A Spatiotemporal Lightning Risk Assessment Using Lightning Mapping Data

Kelley M. Murphy aDepartment of Geosciences, Texas Tech University, Lubbock, Texas

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Eric C. Bruning aDepartment of Geosciences, Texas Tech University, Lubbock, Texas

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Christopher J. Schultz bNASA Marshall Space Flight Center, Huntsville, Alabama

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Jennifer K. Vanos cSchool of Sustainability, Arizona State University, Tempe, Arizona

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Abstract

A lightning risk assessment for application to human safety was created and applied in 10 west Texas locations from 2 May 2016 to 30 September 2016. The method combined spatial lightning mapping data, probabilistic risk calculation adapted from the International Electrotechnical Commission Standard 62305-2, and weighted average interpolation to produce risk magnitudes that were compared with tolerability thresholds to issue lightning warnings. These warnings were compared with warnings created for the same dataset using a more standard lightning safety approach that was based on National Lightning Detection Network (NLDN) total lightning within 5 n mi (1 n mi = 1.852 km) of each location. Four variations of the calculation as well as different units of risk were tested to find the optimal configuration to calculate risk to an isolated human outdoors. The best-performing risk configuration using risk (10 min)−1 or larger produced the most comparable results to the standard method, such as number of failures, average warning duration, and total time under warnings. This risk configuration produced fewer failures than the standard method but longer total time under warnings and higher false alarm ratios. Median lead times associated with the risk configuration were longer than the standard method for all units considered, whereas median down times were shorter for risk (10 min)−1 and risk (15 min)−1. Overall, the risk method provides a baseline framework to quantify the changing lightning hazard on the storm scale and could be a useful tool to aid in lightning decision support scenarios.

Murphy’s current affiliation: Earth System Science Center, The University of Alabama in Huntsville, Huntsville, Alabama.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kelley Murphy, km0109@uah.edu

Abstract

A lightning risk assessment for application to human safety was created and applied in 10 west Texas locations from 2 May 2016 to 30 September 2016. The method combined spatial lightning mapping data, probabilistic risk calculation adapted from the International Electrotechnical Commission Standard 62305-2, and weighted average interpolation to produce risk magnitudes that were compared with tolerability thresholds to issue lightning warnings. These warnings were compared with warnings created for the same dataset using a more standard lightning safety approach that was based on National Lightning Detection Network (NLDN) total lightning within 5 n mi (1 n mi = 1.852 km) of each location. Four variations of the calculation as well as different units of risk were tested to find the optimal configuration to calculate risk to an isolated human outdoors. The best-performing risk configuration using risk (10 min)−1 or larger produced the most comparable results to the standard method, such as number of failures, average warning duration, and total time under warnings. This risk configuration produced fewer failures than the standard method but longer total time under warnings and higher false alarm ratios. Median lead times associated with the risk configuration were longer than the standard method for all units considered, whereas median down times were shorter for risk (10 min)−1 and risk (15 min)−1. Overall, the risk method provides a baseline framework to quantify the changing lightning hazard on the storm scale and could be a useful tool to aid in lightning decision support scenarios.

Murphy’s current affiliation: Earth System Science Center, The University of Alabama in Huntsville, Huntsville, Alabama.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kelley Murphy, km0109@uah.edu

1. Introduction

a. Lightning as a hazard to human safety

Lightning is a threat that exists globally. It is particularly hazardous because of its frequent occurrence and spatial unpredictability. Cloud-to-ground (CG) lightning can kill or injure humans, motivating a desire to find effective means to prevent harm. It is estimated that the number of global annual lightning fatalities ranges from 6000 to 24 000 (Holle 2016).

Within the United States, lightning fatalities have greatly decreased over the last 40 years (Fig. 1). This is due to efforts from the Lightning Safety Awareness Team (LSAT), a shift from rural to urban population with better availability of lightning safe resources (i.e., substantial buildings or vehicles), better medical care, and improved meteorological information about thunderstorms (Holle and Cooper 2016). Although progress has been made to mitigate harm, fatalities and injuries still occur each year. The majority of fatalities are a result of lightning from unorganized convection (Ashley and Gilson 2009). The spatial distribution of these fatalities is well known (Holle 2016), and most occur outdoors during the summer months of June, July, and August, most frequently on Friday, Saturday, and Sunday (Jensenius 2020). Outdoor leisure activities contribute to the greatest number of fatalities in the United States, with water-related activities being the subcategory with the largest number of attributed deaths (Jensenius 2020). Disability from lightning injuries is a far greater problem than lightning fatalities (Cooper 1998), with a lightning injury-to-fatality ratio of 10:1 (Cherington et al. 1999). Injuries vary in severity and often leave victims to deal with long-term side effects (Cooper 1998).

Fig. 1.
Fig. 1.

The annual number of lightning fatalities in the United States since 1940. Data are from National Weather Service (2020b).

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

Lightning is a hazard for reasons beyond the capability to cause physical harm. Because of the unpredictability and frequency of CG flashes, it is both impractical and impossible to warn individuals of every time they could be in danger (Holle et al. 1999). People must be responsible for their own lightning safety, and while this fact is motivating for some, it can cause discomfort for those who would prefer to receive direction from authorities to take action (Roeder et al. 2012). Whereas other meteorological events are larger in space and time and require more ingredients to occur, even a small thunderstorm with minimal lightning can cause harm (Ashley and Gilson 2009). Lightning events are also often very isolated, not broadcast on a mass media platform, and not a criterion for a National Weather Service (NWS) watch or warning. For reasons such as these, Ashley and Gilson (2009) propose that people do not associate the same threat perception for a common or familiar event like lightning as they do for less common events such as hurricanes, tornadoes, and even severe thunderstorms. This could create a psychological disconnect by the public between the actual hazard and its potential impacts, which could lead to a general complacency among the public or cause people to treat lightning as a passive hazard (one that although threatening and possibly lethal, does not typically produce extensive casualties) (Ashley and Gilson 2009).

