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The Madden–Julian Oscillation Recorded in Early Observations from the TropicalRainfall Measuring Mission (TRMM)
HIROHIKO MASUNAGA, TRISTAN S. L’ECUYER, AND CHRISTIAN D. KUMMEROW
Colorado State University, Fort Collins, Colorado(Manuscript received 24 June 2005, in final form 28 February 2006)
ABSTRACT
A satellite data analysis is performed to explore the Madden–Julian oscillation (MJO) focusing on thepotential roles of the equatorial Rossby (ER) and Kelvin waves. Measurements from the Tropical Rainfall
Measuring Mission (TRMM) Precipitation Radar (PR) and Visible/Infrared Scanner (VIRS) are analyzed
in the frequency–wavenumber domain to identify and ultimately filter primary low-frequency modes in the
Tropics. The space–time spectrum of deep-storm fraction estimated by PR and VIRS exhibits notable
Kelvin wave signals at wavenumbers 5–8, a distinct MJO peak at wavenumbers 1–7 and periods of about 40
days, and a signal corresponding to the ER wave. These modes are separately filtered to study the individual
modes and possible relationship among them in the time–longitude space. In 10 cases analyzed here, an
MJO event is often collocated with a group of consecutive Kelvin waves as well as an intruding ER wave
accompanied with the occasional onset of a stationary convective phase. The spatial and temporal relationship between the MJO and Kelvin wave is clearly visible in a lag composite diagram, while the ubiquityof the ER wave leads to a less pronounced relation between the MJO and ER wave. A case study based on
the Geostationary Meteorological Satellite (GMS) imagery together with associated dynamic field captures
the substructure of the planetary-scale waves. A cross-correlation analysis confirms the MJO-related cyclethat involves surface and atmospheric parameters such as sea surface temperature, water vapor, low clouds,
shallow convection, and near-surface wind as proposed in past studies. The findings suggest the possibility
that a sequence of convective events coupled with the linear waves may play a critical role in MJO
propagation. An intraseasonal radiative–hydrological cycle inherent in the local thermodynamic conditions
could be also a potential factor responsible for the MJO by loosely modulating the envelope of the entire
propagation system.

1. Introduction
Since first documented by Madden and Julian (1971,1972), the Madden–Julian oscillation (MJO) has been
extensively studied to explore its physical mechanism.
In contrast to other low-frequency modes such as the
Kelvin wave, however, the MJO has no apparent counterpart in the linear shallow-water theory described by
Matsuno (1966). Numerous attempts have been madeto explain the physical processes that give rise to the
MJO. In the framework of the linear theory, the equatorial Kelvin wave best shares fundamental characteristics with the MJO in reference to the fact that bothpropagate only eastward and are restricted to the Trop-

Corresponding author address: Dr. Hirohiko Masunaga, Dept.
of Atmospheric Science, Colorado State University, Fort Collins,
CO 80523.
E-mail: masunaga@atmos.colostate.edu© 2006 American Meteorological Society

JAS3783

ics. On the other hand, the typical period of the MJO issubstantially longer than expected from the Kelvinwave speed. A variety of theories proposed to date (seereview by Hayashi and Golder 1993) are in agreementon the critical importance of the moist processes. The
MJO has been extensively studied with emphasis on therole of convection by both observational data analyses(e.g., Nakazawa 1988; Takayabu and Murakami 1991;
Hendon and Salby 1994; Yanai et al. 2000) and modelstudies (Hayashi and Sumi 1986; Lau et al. 1989; Bladéand Hartmann 1993; Grabowski 2003; among others).
Consensus, however, has yet to be achieved in thecomprehensive understanding of the MJO. Slingo et al.
(1996) conducted a comparison study using 15 atmospheric general circulation models (AGCMs) to test
their ability to predict the MJO. They found that
AGCMs could typically produce eastward propagation
similar to the MJO, but most of them failed to simulate
periods longer than 30 days. A frequency–wavenumber

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analysis of a long-term (⬃18 yr) record of outgoing
longwave radiation (OLR) found that the spectral peakcorresponding to the MJO clearly does not belong to
the Kelvin wave solution with any equivalent depth(Wheeler and Kiladis 1999, hereafter WK99). A number of papers discussed the MJO in the context of interactions between different types of tropical oscillations (Dunkerton and Crum 1995; Wheeler and Weickmann 2001; Straub and Kiladis 2003; Roundy and Frank
2004b,c). Some observational studies revealed the intraseasonal cycle of local imbalance in the radiation andmoisture budget associated with convective variability(Zhang 1996; Flatau et al. 1997; Stephens et al. 2004).
The present work investigates the MJO as well asother low-frequency tropical waves using precipitation
measurements by satellite remote sensing. The analysis
is based on measurements from the Tropical Rainfall
Measuring Mission (TRMM) satellite, National Oceanic and Atmospheric Administration (NOAA) satellite, and Geostationary Meteorological Satellite (GMS)
data. Section 2 describes the data employed in thiswork. A frequency–wavenumber analysis is performedin section 3 to sort out the MJO and convectively
coupled equatorial waves in the spectral domain. Applying bandpass filters in order to separate different
wave modes, the individual modes as well as the potential interrelationship of planetary-scale waves is investigated in the time–longitude space (section 4). Section
5 is devoted to discussion on the result. The findings are
summarized in section 6.

2. Data
A major part of the analysis is based on a combination of data from the Precipitation Radar (PR) and
Visible/Infrared Scanner (VIRS) onboard the TRMM
satellite. The TRMM orbit is sun-asynchronous and has
the recurrence cycle of about 23 days in local solar time.
This cycle would be twice as long if the ascending anddescending paths are discriminated from each other.
Among the TRMM operational data archives, the PR
echo-top height or storm height is provided by the
TRMM 2A23 product, and the VIRS channel-4 (10.8␮m) radiance (hereafter IR Tb, after conversion tobrightness temperature) is given by the 1B01 dataset.
VIRS pixels are collocated with PR over the inner portion of the VIRS swath that overlaps the narrower PR
swath. Nonoverlapping VIRS pixels are not used in theanalysis to avoid sampling inconsistency with the PR.
In this paper, the deep-storm fraction is used as ameasure of the intensity of active convection. The
deep-storm fraction is the area fraction of precipitation
events having VIRS IR Tb colder than 245 K and PR

