Air Force Manual 91–203 (AFMAN 91–203) directs that a lightning warning be issued when lightning is occurring within a 5 nautical mile (n mi; 1 n mi = 1.852 km) radius of a predetermined location. The 45th Weather Squadron (45 WS), located on the central eastern coast of Florida, provides weather support to Cape Canaveral Air Force Station, NASA Kennedy Space Center, and Patrick Air Force Base. The primary objective of this study is to optimize the lightning warning safety buffer; in particular, to determine if the 5 n mi safety radius can be reduced while maintaining a desired level of safety. The research uses processed Lightning Detection and Ranging II (LDAR-II) data from 2013 to 2016 to map the movement of preexisting lightning storms using ellipses. These ellipses are updated with every lightning flash. The distance from the ellipse boundary of each flash occurring outside the ellipse is recorded. Those exterior flash distances are then used to find the best-fit distribution from which the stand-off distance for the desired level of safety can be calculated. The distances from the edge of the ellipse are fit to a Weibull distribution and a reduction in the radius by 1 to 4 or 5 n mi is selected as the optimized balance between safety and operational impact. The 4 or 5 n mi radii are tested with a resulting failure rate of 3.58%, with an average savings of 130.75 false alarms and 15.7 8-h man days a year for the months of May–September.
Lightning is one of the most powerful and frequent natural phenomena that poses a risk to everyday life. Particularly concerning to the safety of human life, equipment, and machines is the appearance of cloud-to-ground (CG) lightning (Rakov 2016). Due to the severe danger lightning presents for both personnel and equipment, the Air Force (AF) and its civilian counterparts conducted extensive research to ascertain the ideal balance between safety and productivity. Located on the central eastern coast of Florida, the 45th Weather Squadron (45 WS) provides weather services to Cape Canaveral Air Force Station (CCAFS), the NASA Kennedy Space Center (KSC), and Patrick Air Force Base (PAFB). The forecasts, weather warnings, watches, and advisories delivered by the 45 WS provide weather safety for over 25 000 personnel and over $20 billion (U.S. dollars) of resources to include facilities, boosters, and payloads (Roeder et al. 2017).
While an ideal location for mission requirements, the severity and frequency of the weather patterns in this region have earned it the reputation as the thunderstorm capital of the United States (Medici et al. 2017; Orville and Huffines 2001). The more than 2500 lightning watches and warnings per year delivered by the 45 WS result in false alarms 40% of the time. The weather is also a leading source of delays and cancellations of space launch attempts. These numbers, coupled with noted discrepancies between the process of issuing lightning watches and warnings and techniques applied in previous studies, suggest that the current 5 nautical miles (n mi; 1 n mi = 1.852 km) safety standard set by the Air Force Manual 91–203 (AFMAN 91–203) may be reduced to a distance that would incur fewer losses in man hours while still maintaining the necessary level of safety (Department of the Air Force 2018). This paper documents a statistical approach to modeling the distances of lightning strikes outside a preexisting lightning area and comparing the probability of risk to the desired level of safety.
In January of 1998 during the American Meteorological Society’s (AMS) Annual Meeting, an ad hoc Lightning Safety Group (LSG) met to discuss the inconsistent lightning safety recommendations as well as new developments in lightning knowledge (Holle et al. 1999). Referencing advances in the understanding of thunderstorm behavior discovered by López and Holle (1999), the meeting resulted principally in the creation of the 30–30 Rule (Holle et al. 1999). Still relevant to the safety recommendations currently in practice, the 30–30 Rule provides safety guidance for both the onset and cessation of lightning.
The first 30 of the 30–30 Rule refers to the number of seconds between a lightning flash and the subsequent sound of thunder. Based on their findings of the distance subsequent lightning flashes can travel, López and Holle (1999) suggested 6–8 statute miles (mi) was a safer distance for resigning outdoor activities from the previous 2–3 mi, which led to the creation of the first half of the 30–30 Rule by the LSG (Holle et al. 1999). Thus, standard guidance suggests suspending outdoor activities when lightning occurs within 6 mi (5.213 86 n mi), that is, when the time measurement between flash and thunder reaches 30 s or less. The second 30 of the rule references the number of minutes to wait from the last lightning flash or sound of thunder to give a clearance to resume outdoor activities. During the same time frame as the LSG discussion on updating lightning safety rules, the AF also sought to update lightning safety standards based on their own research studies. The lightning strike and subsequent death of an airman in 1996 at Hurlburt Field prompted the beginning of the investigation and resulted in the AF adopting the 45 WS two-tiered lightning watch/warning process using a safety distance of 5 n mi. Subsequent studies of lightning strike distances sponsored by the 45 WS confirmed that 5 n mi effectively balanced safety and operations (Renner 1998; Cox 1999; Parsons 2000; McNamara 2002). These studies incorporated varying techniques that primarily used the distance between successive strikes (DBSS) approach. The DBSS method averages the distance from the storm core for a large number of strikes. Results of these studies proved similar to the results on lightning strike distance documented by López and Holle (1999).
