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Westward Generation of Eastward-Moving Tropical Convective Bands in
TOGA COARESHOICHI SHIGE* AND TAKEHIKO SATOMURA
Graduate School of Science, Kyoto University, Kyoto, Japan(Manuscript received 5 July 2000, in final form 15 June 2001)
ABSTRACT
Mechanisms responsible for westward generation of eastward-moving tropical convective bands in the Tropical
Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE) are investigated using a two-dimensional numerical cloud model. Sequential generation of new convective bands to thewest of an old eastward-moving convective band is successfully simulated in an environment of a convectively
active day during TOGA COARE, characterized by west winds at low levels and strong easterlies aloft.
It is concluded that the westward generation of new convective bands is explained by a gravity wave mechanism. Two westward-propagating modes excited below the convective cells moving westward relative to theconvective bands appear to play an important role. A slow-propagating mode (;15 m s 21 ) excited by a shallow
convective band is ducted in the troposphere under an unstable layer of small Richardson number containing
its critical level. A fast-propagating mode (;25 m s 21 ) excited by a deep convective band is ducted in the
troposphere under the remaining region of the convective cell containing its critical level. These two modes
propagate horizontally to the west and promote the growth of shallow convection into long-lived convective
bands. A dry model with thermal forcing representing the convective cell showed that preferential excitation of
westward-propagating waves below the convective cell is due to westward motion and ascension of the convective
cell. A comparative simulation without the critical level confirms the proposed gravity wave mechanism.

1. Introduction
A hierarchy of tropical convective activity over theequatorial western Pacific has been investigated bymany researchers. Nakazawa (1988) found that ‘‘supercloud clusters’’ (SCC) move eastward with a phasespeed of about 10–15 m s 21 , and disturbances propagate
westward with a lifetime of ;2 days within a supercloud cluster during the active phase of intraseasonal
oscillation (ISO; Madden and Julian 1971), using the
3-hourly satellite infrared data. Takayabu (1994) reported the dominance of a quasi-2-day mode in the cloudfield in the December–February season, and identified
this mode with the westward-propagating n 5 1 inertio–
gravity wave theoretically found by Matsuno (1966).
Although Matsuno (1966) found an eastward-propagating n 5 1 inertio–gravity wave as well as a westward-propagating n 5 1 inertio–gravity wave as linear
solutions under the equatorial beta plane approximation,* Current affiliation: Earth Observation Research Center, National
Space Development Agency of Japan, Tokyo, Japan.
Corresponding author address: Dr. Shoichi Shige, Earth Observation Research Center, National Space Development Agency of Japan, Harumi Island Triton Square, Office Tower X, 1-8-10 Harumi,
Chuo-ku, Tokyo, 104-6023, Japan.
E-mail: shige@eorc.nasda.go.jp

q 2001 American Meteorological Society

an eastward-propagating n 5 1 inertio–gravity wave has
never been observed.1 Yoshizaki (1991) analyticallystudied linear responses to localized heating, whichmoves westward or eastward uniformly on the equatorial beta plane. He showed that the westward-propagating inertio–gravity wave is strongly excited by the
westward-moving heating, while the eastward-propagating wave is not so excited by the eastward-moving
heating. He pointed out that this arises from the difference in meridional structure. His results indicated thepossible dominance of the westward-propagating inertio–gravity wave when the clouds are organized andpropagate westward on the equator.
One might infer that mesoscale convective bands
propagate westward owing to easterly trade winds; thus,
they act as the westward-moving heating that excites
the westward-propagating inertio–gravity wave. Lin andJohnson (1996), however, reported that the typical zonal
wind in the convectively active phase of the ISO waswesterly through the lower troposphere during the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE; Webster
and Lukas 1992). LeMone et al. (1998) demonstrated
1
In the equatorial lower stratosphere, the disturbances that likely
correspond to eastward-propagating n 5 1 inertio–gravity waves wereobserved by Wada et al. (1999).