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echo-top height higher than 4 km. This definition is the
combination of deep stratiform and deep convective
systems in terms of the storm categorization defined by
Masunaga et al. (2005). Although infrared radiance byitself is a reasonable proxy of deep convection, it issensitive to all high clouds including detrained cirrus
clouds, which predominate precipitation cores in spatial
and temporal extent. On the other hand, the deepstorm fraction is more directly linked with the moist
processes. The simultaneous use of the VIRS and PR
excludes both nonprecipitating high clouds and rainfallwith relatively warm cloud tops (i.e., cumulus congestus) from the analysis. The deep-storm fraction is calculated over each 2.5° ⫻ 1-day box in the time–
longitude space with the latitudinal coverage of 10°S–
10°N. The meridional band is divided by the equator
for the symmetric/antisymmetric decomposition in frequency–wavenumber analysis. It is noted that the daily
dataset is longitudinally continuous when integrated
over 10°S–0° and 0°–10°N, although each 2.5° ⫻ 10°
box is only partially sampled, where the subgrid area
coverage is ⬃23% on average. Because no grid box ofthis size is left empty on any given day, spatial interpolation is not required on a daily basis except for some
irregular cases mentioned below.
Two time periods are analyzed: 21 December 1997 to
10 December 1999 (720 days) and 3 December 2000 to
20 June 2001 (200 days). The primary distinction between these periods is that the first encompasses a portion of the 1997–98 El Niño and the subsequent La
Niña phase, while the second represents a normal phaseof the El Niño–Southern Oscillation (ENSO). MJO activity is moderate throughout the both periods except
for the first few months of the second period, which
exhibits a relatively strong peak in terms of the realtime multivariate MJO index computed by Wheeler
and Hendon (2004). This ensures that the analysis conducted here represents average MJO events without
skewing the focus toward extreme cases. The first period contains 16 days of data that are partially missing
and nine other days entirely devoid, primarily due tosensor shutoffs. There are, however, no consecutive periods of missing data in excess of four days, so the missing data can be filled in by linear interpolation in timewith no visible impact on the analysis of low-frequency
oscillations. There are no data missing during the second period.
To assess the magnitude of potential sampling errors
inherent in deep-storm fraction, VIRS IR Tb values are
first compared with the NOAA-interpolated OLR(hereafter NOAA OLR). The NOAA OLR dataset,
constructed from NOAA’s polar-orbiting satellite data,
has been interpolated spatially and temporally to a

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daily, 2.5° ⫻ 2.5° grid. The satellite in use for the time
periods mentioned above is NOAA 14 (NOAA 16)
before (on and after) 1 March 2001. NOAA OLR wasderived from window-channel radiance through an analytic formula (Gruber and Krueger 1984). Since the flux
equivalent blackbody temperature is almost linearly related to the equivalent blackbody window temperaturein their formula, OLR and IR Tb are essentially equivalent in the relative strength of spectral power. These
data are used to ensure that spectral features of interest
are statistically meaningful by identifying satellitedependent spurious peaks in VIRS IR Tb spectra relative to those derived using NOAA OLR. The deepstorm fraction is then examined once spectral artifacts
specific to TRMM measurements are isolated based on
VIRS IR Tb.
Geostationary satellite data are also analyzed for investigating the substructure of convectively coupledwaves. GMS-5, operated by the Japan Meteorological
Agency, is used for a region covering the Maritime
Continent and the west and central tropical Pacific(10°S–10°N and 80°E–160°W) from 21 April to 20 May
2001. Infrared channel-1 (11 ␮m) brightness temperature is gridded on a half-degree scale with a temporal
resolution of 3 h. The daily dataset of 850-hPa horizontal winds is adopted from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data.

3. Frequency–wavenumber analysis
Frequency–wavenumber analysis of satellite measurements has been a popular tool to explore convectively coupled tropical waves in terms of visible brightness (Gruber 1974; Zangvil 1975), infrared flux (Nakazawa 1986; Salby and Hendon 1994; Takayabu 1994;
WK99; Roundy and Frank 2004a), or direct precipitation measurements (Cho et al. 2004; Benedict and Randall 2006, manuscript submitted to J. Atmos. Sci.). In
this study, infrared brightness temperature and the
deep-storm fraction are examined in the space–time
spectral domain utilizing the entire period of 920(720 ⫹ 200) days described in section 2. The method ofanalysis is first described in section 3a, followed by the
results in section 3b.

a. Analysis scheme
Our method of frequency–wavenumber analysis issimilar to the scheme developed by WK99. The only
major difference from WK99 lies in the definition of thereference noise spectrum used to test statistical significance. While WK99 defined the background spectrum

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by smoothing spectral peaks out, the red noise spectrum is employed here as described later. The red noise
spectrum is adopted for the sake of minimizing the arbitrariness in defining the background spectrum. A
background spectrum constructed from multiple passesof smoothing filters solely relies on the number of thefilters applied, which is a rather subjective choice of theuser. The red noise spectrum, on the other hand, provides a more objective basis against which the statisticalsignificance of spectral peaks is tested. Note that a
1–2–1 filter is modestly used in this study to remove
stochastic fluctuation in the red noise spectrum, but it
only plays a minor role in determining the overall structure of the noise spectrum.
The time–longitude sections of the deep-storm fraction, TRMM IR Tb, and NOAA OLR are converted
into the wavenumber–frequency domain in the following manner. First, each variable is decomposed into
symmetric and antisymmetric components about theequator as [ f (NH) ⫹ f (SH)]/ 2 and [ f (NH) ⫺ f (SH)]/ 2,
respectively, where f (NH) and f (SH) denotes the quantity in the Northern and Southern Hemispheres, respectively, at a same longitude. This procedure helps separate different wave modes by the parity of their eigenfunctions as originally demonstrated by Yanai and
Murakami (1970). Next, these datasets are divided into
segments of 80 consecutive days. The beginning datesof sequential segments are selected at an interval of 40days so that each segment overlaps by a half in length.
The overlap is aimed at minimizing the loss of signals
due to the data windowing (described below) and thetruncation of low-frequency waves. Sinusoidal backgrounds with the periods of one, a half, and a quarteryear are removed from OLR data to factor the seasonal
cycle out. This step is skipped for the deep-storm fraction because the seasonal variation has no direct influence on the deep-storm fraction, whereas it periodicallyoffsets OLR. The mean and linear components in time
identified by least square fit are further subtracted ateach longitude. The data are then tapered to zero atboth ends of the time series using the Hanning (or cosine bell) window. This windowing technique is intended to mitigate side lobes in the spectrum cause by
the discontinuity at the ends of a time sequence. Complex fast Fourier transformation (FFT) is applied inlongitude and in time to each 80-day segment. The resulting space–time spectrum, having a bandwidth of
0.0125 (1 /80) cycles per day (cpd) in frequency andone zonal wavenumber, is averaged over all 19 segments formed from the data in the two time periods(section 2).
The statistical significance of the obtained spectral
power is evaluated in comparison with the red noise

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FIG. 1. The symmetric and antisymmetric spectra in the frequency–wavenumber domain of (a), (b) NOAA OLR, (c), (d) TRMM IR
Tb, and (e), (f) deep-storm fraction. Positive (negative) wavenumbers correspond to eastward (westward) propagation. Superimposed
are the theoretical dispersion relations of the Kelvin wave (solid straight lines), MRG and n ⫽ 0 EIG waves (dashed curves), and n ⫽1 ER wave (dotted–dashed curves) for the equivalent depths of 5, 20, and 100 m, from bottom to top. The arrow in (a) indicates a
westward phase speed of 8 m s⫺1. Bandpass filters are designated by thick lines in (e).