The McNamara (2002) study used Lightning Detection and Ranging I (LDAR-I) data to unambiguously determine the lightning strike distance by tracking the lightning from its point of origin, rather than assume it came from the nearest thunderstorm as done in the DBSS method. McNamara (2002) showed that the DBSS method provided very similar results to his higher quality, though more manually intensive process; more specifically, the DBSS assumption of closest thunderstorm, though not technically always valid, did not degrade the results significantly. Subsequently, the AF safety standard settled on 5 n mi as the radius of optimum safety and operational productivity.
The 45 WS bases their weather watches and warnings on the broader AF safety regulation, AFMAN 91–203, which states that for any predesignated locations or activities, a lightning watch is in effect 30 min prior to a thunderstorm being within a 5 n mi radius (Department of the Air Force 2018). A lightning watch does not constitute a halt in activities but paves the way for the official lightning warning. A lightning warning goes into effect once lightning occurs within a 5 n mi radius of predetermined locations and activities and mandates that personnel in affected locations disengage from outdoor activity and seek shelter (Department of the Air Force 2018).
Cessation of AF lightning warnings follows similar protocols to the second half of the 30–30 Rule (Department of the Air Force 2018). The current standards have had the desired effect in regards to maintaining the safety of AF life and property. However, the methods used in the studies that helped form the regulations do not concur with the issuance processes that result in actual watches and warnings. Currently 10 lightning warning circles, pictured in Fig. 1, exist to protect the personnel and equipment responsible for the various missions associated with the 45 WS. The radii of the warning circles vary between 5 n mi for the protection of single small facilities, and 6 n mi for a single large facility or a grouping of several closely located smaller facilities (Roeder et al. 2017).
The lightning warning process employed by the 45 WS is based on the edge of the lightning area, yet the studies that helped to solidify the AFMAN 91–203 safety standards of a 5 n mi warning buffer utilized techniques that determined CG lightning strike distances originating from a storm’s center (Roeder et al. 2017). Because of this difference, the 45 WS lightning warnings incorporate not only the required 5 n mi radius, but also includes the radius of the lightning area, which ranges anywhere from 3 to 7 n mi. While this extra distance does not impinge on the safety concerns of lightning warnings as it allows for a greater safety buffer, it does have a negative effect on productivity. The 45 WS acknowledges that because the operational impact of the lightning warning circles is proportional to the area of the circle, even a relatively small reduction in the size of the warning circle can yield a large savings in lost work time (Roeder et al. 2017).
For their weather watches and warnings, the 45 WS hosts one of the most advanced lightning detection systems in terms of the density of sensors available for data collection. While the primary tool for forecasting locally developing thunderstorms lies in traditional radar, the 45 WS has also historically housed and currently maintains a series of detection tools to assist in forecasting (Roeder and Pinder 1998). Prior to 2008, these tools included the LDAR-I system and the Cloud-to-Ground Lightning Surveillance System (CGLSS). During the period of 2008–16, forecasters relied on the Four-Dimensional Lightning Surveillance System (4DLSS), which consisted of upgraded and combinatorial use of the LDAR-II network and the CGLSS (Roeder 2010). Currently in use since 2016 is the Mesoscale Eastern Range Lightning Information Network (MERLIN) (Roeder and Saul 2017). LDAR-II data are used for the analysis in this paper; any continued use of the term LDAR is referring to LDAR-II unless otherwise stated.