Given the above information, a tool able to quantify the changing lightning threat with respect to human safety would be advantageous. Numerical output would help to further specify and characterize these environments in which lightning is a hazard. This information could then be relayed to help forecasters and others be aware of potential lightning danger.

b. Determining vulnerable environments

To effectively describe environments vulnerable to lightning danger, multiple factors must be considered. An environment vulnerable to lightning danger includes both the presence of lightning itself along with the human(s) at risk. In other words, it is necessary that both the subjective and objective hazards surrounding lightning incidents are accounted for. An objective hazard is one that exists in an environment regardless of a person’s presence, while a subjective hazard is the human behavior that puts people at greater risk of objective hazards (Gookin 2010). It is important to distinguish between, identify, and understand these types of hazards because lightning casualties usually happen at the intersection of the two; natural environment hazards and human behavior (Gookin 2010). This concept is highlighted in Fig. 2. The threat from the lightning itself (objective hazard) is intuitively highest when a thunderstorm is overhead and there is a lot of lightning, but this is not when most lightning casualties occur. Rather, they occur more often at the beginning or end of a storm (Holle et al. 1993), illustrating the importance of subjective hazards (human decision-making and behavior) and exposure. Roeder et al. (2015) is an example of where both hazards are accounted for by combining population density and annual CG lightning flash density to approximate annual risk of lightning fatalities. Last, Fig. 2 also highlights how the lightning hazard fluctuates temporally on the storm scale, therefore evaluating the changing lightning threat over this time frame is important.

Fig. 2.
Fig. 2.

The threat of lightning casualties depends on both the lightning itself and people’s exposure to it. The orange curve shows the risk associated with lightning occurring, and the yellow curve shows exposure to that risk. The majority of lightning casualties occur underneath the intersection of these curves. The figure is from the National Weather Service Lightning Safety web page (National Weather Service 2020a).

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

c. Mitigation strategies

Lightning detection systems paired with varying analysis methods allow for the identification and monitoring of the objective hazard. Some mitigation strategies rely on the use of real-time lightning data to monitor an incoming threat. This type of mitigation strategy is often paired with the concept of “range rings” or lightning warning circles (Holle et al. 2016; Roeder et al. 2017), which involve the monitoring of lightning in an outer region/ring to anticipate lightning that may affect a smaller inner region/ring of concern. In Holle et al. (2016), this technique was applied in airport environments in order to find a balance between safety and efficiency of operations. This study and others use total lightning observations in mitigation systems (Schultz et al. 2017; Elsenheimer and Gravelle 2019; Stano et al. 2019). Total lightning instruments count both CG and intracloud (IC) lightning. Some instruments also spatially map lightning channels, for instance a Lightning Mapping Array (LMA) (Rison et al. 1999). Advantages to using this type of system include being able to see the channel extent of lightning activity within a storm as opposed to a point source indicating where a CG flash has made contact with the surface. This provides a footprint of where lightning is within the cloud, which gives insight as to where a CG flash could potentially come to ground.

Other studies target subjective hazards by focusing on concepts that directly relate to vulnerability, exposure, and decision-making of victims. Jensenius (2020) highlighted some sociodemographic patterns in lightning fatality data (age and gender of the victims) in addition to the previously mentioned finding that leisure activities lead to the highest number of fatalities. To further understand what makes a scenario or particular activity more dangerous than another, factors such as willingness to cancel or postpone activities, the vulnerability of the actual activity, and the ability to get to a safe place quickly must be examined (Jensenius 2020).

d. Lightning risk

The quantification of lightning risk is the mitigation method selected for the present study. The defining determinants of risk are hazard, exposure, and vulnerability (Birkmann et al. 2012), illustrating that risk as a quantity can incorporate both the objective and subjective hazards surrounding the lightning threat. For this research, lightning risk in relation to human safety refers to the probability that an individual will be killed or severely injured by lightning due to the lightning hazard itself as modulated by the individual’s exposure and vulnerability to it. To quantify risk, the structure of the risk assessment in the International Electrotechnical Commission Standard for Lightning Protection, Part II (IEC 62305-2:2010; referred to herein as IEC62305) was used (International Electrotechnical Commission 2010). The risk assessment framework of IEC62305 is intended to produce an annual value of lightning risk for structures. This risk value helps to determine whether or not protection measures are required in order to reduce losses due to lightning. For this research, the risk assessment was adapted to use for application to human safety during storm-scale scenarios. The risk analysis yields a numerical value that is assessed with reference to tolerability thresholds discussed in the following section. The concept of tolerable risk thresholds has been employed in other lightning research as well, such as in Hinkley et al. (2019).

This research focused primarily on assessing lightning risk by quantifying the objective hazard. While some subjective factors are incorporated into the method, future work should aim to achieve a more holistic depiction of risk through increased incorporation of subjective factors. The current risk method was created by blending methods previously listed; using total lightning mapping datasets, the distance dependence encompassed in range rings, and probabilistic risk calculation from IEC62305 to create a spatiotemporal risk analysis and assessment method for use in outdoor vulnerable environments. The method was tested on hypothetical lightning safety scenarios, and it was evaluated against a more standard lightning safety procedure as explained in the following section.

2. Method

a. Risk analysis

As previously mentioned, the structure of IEC62305 was used to quantify risk. This research focused only on the risk of loss of human life or permanent injury, which will be referred to as total risk RT in this research. IEC62305 breaks RT down into the sum of several risk components; however, only two components (RA and RB) were deemed relevant and used for this research while the others were neglected. RA is the component related to loss due to injury of living beings by electric shock and RB is the component related to loss due to physical damage. These risk components were calculated by finding the number of dangerous events ND, probability of damage, and consequent loss associated with a case. The risk calculation procedure and necessary equations are found in the appendix, along with several lookup tables needed to assign values to equation variables. The calculation and selection of variables are case dependent, and the rationale for choices used in this research is found in Table 1. The calculation of ND required the most modification for application to human safety scenarios and is discussed further below.

Table 1.

Selections and assumptions made for risk variables necessary to model risk to a human in this research. Missing from this table is NG because that is dependent on the evolving lightning scenario as discussed in section 2a.

Table 1.

To calculate ND for a case, it was necessary to select a location factor CD, quantify a representative collection area AD, and quantify lightning ground flash density NG. A value was assigned for CD from a lookup table that can be found in the appendix (Table A2). To quantify NG, flash extent density (FED) from the west Texas LMA (WTLMA) was used. This product counts the number of unique flashes per unit time in each 1-km grid box covering a domain of interest. For a flash to count toward a grid box, it must have produced at least one detectable radio noise source within that grid box. The choice of using west Texas LMA total lightning as opposed to only ground strike data (as used in IEC62305) was intentional because of the desire to contrast spatial mapping versus strike-point data in the risk framework and consequently, lightning mitigation methods. Viewing the spatial extent of lightning is advantageous for safety applications because lightning flashes are capable of traveling from tens to hundreds of kilometers (Weiss et al. 2012) and can come to ground outside precipitation structures as a “bolt from the blue” (Tran et al. 2014), or anywhere along very horizontally extensive channels that are sometimes observed (Lyons et al. 2020; Schultz et al. 2021). Further details on the WTLMA sensors and detection efficiency can be found in (Chmielewski and Bruning 2016).

