Numerical Simulations of Lightning and Storm Charge of the 29–30 May 2004 Geary, Oklahoma, Supercell Thunderstorm Using EnKF Mobile Radar Data Assimilation

Kristin M. Calhoun Cooperative Institute for Mesoscale Meteorological Studies, and NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

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Edward R. Mansell NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

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Donald R. MacGorman NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma

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David C. Dowell NOAA/Earth System Research Laboratory, Boulder, Colorado

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Abstract

Results from simulations are compared with dual-Doppler and total lightning observations of the 29–30 May 2004 high-precipitation supercell storm from the Thunderstorm Electrification and Lightning Experiment (TELEX). The simulations use two-moment microphysics with six hydrometeor categories and parameterizations for electrification and lightning while employing an ensemble Kalman filter for mobile radar data assimilation. Data assimilation was utilized specifically to produce a storm similar to the observed for ancillary analysis of the electrification and lightning associated with the supercell storm. The simulated reflectivity and wind fields well approximated that of the observed storm. Additionally, the simulated lightning flash rates were very large, as was observed. The simulation reveals details of the charge distribution and dependence of lightning on storm kinematics, characteristics that could not be observed directly. Storm electrification was predominately confined to the updraft core, but the persistence of both positive and negative charging of graupel in this region, combined with the kinematic evolution, limited the extent of charged areas of the same polarity. Thus, the propagation length of lightning flashes in this region was also limited. Away from the updraft core, regions of charge had greater areal extent, allowing flashes to travel farther without termination due to unfavorable charge potential. Finally, while the simulation produced the observed lightning holes and high-altitude lightning seen in the observations, it failed to produce the observed lightning initiations (or even lightning channels) in the distant downstream anvil as seen in the observed storm. Instead, the simulated lightning was confined to the main body of the storm.

Corresponding author address: Kristin Calhoun, National Severe Storms Laboratory, 120 David L. Boren Blvd., Norman, OK 73072. E-mail: kristin.kuhlman@noaa.gov

Abstract

Results from simulations are compared with dual-Doppler and total lightning observations of the 29–30 May 2004 high-precipitation supercell storm from the Thunderstorm Electrification and Lightning Experiment (TELEX). The simulations use two-moment microphysics with six hydrometeor categories and parameterizations for electrification and lightning while employing an ensemble Kalman filter for mobile radar data assimilation. Data assimilation was utilized specifically to produce a storm similar to the observed for ancillary analysis of the electrification and lightning associated with the supercell storm. The simulated reflectivity and wind fields well approximated that of the observed storm. Additionally, the simulated lightning flash rates were very large, as was observed. The simulation reveals details of the charge distribution and dependence of lightning on storm kinematics, characteristics that could not be observed directly. Storm electrification was predominately confined to the updraft core, but the persistence of both positive and negative charging of graupel in this region, combined with the kinematic evolution, limited the extent of charged areas of the same polarity. Thus, the propagation length of lightning flashes in this region was also limited. Away from the updraft core, regions of charge had greater areal extent, allowing flashes to travel farther without termination due to unfavorable charge potential. Finally, while the simulation produced the observed lightning holes and high-altitude lightning seen in the observations, it failed to produce the observed lightning initiations (or even lightning channels) in the distant downstream anvil as seen in the observed storm. Instead, the simulated lightning was confined to the main body of the storm.

Corresponding author address: Kristin Calhoun, National Severe Storms Laboratory, 120 David L. Boren Blvd., Norman, OK 73072. E-mail: kristin.kuhlman@noaa.gov

1. Introduction

Numerical simulations are valuable tools for three-dimensional (3D) storm-scale analysis. The process of retrieving 3D velocity and thermodynamic fields from radar data alone, namely through dual-Doppler synthesis and analysis, can be subject to errors (particularly when deriving properties from the vertical velocity estimates) and may fall short of providing a complete description of the storm and environment. To examine all processes that may be responsible for producing various storm phenomena, previous studies as early as Gal-Chen (1978), Hane and Scott (1978), and Ziegler (1985) have suggested employing numerical models to retrieve thermodynamic and microphysical variables of convective storms that would be difficult or even impossible to determine otherwise. This idea has been advanced through the introduction of radar data assimilation as a means of reducing the differences between observed and modeled storms (Sun and Crook 1998; Snyder and Zhang 2003; Dowell et al. 2004). Typically, radar data assimilation is employed to improve the initial state of the atmosphere used for forecasts (e.g., Yussouf et al. 2013). For the present study, the ensemble Kalman filter (EnKF) method for data assimilation, described by Dowell et al. (2004), is employed specifically for analysis of the storm state during the period in which radar data were available, similar to Tanamachi et al. (2013).

Lightning is inherently linked to noninductive charging between rebounding ice hydrometeors in the presence of supercooled liquid water (e.g., Takahashi and Miyawaki 2002; Saunders et al. 2006) and, as such, lightning data may prove to be a valuable tool in diagnosing storm intensity. While cloud-to-ground (CG) flash rates show little relationship with storm intensity or severe weather (e.g., Reap and MacGorman 1989; Schultz et al. 2011), the total storm flash rate (in cloud as well as CG) appears to be well correlated with measures of storm intensity including updraft volume and updraft mass flux (e.g., Lhermitte and Krehbiel 1979; Kuhlman et al. 2006; Tessendorf et al. 2007; Deierling and Petersen 2008). Initial conceptual models of storm charge structure involved two or three flat, parallel charge layers (e.g., Simpson and Scrase 1937; Simpson and Robinson 1941; Williams et al. 1989) with later studies adding additional layers in and outside the convective core (e.g., Stolzenburg et al. 1998; Wiens et al. 2005) and the possibility of an “inverted” charge structure in some storms (e.g., Marshall et al. 1995; Rust and MacGorman 2002). Through additional observational research and numerical simulations, it has become apparent that mature thunderstorm charge structure is likely much more complex than these conceptual models portray and is likely primarily driven by the 3D storm flow (e.g., Bruning et al. 2012).

