1. Introduction
The forecasting of cloud-to-ground (CG) lightning flashes is of great importance. Curran et al. (2000) showed that lightning ranked second in weather-related deaths in the United States between 1959 and 1991 and ranked first in some years. Texas was ranked in the top 10 states for the numbers of lightning fatalities (third), casualties (seventh), injuries (eighth), and damage reports (ninth) yet there has been only one study (Clements and Orville 2008) that examined lightning forecasting within the state. The 2008 National Weather Service’s (NWS) 30-yr (1978–2007; NWS 2009) average of weather fatality, injury, and damage statistics indicates that lightning remains the second most frequent cause of weather-related fatalities in the United States with an average of 58 per year. Currently, no automated lightning forecasting algorithm is in operational use.
One of the most widely accepted thunderstorm charging theories is the noninductive graupel–ice collision mechanism, also called noninductive charging (NIC). Laboratory results (e.g., Reynolds et al. 1957; Takahashi 1978; Gaskell and Illingworth 1980; Jayaratne et al. 1983) show that NIC is a more plausible charging mechanism than inductive charging theory, which is theorized to require an initial electric field stronger than the earth’s fair weather electric field (MacGorman and Rust 1998; Rakov and Uman 2006). In situ measurements by Dye et al. (1986) showed that the NIC method is a probable method of charge separation between −10° and −20°C. Studies from several other field campaigns (Goodman et al. 1988; Carey and Rutledge 1996; Carey and Rutledge 2000) also suggest a strong correlation between precipitation-sized ice mass (i.e., graupel) and the production of lightning, which strengthens the viability of the NIC theory. Petersen et al. (2005) give a brief overview of how the NIC theory works within thunderstorms. First, you need a vigorous updraft (also noted in Takahashi 1978), which leads to mixed-phase microphysics. The mixed-phase microphysics then lead to charge separation between the graupel and ice crystals. Storm-scale separation of these ice particles often results in a strong electric field and lightning production. High reflectivities near the elevations of the −10° and −20°C isotherms are indicative of graupel in the mixed-phase region of the storm.
Many studies (Workman and Reynolds 1949; Larsen and Stansbury 1974; Marshall and Radhakant 1978; Dye et al. 1986; Goodman et al. 1988; Dye et al. 1989) have used radar data to study storm electrification and/or infer the presence of mixed-phase particles, especially graupel, at different environmental heights and isotherms (e.g., 0°, −10°, and −20°C). This information was then used to forecast lightning by employing various reflectivity values at various heights by Buechler and Goodman (1990), Michimoto (1991), Hondl and Eilts (1994), Gremillion and Orville (1999), Vincent et al. (2004), Wolf (2007), and Clements and Orville (2008). The results from these studies (Table 1) suggest that using 40 dBZ at −10°C produces the best lightning forecasts in terms of the critical success index (CSI), which will be described in more detail in section 2.
Results from previous studies of lightning forecasting with radar reflectivity.
Using radar-derived parameters such as vertically integrated liquid (VIL; Greene and Clark 1972) to forecast CG lightning has also been attempted. Watson et al. (1995) observed the distribution of VIL and lightning for a storm in central Oklahoma on 9 June 1993. They found that many of the flashes within this particular storm were associated with VIL as low as 1–15 kg m−2 and that there was large scatter in lightning occurrence as VIL values increased. MacGorman et al. (2007) compared the lightning flash rate and VIL values for 1200 cells. Their results show a lack of a clear relationship between VIL and maximum ground flash rates, but that the mean and mode VIL values increase with increasing flash rate. The works of Watson et al. (1995) and MacGorman et al. (2007) suggest that VIL alone cannot be used to forecast lightning. VIL can also be biased by high-reflectivity echo at low levels in storms with warm-rain processes that are not necessarily related to storm electrification (Petersen et al. 1999).
Carey and Rutledge (2000) developed Eq. (1) during the Maritime Continent Thunderstorm Experiment (MCTEX) because no appropriate Z–M relationship for deep, tropical convection existed. Therefore, the constants, ρi and N0, could vary from the values over Houston, Texas. Motley (2006) performed VII sensitivity studies using a range of values for ρi and N0 and showed that the intercept parameter is the most likely source of error. Despite the possible environmental variations, Eq. (1) has been used in numerous other studies (e.g., Petersen and Rutledge 2001; Cifelli et al. 2002; Wang and Carey 2005; Petersen et al. 2005; Motley 2006; Gauthier et al. 2006; Wang et al. 2007) and VII value trends will still be valid.
2. Data and methodology
a. Radar data
Ten years (1997–2006) of level II Houston (KHGX) Weather Surveillance Radar-1988 Doppler (WSR-88D) data from the National Climatic Data Center (NCDC) for summertime (June–August) daylight hours [1400–0000 UTC, 0900 central daylight time (CDT)–1900 CDT] were analyzed within 150 km from the radar site (Fig. 1), amounting to a total of 85 603 radar volumes.
Location of the study area. KHGX indicates the location of the WSR-88D. The range rings are at a distance of 75, 100, 125, and 150 km. IAH is the location of Bush Intercontential Airport, HOU is the location of Hobby Airport, and GLS is the location of Scholes International Airport in Galveston, TX.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
Location of the study area. KHGX indicates the location of the WSR-88D. The range rings are at a distance of 75, 100, 125, and 150 km. IAH is the location of Bush Intercontential Airport, HOU is the location of Hobby Airport, and GLS is the location of Scholes International Airport in Galveston, TX.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
Location of the study area. KHGX indicates the location of the WSR-88D. The range rings are at a distance of 75, 100, 125, and 150 km. IAH is the location of Bush Intercontential Airport, HOU is the location of Hobby Airport, and GLS is the location of Scholes International Airport in Galveston, TX.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
Of great significance to this study is the fact that the radar does not scan at only one level. The NWS uses a total of nine volume control patterns (VCPs) to control the elevation angles used on the WSR-88D (OFCM 2008). The best vertical sampling is provided by VCP 11. VCP 12 has the same number of elevation angles as VCP 11, but concentrates more angles at lower levels. As a result, Gauthier et al. (2006) excluded all non–VCP 11 data from their study. However, this study does not exclude any data based on the VCP. Since the events important to this study occur mainly as a result of convection, it is assumed that the VCP being used during the events provides sufficient vertical sampling. The Houston Weather Forecast Office (WFO HGX) runs VCP 11 in most situations, but will run VCPs 211, 12, and 212 in some circumstances (L. Wood 2009, personal communication).
