1. Introduction
Background
Lightning-producing storms pose a serious hazard to the public and are responsible annually for nearly 1000 fatalities and damages exceeding $1 billion (U.S. dollars) worldwide (Curran et al. 2000; Ashley and Gilson 2009). The occurrence of cloud-to-ground (CG) lightning flashes is especially problematic in semiarid regions where they can occasionally spark forest fires and, concurrently, result in significant damage. Owing to its high economic impact, in the last two decades heightened emphasis has been directed toward improving the community’s ability to forecast lightning using numerical weather prediction (NWP) models. Two separate approaches presently exist for predicting lightning in cloud-scale (i.e., <5 km) models: Lightning is either explicitly predicted using electrification physics or diagnosed via combinations of kinematic and/or microphysical proxy variables known to be well correlated with the occurrence of lightning. Such proxies include graupel volume (Wiens et al. 2005) and ice water content (Petersen et al. 2005).
In the last three decades, several studies successfully implemented lightning parameterization schemes and sophisticated electrification physics within cloud-resolving numerical models (e.g., Takahashi 1984; Helsdon and Farley 1987; Ziegler et al. 1991; Mansell et al. 2005). In the category pertaining to explicit lightning prediction schemes, there exist two distinct types of models: those producing bulk flashes and those explicitly resolving individual lightning channels. The chief advantage and attractiveness of bulk lightning schemes is their relative simplicity and low computational cost.
The present Weather Research and Forecasting (WRF) lightning model makes use of the bulk approximation paradigm and is, therefore, referred to as the bulk lightning model (BLM). Perhaps the simplest bulk lightning parameterization is the scheme developed by Rawlins (1982), whereby the charge densities are reduced upon discharge throughout the entire domain. Takahashi (1987) improved the Rawlins approach by allowing reduction of charge densities only within regions containing the highest magnitude of charge, which would be consistent in nature with regions of the largest electric field magnitudes (Emag). Ziegler and MacGorman (1994) further improved the Takahashi bulk flash model by imposing charge conservation and allowing the space charge to be redistributed within regions exceeding a given charge density threshold. Furthermore, they simplified the ion attachment process of Helsdon et al. (1992) by directly distributing lightning ion charge to each hydrometeor category according to its total surface area. MacGorman et al. (2001) refined the Ziegler and MacGorman scheme by restricting the lightning volume to two regions (defined by ambient charge and electric potential) connected by an initial channel. Explicit branched lightning parameterizations (e.g., Hager 1998; Mansell et al. 2002) are still too computationally expensive for NWP use, though the hybrid scheme from Barthe et al. (2012) adds a kind of channel branching to the MacGorman et al. (2001) approach.
As mentioned earlier, the second category of lightning models pertains to those employing proxy variables to diagnose the occurrence of lightning. Those approaches based on lightning diagnosis are attractive because they do not require inherent knowledge of electrification physics and cloud electrodynamics (i.e., charging and discharge processes) and, consequently, are computationally inexpensive. Bright et al. (2004) utilized mixed-layer convective available potential energy (CAPE) as a proxy for vertical velocity and, ultimately, for the probability of lightning occurrence. Empirically derived statistical methods (based on regression) have also been used to determine the amount of lightning and lightning threats based on storm’s environmental thermodynamic conditions (e.g., Mazany et al. 2002; Burrows et al. 2005; Shafer and Fuelberg 2008). Recently, McCaul et al. (2009, hereafter MC) proposed a lightning flash density prediction method whereby lightning in the convective region is assumed to be proportional to the updraft mass flux of the precipitating ice particles (graupel) in the “mixed-phase region” at the −15°C isotherm (similar to Petersen et al. 1999). They further devised a second proxy that accounts for lightning occurrence in stratiform areas whereby lightning density is a function of the vertically integrated ice mass (e.g., Zipser and Lutz 1994; Petersen et al. 1996, 1999; Cecil et al. 2005; Petersen et al. 2005). Lynn et al. (2012) devised a dynamic lightning prediction algorithm whereby lightning rates are assumed proportional to the so-called potential electrical energy computed through diagnostic relationships between bulk cloud properties and the vertical velocity field.
As an intuitive next step, it is proposed in the present work to implement an explicit, computationally inexpensive, lightning model within a state-of-the-art NWP forecast model. The rationale for developing this modeling capability arises from a need to develop enhanced operational lightning data assimilation tools (e.g., Fierro et al. 2012) prior to the upcoming first launch of the Geostationary Operational Environmental Satellite R series (GOES-R) in 2015, which will be equipped with the Geostationary Lightning Mapper (GLM; Goodman et al. 2013) instrument capable of mapping total lightning (CG + intracloud) day and night, year-round with a nearly uniform resolution over the Americas ranging between 8 and 12 km (Gurka et al. 2006).
2. Description of the lightning model
The model used in this study is the three-dimensional compressible nonhydrostatic WRF Model (version 3.3.1) with Advanced Research WRF (ARW) dynamic solver (WRF-ARW; Skamarock and Klemp 2007). In the following discussion of new physics modules added to WRF-ARW, the charging physics will be described first, followed by the computation of the electric field and the details behind the discharge model.
a. Charging physics
Once the gridcell noninductive and inductive charging rates have been determined, the terms for the total charge production rate increase and decrease are computed for each of the six predicted hydrometeor species x (i.e., the sum of all inductive and noninductive charging rates involving hydrometeor species x). By virtue of the conservation of total charge according to which the domain-integrated charge should be neutral, the amount of space charge gained via inductive and noninductive charging by hydrometeor species x during a given collision between x–y should equal the amount of charge lost by hydrometeor species y. Charges carried on precipitation particles are allowed to pass through the lower boundary by virtue of their fall speed and sedimentation flux, thus leaving the domain.
As a next step, the model computes the amount of charge increase or decrease due to charge separated during mass transfer between hydrometeors, which following mass conservation also conserves charge. The total space charge on each hydrometeor species x is then the sum of the space charge computed at time step t − 1 plus all mass transfer and charge production rate terms.