Developed in 1971 by NASA engineer Carl Lennon and considered one of the first operational systems for detecting in-cloud lightning, the LDAR-I and LDAR-II systems have served the operational and research needs of KSC and CCAFS for over four decades (Starr et al. 1998). The original LDAR-I system employed seven very high frequency radio receivers, six of the receiver stations surround one central site (Starr et al. 1998). When upgrades were made to the system to create the LDAR-II network in 2008, the older receivers were replaced with nine LDAR-II sensors (Roeder 2010).
An accuracy test conducted in 1995 of the legacy LDAR-I system found that when fully operational, flash detection efficiency neared 100% and false alarm rates fell to less than 1% (Mata and Wilson 2012). In his 2010 review of the upgraded system, Roeder confirms that the updated LDAR network’s performance exceeds its earlier edition with a 140% increase in detection. The data from LDAR also provide deeper knowledge into the origin of a lightning flash as it presents a 3D view of numerous data points (Britt et al. 1998). These advantages to LDAR data as opposed to other systems serve as the primary justification for using LDAR data in this study. In addition, this matches how the 45 WS issues lightning warnings by using lightning aloft, as detected by LDAR and now MERLIN, to gain several minutes of extra lead time to take action before the first CG lightning strike.
Limitations to the LDAR system are important to note here. Primarily, the LDAR system does not detect CG lightning strikes. The 4DLSS previously mentioned as a tool for lightning detection by the 45 WS relies on the updated CGLSS portion to provide actual CG strike locations. However, since all CG strikes start as lightning aloft and would have been detected by LDAR, and as the 45 WS issues warnings based on lightning aloft, this weakness of LDAR is not crippling for 45 WS lightning warnings. The other items of concern are the limiting factors of location accuracy and detection efficiency as the radius of inclusion expands beyond the central cluster of sensors. The first limitation of the LDAR system provides the reasoning behind certain assumptions made during this research process, while the second limitation helps in the data reduction decision for this study, as noted in the next section.
a. Data processing
The data source for this study originates from the LDAR network. As the LDAR network registers many in-cloud events and step leaders as lightning sources or source points, a single lightning flash may contain anywhere from several to thousands of source points. The Applied Meteorology Unit provided the LDAR data that were previously converted into lightning flashes for this study. For the years of 2013–16, LDAR data from CCAFS were converted to flashes by grouping source points; if any two source points are within 0.3 s and 3000 m, they are grouped together as part of the same flash.
For every month, January–December, and for years 2013–16, a text file is generated with this flash grouped LDAR data where every line break indicates a new flash. Any source of lightning detected by the LDAR system registers a date/time stamp along with a 3D recording of location and an epoch time. In the provided text files, the data for each source point are in a comma separated format with the following fields: date/time, X, Y, Z, and epoch time. The X, Y, and Z coordinates are in reference to KSC’s LDAR-I central site. Figure 2 illustrates the largest flash from June 2013 containing 1321 source points. For all plots moving forward, including Fig. 2, the X and Y axes are the distance (in km) from the legacy LDAR-I central site.
After consulting with the 45 WS, any event with less than five source points is removed from the data. The principal reasoning for this is that those readings with few to no other nearby source points detected by the LDAR system are generally not considered to be full lightning flashes or could have been erroneous lightning solutions due to radio noise. Also, because the peak lightning season for the central eastern coast of Florida occurs in the summer months (80% of the lightning occurs in 40% of the year), the focus of the analysis is narrowed to the months of May through September for years 2013–16, leaving 20 months of data for the complete analysis process. Last, because the location accuracy and detection efficiency for the LDAR network decrease as the distance from the sensors increases, the 45 WS also suggested a reduction in data with a focus on the flashes that occur within a 25 n mi (46.3 km) radius of the LDAR-I central site. This reduction still covers all 10 lightning warning circles supported by the 45 WS as illustrated in Fig. 3. In total from May to September of 2013–16, 808 430 flashes are extracted to use in the ellipse fitting process detailed shortly. All data processing and analysis is conducted using MATLAB R2015a.
