2006

JOURNAL OF CLIMATEVOLUME 22

Tropical Intraseasonal Variability in the MRI-20km60L AGCM*
PING LIU,1 YOSHIYUKI KAJIKAWA,1 BIN WANG,1 AKIO KITOH,# TETSUZO YASUNARI,@
TIM LI,1 H. ANNAMALAI,1 XIOUHUA FU,1 KAZUYOSHI KIKUCHI,1 RYO MIZUTA,&KAVIRAJAN RAJENDRAN,** DUANE E. WALISER,11 AND DAEHYUN KIM##
1 International Pacific Research Center, SOEST, University of Hawaii at Manoa, Honolulu, Hawaii# Meteorological Research Institute, Tsukuba, Japan@ Frontier Research Center for Global Change, Japan Agency for Marine-Earth Science and Technology, Kanagawa, Japan& Advanced Earth Science and Technology Organization, Meteorological Research Institute, Tsukuba, Japan** Centre for Mathematical Modelling and Computer Simulation, National Aerospace Laboratories, Bangalore, India
11 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California## School of Earth and Environmental Science, Seoul National University, Seoul, South Korea(Manuscript received 4 January 2008, in final form 22 October 2008)
ABSTRACTThis study documents the detailed characteristics of the tropical intraseasonal variability (TISV) in the
MRI-20km60L AGCM that uses a variant of the Arakawa–Schubert cumulus parameterization. Mean states,
power spectra, propagation features, leading EOF modes, horizontal and vertical structures, and seasonality
associated with the TISV are analyzed. Results show that the model reproduces the mean states in winds
realistically and in convection comparable to that of the observations. However, the simulated TISV is lessrealistic. It shows low amplitudes in convection and low-level winds in the 30–60-day band. Filtered anomalies have standing structures. Power spectra and lag correlation of the signals do not propagate dominantly
either in the eastward direction during boreal winter or in the northward direction during boreal summer. A
combined EOF (CEOF) analysis shows that winds and convection have a loose coupling that cannot sustain
the simulated TISV as realistically as that observed. In the composited mature phase of the simulated MJO,
the low-level convergence does not lead convection clearly so that the moisture anomalies do not tilt westward
in the vertical, indicating that the low-level convergence does not favor the eastward propagation. The lessrealistic TISV suggests that the representation of cumulus convection needs to be improved in this model.

1. Introduction
Tropical intraseasonal variability (TISV) exhibits thefollowing two dominant modes: the boreal winterMadden–Julian oscillation (MJO; Madden and Julian
1971, 1972) and the boreal summer intraseasonal oscillations (ISOs; Yasunari 1979; Wang and Rui 1990).
These two modes have both distinct and similar characteristics. The MJO exhibits eastward propagation at
zonal wavenumbers 1–3 and in a 30–60-day period.

* School of Ocean and Earth Science and Technology Contribution Number 7574 and International Pacific Research Center
Contribution Number 556.

Corresponding author address: Ping Liu, 1680 East-West Road,
International Pacific Research Center, University of Hawaii at
Manoa, Honolulu, HI 96822.
E-mail: pliu@hawaii.edu
DOI: 10.1175/2008JCLI2406.1
Ó 2009 American Meteorological Society

Zonal wind anomalies are out of phase in the lower andhigher troposphere; they are closely coupled with convection. The coupled pattern initiates in the western Indian Ocean then slowly propagates eastward at a speedof 5 m s21 in the Eastern Hemisphere. Wind anomalies
in the atmospheric boundary layer lead in the eastward
propagation, building up the moist static energy that
fosters deep convection. In contrast, the ISOs have acomplex structure exhibiting both eastward and northward propagations (Wang and Rui 1990; Annamalai andSlingo 2001; Lawrence and Webster 2002). The northward migration prevails over the Indian Ocean and in thewest Pacific from near the equator to 208–308N so as tomodulate the Asian summer monsoon at a 30–40-day timescale. Winds and convection associated with the ISO arealso closely coupled, moving northward coherently. The
MJO–ISO distinction characterizes the TISV seasonality that is attributed to the changes in the backgroundbasic state of the atmosphere (Wang 2005).

