Mechanisms of westward and northward movement of
sub-monthly scale disturbances over Asian monsoon regions.
*Satoru YOKOI1 and Takehiko SATOMURA1(1:Graduate School of Science, Kyoto University)* Graduate School of Science, Kyoto University, Kitashirakawa-Oiwake cho, Sakyo, Kyoto
606-8502, Japan. e-mail: yokoi@kugi.kyoto-u.ac.jp
Abstract
Sub-monthly scale disturbances, which have time scales between 10 and 25 days, are found frequently
over the Bay of Bengal during the boreal summer. They have strong cyclonic circulation anomaly in thelower troposphere and move north-westward with its speed of about a few meters per second. We discuss
the mechanisms for westward and northward components of the movement in the complex environmental
condition.
The westward component mainly results from balance between advection of the planetary and relative
vorticity. The advection of the planetary vorticity (the beta eﬀect) contributes to the westward movement,
like the Rossby wave dynamics. On the other hand, advection of the disturbance by the environmental
ﬂow tends to move the disturbance eastward, and especially counterbalances the beta eﬀect when the centerof the disturbance is around 10◦ N where low-level westerly jet axis exists. In this case, advection of theenvironmental relative vorticity by the disturbance is second contributor to the westward movement.
For the northward component, both advection of the disturbance by the environmental low-level southerly
wind and tilting eﬀect of the environmental horizontal vorticity vector by the disturbance are main contributors. The former works mainly in the lower troposphere, while the latter works in the middle and upper
troposphere.
keyword: sub-monthly scale disturbance, vorticity budget, the beta term, advection eﬀect, tilting eﬀect

1 Introduction

2 Data and Method

During the boreal summer, sub-monthly scale dis-

ECMWF 40 Years Re-Analysis (ERA40) data wasturbances are frequently observed over the Bay of
Bengal and cause precipitation over the South andused. The used variables for the vorticity budget

Southeast Asia (Chen and Chen, 1993; Yokoi andanalysis are three dimensional wind (u,v,ω), vertical
relative vorticity ζ, and horizontal divergence ∇h · u.

Satomura, 2004). They have typical time scales between 10 and 25 days, typical horizontal scales of

The analyzed period is from May to September in
1979-1999 (total 3213 days). We used a Lanczos

a few thousand kilometers, and accompany cyclonic
circulation in the lower troposphere.

band-pass ﬁlter with cutoﬀ period of 10 and 25 days
to retrieve 10-25-day component, and a low-pass ﬁl-They tend to move westward and slightly northward with time. Because of their time and horizontal

ter with cutoﬀ period of 25 days to retrieve environmental component. The 10-25-day and environ¯
mental components are referred to as (·) and (·),

scales, the disturbances seem to obey Rossby wave
dynamics to some extent. However, in the South

respectively.

and Southeast Asia during the boreal summer, envi-

To clarify eﬀects of the complicated environmen-

ronmental condition is complicated, which inﬂuences
strongly the disturbances’ movement. For example,

tal condition on the disturbances’ movement, we investigate statistical characteristics and mechanisms

strong low-level westerly jet tends to move the disturbances eastward.

from a number of disturbances existed over the Bayof Bengal. We focus on two regions; one is (7.5◦ N-

In the present study, we discuss qualitatively themechanisms for westward and northward movement

12.5◦ N, 80◦ E-100◦E) rectangular region and referred
to as SBB, while the other is (17.5◦ N-22.5◦N, 80◦ E-of the disturbances with use of vorticity budget analysis.

100◦E) and referred to as NBB (Fig. 1). From theanalyzed period, we picked up 158 and 182 days whencenters of the disturbances exist in SBB and NBB regions, respectively (The center of a disturbance wasdeﬁned as a maximum of ζ  at the 850-hPa level).
For each region, the picked days were averaged withrespect to the position of the center.

