The Implementation of an Explicit Charging and Discharge Lightning Schemewithin the WRF-ARW Model: Benchmark Simulations of a Continental

Squall Line, a Tropical Cyclone, and a Winter Storm

ALEXANDRE O. FIERRO

Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National

Severe Storms Laboratory, Norman, Oklahoma

EDWARD R. MANSELL, DONALD R. MACGORMAN, AND CONRAD L. ZIEGLER

NOAA/National Severe Storms Laboratory, Norman, Oklahoma

(Manuscript received 24 September 2012, in final form 30 January 2013)

ABSTRACT

This work describes the recent implementation of explicit lightning physics within the Weather Research

and Forecasting (WRF) Model. Charging of hydrometeors consists of five distinct noninductive parameter-

izations, polarization of cloud water, and the exchange of charge during collisional mass transfer. The three

components of the ambient electric field are explicitly solved for via the computationally efficient multigrid

elliptic solver. The discharge process employs concepts adapted from two well-documented bulk lightning

models, whereby charge reduction is imposed within a prescribed volume centered at grid points charac-

terized by electric field magnitudes exceeding a given breakdown threshold.

This lightning model was evaluated through benchmark convection-allowing (3 km) model simulations of

three contrasting convective systems: a continental squall line, a major hurricane (Rita 2005), and a winter

storm. The areal coverage and magnitude of the simulated hourly flash origin density (FOD) for the conti-

nental squall line are qualitatively comparable to that of the total lightning data observations from Earth

Networks Total Lightning Network (ENTLN). In agreement with the ENTLN observations, no FOD are

simulated for the winter storm case. The simulated spatial FODpattern of the hurricane and the eyewall gross

charge structure were both in reasonable agreement with observations. The simulated FOD for all three cases

were also evaluated against those obtained with the recently developed McCaul diagnostic lightning prediction

schemes and exhibited overall good qualitative agreement with each other for Rita and the continental squall line.

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. dol-

lars) worldwide (Curran et al. 2000; Ashley and Gilson

2009). The occurrence of cloud-to-ground (CG) light-

ning flashes is especially problematic in semiarid regions

where they can occasionally spark forest fires and, con-

currently, result in significant damage. Owing to its high

economic impact, in the last two decades heightened

emphasis has been directed toward improving the com-

munity’s ability to forecast lightning using numerical

weather prediction (NWP) models. Two separate ap-

proaches presently exist for predicting lightning in cloud-

scale (i.e., ,5km) 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 so-

phisticated 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

Corresponding author address: Alexandre O. Fierro, CIMMS,

National Weather Center, Suite 2100, 120 David L. Boren Blvd.,

Norman, OK 73072.

E-mail: alex.fierro@noaa.gov

2390 MONTHLY WEATHER REV IEW VOLUME 141

DOI: 10.1175/MWR-D-12-00278.1

� 2013 American Meteorological Society

producing bulk flashes and those explicitly resolving in-

dividual lightning channels. The chief advantage and at-

tractiveness of bulk lightning schemes is their relative

simplicity and low computational cost.

The presentWeather 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 re-

duced upon discharge throughout the entire domain.

Takahashi (1987) improved the Rawlins approach by

allowing reduction of charge densities only within re-

gions containing the highest magnitude of charge, which

would be consistent in nature with regions of the largest

electric field magnitudes (Emag). Ziegler andMacGorman

(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 sim-

plified 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 expen-

sive for NWPuse, though the hybrid scheme fromBarthe

et al. (2012) adds a kind of channel branching to the

MacGorman et al. (2001) approach.

Asmentioned 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 computa-

tionally inexpensive. Bright et al. (2004) utilized mixed-

layer convective available potential energy (CAPE) as a

proxy for vertical velocity and, ultimately, for the proba-

bility 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 con-

ditions (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 the2158C isotherm (similar to

Petersen et al. 1999). They further devised a second

proxy that accounts for lightning occurrence in strati-

form 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 algorithmwhereby 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 in-

expensive, lightning model within a state-of-the-art

NWP forecast model. The rationale for developing this

modeling capability arises from a need to develop en-

hanced operational lightning data assimilation tools (e.g.,

Fierro et al. 2012) prior to the upcoming first launch of the

Geostationary Operational Environmental Satellite R se-

ries (GOES-R) in 2015, which will be equipped with the

Geostationary Lightning Mapper (GLM; Goodman et al.

