structure and origin of the quasi-biweekly oscillation
TRANSCRIPT
Structure and Origin of the Quasi-Biweekly Oscillation over the Tropical IndianOcean in Boreal Spring
MIN WEN
State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China
TIM LI
Department of Meteorology, and IPRC, University of Hawaii at Manoa, Honolulu, Hawaii
RENHE ZHANG AND YANJUN QI
State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China
(Manuscript received 10 February 2009, in final form 12 August 2009)
ABSTRACT
The structure and evolution features of the quasi-biweekly (10–20 day) oscillation (QBWO) in boreal
spring over the tropical Indian Ocean (IO) are investigated using 27-yr daily outgoing longwave radiation
(OLR) and the National Centers for Environment Prediction–National Center for Atmospheric Research
(NCEP–NCAR) reanalysis data. It is found that a convective disturbance is initiated over the western IO and
moves slowly eastward. After passing the central IO, it abruptly jumps into the eastern IO. Meanwhile, the
preexisting suppressed convective anomaly in the eastern IO moves poleward in the form of double-cell
Rossby gyres. The analysis of vertical circulation shows that a few days prior to the onset of local convection in
the eastern equatorial IO an ascending motion appears in the boundary layer.
Based on the diagnosis of the zonal momentum equation, a possible boundary layer–triggering mechanism
over the eastern equatorial IO is proposed. The cause of the boundary layer convergence and vertical
motion is attributed to the free-atmospheric divergence in association with the development of the baro-
tropic wind. It is the downward transport of the background mean easterly momentum by perturbation
vertical motion during the suppressed convective phase of the QBWO that leads to the generation of a
barotropic easterly—the latter of which further causes the free-atmospheric divergence and, thus, the
boundary layer convergence. The result suggests that the local process, rather than the eastward propagation
of the disturbance from the western IO, is essential for the phase transition of the QBWO convection over
the eastern equatorial IO.
1. Introduction
Atmospheric subseasonal oscillations contain two well-
separated bands with 10–20- and 30–60-day periods, re-
spectively (Chen and Chen 1993; Fukutomi and Yasunari
1999; Annamalai and Slingo 2001; Li and Wang 2005;
Goswami 2005; Li and Zhou 2009). The 30–60-day os-
cillation was first discovered by Madden and Julian (1971,
1972). A major feature of the Madden–Julian oscillation
(MJO) is the eastward propagation along the equator.
The later studies further documented that in addition
to the eastward propagation, the tropical intraseasonal
(30–60 day) oscillation (ISO) also has a distinctive north-
ward propagation in the monsoon region (Yasunari
1979) and a westward propagation off the equatorial
region (Wang and Rui 1990) in boreal summer. In the
present work, we use the term MJO to represent the
general 30–60-day mode of ISO over the tropical region.
The 10–20-day oscillation in the tropics was reported
by several previous studies (e.g., Wallace and Chang
1969; Nitta 1970; Chang et al. 1970; Yanai and Murakami
1970; Murakami 1971). It was referred to as the quasi-
biweekly oscillation (QBWO) by Murakami (1976) and
Krishnamurti and Bhalme (1976), who pointed out the
remarkable QBWOs that exist in the entire monsoon
Corresponding author address: Min Wen, Chinese Academy of
Meteorological Sciences, 46 Zhong-Guan-Cun South Ave., Hai-
dian District, Beijing 100081, China.
E-mail: [email protected]
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DOI: 10.1175/2009JAS3105.1
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region. This oscillation was found to be closely related to
the active and break phases of the summer monsoon
(Yasunari 1979; Krishnamurti and Ardanuy 1980; Chen
and Chen 1993; Zhou and Chan 2005, etc.).
While the MJO exhibits a zonal wavenumber-1 struc-
ture, the QBWO is generally around zonal wavenumber
6 in boreal summer or winter (Kiladis and Wheeler 1995;
Annamalai and Slingo 2001). For the vertical structure,
the MJO has the first baroclinic mode structure, with
a node at about 500 hPa. In contrast, the QBWO ex-
hibits an equivalent barotropic structure, extending
from the lower to the upper troposphere with a reversed
phase near 100 hPa (Chen and Chen 1993; Kiladis and
Wheeler 1995; Annamalai and Slingo 2001; Chatterjee
and Goswami 2004; Fukutomi and Yasunari 2005; Yokoi
and Satomura 2006). Except for the northern spring, the
QBWO is found to have maximum variances off the
equator and propagate westward. For example, in bo-
real summer the QBWO convective activity may prop-
agate all the way from the western tropical Pacific to the
Indian Peninsula, to affect the active and break of the
Indian summer monsoon (Murakami 1980; Annamalai
and Slingo 2001; Chen et al. 2004; Lin and Li 2008). The
phase difference between the boundary layer conver-
gence and the convection may be responsible for the
westward propagation of the QBWO (Goswami 2005).
