1. Introduction
The advent of ground-based lightning detection networks in recent decades has made real-time retrieval of total lightning activity [cloud to ground (CG) and intracloud (IC)] available in both high spatial and temporal resolutions. Although there are uncertainties in the details (Takahashi 1978; Saunders 1993), it is known that rebounding collisions between graupel and ice crystals in the presence of supercooled water is the primary process for thunderstorm electrification (MacGorman and Morgenstern 1998; Saunders et al. 2006; Emersic and Saunders 2010). Several studies have documented a temporal covariability between updraft mass flux, precipitation ice mass, and overall storm depth with the respective total lightning activity (e.g., Goodman et al. 1988; Carey and Rutledge 2000; Chronis et al. 2007; Deierling and Petersen 2008; Bruning and MacGorman 2013). Hence, it would be reasonable to suggest that an abrupt temporal change on the order of a few minutes in the total lightning activity is considered to be a severe weather indicator [lightning jump (LJ); see Schultz et al. (2009), (2011)]. Studies by Williams et al. (1999), Gatlin and Goodman (2010), Carey et al. (2009), Schultz et al. (2009, 2011), and Rudlosky and Fuelberg (2013) document that statistics such as lead time, probability of detection, and false alarm ratio could be improved based on the use of total lightning as a metric for storm intensity. Nonetheless, these methods can be hindered by problems related to uncertainties in severe weather observations at the surface (Trapp et al. 2006; Keene et al. 2008; Schultz et al. 2011). This study puts forward an original comparison between the convective characteristics of storms that did or did not exhibit an LJ throughout their lifetime. This evaluation relies on radar-derived and lightning properties.
2. Data and methods
a. Storm tracking and clustering
The storm identification and tracking have been performed in real time utilizing the Warning Decision Support System–Integrated Information (WDSS-II; Lakshmanan et al. 2007). A storm “cluster” is automatically identified by the reflectivity across the −10°C isothermal layer, following a merger of individual WSR-88D. A combination of watershed segmentation and k-means clustering is employed to identify the storm clusters (Lakshmanan et al. 2009; Kolodziej Hobson et al. 2012; Cintineo et al. 2014). To complete the storm identification, the algorithm searches for local reflectivity Z maxima where Z > 20 dBZ, then incrementally grows the area until it is at least 200 km2. The storm cluster is then matched with a separately identified cluster at the next time step (for our analysis, a 1-min time step was employed) using a cost function, where longer-lived cells are given preference in the case of storm mergers.
Each storm (hereinafter cluster) is described by a geolocated polygon (i.e., footprint). The lifespan is determined by the total time a cluster was tracked by WDSS-II (Lakshmanan and Smith 2009). The maximum vertical integrated liquid (VIL; Greene and Clark 1972) and the maximum expected size of hail (MESH; Witt et al. 1998; Cintineo et al. 2012) are retrieved for each cluster for the duration of its lifetime. Both VIL and MESH have been used as radar-derived intensity metrics for storm properties such as liquid precipitation, updraft strength, and hail growth (Amburn and Wolf 1996; Witt et al. 1998). As with any proxy, there are caveats that reflect the imperfect representations of severe weather potential and these emanate from parameters unrelated to the storm dynamics [e.g., distance from the radar, tilted updrafts, storm speed, etc.; Stumpf et al. (2004)]. To mitigate these effects as much as possible, all available radars in the area are used to retrieve these proxies. Five radars over each of the three locations are employed, namely, KFDR, KTLX, KVNX, KINX, and KSRX for Oklahoma; KHTX, KGWX, KBMX, KOHX, and KFFC for northern Alabama; and KLWX, KDOX, KAKQ, KCCX, and KDIX for Washington, D.C. (Table 1; https://www.ncdc.noaa.gov/nexradinv/map.jsp). The data for the present study extend from 1 April through 14 August 2013.
Acronym and expansion of radars.
b. Total lightning activity and the lightning jump algorithm
This study employs three total lightning detection networks: 1) the Lightning Mapping Array (LMA) networks located in central/southwestern Oklahoma (MacGorman et al. 2008), northern Alabama (Goodman et al. 2005), and Washington, D.C. (Krehbiel 2008); 2) the Earth Networks Total Lightning Network (ENTLN; Liu and Heckman 2011); and 3) the National Lightning Detection Network (NLDN; Cummins et al. 1995, 2006; Cummins and Murphy 2009).
