421.pdf].

    • Search Google Scholar
    • Export Citation
  • Knight, C. A., Cooper W. A. , Breed D. W. , Paluch I. R. , Smith P. L. , and Vali G. , 1982: Microphysics. Hailstorms of the Central High Plains. Volume I: The National Hail Research Experiment, C. A. Knight and P. Squires, Eds., Colorado Associated University Press, 151–193.

    • Search Google Scholar
    • Export Citation
  • Krehbiel, P. R., 1986: The electrical structure of thunderstorms. The Earth’s Electrical Environment, National Academies Press, 90–113.

    • Search Google Scholar
    • Export Citation
  • Krehbiel, P. R., Brook M. , Khanna-Gupta S. , Lennon C. L. , and Lhermitte R. , 1984: Some results concerning VHF lightning radiation from the real-time LDAR system at KSC, Florida. Proc. VIIth Int. Conf. on Atmospheric Electricity, Boston, MA, Amer. Meteor. Soc., 388–393.

    • Search Google Scholar
    • Export Citation
  • Lakshmanan, V., and Stumpf G. J. , 2005: A real-time learning technique to predict cloud-to-ground lightning. Preprints, Fourth Conf. on Artificial Intelligence Applications to Environmental Science/21st Int. Conf. on Interactive Information Processing Systems for Meteorology, Oceanography, and Hydrology, San Diego, CA, Amer. Meteor. Soc., J5.6. [Available online at http://ams.confex.com/ams/pdfpapers/87206.pdf].

    • Search Google Scholar
    • Export Citation
  • Larsen, H. R., and Stansbury E. J. , 1974: Association of lightning flashes with precipitation cores extending to height 7 km. J. Atmos. Terr. Phys., 36 , 15471553.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • MacGorman, D. R., and Rust W. D. , 1998: The Electrical Nature of Storms. Oxford University Press, 422 pp.

  • MacGorman, D. R., and Coauthors, 2008: TELEX: The Thunderstorm Electrification and Lightning Experiment. Bull. Amer. Meteor. Soc., 89 , 9971013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Maekawa, Y., Fukao S. , Sonoi Y. , and Yoshino F. , 1992: Dual polarization radar observations of anomalous wintertime thunderclouds in Japan. IEEE Trans. Geosci. Remote Sens., 30 , 838844.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J. S., and Radhakant S. , 1978: Radar precipitation maps as lightning indicators. J. Appl. Meteor., 17 , 206212.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Michimoto, K., 1991: A study of radar echoes and their relation to lightning discharge of thunderclouds in the Hokuriku district. Part I: Observations and analysis of thunderclouds in summer and winter. J. Meteor. Soc. Japan, 69 , 327335.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Michimoto, K., 1993: A study of radar echoes and their relation to lightning discharges of thunderclouds in the Hokuriku district. Part II: Observation and analysis of “single-flash” thunderclouds in midwinter. J. Meteor. Soc. Japan, 71 , 195204.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mills, B., Unrau D. , Parkinson C. , Jones B. , Yessis J. , Spring K. , and Pentelow L. , 2008: Assessment of lightning-related fatality and injury risk in Canada. Nat. Hazards, 47 , 157183.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Orville, R. E., Huffines G. R. , Burrows W. R. , Holle R. L. , and Cummins K. L. , 2002: The North American Lightning Detection Network (NALDN)—First results: 1998–2000. Mon. Wea. Rev., 130 , 20982109.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pereyra, R. G., Bürgesser R. E. , and Ávila E. E. , 2008: Charge separation in thunderstorm conditions. J. Geophys. Res., 113 , D17203. doi:10.1029/2007JD009720.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reynolds, S. E., Brook M. , and Gourley M. F. , 1957: Thunderstorm charge separation. J. Meteor., 14 , 426436.

