4.1. Optical Observations
 Analysis of recorded video included determination of upward leader initiation and end times as well as quantifying the beginning time and type (i.e., cloud or ground) of any nearby flash activity that preceded upward leader development. There were a total of 81 upward flashes observed over the 7 years of observations, and in all but one of the cases, there was visible brightness associated with nearby flash activity prior to initiation of the upward leader(s). Frequently, video showed a bright flash (cloud or ground) away from the towers followed by in-cloud brightening that propagated from the apparent flash origin toward the towers. As this in-cloud brightening passed near or over the towers, upward leaders would then initiate. This recurring observation suggests that leader development associated with preceding flashes (seen as horizontally propagating in-cloud brightening) created conditions favorable for upward leader initiation and development.
 The time from the first indication of in-cloud visual brightness increase to upward leader initiation was determined for those 80 flashes displaying this preceding activity. The resulting mean, GM, median, maximum and minimum time between the first visual sign of flash activity and upward leader initiation was 181 ms, 112 ms, 109 ms, 918 ms and less than 1 ms respectively. It is interesting to note that the maximum delay was almost an entire second. For the 37 cases (46%) in which there was a preceding visible ground stroke, the mean, GM, median, maximum and minimum time between the visible ground stroke and upward leader initiation was 50 ms, 32 ms, 36 ms, 267 ms and less than 1 ms respectively. Upward flash duration was determined from the first visible evidence of an upward leader until the last visible luminosity in the leader channel following either the initial upward leader development or subsequent return strokes if they occurred after initial upward leader decay. The mean, GM, median, maximum and minimum upward flash duration was 456 ms, 381 ms, 408 ms, 1934 ms and 21 ms respectively.Table 2 summarizes these measurements.
Table 2. Time Summary
|Time from incloud visual brightness to upward leader (uncertainty) (ms)||181 (25)||112 (28)||109 (34)||918 (51)||<1 (0.030)|
|Time from visual CG to upward leader (uncertainty) (ms)||50 (23)||32 (11)||36 (34)||267 (51)||<1 (0.030)|
|Upward flash duration (uncertainty) (ms)||456 (22)||381 (28)||408 (34)||1937 (68)||21 (0.030)|
|Time from preceding NLDN event to upward leader (uncertainty) (ms)||72 (11)||39 (7)||46 (17)||404 (34)||<1 (0.015)|
|Time from upward leader to first subsequent NLDN event (uncertainty) (ms)||324 (10)||271 (2)||256 (17)||745(34)||66 (0.015)|
|Time from upward leader to last subsequent NLDN event (uncertainty) (ms)||459 (10)||389 (2)||401 (17)||1741 (17)||111 (0.015)|
 Uncertainty in the time in which an event started or ended depended on the length of the exposure used in the camera that recorded the event. Since cameras operating at different speeds were used, the exposure times (and therefore the uncertainty) ranged from 34 ms to 0.015 ms. The mean and GM uncertainty values were as follows: time from visual brightness to upward leader (25 and 28 ms), time from visual CG to upward leader (23 and 11 ms), and upward leader duration (22 and 28 ms).