15 APRIL 2009LIU ET AL.

General circulation models (GCMs) have great difficulties in simulating the TISV realistically. Early primitive models that had coarse resolution and simple physical processes produced eastward-propagating MJO-likesignals that are much faster than those observed (Hayashi
and Golder 1986; Lau and Lau 1986). Even the state-ofthe-art GCMs with increased resolution and improved
physical processes show large deficiencies in capturing
the MJO features (Park et al. 1990; Slingo et al. 1996;
Wu et al. 2002; Lin et al. 2006). Some models simulated
an MJO with a standing structure. Others produced theeastward propagation while the amplitude is too low,
the period is too short, or the phase speed is too fast.
The modeled coupling between convection and winds isgenerally weak (Zhang 2005). The simulated ISOs areeven less realistic because of their increasing complexity
consisting of both northward- and eastward-propagating
components (Waliser et al. 2003).
Cumulus convection, which produces latent heat as a
primary driving force to the TISV, is represented byparameterization schemes in the GCMs. Because thecumulus has a small spatial scale and short lifetime, incloud processes are modeled only crudely because of
insufficient observations. As a result, the schemes havea large number of uncertainties, which contributes
greatly to the difficulties of the GCMs in simulating the
TISV. For example, closure conditions of the schemes
contribute differently to the simulated TISV. Slingo
et al. (1996) reported that the signal tends to be relatively more realistic in some of the 15 AGCMs that use
a closure based on buoyancy than in others that have aclosure associated with moisture convergence. However, Lin et al. (2006) suggested that only schemes
having a closure linked to moisture convergence could
produce relatively better MJO. Using a similar buoyancybased closure, Zhang and Mu (2005) showed that thesimulated MJO is more sensitive to the buoyancy tendency in the free atmosphere than to that in the wholecolumn. In contrast, Sperber and Annamalai (2008) did
not find any sensitivity of the simulate ISO to any particular closure.
Cloud-resolving models, which represent the cumulus
explicitly, can overcome some fundamental uncertainties
in the parameterization schemes. These models thus
simulated the TISV more realistically. Ziemiański et al.
(2004) embedded a cloud system–revolving model in a
300-km AGCM over the tropical western Pacific. The
simulated MJO-like disturbances are much more
prominent than in the default model that uses the cumulus scheme only. Miura et al. (2007) reported that an
MJO event was realistically simulated by a 7-km global
cloud-resolving model using the observed initial conditions. Nonetheless, the cloud-resolving models have such

2007

an extraordinarily high resolution that present computing
power can afford a simulation of less than 2 months, whichis too short to disclose the periodicity and seasonality of
the TISV. Conventional AGCMs with increased resolutions and improved cumulus schemes are still necessary
for simulating the long-term climate variability associatedwith the TISV.
The success of the cloud-resolving models suggeststhat the mesoscale circulations associated with the cumulus convection may be important to the simulated
TISV. Gustafson and Weare (2004) supported the importance by showing that a regional model at a 60-km
horizontal resolution can improve the simulated MJO,
even without intraseasonal perturbations prescribed by thelateral boundary conditions. However, cumulus parameterizations (e.g., Arakawa and Schubert 1974) generally
neglect the effect of the mesoscale circulations; this effect can be included by increasing model resolution. A
GCM with finer vertical resolution improved the simulated TISV (Inness et al. 2001), but the dependenceof the simulated TISV on increasing horizontal resolution is inconsistent. Some models show improvement(Hayashi and Golder 1986), while one reported no effect (Martin 1999) and others even deteriorated thesignal (Gualdi et al. 1997; Liess and Bengtsson 2004).
Because the horizontal resolution of these models istypically larger than 200 km, a resolution of tens of kilometers is probably necessary to resolve the mesoscale
circulations, as in Gustafson and Weare (2004).
In spite of the overall nonsuccess, some GCMs at a300-km resolution can improve the simulated TISV
by using alternative cumulus schemes. Maloney andHartmann (2001) demonstrated that the relaxed Arakawa
and Schubert (1974) scheme improved the variance,
periodicity, and eastward propagation of the TISV in the
National Center for Atmospheric Research (NCAR)
Community Climate Model version 3 (Kiehl et al. 1998).
Liu et al. (2005) reported that the Tiedtke (1989)
scheme enhanced the MJO disturbances in the NCAR
Community Atmospheric Model version 2. The improvements in these two schemes were probably achieved by including more sophisticated cloud processes.
For example, a cloud ensemble and different water phases
in clouds, rather than a bulk model, are described by therelaxed Arakawa–Schubert scheme. Turbulent effect andvertically variable entrainment are included in the Tiedtke
scheme. When these relatively successful schemes areused in a GCM that has a resolution that is high enoughto resolve the mesoscale circulations, whether and why
the simulated TISV can be improved are the objectivesof this study.
An AGCM at a horizontal resolution of T956 (approximately 20 km) and with 60 vertical levels using a variant of