2013) instrument capable ofmapping total lightning (CG1intracloud) day andnight, year-roundwith a nearly uniform

resolution over theAmericas ranging between 8 and 12km

(Gurka et al. 2006).

2. Description of the lightning model

The model used in this study is the three-dimensional

compressible nonhydrostatic WRFModel (version 3.3.1)

with Advanced Research WRF (ARW) dynamic solver

(WRF-ARW; Skamarock and Klemp 2007). In the fol-

lowing discussion of new physicsmodules added toWRF-

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

A series of classic laboratory studies using complex

cloud chamber apparatus have suggested that collisions

between riming graupel pellets and ice crystals are the

primary in situ charging mechanism within thunderstorms

(e.g., Takahashi 1978; Saunders et al. 2001; Brooks et al.

1997; Saunders and Peck 1998; Takahashi andMiyawaki

2002; Mitzeva et al. 2006; Saunders et al. 2006; Saunders

2008; Emersic and Saunders 2010). In the last;15 years,

some of these studies have provided increasing evidence

in support of the relative diffusional growth rate hy-

pothesis to account for the microphysics of charging

(e.g., Emersic and Saunders 2010). Assuming a typical

population of mixed-phase particles within a convective

cloud in nature, the integrated effect of themagnitude of

charge separated per collision via this process was able

to generate electric fields comparable in magnitude with

JULY 2013 F I ERRO ET AL . 2391

observations, which was confirmed in cloud-scale simu-

lations of thunderstorms (e.g., Takahashi 1984; Helsdon

et al. 2001; Mansell et al. 2005; Fierro et al. 2006, 2008).

Noninductive charge separation resulting from the re-

bounding collision between graupel–hail and snow–

cloud ice are all parameterized in theWRFModel’s new

BLM module following Eq. (7) of Mansell et al. (2005):

›rxy

›t5bdqxy(12Exy)E

21xy (nxacy) , (1)

where rxy is the space charge (Cm23) separated during

a collision between hydrometeor species x and y, dqxyis the weighted average separated charge (C) per re-

bounding collision between hydrometeor species x and

y, ß is an arbitrary factor limiting charging at low tem-

peratures (owing to lack of experimental data), nxacy is

the number concentration collection rate integral, and

Exy is the collection efficiency.

In this parameterization, the magnitude of charge

separated within a grid cell (dq) is calculated from a poly-

nomial fit of the noninductive critical charging curve as

a function of temperature and graupel–hail riming accre-

tion rate, given by Eq. (18) of Mansell et al. (2005):

dq5BDaI (Vg2VI)

bq(RAR), (2)

whereB, a, and b are a function of crystal size (Table 1 in

Mansell et al. 2005);DI is the mean volume diameter of

the ice crystal–snow, Vg and VI are the mass-weighted

mean terminal fall speeds for graupel and cloud ice (or

snow), respectively; and q(RAR) is the charge separa-

tion as a function of the riming accretion rate (RAR)

from Brooks et al. (1997) modified by Mansell et al.

(2005). The critical RAR curve, which defines the RAR

at which the sign of charge acquired by graupel changes,

is based on the laboratory work of Saunders and Peck

(1998). The polynomial fit of this critical RAR curve as

a function of the temperature T in degree Celsius is

given by Eqs. (21)–(23) in Mansell et al. (2005):

RARcrit 5

8><>:

s(T) : T $ 223:78C

k(T) : 223:78 .T . 240:08C

0 : T # 240:08C

, (3)

where

s(T)5 1:01 7:92623 1022T14:48473 1022T2

1 7:47543 1023T31 5:46863 1024T4

1 1:67373 1025T51 1:76133 1027T6 (4)

and

k(T)5 3:4

�1:02

� jT1 23:7j223:71 40:0

�3�. (5)

Inductive or polarization charging, which arises from the

collision between ice particles and cloud water in the

presence of an electric field is also included in the WRF

Model following Ziegler et al. (1991). The inductive

charging rate primarily depends on the average cosine

of the graupel-droplet impact angle, the rebound prob-

ability, and the vertical component of the electric field.