  • Rust, W. D., and Coauthors, 2005: Inverted-polarity electrical structures in thunderstorms in the Severe Thunderstorm Electrification and Precipitation Study (STEPS). Atmos. Res., 76 , 247271.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Saunders, C. P. R., Bax-Norman H. , Emersic C. , Avila E. E. , and Castellano N. E. , 2006: Laboratory studies of the effect of cloud conditions on graupel/crystal charge transfer in thunderstorm electrification. Quart. J. Roy. Meteor. Soc., 132 , 26532673.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stanski, H. R., Wilson L. J. , and Burrows W. R. , cited. 2009: Survey of common verification methods in meteorology. World Weather Watch Tech. Rep. 8, WMO/TD 358. [Available online at http://www.bom.gov.au/bmrc/wefor/staff/eee/verif/Stanski_et_al/Stanski_et_al.html].

    • Search Google Scholar
    • Export Citation
  • Takahashi, T., 1978: Riming electrification as a charge generation mechanism in thunderstorms. J. Atmos. Sci., 35 , 15361548.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Takahashi, T., 1984: Thunderstorms electrification—A numerical study. J. Atmos. Sci., 41 , 25412558.

  • Takahashi, T., and Miyawaki K. , 2002: Reexamination of riming electrification in a wind tunnel. J. Atmos. Sci., 59 , 10181025.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tomine, K., Michimoto K. , and Abe S. , 1986: Studies on thunderstorm in winter in the area surrounding Komatsu by radar (in Japanese). Tenki, 33 , 445452.

    • Search Google Scholar
    • Export Citation
  • Vincent, B. R., Carey L. D. , Schneider D. , Keeter K. , and Gonski R. , 2004: Using WSR-88D reflectivity data for the prediction of cloud-to-ground lightning: A central North Carolina study. Natl. Wea. Dig., 27 , 3544.

    • Search Google Scholar
    • Export Citation
  • Wallace, J. M., and Hobbs P. V. , 1977: Atmospheric Science. An Introductory Survey. Academic Press, 467 pp.

  • Wolf, P., 2007: Anticipating the initiation, cessation, and frequency of cloud-to-ground lightning, utilizing WSR-88D reflectivity data. Electron. J. Oper. Meteor., 2007-EJ1. [Available online at http://www.nwas.org/ej/2007-EJ1].

    • Search Google Scholar
    • Export Citation
  • Yeung, L. H. Y., Lai E. S. T. , and Chiu S. K. S. , 2007: Lightning initiation and intensity nowcasting based on isothermal radar reflectivity—A conceptual model. Preprints, 33rd Conf. on Radar Meteorology, Cairns, QLD, Australia, Amer. Meteor. Soc., 11A.7. [Available online at http://ams.confex.com/ams/pdfpapers/123157.pdf].

    • Search Google Scholar
    • Export Citation
  • Zipser, E. J., and Lutz K. R. , 1994: The vertical profile of radar reflectivity of convective cells: A strong indicator of storm intensity and lightning probability? Mon. Wea. Rev., 122 , 17511759.

    • Crossref
    • Search Google Scholar
    • Export Citation

APPENDIX

Definition of POD, FAR, and CSI (Stanski et al. 2009)

i1520-0434-25-4-1235-eqa1

Fig. 1.
Fig. 1.

Domain of this study.

Citation: Weather and Forecasting 25, 4; 10.1175/2010WAF2222387.1

Fig. 2.
Fig. 2.

Lightning and radar images at 2130 UTC 18 Aug 2008. Negative and positive CG lightning flashes are marked with yellow minus (−) and red plus (+) signs, respectively. (a) Lightning map. (b) Radar image MAXR. (c) Composite map.

Citation: Weather and Forecasting 25, 4; 10.1175/2010WAF2222387.1

Fig. 3.
Fig. 3.

Box-and-whisker plot of the distance between the initial lightning flash and storm maximum reflectivity on MAXR. The left and right ends of the box are the near first and third quartiles, respectively. The darker line marks the median. At either end of the box, the plot whiskers extend out to 1.5 times the length of the box.

Citation: Weather and Forecasting 25, 4; 10.1175/2010WAF2222387.1

Fig. 4.
Fig. 4.

Average altitudes corresponding to different temperature levels for the time periods examined in the study.

Citation: Weather and Forecasting 25, 4; 10.1175/2010WAF2222387.1

Fig. 5.
Fig. 5.