For all the 808 430 flashes, the X and Y coordinates are converted from meters to kilometers (km) as measured from the legacy LDAR-I central cite. The Z coordinates are removed as the height of a lightning flash is not being considered in this particular study, just the horizontal boundary edge since that is how the 45 WS issues lightning warnings. Each flash is assigned a date/time stamp. Because any two source points for a single flash occur within 0.3 s of each other, the time stamp associated with the first source point of the flash is used. This initial time stamp is associated with all other source points of the flash as a flash is at most a few seconds in duration. Given the nature of the analysis being performed on the dataset, we foresaw the relevance of determining the extreme source points (outer most source points) of each flash. A convex hull MATLAB function is used to ascertain the outer most source points of each flash. The convex hull method was also used by Bruning and MacGorman (2013) and Hinkley et al. (2019) in varying capacities. Figure 4 shows the 13 extreme points for the largest flash in June 2013 and its associated convex hull.
b. Ellipse fitting algorithm
Before detailing how the developed algorithm fits a boundary to the extreme points of the 808 430 flashes, the description of the overarching analytical process is given. First, an ellipse is fitted to the extreme source points of a flash. Second, the distance from the edge of this fitted ellipse to another flash is recorded, if that flash occurs outside of the established ellipse. (The algorithm tracked every flash in order to match the 45 WS process of issuing a lightning warning even if a single total lightning flash enters a warning area.) Third, the fitted ellipse is updated only if another flash occurs outside of the boundary of an established ellipse to approximate a moving and/or developing storm. Fourth, a distribution is fit to all the distances from the edge of a preexisting lightning area. Fifth, this distribution then serves as a proxy for determining how far away the lightning warning boundary should be as to both minimize the probability of a strike occurring at the critical mission units at the center, while maximizing the amount of time operations can continue within the warning boundary. Last, the proposed new lightning warning radii is validated. This analytical process approximates an approaching storm to the protected areas overseen by the 45 WS but does not address a storm developing already within one of the existing lightning warning areas.
Next described is the numerical method by which a boundary around a preexisting lightning area is defined in order to characterize the edge of the storm from which to assess a lightning watch or warning. To contain the extreme flash points, the ellipse with minimum area is selected. The problem of finding a minimum volume enclosing ellipsoid (MVEE) has been studied for decades resulting in a variety of algorithms. Utilized in this study is the Khachiyan algorithm as detailed in Todd and Yildirim (2007). Although only two-dimensional data are being used in this study, a minimum area ellipse will continue to be referred to throughout the rest of this text as MVEE. The main concern in using the MVEE method from the onset is the size of the ellipses, or the amount of area that is contained within these ellipses. For optimum computational speed and accuracy, we used a tolerance of 0.01 (i.e., the ellipses contain at least 99% of the extreme source points of a flash). Recall from earlier that the LDAR network does not produce CG strike data, rather it gives X and Y coordinates for all the source points associated with a lightning strike. Therefore, it is assumed that each source point of a flash is considered as a potential CG strike at each source points X and Y coordinate location. Since LDAR tracks lightning aloft events to within approximately 1 km of the surface, the LDAR events should be reasonably close to where the CG return stroke originated from the ground.
The algorithm functions in accordance with the following series of steps and begins with the first flash from a list of all the flashes for the entire month. When a new flash occurs, if it is the first flash of the month or an existing ellipse is not already present, then an ellipse is drawn around it; if it is not the first flash of the month and an existing ellipse is already present, meaning an ellipse has already been drawn around at least one previous flash, then the time difference between the current flash and the last flash of the current ellipse is found. If the time difference is more than 30 min, the current flash represents the start of a new ellipse. This assumption originates from how the 45 WS issues and cancels lightning warnings. If no additional lightning from a storm cell has occurred after 30 min and no additional lightning is expected, then the warning is usually terminated.
However, if the time difference is less than 30 min, the current flash might potentially belong to the current storm for which the current ellipse was drawn. Therefore, the next step is to determine if the lightning flash occurred within or outside the current ellipse. If the lightning occurred within the ellipse, the algorithm moves on to the next flash. In contrast, if even one extreme source point of the flash occurred outside the ellipse, then the distance from the edge of the ellipse to each source point striking outside the ellipse is determined and the largest distance is recorded as the flash’s distance from the edge of the ellipse. If this distance is not within 16 km of the current ellipse, then the flash is not included in the current ellipse, but rather annotated as still needing assignment to an ellipse (i.e., a new storm in the distance) and the algorithm will then move on to the next flash in the list. If the current flash is within 16 km of the current ellipse then the distance from the edge of the current ellipse and the flash is recorded. Afterward, the ellipse is updated using the MVEE algorithm. The reasoning behind using a 16-km distance threshold is to decipher between different storms that might be active at the same point in time. Previous studies such as Parsons (2000) also referenced similar distance thresholds.
