Wintertime Supercell Thunderstorms in a Subtropical ...web.ntnu.edu.tw/.../CurriculumVita.files/Paper/mwr_09_v137-07_p217… · F IG. 2. Base reﬂectivity (dB Z) observed by the

Wintertime Supercell Thunderstorms in a Subtropical Environment:Numerical Simulation

CHUNG-CHIEH WANG

Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan

GEORGE TAI-JEN CHEN

Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan

SHAN-CHIEN YANG

Department of Atmospheric Sciences, National Taiwan University, Taipei, and National Kinmen

Senior High School, Kinmen, Taiwan

KAZUHISA TSUBOKI

Hydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Japan

(Manuscript received 10 April 2008, in final form 3 December 2008)

ABSTRACT

Following an earlier diagnostic study, the present paper performs numerical simulations of the rare win-

tertime supercell storms during 19–20 December 2002 in a subtropical environment near Taiwan. Using

Japan Meteorology Agency (JMA) 20-km analyses and horizontal grid spacing of 1.5 and 0.5 km, the Cloud-

Resolving Storm Simulator (CReSS) of Nagoya University successfully reproduced the three major storms at

the correct time and location, but the southern storm decayed too early over the Taiwan Strait. The two

experiments produce similar overall results, suggesting that the 1.5-km grid spacing is sufficient even for

storm dynamics. Model results are further used to examine the storm structure, kinematics, splitting process,

and the variation in the mesoscale environment. Over the Taiwan Strait, the strong surface northeasterly flow

enhanced low-level vertical shear and helped the storms evolve into isolated supercells. Consistent with

previous studies, the vorticity budget analysis indicates that midlevel updraft rotation arose mainly from the

tilting effect, and was reinforced by vertical stretching at the supercell stage. As the ultimate source of

vorticity generation, the horizontal vorticity (vertical shear) was altered by the baroclinic (solenoidal) effect

around the warm-core updraft, as well as the tilting of vertical vorticity onto, and rotation of vortex tubes in

the x–y plane, forming a counterclockwise pattern that pointed generally northward (westward) at the right

(left) flanks of the updraft. In both runs, model storms travel about 158–208 to the left of the actual storms,

and they are found to be quite sensitive to the detailed low-level thermodynamic structure of the postfrontal

atmosphere and the intensity of the storms themselves, in particular whether or not the existing instability

can be released by forced uplift at the gust front. In this regard, the finer 0.5-km grid did produce stronger

storms that maintained longer across the strait. The disagreement in propagation direction between the

model and real storms is partially attributed to the differences in environment, while the remaining part is

most likely due to differences not reflected in gridded analyses. Since the conditions (in both the model and

real atmosphere) over the Taiwan Strait are not uniform and depend on many detailed factors, it is antici-

pated that a successful simulation that agrees with the observation in all aspects over data-sparse regions like

this one will remain a challenging task in the foreseeable future.

1. Introduction

Supercell thunderstorms, characterized by a rotating

and persistent updraft, are isolated cumulonimbi capa-

ble of producing damaging winds, large hail, and tor-

nadoes (e.g., Browning 1964; Lemon and Doswell 1979;

Corresponding author address: Prof. George Tai-Jen Chen,

Dept. of Atmospheric Sciences, National Taiwan University.

No. 61, Ln. 144, Sec. 4, Keelung Rd., Taipei 10772, Taiwan.

E-mail: [email protected]

JULY 2009 W A N G E T A L . 2175

DOI: 10.1175/2008MWR2616.1

� 2009 American Meteorological Society

Weisman and Klemp 1986). They have been a focus

of research for several decades (e.g., Browning and

Ludlam 1962; Weisman and Klemp 1982, 1984; McCaul

and Weisman 2001; Wakimoto et al. 2004). Numerous

observational works are found on their characteristics,

structure, and preferred environments (e.g., Charba and

Sasaki 1971; Marwitz 1972; Vasiloff et al. 1986; Doswell

and Burgess 1993), while their evolution, source of rota-

tion, and splitting behavior are studied mainly through

model simulations (e.g., Klemp and Wilhelmson 1978a,b;

Rotunno 1981; Rotunno and Klemp 1982, 1985; Davies-

Jones 1984; Klemp 1987; Bluestein and Weisman 2000).

Considerable success has been achieved through ide-

alized modeling in explaining the behavior of supercells

(e.g., Weisman and Klemp 1986; Klemp 1987). Studies

of real events using single sounding and initial thermal

perturbation have also proven useful, such as Kulie and

Lin (1998), Atkins et al. (1999), van den Heever and

Cotton (2004), and Sun (2005). However, successful sim-

ulations employing three-dimensional (3D), horizontally

varying observations and real terrain without any per-

turbation have been few in number and remain quite

challenging (e.g., Johnson et al. 1993; Finley et al. 2001;

Chancibault et al. 2003). For example, Finley et al. (2001)

utilized interior nudging during the integration in order

to better capture the mesoscale environment in which the

storm developed. The study of a storm over France by

Chancibault et al. (2003), although with a location error

of some 200 km, is also valuable and represents one of

the few studies outside the United States.

In the afternoon of 19 December 2002, severe storms

broke out near the coast of China and subsequently

evolved into supercells that tracked eastward. In a sub-

tropical environment south of 258N, these rare winter-

time supercells were the first near Taiwan to be reported

in the literature. Their environment, initiation, and ev-

olution are documented by Wang et al. (2009, hereafter

W09). In this study, the storms are shown to take place

behind the surface cold front, which provided strong

low-level vertical wind shear (6.4 3 1023 s21 at 0–3 km)

to combine with a weak-to-moderate convective avail-

able potential energy (CAPE) of 887 J kg21 above

the shallow cold air, thus yielding a suitable environ-

ment (e.g., Weisman and Klemp 1982; Rasmussen and

Blanchard 1998; Thompson et al. 2003, 2007). An ap-

proaching upper-level jet (ULJ) also provided deep

shear and drier conditions aloft. Obviously, supercell

storms can develop near Taiwan in winter when both

instability and vertical shear are present.

Near 1400 LST (LST 5 UTC 1 8 h) 19 December

2002, convective storms initiated about 80 km inland

along the southeastern coast of China, where significant

daytime solar heating occurred over the mountain

slopes (cf. Fig. 1; W09). The heating induced upslope/

onshore winds and led to convergence and uplifting

important to storm initiation. The storms evolved into

three isolated supercells about 120 km apart with a

northeast (NE)–southwest (SW) alignment, and trav-

eled eastward across the Taiwan Strait at about 18 m s21

(Figs. 1 and 2). The three primary storms were right

movers and each experienced multiple splits and even-

tually made landfall over Taiwan (Figs. 2h,i and 3). Be-

fore they decayed, all three storms had lasted for about

10 h and traveled more than 550 km (cf. Fig. 2).

As a follow-up study to W09, the present paper ad-

dresses several issues from a modeling aspect. First, can

this rare event in the maritime subtropics be reasonably

simulated (i.e., forecast) in a high-resolution model us-

ing analysis data and real terrain without initial thermal

perturbation? If so, which aspects of the simulation are

more successful and which are less successful? Second,

the storms apparently became isolated supercells over

the Taiwan Strait where data were sparse. Through

modeling, the mesoscale environment can be reproduced

to shed light on their maintenance and the transition

process to supercells. Third, the detailed structure, kine-

matics, and splitting process of storms can be further in-

vestigated using model results, if supercells are indeed

reproduced. To answer these questions, numerical ex-

periments are performed using the Nagoya University

(NU) Cloud-Resolving Storm Simulator (CReSS; Tsuboki

and Sakakibara 2002). This model has been applied

in the past to study high-latitude cloud streets during

cold-air outbreak (Liu et al. 2004), local heavy rainfall

FIG. 1. Model domains of run 1 (light shaded) and run 2 (thin

line), topography (m; shaded as indicated with additional white

contours at 1 and 3 km), and the tracks (dotted) of the three pri-

mary storms (northern, central, and southern) during 1455–2300

LST 19 Dec 2002. The locations of Lungyen Doppler radar (cross),

sounding stations (triangle), and the three storms when they

reached maximum reflectivity (solid dot) are marked.