Case 60 as an example. The altitudes corresponding to the −10°, −15°, and −20°C levels were 5.4, 6.1, and 6.6 km, respectively. The first lightning appeared at 2200 UTC. Case 60 was a hit for almost all predictors but a miss for −10°C–45 dBZ, −15°C–40 dBZ, and −20°C–40 dBZ. (a) Cross section at 2120 UTC 18 Aug 2008. The maximum reflectivities for the −10°, −15°, and −20°C levels were 25 dBZ, 20 dBZ, and unknown, respectively. (b) Cross section at 2130 UTC 18 Aug 2008. The maximum reflectivities for the −10°, −15°, and −20°C levels were 30, 25, and 25 dBZ, respectively. (c) Cross section at 2140 UTC 18 Aug 2008. The maximum reflectivities for the −10°, −15°, and −20°C levels were 40, 35, and 30 dBZ, respectively. (d) Cross section at 2200 UTC 18 Aug 2008. The maximum reflectivities for the −10°, −15°, and −20°C levels were all 35 dBZ.

Citation: Weather and Forecasting 25, 4; 10.1175/2010WAF2222387.1

Fig. 6.
Fig. 6.

Box-and-whisker plots of the lead times for all 77 of the hit cases. The left and right ends of the box are the near first and third quartiles, respectively. The darker line marks the median. At either end of the box, the plot whiskers extend out to 1.5 times the length of the box. Shown are the (a) −10°C, (b) −15°C, and (c) −20°C levels.

Citation: Weather and Forecasting 25, 4; 10.1175/2010WAF2222387.1

Fig. 7.
Fig. 7.

Max echo top prior to or at the start of CG lightning activity.

Citation: Weather and Forecasting 25, 4; 10.1175/2010WAF2222387.1

Fig. 8.
Fig. 8.

Box-and-whisker plot of the current magnitude. The top and bottom ends of the box are the near first and third quartiles, respectively. The darker line marks the median. At either end of the box, the plot whiskers extend out to 1.5 times the height of the box.

Citation: Weather and Forecasting 25, 4; 10.1175/2010WAF2222387.1

Table 1.

Dataset used in this study (N, P, and B denote negative, positive, and both polarities, respectively).

Table 1.
Table 2.

Various radar reflectivity threshold values at different temperature levels studied.

Table 2.
Table 3.

Statistical quantities for all 143 cases.

Table 3.
Table 4.

Fact sheet for comparing different studies correlating radar reflectivity and lightning initiation.

Table 4.
Table 5.

Average lead times in min (±5 min) for different lightning polarities.

Table 5.

1

Note that R is an open-source computer programming language well suited for statistical analysis and graphics (Dalgaard 2008).

2

ImageMagick is a graphics manipulation software package (information online at http://www.imagemagick.org/script/index.php).

Save
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  • Joe, P., Falla M. , Van Rijn P. , Stamadianos L. , Falla T. , Magosse D. , Ing L. , and Dobson J. , 2002: Radar data processing for severe weather in the National Radar Project of Canada. Preprints, 21st Conf. on Severe Local Storms, San Antonio, TX, Amer. Meteor. Soc., P4.13. [Available online at http://ams.confex.com/ams/pdfpapers/47421.pdf].

    • Search Google Scholar
    • Export Citation
  • Knight, C. A., Cooper W. A. , Breed D. W. , Paluch I. R. , Smith P. L. , and Vali G. , 1982: Microphysics. Hailstorms of the Central High Plains. Volume I: The National Hail Research Experiment, C. A. Knight and P. Squires, Eds., Colorado Associated University Press, 151–193.

    • Search Google Scholar
    • Export Citation
  • Krehbiel, P. R., 1986: The electrical structure of thunderstorms. The Earth’s Electrical Environment, National Academies Press, 90–113.

    • Search Google Scholar
    • Export Citation
  • Krehbiel, P. R., Brook M. , Khanna-Gupta S. , Lennon C. L. , and Lhermitte R. , 1984: Some results concerning VHF lightning radiation from the real-time LDAR system at KSC, Florida. Proc. VIIth Int. Conf. on Atmospheric Electricity, Boston, MA, Amer. Meteor. Soc., 388–393.