The LMA detects the very high-frequency (VHF) radiation emitted during the elemental processes that compose a lightning discharge [e.g., the initial breakdown, leader propagation, and other K processes; Uman (1987)] with a location accuracy measured in tens of meters and with a time resolution of 80–100 μs (Thomas et al. 2004). Both IC and CG flashes are detected although the distinction can be dubious because of limitations in range. The location accuracy is also range dependent; however, it is relatively constant to a ~150-km radius from the respective center (Thomas et al. 2004; Koshak et al. 2004). The following analysis relies on the total lightning flashes occurring within ~120 km of the respective LMA center (Thomas et al. 2003). Lightning flashes are retrieved from the LMAs via grouping at least 10 detected VHF radiation sources, using time and space constraints (3 km and 150 ms) between the adjoining points (McCaul et al. 2005). Only flashes that begin within the storm cluster’s footprint are counted toward the total flash rate. No classification between CG and IC flashes is performed using LMA data.
The ENTLN sensors operate over a wide frequency range, spanning from 1 Hz to 12 MHz. According to Liu and Heckman (2011), electric field waveforms are used in locating as well as classifying the IC and CG flashes. Multiple strokes (or individual cloud events) are clustered into a single flash if they are within 700 ms and 10 km of the first detected stroke. A flash that contains at least one return stroke is classified as a CG flash; otherwise, it is classified as an IC flash.
Since the late 1980s, the NLDN has served as the source for many CG lightning-related studies over the United States. The network consists of 113 sensors that combine the advantages of direction finding and time-of-arrival techniques. The NLDN CG detection efficiency ranges between 90% and 95% over the midlatitude continental United States, with a median location error of better than 500 m (Cummins and Murphy 2009; Rudlosky and Fuelberg 2010). Although the NLDN is designed to primarily detect CG flashes, it has been recently reported that IC flashes are also detected, depending on the restrictions applied to the processed waveforms [peak-to-zero rise time; Murphy and Nag (2014)].
The present study employs the total flash activity (IC and CG) for all lightning detection systems. Rudlosky and Fuelberg (2013) use a similar methodology for compiling lightning and radar data. Both NLDN and ENTLN have national (U.S.) coverage. Nevertheless, for this analysis the respective total lightning activity is computed only for the clusters that are identified over a radius around where the optimum LMA operation is ensured. Further detailed comparison (e.g., relative location accuracy and detection efficiency) between the lightning detection systems lies outside the scope of this paper. However, their employment is considered as a preliminary attempt to demonstrate results pertaining to the LJ properties from lightning detection networks of different technical specifications (e.g., detection efficiency).
We note that the above-implemented time window within which we calculate the LJ based on empirical observations of the growth and decay on the convective time scale (<10–20 min). Had we allowed for longer periods (e.g., 40–60 min) into the thunderstorm’s lifetime, we would likely have missed the occurrence of the first LJ and a potentially severe weather occurrence. This is why we have empirically tested this algorithm with over 700 storms in multiple storm environments to help understand the variability of the algorithm (Schultz et al. 2011). The choice of the 2σ (i.e., α = 2) in Schultz et al. (2011) is simply a benchmark to which this study is not tied.
3. Analysis and discussion
a. Data and quality control
As WDSS-II tracks cluster independently of the respective total lightning activity, the number of the identified LJ0 and LJ1 clusters is considerably different. For instance, more than 2000 clusters are classified as LJ0 at α = 2.0 and FRT = 10 flashes min−1, whereas less than 200 are classified as LJ1 for the same α and FRT values. To ensure a comparable sample size and to improve the representativeness of the data, we report on the LJ0 and LJ1 clusters that exhibit sustained total lightning activity for more than 95% during their life span (e.g., if a cluster is tracked for 100 min, the cluster must exhibit total lightning activity greater than zero for at least 95 min). This quality constraint (QC1) may classify a slightly different number of clusters depending on the employed lightning detection system. An additional quality constraint (QC2) is applied to the clusters that start or end at a flash rate that is notably higher than zero (set to >10 flashes min−1). Typically, these cases represent merging or splitting clusters or clusters that entered/exited the effective radius of the LMA with high flash rates. QC2 also takes care of potential problems with MESH/VIL repetitiveness due to distance from the radar. Given that the study explores aspects such as the storm duration, the clusters that failed to conform to QC2 are omitted from the analysis. Examples from a tracked cluster that exhibits a problematic tracking (e.g., cluster entering the area with already high flash rates), a normal tracking (i.e., complies with both QC1 and QC2), and an LJ0 cluster and an LJ1 cluster of comparable flash rates are shown in Figs. 1a–d, respectively.
Tracked cluster that exhibits (a) problematic tracking (e.g., cluster entering the area with already high flash rates) and (b) normal tracking (i.e., complies with both QC1 and QC2). (c) LJ0 and (d) LJ1 clusters of comparable flash rates.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00064.1
All three lightning detection systems indicate that the number of LJ1 clusters decreases as the α and FRT values increase (i.e., fewer clusters at higher α and FRT values; Figs. 2b,d,f). Unlike the LJ1, the number of tracked LJ0 clusters increases as the values of α and FRT increase (Figs. 2a,c,e). The latter result should be expected since an LJ0 at, for example, α = 2.0 and FRT = 10 flashes min−1 will also not exhibit LJs at higher α or FRT values.
