4400

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 64

Seasonality and Regionality of the Madden–Julian Oscillation, Kelvin Wave, andEquatorial Rossby Wave
HIROHIKO MASUNAGA*
Colorado State University, Fort Collins, Colorado(Manuscript received 19 May 2006, in final form 27 March 2007)
ABSTRACTThe Madden–Julian oscillation (MJO), Kelvin wave, and equatorial Rossby (ER) wave—collectively
called intraseasonal oscillations (ISOs)—are investigated using a 25-yr record of outgoing longwave radiation (OLR) measurements as well as the associated dynamical fields. The ISO modes are detected byapplying bandpass filters to the OLR data in the frequency–wavenumber space. An automated wavetracking algorithm is applied to each ISO mode so that convection centers accompanied with the ISOs aretraced in space and time in an objective fashion. The identified paths of the individual ISO modes are firstexamined and found strongly modulated regionally and seasonally. The dynamical structure is composited
with respect to the convection centers of each ISO mode. A baroclinic mode of the combined Rossby and
Kelvin structure is prominent for the MJO, consistent with existing work. The Kelvin wave exhibits a
low-level wind field resembling the shallow-water solution, while a slight lead of low-level convergence overconvection suggests the impact of frictional boundary layer convergence on Kelvin wave dynamics. A laggedcomposite analysis reveals that the MJO is accompanied with a Kelvin wave approaching from the west
preceding the MJO convective maximum in austral summer. MJO activity then peaks as the Kelvin and ER
waves constructively interfere to enhance off-equatorial boundary layer convergence. The MJO leaves a
Kelvin wave emanating to the east once the peak phase is passed. The approaching Kelvin wave prior to thedevelopment of MJO convection is absent in boreal summer and fall. The composite ER wave, loosely
concentrated around the MJO, is nearly stationary throughout. A possible scenario to physically translate
the observed result is also discussed.

1. Introduction
The tropical 40–50-day oscillation originally discovered by Madden and Julian (1971), generally called theMadden–Julian oscillation (MJO), has spawned numerous studies in efforts to understand its physical nature.
The MJO is an eastward-propagating, equatoriallytrapped mode with its vertical structure being dominantly baroclinic (Madden and Julian 1972). These fundamental features are at first glance reminiscent of theconvectively coupled Kelvin wave, but MJO propagation is considerably slower and more dispersive than* Current affiliation: Hydrospheric Atmospheric ResearchCenter, Nagoya University, Nagoya, Japan.

Corresponding author address: Hirohiko Masunaga, Hydrospheric Atmospheric Research Center, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8601, Japan.
E-mail: masunaga@hyarc.nagoya-u.ac.jp
DOI: 10.1175/2007JAS2179.1© 2007 American Meteorological Society

expected for the moist Kelvin wave. Whereas a zonal
wind anomaly is predominant near the equator, a cyclonic (anticyclonic) horizontal circulation in the lower(upper) troposphere off the equator is typically observed in association with the MJO. Many authors discussed this combined Rossby and Kelvin structure interms of the atmospheric response to a local heatanomaly induced by MJO convection (see review by
Zhang 2005 and references therein).
The Rossby and Kelvin waves accompanied with the
MJO are not necessarily only a passive response to convective heating. Masunaga et al. (2006) pointed out thepotential roles of the Kelvin and equatorial Rossby(ER) waves in the MJO propagation mechanism. Satellite precipitation data analyzed by Masunaga et al.
(2006) showed that the MJO envelope occasionally encompasses a group of Kelvin waves as well as incoming
ER waves that often interrupt Kelvin wave propagation. Their result suggests the possibility that neighboring ridges of the interrupted Kelvin wave as a whole
could account for the slow eastward propagation of theDECEMBER 2007

MASUNAGA

MJO. The analysis of Masunaga et al. (2006), however,is limited to subjective diagnosis based on 10 MJO episodes. In this work, long-term outgoing longwave radiation (OLR) data are analyzed to seek climatologicalevidence (or its absence) of the Kelvin and ER waves asa driver of MJO propagation.
Seasonality and regionality of the MJO, which wereoutside the scope of Masunaga et al. (2006), are also amajor interest of the present study. Although the MJO
is a planetary-scale, year-round phenomenon, notableregional and seasonal variability is generally well recognized. MJO activity normally peaks spatially over thewest Pacific warm pool through the South Pacific convergence zone (SPCZ; e.g., Salby and Hendon 1994;
Matthews et al. 1996; Yanai et al. 2000) and seasonallyin austral summer (Madden 1986; Gutzler and Madden
1989; Zhang and Dong 2004). The boreal summer MJO
tends to migrate northward from the Indian Ocean(e.g., Yasunari 1979; Lau and Chan 1986; Lawrence andWebster 2002). The seasonality and regionality of the
MJO imply that the amplitude and propagation direction of the MJO are susceptible to strong modulations
by geophysical conditions such as sea surface temperature (SST) and geographical constraint. Such environmental factors, in addition to atmospheric disturbancesbrought by large-scale waves, likely provide a crucial
physical element that drives the MJO.
The present study analyzes the MJO, Kelvin wave,
and ER wave, which are collectively called the intraseasonal oscillation (ISO) modes for convenience in thispaper. A 25-yr record of satellite-measured OLR isbandpass filtered in the frequency–wavenumber space
to extract each ISO mode. Since OLR is a proxy ofdeep convection, OLR-filtered waves are considered torepresent convectively coupled modes. The Kelvin(ER) wave is therefore meant to be the “moist” Kelvin(ER) wave throughout this paper unless otherwise indicated. The dynamical field associated with each ISO
mode and a possible relationship of the MJO with the
Kelvin and ER waves are explored by a compositing
technique with an automated wave-tracking algorithm.
Data and analysis methods adopted in this study aredescribed in section 2, followed by section 3 where theanalyzed results are presented. The current findings arethen discussed and summarized in the context of a
possible scenario proposed to interpret the results (section 4).

2. Data and method
The daily, 2.5° ⫻ 2.5° global OLR dataset provided
by National Oceanic and Atmospheric Administration(NOAA) is employed. The NOAA OLR is converted

4401

from polar-orbiting satellite measurements at infraredwindow channels through an analytic formula (Gruber
and Krueger 1984). A 25-yr record from 1 January 1980
to 31 December 2004 is analyzed in the present paper.
For investigating dynamical field associated with theISOs, the daily datasets of horizontal winds and geopotential height are taken from the National Centers forEnvironmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data (Kalnay et al. 1996).
Sinusoidal backgrounds with the periods of one, ahalf, and a quarter year are removed in advance fromthe OLR and dynamical fields in order to isolate intraseasonal variations from the contamination of seasonal cycle. It is noted that any seasonal dependence
unaccountable by the first three harmonics of the annual cycle would be left behind in the datasets. Thisremnant component of seasonality in the ISO characteristics is a primary interest of this work. The December–February (DJF) months are denoted as australsummer, March–May (MAM) as austral fall, June–
August (JJA) as boreal summer, and September–
November (SON) as boreal fall, except for the spectral
analysis where a 128-day sequence is assigned to eachseason as described later. El Niño periods are removed
from any seasonal category in order to factor ENSOrelated anomaly out of climatological patterns, as alsodone by Wheeler and Hendon (2004). The standardized
Southern Oscillation index (SOI) is used for identifying
El Niño events (Trenberth 1984). El Niño is considered
to have occurred for months when the standardized
SOI, temporally smoothed by 5-month moving average,
is lower than ⫺1. In total, 60 months are identified as El
Niño between the years of 1980 and 2004.
Frequency–wavenumber analysis of OLR is conducted using the scheme described by Masunaga et al.
(2006), who modified the method originally proposedby Wheeler and Kiladis (1999), except for specific differences mentioned below. In the current analysis, thespace–time spectrum is broken down by three latitudinal sections of 15°–5°S, 5°S–5°⌵, and 5°–15°⌵, and isthen further separated by different seasons. Symmetricand antisymmetric decomposition (Yanai and Murakami 1970) is not performed so that the separated
latitudinal bands are treated independently of eachother. Each season is defined by a 128-day time sequence centered on 15 January, 16 April, 16 July, and15 October for the spectral analysis. Each end of a time
sequence overlaps with the adjacent sequence for thesake of minimizing the data loss by tapering. The statistical significance of spectral power is evaluated basedon the Student’s t test against the red-noise spectrum
from 125 (5 latitudes ⫻ 25 yr) spectral samples for each