spectrum. The explicit form of the red noise spectrum
prn is given as (section 11.2.5 in von Storch and Zwiers
1999)
prn共k, ␻兲 ⫽

2
␴Z
共k兲

1 ⫹ ␣1共k兲2 ⫺ 2␣1共k兲 cos共2␲␻兲

red noise spectrum to purify spectral peaks of interest
from day-to-day weather variations.

b. Results,

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. The amplitude of the red noise
spectrum ␴ 2z is determined so that Eq. (1) is equivalent
to the mean of the symmetric and antisymmetric components of the actual spectra when integrated over frequency. Once ␣1 and ␴ 2z are determined for each wavenumber, the stochastic fluctuation across k in ␣1(k) and␴ 2z(k) is removed by applying multiple passes of a 1–2–1
filter. Statistical significance is then tested against the

Figures 1a–d show the symmetric and antisymmetriccomponents of NOAA OLR and TRMM IR Tb in thefrequency–wavenumber domain. Eastward (westward)
propagation is designated by positive (negative) zonal
wavenumbers. The dispersion relations for some dominant low-frequency modes of tropical waves are also
depicted. These theoretical curves are based on theshallow-water solutions derived by Matsuno (1966), allowing a wide range of equivalent depths h that accountfor various vertical modes with different wavelengths(Lindzen 1967). The thermodynamic environment that
controls the moist wave characteristics is closely linked
with the processes selecting dominant modes with particular equivalent depths. A convectively coupled wave

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is known to have a smaller equivalent depth, or asmaller phase speed, than its dry counterpart (WK99,
and references therein). Emanuel et al. (1994), for example, provided a theoretical basis of the internal wave
propagating in a convecting atmosphere, which is foundto be slower than the corresponding dry mode. The
Kelvin wave (shown as solid, straight lines in Fig. 1) andthe n ⫽ 1 equatorial Rossby (ER) wave (dotted–
dashed) have symmetric eigenfunctions about the equator in pressure and zonal wind. By contrast, they are
antisymmetric for the mixed Rossby–gravity (MRG)
wave (dashed for k ⬍ 0) and n ⫽ 0 eastward inertio–
gravity (EIG) wave (dashed for k ⬎ 0). Three reference
values of h ⫽ 5 m, 20 m, and 100 m, from bottom to top
in Fig. 1, are chosen for the theoretical curves. These
three equivalent depths correspond to 7, 14, and 31
m s⫺1, respectively, in the Kelvin wave speed.
A prominent feature in the symmetric components of
NOAA OLR is the Kelvin wave confined between h ⫽20 m and 100 m, tailed by a weaker component extended down to h ⫽ 5 m. The westward-propagation
domain of Fig. 1a includes another striking signal,loosely centered around ␷ ⫽ ⫺8 m s⫺1 as indicated byan arrow. This signal, without any counterpart of linear
wave modes, might reflect disturbances moving together with the background easterly wind. The speed of
8 m s⫺1 is close to a peak value in climatological zonal
wind in the tropical upper troposphere (Wheeler et al.
2000). The easterly wave as documented by Reed andRecker (1971) also has a phase speed (9 m s⫺1) close tothis spectral mode. The antisymmetric component (Fig.
1b) shows a spectral peak associated with the MRG andn ⫽ 0 EIG waves.
The fact that the satellite-observed area does notcompletely cover the globe within a single day creates aspectral artifact in daily datasets. An observed signal
blinks regularly at a constant longitudinal interval as it
repeatedly appears from and hides behind satellite
blind spots. The temporal and spatial periodicity of thiseffect generates a well-pronounced, spurious peak inspectral space. For the polar-orbiting NOAA satellites,
an artificial peak appears at k ⫽ 14 and ␻ ⫽ 0.11 cpd asseen in Figs. 1a,b, corresponding to the number ofswaths swept per day (⫽14) and the 9-day repeat cycleof satellite zenith overpass.
Spectral power turns out to be generally weaker for
VIRS IR Tb (Figs. 1c,d) than for NOAA OLR. This canbe ascribed to sampling errors specific to the orbital
configuration of the TRMM sensors. Complete observational coverage at tropical latitudes takes about 7
days for the PR swath width of 215 km. (As mentioned
in section 2, the outer portion of the VIRS swath notoverlapping with the PR swath is precluded from analy-

2781sis.) A poorer sampling makes the spectrum noisier andhence reduces the statistical significance of spectral
power particularly for high-frequency modes. The
Kelvin wave nonetheless exhibits a stable signal in the
VIRS IR spectrum although it is narrowed to mostly
above h ⫽ 20 m. The ER wave is readily identifiable atwavenumbers from ⫺4 to ⫺8, barely separable fromthe faster disturbances outside the ER wave domain.
The antisymmetric spectrum has a confined signal of
the MRG/n ⫽ 0 EIG wave around k ⫽ 0. The TRMM
spectrum also has a spectral artifact due to finite orbital
coverage, except that it falls outside the range of Fig. 1
around k ⫽ 15–16 and ␻ ⫽ 0.4–0.45 cpd.
The sun-asynchronous TRMM orbit could yield aresonance effect between the diurnal cycle of convective activity and the TRMM orbital precession: an oscillation with a period close to 23 days can be selectively
amplified. Cho et al. (2004) examined potential sampling errors in a space–time spectrum of TRMM measurements and found no serious contamination by thediurnal cycle for equatorial wave modes. Indeed, Figs.
1c,d shows no apparent spectral peak near 1 / 23 cpd incomparison with Figs. 1a,b.
Finally, frequency–wavenumber analysis is applied tothe deep-storm fraction defined in section 2. Figures
1e,f shows the symmetric and antisymmetric spectra of
the deep-storm fraction. Overall, statistically significant
signals are even more limited than in the VIRS IR spectrum. Cho et al. (2004) also found that spectral peaks
are less distinct for precipitation than for OLR except
at very low frequencies. NOAA OLR and VIRS Tb
indeed lack statistically significant peaks at very low
frequencies (periods longer than 40 days), while thedeep-storm fraction has a strong spectral signal extending down to a period of 80 days. The Kelvin wave is now
shrunk into an island of high-wavenumber modes
around k ⫽ 5–8 and ␻ ⫽ 0.15–0.25 cpd as well as several
isolated spikes. Note that a separate component at k ⫽1–2 in the Kelvin wave domain is categorized into the
MJO as described below. The deep-storm fraction lacks
the Kelvin modes at wavenumbers 3 and 4, for which
infrared spectra exhibit pronounced evidence. This
contrast may suggest that infrared radiance is not necessarily an ideal representative of the convectively
coupled Kelvin wave for k ⫽ 3–4. These wavenumbers
have relatively high equivalent depths of 20–100 m thatare more likely accounted for by dry waves. Remnant
anvil clouds responding to the dry Kelvin wave, therefore, likely make considerable contribution to the
Kelvin wave modes with k ⫽ 3–4 in infrared spectra.
This is also consistent with the fact that observed cloudsystems documented in previous studies have a wavenumber scale of about 6–15 and propagate at a slower