2176 M O N T H L Y W E A T H E R R E V I E W VOLUME 137

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JULY 2009 W A N G E T A L . 2177

FIG. 3. Radar reflectivity (dBZ, contours) and tracks (dotted lines) of the (a) northern, (b) central, and (c) southern storms and

nearby cells at approximately 1-h intervals between 1455 and 2300 LST 19 Dec 2002. The reflectivity contours are drawn at 30, 40,

and 50 dBZ (areas $50 dBZ blackened), and hatched every other time for clarity. The scale of distance, time (LST), cell numbers,

and starting and ending positions of the primary right-moving storms are indicated (adapted from W09).


(Tsuboki 2004), and terrain-induced convective lines in

the mei-yu season (Wang et al. 2005). It is perhaps

worthwhile to note that past modeling studies on con-

vective storms over the Taiwan Strait are also few, with

one such example being Zhang et al. (2003).

This paper is arranged in the following manner. Sec-

tion 2 describes the data used to give a brief overview of

the case and to carry out the numerical study, as well as

the CReSS model and its configuration. The overall

results of model simulation are presented in section 3.

A vorticity budget analysis at the storm scale and the

related discussion on the transition to supercells are

given in section 4. Following an investigation on the

mesoscale environment over the Taiwan Strait and its

effects on storm evolution in section 5, conclusions are

given in section 6.

2. Data and CReSS model

The data used to review the supercell storms on

19 December 2002 in section 1 include base reflectivity by

the Doppler radar at Lungyen, China [25.068N, 117.198E;

1504.9 m above ground level (AGL); cf. Fig. 1], at

roughly 6-min intervals, and vertical maximum-echo

indicator (VMI) radar reflectivity composites over

the Taiwan area every 1 h. To verify model results,

surface and upper-level analyses, Quick Scatterometer

(QuikSCAT) oceanic winds, Geostationary Meteorolog-

ical Satellite-5 (GMS-5) cloud images, and rainfall data

in Taiwan as used in W09 are employed. The objective

analyses from the European Centre for Medium-Range

Weather Forecasts (ECMWF), available every 6 h with

a resolution of 1.1258 latitude–longitude at 11 pressure

(p) levels, are also compared with model outputs.

For model simulation, the Japan Meteorological

Agency (JMA) 6-hourly (at 0200, 0800, 1400, and 2000

LST) gridded regional analyses at 20-km horizontal

resolution at 20 p-levels (1000–10 hPa) during the case

period are used as initial and lateral boundary condi-

tions (IC and LBC, respectively). The variables pro-

vided are geopotential height, temperature (T), u and y

wind components, and specific humidity. The JMA ob-

jective regional analysis is performed by the regional

spectral model using multivariate 3D optimum inter-

polation (OI) to combine first-guess fields with obser-

vations that are free of internal/external quality control

problems from a variety of platforms (Segami et al.

1989; Onogi 1998; Tsuyuki and Fujita 2002).

The CReSS model used in this study (v.2.2) is a non-

hydrostatic, fully compressible, cloud-resolving model

developed at the Hydrospheric Atmospheric Research

Center of NU, Japan (Tsuboki and Sakakibara 2002,

2007). This model employs a terrain-following vertical

coordinate z, defined as z 5 zt[z 2 zs (x, y)]/[zt 2 zs

(x, y)], where zt and zs are heights at the model top and

surface, respectively. Prognostic equations for 3D mo-

mentum, potential temperature (u), p, and mixing ratios

of water vapor (qy) and other hydrometeors (qx, where x

denotes a species) are formulated, and the system in-

cludes all wave modes in the atmosphere. To properly

simulate clouds at high resolution, an explicit bulk cold

rain scheme based on Lin et al. (1983), Cotton et al.

(1986), Murakami (1990), Ikawa and Saito (1991), and

Murakami et al. (1994) are used without any cumulus

parameterization (Table 1). A total of six species (water

vapor, cloud water, cloud ice, rain, snow, and graupel)

with microphysical processes of nucleation (condensa-

tion), sublimation, evaporation, deposition, freezing,

melting, falling, conversion, collection, aggregation, and

liquid shedding are included (Tsuboki and Sakakibara

2002). A bulk warm rain scheme that considers only

liquid and gas phases is also available but not used here.

Subgrid-scale turbulent mixing is parameterized using

1.5-order closure with turbulent kinetic energy (TKE)

prediction (Tsuboki and Sakakibara 2007), and plane-

tary boundary layer (PBL) processes are parameterized

following Mellor and Yamada (1974) and Segami et al.

(1989). The momentum and energy fluxes and radiation

at the surface are also considered with a substrate model

(Kondo 1976; Louis et al. 1981; Segami et al. 1989) but

cloud radiation is neglected.

In the CReSS model, the Arakawa-C staggered and

Lorenz grids are used in the horizontal and vertical with

no nesting. For computational efficiency, a time-splitting

scheme (Klemp and Wilhelmson 1978a) is adopted to

separately integrate fast and slow modes. The filtered

leap-frog method (Asselin 1972) is used for integration

at large time steps (Dt), while the implicit Crank–Nicolson

scheme is used in the vertical at small steps (Dt) by choice

(Table 1). For parallel computing, data exchange be-

tween processing elements (PEs) is performed through

the Message Passing Interface (MPI) and/or Open MP.

Since the version 1.4 used in Wang et al. (2005), options

for different map projections, nudging of radar data,

and specification of sea surface temperature (SST), sea

ice, and land-use types were implemented, augmenting

the model’s applicability to larger domain, more sophis-

ticated lower boundary, and data assimilation.

In this study, two experiments were performed and

named run 1 and run 2. Run 1 had a horizontal grid

spacing of 1.5 km and 65 vertical levels (stretched from a

spacing of 100 m at the bottom to 475 m at the top) and

used the JMA regional analyses as IC/LBCs, and the

integration was from 0800 LST 19 December 2002 for

24 h without initial thermal perturbation (Table 1). At

the lower boundary, terrain elevation at 30 s (;900 m)

JULY 2009 W A N G E T A L . 2179

and weekly SST at 18 3 18 resolution (Reynolds et al.

2002) were provided. No data nudging at model interior

was used and outputs were produced every 15 min.

Afterward, a high-resolution run, run 2, was carried out

with a grid spacing of 0.5 km from 1100 LST for a length

of 14 h, using outputs of run 1 as IC/LBCs also without

nudging (Table 1). The model top of run 2 was slightly

lower, with a total of 63 vertical levels at nearly identical

heights as run 1. Output frequency was also every

15 min, but increased to 5 min over 1400–1900 LST

19 December 2002 for analyses at shorter time intervals.

The model configurations are summarized in Table 1

while domains are shown in Fig. 1. Later in this article,

run 2 results are presented for those aspects at storm-

scale (sections 3b to 4), while the coarser run 1 results

are used in relation to mesoscale environment of storm

initiation and propagation (sections 3a and 5).