4402

JOURNAL OF THE ATMOSPHERIC SCIENCES

meridional band and each season. Since neighboring
latitudinal slips may be somewhat correlated with eachother, the degrees of freedom are chosen to be a conservative value of 50 ⫺ 1 ⫽ 49 when the statisticalsignificance is quantified. The explicit form of the rednoise spectrum prn is given as (section 11.2.5 in vonStorch and Zwiers 1999)
prn共k, ␻兲 ⫽

2
␴Z
共k兲

1 ⫹ ␣1共k兲 ⫺ 2␣1共k兲 cos共2␲␻兲
2

,

共1兲

where k is zonal wavenumber, ␻ is frequency, ␴ 2Z is thevariance of driving white noise, and ␣1 is lag-1 autocorrelation coefficient computed from the observed timeseries whose longitudinal component is transformed
into wavenumber space. In Eq. (1), ␴ 2Z is chosen so that
it is equivalent to the amplitude of the original spectrum when integrated over frequency at each wavenumber. El Niño months are not isolated in the spectral
analysis because otherwise a sufficient number of 128day time series would be difficult to sample.
The ISOs are tracked in space and time by the following procedure. Individual ISO modes are identified
by applying bandpass filters to the time–longitude series of OLR at each latitude (every 2.5°) between 20°S
and 20°⌵. ⌻he filter design adopted in this paper, as
also indicated in the space–time spectrum shown later(Fig. 2), is summarized as follows. The MJO filter isdefined by a rectangular filter bound between 20 and 80
days in cycle and 1 and 7 in wavenumber. This period
range includes a majority of the observed MJO periods(from 22 to 79 days) as documented by Madden andJulian (1994). An alternative MJO filter, slightly narrowed to 30–80 days, was also tried and found to makeno statistically significant change in composite diagrams(not shown). The Kelvin wave filter is bounded by 1 ⱕk ⱕ 10, 0.05 ⱕ ␻ ⱕ 0.25 cycles per day (cpd) (4–20 daysin period), and a pair of theoretical dispersion relations
with the equivalent depths of 5 and 100 m. A smallerequivalent depth, or a lower phase speed, in general
represents a convectively coupled mode. Large-scale
waves are slowed down when coupled with the moist
processes, which may be ascribable to a reduction in theeffective static stability (Chang 1977; Emanuel et al.
1994; Neelin and Yu 1994) and/or to the selection ofshallower vertical modes in response to particular heating profiles (Mapes 2000; Wheeler et al. 2000; see also
review by Wheeler and Kiladis 1999). The n ⫽ 1 ER
wave filter is defined between ⫺10 ⱕ k ⬍ 0 and two
dispersion relations with the equivalent depths of 5 and100 m.
The spatial maximum of convective activity associated with a given ISO mode is located first by the me-

VOLUME 64

TABLE 1. Number of the ISO convection centers identified for
different seasons and regions.
Season/region

MJO

KelvinER

Austral summer
Austral fall
Boreal summer
Boreal fall
Indian Ocean
Pacific Ocean

4962
4976
3271
4159
4365
4230

5933
6675
4937
5040
4656
6245

9170
9126
7191
8556
6109
6974

ridional minimum in the filtered OLR at each longitude. The meridional range to search is from 20°S to20°⌵ for the MJO and ER wave, while a narrower
range of 12.5°S to 12.5°N is chosen for the Kelvin wave
in order to avoid the contamination of extratropical
Rossby wave (Straub and Kiladis 2003a; Roundy andFrank 2004a). The linear shallow-water theory (Matsuno 1966) predicts that the amplitude of the equatorial
Kelvin wave decays poleward at the e-folding scale of(2公gh /␤)1/2, where g, ␤, and h are the gravitational
acceleration, meridional derivative of the Coriolis parameter, and equivalent depth, respectively. This decaying scale varies from 970 to 1390 km for a plausible
range of h between 12 and 50 m (Wheeler and Kiladis1999). The meridional coverage of ⫾12.5° or ⫾1390 km
is thus sufficient to detect a vast majority of real Kelvinwave signals.
Zonal local minima in the filtered OLR are thensought among a series of the meridional minima acrosslongitudes. The local minima are defined within the
search radius of ⫾15° in longitude, ignoring noisy fluctuations on smaller scales. This threshold has been chosen conservatively, given that the ISO filters in use exclude any spatial structures finer than a zonal wavenumber of 10. This procedure to find zonal local
minima is carried out in a way similar to moving averaging, allowing the successive ⫾15° slips to overlap.
The identified OLR minima are considered to represent “ISO convection centers” when the amplitude exceeds twice the standard deviation of the filtered OLR
for individual ISO modes. The standard deviations of
the filtered OLR are 8.90, 9.29, and 9.37 W m⫺2 for the
MJO, Kelvin wave, and ER wave, respectively. The
total number of the ISO convection centers identified
in this study is listed in Table 1. The 2␴ criterion mentioned above, aimed at removing noisy components,
might be thought to put excessive focus on extreme
cases. This criterion is, however, unlikely to damage therepresentativeness of the selected ISO modes. The
numbers listed Table 1 would increase only by a small
factor (⬃1.5–3.5) if the 2␴ threshold were not applied.
The procedure to select the spatial minima of OLR has

DECEMBER 2007

MASUNAGA

FIG. 1. A temporal sequence of MJO events is depicted every 10
days starting from 10 January 1988. MJO-filtered OLR is drawn atintervals of 10 W m⫺2 with solid (dashed) contour for negative(positive) anomalies, where zero contour is omitted. MJO convection centers identified by the tracking algorithm introduced in
section 2 are marked by crosses.

4403

Atlantic Ocean and in the Red Sea through the Arabian Sea, moving eastward in the last two snapshots. A
transient feature that appears over Africa on 20 January vanishes if the MJO filter is cut off at the period of
30 days instead of 20 days, while the major characteristics described above remain the same. Figure 1 demonstrates that the ISO-tracking algorithm is overall successful in capturing the fundamental features of ISO
propagation recorded in the OLR dataset.
A composite analysis is performed to examine thedynamical structure associated with each ISO mode. A
composite diagram is constructed with respect to spatially variable base points given by the ISO convection
centers defined above. A lagged composite analysis anda composite time–longitude analysis are also carriedout to explore possible relationships among different
ISO modes, where filtered OLR variance for the Kelvinand ER waves is composited around the MJO convection centers. Compared to a geographically fixed basepoint commonly used for composite and lagged regression analyses, a movable (or Lagrangian) base point
locked to wave propagation is better suited for tracing
the spatial structure directly coupled with the ISOs.
The composite analysis of Benedict and Randall (2007),using a spatially flexible base point fixed at the observed rainfall maximum, was successful in delineating
the thermodynamic structure associated with the MJO.
Statistical significance is estimated at each location in
the composite domain based on the Student’s t test
against the null hypothesis that the composite variable
is equivalent to the climatological mean (or zeroanomaly). Portions with statistical significances lessthan 95% are not plotted.