Because of the low conductivity of ice and compara-

tively short contact time during collision, inductive

charge separation during ice–ice collision was assumed

negligible (e.g., Gaskell 1981). Therefore, only collisions

between cloud water (subscript c) and ice–graupel–hail

(subscript g) are considered following Eq. (27) of

Mansell et al. (2005):

›rg

›t5

p3

8

"6:0Vg

G(4:5)

#EgcErnt,cn0,gD

2c

3

"pG(3:5)«hcosuiEzD

2n,g2

G(1:5)rg3nt,g

#, (6)

where rg is the charge density carried by graupel; Dc is

the cloud droplet diameter;Egc is the collision efficiency

between graupel and cloud water; Er is the rebound

probability; nt,c and nt,g are the total cloud water and

graupel number densities, respectively; Vg is the mass-

weighted mean fall speed of graupel; G(x) is the com-

plete gamma function; Dn,g is the characteristic diameter

of graupel; n0,g is the number concentration intercept for

graupel; hcosui is the average cosine of the angle of re-

bounding collision; Ez is the vertical component of the

electric field; and « is the electrical permittivity of air.

Brooks and Saunders (1994) suggested that polarization

charging within thunderstorms could be effective in re-

gions with strong electric fields.

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 con-

servation 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 hydro-

meteor species y. Charges carried on precipitation parti-

cles are allowed to pass through the lower boundary by

2392 MONTHLY WEATHER REV IEW VOLUME 141

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 fol-

lowing 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 t2 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 hori-

zontal uses the fifth-order weighted essentially non-

oscillatory (WENO) scheme (Jiang and Shu 1996), with

a positive-definite limiter added for moisture scalars.

Sedimentation for particle mixing ratio, number con-

centration, and charge employ a first-order upwind

scheme.

b. Electric field and electrical potential solver

In this current implementation, the ambient electric

field does not feed back onto the microphysics (e.g.,

enhanced coalescence of oppositely charged cloud drop-

lets). The electric field is obtained by solving the Poisson

equation for the electric potential f (e.g., MacGorman

and Rust 1998):

=2f52rtot«

, (7)

where rtot is the net space charge and, again, « the electric

permittivity of air (8.85923 10212 Fm21). Equation (7) is

solved via a message-passing-interface (MPI) black box

multigrid iterative solver or BoxMG algorithm (Dendy

1987) extended to three-dimensional nonsymmetric

convection-diffusion problems (Dendy and Moulton

2010). The three components of the electric field and its

magnitude are then computed from the negative po-

tential gradient:

E52$f . (8)

The BoxMG algorithm inputs a user-defined matrix on

the fine WRF-ARW grid and constructs coarser grids

and their associated coefficient matrices for the multi-

grid algorithm before returning the solution vector back

onto the fine grid. The method utilizes a Galerkin

coarse-grid approximation with a grid transfer operator

that preserves the fluxes at the interfaces of each grid cell

(e.g., Alcouffe et al. 1981). A Gauss–Seidel relaxation

method is used as a smoother to provide improved ap-

proximation of the solution after each iteration of the

BoxMG algorithm on the coarse grid. The BoxMG al-

gorithm is a robust, computationally efficient solver for

Poisson equations on logically structured grids (Dendy

and Moulton 2010) and typically converges after two to

three iterations.

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 con-

dition (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, high-

lighting 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 parameteri-

zations (e.g., Mansell et al. 2002) are currently imprac-

tical 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 computa-

tionally 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) andMacGorman 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 kVm21, consistent with the break-even field mag-

nitude 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 5 6 km for all

simulations). The simulated lightning trends on the

3-km grids employed for this study remained qualita-

tively 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 sim-

plistic discharge parameterization, it is not possible to

distinguish between flash type or flash polarity.

To determine the charge involved in discharges during

a time step, a two-dimensional (2D) array B(x, y) is set

JULY 2013 F I ERRO ET AL . 2393

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 nCm23 herein) anywhere

within the column and is set to 0 at all other 2Dgrid points

in the model domain (Fig. 1). Considering exclusively all

grid points within the cylinders satisfying B(x, y)5 1, the

discharge model then computes the sum of the space

charge within this discharge volume for all grid cells with

positive charge (S1) and, similarly, the summed magni-

tude for all cells with negative space charge magnitude

(S2). 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 S1 and S2unless that product (e.g., 0.3S1) already exceeds the

summed magnitude of opposite polarity (S2). In that

exceptional case, Qd is simply set to the lesser of S1 and

S2. Then the fraction of positive charge to be superposed

on each grid cell is given by F1 5 Qd/S1 and, similarly,

the fraction of negative charge by F2 5 Qd/S2.