3. Model results

a. Storm initiation

In W09, the convergence and uplifting associated with

the upslope (onshore) flow were found to be vital in the

initiation of storms in our case (section 1). Prior to 1400

LST, solar heating raised surface T and u by about 3 K

over the sloping terrain near the coast under clear-sky

conditions (their Figs. 15 and 17). Here, similar condi-

tions were also reproduced in both runs using the

IC/LBC and setting described in section 2. In the ver-

tical cross section along AA9 that passed through one

storm (storm n1, see next subsection for details) at 1400

LST in run 1 (cf. Fig. 6a), clear onshore flow of about 3–4

m s21 appears below about 1 km over the coastal re-

gion and convective cloud forms at its leading edge

(Fig. 4a). The updraft reaches over 5 m s21 near 3–6 km

(Fig. 4b), which is much stronger than revealed by the

coarse JMA gridded analysis in W09. The increase in

near-surface u since 0800 LST (i.e., u9), on the other

hand, is also about 2–2.5 K and quite comparable to the

analysis.

b. Overall storm evolution

Both run 1 and run 2 successfully reproduced con-

vective storms over the area of interest on 19 December

2002. The overall storm evolution in run 2 is first shown

by column-maximum mixing ratio of precipitating hy-

drometeors (qr 1 qs 1 qg) in Fig. 5. Here, storms are

labeled in a way similar to W09 (and Fig. 3), with odd

(even) numbers for right- (left-) movers but using

lower-case letters. The cells best corresponding to the

three primary storms (Figs. 1–3) are ‘‘n1’’, ‘‘c1’’, and

‘‘s1’’, respectively, and they were initiated over about

238–23.58N in a NE–SW alignment by 1400 LST among

other cells with only small location errors (Fig. 5a; cf.

TABLE 1. Summary of CReSS-model configuration of domain and basic setup, physics, and numerical methods used in experiments

run 1 (1.5 km) and run 2 (0.5 km). The time integration schemes can be classified as horizontal explicit (HE), vertical explicit (VE), and

vertical implicit (VI).

Run 1 Run 2

Domain and basic setup

Projection Lambert conformal, center at 1188E, secant at 208 and 508N

Grid size (km) 1.5 3 1.5 3 100–475 m 0.5 3 0.5 3 100–475 m

Grid number 648 3 450 3 65 1584 3 900 3 63

Domain size (km) 972 3 675 3 20.8 792 3 450 3 19.85

Topography and SST Real at 0.008338, and observed at 18 resolution

IC/LBCs JMA regional analyses (20 3 20 km, 20 levels, 6 h) CReSS run 1 outputs (30 min)

Initial thermal perturbation None

Initial time 0800 LST 19 Dec 2002 1100 LST 19 Dec 2002

Integration length 24 h 14 h

Output frequency 15 min 15 or 5 min

Model physics

Advection, diffusion Fourth-order in H/V, fourth-order in H/V

Cloud microphysics Bulk cold rain scheme (6 species)

Cumulus parameterization None

PBL parameterization 1.5-order closure with TKE prediction

Surface processes Energy and momentum fluxes, and shortwave and longwave radiation

Soil model 41 levels, every 5 cm to 2 m deep

Numerical methods

Time steps (Dt, Dt) 2 s, 1 s 1.5 s, 0.5 s

Integration method Filtered leapfrog for Dt (HE–VE), and leapfrog and Crank–Nicolson for Dt (HE–VI)

Number of PEs 18 108


FIG. 4. Vertical cross sections from 24.108N, 116.658E to 23.638N, 117.258E (AA9 in Fig. 6a) at

0–6 km at 1400 LST 19 Dec 2002. (a) The 2D vectors on the section plane (Vt and w; m s21) with

zero-speed contour (thick dash line) and total mixing ratio of cloud hydrometeors (qc 1 qi;

g kg21; shaded). (b) Speed of horizontal wind normal to section plane (Vn; m s21; thin contour,

zero-line thickened), vertical velocity (m s21; shaded), positive potential temperature pertur-

bation (u9; K; thick dash lines), and outline of cloud approximated by the 0.05 g kg21 value of

qc 1 qi (thick dash–dot gray lines). In (a), reference vector length of 20 m s21 for Vt are indicated,

and a length equivalent to 1 km in the vertical is 4 m s21 for w. In (b), contour intervals are 4 m s21

for Vn and 0.5 K for u9 (starting at 0.5 K).

JULY 2009 W A N G E T A L . 2181

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Figs. 1 and 2). After formation, the three storms also

went through splitting (e.g., n1 at 1645 LST, c1 at 1500

LST, and s1 at 1430 LST) then moved offshore during

1600–1730 LST near 24.58, 23.98, and 23.38N, respectively

(Figs. 5b–h), in good agreement with observation as well

(Figs. 1 and 2). After 1700 LST, n1 and c1 continued to

track toward the ENE over the Taiwan Strait, where the

latter also strengthened to exhibit clear supercell char-

acteristics, while s1 gradually weakened and decayed

(Figs. 5g–k). As their propagation direction was not to-

ward the east as observed, n1 missed Taiwan entirely,

and c1 passed through the northern part of the island

(Fig. 5l). Behind the major storms, several other cells in

run 2 also experienced splitting that produced left movers

of appreciable strength, most notably h1 and i1 (Figs. 5h–

l) that also agree with radar data (see Figs. 8 and 9 of

W09). Thus, although one cannot expect the model to

simulate all individual storms correctly on such local

scale, the overall storm evolution and morphology in run

2 bear close resemblance to the actual event on 19 De-

cember 2002 (Figs. 1–3 and 5).

While the model output does provide an appropriate

analog for our case, especially for c1, differences still

exist in storm tracks and other characteristics (Table 2,

top and middle). Compared to real storms, right movers

in run 2 generally travel about 158–208 too much to the

left (i.e., not right enough) and the southern storm s1

decays too early (Fig. 6b). In run 1, although the major

storms tend to be weaker and less compact as expected,

they are also reproduced with similar tracks (Fig. 6a and

Table 2, bottom). The most notable difference in evolu-

tion is that c1 also weakens too early at 2000 LST (Fig. 6a).

The similar overall results of the two runs suggest that

a horizontal grid spacing of 1.5 km is sufficient to capture

basic storm structure and dynamics. On the other hand,

the high resolution in run 2 is essential in the mainte-

nance of c1 over the strait. The reasons for this and other

discrepancies will be further discussed in section 5.

Figure 7 presents the peak updraft/downdraft strength

(wmax/wmin) and relative vorticity (zmax or zmin) of se-

lected cells in run 2. For the three major storms, the

peak updraft intensity (22–26 m s21) is reached by 1500

LST, within 3–4 h after initiation, then the splitting

starts (Figs. 7a,b). After moving offshore, n1 and c1 ex-

perienced more splits, especially the latter whose updraft

remained stronger, while the left movers (h2 and i2)

over land also exhibit splitting behavior. Consistent

with earlier studies (e.g., Klemp and Wilhelmson 1978b;

Wilhelmson and Klemp 1981), storms split near or

shortly after their updraft intensifies. The peak down-

draft strength of these storms is about 29 to 214 m s21.

The corresponding zmax (or zmin) in run 2 also shows

variation similar to the updrafts, and the peak values

can exceed 2–4 3 1022 s21 (Figs. 7c,d). The above wmax

and zmax values in run 2 are comparable to those found

in U.S. cases at similar grid resolutions (e.g., Weisman

and Klemp 1984; Finley et al. 2001; van den Heever and

Cotton 2004), and are about 1.5–2 times for wmax/wmin

and can be 2–4 times for zmax (or zmin) greater than

those in run 1.

TABLE 2. Comparison between major characteristics of (top) observed and simulated storms by the CReSS model in (middle) run 2 and

(bottom) run 1. For observed cells, radar data were unavailable prior to 1425 and after 2300 LST, 19 Dec 2002.

