GEOPHYSICAL
RESEARCH
LETTERS,
VOL. 19,NO.7, PAGES681-684,
APRIL3, 1992
MECHANISMS
OF SOMETROPICALINTRASEASONAL
OSCILLATIONS
B.N.
Goswami and P.
Indian
Institute
Goswami
of Science
Abstract. A underlying mechanism for
two
westward
propagating
tropical
work by the authors have shown (Goswami
and Goswami, 1991, hereafter referred to
Destabilization
of
equatorial
normal
modesby moist feedbacks, in particular,
by
evaporation-wind
feedback,
is
responsible
for
both of them.
The
westward propagating 4-5 day oscillation
and the quasi-biweekly oscillation
result
from destabilization
of the mixed Rossby
4-5 day oscillation
results
from mixed
Rossby gravity (MRG)wave driven unstable
by the moist processes.
However, no
quantitative
theory was available so far
to explain the frequency selection for
the quasi-biweekly oscillation.
For the
first
time, we provide a mechanism for
intraseasona! oscillations
gravity
(MRG)
is discovered.
wave
by
as GG91) that the westward propagating
the
frequency
evaporation-wind feedback.
The frequency
and scale-selection
of the the unstable
MRG wave depend critically
on the
backgroundmean wind.
In mean easterlies
(as in the Pacific and the Atlantic),
it
results in the 4-5 day oscillation
while
in mean westerlies
(as in the Indian
Ocean during
northern
summer) it
in the quasi-biweekly
Three intraseasonal
the tropics
with well
1972,
Krishnamufti
others).
this
The most
oscillation
over
et
al,
1985,
important
is
the
(hereafter
are
processes.
Emanuel
in
time
of
eastward
Asian
referred
the
normal
to
as
important
(1987)
and
showed that
E-W
moist
Neelin
et
E-W feedback
the
equatorial
Kelvin
wave
However, it does not provide a
scale selection
the effect
of
mechanism.
In general,
E-W feedback depends on
whether
the
background
mean winds are
easterlies
or westerlies.
The studies
cited above (Emanuel, 1987, Neelin et al,
1987)
assume that
the background winds
and many
feature
its
south
(1987)
drives
unstable.
propagation
around
the
globe
over
all
three
oceans
throughout
the
year.
Somewhat less well known are the westward
propagating
quasi-biweekly
(10-20
days)
(Yasunari 1979, Krishnamufti
and Bhalme,
1976, Krishnamurti,
1985) and the 4-5 day
oscillations
(Liebmann and Hendon, 1990;
Takayabu
and
Murakami,
1991).
The
quasi-biweekly
oscillation
is
observed
0nly
during
northern
hemisphere
(NH)
summer
feedback
feedback)
al.
scales
are
well
known.
The
most
extensively
studied
amongst them is the
Madden and Julian
or
the
30-50
day
oscillation
(Madden and Julian,
1971,
the
namely, modification of a tropical
results
oscillations
separated
for
mode by the moist processes.
The
convergence
feedback
(or
wave-CISK)
and
the
evaporation-wind
mode.
Introduction
selection
quasi-biweekly
mode and show that both
the westward propagating
oscillations
arise due to the same physical process
are
mean
Julian
easteries.
oscillation
NH summer
over
the
The
Madden
is
strongest
Indian
Ocean
and
during
where
the
mean winds are westerlies.
We show that
under the influence
of the E-W feedback
the Kelvin
wave decays in westerly
mean
background.
Thus, the E-W feedback,
by
itself,
is unlikely
to explain
the Madden
and Julian
oscillations.
However,
we
show that
the MRG wave is also
driven
unstable
by E-W feedback.
This mechanism
in association
with convergence
feedback
also provides
a natural
scale selection
monsoon
for
the
unstable-MRG
wave
as
it
has
a
low
region while
the 4-5 day oscillation
is
observed
over
the
Pacific
and
the
Atlantic
but not over the Indian
Ocean
frequency
maximum in the
growth
rate.
This
low
frequency
maximum,
however,
depends sensitively
on the nature of the
during NH summer.
background winds.
In
the
recent
years
In easterly
background
many studies have attempted to explain
the Madden and Julian oscillation,
all of
which involve
equatorial
Kelvin wave
modified by moist processes (wave-CISK
and
evaporati on-wind
feedback).
Similarly,
Itoh and Ghil (1988) using a
(as in the central Pacific and Atlantic
throughout the year), this corresponds to
the 4-5 day oscillation.
In mean
westerlies
(as over Indian Ocean during
NH summer
)
it
corresponds
to
the
monsoonal 10-20 day oscillation.
This
processes are essential
for generating
the
4-5
day
westward
propagating
oscillation
in the troposphere.