The KHGX radar data were converted from their native level II format to Universal Format (UF; Barnes 1980). The UF data were then interpolated onto a 150 × 150 × 20 Cartesian grid (or 300 × 300 × 20 km3) using the National Center for Atmospheric Research REORDER software package (Mohr et al. 1986; Oye and Case 1995). A three-dimensional Cressman interpolation scheme, with x, y, and z radii of influence of 1.25, 1.25, and 1.75 km, respectively, was used.
A horizontal resolution of 2 km was found to be adequate for the radar data based on previous studies (Gauthier et al. 2006) and is a commonly used value in other radar studies based on objective statistical methods. However, an appropriate vertical resolution was not as clear. Gauthier et al. (2006) found 1-km vertical resolution to be adequate for their study, but this study includes forecast statistics based on the reflectivity at a given height while their study did not. The vertical resolution of the radar data must be fine enough to utilize available data but not to introduce spurious features via interpolation. If the vertical resolution is too coarse, little differentiation will occur between the height levels in the forecast statistics. Section 3b will describe sensitivity tests that indicate that 1.0-km vertical resolution generally performs better than 0.5-km vertical resolution.
b. Lightning data
The CG lightning data used in this study were provided by the National Lightning Detection Network (NLDN), which is owned by Vaisala of Vantaa, Finland. Biagi et al. (2007) found the NLDN had an average flash detection efficiency of 92% and 86% for 2003 and 2004, respectively, in Arizona, Texas, and Oklahoma. They also found that some positive flashes were actually intracloud (IC) flashes. There is no clear threshold that separates IC flashes from CG flashes, but 15 kA is a value for which 50% were real and 50% were false. Thus, any flashes with positive peak current less than 15 kA were excluded from this study.
c. Sounding data
Sounding data were obtained from the National Oceanic and Atmospheric Administration/Earth System Research Laboratory (NOAA/ESRL) Radiosonde Database for the same time period as the radar data. HGX does not launch a radiosonde, so data were averaged between Lake Charles (LCH), Louisiana; Corpus Christi, Texas (CRP); and Fort Worth, Texas (FWD); to create an HGX sounding. This averaging has been done in previous studies (Vincent et al. 2004; Motley 2006; Clements and Orville 2008) and was the suggestion of the Houston WFO (L. Wood 2009, personal communication). The average was weighted most heavily toward LCH, then CRP, and lastly FWD. Including the FWD sounding was debated since it can be much drier than either LCH or CRP. However, the lack of baroclinic forcing during summer creates a similar environment over much of the southeastern United States. Thus, it was decided to include the FWD sounding, but weight it half as much as CRP and a third as much of LCH. Only the 0000 and 1200 UTC soundings were used. Any special soundings at 0600 and 1800 UTC were not included in the averaging. This resulted in a total of 1840 HGX soundings, or two for each day analyzed during this study. From these soundings, the environmental temperature levels (−10°, −15°, −20°, and −40°C) and updraft temperature levels [−10°C; Wolf (2007)] for the radar analysis were determined.
d. CAPPI-SCIT and cell correlation
Since the lightning forecasts are on a cell-by-cell basis, the ability to identify and track convective cell movement is vital. As such, this study uses a modified version of the Storm Cell Identification and Tracking (SCIT; Johnson et al. 1998) algorithm to identify and track cells in the radar observation. The modified algorithm, called Constant Altitude Plan Position Indicator (CAPPI)-SCIT, is discussed in greater detail in the appendix.
CG lightning flashes were associated with the cells identified by the CAPPI-SCIT algorithm. This process started with identifying all the lightning flashes that occurred within 150 km of the KHGX radar between 2 min before the scan started and 2 min after the scan started. This time frame is chosen since most of the precipitation mode VCPs take approximately 5 min to complete.
Association of the flashes was first attempted within the 30-dBZ boundaries of the CAPPI-SCIT identified cells. If a flash was within the 30-dBZ boundary, it was associated with that cell. Otherwise, the distance between the boundaries of the highest reflectivity threshold of each cell and the lightning flash was calculated. The flash was then associated with the cell with the shortest distance. In this way, every CG flash is associated with a cell, even if the distance was large. However, none of the distances were extremely large.
e. Lightning forecast criteria and statistics
Numerous CG lightning forecast criteria were used in an attempt to establish the best criteria for Houston. Three radar reflectivity thresholds were used (30, 35, and 40 dBZ), as well as three environmental levels (−10°, −15°, and −20°C) and one updraft level (−10°C). The environmental levels were defined as the height for which a temperature is observed on the interpolated HGX sounding. The average heights of the −10°, −15°, and −20°C isotherms for this dataset were 6494, 7381, and 8092 m, respectively. The updraft temperature level was determined by using the sounding to calculate the temperature a surface parcel would be in an updraft assuming adiabatic ascent. The reflectivity values and environmental temperature levels were the same as in previous studies (Gremillion and Orville 1999, Vincent et al. 2004, Clements and Orville 2008; see also Table 1) and the updraft level was used for comparison with Wolf (2007). In addition, forecasts were made based on cell-based VII values. Since appropriate VII test values were not known, the test values were determined by calculating the distribution of VII values for CG-producing cells throughout the entire dataset and using the resulting percentiles (i.e., 5% of lightning-producing cells had a VII value of 0.25 kg m−2 or less before producing a lightning flash; Table 2). Percentile values in 5% increments were used as forecast criteria. These specific test values should be used with caution and could vary from location to location, but they do provide a basis for which values of VII will be significant.
VII percentiles (kg m−2).