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 F1 or F2 (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 hydrome-

teor 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 dis-

tribution 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 dis-

charge 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 every-

where 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 mag-

nitude larger. Owing to the simplicity of this discharge

parameterization, however, the BLM is primarily in-

tended to provide an indication of the direction of

lightning trends, and not to accurately mimic flash

rates within a given storm. Note that this parameteri-

zation differs from the Ziegler and MacGorman

(1994) scheme, in which the discharge process involves

FIG. 1. Sketch illustrating how the lightning scheme selects the grid points participating in an idealized discharge and, subsequently, how

the net total charge density r 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 fieldmagnitude (E) exceeds the breakdown threshold (Ecrit). The gray dots in step 2

show the grid points participating in the discharge (i.e., where r 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 nCm23) are shown in the

red (blue) ovals. The red (blue) ovals in step 3 show examples of space charge areas.0.1 nCm23 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).

2394 MONTHLY WEATHER REV IEW VOLUME 141

all points having excess charge throughout the entire

model domain during each iteration.

Toestablish ameaningful comparisonwith theMcCaul’s

scheme output and, therefore, to provide a lightningmetric

more accessible to forecasters who might wish to use the

BLM output, the following operation was devised to

compute an estimate of flash origin density (FOD) rate

(over a time period T 5 t2 2 t1) per grid cell:

FOD(i, j,T)5G

C

ðt2

t1

B(i, j, t) dt , (9)

where G is the grid cell area [km2 (grid cell)21], C the

cylinder cross sectional area (km2) and the integral on

the right hand side (units of per time interval T) repre-

senting the sum of all discharge (flash) locations counts

for all the time steps within the time intervalT. Following

Eq. (9), the units of FODare in flash per grid cell per time

interval. To provide a rough estimate of lightning flash

activity, we also define lightning discharge events (LDE)

within a subdomain A during the same interval T as fol-

lows:

LDE(A,T)5 �(i,j)2A

FOD(i, j,T) . (10)

From Eq. (10), the units of LDE are in flash per time

interval (over the subdomain A).

3. Brief description of the case studies

To provide a reasonable evaluation of the BLM, the

simulated lightning fields were assessed for three con-

vective systems differing drastically in their internal

dynamics and thermodynamic environments: a conti-

nental squall line, a strong tropic cyclone, and a conti-

nental 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 con-

ducted with the National Severe Storms Laboratory

(NSSL) 4-km WRF-ARW test bed over the contiguous

United States (CONUS).

On 15April 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 sub-

sequent 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 gen-

erate 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 cap-

ture 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 in-

tensification cycle, which was centered near 1200 UTC

21 September 2005, the storm experienced several light-

ning bursts in its eyewall, some of which were docu-

mented by several studies (Shao et al. 2005; Squires and

Businger 2008, hereafter SB08; Fierro et al. 2011, here-

after F11).

Themotivation for selecting Hurricane Rita (2005) is

twofold: (i) as stated above, observations of the dy-

namical 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 continu-

ously 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.

JULY 2013 F I ERRO ET AL . 2395

4. Benchmark simulations setup

a. Physics configuration of the simulations

Abrief summary of the physics andmodel 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 inWRF. 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 pro-

cesses (Chen et al. 1997). Boundary conditions for tur-

bulent 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 pa-

rameterized 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).

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 elec-

trical 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 re-

solve 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 pro-

hibitive 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 than232.58C 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 extrapo-

lations 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 com-

pared 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 estab-

lishing 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 (2403 280)

and (301 3 361), respectively (Table 1). With this con-

figuration, 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 compu-

tational time step of 45 s (15 s) on the 9-km (3 km) grid.

TABLE 1. Summary of the inner nest’s key numerical and physical parameters for all three benchmark simulations. The variable DX 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.