Recent
seen over the
NH Indian
Ocean if
continuous data is taken (e.g. Liebmann
and Hendon, 1990).
numerical
model
indicate
that
moist
may be why the
The
Copyright
!992by theAmerican
Geophysical
Union.
Paper
number92GL00488
To
0094-8534/92/92GL-00488503.00
study
equatorial
681
4-5
model
the
oscillation
and
not
results
modification
waves by the
is
moist
of
the
processes,
682
we
Goswami and Goswami: Mechanisms of tropical
use
model
a
linear
with
a
equatorial
first
beta-plane
baroclinic
F\
mode
vertical
structure.
The model,
the
method
of
nondimensionalization,
the
parameter. ization
of the moist processes
and the parameters
used are discussed
in
detail
in
equations
GG91.
The
may be written
oscillations
D
0'96
r
0.72•-
nondimensional
C
0.48
as
0.24
•5 -
yv/2 + au = •
,
0
I
i,
•
•
4
• + yu/2 + Av = •] ,
88
8u
(1)
1.20
I
0
•
2
4
I
'
8v
•5 - F (• + •)
+ Au+ Be = 0 ,
0 32
where
u and v represent
the
zonal
and
meridional
wind
perturbations,
e,
potential
temperature
prturbation
in the
middle
level
and
A and B represent
Raleigh
friction
and Newtonian
cooling
coefficients
respectively.
The time and
length
scales
used
for
nondimensionalization
in
Eq. (1)
are
approximately
0.22
days
and
1100
km
respectively.
The
nondimensional
parameter
F represents
the reduced static
stability
due to convergence
feedback.
F
=
1
and
F =
0 represent
the
no
convergence
2
feedback
and
the
moist
0.24
--
_
0.4
02
0
0.2
G•owth
Fig.
1:
Non
0.4
rate
dimensional
dispersion
relation
for the MRG wave with A=B=0, F =
0.1 and for A = 0.25 and A = -0.25.
(a)
Dependence
of
real
wavenumber k
on
r
neutral states respectively.
The frequency
part of the
solution
for•. both The
A's real
are identical.
(b)
parameter
A represents
the
strength
of
the E-Wfeedbackand is positive in mean Dependence
of growthrates on •.
easterlies
and
wester!ies.
A
negative
in
nondimensional
mean
value
of
A
=
1 roughlygives an evaporationrate of
about 1 mmday-1 of water vapour from the
surface
for
a
wind
speed
of
5m
s
-1
.
Seekingwavesolution of the form
(u, v, e)
=
(u,
e)
(y) exp
(•+iB)
-
(F k + iA)k
winds
the
Eq.
Kelvin
(1)
mode
contains
also
{ i (kx-•t)
= 0
flow
is
the
Kelvin
unstable.
all
the moist processes.
},
the dispersion relation for the Kelvin
wave(for whichthe meridiona!velocity v
= 0) can be written as
(•+iA)
mean background
wavesdecay and for easterly background
the
dry
tropical
normalmodes(Matsuno,1966), modifiedby
(x, y, t)
v,
westerly
(2)
Assuming
that
there
is
no
Raleigh
friction
(A=0) and no Newtonian
cooling
(B=0) and introducing
• = • + i• , the
r
•
Eq. (2) canbe easily solvedto give
introduce
discusses
relation
for
some
in
The moist processes
new
detail
the
modes.
the
lowest
GG91
dispersion
meridional
mode
(n = 0) in the presence of mean
easterlies. In this study, we compare
the n = 0 equatorial modesmodifiedby
E-W feedback
in the
presence
of mean
easterlies
(A > 0) with
those
in the
presence of mean westerlies
(A < 0).
In
the
dry
atmosphere,
the
n = 0 case
contains only the MRG wave.
The presence
of E-W feedback introduces
an additional
westward
propagating
mode. Assuming
that
the
frequency,
•,
is
positive
definite
•r=-+[ kaF
+ ( k4F2+
kaA
2)1/•'
/•/2 positive
and
allowing
wave-number,
k, tobe
•...................
or the
negative,
the dispersion
relation
k A
and
•i=
i
(3)
(4)
2 o3
r
For the Kelvin waves, Cr= • r / k >- 0.
Whenk is positive,
we have to accept •
>0 solution for Eq (3) while if k is
negative we have to accept the • r <0
solution of Eq. (3). In either case it is
easy to see that the growth rates are
directly proportional to A. Hence, for
for
F
=
0.1
and
for
two
values
of A namely, A = + 0.25 are shownin
figure
1 for
the
case (A = B = 0).
n = 0,
nondissipative
The dependenceof the
real wave number (kr) on frequency
(figure la) showsthat apart from the
modified MRG wave (ABCD), a new westward
propagating mode (EBCF) is
introduced.
