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  • View in gallery

    Peak current vs striking distance. Relationship expressed on curve 1 is adapted from Golde (Golde 1945); curve 2 is from Wagner (Wagner 1963); curve 3 is from Love (Love 1973); curve 4 is from Rühling (Rühling 1972); and points x are from Davis (Davis 1962).

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    Model of the RSM. The RSM defines zones into which CG lightning of certain kiloamp ranges should not strike.

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    Study area within southeast and south-central Colorado.

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    Negative polarity CG flash densities across study area for duration of study period.

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    Section of USGS DEM showing sample locations of GIS-mapped highpoints.

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    Sample of 100-, 200-, and 300-m-radius buffers around highpoints.

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    Zoomed-in section of a set of concentric buffers showing GIS-mapped highpoint as red dot. Actual lightning strike locations are shown as black triangles.

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    CG strikes by kiloamp and buffer size relativized as percents. Green bars above the x axis suggest that highpoint buffers capture more actual CG flashes than random points.

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    Percent change of actual CG strikes over randomly generated points for 300-m buffer only. The gradually increasing trend from right to left trend ceases at the −100- to −109-kA class.

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Exploring Cloud-to-Ground Lightning Earth Highpoint Attachment Geography by Peak Current

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  • 1 Department of Geography and Environmental Studies, University of Colorado at Colorado Springs, Colorado Springs, Colorado
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Abstract

This study applied remotely sensed cloud-to-ground (CG) lightning strike location data, a digital elevation model (DEM), and a geographic information system (GIS) to characterize negative polarity peak current CG lightning Earth attachment behavior. It explored the propensity for (i) flashes to favor topographic highpoint attachment and (ii) striking distance (a near-Earth attachment force) to increase with peak current. On a 16 000 km2 10-m DEM covering a section of southeast and south-central Colorado, a GIS extraction method identified approximately 5000 hilltop and outcrop highpoints containing at least 15 m of vertical gain in a 300-m radius neighborhood with a minimum horizontal separation of 600 m. Flashes with peak currents ranging from −20 to −119 kiloamps (kA), collected between February 2005 and May 2009, were subdivided into 10 kA classes and mapped on this modified DEM. Buffers of 100-, 200-, and 300-m radii created around each highpoint were used to assess the hypothesis that striking distance increases with higher negative peak current. Point-in-polygon counts compared actual CG strike totals to random point totals received inside buffers. CG strikes favored topographic highpoints by as much as 5.0% when compared to random points. Chi-square goodness-of-fit tests further corroborated that actual CG strikes at highpoints were generated by a more nonrandom process. A positive trend between striking distance and peak current was also observed. Although this correlation has been characterized in controlled settings, this study is the first to document this physical process at real-world landscape scales over multiple years.

* Corresponding author address: Brandon J. Vogt, Department of Geography and Environmental Studies, University of Colorado at Colorado Springs, 1420 Austin Bluffs Parkway, Colorado Springs, CO 80918. bvogt@uccs.edu

Abstract

This study applied remotely sensed cloud-to-ground (CG) lightning strike location data, a digital elevation model (DEM), and a geographic information system (GIS) to characterize negative polarity peak current CG lightning Earth attachment behavior. It explored the propensity for (i) flashes to favor topographic highpoint attachment and (ii) striking distance (a near-Earth attachment force) to increase with peak current. On a 16 000 km2 10-m DEM covering a section of southeast and south-central Colorado, a GIS extraction method identified approximately 5000 hilltop and outcrop highpoints containing at least 15 m of vertical gain in a 300-m radius neighborhood with a minimum horizontal separation of 600 m. Flashes with peak currents ranging from −20 to −119 kiloamps (kA), collected between February 2005 and May 2009, were subdivided into 10 kA classes and mapped on this modified DEM. Buffers of 100-, 200-, and 300-m radii created around each highpoint were used to assess the hypothesis that striking distance increases with higher negative peak current. Point-in-polygon counts compared actual CG strike totals to random point totals received inside buffers. CG strikes favored topographic highpoints by as much as 5.0% when compared to random points. Chi-square goodness-of-fit tests further corroborated that actual CG strikes at highpoints were generated by a more nonrandom process. A positive trend between striking distance and peak current was also observed. Although this correlation has been characterized in controlled settings, this study is the first to document this physical process at real-world landscape scales over multiple years.