3 Structure of the disturbances
Composite horizontal and vertical structures of
NBB and SBB are quite similar to each other. They

Fig. 1: Location of NBB and SBB regions.

have zonal and meridional scales of a few thousand
kilometers and about one thousand kilometers, respectively. Anomalous northerly (southerly) wind,whose magnitude is about 1 m s −1 , exists to thewest (east) of the center of ζ  . They move northwestward with their speed of about 2 to 3 degrees
per day in longitude (Figs. 2 a and b) and 1 to 1.5
degrees per day in latitude (Figs. 2 c and d).
Figure 3 shows latitude-height cross sections of ζ and ω  averaged over 10 degrees in longitude aroundthe disturbances’ center. Below the 200-hPa level,ζ  is nearly standing. Negative ω  is found aroundthe center (or a few degree to the south) with its
maximum in the middle troposphere (the 600- and400-hPa levels for NBB and SBB composites, respectively). This negative ω  will be turned out to beimportant for the northward movement.

4 Vorticity budget
In this section, we discuss the mechanisms forwestward and northward movement through vorticity budget analysis.
The vorticity budget equation used in the present

Fig. 2: (a and b) Longitude-time cross sections ofζ  at the 850-hPa level averaged over 20 degrees inlatitude around the center: of (a) SBB and (b) NBB.
Contour interval is 2×10−6 [s−1 ]. (c and d) Latitudetime cross sections of ζ  at the same level averaged
over 20 degrees in longitude around the center of (c)SBB and (d) NBB. Contour interval is the same as(a) and (b).

study isζt = −(ū · ∇)ζ  −(u · ∇)(f + ζ̄)   


A

B

C



−(f ∇h · u + ζ̄∇h · u + ζ  ∇h · ū)



D

+(ωy ūp − ωx v̄p ) +(ω̄y up − ω̄x vp ) +[Res.].





E

F

Subscripts t, x, y and p indicate partial diﬀerentialof time, zonal, meridional and pressure directions,
respectively. The capital letters below the equation
are symbols of the terms. Nonlinear terms, such as−(u · ∇)ζ  , are neglected in the present analysis because they are small compared to the linear terms.
Figure 4 shows horizontal distribution of theseterms of the SBB composite integrated from the sur-Fig. 3: Latitude-height cross sections of ζ  and ω averaged over 10 degrees in longitude around the centers’ longitude: (a) ζ  of NBB, (b) ω  of NBB, (c) ζ of SBB, and (d) ω  of SBB. Contour intervals are
2 × 10−6 [s−1 ] for (a) and (c), and 0.01 [Pa s−1 ] for(b) and (d).

face to the 100-hPa level. In Fig. 4A, which represents tendency of ζ  , positive and negative maxima
exist north-western and south-eastern side of the center, respectively, which are consistent with the northwestward movement.
Looking into positive and negative maxima in Figs.
4B-4F, we can identify which term is a contributor to the westward and northward components ofthe movement. The term B, which represents advection of the disturbances by the environmental
ﬂow, tends to move the disturbances north-eastward
because positive and negative maxima exist northeastern and south-western side of the center, respectively. On the other hand, the term C, which represents advection of the environmental absolute vorticity by the disturbances, tends to move the disturbances south-westward. The term E, which represents tilting eﬀect of the environmental horizontal
vorticity vector by the disturbances, tends to movethe disturbances northward. The terms D and F
seem to hardly contribute to the movement, though
the term D tends to maintain the disturbances because a positive maximum is around the center.
As documented above, diﬀerent terms contributethe disturbances’ movement for diﬀerent directions.
To discuss the relative importance of each term, horizontal gradient vectors of the terms at the center
were calculated. Figure 5 shows zonal and meridional components of the vectors divided by verticallyintegrated ζxx
and ζyyat the center, respectively.
Although the disturbances analyzed in the present

study are not recognized as sinusoidal waves, these
normalization will helpful for us to compare resultsof SBB with those of NBB. The terms B and C are
divided as−(ū · ∇)ζ  
B−(u · ∇)(f + ζ̄)



C

=

     

westward movement, the disturbances can not move
westward by the beta term alone because the advection by the environmental ﬂow counterbalances thebeta term. We can not neglect the contribution of

The relationship between the terms B and C is

B2





= −(u · ∇)ζ̄ −fy v     
C1balances with the term C2. This fact means thatthough the beta term is the best contributor to thethe term C1 which represents the advection of theenvironmental relative vorticity by the disturbances.