The subsequent step of the algorithm is to go through all of the flashes in the current ellipse and remove those that are older than 10 min from the time of the current flash. This step accounts for the movement of a storm over time and also helps to ensure that the ellipses being drawn are not overly large. Removal at both the 5 and 15 min intervals were also attempted and the differences in the distributional results between all three time removal thresholds were minimal. Therefore, removal of flashes at 10 min was selected as the moderate choice. Afterward, a new ellipse is drawn using the MVEE algorithm. The developed algorithm continues this MVEE process until every flash of every month in the database has been included in an ellipse. Figure 5 demonstrates the overall algorithm flowchart process while Fig. 6 gives a basic visual example of the algorithm.
c. Distribution fitting
After the algorithm has concluded, there is a vector containing the distances of all flashes occurring outside the boundary of an establish ellipse generated from the MVEE process. These distances from the edge of a preexisting lightning boundary become the responses to which a stochastic distribution is fit. Due to the nature of the phenomenon being studied, we used the generalized extreme value (GEV) distribution to model the form of the distribution of these lightning strikes outside a preexisting lightning area. The GEV distribution consists of three submodels: the Gumbel distribution (type I), the Fréchet distribution (type II), and the Weibull distribution (type III) (Kotz and Nadarajah 2000). Of these three, the Weibull distribution, which is used primarily to model failure times, is perhaps the most flexible distribution and fits the theme of predicting a failure of a lightning warning circle. Due to the very large sample size involved, a visual check is conducted for assessment of fit in lieu of a statistical goodness-of-fit (GoF) test. Very large samples invariably produce statistically significant lack of fit. Yet the departure from the specified distributions may be very small and technically unimportant to the inferential conclusions (Johnson and Wichern 1992).
After selecting the best distributional representation of these distances, the appropriate distance for initiating a lightning warning given the level of increased risk we are willing to accept is determined. Once this new stand-off distance is ascertained, how often this new stand-off distance fails as opposed to the previous 5 n mi distance is empirically deciphered. To complete this empirical process, the actual warning circles from the 45 WS are used.
d. Validation of new warning distances
To determine how well the newly selected warning radii perform as compared to the previous 5 or 6 n mi radii, the following process is executed for each warning circle for all 20 months of data. The first objective of this process is to establish how much time is saved if the warning circle radius is reduced from 5 or 6 n mi to the newly identified radius length. A second objective of this validation process is to detect how many false alarms are saved using the new radius. A false alarm is defined as a warning that would occur at the current 5 or 6 n mi radii distance but would not be issued using the new radius distance because no flash occurs within the new radius for the duration of the storm. The final objective is to ascertain how many warning failures occur at the new warning radius distance. That is, how many times does a lightning strike occur within 0.5 n mi of the center of a 5 n mi radius warning circle or 1.5 n mi for a 6 n mi radius before a warning would have been called at the new warning radius. The distance of 0.5 or 1.5 n mi is used as a failure radius as the assets actually being protected fall within 0.5 or 1.5 n mi of the center of each warning circle, respectively. From all this information the necessary statistics are gathered on how much time is saved, how many false alarms are averted, and how many failures occur both by month and by warning circle.
a. Ellipse data and distribution fitting
After executing the ellipse fitting algorithm for all 20 months of data, several different outcomes are examined for how the algorithm processes the data. Table 1 provides a compilation of what is found for each month as well as overall for all 20 months. Particularly, column one of Table 1 references the total number of ellipses for each month. Each ellipse represents a single storm since the algorithm processes through all the lightning strikes of one storm using the same ellipse before moving on to another separate set of strikes. Therefore; column one of Table 1 also reflects the total number of storms in each month. August and July of 2015 have the greatest number of storms with 256 and 252, respectively. One especially interesting result of the algorithm is that 25% of all ellipses are ellipses with only one flash. This means that there are single flashes either too far away from another storm and/or the time difference between these flashes and those before or after it are greater than 30 min. A closer examination of the data provides that of the 730 single flash ellipses, 25% of those are a result of time and/or distance isolation. The other 75% are a result of the assumptions and limitations of the algorithm.