15 DECEMBER 2001

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that, consistent with this, 80% of the convective bands
sampled by the aircraft in TOGA COARE propagate
toward the east. Shipboard radar observations (Rickenbach and Rutledge 1998) also suggested that mostmesoscale convective systems moved eastward with
low-level westerlies. Hence it is difficult for COARE
convective bands to act as the westward-moving heatingthat excites the observed westward-propagating inertio–
gravity waves.
Some case studies reported generation of a new convective band to the west of an old convective band in
TOGA COARE. Mori (1995) observed sequential generation of a new convective band to the west of an old
convective band on 10–12 November during TOGACOARE. Lewis et al. (1998) also reported generationof a new convective band to the west of an old convective band on 20 February 1993. Halverson et al.
(1999) examined a convectively active day, 11 February
1993, in which several convective bands evolved andmoved eastward across the TOGA COARE Intensive
Flux Array (IFA) under westerly wind burst conditions.
They reported that a convective band moved eastward
and a new band formed to its west, with zonal separation
between individual bands of 150–200 km. The westward generation of new convective bands observed byMori (1995), Lewis et al. (1998), and Halverson et al.
(1999) occurred in a group of cloud clusters, which isa part of the 2-day westward-propagating disturbance.
Westward generation of new convective bands possibly
acts as the westward-moving heating that excites thewestward-propagating inertio–gravity waves. Thus,
westward generation of new convective bands is not justan interesting phenomena—it is also expected to play
an important role in the interaction between mesoscaleconvective systems and the 2-day westward-propagating
disturbances.
Recently, researchers have focused on the role ofhigh-frequency tropospheric gravity waves in the hierarchy of tropical convective activity. Oouchi (1999)
simulated SCC-like hierarchical cloud organization under easterlies at low levels, using a two-dimensionalmodel. He demonstrated that high-frequency tropospheric gravity waves play the following key role in the
successive formation of cloud clusters to the east. Inner
convective systems of SCC move westward owing toeasterlies at low levels. Gravity waves excited by theseconvective systems propagate eastward, and contributeto the formation of new clouds to the east where thelow-level atmosphere is moistened by the wind-induced
surface heat and moisture exchange (WISHE; Emanuel1987; Neelin et al. 1987). Lin and Johnson (1996), however, reported that observations during TOGA COARE
do not appear to support the WISHE mechanism. Furthermore, the question of why gravity waves propagating opposite to the direction of the motion of the storm
are preferentially excited by inner convective systemsof SCC was not answered.
Recent studies have investigated gravity waves gen-erated by prescribed heating sources resembling a mesoscale convective system (Nicholls et al. 1991; Mapes
1993; Pandya et al. 1993; Pandya and Durran 1996;
McAnelly et al. 1997). Pandya and Durran (1996) demonstrated that gravity waves forced by the low-frequency component of the latent heating and cooling in
the leading edge determined the mesoscale circulation
around squall lines; the mesoscale circulation includes
an ascending front-to-rear flow, a midlevel rear inflow,
and a mesoscale up- and downdraft in the trailing stratiform region. Pandya and Durran (1996) attributed thepreferential rearward excitation of low-frequency tropospheric gravity waves to the tilt of the forcing.
These low-frequency tropospheric gravity waves havelittle resemblance to monochromatic gravity waves, inthe sense that they do not have a periodic structure intime or space, as pointed out by Mapes (1993). In contrast, high-frequency gravity waves are more nearlymonochromatic. The mechanism for excitation of highfrequency gravity waves should therefore be different
from that of low-frequency gravity waves. Fovell et al.
(1992), using a two-dimensional numerical model, demonstrated that the high-frequency stratospheric gravity
waves propagating upward and opposite to the directionof the motion of the storm are preferentially excited bya mesoscale convective storm. Their simulations
showed that the most important factor for the preferential generation of gravity waves was not the tilt of
the forcing, but the presence or absence of horizontal
propagation in the forcing.
In addition to wave generation mechanisms, wave
propagation characteristics are different. The directionof energy propagation for gravity waves in a resting
atmosphere can be described bycot(a) 5v
ÏN 2 2 v 2(1)(Pandya et al. 2000), where a is the angle of energy
propagation measured from the vertical, N is the Brunt–
Väisälä frequency, and v is the frequency of the wave.
Equation (1) predicts that the low-frequency gravity
waves can propagate for long distances while retaining
significant energy and would be expected to influence
tropospheric circulations. Equation (1) also predicts thatthe high-frequency gravity waves would normally lose
their energy through vertical propagation into the middle
atmosphere. A mechanism for trapping wave energy inthe troposphere is therefore necessary for them to playa role in the westward generation of new convective
bands.
Shige (1999) detected mesoscale disturbances in theequatorial western Pacific lower troposphere having periods of 1–2 h in data from wind profilers with fine time
resolution during TOGA COARE. He estimated a disturbance having a 60-min period and a 6-h duration asa gravity wave. He concluded that this gravity wave was
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westward in a wave duct in the troposphere under strong
easterlies aloft, caused by the mechanism proposed by
Lindzen and Tung (1976). The strong easterlies aloft
are common to the westward regeneration convective
activity cases (see Fig. 2 of Mori 1995; Figs. 5 and 6
of Lewis et al. 1998; Fig. 10 of Halverson et al. 1999),
and they are expected to play an important role for thewave duct.
The role of upper-level wind shear in the organizationof mesoscale convective systems has received less attention than those of low- and midlevel wind shear.
Barnes and Sieckman (1984) described two classes oftropical cloud convective lines over the tropical Atlantic
in the GATE,2 so-called fast- and slow-moving lines.
Fast-moving lines developed with strong low-level
shear and were nearly normal to the low-level shear,
while slow-moving lines developed with weak low-level
shear and were parallel to the shear from ;900 to 500
mb. Similar behavior was reported for tropical cloud
convective lines in EMEX3 by Alexander and Young(1992) and in TOGA COARE by LeMone et al. (1998),
but with slow-moving lines parallel to the midlevel
shear from 800 to 400 mb. Furthermore, LeMone et al.
(1998) reported that with appreciable shear at low- andmidlevels, the low-level shear determined the orientation of the primary convective band, while the midlevel
shear determined whether trailing secondary bands
would be present. Although the classification scheme of
LeMone et al. (1998) allows for a more complex, yetstill ordered, structure observed for convective systems
than previous studies, this classification scheme does
not account for the westward regeneration convective
activity cases.
In the present study, we investigate mechanisms responsible for generation of a new convective band to
the west of an old convective band, using a nonhydrostatic cloud model. We focus on the role of highfrequency tropospheric gravity waves generated by convective cells in the westward generation of new convective bands. The effect of the strong easterlies alofton the westward generation of new convective bands isalso examined.
2. Numerical model and initial conditions

VOLUME 58

FIG. 1. Initial thermodynamic soundings used in model simulations,
showing the vertical profiles of potential temperature u (dashed line),
equivalent potential temperature u e (solid line), and saturated equivalent potential temperature u*e (dotted line).

slip. The surface layer fluxes of heat and water vapor
into the atmosphere were computed with the scheme ofLouis (1979). Bulk moist processes, including the formation and interaction of clouds and precipitating liquid
and ice hydrometers, were employed. The model domain was 950 km in the x direction (horizontal) and 27
km in the z direction (vertical). The horizontal resolution
was 500 m. The vertical resolution was expanded from50 m at the lower boundary to 500 m at the top of thedomain; this varying vertical resolution was chosen to
simulate a shallow cold pool near the lower boundary.
A Rayleigh damping layer having a depth of 10 km wasincluded at the top of the domain to reduce the reflectionof gravity waves from the upper boundary. A radiation
condition (Klemp and Wilhelmson 1978) was used forthe lateral boundaries. The model domain was translated
at a constant speed (13.84 m s 21 ) to keep the simulated
convective systems away from the lateral boundaries.