3. Resultsa. Variability in space–time spectrum

already narrowed down the convection center candidates to some extent.
The performance of the ISO-tracking algorithm isdelineated in the sequential maps of sample MJO episodes (Fig. 1). MJO-filtered OLR is depicted every 10
days together with MJO convection centers (marked bycross) identified in the manner described above. On thefirst day (10 January), three convection centers are observed in the Indian Ocean, SPCZ, and intertropicalconvergence zone (ITCZ). The first MJO event, initiated in the Indian Ocean, intensifies as it propagates tothe east, while the other two events die out in the east
Pacific. Convective activity associated with the firstevent eventually peaks in the SPCZ on 19 February,and starts decaying as it proceeds beyond the date line
(29 February). Separate MJO events also appear in the

Seasonal variability of the ISOs at different latitudes
is first outlined based on a frequency–wavenumber
analysis. Figure 2 shows the space–time spectra of OLR
for different seasons and three meridional bands. Spectral signals are scaled by statistical significance tested
against the red noise. The theoretical dispersion relations are depicted in each panel for the Kelvin wave
(solid), n ⫽ 1 ER wave (dash-dotted), and the mixed
Rossby–gravity (MRG) wave (dashed) for equivalent
depths of 5, 20, and 100 m. These dispersion relations
were obtained from the solutions derived by Matsuno(1966). The bandpass filters used later for tracking theISOs are indicated by boxes in Fig. 2.
The MJO is easily recognized across all tropical latitudes and seasons. The MJO signal has a distinct peakat wavenumbers of 1–3 in austral summer, which past

JOURNAL OF THE ATMOSPHERIC SCIENCES

FIG. 2. Space–time spectrum of OLR for (top to bottom) different latitudinal bands and (left to right) different seasons. Eastward (westward) propagation is represented by positive(negative) zonal wavenumbers. Spectral power is shaded in terms of the statistical significance tested against the red-noise spectrum and is shaded only for significance levels of 90%
or higher. Bandpass filters used for the wave-tracking algorithm (see text) are indicated by boxes. The filters are labeled in the top-left panel. Theoretical equivalent depths (Matsuno
1966) of 5, 20, and 100 m, from bottom to top, are plotted for each of the Kelvin, ER, and MRG waves.

4404
VOLUME 64

DECEMBER 2007

MASUNAGA

studies pointed out is the primary peak season of the
MJO (e.g., Madden 1986; Gutzler and Madden 1989;
Zhang and Dong 2004; Roundy and Frank 2004a). A
separate high-wavenumber component (k ⬎ 5) appears
in austral fall, possibly making the MJO more dispersive and thus more quickly broken as it propagates. It
is, however, noted that the high-wavenumber modes
are exaggerated rather than actual, since the spectral
power is normalized by the red-noise spectrum. The
MJO in the Southern Hemisphere weakens in boreal
summer and fall. The Kelvin wave is most prominent inaustral fall, with its spectral power concentrated aroundthe equator as expected by the linear theory (Matsuno
1966). The Kelvin wave remains active through boreal
summer, but its amplitude is somewhat shifted awayfrom the equator in the Northern Hemisphere. This
off-equatorial maximum of the Kelvin wave is related
to the seasonal migration of ITCZ as will become clear
later. Kelvin wave signals are less significant in australsummer and boreal fall.
The ER wave, observed regardless of latitudes andseasons, is the only constituent of westward-propagating low-frequency waves in austral summer and fall.
On the other hand, another westward mode spreadover a broad spectral domain emerges in boreal summer and fall. This mode likely corresponds to the tropical depression (TD)-type disturbance (Takayabu andNitta 1993), as well as the MRG wave where its dispersion relation overlaps, as discussed in the literature(Wheeler and Kiladis 1999; Roundy and Frank 2004a).
The Southern Hemisphere in boreal fall shows clear
evidence for the MRG wave distinct from any otherspectral modes. This is consistent with the result ofHendon and Liebmann (1991), who found the MRG
wave most active in boreal fall. A confined peak at thewavenumber of 14 and the cycle of ⬃9 days is an artifact due to the spatial and temporal regularity in satellite sampling (Wheeler and Kiladis 1999; Masunaga et
al. 2006).

b. Characteristics of individual ISO modes
The individual ISO modes as tracked in the manner
introduced in section 2 are next investigated. Figure 3
depicts the frequency of occurrence of ISO events together with unfiltered OLR flux as a function of longitude. The frequency of occurrence (defined from thenumber of days with the ISO convection centers observed during the entire period studied) and OLR arezonally smoothed by ⫾15° moving average because
smaller-scale fluctuations are ignored in the tracking
algorithm. Overall, the ISOs are most active from theIndian Ocean through the central Pacific (60°E–180°).
The secondary peak appears in the Atlantic Ocean

4405

FIG. 3. Frequency of occurrence (labeled on the left ordinate)
for the MJO (solid), Kelvin wave (dashed), and ER wave (dotted)
convection centers as well as unfiltered OLR flux (dot-dashed,labeled on the right ordinate) as a function of longitude. Different
panels are for different seasons.

around 30°W, most clearly in austral summer, but iscompletely missing in boreal summer. ISO activity
tapers off to minima near 0° and/or in the west of 60°W,
most likely due to the influence of the African andSouth American continents (Knutson and Weickmann
1987).
In addition to these general features, the ISOs shownotable seasonal variations in the frequency of occurrence. In austral summer, the MJO forms a plateau
extending from 60°E to the date line. The Kelvin wave
also exhibits a plateau closely following the MJO. The
MJO plateau is decomposed into a pair of narrower
peaks at 80° and 160°E in austral fall. The second peakin the Pacific Ocean disappears in boreal summer, leaving behind a single maximum in the Indian Ocean witha gradually declining shoulder in its east. The absenceof the second MJO peak sharply contrasts with the
double-peaked distribution of the Kelvin wave in thesame season. The boreal summer MJO exhibits aweaker, separate group in the east Pacific (120°W) as
well. The boreal fall ISOs show an intermediate feature
between the preceding and following seasons. The ER
wave exhibits a pattern generally similar to the othertwo ISO modes. A notable difference is, however, thatthe plateau between 60° and the date line stays
throughout a year for the ER wave without being decomposed into separate peaks.

4406

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 64

FIG. 4. The global distribution of the (left) MJO, (middle) Kelvin wave, and (right) ER wave convection centers in the frequencyof their occurrence. Different panels (top to bottom) are for different seasons.

The fundamental feature of unfiltered OLR is quite
steady throughout the year. OLR is coldest over the
Indo-Pacific warm pool with a slight dip on the Maritime Continent (120°E). Secondary peaks are located in
Africa and South America, as opposed to the ISOfiltered OLR, which is least active over the continents.
This indicates that deep convection developing on
tropical Americas and Africa has little connection withlarge-scale organization associated with the ISOs.
To further investigate these features, the frequencyof ISO occurrence is plotted on a global map (Fig. 4).
The austral summer MJO appears to prefer a narrow
channel around 10°S between Indonesia/New Guinea
and Australia from the Indian Ocean to eventuallyreach SPCZ. This branch is mainly responsible for the
MJO plateau seen in Fig. 3. Together with another (lessconspicuous) branch leading to the northern Pacificthrough the north of the Maritime Continent, typical
MJO trajectories in austral summer resemble the“N(S)E mode” identified by Wang and Rui (1990b). It
is noted that the northwestern Pacific MJO, propagating nearly northward as described by Wang and Rui(1990b), is probably not well detected in this study. In
austral fall, MJO paths constitute a major group in the
Indian Ocean and another in the west Pacific with alocal minimum over the Maritime Continent as was evident in Fig. 3. The “EE mode” defined by Wang andRui (1990b) well shares basic characteristics with the
austral fall MJO. A local minimum of MJO activity
over the Maritime Continent drew the attention ofmany authors in the literature (e.g., Salby and Hendon
1994; Zhang and Hendon 1997; Kemball-Cook andWeare 2001).
The MJO is strictly limited in the east of the central
Pacific in boreal summer, aside from a separate signal
confined in the eastern Pacific ITCZ as also recognizedby Knutson and Weickmann (1987). The disappearanceof the Pacific peak in this season (Fig. 3) reflects thisweakened MJO activity in the west Pacific and SPCZ.
ISO propagation has been known to have a notablenorthward component over the Indian Ocean and subcontinent since early work by Yasunari (1979, 1980,1981) in association with the active and break cycle of
the South Asian summer monsoon. The boreal summer
MJO indeed exhibits a considerable northward extension from the equatorial Indian Ocean across the Bayof Bengal in Fig. 4, although it seems composed of separate bands rather than continuous northward development. Sampling bias may be responsible for the apparent discontinuity, because the bandpass filters used