Storm cell

Time of

initiation

(LST)

Life

span (h)

Distance

traveled (km)

Mean direction

and speed*

(8/m s21) Size $ 40 dBZ (km) Split

Observation N1 By 1425 $8.6 $570 2608/19.6 15–35 Yes

C1 By 1425 $8.7 $518 2688/17.8 15–35 Yes

S1 By 1455 $8.6 $507 2718/17.4 15–40 Yes

N2 1525 4.3 247 2158/19.2 ,20 Yes

Others 2 ;2–6 ;150–400 ;2438/;17–19 #15 2

Model n1 1200 $11.0 $633 2438/16.0 #15 Yes

Run 2 c1 1145 $12.3 $692 2488/15.7 10–20 Yes

(0.5 km) s1 1245 7.0 278 2558/11.0 #20 Yes

h1 1600 $9.0 $391 2598/12.1 10–25 Yes

h2 1830 4.8 237 2328/13.9 #20 Yes

i1 1630 $8.5 $575 2468/18.8 #12 Yes

i2 1730 6.0 377 2328/17.5 10–20 Yes

Model n1 1330 10.5 735 2488/18.3 #15 Yes

Run 1 c1 1400 6.0 313 2478/13.1 #15 Yes

(1.5 km) s1 1400 5.8 324 2508/17.6 10–20 Yes

s2 1530 9.3 623 2278/18.9 10–25 Yes

h1 1500 9.0 410 2588/15.4 10–15 No

* The 500–700-hPa environmental wind was from 2438 at 18.5 m s21 (W09).

JULY 2009 W A N G E T A L . 2183

FIG. 6. Tracks of major storm cells simulated by the CReSS model during 19–20 Dec 2002 in (a) run 1 and (b) run 2 with

topography (km; shaded). Cell locations are marked as open dots at every full hour, and labeled with their assigned name (as in

Fig. 5) and time (LST) every 3 h. End points are marked as solid dots and also labeled. Dotted line AA9 in (a) depicts the vertical

cross section used in Fig. 4. The domain of run 2 is also plotted in (b).


c. Storm structure and morphology

In section 3b, it was shown that c1 is reproduced more

successfully among the three major storms, and it un-

dergoes a transition into an isolated supercell after

moving offshore (Fig. 5). The structure of this storm on

land at 1445 LST is revealed by Fig. 8 for an area of

roughly 50 3 50 km2. At this time, wmax of c1 reaches its

peak (;26 m s21) after initiation (cf. Fig. 7b) and the

storm is traveling at 2438/13.9 m s21. From low to mid-

levels (Figs. 8a,b), multiple updraft centers exist slightly

to the east and southeast (at the front to right-front side)

of the precipitation (shown by qr 1 qs 1 qg). At 2.4 km,

the rear-flank downdraft (RFD) is also visible north of

the updraft (reaching 25 m s21), and coincides with the

precipitation (Fig. 8a). Although not evident at low

levels, it is clear that the main updraft of c1 exhibits cy-

clonic rotation at 4.8 km (with z reaching 1022 s21) while

z , 0 appears to the north (Figs. 8c,d). In a relative sense,

the updrafts are also associated with negative pressure

perturbation (p9) at the front side (to the E-NE) and

positive p9 at the rear [to the west-southwest (W-SW)], a

configuration consistent with the horizontal gradient of

vertical pressure gradient force that leads to downstream

propagation of supercell storms (e.g., Rotunno and

Klemp 1985; Klemp 1987; Cai and Wakimoto 2001).

The vertical cross sections through the main updraft

of c1 at 1445 LST along lines BB9 and CC9 in Fig. 8b are

presented in Fig. 9. Along BB9, strong storm-relative

low-level inflow (from the E-NE) and upper-level out-

flow (from the W-SW) both exceed 20 m s21 (Fig. 9a), in

accordance to the strong vertical shear. The rain (qr,

peaking near 7 g kg21) mainly appears below 5 km,

snow (qs) above 7 km, and graupel over 4–9 km (also

$7 g kg21). While the main updraft is over 15 m s21 at

4–7 km, several other updrafts are also developing

nearby with the closest only 12 km ahead (Fig. 9a).

Thus, c1 still displays some multicell characteristics and

has yet to become an isolated and quasi-steady supercell

at 1445 LST. Associated with the updraft and conden-

sational heating, increase in u (downward intrusion of

adiabats) is seen at 4–9 km in section CC9, while some

cooling exists near cloud edges (Fig. 9b).

At 1730 LST, storm c1 is moving at 2598/17.3 m s21

over the Taiwan Strait and has become more isolated in

run 2 (cf. Fig. 5). From 2.4 to 7.2 km, the relative flow

changes from about 25 m s21 from the east to nearly

20 m s21 from the southwest (Figs. 10a–c), veering

clockwise and consistent with the right-moving behavior

of c1. At low levels, the strong inflow is collocated with

the main updraft with an inflow notch at the immediate

FIG. 7. Maximum updraft (wmax; m s21) and downdraft velocity (wmin) associated with (a) cells n1, s1, and i2, and (b) c1, h1,

and h2 from 1100 LST 19 to 0100 LST 20 Dec 2002. (c),(d) Same as (a),(b) but for relative vorticity extrema (zmax or zmin;

1023 s21). For the two left-moving (anticyclonic) cells (i2 and h2), zmin is shown while zmax is plotted for all other (cyclonic) cells.

Arrows with time (LST) indicate storm splitting (boxed time for result from a split), and large open circles indicate the time

when storms moved offshore.

JULY 2009 W A N G E T A L . 2185

right-front side of the precipitation area. At 7.2 km,

however, the updraft becomes coincident with precipi-

tation (Fig. 10c). The RFD at 2.4 km and the forward-

flank downdraft (FFD) at 4.8 km (near 24.018N,

118.318E) are both visible (Figs. 10a,b). At this time, a

single, strong updraft is associated with c1 while a left-

moving cell c4 is under development (near 24.058N;

Figs. 10b,c). As expected, both the updrafts of c1 and c4

are rotating, with z reaching 1022 s21 for the former and

25 3 1023 s21 (anticyclonic) for the latter (Figs. 10d–f).

Again, the forward-directed pressure gradient force is

clear, especially at 4.8 km, with a horizontal gradient of

about 2 hPa over only 3 km (0.67 Pa km21) across the

updraft. The pressure gradient also rotates clockwise

with height as observed (Figs. 10d–f), which favors right

movers (e.g., Weisman and Klemp 1984; Klemp 1987).

In the vertical cross section along line DD9 (Fig. 10b),

again, a single and strong updraft is present (Figs. 11a,b).