a. Numerical modelb. Initial conditions

The present study uses a nonhydrostatic cloud model,
the Regional Atmospheric Modeling System (RAMS),
developed at Colorado State University. The computation was carried out under a two-dimensional configuration. The Coriolis terms were neglected. The lower
and upper boundary conditions were flat, rigid, and free-

For all simulations discussed herein, the thermodynamic structure was specified according to the soundingof R/V Vickers at 0600 UTC 11 February 1993 (Fig.
1). The surface temperature was fixed at 302.15 K fromthe Integrated Sounding System (ISS) sea-surface temperature observation of R/V Vickers on 11 February
1993. It was the convectively active day during TOGACOARE examined by Halverson et al. (1999). They
documented that nine convective bands evolved andmoved from the direction of 2558 (toward the east-northeast) across the region of shipboard radar in the TOGA2
GATE: (Global Atmospheric Research Program) Atlantic Tropical
Experiment, conducted in the tropical Atlantic in 1974.
3
EMEX: Equatorial Mesoscale Experiment, conducted north ofAustralia in 1987.

15 DECEMBER 2001

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FIG. 2. Initial wind profiles for the CONTROL case (thick solidline) and NOEAST case (dotted line). The thin solid line indicates
the translation speed of the model domain (13.84 m s 21 ).

COARE IFA. These bands initiated from scattered convection in the western portion of the IFA, and with timethey gradually intensified and grew to large convective
bands before exiting the IFA to the east (see Fig. 4 ofHalverson et al. 1999). The zonal separation between
individual bands was characteristically on the order of
150 km.
We compared two simulations to examine the influence of upper tropospheric winds on the westward generation of new convective bands. The examined horizontal wind profiles are shown in Fig. 2. In the firstcase (CONTROL), the wind profile was specified according to the wind sounding in the storm motion direction of 758 of R/V Vickers at 0600 UTC 11 February
1993. Horizontal winds are westerlies at low to middle
levels and easterlies aloft. Lin and Johnson (1996) reported that this is a typical profile in the convectively
active phase of the ISO. In the other case (NOEAST),
easterlies aloft are artificially reduced.
Convection was initiated by placing a warm thermal(a potential temperature excess of 4 K) having a horizontal width of 20 km and a vertical width of 3.2 km.
This thermal was centered at 550 km from the left
boundary (hereafter x 5 0 km), and z 5 1.6 km. The
initial sounding used here was not moist enough to support the rate of development and strength of the observed convection. The above strong thermal was therefore used. It should be noted that the numerically simulated features did not vary qualitatively if the potential
temperature excess is 2 K.
3. Results
A time-zonal cross section of the mixing ratio of rain
at z 5 23.9 m in the CONTROL case is shown in Fig.

3727

3. The thin line in this figure indicates 0 m s 21 relative
to the ground. The primary band near x 5 0 km wasinitialized by the thermal bubble. Figure 3 clearly shows
an asymmetry of precipitating clouds between the primary band’s western and eastern sides. On the westernside of the primary band, precipitating clouds became
organized into long-lived bands B2 and B3. New bands
sequentially developed to the west of old bands. Longlived band B2 developed to the west of short-lived band
B1, then long-lived band B3 developed to the west ofband B2. In contrast, none of the small precipitating
clouds become organized into long-lived bands on theeastern side.
The overall structures of the primary band’s westernand eastern sides are illustrated in Figs. 4a–c and 4d–f. These figures show vertical cross sections of the vertical velocity field superposed on the cloud outline. The
cloud outline, defined as the region in which the mixing
ratio of condensates exceeds 0.1 g kg 21 , is shown by abold line. It is clear from Fig. 4 that there are differencesin the horizontal scale and height of clouds between thewestern side and eastern side. The western side clearly
exhibits sequential growth of shallow convection into
deep convection to the west of old bands. At t 5 330
min, the heights of short-lived band B1 and earlier B2
were about 10 km (Fig. 4a). Short-lived band B1 dissipated without growing into a large and deep convective system. After band B1 dissipated, band B2 became
organized into a large, long-lived system, and its height
reached about 14 km (Fig. 4b). After band B2 decayed
in intensity, band B3 became organized into a large,
long-lived system, and its height reached about 14 km(Fig. 4c). On the eastern side, however, small clouds
were not organized on the mesoscale and their heights
were less than 10 km (Figs. 4d–f).
Shipboard radar data collected during TOGA COARE
provided evidence of abundant populations of midlevel
cumulus congestus clouds in addition to the well-known
large populations of shallow cumulus clouds, and deep
cumulonimbus clouds in the tropics (DeMott and Rutledge 1998; Johnson et al. 1999). Although the cumulus
congestus clouds with tops between 4.5 and 9.5 km do
not produce heavy rain as the deep cumulonimbus
clouds with tops near the tropopause, congestus are themost abundant of all precipitating clouds in TOGACOARE. Short-lived band B1, earlier B2, and earlier
B3 on the western side, and all precipitating clouds onthe eastern side can be classified into cumulus congestus
clouds, while later B2 and later B3 can be classified as
deep cumulonimbus counterparts. Johnson et al. (1999)
pointed out that restriction of growth of congestus
clouds to just above the 08C level limits further enhancement of cloud buoyancy through glaciation.
We now focus on why cumulus congestus clouds cangrow into deep, long-lived convective bands only on
the western side. A possible explanation for the asymmetry of precipitating clouds between the western andeastern sides lies in the difference of surface thermo-

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FIG. 3. Time-zonal cross section of mixing ratio of rain (g kg 21 ) at z 5 23.9 m in the CONTROL case. The degree of shading denotes
the range of mixing ratio of rain, as indicated by the value bar at the bottom of the figure. The rectangle indicates the region that is expanded
in Fig. 5. The thin line indicates 0 m s 21 relative to the ground. B1, B2, and B3 indicate precipitating bands.