2008

JOURNAL OF CLIMATE

the Arakawa–Schubert scheme has been developed withjoint efforts of the Japan Meteorological Agency (JMA)and Meteorological Research Institute (MRI) of Japan;
this model is termed the MRI-20km60L AGCM. Earlier, a 10-yr run was carried out using the climatological
SST as external forcing. Rajendran et al. (2008) examined the TISV partially in power spectra and eastward
propagation in this particular run. They reported thatthe simulated TISV exhibits eastward propagation in
200-hPa velocity potential, while the power spectra
concentrate on periods longer than 90 days. This study
continues to investigate the simulated TISV in detailand understand why the simulated TISV is less realistic
in a 27-yr Atmospheric Model Intercomparison Project(AMIP; Gates 1992) run using the monthly evolving
SST as external forcing. Variance, power spectra, andlag correlation are diagnosed to disclose the modeled
TISV features. Following Wheeler and Hendon (2004,
hereafter WH04), a composited phase 3 of the MJO
is constructed to investigate the simulated convection–
circulation interaction. This MJO phase has a convection
maximum along the equator near 908E and a minimum tothe west of the date line. Section 2 briefly introduces themodel and methodology. Section 3 presents the TISV
characteristics and the horizontal and vertical structuresof the constructed MJO in phase 3. Section 4 discusses
possible causes of the nonsuccess.

2. Model and methodology
a. ModelThe MRI-20km60L AGCM is developed for bothclimate simulation and weather prediction. It is based
upon the global numerical weather prediction (NWP)
model of the JMA, version JMA-GSM0103, with modifications and improvements. A detailed description of
the model can be found in Mizuta et al. (2006); a summary is presented here.
This model uses a spectral transform on the spheretriangularly truncated at 959 waves on 1920 3 960 gridcells (approximately 20 3 20 km2) and a sigma-pressure
hybrid coordinate with 60 vertical levels. The 20-km
horizontal resolution is able to resolve the mesoscale circulations associated with the cumulus convection, which isrepresented by the Arakawa–Schubert scheme with somerevisions. The cloud-base mass flux is determined bysolving a prognostic equation (Pan and Randall 1998).
The upward mass flux has a profile linearly related toheight (Moorthi and Suarez 1992). Effects of entrainmentand detrainment in downdraft are included between thecloud base and cloud top (Nakagawa and Shimpo 2004),
which reduces the cooling bias in the tropical lower tro-

VOLUME 22

posphere. In addition, clouds are formed prognostically(Smith 1990); cloud amount and cloud water content are
statistically estimated (Sommeria and Deardorff 1977).
Cloud water is in liquid state above 08C and in ice state
below 2158C; between 2158 and 08C the fraction changes
linearly with temperature. A quasi-conservative semiLagrangian scheme (Yoshimura and Matsumura 2003)
is implemented for stable and efficient time integrations
so that the model is able to use a 6-min time step.
The model is forced with monthly SST evolving from1979 to 2005. Six-hourly outputs are archived, fromwhich daily mean is derived. A two-step box-mean linear
interpolation is used to convert the high-resolution data
to 18 3 18 then 2.58 3 2.58 for analysis. The December–
February (DJF) and June–August (JJA) climatology isderived from the daily output.

b. Methodology
The U.S. Climate Variability and Predictability (CLIVAR) MJO Working Group has developed a standard
software package for evaluating both the MJO and ISO
in GCMs. The variables in the package include observational datasets of the National Oceanic and Atmospheric Administration (NOAA)-interpolated outgoing
longwave radiation (OLR) and the National Centers forEnvironmental Prediction (NCEP)–NCAR reanalysis(Kalnay et al. 1996) products of 850- and 200-hPa zonal
winds at a 2.58 3 2.58 resolution for the period of 1979–
2005. Daily anomalies are derived by subtracting thelong-term mean. A 20–100-day bandpass filter is thenapplied to the daily anomalies. Standard metrics, including estimation of variance, power spectra, lag correlation, EOF analysis, and combined EOF (CEOF)
analysis, are applied to the filtered series. Apart fromthese metrics, by incorporating the methods outlined in
WH04, modeled anomalies of 200-hPa zonal wind areprojected onto the observed first two CEOFs to select
events for constructing the horizontal and verticalstructure of the MJO in phase 3. Section 3d describes
the procedure in detail.

