VIII International Symposium on Lightning Protection 21st-25th November 2005 – São Paulo, Brazil
EVALUATION OF THE PERFORMANCE CHARACTERISTICS OF LIGHTNING LOCATING SYSTEMS USING ROCKET-TRIGGERED LIGHTNING Vladimir A. Rakov Department of Electrical and Computer Engineering, University of Florida 553 Engineering Building #33, PO Box 116130, Gainesville, FL 32611-6130, USA
[email protected] Abstract – In this lecture, two studies aimed at evaluation of the performance characteristics of lightning locating systems using rocket-triggered lightning are reviewed. Both studies were conducted in the United States and the tested lightning locating system was the U.S. National Lightning Detection Network (NLDN) or its predecessor. The first study (1985-1991; Orville [1991], Idone et al. [1993]) involved data from rocket-triggered lightning experiments at the NASA Kennedy Space Center (KSC) and the second one (2001-2003; Jerauld et al. [2004, 2005]) data from similar experiments at the International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, Florida. From the latter study, the NLDN in Florida is characterized by flash and stroke detection efficiencies of about 84% and 60%, respectively (probably lower bounds, since triggered-lightning strokes are similar to subsequent strokes in natural lightning, and the natural-lightning first strokes typically have larger peak currents than subsequent strokes). Median location error is about 600 m, with larger location errors (greater than 2 km) being associated with strokes having smaller peak currents (5-10 kA). The NLDN in 2001-2003 had been found to underestimate peak currents by about 18% (median value), but this error was apparently reduced due to a recent change, from power-law to “exponential”, of the assumed distance dependence of signal strength (propagation model) [Cummins et al. 2004] that is used in computing the range-normalized signal strength (RNSS). The field-to-current conversion equation, I = 0.185 RNSS (where I is the peak current in kiloamperes, and the field is represented by the RNSS in LLP units), that is presently employed by the NLDN, is based on the 1985-1991 KSC study and has been the same since 1996.
1 INTRODUCTION Locating lightning discharges with reasonable accuracy requires the use of multiple-station networks. Such networks are currently operating in nearly 40 countries on all continents except Antarctica, including, for example, USA, Canada, many European countries, Japan, and Brazil. The Canadian Lightning Detection Network (CLDN) and the U.S. National Lightning Detection Network (NLDN) have been combined since 1998, and the resultant North American Lightning Detection Network (NALDN) employs 187 sensors and monitors 20 million square kilometers [Cummins 2000]. A bibliography on real-time lightning detection networks worldwide, including networks instrumentation, applications of lightning data, and network performance, is maintained on the Web (http://www.nssl.noaa.gov/users/holle/public_html/) by R.L. Holle. In addition to locating individual lightning strokes, lightning locating systems (LLS) can group strokes into flashes and determine polarity and a peak current estimate for each stroke, using the measured electric and magnetic radiation field peaks. The proper interpretation of LLS’s output requires knowledge of system’s performance characteristics, such as flash detection efficiency, stroke detection efficiency, location accuracy, and errors in peak current estimates. Although theoretical models can be used to evaluate the LLS performance characteristics, ultimately ground-truth data are needed to verify model-predicted results. Such data should include the measured time, position, and peak current of lightning discharges in a region covered by LLS and can be obtained using instrumented towers or rocket-triggered lightning. Only the use of rocket-triggered lightning will be discussed in this lecture. Section 2 contains the results of calibration of the NLDN (or its predecessor before 1989) using rocket-triggered lightning data obtained at the NASA Kennedy Space Center (KSC), Florida, in 1985-1988 [Orville, 1991] and in 19851991 [Idone et al. 1993]. A total of 18 strokes in 18 flashes were analyzed by Orville and 57 strokes in 36 flashes by Idone et al. Section 3 covers the results of recent joint University of Florida/Vaisala study, presented by Jerauld et al. [2004, 2005]. In the latter project, the performance characteristics of the NLDN were evaluated using rocket-triggered lightning data acquired in the summers of 2001-2003 at the International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, Florida. A total of 159 strokes in 37 flashes were analyzed. Directly measured currents were obtained for 122 strokes in 29 flashes.