dynamic conditions between the western and easternsides due to an effect similar to WISHE (Emanuel 1987;
Neelin et al. 1987). In order to examine the influenceof the WISHE-like effect on the asymmetry of clouds
between the western and eastern sides, we performed
an additional simulation (NOWISHE). This simulationis the same as the CONTROL case except that the surface heat and moisture fluxes are calculated using a
constant surface wind of 8.4 m s 21 , which is the averaged wind speed on the western side at t 5 240 min
in the CONTROL case. Precipitating clouds on the western side are still stronger than those on the eastern side
as in the CONTROL case (not shown). Thus, the asymmetry of clouds between the western and eastern sides
is not due to the WISHE-like effect.
An expanded view of the rectangle in Fig. 3 is illustrated in Fig. 5, which shows the time-zonal cross section of vertical velocity at z 5 6.675 km and the mixing
ratio of rain at z 5 23.9 m. It is clear from Fig. 5 thatthe wave activity generated by the convective bands isbiased to the western side. Disturbance D1 propagates
westward from the band B1 and promotes the development of the band B2. Disturbance D3 then propagates
westward from band B2 and promotes the developmentof band B3. Disturbance D1 has a horizontal wavelength
L x 5 12 to 14 km and horizontal phase speed c x 5 215

to 216 m s 21 relative to the ground, while disturbanceD3 has L x 5 20 to 21 km and c x 5 224 to 227 m s 21 .
Additionally, disturbance D2 has a phase speed similar
to that of disturbance D1, and disturbance D4 has aphase speed similar to that of disturbance D3, as shownin Fig. 5. These results suggest that slow-propagatingwaves (D1 and D2) are excited by shallower bands (B1and earlier B2), and fast-propagating waves (D3 andD4) by deeper bands (later B2 and later B3). Once they
have excited waves, these bands decay in intensity.
Figure 6 is the same as in Fig. 5 but for potential
temperature and rain mixing ratio at z 5 23.9 m in the
CONTROL case. The cold pool spreading rearwardfrom the primary band initialized by the thermal bubble
is responsible for the initiation of band B1. Moncrieffand Liu (1999) showed that when the shear and surface
flow vectors are in the same direction, lifting is generated in the upstream-propagating currents. This is thecase here because the westerly shear at low levels andsurface westerly can be seen in Fig. 2. However, thecold pool spreading rearward from the primary band
was very shallow (about 500 m thick) and therefore, thespeed was very slow. It should be noted that the westernedge of the cold pool spreading from the primary bandpropagates eastward relative to the ground at a speedof 2 m s 21 . These characteristics of the simulated cold

15 DECEMBER 2001

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3729

FIG. 4. Contours of vertical velocity (contour interval 1.0 m s 21 ) and cloud outline (bold line) defined as the region in which the mixing
ratio of condensates exceeds 0.1 g kg 21 ; for (a)–(c) the western side and (d)–(f ) the eastern side in the CONTROL case at t 5 330, 380,
and 430 min. Positive (negative) values are solid (dashed). Updrafts greater than 1.0 m s 21 are heavily shaded, and downdrafts less than
21.0 m s 21 are lightly shaded.

pool agree with the observation over the western Pacificocean (Parsons et al. 1994). Thus, the cold pool spreading rearward from the primary band could not develop
deep bands, or it does not account for westward generation speed of new convective bands. In fact, it isclear from Fig. 6 that the cold pool spreading rearwardfrom the primary band is not responsible for the development of long-lived band B2. The initiations of convection are not always attributed to the cold pool, anddiffer from case to case. For example, disturbance D2
appears to contribute to the initiation of band B3 (Fig.
5).
The time sequence of westward-propagating disturbance D3 with a time interval of 6 min is illustrated inFig. 7, which shows vertical cross sections of the verticalvelocity field superposed on the cloud outline. Convective band B2 at x 5 2240 km propagated eastward by
discrete growth of new convective cells at the leadingedge of the gust front. An old convective cell denotedby ‘‘C’’ separated from the leading edge of band B2 at
x 5 2240 km and moved westward relative to band
B2, as shown in Figs. 7a,b. This behavior is typical of
multicell storms and has been simulated by previous
modeling studies (Rotunno et al. 1988; Fovell and Ogura
1988; Tao and Simpson 1989; Lafore and Moncrieff
1989; and many others). From model outputs at 2-minintervals (not shown), we see that cell C ascended withwestward acceleration. Westward-propagating disturbance D3 of upward motion is produced below cell C.
Figure 8 shows the vertical velocity fields superimposed in potential temperature fields. The cold pool extends from the leading edge of the band B2 at x 5 2240
km to x 5 2280 km and does not pass under the shallow
convection at x 5 2305 km (Fig. 8f). Thus, the cold
pool of band B2 does not promote the growth of shallow
convection into a long-lived convective band B3 at x 52305 km, as mentioned earlier. Cell C dissipates nearz 5 14.5 km until t 5 390 min (Fig. 8c), since its closed
contour region of high potential temperature has disappeared. The level where cell C dissipated roughly
corresponds to the equilibrium level where the equivalent potential temperature of the parcel ascending fromthe surface crosses the environmental potential temperature (Fig. 1). The contours of potential temperature in
Figs. 8c–e clearly show that the unstable region denotedby R remains after cell C has dissipated. Remaining
region R moves near z 5 14.5 km with a speed of about
221 m s 21 relative to the ground. Since this speed
roughly corresponds to the mean horizontal wind nearz 5 14.5 km, remaining region R is considered to bepassively advected by the mean horizontal wind. Even
though cell C has dissipated, disturbance D3 propagates

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FIG. 5. Time-zonal cross section of vertical velocity (m s 21 ) at z 5 6.675 km and rain mixing ratio (g kg 21 ) at z 5 23.9 m in the CONTROL
case illustrating an expanded view of the rectangle in Fig. 3. The degree of shading denotes the range of vertical velocities, as indicated by
the value bar at the bottom of the figure. The heavy (light) solid lines indicate the region in which the rain mixing ratio exceeds 0.3 g kg 21(0.05 g kg 21 ). The thick dashed lines indicate 0, 215, and 225 m s 21 relative to the ground. D1, D2, D3 and ‘‘D4’’ indicate westwardpropagating disturbances.