3. Resultsa. Mean states
A necessary, but perhaps not a sufficient, condition
for GCMs to represent the TISV is the capture of thetime-mean climatology in precipitation and zonal wind(Slingo et al. 1996; Wang and Xie 1997; Inness et al.
2003; Jiang et al. 2004). The MRI-20km60L AGCM has
simulated realistic mean states in equatorial zonal winds
during both the DJF and JJA seasons (Fig. 1). The
westerly winds at 850 hPa during DJF (Fig. 1a) over

15 APRIL 2009LIU ET AL.

2009

FIG. 1. Long-term-mean (1979–2005) zonal wind at 850 hPa in the MRI-20km60L AGCM for(a) DJF and (b) JJA. Contours are 220, 210, 25, 0, 2.5, 5, 10, and 20 m s21, with dashed as
negative and the first solid line adjacent to a dashed as zero. The thick gray curve corresponds tozero from the NCEP–NCAR reanalysis.

southern equatorial areas in Africa and the Indian
Ocean up to the date line is realistically simulated inboth spatial range and magnitude compared to the
NCEP–NCAR reanalysis. The gray thick curve, which
represents the zero line for the reanalysis, mostly coincides with that in the model and extends over the entire
southern equatorial areas in the Eastern Hemisphere.
The westerly winds in this area are essential for the
MJO in eastward propagation (e.g., Slingo et al. 1996;
Inness et al. 2003). Many GCMs with coarse resolution,
typically 300 km, are able to simulate the westerly winds
in only part of the area (e.g., Maloney and Hartmann2001; Inness et al. 2003).
The zonal wind shear between 200 and 850 hPa fromthe northern Indian Ocean to the South China Sea traps
the equatorial waves in the Asian summer monsoon
region, thereby promoting the northward propagationof the ISO mode (e.g., Wang and Xie 1997; Jiang et al.
2004). Here we only show the zonal wind at 850 hPa forclarity; that at 200 hPa has a similarly realistic pattern.
As shown in Fig. 1b, the model has produced comparable westerly jets at 850 hPa from Africa to the west
Pacific. The simulated zero, indicated by the first solidline adjacent to the dashed line, is collocated with that in
the reanalysis (the thick gray line); the modeled westerly winds fall within the same range as the reanalysis inwestern Africa, the equatorial Indian Ocean, and thewestern Pacific.
Mean-state OLR in the MRI-20km60L AGCM has apattern comparable to observations as reported by
Rajendran et al. (2008). This is also supported by thetwo nearly coincident bold contours in Fig. 2 that represent the 230 W m22 of OLR in the NOAA satellite

observations (gray) and in the model (black). Nonetheless, differences exist between the model and theobservations during DJF and JJA. For example, during
DJF (Fig. 2), the model produces somewhat higher
OLR, indicating less active convection, over the tropics
in Africa, eastern Indian Ocean, and South America.
The Indian Ocean, in particular, displays a dipole of
622 W m22 deficit, indicating more active (suppressed)
convection in the west (east). This biased convection
dipole also occurs in the composited phase 3 of themodel MJO. During JJA (not shown), convection overthe Bay of Bengal, Indo-China Peninsula, and South
China is weaker than observed, while it is stronger overthe central Indian Ocean along 608E. Such deficiencies
in mean OLR correspond to unrealistic TISV features
as described below.

b. Variance, power spectra, and lag correlation
The climatology in winds and convection are simulated well by the MRI-20km60L AGCM, but the TISV
variance (filtered 20–100 day) is much lower than that in
the observations. To assess the zonal extent and magnitude of the TISV, in Fig. 3 we show the model-toobservation ratio in the OLR variance. In both seasons,the zonal extent in variance is fairly well captured, but adeficiency in the amplitude is noted. In boreal winter,over the known MJO active regions of the deep tropical(108S–108N) Indian and western Pacific Oceans, theratio is around 0.5, suggesting that the model is only able
to produce about 50% of the observed variance. Similarly, in boreal summer (Fig. 3b), about 40%–60% of
the variance is simulated in the ISO active regions of
the eastern Indian Ocean, South China Sea, and western

2010

JOURNAL OF CLIMATEVOLUME 22

FIG. 2. Long-term-mean (1979–2005) OLR differences between the MRI-20km60L AGCM
and the NOAA satellite observations for DJF. Contour interval is 7.5 W m22, with dashed as
negative and zero line omitted. The thick contours correspond to 230 W m22 for the observation (gray) and in the model (black).

