MARCH 2011 F I E R R O A N D R E I S N E R 477

High-Resolution Simulation of the Electrification and Lightning of during the Period of Rapid Intensification

ALEXANDRE O. FIERRO Earth and Environmental Sciences Division/Space and Remote Sensing Group, Los Alamos National Laboratory, Los Alamos, New

JON M. REISNER Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico

(Manuscript received 31 August 2010, in final form 15 November 2010)

ABSTRACT

In this paper, a high-resolution simulation establishing relationships between lightning and eyewall con- vection during the rapid intensification phase of Rita will be highlighted. The simulation is an attempt to relate simulated lightning activity within strong convective events (CEs) found within the eyewall and general storm properties for a case from which high-fidelity lightning observations are available. Specifically, the analysis focuses on two electrically active eyewall CEs that had properties similar to events observed by the Los Alamos Sferic Array. The numerically simulated CEs were characterized by updraft speeds exceeding 10 m s21, a relatively more frequent flash rate confined in a layer between 10 and 14 km, and a propagation speed that was about 10 m s21 less than of the local azimuthal flow in the eyewall. Within an hour of the first CE, the simulated minimum surface pressure dropped by approximately 5 mb. Concurrent with the pulse of vertical motions was a large uptake in lightning activity. This modeled relationship between enhanced vertical motions, a noticeable pressure drop, and heightened lightning activity suggests the utility of using lightning to remotely diagnose future changes in intensity of some tropical cyclones. Furthermore, given that the model can relate lightning activity to latent heat release, this functional relationship, once validated against a derived field produced by dual-Doppler radar data, could be used in the future to initialize eyewall convection via the introduction of latent heat and/or water vapor into a hurricane model.

1. Introduction and background on hurricane making landfall, hurricanes1 undergo rapid intensifi- electrification cation (RI), which is defined as any hurricane showing a 30 kt (or more) increase in 10-m maximum sustained Tropical cyclones (TCs) are among the most destructive wind speed in a 24-h period or less (Kaplan and DeMaria natural forces on the earth and many coastal commu- 2003). nities worldwide are threatened yearly by these extreme Though many recent observational studies (e.g., events. Hence, it is vital to advance our knowledge on Molinari et al. 1994, 1999; Price et al. 2009) have revealed the internal and external dynamical processes governing that rapidly intensifying hurricanes occasionally produce their evolution and especially their intensity, which is abundant eyewall lightning activity, only one highly ide- currently poorly forecast (e.g., Davis et al. 2008). This alized study, Fierro et al. (2007, hereafter F07), so far knowledge becomes especially critical when, before focused on modeling hurricane electrification. This work improves upon F07 by simulating Hurricane Rita (2005), Corresponding author address: Alexandre O. Fierro, Cooper- a hurricane that produced frequent eyewall lightning ative Institute for Mesoscale Meteorological Studies, National Weather Center, Suite 2100, 120 David L. Boren Blvd., Norman, OK 73072. 1 The terms ‘‘hurricanes’’ and ‘‘tropical cyclones’’ will be used E-mail: afi[email protected] interchangeably throughout this paper.

DOI: 10.1175/2010JAS3659.1

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(e.g., 2003) were shown to produce little lightning in the eyewall (Molinari et al. 1999; Demetriades and Holle 2005). Price et al. (2009) analyzed the cloud-to- ground (CG) lightning flash rate of 56 tropical cyclones around the globe using the World Wide Lightning Loca- tion Network (WWLLN; Jacobson et al. 2006; Lay et al. 2007), with their study revealing a strong correlation be- tween hurricane intensification rate and CG lightning ac- tivity. Furthermore, Cecil and Zipser (1999) found that a temporal lag existed between the production of ice scat- tering signature (proportional to convective intensity and lightning production) and the TC intensifying. Therefore, FIG. 1. (left) Horizontal projection of narrow bipolar events they also argued that lightning activity could be used as a (NBEs) with the time of observation specified at the top. The flashes reliable forecast tool as any changes in lightning frequency were color coded in time for each event, where blue represents early in time and red represents later in time. The circle shows the esti- were likely associated with future changes in the intensity mated location and size of the of Rita based on NHC best-track of a given TC. data. (right) Corresponding evolution of the heights of the NBE Because electrical activity is relatively infrequent within discharges. (Figure adapted from F11 and used with permission.) the eyewall, lightning associated with the convective bursts are easily observed by detection networks such as activity during its intensification cycle and from which LASA. Eyewall updrafts are too weak in the mixed phase very good lightning observations are available from a region to allow sufficient production and lofting of grau- broad array of platforms (Shao et al. 2005; Squires and pel particles and supercooled water (Black 1984; Black Businger 2008; Solorzano et al. 2008; Fierro et al. 2011, and Hallett 1986) that are necessary for the generation of hereafter F11). By comparing the simulated lightning be- strong electric fields via the noninductive charging process havior with available three-dimensional lightning obser- (Takahashi 1978; Saunders et al. 1991; Saunders and Peck vations from the Los Alamos Sferic Array (LASA; F11), 1998, hereafter SP98). For example, Black et al. (1996) this work provides hypotheses on the evolution of the found that 70% of the eyewall vertical velocities from microphysical/convective state of the hurricane as its in- seven Atlantic hurricanes ranged between 22and2 m s21 tensity changes. In particular, the work of F11, which is the with only about 5% of vertical motions exceeding 5 m s21. first presenting three-dimensional flash data within a hur- Stronger and wider updrafts capable of producing no- ricane, shows that during the period of rapid intensifica- table lightning bursts, such as those reported in F11, are tion, Rita produced several episodic and isolated lightning rare, except in some hurricanes undergoing rapid inten- bursts that rotated around the eyewall at a speed within sification: for example, Black et al. (1994) reported up- 10% to that of the local azimuthal flow (see Fig. 1 for an draft (downdraft) speeds reaching 24 (219) m s21 in example of those events) and had a life time between 15 (1987) during its deepening phase. and 25 min. Other examples of deep convective updrafts within TC Besides F11, many studies reported that the occurrence undergoing RI are documented in Eastin et al. (2005a,b) of lightning bursts near the TC center was often associated for Hurricane Guillermo (1997) and in Guimond et al. with intensification of the system and that these episodic (2010) for (2005). lightning bursts were associated with deep convection This modeling study builds upon the observational (e.g., Lyons et al. 1989; Black et al. 1993; Lyons and Keen work of F11 by relating modeled lightning to key prop- 1994; Simpson et al. 1998; Rodgers et al. 2000; Heymsfield erties of the eyewall convection with focus on convective et al. 2001). Consistent with this, Kelley et al. (2004) events (CEs) and attempts to address questions that could suggested that extremely deep eyewall clouds (most likely not be easily answered by the observations. In this work, to produce lightning) observed via the Tropical Rainfall a CE is defined as an isolated convective entity in the Measuring Mission (TRMM) satellite in the eyewall were eyewall characterized by the following: 1) an instanta- coincident with a 70% likelihood of storm intensification. neous updraft speed greater than 10 m s21 anywhere It is also well recognized that RI often relies on the oc- above the freezing level, 2) a minimum depth of the currence of small-scale hard-to-forecast convective bursts 7ms21 isosurface of 5 km, 3) minimum horizontal di- (e.g., Steranka et al. 1986; Rodgers et al. 1998, 2000; mensions of 10 km 3 10 km, and 4) a minimum lifetime Reasor et al. 2009; Guimond et al. 2010) in the eyewall of of 15 min. The questions to be addressed include the the hurricane. In contrast to hurricanes undergoing RI, following: how strong is the convection within the mod- strong mature hurricanes remaining in a quasi–steady state eled CEs? How frequent are these events? What is their