The use of WTLMA data enabled monitoring of the changing lightning hazard to be incorporated into the risk calculation rather than a single value representing the annual lightning flash density for a particular location. Lightning was constantly monitored within a 40-km radius surrounding a location designated by latitude and longitude coordinates. The flashes occurring in the radius were weighted based upon distance from the center point in order to convey that lightning closer to the center is more dangerous to someone located there than flashes farther away. To do this, a Gaussian distribution filter was applied to the lightning appearing within the radius, as described in the equation below. Here, R was set to 40 km and is a normalization distance, r is distance away from the center of the radius, and alpha is the reciprocal of the standard deviation:
fgauss=exp[12(αrR)2].

This filtering technique matches that of the Barnes (1964) scheme that is used to obtain data at a desired point in a variety of meteorological analyses through weighted averaging interpolation, and it is also known as kernel density estimation. An example of this technique applied to LMA data can be seen in Fig. 3. Two tests were applied to the above method to confirm that the filtering mechanism performed accurately. First, a uniform flash rate of 1 flash per kilometer squared was imposed over the entire domain with uniform coverage. Next, the same setup was repeated but with 25% coverage over the domain (Fig. 4). Flash density values per minute were output for both tests. The resultant output was as expected: 1 flash per kilometer squared per minute for uniform coverage and 0.25 flashes per kilometer squared per minute for 25% coverage.

Fig. 3.
Fig. 3.

An example of WTLMA data visualized for an individual minute at 2326 UTC 22 May 2016. Colored grid boxes represent weighted FED values that fall within the 40-km radius and contribute to the risk calculation, and gray grid boxes represent nonweighted FED values that do not affect the risk analysis. The x and y axes indicate distance in kilometers away from the WTLMA. The legend in the top right helps identify the distances of 40 km, 5 n mi, and 0.5 n mi used in this research.

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

Fig. 4.
Fig. 4.

As in Fig. 3, but an illustration of the uniform-flash-rate, 25%-domain-coverage test performed on the Gaussian filter.

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

A conservative distance of 40 km was chosen for R to account for lower probability scenarios in which lightning extends far beyond its parent storm. This way, if a storm were right on the 40-km edge of the radius, it would produce a nonzero, very low risk to account for situations in which long flashes (Schultz et al. 2017; Lang et al. 2017; Lyons et al. 2020; Peterson et al. 2020) could potentially produce a ground flash at the center of the radius. The selection of alpha dictated the placement of the weights within the 40-km radius, essentially deciding the impact of flashes on the risk relative to their distance from the radius center point. Values of 2 and 6 were both tested (α = 2; α = 6) as seen in Fig. 5. These values were selected on the basis of visual inspection of their associated Gaussian curve with respect to depictions of horizontal extent of lightning flashes and flash size distributions (Fuelberg et al. 2014; Parsons 2000; Sanderson et al. 2020). In general, shorter flash distances and sizes (these can be measured various ways, i.e., from a storm center point, reflectivity contour, existing lightning ellipse, etc.) are more common than longer flash distances and therefore should be weighted more heavily by the Gaussian filter. An α = 6 weights FED with near 0 values as distances approach 20 km, reflecting the fact that a storm around this distance away from the center is less likely to produce lightning that reaches the radius center. An α = 2 was chosen as an alternate conservative method to weight all flashes at the radius with a value of near 0.1. Ultimately, the weighted flashes in the radius were summed each minute and divided by the sum of the weights within the radius to get a representative weighted FED value for that minute. These values were then summed over a desired risk duration/unit to yield NG. For this research, in addition to risk per minute, risk units were evaluated in increments of 5 min up to a maximum unit of risk per 30 minutes [hereinafter, such risk units will be expressed as, e.g., risk (30 min)−1].

Fig. 5.
Fig. 5.

An illustration of the Gaussian filter applied to FED. The choice of α impacts the distribution of weights applied to FED within the 40-km radius.

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

It is important to note that, along with gaining spatial awareness of lightning channels, a lightning quantity was also inherently incorporated into the risk framework by utilizing FED. In other words, the risk framework did not only rely on where lightning was relative to a location, but how much of it was present. At a given distance away from a radius center, a FED value of 1 flash per kilometer squared would produce a lower risk magnitude than a FED value of 5 flashes per kilometer squared at that same distance. In other lightning mitigation methods using distance dependence, the lightning threat may be implied to be the same in both of those scenarios as the flashes would be the same distance away from the radius center.

The last component needed to calculate ND was AD, which was modeled in two different manners. The first AD modeled, ADP, was created as a best effort to match the dimensions of a human who was assumed to be standing at the location centers. This was done by choosing estimate measurements of the height (1.74 m), width (0.837 m), and wingspan (0.837 m) of an average male to replace the height, width, and length of a structure. The second method of modeling AD, ADR, was calculated by considering a radius of 100 ft (~30 m) from the human assuming that within this distance, a CG lightning strike could be fatal (Hinkley et al. 2019). Note that ADP uses appendix Eq. (A5), but ADR simply calculates the area of a circle with a radius of 100 ft. These two choices of AD in combination with two choices for α created four separate risk configurations to be tested (Table 2).

Table 2.

The four risk configurations tested in this research. Other than the variables listed here and lightning input (NG), all other risk variables are held constant in the calculation and are listed in Table 1.

Table 2.

To summarize, the risk analysis calculates lightning risk to a human being per unit time. It does this by finding a collection area representative of a human (two possible areas are tested, ADP and ADR), monitoring and weighting WTLMA FED within 40 km of that human (two alphas were tested to distribute the weights within the 40-km radius, α = 2 and α = 6), and inputting these parameters into the IEC62305 risk assessment framework in place of AD and NG. The remainder of the variables needed for the calculation are discussed in the appendix, and their associated values chosen for this research are shown Table 1. The risk unit is determined by the amount of time over which FED is summed. For example, risk (10 min)−1 is found by summing the weighted FED within the 40-km radius over 10 min and using that value within the assessment.

b. Risk assessment

The last step in the risk framework was to assess the values output from the risk calculation. These values were compared to tolerability thresholds to draw conclusions about safety. IEC62305 uses a single threshold for tolerable risk of 10−5 yr−1, where values that exceed this threshold would be considered unacceptable and values that are at or below it are tolerable. This is also the desired safety threshold in Hinkley et al. (2019). This research utilized a different framework from the Health and Safety Executive (HSE), called tolerability of risk (TOR) (Health and Safety Executive 2001). TOR employs thresholds to classify risk as unacceptable, tolerable, or broadly acceptable and is further explained in Fig. 6. This framework not only allows for classification of numerical risk, but also provides a graduated scale that enables interpretation of an individual’s risk perception (this is not considered in this research but could be examined in future work). To appropriately apply these thresholds to calculated risk values on shorter time intervals, they were prorated dependent upon the unit of risk desired. Table 3 illustrates these prorated values for the units of risk considered in this study.