Pacific. The simulated 850-hPa zonal wind variance (notshown) also has patterns similar to the observations, butwith low amplitudes.
Corresponding to the low variances, the power spectra of the simulated TISV are low. Modeled zonal winds
at the upper troposphere have patterns in power spectrain this Atmospheric Model Intercomparison Project(AMIP) run, similar to those in the climatological run
reported by Rajendran et al. (2008). The power is prominent at zonal wavenumbers 1–3 during boreal winter,
while it is concentrated on time scales greater than
90 days, much longer than the 30–60 days in the observations (not shown). The simulated power spectra in
low-level winds are even less realistic. For comparison,Fig. 4a shows the frequency–wavenumber power spectrain the observed 850-hPa zonal wind along the equatoraveraged between 158S and 158N in November–April
seasons during 1979–2005. In the observations (Hendon
and Salby 1994), the power is concentrated at 30–60
days and at zonal wavenumbers 1–3. Specifically, thecentral value is above 0.08 m2 s22 at a 60-day period andat zonal wavenumber 1, which is dominant in the east-

ward direction. In contrast in the model, although theeastward component at zonal wavenumber 1 dominates (Fig. 4b), the amplitude is substantially lower(0.02 m2 s22 versus about 0.08 m2 s22) and distributed
over a wider time scale (30–100 days). The simulated
power for westward direction is comparable to the reanalysis but is almost as large as its eastward counterpart, unlike in the observations.
The MJO is weaker during boreal summer (May–
October) than winter, which can be shown by the lower
power spectra of zonal wind at 850 hPa (Fig. 5a). The
power spectra have a central value of 0.05 m2 s22 in theeastward component, about 60% of which is in winter (cf.
Fig. 4a). In contrast, the westward component is nearly0.01 m2 s22, indicating dominant eastward propagation.
The difference between power spectra during boreal
winter and summer partially characterizes the seasonalityof the TISV. The simulated MJO in power spectra in JJA(Fig. 5b), however, is less than 1/5 of that observed in theeastward propagation. The spread is near zonal wavenumber 1 at periods longer than 90 days. Such weak power
spectra in both seasons suggest that the model does not

FIG. 3. Model-to-observation ratio of 20–100-day-filtered variance in the NOAA OLR for (a)November–April and (b) May–October averaged in 1979–2005. Model variance less than 150
W2 m24 is masked out and ratio # 0.6 is shaded.

15 APRIL 2009LIU ET AL.

2011

FIG. 4. Frequency–wavenumber power spectra (m2 s22) of the 850-hPa zonal wind along theequator (158S–158N mean) during November–April averaged in 1979–2005 for (a) the reanalysis and (b) the MRI-20km60L model.

realistically reproduce the seasonality of the TISV. The
simulated OLR has similarly weak power spectra as thezonal wind at 850 hPa (not shown).
The simulated weak power spectra in zonal winds andconvection suggest either the propagating signal is too
weak or the signal does not strongly propagate at all.
Lag correlation can more clearly disclose either propagating or standing structures. Figure 6a demonstrates

the lag correlation of OLR during the November–April
season in the observations with the mean of 108S–108N
on 908E as the reference point where the OLR has amaximum variance. An eastward-propagating signal starts
from day 220 in Africa to the western Indian Ocean,moves slowly eastward at about 5 m s21, crosses thereference point at day 0, and reaches the date line on thenext day 215, showing a 60-day period. The simulated

2012

JOURNAL OF CLIMATEVOLUME 22

FIG. 5. Same as Fig. 3, but for May–October.

OLR (Fig. 6b), however, has a dominant standing structure centered at 908E. Isolated moving patches are seen
in both eastward and westward directions. In particular,
signals in Africa and the western Indian Ocean are completely separated from those of the reference point. Thismodeled standing structure also occurs in zonal winds at
850 hPa (not shown), although the signals are more connected with the reference in both eastward and westward
directions than in OLR. Lag correlation in zonal winds at
200 hPa has more organized eastward propagation fea-tures than those in OLR and 850-hPa zonal wind, eventhough the overall pattern is still less realistic, similar tothe climatological run (Rajendran et al. 2008). We will
use the relatively better simulated anomalies in 200-hPa
zonal wind to derive the MJO events.
The ISO in the observations dominates in the northward propagation separately in the Indian Ocean and in
the west Pacific (Yasunari 1979; Wang and Rui 1990).
The lag correlation of filtered OLR during May–
October in the Indian Ocean sector is shown in Fig. 7, with