Unauthenticated | Downloaded 10/06/21 09:49 PM UTC MARCH 2011 F I E R R O A N D R E I S N E R 479 microphysical and electrical structure and in turn how do Mansell et al. (2005), which was adapted from Ziegler et al. these structures differ from that of the bulk of the eyewall (1991). Lightning initiation/discharge in the model occurs convection? How much latent heat is being released whenever the ambient electric field exceeds the breakeven within the simulated CEs? Note that the latter question is (or fair weather) electric field threshold, which was as- important with regard to relating observed lightning sumed to decrease exponentially with height, as in Mansell withinCEstoaquantitythatcanbeusedtoinitializeCEs et al. (2002), with the electric field and space charge den- within a model. Furthermore, though at least 4 distinct sities being decreased by a constant value of 10% through CEs were observed by LASA during a 24-h period, this the column upon discharge. Although more sophisticated paper will focus on the period in which two CEs were lightning models could have been used in the simulations, evident over a short period, from 1800 UTC 21 September given the cost of the calculations, the reality that modeled to 0200 UTC 22 September, during Rita’s most rapid in- collision rates between various hydrometers in hurricanes tensification phase. The remainder of the paper is de- contain some uncertainty, and the simple desire to relate signed to address these questions by first presenting the only the relative change in lightning flash rate to hurricane hurricane model in the next section, the results in the intensity fluctuations, this important piece of work will be subsequent section, and the final section providing a brief deferred for a subsequent study. Likewise, because the summary and future directions. current lightning model makes no distinction between in- cloud (IC) and CG flashes, the simulated lightning pro- 2. The numerical model and initialization duced by the current model will be simply referred to as procedures lightning discharges. For point of comparison it is also be- ing assumed that the cell-by-cell lightning predicted by the a. Equation set model is a rough surrogate for the intense in-cloud dis- The hurricane model is based on the Los Alamos Na- charges (narrow bipolar events; Smith et al.1999) observed tional Laboratory’s (LANL) High Gradient (HIGRAD) by LASA. large-eddy ‘‘smooth’’ cloud model (Reisner and Jeffery b. Discrete model 2009). The equation set for the hurricane model is similar to what is described in section 2a of Reisner and Jeffery The discrete version of the hurricane model is iden- (2009), except that additional conservation equations were tical to what was described in section 2c of Reisner and added for the microphysics and space charge. Specifically, Jeffery (2009) with each conservation equation being the model includes conservation equations for the three written in finite volume form on a collocated mesh (A momentum fields, potential temperature, gas density, water grid) within a terrain-following coordinate framework. vapor density, number and density of cloud water, rain- As explained in more detail in section 2c, two simulations water density, number and density of cloud ice, snow den- were analyzed in this work with the first simulation pri- sity, graupel density, turbulence kinetic energy density, and marily being run to provide reasonable initial conditions the space charge densities associated with each hydrome- for the second higher-resolution simulation that resolves ter. Besides the momentum equations, each conservation the CEs. The first simulation made use of a flux-limited equation includes terms for advection (including those form of the quadratic upstream interpolation for convec- associated with precipitation fall terms), diffusion, and tive kinematics scheme including estimated streaming sources [see Eq. (6) within Reisner and Jeffery (2009)]. The terms (QUICKEST; Leonard and Drummond 1995) for sources and sinks found within the various microphysical advection of all model fields with the discrete conserva- conservation equations utilize a hybrid of the activation tion equations utilizing a first-order forward Euler time- and condensation model found in Reisner and Jeffery stepping procedure within a semi-implicit method to step (2009) together with all of the other relevant bulk param- over sound waves. The second simulation used a less dif- eterizationsfoundinThompsonetal.(2004).Themo- fusive form of QUICKEST, QUICK (Leonard 1979), in mentum equations forgo the microphysical source terms, combination with an explicit fourth-order Runge–Kutta but insert additional terms representing forcing due to time-stepping process. As shown in Reisner and Jeffery pressure gradients, buoyancy, and the earth’s rotation. (2009), the numerical approach utilized in the second Space charge density equations in the hurricane model simulation results in less numerical diffusion near cloud are included as an option within a relatively simple boundaries and hence should adequately resolve CEs found lightning module that simulates the local time rate of near the very small eye of Rita. However, although numer- change of a one-dimensional form of the electric field ical diffusion is lower, the use of an explicit time-stepping due to charging and discharging (lightning). The charg- procedure requires sound waves to be resolved and hence ing model uses the SP98 noninductive charge separation the computational cost of this simulation prevents numer- parameterization and polarization charging following ous sensitivity simulations from being undertaken.