* Corresponding author address: Brandon J. Vogt, Department of Geography and Environmental Studies, University of Colorado at Colorado Springs, 1420 Austin Bluffs Parkway, Colorado Springs, CO 80918. bvogt@uccs.edu

1. Introduction and background

Lightning attachment to the ground is “one of the least understood and most poorly documented processes of the cloud-to-ground lightning discharge.” (Rakov and Uman 2003, p. 137). Whereas much of research on lightning attachment theory has taken place in a research domain dominated by laboratory-based numerical modeling, controlled simulation, and monitoring of individual lightning strikes at specialized field facilities, this paper uses remotely sensed cloud-to-ground (CG) lightning strike location data, a digital elevation model (DEM), and a geographic information system (GIS) to empirically document long-standing assumptions about lightning attachment behavior. Although this work supports extant lightning theory, it illustrates how GIS may be employed to examine theoretical questions about lightning and to enhance applied concerns related to lightning protection system design and structure site selection.

Since Benjamin Franklin’s work with electricity (Franklin 1774), air terminals (lightning rods) atop buildings and structures have intercepted and safely routed CG lightning current into the ground. Criteria for air terminal height, placement, and spacing distance were based on the cone of protection concept. This concept fixed the apex of an imaginary skyward-pointing cone to the tip of a grounded air terminal (Golde 1977). Objects in the cone’s interior space were thought to be protected from CG strikes. From Franklin’s time through the late 1930s, cone angle ratios (cone base radius to cone height) described in lightning protection literature varied from 0.125 to 9.0 (Schwaiger 1938). The large variation in cone angle ratios and associated uncertainty of air terminal effectiveness was likely a function of the reduced scales and reduced voltages used in laboratory tests that simulated lightning behavior. In a discussion of zones of protection from lighting, Rakov and Uman (Rakov and Uman 2003) question the soundness of any reduced-scale laboratory-based study that simulates the lightning attachment process (Rakov and Uman 2003).

Throughout the twentieth century and into the twenty-first century, lightning scientists continue to refine the Franklin-era cone of protection concept. Researchers have developed sophisticated physics and electrogeometrically based models to better understand lightning attachment behavior and to improve lightning protection system designs. Much of this research has been tied to models tested in downscaled laboratory conditions or in field campaigns where CG flashes are triggered or monitored and studied individually over relatively small spatial and temporal scales. These foundational works on CG attachment behavior are organized around the concepts of lightning “leaders” and “striking distance.” Leaders, a precursor to lightning, are self-propagating electrical discharges creating a channel in the atmosphere with enhanced electrical conductivity (Rakov and Uman 2003). In about 90% of all CG lightning, the strike involves the attachment of a descending leader from a negatively charged cloud base to an ascending leader from a positively charged area on the Earth below a storm (Rakov and Uman 2003). These are negative CG strikes. For negative CG strikes, striking distance is a measure of how far skyward an ascending Earth-connected positively charged leader extends before it reaches a breakdown value and attaches to a descending negatively charged leader (Cooray et al. 2007).

