In this paper, a high-resolution simulation establishing relationships between lightning and eyewall convection 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 s−1, a relatively more frequent flash rate confined in a layer between 10 and 14 km, and a propagation speed that was about 10 m s−1 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 electrification
Tropical cyclones (TCs) are among the most destructive natural forces on the earth and many coastal communities worldwide are threatened yearly by these extreme events. Hence, it is vital to advance our knowledge on the internal and external dynamical processes governing their evolution and especially their intensity, which is currently poorly forecast (e.g., Davis et al. 2008). This knowledge becomes especially critical when, before making landfall, hurricanes1 undergo rapid intensification (RI), which is defined as any hurricane showing a 30 kt (or more) increase in 10-m maximum sustained wind speed in a 24-h period or less (Kaplan and DeMaria 2003).
Though many recent observational studies (e.g., Molinari et al. 1994, 1999; Price et al. 2009) have revealed that rapidly intensifying hurricanes occasionally produce abundant eyewall lightning activity, only one highly idealized study, Fierro et al. (2007, hereafter F07), so far focused on modeling hurricane electrification. This work improves upon F07 by simulating Hurricane Rita (2005), a hurricane that produced frequent eyewall lightning activity during its intensification cycle and from which very good lightning observations are available from a broad array of platforms (Shao et al. 2005; Squires and Businger 2008; Solorzano et al. 2008; Fierro et al. 2011, hereafter F11). By comparing the simulated lightning behavior with available three-dimensional lightning observations from the Los Alamos Sferic Array (LASA; F11), this work provides hypotheses on the evolution of the microphysical/convective state of the hurricane as its intensity changes. In particular, the work of F11, which is the first presenting three-dimensional flash data within a hurricane, shows that during the period of rapid intensification, Rita produced several episodic and isolated lightning bursts that rotated around the eyewall at a speed within 10% to that of the local azimuthal flow (see Fig. 1 for an example of those events) and had a life time between 15 and 25 min.
Besides F11, many studies reported that the occurrence of lightning bursts near the TC center was often associated with intensification of the system and that these episodic lightning bursts were associated with deep convection (e.g., Lyons et al. 1989; Black et al. 1993; Lyons and Keen 1994; Simpson et al. 1998; Rodgers et al. 2000; Heymsfield et al. 2001). Consistent with this, Kelley et al. (2004) suggested that extremely deep eyewall clouds (most likely to produce lightning) observed via the Tropical Rainfall Measuring Mission (TRMM) satellite in the eyewall were coincident with a 70% likelihood of storm intensification. It is also well recognized that RI often relies on the occurrence of small-scale hard-to-forecast convective bursts (e.g., Steranka et al. 1986; Rodgers et al. 1998, 2000; Reasor et al. 2009; Guimond et al. 2010) in the eyewall of the hurricane. In contrast to hurricanes undergoing RI, strong mature hurricanes remaining in a quasi–steady state (e.g., Hurricane Isabel 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 Location Network (WWLLN; Jacobson et al. 2006; Lay et al. 2007), with their study revealing a strong correlation between hurricane intensification rate and CG lightning activity. Furthermore, Cecil and Zipser (1999) found that a temporal lag existed between the production of ice scattering signature (proportional to convective intensity and lightning production) and the TC intensifying. Therefore, they also argued that lightning activity could be used as a reliable forecast tool as any changes in lightning frequency were likely associated with future changes in the intensity of a given TC.
Because electrical activity is relatively infrequent within the eyewall, lightning associated with the convective bursts are easily observed by detection networks such as LASA. Eyewall updrafts are too weak in the mixed phase region to allow sufficient production and lofting of graupel particles and supercooled water (Black 1984; Black and Hallett 1986) that are necessary for the generation of strong electric fields via the noninductive charging process (Takahashi 1978; Saunders et al. 1991; Saunders and Peck 1998, hereafter SP98). For example, Black et al. (1996) found that 70% of the eyewall vertical velocities from seven Atlantic hurricanes ranged between −2 and 2 m s−1 with only about 5% of vertical motions exceeding 5 m s−1. Stronger and wider updrafts capable of producing notable lightning bursts, such as those reported in F11, are rare, except in some hurricanes undergoing rapid intensification: for example, Black et al. (1994) reported updraft (downdraft) speeds reaching 24 (−19) m s−1 in Hurricane Emily (1987) during its deepening phase. Other examples of deep convective updrafts within TC undergoing RI are documented in Eastin et al. (2005a,b) for Hurricane Guillermo (1997) and in Guimond et al. (2010) for Hurricane Dennis (2005).