The Thunderstorm Electrification and Lightning Experiment (TELEX; MacGorman et al. 2008) field program in Oklahoma was established to further explore the relationship of storm electrification and lightning to storm dynamics and microphysics. During the field campaign multiple observational systems were employed, including a Lightning Mapping Array (LMA) to monitor total lightning activity and the two C-band Shared Mobile Atmospheric Research and Teaching (SMART) radars, described by Biggerstaff et al. (2005). A long-lived, tornadic, high-precipitation supercell storm crossed through the TELEX domain on 29–30 May 2004. The availability of nearly continuous radar data from one of the SMART radars during a particularly intense period of this storm provides high-resolution (in both time and space) reflectivity and velocity data for assimilation. This radar data assimilation combined with numerical parameterizations for storm electrification and lightning provides a unique opportunity to provide a comprehensive analysis of the electrical activity of the 29–30 May 2004 high-precipitation supercell storm relative to behavior and location noted by Calhoun et al. (2013). To our knowledge, this is the first study that uses storm-scale data assimilation to produce a storm consistent with the observations in order to further our understanding of the associated storm electrification and lightning processes. The details of the model and data assimilation system are discussed below, followed by comparisons of the simulated storm to observations and discussion of the results.

2. Data and methods

a. Model background: Dynamics and microphysics

The Collaborative Model for Multiscale Atmospheric Simulation (COMMAS) uses the basic kinematic equation set from Klemp and Wilhelmson (1978) with prediction equations for momentum, pressure, potential temperature, and turbulence kinetic energy (Coniglio et al. 2006; Dowell and Wicker 2009). The numerical integration scheme follows the methodology of Wicker and Skamarock (2002) and Bryan (2005): a third-order Runge–Kutta scheme is used with fifth-order differencing on the first two iterations followed by sixth-order finite differencing for scalar quantities on the final step. Wind components are advected by using a fifth-order nonoscillatory scheme (Bryan 2005).

The microphysics package employed in the COMMAS model is described in detail in the appendix of Mansell et al. (2010); however, it is also briefly summarized below. The microphysics scheme used in the current simulations was adapted from Ziegler (1985) with modifications from Straka and Mansell (2005) for additional diversity in graupel and hail fall speed. A two-moment scheme predicts both the mixing ratio and number concentration for the six hydrometeor categories (shown in Table 1, along with the assumed density or range of densities for water in each category). In addition, the scheme also predicts the number concentration of cloud condensation nuclei (CCN) and the average bulk densities of graupel and hail. Graupel density varies and can range from low-density graupel to high-density frozen drops [or small hail, as in Mansell et al. (2010)]. The conversion of graupel to hail occurs under wet growth conditions, as done by Milbrandt and Yau (2005), but with the additional constraints provided by Mansell et al. (2010). The two-moment scheme utilized in this study has been shown to compare better with observations than a single-moment scheme, in terms of both supercell storm structure and behavior, even when employing an EnKF for radar data assimilation (Dawson et al. 2012; Yussouf et al. 2013).

Table 1.

Hydrometeor categories and densities. A range in values signifies imposed limits on hydrometeor densities in the two solid categories for which density is predicted. [Adapted from Mansell et al. (2010).]

Table 1.

b. Model background: Charging, electrification, and lightning

To produce a hydrometeor charge and, thus, storm electrification, the COMMAS model features several noninductive charging parameterizations as well as an option for inductive charging. The results of laboratory and modeling studies strongly suggest that noninductive charging plays the primary role in generating electric fields comparable to those of observed storms (e.g., Saunders and Peck 1998; Takahashi and Miyawaki 2002; MacGorman and Rust 1998). However, it is believed that inductive charging could also play a role (Mason 1988; Brooks and Saunders 1994). Inductive charging occurs in the presence of an electric field, when a rebounding collision occurs between two polarized particles. In the model, inductive charging occurs when graupel and hail undergoing dry growth collide with water droplets. Noninductive charging (independent of the electric field) occurs during rebounding collisions between riming graupel–hail and ice particles (snow and ice crystals) in the presence of liquid water and is the primary driver of storm electrification in the model. More details on both the inductive and noninductive parameterizations used in the model can be found in Mansell et al. (2005). Differential sedimentation of the graupel and small cloud particles separates the opposite polarities of charge into regions of net charge. As the magnitudes of the net charges in various regions increase, the electric field also tends to increase. With enough charging, the electric field eventually increases to the point that it produces lightning.

Based on previous sensitivity tests of multiple noninductive charging parameterizations (Mansell et al. 2005; Kuhlman et al. 2006; Fierro et al. 2006), it was found that the schemes incorporating rime accretion rate better reproduced observations. As developed by Mansell et al. (2010), this study uses a hybrid parameterization of the noninductive charging mechanism based on the Saunders and Peck (1998) laboratory results, with an adjustment for warmer temperatures (T > −15°C) following Brooks et al. (1997) (Fig. 1). The Saunders and Peck (1998) parameterization is described in more detail in the subsection below.

Fig. 1.
Fig. 1.

Noninductive charge separation sign-reversal curve. The critical RAR curve follows Saunders and Peck (1998) for T < −15°C (shown as dashed curve for T > −15°C) and Brooks et al. (1997) at warmer temperatures. Charge transfer is set to zero for T < −33°C. [Adapted from Mansell et al. (2010).]

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

1) Saunders and Peck charging scheme (SP98)

The noninductive charging rate in the scheme in Saunders and Peck (1998, hereafter SP98) is based on their laboratory charging measurements as a function of temperature and rime accretion rate (RAR). The critical RAR value (RARcrit, g m−2 s−1) is dependent on ambient temperature and delineates positive and negative charging regions in temperature and RAR space (Fig. 1). The sign of the charge transferred to the graupel during a rebounding collision in the SP98 scheme is strongly influenced by the amount of water accreted on the graupel (i.e., the rimer). The charge separated per collision (δq, fC) is calculated according to Brooks et al. (1997) as
e1
where B, a, and b are constants that depend on crystal size (Table 2); Dn,I is the diameter of the cloud ice or snow; and and are the mass-weighted mean terminal speeds for graupel and ice crystals. If RAR > RARcrit, the graupel charges positively according to
e2
If RARcrit > RAR > 0.1 g m−2 s−1, the graupel charges negatively as
e3
Charging is set to zero for RAR < 0.1 g m−2 −1.
Table 2.

Values of constants for the riming-rate charging scheme (from Brooks et al. 1997).