Sedimentation and advection of space charge is treated in an identical manner as the predicted scalars. In this work, scalar advection in the vertical and horizontal uses the fifth-order weighted essentially nonoscillatory (WENO) scheme (Jiang and Shu 1996), with a positive-definite limiter added for moisture scalars. Sedimentation for particle mixing ratio, number concentration, and charge employ a first-order upwind scheme.
b. Electric field and electrical potential solver
The bottom and top of the model domain employ Dirichlet boundary conditions (zero potential at the ground and fair-weather potential at the top), while the lateral boundaries employ the Neumann boundary condition (zero normal derivatives). For a first-guess solution and for the lateral boundary conditions, the fair-weather electric field formulation of Gish (1944) is employed. In all convection allowing simulations conducted herein [O(106) grid cells], the computational time of the solver is about 10%–13% of the total computational time, highlighting its efficiency.
c. Discharge model
As mentioned in the introduction, several discharge models with varying degrees of complexity have been developed in the last three decades. The most realistic, explicit branched “fractal-like” lightning parameterizations (e.g., Mansell et al. 2002) are currently impractical for even regional forecast applications due to the high computational cost of solving Eq. (7) after adding each small channel segment for every flash. One of the primary goals of this work is to implement a computationally inexpensive physics-based lightning model for use in operational forecasts as a significant step toward the upcoming launch of GOES-R.
The discharge model implemented in this study is a “bulk” type adapted from Ziegler and MacGorman (1994) and MacGorman et al. (2001). First, the lightning discharge scheme identifies lightning initiation points at all grid cells at which Emag exceeds a prescribed critical threshold Ecrit [set in the following simulations to 120 kV m−1, consistent with the break-even field magnitude indicated by Gurevich et al. (1992) for middle levels of the troposphere; Fig. 1]. A discharge is centered around each initiation point and involves all points within a cylinder of fixed radius R extending vertically through the entire depth of the simulation domain (Fig. 1). For cloud-scale simulations, R is typically on the order of a few kilometers (set here to R = 6 km for all simulations). The simulated lightning trends on the 3-km grids employed for this study remained qualitatively similar in shape when R was varied between 2 and 12 km. When R extends beyond the tile of the initiation point, MPI subroutines ensure that the occurrence of a discharge is communicated to all the points involved in the cylinder in neighboring tiles. By virtue of this simplistic discharge parameterization, it is not possible to distinguish between flash type or flash polarity.
Sketch illustrating how the lightning scheme selects the grid points participating in an idealized discharge and, subsequently, how the net total charge density ρ is altered after the discharge. The discharge cylinder axis (boundary) is shown in a dashed (solid gray) line. The black dots represent grid points where the electric field magnitude (E) exceeds the breakdown threshold (Ecrit). The gray dots in step 2 show the grid points participating in the discharge (i.e., where ρ will be reduced in step 3). Note that in step 2, discharge points located within overlapping cylinders are counted only once. Total positive (negative) net space charge regions are shown in the orange (light blue) shaded ovals. Positive (negative) net space charge regions exceeding the minimum threshold for discharge (0.1 nC m−3) are shown in the red (blue) ovals. The red (blue) ovals in step 3 show examples of space charge areas >0.1 nC m−3 not affected by the discharge because of being located outside the cylinders. The areas outlined in black in steps 1 and 2 denote the boundary on the model grid where E > Ecrit. Last, the black arrow represents the radius of the discharge cylinders (of 6 km in the three benchmark simulations herein).
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
To determine the charge involved in discharges during a time step, a two-dimensional (2D) array B(x, y) is set to 1 at all 2D grid points within all the cylinders where the space charge magnitude exceeds a small nominal space charge threshold (0.1 nC m−3 herein) anywhere within the column and is set to 0 at all other 2D grid points in the model domain (Fig. 1). Considering exclusively all grid points within the cylinders satisfying B(x, y) = 1, the discharge model then computes the sum of the space charge within this discharge volume for all grid cells with positive charge (S+) and, similarly, the summed magnitude for all cells with negative space charge magnitude (S−). The total magnitude of charge Qd to be superposed upon each polarity is set to 30% (Rawlins 1982; Ziegler and MacGorman 1994) of the maximum of S+ and S− unless that product (e.g., 0.3S+) already exceeds the summed magnitude of opposite polarity (S−). In that exceptional case, Qd is simply set to the lesser of S+ and S−. Then the fraction of positive charge to be superposed on each grid cell is given by F+ = Qd/S+ and, similarly, the fraction of negative charge by F− = Qd/S−.
The lightning charge is distributed throughout all discharge volumes during a time step. In each grid cell within the discharges, the magnitude of space charge to be deposited is F+ or F− (if the polarity of net space charge in that cell is positive or negative, respectively) times the magnitude of net space charge above the threshold in that grid cell. This magnitude of opposite-polarity space charge is distributed across all hydrometeor species in the grid cell. The magnitude placed on a specific hydrometeor species is proportional to the fraction of surface area of that species relative to the total surface area of all species in that grid cell. As explained by Ziegler and MacGorman (1994), this distribution mimics the capture of free-ion space charge by each hydrometeor species, but is done instantaneously, rather than by explicit ion processes (e.g., Helsdon et al. 1992). In other words, the transfer of charge from lightning channels to hydrometeors is done within the model time step in which the flash occurs.
The discharge procedure is repeated iteratively in a time step until the maximum Emag no longer exceeds Ecrit anywhere in the domain. In other words, the discharge first determines the locations of Emag exceeding Ecrit, then redistributes the charge, and as a last step updates the electric field solution across the domain. If Emag from the updated electric field solution exceeds Ecrit anywhere in the domain the discharge process is repeated. Typically, no more than three iterations are required to relax the maximum Emag below Ecrit everywhere in the domain. As explained in the following section, the simulated lightning was evaluated on the domain’s inner nest, which had a horizontal grid spacing of 3 km and used a computational time step of 15 s. Relative to the time scale of a typical lightning discharge (on the order of a few hundred milliseconds), this computational time step is a couple of orders of magnitude larger. Owing to the simplicity of this discharge parameterization, however, the BLM is primarily intended to provide an indication of the direction of lightning trends, and not to accurately mimic flash rates within a given storm. Note that this parameterization differs from the Ziegler and MacGorman (1994) scheme, in which the discharge process involves all points having excess charge throughout the entire model domain during each iteration.
3. Brief description of the case studies
To provide a reasonable evaluation of the BLM, the simulated lightning fields were assessed for three convective systems differing drastically in their internal dynamics and thermodynamic environments: a continental squall line, a strong tropic cyclone, and a continental winter storm.
The chief motivation behind the choice of each case study differs. For the severe continental squall line (15 April 2012) and the continental winter storm (1 January 2012) cases, the main criterion for selection was the production of a reasonable forecast of the convection with a cold start beginning at 0000 UTC to mimic the situation under which experimental forecasts are conducted with the National Severe Storms Laboratory (NSSL) 4-km WRF-ARW test bed over the contiguous United States (CONUS).