 Figure 4 shows the number of flashes each tower experienced along with a) the tower heights above ground level (AGL) and b) tower tip elevations above mean sea level (MSL). Tower 4 experienced the most upward flashes at 40 (49%). This tower extends to the highest elevation at 1341.4 m MSL as shown in Table 1, but is 6.1 m shorter in height than the tallest tower (Tower 6). The tip of Tower 6 is 18.0 m lower in elevation than Tower 4 and has experienced 26 upward flashes (32%). Interestingly, Tower 1's tip, which is lower in elevation than Tower 6 by 14.3 m and is lower in height by 27.7 m, has experienced 34 upward flashes (42%), which is 8 more than Tower 6. The ridge topography near Tower 1 has much steeper elevation change near the tower when compared to the other towers (see Figure 2). It is also isolated from the location grouping of Towers 2–6. Tower 1 may have an effective height [e.g., Eriksson, 1978; Pierce, 1971] that is greater than Tower 6 and there may be some shielding interaction among Towers 2–6 due to their close relative locations. Shielding from Tower 4 seems the likely cause for the low number of upward flashes for Tower 5. Even though Tower 5 is the third tallest in height and second tallest in elevation, it has only experienced one upward flash. Tower 4, which is 56 m away and 10.6 m taller in elevation than Tower 5, is likely acting as a protection tower for Tower 5. Furthermore, Tower 4 sits closer to the steeper west side of the ridge, which might result in greater field enhancement for Tower 4 relative to Tower 5 (see Figure 2b). A scatterplot of tower height and corresponding number of upward flashes is shown in Figure 5. This plot does not include Tower 5 due to the apparent shielding provided by Tower 4. A best fit trend line is a second order polynomial with an R2 value of 0.7371. Interestingly, the trend line goes to zero near a height of 100 m, which is consistent with previous studies that provide an expected minimum height for upward flashes [Eriksson, 1978; Rakov and Uman, 2003]. When Tower 5 is included in the data, the R2 value drops to 0.4728.
Figure 4. (a) Number of upward flashes by tower (left axis and top row) and tower heights in meters above ground level, AGL (right axis). (b) Number of upward flashes (left axis) and tower elevations in meters above mean sea level, MSL (right axis). After experiencing 3 upward flashes in 2004, Tower 9 was lowered to 54.9 m AGL (1200 m MSL) and experienced no upward flashes since.
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Figure 5. Number of upward flashes versus tower height (AGL). Tower 5 is removed since Tower 4 appears to shield it.
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 More than one tower initiated an upward leader during a flash in 37 cases (46%). Figure 6 shows the number of flashes involving more than one tower by the number of towers involved. The maximum number of towers that developed upward leaders during a single flash was seven. Figure 7shows how many times each tower participated in a multiple upward leader flash MULF, (i.e., a flash with upward leaders that develop from at least two towers). Analysis of high-speed camera observations from nine MULFs between 2008–2010 indicate that the multiple upward leaders initiated simultaneously or nearly simultaneously and were of the same polarity (i.e., positive). A detailed analysis of one MULF is given inWarner .
Figure 6. Histogram showing the number of upward flashes versus the number of towers with upward leaders during a flash.
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 Recoil leaders, which have been shown to be associated with positive leader development [e.g., Mazur, 2002; Saba et al., 2008], were identified optically in 73 (90%) of the upward flashes suggesting that UPLs developed in those cases. This high percentage of upward leader positive polarity is consistent with previous observations [e.g., Berger, 1967; Diendorfer et al., 2009]. Furthermore, upward leaders in the remaining 10% of the flashes did not exhibit optical characteristics of negative leaders (e.g., erratic leader tip directional change, localized branching and sustained stepping) suggesting they too were positive polarity.
4.2. NLDN Comparison
 Once the optical characteristics were quantified, a comparison with NLDN data was made. NLDN data included both cloud events and cloud-to-ground (CG) strokes within a 200 km radius of the towers. For each upward flash, NLDN-indicated events from 2 s prior to 3 s after the upward leader initiation time were identified and plotted relative to the tower locations. The resulting NLDN events were then correlated with standard- and high-speed video to specifically identify those that appeared to be associated with the upward flashes. This process resulted in the identification of 67 of the 81 upward flash cases (83%) in which a flash with a correlated NLDN event preceded upward leader development from the towers. A preceding positive cloud-to-ground stroke (+CG) was detected in 57% (46/81) of the cases, and a preceding positive intracloud event (+IC) in 23% (19/81) of the cases. However, 8 of the 19 NLDN-indicated +IC events were actually +CG strokes based on optical observations. A preceding negative intracloud event (−IC) was recorded for 2% (2/81) of the cases. All but one video-validated preceding CG stroke had a corresponding NLDN report. For the 14 cases (17%) in which there was no preceding NLDN-indicated event, optical evidence showed there was preceding flash activity in all but one case. In one of these 14 cases, there was a non-detected CG stroke observed by a standard-speed camera, however the polarity could not be determined from the optical assets.