15 APRIL 2009LIU ET AL.

2013

FIG. 6. Lag correlation in OLR along the equator during November–April in 1979–2005 for (a)the NOAA observations and (b) the MRI-20km60L model. Reference point is the mean of 108S–
108N on 908E. Shaded values are above 99% significance level.

the equator as the reference point averaged between 808
and 1008E. In the observation (Fig. 7a), the ISO initiateswith a suppressed phase just south of the equator on day
225, and then strengthens and matures around day 215.
The signal moves in both southward and northward directions. The southward branch reaches 208S on day 25,
which is sooner than the northward branch that reaches
228N on day 0. The active phase of the oscillation reaches
its maxima on day 0 at the equator and also moves in boththe southward and northward directions. However, thisphase can reach 308N, much farther northward than the
suppressed phase. The active phase decays on the equator
near day 10, showing a 35-day period.
The simulated ISO in the Indian Ocean sector (Fig.
7b) oscillates similarly to that in the observations on theequator. A suppressed phase starts on day 225, matures

on day 215, and switches to an active phase on day 210.
The successive active phase on the equator matures on
day 0 and decays on day 10. Thus, the oscillation has aperiod of 35 days, comparable to that observed. In spiteof the similar periodicity, the simulated ISO in the
Indian Ocean sector has centers of 20.2 for the suppressed phase and 0.5 for the active, which is weaker thanthose observed. The northern branches in both suppressed
and active phases can only reach 108N, while the southernbranches can propagate as far as 308S. The main signal isconfined within 128S and 108N, which is much narrower
than that observed, and it has a standing structure.
Observed ISO in the west Pacific sector has distinct
features compared to that in the Indian Ocean sector.
The lag correlation in Fig. 8 uses a reference point averaged between 1158 and 1358E on the equator during

2014

JOURNAL OF CLIMATEVOLUME 22

FIG. 7. Lag correlation in OLR during May–October along the Indian Ocean sector for(a) the NOAA observations and (b) the MRI-20km60L model. The reference point is the meanof 808–1008E on the equator. Shaded values are above 99% significance level.

the May–October season. The observed ISO (Fig. 8a)
has a 40-day period on the equator, but its center value
is about 20.2 for the suppressed phase and 0.3 for theactive phase, which is much weaker than that in the
Indian Ocean sector. The oscillation propagates prominently northward and can reach beyond 408N. The
southern branch is predominately a standing feature
with lower value during the suppressed phase. During
the active phase, north and south signals are separated
near 108S. In this sector at the equator, the simulated
ISO (Fig. 8b) starts on day 210 with a suppressed phase,and then switches to an active phase on day 5 and ends
on day 20, indicating a period of about 30 days. Minimum and maximum correlation amplitudes, however,are around 20.1 and 0.1, which is about 1/3–1/2 of thoseobserved. The northward part is connected with thesouthward branch and can reach 308N, not as far as in

the observation. Unlike the relatively static structure in
the Indian Ocean sector, the ISO here has discernablenorthward-propagating features. Because the lag correlation includes all propagating information, an EOF
analysis in the following section will effectively isolate
the dominant modes of the TISV.

c. Leading EOFs and the coupled pattern
EOF analysis has been widely used to separate thephase structures of the TISV from the filtered time series (e.g., Lau and Chan 1985; Knutson and Weickmann
1987; Maloney and Hartmann 1998). Rajendran et al.
(2008) applied the extended EOF analysis to the filteredvelocity potential at 200 hPa of the 10-yr climatologicalrun from the MRI-20km60L AGCM. They obtained
MJO propagating structures similar to that observed,
except the spatial scale is smaller. However, when the15 APRIL 2009LIU ET AL.

2015

FIG. 8. Same as Fig. 7, but in the west Pacific sector and the reference point is the average
between 1158 and 1358E on the equator.