On 15 April 2012, during the late afternoon and evening hours, the collision of a retrogressing dryline with an eastward-moving cold front in the Texas Panhandle resulted in the rapid development of a large squall-line mesoscale convective system (MCS) over northwest Texas, western Oklahoma, and central Kansas. The merging mesoscale boundaries were reasonably well resolved in the National Centers for Environmental Prediction (NCEP) North American Mesoscale Model (NAM) analysis and forecast fields that were used to initialize and provide time-dependent lateral boundary conditions for experimental forecasts conducted with the NSSL 4-km WRF-ARW test bed over CONUS. Thus, the NSSL-WRF was able to forecast the timing and location of convection initiation (CI) and subsequent upscale development of this squall line with reasonable accuracy.
On 1 January 2012, strong northerly flow wrapping around the northern and northwestern side of a strong low pressure system over the northern Great Plains resulted in sufficient cold air advection and lift to generate a snow storm. Because synoptic-scale ingredients were the primarily driver for this winter storm event, the NSSL 4-km WRF-ARW test bed was also able to capture the evolution of this system reasonably well. Moreover, since no lightning was detected in this winter storm during the simulation period (see section 5c), this case was selected to further document the performance of the BLM in simulating a null case.
The 2005 hurricane season was one of the most active in recorded history with a total of 31 named storms, 7 of which were classified as major hurricanes (category 3 or greater on the Saffir–Simpson scale). One of those major hurricanes, Rita, made landfall on the Texas coast and in South Florida resulting in an estimate of $12 billion (U.S. dollars) in damage. During its journey in the Gulf of Mexico between 20 and 24 September 2005, Rita rapidly intensified from a category 2 to a category 5 storm reaching maximum sustained winds near 155 kt (Knabb et al. 2005). During this rapid intensification cycle, which was centered near 1200 UTC 21 September 2005, the storm experienced several lightning bursts in its eyewall, some of which were documented by several studies (Shao et al. 2005; Squires and Businger 2008, hereafter SB08; Fierro et al. 2011, hereafter F11).
The motivation for selecting Hurricane Rita (2005) is twofold: (i) as stated above, observations of the dynamical and electrical evolution of this category five storm during its rapid intensification cycle have been well documented in the literature and, additionally, have been well simulated in other studies (Fierro et al. 2009, hereafter F09; Fierro and Reisner 2011); (ii) the solutions are integrated over a long period (3 days), so many electrically active thunderstorms will continuously interact with each other during the forecast and provide, therefore, a considerable range of conditions over which to evaluate the performance of the lightning code.
4. Benchmark simulations setup
a. Physics configuration of the simulations
A brief summary of the physics and model parameters employed for all three simulations are shown in Table 1. The simulations employ the two-moment, six-class bulk microphysical scheme of Mansell et al. (2010) recently implemented in WRF. The six bulk hydrometeor species are rain, cloud water, cloud ice, snow, graupel, and hail. The boundary layer was parameterized following the Eta implementation of the 1.5-order closure Mellor and Yamada (1982) turbulence kinetic energy scheme adapted by Janjic (1994) with Monin–Obukhov–Janjic similarity theory for the subgrid-scale turbulence processes (Chen et al. 1997). Boundary conditions for turbulent fluxes are provided by the Unified Noah land surface model (Chen and Dudhia 2001; Ek et al. 2003). The longwave and shortwave radiation were both parameterized following the Goddard scheme (adapted from Mlawer et al. 1997). Note that the above physics options were used on both the parent and the nested grid for consistency. Because the horizontal grid spacing of the parent domain (9 km) is in principle too coarse for the use of an explicit microphysics scheme, the Kain–Fritsch (Kain and Fritsch 1993) subgrid convective parameterization scheme was also activated to assist in triggering the convection in the large-scale environment (Wyngaard 2004).
Summary of the inner nest’s key numerical and physical parameters for all three benchmark simulations. The variable ΔX is the horizontal grid spacing; NX, NY, and NZ are the number of grid points in the zonal, meridional, and vertical directions, respectively; and dt is the computational time step. MYJ: Mellor–Yamada–Janjic.
Since charge separation (and lightning) is a cloud-scale process, the lightning physics were only activated on the inner 3-km nest of all simulations and all electrical variables on the parent 9-km domain were set to zero. The horizontal grid spacing of the inner nest for all three simulations was set to 3 km to closely match that of current experimental NWP forecast models. While the use of a 1-km horizontal grid spacing would better resolve individual convective updrafts and the small-scale gradients in the charge and microphysics, such finescale simulations and their accompanying sensitivity tests were not conducted because of their relatively prohibitive computational costs with the current two-moment microphysics scheme as discussed in section 4. All three simulations employ the Saunders and Peck (1998) noninductive charging scheme with adjustments for ambient temperatures colder than −32.5°C following Eq. (23) in Mansell et al. (2005), shown here in Eqs. (3)–(5). Note that these temperature adjustments are not based on laboratory observations, but on extrapolations to lower temperatures, which are believed to offer a reasonable best guess for now. In addition to comparing model results with available observations for evaluation, the simulated FOD rates were also compared against the proxy-derived lightning diagnostic schemes of MC.
It is relevant to stress that emphasis will be placed on the simulated lightning and electric fields after establishing that the simulated storms reasonably reproduce the observed storms. As mentioned earlier, the present simulations were primarily designed to evaluate the BLM rather than focusing on details behind factors influencing errors in the forecast evolution of a storm’s circulation intensity, precipitation content, and path. For this reason, the simulations do not make use of any specialized initialization procedures involving radar or lightning observations.
b. 15 April 2012
The simulation domain (shown in Fig. 2a) features one two-way interactive nested grid. The domains have horizontal grid spacings of 9 km (D01) and 3 km (D02), with horizontal dimensions in grid points of (240 × 280) and (301 × 361), respectively (Table 1). With this configuration, the nested grid represents convection-allowing (3 km) scales as used in several experimental NWP models. The stretched vertical grid has 46 levels with finest (coarsest) spacing right above the surface (below model top, set to 50 hPa). The simulation use a computational time step of 45 s (15 s) on the 9-km (3 km) grid. The initial and boundary conditions use the 6-hourly, 40-km NAM reanalysis data for an entire 12-h period starting at 0000 UTC 15 April 2012. The fields on the nested grid (D02) were initialized by interpolating fields from the parent grid (D01) at the time the nested grid was spawned (set at 0200 UTC) with the NAM-derived time-dependent boundary conditions used every 6 h.