DECEMBER 2007

MASUNAGA

here do not detect any northward propagation unless it
is accompanied with a zonal component. Eastward
propagation is present or absent in association with thenorthward movement, depending systematically on thephase of the ISO cycle (Lau and Chan 1986; Lawrence
and Webster 2002). The presence of gaps could be also
because the northward migration of cloud systems is
not meridionally uniform in this area (Sikka and Gadgil
1980). It is also noted that meridional scale is exaggerated compared to zonal scale in Fig. 4, which makes thelatitudinal gaps look wider than actual. The generalproperties possessed by the boreal summer MJO are
still observed in boreal fall, except that eastward penetration into the SPCZ starts to develop again.
The Kelvin wave exhibits a relatively consistent geographical pattern throughout the year. A Kelvin wave
signal in the Indian Ocean shifts slightly in the north as
it proceeds eastward in the west Pacific to eventually
join the Pacific ITCZ. The Kelvin wave weakens in theeast Pacific (near 90°W) in austral summer (Fig. 3). The
Kelvin wave tends to propagate across a wider zonal
extent in austral fall, which makes a stronger spectral
signal in the Kelvin wave domain for austral fall thanfor austral summer (Fig. 2). The Kelvin wave in the
Atlantic Ocean through central Africa constitutes aseparate group in austral summer and fall, while theKelvin wave seems to be directly extended from the
Pacific ITCZ to the Atlantic Ocean across SouthAmerica in boreal summer and fall. Notable is theasymmetry about the equator in the global distribution,
unlike the theoretical eigenfunctions of the equatorial
waves. The absence of symmetry in Kelvin wave convection, also pointed out by Straub and Kiladis (2002)
and Roundy and Frank (2004a), suggests that regionality in the background states such as SST and atmospheric dynamical fields plays a crucial role in modulating the moist processes coupled with the large-scale
waves.
The ER wave has broad maxima in the southern Indian Ocean and SPCZ as well as in the west Pacific in
austral summer. The off-equatorial maxima in eachhemisphere are as theoretically expected, although meridional asymmetry is prominent here again. The ER
wave becomes more frequent in the Northern Hemisphere across the Pacific Ocean and less frequent in theSouthern Hemisphere as seasons change to boreal summer.

c. Dynamical structure associated with the ISOs
Seasonal variability of the ISOs is further examinedin terms of the associated dynamical fields in this section. Figure 5 demonstrates geopotential height(shaded), horizontal winds (vectors), and horizontal

4407

convergence (contours) anomalies at 850 hPa composited with respect to each of the three ISO modes. To
obtain these diagrams, the ISO bandpass filters used to
identify the convection centers (i.e., boxes in Fig. 2) are
not applied directly to the space–time fields of geopotential height and horizontal winds. Nevertheless, distinct dynamical features specific to each ISO mode
manifest themselves in the composite diagrams as described below. This implies that the ISO convection
center used as the base point for compositing procedure
is efficient at capturing the associated dynamical fields.
The composite MJO in Fig. 5 shows the basic dynamical characteristics well recognized in the literature(Zhang 2005): low-level easterlies to the east, westerlies
to the west, and a pair of cyclonic circulations off theequator to the west of the MJO convection center, thatis, 0° in abscissa by definition. This combined Rossby
and Kelvin structure is most striking for the australsummer MJO, associated with strong low-level convergence confined in the Southern Hemisphere. The combined Rossby and Kelvin pattern retains also in theother seasons, although Rossby wavelike gyres are lessprominent in boreal summer and fall at least within themeridional range investigated.
The horizontal wind field of the Kelvin wave at 850
hPa closely follows the shallow-water solution: wind
anomaly is predominantly zonal and the amplitude declines poleward from the equator. The overall structureis nearly symmetric about the equator and shows little
annual variability. The meridional symmetry in the
Kelvin wave dynamical field exhibits a remarkable contrast to the asymmetry in Kelvin-filtered OLR as mentioned earlier. This contrast seems to imply that theatmospheric response to Kelvin wave convection
closely follows the linear theory even though convective heating is not symmetrically distributed about theequator. A similar observational result was also obtained by Straub and Kiladis (2002). Some discrepancies from the inviscid wave theory, however, are recognizable in the composite Kelvin wave structure. For
example, the convergence maximum is not precisely
collocated with the convection center but leads convection in its east by ⬃10°. The negative anomaly field ofgeopotential height, furthermore, is latitudinally tilted
to the west. The departure from the shallow-water
structure will be discussed later in section 4.
A cyclonic gyre to the west and an anticyclonic counterpart to the east together characterize the composite
ER wave structure. A pair of gyres is observable ineach hemisphere as theoretically predicted although
the amplitude is greater in the summer hemispherethan in the winter hemisphere.
A composite diagram for the upper-tropospheric dy-

4408

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 64

FIG. 5. Composite diagrams of 850-hPa geopotential height (shaded) and horizontal wind anomalies for the (left) MJO, (middle)
Kelvin wave, and (right) ER wave. Darker (lighter) shade represents positive (negative) geopotential height anomalies. Different
panels (top to bottom) are for different seasons. Horizontal axis is zonal coordinate relative to the base point or ISO convection center(see text). Contour is anomalous horizontal convergence at the same pressure level, drawn at intervals of 5 ⫻ 10⫺8 s⫺1 for positive
convergence only. Wind and geopotential height are not plotted where local statistical significance is lower than the 95% level.

namical field at 200 hPa and OLR anomaly is provided
in Fig. 6. The lower- and upper-tropospheric fields ofthe MJO are nearly 180° out of phase as reported since
the earliest work (Madden and Julian 1971, 1972), suggesting the predominance of baroclinic modes. The
dominant baroclinic structure is also evident for the
Kelvin wave. Irregular disturbances resembling the
Rossby wave intruding into the upper-troposphericfield in the winter hemisphere presumably arise fromsubtropical jet activity (Straub and Kiladis 2003a). The
composite OLR anomaly has a spatial pattern in phasewith the 200-hPa divergence field (not shown), suggesting that the upper-tropospheric divergence peak is centered on the convection maximum, as consistent withthe result of Kiladis et al. (2005).
The baroclinic structure is not as clear for the ER
wave. A cyclonic (anticyclonic) circulation at 850 hPa
spatially matches with an anticyclonic (cyclonic) gyre at
200 hPa only in the boreal summer Northern Hemisphere. The vertical structure of the ER wave is otherwise heavily tilted, where the upper- and lowertropospheric Rossby structures are roughly in quadrature or almost barotropic in austral summer and fall. A

barotropic ER wave was also observed by Kiladis andWheeler (1995) and Wheeler et al. (2000). The barotropic ER wave might result from the vertical shear inmean zonal wind, which invokes a coupling between
barotropic and baroclinic ER modes (Wang and Xie
1996).

d. Relationship of the MJO with the Kelvin andER waves
The combined Rossby and Kelvin structure is typicalof the composite MJO (Figs. 5 and 6), similar to thesteady solution of heat-induced atmospheric response(Gill 1980). The Kelvin and ER waves together, in addition, have been examined in the context of the driving
mechanism of MJO propagation (e.g., Salby et al.
1994). Several observational studies have pointed out
the possibility that interactions between multiple equatorial waves could play an important role in MJO
propagation (e.g., Dunkerton and Crum 1995; Strauband Kiladis 2003b; Roundy and Frank 2004b). Whiledifferent authors investigated different modes to shedlight on different aspects of MJO propagation, thepresent paper focuses on the roles of the Kelvin and ER

DECEMBER 2007

MASUNAGA

4409

FIG. 6. Same as in Fig. 5 but for 200 hPa. Horizontal convergence has been replaced with the composite OLR anomaly, contoured
every 2 K where negative.