It is widely recognized in lightning attachment research that a correlation exists between striking distance and the current in negative polarity CG flashes (Golde 1945; Wagner 1963; Rühling 1972; Love 1973; Eriksson 1974; Lee 1978; Mousa and Wehling 1993; Petrov and Waters 1995; D’Alessandro and Petrov 2006; Cooray et al. 2007) (Figure 1). A strike’s peak current, which is measured in kiloamps (kA), is visually the brightest lightning process and represents the largest waveform in a series of nearly instantaneous strokes that occur in CG flashes (Rakov and Uman 2003). Mathematical and reduced-scale laboratory-generated values (Rakov and Uman 2003) have documented a positive, curvilinear relationship between striking distance and peak current that deviates considerably in slope, especially with higher peak current (Figure 1). For example, at approximately −90 kA, a striking distance ranges from just under 100 m (Wagner 1963) to approximately 340 m (Rühling 1972). Understanding how these two flash parameters covary is important because it forms the basis for lightning protection strategies that dictates, among other key safety criteria, the gauge, placement, and spacing of air terminals and other CG-intercepting objects.

A common and practical means to visualize striking distance is through the “rolling-sphere method” (RSM) (Szedenik 2001), a model introduced by Lee in 1978 (Lee 1978) (Figure 2). The concept of striking distance rests at the core of the RSM. Following the RSM, the terminus of the upward, positively charged propagating leader resides in the center of an imaginary sphere with a radius equaling the striking distance (Rakov and Uman 2003). Thus, if an imaginary sphere whose radius represented a striking distance were rolled along the ground, any point of contact would represent a potential CG strike location. Low peak current rolling spheres, which are smaller in diameter than high peak current rolling spheres, contour more closely to the ground and may not sense taller objects that are nearby but lie beyond their striking distance. Reciprocally, based on the geometry of a sphere, the RSM presumes that higher peak current flashes are more likely to sense and potentially strike objects that protrude high above Earth’s surface.

As suggested above, major weaknesses in understanding the peak current–striking distance relationship are (i) the fact that conclusions drawn from reduced-scale lightning models are not particularly reliable and (ii) the theoretical basis from which CG attachment behavior is derived. A third constraint in understanding attachment behavior is related to the small number of data-driven case studies in which a direct link is made between peak current and the specific Earth surface configuration where CG attachment occurred. Exceptions include investigations at documented strike locations (Hodanish et al. 2004; Holle 2005; Baba and Rakov 2007; Loendorf 2008; Hodanish 2009; Mäkelä et al. 2009; Shindo and Suda 2009). This weakness in understanding the geography of CG attachment through empirical means is largely due to the hazardous, capricious, and fleeting nature of lightning. Examining the spatial relationship between thousands of CG flashes (by peak current) and thousands of isolated salient landscape features will assess (i) the propensity for lightning to favor highpoint attachment and (ii) the postulation that a positive relationship exists between striking distance and peak current.

Because theory dictates that striking distance depends on the peak current, it is assumed that higher peak current flashes, with their larger RSM diameters, should sense and strike protruding near-Earth objects more frequently than featureless areas. This idea is based on the assumption that downward-propagating leaders, as they approach upward leaders attached to ground objects, will be redirected at their near-Earth striking distance and thus attach more frequently at highpoints. The near-Earth attractive effect of lightning has been visually confirmed in a small number of photographs as an abrupt change in direction in the CG channel (at a node called the orientation point) where the descending leader enters its striking distance and attaches to isolated, tall Earth-grounded objects (Gulyás and Szedenik 2009). If a tendency for topographic highpoints to attract more CG flashes than surrounding areas is observed, the concept of striking distance and the associated RSM will be supported empirically. More importantly, if highpoints are found to attract higher concentrations of high peak current flashes, then the longstanding assumption that a positive relationship exists between striking distance and peak current will also gain support. These relationships have been confirmed in controlled settings, but they have not been validated in actual landscapes over extended periods of time.

2. Study area

A 16 000 km2 section of southeast and south-central Colorado (bound by 37.00°–37.90°N, 103.90°–105.75°W) serves as the study site for this research (Figure 3). The region is well situated between four ground-based lightning sensors. One is located near La Junta, Colorado, and the others reside in New Mexico and northern Texas (USPLN 2010).