The maximum concentrations of graupel and rain are

about 10 and 4 g kg21, respectively, and snow particles

FIG. 8. Plain views of storm c1 in run 2 at 1445 LST 19 Dec 2002, of storm-relative horizontal winds (m s21; vectors),

vertical velocity (w; m s21; thick contours), total mixing ratio of rain, snow, and graupel (qr 1 qg 1 qs; g kg21; shaded),

and cloud boundary (thick dash–dot lines) approximated by 0.5 g kg21 of the column-maximum total mixing ratio of

all five species of hydrometeors, at (a) 2366 and (b) 4829 m. (c),(d) Same as (a),(b) but for pressure perturbation (hPa;

shaded), the vertical component of relative vorticity (z; 1023 s21; thin contours), positive w (thick contours), and

cloud boundary. Shading scales and reference vectors of 20 m s21 are indicated. Contours for w are every 5 m s21 plus

one additional level at 22 m s21, and those for z are every 5 3 1023 s21 plus 62 3 1023 s21 (dashed for negative

values and zero-line omitted for both). Straight dash lines BB9 and CC9 in (b) are used to construct the vertical cross

sections shown in Fig. 9.


are mostly within the anvil farther downstream. Within

the updraft, the warming as shown by u9 (perturbation

since 1100 LST in run 2) can reach almost 4 K in upper

levels. On the other hand, evaporative cooling also oc-

curs in association with rain at low levels as well as

below the anvil (both over 22 K; Fig. 11b). Along sec-

tion EE9 (Fig. 11c), it can be seen that the updraft of c1

tilts toward the NNW (left) with height and keeps a

large amount of graupel suspended aloft, forming a

clear vault that corresponds to the bounded weak echo

region (BWER). The rain falls below the strongest as-

cent, over a region of transition from updraft to down-

draft. The developing updraft of c4 (.5 m s21) from a

splitting process is also depicted (Figs. 11c,d).

d. Storm splitting process

The storm splitting process is also well reproduced

in both runs, as predicted when significant vertical shear

is present from previous studies (e.g., Klemp and

Wilhelmson 1978b; Wilhelmson and Klemp 1981;

Rotunno 1981; Rotunno and Klemp 1982; Klemp 1987).

Distributions of 1-h rainfall for four selected periods

and areas are shown in Fig. 12. With a 500–700-hPa

environmental wind of 2438/18.5 m s21 (cf. Table 2), the

separation of storm tracks into right and left branches is

clearly depicted during the split of s1 and s2 and h1 and

h2 (Figs. 12a,c). The rainfall resulted from c1 has sig-

nificantly wider swath (over 20 km for amount $5mm)

after it becomes more isolated (Fig. 12b), in agreement

with Fig. 10a of W09. In Fig. 12d, the split of h3 from

left-moving h2 during 2000–2100 LST is also visible (cf.

Figs. 5j,k).

The splitting process for storm c1 during a 25-min

period in its mature stage from 1715 to 1740 LST at

midlevel in run 2 is presented in Fig. 13. At 1715 LST,

the main updraft is located at the right flank (southeast

side) of the storm complex and clearly associated with

cyclonic rotation (Fig. 13a). North of the updraft at

the left flank, an area of anticyclonic rotation exists

where ascending motion gradually forms at 1725 LST

(Fig. 13b). This updraft and its accompanying precipi-

tation north of 248N continue to develop, and become

well established as c4 (.5 m s21) at 1730 LST (Fig. 13c).

With wmax . 5 m s21 and qr 1 qg . 5 g kg21, cell c4

further separates from c1 at 1740 LST after the split

(Fig. 13d).

The splitting of h1 during 1820–1855 LST at 4.8 km is

shown in Fig. 14. Not long after its initiation (Figs. 5h,i),

this storm is mainly composed of a single updraft at 1820

LST (Fig. 14a). At 1830 LST, the precipitation grows

and extends toward the rear of the storm, and a new

updraft h2 develops (Fig. 14b). The distance between

old and new updrafts gradually increases through 1855

LST and the split is completed (Figs. 14c,d). Afterward,

both h1 and h2 continue to intensify (Figs. 5i–l) and the

left-moving h2 also experiences splitting (Fig. 12d). In

Figs. 13 and 14, it is quite clear that storm updrafts tend

to strengthen at the forward flank of the precipitation,

FIG. 9. Vertical cross sections at 1445 LST 19 Dec 2002 of (a) 2D storm-relative vectors on the section plane (Vt and w; m s21), mixing

ratios of rain (qr; g kg21; solid), snow (qs; dashed), and graupel (qg; shaded as indicated), and outline of cloud approximated by the 0.05

g kg21 value of mixing ratio of cloud hydrometeors (qc 1 qi; thick dash–dot lines) along line BB9, and (b) positive w (m s21; shaded),

outline of cloud, and potential temperature perturbation (u; K; thick gray dashed lines) along line CC9 in Fig. 8b. In (a), reference vector

of 20 m s21 for Vt is indicated, and a length equivalent to 1 km in the vertical is 10 m s21 for w. Contour intervals for qr are the same as

qg, and 0.2 g kg21 for qs, and 4 K for u. Vertical arrows at the bottom mark the location where BB9 and CC9 intersect.

JULY 2009 W A N G E T A L . 2187

FIG. 10. (a)–(c) Same as Figs. 8a,b, but for storm c1 at 1730 LST 19 Dec 2002 at (a) 2366, (c) 4829, and (e) 7105 m.

(d)–(f) Same as Figs. 8c,d, but for c1 at 1730 LST at 2366, 4829, and 7105 m, respectively. Straight dash lines DD9

and EE9 in (b) are used to construct the vertical cross sections shown in Fig. 11.


which in turn often intensifies within several minutes

after the updraft enhanced, in agreement with earlier

studies (e.g., Weisman and Klemp 1986).

4. Storm vorticity budget analysis

To understand whether supercell-like structure can

be replicated by the CReSS model, a vorticity budget

analysis is performed for the period of 1600–1800 LST,

where storm c1 evolved into an isolated supercell

(cf. Fig. 5) and outputs at 5-min intervals are available

in run 2. The vorticity equations commonly used to in-

terpret supercell dynamics are obtained by taking the

curl of the Boussinesq equations of motion (e.g., Klemp

1987; Weisman and Rotunno 2000; Chancibault et al.

2003). When transformed into a storm-relative (quasi-

Lagrangian) frame for interpretation (e.g., Lee and

Wilhelmson 1997), they can be written as

›z

›t

� �SR

5�[(vH � c) � =H]z � w›z

›z

1 (vH � =H)w 1 z›w

›z1 Fz, (1)

FIG. 11. (a),(d) Same as Figs. 9a,b, but for 1730 LST 19 Dec 2002 along lines DD9 and EE9 in Fig. 10b, respectively. (b) Same as (a), but

for positive w (m s21; shaded), outline of cloud, and potential temperature perturbation (u9; K; contour; dashed for negative values). (c)

Same as (a), but for along line EE9 in Fig. 10b. Vectors for Vt and w, and contour intervals for qr, qs, and u are the same as in Fig. 9, while

intervals are 1 K for u9 in (b). Vertical arrows at the bottom mark the location where DD9 and EE9 intersect.

JULY 2009 W A N G E T A L . 2189

›vH

›t

� �SR

5�[(vH � c) � =H]vH � w›vH

›z

1 (v � =)VH 1 = 3 (Bk) 1 FvH , and (2)

= 3 (Bk) 5R

p=p 3 =T, (3)

where (›/›t)SR is the local derivative in the storm-relative

frame, vH is the horizontal velocity vector (relative to

the ground), c is the (constant) storm-motion vector,

vH 2 c is the storm-relative horizontal velocity, w is

vertical velocity, v 5 (j, h, z) is the 3D vorticity vector

while vH 5 (j, h) is the 2D vector on the plane, and VH

is u or y. The terms Fz and FvH represent mixing, and B

is buoyancy, R the gas constant, and k the unit vector in

z direction. In both equations, the first two terms on the

rhs are horizontal and vertical advection, respectively.

In Eq. (1), the third and forth terms are the generation

of vertical vorticity by tilting of horizontal vorticity into

the vertical [vH �=Hw 5 j(›w/›x) 1 h(›w/›y)] and by

stretching of existing vertical vorticity. Equation (2) has

two components (›j/›t, ›h/›t), and the third term is the

combined effect of stretching [j(›u/›x), h(›y/›y)] and

rotation [h(›u/›y), j(›y/›x)] of vortex tubes in the x–y

plane, and tilting of vertical vorticity onto the x–y plane

[z(›u/›z), z(›y/›z)]. The fourth term on the rhs of

Eq. (2) is the baroclinic (or solenoidal) generation due

to a buoyancy gradient, and can be expressed as Eq. (3).