waves. In this subsection, a lagged composite analysis isapplied to the Kelvin- and ER-filtered OLR varianceswith respect to the MJO convection centers in an attempt to explore the relationship among the different
ISO modes.
Figure 7 shows the lagged composite diagram for different seasons. Portions with local statistical significances lower than 95% are blanked out. In austral summer,
the Kelvin wave power is concentrated around theequator and is limited to the west of the MJO convection center on day ⫺10. The Kelvin wave peak moves
closer to the MJO convection center on day 0. The
Kelvin wave is spread across a wide zonal range on day⫹10. The composite ER wave exhibits no notablechange throughout this 20-day sequence, with a pair ofzonally broad maxima on both sides of the equator thatare roughly centered on the MJO convection center.
These results are consistent with a preceding study
based on a 2.5-yr record of precipitation data by Masunaga et al. (2006).
The Kelvin wave is much larger in amplitude during
austral fall than is in austral summer, as found in thefrequency–wavenumber space (Fig. 2). The composite
temporal evolution is otherwise qualitatively in parallelwith what is observed for austral summer. In contrast,

boreal summer and fall are quite different from theother two seasons. The Kelvin wave has the outstanding component emanating to the east of the MJO convection center, while there is no strong sign of an incident Kelvin wave in advance of the maximum MJO
activity. Straub and Kiladis (2003b) observed a similar
structure of the Kelvin wave in association with theboreal summer MJO. The ER wave has a timeindependent, broad maximum off the equator similar to
the result for the preceding seasons, but is limited in the
Northern Hemisphere during boreal summer and fall.
The temporal evolution of the Kelvin and ER waves
in reference to the MJO is further examined in thecomposite time–longitude diagram shown in Fig. 8. The
zonal cross section of the Kelvin (ER) wave at theequator (10°N), around which each wave reaches the
maximum in amplitude, is used to plot Fig. 8. The
Kelvin wave component approaching from the west of
the MJO convection center, as implied by the day ⫺10
diagram in Fig. 7, is traceable along the ridge of thecomposite Kelvin wave in austral summer and fall. The
propagation speed of the composite Kelvin wave is estimated from the inclination of the Kelvin wave ridge in
Fig. 8 as approximately 4° day⫺1. This is roughly consistent with the Kelvin wave speed of 11° day ⫺1

4410

JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 64

FIG. 7. Filtered OLR variance for the Kelvin and ER waves composited with respect to the MJO convection center, lagged by (left)⫺10, (middle) 0, and (right) ⫹10 days. Different panels (top to bottom) are for different seasons. OLR variance is standardized by the
all-season mean variance, or 86.2 and 85.9 W2 m⫺4 for the Kelvin and ER waves, respectively. The composite Kelvin wave is shaded
while the ER wave is contoured at intervals of 0.1 starting at 1.1. The composite Kelvin and ER waves are plotted only where local
statistical significance is greater than 95%.

(⫽公gh for h ⫽ 20 m) relative to the MJO convection
center moving at 7° day⫺1, which corresponds to thewavenumber-1 mode with the period of 50 days. In
boreal summer, on the other hand, the Kelvin wave
power tends to be concentrated near the MJO convection center with weaker evidence of the approachingcomponent. The approaching Kelvin wave completely
vanishes in boreal fall. A systematic trend of ER wave
propagation is unclear throughout the year. The amplitude maximum of the ER wave mostly stays around the
MJO convection center, although short-lived segmentsof westward propagation are barely recognized, particularly in boreal fall.
Figure 9 shows a composite time–longitude diagram
constructed from all-season data but regionally isolated
for the Indian Ocean (20°S–10°N, 50°–100°E) and thewest and central Pacific Ocean (20°S–10°N, 150°E–
150°W). In the Indian Ocean, both the Kelvin and ER
waves are consistently weak in the west of MJO convection, as expected by Figs. 3 and 4 where the ISOs areconstantly inactive over Africa. In the Pacific Ocean, in
contrast, the Kelvin wave propagating toward the MJO
convection center is evident, while no emanating com-ponent exists farther east. The seasonal and regional
contrasts in the changing roles of the Kelvin wave will
be discussed in section 4 below.

4. Discussion and conclusions
Many theories have been proposed over decades tophysically interpret the slow, eastward propagation andperiodicity of the MJO (see reviews by Wang 2005 andZhang 2005). While some of them are successful in explaining certain aspects of the MJO, no single theory todate is satisfactorily comprehensive to elucidate a variety of diverse properties of MJO mechanism. In thissection, possible physical processes involved in the
MJO are discussed as inferred from the present findings.
An intriguing implication of the current analysis isthat the Kelvin wave leads the MJO as it approaches
from the west, while the Kelvin wave extends further tothe east of MJO convection at a later phase of the MJO
life cycle (Figs. 7 and 8). The leading component of the
Kelvin wave is well established in the Pacific Ocean,
while it is only barely discernible in the Indian Ocean

DECEMBER 2007

MASUNAGA

4411

FIG. 8. Time–longitude diagram of filtered OLR variance for the Kelvin (ER) waves at the equator (10°N)
composited with respect to the MJO convection center with lags from ⫺15 to 15 days. Different panels are fordifferent seasons. OLR variance is standardized by the all-season mean variance as done for Fig. 7. The composite
Kelvin wave is shaded and contoured (dashed) while the ER wave is contoured in solid lines. Contour is drawn at
the interval of 0.05 starting at 1.1. The composite Kelvin and ER waves are plotted only where local statisticalsignificance is greater than 95%.

(Fig. 9). In this section, the role of the Kelvin wave in
MJO propagation is discussed in further detail.

a. MJO propagation
Low-level convergence was found to slightly lead
convection and, on the other hand, upper-level divergence precisely overlies convection for the observed
Kelvin wave (section 3c). Such a westward vertical tilt
in the convergence field is as predicted for a Kelvinmode in the presence of boundary layer convergence
due to surface friction. A theoretical framework of thefrictional wave-conditional instability of the second
kind (CISK) or frictional convergence feedback was
originally developed for equatorially trapped waves by
Wang (1988). Wang (1988) showed that wave-induced
convergence and frictional convergence working together suppress local convective instability but could
amplify planetary-scale modes of the moist Kelvin

FIG. 9. Same as in Fig. 8 but for selected geographical regions. (left) Diagram composited with respect to the
MJO convection centers located in the Indian Ocean (20°S–10°N, 50°–100°E). (right) The western and central
Pacific Ocean (20°S–10°N, 150°E–150°W). Contour interval is 0.1.

4412

JOURNAL OF THE ATMOSPHERIC SCIENCES

wave. The meridional tilt in Kelvin-composite geopotential anomaly (Fig. 5) is also reminiscent of the pattern simulated in frictional wave-CISK models (e.g.,
Fig. 5 of Wang and Li 1994). More recent studies basedon refined frictional wave-CISK models discovered diverse results in terms of growth rate and scale selection
but all agreed in the overall dynamical structure of thefrictionally modified Kelvin wave (Wang and Rui
1990a; Xie and Kubokawa 1990; Salby et al. 1994; Ohuchi and Yamasaki 1997; Moskowitz and Bretherton
2000).
Boundary layer convergence associated with each
ISO mode is depicted in Fig. 10, where composite 1000hPa convergence anomaly is shown. It is noted that
surface winds largely depend on model-specific dynamics in the reanalysis dataset and represent observations
only to this extent. The Kelvin wave convergence has
the maximum on the equator leading the convection
center by ⬃15°, similar to the 850-hPa convergence
field (Fig. 5). Unlike 850-hPa convergence, however,Fig. 10 exhibits tongues of boundary layer convergenceextending from the equatorial maximum to its poleward west. Theoretical studies of the frictionally modified Kelvin wave indeed imply the presence of an offequatorial component of boundary layer convergence[e.g., Fig. 9e of Wang and Rui (1990a), in terms ofvertical motion at the boundary layer top, and Fig. 9c of
Salby et al. (1994)]. It does not contradict the absenceof the corresponding off-equatorial feature in the 850hPa Kelvin wave convergence (Fig. 5), given that ISO
convergence field has a strong vertical gradient fromthe surface to the 850-hPa level (Hendon and Salby
1994; Kiladis et al. 2005). In austral summer, a tongueof convergence develops down to 15°S, where it forms
a distinct peak. This off-equatorial peak of Kelvin wave
surface convergence is collocated with the surface convergence maximum of the ER wave. The Kelvin wave istherefore potentially interactive with the ER wave toreinforce frictional convergence when convection centers associated with the two waves encounter eachother. It is further suggested that such collaborative
enhancement of boundary layer convergence, if it occurs, may have some physical connection with the MJO,
given that the MJO-composited 1000-hPa convergenceis also in harmony with the Kelvin and ER wave convergence.
This hypothetical relationship of the MJO with the
Kelvin and ER waves does not contradict the laggedcomposite analysis outlined in section 3d. Figure 7
shows that the ER wave power is in general loosely
concentrated in longitude around MJO convection. The
ER wave maximum stays close to the MJO convection
center even as early as 10 days before the peak MJO