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output data was saved every 150 s, while for the 2-km simulation each 12-Gb output file was saved every 50 s to allow for a detailed analysis of the evolution of smaller- scale CEs and the corresponding lightning. Examining vertical profiles from ECMWF data at 1200 UTC 20 September and using a representative com- posite achieved the initialization of the horizontally ho- mogeneous horizontal momentum, potential temperature, water vapor, and total gas density fields for the 4-km simulation. To initialize the momentum fields associated with Rita, a composite of surface wind data obtained at 1200 UTC 20 September and a bogus vortex were in- corporated into the 4-km simulation via a simple nudging procedure that was active for the first hour of the simu- lation. Note the minimum surface pressure of the resulting hurricane that develops in response to this nudged wind FIG. 2. Simulation domain and horizontal projection of the in- field is relatively sensitive to the time period over which terpolated LASA lightning for the four consecutive 3-h periods used for the initialization of the rainbands in the 4-km simulation. this nudging takes place and for the current simulation it The LASA lightning data were summed from the times shown in was decided that this nudging be of sufficient duration the legend. The location of the Key West Weather Surveillance (3 h) to induce a vortex stronger than the observed vortex Radar-88 Doppler (WSR-88D; BYX) is denoted by a black star. The (by about 10 m s21). Given that the period of interest is small disks denote the NHC best-track storm center estimates using still 30 h away, the introduction of a stronger vortex the same color code for time as for the lightning. The horizontal axes simultaneously show the lat–lon and X–Y Cartesian coordinate used makes sense in that a stronger initial vortex can induce the in the model. formation of rainbands over a larger horizontal extent such that the modeled hurricane at 1800 UTC 21 September contains a reasonable structure (i.e., the balance between eyewall and rainband convection is not entirely skewed c. Model setup and initialization toward having all the convection within the eyewall). As discussed at the end of the introduction, the goal of To further facilitate the balance between eyewall and this work is to examine the lightning within Rita during a rainband convection a combination of the Next Genera- 8-h window starting at 1800 UTC 21 September using high tion Weather Radar (NEXRAD) radar data (primarily enough resolution (2 km) to adequately resolve small- used for initialization of the eyewall convection) obtained scale CEs (e.g., Davis et al. 2008; Fierro et al. 2009; Gentry from Key West, , at 1200 UTC 21 September and and Lackmann 2010). However, in order to produce a integrated-in-time LASA lightning data obtained for four reasonable looking facsimile of Rita at 1800 UTC 3-h intervals starting at 1200 UTC 21 September (pri- 21 September and to reduce the overall computational marily employed for initialization of the rainband con- burden, a 4-km simulation was first conducted and ini- vection, see Fig. 2b) were used to initialize rainwater, tialized at 1200 UTC 20 September with this simulation snow, and graupel fields over the first hours of the 4-km then running for 38 h. The 2-km simulation then utilized simulation. Microphysical fields were initialized with the output from the 4-km run for its initialization at 1800 UTC NEXRAD radar data via dBZ-to-mass relationships 21 September (or 30 h into the 4-km simulation). along with the addition of water vapor to ensure satura- The 2- and 4-km simulations were carried out in the same tion of the column. To utilize the LASA lightning data domain having geographical dimensions of 2000 km 3 within the model, the data were first interpolated onto the 1600 km 3 21.3 km (Fig. 2a). For the 2- (4 km) simulations 4-km grid and represented within a two-dimensional bi- this corresponds to grid sizes of 1000 3 800 3 86 (500 3 nary array (containing zeros for no lightning and ones for 400 3 86) with the vertical grid using a stretched mesh with lightning). Then, for the columns for which lightning was highest resolution near the surface (50 m) and coarsest near present water vapor was added from z 5 3kmtoz 5 11 km the model top (440 m). The time step for the 4-km simu- to ensure saturation within this layer. lations was 1 s, while for the 2-km simulation the time step was 0.25 s. All simulations utilized the Department 3. Results of Energy’s (DOE’s) XT-5 Cray machine (Jaguar) hos- ted at the Oak Ridge National Laboratory using be- As previously discussed, the simulated intensity in the tween 2000 and 32 000 processors. For the 4-km run 4-km simulation is initially stronger than the observations

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FIG. 4. Simulated 5-min flash rate and 5-min simulated pressure trace overlaid with the 3-hourly pressure trace from the NHC ad- visories for (a) the last 8 h of the 4-km run and (b) for the entire duration of the 2-km simulation. The flash rate in the 2-km run was scaled by a factor of 100. FIG. 3. (a) Simulated (gray) and storm tracks obtained from the 3-hourly NHC public advisories (black). (b) Simulated hourly flash rate in the rainbands (white bars) and the eyewall (gray bars) (Fig. 3b). The largest track differences (observed vs simu- overlaid with the simulated pressure trace (solid line) and the lated) occurred during the last few hours of the simulation pressure trace estimate from the 3-hourly NHC advisories (dashed and were caused by a slightly inaccurate representation of line; hPa). The sum of the white and gray bar flash rate is the storm total hourly flash rate, which is shown on the left axis. (c) LASA the large-scale steering environment that was held con- observations of eyewall hourly flash rate overlaid with the standard stant during the simulation. best-track pressure trace (black) and 3-hourly NHC advisories To further illustrate the lightning bursts, 5-min flash (gray triangles). The time axis in (c) shows the real time of obser- rate and pressure traces for the 2-km run are presented vations (UTC) and corresponding simulation time (h) for refer- (see Fig. 4a) and are compared to the last 8 h of the 4-km ence. [(c) is from F11 and used with permission.] simulation (see Fig. 4b). A 5-min interval was chosen to be able to properly resolve smaller-scale fluctuations within the eyewall, given that the life cycle of the CEs was until near the time in which the 2-km simulation was ini- approximately 15 min. The boundary between the eye- tiated, after which the simulated hurricane was weaker wall and rainbands for the lightning computations was than the observations (Fig. 3b). The simulated track is based on horizontal cross sections of average updraft close to the observed track during the course of the 4-km speeds in the 10–14-km layer in order to account for the simulation (Fig. 3a) with a few bursts of lightning oc- outward tilt of the convection and also because, as shown curring near periods of small drops in surface pressure later in this section, most simulated flashes were found to