It can be easily shownthat this mode
(not allowed
in the dry caseas its eigen
functions
are unbounded) has bounded
eigen functions in the presence of the
moist feedbacks. As long as the stren•
of the E-W feedback remains the same (IAI
Goswami
and Goswami:
Mechanisms
of tropical oscillations
= const.),
the
dependence
of
k
on
•
683
is
1.8
not affected
by whether the background
wind is easterly
(A > 0) or westerly
(A <
0).
E1 and W1 in figure
l(b) represent
.-
2.4
1.4
the growth rates
for the MRG wave when A
= +0.25 and A = -0.25
respectively.
In
the
presence
of
mean westerlies,
the
I.O
growth rate curve for the MRG wave is a
mirror image of the corresponding growth
rate
curve
in
the
mean easterlies
damped (not
case is
mean
the
shown) .
unstable
domain with
a
easter
lies.
The MRG wave
in
low
In
new wave is
the
low
0.2
always
in
this
frequency
frequency
maximum in
the growth rate
(around
nondimensional
•
= 0.3) .
This corresponds
to a westward
propagating
4.5
days
wave with
and
a period
wavelength
thousand kilometers.
ßof
of
about
about
nine
In mean westerlies,
on the other
hand, the MRG (Wl) wave is
unstable with two maxima, one in the low
frequency (around nondimensional • • 0.1)
and the
other
in the
high
frequency
(around nondimensional • • 0.5) regime.
The low frequency maximumcorresponds to
a westward propagating wave with a period
Fig. 2:Dependence of the period (a) and
wavelength (b) of the maximally growing
low frequency wave in mean easterlies.
of about 14 days and wavelength of about
three thousand kilometers.
In mean
Periods are in days with contour interval
0.25.
Wavelengths are in thousand km
westerlies,
the
nondissipative
unstable
new
case
but
branch
(not
with
no
shown)
maximum
in
the
is
also
in
the
growth rates.
The presence of a small
amount of dissipation
(A=B•0), makes this
branch neutral but does not change the
low frequency maximumin the other branch
appreciab•ly.
The characteristics
of the
maximally growing wave in the easterlies
agree extremely well with the observed
westward propagating 4-5 day wave in the
Pacific
and Atlantic
(Liebmann and
Hendon,1990). The maximally growing low
frequency
agree
wave
well
observed
in
with
over
mean
the
south
westerlies
summer
is
observed.
we
believe
physical
somewhat
Our model
that
agreement
very
inclusion
processes
of
may
the
these
processes may vary
from one
equatorial region to another and from one
season to another.
We envisage that the
observed
quasi-periodicity
of
the
tropical
intraseasonal oscillations
may
be due to the variations of the strength
of the moist feedbacks. In figure 2 and
figure 3, we show how the period and
wavelength of the maximally growing low
frequency wave vary with strengths of
1976,
The
than
simple,
of
other
provide
better
wavelength
with
observations.
Thus, the destabilization
of the MRG wave by the
E-W feedback
provides the long sought mechanism for
the frequency
as well
selection
as in the
Another
of
is their
these
4-5
feature
oscillations
be explained
the
-0.2
days
days.
characteristic
intraseasonal
Most
10-20
in
that
of
needs
the
to
- 0,8
quasi-periodicity.
oscillations
occur
over
a
band of frequencies rather than a single
frequency.
While the 4-5 day oscillation
show relatively
lower variation,
it is
quite
large
for
the
quasi-biweekly
oscillation
( 10-20 day) .
Our theory
offers
a natural
explanation
of this
quasi-periodicity
dependence of
feedbacks
on
conditions,
mean winds,
when we
consider
the strength of
the
prevailing
-14
-•0
0 08
0 28
0 48
the
these
mean
such as the strength of the
static
stability,
sea surface
temperature etc.
2.
monsoon
shorter
being
interval
mode
region
(Krishnamurti
and Bhalme,
Krishnamurti
and Ardunay,
1980).
wavelength
contour
also
quasi-biweekly
Asian
with
Thus, the strengths of
0 68
0 88
r
Fig. 3: Same as in Figure 2 but for the
maximally growing low frequency wave in
mean westerlies.
Contour interval
for
periods
0.4
is
5 and that
for
wavelength
is
684
Goswami and Goswami: Mechanisms of tropical
convergence feedback (F) and E-W feedback
(A)
in
mean
westerlies
easterlies
and
respectively.
in
mean
Hatchings
in
the
oscillations
tropics.
2324-2340,
J.
1987.
Atmos.
Goswami,Prashanth
and
sci____=.,
44,
B.N. Goswami,
figure
2a
and
figure
3a
show the
approximate range of the strengths of the
feedbacks
that
provide
the
observed
periods.
We also note that the period
and wavelength
of the
low frequency
maximumin wester!ies is rather sensitive
to
the
variation
of
the
feedback
strengths but those for the low frequency
maximum in mean easterlies
vary little
over a wide range of variations
of A and
F.