VOLUME 64

FIG. 10. Horizontal convergence anomaly at 1000 hPa composited with respect to the MJO (shaded), Kelvin wave (solid contour), and ER wave (dashed contour). Contour interval is 5 ⫻10⫺8 s⫺1 with only positive convergence drawn. Different panels(top through bottom) are for different seasons.

convection, when the Kelvin wave is still far away to thewest in austral summer. This might be translated as astage when an ER wave “awaits” an incoming Kelvinwave preceding the peak phase of MJO convection.
The equatorial maximum of Kelvin wave convergencein the east of convection favors its eastward propagation by accumulating low-level moisture ahead (Hendon and Salby 1994; Maloney and Hartmann 1998;
Kiladis et al. 2005). Figure 7 suggests that the Kelvinwave finally arrives to join the ER wave around day 0,
when MJO convection peaks. This is also the time when

DECEMBER 2007

MASUNAGA

the Kelvin and ER waves are in tandem capable ofstrengthening boundary layer convergence (Fig. 10).
Given this result, the combined Rossby and Kelvinstructure in the composite MJO (Fig. 5) can be viewed
as a trace of the Kelvin and ER waves met together,while a heat-induced response to MJO convection isprobably superposed on it as well. The Kelvin wave,
separated away from the ER wave again, is left emanating eastward once the peak phase is passed. The
emanating Kelvin wave corresponds to the “propagating response” to MJO convection reported by Salby
and Hendon (1994). The ER wave is virtually stationary during the entire cycle.
The frictionally modified Kelvin wave is accompanied with finite meridional wind component off theequator, which, Wang and Rui (1990a) and Salby et al.
(1994) argued, probably arises from mode couplingwith the Rossby wave. The Rossby-like element inherent in the frictionally modified Kelvin wave is presumably augmented by an ER wave intruding into an incident Kelvin wave. The interference of the ER wave
therefore could positively feed back the Kelvin wave
through off-equatorial boundary layer convergence. As
implied from normal mode analyses and linearized numerical models (Wang and Rui 1990a; Salby et al. 1994;
Wang and Li 1994), a frictionally modified Kelvin mode
grows in amplitude and lowers in phase speed for SSTs
higher than a critical value around 29°C, where convective heating and large-scale warming are positively correlated, letting them amplify each other. As such, an
external trigger brought by interacting Kelvin and ER
waves and the wave-intrinsic instability supported bywarm sea surface together is capable of giving rise to aconvective burst that peaks MJO activity. The quick
growth of convection would not be as efficient outside
the tropical warm pool because subcritical SSTs damp
the frictionally modified Kelvin wave (Wang and Rui
1990a; Salby et al. 1994).
A near-zero group velocity of the ER wave (Wheeler
et al. 2000) is a part of the reason why the composite
ER wave exhibits little systematic temporal variation.
Another plausible factor is that ER wave propagation is
likely trapped within a limited zonal span because thefrictionally modified ER wave is always a damping
mode by itself (Wang and Rui 1990a; Moskowitz andBretherton 2000). The theoretical implication that frictional convergence works favorably to the Kelvin wave
but not to the ER wave seems to dictate the direction of
MJO propagation (Wang 2005).
Masunaga et al. (2006) investigated 10 individual
MJO events together with the Kelvin and ER waves
based on bandpass-filtered precipitation data from theTropical Rainfall Measuring Mission (TRMM). Their

4413

time–longitude analysis discovered a number of cases
where the Kelvin wave appears to be interrupted byintruding ER waves with the occasional onset of intensified convective episodes, which occurs within the
MJO envelope over the Indo-Pacific warm pool. Kelvinwaves approaching from the west and emanating to theeast of the MJO envelope are individually visible intheir dataset. The “stationary convective phase” theyfound in the MJO envelope could have been invokedby the unstable growth of a frictionally modified Kelvinmode. No apparent counterpart of the stationary convective phase, however, has been discussed in pasttheoretical work. This may be because the stationary
convective phase is not reproducible by linearized models. Nonlinearity might be indeed crucial for the maintenance of the stationary convection phase, given the
result of Oouchi and Yamasaki (2001) who discovered
quasi-stationary convection as well as eastwardpropagating convective envelopes in their global-scale
two-dimensional cloud-resolving model simulation.
The spatial coherence in boundary layer convergenceamong the different ISO modes is generally not as evident as found in austral summer (Fig. 10). Even in austral summer, the composite MJO convergence is much
weaker in the Northern Hemisphere than in the Southern Hemisphere. The absence of the northern counterpart may be attributed to the colder ocean as well as thelarger landmass in the Northern Hemisphere. The austral summer Southern Hemisphere serves as an ideal
environment for the frictional destabilization, whileotherwise the warmest sector of the tropical oceans
tends to be disrupted by land barriers such as the Maritime Continent and Indian subcontinent. This is perhaps a major reason why the MJO is most active during
austral summer (section 3b).
In addition to (and in part because of) the geographical constraint, the MJO in boreal summer and fall typically moves to north or northeast from the Indian
Ocean, leaving behind no substantial fraction of the
MJO propagating deep into the Pacific Ocean (Fig. 4).
The boreal summer/fall MJO is therefore expected tomostly mirror the characteristics in the Indian Ocean
and to be scarcely affected by those specific to the Pacific Ocean. This indeed accounts for the seasonal cyclein Fig. 7, where the MJO is not led by the Kelvin wave
approaching from the west but only emanates a Kelvinwave to the east in boreal summer and fall. The radiating Kelvin wave contributes, to some extent, to thesecond maximum near the date line in the zonallydouble-peaked histogram (Fig. 3). A corresponding
peak is missing for the MJO in boreal summer reflecting the fact that the MJO itself rarely propagates down
to the central Pacific during this season.

4414

JOURNAL OF THE ATMOSPHERIC SCIENCES

b. MJO onset
The absence of a triggering Kelvin wave for the MJO
in the Indian Ocean leads to the question of what initiates the MJO there. Whereas the MJO onset is outside the scope of this paper, possible onset mechanisms
are briefly reviewed below.
An observational data analysis conducted by
Kemball-Cook and Weare (2001) implied a gradual andcontinuous buildup of moist static energy that guides
convection deepening toward the peak MJO activity.
They hypothesized that the onset of MJO convection ispreconditioned by surface evaporation moistening theboundary layer, followed by the destabilization of thefree troposphere through shallow convection, which
eventually primes the atmosphere for deep convection.
A similar intraseasonal cycle inherent in the ocean–
atmosphere system is commonly recognized in a number of observations (Lin and Johnson 1996; Zhang
1996; Kikuchi and Takayabu 2004; Stephens et al. 2004;
Benedict and Randall 2007; Masunaga et al. 2006). The
relevance of such a locally regulated cycle to the MJO
has been explored also by modeling studies (e.g.,
Yamagata and Hayashi 1984; Bladé and Hartmann
1993; Hu and Randall 1994; Sobel and Gildor 2003).
Another potential trigger of the MJO onset could be
brought by dry waves. Although convective activity associated with the MJO is localized in the eastern hemisphere, dry atmospheric disturbances can travel beyond
the convectively active region (e.g., Milliff and Madden
1996). A dry wave propagating across the globe may
take part in triggering the next cycle of the MJO when
it arrives back in the Indian Ocean (Knutson and Weickmann 1987; Yanai et al. 2000; Kikuchi and Takayabu
2003). Interaction between eastward- and westwardpropagating ISOs together with partial reflection of the
waves from the land barrier over Africa could be another factor that induces MJO convection in the Indian
Ocean (Roundy and Frank 2004b). Further investigations have yet to be done to conclude whether (and, if
so, how) a dry remnant from the previous convective
cycle helps trigger the MJO.