First CG lightning flash forecasts were made on a cell-by-cell basis. A forecast was a yes–no product on whether or not the cell was expected to produce a CG lightning flash. A typical forecast used the following steps: 1) CAPPI-SCIT was run on a radar volume to identify and track cells; 2) environmental temperature levels were obtained from an area-averaged sounding; 3) for each cell, the reflectivity values were obtained at the environmental and updraft levels; 4) if the reflectivity values met the given thresholds, a yes forecast was made, and 5) cell-based VII was calculated and if the values met the given percentile, a yes forecast was made.
The forecast statistics for this study used a simple 2 × 2 contingency table to determine the forecast skill of each predictor. Since this study was intended to evaluate the operational significance of various forecast criteria, only the first CG flash from each cell was considered. As a result, only one value (i.e., hit, miss, or false alarm) was added to the contingency table for each cell. For example, if the first CG lightning flash occurred before it was forecast, a miss was added to the contingency table, regardless of whether additional flashes occurred after a forecast was made. From the data in the table, three variables were used in computing the skill of the forecasts. The first was the probability of detection (POD), the second was the false alarm ratio (FAR), and the last was CSI (see Wilks 1995 for definitions). The lead time between the forecast and the lightning flash was also noted. POD provides a general measure of how well a predictor can detect an event. FAR provides a skill assessment on the accuracy of a predictor. Schaefer (1990) showed that CSI is a good indicator of the usefulness of different forecast techniques when applied to a consistent environment, including the effectiveness of various WSR-88D algorithms for a given WFO. However, caution should be used when comparing CSIs between two different environments.
Since the lightning forecast is based on radar data, the actual time the forecast is made needs to be considered. Gremillion and Orville (1999) and Clements and Orville (2008) used the difference between the time the volume scan started and the time of the first CG flash to calculate the lead time. To maintain consistency with the previous study over Houston (Clements and Orville 2008), the lead time in this study will be the difference between the time when the scan began and when the flash occurred. However, caution should be used since the times are slightly longer (2.5–4.5 min) than could be realized in an operational setting (Vincent et al. 2004).
3. Results
a. Radar reflectivity forecast method
The 10-yr WSR-88D and NLDN datasets were analyzed using the radar reflectivity forecast method; results are shown in Figs. 2–4. The environmental levels are labeled such that E10, E15, and E20 represent the −10°, −15°, and −20°C isotherm levels, respectively, and U10 represents the updraft −10°C level. The range was delineated by radial distance from the radar location (i.e., 75, 100, 125, and 150 km). The track count is the number of times the cell was identified and tracked by the CAPPI-SCIT algorithm. Thus, 0 indicates one radar volume (the identification scan), 1 indicates two radar volumes, etc. The dBZ test values are the radar reflectivity values used in the forecast criteria. The statistic of the greatest interest is the CSI (Fig. 2) because it combines both the POD and FAR, but an analysis of POD (Fig. 3) and FAR (Fig. 4) is also essential since it provides additional understanding of how a specific CSI value was obtained.
CSI values as a result of the analysis of the entire dataset, from 1997 through 2006. Count represents the minimum number of times a cell must be tracked to be considered. Range represents the range a cell must be within to be considered.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
CSI values as a result of the analysis of the entire dataset, from 1997 through 2006. Count represents the minimum number of times a cell must be tracked to be considered. Range represents the range a cell must be within to be considered.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
CSI values as a result of the analysis of the entire dataset, from 1997 through 2006. Count represents the minimum number of times a cell must be tracked to be considered. Range represents the range a cell must be within to be considered.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 2, but for the POD values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 2, but for the POD values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 2, but for the POD values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 2, but for the FAR values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 2, but for the FAR values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 2, but for the FAR values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As shown in Fig. 2, two predictor combinations, 30 dBZ at E15 and E20 used on cells within 75 km of the radar with a track count of at least 2, had the highest CSI value of 0.68. It is interesting to note that E20 had the lowest overall CSI compared to the other environmental levels, highlighting the usefulness of combining forecast criteria. In addition, 40 dBZ at E20 within 150 km and a track count of 0 is the worst overall combination, with a CSI of 0.26. Thus, the specific choice of forecast criteria is critical.
Even though the best CSI value is 0.68, other predictors were close to this maximum value. At E10, the best predictor combination (CSI = 0.67) is 35 dBZ used on cells within 75 km with a minimum track count of 2. At the U10 level, the best predictor combination uses 30 dBZ on cells within 75 km with a minimum track count of 2 (CSI = 0.66). In all, 29 (or 20%) of the possible 144 predictor combinations had a CSI greater than or equal to 0.60. None of these combinations included a track count of 0. Two instances (30 dBZ at E15 and 30 dBZ at E20) including cells out to 150 km yielded a CSI over 0.60. The greatest CSI (0.62) using 40 dBZ was found at the E10 level when considering only cells within 75 km with a minimum track count of 2. Figure 4 shows that 40 dBZ generally performs better at E10 because of low FAR values (whereas 30 dBZ at this height can sometimes have unacceptably high FAR values). Out of all the predictor combinations, 17 (or 12%) have a CSI less than or equal to 0.40. All but one of these combinations uses 40 dBZ as a reflectivity threshold.
The average CSI increased from 0.44 for all identified cells to 0.56 when considering only cells with a minimum track count of 2. This increase is a result of the reduction of the FAR values. The cells remaining after those with a track count of 0 or 1 are eliminated are more robust and exhibit a greater likelihood of maintaining a strong enough updraft to create the mixed-phase microphysics needed for storm electrification.
The increase in CSI when restricting cells to within 75 km (versus 150 km) of the radar was less pronounced at only 0.06. As a result, confidence in lightning forecasts for cells close to the radar is similar to lightning forecasts for cells far from the radar. Monthly variability exists within the dataset (not shown), but overall the distance from the radar and hence the beam resolution appear to have a relatively small impact on the accuracy of the CG lightning forecasts. Additionally, the difference between the results using E15 and U10 levels was insignificant. In most cases the statistics were the same or very close. The complexities of the methodology introduced by calculating the updraft temperature can be simplified by using the E15 as a proxy.