Fig. 6.
Fig. 6.

A visual representation of the TOR framework. Green, yellow, and red areas designate the acceptable, tolerable, and unacceptable regions, respectively. The red/unacceptable region is risk associated with an activity that would be taken under no circumstance unless the risk were lowered to tolerable or broadly acceptable levels. The green/acceptable region is insignificant and accurately controlled risks, or ones that would regularly be dismissed in everyday life. The yellow/tolerable region is associated with risks from activities that people may tolerate in order to secure benefits. The suggested threshold values between the broadly acceptable and tolerable region as well as the tolerable and unacceptable region are shown to the right of the thick, horizontal arrows. To the right of the dotted horizontal arrow is the tolerable risk threshold used in IEC62305 and Hinkley et al. (2019). The figure is adapted from Health and Safety Executive (2001).

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

Table 3.

Values for the TOR thresholds. The two columns on the right represent the two suggested thresholds within the TOR framework. The rows show these thresholds prorated for each risk unit considered in this research, with risk per year as a reference at the bottom.

Table 3.

c. Lightning safety test and comparison with a standard method

For this research, the risk method configurations were evaluated against a more standard lightning safety protocol to assess performance. Ten locations within the WTLMA domain were used to monitor lightning activity (Fig. 7). For both methods, the risk method (including all four configurations) and more standard protocol, lightning was monitored for all locations from 2 May to 30 September 2016 at all hours. This produced a database of 1520 “case days” spanning 36 480 h over which to evaluate the lightning safety methods based upon lightning warnings that would have been issued during this time.

Fig. 7.
Fig. 7.

Locations selected within the WTLMA domain to evaluate both lightning safety methods. The table on the right lists the latitude, longitude coordinates of the locations. The yellow star is the location of the WTLMA.

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

The more standard lightning safety protocol (referred to as the standard method) used the National Lightning Detection Network (NLDN) (Cummins et al. 1998; Cummins and Murphy 2009) total lightning data in combination with a 5 n mi (1 n mi = 1.852 km) warning radius and 0.5 n mi inner radius of concern. Using a 5 n mi warning radius is the current safety standard set by the Air Force Manual 91-203 (Department of the Air Force 2018). This is also close to the threshold of 6–8 (statute) mi (1 mi = 1.6 km) that coincides with the first part of the “30–30” rule created by the LSAT (Holle et al. 1999). A small 0.5 n mi inner warning radius was selected to designate where lightning strikes would pose a danger. This is the same inner radius distance used in tandem with a 5 n mi warning radius in Sanderson et al. (2020).

A standard method “lightning warning” was issued when any NLDN flash occurred at or within the 5 n mi radius of a location. This warning ended once there were no flashes within that radius for 30 min following the last flash within the radius, thereby adopting the second half of the “30–30” rule (Holle et al. 1999). A successful warning was defined as a warning in which at some point in its duration, any NLDN lightning flash came within the inner 0.5 n mi radius. A false alarm was defined as a warning in which no flashes ever entered the inner radius. A failure was defined as any warning period in which the warning began with a flash inside of the inner radius, indicating that there would have been no prior warning to this flash occurring within the area of concern. The number of total warning periods, false alarm ratio (FAR), average duration of a warning period, and total time spent under warning periods were also calculated. Last, lead time and down time were calculated on all validated (nonfalse alarm) warning periods. Lead time represented the amount of time elapsed from the start of the warning period to the first flash occurring within the inner radius. Down time represented the amount of time elapsed from the last flash within the warning period and inner radius to the end of the warning period.

Risk was calculated as highlighted in the appendix with the additional modifications discussed prior in section 2a. This risk in relation to the TOR framework was used to issue lightning warnings. A lightning warning was issued as soon as the unacceptable threshold was met or exceeded and ended when risk fell back into the tolerable or acceptable range. Successful warnings, false alarms, FAR, average duration of a warning period, total time spent under warning periods, lead time, and down time for the risk method were defined in the same manner as for the standard method. This is intentional as it was desired to see how the risk method (including its use of WTLMA FED) performed against a more widely used standard method. In contrast to the standard method, the risk method could have two failure types. The first type of failure, a “start failure,” was similar to that of the standard method where a warning period began with a flash inside of the inner radius. The second type of failure, a “general failure,” was when any NLDN flash occurred within the inner radius but the risk was not unacceptable. In other words, a general failure indicated any time in which the risk method did not issue a warning when a NLDN lightning flash was within 0.5 n mi of a location center. As a further diagnostic, the number of times that lightning occurred within the 5 n mi radius but risk was not unacceptable was also recorded; this situation was not considered a failure. Last, lead time and down time were found only for the best-performing risk configuration as determined by the other statistics calculated.

3. Lightning safety test results

a. Standard method

For the entirety of the database, the standard method issued 638 warning periods. Of these warning periods, 493 were false alarms, creating a FAR of 0.772. The average duration of a warning period was 01:12:50 [all durations in this paper use the format “(days,) hours:minutes:seconds”], and the total time spent under a warning period was 32 days, 06:27:00. There were five failures that occurred. The lead time and down time averaged over all validated periods (nonfalse alarm periods) were 00:35:29 and 01:14:48, respectively. This information is summarized in Table 4.

Table 4.

Lightning safety results for the standard method.

Table 4.

b. Risk method

Tables 58 highlight the safety test results for each risk configuration. Each table column corresponds to each risk unit calculated.

Table 5.

Lightning safety test results for configuration 1 (α = 2; ADP).

Table 5.
Table 6.

Lightning safety test results for configuration 2 (α = 6; ADP).

Table 6.
Table 7.

Lightning safety test results for configuration 3 (α = 2; ADR).

Table 7.
Table 8.

Lightning safety test results for configuration 4 (α = 6; ADR).

Table 8.

A few general observations can first be drawn on varying risk units by looking at all four tables together. For all risk method configurations, as the risk unit gets larger there are fewer warning periods. These fewer warning periods are also longer in duration on average than those of smaller risk units. Risk per minute and risk (5 min)−1 most often have a higher number of start failures compared to the other risk units, indicating instances where there was no warning given prior to lightning occurring within the 0.5 n mi inner radius. General failures increased with increasing risk unit with ADP (Tables 5 and 6), suggesting that higher risk units paired with this collection area smooth the risk curve and could contribute to a dampening of the risk magnitude. Risk per minute and risk (5 min)−1 will be excluded in further discussion when referring to the risk method, as the associated results for almost all statistics listed are nonrealistic or highlight poor performance. For either unit in any configuration, there were too many failures, FAR greater than 90%, or average warning durations less than 10 min.