This modeling study builds upon the observational work of F11 by relating modeled lightning to key properties of the eyewall convection with focus on convective events (CEs) and attempts to address questions that could not be easily answered by the observations. In this work, a CE is defined as an isolated convective entity in the eyewall characterized by the following: 1) an instantaneous updraft speed greater than 10 m s−1 anywhere above the freezing level, 2) a minimum depth of the 7 m s−1 isosurface of 5 km, 3) minimum horizontal dimensions of 10 km × 10 km, and 4) a minimum lifetime of 15 min. The questions to be addressed include the following: how strong is the convection within the modeled CEs? How frequent are these events? What is their microphysical and electrical structure and in turn how do these structures differ from that of the bulk of the eyewall convection? How much latent heat is being released within the simulated CEs? Note that the latter question is important with regard to relating observed lightning within CEs to a quantity that can be used to initialize CEs within a model. Furthermore, though at least 4 distinct CEs were observed by LASA during a 24-h period, this paper will focus on the period in which two CEs were evident over a short period, from 1800 UTC 21 September to 0200 UTC 22 September, during Rita’s most rapid intensification phase. The remainder of the paper is designed to address these questions by first presenting the hurricane model in the next section, the results in the subsequent section, and the final section providing a brief summary and future directions.
2. The numerical model and initialization procedures
a. Equation set
The hurricane model is based on the Los Alamos National Laboratory’s (LANL) High Gradient (HIGRAD) large-eddy “smooth” cloud model (Reisner and Jeffery 2009). The equation set for the hurricane model is similar to what is described in section 2a of Reisner and Jeffery (2009), except that additional conservation equations were added for the microphysics and space charge. Specifically, the model includes conservation equations for the three momentum fields, potential temperature, gas density, water vapor density, number and density of cloud water, rainwater density, number and density of cloud ice, snow density, graupel density, turbulence kinetic energy density, and the space charge densities associated with each hydrometer. Besides the momentum equations, each conservation equation includes terms for advection (including those associated with precipitation fall terms), diffusion, and sources [see Eq. (6) within Reisner and Jeffery (2009)]. The sources and sinks found within the various microphysical conservation equations utilize a hybrid of the activation and condensation model found in Reisner and Jeffery (2009) together with all of the other relevant bulk parameterizations found in Thompson et al. (2004). The momentum equations forgo the microphysical source terms, but insert additional terms representing forcing due to pressure gradients, buoyancy, and the earth’s rotation.
Space charge density equations in the hurricane model are included as an option within a relatively simple lightning module that simulates the local time rate of change of a one-dimensional form of the electric field due to charging and discharging (lightning). The charging model uses the SP98 noninductive charge separation parameterization and polarization charging following Mansell et al. (2005), which was adapted from Ziegler et al. (1991). Lightning initiation/discharge in the model occurs whenever the ambient electric field exceeds the breakeven (or fair weather) electric field threshold, which was assumed to decrease exponentially with height, as in Mansell et al. (2002), with the electric field and space charge densities being decreased by a constant value of 10% through the column upon discharge. Although more sophisticated lightning models could have been used in the simulations, given the cost of the calculations, the reality that modeled collision rates between various hydrometers in hurricanes contain some uncertainty, and the simple desire to relate only the relative change in lightning flash rate to hurricane intensity fluctuations, this important piece of work will be deferred for a subsequent study. Likewise, because the current lightning model makes no distinction between in-cloud (IC) and CG flashes, the simulated lightning produced by the current model will be simply referred to as lightning discharges. For point of comparison it is also being assumed that the cell-by-cell lightning predicted by the model is a rough surrogate for the intense in-cloud discharges (narrow bipolar events; Smith et al.1999) observed by LASA.