Table 2.
In the model, the curve RARcrit in the SP98 scheme (Fig. 1) is calculated as a piecewise continuous function as given by Mansell (2000):
e4
where s(T) is the sixth-order polynomial function given by Saunders and Peck (1998) as
e5
Since the function s(T) becomes negative at temperatures less than −32.45°C and liquid droplets can exist at temperatures as low as −40°C, the function k(T) is used for T < −23°C to keep the critical RAR positive down to T < −33°C:
e6

The reader is strongly encouraged to review appendix A of Mansell et al. (2010) for details of the two-moment microphysics scheme (e.g., hydrometeor diameters and calculation of terminal fall speeds) used within the charging parameterization above.

2) Charge conservation, advection, and ions

The charge density on each of the six hydrometeor types is explicitly predicted. As mass is exchanged between categories in the microphysics, the corresponding amount of charge also is transferred from one category to another (e.g., mass from ice to rain). Although charge is conserved in the model domain, charge is not absolutely conserved due to charge movement from ion currents (including surface corona discharge) entering or exiting the domain, advection through a lateral boundary, or transport to ground by lightning. The charge continuity equation from Mansell et al. (2005) resembles a typical conservation equation with treatment of advection, diffusion, and particle sedimentation. The model neglects the accelerations of charged particles and enhanced coalescence effects in an electric field. The three components of the ambient electric field are explicitly solved via a computationally efficient elliptic multigrid solver.

Small ion processes are also included in the model (Mansell et al. 2005). Conservation equations are defined for both positive and negative ion concentrations. The equations take into account advection, mixing, drift motion (ion motion induced by the electric field), cosmic ray generation, ion recombination, ion attachment to hydrometeors, corona discharge from the ground, and release of ions from evaporating hydrometeors. This work follows Mansell et al. (2005) and uses a fair-weather state from Gish (1944) as expressed by Helsdon and Farley (1987) to incorporate sources of ions unrelated to thunderstorms.

3) Lightning parameterization

Lightning flashes are parameterized by a stochastic dielectric breakdown model as described by Mansell et al. (2002, 2005), a version of which has been employed, for example, by Kuhlman et al. (2006), Fierro et al. (2006), Riousset et al. (2007), Krehbiel et al. (2008), and Mansell et al. (2010). The lightning develops bidirectionally across a uniform grid with each step chosen randomly from among the surrounding points at which the electric field meets or exceeds a fixed, height-dependent threshold value for propagation. After each step, the electric field is recalculated to include the contribution of the lightning channel to the electric field. The end result is a branched, fractal-like leader structure of each flash in three dimensions.

Following Mansell et al. (2010), flash initiation occurs if the electric field reaches the threshold Ebe for runaway air breakdown determined by Dwyer (2003). A particular initiation point is chosen randomly from all the points that exceed 0.9Ebe and the flash maintains an overall charge neutrality. The critical threshold for continued channel propagation is assumed to be a fraction of the initiation threshold. Continuation of lightning propagation is quite sensitive to the grid resolution (Tan et al. 2006). Even though the lightning grid spacing is smaller in the horizontal (500 m) than the dynamics grid spacing (1 km), it still does not approach the 250- or 12.5-m resolutions that were tested by Tan et al. (2006). Thus, the threshold for the continued breakdown of lightning leaders relative to initiation is set to be quite small in this study to compensate for the inadequate resolution (e.g., Mansell et al. 2010).

Positive (negative) leaders carry positive (negative) charge and tend to propagate preferentially through regions of net negative (positive) charge density (Mansell et al. 2002). Therefore, the polarity of the simulated lightning channels tends to reflect the storm’s charge structure. As in Mansell et al. (2005, 2010), a flash is declared to be a CG if it descends to a height threshold of 500 m (or three grid points above ground herein). Even with this addition, the model still underpredicts the fraction of flashes that strike ground relative to the observations.

c. Radar data

This study utilizes data from one of the two mobile C-band SMART radars (SR1 and SR2), described by Biggerstaff et al. (2005). The SMART radars completed volume scans every 3 min for over 2 h as the storm passed through central Oklahoma. For the majority of data in this study, sector volume scans of approximately 120° were used, with the radar completing an entire volume scan in 1 min 50 s. Elevation angles ranged from 0.5° to 59° with increments of 0.3°–3.0°. Both SMART radars had a 1.5° beamwidth (Biggerstaff et al. 2005). This study uses the same data, including all manual editing processes, as in Calhoun et al. (2013). However, data from only SR2 was assimilated whereas both SR1 and SR2 were used in the dual-Doppler analyses completed by Calhoun et al. (2013).

d. Data assimilation

Following the methodology of Dowell et al. (2004) and Yussouf et al. (2013), each sweep of edited SR2 data was objectively analyzed separately onto a horizontal Cartesian grid, maintaining the conical distribution of the data and reducing vertical interpolation errors. To complete this interpolation of reflectivity and velocity prior to data assimilation, a Cressman weighting function with a 1000-m radius of influence was used with grid points spaced 2000 m apart in the horizontal, corresponding to every other model grid point in the x and y directions. The vertical height of each data point corresponds to the actual height of the observation on the conical scan at the (x, y) location. Reflectivity and radial velocity data from SR2 were assimilated in approximately 5-min intervals from 2320 UTC (15 min after the start of the simulation) to 0040 UTC. Only data occurring within 60 s of the assimilation time and under 8.5 km in height was included in the assimilation. The EnKF methodology (specifically, an ensemble square root filter or EnSRF) was used to assimilate the observations following the process described by Dowell and Wicker (2009) and Dawson et al. (2012). The EnSRF uses the traditional Kalman gain for updating the ensemble mean but uses a “reduced” Kalman gain to update deviations from the ensemble mean (Whitaker and Hamill 2002). As completed by Dowell et al. (2004), observations were processed serially, under the assumption that observational errors are uncorrelated in space and time. Values of (2.0 m s−1)2 and 5 dBZ were used for the observation-error variance in the Doppler velocity and reflectivity observations, respectfully, following Dowell et al. (2004), Dowell and Wicker (2009), and Dawson et al. (2012).

e. Model configuration

This analysis 1) created an ensemble of model states starting at 2305 UTC, 2) advanced the ensemble to the first observation time (2320 UTC, 15 min into the simulation), 3) assimilated all observations within 60 s of the time, 4) advanced the ensemble to the next observation time, and 5) repeated the process as the ensemble reached each observation time, until the last observation was assimilated at 0041 UTC (96 min into the simulation). The simulation continued to run without data assimilation until 0055 UTC (110 min from the start of the simulation).