Unauthenticated | Downloaded 10/06/21 09:49 PM UTC 482 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 68 initiate at those altitudes. In the 2-km case, a constant three-dimensional tail radar data [the National Oceanic radius of 100 km from the storm center (defined by the and Atmospheric Administration (NOAA) Hurricane minimum surface pressure) was selected because the Research Division (HRD)] obtained at 1915 UTC eyewall size of the 2-km storm remains nearly constant. 21 September (Fig. 5). It is important to note that an 8-dBZ Because the 4-km simulation was run for a longer period offset was added to the raw observational data shown in and was designed to include the development and in- Figs. 5a,c,e. This is because the generally low reflectivity tensification stage of the storm, the eyewall size did vary values in the observations are caused by low calibration and for this reason the radius of the box encompassing the of the tail and low-fuselage radars mounted on the eyewall was set to 100 km during the first 24 h, 120 km NOAA WP-3D aircraft. For instance, Marks et al. (1993) between 24 and 26 h, and 148 km after that time. found a 28.2-dBZ calibration error for low-fuselage radar As compared to the 4-km run, the 2-km simulation data of Hurricane Anita (1977). Consistent with Kabe`che produces a stronger storm with a simulated minimum and Testud (1995), a more recent study from Protat et al. surface pressure of about 908 hPa (cf. Figs. 4a,b). Unlike (2000) reported an improved 25-dBZ calibration error of the 4-km simulation, the 2-km run also produces between the NOAA WP-3D radars, which value lies within a rea- 5 and 6 h a relatively large eyewall lightning burst, which sonable range of the 8-dBZ offset used herein. Below is followed by a small but noticeable 4–5-hPa minimum 2 km AGL, the true dBZ readings are compromised due surface pressure drop. Additionally, after 4 h, both sim- the presence of sea clutter. However, corrections were not ulations produced overall less lightning in the rainbands made to account for this effect since this work focuses on than in the eyewall, consistent with observations (e.g., electrification processes, which occur within and above Shao et al. 2005; Squires and Businger 2008). Further- the mixed-phase region of updrafts (between about 08 and more, though the 2-km simulation did not produce a hur- 2208C). Given the above corrections of the observed ricane as intense as the observations, preliminary analysis dBZ, the model underestimates the 15–30-dBZ echo tops, of an additional 2-km simulation, whereby spurious evap- while the 35-dBZ top, a threshold for significant hydro- oration near cloud edges was limited (Reisner and Jeffery meteor mass in tropical convection (and hence lightning; 2009) resulted in a hurricane with a steeper pressure trace Petersen et al. 1999) shows reasonable agreement with slope and a lower minimum surface pressure during max- the observations (Figs. 5a–d). The simulated eye size imum intensity (i.e., 898 compared with 908 hPa). The near the surface (;20 km in diameter) is slightly larger overall structure, evolution, and lightning activity re- than the observations (;12 km in diameter). Also, the mained very similar to that of the 2-km simulation pre- simulated radar reflectivity slope in the eyewall, measured sented herein. from the vertical axis, ranges between 708 and 808,which Noteworthy differences are also seen between observed is approximately twice the values of 408–458 observed by and modeled lightning rates. Clearly, while the hourly flash the NOAA WP-3D radars in weakly sheared environ- rates for the 4-km case are comparable to observations ments (Marks 1985). The model also consistently produces (Fig. 3), the 2-km run produces much larger flash rates higher reflectivity than the observations especially at lower greater by as much as a factor of 100 (Figs. 3–4). While it is levels below z 5 5 km, which is a well-documented prob- possible that further tuning of the magnitude of charge lem within models and has been attributed primarily to separated per collision within the noninductive charging biases in the functions used to compute reflectivity and parameterization would reduce the modeled flash rate, the terminal fall speeds of precipitation particles (Rogers et al. focus here is on the trends and associated relative increase/ 2007). Also, the simulated eyewall width is larger than the decrease of the modeled flash rate and their relationship observations by as much as a factor of 5, with this differ- to storm intensity rather than reproducing reasonably the ence possibly being attributed to numerical diffusion near observed amount of flashes. There are many factors that cloud edges (Reisner and Jeffery 2009) and/or too small of could cause this scale dependency on the modeled flash a surface friction coefficient (Davis et al. 2008). rate. One of which is undoubtedly related to the rather Horizontal cross sections from the 2-km simulation (see simplistic electrification processes implemented in this code, Fig. 6) taken at different times of modeled radar reflec- which do not take into account ion attachments, recoil tivity overlaid with a horizontal projection of modeled streamers, stochastic branching of lightning channels (re- 50-s accumulated lightning discharge show evidence of sulting, again, in no possible distinction between IC and CG CEs located inside areas of radar reflectivity exceeding flashes), and corona discharges as in Mansell et al. (2002). 45 dBZ within the simulated eyewall of Rita. Of impor- Before relating the simulated lightning to modeled tant note are the three CEs found at hour 5 that roughly microphysical/kinematic fields in the 2-km simulation, correspond with the onset of the lightning burst shown in basic storm attributes were evaluated by comparing the Fig. 4b. Because the evolution of these CEs bear some simulated hurricane radar reflectivity structures to in situ resemblance to what was suggested by the LASA lightning

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FIG. 5. (right) Simulated and (left) observed (a),(b) vertical cross section; (c),(d) radius–height; and (d),(e) contour– frequency plots of radar reflectivity. For the simulation, black contours show 5-min accumulated lightning discharges. A thick dashed line highlights the 60-km radius mark in the azimuthal plot of simulated radar reflectivity as reference for comparisons with observations. The legend for the color and shadings of reflectivity, which is shown in the top right, is the same for observations and the simulation. On the other hand, the legend for the color and shadings of the contour frequency plots differ between the observations and the simulation. Each is shown in (e) and (f), respectively. array, their evolution and potential impact on intensifica- averaged but simply summed in azimuth after interpola- tion is highlighted later in this section. tion. And for the subsequent Hovmo¨ller plots, the light- To provide a broader view of the averaged storm ning datum at each grid point on the cylindrical grid properties and its relationship to lightning, azimuthally represents the sum of all discharges in the vertical. averaged diagrams were produced onto which simulated Figure 7 shows radius–height diagrams of vertical ve- lightning discharges were overlain. At each time of inter- locity, 5-min accumulated lightning flashes, liquid water est, the data were interpolated onto a cylindrical grid cen- content (LWC), and radar reflectivity for the same four tered on the storm’s minimum surface pressure and then times shown in Fig. 6. Lightning is primarily found in the averaged in azimuth. Since lightning discharges consist eyewall between z 5 10 and 14 km where azimuthal up- of discrete integer values, the data were not azimuthally drafts reach their maximum and the bulk of the graupel is

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produced by riming with supercooled droplets (i.e., non- inductive charging is directly a function of the riming rate). In agreement with observations, the simulated storm pro- duced overall weak-to-absent lightning activity in the outer bands (radii greater than 90 km) with this behavior being clearly evident in the Hovmo¨ller diagram (see Figs. 8a,b). As time progresses, the eye and eyewall size remain con- stant with a diameter of about 20 km at 1 km AGL, while lightning is generally found at a radius of 60 km (see Figs. 8a,b) due to the simulated large eyewall slope (Fig. 5). Again, the large eyewall lightning burst mentioned earlier between 5 and 6 h is clearly evident in Fig. 8b at radii be- tween 70 and 110 km with flash counts exceeding 180 h21. The three CEs found at hour 5 are associated with rela- tively higher 5–9-km layer averaged equivalent potential

temperature (ue)valuesatradiibetween40and50km, which progressively propagate radially inward toward the storm’s center between 5 h 30 min and 6 h, the time at which the eyewall mass flux dramatically increases (Fig. 9). This behavior would support storm intensification by axisymmetrization of asymmetric heating of relatively

higher ue parcels within CEs (Nolan et al. 2007). In agreement with what was suggested by the LASA observations, the 2-km simulation produced CEs rotating around the eyewall at a speed of about 10 m s21 less than the local azimuthal flow. For example, Fig. 9 shows distinct episodic periods of enhanced vertical mass flux occurring within the eyewall convection with the most distinct in- crease occurring between 5 h and 6 h 30 min. To examine two such events in detail, horizontal cross sections of layer- averaged updraft speed between 7 and 9 km were overlaid with projected 50-s accumulated lightning discharge in Fig. 10. This figure shows two isolated CEs with 7–9-km layer averaged vertical velocities exceeding 11 m s21 mov- ing around the eyewall. The propagation speeds of the CEs shown here are about 10 m s21 less than the local azimuthally flow in the eyewall. The lifetime of those events range between 15 and 30 min, which is in good agreement with the LASA observations of F11. Recent theoretical modeling work (C. M. Nguyen and M. J. Reeder 2010, personal communication) showed that as a simulated eyewall undergoes a transition from a symmetric to an asymmetric mode (which is seen in Fig. 6), the latter is accompanied with the formation of CEs within the eyewall. They revealed that the initial growth of the flow asymmetries within the eyewall are associated with barotropic instability of the potential vorticity ring structure (following the work of Schubert et al. 1999),

FIG. 6. Horizontal cross sections of simulated radar reflectivity which, in turn, initiate CEs where the inertial instability is (dBZ) for the 2-km run at t 5 2, 5, and 7 h overlaid with horizontal sufficient. As time progresses and the eyewall reaxisym- projections of the modeled 50-s lightning flashes/discharges. The metrizes, the CEs progressively weaken due to local con- legend for colors and shadings is shown on the right. sumption of convective available potential energy and the angular shear of the primary vortex.

