Correlation between lightning types

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 34,, doi: /2007gl029476, 2007 Correlation between lightning types J. L. Lapp 1 and J. R. Saylor 1 Received 25 January 2007; revised 21 February 2007; accepted 20 March 2007; published 2 June [1] The spatial correlation of cloud-to-ground (CG), intracloud (IC), and narrow-bipolar event (NBE) lightning was investigated. Lightning data were collected for a two-month period in Florida. Separate analyses were performed for lightning over land and lightning over water. Space-time cells were defined, and lightning flash density was computed on each cell for the three lightning types. Correlation coefficients were computed for each of the three pairs of lightning types: CG-IC, IC-NBE, and CG- NBE. The CG-IC lightning pair was correlated most strongly. Best fit curves were also produced for each pair of lightning densities. These were second order polynomial fits in log space. These fits displayed curvature on log-log axes, signifying that the relative fractions of lightning types vary with storm intensity. The land/water separation did not have a strong effect on the relationships. Citation: Lapp, J. L., and J. R. Saylor (2007), Correlation between lightning types, Geophys. Res. Lett., 34,, doi: /2007gl Introduction [2] Significant research has been conducted on the relationship between rain rate and the amount of cloudto-ground (CG) lightning [Battan, 1965; Kinzer, 1974; Piepgrass and Krider, 1982; Williams et al., 1991; Petersen and Rutledge, 1998] and, to a lesser extent, intra-cloud (IC) lightning [Soula and Chauzy, 2001]. This research has not included narrow-bipolar event(nbe) lightning, a specific type of impulsive lightning [Jacobson and Light, 2003; Smith et al., 1999]. NBE lightning is less common (about 1% of total lightning) than IC or CG lightning, in physical occurrence, and detection by ground-based sensors [Smith et al., 1999], but can comprise over 40% of the VHF lightning seen by space-based sensors [Light and Jacobson, 2002]. Hence, a knowledge of how CG and IC lightning are related to NBE lightning would provide a way to connect current and future space-based measurements to the extensive body of literature relating IC and CG lightning to characteristics of rainfall. [3] NBE s are lightning discharges of very intense radiofrequency radiation that have a short duration (<20 ms) [Suszcynsky and Heavner, 2003], are spatially compact [Smith et al., 1999], are optically weak [Light and Jacobson, 2002], and are of particular interest because of their efficiency in being detected from space. Suszcynsky and Heavner [2003] compared NBE lightning flash rates to CG lightning flash rates. These authors noted that CG lightning is an indicator of convective updraft [Ushio et al., 2001; Williams, 1985], 1 Department of Mechanical Engineering, Clemson University, Clemson, South Carolina, USA. Copyright 2007 by the American Geophysical Union /07/2007GL and hence relating NBE lightning to CG lightning would be a method of quantifying thunderstorm convective strength using NBE lightning. Suszcynsky and Heavner [2003] counted lightning flashes in each of 36 spatial cells over Florida, which were approximately 50 km square, and found that CG and NBE counts were correlated. However, numerical correlation coefficients were not provided. Their work did not consider IC lightning, nor did it reveal whether correlations differ over land and water (an important next step, as suggested by these authors). The work presented herein extends that of Suszcynsky and Heavner [2003] by computing correlation coefficients r for the CG-NBE pair, and for the IC-NBE pair, and shows how r varies over land and water. Values of r for the CG-IC pair are also presented, since this is a correlation of fundamental interest. [4] Jacobson and Heavner [2005] compared NBE to CG lightning and cloud-top-temperature to test the utility of NBE lightning as a proxy for deep convection. It was found that NBE lightning performs similarly to CG lightning in this regard. IC lightning was not investigated. 2. Method [5] Lightning data were collected by Los Alamos National Laboratories (LANL) using the Los Alamos Sferic Array (LASA) lightning detection array [Smith et al., 2002; Shao et al., 2006]. This is the same array used by Suszcynsky and Heavner [2003] and Jacobson and Heavner [2005], but through a 2004 upgrade it gained the ability to identify IC lightning. [6] The Florida LASA consists of eight electric field change sensor stations shown in Figure 1. The array has a theoretical location accuracy of 10 km or more on portions of this work s domain, however, experiments show that the actual location accuracy is much better [Shao et al., 2006]. It is possible that, due to location inaccuracy, some lightning flashes are placed in the wrong space-time cell, and have an influence on the results of this work, although increased scatter is the only expected effect. [7] Waveforms recorded by