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speed than inferred by the infrared spectrum of the
Kelvin wave (WK99). In the spectrum of the deepstorm fraction, the equivalent depth spread across bothsides of 20 m at wavenumbers larger than 5.
A most remarkable feature is a slow eastward mode
at periods around 40 days that extends from wavenumber 1 to 7, leading itself to a domain prohibited for the
Kelvin wave. This feature is recognized as the spectral
representation of the MJO, as originally indicated by
WK99. Wheeler and Hendon (2004) confirmed that thisspectral peak is obtained when the MJO is singled out
by an EOF analysis based on a long-term record of
zonal wind and OLR. Note that the apparent strengthof spectral peaks can vary with different definitions of
the reference noise spectrum. The red noise spectrum
defined here, for example, tends to have spectral power
more concentrated around low frequencies in comparison with the background spectrum as derived by WK99.
This explains why the MJO peak in Fig. 1a is weaker
than obtained by WK99.
Westward propagation is fainter in spectral power
than the eastward modes. The ER wave is, however,noticeable around k ⫽ ⫺5. The contrast in spectral
strength between the Kelvin and ER waves occurs inpart because the latitudinal range chosen in the analysis
favors the Kelvin wave. The amplitude of the Kelvinwave is concentrated near the equator, while the ER
wave has the maximum amplitude off the equator. Extending the meridional range to 15°S–15°N (not shown)actually results in a slightly stronger ER peak and alittle weaker Kelvin signal in the frequency–wavenumber domain than seen in Fig. 1. General conclusions drawn from the present analysis, however, do notdepend on the choice of meridional range.
In summary, the planetary-scale eastward propagation coupled with deep convection has a pair of distinct
constituents: high-wavenumber (k ⫽ 5–8) harmonics ofthe Kelvin wave and the MJO mode with periods ofabout 40 days. The ER wave at a wavenumber of about⫺5 is also present but not as intense as the other twomodes.

4. Time–longitude analysis
Given this identification of the dominant wave
modes in the TRMM dataset, this section further examines the Kelvin wave, MJO, and ER wave in thetime–longitude space and seeks to explore possible relationships between them. The filtering technique used
for the time–longitude analysis is introduced in section
4a, and results are presented in section 4b. The internal
structure of the planetary-scale waves are studied for asingle case in section 4c to support the findings based

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on two-dimensional cloud images and associated dynamic field.

a. Filtering technique
The MJO, Kelvin wave, and ER wave are investigated in the time–longitude diagram by applying bandpass filters defined in the wavenumber–frequency domain. The basic method parallels that introduced by
WK99, which has been widely used to date (e.g.,
Wheeler et al. 2000; Wheeler and Weickmann 2001;
Straub and Kiladis 2003; Roundy and Frank 2004a).
Each of the undivided 720-day and 200-day time seriesof the deep-storm fraction averaged over 10°S–10°N is
decomposed into the frequency–wavenumber space after the windowing is performed in time. Data near bothends of the time series are lost due to the windowing
and hence are not used in the analysis. Spectral signals
bound in a given filter, with all the others eliminated,
are transformed back in the time–longitude domain by
backward FFT. The frequency bandwidth (1 /720 or
1 / 200 cpd) is sufficiently small to recover all the filteredwaves without the truncation of low-frequency modes.
Filters in use are designated by thick lines in Fig. 1e.
The Kelvin wave filter is bounded by 1 ⱕ k ⱕ 10, 0.05
cpd ⱕ ␻ ⱕ 0.25 cpd (4–20 days in period), and a pair oftheoretical dispersion relations with the equivalent
depths of 5 m and 100 m. Periods shorter than 4 days
are not used to avoid sampling noise in TRMM measurements. The MJO filter is defined as 1 ⱕ k ⱕ 7,
0.0125 cpd ⱕ ␻ ⱕ 0.05 cpd (20–80 days in a period),targeted on the low-frequency oscillation distinct fromthe Kelvin wave. The range of 20–80 days covers amajority of the observed MJO periods documented in
the literature (Madden and Julian 1994). It is noted thatthe theoretical solution of the Kelvin wave at low wavenumbers falls within the MJO filter particularly forsmall equivalent depths. The n ⫽ 1 ER wave filter isdefined between ⫺10 ⱕ k ⬍ 0 and two dispersion relations with the equivalent depths of 5 m and 100 m.

b. Planetary-scale waves
Six 50-day time series are chosen to demonstrate thefiltered MJO and Kelvin wave (in red and blue) as wellas the unfiltered field (contoured) of the deep-storm
fraction (Figs. 2a,b). The unfiltered field has beensmoothed by running mean over 3 days in time and 15°
in longitude to eliminate small-scale fluctuations. Notethat this smoothing technique is not applied to the filtered waves. The subsequent analysis focuses on the 10
MJO events marked in Fig. 2, identified based on positive phases of the filtered MJO. The first three eventsoccurred at the end of the 1997–98 El Niño, playing an

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important role in the termination of the El Niño as
discussed by Takayabu et al. (1999). The next three
MJO events fall during the subsequent La Niña event.
The remaining events are selected from a normal
ENSO phase in 2001.
With the exceptions of those that occur during the El
Niño (MJO-1–3), all the MJO events but MJO-8 arecentered around 120°E over the Maritime Continent(Fig. 2a) and confined between the Indian Ocean(⬃60°E) and the date line. The regionality of convective activity associated with the MJO has been wellrecognized in the literature (e.g., Hendon and Salby
1994; Yanai et al. 2000; Wheeler and Hendon 2004).
The visibly dominant mode of the MJO is typicallywavenumber 1, while higher wavenumbers up to 7 areas pronounced as the lowest for the MJO in the space–time spectrum (Fig. 1e). The high-wavenumber modes
are exaggerated than actual in the frequency–
wavenumber space since the spectral power is normalized by the red noise spectrum (section 3a). Salby andHendon (1994) pointed out that the high-wavenumber
components contribute to the highly dispersive natureof the MJO, which is responsible for its regionality.
The Kelvin wave propagates at a consistently larger
speed (about 15 m s⫺1 as inferred from the average
equivalent depth of ⬃20 m) than the MJO (Fig. 2b).
The Kelvin wave is occasionally visible even in the unfiltered pattern. The most conspicuous case is the onethat penetrates MJO-2 through MJO-3. Intensified convection at the end of MJO-2 anchors this MJO event in
the east of 60°E, making this MJO event slower thanthe Kelvin wave that propagates further through a subsequent ridge of the MJO. Another dramatic case is
MJO-9 and MJO-10, where three notable branches of
the Kelvin wave are emanated one after another at a
temporal interval of about a week. A similar trend isalso seen in association with other MJO events, although the Kelvin wave is less apparent in the unfiltered field. In these cases, the embedded Kelvin wave isloosely modulated in amplitude as if a few or several
neighboring Kelvin waves together constitute a single
MJO event.
As expected from the relatively weak spectral peak(Fig. 1), the ER mode is not a primary constituent of
convectively coupled tropical waves. The ER wave
(dotted in Fig. 2c) would be barely traceable from theunfiltered deep-storm fraction without contoured guidance. The ER wave, nevertheless, occasionally includes
distinct spots of the enhanced deep-storm fraction
when the ER wave intersects with the Kelvin wave.
Figure 2d schematically illustrates the behavior of the
ER and Kelvin waves in the vicinity of individual MJO
events. Interestingly, each event exhibits at least one