So far the understanding of the cause of the QBWO is
limited. Krishnamurti and Bhalme (1976) proposed that
the cloud–radiation–convection feedback may maintain
the QBWO over the Indian monsoon region. Goswami
and Mathew (1994) and Chatterjee and Goswami (2004)
suggested that the QBWO is an intrinsic mode of the
tropical atmosphere driven by evaporation–wind feed-
back in the presence of the mean westerly or boundary
layer convergence–induced convective heating. Chen
and Chen (1993) noted that low-level circulation asso-
ciated with the QBWO in boreal summer exhibits
a double cyclonic–anticyclonic cell structure, with the
northern structure centered at about 158–208N and the
southern one at the equator. This equatorially asym-
metric structure is possibly attributed to the influence
of the background summer mean flow (Chatterjee and
Goswami 2004). Kiladis et al. (1994) and Kiladis and
Wheeler (1995) noted that equatorially symmetric
Rossby waves in the period of 6–30 days appear over the
tropical Pacific, and those waves move westward with
eastward energy dispersion. Wen and Zhang (2008)
detected Rossby wave–like circulation related to the
QBWO over the eastern tropical Indian Ocean (IO) in
boreal spring. They suggested that feedbacks among the
convection, Rossby wave response, and associated low-
level circulation are crucial in maintaining the observed
QBWO structure.
Given the distinctive propagation characteristics of
the QBWO in different seasons, it is anticipated that the
origin of the QBWO might be different. In this study,
we focus on the equatorially symmetric mode of the
QBWO in boreal spring. The objective of the current
study is to explore the 3D structure and propagation
features of the QBWO over the tropical IO and to in-
vestigate the specific physical mechanism that gives rise
to the QBWO over the tropical IO. The rest of this pa-
per is organized as follows: In section 2, we describe
datasets and methods used. The seasonal characteristics
of the QBWO activity over the tropical IO are com-
pared in section 3. The evolution of the 3D structure of
the atmospheric circulation associated with the QBWO
in boreal spring is examined in section 4, and a mecha-
nism for the origin of the QBWO in the tropical IO is
proposed in section 5. Finally, discussion and conclu-
sions are given in section 6 and section 7, respectively.
2. Data and methodology
Two major datasets are used in this work. One is the
daily reanalysis from the National Centers for Envi-
ronment Prediction–National Center for Atmospheric
Research (NCEP–NCAR; Kalnay et al. 1996), including
zonal and meridional winds u and y, geopotential height
z, specific humidity q, and vertical velocity v at pres-
sure levels. The other is the daily National Oceanic and
Atmospheric Administration (NOAA) outgoing long-
wave radiation (OLR) data, used as a proxy for the
tropical convection (Liebmann and Smith 1996). Both of
the datasets have a global coverage with a 2.58 longitu-
dinal and latitudinal resolution, spanning from 1979 to
the present. [Datasets are provided by the NOAA’s Of-
fice of Oceanic and Atmospheric Research/Earth System
Research Laboratory (NOAA/OAR/ESRL) Physical
Sciences Division (PSD), Boulder, Colorado, available
online at http://www.cdc.noaa.gov/.]
Lanczos filtering is used on the daily data to get the
subseasonal signals. As introduced by Duchon (1979),
the Lanczos filtering is digital filtering that uses a linear
relationship to transform the raw data sequence xt into
a filtered data sequence yt as
yt5 �
n
k5�nw
kx
t1k, (1)
where the wk are smoothed weights. For bandpass fil-
tering, the smoothed weights are written as
wk
5sin2p f
c2k
pk�
sin2p fc1
k
pk
� �sinpk/n
pk/n,
k 5�n, . . . , 0, . . . n. (2)
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Here, two the cutoff frequencies fc2 and fc1 are 0.1
and 0.05 day21 for QBWO, respectively, and 0.033 and
0.017 day21 for MJO, respectively. The total number of
weights n are chosen in such a way that the response
functions are close to 1 between two cutoff frequencies
and to 0 beyond (for QBWO, n 5 44 and for MJO, n 5
79). Limited by the values of n, the valid filtered data
used in this analysis are from 1980 to 2006.
A lagged regression is applied to the 27-yr daily data
to examine the evolution of the coherent 3D atmo-
spheric circulation patterns associated with the QBWO
convection. A t test is used to determine the statistical
significance of the regressed fields. As for the effective
sample size (ESS) for the t test, we adopt a method in-
troduced by Bretherton et al. (1999), as Wen and Zhang
(2008) also did. Considering the discontinuity of the daily
time series (only 92 days from 1 March to 31 May are
used each year), the ESS is first calculated individually for
each year, and then the sum of them is regarded as the
total ESS. For the current study, a time series of 27 3 92
days corresponds to a mean ESS of 500.
3. Seasonal dependence of the QBWO over thetropical IO
Figure 1 shows the climatological mean of OLR and
the QBWO and MJO variances for annual mean and four
natural seasons, respectively. For the climatological an-
nual mean field, the most vigorous convection appears
over the eastern and central tropical IO, with a minimum
OLR center over Sumatra. Strong convective activities
associated with MJO and QBWO also appear in the region
where the mean convection is pronounced. In general, the
variance distributions of QBWO and MJO resemble each
other over the IO, except that the QBWO variance center
extends farther northward to the Bay of Bengal (BOB).