The identified number of LJ0/LJ1 clusters as a function of FRT (x axis; flashes min−1) and α (y axis) for (a),(b) LMA; (c),(d) ENTLN; and (e),(f) NLDN.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00064.1
b. The autocorrelation function of LJ0 and LJ1 flash time series
Autocorrelation is an essential tool for describing the independence of sequential values in a time series. A slow (fast)-decaying autocorrelation function with time (i.e., lag) indicates a consistent (random) pattern of behavior of the variable under consideration (Bowerman and O’Connell 1979). For example, a slow-decaying autocorrelation function of lightning activity time series would signal coherent behavior in the storm’s updraft speed and volume (e.g., Schultz et al. 2009, 2011, 2014). Consequently, autocorrelation can elaborate on whether the presence of an LJ relates to a numerically random increase in the total lightning activity or points to a more persistent feature of the storm’s dynamical evolution. The autocorrelation function is computed for the flash rates of LJ0 and LJ1, by introducing a time lag that ranges from 1 to +N/2 min, where N is the number of 1-min intervals during which the cluster is tracked (i.e., life span). The lag at which the Pearson correlation is reduced below the 95% significance level denotes the e-folding time. Figure 3 illustrates the average e-folding times for the LJ0 and LJ1 clusters for different α and FRT values. The corresponding results (Fig. 3) show longer e-folding times for the LJ1 clusters. For example, the e-folding times for the LJ1 at α = 2.0 and FRT = 15 flashes min−1 are computed as ~12 min for LMA, 12.7 min for the ENTLN, and 11.5 min for the NLDN. Conversely, the e-folding times for the LJ0 for the same α and FRT values are consistently less than ~4.0 min for all three lightning detection systems and any given α and FRT value. Moreover, the fact that the e-folding times for LJ1 clusters increase as both α and FRT values also increase illustrates a key observation that emphasizes the nonredundant numerical role of both variables α and FRT in the LJ algorithmic implementation (Schultz et al. 2009, 2011).
Mean e-folding time (min) for LJ0/LJ1, as a function of FRT (x axis; flashes min−1) and α (y axis) for (a),(b) LMA; (c),(d) ENTLN; and (e),(f) NLDN.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00064.1
c. Comparison of storm severity potential and physical characteristics between the LJ0 and LJ1 clusters
The previous section studied the LJ0 and LJ1 clusters exclusively from the viewpoint of the flash rate temporal variation. This section explores the mean values of storm attributes derived from WDSS-II. As Fig. 4 demonstrates, the LJ1 clusters exhibit a longer life span than do the respective LJ0 cases, and this observation is consistent throughout the three lightning detection systems and all α and FRT values. For example, for α = 2.0 and FRT = 15 flashes min−1, the average life span is 80 min, whereas the respective LJ0 life span is approximately 35 min. Similar behavior is evident for the mean flash rate (normalized by the cluster’s footprint area; flashes min−1 km−2; Fig. 5), MESH (Fig. 6), and VIL (Fig. 7) values.
Mean life span (min) for LJ0/LJ1, as a function of FRT (x axis; flashes min−1) and α (y axis) for (a),(b) LMA; (c),(d) ENTLN; and (e),(f) NLDN.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00064.1
Mean area-normalized flash rate (flashes min−1 km−2) for LJ0/LJ1, as a function of FRT (x axis; flashes min−1) and α (y axis) for (a),(b) LMA; (c),(d) ENTLN; and (e),(f) NLDN.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00064.1
Mean MESH (mm) for LJ0/LJ1, as a function of FRT (x axis; flashes min−1) and α (y axis) for (a),(b) LMA; (c),(d) ENTLN; and (e),(f) NLDN.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00064.1
Mean VIL (kg m−2), for LJ0/LJ1, as a function of FRT (x axis; flashes min−1) and α (y axis) for (a),(b) LMA; (c),(d) ENTLN; and (e),(f) NLDN.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00064.1
In particular, Fig. 5 indicates that on average, the LJ1 clusters exhibit ~4–5 times higher flash rates than do the respective LJ0 cases. For instance, the average LJ1 flash rates for α = 2.0 and FRT = 15 flashes min−1 are ~0.054 flashes min−1 km−2 as opposed to ~0.015 flashes min−1 km−2 for the LJ0, an observation that is also consistent across all networks. In turn, the MESH values for the LJ1 clusters range from ~11 to 18 mm whereas the corresponding LJ0 values range from ~6.5 to 10 mm (Fig. 6). Likewise, the mean values of VIL are ~18 kg m−2 for the LJ0 clusters and ~25 kg m−2 for the respective LJ1 cases (Fig. 7). As is also highlighted in section 3b, higher flash rates and larger MESH and VIL values (Figs. 5–7) are found with increasing α and FRT thresholds. One could argue that it would be expected to have higher magnitudes of weather severity proxies (e.g., MESH, VIL, etc.) with higher flash rates. Nevertheless, the previous results also suggest that it is not only the flash rate (i.e., FRT) that exhibits a fundamental physical link to storm intensity but also its temporal evolution (i.e., α). The above results are also in agreement with the findings by Rudlosky and Fuelberg (2013).