Sketch of the WRF-ARW simulation 9-km parent domain (D01) with the 3-km (D02) inner domain for (a) 15 Apr 2012, (b) Hurricane Rita (2005), and (c) 1 Jan 2012. States are indicated by their usual abbreviations and a black star shows the location of the Oklahoma City metro area for reference in (a). The moving inner mesh (D02) for the Hurricane Rita case in (b) is shown at 0600 UTC 20 Sep 2005 when first spawned into the simulation. All times in this and subsequent figures are UTC.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
c. Hurricane Rita (2005)
The initial and boundary conditions for this simulation were derived using the 6-hourly, 1° NCEP aviation (AVN) final analyses (FNL) reanalysis data for a 3.5-day period starting at 0000 UTC 20 September 2005. The latter date is about 1.5 days prior to Hurricane Rita’s rapid intensification cycle (RI; e.g., Knabb et al. 2005; F09; F11).
The domain configuration follows the treatment of F09. The simulation domain is comprised of a two-way interactive vortex-following inner nest (Michalakes et al. 2005). The two domains have horizontal grid spacing of 9 and 3 km, with horizontal dimensions in grid points of (266, 124) and (139, 139), respectively (Table 1 and Fig. 2b). For simplicity, both grids were named in a way consistent with the squall-line case, namely, D01 and D02. The vertical grid consists of 43 levels, with spacing stretching from about 50 m right above the surface to about 500 m at the midlevels and, in contrast to the vertical grid of the continental squall-line case, contracts back to finer spacings above 15 km as in Dougherty and Kimball (2006). Their study found that using finer grid spacings near and a few kilometers below the tropopause resulted in a better representation of the outflow layer of the hurricane, which is a key component for storm intensity (e.g., Emanuel 1986; Camp and Montgomery 2001).
The 3-km (D02) inner nest was introduced 6 h into the simulation, namely at 0600 UTC 20 September, allowing a few hours of spin up for the incipient vortex on the 9-km grid. The simulation was run for a 3-day period (until 0600 UTC 23 September) and, as for the 15 April case, used a computational time step of 45 s (15 s) on the 9-km (3 km) grid.
d. 1 January 2012
The domain configuration, initialization procedure, physics settings, and numerical configurations are identical to the 15 April 2012 case (Table 1). The simulation domains are shown in Fig. 2c. The horizontal dimensions in grid points of the parent domain and inner nest are (400, 200) and (601, 331), respectively. The simulation was run for a 12-h period starting at 0000 UTC 1 January with the inner nest spawned 2 h into the simulation.
5. Results
For both the 15 April and 1 January case, the simulated FOD are compared to available total lightning observations from the Earth Networks Total Lightning Network (ENTLN), which consists of over 150 sensors deployed over CONUS alone (http://weather.weatherbug.com/weatherbug-professional/products/total-lightning-network) able to detect both IC and CG flashes with a national average detection efficiency exceeding 95% for typical CG return strokes and about 50% for typical IC flashes (see Fig. 6 in Fierro et al. 2012). The ENTLN location accuracy varies from tens of meters in dense areas of the network to about 500 m elsewhere. Given that ENTLN typically detects 1–2 points per flash, their data provide a reasonable surrogate for FOD if one makes allowances for its detection efficiency. The simulated radar reflectivity is evaluated against the NSSL’s three-dimensional National Mosaic and Multisensor Quantitative Precipitation Estimation (QPE) or 3D NMQ product (Zhang et al. 2011). For Rita, the simulated lightning will be evaluated against the comparatively very limited lightning observations presented in SB08 and F11.
a. 15 April 2012
The formation of the squall-line MCS in the model was found to lag observations by up to about 1 h (i.e., 0400 UTC in the observations versus 0500 UTC in the model). A likely cause for the delay in upscale development of convection to form the MCS is a delay in the timing of CI owing to the use of relatively coarse initial reanalysis fields (40 km), which tend to underresolve the sharp gradients along mesoscale boundaries such as drylines or cold fronts (e.g., as seen in Fierro et al. 2012), and the time required for mesoscale boundary layer solenoids in the initial model state to generate convergence and shear required to help force CI. It is likely that the assimilation of lightning observations (Fierro et al. 2012) and radar data (e.g., Aksoy et al. 2009) at the 0000 UTC analysis time would have helped improve the representation of the convection and associated outflow boundaries during the first hours of the simulation. Simulated radar reflectivity fields of the squall line, however, show overall good agreement with the 3D NMQ observations, particularly at and after 0600 UTC (Fig. 3). The WRF Model also captures the gradual weakening of the system after 0800 UTC as evidenced by the weakening of the simulated reflectivities (Figs. 3b,d).
The horizontal cross section of the simulated radar reflectivity at z = 4 km AGL (dBZ) at (a) 0600 and (b) 0800 UTC 15 Apr 2012. (c),(d), As in (a),(b), but for 1-km resolution three-dimensional observations from the NSSL NMQ product interpolated onto the local 3-km (D02) domain. A thick black horizontal line and a black arrow in (a) denote the location of the vertical cross sections shown in Fig. 6 (i.e., 36.5°N latitude).
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
Given a reasonable reproduction of the observed storms, the simulated 1-h accumulated FOD spatial pattern shows overall reasonable agreement with the total lightning observations from ENTLN (Fig. 4). In particular, the evolution of the simulated FOD rates exhibits a gradual decrease over Oklahoma and central Kansas, consistent with a weakening squall line (Fig. 3). Similar to the radar reflectivity fields, the simulated FOD also show a slight westward displacement relative to the observations especially at 0800 UTC (Figs. 3, 4) as well as an overall lack of lightning activity in the southern Texas Panhandle compared to the observations at both times (Fig. 4). The largest differences between the BLM lightning fields and the ENTLN observations are seen at 0800 UTC with one distinct FOD maximum in northeast Kansas, which is absent in the simulation (Figs. 4b,d) as evidenced by the simulated reflectivity fields (Figs. 3b,d). Overall, the simulated FOD values are in remarkably good agreement with the ENTLN densities.