    • Search Google Scholar
    • Export Citation
  • Lakshmanan, V., and Stumpf G. J. , 2005: A real-time learning technique to predict cloud-to-ground lightning. Preprints, Fourth Conf. on Artificial Intelligence Applications to Environmental Science/21st Int. Conf. on Interactive Information Processing Systems for Meteorology, Oceanography, and Hydrology, San Diego, CA, Amer. Meteor. Soc., J5.6. [Available online at http://ams.confex.com/ams/pdfpapers/87206.pdf].

    • Search Google Scholar
    • Export Citation
  • Larsen, H. R., and Stansbury E. J. , 1974: Association of lightning flashes with precipitation cores extending to height 7 km. J. Atmos. Terr. Phys., 36 , 15471553.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • MacGorman, D. R., and Rust W. D. , 1998: The Electrical Nature of Storms. Oxford University Press, 422 pp.

  • MacGorman, D. R., and Coauthors, 2008: TELEX: The Thunderstorm Electrification and Lightning Experiment. Bull. Amer. Meteor. Soc., 89 , 9971013.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Maekawa, Y., Fukao S. , Sonoi Y. , and Yoshino F. , 1992: Dual polarization radar observations of anomalous wintertime thunderclouds in Japan. IEEE Trans. Geosci. Remote Sens., 30 , 838844.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Marshall, J. S., and Radhakant S. , 1978: Radar precipitation maps as lightning indicators. J. Appl. Meteor., 17 , 206212.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Michimoto, K., 1991: A study of radar echoes and their relation to lightning discharge of thunderclouds in the Hokuriku district. Part I: Observations and analysis of thunderclouds in summer and winter. J. Meteor. Soc. Japan, 69 , 327335.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Michimoto, K., 1993: A study of radar echoes and their relation to lightning discharges of thunderclouds in the Hokuriku district. Part II: Observation and analysis of “single-flash” thunderclouds in midwinter. J. Meteor. Soc. Japan, 71 , 195204.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mills, B., Unrau D. , Parkinson C. , Jones B. , Yessis J. , Spring K. , and Pentelow L. , 2008: Assessment of lightning-related fatality and injury risk in Canada. Nat. Hazards, 47 , 157183.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Orville, R. E., Huffines G. R. , Burrows W. R. , Holle R. L. , and Cummins K. L. , 2002: The North American Lightning Detection Network (NALDN)—First results: 1998–2000. Mon. Wea. Rev., 130 , 20982109.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pereyra, R. G., Bürgesser R. E. , and Ávila E. E. , 2008: Charge separation in thunderstorm conditions. J. Geophys. Res., 113 , D17203. doi:10.1029/2007JD009720.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reynolds, S. E., Brook M. , and Gourley M. F. , 1957: Thunderstorm charge separation. J. Meteor., 14 , 426436.

  • Rust, W. D., and Coauthors, 2005: Inverted-polarity electrical structures in thunderstorms in the Severe Thunderstorm Electrification and Precipitation Study (STEPS). Atmos. Res., 76 , 247271.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Saunders, C. P. R., Bax-Norman H. , Emersic C. , Avila E. E. , and Castellano N. E. , 2006: Laboratory studies of the effect of cloud conditions on graupel/crystal charge transfer in thunderstorm electrification. Quart. J. Roy. Meteor. Soc., 132 , 26532673.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stanski, H. R., Wilson L. J. , and Burrows W. R. , cited. 2009: Survey of common verification methods in meteorology. World Weather Watch Tech. Rep. 8, WMO/TD 358. [Available online at http://www.bom.gov.au/bmrc/wefor/staff/eee/verif/Stanski_et_al/Stanski_et_al.html].

    • Search Google Scholar
    • Export Citation
  • Takahashi, T., 1978: Riming electrification as a charge generation mechanism in thunderstorms. J. Atmos. Sci., 35 , 15361548.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Takahashi, T., 1984: Thunderstorms electrification—A numerical study. J. Atmos. Sci., 41 , 25412558.