EOF analysis is applied to the model OLR and zonal
wind at 850 hPa, the leading EOFs demonstrate quite
different spatial patterns from those in the observations.
Generally, the modeled EOFs have zonally asymmetricstructures that are flatter than those observed in convection and winds. The variance of the first two EOFs is
too small to separate them from the rest with a statistical significance. These values are listed in Table 1 withthe observations for comparison.
The first two EOFs in the observations explain 6.1%–
7.6% of the variance in OLR and 9.4%–14.8% of thevariance in zonal wind at 850 hPa. Both EOFs are
separated from the rest at a significance level with thecriterion of North et al. (1982) as disclosed in previous
studies (e.g., WH04). The corresponding two EOFs in
the model, however, explain 3%–4% of the variance in
OLR and 5.5%–6.8% of the variance in zonal wind at
850 hPa, which is about half of that observed. They arevery close to the third and fourth EOFs, so they cannot
be separated statistically. These inseparable EOFs inboth OLR and 850-hPa zonal winds suggest that the
coupling among the convection and dynamical fields canbe weak, which is demonstrated in a CEOF analysis
using OLR and zonal winds at both 850 and 200 hPa.
WH04 tested different combinations of variables for
the CEOF analysis optimizing the CEOFs to represent
the TISV for real-time monitoring and prediction. They
found out that the optimal combination is OLR and
850- and 200-hPa zonal winds, each averaged over thelatitudes of 158S–158N. They excluded the seasonalmean and ENSO components before analysis without
bandpass filtering. The latitude average implicitly filters
out small-scale disturbances as indicated in WH04. Here
we use the bandpass-filtered data for the CEOF analysis,
which produces observed CEOFs almost identical to thosein WH04. The two leading CEOFs in the observations are

2016

JOURNAL OF CLIMATEVOLUME 22

TABLE 1. Explained variance of the first four leading EOFs either in the observations or in the reanalysis and the MRI-20km60L AGCM.
EOF analysis is applied to OLR in 308N–308S, 08–3608, and to zonal wind at 850 hPa in 208N–208S, 08–3608.
OLR

850-hPa zonal wind

NOAA

EOF 1
EOF 2
EOF 3
EOF 4

MRI

Reanalysis

MRI

WinterSummer

WinterSummer

WinterSummer

WinterSummer

7.5%
7.2%
4.1%
3.3%

7.6%
6.1%
4.2%
3.0%

4.1%
3.0%
2.6%
2.5%

3.0%
2.8%
2.7%
2.4%

12.3%
9.4%
6.3%
4.5%

14.8%
11.9%
5.5%
4.8%

6.8%
6.1%
6.1%
4.7%

6.8%
5.5%
5.3%
4.4%

plotted in Fig. 9 for comparison. The first mode (Fig. 9a)
starts an active MJO cycle in OLR (solid line) near
608E, where the 200-hPa zonal wind (short dashed line)
is at a negative maximum, while the 850-hPa zonal wind(long dashed line) almost reaches a positive maximum.
The winds are in a baroclinic structure and lead convection by about 908 phase. The OLR reaches its maximum at 908–1308E, where the zonal winds at both 850
and 200 hPa restore back to 0. At 1808 longitude, the
OLR restores to 0 while the winds almost reach theiropposite maxima. The second mode nearly mirrors thefirst for a suppressed MJO cycle. Both CEOF modes
show an apparent quadrature between winds and convection, which is a typical structure of the MJO (e.g.,
Hendon and Salby 1994). The CEOFs in Fig. 9 coincidewith those in WH04 (their Fig. 1), where shorter timeseries were used, indicating the robustness of the structure.
The two leading CEOFs in the MRI-20km60L
AGCM, however, are quite different. In the first mode
(Fig. 10a), zonal winds at 850 and 200 hPa have the same
sign from 508–1508E, indicating a barotropic structure
rather than a baroclinic structure, as in the reanalysis.
Both winds are weak easterly and almost collocatedwith the OLR from 608 to 1208E, where the observations
are separated and in quadrature (Fig. 9a). The OLR
amplitude here is barely lower than 20.4, about half ofthat observed. The second CEOF is also quite different
from that in the observations. The simulated OLR has
amplitudes between 20.3 and 0.3, which is smaller thanthat observed. Even though the zonal winds have a baroclinic structure, they are still in phase with the OLR.
Such weak coupling among convection and zonal
winds corresponds to the low explained variances by
each EOF as listed in Table 2. The first two CEOFs
explain about 22% of the variance in the observations,but only 12% in the model. The first two EOFs of the
OLR in the model explain only 3%–4% variance, which
is much lower than the 13%–15% in the observations.
The EOFs for the simulated winds are also lower thanthose observed. It is noteworthy that the EOFs for the
200-hPa zonal winds have explained a variance almost
comparably to observations. This is consistent with thevelocity potential at 200 hPa reported by Rajendran
et al. (2008). The standard deviations for the OLR and
850- and 200-hPa zonal winds in the model are allsmaller than those in the observations. From Figs. 9 and
10, and Tables 1 and 2, the model has simulated generally weak coupled patterns for the TISV.