 Figure 8shows a plot of the preceding NLDN-indicated events relative to the towers. +CGs are indicated as a red circle, +ICs as a light red circle and −ICs as a light blue triangle. The 8 misclassified +ICs, which were +CG strokes based on optical evidence, are shown as +CGs in the plot. The symbol size is proportional to the estimated peak current as shown in the legend. The mean distance of these NLDN-indicated events from the closest participating tower was 17.5 km and the GM, median, maximum and minimum distance was 14.7 km, 14.8 km, 50.5 km and 3.5 km respectively. The mean time between the preceding NLDN-indicated event and upward leader initiation was 72 ms with the GM, median, maximum and minimum being 39 ms, 46 ms, 404 ms and less than 1 ms respectively (seeTable 2). Table 3summarizes the estimated peak current and distance parameters for each type of NLDN-indicated preceding event. Distances are from the nearest tower that developed an upward leader.
Figure 8. Plot of NLDN-indicated events relative to the towers. Dark and light blue triangles clustered near the towers were subsequent events and all others were preceding events.
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Table 3. NLDN Event Summary (Optically Adjusted)
|Peak Current (kA)|
|Peak Current (kA)|
 A subjective look at the distribution of preceding events does suggest events are grouped to the east and southeast of the towers with a more widely spaced distribution to the north and west. However, an objective evaluation of the distribution pattern would require a correlated analysis with weather data to determine the storm characteristics (e.g., type, coverage and movement) present during the upward flashes. This analysis is beyond the scope of this paper but is ongoing and will be reported in the future.
 There were no NLDN-indicated events that coincided with initial upward leader development. This is not surprising since the current associated with initial upward leader development rises slowly compared to that of the impulsive dart leader/return stroke processes that the NLDN is optimized to detect [Cummins and Murphy, 2009; Cummins et al., 1998]. However, there were a total of 151 negative cloud-to-ground strokes (−CGs) and negative cloud events (−ICs) recorded at the tower locations after initial upward leader formation. These subsequent events, as they will be referred to here, were present in 36 (44%) of the upward flashes.
 The process of determining subsequent NLDN events first involved identifying those detections that occurred within the duration of the optical observations, and second, those that were also located within 1 km of a tower that developed an upward leader. For those flashes observed with high-speed cameras, the subsequent events were further correlated with the higher time-resolved optical observations. The high-speed video analysis showed that these subsequent events were detections resulting from either 1) the connection of a recoil leader, which formed on a cutoff UPL branch, with a main luminous upward channel at the branch point or the tower tip when the main upward channel was weakly luminous or 2) a dart leader connection with the tip of a tower after complete current cutoff.
 Figure 8shows a plot of the NLDN-indicated subsequent events relative to the towers. All the subsequent events are clustered around the 10 towers as identified by the dark blue triangles (−CG) or light blue triangles (−IC). There were 105 −CG and 46 −IC events recorded representing 70% and 30% of the 151 respectively. Since the subsequent events involve known locations (i.e., the towers), an evaluation of the NLDN location accuracy was possible. The mean, GM, median, maximum and minimum distances for all the subsequent events were found to be 246 m, 194 m, 206 m, 2280 m, and 7 m respectively. Notice that the maximum distance (2.28 km) was greater than the 1 km used in selecting subsequent events. There was a single subsequent event that was clearly correlated with high-speed video and so this was included in the location accuracy calculations. All other subsequent events fell within 1 km of the towers.Table 3summarizes the estimated peak current and distance parameters for each type of NLDN-indicated subsequent event. Distances are from the tower that developed the upward leader.