As in Fig. 3, but for the simulated flash origin density [FOD per grid cell per hour] with the BLM in (a),(b) and the ENTLN total lightning data interpolated onto the local 3-km domain (D02) in (c),(d). The FODs were summed for 1 h prior to the times shown in the figures.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
Figure 5 shows the FOD from the three diagnostic schemes of MC at the same times as in Fig. 4. The derived FOD values for each of the MC schemes, namely, the maximum FOD per 5-min per grid cell, were multiplied by a factor of 12 to provide an estimate of the upper limit of the maximum FOD per hour per grid cell. The first MC scheme (F1) is proportional to the vertical graupel mass flux at −15°C and the second MC scheme (F2) is proportional to the total ice mass in the column. Scheme F1 is suited for forecasting lightning near and within the updraft cores, while scheme F2 is designed to account for flashes occurring within stratiform regions. The third MC scheme (F3) is a linear combination of F1 and F2 (i.e., 0.95F1 + 0.05F2), to account for both regions. The overall spatial patterns of the lightning from the BLM and the MC schemes are in accord, particularly with scheme F3 (cf. Figs. 4a,b and 5c,d). The difference in locations of areas of maximum lightning activity and areal coverage of the simulated FOD show overall negligible differences between the BLM and all three MC schemes (Fig. 4a vs Figs. 5a–c). Quantitatively, provided that (i) the plotted MC FOD values represent an upper limit for maximum hourly rates; (ii) the constants in the MC diagnostic relationships were not specifically calibrated for two-moment microphysics schemes; and (iii) that their lightning threats were calibrated using the Lightning Mapping Array (LMA; MacGorman et al. 2008) data and not ENTLN, their simulated values are overall in relatively good agreement with the BLM’s and the ENTLN observations (e.g., Fig. 4 vs Fig. 5). Keeping the above in mind and that the IC detection efficiency of ENTLN over Oklahoma is about 75% (see Fig. 6 in Fierro et al. 2012) some quantitative differences ought to be noted, however. For instance, at 0600 UTC in central Oklahoma, the BLM produces (hourly) FOD rates ranging between 25 and 50 in agreement with ENTLN observations (Figs. 4a,c) while the rates of MC scheme F3 often exceed 75 (with local maxima above 100; Fig. 5c). This quantitative difference is further exacerbated during the weakening stage of the squall line: at 0800 UTC, observations show maximum FOD rates rarely exceeding 10 while MC scheme F3 generates rates often exceeding 25 in contrast to the BLM, which FOD rates essentially remain between 10 and 25 in closer agreement with the observations (cf. Figs. 4b,d and 5d).
As in Fig. 4, but for the simulated FODs obtained with the McCaul et al. (2009) schemes converted to an upper limit of maximum FOD per grid cell per hour. Scheme F1 is proportional to the graupel flux at −15°C, scheme F2 to the total ice mass in the column, and F3 is a linear combination of F1 and F2, namely, 0.95F1 + 0.05F2. FODs at 0600 UTC using (a) F1 and (b) F2. (c),(d) As in (a),(b), but for F3 at (c) 0600 and (d) 0800 UTC. To facilitate comparisons of the simulated FOD between the McCaul schemes and the BLM, the legend for colors and shadings use the same scale as in Fig. 4.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
Vertical cross sections of key microphysical and electric variables through a mature convective cell in the MCS provide a more detailed insight on the modeled lightning production process via the BLM (Fig. 6). The updrafts and graupel mixing ratio in this intense leading-line cell exceed 10 m s−1 and 4 g kg−1 (Fig. 6a), respectively, with 30-dBZ echo tops reaching an altitude of 12 km (Fig. 6a). From the Saunders and Peck (1998) charging curve, graupel charges positively within regions of relatively strong updrafts and larger LWC (≥0.5 g m−3) such as at 99.1°W and 5 km AGL (Figs. 6a,c). Conversely, graupel charges negatively in relatively lower LWC at 99.2°W and 7 km AGL (Figs. 6a,c). Inductive charging rates (ICR) in this convective cell are overall one order of magnitude smaller than noninductive charging rates (NICR) and are primarily positive (Fig. 6c). The spatial sign–magnitude distribution of NICR and ICR accounts for the presence of distinctive pockets of strong magnitude (>100 pC m−3) net negative and positive space charge below the −20°C level (Fig. 6d). Other charge pockets such as seen at 99.6°W above 8 km are likely due to advection and/or are leftover charge from a decaying cell in the trailing stratiform region of the MCS (between 99.4° and 99.6°W) as evidenced for example by the weak vertical velocities (<5 m s−1) and small graupel mixing ratios (<1.5 g kg−1) in this region (Fig. 6a). The simulated charge structure in this convective cell is generally complex and comprises several charge layers. The simulated vertical arrangement of net charge cannot be classified as simple dipoles or tripoles (Williams 1989) and, therefore, would be more consistent with the conceptual model of Stolzenburg et al. (1998) for continental MCS. Regions of relatively large Emag exceeding 75 kV m−1 are generally found between opposite-sign space charge centers such as at (99°–98.4°W, z = 8–12 km AGL, Figs. 6b,d) and (99.7°–99.5°W, z = 8–11 km AGL, Figs. 6b,d). Because the cross sections in Fig. 6 are shown after the discharge, smaller Emag values are generally collocated over and around updraft core regions (e.g., 99.4°–99.1°W, z = 5–12 km AGL, Fig. 6b).
Vertical cross sections in the X–Z plane through the convective cell shown in Fig. 3a (0600 UTC) of main simulated electrical and microphysical variables with (a) showing vertical velocities (m s−1, shading), 30-dBZ echo top (thick black contour), 0.5 g m−3 LWC (green contour), and graupel mixing ratio contours in 1 g kg−1 increments with the 0.5 g kg−1 contour also shown (thin black lines). The cloud outline is delineated by the gray shaded contour in both (a),(c); and in (b),(d) by a thick black line that shows reflectivity echoes ≥5 dBZ. The 0°, −10°, and −20°C isotherms are also shown by the thin dashed black lines in (a)–(d). (b) As in (a), but for the simulated electric field magnitude starting at 25 kV m−1 by increment of 25 kV m−1 (gray shading). Note that the due to terrain in northwest Oklahoma (location of this cross section), the lowest height level above sea level is set at z = 0.75 km. (c) Noninductive (color shading) and inductive (thick black line) charging rate (pC m−3 s−1) and (d) total space charge (pC m−3, color shading). Inductive charging rate contour intervals are the same as noninductive charging. Note that the electric field magnitude in (b) and the space charge in (d) are shown after discharge.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
b. Hurricane Rita (2005)
Owing to the model configuration being similar to F09, the simulated storm track (Fig. 7a) and intensity (Fig. 7b) both exhibit overall similar evolution (cf. with Figs. 1a–c in F09). The simulated track, nonetheless, shows a noteworthy difference with F09’s during the last 9 h of simulation with a well-defined southward deviation from the observations by up to 1° of latitude (Fig. 7a). The relatively large track deviations also found during the first 12 h are associated with the initial spinup of the incipient vortex on the finer resolution grid. The simulated intensity as measured by the minimum sea level pressure is in relatively good agreement with the observations during the first 30 h of integration (i.e., until 1200 UTC 21 September; Fig. 7b). Similar to F09, however, the model is unable to capture the rapid deepening of Rita in the subsequent 10 h. Also, the simulated storm reaches its maximum intensity (about 895 hPa) about 24 h later than the observations (Fig. 7b). Despite these noteworthy discrepancies between observations and the simulation, the model successfully reproduces an intense, nearly axisymmetric category-5 storm (Knabb et al. 2005) whose key structural traits are sufficiently realistic for the evaluation of the BLM.