b. Discrete model
The discrete version of the hurricane model is identical to what was described in section 2c of Reisner and Jeffery (2009) with each conservation equation being written in finite volume form on a collocated mesh (A grid) within a terrain-following coordinate framework. As explained in more detail in section 2c, two simulations were analyzed in this work with the first simulation primarily being run to provide reasonable initial conditions for the second higher-resolution simulation that resolves the CEs. The first simulation made use of a flux-limited form of the quadratic upstream interpolation for convective kinematics scheme including estimated streaming terms (QUICKEST; Leonard and Drummond 1995) for advection of all model fields with the discrete conservation equations utilizing a first-order forward Euler time-stepping procedure within a semi-implicit method to step over sound waves. The second simulation used a less diffusive form of QUICKEST, QUICK (Leonard 1979), in combination with an explicit fourth-order Runge–Kutta time-stepping process. As shown in Reisner and Jeffery (2009), the numerical approach utilized in the second simulation results in less numerical diffusion near cloud boundaries and hence should adequately resolve CEs found near the very small eye of Rita. However, although numerical diffusion is lower, the use of an explicit time-stepping procedure requires sound waves to be resolved and hence the computational cost of this simulation prevents numerous sensitivity simulations from being undertaken.
c. Model setup and initialization
As discussed at the end of the introduction, the goal of this work is to examine the lightning within Rita during a 8-h window starting at 1800 UTC 21 September using high enough resolution (2 km) to adequately resolve small-scale CEs (e.g., Davis et al. 2008; Fierro et al. 2009; Gentry and Lackmann 2010). However, in order to produce a reasonable looking facsimile of Rita at 1800 UTC 21 September and to reduce the overall computational burden, a 4-km simulation was first conducted and initialized at 1200 UTC 20 September with this simulation then running for 38 h. The 2-km simulation then utilized output from the 4-km run for its initialization at 1800 UTC 21 September (or 30 h into the 4-km simulation).
The 2- and 4-km simulations were carried out in the same domain having geographical dimensions of 2000 km × 1600 km × 21.3 km (Fig. 2a). For the 2- (4 km) simulations this corresponds to grid sizes of 1000 × 800 × 86 (500 × 400 × 86) with the vertical grid using a stretched mesh with highest resolution near the surface (50 m) and coarsest near the model top (440 m). The time step for the 4-km simulations was 1 s, while for the 2-km simulation the time step was 0.25 s. All simulations utilized the Department of Energy’s (DOE’s) XT-5 Cray machine (Jaguar) hosted at the Oak Ridge National Laboratory using between 2000 and 32 000 processors. For the 4-km run 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 composite achieved the initialization of the horizontally homogeneous 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 incorporated into the 4-km simulation via a simple nudging procedure that was active for the first hour of the simulation. Note the minimum surface pressure of the resulting hurricane that develops in response to this nudged wind field is relatively sensitive to the time period over which this nudging takes place and for the current simulation it was decided that this nudging be of sufficient duration (3 h) to induce a vortex stronger than the observed vortex (by about 10 m s−1). Given that the period of interest is still 30 h away, the introduction of a stronger vortex makes sense in that a stronger initial vortex can induce the 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 toward having all the convection within the eyewall).
To further facilitate the balance between eyewall and rainband convection a combination of the Next Generation Weather Radar (NEXRAD) radar data (primarily used for initialization of the eyewall convection) obtained from Key West, Florida, at 1200 UTC 21 September and integrated-in-time LASA lightning data obtained for four 3-h intervals starting at 1200 UTC 21 September (primarily employed for initialization of the rainband convection, see Fig. 2b) were used to initialize rainwater, snow, and graupel fields over the first hours of the 4-km simulation. Microphysical fields were initialized with the NEXRAD radar data via dBZ-to-mass relationships along with the addition of water vapor to ensure saturation of the column. To utilize the LASA lightning data within the model, the data were first interpolated onto the 4-km grid and represented within a two-dimensional binary array (containing zeros for no lightning and ones for lightning). Then, for the columns for which lightning was present water vapor was added from z = 3 km to z = 11 km to ensure saturation within this layer.