Using the results of the ellipse fitting algorithm a total of 48 134 distances from the edge of an ellipse are extracted. A histogram of these distances can be seen in Fig. 7. The maximum distance being less than 16 is due to the distance between storms restriction that was included in the ellipse fitting algorithm. The two primary distributions under consideration when fitting this data are the GEV and the Weibull. The application of the GEV to the data can be seen in Fig. 8, while Fig. 9 highlights fitting a Weibull distribution. The GEV fits fairly well; however, it does not capture the full extent of the higher number of observations at shorter distances. Therefore, the Weibull distribution offers a more adequate fit while capturing the higher frequency of shorter distances.
As discussed in the methodology section, any GoF test applied to the data would result in a rejection of the null hypothesis. That is, the p values from any GoF test would be so low that any test would determine the hypothesized distribution is not an adequate fit as discussed in Johnson and Wichern (1992). The estimated shape and scale parameters of the fitted Weibull distribution are 0.833 and 2.124, with the associated 95% confidence intervals of (0.827, 0.839) and (2.093, 2.170), respectively. The mean and associated 95% confidence interval for this Weibull distribution are 2.36 and (2.334, 2.388), respectively.
b. Establishing new warning radii
The next step of the analysis process is to determine if a new warning distance may be safely established. The primary concern in decreasing the distance of warning for lightning strike is the extra risk incurred with such a reduction. As warning distance decreases it can be determined from the established Weibull distribution the percentage of risk increase. This percentage of risk increase is then compared to the amount of area decreased when considering the warning distance as the radius of a warning circle as utilized by the 45 WS. Table 2 displays the percentage of risk increase and area decrease from the current 5 n mi radius. From this table, the percentage of the rate of diminished returns (rate gained) is calculated for both the risk increase and area reduction. The plot of these percentages can be seen in Fig. 10. From this figure, we see that the amount of rate gained for both risk and area diminishes substantially around 4 n mi. Therefore, 4 n mi is elected as the new proposed alternative warning distance for the current 5 n mi warning radii circles and 5 n mi for the current 6 n mi warning radii.
c. Empirical validation results
Now that a new radius has been established (reducing current warning radii by 1 n mi), testing this radius empirically using the 45 WS warning circles is the next step. It is important to note here that the specific Weibull distribution that is fit to this set of data is not intended to perfectly model the strike distance of lightning outside a preexisting area; rather, this distribution serves as a stepping tool to select a new potential radius. The results of the empirical validation process provide the strongest justification for accepting or rejecting a shorter warning distance. The first empirical testing applied is the chosen 4 or 5 n mi radii for the current 5 or 6 n mi warning radii. While a large number of simulated lightning warning circles across CCAFS/KSC could have been used, the authors chose to use the current operational lightning circles since that will help advocate the new warning radii to the space launch customers.
Tables 3 and 4 provide a breakdown of the results of this test by warning circle and month, respectively. From Table 4, we find a reduction for all the warning circles provides a savings of 502.58 h or 62.82 8-h man days with 142 failures. This is an average savings of 15.7 8-h man days a year just in the five summer months. When considering the number of failures as a percentage of the total number of storms experienced in all 10 warning circles over the 20-month period the resulting percentage of risk, or failure rate is 3.58%. It is also found that the new warning radii produce a total of 523 false alarms saved; this gives an average of 130.75 false alarms saved a year in the five summer months. The hours saved from these prevented false alarms are included in the overall time savings and account for roughly 58% of the total time saved. The breakdown by circle reveals that all 10 warning circles experienced at least 3 failures, with the SLF circle having the largest number of failures at 32. The SLF circle also had the highest percentage of failures at 7.13% as it saw 32 failures out of 449 total storms. Table 3 also supplies that the four circles that are 6 n mi in radius and thus require a larger radius of protection at 1.5 n mi accounted for 76.06% of the total failures.
It is important to note that the failures and failure rate referenced previously are simulated failures using only observed lightning data and not actual failures accrued by real-world lightning warnings issued by the 45 WS. Indeed, upon consulting the 45 WS with a list of the circle, date, and time of each simulated failure, the 45 WS reported that in all 142 instances, a lightning warning was properly issued resulting in no actual failures or a real-world failure rate of 0%. These warnings were correctly issued by using other local weather data, especially weather radar, capable of observing locally developing cumulus that would be expected to continue to grow and produce lightning.