Figure 15 presents the results of the vorticity budget

analysis for the major terms in Eq. (1) for c1 near 4 km at

FIG. 12. Model-simulated 1-h accumulative rainfall over selected areas for (a) 1415–1515, (b) 1715–1815, (c) 1815–1915, and (d)

2000–2100 LST 19 Dec 2002 in run 2. Shading scale is indicated to the lower right of (c),(d), and isohyets at 1, 10, and 30 mm are drawn.

Maximum rainfall areas caused by different cells are also marked.


1630 LST, when the storm is moving offshore (cf. Fig. 5).

In Fig. 15a, the main updraft is elongated and peaks at

about 7 m s21. Since the vorticity vector vH usually has

a northward component associated with westerly shear,

tilting from updrafts generates positive (negative) z at

the southern (northern) flank (and the opposite for

downdrafts) as expected (Fig. 15a). The peak value just

south of the main updraft is almost 4 3 1025 s22. Near

updraft centers of c1 (within ;3 km) and also to their

south, the stretching effect has opposite sign to vorticity;

that is, ›z/›t , 0 over regions of z . 0 and vice versa,

with a maximum rate of about 24 3 1025 s22 (Fig. 15b).

This is because the updraft tilts northward with height

and ›w/›z at 4 km AGL is in fact negative, resulting

in vertical shrinking of vortex tubes. When the two effects

are combined (Fig. 15c), the pattern of z generation

agrees more with that in Fig. 15a (and the pattern of

z itself), confirming that the tilting effect is the primary

FIG. 13. Same as Fig. 8b, but for storm relative winds (m s21; vectors), vertical velocity (w; m s21; thick lines), column-maximum mixing

ratio of rain and graupel (qr 1 qg; g kg21; shaded), and cloud boundary (thick dash–dot lines) approximated by the 0.5 g kg21 value of the

column-maximum total mixing ratio of all five species of hydrometeors for storm c1 at 4829 m at (a) 1715, (b) 1725, (c) 1730, and (d) 1740

LST 19 Dec 2002. For w, contour intervals are drawn every 5 m s21 (starting from 5 m s21), while shading scales and reference vectors of

20 m s21 are indicated.

JULY 2009 W A N G E T A L . 2191

source for the storm’s overall rotation at midlevels. Once

positive z is generated, it is advected by the storm-relative

flow toward the updraft from the south/southeast

(Fig. 15d). On the other hand, vertical advection tends

to cancel with stretching (Fig. 15e). When all effects

in Eq. (1) are combined (except friction), the total

tendency (›z/›t)SR is mostly positive at updraft centers

and thus tends to enhance existing z (Fig. 15f). At a

FIG. 14. Same as Fig. 13, but for storm h1 at (a) 1820, (b) 1830, (c) 1840, and (d) 1855 LST 19 Dec 2002.

FIG. 15. (a) The w (m s21; shading), generation of z by tilting (1025 s22; contours), and horizontal vorticity vector vH [vH 5 (j, h);

1023 s21]; (b) z (1023 s21, shading), generation of z by vertical stretching (1025 s22; contours), and storm-relative horizontal wind vector

(vSR 5 vH 2 c; m s21); (c) w, generation of z by both tilting and vertical stretching, and vH; (d) z, horizontal advection of z (1025 s22;

contours), and vSR; (e) w, vertical advection of z (1025 s22; contours), and vSR; and (f) z, total local tendency of z (1025 s22; contours), and

vSR for storm c1 at 3984 m at 1630 LST 19 Dec 2002. Contour intervals are 3 3 1025 s22 plus two additional levels at 61 3 1025 s22 in all

panels, with solid (dotted) lines for positive (negative) values (thickened every 6 3 1025 s22, zero-line omitted). Reference vector and

shading scale are indicated, with white contours added between shades of positive values. (b),(d),(f) Solid dots (crosses) indicate updraft

(downdraft) centers.

!


JULY 2009 W A N G E T A L . 2193

maximum rate of 6 3 1025 s22, only 2.5 min are needed

to generate a vertical vorticity close to 1022 s21, which is

roughly the peak value in Fig. 15b.

At 1730 LST when c1 has moved offshore and be-

comes an isolated supercell (Fig. 16a; cf. Figs. 5, 10, and

13), its updraft reaches 14 m s21 near 4 km (Fig. 11),

twice than that at 1630 LST. The tilting effect is also

more effective and can reach 9 3 1025 s22, consistent

with the acceleration in storm rotation with a peak z of

;1.4 3 1022 s21 (Fig. 16b). The stretching effect con-

tinues to destroy z along the southern flank because the

updraft still tilts northward with height. However, it

starts to reinforce existing z near the center and along

the northern flank (Fig. 16b), as the updraft becomes

significantly wider (cf. Figs. 10 and 11). Thus, the com-

bined effect of tilting and stretching becomes strongly

positive near the updraft center (Fig. 16c). The hori-

zontal advection effect near 4 km is now somewhat re-

duced because of less penetration by the relative flow

through the updraft, while vertical advection continues

to counteract the stretching term (Figs. 16e,f). Finally,

the resulted total z tendency in the storm-relative frame,

still dominant by tilting among all terms, is positive over

the region of z . 0, at the updraft center, and along its

right flank (Fig. 16f).

From low levels up to 9 km, the budget terms in

Eq. (1) reveal that the tilting effect is significant above

2.5 km and becomes strong at midlevels (up to 6 km, not

shown). In the upper troposphere where =Hw is large

(cf. Figs. 11b,d), it can also be significant. The positive

stretching effect close to the updraft center, once z is

produced, is typically maximized near 3.5 km (not

shown), where the upward acceleration is more intense

(cf. Fig. 11). The combined effect from both terms,

therefore, usually peaks near 3–4 km.

As the source for z generation, the horizontal vor-

ticity vector vH (i.e., vertical shear) is clearly not uni-

formly distributed on the x–y plane and typically points

northward (westward) at the right- (left-) front flank

of the updraft (Figs. 15a and 16a). This counterclock-

wise (cyclonic-rotating) pattern indicates that westerly

(southerly) shear is enhanced at the right (left) flank. To

a lesser degree, vH generally has an anticyclonic pattern

near downdrafts. The rates of vH generation from in-

dividual effects in Eq. (2) at 1730 LST are shown in

Fig. 17. The combined effect from the third and forth

terms (Fig. 17a) shows that (›vH/›t)SR usually has an

eastward or forward (westward to southward or back-

ward) component at the right (left) flank of the updraft,

over the area where z . 0 (,0), also forming a coun-

terclockwise pattern for vH tendency. This distribution

of ›vH/›t, thus, tends to reinforce existing vortex tubes

at both flanks (gray shades), in agreement with Brandes

et al. (1988), who noted a similar vH pattern near the

updrafts. For individual components, the horizontal

stretching effect [j(›u/›x), h(›y/›y)], produced by speed

change in the direction of vortex tubes, tends to be

slightly negative (i.e., weakening existing vH) since air

usually decelerates (on the x–y plane) when entering the

updraft (Fig. 17b). The combined effect of horizontal

rotation [h(›u/›y), j(›y/›x)] and the tilting of z onto the

x–y plane [z(›u/›z), z(›y/›z)] is dominated by the latter.