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FIG. 7. Radius–height plots of (left) azimuthally averaged radar reflectivity and (right) azimuthally averaged vertical velocity at the same three times shown in Fig. 6. Both the azimuthally averaged radar reflectivity and azimuthally averaged vertical velocity are overlaid with the azimuthal sum of simulated total 5-min lightning discharge with the 1, 5, and 10 contours shown. The azimuthally averaged vertical velocity is also overlaid with azimuthally averaged LWC using gray contours of 0.1, 0.5, and 1 g m23. The legends for colors and shadings are shown at the bottom of each column.

While the above mechanisms have not been yet veri- and Eastin 2001). Evidence of this mechanism can be seen fied against observations of CEs within rapidly intensi- in Fig. 6 by the polygonal eyewall structure and episodic fying hurricanes, which are at present very limited, an mixing of radar reflectivity from the eyewall into the eye alternative explanation that could support the formation (implying a compensating outward mixing of air found of those strong CEs would involve asymmetric mixing within the eye; Fig. 8). between relatively high entropy air at low levels in the eye Vertical cross sections of the simulated net space and the eyewall. Once this entropy-rich air is transported charge across the two simulated CEs of Fig. 10 (location outward near the radius of maximum wind, the latter could denoted by a thick horizontal black line) and across the enhance/boost convective development in that region eyewall are shown in Fig. 11. The simulated gross charge (Barnes and Fuentes 2010; Reasor et al. 2009; Braun and structure in the CEs resembles an inverted tripole, which Wu 2007; Braun et al. 2006; Eastin et al. 2005b; Kossin consists of a main positive charge region sandwiched in

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FIG. 8. Hovmo¨ ller plots for (a) radar reflectivity and (b) layer-averaged 5–7-km vertical velocity overlain with the azimuthal sum of simulated total hourly lightning discharges contoured by increments of 10. The azimuthal lightning shown here was also summed in the vertical. The frequency of plotting is at a 5-min interval in order to resolve convective events. (c) Hovmo¨ller plot of 5–9-km layer-averaged ue (K). Leg- ends are shown to the right of each panel.

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To illustrate specific aspects of the charge structure and how it relates to microphysical quantities, Fig. 11 shows that most space charge in the simulated eyewall is found within regions having LWC of about 0.5 g m23 and graupel mixing ratios ranging between 2.5 and 5 g kg21, which are generally located atop updrafts between z 5 10 and 14 km. Those mixing ratios are somewhat larger than typically observed and suggests the model may be producing too much supercooled water within CEs, in turn leading to large graupel production via enhanced riming with ice crystals and/or frozen drops. For in- stance, Black and Hallett (1999) noted the abundant concentration (100–300 L21) of ice crystals in this region that appeared to lead to the depletion of liquid water (i.e., this microphysical structure, lack of supercooled water, typically accounts for the infrequent lightning activity within hurricane eyewalls). But, as shown by Houze et al. (1992) and Black and Hallett (1986), the dominant particle types at upper levels in the eyewall (and the inner band stratiform region defined as the area just radially outside the eyewall convection) are ice crystals and aggregates, which are well reproduced by the model (Fig. 12). Hence, both the overall and detailed charge structure suggests that future simulations should be conducted us- ing other critical charging curves and/or adjusting various microphysical parameterizations to examine how these highly nonlinear relationships affect charge structure and/ 10 21 FIG. 9. Time–height plot of eyewall updraft mass flux (10 kg s ) or lightning activity within the CEs. Though these simu- for vertical velocities greater than (top) 5 m s21 and (bottom) 9 m s21 lations should help pinpoint what combination is needed for the 2-km simulation. Legends are shown to the right of each panel. to reproduce the observed charge structure of Rita, without observations of microphysics in the critical riming regions of CEs to validate the microphysics of the model, between two layers of negative charge. The recent ob- the model could still produce the right charge structure for servational study of F11 found, however, that the gross the wrong reasons. Furthermore, though these simulations charge structure in Rita’s eyewall was of opposite po- will probably produce lightning at heights within the CEs larity, namely a normal tripole. Previous high-resolution that are different than the current simulation, the primary modeling studies on thunderstorm electrification showed results of this paper should still stand (i.e., a majority of the that the simulated gross charge structure of a thunder- simulated lightning is found within the CEs). storm was very sensitive to the noninductive charging Another interesting aspect of Fig. 11 is that, despite scheme selected in the model (e.g., Fierro et al. 2006; noteworthy differences in lightning flash rate between CEs Kuhlman et al. 2006). Such discrepancies in simulated and the bulk of the eyewall convection, their differences in charge structures are mainly attributed to the different in- space charge magnitude and vertical motions can be rela- cloud conditions and apparatus used to reproduce the tively small. Because the simulated CEs lasted 15–30 min critical charging curves of riming graupel (e.g., Takahashi compared to about 5–10 min for the bulk eyewall con- 1978; Jayaratne et al. 1983; Saunders et al. 1991; SP98). vection, CEs are able to build up charge and hence the Because induction in the model is only allowed to occur necessary electric fields that are able to exceed the break- during graupel–rainwater collision, the main negative even threshold for lightning initiation/production (not charge region in Fig. 11, which is located well above the shown). Figure 12 also confirms that CEs are characterized freezing level, is principally attributed to noninductive by relatively higher ue values with the highest values charging of graupel, with snow and cloud ice carrying the confined at upper levels between z 5 10 and 14 km where corresponding amount of opposite charge (i.e., positive the great majority of the ice-phase hydrometeors reside charge; Fig. 12). (Figs. 11 and 12).

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21 FIG. 10. Horizontal cross sections of 7–9-km layer-averaged vertical velocity (m s ) at selected times of the 2-km simulation (time shown in the top-right corner of each frame) overlaid with horizontal projections of accumulated 50-s lightning discharges zoomed over the eyewall. Two examples of convective events moving around the eyewall with the primary circulation are shown. The black arrow indicates the location of the convective event of interest, whereas the thick horizontal black line denotes both the location and length of the cross sections shown in Fig. 11.