As previously discussed, the simulated intensity in the 4-km simulation is initially stronger than the observations until near the time in which the 2-km simulation was initiated, after which the simulated hurricane was weaker than the observations (Fig. 3b). The simulated track is close to the observed track during the course of the 4-km simulation (Fig. 3a) with a few bursts of lightning occurring near periods of small drops in surface pressure (Fig. 3b). The largest track differences (observed vs simulated) occurred during the last few hours of the simulation and were caused by a slightly inaccurate representation of the large-scale steering environment that was held constant during the simulation.
To further illustrate the lightning bursts, 5-min flash rate and pressure traces for the 2-km run are presented (see Fig. 4a) and are compared to the last 8 h of the 4-km 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 approximately 15 min. The boundary between the eyewall and rainbands for the lightning computations was based on horizontal cross sections of average updraft speeds in the 10–14-km layer in order to account for the outward tilt of the convection and also because, as shown later in this section, most simulated flashes were found to initiate at those altitudes. In the 2-km case, a constant radius of 100 km from the storm center (defined by the minimum surface pressure) was selected because the eyewall size of the 2-km storm remains nearly constant. Because the 4-km simulation was run for a longer period and was designed to include the development and intensification stage of the storm, the eyewall size did vary and for this reason the radius of the box encompassing the eyewall was set to 100 km during the first 24 h, 120 km between 24 and 26 h, and 148 km after that time.
As compared to the 4-km run, the 2-km simulation produces a stronger storm with a simulated minimum surface pressure of about 908 hPa (cf. Figs. 4a,b). Unlike the 4-km simulation, the 2-km run also produces between 5 and 6 h a relatively large eyewall lightning burst, which is followed by a small but noticeable 4–5-hPa minimum surface pressure drop. Additionally, after 4 h, both simulations produced overall less lightning in the rainbands than in the eyewall, consistent with observations (e.g., Shao et al. 2005; Squires and Businger 2008). Furthermore, though the 2-km simulation did not produce a hurricane as intense as the observations, preliminary analysis of an additional 2-km simulation, whereby spurious evaporation near cloud edges was limited (Reisner and Jeffery 2009) resulted in a hurricane with a steeper pressure trace slope and a lower minimum surface pressure during maximum intensity (i.e., 898 compared with 908 hPa). The overall structure, evolution, and lightning activity remained very similar to that of the 2-km simulation presented herein.
Noteworthy differences are also seen between observed and modeled lightning rates. Clearly, while the hourly flash rates for the 4-km case are comparable to observations (Fig. 3), the 2-km run produces much larger flash rates greater by as much as a factor of 100 (Figs. 3 –4). While it is possible that further tuning of the magnitude of charge separated per collision within the noninductive charging parameterization would reduce the modeled flash rate, the focus here is on the trends and associated relative increase/decrease of the modeled flash rate and their relationship to storm intensity rather than reproducing reasonably the observed amount of flashes. There are many factors that could cause this scale dependency on the modeled flash rate. One of which is undoubtedly related to the rather simplistic electrification processes implemented in this code, which do not take into account ion attachments, recoil streamers, stochastic branching of lightning channels (resulting, again, in no possible distinction between IC and CG flashes), and corona discharges as in Mansell et al. (2002).
Before relating the simulated lightning to modeled microphysical/kinematic fields in the 2-km simulation, basic storm attributes were evaluated by comparing the simulated hurricane radar reflectivity structures to in situ three-dimensional tail radar data [the National Oceanic and Atmospheric Administration (NOAA) Hurricane Research Division (HRD)] obtained at 1915 UTC 21 September (Fig. 5). It is important to note that an 8-dBZ offset was added to the raw observational data shown in Figs. 5a,c,e. This is because the generally low reflectivity values in the observations are caused by low calibration of the tail and low-fuselage radars mounted on the NOAA WP-3D aircraft. For instance, Marks et al. (1993) found a −8.2-dBZ calibration error for low-fuselage radar data of Hurricane Anita (1977). Consistent with Kabèche and Testud (1995), a more recent study from Protat et al. (2000) reported an improved −5-dBZ calibration error of the NOAA WP-3D radars, which value lies within a reasonable range of the 8-dBZ offset used herein. Below 2 km AGL, the true dBZ readings are compromised due the presence of sea clutter. However, corrections were not made to account for this effect since this work focuses on electrification processes, which occur within and above the mixed-phase region of updrafts (between about 0° and −20°C). Given the above corrections of the observed dBZ, the model underestimates the 15–30-dBZ echo tops, while the 35-dBZ top, a threshold for significant hydrometeor mass in tropical convection (and hence lightning; Petersen et al. 1999) shows reasonable agreement with the observations (Figs. 5a–d). The simulated eye size near the surface (∼20 km in diameter) is slightly larger than the observations (∼12 km in diameter). Also, the simulated radar reflectivity slope in the eyewall, measured from the vertical axis, ranges between 70° and 80°, which is approximately twice the values of 40°–45° observed by the NOAA WP-3D radars in weakly sheared environments (Marks 1985). The model also consistently produces higher reflectivity than the observations especially at lower levels below z = 5 km, which is a well-documented problem within models and has been attributed primarily to biases in the functions used to compute reflectivity and terminal fall speeds of precipitation particles (Rogers et al. 2007). Also, the simulated eyewall width is larger than the observations by as much as a factor of 5, with this difference possibly being attributed to numerical diffusion near cloud edges (Reisner and Jeffery 2009) and/or too small of a surface friction coefficient (Davis et al. 2008).