At the right flank, the westerly vertical shear tends to

twist the positive (upward pointing) z into (eastward

pointing) j, which is then rotated cyclonically toward

the north (because z . 0), thus strengthening existing

vH (Fig. 17c). At the left flank, likewise, the southerly

shear tends to twist negative z (pointing down) into

negative h (pointing south) that is then rotated toward

the west. Therefore, this combined effect corresponds to

a cyclonic pattern for ›vH/›t that bares similarity to the

total effect in Fig. 17a. The baroclinic effect, with strong

ascent within a warm-core updraft and descent (or

weaker ascent) farther away, also produces cyclonic vH

turning tendency (Fig. 17d; Brandes et al. 1988) that

contributes toward the total effect. Considering also

horizontal advection, which tends to be positive near

the updraft center (Fig. 17e), and vertical advection (not

shown), the total tendency (›vH/›t)SR exhibits a cy-

clonic pattern over the region of z . 0 near the main

updraft (Fig. 17f). It is noted that all terms in Fig. 17

have similar peak magnitude of about 5–10 3 1025 s22,

in the same order as the terms in Eq. (1). Consis-

tent with previous studies (e.g., Kulie and Lin 1998;

Chancibault et al. 2003), the baroclinic generation of vH

is identified to be an important source for local en-

hancement of vertical shear, which then can be tilted

near and stretched inside the updraft to produce storm

rotation. Based on Fig. 17, however, once appreciable z

is present, regardless of its sign, it can also be tilted onto

the x–y plane and then rotated, and contributes toward

the modification of vertical shear (i.e., vH) into the

horizontally varying, cyclonic pattern as seen in Fig. 16a.

In other words, there exists complex interaction among

the three v components (j, h, z) through kinematics that

readily affect one another near the rotating updraft of

supercell thunderstorms. The roles of tilting effect (from

z into j or h) and horizontal rotation in mature storms

have not been emphasized recently in the literature.

5. Mesoscale environment over the Taiwan Strait

One of the major differences between modeled and

observed storms is the shorter lifespan of ‘‘s1’’ in the

model. While ‘‘n1’’ and ‘‘c1’’ last much longer in run 2,

one wonders why these model storms behave differently.


FIG. 16. Same as Fig. 15, but for storm c1 at 3984 m at 1730 LST 19 Dec 2002.

JULY 2009 W A N G E T A L . 2195


As c1 improved in total lifespan using a finer grid, fur-

ther increase in resolution from run 2 may help s1 last

longer, but some reasons related to the variation in me-

soscale environment must also exist. Using QuikSCAT

oceanic winds at 1825 LST and largely land-based obser-

vations at 2000 LST, the surface mesoscale environment

over the Taiwan Strait was manually analyzed and

compared with the model fields in run 1 in Fig. 18. Only

subtle differences exist between the two, as the ob-

served winds appeared slightly stronger over the strait

while the model surface air of 198–228C seemed to have

advanced more to the south. The strong northeasterly

flow over the strait, in contrast to the weak onshore flow

along the coast of China, indicates that the low-level

vertical shear was much stronger over the ocean. This

explains why the storms evolved into isolated supercells

once they moved offshore in the current case.

To further shed light on the differences in mesoscale

environment in the model, five points over the strait,

marked ‘‘A’’ through ‘‘E’’ from north to south in Fig. 18b,

are selected to compute several thermodynamic and

shear parameters. These include CAPE and convective

inhibition [CIN (J kg21); Weisman and Klemp 1982;

Colby 1984] at the most unstable level, the distance to

the level of free convection (LFC), 0–3 km mean shear

(Thompson et al. 2007) and storm relative helicity

(SRH; Davies-Jones et al. 1990), bulk Richardson

number (Moncrieff and Green 1972), energy–helicity in-

dex (Hart and Korotky 1991; Davies 1993), and super-

cell composite parameter (SCP; Thompson et al. 2003).

As shown in Fig. 6b, storm n1 passed near point B

(258N, 1208E) at around 1945 LST and point A (25.58N,

1218E) at around 2115 LST, while c1 passed near point

C (248N, 1198E) around 1845 LST in run 2. On the other

hand, s1 dissipated when approaching point D (23.58N,

118.58E) at about 2000 LST, and h1 passed near the

same point later at 2330 LST. Point E (22.58N, 1188E),

slightly farther to the south, is chosen for comparison.

Time series of selected parameters, computed from run

1 results, are shown in Fig. 19, in which the occurrences

noted above are also marked.

In the late afternoon/early evening of 19 December,

maximum CAPE increased from north to south (Fig. 19a)

as the surface cold air was thicker (and colder) to the

north (cf. Fig. 18). At points A and B, CAPE was almost

nonexistent initially but increased after 2100–2300 LST.

Similarly, CAPE at C and D decreased before 1700 LST

to about 200 J kg21 and increased after 2000 LST. The

CAPE values decreased because of the southward ad-

vance of cold air, but were slowly restored as the near-

surface air was gradually warmed and moistened by

ocean fluxes. However, since the southern storm s1

dissipated near D at 2000 LST (CAPE ;170 J kg21)

while n1 passed A and B during 1945–2115 LST (CAPE

,100 J kg21), there appears to be a paradox. Therefore,

CIN and the distance to LFC are also examined to yield

information about how easily CAPE can be released

(Figs. 19b,c). Consistent with earlier discussion, both

CIN and the distance to LFC at A and B were very

large in the afternoon with no chance for convection,

but decreased drastically to within 50 J kg21 and 100

hPa prior to 2000 LST. For this reason, convection

could occur, though with only limited CAPE, given the

strength of storm n1 around 2000 LST (cf. Fig. 7a).

When other storms appeared near A and B later around

2300 LST (cf. Fig. 5l), CIN became small (,40 J kg21)

while CAPE grew further, and the distance to LFC re-

duced to #200 hPa (Figs. 19a–c). This indicates only

weak stability with respect to saturated ascent. At point

C at 1845 LST and point D at 2000 LST, some CAPE

(;200 J kg21) existed and CIN was less than 75 J kg21,

and the distance to LFC was about 120 hPa at C but

almost 200 hPa at D (Figs. 19b,c). Thus, whether the

limited CAPE can be released at C and D through

forced uplift at the gust front depends heavily on the

strength of the passing storm. Therefore, the stronger

storm c1 in run 2, with a finer grid and an inflow layer

at least 3 km in depth (cf. Figs. 10 and 11), could be

maintained when it propagated across the strait. On the

contrary, storms s1 in both runs and c1 in run 1, once

becoming too weak, cannot sustain themselves in such

an environment with a long path to LFC. Slightly farther

south at point E, CAPE decreased from 1400 LST but

still remained at 400–600 J kg21 after 1900 LST, and

CIN increased to 50–70 J kg21. The distance to LFC

was also large (.200 hPa) during 1600–2300 LST, but

FIG. 17. (a) Vertical velocity w (m s21; contours) and generation of horizontal vorticity vH [(›vH/›t)SR in Eq. (2); vector; 1025 s22] by

all three effects in (b)–(d), vertical component of vorticity z (1023 s21, contours) and generation of vH by (b) stretching by horizontal

wind and (c) horizontal rotation and tilting of z onto x–y plane (vector; 1025 s22), (d) w and generation of vH by the buoyancy

(solenoidal) effect (vector; 1025 s22); (e) w and total advection of vH by storm-relative wind vH and w; and (f) z and total (›vH/›t)SR

(1025 s22; contours), for storm c1 at 3984 m at 1730 LST 19 Dec 2002. For w and z, contour levels are the same as the shading levels in

Figs. 16a,b, respectively, and thick solid (dotted) lines indicate positive (negative) values. Reference vectors are drawn at the bottom. The

gray shade indicates the area where the dot product of vH (as shown in Fig. 16a) and its tendency (›vH/›t)SR by the respective effect (or

process) is positive (i.e., enhances existing vH), while no shade indicates the opposite (i.e., weakens existing vH). (b),(c),(f) Solid dots

(crosses) indicate updraft (downdraft) centers.