The size of the model domain was 140 km × 140 km × 22 km, with a horizontal grid spacing of 1 km and a vertical grid spacing of 200 m stretched to a maximum of 500 m at 20 km over 53 grid points. Lightning propagation was calculated on a grid having higher resolution (500 m spacing) in the horizontal, with the lateral domain extended 10 km at 500-m spacing surrounding the dynamics domain. The environment over the domain was initialized to be horizontally homogeneous and was based on a combination of two soundings (Fig. 2). Below 400 mb, the sounding was taken from an environmental sounding released near Weatherford, Oklahoma. Above 400 mb, the data were from the sounding released at the Norman, Oklahoma, National Weather Service Forecast Office at 0000 UTC.

Fig. 2.
Fig. 2.

Skew T–logp diagram for the base state in the assimilation experiments. Below 400 mb, the sounding is taken from an environmental sounding released near Weatherford. Above 400 mb, the sounding is from data from the National Weather Service Norman sounding released at 0000 UTC. Winds are plotted with a filled flag = 25 m s−1, full barb = 5 m s−1, and half-barb = 2.5 m s−1.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

A 24-member ensemble was used; convective storms developed in the ensemble members through the random bubbles, model advance, and data assimilation. Since the members were initialized with horizontally homogeneous base states, thermal bubbles were used to initialize convection. The process of inserting these warm (4 K) bubbles was automated: they were inserted into the boundary layer where observations indicated strong convection that was not yet represented in the ensemble mean (i.e., >30-dBZ difference). The bubbles had a horizontal radius of 7.5 km and a vertical radius of 2 km and were added throughout the simulation; for the first time steps of the simulation, 18–20 bubbles were required, but this was quickly reduced to less than 7 by the time electrification began at 40 min and no more than 2 were required at any time step shortly thereafter. This methodology to populate the ensemble follows that described by Dawson et al. (2012) and Tanamachi et al. (2013).

3. Results and discussion

a. Comparison with dual-Doppler observations

All members of the ensemble exhibited smaller reflectivity values than had been found in the dual-Doppler analyses presented in Calhoun et al. (2013). This was especially true at midlevels of the storm, where the reflectivity was particularly deficient in the region of the southern overhang and within the back shear anvil. The smaller reflectivity values are due in part to signal attenuation in the C-band observations from SR2, which was located southwest of the reflectivity core throughout the assimilation period, while the observations in Calhoun et al. (2013) used the maximum reflectivity at a given location from either radar. Therefore, in both the SR2 data and all of the ensemble members, the reflectivities directly along the path of the radar beam behind the storm hail core were too weak.

On average, the mesocyclone strength in the simulations was considerably weaker than the dual-Doppler derived mesocyclones noted by Calhoun et al. (2013), though the location and shape are generally well matched. The vertical velocities of the main updraft in all members of the simulation were slightly smaller at low levels, but nearly identical at mid- and upper levels of the storm (Fig. 3). The differing values of the mesocyclone strength, in particular the lower values in the simulations, are somewhat expected with a 1-km grid spacing, as smaller grid spacing (such as the 500 m used in the dual-Doppler analyses) may have enabled the simulation to produce slightly higher values (e.g., Adlerman and Droegemeier 2002). Throughout the remainder of this work (including all figures), comparisons with dual-Doppler analyses are made primarily with member 1 of the ensemble, though the ensemble spread is presented in many of the figures and the analysis. (Note: all members provide similar kinematic results, but only members 1–4 included electrification processes to conserve computing resources.)

Fig. 3.
Fig. 3.

Maximum vertical velocity (m s−1) in member 1 of the EnKF simulations (solid lines) and dual-Doppler analyses (points) at 1.5 km (bottom values) and 9 km (top values) AGL. Ensemble spread is represented by the shaded regions at both 1.5 and 9 km.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

At 73 min (Fig. 4; corresponding to 0018 UTC in the observations), member 1 appears to match the dual-Doppler reading at 0016–0019 UTC reasonably well. Although reflectivity values in the simulation are about 5 dBZ less and not as large in areal extent as observed, the overall shape of the storm and hook echo, as well the location of the maximum of the forward-flank downdraft (FFD), are reproduced quite well by the model. The mesocyclone size, shape, and strength were also replicated well in the simulation. The maxima of the updraft at low levels along the edge of the outflow and the hook echo, as well as the location of the updraft associated with the bounded weak-echo region (BWER) at midlevels, were also captured.

Fig. 4.
Fig. 4.

The 0016–0019 UTC dual-Doppler analysis at (a)–(c) 1 km AGL from Calhoun et al. (2013) and member 1 at 0018 UTC (72 min into simulation) at (d)–(f) 1.1 and (g)–(i) 5.8 km. (a),(d),(g) Reflectivity (color fill, dBZ). (b),(e),(h) Reflectivity, horizontal wind vectors (m s−1), and vertical vorticity (contoured every 10 × 10−3 s−1, beginning at 10 × 10−3 s−1). (c),(f),(i) Vertical velocity (color fill, m s−1) and reflectivity (contoured every 20 dBZ).

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

At 83 min into the simulation (Fig. 5), the two observed regions of the rear-flank downdraft (RFD) of the dual-Doppler analyses at 1 km are also well reproduced: one with the peak reflectivity near the tip of the hook and another extending along the southern semicircle of the hook from the core (cf. with Fig. 7 of Calhoun et al. 2013). The simulated reflectivities in the FFD, which are collocated with the surface reflectivity maximum, are slightly smaller in the simulation than was found in the dual-Doppler analysis. The size and shape of the main updraft at low levels was well approximated with similar peak values at similar locations: above the tip of the hook and following the outflow boundary along the reflectivity edge around to the south side. However, the simulated storm was smaller than observed at midlevels (in terms of 40+ dBZ areal coverage), and the simulated mesocyclone was neither as strong nor as circular as observed during this time period.

Fig. 5.
Fig. 5.

As in Fig. 4, but at 0028 UTC.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

By 95 min (Fig. 6), the simulated storm resembled the observations in terms of size and shape, with relatively larger reflectivity values (i.e., >50 dBZ) extending through the hook echo and reflectivity values at midlevels closer to what was observed by radar than during earlier time periods. The simulation captured the observed occlusion of the mesocyclone at this time and also produced additional wrapping of the main updraft and an intrusion of the RFD into the region.

Fig. 6.
Fig. 6.