horizontally with remaining region R. Its upward motion
then promotes the growth of shallow convection into
long-lived convective band B3 at x 5 2305 km (Figs.
7e and 7f).
Figure 9 shows the vertical cross section of windvectors superimposed on temperature perturbation at t
5 390 min just after the dissipation of cell C. The windvectors and temperature perturbation were extracted byusing a bandpass filter with cutoff horizontal wavelengths of 10 and 30 km. In this figure, the antinodeand node of vertical velocity are clearly seen at z 5 6
and 10 km. Maximum (minimum) in temperature perturbations is centered one-quarter wavelength ahead of(i.e., to the left of ) the updraft (the downdraft) at z 5
6 km. In addition, the updraft is located one-quarter
wavelength behind a maxima in horizontal wind perturbations below and a minimum in horizontal wind
perturbations above. A vertically standing structure withthe above quadrature relationship indicates that disturbance D3 is a ducted gravity wave, and thus could reachshallow convection at x 5 2305 km without propagating into the middle atmosphere. The vertical wave
length is calculated as about 16 km.
The wave parameters for disturbance D3 can beroughly estimated from the linear dispersion relation forinternal gravity waves under the Boussinesq approximation as
m2 5

N2
d 2 U/dz 2
2
2 k2(U 2 cx ) 2
U 2 cx(2)where m (52p/L z ) is the vertical wave number, k (52p/
L x ) the horizontal wave number, and U the backgroundwind speed. The vertical profiles of the horizontal wind
relative to the ground U (m s 21 ) and the square of theBrunt–Väisälä frequency N 2 (s 22 ) averaged from x 52300 km to x 5 2260 km at t 5 360 min before thepassages of disturbance D3 are shown in Fig. 10. The
Brunt–Väisälä frequency is calculated for saturated fair,
following Durran and Klemp [1982, see their Eq. (36)].
From the soundings shown in Fig. 10, N 2 (9.9 3 10 25
s 22 ), U (22.9 m s 21 ) and d 2 U/dz 2 (29.2 3 10 28 m 21
s 21 ) are obtained by averaging from z 5 2.0 km to z
5 14.5 km. For a horizontal phase speed c x 5 224 to
227 m s 21 and a horizontal wavelength L x 5 20 to 21
km, vertical wavelength L z is calculated from (2) as 18
to 22 km, in fair accord with the result from Fig. 9. This
result confirms that westward-propagating disturbance15 DECEMBER 2001

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FIG. 6. As in Fig. 5 but for potential temperature (K) and rain mixing ratio (g kg 21 ) at z 5 23.9 m in the CONTROL case. The degreeof shading denotes the range of potential temperature, as indicated by the value bar at the bottom of the figure. The heavy (light) solid lines
indicate the region in which the rain mixing ratio exceeds 0.3 g kg 21 (0.05 g kg 21 ). The thick dashed lines indicate 0 and 12 m s 21 relative
to the ground.

D3 is a gravity wave. The increasing rate of easterly
wind shear (2d 2 U/dz 2 ) used for calculating the vertical
wavelength is possibly underestimated by averaging
from z 5 2.0 km to z 5 14.5 km, so the calculated
vertical wavelength may be overestimated. In the sameway for the disturbance D3, vertical wavelength L z of
disturbance D1 is calculated as 11 to 12 km, in fairaccord with the estimated value of 12 km from the vertical cross section (not shown).
4. Discussions
a. Wave excitation below the convective cell
Fovell et al. (1992), using a two-dimensional numerical model, demonstrated that the high-frequency
stratospheric gravity waves propagating upward and opposite to the direction of the motion of the storm are
preferentially excited by a mesoscale convective storm.
They attributed the preferential excitation of rearwardpropagating waves to the rearward storm-relative motion of convective cells. Although the preferential excitation of the westward-propagating waves in CONTROL is similar to that in Fovell et al. (1992), the waves
in CONTROL propagate below the convective cells incontrast to the waves in Fovell et al. (1992) propagating
upward.
To investigate preferential excitation mechanisms ofwestward-propagating waves below the convective cell,
we conducted a series of simulations in which gravity
waves are excited by thermal forcing (‘‘DRY’’). The
model is the same as that used in the CONTROL case
except for a constant vertical resolution of 500 m andexclusions of cloud microphysics and the model-domaintranslation. The static stability profile has a constant
Brunt–Väisälä frequency N (50.01 s 21 ). The horizontal
wind profile examined in the DRY0 and DRY1 cases
is shown in Fig. 11. The wind speed is set to 0 m s 21
below z 5 5 km and easterly shear of 4 m s 21 per 1
km above z 5 5 km, which is a simplified wind profilein the CONTROL case. In the DRY2 case, the windspeed is set to 0 m s 21 in the whole domain. The thermal
forcing function is given as
Q(x, z, t) 5 Q 0
31[1 1 (x 2 x 0 ) /a 1 (z 2 z 0 ) 2 /a 2 ] 3/22

2

1 2 cos(2p t/T )
,
2

(3)

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FIG. 7. Time sequence of vertical cross sections of vertical velocity (contour interval 1.0 m s 21 ) superposed on cloud outline (bold line),
defined as the region in which the mixing ratio of condensates exceeds 0.1 g kg 21 , for the CONTROL case. Positive (negative) values are
solid (dashed). Updraft greater than 1.0 m s 21 is heavily shaded, and downdraft less than 21.0 m s 21 is lightly shaded. C indicates an old
convective cell separating from the leading edge of band B2 at x 5 2240 km.

where the magnitude of the thermal forcing Q 0 5 1 J
kg 21 , the half-width a 5 1 km, T 5 10 min,


[

]