Given the reduction in pressure that may occur after the time frame. Note, because the 2-km simulation pro- short-lived mass flux increases within the eyewall, which in duced more flashes (Fig. 4), the time interval was re- allprobabilityareentirelyrandominnature(Zhangand ducedfrom1000sinthe4-kmsimulationto100s. Sippel 2009), it is important that hurricane forecast models Specifically, during this time interval, each modeled be properly initialized before this time so that accurate lightning discharge was correlated with the following four forecasts can be made. But, in order to utilize observed variables (see Fig. 13): vertical velocity (W), water vapor lightning within models for initialization purposes, proxies supersaturation (QVS), water vapor supersaturation over must be developed. Toward this goal, model results from ice (QVSI), and latent heat (LH). The four histograms of both the 2- and 4-km simulations were averaged over a 9 3 these variables from both the 2- and 4-km simulations show 9 3 9 grid volume (;535 km3) within either a 100- or 1000-s that lightning in the model was primarily associated with

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23 FIG. 11. (top) Vertical cross sections in the zonal direction of simulated net space charge (10 nC m ) along the thick black line highlighted in Fig. 10. Thin black contours show the 2.5 and 5 g kg21 graupel mixing ratios and the thick dark gray contours denote LWC of 0.5 and 2.5 g m23. (bottom) Vertical cross sections in the zonal direction of simulated vertical velocities overlaid with X–Z projections of 3D wind vectors with the scale for the wind vectors shown at the bottom. Legends are shown to the right of each row. updraft speeds on the order of 2–4 m s21, latent heat values relate simulated eyewall lightning activity to the convec- of about 100 K h21, and supersaturation (over ice and tive state of the storm and intensity fluctuations. The 2-km water) on the order of 0.5 g kg21. After being validated simulation is the first relating simulated lightning activity against observations (i.e., latent heat derived from dual- and general storm (azimuthally averaged) properties for Doppler aircraft data), the values shown in Fig. 13 could be a case from which high-quality lightning observations are utilized to help initialize CEs within a model by both satu- available from many platforms (F11; Squires and Businger rating and/or introducing heat into a column via a data as- 2008; Solorzano et al. 2008; Shao et al. 2005). A key finding similation procedure. from the 2-km simulation, suggested as well by lightning observations in Rita, was the occurrence of lightning bursts within CEs found within the eyewall. 4. Discussion and conclusions Specifically, the 2-km simulation was able to resolve Cloud-resolving numerical simulations of the electrifi- individual electrically active strong convective updrafts cation and lightning in Hurricane Rita were carried out to exceeding 11 m s21 rotating around the eyewall at a speed

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21 FIG. 12. (top) Equivalent potential temperature (color shading; K), snow mixing ratio (gray contours; g kg ), and cloud ice mixing ratio (black contour; g kg21). The contours for snow (cloud ice) mixing ratio start at 1 (0.12) g kg21 and increase by increments of 1 (0.02) g kg21. (bottom) Simulated space charge of graupel (blue shading; 10 nC m23), cloud ice (black contours, 10 nC m23), and snow (red contours; 10 nC m23). The horizontal dimensions on the X axis and cross section location are the same as in Fig. 11. Note the difference in the scale of the z axis between (top) and (bottom). about 10 m s21 less than the local azimuthal flow, con- under grid refinement. Likewise, it is hoped that the sistent with observations. The characteristic width of most results from the current simulation will help guide of these CEs was about 10–15 km, consistent with obser- the setup of these future high-resolution simulations; vations of Black et al. (1996) and in turn explaining why resulting in simulations that not only better reproduce the 4-km simulation failed to adequately resolve the CEs. the narrow eye of Rita and the tilt of the eyewall con- But, given the small spatial scale of these CEs and that vection, but the observed charge structure as well. Fur- their dynamical structure is just resolved using a 2-km thermore, the lightning discharge model used in the stencil, future simulations are needed, whereby even current simulations was relatively crude and more so- higher resolution near the eye is employed to understand phisticated lightning models such as Mansell et al. (2002) how the nature of both the lightning and CEs change that can simulate branched lightning should be next

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21 FIG. 13. Histograms of latent heat (K h ), supersaturation over water, supersaturation over ice, and vertical velocity for (a) the 4- and (b) the 2-km simulation. For the 4-km run, the data were averaged over 1000 time steps (1000 s) vs 400 time steps (100 s) for the 2-km run. Whenever lightning flashes occur at a given grid point, the data from each of the above four variables were averaged over a 9 3 9 3 9 grid box (equivalent to an average grid volume of ;535 km3). carried out in order to relate hurricane intensity changes This capability could prove itself very valuable over the with lightning type and polarity. Pacific Ocean, where data availability is sparse or in situ- Another aspect of this work was to begin determining ations for which more than one hurricane is occurring over proxies for lightning that could be used in operational the Atlantic basin. Note that, as described in the model hurricane models to assimilate near-real-time observed setup section, observed lightning from the LASA array has lightning data (i.e., from geostationary lightning mappers). already been used to help initialize the rainbands in the