As in Fig. 4, but at 0040 UTC.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

By 105 min, the older of the two mesocyclones was completely occluded in the simulations (Fig. 7), consistent with in the observations (Fig. 8 of Calhoun et al. 2013). As evident in both the observations and the ensemble members, the mesocyclone at this time was not associated with the main updraft, but instead was completely immersed within the RFD. As the simulated mesocyclone became fully wrapped by the downdraft, it weakened and decayed more rapidly than in the observed storm. Meanwhile, a new mesocyclone developed in the simulation in a new main updraft region farther east along the gust front. At this point, without the continued data assimilation, it is evident that the storm is rapidly decaying from the mature stage noted just 10 min prior.

Fig. 7.
Fig. 7.

As in Fig. 4, but at 0050 UTC.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

b. Microphysical and electrical evolution

Throughout the analysis period, the storm can be considered a well-developed, mature, supercell storm. For the simulations, it was necessary first to initialize storms where they were observed and then allow the simulated storms to take on the character of the observed storms through the data assimilation process. Due to artifacts in the behavior of the lightning in early trial runs, electrification processes were started at 40 min into the simulation, after the subject storm had relatively stabilized. At that time, the storm was large, with core reflectivities greater than 60 dBZ and updrafts as large as 70 m s−1 at midlevels. A hook echo and low-level mesocyclone were simulated as early as 56 min. Because all the electrified members (1–4) provided very similar results, the majority of the results presented in this section focus on member 1, for brevity.

A charge structure could be discerned in the simulated updraft at 42 min, only 2 min after electrification processes started. The charge structure at this time consisted of an inverted polarity tripole, with a main positive charge region (between 9 and 11 km in height), sandwiched between a small upper negative region (11–13 km) and a large lower negative region (5–9 km). This charged region covered about 10 km horizontally. Less than 2 min later (at approximately 44–46 min into the simulation), the charge structure had evolved dramatically: the core of the storm contained six layers of charge, as an additional small lower positive region (below 4 km) and an upper dipole (between 13 and 16 km) developed. The center of the charge structure was still dominated by the inverted tripole, but the main positive charge region had expanded in depth and width while the lower negative charge region moved farther downward and outward into the FFD. Over this first 10-min period, the amount of both positive and negative charge increased quickly, doubling from 1000 nC m−3 of each polarity at 42 min to nearly 2000 nC m−3 within the entire storm by 50 min in almost all members (Fig. 8). By this point in the simulations, the storm charge spanned about 20 km horizontally. It is also at this point that the first lightning flashes were initiated.

Fig. 8.
Fig. 8.

(top) Positive storm and (bottom) negative storm charges (nC m−3). Ensemble spread from the explicitly electrified members (members 1–4 and ensemble mean) is depicted by the purple (positive charge) and blue (negative charge) shaded regions.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

The charge structure continued its complex evolution (Fig. 9) through 60–70 min; charged hydrometeors were advected farther away from the updraft core and recycled through the updraft while lightning activity neutralized pockets of charge. While the overall charge structure continued its elaborate evolution, the overall amount of positive and negative charge in the storm stayed nearly steady state (Fig. 8). As the simulation progressed, little charge existed below 4 km in the region of the main updraft core. However, above this level within the updraft, there were more than five or six distinct charge layers all characterized by small horizontal extent (some less than 5 km wide and all smaller than 10 km). In the forward-flank downdraft, six to seven different charge layers were frequently present. These tended to exhibit a relatively longer horizontal extent, reaching as far as 30 km horizontally from the region of active charging within the main core updraft. Overall, the charge structure at this time was more complex than a dipole or tripole structure (Fig. 9e). The complexity of the storm charge structure was apparent throughout the rest of the simulation time (e.g., Fig. 10) and in all electrified members (Fig. 11).

Fig. 9.
Fig. 9.

Data from ensemble member 1 at 0018 UTC. (a)–(d) Net charges at 0.1 and 1.0 nC m−3, with positive in purple/red and negative in blue. Reflectivity contours are at 20, 40, and 60 dBZ. Lightning initiation locations within 1 km of each level are in green fill. Shown are z = (a) 14.3, (b) 10.3, (c) 5.8, and (d) 1.1 km. (e)–(g) Cross section through storm at y = 60 km. (e) Storm charge at 0.1 (light shading) and 1.0 (dark shading) nC m−3, with positive in purple/red and negative in blue. (f) Noninductive charge separation rates between graupel–hail and ice crystals–snow at 50, 100, 200, 300, 400, 600, 800, and 1000 pC m−3 s−1. Polarity (red, positive; blue, negative) indicates the sign of charge gained by graupel–hail. Lightning initiation regions (green), areas of positive leaders (red contour, yellow fill), negative leaders (blue contour, gray fill), and 20-dBZ reflectivity contour also shown. (g) Reflectivity (dBZ, color scale Fig. 4) and wind vectors, with the cloud boundary (gray contour).

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

Fig. 10.
Fig. 10.

As in Fig. 9, but at 0028 UTC (82 min).

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

Fig. 11.
Fig. 11.

Noninductive charge separation rates between graupel and ice crystals–snow; polarity (contoured: red, positive; blue, negative) indicates the sign of the charge gained by graupel. For storm charge (>0.1 nC m−3), positive is shown in the purple-shaded region and negative in the blue-shaded region.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

Laboratory experiments (Takahashi and Miyawaki 2002; Saunders et al. 2006) show that the graupel within and surrounding the main updraft gains negative charge over much of the mixed-phase region at moderate cloud water content, but gains positive charge at warmer temperatures and higher cloud water content (following the critical RAR curve as shown in Fig. 1). Both positive and negative charging of the large ice hydrometeors occurred within different parts of the main updraft region: on the east side and within the core of the updraft at high liquid water contents, the larger ice hydrometeors gained positive charge (Fig. 11). On the periphery of the updraft and on the west side of the updraft, strong negative charging of graupel and hail was simulated owing to relatively lower cloud water content and colder ambient temperatures (Figs. 9f, 12, and 10f).

Fig. 12.
Fig. 12.