While the patterns of the mean OLR and the QBWO
and MJO variances in boreal spring [March–April–May
(MAM)] are similar to those of the annual mean, being
symmetric about the equator, they are quite asymmetric
in other seasons. For instance, in boreal summer [June–
July–August (JJA)] the most vigorous convection shifts
northward to the Indian Peninsula, BOB, and the Indo-
china Peninsula, while the maximum QBWO variances
appear over the BOB and the eastern part of the Arabian
Sea. In northern autumn [September–October–November
(SON)], the mean convective belt shifts to the equatorial
region, but the maximum variances of QBWO and MJO ap-
pear north of 108N. In boreal winter [December–January–
February (DJF)], both the mean convection and the maxi-
mum variance centers lie over the southern tropical IO.
For all seasons, the amplitude of the QBWO is similar
to that of MJO. This indicates that the QBWO is equally
important in contributing to the atmospheric variability
in the tropics.
The empirical orthogonal function (EOF) analysis
method is employed to reveal the dominant patterns of
the QBWO over the tropical IO at each season. The
structures of the first and second EOF modes (EOF1
and EOF2) of the 10–20-day-filtered OLR field and the
time-lag correlation coefficients between the two prin-
cipal components (PCs) are shown in Fig. 2. The positive
(negative) lagged time denotes that PC2 lags (leads)
PC1. Also, illustrated in Fig. 2 are the regressed 850-hPa
wind fields. Note that in boreal spring both the first and
second EOF modes represent an equatorially symmetric
pattern over the tropical IO, which is distinctive from
the other seasons.
In EOF1, an active convection (negative OLR) center
appears east of 808E and a suppressed convection (posi-
tive OLR) center appears in the western IO. The in-
tensity of the former is much stronger than that of the
latter. On the east edge of the negative OLR center, the
contours are approximately parallel to the shoreline of
Sumatra Island, implying a possible impact of Sumatra
on local convective activities (Nitta et al. 1992). The as-
sociated 850-hPa winds over the eastern IO exhibit a
double-cell cyclonic Rossby gyre structure symmetric
about the equator, with anomalous westerlies being right
over the equator. A weak anticyclonic Rossby gyre pat-
tern may be identified over the western IO, in association
with the suppressed convection there. The symmetric
OLR and wind patterns resemble those shown in Kiladis
and Wheeler (1995) and Wen and Zhang (2008).
In EOF2, a broadscale positive OLR anomaly occurs
over the equatorial IO, with a maximum center around
808E. Over the eastern IO, this positive OLR anomaly is
accompanied by two negative centers at 158S and 158N,
making up a ‘‘sandwich’’ pattern there. The negative
OLR centers are associated with cyclonic Rossby gyre
pairs at 850 hPa. An interesting feature is the in-phase
relationship between the positive OLR and westerly
anomalies over the equatorial eastern IO. The possible
mechanism for such an in-phase relationship will be
discussed in the following sections.
A significant lagged correlation between EOF1 and
EOF2 suggests that physically they represent the dif-
ferent phases of the same QBWO cycle (Lau and Lau
1990; Plaut and Vautard 1994; Jiang et al. 2004; Jiang
and Li 2005). Thus, one may use the time series of EOF1
to reveal the evolution characteristics of the entire
QBWO cycle.
The EOF patterns in boreal summer show a more
asymmetric structure, with the centers of negative and
positive OLR anomalies shifting northward to 58–108N.
Accordingly, the 850-hPa winds exhibit double Rossby
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FIG. 1. (left) Climatological mean of OLR (W m22) , (middle) QBWO (10–20 day) variance (W2 m24), and (right)
MJO (30–60 day) variance (W2 m24) for (a) annual mean, (b) MAM, (c) JJA, (d) SON, and (e) DJF.
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gyre cells, with the axis along 58–108N. When the anal-
ysis domain is extended eastward to include the tropical
western Pacific, the maximum activity center is found off
the equator in the western Pacific. This is consistent with
Chen and Chen (1993), who found that the QBWO
OLR anomalies in boreal summer originate over the
western tropical Pacific and move westward. Having
the similar amount of variances, the EOF1 and EOF2
FIG. 2. Patterns of the (left) EOF1 and (middle) EOF2 modes of the 10–20-day filtered OLR (contours; W m22)
and associated 850-hPa winds (vectors; m s21), and (right) their PCs correlation coefficients in (a) MAM, (b) JJA,
(c) SON, and (d) DJF. The two EOF modes have been scaled by standard deviation of the corresponding time series
with a unit of W m22 and the percentages of the total variance are written in the upper-left corner of (a)–(d). For the
PC correlation, a positive (negative) lagged time (day) denotes that PC2 lags (leads) PC1.
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modes in boreal summer over the IO are not signifi-
cantly correlated.
Similar to the wind patterns in summer, the axis of
the double cells in northern fall is about 58–108N of the
equator. The significant lagged correlation between
the first and second EOF modes in autumn implies that
the OLR anomalies move northeastward from the equa-
torial IO to the west coast of Indochina Peninsula.
In DJF, the major QBWO activity is confined at and
south of the equator. It again exhibits an equatorial
asymmetric feature. The lagged correlation between the
two dominant EOF modes is not significant.