1) ADP results: Configurations 1 and 2

Results for configurations 1 and 2 can be seen in Tables 5 and 6. Using estimates of the height, length, and width of a human being resulted in a small collection area and consequently, lower risk magnitudes. Overall, ADP produced fewer warning periods compared to those created by the standard method and ADR, as well as shorter average warning durations and total time spent under warnings. While a shorter time spent in a warning period might have been considered to be a positive result with no other context, the number of false alarms and failures illustrated that ADP was an ineffective choice for AD. Both types of failures were present across all risk units and both alphas. General failures were more prevalent than start failures, strongly suggesting that ADP was too small, leading to risk magnitudes that were too low and not representative of the danger associated with lightning overhead within the inner radius.

2) ADR results: Configurations 3 and 4

Results for configurations 3 and 4 using ADR (Tables 7 and 8) were more comparable to the results of the standard method, with configuration 4 being closest (Table 8). FAR was generally higher with ADR than with ADP, however, the number of failures (both types) decreased significantly. The total time under warnings increased, coinciding with an increase in the total number of warning periods. Results for configuration 3 showed higher FAR, number of warning periods, and longer total time under warning periods. Configuration 4 was comparable to the standard method for total time under warnings and average warning durations, but with more warning periods at risk units lower than risk (30 min)−1. The number of warning periods for risk (30 min)−1 was close to that of the standard method with 15 fewer warning periods. FAR was lower with configuration 4, although still higher than the standard method, possibly because of the higher number of warning periods. Configuration 3 had 0 general failures across all risk units, indicating that every time there was a lightning flash that occurred within the inner radius, the risk was unacceptable. Notably, there were 0 start failures for configuration 4, but 1 general failure that persisted through every risk unit. From the higher FAR, number of warning periods, and total time under warnings associated with configuration 3, it appears to be too conservative. This leaves configuration 4 (ADR, α = 6) to be the best-performing risk configuration with reference to the standard method, and it is selected for further discussion.

c. Closer comparison of risk configuration 4 with the standard method

1) Lead time and down time

Lead time, down time, and lightning flash distance comparisons were evaluated for the standard method and risk configuration 4. Figures 8 and 9 show lead time and down time comparisons, respectively, between risk (of varied units) and the standard method. The standard method had the lowest median lead time of 26 min, and the highest median lead time was risk (25 min)−1 with 41.5 min. The spread between the upper and lower extreme values for the risk method was larger, with a noticeable elongation toward longer lead times. The interquartile range (IQR) was also larger for the risk method. Risk (10 min)−1 had the smallest median down time of 58 min, followed by the standard method with a median of 66 min. The highest down time was risk (30 min)−1 with 83 min. Again, the spread between the upper and lower extreme values and IQR for down time was larger with the risk method.

Fig. 8.
Fig. 8.

Lead times for both the standard method and configuration 4 of the risk method; N is the number of samples considered, or the number of verified warning periods.

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

Fig. 9.
Fig. 9.

As in Fig. 8, but for down times.

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

2) Failures

The standard method had five failures for which there was no prior warning to a flash being within the inner radius. Two of the failures were associated with flashes of a nearby storm reaching the inner radius (one of these is shown in Fig. 10a), another two were due to large flashes associated with a stratiform region (one of these is shown in Fig. 10b), and one failure was from a combination of lightning in a stratiform region and secondary convection (Fig. 10c). Figure 11 shows the warning periods issued by both the standard method and risk configuration 4 for the failure shown in Fig. 10c, which occurred at location 4 on 14 May 2016. The standard method had issued a warning that eventually expired at 0249 UTC, shortly before the failure at 0255 UTC. Risk (10 min)−1 similarly had a warning period that expired before the one encompassing the standard method failure; however, it started a new warning with 8 min of prior lead time. For the units of risk (15 min)−1–risk (25 min)−1, there was one long warning period mostly encompassing the first three standard method warning periods. Risk (30 min)−1 had a very long first warning period encompassing all four of the standard method warning periods issued. Notably, the risk method produced three–five extra warning periods encompassing a period of time for which the standard method did not issue any warnings. During this time, stratiform lightning as seen by the WTLMA FED periodically occurred overhead of the location, but no NLDN flashes were seen within 5 n mi. Note that the failure time of 0255 UTC is 1 min later than shown in Fig. 10. This is because at any given time, risk encompasses the previous minutes corresponding to unit. For example, risk (10 min)−1 at 0254 UTC encompasses lightning occurring from 0244 to 0254 UTC but does not include lightning occurring from 0254 to 0255 UTC, which is when the dangerous flash occurred.

Fig. 10.
Fig. 10.

As in Fig. 3, but with added NLDN IC and CG flash locations (shown in the legend by gray or green diamonds). Shown is the lightning activity occurring at failure times associated with the standard method. The lightning activity at the failure times was associated with (a) flashes from a nearby storm, (b) large flashes from a stratiform region, or (c) a combination of lightning in a stratiform region and secondary convection.

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

Fig. 11.
Fig. 11.

Warning periods for the standard method and risk method at location 4 on 14 May 2016. All times listed are UTC. A standard method failure occurred on this day at 0255 UTC, as indicated by the red text and arrow. This meant that there was no prior warning to lightning being within the 0.5 n mi radius, and the failure event itself initiated this warning period. The yellow highlighted periods show the warning periods that encompass the failure time.

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

The risk method had one general failure persist through all risk units, indicating one instance in which, even with a flash inside of the 0.5 n mi radius, risk was not considered unacceptable. For further investigation of how the risk method functioned relative to lightning flash distances, risk (10 min)−1 was used to find the number of times [representing a period of risk (10 min)−1] that lightning (NLDN total lightning flashes) fell within the standard method 5 n mi warning radius but risk was not unacceptable. In other words, this showed situations in which the standard method would issue a warning but the risk method would not. Figure 12 illustrates the closest nonzero WTLMA FED pixel distance to the location center versus the closest NLDN flash distance for each of these times. There are 219 times total; 166 times for which the closest WTLMA FED pixel distance is greater than 5 n mi and 53 times for which the distance is smaller than or equal to 5 n mi. The times for which the distance is smaller than or equal to 5 n mi indicate where risk could be underestimated; however, lightning only entered into the inner radius once during these times when the risk method did not issue a warning; this was the single general failure (Figs. 12 and 13).

Fig. 12.
Fig. 12.