The best predictor result was surprising. Previous studies suggested a forecast criteria of 40 dBZ at the E10 as optimal, while our best predictor combinations were higher in the storm (E15 and E20) but with lower reflectivity (30 dBZ). As noted, other predictor combinations provided similar results (i.e., similar CSI values), so focusing on particular forecast criteria could be ineffective. However, Figs. 2–4 show that using 40 dBZ, rather than 30 or 35 dBZ, as the reflectivity value reduces the forecast skill. More comparisons to previous studies are discussed in section 3c.
b. Sensitivity to vertical resolution
Forecast statistics using vertical resolutions of 0.5 and 1 km were compared to determine if a 1-km vertical resolution (the typical resolution used by previous studies) is sufficient to calculate robust radar forecast statistics or if a finer resolution should be used. August 2006 was chosen as the time period for the data comparison since the month exhibited general storm characteristics expected during the summer months in Houston. Figure 5 shows that CSI1.0km–CSI0.5km values generally favor the 1.0-km resolution dataset. At E10, CSI1.0km is about 0.1 greater than CSI0.5km when a cell is only identified for one scan, but the difference is close to zero when cells are tracked at least once. The CSI1.0km–CSI0.5km values are more variable at E15 and U10, although the use of 40 dBZ strongly favors the 1.0-km-resolution dataset at both environmental levels. Here, CSI1.0km shows the most consistent improvement over CSI0.5km at E20, with most differences ranging from 0.02 to 0.13. Similar results were found when comparing the POD and FAR values. All three statistics favored the 1.0-km vertical resolution. As a result, 1.0 km was used as the vertical resolution for the CAPPI data.
Differences (1.0-km vertical resolution − 0.5-km vertical resolution) in the CSI values from August 2006.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
Differences (1.0-km vertical resolution − 0.5-km vertical resolution) in the CSI values from August 2006.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
Differences (1.0-km vertical resolution − 0.5-km vertical resolution) in the CSI values from August 2006.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
c. Comparison to previous studies
This section will focus on comparing results from previous studies (Table 1) with the results of this study. For example, Buechler and Goodman (1990) found a POD of 1.00, an FAR of 0.20, and a CSI of 0.80 when using 40 dBZ at −10°C, while this study found an average CSI of 0.51 for the same criteria. Considering only cells with a minimum track count of 2 increases the average to 0.57. It is likely that this discrepancy is a result of the number of cells analyzed and the method of determining the forecast criteria. Buechler and Goodman (1990) analyzed 20 subjectively chosen cells and then determined their best predictor combination, while this study analyzed 67 384 objectively chosen cells with a priori predictor combinations.
Results from Gremillion and Orville (1999) are directly compared to the results from this study in Table 3. Their criteria were slightly different than those used in this study since they required the criteria to be met for at least two consecutive scans, while this study only required for it to be met for one scan. Therefore, comparison between the two results should be used cautiously, but the results are presented and compared here because of the study’s prominence in lightning forecasting (T. Oram 2009, personal communication). All of the comparable CSI values are higher for the Gremillion and Orville (1999) study except when using 30 dBZ at −20°C. The FAR values are higher in this study because Gremillion and Orville required the criteria to be met for at least two consecutive scans. Gremillion and Orville found 40 dBZ at −10°C to be the best predictor pair while this study found 30 dBZ at −20°C to be the best. As with Buechler and Goodman (1990), the number of cells analyzed by Gremillion and Orville (1999) is much less than the number analyzed by this study (39 compared to 67 384). This is likely the main cause of the differences between the two studies.
Comparison between the results of this study and the results of Gremillion and Orville (1999, hereafter GO).
Results from Vincent et al. (2004) are directly compared to the results of this study in Table 4. The difference in dataset size and the more subjective nature of their study likely resulted in higher POD values and therefore higher CSI values. Many of the days analyzed for this study showed results similar to those of Vincent et al., suggesting that it is necessary to include a large number of cells to produce lightning forecasting criteria that will be robust in varying scenarios. Again, the number of cells analyzed is very different (50 compared to 67 384) and is likely the main cause of the statistical differences.
Comparison between the results of this study and the results of Vincent et al. (2004, hereafter V).
Wolf (2007) analyzed 1100 cells using 40 dBZ at the −10°C updraft level and found a POD of 0.96, an FAR of 0.11, and a CSI of 0.83 (Table 1). This study found a POD of 0.51, an FAR of 0.26, and a CSI of 0.44 for similar criteria. If only cells within 75 km with a minimum track count of 2 are considered, the POD becomes 0.69, the FAR becomes 0.16, and the CSI becomes 0.53. The difference in these results is much greater than the difference in the results from the other studies. There are a few possible explanations: 1) the convection in Florida, the main location of Wolf’s study, could be more robust, therefore reaching the updraft −10°C more frequently; 2) the subjective nature of using the −10°C updraft level; and/or 3) the difference in the number of cells analyzed. The most likely explanation appears to be the first. Wolf’s results showed a POD of 0.99 when using 40 dBZ at the −6°C updraft level, which is near the location of the −10°C isotherm. The results from this study showed an average POD at this level of 0.67. This difference alone shows that the cells considered for Wolf’s study were more robust, since almost all of them had 40-dBZ reflectivity at approximately the −10°C level.
An overarching issue here is that different locales may have fundamental and statistically significant differences in various kinematic and microphysical properties critical for lighting production. Ultimately, simple reflectivity thresholds (and VII), while very effective, are imperfect and incomplete metrics for conditions leading to lightning. Hence, even if you had order 10^4 samples for each region using the same methods and data sources, you might still have some differences.
d. VII forecast method
The analysis of the entire dataset using the VII forecast method is shown in Figs. 6–8. The VII forecast method compares the cell-based VII values to the probability distribution function percentile values to make a lightning forecast. As in the radar reflectivity method, the forecasts are separated by range from the radar and how many times a cell was tracked by the CAPPI-SCIT algorithm. In Figs. 6–8, only those cells with a minimum track count of 2 were considered since it was determined to provide the most accurate forecasts. Forecast variations by range from the radar and VII percentile value will be considered.