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case where an ER wave intersects a moist Kelvin wave,
accompanied with the interruption of the eastward
propagation of convective systems or its slight westward retrogression (MJO-6, MJO-7, and MJO-10). Intensified convective systems are sometimes left behindthe outgoing waves and remain unmoved (MJO-4,
MJO-5, and the eastern end of MJO-7). The resulting
apparent stationary convective phases always build up(besides the El Niño period) over the Indo-Pacificwarm pool. Such phases, however, eventually start
propagating again when they encounter an incoming
Kelvin wave. A stationary convective phase otherwise
dies out as seen in MJO-2, MJO-8, and MJO-9. Intensified convection is also frequently observed at the termination of entire propagation as observed at the endof MJO-6, MJO-7, and MJO-10.
To establish the statistical significance of this apparent relationship between the MJO and Kelvin/ER
waves, a lag composite analysis is performed. MJO
peaks are first identified as local longitudinal maxima in
the MJO-filtered deep-storm fraction. The MJO peak isdefined only when it exceeds ⫹2␴ of the filtered MJO
in order to assure a high signal-to-noise ratio. Fluctuations with zonal scales smaller than 30° are excluded
when defining the local maxima. Higher-wavenumber
fluctuations are ignored to avoid spurious signals because any spectral components with wavenumbers
greater than 10 are excluded by the filters used in thisstudy. The Kelvin and ER wave powers, that is, thesquare of filtered deep-storm fraction anomaly, arethen composited in reference to the MJO peak withdifferent time lags of ⫾7, ⫾3, and 0 days. The composite diagram is constructed so that the reference point(0°) coincides with the MJO peak at lag 0. All the dataconsidered in this study (the whole globe between 10°S
and 10°N for the two time series defined in section 2)
are employed for the result shown in Fig. 3.
The Kelvin wave exhibits a striking peak in the vicinity of the MJO peak particularly for small time lags
(within ⫾3 days). The Kelvin wave power at an earlier
or later time (⫾7 days) has a weaker peak with abroader shoulder, which extends eastward (westward)
for a positive (negative) lag. The MJO, in other words,
tends to be accompanied with the Kelvin wave approaching from the west prior to the peak activity, after
which the MJO emanates the Kelvin wave in the east.
The composite series of the ER wave only shows asmall, broad hump in the east of the MJO maximum
with no discernible temporal evolution. The weak correlation with the MJO reflects the relatively ubiquitous
nature of the ER wave, as seen, for example, around
MJO-6 in Fig. 2c. The absence of temporal variability

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FIG. 2.1. Time–longitude diagram of deep-storm fraction for different time periods. (a) The MJO-filtered anomaly (color) andunfiltered field contoured at an interval of 2.5% starting with 5%. (b) The Kelvin-filtered anomaly (color) as well as the unfiltered field.
The MJO-filtered anomaly at the ⫹1.5% level is superimposed for reference. (c) The unfiltered field in colors superimposed with theanomalies of the filtered Kelvin wave (at ⫹2% in dashed contour) and ER wave (at ⫹1% in dotted contour). (d) A schematic
representation of wave interactions and a resultant stationary convective phase. The dry Kelvin wave is simply extrapolated from themoist counterpart in the schematic, where difference in propagation speed between the dry and moist waves is ignored for brevity.

may be explained by a near-zero group velocity of the
ER wave as indicated by Wheeler et al. (2000).

c. Internal structure of the waves
Figure 4 shows daily infrared images with 850-hPa
horizontal wind anomaly and the 3-hourly time–
longitudinal section averaged over 10°S–10°N. In thetime–longitude diagram, the westward migration ofcloud systems constitutes a fine structure embedded ineastward propagating mesoscale convective systems(MCS) as originally discovered by Nakazawa (1988).
Westward-moving cloud systems are also evident in theenvelope of the stationary convective phase that belongs to MJO-9, staying active to the west of 100°E
until 5 May. This stationary convective phase is associated with strong westerly wind anomaly after 28 April
as seen in the daily images. The westerly anomaly gains

a southward component and eventually turns into aneasterly anomaly as it goes on through the Southern
Hemisphere.
An MCS originating from the Maritime Continent
moves to the east together with the Kelvin wave andeventually reaches beyond the date line on 4 May. ThisMCS is primarily centered between 5°N and the equator throughout the propagation, where the intertropicalconvergence zone (ITCZ) is located during this period.
A notable exception is that the MCS expands northward up to 10°N in a cyclonic motion from 29 to 30
April, when the ER wave intersects the Kelvin wave as
indicated in the time–longitude diagram. The MCS
then breaks up into a pair moving in opposite directions: an MCS continuously brought to the east by the
Kelvin wave and another to the west by the ER wave.
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FIG. 2.2. Same as Fig. 2.1, except for the different dates shown. The dashed box in the lower panel of (c) indicates the spatial andtemporal coverage used for GMS analysis (Figs. 4 and 5).

waves generally shows patterns typical to each mode. In
3 May, for instance, a gyre is readily identified for an
MCS accompanied with the ER wave at 5°N and 135°E,
while another MCS linked with the Kelvin wave

(2.5°N and 170°W) is associated with zonally dominantwind anomaly as expected.
The subsequent evolution is shown in Fig. 5. The
MCS that arrived from the east at the Maritime Con-

FIG. 3. Lag composite for (left) the Kelvin-wave power and (right) ER wave power with respect to the MJO peak,defined by local maxima in the filtered MJO field of the deep-storm fraction. The ordinate shows the square ofdeep-storm fraction anomaly [in (%)2] filtered by each wave. The abscissa represents zonal coordinate [in (°)]
relative to the MJO maximum.