Each blue point represents a period of risk (10 min)−1 for configuration 4 during which risk was not unacceptable but an NLDN flash was within 5 n mi of a center location. Each point is plotted with respect to the closest WTLMA flash distance (y axis) vs the closest NLDN flash distance (x axis) at that minute. The dotted gray line represents the 5 n mi distance with respect to the WTLMA flash distances, and the dotted red line represents the 0.5 n mi distance with respect to NLDN flash distances. The red dot is the general failure that occurred with the risk method (NLDN flash was within 0.5 miles but risk was not unacceptable).

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

Fig. 13.
Fig. 13.

As in Fig. 10, illustrating the risk general failure. Risk was tolerable at this time, but an NLDN IC flash was within the inner radius.

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

The risk calculation is based on the location and intensity of WTLMA FED. For this reason, a level of risk other than unacceptable for the 166 times for which the closest WTLMA FED pixel distance was farther than 5 n mi seems appropriate. At these times, the risk method did not “see” lightning within 5 n mi and therefore did not produce a large risk magnitude. However, because these times have an associated NLDN IC or CG flash within 5 n mi, it shows there is disagreement in flash locations between the WTLMA and NLDN. Perhaps these were CG flashes not detected by the WTLMA, or the NLDN falsely identified flashes. Future work should look more closely at this data subset. Future attention could also be given to the 53 times for which the closest WTLMA FED pixel was equal to or less than 5 n mi to determine why the unacceptable threshold was not exceeded.

4. Utility of risk in an operational setting

Using the lightning risk method in real time and in an operational setting could prove to be useful for monitoring dangerous lightning trends in locations of interest. The risk method produces a risk magnitude that changes with time, which can be easily visualized with time series plots (Fig. 14). These risk time series plots could be implemented as an added forecasting tool to help a forecaster evaluate current lightning risk, place it in the context of tolerability thresholds, and identify whether that risk is increasing or decreasing. Figure 14 is an example of a lightning risk time series plot generated from 2200 UTC 13 May to just past 1000 UTC 14 May for location 1 (Fig. 7). Forecasters may start to be concerned about issuing a lightning warning at around 2200 UTC as there is a large jump in risk magnitude toward the unacceptable region. Contrarily, they may begin to feel comfortable about ending that warning period around 0100 UTC after seeing that the risk dropped into the tolerable region and had been steadily decreasing over the last hour. The same concept applies when risk started to increase again around 0345 UTC and they might anticipate a warning. During this second warning period, they might watch risk begin to decrease around 0430 UTC, but it never leaves the unacceptable range [with risk (20 min)−1 and risk (30 min)−1], possibly helping them decide to continue the warning. While viewing lightning flash locations on a map is an invaluable resource, it is not always easy to tell whether the lightning threat has increased or decreased with passing time. These time series plots implemented in real time could be a useful complement to real-time lightning location data to help forecasters in decision-making scenarios.

Fig. 14.
Fig. 14.

Risk time series plots for configuration 4. Risk (10 min)−1, risk (20 min)−1, and risk (30 min)−1 are shown from 2200 UTC 13 May 2016 to just after 1000 UTC 14 May 2016. The colored background corresponds to the tolerability thresholds in Fig. 6.

Citation: Weather, Climate, and Society 13, 3; 10.1175/WCAS-D-20-0021.1

5. Discussion, limitations, and future work

The risk method applied in this study was shown to be comparable to the standard method and effectively issued warnings when lightning danger was present. Configuration 4 performed best of all risk configurations considered. While this risk method and configuration were effective for this research, below we highlight areas in which continued work is needed as well as limitations to this study.

To the authors’ knowledge, this study was the first to apply lightning mapping data to quantify risk and showed the benefits of spatial extensive mapping. However, the use of total lightning within the risk assessment framework could overestimate the magnitude of risk in some cases as IEC62305 uses only ground flashes, and IC flashes are not a direct danger to a human on the ground. This is partially mitigated through the use of the Gaussian filter. Another way to potentially mitigate this would be through the use of an IC to CG ratio. This could be implemented to obtain a representative ground flash value by applying a known IC-to-CG ratio such as those presented in Medici et al. (2017) for the corresponding region of interest, causing risk to decrease by a value corresponding to that ratio. Note also that previous work has highlighted the importance of factoring in the actual number of ground contacts per lightning flash into quantitative risk assessments, as flashes can produce multiple strokes that can lead to lightning striking the ground in more than one place (Stall et al. 2009). Anywhere that a channel comes to ground poses a risk for humans; therefore, incorporating ground contacts is an additional way to modify the risk method for future calculations. This also illustrates that risk may not be as overestimated as initially presumed. In fact, using total lightning in this research actually resulted in risk magnitudes that were too low with selection of ADP. Further testing would be required to evaluate how changes to total lightning input would impact the performance of the method.

Next, while the use of total lightning was beneficial to see the spatial extent of lightning, the lack of CG specific lightning data within the risk method limited the ability to see the location of flashes that could have a direct impact on humans. Being able to incorporate the specific ground contact locations of CG lightning flashes could enhance the risk calculation, perhaps by increasing risk with the presence of a CG flash a certain distance away from a location center point. Total lightning could provide a baseline risk value, with the presence of CG flashes enhancing that risk.

As mentioned previously, the risk method calculates a risk magnitude that is based on lightning location and quantity, which is unique relative to other lightning safety mitigation methods that often rely primarily on the location of lightning. By factoring in lightning quantity, two storms at the same distance away from a radius center may have different associated risks if one storm has more lightning than the other. This was intentional because it was deemed likely beneficial to capture an increasing or decreasing lightning trend relative to storm intensification or decay. However, this means particular storm modes with more lightning (i.e., supercells) will likely create larger risk magnitudes than those with less lightning. It is important to note, however, that the magnitude in relation to tolerability thresholds is more important than the magnitude alone. Supercells could create higher risk magnitudes because of more lightning; however, isolated convection (likely with less lightning) is responsible for the majority of lightning fatalities (Ashley and Gilson 2009). Future work should investigate how the risk method works for varied storm modes.

Further testing needs to be done to find a base configuration that is appropriate for varying lightning safety situations. While configuration 4 produced results similar to the standard method, only thunderstorms within the WTLMA domain were considered during 5 months of the year and other risk terms (see the appendix) were not varied. While ultimately more testing is required to fully validate model use in varied scenarios, the ability to adjust the risk configuration adds flexibility while closely matching the performance of the standard method. Configuration of variables based on local or storm specific lightning characteristics (α) and area of concern (AD) could allow for a more tailored approach to lightning safety. In addition to this, tolerability thresholds could be changed to match a user-determined unacceptable risk level dependent upon a given application. The thresholds used within the TOR framework are guidelines that are not meant to be rigid benchmarks for use in all circumstances (Health and Safety Executive 2001). While the suggested thresholds are efficient in this research, application of the risk analysis to a larger database could help to better define these risk thresholds to be more specifically suited to lightning safety scenarios.