Horizontal cross sections from the 2-km simulation (see Fig. 6) taken at different times of modeled radar reflectivity overlaid with a horizontal projection of modeled 50-s accumulated lightning discharge show evidence of CEs located inside areas of radar reflectivity exceeding 45 dBZ within the simulated eyewall of Rita. Of important note are the three CEs found at hour 5 that roughly correspond with the onset of the lightning burst shown in Fig. 4b. Because the evolution of these CEs bear some resemblance to what was suggested by the LASA lightning array, their evolution and potential impact on intensification is highlighted later in this section.
To provide a broader view of the averaged storm properties and its relationship to lightning, azimuthally averaged diagrams were produced onto which simulated lightning discharges were overlain. At each time of interest, the data were interpolated onto a cylindrical grid centered on the storm’s minimum surface pressure and then averaged in azimuth. Since lightning discharges consist of discrete integer values, the data were not azimuthally averaged but simply summed in azimuth after interpolation. And for the subsequent Hovmöller plots, the lightning datum at each grid point on the cylindrical grid represents the sum of all discharges in the vertical.
Figure 7 shows radius–height diagrams of vertical velocity, 5-min accumulated lightning flashes, liquid water content (LWC), and radar reflectivity for the same four times shown in Fig. 6. Lightning is primarily found in the eyewall between z = 10 and 14 km where azimuthal updrafts reach their maximum and the bulk of the graupel is produced by riming with supercooled droplets (i.e., noninductive charging is directly a function of the riming rate). In agreement with observations, the simulated storm produced overall weak-to-absent lightning activity in the outer bands (radii greater than 90 km) with this behavior being clearly evident in the Hovmöller diagram (see Figs. 8a,b). As time progresses, the eye and eyewall size remain constant 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 between 70 and 110 km with flash counts exceeding 180 h−1. The three CEs found at hour 5 are associated with relatively higher 5–9-km layer averaged equivalent potential temperature (θe) values at radii between 40 and 50 km, 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 θe 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 s−1 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 increase 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 s−1 moving around the eyewall. The propagation speeds of the CEs shown here are about 10 m s−1 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), which, in turn, initiate CEs where the inertial instability is sufficient. As time progresses and the eyewall reaxisymmetrizes, the CEs progressively weaken due to local consumption of convective available potential energy and the angular shear of the primary vortex.
While the above mechanisms have not been yet verified against observations of CEs within rapidly intensifying hurricanes, which are at present very limited, an alternative explanation that could support the formation of those strong CEs would involve asymmetric mixing between relatively high entropy air at low levels in the eye and the eyewall. Once this entropy-rich air is transported outward near the radius of maximum wind, the latter could enhance/boost convective development in that region (Barnes and Fuentes 2010; Reasor et al. 2009; Braun and Wu 2007; Braun et al. 2006; Eastin et al. 2005b; Kossin and Eastin 2001). Evidence of this mechanism can be seen in Fig. 6 by the polygonal eyewall structure and episodic mixing of radar reflectivity from the eyewall into the eye (implying a compensating outward mixing of air found within the eye; Fig. 8).