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4-km simulation using a simple nudging procedure; how- Guimond for providing the wind, radar, and environmental ever, considerable research is still required to determine the observations and to Dr. Edward ‘‘Ted’’ Mansell for his values of latent heat and/or water vapor introduced within guidance toward the elaboration of the HIGRAD elec- a given model volume that produces results that ‘‘opti- trification model. The authors would also like to thank mally’’ agree with observations (i.e., these values could be Dr. Robert Rogers at HRD, NOAA, for providing the determined by the use of an ensemble Kalman filter). Fortran subroutine that interpolates the model data from Since lightning data is nearly continuous over long a Cartesian to a cylindrical grid. time periods, the data could be readily incorporated into advanced four-dimensional data assimilation procedures REFERENCES to help determine the true convective state of a hurricane Barnes, G. M., and P. Fuentes, 2010: Eye excess energy and the at a given moment for short-term high-resolution re- rapid intensification of (2002). Mon. Wea. Rev., search simulations. The nudging procedure via proxies 138, 1446–1458. could, for example, alter the supersaturation field in a Black, M. L., R. W. Burpee, and F. D. Marks, 1996: Vertical motion given layer as done herein, or artificially increase the characteristics of tropical cyclones determined with airborne mixing ratio of a predicted variable known to be well cor- Doppler radial velocities. J. Atmos. Sci., 53, 1887–1909. Black, R. A., 1984: Distribution of particles types above 6.0 km in related with lightning, such as graupel content or LWC two Atlantic hurricanes. Preprints, 16th Conf. on Hurricanes within the mixed phase region (defined here as the layer and Tropical Meteorology, San Diego, CA, Amer. Meteor. between z 5 5 and 7 km). However, given the relative Soc., 537–541. short lifetime of CEs, current operational hurricane ——, and J. Hallett, 1986: Observations of the distribution of ice in models may require at least 6–12 h for spinup, and given hurricanes. J. Atmos. Sci., 43, 802–822. ——, and ——, 1999: Electrification of the hurricane. J. Atmos. Sci., that these simulations typically make use of a horizontal 56, 2004–2028. grid spacing that is too coarse to resolve CEs, the assim- ——, ——, and C. P. R. Saunders, 1993: Aircraft studies of pre- ilation of the small-scale CEs raises important questions cipitation and electrification in hurricanes. Preprints, 17th with regard to the community’s ability to predict hurri- Conf. on Severe Local Storms/Conf. on Atmospheric Elec- cane intensification. Chief among them is whether hurri- tricity, St. Louis, MO, Amer. Meteor. Soc., J20–J25. ——, H. B. Bluestein, and M. L. Black, 1994: Unusually strong cane models must accurately resolve the evolution of the vertical motions in a Caribbean hurricane. Mon. Wea. Rev., CEs or just capture the integrated impact of these events 122, 2722–2739. on the overall intensity of the eyewall convection. For Braun, S. A., and L. Wu, 2007: A numerical study of Hurricane instance, the latter approach could employ a simple con- Erin (2001). Part II: Shear and the organization of eyewall tinuous nudging procedure that introduces both a sym- vertical motion. Mon. Wea. Rev., 135, 1179–1194. ——, M. T. Montgomery, and Z. Pu, 2006: High-resolution simu- metric and an asymmetric water vapor source into a given lation of Hurricane Bonnie (1998). Part I: The organization of simulation with the magnitude of this source correlated to eyewall vertical motion. J. Atmos. Sci., 63, 19–42. the amount of observed lightning found within the CEs. In Cecil, D. J., and E. J. Zipser, 1999: Relationships between tropical the present simulation, the supersaturation field was cyclone intensity and satellite-based indicators of inner core maintained for 3 h in order for the rainband convection convection: 85-GHz ice-scattering signature and lightning. Mon. Wea. Rev., 127, 103–123. to persist. Hence, tests similar to these need to be con- Davis, C., and Coauthors, 2008: Prediction of landfalling hurri- ducted in the future to determine both the time period canes with the Advanced Hurricane WRF model. Mon. Wea. and amount of water vapor required to reasonably Rev., 136, 1990–2005. capture the integrated impact of the CEs within a given Demetriades, N. W. S., and R. L. Holle, 2005: Long-range light- hurricane simulation. ning applications for hurricane intensity. Preprints, Conf. on Meteorological Applications of Lightning Data, San Diego, CA, Amer. Meteor. Soc., P2.8. [Available online at http://ams. Acknowledgments. This work was supported by the confex.com/ams/Annual2005/techprogram/paper_84498.htm.] Laboratory Directed Research and Development Eastin, M. D., W. M. Gray, and P. G. Black, 2005a: Buoyancy Program of the Los Alamos National Laboratory, which of convective vertical motions in the inner core of intense is under the auspices of the National Nuclear Security hurricanes. Part I: General statistics. Mon. Wea. Rev., 133, 188–208. Administration of the U.S. Department of Energy under ——, ——, and ——, 2005b: Buoyancy of convective vertical mo- DOE Contracts W-7405-ENG-36 and LA-UR-10-04291. tions in the inner core of intense hurricanes. Part II: Case Computer resources were provided both by the Com- studies. Mon. Wea. Rev., 133, 209–227. puting Division at Los Alamos and the Oak Ridge Na- Fierro, A. O., M. S. Gilmore, E. R. Mansell, L. J. Wicker, and tional Laboratory Cray clusters. The authors would also J. M. Straka, 2006: Electrification and lightning in an idealized boundary-crossing supercell simulation of 2 June 1995. Mon. like to thank Dr. Gary Barnes and one anonymous re- Wea. Rev., 134, 3149–3172. viewer for providing helpful suggestions on an earlier ——, L. M. Leslie, E. R. Mansell, J. M. Straka, D. R. MacGorman, version of the manuscript. Thanks also go out to Steve and C. Ziegler, 2007: A high-resolution simulation of