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FIG. 4. Daily-averaged GMS infrared images on a half-degree grid superposed (left) by 850-hPa horizontal wind
anomaly on a 2.5-degree grid and (right) by 3-hourly time–longitude diagram for the 10S°–10°N latitudinal bandfrom 21 April to 20 May 2001. Contour lines are taken from Fig. 2c. The time period covered by the left panels is
indicated by thick-framed box. Arrows indicate the movement of mesoscale convective systems (see text).

tinent on 4 May (Fig. 4) is split again on 5 May. A new
MCS is born and heads east in response to the Kelvinwave. The old MCS continues moving slowly to thewest and spawns another MCS heading east on 9 May,
when the ER wave meets the next ridge of the Kelvinwave. The newest MCS quickly grows in size immediately after it merges with another system approachingfrom the east on 10 May. This westward-moving MCS,
designated by dashed arrow, does not belong to the ER
wave, because it is located in a trough of the filtered ER
wave and concentrated within ⫾5° in latitude dissimilarly to the ER wave. This system is more likely associated with a tropical depression (TD)-type disturbance(Takayabu and Nitta 1993). The merged MCS keeps

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FIG. 5. Same as Fig. 4 but daily images for a subsequent time period.

heading east and develops to a very intense system in
the west Pacific by 14 May. It can be seen in the time–
longitude diagram that this intensified MCS is locatedwhere the Kelvin wave meets an incoming ER wave.
Interestingly, although the ER wave involved here isnot clearly visible in the infrared images, it is traceable
in wind anomaly as a gyre moving to the west in theSouthern Hemisphere from 180° on 9 May to 160°E on
13 May. The final stage of the MCS on 14 May turns out
to be part of MJO-10 together with another MCS thatbuilds up over the Maritime Continent earlier on 3 and
4 May.

5. Discussiona. Interrelationship among different waves
The case studies and a brief composite analysis demonstrated in the previous section motivate us to givesome thought to the possible relationship between the
Kelvin and ER waves and the MJO. A number of pre-

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vious studies have pointed out the critical roles of boththe Kelvin and ER waves in association with the MJO.
Hayashi and Sumi (1986) discovered in their aquaplanet simulations that the eastward convectively
coupled wave with a period of 30 days is disintegrated
into the Kelvin and Rossby waves as soon as the moist
processes are turned off. A model study by Lau et al.
(1989) demonstrated that the Kelvin and Rossby waves
take part in the dynamical adjustment to reconcile animbalance between large-scale circulation and heating
fields. Observational studies also found evidence for acoupled Rossby–Kelvin wave in composite analyses ofthe MJO (Nakazawa 1988; Hendon and Salby 1994;
Salby and Hendon 1994; Takayabu et al. 1999).
Some preceding studies have also focused on the interactions between different modes of the tropical oscillations. Dunkerton and Crum (1995) analyzed a 10-yr
record of OLR measurement to find some evidence forlow-frequency (⬃30–60 days) oscillations interactingwith high-frequency (⬃2–15 days) eastward propagation. Considering that their high-frequency propagation
is likely the Kelvin wave, their findings support ourcomposite analysis (Fig. 3) showing a strong Kelvinwave peak collocated with the MJO maximum. Strauband Kiladis (2003) discovered that the MRG and TDtype activity is enhanced with the MJO convective envelope, and that the Kelvin wave is more active in theeast of the MJO than within the MJO envelope. Whilethe notable Kelvin wave activity in the east of the MJO
is also seen in Fig. 3 of this paper, the present resultshows a high concentration of the Kelvin wave within
the MJO envelope in contrast to Straub and Kiladis(2003). The disagreement is perhaps because Strauband Kiladis (2003) focused their analysis on boreal summers, when the MJO is not active in general (Madden
1986; Roundy and Frank 2004a). Preliminary resultsfrom an OLR-based long-term analysis underway indicate the significant seasonal variation that the Kelvinwave is in the east of the MJO for boreal summer, while
the Kelvin wave is clearly located within the MJO envelope during austral summer (not shown). Figure 3
exhibits both these aspects because it is based on allseasons together. Roundy and Frank (2004b,c) demonstrated that interactions between the eastward- andwestward-propagating intraseasonal oscillations(roughly corresponding to the MJO and ER wave, respectively, by the current definition) modulate the amplitudes of these waves. These existing studies all seemto imply that interactions between different tropicalwaves are commonly observed and can play some role
in MJO propagation. In this study, it is found in Fig. 2that distinct spots of enhanced convection are often
collocated with areas where a ridge of the Kelvin wave

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intersects with an intruding ER wave. The convective
amplification may be induced by the Kelvin and ER
waves interacting with each other in a way similar tothat discussed by Dunkerton and Crum (1995) andRoundy and Frank (2004b,c).
It is beyond the scope of this paper to extensively
explore the physical basis behind the present results.
We, nevertheless, forward a hypothesis concerning
MJO propagation, where a group of consecutive ridgesof the convectively coupled Kelvin wave are presumed
to be a seed of the MJO formation. The ignition andmaintenance of convective activity associated with the
MJO are in part brought by the interaction of the
Kelvin wave with the ER wave. Convection occasionally remains intensive beyond the control of the largescale waves, which forms a stationary convective phase.
It is speculated that stationary convective phase ismaintained by a convective system driven by selfgenerated diabatic circulation that has grown strong
enough to overwhelm the wave-induced circulation. An
entire system including intensified convection and stationary convective phase(s) slowly moves to the east,
because the Kelvin wave dominates the ER wave inboth speed and amplitude. The predominance of the
Kelvin wave over the ER wave in association with the
MJO is implied by Fig. 3. This whole propagation system is unlikely ascribable to a linear superposition of
the Kelvin and ER waves because of the nonlinearity
involved in the moist processes as well as the presenceof the stationary convective phase. The resultant
unique mode orthogonal to both the Kelvin and ER
waves is presumably responsible for the distinct MJO
peak found in the space–time spectrum.
This idea, if true, raises some important questions.
What modulates neighboring Kelvin waves so that they
are grouped around the MJO? What determines theefficiency with which the wave interaction controls convective intensity, if the ER wave is ubiquitous both
inside and outside the MJO envelope as observed inFig. 2? Physical factors beyond wave dynamics perhaps
need to be considered to address these questions. The
development of deep convection is, for example, closely
related to local geophysical conditions such as SST. Masunaga et al. (2005) suggested the existence of a regimeindependent threshold of 28°–29°C above which SST
favors deep storm systems in the tropical Pacific.
Lower-tropospheric moisture and radiative processes
are also potential key parameters characterizing environmental states that affect convective activity.
The linear theory of the Kelvin and ER waves, moreover, involves no intrinsic mechanism to preferentiallyselect a particular intraseasonal time scale. A typical
MJO period of 40–50 days is too slow to be attributed

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to any linear waves in the Tropics. On the other hand,
this time scale allows a cyclic change in environmental
conditions between those favorable and unfavorable tothe development of active convection (Bladé and Hartmann 1993; Hu and Randall 1994; Flatau et al. 1997;
Sobel and Gildor 2003). This locally regulated thermodynamic system associated with the MJO manifests itself in observed geophysical parameters such as SST,
wind speed, surface heat flux, humidity, precipitation,
OLR, and solar insolation (Lin and Johnson 1996;
Zhang 1996; Kemball-Cook and Weare 2001; Stephenset al. 2004). Section 5b reexamines the connection between the observed MJO time scale and backgroundgeophysical parameters derived from satellite measurements.