2 TRIGGERED-LIGHTNING EXPERIMENTS AT KSC, FLORIDA (1985-1991) Triggered-lightning data from KSC were used specifically for evaluating the field-to-current conversion equation, I = 0.2 RNSS
(1)
where I is the current in kA, and RNSS is the range-normalized (to 100 km) signal strength in so-called LLP units. Initial results were presented by Orville [1991]. These have been reexamined, based on a larger data set, by Idone et al. [1993]. Equation (1) was employed by the NLDN until 1993 [Cummins et al. 1996]. The 0.2 conversion factor was obtained by Orville et al. [1987] by equating the observed median value of RNSS, based on reports of the SUNYA network (predecessor of the NLDN) in 1984-1985, to the median peak current of 30 kA direclty-measured in Switzerland by Berger et al. [1975]. Evaluation of flash or stroke detection efficiency, or of location accuracy were not stated as objectives of the studies conducted by Orville [1991] and Idone et al. [1993]. Before presenting results of testing the validity of equation (1) we briefly review the concept of estimating lightning currents from measured fields (that is, the concept of “remote” lightning current measurements) and its implementation in the NLDN. There have been many attempts to infer lightning currents from remotely measured electric and magnetic fields [e.g., Norinder and Dahle 1945; Uman and McLain 1970b; Uman et al. 1973a,b; Dulzon and Rakov 1980; Krider et al. 1996]. For example, Krider et al. [1996], using measured electric field derivatives and the simple transmission line model [Uman and McLain 1969], inferred the average values of the peak of the dI/dt waveform and its duration at half-peak value for first return strokes to be 115 kA/ s and 75 ns, respectively. Such "remote" measurements are model dependent and, therefore, inferior to direct measurements. However, triggered-lightning studies indicate that a reasonable estimate of the subsequent return-stroke peak current I can be obtained from the electric field E measured at a distance D using the following regression equation [Rakov et al. 1992]. I = 1.5 - 0.037 x E x D
(2)
where I is in kA and taken as negative, E is positive and in V/m, and D is in km. Triggered-lightning data (28 events) used to derive equation (2) were obtained by Willett et al. [1989], and the range of peak field values was from 1.9 to 11 V/m (normalized to 100 km). For 18 out of 28 strokes used to derive equation (2) the two-dimensional return-stroke speed, averaged over 457-625 m, was measured and found to vary in a relatively narrow range, from 1.2 x 108 to 1.9 x 108 m/s with a mean value about 1.5 x 108 m/s. The NLDN outputs a peak current estimate for each stroke using the measured magnetic radiation field peaks and distances to the ground strike point. As noted above, equation (1) was used until 1993 to translate peak radiation field to current. This formula may be viewed as equivalent to the following equation derived for the transmission line model [Uman and McLain 1969] of the lightning return stroke.
I (0, t − D c) =
2π cD B ( D, t ) µo v
(3)
where B is the magnetic radiation field at ground at a distance D from the lightning channel base, o = 4 x 10-7 H/m is the permeability of free space, v is the return-stroke propagation speed, and c is the speed of light (3 x 108 m/s) . Note that v in equation (3) is not measured by the NLDN (or by any other LLS) and varies from stroke to stroke up to an order of magnitude [e.g., Rakov 2004], while equation (1) implies that v is the same for all lightning strokes. In 1985-1991, the testing period of Orville [1991] and Idone et al. [1993], all NLDN (or its predecessor) sensors were magnetic direction finders. Six direction finders, whose locations are shown in Fig. 1, responded to triggered-lightning strokes at KSC, one in Georgia and five in Florida. All strokes analyzed lowered negative charge to ground. The range of variation of currents directly measured at KSC (stated measurement error of 10%) was 7 to 60 kA. Scatter plot of directly measured current versus RNSS for 18 strokes analyzed by Orville [1991] is shown in Fig. 2. The corresponding linear regression equation has an intercept of 2.3 kA and a slope of 0.19 kA/(LLP units). Peak currents predicted by this regression equation differ from those predicted by equation (1) by typically less than 6%. If the intercept is ignored, then the regression equation becomes essentially identical to equation (1). Orville [1991] also examined the signal strength reported by individual direction finders as a function of distance from the lightning channel for seven strokes. Assuming the power-law dependence, he found the mean exponent to be -1.13, with the range of variation being from -0.96 to 1.20. Distance dependence of the signal strength for one of these strokes is shown in Fig. 3.
Figure 1. Map showing the locations of six direction finders, data from which were used in studies of Orville [1991] and Idone et al. [1993]. One direction finder was located in Georgia, Sa (Savannah), and the remaining five were in Florida, Qu (Quincy), Jk (Jacksonville), LA (Lake Alfred), FP (Fort Pierce), and Im (Immokalee). Also shown is the location of lightning triggering site, labeled “Trig”, at the NASA Kennedy Space Center. Four dotted circles show distances, 100, 200, 300, and 400 km, from the triggering site. Adapted from Orville [1991].
Figure 2. Directly measured peak current (labeled “French Current Measurement”) versus mean range normalized signal strength (RNSS, labeled “Normalized Amplitude”) for 18 strokes analyzed by Orville [1991]. Also given are the linear regression equation for the directly measured current (y) vs. RNSS (x), correlation coefficient (R) and standard deviation, (s, in kA), relative to the shown regression line. Adapted from Orville [1991]. Additionally, the results presented by Orville (1991) can be used to estimate the (subsequent) stroke detection efficiency. The total number of strokes in the 18 triggered-lightning flashes was 92, 40 of which were recorded by the network (only
for 18 of them peak currents were reported by the network). Thus, the stroke detection efficiency is 40/92 = 0.43 (43%), which is consistent with the estimate, 40%, obtained for Florida by Rakov and Huffines [2003], who used stroke counts in 1995-2001 NLDN data and ground-truth electric field and optical observations found in the literature, assuming the same detection efficiency for first and subsequent strokes. Idone et al. [1993] extended the analysis of Orville [1991] including additional KSC triggered-lightning strokes (up to a total of 57 in 36 flashes triggered during 1985-1991). Data from the same six direction finders (see Fig. 1) were used, although since June of 1989 they reported signal strength measurements for each detected stroke, as opposed to the first detected stroke only in Orville’s [1991] study. All strokes analyzed lowered negative charge to ground, similar to the study of Orville [1991]. Further, Idone et al. [1993] corrected the distance to the Jacksonville (Jk, see Fig. 1) direction finder. This distance is 220 km, not 197 km as cited by Orville [1991], although this correction causes a change of typically as small as a few percent in the RNSS. Exponents in the distance dependence of signal strength for two out of seven events analyzed by Orville [1991] (including that shown in Fig. 3) after the correction remain the same, and exponents for the other five events changed by less than 15%. The range of variation of directly measured peak currents was the same as in Orville’s [1991] study, 7 to 60 kA, although one event having a peak current of 3.4 kA was excluded from the analysis as “an obvious outlier”. After this exclusion the sample size reduced from 57 to 56.