c. Summary
In summary of the findings from the current analysis,
the dynamical processes involved in MJO propagation
may be speculated as follows.
The life cycle of the MJO starts with the onset overthe Indian Ocean, followed by its propagation to theeast. In austral summer, the Kelvin wave is involved in
the eastward propagation of the MJO preceding its
peak activity. The MJO convection centers preferably
go through the narrow oceanic channel near 10°S be-

VOLUME 64

tween Australia and Indonesia/New Guinea to eventually penetrate deep into the Pacific Ocean. When an
incoming Kelvin wave encounters an ER wave, theKelvin and ER waves are allowed to be dynamicallylinked with each other through off-equatorial boundary
layer convergence within the MJO envelope. As expected from the frictional wave-CISK theory, a frictionally modified Kelvin mode can be destabilized overtropical warm pools, capable of seeding intensive convective episodes as it decelerates the eastward propagation. As such, large-scale disturbances amplified
jointly by interacting Kelvin and ER waves and by afavorable SST condition lead to a burst of MJO convection, which makes the MJO most distinctive fromindividual modes of the Kelvin and ER waves.
The austral fall MJO holds most of the propagation
characteristics as described for austral summer. The
seasonal migration of MJO paths, however, results in aless favorable condition for MJO propagation as the
Maritime Continent stands in its way. While the equinoctial SST distribution favors Kelvin wave propagation, its interaction with the ER wave does not work as
effectively as in austral summer because frictional moisture convergence is inefficient over a landmass. The
oceanic channel in the north of Australia is almost completely shut off for MJO propagation in boreal summer,
during which the northward or northeastward propagation to the Asian continent dominates the eastward
propagation of the MJO. The overall pattern remains
unchanged from boreal summer to fall, although theextensive eastward propagation begins to recover toward the austral summer to come.
There are some related problems unaddressed in thepresent paper. The mechanism of the northward propagation in boreal summer is beyond the scope of thisstudy, since the bandpass filter we employ is only sensitive to a zonal component of propagation. The role offrictional convergence needs to be quantitatively assessed for its role in explaining the observed MJO
structure. The present study does not rule out the potential significance of any other theories. The onset
mechanism of the MJO is another outstanding issue,
which is critical for understanding the periodicity of the
MJO. ENSO-related variability of the MJO was notdiscussed either in this paper. Although it is unlikelythat the MJO is a key agent that regulates ENSO, the
MJO and other ISO modes could indirectly contributeto the maintenance of the ENSO cycle (Lau 2005).
Acknowledgments. The author thanks Chris Kummerow and Jim Benedict for reading the manuscript
and providing suggestions for improvement. Detailed
comments given by anonymous reviewers are also ap-

DECEMBER 2007

MASUNAGA

preciated. NOAA-interpolated OLR data and NCEP–
NCAR Reanalysis data were provided by the NOAA
Cooperative Institute for Research in Environmental
Sciences (CIRES) Climate Diagnostics Center (CDC),
Boulder, Colorado, from their Web site at http://www.
cdc.noaa.gov/. This research is in part supported by
NOAA’s office of Global Program Grant NA17RJ1228#15
and NASA’s Precipitation Program Grant NAG5-13694.
REFERENCES
Benedict, J. J., and D. A. Randall, 2007: Observed characteristicsof the MJO relative to maximum rainfall. J. Atmos. Sci., 64,
2332–2354.
Bladé, I., and D. L. Hartmann, 1993: Tropical intraseasonal oscillations in a simple nonlinear model. J. Atmos. Sci., 50, 2922–
2939.
Chang, C.-P., 1977: Viscous internal gravity waves and lowfrequency oscillations in the tropics. J. Atmos. Sci., 34, 901–
910.
Dunkerton, T. J., and F. X. Crum, 1995: Eastward propagating⬃2- to 15-day equatorial convection and its relation to thetropical intraseasonal oscillation. J. Geophys. Res., 100,
25 781–25 790.
Emanuel, K. A., J. D. Neelin, and C. S. Bretherton, 1994: On
large-scale circulations in convecting atmospheres. Quart. J.
Roy. Meteor. Soc., 120, 1111–1143.
Gill, A. E., 1980: Some simple solutions for heat-induced tropicalcirculation. Quart. J. Roy. Meteor. Soc., 106, 447–462.
Gruber, A., and A. F. Krueger, 1984: The status of the NOAA
outgoing longwave radiation data set. Bull. Amer. Meteor.
Soc., 65, 958–962.
Gutzler, D. S., and R. A. Madden, 1989: Seasonal variations in thespatial structure of intraseasonal tropical wind fluctuations. J.
Atmos. Sci., 46, 641–660.
Hendon, H. H., and B. Liebmann, 1991: The structure and annual
variation of antisymmetric fluctuations of tropical convection
and their association with Rossby–gravity waves. J. Atmos.
Sci., 48, 2127–2140.
——, and M. L. Salby, 1994: The life cycle of the Madden–Julian
oscillation. J. Atmos. Sci., 51, 2225–2237.
Hu, Q., and D. A. Randall, 1994: Low-frequency oscillations inradiative-convective systems. J. Atmos. Sci., 51, 1089–1099.
Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437–471.
Kemball-Cook, S. R., and B. C. Weare, 2001: The onset of convection in the Madden–Julian oscillation. J. Climate, 14, 780–
793.
Kikuchi, K., and Y. N. Takayabu, 2003: Equatorial circumnavigation of moisture signal associated with the Madden-Julian
Oscillation (MJO) during boreal winter. J. Meteor. Soc. Japan, 81, 851–869.
——, and ——, 2004: The development of organized convection
associated with the MJO during TOGA COARE IOP: Trimodal characteristics. Geophys. Res. Lett., 31, L10101,
doi:10.1029/2004GL019601.
Kiladis, G. N., and M. Wheeler, 1995: Horizontal and verticalstructure of observed tropospheric equatorial Rossby waves.
J. Geophys. Res., 100, 22 981–22 997.
——, K. H. Straub, and P. T. Haertel, 2005: Zonal and vertical