JULY 2009 W A N G E T A L . 2197

FIG. 18. (a) QuikSCAT oceanic winds with isotach (kt; thick solid lines) over the Taiwan area

at 1825 LST and manual mesoscale surface analysis of MSL temperature (8C; dashed) at 2000

LST 19 Dec 2002. (b) Model-simulated surface winds (barbs in knots) with isotach (m s21;

shading) at 10-m height at 1830 LST, and temperature (8C; contour) at the lowest model level of

50 m at 2000 LST 19 Dec 2002 in run 1. Isotherm intervals are 28C in (a) and 18C in (b), and solid

dots mark the position of the three primary storms at 1830 LST. Letters A through E indicate

the locations of model sounding used in Fig. 19.


FIG

.1

9.S

ele

cte

dth

erm

od

yn

am

ica

nd

shea

rp

ara

me

ters

at

po

ints

Ath

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Fig

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ure

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.

JULY 2009 W A N G E T A L . 2199

gradually lowered afterward also because of surface

fluxes.

In contrast to CAPE, low-level mean vertical wind

shear generally decreased from north to south, but was

significant (5–10 3 1023 s21) over the Taiwan Strait at

all five points (Fig. 19d). The perturbation in shear

caused by n1 at point B at 2000 LST was also clear. The

0–3 km SRH generally peaked at 73–82 m2 s22 during

1700–2000 LST at points A through D, but the same

level was not reached at point E until 0100 LST

20 December (Fig. 19e). The time series of SCP shows

that its value increased to 0.7 at point B, but only 0.3 at

point A as n1 moved close. At C and D, SCP was about

0.6–1.0 when c1, s1, and h1 moved through or dissipated

nearby. Thus, it is impossible to distinguish which storm

environment among the five points was suitable for su-

percell maintenance based merely on low-level shear,

SRH, or SCP values (Figs. 19d–f). Rather, the more

detailed structure of sounding profile, especially at low

levels, must be taken into account to give information

about not only whether instability exists, but also how

easily it can be released as shown here. From Figs. 18

and 19, for the present case, it can be identified that each

point over the Taiwan Strait only experienced a certain

period of time from the afternoon of 19 to early morning

of 20 December 2002, perhaps no longer than 6–10 h,

that was favorable for supercells. Given sufficient low-

level shear (and SRH), the CAPE must exist and its

release was achievable; that is, the surface cold air was

still shallow enough (so that convection could occur

above it), or a sufficient period of time had elapsed to

allow the ocean fluxes to modify the near-surface air

inside the marine PBL and reduce CIN to a level that

could be overcome.

The previous analysis shows that in this case, in ad-

dition to the common ingredients of sufficient shear

and instability, the evolution of model storms depends

heavily on the detailed low-level vertical structure of

storm environment, which varies horizontally and is

linked to the rapid evolution of surface cold air. Over

the Taiwan Strait, the environmental vertical profile at

any given point and time was dictated by a number of

factors, including the depth and advancing speed of the

cold air, and the modification rate (in both temperature

and moisture) from the underlying ocean. Thus, inac-

curate representation or simulation in any of these fac-

tors or processes in the model from reality can alter the

time window in the environment suitable for supercells

and hamper storm evolution, thereby presenting serious

challenges for a successful simulation that agrees with

the observation in almost all aspects.

The averaged environmental wind near 600 hPa

among points B through D in the model is from 2378,

which is about 68 to the left of the observed wind at

Shantou (from 2438; cf. Table 1). This only partially

accounts for the difference in storm propagation direc-

tion. When Figs. 1 and 6 are compared in more detail, it

is found that storm h1 travels more to the right, almost

eastward, during 1900–2200 LST in run 2 when it de-

velops into an isolated supercell (cf. Figs. 5i–l). How-

ever, the tracks of the weaker n1 and stronger c1 over

the Taiwan Strait in run 2, as well as those in run 1 using

a coarser grid, show virtually no difference. Therefore,

it is unlikely that the propagation direction is dictated

by the intensity of the storm in the model. It can only be

hypothesized that the remaining part of the difference

between the observed and modeled propagation direc-

tion is due to a deviation of low-level shear profile in

the model from the real atmosphere, which was by no

means adequately represented over the data-sparse, or

even data-lacking, Taiwan Strait in this case. Thus, if

detailed observations were available and assimilated

into the model, it is quite likely that the overall results

will further improve.

6. Conclusions

The present paper is a follow-up numerical study on

the rare wintertime supercell thunderstorms that oc-

curred during 19–20 December 2002 near Taiwan in a

maritime subtropical environment, which were docu-

mented and studied by Wang et al. (2009). Using the

NU CReSS model at grid spacing of 1.5 (run 1) and

0.5 km (run 2), both simulations successfully reproduced

the three primary storms at correct time and location

with multiple splits as observed, using real terrain and

JMA (20 km) regional analyses as IC/LBC with no

initial perturbation. However, when compared to ob-

servation of the actual event, the model storms travel

about 158–208 too much to the left and the southern

storm diminishes too early over the Taiwan Strait. The

model results are described and used to perform a

vorticity budget analysis on a storm during its transition

to an isolated supercell, and to diagnose on the meso-

scale environment over the strait.

The vorticity budget analysis suggests that the tilting

from horizontal into vertical vorticity is the major

source of midlevel storm rotation, producing positive

(negative) z at the right (left) flanks, while vertical

stretching also strengthens existing z in the lower parts

of updrafts at supercell stage, consistent with previous

studies. As the source of z generation, the horizontal

vorticity (i.e., vertical shear) usually points northward

(westward) [i.e., enhancing westerly (southerly) shear]

at the right (left) flanks, forming a counterclockwise pat-

tern across the updrafts. This pattern is largely attributed


to the combined effect of baroclinic (solenoidal) gen-

eration, tilting of vertical vorticity onto, and rotation of

vortex tubes in the x–y plane. Except for the baroclinic

generation, roles of the other two kinematic effects in

mature storms have not been emphasized recently in the

literature.

Over the Taiwan Strait, the strong surface north-

easterly flow enhanced low-level vertical shear, and

helped the storms evolve into isolated supercells once

they moved offshore in the present case. Through the

diagnosis on storm environment over the strait, it is

shown that the evolution of model storms is quite sen-

sitive to the detailed low-level structure of the post-

frontal environment and the intensity of the storms

themselves. While traveling, storms are sustained only

when CAPE exists and can be released through forced

uplift at the gust front, in addition to the common

conditions of sufficient vertical shear and instability.

The horizontal heterogeneity in mesoscale conditions

over the strait caused the storms to behave differently,

and potentially explains the differences between mod-

eled and observed storms. Furthermore, the fact that

these conditions are dictated by a number of factors not

resolved by the observation (and inadequately repre-

sented in gridded data) suggests that a successful sim-

ulation of supercell storms that agrees with observations

in almost every aspect will likely remain difficult in the

near future, at least in cases over data-lacking oceans

similar to the present one.

Acknowledgments. The authors thank the three anon-

ymous reviewers for their constructive comments that

helped improve the content of this paper. Thanks are also

due to Mr. Joe Harwood for proofreading the manuscript,

Ms. Casey C.-Y. Her for assistance in sounding analysis,

Mr. J.-S. Yang for drafting Fig. 3, and Ms. Y.-W. Huang for

figure editing. This study was supported by the National

Science Council of Taiwan jointly under Grants NSC-96-

2111-M-002-010-MY3, NSC-97-2625-M-002-001, NSC-97-

2111-M-003-005-MY2, and NSC-97-2625-M-003-004.

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