The study area displays a varied range of topographic features. These include high mountain peaks that extend above tree line, high basins, basalt capped plateaus, steeply incised canyons, and protruding volcanic dikes. Climate types range markedly from arid (<25 cm annually) in the western San Luis Valley region to moist (89–101 cm annually) in the high elevations to semiarid (25–38 cm annually) in the northeastern two-thirds of the area (USDA–NRCS 1997). Mountainous and south-central sections of the study area receive frequent thunderstorms during the spring and summer months. The section of the study area extending from the southern Sangre de Cristo mountain range across the Raton Mesa boasts some of the highest CG flash densities in Colorado (Hodanish and Wolyn 2006). From the period 1985 to 2005 (missing year 2000 data), Hodanish and Wolyn (Hodanish and Wolyn 2006) measured greater than five CG strikes per square kilometer per year in south-central sections of the study area. This study, covering the period February 2005 through May 2009, measured as high as 8.1 negative polarity CG strikes per square kilometer per year in climatologically and topographically favorable areas (Figure 4).

3. Methods

3.1. Overview

The first step in the GIS workflow required derivation of local highpoints on a DEM (Figure 5). Some highpoints fell on actual summits, whereas others were located along ridges or on steep, convex slopes. Subsequent steps created circular buffers of three different radii surrounding all highpoints (Figure 6). The buffers served as containers for tallying and comparing the number of actual strikes to the number of random points that fell in the buffer (Figure 7). Two methods—one descriptive and one statistical—compared differences between actual strikes and random points captured within the buffers. The multistep GIS workflow, described in detail below, was executed using Environmental Systems Research Institute (ESRI) ArcGIS 9.3.1 GIS software environment.

3.2. Data and data preparation

To analyze the spatial relationship between landscape highpoints and CG strike locations by peak current, two geospatially referenced datasets were assembled in a GIS: (i) a mosaicked ⅓ arc sec, 10-m resolution U.S. Geological Survey (USGS) National Elevation Dataset (NED) DEM and (ii) U.S. Precision Lightning Network (USPLN) negative polarity CG strike locations with peak current values as attributes. The USPLN advertises strike location spatial accuracy of 250 m (USPLN 2010). The CG lightning data utilized in this study were collected continuously from February 2005 through May 2009. Rare (1.2% of sample) positive flashes were removed from the dataset because their ground attachment behavior varies from negative flashes (Berger and Vogelsanger 1969). Positive CG strikes often follow a horizontal trajectory through clear air before striking the ground several kilometers to 40 km (NOAA 2010) away from the parent storm (Carey et al. 2003). Known as “bolts from the blue” (Hodanish 1996), the tendency for positive CG flashes to travel great distances compromises the ability of ground sensors to determine x, y attachment location with the same accuracy as negative CG flashes.

Following a raster-based point extraction method developed by Wentz et al. (Wentz et al. 2001), 5118 topographic highpoint features were identified and mapped on the DEM (Figure 5). Highpoint mapping was achieved using a series of raster reclassifications with input parameters as follows: A highpoint must have at least 15 m of vertical gain in a 300-m-radius neighborhood and must contain a horizontal separation from other highpoints of at least 600 m. The vertical gain setting of 15 m was used to ensure that the lowest highpoints extend into a realistic rolling-sphere-intercepting striking distance. Also, an elevation gain value of 15 m created a total number of highpoints that roughly corresponds to the observed highpoint distribution of the study area (e.g., 5118 highpoints creates a highpoint, on average, every 3 km2 across the landscape).

The 5118 highpoints mapped in the previous step were not initially derived as true points. Rather, they were selected grid cells on a raster image. Thus, the first step in the buffer process involved converting the set of selected cells to discrete vector-based points whose location is the center of each highpoint cell. Around each highpoint (now a true point), 100-, 200-, and 300-m-radius buffers were created (Figures 6 and 7). The 300-m-radius (600-m diameter) buffers, which are 350 m larger than the documented 250-m mean location accuracy of the CG strike data (USPLN 2010), served as a catch-all container to test the notion that CG strikes concentrate near highpoints. The 200- and 100-m-radius buffer sizes, with their 400- and 200-m diameters, most closely matched the 250-m mean accuracy of the CG strike location data. Assuming CG strikes do indeed favor attachment to local highpoints, the smallest buffer size should show higher strike clustering than the larger two.