To summarize, the QBWO convection and low-level
circulation exhibit distinct characteristics in the four
seasons. Only in boreal spring are the patterns of both
the convection and low-level circulation anomalies sym-
metric about the equator for both the EOF1 and EOF2
modes. In the rest of this paper, we will focus on the
QBWO in boreal spring.
4. 3D circulation patterns associatedwith QBWO in boreal spring
A linear-lagged regression is used to reveal the cir-
culation pattern associated with a full cycle of the
QBWO. As shown in Fig. 2a, the first two PCs have
a significant correlation, with the peak of PC1 leading
that of PC2 by 3–4 days. Thus, one may simply choose
PC1 as the reference time series and reveal the QBWO
evolution with the application of a linear-lagged re-
gression method. Figure 3 illustrates the evolution of the
OLR and the low-level (850 hPa) circulation associated
with a half cycle of the QBWO from day 27 to day 0.
Here, day 0 (day 27) represents the strongest (most
suppressed) convective phase of the QBWO over the
eastern equatorial IO. Before conducting the lagged
regression, both the OLR and 850-hPa wind fields are
subjected to a 10–20-day bandpass filter. In the rest of
this study, without being mentioned specifically, all
discussions are for the QBWO and all regression co-
efficients are relevant to PC1.
At day 27, a strong positive OLR center, representing
the suppressed convection, appears over the eastern
equatorial IO. Correspondingly, low-level easterlies are
pronounced in situ. A weak negative OLR anomaly oc-
curs in the western IO. In the subsequent days (days 26
to 25), the positive anomaly over the eastern IO tends to
separate into two symmetric parts in association with two
anticyclonic gyres, whereas the negative anomaly in the
west propagates slowly toward the east.
From days 24 to 23, the negative OLR anomaly
rapidly shifts into the eastern equatorial IO, while the
two positive OLR anomaly centers, along with two
anticyclonic gyres, move poleward. An interesting fea-
ture of the low-level circulation at this transition phase is
the easterly anomaly overlapping with the enhanced
convection in the eastern equatorial IO. This structure
is contradictory to a conventionally held Gill-type dy-
namic pattern of the westerly anomaly being in phase
with the enhanced convection anomaly. As will be dis-
cussed in the next section, the equatorial easterly anomaly
(associated with the two off-equatorial anticyclonic
gyres) is a cause rather than a result of the local con-
vection anomaly.
Two days later (days 21 and 0) when the equatorial
convection is further enhanced and the impact of the off-
equatorial gyres is weakened, the low-level westerly
anomaly forms and is in phase with the negative OLR
center. The spatial patterns of the OLR and 850-hPa
winds at day 0 are a mirror image of those at day 27,
indicating a completion of a half cycle of the QBWO
from days 27 to 0.
One may note from Fig. 3 that the OLR patterns at
day 0 (day 24) are similar (opposite) to the first (second)
leading EOF patterns shown in Fig. 2a. This again in-
dicates that the two leading EOF modes reflect the dif-
ferent phases of the same dynamic mode.
A key question related to the formation of the QBWO
convection in the eastern equatorial IO is whether it is
generated locally or attributed to the eastward propa-
gation of the disturbance from the western IO. Note that
the negative OLR center is located at 658E in the
western equatorial IO at day 27 and moves to 758E at
day 24, with an averaged phase speed of 3.38 day21.
However, at day 23, it suddenly jumps to 908E, 4–5
times faster than the previous propagation speed. To
reveal the cause of this ‘‘odd’’ feature, we examine the
longitude–vertical section of the regressed zonal and
vertical winds at each phase (Fig. 4).
At day 27, a strong subsidence is pronounced
throughout the troposphere over the eastern equatorial
IO (80821008E), coinciding with the positive OLR
anomaly in situ. This subsidence weakens from days 27
to 25 and, meanwhile, a local-ascending branch de-
velops in the planetary boundary layer (PBL), gradually
penetrating into the upper levels. To the west of the
midtropospheric subsidence, there is an updraft over
the western IO, which moves slowly eastward. Its loca-
tion coincides with that of the negative OLR center (see
Fig. 3). At day 24, the western and eastern branches of
the updrafts are well connected at low levels, while the
downdraft in between weakens and can only be detected
at upper levels. At day 23 when the equatorial eastern
IO is overwhelmed by large-scale ascending motion, one
may still discern two ascending centers, with one be-
ing near 708E and the other near 1008E. The former is
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initiated from the western IO, whereas the latter de-
velops locally, as viewed clearly from the vertical–lon-
gitude maps. The local ascending motion initially
develops at PBL (below 800 hPa), and it grows rapidly
and reaches to the middle troposphere at day 24. As the
eastern convective branch continues growing from days
23 to 0, the western one decays gradually.
Therefore, the evolution of the zonal and vertical
circulation along the equatorial plane reveals the
cause of the sudden ‘‘jump’’ of the OLR anomaly from
the western to eastern IO. It provides a physical
clue of how the local convection in the eastern IO
is generated—it is primarily attributed to the local
processes associated with the atmospheric boundary
FIG. 3. Lagged regression of the 10–20-day filtered OLR (contours; W m22) and 850-hPa winds (vectors; m s21) on
the PC1. The contour interval of OLR is 2 W m22 and the zero contours have been omitted. Shading indicates the
regression of OLR passing the 95% significance level, and vectors below the 95% significance level are omitted.