Parameter/case 15 Apr 2012 Hurricane Rita (2005) 1 Jan 2012

DX (m) 3000 3000 3000

NZ 46 43 40

NX 3 NY 301 3 361 139 3 139 601 3 331

dt (s) 15 15 15

Boundary layer scheme MYJ MYJ MYJ

Radiation scheme Goddard Goddard Goddard

Microphysics scheme NSSL two-moment NSSL two-moment NSSL two-moment

Land surface model Noah Noah Noah

Initial–boundary conditions 40-km NCEP NAM 18 NCEP AVN/FNL 40-km NCEP NAM

2396 MONTHLY WEATHER REV IEW VOLUME 141

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.

c. Hurricane Rita (2005)

The initial and boundary conditions for this simulation

were derived using the 6-hourly, 18NCEP 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 in-

tensification 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 50m right above the

surface to about 500m 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

FIG. 2. 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.

JULY 2013 F I ERRO ET AL . 2397

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 0600UTC 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 iden-

tical 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 0000UTC 1 January

with the inner nest spawned 2 h into the simulation.

5. Results

For both the 15 April and 1 January case, the simu-

lated 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 500m elsewhere. Given

that ENTLN typically detects 1–2 points per flash, their

data provide a reasonable surrogate for FOD if onemakes

allowances for its detection efficiency. The simulated

radar reflectivity is evaluated against the NSSL’s three-

dimensional National Mosaic and Multisensor Quantita-

tive 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 de-

velopment of convection to form theMCS is a delay in the

timing of CI owing to the use of relatively coarse initial

reanalysis fields (40km), 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 con-

vergence 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. Sim-

ulated radar reflectivity fields of the squall line, however,

show overall good agreement with the 3D NMQ obser-

vations, 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).

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.

Figure 5 shows the FOD from the three diagnostic

schemes ofMC 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 themaximumFODper hour per grid cell. The firstMC

scheme (F1) is proportional to the vertical graupel mass

flux at 2158C and the second MC scheme (F2) is pro-

portional 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 1 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

2398 MONTHLY WEATHER REV IEW VOLUME 141

locations of areas ofmaximum 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-momentmicrophysics 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 rela-

tively 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 con-

trast to the BLM, which FOD rates essentially remain

FIG. 3. The horizontal cross section of the simulated radar reflectivity at z 5 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 theNSSLNMQproduct 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., 36.58N latitude).

JULY 2013 F I ERRO ET AL . 2399

between 10 and 25 in closer agreement with the ob-

servations (cf. Figs. 4b,d and 5d).

Vertical cross sections of key microphysical and

electric variables through amature 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 10ms21 and 4gkg21 (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 rel-

atively strong updrafts and larger LWC ($0.5 gm23)

such as at 99.18W and 5 km AGL (Figs. 6a,c). Con-

versely, graupel charges negatively in relatively lower

LWC at 99.28W and 7km 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 pCm23) net negative and

positive space charge below the 2208C level (Fig. 6d).

Other charge pockets such as seen at 99.68W above

8 km are likely due to advection and/or are leftover

charge from a decaying cell in the trailing stratiform re-

gion of the MCS (between 99.48 and 99.68W) as evidenced

for example by the weak vertical velocities (,5ms21)

and small graupel mixing ratios (,1.5 g kg21) in this

FIG. 4. As in Fig. 3, but for the simulated flash origin density [FODper 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.

2400 MONTHLY WEATHER REV IEW VOLUME 141

region (Fig. 6a). The simulated charge structure in this

convective cell is generally complex and comprises

several charge layers. The simulated vertical arrange-

ment of net charge cannot be classified as simple di-

poles or tripoles (Williams 1989) and, therefore, would

be more consistent with the conceptual model of

Stolzenburg et al. (1998) for continentalMCS. Regions of

relatively large Emag exceeding 75kVm21 are generally

found between opposite-sign space charge centers such

as at (998–98.48W, z 5 8–12 km AGL, Figs. 6b,d) and

(99.78–99.58W, z 5 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., 99.48–99.18W, z5 5–

12 km AGL, Fig. 6b).

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 de-

viation from the observations by up to 18 of latitude

(Fig. 7a). The relatively large track deviations also found

during the first 12 h are associated with the initial spinup

FIG. 5. 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 at2158C, scheme F2 to the total ice mass in the column, and F3 is a linear combination of F1

and F2, namely, 0.95F11 0.05F2. FODs at 0600UTC 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.