d. LJ strength and storm decay time
The results shown in Fig. 4 support that the LJ1 clusters with larger α and FRT relate to storms with longer durations (Fig. 4). Approaching the latter from a different perspective, one can raise the following question: Does the strength of the final LJ occurrence relate to the remaining life span of the cluster? To address the above, we compute the time elapsed from the last LJ occurrence to the last time step that a cluster is tracked. Arguably, the results in Fig. 8 corroborate that both α and FRT play a role in the storm’s remaining duration, which shows to increase from around 30–35 min for LJ1 of α = 1.0 and FRT = 10 flashes min−1 to over 45–60 min for higher α and/or FRT values.
Time elapsed until the storm dissipation for LJ1 (min) from (a) LMA, (b) ENTLN, and (c) NLDN, as a function of FRT (x axis; flashes min−1) and α (y axis).
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00064.1
4. Conclusions
The observations herein indicate that the presence of an LJ has implications for a storm’s dynamics, intensity, and evolution. The e-folding times are lower for the LJ1 clusters. For example, the e-folding times for the LJ1 at α = 2.0 and FRT = 15 flashes min−1 are computed as ~12 min for LMA, 12.7 min for the ENTLN, and 11.5 min for the NLDN. Conversely, the e-folding times for the LJ0 for the same α and FRT values are consistently less than ~4.0 min for all three lightning detection systems. Through the enhanced updraft hypothesis, these findings indicate that the presence of an LJ signals the storm’s ability to sustain convection.
The study also documents that LJ1 clusters last longer and exhibit higher flash rates (area normalized), as well as larger MESH and VIL values, further corroborating previous studies that also suggest that the temporal total lightning variability is a dependable proxy for severe weather risk assessment (Williams 2001; Schultz et al. 2009, 2011; Rudlosky and Fuelberg 2013). In addition, the MESH values for the LJ1 clusters range from ~11 to 18 mm whereas the respective LJ0 values range from ~6.5 to 10 mm (Fig. 5). The mean values of VIL are ~18 kg m−2 for the LJ0 cases and ~25 kg m−2 for the LJ1 clusters.
The results throughout this analysis consistently suggest that there is no redundancy in the role of α and FRT in the LJ numerical implementation. This is shown by the increasing magnitudes of the implicated variables (e.g., e-folding time, MESH, flash rate, etc.; see Figs. 2–7) for LJ1 clusters increase as both α and FRT values also increase. Finally, the study offers further evidence that the presence and temporal coincidence of an LJ could be viewed as a proxy for the storm’s expected dissipation. Typically, these values range between 20 and 60 min, depending on the LJ strength, with stronger jumps indicating more time until storm decay.
Ongoing efforts are exploring the value of the LJ as a component in operational severe weather watch/warning issuances (Schultz et al. 2014). The upcoming Geostationary Lightning Mapper (GLM) on board the GOES-R mission (Goodman et al. 2013) will provide continuous monitoring of total lightning activity across the Western Hemisphere. GLM will provide even greater detail on the linkage between temporal lightning variability and the storm evolution over areas where currently related information, including radar, is limited or nonexistent. Importantly, GLM will provide continuous coverage of total lightning over a large domain to evaluate this study on the global scale.
Acknowledgments
We acknowledge the support by the GOES-R System Program as part of the Proving Ground and Risk Reduction programs. The first and second authors also acknowledge the support by the UAH Individual Investigator Distinguished Research awards for 2014. CJS would like to acknowledge the NASA Pathways Intern Program, which provided the funding for support of this work. Sincere thanks to 1) Geoffrey Stano and the NASA Short-Term Prediction Research and Transition Center (SPoRT) for the NA LMA, 2) Earth Networks for the ENTLN data, 3) Vaisala for the NLDN data, 4) Donald R. MacGorman for the Oklahoma LMA data, and 5) Monte Bateman for the ENTLN processing. We would also like to extend our sincere thanks to the three anonymous reviewers who helped us improve this paper.
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