 The results from statistical analysis in the NLDN-indicated subsequent event occurrence times relative to upward leader initiation is given inTable 2. The mean and GM time delay between upward leader initiation and the first NLDN-indicated subsequent event was 324 ms and 271 ms respectively with the shortest differential being 66 ms. The mean and GM delay between upward leader initiation and the last NDLN-indicated subsequent event was 459 ms and 389 ms respectively. The longest time differential was 1.741 s.
 An NLDN-indicated event density analysis was made to determine if there was enhanced event density near the tower locations due to the upward flashes. Given that the mean distance of the subsequent events was 246 m, the NLDN-indicated events that fell within a 500 m radius of each of the towers during the seven summer storm seasons (Apr–Sep, 2004–2010) were identified and used to determine an annualized number of events/km2/summer season. The density was calculated for all of the 500 m radii cumulatively and for Tower 1's radius individually as this radius did not intersect with any of the other towers' radii. Figure 9shows the tower relative locations and 500 m radius circles. For comparison, NLDN-indicated events that fell within a 10 km radius of Tower 6 but outside of the cumulative 500 m radii around the towers were also identified. The number of events/km2/summer season was determined for this area as well and is considered representative of the event density not influenced by upward lightning from the towers [e.g., Diendorfer and Schulz, 1998].
Figure 9. Layout showing the areas used for event density calculations. Light red area is 500 m radius of each tower. Light green area is 10 km radius of Tower 6, not including the 500 m radii around the towers (light red area).
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 Figure 10 shows the annualized density of all events as well as individual event categories for a 500 m radius around Tower 1, a cumulative 500 m radii around all the towers and a 10 km radius around Tower 6 (not including the cumulative 500 m radii around all the towers). The positive polarity event density did not show a statistically significant difference between the three selected areas. However, the negative polarity event density was significantly higher in the Tower 1 500 m radius area as well as the cumulative 500 m radii area around all the towers. Specifically, the −CG density in the Tower 1 500 m radius area was 4.9 times greater than the exclusive 10 km radius area around Tower 6, and the −IC density was 14.4 times greater. The −CG density in the cumulative 500 m radii around all the towers was 2.8 times greater than the exclusive 10 km radius area around Tower 6, and the −IC density was 6.5 times greater. Based on this analysis, the subsequent events resulting from the upward flashes clearly enhanced the event density (specifically the negative event density) near the towers.
Figure 10. Event density (number of NLDN-indicated events per km2 per summer) versus event category. Black shaded is for 500 m radius area around Tower 1 only. White shaded area is for cumulative 500 m radii around all towers. Gray shaded area is for 10 km radius area around Tower 6, not including cumulative 500 m radius around towers.
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 A total number of +CG and −CG NLDN-indicated strokes for a 50 km radius of Tower 6 for the entire observation period was determined for comparison. There were 20500 +CG strokes and 280895 −CG strokes. The −CG to +CG stroke ratio was 13.7 to 1 and the percentage of +CG strokes to the total number of CG strokes was 7%. With 54 of the 81 upward flashes preceded by +CG strokes, the percentage of triggering +CGs within 50 km for the entire observation period is only 0.29% for all +CGs and 0.0008% for all CGs.
 Interestingly, there were no upward flashes associated with preceding −CG return strokes. Zhou et al. reported that one of 26 observed lightning-triggered upward flashes was preceded by a negative ground flash. Although the development of upward positive leaders following positive triggering flashes appears significantly more common than upward negative leaders following negative triggering flashes (e.g., this study andZhou et al. ), it is unclear why there have been no observed triggered upward negative leader cases in Rapid City. One possibility, based on visual observation, is that negative ground flashes tend to lack the horizontally extensive leader development frequently seen with positive flashes. Negative flashes also tend to occur in the convective core of mesoscale convection systems whereas positive flashes are frequently seen in the trailing stratiform precipitation area, which has been shown to contain horizontally stratified charge layers favorable for horizontally extensive flashes [e.g., Lang et al., 2010].