JULY 2013 F I ERRO ET AL . 2401

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 deep-

ening of Rita in the subsequent 10 h. Also, the simulated

storm reaches its maximum intensity (about 895hPa)

about 24h later than the observations (Fig. 7b). Despite

these noteworthy discrepancies between observations

FIG. 6. Vertical cross sections in theX–Z plane through the convective cell shown in Fig. 3a (0600UTC) ofmain simulated electrical and

microphysical variables with (a) showing vertical velocities (m s21, shading), 30-dBZ echo top (thick black contour), 0.5 gm23 LWC (green

contour), and graupelmixing ratio contours in 1 gkg21 incrementswith the 0.5 g kg21 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

08, 2108, and 2208C 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 kVm21 by increment of 25kVm21 (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 z5 0.75km. (c) Noninductive (color shading) and inductive (thick black

line) charging rate (pCm23 s21) and (d) total space charge (pCm23, 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.

2402 MONTHLY WEATHER REV IEW VOLUME 141

FIG. 7. (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 accumu-

lated 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 di-

mensions of 270 km 3 270 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 outwardwith height. (c) The corresponding

observations (adapted from F11, used with permission). The time axis in (b),(c) is in day–UTC

format.

JULY 2013 F I ERRO ET AL . 2403

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.

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 be-

tween 1800 UTC 22 September and 0600 UTC 23 Sep-

tember. 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

FIG. 8. (a) Horizontal cross section at z5 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., atY5 24.818N). (c),(d) As in (a),(b), but for in-situ tail Doppler radar data fromNOAA/Hurricane Research

Division aircraft reconnaissance mission flown on 1915 UTC 21 Sep 2005. Note the difference in horizontal scaling between the obser-

vations and the simulations (using 18 ’ 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 bemultiplied by a factor 2 (as done herein). Accounting

for this brings their simulated eye size and eyewall slope in excellent agreement with the observations.

2404 MONTHLY WEATHER REV IEW VOLUME 141

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 eye-

wall 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, how-

ever, is about 2 times larger than observed (Fig. 8), which

was also reported in F09. Fierro and Reisner (2011) sug-

gested 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 re-

flectivity (Figs. 8b,d) and the maximum reflectivity below

themelting level by about 10 dB (F09;Rogers et al. 2007).

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 re-

produced 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).

The 1-h accumulated FOD exhibits a distinct maxi-

mum in the eyewall with a relatively much weaker sec-

ondarymaximum 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

FIG. 9. 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 5 0.95F1 1 0.05F2.

JULY 2013 F I ERRO ET AL . 2405

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 5 1km in the eyewall

(;80km, Fig. 8). At 0200 UTC 22 September, the sim-

ulated FOD patterns of the BLM exhibit overall good

quantitative and qualitative agreement with the three

MC lightning schemes, especially F1 and F3, which pri-

marily 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 semi-

circle. 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., .100kVm21) and, hence,

lightning activity there (Fig. 9).

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 kg21. 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. Further-

more, vertical velocity magnitudes in eyewalls of mature

FIG. 10. (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.

2406 MONTHLY WEATHER REV IEW VOLUME 141

hurricanes were shown to be rather small with about

90% of the magnitudes not exceeding 2m s21 (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 gm23) and hence, the graupel

mixing ratio (.5 g kg21) 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 s21 (not shown) with local maximum updraft ve-

locities sometime exceeding 10ms21 (Fig. 11a). The

above limitations were also reported in Fierro and Re-

isner (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 par-

ticles and LWC (Fig. 11a). Positive NICR exceeding

FIG. 11. As in Fig. 6, but for the vertical cross section through the eyewall (Y 5 24.818N) at the location and time shown in Fig. 8a.

JULY 2013 F I ERRO ET AL . 2407

100 pCm23 s21 are found in a confined region within the

eyewall between 6 and 8.5 km. Negative NICR of sim-

ilar magnitudes are typically found near the top of and

slightly radially outward from the region of maximum

positiveNICR, namely, between 7.5 and 10km (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 ob-

servations (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 con-

vection 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., 88.38W in

Fig. 11d), where a ‘‘main charge region’’ herein refers

to a volume containing charge density magnitudes ex-

ceeding 0.25 nCm23. Observations also suggested the

presence of a normal tripolar gross charge structure in

the eyewall of Rita as inferred from the respective lo-

cations 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

0.1nCm23 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

5–7km inside the eyewall (Figs. 11d and 12a). The large

volume of positive charge at 9–14km is carried primarily

by snow particles and ice crystals (Fig. 12a). While there

also exist regions characterized by negative charge on

graupel above 9km, 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 5km (Fig. 12),

with rain carrying comparable negative charge radially

outward away from the lowest positive charge areas (i.e.,

86.88W 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).

c. 1 January 2012

The evolution of the areal coverage and placement of

the winter storm is captured reasonably well by the

FIG. 12. As in Fig. 11, but for the6100pCm23 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.