b. Variability in environmental conditions
Geophysical parameters examined here include SST,
low (liquid) clouds, columnar water vapor (CWV),
near-surface wind speed, latent heating, net atmospheric radiative heating by clouds, and cloud shortwave forcing at the surface. These variables are derived
primarily from TRMM measurements from the methodology described by L’Ecuyer and Stephens (2003). In
brief summary, the algorithm first retrieves ice clouds,
liquid clouds, and precipitation from TRMM infraredand microwave radiometric measurements. Background atmosphere and surface parameters are obtained from the data archives provided by European
Centre for Medium-Range Weather Forecasts (ECMWF) as well as the TRMM Microwave Imager(TMI)-based datasets produced by Remote Sensing
Systems (RSS). Broadband shortwave and longwave
fluxes are then synthesized by forward radiative transfer calculations. A complete description of the algorithm with error analysis can be found in L’Ecuyer andStephens (2003). The area fractions of shallow anddeep precipitation systems are determined using theMasunaga et al. (2005) categorization based on VIRS
IR Tb and PR echo-top height: shallow rain is identified
by VIRS IR Tb warmer than 260 K and PR echo-top
height lower than 4 km, while the deep category is as
defined earlier in section 2.
For the cross-correlation analysis performed below,
all variables are averaged over oceanic scenes acrossthe whole globe between 10°S and 10°N at the zonal
and temporal resolutions of 1° and 1 day, respectively.
The cross-correlation function between each variable
and the MJO-filtered deep-storm fraction is computed.
Time series at different longitudes are considered independent samples. The 2-yr period from January 1998 to
December 1999 is analyzed, but the first and last 60

FIG. 6. Cross-correlation function of the MJO-filtered deepstorm fraction with (a) (unfiltered) deep-storm fraction (rescaled
by a factor of 0.5), SST, shallow-cumulus fraction, and low-cloud
fraction, and with (b) deep-storm fraction, CWV, and nearsurface wind speed. A negative lag means that the MJO-filtereddeep-storm fraction lags. Vertical bars at the abscissa indicate thesignificance level at 95%.

days are removed from the filtered deep-storm fraction
due to the data loss by the windowing (see section 4a).
The cross-correlation functions are shown in Fig. 6.
Correlation is statistically significant beyond the 95%
level outside the range indicated by vertical bars. Deep
storm systems have a nearly symmetric crosscorrelation function with a pronounced maximum at lag
0, reflecting the MJO cycle itself. The cross correlationof SST indicates that sea surface exhibits a gradualwarming trend in advance of the MJO maximum (at lag0) by more than 10 days. Low clouds are negatively
correlated during the SST warming period. During thesame period, shallow convection gradually increases
peaking 10 days prior to the MJO maximum. The lackof an accompanying increase during this period in low
cloudiness suggests an increasingly efficient conversion

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MJO. The cloud shortwave forcing at the surface is alsoin phase.
A closer examination reveals that the cloud heating
and latent heating are not precisely symmetric aboutlag 0. The latent heating slightly (by a day) leads thecloud heating, and the influence of the cloud heating
remains longer after the MJO maximum than that of
the latent heating. This reflects the fact that the cloudheating is enhanced as high clouds detrained from precipitation cores develop behind the convectively matured stage. The role of cloud heating relative to latentheating is most clearly evident in terms of the atmospheric heating efficiency, rH, defined as the ratio ofcloud heating to latent heating (L’Ecuyer et al. 2005).
While rH has a close connection to the conventional
precipitation efficiency defined as the ratio of precipitation to total condensate, rH is a more direct representative of the local gradient of atmospheric heating,which ultimately leads to changes in the troposphericstability associated with precipitating cloud systems.
Although the phase difference between latent heating
and cloud heating is as small as a day or two, their ratioor rH could have a critical impact on an intraseasonal
time scale typical of the MJO. It can be demonstrated
by a simple mathematical model as follows. Consider
two sinusoidal functions with a phase lag ␦␪ with a constant offset a. For | ␦␪ | K 1,

FIG. 7. Same as Fig. 6 but for (a) latent heating (LH), net
atmospheric radiative heating by clouds (CNH), cloud shortwave
forcing (CSW) at the surface, and SST, and for (b) atmosphericheating efficiency rH.

from cloud liquid water to precipitation. The resultant
lower-tropospheric moistening is observed in the crosscorrelation of CWV (Fig. 6b). The fact that nearsurface wind increases in phase with CWV implies thatwind-induced evaporation is important as well formoistening the lower troposphere. Both the wind speed
and CWV lead deep storm systems by a few days. SST
starts to decrease as deep convection intensifies. A
warm ocean surface begins to recover about 10 days
after the MJO maximum as the sky clears, the air dries,
and the wind calms.
In Fig. 7a the latent heating, net atmospheric heatingby clouds (hereafter the cloud heating), and cloud
shortwave forcing at the surface are plotted as crosscorrelation functions. The cross correlation of SST is
duplicated from Fig. 6 for reference. The latent heating
and cloud heating closely reflect the development anddissipation of convective activity associated with thesin␪
a ⫹ cos共␪ ⫹ ␦␪兲⬇ 1 ⫺ ␦␪.
a ⫹ cos␪a ⫹ cos␪
The resultant function oscillates at the period of 2␲
independently of ␦␪. The smaller ␦␪ is, the smaller theamplitude is while it does not affect the period at all. As
such, the leading oscillation dominates the other in theratio, whatever small the lead is, throughout the firsthalf of the cycle and the relation is turned over during
the rest of the period.
This conceptually explains a fundamental trend in
the correlation of rH with the MJO cycle as shown in
Fig. 7b, which shows that rH is anticorrelated with the
MJO-filtered deep-storm fraction for 15 days preceding
the MJO maximum, while the correlation is positive forthe following 15 days. The antisymmetric pattern in rH
suggests the contrasting roles of cloud heating between
the destabilization that primes the atmosphere for convection prior to the maximum convective activity andthe subsequent stabilizing influence of the cloud longwave heating of the upper troposphere.
Figures 6 and 7 support the MJO-related cycle swinging between stable and unstable atmospheric environments as suggested by previous work. An increase of
SST in advance of the MJO maximum was found in the