Figure 3. Signal strengths (labeled “Amplitude”) reported by five direction finders, LA, FP, Jk, Im, and Sa (see Fig. 1), versus distance (labeled “Range”) from the lightning channel for Flash 8620, Stroke 1. Also given are the exponent (labeled “b”) of the shown best-fit power law curve and correlation coefficient, R. Adapted from Orville [1991].
A scatter plot of directly measured current versus RNSS for the 56 strokes is shown in Fig. 4. The corresponding linear regression equation (for all data combined) has an intercept of 4.20 kA and a slope of 0.171 kA/(LLP units). In this analysis, similar to that of Orville [1991], the RNSS was obtained assuming the inverse distance dependence (D-1), which ignores any signal attenuation due to propagation over lossy ground. Idone et al. [1993] also examined the signal strength reported by individual direction finders as a function of distance from the lightning channel for 12 strokes (7 of which were the same as those analyzed by Orville [1991], but with the distance to the Jk direction finder corrected). Both power-law, D- , and “exponential”, D-1exp(- D), distance dependences were considered. For the power-law distance dependence the mean exponent value was found to be -1.09 with the range of variation from -0.82 to -1.34. The maximum linear correlation coefficient (although its range of variation was rather small) between the directly measured current and RNSS was achieved for = -1.13, which is equal to the mean value of reported by Orville [1991]. The corresponding regression equation is as follows: I = 5.20 + 0.148 RNSS.
(4)
Figure 4. Directly measured peak curent versus mean RNSS (labeled “Mean Normalized Magnetic Signal Strength”) for 56 strokes analyzed by Idone et al. [1993]. The total data set is segregated into two subsets, 1985-1988 (21 points, asterisks) and 1989-1991 (35 points, squares). The regression lines for the total data set (solid line) and for the 1985-1988 data set (dash-dot line) are shown. The regression line for the 1989-1991 data set is not shown since it is nearly identical to that for the total data set. Regression parameters for the three data sets are given in the upper left. The two parallel dashed lines represent the standard deviation of the directly measured peak current values about the regression line for the total data set. Adapted from Idone et al. [1993].
For the “exponential” distance dependence, values of between (1/400) km-1 and (1/2000) km-1 were considered with = (1/1050) km-1 resulting in the maximum linear correlation coefficient between the directly measured peak current and RNSS. The corresponding regression equation is as follows: I = 5.90 + 0.140 RNSS.
(5)
In 1993, Global Atmospherics, the operator of the NLDN at that time, has adopted the power-law dependence of signal strength on distance with = -1.13 and equation (4) for evaluating peak currents by the NLDN [Cummins et al. 1996]. Note that the RNSS is averaged over all sensors that reported the event within 625 km, in order to minimize errors in polarity identification due to ionospheric reflections. Beginning on May 1, 1996, a modification of equation (4), which is based on the same data of Idone et al. [1993] but with the intercept forced to be zero (in order to satisfy the condition that zero current corresponds to zero field) has been implemented in the NLDN, I = 0.185 RNSS.
(6)
Note that equation (6) is not much different from the original equation (1). Forcing the intercept (5.2 kA in the original equation (4)) to be zero changed the slope from the original 0.148 to 0.185 kA/LLP units, this change introducing an error with respect to the original, best-fit equation. Idone et al. [1993] stated that the 95% confidence bounds for peak current prediction in the mean (using the regression equation with an intercept of 4.20 kA and a slope of 0.171 kA/(LLP units)) suggested a percent uncertainty of 10-15% for peak currents between 15 and 60 kA. Below 15 kA, the percent uncertainty rapidly increased suggesting that it is
unlikely that an accurate evaluation of the distribution of lightning peak currents below about 15 kA can be obtained from the NLDN data. No "ground truth" data for the NLDN current estimates exist for (1) first strokes in natural lightning, (2) natural positive strokes, or (3) triggered lightning peak currents exceeding 60 kA, triggered-lightning strokes being probably representative of natural subsequent strokes. It follows that the NLDN current estimates should be viewed with caution for strokes other than negative subsequent strokes. 3 TRIGGERED-LIGHTNING EXPERIMENTS AT CAMP BLANDING, FLORIDA (2001-2003) In 2001-2003, some of the NLDN sensors were of the time-of-arrival type (LPATS), while others used a combined timeof-arrival/magnetic direction finding technology (IMPACT). Lightning was triggered at the International Center for Lightning Research and Testing at Camp Blanding, Florida [e.g., Rakov 1999; Rakov et al. 2005]. A map showing the locations of NLDN sensors (as of late 2003) responding to triggered-lightning flashes at Camp Blanding is found in Figure 5. During the evaluation period (2001-2003), a network-wide upgrade was under way and was near completion at the end of 2003. A detailed discussion of the NLDN upgrade is found in Cramer et al. [2004] and Cummins et al. [2004]. A summary of this upgrade for the Florida region is presented in Table 1. The year of 2003 was essentially post-upgrade.
Figure 5. Map showing the locations of NLDN sensors, data from which were used in the study of Jerauld et al. [2004, 2005]. Also shown is the location of lightning triggering site, labeled “Camp Blanding”. Sensor type, its distance from Camp Blanding, and other pertinent information are given in Table 1. Adapted from Jerauld et al. [2005].