Further research needs to be done to evaluate the optimal choice of risk unit. As shown in the results, the risk unit dictates how many warning periods will be issued and can likely cause there to be multiple warning periods during a time frame in which the standard method may have only had one continuous warning period (Fig. 11). Perhaps a buffer could be added to smaller risk units in which a warning period only ends once risk has been tolerable or acceptable for an allotted amount of time. This could lead to a better performance from risk min−1 and risk (5 min)−1. Had this been applied to the results seen in Fig. 11, the first few warning periods for the risk method (dependent on risk unit) would likely be combined. The concept of using one risk unit to start warnings and another to end warnings [i.e., use risk (10 min)−1 to issue but use risk (30 min)−1 to end] could also be explored.

Risk was chosen as the lightning safety mitigation method due to its ability to capture both the objective and subjective factors surrounding lightning casualties, thereby incorporating hazard, exposure, and vulnerability. As stated in the goals of this research, the current model configuration was focused on quantifying the objective hazard and as it stands, mostly disregards elements of exposure and vulnerability. Exposure can be modified in the last term of appendix Eqs. (A7) and (A8); however, this research assumed constant exposure. If more ways to quantify these other components of risk were incorporated, it is possible that risk could better highlight times when people are more likely to be struck rather than only putting emphasis on times when the lightning threat is highest (a risk curve that illustrates the highlighted portion of Fig. 2, and not just the curve labeled “lightning risk”). Factors that could be considered in the future to account for vulnerability include demographic information discussed in section 1c from Jensenius (2020). Overall, for a more complete depiction of lightning risk, elements of exposure and vulnerability should be incorporated into the model.

Future work is being done to apply the risk method in a real-time setting and incorporate the use of Geostationary Lightning Mapper (GLM) data (Schultz et al. 2021). While this research was limited to investigating cases within the domain of the WTLMA, utilizing GLM flash extent density data would enable calculation of risk anywhere within its field of view, including areas outside the United States. It would also enable a larger database over which to apply the risk method in order to better understand and characterize lightning danger in varied geographic locations. While work is ongoing to transition the risk method for use with the GLM data stream, the method could work with any lightning mapping dataset.

6. Summary

A unique method was created to assess lightning risk in 10 locations within the WTLMA domain from 2 May to 30 September 2016. Using a combination of WTLMA data, the IEC62305 risk assessment structure, and weighted averaging interpolation, the method produced risk magnitudes that were compared to tolerability thresholds to issue lightning warnings. These warnings were compared with warnings issued for the same time frame and locations by a more standard lightning safety method that used the location of NLDN total lightning flashes with respect to a 5 n mi radius. The best design of the risk method was chosen based upon which configuration produced the most similar or improved lightning safety test results relative to those of the standard method. The following are key conclusions:

  • The best risk configuration was number 4, which utilized α = 6 and ADR. Results were comparable to the standard method with regard to total time under lightning warnings issued and average warning durations. This risk method configuration led to fewer failures than the standard method but had a higher FAR. There were also more warning periods for the risk method for all units except risk (30 min)−1.

  • The temporal resolution of risk min−1 and risk (5 min)−1 was too high and produced highly variable risk magnitudes. Because of this, these units did not accurately define warning periods, causing too many failures and a high FAR.

  • Configuration 4 produced longer median lead times than the standard method across all risk units. The IQR was larger and shifted toward longer lead times than the standard method. Median down times for risk (10 min)−1 and risk (15 min)−1 were shorter than the standard method, but risk (20 min)−1 and greater were longer. The spread between minimum and maximum values for both lead time and down time was larger for risk than for the standard method.

  • Although the risk method had only one failure, there were times when risk produced a nonunacceptable value when lightning fell within 5 n mi. This needs to be investigated further to determine whether the associated magnitudes at these times are appropriate or if risk is being underestimated in certain scenarios.

  • Risk configuration 4 adds flexibility to lightning safety monitoring while closely matching the performance of the standard method. In addition, the data themselves start and end warnings without the need for a predetermined time threshold for resuming activities.

  • Looking at an evolving time series of risk could be a useful tool for forecasters in decision-making scenarios. Identifying risk trends relative to tolerability thresholds could help to increase confidence in decisions to start or end lightning warnings.

Future work should aim to further test the risk method and its flexibility in varying scenarios and to implement GLM data so as to expand the geographic reach of its application.

Acknowledgments

The authors thank Dr. Vicente Salinas and Dr. Karin Ardon-Dryer for their support, helpful ideas, and comments that greatly improved the content of this research. In addition, we thank two anonymous reviewers for their comments and suggestions that greatly helped the clarity and presentation of the paper.

Data availability statement

The WTLMA data used in this research were obtained with permission from Dr. Eric Bruning. These data are available by email request to him (eric.bruning@ttu.edu) or the first author (km0109@uah.edu). NLDN lightning data are available through Vaisala, Inc., and the Global Hydrology Resource Center (https://ghrc.nsstc.nasa.gov/home/). Links for obtaining access to the HSE TOR framework or IEC62305 are provided in the citations.

APPENDIX

Lightning Risk Calculation

Because IEC62305 is meant for structures, an exact application of the risk assessment to this research was not practical. In addition to the methods section of this paper, this appendix summarizes the decisions made to adapt and simplify IEC62305 for the purpose of this research. Only risk terms deemed relevant to human safety in outdoor vulnerable environments are included. Other terms that are found in IEC62305 but not listed here are neglected. Additionally, some variable options in lookup tables are intentionally left out because they are deemed not relevant to the given research application.

A type of risk and source of damage were first identified, which coincide with a type of damage and consequent loss (Table A1). From these selections, the formula for total risk RT becomes the sum of risk components relevant to risk of loss of human life R1 [RA (the risk component related to loss due to injury of living beings by electric shock; variables with subscript A pertain to this component) and RB (the component related to loss due to physical damage; variables with subscript B pertain to this component)]:
R1=RT=RA+RB.
These risk components are solved using
RA=NDPALAand
RB=NDPBLB.
The components are the product of the number of dangerous events per unit time ND, a probability of damage (PA or PB), and consequent loss (LA or LB). The sections below outline how to find values for each of the above terms. Most variables required for these calculations vary by case and are either described in the methods or selected via lookup tables. Variable selections for this research study are listed in Table 1.
Table A1.

Type of risk, source(s) of damage, type(s) of damage, and type of loss chosen from IEC62305 for this research application.