4415

structure of the Madden–Julian oscillation. J. Atmos. Sci., 62,
2790–2809.
Knutson, T. R., and K. M. Weickmann, 1987: 30–60 day atmospheric oscillations: Composite life cycles of convection andcirculation anomalies. Mon. Wea. Rev., 115, 1407–1436.
Lau, K.-M., 2005: El Niño Southern Oscillation connection. Intraseasonal Variability in the Atmosphere-Ocean Climate System, Springer-Verlag, 271–305.
——, and P. H. Chan, 1986: Aspects of the 40–50 day oscillation
during the northern summer as inferred from outgoing longwave radiation. Mon. Wea. Rev., 114, 1354–1367.
Lawrence, D. M., and P. J. Webster, 2002: The boreal summer
intraseasonal oscillation: Relationship between northwardand eastward movement of convection. J. Atmos. Sci., 59,
1593–1606.
Lin, X., and R. H. Johnson, 1996: Kinematic and thermodynamic
characteristics of the flow over the western Pacific warm pool
during TOGA COARE. J. Atmos. Sci., 53, 695–715.
Madden, R. A., 1986: Seasonal variations of the 40–50 day oscillation in the tropics. J. Atmos. Sci., 43, 3138–3158.
——, and P. R. Julian, 1971: Detection of a 40–50 day oscillationin the zonal wind in the tropical Pacific. J. Atmos. Sci., 28,
702–708.
——, and ——, 1972: Description of global-scale circulation cells
in the tropics with a 40–50 day period. J. Atmos. Sci., 29,
1109–1123.
——, and ——, 1994: Observations of the 40–50-day tropical oscillation—A review. Mon. Wea. Rev., 122, 814–837.
Maloney, E. D., and D. L. Hartmann, 1998: Frictional moisture
convergence in a composite life cycle of the Madden–Julian
oscillation. J. Climate, 11, 2387–2403.
Mapes, B. E., 2000: Convective inhibition, subgrid-scale triggering
energy, and stratiform instability in a toy tropical wave
model. J. Atmos. Sci., 57, 1515–1535.
Masunaga, H., T. S. L’Ecuyer, and C. D. Kummerow, 2006: The
Madden–Julian oscillation recorded in early observations
from the Tropical Rainfall Measuring Mission (TRMM). J.
Atmos. Sci., 63, 2777–2794.
Matsuno, T., 1966: Quasi-geostrophic motions in the equatorial
area. J. Meteor. Soc. Japan, 44, 25–43.
Matthews, A. J., B. J. Hoskins, J. M. Slingo, and M. Blackburn,
1996: Development of convection along the SPCZ within a
Madden-Julian oscillation. Quart. J. Roy. Meteor. Soc., 122,
669–688.
Milliff, R. F., and R. A. Madden, 1996: The existence and verticalstructure of fast, eastward-moving disturbances in the equatorial troposphere. J. Atmos. Sci., 53, 586–597.
Moskowitz, B. M., and C. S. Bretherton, 2000: An analysis of frictional feedback on a moist equatorial Kelvin mode. J. Atmos.
Sci., 57, 2188–2206.
Neelin, J. D., and J.-Y. Yu, 1994: Modes of tropical variability
under convective adjustment and the Madden–Julian oscillation. Part I: Analytical theory. J. Atmos. Sci., 51, 1876–1894.
Ohuchi, K., and M. Yamasaki, 1997: Kelvin wave-CISK controlled
by surface friction: A possible mechanism of super cloud cluster. Part I: Linear theory. J. Meteor. Soc. Japan, 75, 497–511.
Oouchi, K., and M. Yamasaki, 2001: An MJO-like gravity wave
and superclusters simulated in a two-dimensional cumulusscale-resolving model under a warm pool condition. J. Meteor. Soc. Japan, 79, 201–218.
Roundy, P. E., and W. M. Frank, 2004a: A climatology of waves inthe equatorial region. J. Atmos. Sci., 61, 2105–2132.

4416

JOURNAL OF THE ATMOSPHERIC SCIENCES——, and ——, 2004b: Effects of low-frequency wave interactions
on intraseasonal oscillations. J. Atmos. Sci., 61, 3025–3040.
Salby, M. L., and H. H. Hendon, 1994: Intraseasonal behavior ofclouds, temperature, and motion in the tropics. J. Atmos. Sci.,
51, 2207–2224.
——, R. R. Garcia, and H. H. Hendon, 1994: Planetary-scale circulations in the presence of climatological and wave-induced
heating. J. Atmos. Sci., 51, 2344–2367.
Sikka, D. R., and S. Gadgil, 1980: On the maximum cloud zone
and the ITCZ over Indian longitudes during the Southwest
monsoon. Mon. Wea. Rev., 108, 1840–1853.
Sobel, A. H., and H. Gildor, 2003: A simple time-dependent
model of SST hot spots. J. Climate, 16, 3978–3992.
Stephens, G. L., P. J. Webster, R. H. Johnson, R. Engelen, and T.
L’Ecuyer, 2004: Observational evidence for the mutual regulation of the tropical hydrological cycle and tropical sea surface temperatures. J. Climate, 17, 2213–2224.
Straub, K. H., and G. N. Kiladis, 2002: Observations of a convectively coupled Kelvin wave in the eastern Pacific ITCZ. J.
Atmos. Sci., 59, 30–53.
——, and ——, 2003a: Extratropical forcing of convectively
coupled Kelvin waves during austral winter. J. Atmos. Sci.,
60, 526–543.
——, and ——, 2003b: Interactions between the boreal summer
intraseasonal oscillations and higher-frequency tropical wave
activity. Mon. Wea. Rev., 131, 945–960.
Takayabu, Y. N., and T. Nitta, 1993: 3–5 day-period disturbances
coupled with convection over the tropical Pacific Ocean. J.
Meteor. Soc. Japan, 71, 221–246.
Trenberth, K. E., 1984: Signal versus noise in the Southern Oscillation. Mon. Wea. Rev., 112, 326–332.
von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in
Climate Research. Cambridge University Press, 484 pp.
Wang, B., 1988: Dynamics of tropical low-frequency waves: An
analysis of the moist Kelvin wave. J. Atmos. Sci., 45, 2051–
2065.
——, 2005: Theory. Intraseasonal Variability in the AtmosphereOcean Climate System, Springer-Verlag, 307–360.
——, and H. Rui, 1990a: Dynamics of the coupled moist Kelvin–
Rossby wave on an equatorial ␤-plane. J. Atmos. Sci., 47,
397–413.
——, and ——, 1990b: Synoptic climatology of transient tropicalintraseasonal convection anomalies: 1975–1985. Meteor. Atmos. Phys., 44, 43–61.
——, and T. Li, 1994: Convective interaction with boundary-layer

VOLUME 64

dynamics in the development of a tropical intraseasonal system. J. Atmos. Sci., 51, 1386–1400.
——, and X. Xie, 1996: Low-frequency equatorial waves in vertically sheared zonal flow. Part I: Stable waves. J. Atmos. Sci.,
53, 449–467.
Wheeler, M., and G. N. Kiladis, 1999: Convectively coupled equatorial waves: Analysis of clouds and temperature in the wavenumber–frequency domain. J. Atmos. Sci., 56, 374–399.
——, and H. H. Hendon, 2004: An all-season real-time multivariate MJO index: Development of an index for monitoring andprediction. Mon. Wea. Rev., 132, 1917–1932.
——, G. N. Kiladis, and P. J. Webster, 2000: Large-scale dynamical fields associated with convectively coupled equatorial
waves. J. Atmos. Sci., 57, 613–640.
Xie, S.-P., and A. Kubokawa, 1990: On the wave-CISK in thepresence of a frictional boundary layer. J. Meteor. Soc. Japan,
68, 651–657.
Yamagata, T., and Y. Hayashi, 1984: A simple diagnostic modelfor the 30–50 day oscillation in the tropics. J. Meteor. Soc.
Japan, 62, 709–717.
Yanai, M., and M. Murakami, 1970: Spectrum analysis of symmetric and antisymmetric equatorial waves. J. Meteor. Soc.
Japan, 48, 331–347.
——, B. Chen, and W.-W. Tung, 2000: The Madden–Julian oscillation observed during the TOGA COARE IOP: Global
view. J. Atmos. Sci., 57, 2374–2396.
Yasunari, T., 1979: Cloudiness fluctuations associated with theNorthern Hemisphere summer monsoon. J. Meteor. Soc. Japan, 57, 227–242.
——, 1980: A quasi-stationary appearance of 30 to 40 day period
in the cloudiness fluctuations during the summer monsoon
over India. J. Meteor. Soc. Japan, 58, 225–229.
——, 1981: Structure of an Indian summer monsoon system witharound 40-day period. J. Meteor. Soc. Japan, 59, 336–354.
Zhang, C., 1996: Atmospheric intraseasonal variability at the surface in the tropical western Pacific Ocean. J. Atmos. Sci., 53,
739–758.
——, 2005: Madden–Julian Oscillation. Rev. Geophys., 43,
RG2003, doi:10.1029/2004RG000158.
——, and H. H. Hendon, 1997: Propagating and standing components of the intraseasonal oscillation in tropical convection. J.
Atmos. Sci., 54, 741–752.
——, and M. Dong, 2004: Seasonality in the Madden–Julian oscillation. J. Climate, 17, 3169–3180.