Structure and Origin of the Quasi-Biweekly Oscillation

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]

JUNE 2010 W E N E T A L . 1965

DOI: 10.1175/2009JAS3105.1

� 2010 American Meteorological SocietyUnauthenticated | Downloaded 06/08/22 11:44 PM UTC

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

JUNE 2010 W E N E T A L . 1967


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.



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.

JUNE 2010 W E N E T A L . 1969


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



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.

JUNE 2010 W E N E T A L . 1971


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.



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.

JUNE 2010 W E N E T A L . 1973


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.



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).

JUNE 2010 W E N E T A L . 1975


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.



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.

JUNE 2010 W E N E T A L . 1977


(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.



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.

JUNE 2010 W E N E T A L . 1979


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.



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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Structure and Origin of the Quasi-Biweekly Oscillation