H
1 2 cos 1 2 1 x DRY0

dz p
2T
x 5
(4)
Ut1x
DRY1
x
DRY2
0

dU 2T



c

pt

s

s

 s

and


12T 2 1 z DRY0
pt


 1 2
H sin

z 0 5 z c

H sin



s

DRY1

(5)

pt
1 z s DRY2.
2T

Here dU/dz 5 24 3 10 23 s 21 , x s 5 0 km, z s 5 5 km,
H 5 10 km, z c 5 10 km, and U c 5 220 m s 21 .
In DRY0, the source function has the form of anascending and westward-accelerated thermal restricted
to a small region in space centered at (x 0 , z 0 ). The horizontal velocity of the ascending thermal is the same asthat of the wind at z 0 (t). This form of source function
approximates the characteristics of the convective cell

separating from the leading edge of a multicell storm;
it ascends with westward acceleration and then dissipates. The DRY1 and DRY2 cases are conducted to
examine the role of westward motion and ascending of
the forcing in the preferential generation of the westward-propagating wave below the cell. In DRY1, thethermal forcing is fixed at a constant height, but it moves
westward. In DRY2, the thermal forcing is fixed in thex direction, but it ascends until z 5 15 km the same as
in DRY0.
The vertical velocity at t 5 10 min in the DRY0 caseis shown in Fig. 12b. A strong updraft is seen at x 5
213 km and z 5 13 km. Below this strong updraft,
upward motion is produced upstream relative to the thermal forcing (to the west). This pattern of updraft issimilar to that in the CONTROL case (Fig. 12a).
Figures 12c and 12d show the vertical velocity at t
5 10 min in DRY1 and DRY2, respectively. In DRY1,
the disturbances with upward motion are produced upstream both below and above the forcing. These disturbances in DRY1 propagate westward relative to theground. In DRY2, upward motion below the forcing ispreferentially generated. The response in DRY2 is, however, symmetric about the forcing. These results suggestthat two factors contribute to preferential generation of
westward-propagating waves below the cell (forcing) in15 DECEMBER 2001

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FIG. 8. As in Fig. 7 but for vertical velocities and potential temperature (contour interval 5 K). Updraft greater than 1.0 m s 21 is heavily
shaded, and downdraft less than 21.0 m s 21 is lightly shaded. R indicates the remaining unstable region of cell C.

CONTROL and DRY0: westward motion of the cell
excites westward-propagating waves, and ascension of
the cell excites waves below the cell.
Generally, the phase of the wave locks onto the motion of the forcing in a steady state. Thus waves excitedby a westward-moving source naturally propagate westward. Lin and Li (1988), investigating the steady re-sponse of the atmosphere to an elevated stationary heatsource, showed that the wave energy propagates downward and upstream relative to the air in an unbounded
steady shear flow, but is advected downstream by thebasic flow. The wave activity is thus found downstream
relative to the source, which is similar to the mountainwave. In contrast to Lin and Li (1988), the wave activity

FIG. 9. Vertical cross section of wind vectors and temperature perturbation (contour interval 0.5 K) at t 5 390 min for the CONTROL
case. Rightward and upward unit vectors show horizontal wind (u9) and vertical velocity (w9) perturbations of 1.0 m s 21 , respectively.
Temperature perturbations greater than 0.5 K (less than 20.5 K) are heavily (lightly) shaded. The wind vectors and temperature perturbation
are extracted by using a bandpass filter with cutoff horizontal wavelengths of 10 and 30 km.

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FIG. 11. Initial wind profile for DRY0 and DRY1.

FIG. 10. (left) Vertical profiles of horizontal wind relative to theground and (right) square of the Brunt–Väisälä frequency averaged
from x 5 2300 km to x 5 2260 km at t 5 360 min for the CONTROL
case. The thin vertical line in the left panel indicates U 5 225 m
s 21 .

is found upstream relative to the source in CONTROL
and DRY0. Studies on the transient response of the atmosphere to a spatially and temporally localized heatsource showed that, when the intensity of the heat source
decays, upward motion develops in the adjacent region
and propagates outward as a gravity wave (e.g., Nicholls
et al. 1991; Shige and Satomura 2000); therefore, thephase of the disturbance does not lock onto the source.
Since the intensity of the heat source in CONTROL and

FIG. 12. (a) As in Fig. 7 but for t 5 386 min in CONTROL. Vertical cross section of vertical velocity (contour interval 0.01 m s 21 ) in(b) DRY0, (c) DRY1, and (d) DRY2. Positive (negative) values are solid (dashed). Updraft greater than 0.01 m s 21 is heavily shaded, anddowndraft less than 20.01 m s 21 is lightly shaded.

15 DECEMBER 2001

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3735

and DRY0, the wave activity was, therefore, found below the source.
The dominant horizontal phase speeds of excitedwaves near their source region deeply depend on themoving speed of their source. Waves of fast (slow) horizontal phase speed are excited by a fast (slow) moving
source. In deeper bands (later B2 and later B3; Figs. 4band c), convective cells ascend higher and are accelerated by stronger easterlies; thus they generate fastpropagating waves (D3 and D4; Fig. 5). In shallower
bands (B1 and earlier B2; Fig. 4a), convective cells
ascend lower and are accelerated by weaker easterlies;
thus they generate slow-propagating waves (D1 and D2;
Fig. 5).
b. Wave duct

FIG. 13. Vertical profiles of the Richardson number Ri averaged(a) from x 5 2240 km to x 5 2200 km at t 5 300 min before thepassage of disturbance D1 and (b) from x 5 2300 km to x 5 2260
km at t 5 360 min before the passage of disturbance D3 for the
CONTROL case. The thin lines indicate the levels of the mean windspeed of (a) 215 m s 21 and (b) 225 m s 21 . The dotted lines indicate
the Richardson number value of 0.25.