LASA sensors are processed by differential time of arrival techniques, providing time stamps, latitude, and longitude for each lightning event, as well as classifying each event as CG, IC, or NBE lightning [Shao et al., 2006]. Data were collected from 15 May 2005 to 17 July 2005, and include all lightning which occurred between latitudes 25 N and 33 N, and between longitudes 78 W and 88 W as shown in Figure 1. [8] Lightning strokes were first grouped into flashes, and the flash location was defined as that of the first stroke in the flash. Successive strokes were grouped into a flash if they occurred within 500 meters of the previous stroke, and occurred one half second or less after the previous stroke and two seconds or less from the first stroke in the flash. If an initial stroke in a flash was identified to be an IC stroke, 1of5

2 LAPP AND SAYLOR: CORRELATION OF LIGHTNING Figure 1. Map of the region studied. Circles indicate LASA lightning detection array sensor locations. Dashed box indicates the data collection area (25 33N Lat, 78 88W Lon). One analysis cell is shown for size comparison. then any subsequent IC or CG strokes which met the criteria outlined above were added to the flash, and if any of these strokes were CG strokes, the flash was designated to be a CG flash. Otherwise the flash was designated to be a IC flash. If the initial stroke was a CG stroke, the same procedure was used, with IC and CG strokes grouped into the flash, which would be a CG flash. NBE strokes were kept separate, so if the initial stroke was a NBE stroke, then only other NBE strokes would be grouped into the flash. [9] A summary of the lightning collected for this study is presented in Table 1. A total of 1,224,264 lightning flashes were observed. As with many studies based on electric field change sensor network data, the detection efficiency of the LASA is not accounted for in this study, and is only discussed briefly by Shao et al. [2006]. It should still be noted that the detection efficiency may have affected the results of this study. The primary manifestation of detection efficiency is likely the underestimation of the total number of IC flashes, which make up 55.7% and 51.2% of total lightning over land and water respectively. This compares to a value of 80% found near the LASA by Shao et al. [2006] or 60 91% found by Soula and Chauzy [2001]. [10] The data collection area was divided into rectangular cells 0.2 degrees latitude by 0.2 degrees longitude in extent. These cells are approximately 20 km 20 km; the area of Table 1. Flash Totals for Lightning Types Collected Over the Two Month Period of This Study CG a +CG IC NBE Total Land 279,225 80, ,946 11, ,077 Water 273,116 56, ,538 3, ,187 a +CG and -CG. each cell varies slightly with latitude. Cells were indexed as either land or water to permit separate analyses for each environment. Cells containing coastline were divided along the coastline into two smaller cells, one for land, and one for water. Herein, analyses are performed for lightning flash densities (flashes/area/time), so these smaller coastal cells, and the variation in cell area with location in the domain, do not create a bias in the coefficients. 3. Results and discussion [11] Lightning flash densities s were computed over one hour intervals and 15 minute intervals for each cell and had the units of flashes/km 2 /hour. Previous studies have used 15 minute [Suszcynsky and Heavner, 2003] or 10 minute [Jacobson and Heavner, 2005] intervals, small enough to permit resolution of temporal changes in convective storms. Values of r are shown in Table 2 for both hourly and 15 minute intervals. Hour intervals are large enough to Table 2. Total Number of Data Points and r of Relationships Examined for One Hour and 15 Minute Time Intervals Time Interval Lightning Types Location Data Points r 1 Hour CG & IC Land 20, Water 20, CG & NBE Land 1, Water 1, IC & NBE Land 1, Water 1, Minute CG & IC Land 32, Water 31, CG & NBE Land 2, Water 1, IC & NBE Land 1, Water 1, of5

3 LAPP AND SAYLOR: CORRELATION OF LIGHTNING Figures 2 4, two plots are presented: (top) corresponding to land, and (bottom) corresponding to water. [13] The quantization of points which can be seen for small values of s on both axes is a result of data where few flashes occurred within a cell. Because the time period is fixed and the box area is nearly constant, there are discrete values for lightning density which correspond to very small numbers of flashes in the cell during one interval. Some points deviate from this quantization, however, because of splitting coastline-containing cells into two smaller cells for land and water. [14] IC and CG lightning occur more often than NBE lightning [Smith et al., 1999], and this is seen in Figures 2 4. Value of r for the sic versus scg plots are much higher (0.805 and for land and water, respectively) than those for the snbe plots. The correlation between snbe and sic is slightly stronger than the correlation between snbe and scg