This
also
agrees well
with the
Modification
of n = 0 equatorial
waves
due to interaction
between convection
and dynamics. J• .A.t.
mos. sci____=.,
48,
2231-2244, 1991.
Itoh, H.J.
and M.J. Ghil,
The generation
mechanism of mixed Rossby gravity
waves in the equatorial
troposphere.
J• Atmos. Sci., 45, 585-604, 1988.
Krishnamurti,T.N.
and
H.N.Bhalme,
Oscillations
of a monsoon system, Part
I : Observation
aspects.
J_=. Atmos
observation
4-5 day is
Sci.,
33, 1937-1954,
1976.
Krishnamurti,T.N.
and P.Ardunay,
10-20
day westward
propagating
mode and
"Breaks" in the monsoons. Tellus,
32,
15-26,
1980.
Krishnamurti, T. N.,
P.K. Jayakumar,
J. Sheng,
N. Surgi
and
A. Kumar,
that
the spectrum around the
rather
sharp while the period
for the quasi-biweekly
mode varies
from
10 to 20 days.
The moist feedbacks also
modify
the
eigen
functions
of the MRG
wave
and
introduce
a
meridional
propagation
which
also
agrees
with
observations.
Further
modification
of
the
feedback
in
published
elsewhere.
details
on
the
n = 0 waves by E-W
mean
westerlies
will
be
Divergent
time
circulation
scale.
364-375,
J.
T. N.,
experiment113,
It
is shown here
westward propagating
the 10-20 day oscillation and the 4-5
oscillation
both
result
from
day
Sci.
42,
Summer
A review.
1590-1625,
Liebmann, B.
that
two equatorial
oscillations
namely,
30-50
1985.
Krishnamurti,
Conclusions
on
Atmos.
monsoon
Mon. Wea. Rev.,
1985.
and
H.H. Hendon,
scale
disturbances
J. Atmos. sci.,
47,
--
Synoptic
near
the
1463-1479,
equator.
1990.
Madden,R.A.and P.R.Julian, Detection of
a 40-50 day oscillation
in the zonal
destabilization equatorial normal modes
wind in the tropical Pacific. J_•.
(MRG) by E-W feedback.
The moist
Atmos.Sci., 28, 702-708, 1971.
processes introduce the
required Madden,R.A.and P.R.Julian, Description
frequencyselection in case of both these
of global scale circulation cells in
oscillations. In addition, they give rise
the tropics with a 40-50 day period.
to latitudinal
phase propagation as
J. Atmos. Sci., 29, 1109-1123, 1972.
observed. The observedquasi-periodicity
Matsuno,
T, Quasigeostrophic motions in
of
these
spatial
waves is
a reflection
and temporal variations
of
the
of the
strengths of the moist feedbacks. The
mechanism for
the
4-5
day lower
tropospheric wave discussedhere also
provides a long sought explanation for
the forcing required for the observed 4-5
day lower stratospheric wave. Webelieve
that the discovery of this commonalityin
the mechanisms for
westward
these two classes of
propagating
oscillations
is
understanding
an
intraseasonal
advance
of
in
our
intraseasonal
variability
in
the
tropics.
We also
predict
that
if data for only winter
is
examined over the equatorial
Indian Ocean
(when the mean winds are easterlies),
the
4-5 day oscillation
should be seen even
over
the
Indian
Ocean.
The
authors
preparing
the
of
authors
Ocean
India
for
a grant.
The
grateful
to
an anonymous
some interesting
comments.
also
thank
Mrs.
R
Rama
for
the manuscript.
area.
J_=.Meteorol.
Neelin,J.D.,
I.M.Held
and K.H.Cook,
Evaporation wind feedback and low
frequencyvariability in the tropical
atmosphere. J_=. Atmos. Sci.,
2341-2348, 1987.
Takayabu,Y.N.
structure
and
of
An air
intraseasonal
sea
interaction
oscillations
in
44,
M.Murakami, The
super cloud
clusters
observed in 1-20 June 1986 and their
relationship
Meteorol.
Soc.
Yasunari, T .J.,
to
easterly
Japan,
69,
Cloudiness
associated
with
hemisphere
Meteorol.
the
waves. J_•.
1991.
fluctuations
northern
summer
monsoon.
J__.
Sco.
Ja__a•,
57,
227-262,
1979.
Goswami
and
Centre
for
indian
Institute
Bangalore
Present
Prashanth
Atmospheric
560
of
012,
Goswami
Sciences
Science
india.
affiliation:
Department
of Physics
Indian
Institute
of Technology
Kanpur 208 016, india.
References
Emanuel,K.A.,
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B.N.
Acknowledqements
One of
(BNG)
thanks
Department
Development,
authors
are
reviewer
for
the equatorial
Received
Revised
: November 13, 1991
: January 21, 1992
Accepted
: February
19,
1992