(a) Plot of Hurricane Rita’s track between 0600 UTC 20 Sep and 0600 UTC 23 Sep 2005 on the parent 9-km domain (D01). The best track from the National Hurricane Center (NHC) 3-hourly advisories is shown in black and the simulated track in blue. (b) Time series of the NOAA/NHC 6-hourly best-track (black line) minimum surface pressure (hPa) overlaid with the simulated hourly minimum surface pressure (dashed line, hPa) and the 1-h accumulated lightning discharge events (LDE) scaled by a factor of 1000 for the eyewall (gray bars) and the rainbands (white bars). The eyewall LDE were summed within a subdomain having dimensions of 270 km × 270 km centered at the midpoints of D02. The large dimensions of the subdomain relative to the eyewall size at 1-km AGL were warranted to properly capture the upper portion of the eyewall convection, which tilts outward with height. (c) The corresponding observations (adapted from F11, used with permission). The time axis in (b),(c) is in day–UTC format.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
The simulated lightning exhibits a gradual increase in eyewall hourly LDE throughout its intensification stage between 1200 UTC 21 September and 0000 UTC 23 September (Fig. 7b). A peak in LDE activity occurs during the period of simulated maximum intensity between 1800 UTC 22 September and 0600 UTC 23 September. Although the lightning observations from the Los Alamos Sferics Array (LASA; Shao et al. 2006) do not include the vast majority of intracloud flashes, lightning observations in Rita’s eyewall nevertheless imply that the flash rates also peaked during the period of maximum intensity (Fig. 7c; SB08; F11). Similar to Fierro and Reisner (2011, see their Fig. 4), the simulated maximum eyewall LDE hourly rates overestimate the observed maximum hourly flash counts by about two orders of magnitudes (SB08; F11; Fig. 7c), assuming a typical IC:CG ratio of 3:1 (Boccippio et al. 2001). The likely causes for the overestimate of the LDE rates are stated later in the section.
Overall, the simulation is also consistent with Rita’s observed horizontal precipitation structure between 1800 UTC 21 September and 1800 UTC 22 September, which was characterized by a nearly axisymmetric eyewall and a radially extensive, dense stratiform overcast in the storm’s core region with comparatively little convective activity in the rainbands (Knabb et al. 2005; Figs. 8a,c). The diameter of the simulated eyewall, however, is about 2 times larger than observed (Fig. 8), which was also reported in F09. Fierro and Reisner (2011) suggested that one possible factor for this discrepancy arose from overestimating horizontal diffusion in the model and spurious evaporation at cloud edges (Reisner and Jeffery 2009; particularly between the eye–eyewall interface). The simulation also overestimates the echo tops of reflectivity (Figs. 8b,d) and the maximum reflectivity below the melting level by about 10 dB (F09; Rogers et al. 2007).
(a) Horizontal cross section at z = 1 km AGL and (b) vertical cross section in the X–Z plane of the simulated radar reflectivity (dBZ) at 0200 UTC 22 Sep 2005. The black horizontal line in (a) denotes the location of the eyewall vertical cross section in (b) and the subsequent figures (i.e., at Y = 24.81°N). (c),(d) As in (a),(b), but for in-situ tail Doppler radar data from NOAA/Hurricane Research Division aircraft reconnaissance mission flown on 1915 UTC 21 Sep 2005. Note the difference in horizontal scaling between the observations and the simulations (using 1° ≈ 100 km). Panel (d) adapted from Fig. 1d of Fierro and Reisner (2011). Note that the horizontal scale of this figure in Fierro and Reisner (2011) contains a minor error and should be multiplied by a factor 2 (as done herein). Accounting for this brings their simulated eye size and eyewall slope in excellent agreement with the observations.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
The region outside the eyewall convection is mainly composed of aggregates, snow particles, and cloud ice (not shown, Marks 1985; Marks and Houze 1987; Heymsfield et al. 2006). Consequently, this region of the hurricane often exhibits a distinct minimum in lightning activity (Molinari et al. 1999; Cecil et al. 2002), which is well reproduced in the present simulation by the BLM and the MC schemes (Fig. 9) and remains consistent with the observations (Fig. 10; SB08, see their Fig. 2).
As in Fig. 5, but at 0200 UTC 22 Sep 2005 for (a) the BLM, (b) the MC scheme F1, (c) F2, and (d) F3 = 0.95F1 + 0.05F2.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
(a)–(f) Map of 2-h accumulated IC (red) and CG (blue) lightning flashes for Rita overlain with the NHC best track (black line). The UTC times define the period of analysis of the lightning. Adapted from F11 and used with permission.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
The 1-h accumulated FOD exhibits a distinct maximum in the eyewall with a relatively much weaker secondary maximum in the rainbands similar to observations (cf. Figs. 9 and 10; SB08; F11). Note that because of the outward tilt of the eyewall convection (e.g., Stern and Nolan 2009) and the lightning initiating in the midlevel graupel-rich regions where the Emag are largest (see later in the section), the mean diameter of the eyewall FOD ring (~100 km) is larger than the mean diameter of the simulated reflectivity field at z = 1 km in the eyewall (~80 km, Fig. 8). At 0200 UTC 22 September, the simulated FOD patterns of the BLM exhibit overall good quantitative and qualitative agreement with the three MC lightning schemes, especially F1 and F3, which primarily concentrate on convectively active regions (Fig. 9). In particular, the BLM and the MC schemes capture the asymmetry in the lightning at this time, with a distinct FOD minimum primarily confined in the western semicircle. However, the spatial locations of the relative maxima in lightning activity between the MC schemes and the BLM exhibit noteworthy differences. The MC schemes produce a maximum FOD activity on the right-front quadrant (i.e., northwest) where simulated updraft velocities are largest (not shown), while the BLM FOD maximum is located on the left-front quadrant (southwest), a result more consistent with observations (Corbosiero and Molinari 2003) for a storm track nearly due west (Fig. 7a). Convective updrafts, echo tops, and graupel mixing ratios at 0200 UTC are largest on the western side of the storm (e.g., Figs. 11a,b), which accounts for the larger Emag contours (i.e., >100 kV m−1) and, hence, lightning activity there (Fig. 9).