Vertical cross sections of the simulated net space charge across the two simulated CEs of Fig. 10 (location denoted by a thick horizontal black line) and across the eyewall are shown in Fig. 11. The simulated gross charge structure in the CEs resembles an inverted tripole, which consists of a main positive charge region sandwiched in between two layers of negative charge. The recent observational study of F11 found, however, that the gross charge structure in Rita’s eyewall was of opposite polarity, namely a normal tripole. Previous high-resolution modeling studies on thunderstorm electrification showed that the simulated gross charge structure of a thunderstorm was very sensitive to the noninductive charging scheme selected in the model (e.g., Fierro et al. 2006; Kuhlman et al. 2006). Such discrepancies in simulated charge structures are mainly attributed to the different in-cloud conditions and apparatus used to reproduce the critical charging curves of riming graupel (e.g., Takahashi 1978; Jayaratne et al. 1983; Saunders et al. 1991; SP98). Because induction in the model is only allowed to occur during graupel–rainwater collision, the main negative charge region in Fig. 11, which is located well above the freezing level, is principally attributed to noninductive charging of graupel, with snow and cloud ice carrying the corresponding amount of opposite charge (i.e., positive charge; Fig. 12).
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 m−3 and graupel mixing ratios ranging between 2.5 and 5 g kg−1, which are generally located atop updrafts between z = 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 instance, Black and Hallett (1999) noted the abundant concentration (100–300 L−1) 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 using other critical charging curves and/or adjusting various microphysical parameterizations to examine how these highly nonlinear relationships affect charge structure and/or lightning activity within the CEs. Though these simulations should help pinpoint what combination is needed 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, the model could still produce the right charge structure for the wrong reasons. Furthermore, though these simulations will probably produce lightning at heights within the CEs that are different than the current simulation, the primary results of this paper should still stand (i.e., a majority of the simulated lightning is found within the CEs).
Another interesting aspect of Fig. 11 is that, despite noteworthy differences in lightning flash rate between CEs and the bulk of the eyewall convection, their differences in space charge magnitude and vertical motions can be relatively small. Because the simulated CEs lasted 15–30 min compared to about 5–10 min for the bulk eyewall convection, CEs are able to build up charge and hence the necessary electric fields that are able to exceed the breakeven threshold for lightning initiation/production (not shown). Figure 12 also confirms that CEs are characterized by relatively higher θe values with the highest values confined at upper levels between z = 10 and 14 km where the great majority of the ice-phase hydrometeors reside (Figs. 11 and 12).
Given the reduction in pressure that may occur after the short-lived mass flux increases within the eyewall, which in all probability are entirely random in nature (Zhang and Sippel 2009), it is important that hurricane forecast models be properly initialized before this time so that accurate forecasts can be made. But, in order to utilize observed lightning within models for initialization purposes, proxies must be developed. Toward this goal, model results from both the 2- and 4-km simulations were averaged over a 9 × 9 × 9 grid volume (∼535 km3) within either a 100- or 1000-s time frame. Note, because the 2-km simulation produced more flashes (Fig. 4), the time interval was reduced from 1000 s in the 4-km simulation to 100 s.
Specifically, during this time interval, each modeled lightning discharge was correlated with the following four variables (see Fig. 13): vertical velocity (W), water vapor supersaturation (QVS), water vapor supersaturation over ice (QVSI), and latent heat (LH). The four histograms of these variables from both the 2- and 4-km simulations show that lightning in the model was primarily associated with updraft speeds on the order of 2–4 m s−1, latent heat values of about 100 K h−1, and supersaturation (over ice and water) on the order of 0.5 g kg−1. After being validated against observations (i.e., latent heat derived from dual-Doppler aircraft data), the values shown in Fig. 13 could be utilized to help initialize CEs within a model by both saturating and/or introducing heat into a column via a data assimilation procedure.
4. Discussion and conclusions
Cloud-resolving numerical simulations of the electrification and lightning in Hurricane Rita were carried out to relate simulated eyewall lightning activity to the convective state of the storm and intensity fluctuations. The 2-km simulation is the first relating simulated lightning activity and general storm (azimuthally averaged) properties for a case from which high-quality lightning observations are available from many platforms (F11; Squires and Businger 2008; Solorzano et al. 2008; Shao et al. 2005). A key finding 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.