To ensure that a reduction of 1 n mi from the current lightning warning radii is the appropriate choice, empirical testing was also completed for several other reductions. Specifically tested was a reduction of the 5 or 6 n mi radii in 0.25 n mi increments down to 3.5 or 4.5 n mi, respectively. A comparison was also made between the 4 or 5 n mi reduction failure count to the current number of failures. The results of these tests can be seen in Table 5.
From Table 5 we see that the current radii of 5 and 6 n mi produce 113 failures or a failure rate of 2.85%, only 29 fewer than the newly selected 4 and 5 n mi radii. A visualization of the data from Table 5 can be seen in Fig. 11 where we see the number of failures at each new warning distance plotted simultaneously with the number of 8-h man days saved and tens of false alarms saved. The scaling of the number of false alarms saved by 10 was made to allow for concurrent plotting of the three statistics. From Fig. 11 we see that when specifically considering the number of failures at each warning distance, 4 and 5 n mi again prove to be the pivotal distances. This is primarily due to the number of increased failures more than doubling when moving from 4 and 5 n mi to 3.75 and 4.75 n mi. The appropriateness of this choice is further illustrated with Fig. 12, which displays the percentage increase in the number of failures from the current 5 and 6 n mi to each test radius.
It was previously stated that at the chosen distance of 4 or 5 n mi, the four larger circles contributed to 76.06% of the total number of failures. This same pattern can be seen in Table 6 where the number of failures as the warning circle radius changes is broken down by initial circle size. Figure 13 gives a visual representation of the data from Table 6. Although there are only four circles with an original radius of 6 n mi, we see that on average, those four circles are responsible for 75% of the total number of failures. While this percentage seems excessive, it is entirely reasonable as the inner failure radius of 1.5 n mi for the larger circles results in a failure area nine times larger than the failure area of the smaller circles that have a failure radius of 0.5 n mi.
In conclusion, it was found that completing the process of fitting the distances from the edge of a preexisting lightning area can be closely approximated as a Weibull distribution. Though the particular Weibull distribution chosen was not meant to be a precise model of the actual probability of strike, it was used as a tool to determine the increase in probability of strike. Comparing the rate gained of risk increase and area reduction led to the selection of reducing the warning radius by 1 n mi. Finally, the empirical validation results confirmed the selection of a 1 n mi reduction to the warning radius as the best choice when considering the amount of time and the number of false alarms saved versus the extra risk incurred.
5. Comparative and future research
a. Comparison of research techniques
The research in this paper has similarities to that of Holle et al. (2016). However, there are significant differences. The work in Holle et al. (2016) applied to an automated process where an inner circle was warned whenever lightning was detected within a larger circle with the same center point. The 45 WS lightning warning process uses a single circle and human forecasters with a wide range of weather sensors (e.g., radar, satellite, local skew T–logp) beyond just lightning to make the warning decision. The biggest difference with the research presented here is that Holle et al. (2016) showed the impact on warning performance with just a few radii based on previous choices without optimizing those radii. The main point of the research here is that the radii were optimized. Indeed, that was the main motivation for this project.
Another difference was that Holle et al. (2016) used lightning aloft from a system with flash detection efficiency of only about 50%, while the 45 WS lightning aloft system is close to 100% inside the small network (Roeder and Saul 2017). The research in this paper also has similarities to recent work on lightning safety at NASA Marshall Spaceflight Center, but that work also used preexisting lightning warning distances and did not attempt to optimize those distances, which is the main point of the research in this paper (Schultz et al. 2017; Stano et al. 2019).
b. Corroborating research
The Applied Meteorology Unit has recently completed similar research that corroborates these results (Hinkley et al. 2019). They used the same lightning data as in this study but used differing analysis methods. In particular, they used a convex hull to define the preexisting lightning area. In addition, they used the national safety standard for death rate (less than 10−4 deaths yr−1 or 1 in 10 000) to define the stand-off distance for lightning warnings for the optimum balance between safety and operational availability. Despite using different methods, their final recommendation for lightning safety was identical to this study at 4 or 5 n mi. The authors are encouraged that the different approaches using identical data converged to the same answer, bolstering the confidence in the final recommendation.
c. Future studies
There are several additional studies that should be considered before implementing the new lightning safety stand-off distance elsewhere from CCAFS/KSC. Most importantly for 45 WS operations, the study should be repeated with more recent data from the current system MERLIN. This is important since LDAR and MERLIN detect very different parts of lightning aloft. LDAR tends to detect smaller sized features such as stepped leaders, while MERLIN tends to detect larger sized features such as recoil streamers and dart leaders. Overall, both systems should adequately portray the horizontal extent of lightning aloft and produce similar results. However, this still needs to be verified.