As in Fig. 6, but for the vertical cross section through the eyewall (Y = 24.81°N) at the location and time shown in Fig. 8a.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
Observations of mixed-phase particle mixing ratios and concentrations in the eyewalls of mature hurricanes are rare. Seminal works from Marks and Houze (1987) and Black and Hallett (1986, 1999) suggested that peak graupel mixing ratios in mature hurricanes are likely not in excess of 2.5 g kg−1. This is a result of the rather small residence times of frozen drop embryos in the strongly azimuthally sheared environment of the eyewall and the lack of supercooled LWC above the melting level due to rapid depletion by advection and scavenging. Furthermore, vertical velocity magnitudes in eyewalls of mature hurricanes were shown to be rather small with about 90% of the magnitudes not exceeding 2 m s−1 (Black et al. 1996). Therefore, it is clear from Fig. 11 and from additional azimuthally averaged diagrams not shown here that the model generally overestimates the updraft speeds, the LWC (>0.5 g m−3) and hence, the graupel mixing ratio (>5 g kg−1) and the simulated echo tops (30 dBZ) in the eyewall of Rita (as seen in Figs. 8b,d). Azimuthally averaged updraft speeds at the time of this analysis (and during the great majority of the simulation after 1200 UTC 21 September) range between 4 and 5 m s−1 (not shown) with local maximum updraft velocities sometime exceeding 10 m s−1 (Fig. 11a). The above limitations were also reported in Fierro and Reisner (2011) and in many other hurricane modeling studies using the WRF-ARW model at similar grid spacings (e.g., Rogers et al. 2007; F09; Davis et al. 2010; Rogers 2010).
The eyewall updrafts offer the necessary and sufficient conditions for the occurrence of in situ NICR (Fig. 11c) due to the simultaneous presence of mixed-phase particles and LWC (Fig. 11a). Positive NICR exceeding 100 pC m−3 s−1 are found in a confined region within the eyewall between 6 and 8.5 km. Negative NICR of similar magnitudes are typically found near the top of and slightly radially outward from the region of maximum positive NICR, namely, between 7.5 and 10 km (Fig. 11c). Secondary regions of weaker NICR are also seen within isolated convective cells embedded within the weak rainbands (not shown). These results are consistent with previous simulations (Fierro et al. 2007; Fierro and Reisner 2011) and the conceptual model based on observations (see Fig. 16 in Black and Hallett 1999). In the present simulation, the maximum magnitude of ICR is about two orders of magnitude weaker than NICR and is mainly negative (Fig. 11c).
The simulated charge structure in the eyewall convection resembles a radially outward-tilted variant of the classic normal tripolar charge arrangement in garden variety airmass thunderstorms (Williams 1989). The normal tripolar charge structure is defined as a main midlevel negative charge region sandwiched in between two main regions of positive charge (e.g., 88.3°W in Fig. 11d), where a “main charge region” herein refers to a volume containing charge density magnitudes exceeding 0.25 nC m−3. Observations also suggested the presence of a normal tripolar gross charge structure in the eyewall of Rita as inferred from the respective locations and dominant polarities of CG flashes and a few intense intracloud discharges (F11). In nature, such charge structures would be conducive for the occurrence of negative CG flashes in the eyewall (Williams 1989; Mansell et al. 2002; Fierro et al. 2006, 2007; Mansell et al. 2010), consistent with observations (SB08; F11).
The origins of the simulated hurricane charge regions (e.g., Fig. 11d) may be explored by examining the charge carried on each of the six predicted hydrometeor species (Fig. 12). A nominal charge density magnitude of 0.1 nC m−3 was selected to also determine the origin of charge outside the eyewall convection region. Positive net space charge on hail and graupel dominate at around 5–7 km inside the eyewall (Figs. 11d and 12a). The large volume of positive charge at 9–14 km is carried primarily by snow particles and ice crystals (Fig. 12a). While there also exist regions characterized by negative charge on graupel above 9 km, the upper negative graupel charge magnitudes are comparatively much smaller than that of snow and ice crystals combined (not shown). Most of the positive charge (Fig. 12) in the eyewall is carried by hail and graupel below the melting level near 5 km (Fig. 12), with rain carrying comparable negative charge radially outward away from the lowest positive charge areas (i.e., 86.8°W in Fig. 12b). The main negative charge region in the 6–8-km layer is mainly attributed to ice crystals and snow inside the eyewall and to graupel outside the eyewall (Figs. 11d and 12b).
As in Fig. 11, but for the ±100 pC m−3 space charge density contours for graupel (black), snow (blue), rain (red), cloud ice (orange), cloud water (green), and hail (purple). Positive (negative) charge density contours are denoted by a solid (dashed) line, respectively.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
c. 1 January 2012
The evolution of the areal coverage and placement of the winter storm is captured reasonably well by the model between 0200 and 1200 UTC (Fig. 13). There are, however, noteworthy differences to underline: first, the simulated reflectivity fields are about 5–10 dB larger than observed; second, the model develops cellular convection in northern Missouri at 0300 UTC, which was absent in the observations (Figs. 13a,c); and, third, the tail end of the simulated snowband at 0800 UTC extends farther south than observed (Figs. 13b,d). Last the snowband in the simulation is more prominent northeast of Lake Superior at 0800 UTC (Figs. 13b,d).
Radar reflectivity (z = 4 km) on the local 3-km grid (D02) as in Fig. 3, but for the 1 Jan 2012 winter storm case at (left) 0300 and (right) 0800 UTC. (c),(d) As in (a),(b), but for the interpolated NMQ observations. As in Figs. 3a, the thick black line in (b) highlights the location of the vertical cross section in Fig. 15.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
Owing to a reasonable reproduction of the observed reflectivity fields, both the BLM and the ENTLN observations show no lightning (Figs. 14a,b) during the time period considered herein (i.e., 0200–1200 UTC). Although small, the MC schemes, on the other hand, show nonzero FOD values on the order of 1 (grid cell)−1 h−1 (Figs. 14c,d shown for scheme F3). This is because the MC scheme designed for stratiform regions, namely F2 (and hence, F3), assumes the presence of lightning whenever ice and mixed-phase particles are simulated. In contrast, the BLM requires the simultaneous presence of mixed-phase particle and supercooled (LWC) water, both of which are small in the simulated winter band convection. The small amount of mixed phase particles and rain (Fig. 15b), accounts for the simulated weak reflectivities (Figs. 13 and 15a) and echo tops rarely exceeding 6 km with the exception of a deeper convective cell on the southern warmer (above freezing) tip of the band as seen at latitude 43°N (Fig. 15a). This cell is characterized by vertical velocities on the order of 1–2 m s−1 (Fig. 15b), graupel mixing ratios on the order of 0.01 g kg−1, and isolated pockets of LWC reaching 0.2 g m−3 (Fig. 15b).