Table 1. The NLDN configuration in and around the Florida region for the Camp Blanding triggering seasons in 2001-2003. The sensor locations given here correspond to those shown in Figure 5 (except for Jackson, Rockwood, and Russellville). 2001 NLDN Sensor Distance from 2002 2003 Location Camp 20 July – 18 August 2001 9 July – 13 September 2002 30 June – 15 August 2003 Blanding, km Marion Junction, AL 571 LPATS IV LPATS IV / IMPACT-ESPa IMPACT-ESP Homestead, FL 517 IMPACT IMPACT-ESP IMPACT-ESP Naples, FL 422 LPATS IV LPATS IV IMPACT-ESP Ocala, FL 89 IMPACT IMPACT-ESP IMPACT-ESP Palm Bay, FL 257 IMPACT IMPACT-ESP IMPACT-ESP Quincy, FL 256 LPATS IV LPATS IV Tampa, FL 227 LPATS IV LPATS IV LPATS IVb Wakulla, FL 228 IMPACT-ESP Beckham Farms, GA 424 IMPACT IMPACT Bledsoe Farms, GA 426 IMPACT-ESP Savanna, GA 255 LPATS IV LPATS IV IMPACT-ESP Lenoir, NC 660 IMPACT IMPACT IMPACT-ESP Greenwood, SC 481 IMPACT IMPACT IMPACT-ESP Myrtle Beach, SC 533 LPATS IV LPATS IV IMPACT-ESP a Sensor was upgraded on 28 August 2002, during the Camp Blanding lightning triggering season. b Sensor was upgraded and moved to a nearby location in November 2003, after the Camp Blanding lightning triggering season.
The time-correlated Camp Blanding and NLDN events were examined to determine the following NLDN performance characteristics: (1) flash detection efficiency, (2) stroke detection efficiency, (3) location accuracy, and (4) errors in peak current estimates. These characteristics were evaluated for each of the three evaluation years (2001, 2002, and 2003), as well as for all data combined. During the three-year period, 37 flashes, containing a total of 159 (158 negative and 1 positive) strokes, were triggered at Camp Blanding. Of these 37, 36 were classically triggered and one flash (containing 4 strokes) was the result of an unintentional altitude (ungrounded wire) trigger. The average number of strokes per flash was 4.3. Directly measured currents were obtained for 122 of the 159 strokes in 29 flashes. The NLDN recorded 95 Camp Blanding strokes in 31 flashes. Of these 95, directly-measured currents were obtained for 70 strokes in 22 flashes. Camp Blanding return-stroke current waveforms were recorded on high-bandwidth (5 or 12 MHz -3 dB upper-frequency response) LeCroy digitizers and low-bandwidth (500 kHz -3dB upper-frequency response) Yokogawa digitizers, the latter of which acquired continuous, full-flash records. For some flashes, only Yokogawa data were obtained, and for a few flashes, only LeCroy data were obtained. When only one type of record existed, that value of peak current was taken as the ground-truth for comparison with the NLDN estimate. When both types of records existed, the two peak current values (which usually agree very well) were averaged. The justification for this is based on the fact that while the 12-bit Yokogawa digitizer may somewhat underestimate the peak current (due to the limited bandwidth), the signal-tonoise ratio of the 8-bit LeCroy digitizer often yielded an overestimate of the peak due to the inclusion of bit noise. To establish a correlation between Camp Blanding and NLDN events, the time-stamps on each event were compared. The Camp Blanding system is capable of recording GPS (Global Positioning System) times, having about 1 µs accuracy, for individual strokes, although times are typically only recorded for strokes having peak currents exceeding the trigger threshold of the LeCroy digitizers that triggered on individual strokes. When GPS timing was not available for individual strokes within a flash, interstroke interval timing was used to calculate the stroke times. The Yokogawa digitizers recorded full-flash current waveforms, and interstroke intervals could be determined with about 1 µs accuracy. Interstroke interval timing was also extracted from the LeCroy records, which were much more precise, but not available
for all strokes. For flashes with Camp Blanding GPS timing, the search scope in the NLDN database was usually limited to within one second of the Camp Blanding time and within a 20 km radius of the launcher. If a stroke was not found, the radius was expanded. In the few cases when Camp Blanding GPS timing was not available for an entire flash, the approximate flash time (usually taken from video records), in conjunction with interstroke intervals, was used to search the NLDN records, although the scope of the search was increased to within 2-3 seconds of the Camp Blanding time. In general, the Camp Blanding and NLDN times differed by only a few microseconds, although timing differences could be as high as some tens of microseconds, especially for strokes with relatively high location errors. Since the NLDN stroke times are determined from the stroke location algorithm (i.e., they are part of the stroke location solution), a relatively large location error typically results in a relatively large NLDN timing uncertainty. Once correlated strokes were identified, detection efficiency values were computed as ratios of the numbers of NLDN-detected events and all triggered-lightning events. Location accuracy was evaluated for all events reported by the NLDN. The location of the rocket launcher was taken as the ground strike point (except in the case of the altitude trigger, where the ground strike point was approximately 50 m from the launcher) and that position (accurate within a few meters) was compared with the NLDN-reported location, which corresponds to the centroid of the NLDN error ellipse. For a given stroke, the distance between these two locations was defined to be the stroke location error. The location errors were compared to the semi-major axis lengths of the corresponding NLDN 50% error ellipses as well as to the stated median location accuracy of the NLDN in the region. In addition to the absolute magnitude of the location error, the individual components (north-south and eastwest) of the location error were also examined. 