CSI values using the VII percentile values for the entire dataset (1997–2006) when considering only cells with a minimum track count of 2. (top) Data including cells within 150 km. (bottom) Data including only cells within 75 km.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
CSI values using the VII percentile values for the entire dataset (1997–2006) when considering only cells with a minimum track count of 2. (top) Data including cells within 150 km. (bottom) Data including only cells within 75 km.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
CSI values using the VII percentile values for the entire dataset (1997–2006) when considering only cells with a minimum track count of 2. (top) Data including cells within 150 km. (bottom) Data including only cells within 75 km.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 6, but for the POD values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 6, but for the POD values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 6, but for the POD values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 6, but for the FAR values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 6, but for the FAR values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
As in Fig. 6, but for the FAR values.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
The best VII predictors were found when using a test values of 0.42 kg m−2 (10th percentile) and 0.58 kg m−2 (15th percentile) in cells within 75 km of the radar, resulting in a CSI of 0.68. The best predictor combination using the radar reflectivity method had a CSI of 0.68, so the values are comparable. Figure 6 shows a gradual increase in the CSI values from the lowest VII percentile (i.e., >0.25 kg m−2) to the 15th VII percentile (i.e., >0.58 kg m−2), a gradual decrease from the 15th percentile to the 40th percentile (1.50 kg m−2), and then a sharper decrease thereafter. The VII percentiles used are shown in Table 2. This plateau likely represents the optimum amount of precipitation ice mass needed for lightning production. As mentioned earlier, the assumptions made in creating this product likely restrict its ability to measure the actual amount of precipitation ice mass between −10° and −40°C. Therefore, though the plateau occurs near 1.0 kg m−2, it is more important to note the plateau instead of the actual values. The lower-percentile (below 50%) forecasts show approximately the same level of skill as the radar reflectivity method forecasts, resulting from high POD instead of low FAR (Figs. 7 and 8).
As in the radar reflectivity method, VII-based CSI values indicate only a small range dependency; that is, CSI increases slightly as the range decreases (Fig. 6). This result suggests that while considering the range is beneficial, it is a secondary consideration. If a maximization of CSI is desired, only cells within 75 km should be analyzed.
An interesting result is the CSI average near 0.65 for the lower percentile values. Since VII is only calculated between the −10° and −40°C environmental levels, which are at approximately 7 and 11 km in height, respectively, the results show that for any time echo reaches near 7 km, there is a potential for CG flashes This is similar to the “Larsen area” of Larsen and Stansbury (1974), which was defined as an area with greater than 43 dBZ above 7 km. This information is very valuable when considering the ease with which a lighting forecast can be made. The plateau of CSI values suggests that the daily environmental level does not need to be explicitly known. Instead, climatological heights could be used. Additionally, combining VII values with the reflectivity threshold method shows promise.
e. First flash forecast time
In addition to testing the accuracy of the lightning forecast, the lead time to the first flash was calculated for the reflectivity threshold and VII methods (Figs. 9 and 10). For the radar reflectivity method, the maximum forecast time of 19.0 min occurred using 30 dBZ at E10 within 150 km of the radar on cells that have been tracked for at least two consecutive scans. Average forecast times were 11.0, 8.9, 6.0, and 9.1 min for E10, E15, E20, and U10, respectively. Forecast times also decreased as the reflectivity threshold increased and the number of tracked scans decreased. For the VII method, the maximum forecast time of 13.5 min occurred when using the 5th percentile within 150 km of the radar. The 5th–25th, 25th–50th, 50th – 75th, and 75th–95th percentile VII ranges were averaged and yielded average forecast times of 11.7, 7.3, 3.6, and 1.4 min, respectively. As shown in Figs. 3 and 7, both the radar reflectivity and VII method forecast times follow the POD values. This is to be expected since higher POD values signal that a predictor is easily met, which in turn creates a longer forecast time. The only difference is that the forecast time is maximized at larger distances while the POD decreases slightly as range increases. Since the differences are minor, a maximization of the POD can be used as a maximization of the forecast time.
Average lead time for 1997–2006 (min) using the radar reflectivity method. Count represents the minimum number of times a cell must be tracked to be considered. Range represents the range a cell must be within to be considered.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
Average lead time for 1997–2006 (min) using the radar reflectivity method. Count represents the minimum number of times a cell must be tracked to be considered. Range represents the range a cell must be within to be considered.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
Average lead time for 1997–2006 (min) using the radar reflectivity method. Count represents the minimum number of times a cell must be tracked to be considered. Range represents the range a cell must be within to be considered.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
Average lead time for 1997–2006 (in min) using the VII percentile values for the entire dataset (1997–2006) when considering only cells with a minimum track count of 2 for data within (top) 150 and (bottom) 75 km.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
Average lead time for 1997–2006 (in min) using the VII percentile values for the entire dataset (1997–2006) when considering only cells with a minimum track count of 2 for data within (top) 150 and (bottom) 75 km.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
Average lead time for 1997–2006 (in min) using the VII percentile values for the entire dataset (1997–2006) when considering only cells with a minimum track count of 2 for data within (top) 150 and (bottom) 75 km.
Citation: Weather and Forecasting 26, 2; 10.1175/2010WAF2222431.1
The average forecast time using the VII method on the 5th–25th percentile was higher than the average of using any of the environmental test levels for the radar reflectivity method. This is encouraging because, as mentioned earlier, the VII forecast method is simpler than the radar reflectivity method. In fact, the best lead times for the VII forecast method were found when using 0.25 kg m−2 as the threshold value. This means that for the highest lead times the only test that is needed is whether any 30-dBZ echo is above the −10°C environmental level, which is confirmed by the lead times using the reflectivity forecast method The average FAR when using 0.25 kg m−2 as the test value is 0.33, which is not unacceptably high. Therefore, the VII method provides an easy and reliable tool that can be used to maximize forecast time.