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layer dynamics. Note that after the low-level westerly
is established in response to the local convective heat-
ing at day 0, a new downdraft is formed at the bound-
ary layer around 1008E, indicating the subsequent
development of a suppressed convective phase over the
region.
Figure 5 further illustrates the evolution of the
QBWO circulation in the vertical–latitude section along
FIG. 4. Regressed zonal–vertical circulations (vectors) and vertical velocity (contours) on the PC1 along 58S–58N.
The contour interval of vertical velocity is 0.1 3 1024 hPa s21. Shading denotes the regression of vertical velocity
passing the 95% significance level, and vectors below the 95% significance level are omitted.
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1008E. The circulation is approximately symmetric
about the equator. As in the vertical–longitude section,
the local ascending motion is first found at PBL during
the suppressed convective phase over the eastern equa-
torial IO. It enhances and extends upward. Meanwhile,
the downdrafts at both sides of the equator weaken
gradually. Therefore, both the vertical–longitude and
vertical–latitude profiles reveal that even though there
are obvious eastward-propagating signals along the equa-
torial IO, the formation and phase transition of convection
FIG. 5. As in Fig. 4, but for meridional–vertical circulations.
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in the eastern equatorial IO are primarily attributed to
local processes. In the next section, we will investigate
how the boundary layer ascending motion is generated.
5. Mechanism for the boundary layer triggeringoff Sumatra
As shown in Figs. 3–5, the ascending motion first de-
velops in the boundary layer at days 27 to 26 when
suppressed convection and descending anomalies ap-
pear over the equatorial eastern IO. How does the
vertical motion form in the boundary layer? As we
know, in the absence of the background mean flow, the
free-atmospheric response to a midtropospheric heat-
ing/cooling is baroclinic, that is, the upper and lower
tropospheric circulations are reversed (Gill 1980). In
the presence of the background vertical shear, the free-
atmospheric barotropic flow may be generated because
of the coupling between the barotropic and baroclinic
flows (Wang and Xie 1996; Jiang et al. 2004). The di-
vergence of the free-atmosphere barotropic flow may
further induce the boundary layer convergence accord-
ing to the mass continuation. Thus, it is critical to ex-
amine the evolution of the barotropic flow associated
with the QBWO, and its phase relationship with the
baroclinic flow and PBL divergence.
A dependent variable may be decomposed into a
barotropic (1) and a baroclinic (2) part (Peixoto and
Oort 1992) as
A(x, y, z, t) 5 A1
(x, y, t) 1 A�(x, y, z, t), (3)
where A1
5Ð Pb
PtA dp/(P
b� P
t) and
Ð Pb
PtA� dp 5 0. Pt
and Pb are pressures at the top and bottom of the free
atmosphere, respectively. Here we set Pb 5 850 hPa and
Pt 5 100 hPa.
Our diagnosis reveals that at the equator the zonal
wind component primarily contributes to the free-
atmosphere barotropic divergence field. Figure 6 illus-
trates the evolution of the free-atmospheric barotropic
zonal wind along the equator in a full cycle of the
QBWO. The amplitude of the barotropic zonal wind is
about 0.5 m s21, being close to that of the baroclinic
counterpart. The maximum barotropic easterly occurs at
day 26 and is located at 908E. The maximum barotropic
easterly appears 1–2 days after the weakest convective
phase over the region, implying that the barotropic flow
is possibly triggered by the anomalous descending mo-
tion associated with the QBWO. Unlike the behavior of
the OLR anomaly, the barotropic flow propagates slowly
westward along the equator, possibly caused by the
Rossby wave emanation from the anticyclonic gyres off
the equator (Wang and Xie 1997).
To understand the specific process that generates the
barotropic zonal wind, we diagnose the zonal momen-
tum budget using the NCEP–NCAR reanalysis data. All
dependent variables are decomposed into a basic state
and a perturbation field as
A 5 A 1 A9. (4)
FIG. 6. Free-atmospheric barotropic zonal wind (1021 m s21)
along 58S–58N regressed onto the PC1 from days 27 to 7. The light-
filled area denotes easterlies and the dark-filled area denotes
westerlies.
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Substituting Eq. (4) into the zonal momentum equation,
considering that the mean state satisfies the equation
and integrates vertically from 850 to 100 hPa, one may
derive the barotropic zonal wind tendency equation as
›u91
›t5
ðPb
Pt
›u9
›tdp=(P
b� P
t)
5�Uu� V
u�W
u1 F
y�F
x, (5)
where
Uu
5
ðPb
Pt
u›u9
›x1 u9
›u
›x1 u9
›u9
›x
� �dp=(P
b� P
t), (6)
Vu
5
ðPb
Pt
y›u9
›y1 y9
›u
›y1 y9
›u9
›y
� �dp=(P
b� P
t), (7)
Wu
5
ðPb
Pt
�v›u9
›p1 v9
›u
›p1 v9
›u9
›p
� �dp=(P
b� P
t), (8)
Fy5
ðPb
Pt
f y9dp/(Pb� P
t), (9)
and
Fx
5
ðPb
Pt
›u9
›xdp=(P
b� P
t). (10)
For simplicity, we define A as the climatological mean
from 1 March to 31 May and A9 as the 10–20-day filtered
field.