for both land and water. An important observation from Figures 2 4 is that, at high densities, the variation in the density of IC lightning, for a given CG density, is far less than the variation in NBE density, for a given IC or CG Figure 2. Plots of CG lightning density versus IC lightning density for (top) land and (bottom) water. Small circles represent individual space-time cells. Large dots are averages over equally spaced CG density bins. allow significant convective changes, but collect more lightning per space-time cell. In this work, hour intervals produce slightly stronger correlations, perhaps by exposing more long term trends rather than short term effects. Plots for the two time intervals appeared similar, and only plots for the hour interval are presented here. [12] Figures 2, 3, and 4 present plots of sic versus scg, snbe versus sic, and snbe versus scg, respectively. Each data point in these plots corresponds to a space-time cell where at least one flash occurred for each of the two types of lightning being considered. These data points are presented as small circles in Figures 2 4, and were used in computing r. For all cases, r was computed from the log of s, and was defined as [Miller and Miller, 2004]: S Xi X ðyi Y Þ r¼h i 2 2 1=2 S Xi X SðYi Y Þ ð1þ where X and Y are the variables being correlated (which are assumed to be random and normally distributed). In Figure 3. Plots IC lightning density versus NBE lightning density for (top) land and (bottom) water. Small circles represent individual space-time cells. Large dots are averages over equally spaced IC density bins. 3 of 5

4 LAPP AND SAYLOR: CORRELATION OF LIGHTNING to infer the overall trend between lightning types. The curvature in the s NBE plots observed by Suszcynsky and Heavner [2003] is also observed in this study (we note that our axes are switched compared to those by Suszcynsky and Heavner [2003]). Low flash rates were dominated by individual flashes (1 or 2 per space-time cell), as given by Suszcynsky and Heavner [2003]. [17] Data which are well-fit by a line on log-log axes are well-represented by a power law. The average values plotted in Figures 2 4 show that CG and IC lightning scale more closely to a power law than do NBE and IC or NBE and CG. However, some curvature is apparent in all of these plots, and so the averaged data were fit to a second-order polynomial in log space. This fit is defined in equation (2), where y and x are the densities of the pair of lightning types, and a, b, and c are the polynomial coefficients obtained from the least squares curve fitting procedure. lnðyþ ¼ a þ b½lnðþ x Šþc½lnðÞ x Š 2 ð2þ Figure 4. Plots of CG lightning density versus NBE lightning density for (top) land and (bottom) water. Small circles represent individual space-time cells. Large dots are averages over equally spaced CG density bins. density. At a CG density of 0.5 flashes/km 2 /hr, IC density varies by less than one order of magnitude, while NBE density varies by about two orders of magnitude. The IC and CG lightning formation process may be more directly related than either is to NBE lightning. Using NBE lightning density as a proxy for CG lightning density, and convective activity, may not be justified based on the amount of scatter in these analyses. [15] Values of r for lightning type pairs are similar for lightning over both land and water, and are slightly higher over land for both NBE lightning data pairs, but slightly higher over water for the IC and CG lightning pair. These differences are small in comparison to the difference between r for different lightning type pairs. If there is any consistent effect on lightning relationships cause by the land/water separation, it is that, over water, NBE density becomes less related to the total lightning density. [16] The data presented in Figures 2 4 were also averaged on equally spaced bins along the x-axis of the plots. These average values are shown as large dots, and are used [18] Asc approaches zero, the curve fit approaches power law behavior. Hence, the value of c in Table 3 is a measure of the curvature seen in Figures 2 4. For all cases, c is nonzero, confirming curvature is present for all lightning pairs. The fits presented in Table 3 are similar for the land and water cases for the same lightning pair, and differences in the fits between different lightning pairs are much greater that the differences between the land and water fits for the same pair. [19] The curvature in lightning density plots necessarily results in a variation in the ratio between lightning types at different densities. For CG and IC lightning over land, at low flash densities ( flashes/km 2 /hour) and high flash densities (1 flashes/km 2 /hour) IC lightning outnumbers CG lightning by factors of 1.29 and 1.42, respectively, but at mid flash densities (10 1 flashes/km 2 /hr), CG lightning outnumbers IC lightning by a factor of For IC and NBE lightning over land, IC always outnumbers NBE lightning, but the ratio