Specifically, the 2-km simulation was able to resolve individual electrically active strong convective updrafts exceeding 11 m s−1 rotating around the eyewall at a speed about 10 m s−1 less than the local azimuthal flow, consistent with observations. The characteristic width of most of these CEs was about 10–15 km, consistent with observations of Black et al. (1996) and in turn explaining why the 4-km simulation failed to adequately resolve the CEs. But, given the small spatial scale of these CEs and that their dynamical structure is just resolved using a 2-km stencil, future simulations are needed, whereby even higher resolution near the eye is employed to understand how the nature of both the lightning and CEs change under grid refinement. Likewise, it is hoped that the results from the current simulation will help guide the setup of these future high-resolution simulations; resulting in simulations that not only better reproduce the narrow eye of Rita and the tilt of the eyewall convection, but the observed charge structure as well. Furthermore, the lightning discharge model used in the current simulations was relatively crude and more sophisticated lightning models such as Mansell et al. (2002) that can simulate branched lightning should be next carried out in order to relate hurricane intensity changes with lightning type and polarity.
Another aspect of this work was to begin determining proxies for lightning that could be used in operational hurricane models to assimilate near-real-time observed lightning data (i.e., from geostationary lightning mappers). This capability could prove itself very valuable over the Pacific Ocean, where data availability is sparse or in situations for which more than one hurricane is occurring over the Atlantic basin. Note that, as described in the model setup section, observed lightning from the LASA array has already been used to help initialize the rainbands in the 4-km simulation using a simple nudging procedure; however, considerable research is still required to determine the values of latent heat and/or water vapor introduced within a given model volume that produces results that “optimally” agree with observations (i.e., these values could be determined by the use of an ensemble Kalman filter).
Since lightning data is nearly continuous over long time periods, the data could be readily incorporated into advanced four-dimensional data assimilation procedures to help determine the true convective state of a hurricane at a given moment for short-term high-resolution research simulations. The nudging procedure via proxies could, for example, alter the supersaturation field in a given layer as done herein, or artificially increase the mixing ratio of a predicted variable known to be well correlated with lightning, such as graupel content or LWC within the mixed phase region (defined here as the layer between z = 5 and 7 km). However, given the relative short lifetime of CEs, current operational hurricane models may require at least 6–12 h for spinup, and given that these simulations typically make use of a horizontal grid spacing that is too coarse to resolve CEs, the assimilation of the small-scale CEs raises important questions with regard to the community’s ability to predict hurricane intensification. Chief among them is whether hurricane models must accurately resolve the evolution of the CEs or just capture the integrated impact of these events on the overall intensity of the eyewall convection. For instance, the latter approach could employ a simple continuous nudging procedure that introduces both a symmetric and an asymmetric water vapor source into a given simulation with the magnitude of this source correlated to the amount of observed lightning found within the CEs. In the present simulation, the supersaturation field was maintained for 3 h in order for the rainband convection to persist. Hence, tests similar to these need to be conducted in the future to determine both the time period and amount of water vapor required to reasonably capture the integrated impact of the CEs within a given hurricane simulation.
This work was supported by the Laboratory Directed Research and Development Program of the Los Alamos National Laboratory, which is under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy under DOE Contracts W-7405-ENG-36 and LA-UR-10-04291. Computer resources were provided both by the Computing Division at Los Alamos and the Oak Ridge National Laboratory Cray clusters. The authors would also like to thank Dr. Gary Barnes and one anonymous reviewer for providing helpful suggestions on an earlier version of the manuscript. Thanks also go out to Steve Guimond for providing the wind, radar, and environmental observations and to Dr. Edward “Ted” Mansell for his guidance toward the elaboration of the HIGRAD electrification model. The authors would also like to thank Dr. Robert Rogers at HRD, NOAA, for providing the Fortran subroutine that interpolates the model data from a Cartesian to a cylindrical grid.
Corresponding author address: Alexandre O. Fierro, Cooperative Institute for Mesoscale Meteorological Studies, National Weather Center, Suite 2100, 120 David L. Boren Blvd., Norman, OK 73072. Email: email@example.com
The terms “hurricanes” and “tropical cyclones” will be used interchangeably throughout this paper.