Figure 7 shows the barotropic zonal wind, and its
tendency averaged over the eastern equatorial IO (be-
tween 808 and 1008E). Note that the maximum barotropic
easterly appears at day 26, while the peak of the baro-
tropic westerly occurs at day 1. To understand the gen-
eration mechanism for the barotropic easterly–westerly,
we diagnose each term at the right-hand side of Eq. (5)
and a composite is made for a 2-day period prior to the
peak of the barotropic easterly and westerly.
Figure 8a shows the composite differences between
the barotropic easterly and westerly phases. Note that
the vertically integrated horizontal advection and pres-
sure gradient force terms are all small. The dominant
contribution comes from the vertical advection term.
The zonal momentum budget is not exactly in balance,
possibly due to finite difference errors, vertical in-
terpolation from a sigma to a pressure coordinate, and/
or the neglecting of horizontal and vertical diffusions in
the momentum equation. A further discussion of this
discrepancy can be found in the next section.
According to Eq. (8), the vertical momentum trans-
port consists of the following three terms: 1) the vertical
FIG. 7. Time series of the barotropic zonal wind (solid line;
1021 m s21) and its tendency (dashed line; 1027 m s22) over the
equator between 808 and 1008E.
FIG. 8. (a) Relative contributions of the barotropic zonal wind
tendency difference terms averaged over the equator between 808
and 1008E. (b) As in (a), but for each vertical advection term
(1027 m s22). The difference is based on 2-day composites prior to
the peaks of the maximum barotropic easterly (at day 26) and
westerly (at day 1).
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advection of the perturbation zonal wind by the back-
ground mean vertical motion Wu,1, 2) the vertical ad-
vection of the mean zonal wind by the perturbation
vertical motion Wu,2, and 3) the vertical transportation
of the perturbation zonal wind by the perturbation
vertical motion Wu,3, respectively. The physical in-
terpretation of Eq. (8) is that a baroclinic perturbation
may interact with either a baroclinic mean flow, or the
baroclinic perturbation itself, to lead to the generation
of the barotropic motion in the free atmosphere.
The relative contributions of the three vertical advec-
tion terms are diagnosed and the result is illustrated in
Fig. 8b. It is found that the vertical transportation of the
background mean zonal wind by Wu,2 contributes mostly
to the vertical momentum transport, whereas the other
two terms play a minor role. As shown in Fig. 4, at day
27, strong descending motion occupies the whole tropo-
sphere east of 808E. The background mean flow in boreal
spring over the eastern equatorial IO exhibits an easterly
shear feature with low-level westerlies (Zhang et al. 2002;
He et al. 2006) and upper-level easterlies (Fig. 9). As
a result, the contribution to the tendency of the barotropic
zonal wind �v9(›u/›p) is negative. Thus, during the
strongest suppressed convective phases at days 27 and
26, the perturbation descending motion advects the mean
easterly momentum downward, leading to the generation
of the free-atmospheric barotropic easterly. The opposite
process is found during the generation of the barotropic
westerly.
The result shown previously suggests that the free-
atmospheric barotropic motion may be generated through
the interaction between the QBWO baroclinic motion
and the baroclinic mean flow. How does the generated
barotropic flow further impact the boundary layer cir-
culation? Note that the strong barotropic easterly occurs
at days 27 and 26 around 908E. To the east of the
maximum easterly, the zonal gradient of the barotropic
wind is divergent. In addition, the barotropic easterly at
the equator may also induce a tendency of the meridi-
onal wind divergence (i.e., the b divergence) in the free
atmosphere as
›
›t
›y1
›y
� �}�bu
1. (11)
Our calculation indicates that in the eastern equato-
rial IO the zonal wind component dominates the free-
atmospheric divergence field. According to the mass
continuity, this free-atmospheric divergence needs be
balanced by a boundary layer convergence so that the
total column mass divergence vanishes. Figure 10 shows
the evolution of the free atmosphere and PBL di-
vergence patterns from days 27 to 0. Note that they in
general have opposite signs. The near-surface conver-
gence is approximately in phase with anomalous as-
cending motion at top of the atmospheric PBL.
The previous argument suggests a possible scenario for
the local origin of the QBWO off Sumatra. Prior to day
26, there is a pronounced descending anomaly in the
equatorial eastern IO in association with the suppressed
convective phase of the QBWO. The strong descending
motion advects the mean easterly momentum down-
ward, leading to the formation of the free-atmospheric
barotropic easterly in situ (Figs. 4 and 6). The barotropic
easterly further causes the free-atmospheric divergence
and the boundary layer convergence. As a result, a
marked updraft is observed first at the top of the boundary
layer around 1008E, and then it penetrates into the upper
troposphere (Fig. 4). Thus, it is the local PBL process
that leads to the phase change of the QBWO convection
in the eastern equatorial IO from a break phase at
day 27 to an active phase at day 0. A reversed process
is followed as the anomalous convection leads to the
formation of the free-atmospheric barotropic westerly.