Cross sections through member 1 at (a),(b) 0018 UTC (as shown in Fig. 9) and (c),(d) 0028 UTC (as shown in Fig. 10). (a),(c) Mixing ratio contours of rain (0.5, 1.0, 3.0, 5.0, 9.0, and 13.0 g kg−1) and cloud ice (0.5, 1.0, 1.5, 2.0, and 4.0 g kg−1). Gray fill indicates areas of updraft >15 m s−1. Cloud outline indicated by gray contour. (b),(d) Mixing ratio contours of hail (1.0, 3.0, 5.0, 9.0, 13.0, and 17.0 g kg−1). Gray fill is cloud water content (0.1, 0.5, and 1.5 g m−3). The 20-dBZ outline is indicated by the dark gray contour. Rain, cloud ice, and hail contours are green, blue, and orange, respectively.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

As seen in Fig. 12, the availability of relatively high liquid water contents in the simulated storm contributed greatly to the positive noninductive charging rates of graupel and frozen drops. However, this did not result in a strictly inverted vertical tripole (i.e., having a positive charge region between two negative charge regions). As evident in all electrified members, at midlevels, while parts of the storm do contain a net positive polarity charge, substantial regions of the storm at the same altitude contain negative charge instead (Fig. 11). Thus, the resulting charge structure between 6 and 12 km of the main updraft region cannot be succinctly described as inverted or normal polarity, as inverted and normal polarity structures both exist side by side near the main updraft region as well as throughout the storm, as found in other observed storms documented by Weiss et al. (2008) and Emersic et al. (2011).

It is this complexity of the charge structure that supports CG flashes of both polarities, as both positive and negative charge regions exist in different areas of the lowest levels of the storm. Because of this evolving complex charge structure, it is apparent that the polarity of a particular ground flash depends directly on the time and location at which it initiated. Once electrification processes were allowed in the simulation, pockets of negative charge were consistently seen at lower levels on the northern side of the storm, each surmounted by regions of positive charge. Several studies have suggested that such a charge configuration is conducive to +CG production (e.g., Mansell et al. 2002; MacGorman et al. 2005; Wiens et al. 2005). All CG flashes produced by the simulation between 45 and 70 min were +CG flashes and were coincident with the aforementioned charge configuration. From 75 to 105 min, the majority of the simulated CG flashes were negative polarity, with all of the −CG flashes occurring in the hook echo and RFD region of the storm through 105 min. In these regions below 4 km, there was positive charge throughout the simulation (Figs. 9d and 10d) that triggered initiation of the downward negative channels that connected with the ground.

Most simulated flashes were initiated at altitudes between 8 and 11 km (Fig. 13), in regions of active charging immediately surrounding the updraft region, with leaders predominately progressing through regions of graupel and hail mixing ratios greater than 1 kg m3. All flashes remained in relatively close proximity to the storm core with very few leaders traveling into the glaciated anvil region. As noted by MacGorman et al. (1981, 2001), Williams (1985), and Mansell et al. (2002) lightning propagation is primarily restricted to regions of substantial charge density. Thus, the limited extent of the simulated lightning is consistent with substantial charge densities extending only about 30 km from the updraft region in the simulated storm. To replicate the anvil lightning noted in the observed storm (Kuhlman et al. 2009), an additional charging parameterization, possibly involving ice–ice particle interaction in regions of supersaturation with respect to ice, as discussed by Mitzeva et al. (2006), is likely needed.

Fig. 13.
Fig. 13.

Log density plot of initiations per time step (3 s) per grid height (500 m) over the time of active electrification in member 1.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

A secondary region of charging (and lightning activity) separate from the main updraft region occurred sporadically throughout the simulation. One example occurred at 0018 UTC and (x, y) = (65 km, 60 km) with active charging at altitudes between 6 and 8 km and lightning leaders traveling within an altitude range of 4–10 km (Fig. 9f). This secondary region of charging was not located in a significant updraft region, but occurred within the FFD. During the periods of active charging, a higher concentration of cloud water existed in this region in addition to the large mixing ratios of hail and graupel (Fig. 12b). This additional region of charging was rare and appeared intermittently during the simulation.

Although reflectivity values at altitudes between 5 and 7 km remained between 30 and 50 dBZ, very little to no lightning was seen below 7 km on the southeast side of the storm. As noted above, lightning was essentially restricted to regions of substantial charge density, and, thus, the lack of lightning noted above was due to the relative lack of charge in this region (Figs. 9 and 10c,d). Charging rates on the southeast side of the main updraft core were much lower to nearly nonexistent relative to those simulated on the northwest portion of the main updraft and downshear to the northeast. The southeast region of the storm lacked the higher concentrations of water vapor and cloud ice that were present on the northwest side—a necessary ingredient for noninductive charging in the model parameterization and in laboratory experiments, as discussed previously. Above 9 km, an increase in charge density and lightning activity are noted, though the majority of flash initiations still occurred on the north and northeast side of the updraft core (Figs. 9 and 10a,b). The distribution of lightning in the observed storm had a comparable deficit below 7 km on the south side of storm (Calhoun et al. 2013). The increase in lightning activity between 9 and 11 km in the observations was much greater than produced by the model simulations. It is possible that both discrepancies were a consequence of the model tracking only the mean motion of each particle category and, thus, underestimating or even missing altogether the trajectories of larger and smaller particles. It is also possible that the lack of a lightning maximum at higher altitudes in the simulation was again a result of the lack of charging at low-liquid water content not accounted for in the current modified SP98 noninductive charging parameterization, as suggested above to explain the lack of anvil lightning.

The majority of both observed and simulated flashes was small and was contained within the region of the main updraft core. More than 65% of the simulated flashes were less than 10 km in total channel length, and more than 55% spanned 5 km or less. Less than 3% of simulated flashes were long enough to connect more than 200 grid points in the flash; these may correspond to the exceptionally long observed flashes. Though these long flashes were relatively rare and there was some scatter in the location at which they were initiated, the majority initiated in the north-to-northeast portion of the storm within reflectivities ranging between 55 and 60 dBZ within a layer confined between about 9 and 12 km. Similar to the region with predominately smaller flashes, the region with very large flashes tended to receive a continuous influx of charge from the active charging region in the periphery of the main updraft. However, in contrast to the small pockets of opposing charge polarity in the updraft region, this region of the storm contained larger, more continuous horizontal regions of each charge polarity that allowed flash leaders to propagate farther before terminating.

As in the observed storm, a transient lightning hole was present in all four electrified members of the simulations. The lightning hole appeared at similar times in the different members, typically within 2–3 min of each other. However, some members produced larger and more persistent holes than others. This feature first appeared around 2355–0010 UTC (49–64 min into the simulation) in a couple of the members and another short-lived hole appeared around 0015–0023 UTC in almost all of the electrified members. The feature was not seen again until 0038 UTC in member 1 and then appeared again in all the members around 0048–0054 UTC.