4. Conclusions
Previous research has shown the potential of forecasting CG lightning using radar reflectivity thresholds at various isothermal heights. This study extends those results for Houston, Texas, by objectively analyzing a multiyear summertime dataset that includes a factor of 500 more cells than in any previous publication. This study also incorporates a new radar-derived parameter, vertically integrated ice (VII), into the radar-based first flash CG lightning forecasting method. It was found that using 30 dBZ at the 15° or −20°C isotherm on cells within 75 km of the radar and with a minimum track count of 2 is the best predictor combination for the Houston area, producing an average CSI of 0.68. These results suggest different criteria than Gremillion and Orville (1999) and Vincent et al. (2004), which both recommend 40 dBZ at the −10°C isotherm as the best predictor combination. Using those criteria produced an average CSI of 0.51 in this study. For most predictor combinations in this study, 40 dBZ had significantly lower CSIs than either 30 or 35 dBZ, while the CSI values when using 30 and 35 dBZ were similar. This difference suggests 1) cells reaching 40 dBZ occur less frequently over Houston than either Florida [the location of Gremillion and Orville (1999)] or North Carolina [the location of Vincent et al. (2004)] and/or 2) the more objective algorithm of this study resulted in more weak cells compared to the subjective cell identification in the other studies. The main difference between this study and all other previous studies is the amount of cells analyzed. A large number of cells is much more likely to fully represent the environment since studies with a small number of cells are rarely unbiased. The optimal environmental level in this study (−20°C isotherm) likely better represents the depth mixed-phase hydrometeors need for sufficient cloud electrification. Note that 30 dBZ at −10°C (the beginning of the “charging zone”) is not as likely to produce as ample a cloud electrification as 30 dBZ at −20°C. A test analyzing instability at the −10°C level may be more appropriate to show the likelihood of continued convection if −10°C is the desired forecast level.
Limiting the analysis to include only cells that had been tracked for at least two scans improved the forecast statistics more than varying the range from the radar or the reflectivity threshold. The CSI average increased from 0.44 when considering all identified cells to 0.56 when considering only cells with a minimum track count of 2. In addition, the best CSI values at every level were found when considering only cells with a minimum track count of 2. Strong, long-lived cells are more likely to have time to loft the amount of hydrometeors needed for ample cloud electrification.
Using radar-derived VII values to forecast CG lightning shows promise. VII-based CSI values were often comparable to the reflectivity threshold method and the ease of the VII forecast method provides the NWS an easy to implement and effective method of forecasting CG lightning. Forecasts made using the predictor of VII greater than 0.25 kg m−2 produced an average CSI of 0.65. The best forecast values for this study were using the 10th percentile value of 0.42 kg m−2 or 15th percentile value of 0.58 kg m−2, which both produced an average CSI of 0.67. The CSI values stay above 0.60 until after the 35th percentile VII value. Since VII only considers reflectivity above the −10°C environmental level, any time VII is greater than zero, the precipitation mass (i.e., rain, snow, graupel, and/or hail) has reached a height needed for cloud electrification, while any increase of VII over 0.42 kg m−2 is shown to represent a sufficient amount of precipitation mass for cloud electrification.
The best first flash forecast time was 19.1 min when using 30 dBZ at −10°C on all cells within 150 km with a minimum track count of 2. This forecast time was greater than in any previous study. If the number of times a cell is tracked is not considered (i.e., it only needs to be identified, not necessarily tracked between radar volume scans), the forecast time is 10.0 min. The results found by Clements and Orville (2008) had an average forecast time of 16.1 min, which is within the range presented in this study. The average forecast time when using the 5th–25th percentile VII values was 11.7 min.
A combination of the radar reflectivity forecast method and the VII forecast method can potentially be used to provide better results. Case studies (not discussed) generally showed improvement in their average CSI values when including the 20th percentile VII value, especially when there was a large amount of lightning.
While this study provides the most thorough and objective analysis to date using radar reflectivity at an isothermal level to forecast lightning, more work still needs to be done to find the best predictors at different locations. This study was designed to be easily reproducible so that other WFOs could perform their own analysis and find the criteria that work best for their area. Additional research also needs to be done with VII, including correlation of VII with various atmospheric parameters such as convective available potential energy (CAPE), the lifted index, and wind shear to potentially provide longer forecast times and forecast products such as lightning “outlooks” for “frequent” or “numerous” lightning events. Carey and Rutledge (2000) found a strong correlation between the total lightning flash rate and total mixed-phase ice mass. Therefore, VII, which is a measure of mixed-phase ice mass, particularly graupel mass, could be used to nowcast frequent or numerous lightning events once local criteria are established for those types of events. More work also needs to be done with rapid changes in VII. Case studies of this dataset showed VII “jumps” often precede cloud-to-ground flashes. There is also a possibility that rapid changes in VII could signal lightning cessation.
Acknowledgments
We gratefully acknowledge support by the National Oceanic and Atmospheric Administration under an award entitled Lightning in the Nowcasting and Warning Process: Cooperative Research Applied to NWS Needs and Priorities (NA08NWS4680034). Lawrence Carey acknowledges support from the NASA MSFC Earth Sciences Office under the space shuttle program (NNM05AA22A). We would also like to thank Lance Wood at WFO Houston and Greg Patrick at WFO Fort Worth for many meaningful discussions and suggestions, Mark Keehn at WFO Houston for all his work in getting VII data to display in the Advanced Weather Interactive Processing System (AWIPS), and Greg Seroka at Texas A&M University for his help debugging much of the code used in this project.
APPENDIX
CAPPI-SCIT Algorithm
This study uses a modified version of the Storm Cell Identification and Tracking (SCIT; Johnson et al. 1998) algorithm. The original SCIT algorithm was designed to work in polar format while the data in this study are in Cartesian form. Therefore, the algorithm was modified to work on Cartesian data and a few changes in the cell identification and tracking methods were made. The modified algorithm, called Constant Altitude Plan Position Indicator (CAPPI)-SCIT, alters the SCIT algorithm in three ways.