To demonstrate clearly the phase relationship among
the OLR, the barotropic wind, and the boundary layer
divergence, we show the time evolution of these fields
averaged in the eastern equatorial IO in Fig. 11. Here,
the 10–20-day-filtered 925-hPa specific humidity and
winds are used to represent the boundary layer moisture
and wind fields. Note that the maximum positive OLR
anomaly (and anomalous descending motion at 500 hPa)
leads the peak of the barotropic easterly by one day
FIG. 9. Vertical profile of the climatological mean zonal wind
(m s21) in boreal spring (MAM) over 58S–58N, 808–1008E.
1976 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 67
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FIG. 10. Free-atmosphere (averaged over 850–100 hPa) and PBL (at 925 hPa) divergence associated with QBWO. The contour interval is
1 3 1025 hPa s21.
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(Fig. 11a), whereas the barotropic easterly leads the free-
atmospheric divergence by a couple of days (Fig. 11b).
The free-atmospheric divergence, on the other hand, is
in phase with the boundary layer convergence (Fig. 11b).
The near-surface specific humidity increases from days
26 to 1, when the boundary layer flow is convergent
(Fig. 11c). The increase of the moisture resulting from
the boundary layer convergence may further destabilize
the local atmosphere, leading to the upward develop-
ment of the ascending branch (Fig. 4). The enhanced
surface moist static energy eventually leads to a con-
vectively unstable stratification and triggers the onset of
convection. Therefore, the boundary layer divergence
induced by the free-atmospheric barotropic winds over
the eastern equatorial IO is a direct cause of the phase
transition of the QBWO.
6. Discussion
Most of the previous works are focused on QBWO
in boreal summer or winter, which has the maximum
amplitude off the equator, with a typical Rossby wave
structure, and propagates westward. The present study
shows that the structure and generation mechanism of
the boreal spring QBWO are different from those in
boreal summer and winter. In boreal spring, QBWO is
approximately symmetric about the equator, and it orig-
inates from local processes over the eastern equatorial
IO, not signals propagating from the western IO. The
cause of the structure difference between the boreal
spring and summer/winter QBWO is likely attributed
to the mean state distribution (the spring mean state is
approximately symmetric, whereas the summer–winter
mean state is quite asymmetric relative to the equator). A
further study is needed to understand the dynamic cause
of structure asymmetry and temporal-scale selection.
A relevant question is what differentiates QBWO and
MJO in boreal spring? To show their differences, we
extract the EOF modes of MJO in boreal spring (MAM)
in the same way as we did for the QBWO analysis. Then,
we regress the OLR and circulation fields onto PC1 for
both the MJO and QBWO modes.
Figure 12 illustrates the regressed OLR and 850-hPa
wind fields for both the MJO and QBWO modes in the
global tropics domain. It is clearly seen from Fig. 12
that the spatial scale of MJO is much larger than
that of QBWO. While dominant convective activity
associated with QBWO is confined in the tropical
IO and western Pacific warm pool, MJO convection
shows a more pronounced global-circumnavigating
characteristic. Figure 13 further illustrates the evolu-
tion of the 200-hPa velocity potential field associated
with the MJO and QBWO modes. While the MJO is
dominated by a zonal wavenumber-1 structure, the
QBWO has a remarkable wavenumber-2 pattern.
Therefore, the previously stated analysis clearly illus-
trates the marked differences between QBWO and
MJO in spatial structure, zonal wavelength, and prop-
agation speed.
Despite the difference in zonal wavelength and fre-
quency, QBWO and MJO exhibit a similar horizontal
Kelvin–Rossby wave couplet pattern. This implies that
the fundamental mechanism that causes the eastward
propagation for the two modes may be similar.
An interesting feature is the sinusoidal nature of the
time variations of QBWO, even though they contain
a highly nonlinear moist process, which is characterized
by an asymmetric nature associated with upward and
downward motions. It is argued that the moist process is
nonlinear or asymmetric in association with the total up-
ward and downward motions. However, for the pertur-
bation it will depend on the background mean state under
which the perturbation evolves. During boreal spring,
the pronounced seasonal mean large-scale convection
FIG. 11. Evolutions of (a) the OLR (solid line) and barotropic
zonal wind anomalies (dashed line), (b) the anomalous divergence
of the free atmosphere (solid line) and PBL (dashed line), and (c)
vertical velocity (solid line) and the tendency of specific humidity
(dashed line) at 925 hPa averaged over the equator between 808
and 1008E.
1978 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 67
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and upward motion are often observed over the equa-
torial IO. As a result, anomalous downward (upward)
motion may lead to a negative (positive) heating anom-
aly. This indicates an approximately linear process.
However, there is still an asymmetry in the zonal ex-
tension between the convective and nonconvective
regions—a narrower rising branch is accompanied by
a wider subsidence branch. Such a zonal asymmetry,
however, was largely reflected by the EOF1 and EOF2
patterns, so that the time series of their principal com-
ponents remain sinusoidal. It is possible that a bandpass
filter may help smooth out some temporally asymmetric
features.