The lightning hole produced by member 1 near the end of the simulation (at 0049–0052 UTC; 103–106 min) corresponded with the BWER (on the southeast edge) and with the main updraft core (Fig. 14), as found by the dual-Doppler and LMA analysis of Calhoun et al. (2013). The charge density in the lightning hole, while not zero, was smaller during this time period than was found in this region during periods not containing a lightning hole. There was a complete absence of charge and active noninductive charging below 8 km in regions where vertical velocities exceeded 40 m s−1 (Fig. 15). The central region of the lightning hole lacked significant concentrations of large ice particles; mixing ratios for hail were below 2 g kg−1 in the center of the hole.

Fig. 14.
Fig. 14.

Data from ensemble member 1 at 0050 UTC, 104 min into the simulation. (a) Composite of lightning initiations (green), positive leaders (yellow fill, red contour), and negative leaders (gray fill, blue contour) within 2.5 km from 8.8 km. (b) Reflectivity at 8.8 km (grayscale) with positive (red) and negative (blue) leaders contoured. Solid black line is referenced in Fig. 15.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

Fig. 15.
Fig. 15.

Data from ensemble member 1 at 0050 UTC, 104 min into the simulation. (a) Net charge density with positive shown in purple and negative in blue, as well as wind vectors. (b) Contours for hail mixing ratio (orange), cloud outline (gray), and gray fill of vertical velocities at 25 and 40 m s−1 (light and dark gray, respectively). (c) Contours of noninductive charging rate of graupel–hail for positive in red and negative in blue, as well as the 20-dBZ reflectivity (dark gray). Gray-fill patterns of negative (light) and positive (dark gray) charge densities. Cross section for all panels is along the solid black line in Fig. 14.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

The heights of the flash initiations in the simulations were similar to those in the observed storm. Throughout the simulation, lightning initiations peaked near 10 km (maxima typically at the 9.8- and 10.3-km grid heights) (Fig. 13); this roughly the same height as the majority of the lightning initiations in the observed storm. This height also marks the boundary between large concentrations of cloud ice (above) and regions of rain and water vapor below (Fig. 12). During the time of early electrification (prior to 60 min), this region above 10 km consisted primarily of positive lightning breakdown through regions of negative charge associated with cloud ice. As the simulations progressed, the majority of initiations remained near 10 km, though, as mentioned previously, depending on the specific region of the updraft, cloud ice gained either positive or negative charge (e.g., Fig. 11). More importantly than the specific charge attached to the hydrometeors, the region of peak initiations was just below the region of largest cloud ice mixing ratio, where cloud ice was the dominant species, and just above the region of highest mixing ratio of graupel and hail around −30° to −40°C in the storm core. As a result, the region of peak initiations was within and just above the region of highest charging rates.

High-altitude lightning (i.e., above 13 km), though usually infrequent, did occur in the simulations, similar to the observed storm, but not as often. Less than 3% of the total flashes initiated at heights greater than 13 km. Above 15 km, the percentage was even smaller, with only 0.3% of all flashes in the storm. Lightning initiations at these heights were located primarily above the main updraft region, where vertical velocities greater than 35 m s−1 reached at least 13 km in the overshooting top. However, in contrast to the uniformly small flashes observed in the overshooting storm top, the simulated high-altitude flashes varied markedly in size: the smallest flashes were only 2–3 km in total length (adding together the length of all channel steps, including those in all branches) while the largest were as long as 150 km. The size of the majority of high-altitude flashes fell in between, typically less than 45 km of total leader channel length. After initiation, leaders normally followed the cloud boundary directly downshear from the overshooting top and tapped the charge regions advected downshear from the main updraft. It appears that the lightning in this region was most commonly initiated between charge regions of opposite polarity created within the updraft core at temperatures warmer than −40°C. The charged particles were lofted above 14 km by the updraft at the time. Occasionally, the lightning was possibly initiated between the screening-layer charge at the cloud boundary and the upper charge transferred by the noninductive mechanism to cloud particles, though this was quite rare.

The pattern of evolution of flash rates in the simulated storm had features similar to those of the observed storm (Fig. 16). While the observed flash rate was not at all correlated to the simulated flash rates in any of the electrified members (correlations ranged from 0.14 to 0.18 for each member and the observed flash rate), all of the members produced considerably high flash rates similar to the observed storm: between 300 and 600 flashes min−1. The flash rates also had episodic behavior in each simulation, with lower flash rates between 2355 and 0000 UTC and again from 0030 to 0040 UTC, similar to the observed storm, however not with the same timing, accounting for the low correlations between the two. In the simulation, the second period of lower flash rates coincided with a decrease in updraft mass flux and graupel volume in the simulation (Fig. 17). However, the correspondence with kinematic properties was not as clear for the first period of smaller flash rates. Although updraft mass flux decreased slightly during the period of the first decrease in flash rate, the flash rate rapidly increased between 0000 and 0005 UTC without a corresponding increase in updraft mass flux or graupel volume. While both updraft mass flux and graupel volume show moderate to strong correlations with the flash rate of member 1, 0.46 and 0.61, respectively, this is a bit lower than noted in previous studies (e.g., Wiens et al. 2005; Kuhlman et al. 2006; Deierling and Petersen 2008).

Fig. 16.
Fig. 16.

Flash rate from member 1 (solid line) and observed storm (dashed line) for the same time period. Ensemble spread (includes members 1–4 and the ensemble mean, which was explicitly electrified) is represented by the shaded region. Note that electrification was not started until 2345 UTC and the initial maximum in the simulated flash rate may have been a result of artifacts due to the sudden onset.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

Fig. 17.
Fig. 17.

Updraft mass flux: (a) time series of member 1 within the mixed-phase region (0°–40°C, black), ensemble spread shown in gray and (b) time–height, contoured every 1 × 109 kg s−1, beginning at 1 × 109 kg s−1. Graupel volume: (c) time series of member 1 within the mixed-phase region (black), and ensemble spread shown in gray, and (d) time–height, contoured at 5, 50, 125, 200, 300, 450, and 550 (red) km3. Corresponding heights of temperatures in the mixed-phase region are noted along the right y axis.