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microphysics and electrification in an idealized hurricane- modeling—There are better alternatives. Int. J. Numer. like vortex. Meteor. Atmos. Phys., 98, 13–33, doi:10.1007/ Methods Fluids, 20, 421–442. s00703-006-0237-0. Lyons, W. A., and C. S. Keen, 1994: Observations of lightning in ——, R. Rogers, F. Marks, and D. Nolan, 2009: The impact of convective supercells within tropical storms and hurricanes. horizontal grid spacing on the microphysical and kinematic Mon. Wea. Rev., 122, 1897–1916. structures of strong tropical cyclones simulated with the WRF- ——, M. G. Venne, P. G. Black, and R. C. Gentry, 1989: Hurricane ARW model. Mon. Wea. Rev., 137, 3717–3743. lightning: A new diagnostic tool for tropical storm fore- ——, X.-M. Shao, J. M. Reisner, J. D. Harlin, and T. Hamlin, 2011: casting? Preprints, 18th Conf. on Hurricanes and Tropical Evolution of eyewall convective events as indicated by intra- Meteorology, San Diego, CA, Amer. Meteor. Soc., 113–114. cloud and cloud-to-ground lightning activity during the rapid Mansell, E. R., D. R. MacGorman, C. L. Ziegler, and J. M. Straka, intensification of Hurricanes Rita, Katrina, and Charley. Mon. 2002: Simulated three-dimensional branched lightning in a nu- Wea. Rev., in press. merical thunderstorm model. J. Geophys. Res., 107, 4075, doi:10. Gentry, M. S., and G. Lackmann, 2010: Sensitivity of simulated 1029/2000JD000244. structure and intensity to horizontal resolu- ——, ——, ——, and ——, 2005: Charge structure and lightning tion. Mon. Wea. Rev., 138, 688–704. sensitivity in a simulated multicell storm. J. Geophys. Res., Guimond, S. R., G. M. Heymsfield, and F. J. Turk, 2010: Multi- 110, D12101, doi:10.1029/2004JD005287. scale observations of Hurricane Dennis (2005): The effects Marks, F. D., 1985: Evolution of the structure of precipitation in of hot towers on rapid intensification. J. Atmos. Sci., 67, (1980). Mon. Wea. Rev., 113, 909–930. 633–654. ——, D. Atlas, and P. T. Wills, 1993: Probability-matched Heymsfield, G. M., J. B. Halverson, J. Simpson, L. Tian, and T. P. Bui, reflectivity–rainfall relations for a hurricane from aircraft ob- 2001: ER-2 Doppler radar investigations of the eyewall of servations. J. Appl. Meteor., 32, 1134–1141. Hurricane Bonnie during the Convection and Moisture Ex- Molinari, J., P. K. Moore, V. P. Idone, R. W. Henderson, and periment-3. J. Appl. Meteor., 40, 1310–1330. A. B. Saljoughy, 1994: Cloud-to-ground lightning in Hurricane Houze, R. A., F. D. Marks, and R. A. Black, 1992: Dual-aircraft Andrew. J. Geophys. Res., 99, 16 665–16 676. investigation of the inner core of Hurricane Norbert. Part II: ——, ——, and ——, 1999: Convective structure of hurricanes as Mesoscale distribution of ice particles. J. Atmos. Sci., 49, revealed by lightning locations. Mon. Wea. Rev., 127, 520– 943–963. 534. Jacobson, A. R., R. Holzworth, J. Harlin, R. Dowden, and E. Lay, Nolan, D. S., Y. Moon, and D. P. Stern, 2007: Tropical cyclone 2006: Performance assessment of the World Wide Lightning intensification from asymmetric convection: Energetics and Location Network (WWLLN), Using the Los Alamos Sferic efficiency. J. Atmos. Sci., 64, 3377–3405. Array (LASA) as ground truth. J. Atmos. Oceanic Technol., Petersen, W. A., R. C. Cifelli, S. A. Rutledge, B. S. Ferrier, and 23, 1082–1092. B. F. Smull, 1999: Shipborne dual-Doppler operations and Jayaratne, E. R., C. P. R. Saunders, and J. Hallet, 1983: Laboratory observations during TOGA COARE. Bull. Amer. Meteor. studies of the charging of soft hail during ice crystals in- Soc., 80, 81–97. teractions. Quart. J. Roy. Meteor. Soc., 109, 609–630. Price, C., M. Asfur, and Y. Yair, 2009: Maximum hurricane in- Kabe`che, A., and J. Testud, 1995: Stereoradar meteorology: A new tensity preceded by increase in lightning frequency. Nat. Geo- unified approach to process data from airborne or ground- sci., 2, 329–332, doi:10.1038/NGEO477. based meteorological radars. J. Atmos. Oceanic Technol., 12, Protat, A., Y. Lemaitre, D. Bouniol, and R. A. Black, 2000: Mi- 783–799. crophysical observations during FASTEX from airborne Kaplan, J., and M. DeMaria, 2003: Large-scale characteristics of Doppler radar and in-situ measurements. Phys. Chem. Earth rapidly intensifying tropical cyclones in the North Atlantic B. Hydrol. Oceans Atmos., 25 (10–12), 1097–1102. basin. Wea. Forecasting, 18, 1093–1108. Reasor, P. D., M. D. Eastin, and J. F. Gamache, 2009: Rapidly in- Kelley, O. A., J. Stout, and J. B. Halverson, 2004: Tall precipitation tensifying Hurricane Guillermo (1997). Part I: Low-wavenumber cells in tropical cyclone eyewalls are associated with tropi- structure and evolution. Mon. Wea. Rev., 137, 603–631. cal cyclone intensification. Geophys. Res. Lett., 31, L24112, Reisner, J. M., and C. A. Jeffery, 2009: A smooth cloud model. doi:10.1029/2004GL021616. Mon. Wea. Rev., 137, 1825–1843. Kossin, J. P., and M. D. Eastin, 2001: Two distinct regimes in the Rodgers, E. B., W. S. Olson, V. M. Karyampudi, and H. F. Pierce, kinematic and thermodynamic structure of the hurricane eye 1998: Satellite-derived latent heating distribution and envi- and eyewall. J. Atmos. Sci., 58, 1079–1090. ronmental influences in (1995). Mon. Wea. Kuhlman, K. M., C. L. Ziegler, E. R. Mansell, D. R. MacGorman, Rev., 126, 1229–1247. and J. M. Straka, 2006: Numerically simulated electrification ——, J. Weinman, H. Pierce, and W. Olson, 2000: Tropical cyclone and lightning of the 29 June 2000 STEPS supercell storm. lightning distribution and its relationship to convection and Mon. Wea. Rev., 134, 2734–2757. intensity change. Preprints, 24th Conf. on Hurricanes and Lay, E. H., A. R. Jacobson, R. H. Holzworth, C. J. Rodger, and Tropical Meteorology, Ft. Lauderdale, FL, Amer. Meteor. R. L. Dowden, 2007: Local time variation in land/ocean Soc., 537–541. lightning count rates as measured by the World Wide Light- Rogers, R. F., M. L. Black, S. S. Chen, and R. A. Black, 2007: An ning Location Network. J. Geophys. Res., 112, D13111, evaluation of microphysics fields from mesoscale model sim- doi:10.1029/2006JD007944. ulations of tropical cyclones. Part I: Comparisons with ob- Leonard, B. P., 1979: A stable and accurate convective modelling servations. J. Atmos. Sci., 64, 1811–1834. procedure based on quadratic upstream interpolation. Com- Saunders, C. P. R., and L. S. Peck, 1998: Laboratory studies of the put. Methods Appl. Mech. Eng., 19, 59–98. influence of the rime accretion rate on charge transfer during ——, and J. Drummond, 1995: Why you should not use ‘‘hybrid,’’ crystal-graupel collisions. J. Geophys. Res., 103, 13 949– ‘‘power-law’’ or related exponential schemes for convective 13 956.

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——, W. D. Keith, and R. P. Mitzeva, 1991: The effect of liquid water Meteor. Soc., 1.4. [Available online at http://ams.confex.com/ on thunderstorm charging. J. Geophys. Res., 96, 11 007–11 017. ams/88Annual/techprogram/paper_134367.htm.] Schubert, W. H., M. T. Montgomery, R. K. Taft, T. A. Guinn, Squires, K., and S. Businger, 2008: The morphology of eyewall S. R. Fulton, J. P. Kossin, and J. P. Edwards, 1999: Polygonal lightning outbreaks in two category 5 hurricanes. Mon. Wea. eyewalls, asymmetric eye contraction, and potential vorticity Rev., 136, 1706–1726. mixing in hurricanes. J. Atmos. Sci., 56, 1197–1223. Steranka, J., E. B. Rodgers, and R. C. Gentry, 1986: The relationship Shao, X. M., and Coauthors, 2005: Katrina and Rita were lit up between satellite measured convection burst and tropical cy- with lightning. Eos, Trans. Amer. Geophys. Union, 86, 398, clone intensification. Mon. Wea. Rev., 114, 1539–1546. doi:10.1029/2005EO420004. Takahashi, T., 1978: Riming electrification as a charge generation Simpson, J., J. B. Halverson, B. S. Ferrier, W. A. Petersen, mechanism in thunderstorms. J. Atmos. Sci., 35, 1536–1548. R. H. Simpson, R. Blakeslee, and S. L. Durden, 1998: On the Thompson, G., R. M. Rasmussen, and K. Manning, 2004: Explicit role of ‘‘hot towers’’ in tropical cyclone formation. Meteor. forecasts of winter precipitation using an improved bulk mi- Atmos. Phys., 67, 15–35. crophysics scheme. Part I: Description and sensitivity analysis. Smith, D. A., and Coauthors, 1999: A distinct class of isolated in- Mon. Wea. Rev., 132, 519–542. tracloud lightning discharges and their associated radio Zhang, F., and J. A. Sippel, 2009: Effects of moist convection on emissions. J. Geophys. Res., 104, 4189–4212. hurricane predictability. J. Atmos. Sci., 66, 1944–1961. Solorzano, N. N., J. N. Thomas, and R. H. Holzworth, 2008: Global Ziegler, C. L., D. R. MacGorman, J. E. Dye, and P. S. Ray, 1991: A studies of tropical cyclones using the World Wide Lightning model evaluation of non-inductive graupel-ice charging in the Location Network. Preprints, Third Conf. on Meteorological early electrification of a mountain thunderstorm. J. Geophys. Applications of Lightning Data, , LA, Amer. Res., 96, 12 833–12 855.

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