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literature (e.g., Nakazawa 1995; Zhang 1996; Hendon
and Glick 1997). The anticorrelation of low clouds with
SST is indicative of strong insolation under suppressedboundary layer clouds as discussed by Flatau et al.
(1997), Hendon and Glick (1997), and Stephens et al.
(2004). The moistening of the free troposphere in response to increasing shallow convection is pointed out
by Kemball-Cook and Weare (2001). The rapid increase of wind speed and water vapor ahead of the
MJO maximum supports the result of Zhang (1996)
that the surface latent-heat flux slightly leads the mostactive convection. It is noted, however, that the phaselag is not distinct enough to let an evaporation–wind
feedback mechanism (Emanuel 1987; Neelin et al.
1987) alone drive the MJO. The decrease of SST withintensifying convection is presumably due to the combined effects of the oceanic vertical mixing, windinduced evaporative cooling, and reduced insolation by
cloud shielding (Flatau et al. 1997). The close correlation between the latent heating and radiative heating is
consistent with the findings by Lin and Mapes (2004).
The whole picture suggested by the present resultclosely resembles the humidistat theory proposed by
Stephens et al. (2004).
In section 5a we discussed the possibility that a sequence of consecutive Kelvin waves could be a key toaccount for MJO propagation. The above radiative–hydrological cycle may serve as a modulator that controls the amplitude of convectively coupled waves
quasi-periodically on an intraseasonal time scale. Thisis possibly a mechanism by which neighboring Kelvinwave ridges are grouped together. Furthermore, lowlevel convergence brought by the Kelvin wave, especially when it coincides with that due to the ER wave,
could intensify convection more efficiently if it takes
place in a more unstable phase of the atmosphericcycle. This may also be a part of the cycle of convective
variation associated with the MJO. The combination of
locally induced oscillation and wave-driven propagation as a forced response is essentially an observational
realization of the discharge–recharge theory of Bladéand Hartmann (1993) aside from differences in details.
The observed thermodynamic structure of the MJO
was found to be supportive of the discharge–recharge
hypothesis also in the analysis performed by Benedict
and Randall (2006, manuscript submitted to J. Atmos.
Sci.).

c. Implications for model studies
These results emphasize the fact that for model simulations to reproduce the MJO it is critical that theyaccount for all factors controlling convective activity
with proper flexibility. The convective response to low-2791

level convergence can be either reinforced or weakened
depending on the environmental conditions involving
SST, moisture, surface wind, solar insolation, and longwave atmospheric cooling. Without the modulation by
these conditions, the MJO would be resolved into linear waves propagating independently (e.g., Hayashi
and Sumi 1986). Slingo et al. (1996) concluded that
AGCMs generally have difficulty in simulating intraseasonal oscillations with periods slower than 30
days. This may indicate that while climate models haveachieved overall success in reproducing the moist
Kelvin wave (which has a period of 30 days for h ⫽ 24
m at k ⫽ 1), the modulation of convective activity bychanges in the background state is not appropriately
modeled. More recent work indicates that the nature ofsimulated eastward propagation is significantly affectedby introducing a wind–SST interaction (Flatau et al.
1997), a cloud–radiation interaction (Lee et al. 2001;
Raymond 2001), or their combination (Sobel and
Gildor 2003).
As an alternative to conventional cloud-parameterization schemes, multiscale modeling framework(MMF) or superparameterization (Grabowski 2001;
Randall et al. 2003) allows a flexible treatment of theconvective response to the environmental conditions.
Grabowski (2003), investigating an MJO-like structure
simulated in a superparameterized aquaplanet model,
discovered that its development exhibited a strong sensitivity to the free-tropospheric moisture. This confirms
the importance of the moistening by shallow convection(section 5b) that preconditions the development of the
MJO. Further progress in the model capability of realizing the MJO will be critical since only a limited number of variables can be extracted directly from observations. Applying a frequency–wavenumber analysis
and a filtering technique to simulated outputs would
help diagnose the model performance in comparison
with observations.

6. Summary
The present paper examines observed properties ofthe MJO by analyzing TRMM PR and VIRS measurements acquired from December 1997 to December
1999 and from December 2000 to June 2001. A frequency–wavenumber analysis of these datasets reveals
general spectral features relevant to convectively
coupled equatorial waves that are consistent with previous work. The PR swath is so narrow that TRMM
sampling errors tend to degrade the statistical significance of spectral signals for high-frequency modes relative to the NOAA OLR product, while lowerfrequency modes are still prominent in the TRMM

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spectrum. Deep-storm fraction estimated by PR and
VIRS in the frequency–wavenumber domain shows the
predominance of wavenumbers 5–8 for the moist
Kelvin wave. Another outstanding spectral feature appears at a period of about 40 days and wavenumbers
1–7, recognized as the spectral representation of the
MJO. A weaker spectral signal corresponding to then ⫽ 1 ER wave is also identified.
A filtering analysis of 10 MJO events in time–
longitude space suggests that a group of consecutive
Kelvin waves are often collocated with an MJO envelope. These Kelvin waves encompass distinct regions ofenhanced convection at the intersection with an intruding ER wave, launching a stationary convective phase,or an intensive convective event left behind outgoingwaves, in some cases. A lag composite diagram indicates that the Kelvin wave, approaching the MJO fromthe west before the MJO grows most active, is strongest
when it spatially and temporally coincides with the
MJO peak. The Kelvin wave emanating in the east of
the MJO is observed once the peak phase of MJO activity passed. The composite ER wave exhibits much
weaker correlation with the MJO peak with no temporal variation to its east. A case study based on GMS
imagery and 850-hPa winds confirms a coherent trend
in the behavior of MCSs.
Cross-correlation analysis of observed geophysicalparameters yields a result consistent with existing scenarios on the intraseasonal cycle regulating atmospheric stability. Sea surface exhibits a warming trend
for 10 days or more prior to the MJO maximum, while
low clouds are anticorrelated with the MJO-filtereddeep-storm fraction during this period. Following an
increase of shallow convection, CWV increases andnear-surface winds intensify, leading deep convection
by a few days. All the parameters return to their initialstate when about 30 days passed after the MJO maximum. The net atmospheric heating by clouds and cloud
shortwave forcing at the surface exhibit nearly coherent
correlation with latent heating. A slight phase lag, however, between cloud atmospheric heating and latentheating results in a cross-correlation function antisymmetric about lag 0 for the atmospheric heating efficiency rH, suggesting a dramatic shift in the role ofcloud radiative heating before and after the peak indeep convective activity.
As the time period analyzed in the present paper islimited, further investigations based on a longer-term
data analysis are required to ensure statistical robustness. It is, moreover, beyond the scope of the present
paper and possible the observations employed to determine a specific mechanism that provides a comprehensive explanation for the above findings. Future model

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studies with improved capability of resolving the moistconvective processes at the root of the MJO are therefore crucial. A hypothetical explanation, nevertheless,emerges from the current results that the MJO may beunderstood in terms of a series of active convection
associated with a group of the Kelvin wave. The interaction of the Kelvin wave with the ER wave might
assist the triggering and maintenance of convective activity within the MJO envelope. These linear waves
coupled with convection as well as the occasional onsetof the stationary convective phase behave as if they
together constitute a slow propagation system, whichappears to be loosely modulated by a locally regulated
radiative-hydrological cycle. We speculate that this system is responsible for the distinct spectral mode corresponding to the MJO.
Acknowledgments. The authors are grateful to T. Inoue at Meteorological Research Institution, Japan Meteorological Agency for his providing GMS data.
TRMM VIRS (1B01) and PR (2A23) data were obtained from National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC).
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 supported by NOAA’s office of Global Program Grant NA17RJ1228#15,
NASA’s Precipitation Program Grant NAG5-13694,
and NASA Research Grant NNG04GB97G.
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