First, CAPPI-SCIT uses a different 2D association method than SCIT. The 1D segment data are placed into an array the same size as the CAPPI grid (150 × 150 × 20) with an additional dimension that has the same number of elements as reflectivity threshold categories. This array contains the locations of all the reflectivity threshold segments. To create the 2D components, a contour function is run on the array for each of the reflectivity thresholds. This contour function returns the boundaries of the contours and these boundaries define each of the 2D components for each reflectivity threshold. As in the SCIT algorithm, if a component boundary of higher reflectivity is found within a component boundary of lower reflectivity, the component of lower reflectivity is ignored. Also similar to SCIT, the 2D components are defined with the highest reflectivity threshold for that particular component and an area criterion is used to eliminate very small cells. However, CAPPI-SCIT uses no separation or overlap criteria as in the SCIT algorithm since the contour function requires the segments to be adjacent.
Second, for the 3D association, only one vertical association range, 6 km, is used in the attempt to associate cells while SCIT uses 5, 7.5, and 10 km. This range is also not calculated from the individual component centroids, but from the boundaries of the components to allow for a greater search area. If the search from the component boundary point yields another point in a component within 6 km at the next height, that component boundary point is kept.
Third, the methodology between the tracking for SCIT is slightly different than that for CAPPI-SCIT. In both algorithms, the first step is to determine the time difference between the volume scans. If the difference is greater than a user-defined value (default = 10 min), time association is not utilized; all the cells are treated as if it was the first time they have been identified. Next, a first guess, based on the cell’s previous centroid and movement, is generated. The cell’s movement is determined by its average movement in the previous scans or a default motion vector if the cell was first detected on the previous volume scan. This default motion vector can be user defined, for situations when no other cells have been tracked, or based on the average motion vector of all the other detected cells, which can be used to determine `a default cell motion.
After a first guess is generated for all of the cells, correlation between the first guesses and the current centroids is attempted. The distance between all current centroids and first guesses is calculated. For both algorithms, if the difference between the current centroid and a first guess is within a certain threshold, the cells are correlated. If more than one correlation is possible, the possibility with the smaller difference is considered to be best. This is the only correlation done by the SCIT algorithm, but the CAPPI-SCIT algorithm adds an additional step. The 30-dBZ boundary of the cell on the previous volume scan is used as a search area for cells on the current scan. If a cell on the current scan is found within the 30-dBZ boundary of a cell on the previous scan, those cells are correlated in favor of a distance correlation. This is motivated by the fact that the cell centroids can be located in larger areas of reflectivity and will not move outside of that area. If more than one cell is found within the 30-dBZ boundary of a previous scan’s cell, the distance correlation method is used for the corrected correlation.
REFERENCES
Barnes, S. L., 1980: Report on a meeting to establish a common Doppler radar data exchange format. Bull. Amer. Meteor. Soc., 61, 1401–1404.
Biagi, C. J., Cummins K. L. , Kehoe K. E. , and Krider E. P. , 2007: National Lightning Detection Network (NLDN) performance in southern Arizona, Texas, and Oklahoma in 2003–2004. J. Geophys. Res., 112, D05208, doi:10.1029/2006JD007341.
Black, R. A., 1990: Radar reflectivity–ice water content relationships for use above the melting level in hurricanes. J. Appl. Meteor., 29, 955–961.
Buechler, D. E., and Goodman S. J. , 1990: Echo size and asymmetry: Impact on NEXRAD storm identification. J. Appl. Meteor., 29, 962–969.
Carey, L. D., and Rutledge S. A. , 1996: A multiparameter radar case study of the microphysical and kinematic evolution of a lightning producing storm. Meteor. Atmos. Phys., 59, 33–64.
Carey, L. D., and Rutledge S. A. , 2000: The relationship between precipitation and lightning in tropical island convection: A C-band polarimetric study. Mon. Wea. Rev., 128, 2687–2710.
Cifelli, R., Petersen W. A. , Carey L. D. , and Rutledge S. A. , 2002: Radar observations of the kinematic, microphysical, and precipitation characteristics to two MCSs in TRMM LBA. J. Geophys. Res., 107, 8077, doi:10.1029/2000JD000264.
Clements, N. C., and Orville R. E. , 2008: The warning time for cloud-to-ground lightning in isolated, ordinary thunderstorms over Houston, Texas. Preprints, Third Conf. on Meteorological Applications of Lightning Data, New Orleans, LA, Amer. Meteor. Soc., 6.4. [Available online at http://ams.confex.com/ams/pdfpapers/132309.pdf.]
Curran, E. B., Holle R. L. , and Lopez R. E. , 2000: Lightning casualties and damages in the United States from 1959 to 1994. J. Climate, 13, 3448–3464.
Deierling, W., Petersen W. A. , Latham J. , Ellis S. , and Christian H. J. , 2008: The relationship between lightning activity and ice fluxes in thunderstorms. J. Geophys. Res., 113, D15210, doi:10.1029/2007JD009700.
Dye, J. E., and Coauthors, 1986: Early electrification and precipitation development and precipitation development in a small, isolated Montana cumulonimbus. J. Geophys. Res., 91, 1231–1247.
Dye, J. E., Winn W. P. , Jones J. J. , and Breed D. W. , 1989: The electrification of New Mexico thunderstorms, 1. Relationship between precipitation development and the onset of electrification. J. Geophys. Res., 94, 8643–8656.
Gaskell, W., and Illingworth A. J. , 1980: Charge transfer accompanying individual collisions between ice particles and its role in thunderstorm electrification. Quart. J. Roy. Meteor. Soc., 106, 841–854.
Gauthier, M. L., Petersen W. A. , Carey L. D. , and Christian H. J. Jr., 2006: Relationship between cloud-to-ground lightning and precipitation ice mass: A radar study over Houston. Geophys. Res. Lett., 33, L20803, doi:10.1029/2006GL027244.
Goodman, S. J., Buechler D. E. , Wright P. D. , and Rust W. D. , 1988: Lightning and precipiation history of a microburst-producing storm. Geophys. Res. Lett., 15, 1185–1188.