3.1. Flash and stroke detection efficiencies Table 2 gives the number of Camp Blanding flashes and strokes detected by the NLDN for each of the summers of 20012003, along with data for all three years combined. Since all classically-triggered flashes contain only strokes similar to subsequent strokes in natural negative downward lightning (i.e. contain no first strokes), the flash detection efficiency reported here is likely to be an underestimate of the true value for natural negative lightning flashes in Florida, since first strokes typically have larger peak currents than subsequent ones and thus should be associated with higher detection efficiency. However, the stroke detection efficiency reported here is probably representative of the true subsequent stroke detection efficiency for natural lightning in Florida (but not necessarily overall stroke detection efficiency). Also, the flash and stroke detection efficiencies reported here may be applicable to upward lightning (containing return strokes) initiated from tall objects, since upward flashes are thought to be similar to classically-triggered flashes [Miki et al., 2005]. Table 2. Summary of flashes and strokes recorded at Camp Blanding during the summers of 2001-2003, along with the corresponding NLDN detection efficiencies. Note that flashes consisting of the initial stage only (having no return strokes) were not considered in this study. Year Number of Number of NLDN Flash Number of Number of NLDN NLDN Stroke Flashes NLDN Detection Strokes Detected Strokes Detection Efficiencya a Triggered Detected Efficiency Flashes 2001 11 9 82% 33 17 52% 2002 14 12 86% 77 44 57% 2003 12 10 83% 49b 34 69% 2001-2003 37 31 84% 159b 95 60% a The NLDN flash and stroke detection efficiencies for natural downward lightning are expected to be higher due to the presence of first strokes that typically have higher peak currents than subsequent strokes. b Includes one +5 kA positive stroke which was not detected by the NLDN.
As shown in Table 2, the flash detection efficiency was 82% (9 out of 11) in 2001, 86% (12 out of 14) in 2002, and 83% (10 out of 12) in 2003, with an overall flash detection efficiency of 84% (31 out of 37) for the 3-year period. The flash detection efficiency appears to be more or less constant over the 3-year period, and is consistent with the expected flash detection efficiency of 80% to 90% estimated by Cummins et al. [1998]. The observed (subsequent) stroke detection efficiency was 52% (17 out of 33) in 2001, 57% (44 out of 77) in 2002, and 69% (34 out of 49) in 2003, with an overall (subsequent) stroke detection efficiency of 60% (95 out of 159) for the 3year period. The 2003 and 2001-2003 data include the one +5 kA positive stroke noted above, which was not detected
by the NLDN; omitting this event results in a slightly higher stroke detection efficiency for 2003 (34 out of 48, or about 71%) and virtually no change in the overall 2001-2003 stroke detection efficiency. The expected pre-upgrade stroke detection efficiency, according to Cummins et al. [1998], is about 50%, which is consistent with the value observed for 2001. The mean stroke multiplicity at Camp Blanding (defined as the total number of strokes divided by the number of flashes triggered) was about 3.0 in 2001, 5.5 in 2002, and 4.1 in 2003, with a combined 3-year average stroke multiplicity of about 4.3. This latter value is close to the average number of strokes per flash, 4.6, reported for natural lightning in Florida by Rakov et al. [1994]. The smallest Camp Blanding stroke multiplicity was 1 and the largest was 17, which is the largest value recorded at Camp Blanding to date. The corresponding mean NLDN stroke multiplicity (defined as the total number of strokes detected divided by the total number of flashes detected) was approximately 1.9 in 2001, 3.7 in 2002, and 3.4 in 2003, with a 3-year average stroke multiplicity of about 3.1. Cummins et al. [1998] report average NLDN stroke multiplicities (for natural lightning), measured over a 2-year period, ranging from 1.9 to 2.1 (2.37 for Florida in 1995-2001 according to Rakov and Huffines, 2003), which is consistent with the value observed for 2001. However, in 2002 and 2003, the average stroke multiplicity almost doubles, and this is likely related to the observed increase in stroke detection efficiency for those 2 years.
Figure 6. NLDN stroke detection efficiency as a function of peak current measured at Camp Blanding. For each peak current range (bin size of 5 kA), the ratio given inside the column indicates the number of strokes detected by the NLDN (numerator) and the number of strokes recorded at Camp Blanding (denominator), for that peak current range. The total number of strokes whose currents were measured at Camp Blanding is 122, of which 70 were detected by the NLDN. Adapted from Jerauld et al. [2005].
Figure 6 gives the NLDN stroke detection efficiency as a function of peak current measured at Camp Blanding. Note that strokes for which no directly measured currents were obtained are not included, hence reducing the total number of strokes recorded at Camp Blanding in Figure 6 to 122, although some of these strokes without measured currents may have been detected by the NLDN. Since the strokes for which no peak current was measured do not belong to any specific peak current range (since the loss of peak current measurement is due to instrumentation failure and not trigger thresholds or saturation), the results presented in Figure 6 should not be biased. The combined data for 2001-2003 suggest that the detection efficiency is probably near 100% for strokes having peak currents in excess of 30 kA, although the data set is quite small for that peak current range. The stroke detection efficiency decreases to 60-70% as current decreases from 30 to 10 kA, and drops to less than 30% for currents in the 5
to 10 kA range. No strokes with measured peak currents below 5 kA were detected by the NLDN. The detection efficiency for strokes in the range of 5 to 15 kA increased between 2001 and 2003.