(a),(b) BLM and ENTLN observations and (c),(d) as in Figs. 5c,d for the 1 Jan 2012 winter storm case at (left) 0300 and (right) 0800 UTC.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
(a) As in Fig. 8b, (b) as in Fig. 6a, (c) as in Fig. 6b, and (d) as in Fig. 6d, but for the 1 Jan 2012 winter storm case at 0800 UTC. Note the reduced order of magnitude of the scaling units used for the electrical variables compared to all previous corresponding figures.
Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-12-00278.1
Despite the lack of simulated lightning, the snow clouds exhibit some degree of electrification with weak Emag rarely reaching 50 V m−1. For instance, in the cross section shown in Fig. 15, the simulated Emag ranges between 10 and 20 V m−1 (Fig. 15c), which are associated with small space charge values ranging between 0.25–0.5 pC m−3 (Fig. 15d). Those space charge (electric field) values are about three (four) orders of magnitudes smaller than those simulated in the continental MCS and Hurricane Rita (cf. Figs. 15c,d and 6b,d).
6. Summary
A computationally inexpensive electrification model with explicit charging and discharge physics has been implemented within the WRF-ARW numerical prediction model. In situ charging of hydrometeors was parameterized following laboratory work, which demonstrated the effectiveness of noninductive charging in generating Emag comparable to those reported within thunderstorms in nature. The amount and polarity of charge separated during individual collisions between mixed-phased particles (graupel or hail) and ice crystals (cloud ice and snow) are functions of the ambient temperature and the growth rate of the graupel or hail particles (e.g., Brooks et al. 1997; Saunders and Peck 1998; Saunders 2008; Emersic and Saunders 2010). Once the electric field generated by the noninductive charging process becomes large enough (typically >1 kV m−1), polarization charging of cloud water was also allowed to occur following the parameterization of Ziegler et al. (1991). Advection of charge was treated identically to all other moisture scalars. The electric field potential (and three components of the ambient electric field) was solved explicitly via a computationally efficient multigrid or BoxMG elliptic iterative solver (Dendy 1987; Dendy and Moulton 2010). The discharge model is adapted from Ziegler and MacGorman (1994), whereby lightning-deposited charge is made proportional to the total hydrometeor surface area and the domain-integrated positive and negative charges. Simulated discharges occur within cylinders of constant prescribed radii centered at grid points characterized by Emag exceeding a fixed critical breakdown threshold.
The efficiency and performance of the BLM was tested through convective-allowing (dx = 3 km) model simulations of three contrasting cases: a continental squall-line case, a strong tropical cyclone, and a continental winter storm. Overall, the simulated spatial flash pattern for all three cases exhibited reasonable agreement with observations. Owing to imperfect forecast of the placement and strength of the convection, the locations of the simulated FOD maxima that are associated with deep convective cloud entities did not exactly match those from the observations. Although weather forecasts are improving, shortcomings in our ability to forecast the deep convection itself are a major obstacle to reliable forecasts of lightning. For the tropical cyclone, the simulated gross charge structure, namely, an outwardly tilted normal tripole, was in accord with the very limited observations. The deeper convective cells composing the continental MCS, however, exhibited complex vertical charge structures that could not be classified as simple dipoles or tripoles. This result is consistent with a conceptual model derived from observations within deep continental storms, which often indicated the existence of various charge structures within a single storm, some of which are composed of more than five charge layers with varying degrees of horizontal slant (Stolzenburg et al. 1998). The simulated FOD from the BLM were also evaluated against those obtained from the recently developed diagnostic lightning algorithm of McCaul et al. It was found that for all three case studies analyzed herein, the simulated FOD showed overall good qualitative agreement between the BLM and the MC schemes owing to the strong relationship between lightning and mixed-phase particles. Quantitatively, the MC schemes produced FOD values in reasonable agreement with the observations, with the exception of the winter storm case.
The present WRF lightning model could be easily ported to other versions of WRF or to the Hurricane-WRF model (HWRF), because the solver and the discharge code each consist of a single external FORTRAN module. The noninductive and inductive charging parameterizations, however, are currently coupled with the NSSL two-moment microphysics code and, therefore, cannot be currently used with the other microphysics schemes. If initial comparisons with simpler lightning forecast schemes demonstrate that our new scheme provides improved lightning forecasts in enough situations to be worth its extra computational cost, the technical task of extending the BLM to other versions of WRF will be addressed in subsequent work.
Steadily increasing computer power will eventually facilitate the application of the BLM in operational forecasts. In advance of the launch of GOES-R, the simulated lightning fields from both the BLM and McCaul scheme could be readily incorporated into a statistical ensemble Kalman filter (EnKF) package through an operator linking flash rate density and given microphysical–kinematic variables to assist in improving the spatial location of the simulated storms and, concurrently, to limit the presence of spurious convection.
Currently, the MacGorman et al. (2001) discharge scheme has been implemented and is being tested as an alternate lightning parameterization that does consider individual discharge event one at a time (during a computational time step) rather than computing the bulk effect of all discharge events throughout the entire domain instantaneously. It could be used in the future to estimate flash type if it can be suitably adapted to produce CG flashes. Such improvements would also better represent lightning propagation within anvils and better constrain the height distribution of lightning effects. More refined estimates than provided by MacGorman et al. (2001) would require, however, treatment of detailed channel propagation, which are currently computationally prohibitive for national weather predictions.
Acknowledgments
Funding was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA-University of Oklahoma Cooperative Agreement NA11OAR4320072, U.S. Department of Commerce. This work was also supported by the NESDIS program, which is under the auspices of the National Oceanic and Atmospheric Administration of the U.S. Department of Commerce under Grant NOAA-NESDIS-OAR-NA08OAR4320904. Computer resources were provided by the Oklahoma Supercomputing Center for Education and Research (OSCER) hosted at the University of Oklahoma. The authors thank Scott Dembek for providing the 40-km NAM data and Ami Arthur for providing the NSSL three-dimensional NMQ radar mosaic data. Thanks also go out to Bill Callahan, Benny Chukrun, Stan Heckman, and Jim Anderson from Earth Networks for providing the total lightning data for two of the case studies. The authors would also like to thank Dr. Eugene McCaul and two anonymous reviewers for providing helpful suggestions on an earlier version of the manuscript.
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