All CG strikes recorded in the study area between −20 and −119 kA were divided into 10 kiloamp classes in the following format: −20 to −29 kA, −30 to −39 kA, −40 to −49 kA, … , and −110 to −119 kA. The data were broken into exactly 10 sets for ease of data analysis and to ensure that the sample size of CG flashes and random numbers did not exceed the processing capacity of the computer hardware used for this study. All strikes were then summed by kiloamp class. Parsing, ordering, and summing CG strikes by peak current provided the necessary organization to explore the notion that a positive relationship exists between striking distance and peak current.

The last data preprocessing step placed random points across the entire study area. Using the totals for actual strikes in each kiloamp class, six sets of random points were mapped for each kiloamp class and for each buffer size (six sets of random numbers × 10 kiloamp classes × three buffer sizes). All 180 sets of random points were spatially constrained to fall within the precise coordinate boundaries of the study area. Comparing the sums of actual strikes (actual distribution) to randomly generated points (expected distribution) collected in the buffers served as the basis to confirm or reject the notion that CG strikes favor highpoints. These actual-to-random comparisons by buffer size and by kiloamp class served as the basis to evaluate the notion that a positive relationship exists between striking distance and peak current.

3.3. Data analysis techniques

Two types of data analyses were performed in this study: one descriptive and one statistical. The descriptive analysis graphically compared the percent of actual CG strikes that fell within the buffers to random points that fell within the buffers. This facilitated comparisons of actual versus random totals for all kiloamp classes and for all three buffer sizes. Results were expressed as percent changes between actual strikes and random points as captured in buffers. The second analysis, a Pearson’s chi-square goodness-of-fit test, quantified how the actual distribution of CG strikes in all kiloamp classes collected in the three buffer sizes at highpoints varied from the expected (random) distribution. The Pearson’s chi-square goodness-of-fit test was also used to examine the extent that highpoints attracted a larger percentage of CG strikes with higher peak currents given that striking distance increases as peak currents become more strongly negative.

4. Results

4.1. Descriptive results

The total strikes received in the study area for the duration of the study period were summed by kiloamp class (Table 1). From these values, change between (i) the percent of actual CG strikes captured in all buffer sizes and (ii) the percent of random points captured in buffers was calculated. With the exception of 3 of the 30 combinations of buffer size and kiloamp range [(i) 200-m buffer at −100 to −119 kA, (ii) 100-m buffer at −100 to −119 kA, and (iii) 100-m buffer at −80 to −89 kA], highpoint buffers captured more actual strikes than randomly generated point locations (Figure 8).

For all 10 kiloamp classes, an average of 2.6% more actual strikes than random points fell within 300-m buffers, 1.5% more actual strikes than random points fell within 200-m buffers, and 0.6% more actual strikes than random points fell within 100-m buffers. For the 300-m buffers only, percentages gradually increased from 1.25% at the −20- to −29-kA range up to 5.19% in the −80- to −89-kA range (Figure 8). Tracking from the small kiloamp classes to the largest shows a gradual increase in the difference between observed and randomized flashes. At the 100-kA level, this relationship begins to weaken. This trend confirms that, as the kiloamp increases, there is a greater attraction of CG flashes to highpoints, thus descriptively validating the positive peak current to striking distance relationship posited largely in controlled settings (Golde 1945; Wagner 1963; Rühling 1972; Love 1973; Eriksson 1974; Lee 1978; Mousa and Wehling 1993; Petrov and Waters 1995; D’Alessandro and Petrov 2006; Cooray et al. 2007) (Figures 8 and 9).