Figure 7. Plot of NLDN stroke locations for 95 strokes in 31 flashes triggered during 2001-2003 at Camp Blanding. The origin corresponds to the actual stroke location (lightning triggering location). The horizontal axis corresponds to the east-west component of the location error, with positive values corresponding to east. The vertical axis corresponds to the north-south component of the location error, with positive values corresponding to north. The total area covered by the plot is 576 km2 (24 km × 24 km), with the inset showing the central 16 km2 (4 km × 4 km). Statistics given are arithmetic mean (AM), median, and standard deviation (SD), for each location error component. Adapted from Jerauld et al. [2005].
3.2. Location accuracy Figure 7 is a plot of the NLDN stroke location errors for 95 strokes in 31 flashes triggered during 2001-2003 at Camp Blanding. The origin corresponds to the actual strike location that was known within a few meters. The horizontal and vertical axes correspond to the east-west (east being positive) and north-south (north being positive) error components, respectively. For the 2001 and 2003 data, the location errors are distributed more or less uniformly about the strike location. The 2002 data appear to be divided into two major clusters, one of which is very similar to the 2001 and 2003 data (with a slight bias towards the west). The second cluster in the 2002 data appears to have the roughly same westward bias as the first cluster, but also contains a large bias towards the north. The north component of these large location errors ranges from about 2 km to about 11 km. Figure 8 is a histogram of the NLDN absolute stroke location errors for the 95 strokes shown in Figure 7. The overall distribution has a long “tail” due to the relatively large location errors observed in 2002. The inset of the figure shows the distribution of stroke location errors up to 1 km. The median stroke location errors are 0.3 km, 0.8 km, 0.5 km, and 0.6 km, for 2001, 2002, 2003, and 2001-2003, respectively. The corresponding arithmetic means are 0.7 km, 2.4 km, 0.6 km, and 1.5 km, respectively. The relatively large arithmetic mean location errors observed for the combined data are mostly due to the relatively large location errors (>2 km) observed for some of the 2002 events.
Figure 8. Histogram of the NLDN absolute location errors for 95 strokes in 31 flashes triggered during 2001-2003 at Camp Blanding. All bins are 0.25 km except for the last bin, which includes all errors greater than 5 km, with a maximum of 11 km. The inset shows the histogram with bins of 0.1 km for errors less 1 km. Corresponding statistics are given below the histogram. Adapted from Jerauld et al. [2005].
Figure 9 gives the NLDN absolute location error plotted versus the peak current, measured at Camp Blanding, for 70 strokes in 22 flashes. Note that the sample size of 70 in Figure 9 is smaller than the sample size of 95 in Figure 8 because, as stated previously, the number of strokes for which peak currents were obtained is smaller than the number of triggered-lightning strokes recorded at Camp Blanding. The majority of large (>2 km) location errors occur in the 5-10 kA range during 2002 (no strokes were detected with peak currents below 5 kA). Between 10 and 35 kA, most of the 2002 location errors are below 1 km. For 2003, the location accuracy for smaller peak currents appears to have improved, although there are not as much data in that range as in 2002. For 2001, all detected strokes were above 15 kA, so no conclusions can be drawn regarding the location accuracy for small strokes during that year.
Figure 9. NLDN absolute location error versus Camp Blanding peak current, for 70 strokes with measured peak currents in 22 flashes triggered during 2001-2003. Adapted from Jerauld et al. [2005].
Figure 10 gives the NLDN absolute location error plotted versus the number of NLDN sensors which were involved in the location solution, for 95 strokes in 31 flashes. The number of reporting sensors ranged from 2 to 14 during 20012003. Figure 10 provides crude estimates of the apparent upper and lower location error boundaries for a given number of sensors. For example, for strokes detected by only 2 sensors, the smallest location error observed was above 2 km. For strokes detected with 3 sensor solutions, the majority of location errors fall between 0.1 and 3 km, although some outliers exist beyond 3 km. As the number of reporting sensors increases, the upper bound on location error appears to decrease. It should be noted that all of the two-sensor locations in 2002 were located by the Ocala and Palm Bay sensors (see Figure 5 and Table 1), resulting in large location errors, apparently due to the baseline orientation relative to the source location (Camp Blanding). The NLDN 50% error ellipse, calculated for each stroke location solution, is defined as a confidence region for which there is a 50% probability that the actual stroke location lies within the area circumscribed by the ellipse, with the center of the ellipse being the most-probable (reported) stroke location. Hence, the 50% ellipse is usually viewed as a measure of the median location (50%) error. Corresponding error ellipses for any probability level (e.g., 90%) can be derived by multiplying the semi-major and semi-minor axes of the 50% ellipse by an appropriate scaling factor. The two-dimensional Gaussian distribution of errors in latitude and longitude is based on the assumption that the random errors in sensor time and angle measurements are uncorrelated and their distributions are approximately Gaussian [Cummins et al., 1998]. Strokes located within a group of several sensors typically have relatively small near-circular error ellipses, whereas strokes detected by only 2 or 3 sensors typically have very large, elongated ellipses. A stroke detected by only two sensors, when that stroke is located near the line joining the two sensors (base line), typically has an elongated ellipse whose major axis is along the base line.
Figure 10. NLDN absolute location error versus the number of reporting NLDN sensors, for 95 strokes in 31 flashes triggered during 2001-2003. Adapted from Jerauld et al. [2005].