Greene, D. R., and Clark R. A. , 1972: Vertically integrated water—A new analysis tool. Mon. Wea. Rev., 100, 548–552.
Gremillion, M. S., and Orville R. E. , 1999: Thunderstorm characteristics of cloud-to-ground lightning at the Kennedy Space Center, Florida: A study of lightning initiation signatures as indicated by the WSR-88D. Wea. Forecasting, 14, 640–649.
Hondl, K. D., and Eilts M. D. , 1994: Doppler radar signatures of developing thunderstorms and their potential to indicate the onset of cloud-to-ground lightning. Mon. Wea. Rev., 122, 1818–1836.
Jayaratne, E. R., Saunders C. P. R. , and Hallett J. , 1983: Laboratory studies of the charging of soft hail during ice crystal interactions. Quart. J. Roy. Meteor. Soc., 109, 609–630.
Johnson, J. T., MacKeen P. L. , Witt A. , Mitchell E. D. , Stumpf G. J. , Eilts M. D. , and Thomas K. W. , 1998: The Storm Cell Identification and Tracking algorithm: An enhanced WSR-88D algorithm. Wea. Forecasting, 13, 263–276.
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, 1547–1533.
Liu, C. L., and Illingworth A. J. , 2000: Toward more accurate retrievals of ice water content from radar measurements of clouds. J. Appl. Meteor., 39, 1130–1146.
MacGorman, D. R., and Rust W. D. , 1998: The Electrical Nature of Storms. Oxford University Press, 422 pp.
MacGorman, D. R., Filiaggi T. , Holle R. L. , and Brown R. A. , 2007: Negative cloud-to-ground lightning flash rates relative to VIL, maximum reflectivity, cell height, and cell isolation. J. Lightning Res., 1, 132–147.
Marshall, J. S., and Radhakant S. , 1978: Radar precipitation maps as lightning indicators. J. Appl. Meteor., 17, 206–212.
McCaul, E. W., Jr., 2008: Use of vertically integrated ice in WRF-based forecasts of lightning threat. Preprints, 24th Conf. on Severe Local Storms, Savannah, GA, Amer. Meteor. Soc., 3B.3. [Available online at http://ams.confex.com/ams/pdfpapers/142219.pdf.]
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, 327–335.
Mohr, C. G., Miller L. J. , Vaughn R. L. , and Frank H. W. , 1986: On the merger of mesoscale data sets into a common Cartesian format for efficient and systematic analysis. J. Atmos. Oceanic Technol., 3, 143–161.
Motley, S. M., 2006: Total lightning characteristics of ordinary convection. M.S. thesis, Dept. of Atmospheric Sciences, Texas A&M University, 165 pp.
NWS, cited 2009: 2008 NWS weather fatalities, injury, and damage statistics. [Available online at http://www.nws.noaa.gov/om/hazstats.shtml.]
OFCM, 2008: Doppler radar meteorological observations. Part A: System concepts, responsibilities, and procedures. Federal Meteorological Handbook 11, FCM-H11A-2008, 53 pp. [Available from Office of Federal Coordinator for Meteorology, 8455 Colesville Rd., Ste. 1500, Silver Springs, MD 20910.]
Oye, D., and Case M. , 1995: REORDER: A program for gridding radar data. Installation and use manual for the UNIX version. NCAR Atmospheric Technology Division, 19 pp.
Petersen, W. A., and Rutledge S. A. , 2001: Regional variability in tropical convection: Observations from TRMM. J. Climate, 14, 3566–3586.
Petersen, W. A., and Coauthors, 1999: Mesoscale and radar observations of the Fort Collins flash flood of 28 July 1997. Bull. Amer. Meteor. Soc., 80, 191–216.
Petersen, W. A., Christian H. J. , and Rutledge S. A. , 2005: TRMM observations of the global relationship between ice water content and lightning. Geophys. Res. Lett., 32, L14819, doi:10.1029/2005GL023236.
Rakov, V. A., and Uman M. A. , 2006: Lightning: Physics and Effects. Cambridge University Press, 687 pp.
Reynolds, S. E., Brook M. , and Gourley M. F. , 1957: Thunderstorm charge separation. J. Meteor., 14, 426–436.
Sassen, K., 1987: Ice cloud content from radar reflectivity. J. Appl. Climate Meteor., 26, 1050–1053.
Schaefer, J. T., 1990: The critical success index as an indicator of warning skill. Wea. Forecasting, 5, 570–575.
Takahashi, T., 1978: Riming electrification as a charge generation mechanism in thunderstorms. J. Atmos. Sci., 35, 1536–1548.
Vincent, B. R., Carey L. D. , Schneider D. , Keeter K. , and Gonski R. , 2004: Using WSR-88D reflectivity for the prediction of cloud-to-ground lightning: A central North Carolina study. Natl. Wea. Dig., 27, 35–44.
Wang, J. J., and Carey L. D. , 2005: The development and structure of an oceanic squall-line system during the South China Sea Monsoon Experiment. Mon. Wea. Rev., 133, 1544–1561.
Wang, J. J., Li X. , and Carey L. D. , 2007: Evolution, structure, cloud microphysical, and surface rainfall processes of monsoon convection during the South China Sea Monsoon Experiment. J. Atmos. Sci., 64, 360–380.
Watson, A. I., Holle R. L. , and Lopez R. E. , 1995: Lightning from two national detection networks related to vertically integrated liquid and echo-top information from WSR-88D radar. Wea. Forecasting, 10, 592–605.
Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, 467 pp.
Wolf, P., 2007: Anticipating the initiation, cessation, and frequency of cloud-to-ground lightning, utilizing WSR-88D reflectivity data. NWA Electron. J. Oper. Meteor., 2007-EJ1. [Available online at http://www.nwas.org/ej/pdf/2007-EJ1.pdf.]
Workman, E. J., and Reynolds S. E. , 1949: Electrical activity as related to thunderstorm cell growth. Phys. Rev., 74, 1231–1232.