Comparable studies should be conducted in many locations with weather that differs significantly from CCAFS/KSC. Other studies should also be conducted in different seasons. Likewise, many different types of thunderstorms under diverse driving mechanisms should be analyzed. In addition, the optimum lightning stand-off distance should be determined for when only CG lightning location systems are available. In most of these cases, similar lightning strike distance distributions are reasonably expected to occur. But, with a phenomenon as powerful and impactful as lightning, it is prudent to verify these expectations before making such a large change to a long-held safety procedure. This is especially true since few locations have a high performance local lightning location system similar to LDAR on which these results were based. Finally, alternative analysis methods should be considered. In particular, dynamic clustering analysis may produce more accurate preexisting lightning areas and overcome some of the problems from closely located thunderstorms, such as often occur in the CCAFS/KSC area due to thunderstorms forming along low-level boundaries such as sea-breeze front.
Because of the discrepancy of past research methodologies and the manner in which lightning warnings are issued, meteorologists at the 45 WS recognized the need for a study that considered the distribution of the distance lightning travels beyond the edge of a preexisting area. It was found in this study using ellipses that an extreme value distribution, specifically the Weibull distribution, may be used to fit the distance lightning strikes beyond the edge of a preexisting area. Applying the Weibull distribution and ascertaining the amount of additional risk incurred at shorter distances, the distances of 4 or 5 n mi were chosen as the new radii to empirically test. Comparing the empirical results of 4 or 5 n mi to various other choices, the 4 or 5 n mi radii continued to present as the appropriate choice based on the amount of additional risk they produced.
Past studies focused on the distance lightning travels as averaged from the distance to the core of the thunderstorm; thus, there were no similar studies to this work except Hinkley et al. (2019), which was completed about the same time. Similar time and spatial constraints were applied to the data in this study as that of previous work. A total of 20 months of data were used from a single location, a considerable amount more than most other studies. The amount of data used in this study fell third in magnitude behind Parsons (2000) who used 4 years’ worth of data covering the majority of the United States and McNamara (2002) whose study also included nearly 4 years’ worth of data from the 45 WS. The omission in this study of the concept of storm origin was opposite that of the other studies in that this research used the in-cloud data and assumed ground strike location at any of the various LDAR source point locations.
While there is further research to be done on this particular topic, the results of this study are very revealing. The amount of risk incurred with a reduction of 4 or 5 n mi from the current 5 or 6 n mi lightning warning distance of 3.58% may be acceptable, especially given that there is presently a 2.85% risk of failure at the current distance. Emphasized again here is the concept that this is theoretical risk, as it was already confirmed that none of the simulated failures resulted in real-world failures at the 45 WS. Results from the 4 or 5 n mi warning radii at the 45 WS provided a substantial reduction in the amount of lost man days with an average of 15.7 8-h man days recovered as well as an average of 130.75 false alarms saved in five months a year alone. As suggested previously, further studies of different locations and storm types would offer even greater support of a reduction in the lightning warning radius. However, because the 45 WS has so much invested in the assurance of safety of life and property due to the nature of their mission, much of the decision to update the AFMAN 91–203 lightning safety standards has historically been adopted from the 45 WS procedures. Therefore, with the results of this study, the authors suggest that a waiver to the AFMAN 91–203 be pursued by the 45 WS to reduce the lightning safety stand-off distance by 1 n mi, from 5 to 4 n mi. Upon further study of other locations, types of thunderstorms, seasons, and lightning location systems, a change to the AFMAN 91–203 for all locations may be justified.
Many thanks to friends and colleagues who assisted in this research, and in particular, the reviewers for their constructive comments and suggestions. This work was partially supported by the 45th Weather Squadron.
Current affiliation: Department of Mathematics and Statistics, Air Force Institute of Technology, Wright Patterson Air Force Base, Dayton, Ohio.
Current affiliation: 45th Weather Squadron, Cape Canaveral Air Force Station, Patrick Air Force Base, Florida.
Current affiliation: Department of Operational Sciences, Air Force Institute of Technology, Wright Patterson Air Force Base, Dayton, Ohio.
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