4.2. Statistical results

To more thoroughly characterize how well buffers capture distributions of random points compared to actual CG strikes, a statistical measure was utilized. A Pearson’s chi-square goodness-of-fit test compared expected number of random flashes collected in each of the 10 kiloamp classes to actual CG strikes for the three buffer sizes (Table 2). The null hypothesis is rejected when p values are less than or equal to 0.05. The test demonstrated that a nonrandom process is responsible for the clustering of strikes near highpoints in all three buffer sizes. All three buffer size classes had test statistics with p values less than 0.01 (Table 2). In each test, a series of 10 random flash counts were compared to the corresponding series of 10 observed flash counts.

The chi-square goodness-of-fit test was also applied to statistically confirm the relationship between striking distance and peak current (Table 3). Randomized distributions of flashes were compared to their actual strike totals in each of the 10 kiloamp classes for all three buffer sizes. Like the descriptive percentage-based analysis, the statistical test confirmed that the two highest kiloamp classes do not follow the same trend in terms of higher peak currents favoring highpoints more than weaker peak currents. These two classes—especially the highest class—revealed p values that were not significant (−110 to −119 kA: p = 0.47; −100 to −109 kA: p = 0.20). Unlike the descriptive percentage-based analysis that showed a general increase percent in strike concentrations with increased kiloamp, the statistical test identified two additional outliers: the −30- to −39-kA and −40- to −49-kA classes revealed p values of 0.25 and 0.97, respectively.

5. Discussion

This GIS analysis of lightning attachment patterns, one of the first conducted at landscape scales spanning kilometers and over a time period of several years, confirmed that CG lightning channels, as they zigzag randomly Earth bound (Rakov and Uman 2003, p. 378), are influenced when the channel enters the near-surface striking distance and makes changes in a direction for highpoint attachment. Despite the low percentage difference between CG strikes and random points captured in buffers (e.g., 2.49% in 300-m buffers to 1.47% in 200-m buffers to 0.56% in 100-m buffers), the difference between observed and randomized CG flashes was consistent across all kiloamp classes. Chi-square tests further validated this trend.

A positive relationship between peak current and striking distance was also documented. With the exception of the two highest kiloamp classes, a greater than expected number of flashes were attracted to highpoints in moving from a weaker to stronger kiloamp class. Chi-square tests to validate this were also supportive of this trend; however, there were some outliers. The arbitrary division of kiloamp classes may in part explain these departures, because the 10 kiloamp intervals for binning flashes do not necessarily have any meaning in the continuous-scale world. Other explanations for these departures may be a result of small sample sizes, polarity errors in raw data provided, or the presence of different attachment behavior processes in the highest kiloamp classes, as suggested in engineering-based studies.

Other factors to consider when viewing these results relate to the use of real-world data and surfaces. The distribution of flashes over the study area is responding to a heterogeneous forcing environment; thus, randomized distributions of flashes may not necessarily capture the contingencies of flash location arising from real-world thunderstorms and their flashes. Individual thunderstorms can vary significantly in their polarity structure, thus introducing variability in the types of flashes lowered to the ground. Nonetheless, these shortcomings are recognized as necessary when conducting field-based geographic research and, like the controlled engineering studies from which this GIS analysis builds, no single methodology or scale of analysis lacks its criticisms (Stallins and Rose 2008).

6. Conclusions and implications

For negative polarity CG lightning, this research examined patterns of CG attachment to topographic highpoints and explored the relationship between peak current and striking distance. Using a GIS, this work empirically documented CG attachment behavior to support extant studies of lightning attachment theory. Integration of spatial data was undertaken to illustrate how real-world surfaces and atmospheric processes can be configured to test standing assumptions about CG flash behavior derived from controlled settings. The basic tenets underlying the design of lighting protection systems—the concept of the striking distance and the rolling-sphere method—were shown valid over the larger spatial and temporal scales of the Colorado study area employed in this paper. Although these tenets have provided and will likely continue to provide the basis for authoritative lightning protection system design (ASABE 1988; USDA 2001; IEEE 2004; NFPA 2008), geographic approaches such as the one employed in this paper may be useful for extending the ideas that originate in engineering contexts. Exploring the attachment geography of hundreds of thousands of CG flashes confirmed anomalies related to attachment behavior of the highest kiloamp flashes. In an inductive sense, the GIS-based investigation presented could stimulate research questions that could be addressed using deductive, more traditional laboratory-based approaches. A geographic approach to the study of lightning may also be useful to identify how lightning safety standards could (and should) vary in different regions and at different times. There are not only seasonal differences in lightning but also weekly differences. Weekend and weekdays, for example, have been identified as having different lightning regimes because of air pollution attributed to automobile traffic volumes (Bell et al. 2008).