Figure 11a gives the NLDN absolute location error plotted versus NLDN 50% semi-major axis length, for 95 strokes in 31 flashes triggered during 2001-2003. Data for semi-major axis lengths and location errors less than 2 km (73 strokes total) are given in Figure 11b. Strokes with absolute location errors less than 2 km are typically associated with semimajor axis lengths between 0.4 and 1.5 km. No semi-major axis lengths between 2 and 4 km were observed, although 20 strokes were found to have semi-major axis lengths between 4 and 8 km, with most of those strokes having location errors greater than 2 km. The slanted solid line (slope = 1) on each plot is the locus of points for which the NLDN 50% semi-major axis length and corresponding location error are equal, that is, represents the boundary of the 50% error ellipse. If the error ellipses are assumed to be nearly circular, then data points below this line correspond to strokes with ground-truth locations enclosed by the 50% error ellipse and strokes above it are outside the 50% error ellipse. Using only the data shown in Figure 11b, where the assumption of nearly circular error ellipses is most-likely valid, it was found that about 63% (46 out of 73) of those strokes had ground-truth locations enclosed by the 50% error ellipse. Data points below the dashed line (slope = 1.82) on each plot of Figure 11 correspond to strokes with ground-truth locations enclosed by the 90% (assumed to be nearly circular) error ellipse. It was found that about 96% (70 out of 73) of those strokes shown in Figure 10b had ground-truth locations enclosed by the 90% error ellipse. If this analysis is extended to all strokes, including those with large (>2 km) semi-major axes and location errors (Figure 11a), and the nearly circular error ellipse assumption is kept, then about 66% (63 out of 95) and 96% (91 out of 95) of stroke locations are enclosed by the 50% and 90% error ellipses, respectively. Hence, the results are more or less the same regardless of whether strokes with large semi-major axes (for which the nearly circular ellipse assumption is likely to be invalid) are included, and may be due to the ellipse major axis orientation being consistent with the orientation of the line joining the NLDNreported and ground-truth locations. These results suggest that the ellipse semi-major axis is a conservative estimate of the location error, at least in north-central Florida. In order to perform a more detailed analysis, the actual shape and orientation of each individual error ellipse must be considered. 3.3. Peak current estimates Figure 12 shows the NLDN-estimated peak current plotted versus peak current measured directly at Camp Blanding, for 70 strokes in 22 flashes. There is a strong positive linear relationship between the measured and NLDN-estimated peak currents for all 3 years, which is stronger in 2002 and 2003 than in 2001. It is clear that the NLDN tends to underestimate the actual peak current. For all data combined, a crude “correction factor” for the NLDN peak current estimates can be obtained by taking the mean of the ratio ICB/INLDN, which is about 1.2 for the combined data, and is presumably applicable to subsequent strokes in natural lightning. Note that this result might be valid only for the
configuration and settings used in the NLDN in 2001-2003. No attempt is made in this paper to re-process the raw NLDN data. According to Cummins et al. [2004], the mismatch seen in Figure 12 can be significantly reduced by simply employing the “exponential” dependence of signal strength, D-1exp (-D/1000), where D is the distance from the source in kilometers, rather than the power-law dependence, D-1.13, used in the NLDN in 1993-2003.
Figure 11. Part (a) gives the NLDN absolute location error plotted versus NLDN 50% error ellipse semi-major axis length, for 95 strokes in 31 flashes triggered during 2001-2003. Part (b) is an expansion of (a) that shows data only for location errors and semimajor axis lengths less than 2 km. The NLDN-calculated stroke location corresponds to the centroid of the error ellipse. The slanted solid line (slope = 1) is the locus of points for which the NLDN 50% semimajor axis length and corresponding location error are equal. If the error ellipses are assumed to be nearly circular, then points below this line correspond to strokes with ground-truth locations enclosed by the 50% error ellipse and strokes above are outside the 50% error ellipse. Points below the dashed line (slope = 1.82) correspond to strokes with ground-truth locations enclosed by the 90% (assumed to be nearly circular) error ellipse. Adapted from Jerauld et al. [2005].
Figure 13 gives histograms the NLDN peak current estimation errors (defined here as I = INLDN - ICB), both signed (Figure 13a) and absolute values (Figure 13b). Note that only negative events are considered here, since the positive stroke in the Camp Blanding data was not detected by the NLDN. The arithmetic mean values of I are -6.0 kA, -1.3 kA, -2.6 kA, and -2.9 kA, for 2001, 2002, 2003, and 2001-2003, respectively. The corresponding median values are -8.2 kA, -2.1 kA, -2.9 kA, and -2.9 kA, respectively. This is consistent with the observation that, in general, the NLDN underestimated the actual peak current. If the absolute value of I is considered (Figure 13b), the arithmetic mean values are 6.0 kA, 2.6 kA, 2.9 kA, and 3.4 kA, for 2001, 2002, 2003, and 2001-2003, respectively. The corresponding median values are 8.2 kA, 2.5 kA, 2.9 kA, and 2.9 kA, respectively. Note that the mean and median peak current estimation errors are somewhat lower for 2002 and 2003, compared to those for 2001. This observation is consistent with the plots of NLDN peak current versus Camp Blanding peak current shown in Figure 12.
Figure 12. NLDN-reported peak current versus peak current directly measured at Camp Blanding for (a) 2001, (b) 2002, (c) 2003, and (d) 2001-2003. There were a total of 70 strokes with directly measured current in 22 flashes triggered during 2001-2003. The slanted line (slope = 1) is the locus of points for which the NLDN peak current is equal to the Camp Blanding peak current. Also given for each data set are the coefficient of determination (R2) and sample size (n).