2408 MONTHLY WEATHER REV IEW VOLUME 141

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, themodel 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).

Owing to a reasonable reproduction of the observed

reflectivity fields, both the BLM and the ENTLN ob-

servations show no lightning (Figs. 14a,b) during the

time period considered herein (i.e., 0200–1200 UTC).

Although small, theMC schemes, on the other hand, show

nonzero FOD values on the order of 1 (grid cell)21 h21

(Figs. 14c,d shown for schemeF3). This is because theMC

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 ofmixed 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 lati-

tude 438N (Fig. 15a). This cell is characterized by vertical

velocities on the order of 1–2ms21 (Fig. 15b), graupel

mixing ratios on the order of 0.01 gkg21, and isolated

pockets of LWC reaching 0.2 gm23 (Fig. 15b).

Despite the lack of simulated lightning, the snow

clouds exhibit some degree of electrification with weak

Emag rarely reaching 50Vm21. For instance, in the cross

section shown inFig. 15, the simulatedEmag ranges between

10 and 20Vm21 (Fig. 15c), which are associated with small

space charge values ranging between 0.25–0.5 pCm23

(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).

FIG. 13. Radar reflectivity (z5 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.

JULY 2013 F I ERRO ET AL . 2409

6. Summary

A computationally inexpensive electrification model

with explicit charging and discharge physics has been

implementedwithin theWRF-ARWnumerical prediction

model. In situ charging of hydrometeors was parame-

terized following laboratory work, which demonstrated

the effectiveness of noninductive charging in genera-

ting Emag comparable to those reported within thun-

derstorms 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 kVm21), polariza-

tion 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

andMoulton 2010). The dischargemodel is adapted from

Ziegler and MacGorman (1994), whereby lightning-

deposited charge is made proportional to the total hydro-

meteor 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 5 3 km) model

simulations of three contrasting cases: a continental

squall-line case, a strong tropical cyclone, and a conti-

nental winter storm. Overall, the simulated spatial flash

pattern for all three cases exhibited reasonable agree-

ment with observations. Owing to imperfect forecast of

the placement and strength of the convection, the loca-

tions of the simulated FOD maxima that are associated

with deep convective cloud entities did not exactly

match those from the observations. Although weather

FIG. 14. (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.

2410 MONTHLY WEATHER REV IEW VOLUME 141

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 cy-

clone, 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 ob-

servations 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 simu-

lated FOD from the BLM were also evaluated against

FIG. 15. (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 0800UTC. Note

the reduced order of magnitude of the scaling units used for the electrical variables compared to all previous corresponding figures.

JULY 2013 F I ERRO ET AL . 2411

those obtained from the recently developed diagnostic

lightning algorithm ofMcCaul et al. It was found that for

all three case studies analyzed herein, the simulated

FOD showed overall good qualitative agreement be-

tween the BLMand theMC schemes owing to the strong

relationship between lightning and mixed-phase parti-

cles. 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 ofWRFor to theHurricane-WRF

model (HWRF), because the solver and the discharge

code each consist of a single external FORTRAN mod-

ule. The noninductive and inductive charging parame-

terizations, 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 pro-

vides 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 sim-

ulated lightning fields from both the BLM and McCaul

scheme could be readily incorporated into a statistical

ensemble Kalman filter (EnKF) package through an op-

erator 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 com-

putational 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 pro-

duce 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 de-

tailed channel propagation, which are currently compu-

tationally prohibitive for national weather predictions.

Acknowledgments. Funding was provided by NOAA/

Office of Oceanic and Atmospheric Research under

NOAA-University of OklahomaCooperativeAgreement

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 pro-

viding the 40-kmNAMdata andAmiArthur 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 themanuscript.

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