ranges from about 3 at low flash densities, to over 100 at mid flash densities, and is about 30 at high flash densities. These ratios differ even more for CG and NBE lightning, ranging from 2 at low flash densities, to 224 near a CG density of flashes/km 2 /hour. Ratios at low flash densities are systematically low, because at a density which corresponds to 4 flashes in a space-time cell, for example, the maximum ratio will be 4, because both lightning types must have at least one flash. Over water, the fractions of NBE lightning are decreased. For example, Table 3. Log Space Second-Order Polynomial Fits of Lightning Type Relationships for Averaged Space-Time Cells Over Land and Water a Lightning Types Location a b c CG & IC Land Water IC & NBE Land Water CG & NBE Land Water a Fits are of form ln(y) =a + b[ln(x)] + c[ln(x)] 2. 4of5

5 LAPP AND SAYLOR: CORRELATION OF LIGHTNING where CG lightning outnumbers NBE lightning by a factor of 224 over land, the ratio is 450 over water. [20] In summary, of CG, IC and NBE lightning, CG and IC are the most correlated pair. The relationships were fit with a second-order polynomial in log space. These fits showed that curvature is significant in log space for all lightning type pairs, so power law or linear relationships are inadequate. The relationship between CG and IC lightning exhibited the least scatter, so the formation processes of these lightning types appear more linked than either process is to the formation of NBE lightning. This suggests that NBE lightning may not be suitable to use as a proxy for other lightning types and convective activity, in disagreement with previous results. The relative fractions of lightning types were found to be specific to lightning density, or storm intensity, and change for lightning over land and lightning over water. The relationships change slightly between lightning over land and lightning over water, and these changes are small compared to the differences between relationships of different lightning types. [21] Acknowledgments. The authors would like to acknowledge the support of LANL, including T. E. Lavezzi Light and Jeremiah Harlin. LASA data was acquired and provided by LANL. References Battan, L. J. (1965), Some factors governing precipitation and lightning from convective clouds, J. Atmos. Sci., 22, Jacobson, A. R., and M. J. Heavner (2005), Comparison of narrow bipolar events with ordinary lighting as proxies for severe convection, Mon. Weather Rev., 133, Jacobson, A. R., and T. E. L. Light (2003), Bimodal radio frequency pulse distribution of intracloud lightning signals recorded by the FORTE satellite, J. Geophys. Res., 108(D9), 4266, doi: /2002jd Kinzer, G. D. (1974), Cloud-to-ground lightning versus radar reflectivity in Oklahoma thunderstorms, J. Atmos. Sci., 31, Light, T. E. L., and A. R. Jacobson (2002), Characteristics of impulsive VHF lightning signals observed by the FORTE satellite, J. Geophys. Res., 107(D24), 4756, doi: /2001jd Miller, I., and M. Miller (2004). John E. Freund s Mathematical Statistics With Applications, Pearson Education, Upper Saddle River, N. J. Petersen, W. A., and S. A. Rutledge (1998), On the relationship between cloud-to-ground lightning and convective rainfall, J. Geophys. Res., 103, 14,025 14,040. Piepgrass, M. V., and P. E. Krider (1982), Lightning and surface rainfall during Florida thunderstorms, J. Geophys. Res., 87, 11,193 11,201. Shao, X. M., M. Stanley, A. Regan, J. Harlin, M. Pongratz, and M. Stock (2006), Total lightning observations with the new and improved Los Alamos Sferic Array (LASA), J. Atmos. Oceanic Technol., 23, Smith, D. A., X. Shao, D. Holden, C. Rhodes, M. Brook, P. Krehbiel, M. Stanley, W. Rison, and R. Thomas (1999), A distinct class of isolated intracloud lightning discharges and their associated radio emissions, J. Geophys. Res., 104, Smith, D. A., K. B. Eack, J. Harlin, M. J. Heavner, A. R. Jacobson, R. S. Massey, X. M. Shao, and K. C. Wiens (2002), The Los Alamos Sferic Array: A research tool for lightning investigations, J. Geophys. Res., 107(D13), 4183, doi: /2001jd Soula, S., and S. Chauzy (2001), Some aspects of the correlation between lightning and rain activities in thunderstorms, Atmos. Res., 56, Suszcynsky, D. M., and M. J. Heavner (2003), Narrow Bipolar Events as indicators of thunderstorm convective strength, Geophys.Res.Lett., 30(17), 1879, doi: /2003gl Ushio, T., S. Heckman, D. Boccippio, and H. Christian (2001), A survey of thunderstorm flash rates compared to cloud top height using TRMM satellite data, J. Geophys. Res., 106, 24,089 24,095. Williams, E. R. (1985), Large scale charge separation in thunderclouds, J. Geophys. Res., 90, Williams, E. R., S. A. Rutledge, S. G. Geotis, N. Renno, E. Rasmussen, and T. Rickenbach (1991), A radar and electrical study of tropical hot towers, J. Atmos. Sci., 49, J. Lapp and J. R. Saylor, Department of Mechanical Engineering, Clemson University, 102 Fluor Daniel Building, Box , Clemson, SC 29634, USA. (jlapp@clemson.edu) 5of5