DRY0 decayed, the wave energy could propagate upstream relative to the source as a transient response to
the decaying source.
In contrast, for an ascending source, the phases of theexcited waves propagate upward. The vertical groupvelocity has a sign opposite to the vertical phase speed.
Thus, for an ascending source, waves with upward phasepropagation should be observed below the source because their energy propagates downward. In CONTROL

Lindzen and Tung (1976) proposed four conditions
necessary for a duct in which gravity waves are trapped:
1) a statically stable duct layer, in which gravity waves
could propagate, is adjacent to the ground; 2) the duct
is deeper than one quarter of the vertical wavelength of
the gravity waves; 3) the duct is topped by an unstablelayer of Richardson number Ri[5N 2 /(dU/dz) 2 ] , 0.25;
and 4) the unstable layer contains a critical level where
the mean wind speed is equal to, or nearly equal to, theground-relative phase speed of the gravity wave.
As shown in Fig. 10, the mean profile of N 2 below
z 5 10 km is favorable for wave propagation. The vertical profile of Richardson number Ri averaged from x
5 2240 km to x 5 2200 km at t 5 300 min before
the passage of disturbance D1 is shown in Fig. 13a. The
critical level at z 5 12.3 km where the mean wind speed(215 m s 21 ) is nearly equal to the phase speed of disturbance D1 (215 to 216 m s 21 ) is illustrated by thehorizontal thin line in Fig. 13. Although the layer containing the critical level has Ri . 0.25, the Richardson
number is small (about 0.5). Disturbance D1 is consid-

FIG. 14. As in Fig. 9 but for regions having Ri , 0.25 (contour) superposed on vertical velocity field at t 5 390 min for the CONTROL
case. A bold line indicates the critical levels where the horizontal wind (225 m s 21 ) is nearly equal to the phase speed of disturbance D3(224 to 227 m s 21 ). Updrafts greater than 1.0 m s 21 are heavily shaded, and downdrafts less than 21.0 m s 21 are lightly shaded.

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FIG. 15. As in Fig. 3 but for the NOEAST case. The rectangle indicates the region that is expanded in Fig. 16. S indicates a precipitating
band.

ered to be trapped in the troposphere because the ducting
conditions proposed by Lindzen and Tung (1976) areroughly satisfied.
The vertical profile of the Richardson number averaged from x 5 2300 km to x 5 2260 km at t 5 360
min before the passage of disturbance D3 is shown in
Fig. 13b. The critical level at z 5 14.5 km where themean wind speed (225 m s 21 ) is nearly equal to thephase speed of disturbance D3 (224 to 227 m s 21 ) is
illustrated by the horizontal thin line in Fig. 13b. It isclear from this figure that the layer containing the criticallevel has a large Richardson number (about 3.0). According to Booker and Bretherton’s theory (1967),
waves should be absorbed by the critical level for alarge Richardson number flow.
Figure 14 shows the regions having Ri , 0.25 superposed on the vertical velocity field at t 5 390 min
just after the dissipation of cell C. A local region having
Ri , 0.25 at x 5 2280 to 2275 km just above disturbance D3 is noticed around the critical levels where
the horizontal wind (225 m s 21 ) is nearly equal to thephase speed of the disturbance D3 in Fig. 14. This region
with Ri , 0.25 is remaining region R (Fig. 8c) of convective cell C that excited disturbance D3 and dissipatednear z 5 14.5 km. Remaining region R is passively
advected by the mean flow near the equilibrium level(z 5 14.5 km). Thus, disturbance D3, with a horizontal

phase speed that happens to match the mean flow near
the equilibrium level, is trapped in the troposphere owing to remaining region R because the ducting conditions proposed by Lindzen and Tung (1976) are locallysatisfied. Lindzen (1988) noted that, for the reflectionof a wave, the wave must tunnel through the layer of
Ri , 0.25 to reach the critical level, thus the layer of
Ri , 0.25 must not be too deep. Therefore, the shallowness of remaining region R is rather favorable forthe trapping and reflection of the wave.
For the slow-propagating waves generated by theshallow bands (B1 and earlier B2) whose heights areless than 12 km, waves (D1 and D2) having their criticallevels within the small Richardson number layer at z 5
12 km are ducted. The ducting situation of the slowpropagating mode is similar to that in Shige (1999). On
the other hand, for fast-propagating waves (D3 and D4)
generated by the deep bands (later B2 and B3) whose
heights exceed than 12 km, waves (D3 and D4) having
their critical levels within the remaining region of convective cells are ducted.
c. Effect of strong easterlies aloft
In order to examine the effect of the strong easterlies
aloft on the westward generation of new convective
bands, we performed an experiment with a wind profile15 DECEMBER 2001

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3737

FIG. 16. As in Fig. 5 but for the NOEAST case, illustrating an expanded view of the rectangle in Fig. 15. The thick dashed line indicates
210 m s 21 relative to the ground. E indicates a westward-propagating disturbance.

in which easterlies aloft are reduced (NOEAST). The
initial wind profile used in the NOEAST case is shown
Fig. 2. The wind speed in the NOEAST case is 0 m s 21
relative to the ground above z 5 11 km. Figure 15 showsa time-zonal section of the mixing ratio of rain at z 5
23.9 m in the NOEAST case. Discrete generation of
new convective bands to the west of an old convective
band is much weaker than the CONTROL case.
An expanded view of the rectangle in Fig. 15 is illustrated in Fig. 16, which shows a time-zonal crosssection of vertical velocity at z 5 6.675 km and mixing
ratio of rain at z 5 23.9 m. Band S remained nearly

FIG. 17. Peak vertical velocities associated with disturbances D1(dotted), D3 (dashed), and E (solid). The horizontal axis indicatesthe horizontal distance from the leading edge of the bands that excitedwaves.

stationary at x 5 2180 km in the moving frame. The
time-zonal cross section of potential temperature (notshown) indicates that band S was initiated by the cold
pool spreading rearward from the primary band initiatedby the thermal bubble, the same as band B1 in the CONTROL case. Band S was also a short-lived band, confirming that the cold pool spreading rearward from theprimary band cannot develop long-lived bands. Westward-propagating disturbance E has horizontal phasespeed c x 5 29 to 210 m s 21 relative to the ground,and horizontal wavelength L x 5 11 to 12 km. The vertical wave length is calculated as 8 to 9 km. Disturbance
E does not promote the development of convection to
the west of band S.
Figure 17 shows the peak vertical velocities associated with disturbances D1, D3, and E. Vertical velocities
for disturbances D1, D2, and E were extracted by using
bandpass filters with cutoff horizontal wavelengths of
10 and 30 km (D1), 6 and 18 km (D2), and 5 and 15
km (E). Disturbances D1 and D3 still have peak verticalvelocities exceeding 1.0 m s 21 even after they propagate
horizontally about 60 km from the bands that excitedthem. In contrast, the peak vertical velocity of disturbance E is less than 1.0 m s 21 when it propagates about
60 km from the band that excited it. Thus, even if ashallow convection exists to the west of band S, dis-