Figure 13. Histograms of NLDN peak current estimation errors (defined as I = INLDN - ICB), for 70 negative strokes in 22 flashes triggered during 2001-2003. Part (a) gives the distribution for signed errors with a bin size of 2 kA and part (b) gives the distribution for the magnitudes of the errors (absolute values) with a bin size of 1 kA. Statistics given are arithmetic mean (AM), standard deviation (SD), geometric mean (GM), median, minimum, and maximum vaules. Adapted from Jerauld et al. [2005].
Figure 14 is similar to Figure 13, except that the NLDN peak current estimation error ( I) is now expressed as a percentage of the measured Camp Blanding peak current ( I %=100 I /ICB). As with Figure 13, histograms are given for both signed (Figure 14a) and absolute (Figure 14b) errors. For all 3 years, the percentage errors never exceeded 50%, with the median signed errors being -25%, -11%, -22%, and -18%, for 2001, 2002, 2003, and 2001-2003, respectively. The arithmetic mean values were generally similar to the corresponding median values. For the unsigned (absolute) percentage errors, the median values were 25%, 17%, 23%, and 20%, for 2001, 2002, 2003, and 2001-2003, respectively. Hence, it appears that the median absolute peak current estimation error is roughly 20% for the data analyzed by Jerauld et al [2005].
Figure 14. Histograms of NLDN peak current estimation errors (defined as I = INLDN - ICB), given as a percentage of the directly measured Camp Blanding current ( I% = 100 I/ICB) , for 70 negative strokes in 22 flashes triggered during 2001-2003. Part (a) gives the distribution for signed percentage errors and part (b) gives the distribution for the magnitudes of the percentage errors (absolute values). Both histograms have a bin size of 10%. Corresponding statistics are given below each histogram. Adapted from Jerauld et al. [2005].
3.4. Summary of the 2001-2003 evaluation For 2001-2003, the following NLDN performance characteristics have been found by Jerauld et al. [2005]: • A flash detection efficiency of about 84% (31 flashes detected out of 37 triggered at Camp Blanding). • A stroke detection efficiency of about 60% (95 strokes detected out of 159 recorded at Camp Blanding). • A median location error of about 600 m. Larger location errors (>2 km) are observed for strokes having smaller peak currents (5-10 kA). • A median peak current estimation error of about -18%. Since first strokes in natural lightning typically have larger peak currents than subsequent strokes, and the triggered lightning strokes studied here are similar to subsequent strokes in natural lightning, the observed values of flash (84%) and stroke (60%) detection efficiencies should probably be viewed as lower bounds. Further, since location error generally decreases with increasing peak current, the lack of typically larger first strokes can be interpreted to indicate that the observed median location error (600 m) is an upper bound. It has been observed that stroke detection efficiency systematically increased between 2001 and 2003, this trend being probably attributable to the 2002-2003 NLDN upgrade. Strictly speaking, the results listed above are valid only for negative subsequent strokes and for the configuration and settings used in the NLDN in 2001-2003. A new configuration and/or settings would generally require another groundtruth evaluation. Further, all of the strokes analyzed by Jerauld et al. [2005] had peak currents less than 50 kA, with the majority having peak currents below 30 kA, and hence the NLDN peak current error estimates presented by them may not be applicable to strokes with larger peak currents. 4 CONCLUDING REMARKS Since 1989, the NLDN has provided lightning data covering the contiguous United States. Its performance characteristics were evaluated in two major studies based on the use of rocket-triggered lightning as the source of ground-truth data. The first study (1985-1991; Orville [1991], Idone et al. [1993]) employed data from the triggeredlightning experiments at the NASA Kennedy Space Center (KSC) and the other one (2001-2003; Jerauld et al. [2004, 2005]) used data from similar experiments at the International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, Florida. From the latter study, the NLDN (in its current configuration) in Florida is characterized by flash and stroke detection efficiencies of about 84% and 60%, respectively. Median location error is about 600 m, with larger location errors (greater than 2 km) being associated with strokes having smaller peak currents (5-10 kA). The NLDN had been found to underestimate peak current by about 18% (median value), but this error was apparently reduced due to a recent change of the assumed distance dependence of signal strength (propagation model), from powerlaw with an exponent equal -1.13 to “exponential”. The new distance dependence is D-1exp (-D/1000), where D is the distance from the source in kilometers [Cummins et al. 2004]. The field-to-current conversion equation, I = 0.185 RNSS, presently employed by the NLDN, is based on the 1985-1991 KSC study and has been the same since 1996. The evolution of the NLDN current estimation algorithm is summarized in Table 3.
Table 3. Estimation of lightning peak currents by the NLDN (or its predecessor prior to 1989). Period 1982-1993 1993-1996 1996-2003 2003-present Assumed distance dependence of -1 -1.13 -1.13 -1 D D D D exp (-D/1000) signal strength Field-to-current conversion 0.2 RNSS 5.20 + 0.148 RNSS 0.185 RNSS 0.185 RNSS equation D is the distance from the lightning channel in kilometers, and RNSS is the range-normalized (to 100 km) signal strength in LLP units.
ACKNOWLEDGEMENTS This lecture is based on works of Orville [1991], Idone et al. [1993], and Jerauld et al. [2004, 2005]. NSF support (grant ATM-0346164) is acknowledged. Special thanks are due Jason Jerauld and Ken Cummins for their help with preparing this review.
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