Table A1.

a. Number of dangerous events

To solve for ND requires a collection area AD, the number of flashes for the location NG, and a structure location factor CD:
ND=NGADCD106.
The input for NG is modified as discussed in the methods. The value for CD is selected from Table A2. A value for AD is found through the use of
AD=LW+2(3H)(L+W)+π(3H)2.
Modifications to this equation are discussed in the methods section. The unit for ND is number of dangerous events per unit time, where the time matches the desired risk unit.
Table A2.

Choices for structure location factor CD, which describes the surroundings of the structure (in this research, a person) at risk.

Table A2.

b. Probability of damage

To solve for the probability of damage for both risk components requires the use of
PA=PTA+PB.
and values selected for PTA from Table A3. Varying values assigned for PB in IEC62305 pertain to existing lightning protection levels. It is assumed none are present for this research, which assigns a value of 1 for PB in all scenarios.
Table A3.

Choices for PTA, which is assigned on the basis of additional protection measures present against touch and step voltages.

Table A3.

c. Consequent loss

Consequent loss for both components is found through the use of
LA=rtLTnZnttz8760hand
LB=rprfhzLFnZnttz8760h.
Tables A4A8 are lookup tables for rt, rp, rf, and hz in the above equation. Each table defines the term and lists options for selection. Here, LT is the typical mean relative numbers of victims injured by D1 due to one dangerous event, which is selected to always equal 10−2 to represent all types of structures (or scenarios for the purpose of this research). The variables nz and nt are the number of people in a specific zone within the area of interest and the total number of people in that area, respectively. This research does not define zones and always calculates the risk for one individual, so these two terms are always equal to 1. The final term in Eqs. (A7) and (A8) is modified so that tz (the time exposed) and the denominator both match the desired unit of risk to reflect constant exposure. For example, for risk per 10 minutes, tz/(8760 h) becomes (10 min)/(10 min) = 1.
Table A4.

Choices for rt, a reduction factor that is based upon the type of soil or floor in the location. The values are based upon contact resistance of a particular surface type.

Table A4.
Table A5.

Choices for the reduction of loss due to physical damage depending on provisions taken to reduce the consequences of fire (rp).

Table A5.
Table A6.

Choices for reducing loss due to physical damage depending on the risk of fire (rf).

Table A6.
Table A7.

Choices for any special hazards present (hz).

Table A7.
Table A8.

Choices for the typical mean relative number of victims by physical damage due to one dangerous event (LF).

Table A8.

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  • Fig. 1.

    The annual number of lightning fatalities in the United States since 1940. Data are from National Weather Service (2020b).

  • Fig. 2.

    The threat of lightning casualties depends on both the lightning itself and people’s exposure to it. The orange curve shows the risk associated with lightning occurring, and the yellow curve shows exposure to that risk. The majority of lightning casualties occur underneath the intersection of these curves. The figure is from the National Weather Service Lightning Safety web page (National Weather Service 2020a).

  • Fig. 3.

    An example of WTLMA data visualized for an individual minute at 2326 UTC 22 May 2016. Colored grid boxes represent weighted FED values that fall within the 40-km radius and contribute to the risk calculation, and gray grid boxes represent nonweighted FED values that do not affect the risk analysis. The x and y axes indicate distance in kilometers away from the WTLMA. The legend in the top right helps identify the distances of 40 km, 5 n mi, and 0.5 n mi used in this research.

  • Fig. 4.

    As in Fig. 3, but an illustration of the uniform-flash-rate, 25%-domain-coverage test performed on the Gaussian filter.

  • Fig. 5.

    An illustration of the Gaussian filter applied to FED. The choice of α impacts the distribution of weights applied to FED within the 40-km radius.

  • Fig. 6.

    A visual representation of the TOR framework. Green, yellow, and red areas designate the acceptable, tolerable, and unacceptable regions, respectively. The red/unacceptable region is risk associated with an activity that would be taken under no circumstance unless the risk were lowered to tolerable or broadly acceptable levels. The green/acceptable region is insignificant and accurately controlled risks, or ones that would regularly be dismissed in everyday life. The yellow/tolerable region is associated with risks from activities that people may tolerate in order to secure benefits. The suggested threshold values between the broadly acceptable and tolerable region as well as the tolerable and unacceptable region are shown to the right of the thick, horizontal arrows. To the right of the dotted horizontal arrow is the tolerable risk threshold used in IEC62305 and Hinkley et al. (2019). The figure is adapted from Health and Safety Executive (2001).

  • Fig. 7.

    Locations selected within the WTLMA domain to evaluate both lightning safety methods. The table on the right lists the latitude, longitude coordinates of the locations. The yellow star is the location of the WTLMA.

  • Fig. 8.

    Lead times for both the standard method and configuration 4 of the risk method; N is the number of samples considered, or the number of verified warning periods.

  • Fig. 9.

    As in Fig. 8, but for down times.

  • Fig. 10.

    As in Fig. 3, but with added NLDN IC and CG flash locations (shown in the legend by gray or green diamonds). Shown is the lightning activity occurring at failure times associated with the standard method. The lightning activity at the failure times was associated with (a) flashes from a nearby storm, (b) large flashes from a stratiform region, or (c) a combination of lightning in a stratiform region and secondary convection.

  • Fig. 11.

    Warning periods for the standard method and risk method at location 4 on 14 May 2016. All times listed are UTC. A standard method failure occurred on this day at 0255 UTC, as indicated by the red text and arrow. This meant that there was no prior warning to lightning being within the 0.5 n mi radius, and the failure event itself initiated this warning period. The yellow highlighted periods show the warning periods that encompass the failure time.

  • Fig. 12.

    Each blue point represents a period of risk (10 min)−1 for configuration 4 during which risk was not unacceptable but an NLDN flash was within 5 n mi of a center location. Each point is plotted with respect to the closest WTLMA flash distance (y axis) vs the closest NLDN flash distance (x axis) at that minute. The dotted gray line represents the 5 n mi distance with respect to the WTLMA flash distances, and the dotted red line represents the 0.5 n mi distance with respect to NLDN flash distances. The red dot is the general failure that occurred with the risk method (NLDN flash was within 0.5 miles but risk was not unacceptable).

  • Fig. 13.

    As in Fig. 10, illustrating the risk general failure. Risk was tolerable at this time, but an NLDN IC flash was within the inner radius.

  • Fig. 14.

    Risk time series plots for configuration 4. Risk (10 min)−1, risk (20 min)−1, and risk (30 min)−1 are shown from 2200 UTC 13 May 2016 to just after 1000 UTC 14 May 2016. The colored background corresponds to the tolerability thresholds in Fig. 6.

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