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VOLUME 58

erlies (Lin and Johnson 1996). Murakami and Wang
(1993), using 10 years of data for outgoing long radiation (OLR) and 8 years of data for 200-mb winds,
showed that easterlies in the equatorial upper troposphere are strongest above the convective center overthe maritime continent (1008–1508E). Their results indicate that the climatic wind profile in this area favors
the trapping of westward-propagating gravity waves inthe troposphere. Thus, we consider that westward generation of new convective bands by ducted gravity
waves occurs in convectively active regions over theequatorial western Pacific.
5. Summary and concluding remarks

FIG. 18. (left) Vertical profiles of horizontal wind relative to theground and (right) Richardson number Ri averaged from x 5 2250
km to x 5 2210 km at t 5 270 min for the NOEAST case. The thin
vertical line in the left panel indicates U 5 210 m s 21 . The dottedlines indicates Ri 5 0.25.

turbance E cannot promote its growth to a long-lived
band.
The vertical profile of horizontal wind speed relative
to the ground U (m s 21 ) and Richardson number Ri
averaged from x 5 2250 km to x 5 2210 km at t 5
270 min before the passages of disturbance E are shownin Fig. 18. There are no critical levels of disturbance E,
although there is a relatively small Richardson number
layer at z 5 10 km. Thus disturbance E is not trapped
and loses its energy. These results confirm that strong
easterlies are very important for discrete generation ofa new convective band to the west of an old convective
band in the CONTROL case.
As mentioned in the Introduction, Mori (1995) andLewis et al. (1998) also reported generation of a newconvective band to the west of an old convective bandin TOGA COARE. The wind profile characterized bywest winds at low levels and strong easterlies aloft (;20m s 21 ) is common to these cases (see Fig. 2 of Mori
1995, and Figs. 5 and 6 of Lewis et al. 1998). The strong
easterlies are likely to match the phase speeds of the
westward-propagating gravity waves generated by eastward-moving convective bands. Thus, these cases arealso possibly explained by the convectively generated
gravity wave mechanism proposed in this paper.
The typical zonal wind in the convectively active
phase of the ISO during TOGA COARE was characterized by strong easterlies aloft with low-level west-

Mechanisms responsible for westward generation of
eastward-moving tropical convective bands over theequatorial western Pacific were investigated using a numerical cloud model. A simulation was initialized withthe sounding of R/V Vickers on 11 February 1993 during TOGA COARE, with west winds at low levels andeasterlies aloft. It was a convectively active day on
which discrete generation of a new convective band to
the west of an eastward-moving convective band wasobserved (Halverson et al. 1999).
In this paper, the westward generation of new convective bands was explained by a gravity wave mechanism. Two westward-propagating modes excited below
cells moving rearward relative to eastward-moving convective bands appeared to play an important role. A
slow-propagating mode (;15 m s 21 ) was ducted in the
troposphere owing to an unstable layer of small Richardson number containing its critical level (Fig. 19a).
The slow-propagating mode was excited by the cell ina shallow convective band whose height was less thanthe unstable layer. A fast-propagating mode (;25 m s 21 )was excited by the cell in a deep convective band whose
height exceeded than the unstable layer (Fig. 19b). The
fast-propagating mode was ducted in the troposphereowing to the remaining region of the cell containing its
critical level (Fig. 19c). These two modes thus propagated horizontally with no significant energy leak into
the stratosphere and promoted the growth of shallow
convections into long-lived convective bands.
In order to investigate preferential excitation mechanisms of westward-propagating waves below the cell(Fig. 19b), we conducted a series of simulations inwhich gravity waves were excited by a thermal forcing
representing the cell (‘‘DRY’’). These simulations
showed that preferential excitation of westward-propagating waves was due to westward motion of the cell,while that of waves below the cell was due to ascensionof the cell.
A comparative simulation (NOEAST) showed that a
new convective band was not generated to the west ofan old convective band when the critical level was removed. This result confirms strong easterlies are very

15 DECEMBER 2001

SHIGE AND SATOMURA

FIG. 19. A schematic model for generation of a new convective
band to the west of an old convective band in a moving frame. Solidarrows indicate upward motion. Bold lines indicate cold pool outlines.
The regions of small Richardson number (,.0.25) are shaded. (a)A slow-propagating mode, which has its critical level within the small
Ri layer, propagates horizontally and promotes the growth of shallow
convection to a long-lived convective band. (b) A fast-propagating
mode is excited below an old convective cell in a deep convective
band whose height is higher than the small Ri layer. (c) The fastpropagating mode, which has its critical level within the remaining
region of the cell, propagates horizontally and promotes the growthof shallow convection into a long-lived convective band.

important for discrete generation of a new convective
band to the west of an old convective band.
Acknowledgments. Discussions with Mr. Noriyuki Nishi and Dr. Toru Terao, and comments by Dr. Takeshi
Horinouchi, are greatly appreciated. We thank Drs.
George N. Kiladis and Mitchell W. Moncrieff and an
anonymous reviewer for their helpful reviews of thismanuscript, and Drs. Timothy J. Dunkerton and Kazuyoshi Oouchi for additional comments. The simulations were made using the Regional Atmospheric Modeling System (RAMS) developed at Colorado State University. GFD-DENNOU was utilized for graphics. This
work was supported by a research fellowship from theJapan Society for the Promotion of Science for Young
Scientists (SS).
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