−ūζx −v̄ζy
B1Fig. 4: Spatial distributions of each term of thevorticity budget equation of SBB. The term symbols
are explained in the text. Abscissas and ordinates
indicate relative longitude and latitude to the center, respectively. The contour interval is 4 × 10−7
[Pa s−2 ]. Color tone marks signiﬁcance greater than
99%.

C2

diﬀerent for the case NBB (Fig. 5a). While the term
C2 of NBB is about 1.3 m s−1 smaller than that ofwhere the vertical advection term in the term B is
not displayed because it turns out to be small.

SBB, the term B of NBB is about 2.4 m s−1 smaller
than that of SBB. On the other hand, the term C1 of

The zonal components of the gradient of SBB composite are shown in Fig. 5c. As recognized in Fig.

NBB is positive and tends to make the disturbances
move eastward.

4C, the term C contributes to the westward movement. The zonal component of the term C2 is about

This diﬀerence of relation between the term B and
C is due to the latitude where the disturbances exist.

three times larger than that of the term C1. The
term B hinders the westward movement, and nearly

The centers of the SBB disturbances are in 7.5◦ N12.5◦ N band where the low-level westerly jet axis

exists, while that of NBB disturbances are at 17.5◦ N22.5◦ N, where the environmental westerly is weaker.
Figures 5b and 5d show the meridional components of the gradient vectors of NBB and SBB, respectively. They show quite similar characteristics
to each other. The term A is positive, which means
the northward movement. The contributors to thenorthward movement are the terms B2 and E. The
term B2 is due to the environmental southerly windin the lower troposphere over the Bay of Bengal, thus
it contributes to the northward movement mainly inthe lower troposphere (Fig. 6a). On the other hand,Fig. 6b shows that the term E contributes to thenorthward movement mainly in the middle and upper troposphere. The terms B2 and E work at diﬀerent height, though their integrated magnitudes are
similar to each other. The physical explanation of
the eﬀect of the term E is as follows. As shown in
Fig. 3, negative ω  exists at the same latitude of
positive ζ  and positive meridional gradient of ω  isFig. 5: Zonal and meridional components of gradient vectors of the terms: (a) zonal component of
NBB, (b) meridional component of NBB, (c) zonal
component of SBB, and (d) meridional component of
SBB. Symbols on the abscissas are explained in the
text. The dimension of ordinates is [m s−1 ]. Positive
value of zonal and meridional components indicatethat the term tends to move the disturbances eastward and northward, respectively.

found at the northern side of the positive ζ  . This
meridional gradient of ω  twists the environmental
horizontal vorticity vector which points toward south
because of vertical easterly shear, produces positiveζ  tendency, and thus move the disturbance northward.

5 Conclusion
Sub-monthly scale disturbances over the Bay of
Bengal during the boreal summer tend to movenorth-westward with their speed of a few meters per

Fig. 6: Vertical distribution of meridional components of the gradient vectors of the terms (a) B2 and(b) E of SBB. The abscissas indicate pressure, andthe dimension of the ordinates is [m s−1 ]. Each comat the 850-hPa level at theponent is divided by ζyycenter for normalization.

second. The vorticity budget analysis revealed thecontributors to the westward and northward compo-

over the Bay of Bengal and tilting eﬀect of the en-nents of the movement. The main contributor to thewestward movement is the beta term, while strong

vironmental horizontal vorticity vector. The former
eﬀect mainly works at lower troposphere, while thelow-level westerly jet tends to move the disturbances
eastward. When the centers of the disturbances arelatter at middle and upper troposphere. The magnitudes of northward forcing is similar to each other.

around 10◦ N where the axis of the westerly jet locates, the eastward advection nearly counterbalances

References

the beta term, and advection of the environmental
relative vorticity by the disturbances is the second
contributor to the westward movement. For the disturbances which have their centers at 20◦ N, the advection eﬀect by the westerly jet is weaker than thebeta eﬀect.
For the northward movement, the main contributors are advection by the low-level southerly wind

Chen, T.-C., and J.-M. Chen, The 10-20-day mode of
the 1979 Indian monsoon: Its relation with the time
variation of monsoon rainfall. Mon. Wea. Rev.,
121, 2465-2482, 1993.
Yokoi, S., and T. Satomura, An Observational Study ofIntraseasonal Variations over Southeast Asia during
the 1998 Rainy Season. Mon. Wea. Rev., revised.