  • Takahashi, T., and Miyawaki K. , 2002: Reexamination of riming electrification in a wind tunnel. J. Atmos. Sci., 59 , 10181025.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tomine, K., Michimoto K. , and Abe S. , 1986: Studies on thunderstorm in winter in the area surrounding Komatsu by radar (in Japanese). Tenki, 33 , 445452.

    • Search Google Scholar
    • Export Citation
  • Vincent, B. R., Carey L. D. , Schneider D. , Keeter K. , and Gonski R. , 2004: Using WSR-88D reflectivity data for the prediction of cloud-to-ground lightning: A central North Carolina study. Natl. Wea. Dig., 27 , 3544.

    • Search Google Scholar
    • Export Citation
  • Wallace, J. M., and Hobbs P. V. , 1977: Atmospheric Science. An Introductory Survey. Academic Press, 467 pp.

  • Wolf, P., 2007: Anticipating the initiation, cessation, and frequency of cloud-to-ground lightning, utilizing WSR-88D reflectivity data. Electron. J. Oper. Meteor., 2007-EJ1. [Available online at http://www.nwas.org/ej/2007-EJ1].

    • Search Google Scholar
    • Export Citation
  • Yeung, L. H. Y., Lai E. S. T. , and Chiu S. K. S. , 2007: Lightning initiation and intensity nowcasting based on isothermal radar reflectivity—A conceptual model. Preprints, 33rd Conf. on Radar Meteorology, Cairns, QLD, Australia, Amer. Meteor. Soc., 11A.7. [Available online at http://ams.confex.com/ams/pdfpapers/123157.pdf].

    • Search Google Scholar
    • Export Citation
  • Zipser, E. J., and Lutz K. R. , 1994: The vertical profile of radar reflectivity of convective cells: A strong indicator of storm intensity and lightning probability? Mon. Wea. Rev., 122 , 17511759.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Domain of this study.

  • Fig. 2.

    Lightning and radar images at 2130 UTC 18 Aug 2008. Negative and positive CG lightning flashes are marked with yellow minus (−) and red plus (+) signs, respectively. (a) Lightning map. (b) Radar image MAXR. (c) Composite map.

  • Fig. 3.

    Box-and-whisker plot of the distance between the initial lightning flash and storm maximum reflectivity on MAXR. The left and right ends of the box are the near first and third quartiles, respectively. The darker line marks the median. At either end of the box, the plot whiskers extend out to 1.5 times the length of the box.

  • Fig. 4.

    Average altitudes corresponding to different temperature levels for the time periods examined in the study.

  • Fig. 5.

    Case 60 as an example. The altitudes corresponding to the −10°, −15°, and −20°C levels were 5.4, 6.1, and 6.6 km, respectively. The first lightning appeared at 2200 UTC. Case 60 was a hit for almost all predictors but a miss for −10°C–45 dBZ, −15°C–40 dBZ, and −20°C–40 dBZ. (a) Cross section at 2120 UTC 18 Aug 2008. The maximum reflectivities for the −10°, −15°, and −20°C levels were 25 dBZ, 20 dBZ, and unknown, respectively. (b) Cross section at 2130 UTC 18 Aug 2008. The maximum reflectivities for the −10°, −15°, and −20°C levels were 30, 25, and 25 dBZ, respectively. (c) Cross section at 2140 UTC 18 Aug 2008. The maximum reflectivities for the −10°, −15°, and −20°C levels were 40, 35, and 30 dBZ, respectively. (d) Cross section at 2200 UTC 18 Aug 2008. The maximum reflectivities for the −10°, −15°, and −20°C levels were all 35 dBZ.

  • Fig. 6.

    Box-and-whisker plots of the lead times for all 77 of the hit cases. The left and right ends of the box are the near first and third quartiles, respectively. The darker line marks the median. At either end of the box, the plot whiskers extend out to 1.5 times the length of the box. Shown are the (a) −10°C, (b) −15°C, and (c) −20°C levels.

  • Fig. 7.

    Max echo top prior to or at the start of CG lightning activity.

  • Fig. 8.

    Box-and-whisker plot of the current magnitude. The top and bottom ends of the box are the near first and third quartiles, respectively. The darker line marks the median. At either end of the box, the plot whiskers extend out to 1.5 times the height of the box.

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