Citation: Monthly Weather Review 142, 11; 10.1175/MWR-D-13-00403.1

The simulations also captured an increase in the rate of flash initiations at lower elevations and an increase in −CG flash rates, both of which occurred in the observed storm around 0040 UTC. In the simulations, these flash-rate increases occurred at about the same time as the updraft mass flux and graupel volume began to increase again, though the increase in these parameters was not as great as seen earlier in the simulations. Note, however, that the CG lightning rate of the simulations was hampered by a known underproduction of CG flashes by the lightning parameterization related to insufficiently small vertical grid spacing (Mansell et al. 2002, 2010). So, while the −CG rate for the observed storm at this time was 10–15 min−1, the simulations never produced more than 3 min−1.

As expected with an HP supercell, this simulation exhibited relatively high concentrations of large ice hydrometeors (Fig. 12). The flash rates are in no way tuned via any type of scaling factor; instead, they are controlled completely within the model by the amount of charge produced by the charging parameterization. The large concentrations of precipitating ice contributed to a large noninductive charging rate (Figs. 9f and 10f), ultimately providing the large rate of charge replenishment needed to maintain the extremely high flash rates produced both in the simulations and in the observed storm (Fig. 16). Throughout the analyzed period, flash rates remain above 200 min−1 and at times peaked at 400–600 min−1. (Note, however, that the first peak near 700 min−1 in the simulation occurred at the beginning of the analyzed period, between 2345 and 2355 UTC, shortly after electrification was started, and was likely inflated by artifacts relating to the sudden start of electrification.) The difference from previous simulations, and the probable cause of large flash rates in the present simulations, was in the very large amount of precipitating ice in the mixed-phase region, coincident with the prediction of ice crystal concentrations by the microphysics parameterization, and the exceptionally large updraft mass flux and, similar to the observed storm, many small, compact flashes neutralizing limited amounts of charge.

4. Summary and conclusions

As noted in both the observations and the simulations, this supercell produced exceptionally large flash rates, dominated by flashes in the inner core of the storm that were small in overall leader extent. The updraft core was the predominant region of active charging and, when combined with the turbulence due to updraft–downdraft interaction, led to small pockets of high charge density of opposite sign in close proximity to each other. The resulting strong electric fields allowed frequent flash initiation, but the leaders in these flashes had little room to travel before reaching an area of unfavorable electric potential. The combination of the small amount of charge neutralized by each of these flashes, the large noninductive charging rates, and the rapid charge replenishment provided by the substantial updraft mass flux were the main factors that enabled such high flash rates to persist throughout the simulation in a manner similar to that of the observed storm. After the first 10 min of electrification, the amount of charge in the storm remained relatively steady state, emphasizing the charge replenishment process. Moving away from the storm core and toward the anvil region, regions of charge were larger with greater areal extent, and this allowed flashes to travel farther without termination.

The region of highest flash density, surrounding and just downshear from the updraft core in both the observed and simulated storms, is representative of the region of maximum charge replenishment. Due to the strong, persistent, and sizable updraft, the peak region of flash initiations in both the observed and simulated storms was centered near 10 km, higher in altitude than observed or simulated for less severe storms. In the simulations, this region contained the highest concentrations of large ice hydrometeors (graupel and hail) overlapping the edge of the cloud ice concentrations just above. The highest noninductive charging rates occurred within or immediately below this region in and surrounding the main updraft, in regions of high liquid water contents. Noninductive charging led to both positive and negative charging of graupel in and around the main updraft, with the polarity depending on the temperature and liquid water content of the region. The decidedly large concentrations of ice hydrometeors and cloud water content, combined with the large, steady updraft for this HP supercell (reflected in the large values of updraft mass flux and graupel volume seen in Fig. 17), maintained the charging rates at a consistently high level throughout the simulations.

A lightning hole was noted in both the observations and simulations of the 29–30 May 2004 supercell. In both cases, the lightning hole was collocated with the BWER and maxima of the updraft, though not taking on the exact shape of either. The dual-Doppler analyses depicted divergence and circulation around the lightning hole, suggesting that charged hydrometeors were actually being swept out from and around this area. Though the lightning hole in the simulations was not as consistently present as in the observations, when it did occur, there was a complete absence of charge and active noninductive charging through the region of the main updraft core directly below the lightning hole. Vertical velocity in the region of the lightning hole in the simulations generally exceeded 40 m s−1.

The simulations also reproduced the high-altitude lightning seen in the observations, though its nature was different than observed. The simulated flashes were typically of greater spatial extent than the singular VHF emissions seen by the Lightning Mapping Array (note, however, that simulated flashes are at least 1 km in length due to grid resolution): simulated flashes were generally around 45 km in total leader length, though they ranged from as small as 2–3 km to as large as 150 km in total branched length. However, both the simulated and observed flashes initiated at similar altitudes directly above the main updraft region. Here, velocities greater than 35 m s−1 reached at least 13 km. Consistent with the observed distribution of mapped VHF sources, simulated leaders typically followed the reflectivity gradient downward east-northeast from the overshooting top.

The storm simulations did not contain any substantial charge in the anvil region beyond 30 km from the storm core and thus did not reproduce any of the anvil lightning seen in the observations. It seems likely that some charging mechanism besides the included noninductive graupel–ice mechanism was active inside the anvil, such as charging by ice–ice particle interactions in regions of supersaturation with respect to ice, as discussed by Mitzeva et al. (2006) and Dye and Willett (2007).

Though not within the scope of this research, future data assimilation work may be able to utilize the high spatial and temporal resolutions of the Lightning Mapping Array data in addition to or instead of radar data. However, initial data assimilation of lightning data has focused only on flash rates for nudging model variables such as water vapor (e.g., Fierro et al. 2012) and as of yet has not been able to match the results from radar data assimilation, particularly data assimilation utilizing mobile radars rapidly scanning all levels of a storm such as in the current study. However, with the strong relationship between lightning and storm intensity as noted here and in previous studies, it appears that lightning data assimilation could be advantageous, particularly in regions where radar coverage is sparse to nonexistent.

Acknowledgments

This research was supported in part by National Science Foundation Grants ATM-0233268 and ATM-0802717. Funding was also provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA11OAR4320072, U.S. Department of Commerce. The authors thank Conrad Ziegler, Alex Fierro, Michael Biggerstaff, Jerry Straka, Stewart Ryan, and William Beasley for comments and suggestions regarding this work. The authors would also like to acknowledge the three anonymous reviewers whose comments helped strengthen the content of this manuscript. This study would not have been possible without the participants in the TELEX field program, including more than 30 students from the University of Oklahoma.

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