The relatively large residual term in the momentum
budget analysis is possibly attributed to the neglecting of
the variability with time scales longer than 20 days in the
background mean flow. The effect of this slowly varying
background state was revealed from the composite
analysis of Fukutomi and Yasunari (2005) and Yokoi
and Satomura (2006). However, in the current work the
budget analysis is done at each phase of QBWO, which
is derived previously, based on regressed coefficients in
boreal spring during the entire 27-yr period. As a result,
for each phase there is no specific information about the
timing of the background state and only a seasonal mean
background state was used in the calculation. Another
possible cause is the neglecting of the PBL dissipation.
7. Conclusions
The spatial and temporal characteristics of the QBWO
are investigated over the tropical IO using 27-yr daily
FIG. 12. Lagged regression of filtered OLR and 850-hPa wind fields for (left) QBWO and (right) MJO onto their PC1: lags (top to
bottom) (left) 28 to 6 days and (right) 220 to 15 days. The contour interval of OLR is 2 W m22 and the zero contours have been omitted.
Shading is for the absolute values of OLR to be greater than 1 W m22.
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OLR and NCEP–NCAR reanalysis data. The QBWO
convective activity is closely related to the climatologi-
cal mean convective activity, with active centers shifting
seasonally along with the mean convection centers. There
is a permanent QBWO activity center over the equatorial
eastern IO. The intensity of QBWO is in general com-
parable with that of MJO. A double-cell Rossby gyre
structure is often observed at low levels in association
with the QBWO convective anomaly, whose axis is
shifting meridionally with each season. The most equa-
torially symmetric patterns for both the OLR and wind
fields are found in boreal spring over the tropical IO.
The detailed 3D structure and evolution characteris-
tics of the symmetric QBWO mode in boreal spring are
examined. It is found that the QBWO convection first
appears over the western equatorial IO and then moves
eastward slowly. After passing the central IO, the dis-
turbance suddenly speeds up and jumps into the eastern
equatorial IO. Meanwhile, the preexisting suppressed
convective disturbance in the eastern IO shifts poleward,
accompanied by low-level anticyclonic Rossby gyres.
The evolution of the circulation along the longitude–
vertical section reveals that prior to the phase transition
of the QBWO from a suppressed to an active convective
phase, an ascending motion (and convergence) anomaly
emerges first in the atmospheric PBL around 1008E. The
increase of the surface moisture (resulting from the PBL
convergence) further leads to the convectively unstable
stratification and, thus, the upward development of the
ascending motion and convection. Therefore, the QBWO
convection over the eastern equatorial IO is primarily
triggered by local processes in the PBL, rather than
resulting from the propagation of convective distur-
bances from the western IO.
A zonal momentum budget analysis using the NCEP–
NCAR reanalysis data is conducted to reveal the cause
of the free-atmospheric barotropic flow and associated
divergence. The result indicates that the downward
transport of the background mean easterly by pertur-
bation vertical motion leads to the generation of the
barotropic easterly in the free atmosphere. The di-
vergence of the barotropic easterly to the east of the
maximum zonal wind further leads to a convergence and
ascending motion at the atmospheric boundary layer.
The PBL convergence causes the increase of the surface
moisture and, thus, the convective instability in situ.
Therefore, through anomalous downward easterly mo-
mentum transport, and its associated impact in the at-
mospheric PBL, a suppressed convective anomaly over
the eastern equatorial IO may lead to the onset of a new
opposite-phase convective anomaly in situ.
The previously stated observational analysis reveals
that the phase transition of the QBWO convection over
the eastern equatorial IO is primarily attributed to the
local boundary layer process. The eastward propagation
of convective disturbances along the equatorial IO plays
a minor role in the phase transition.
The study of the QBWO in boreal spring is useful
because it may significantly impact the Asian monsoon
onset (Zhang et al. 2002; Wen and Zhang 2007). The
generation mechanism for QBWO in boreal spring
might be different from that in other seasons. How and
to what extent does the local triggering mechanism op-
erate in other seasons requires further observational
analyses and modeling studies.
Acknowledgments. The authors thank the editor
Dr. Shigeo Yoden and two anonymous reviews for their
constructive comments that improved the overall quality
of the paper. The authors also thank Dr. Xianan Jiang
for discussions. This study was jointly supported by the
National Natural Science Foundation of China under
Grant 40775039, the National Basic Key Research
Program (973) under Grant 2006CB403602, and the
International S&T Cooperation Project of the Ministry
of Science and Technology of China under Grant
FIG. 13. Time–longitude sections of lagged regression of the
200-hPa velocity potential along the 108S–108N for (a) QBWO and
(b) MJO onto their PC1. The contour interval is 1 3 105 m2 s21 for
QBWO and 5 3 105 m2 s21 for MJO.
1980 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 67
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2009DFA21430. TL was supported by CMA and
NSFC Grants 40628006/40675055 and ONR Grants
N000140710145/N000140810256 and by the Interna-
tional Pacific Research Center that is sponsored by the
Japan Agency for Marine–Earth Science and Technol-
ogy (JAMSTEC), NASA (NNX07AG53G), and NOAA
(NA17RJ1230).
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