Integrating field-based analyses with theory and hypotheses obtained from controlled settings may be a productive means to extend our understanding of lightning attachment theory. Although a field-based geographic approach to lightning pattern and process may not provide direct insight into lightning physics, this paper shows how it can provide lightning scientists with an example of the real-world manifestation of their specialized research.

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Figure 1.
Figure 1.

Peak current vs striking distance. Relationship expressed on curve 1 is adapted from Golde (Golde 1945); curve 2 is from Wagner (Wagner 1963); curve 3 is from Love (Love 1973); curve 4 is from Rühling (Rühling 1972); and points x are from Davis (Davis 1962).

Citation: Earth Interactions 15, 8; 10.1175/2010EI357.1

Figure 2.
Figure 2.

Model of the RSM. The RSM defines zones into which CG lightning of certain kiloamp ranges should not strike.

Citation: Earth Interactions 15, 8; 10.1175/2010EI357.1

Figure 3.
Figure 3.

Study area within southeast and south-central Colorado.

Citation: Earth Interactions 15, 8; 10.1175/2010EI357.1

Figure 4.
Figure 4.

Negative polarity CG flash densities across study area for duration of study period.

Citation: Earth Interactions 15, 8; 10.1175/2010EI357.1

Figure 5.
Figure 5.

Section of USGS DEM showing sample locations of GIS-mapped highpoints.

Citation: Earth Interactions 15, 8; 10.1175/2010EI357.1

Figure 6.
Figure 6.

Sample of 100-, 200-, and 300-m-radius buffers around highpoints.

Citation: Earth Interactions 15, 8; 10.1175/2010EI357.1

Figure 7.
Figure 7.

Zoomed-in section of a set of concentric buffers showing GIS-mapped highpoint as red dot. Actual lightning strike locations are shown as black triangles.

Citation: Earth Interactions 15, 8; 10.1175/2010EI357.1

Figure 8.
Figure 8.

CG strikes by kiloamp and buffer size relativized as percents. Green bars above the x axis suggest that highpoint buffers capture more actual CG flashes than random points.

Citation: Earth Interactions 15, 8; 10.1175/2010EI357.1

Figure 9.
Figure 9.

Percent change of actual CG strikes over randomly generated points for 300-m buffer only. The gradually increasing trend from right to left trend ceases at the −100- to −109-kA class.

Citation: Earth Interactions 15, 8; 10.1175/2010EI357.1

Table 1.

Differences between the percent actual negative CG strikes received in buffers and the percent random points captured in buffers. Positive percentages indicate that highpoint buffers capture more actual strikes than randomly generated points. Combinations shown in italics show positive percentages or no change.

Table 1.
Table 2.

Pearson chi-square goodness-of-fit test statistics for each buffer distance. Each test represents a comparison of flash count totals derived from randomized data (n = 10) with the count totals derived from the actual observed flashes (n = 10).

Table 2.
Table 3.

Pearson chi-square goodness-of-fit test statistics for each of the 10 kiloamp classes. Each test represents a comparison of flash count totals derived from randomized data (n = 18; six count totals for each of the three buffer distances) with the count totals derived from the actual observed flashes (n = 18). With a few exceptions, these results corroborate the positive trend between peak current and striking distance evident in the count data (D’Alessandro and Petrov 2006; Cooray et al. 2007).

Table 3.
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