d. Horizontal and vertical structure of themodeled MJO
The frictional convergence mechanism (Wang 1988)
explains why the MJO exhibits eastward propagation.
During an MJO life cycle, the convergence in the atmospheric boundary layer is observed to lead in theeastward propagation for building up the moist static
energy that fosters the deep convection (Rui and Wang
1990; Hendon and Salby 1994; Maloney and Hartmann1998). As a result, the anomalous moisture and latentheating have a westward-tilted structure in the verticalwith respect to the convection maximum (Sperber 2003;
Kiladis et al. 2005). The low-level convergence andvertically westward-tilted pattern associated with the
MJO are absent (see Figs. 12 and 13) in the MRI20km60L AGCM so that the simulated signal has astanding structure.
WH04 derived a TISV index for real-time monitoringand prediction. By projecting the real-time anomalies
onto the two leading CEOFs, they derived two principal
components as RMM1 and RMM2. A phase map of theRMM1 and RMM2 effectively defines the eight phasesof a TISV event. Details about the phase definition canbe found in their literature. We next follow their procedure to derive a composited phase 3 of the MJO byprojecting the zonal winds at 200 hPa in both the modeland the reanalysis onto the observed CEOFs. Because the
CEOFs are derived from the 20–100-day bandpass-filtereddatasets where components other than the TISV havebeen excluded, the anomalies used for projection are calculated by simply subtracting climatology from the daily
mean. The derived phase 3 of the MJO has a convection
maximum in the eastern Indian Ocean and a minimum
near the date line as shown by WH04 (their Fig. 5).

15 APRIL 2009LIU ET AL.

2017

FIG. 9. The first two CEOF modes of 20–100-day filtered 850- and 200-hPa zonal winds and
OLR in the observations averaged between 158N and 158S from 1979 to 2005.

Figure 11 shows the first two projected principal
components RMM1 and RMM2 in the model. Only a
few labels are marked for simplicity. The inner circle
includes the RMM1 and RMM2 less than one standard
deviation. To isolate phases as clearly as possible, wechoose points that are over one standard deviation inboth the RMM1 and RMM2 to represent the MJO
phase 3. These points fall in the small triangle marked
with ‘‘Ph3.’’ There are about 100 points selected in themodel. Using the time indices of these selected events,
composites of the OLR, low-level convergence, andvertical structure of the moisture anomalies are derived
and shown in Figs. 12 and 13.
Figure 12 shows the composited anomalies of OLR,
850-hPa velocity potential, and divergent wind vectors
during the MJO phase 3. The OLR in the observations(shaded in Fig. 12a) clearly displays a dipole structure(cf. Fig. 9b) in the Indian and western Pacific Oceans.
The minimum OLR, indicating a maximum convection,is less than 240 W m22 near 908E. The nonrotatedconvergence at 850 hPa in the reanalysis, indicated by thesolid contours in Fig. 12a, extends from 308E to 1608W in
the 158S–158N latitudes, covering the entire tropical Indian Ocean and west Pacific. The convergence center,
which is represented by the velocity potential larger than
1 3 107 m2 s21 and the intersection of divergent easterly
and westerly winds, is located near 1208E, about 308 in
longitude to the east of the maximum convection. Thisquadrature pattern indicates that the low-level convergence leads the convection in the eastward propagation.
In contrast, Fig. 12b shows the situation in the model.
The simulated convection has two maxima in the Indian
Ocean, which is different from the one in the observations. The positive 850-hPa velocity potential extends
only from 908 to 1408E with values no larger than 2 3 106m2 s21, elucidating a weaker amplitude and narrower
range in the simulated low-level convergence than in thereanalysis. This less realistic low-level convergence contributes to a quasi-barotropic vertical structure in the
moisture anomalies as shown in Fig. 13.
The thick gray line in Fig. 13 represents the composited OLR anomalies averaged in 158S–158N

2018

JOURNAL OF CLIMATEVOLUME 22

FIG. 10. Same as Fig. 9, but in the MRI-20km60L AGCM.

latitudes in the NOAA observations during this MJO
phase. Clearly, a 240 W m22 minimum occurs near
908E and a 20 W m22 maximum occurs near 1808 longitude, which has been shown in Fig. 12a. These two
extremes characterize the MJO zonal asymmetry (e.g.,
Madden and Julian 1971). The modeled OLR (thickblack line), however, has two approximately 220 W m22
minima from 308 to 1208E, which is much higher thanthat in the observations. Corresponding to these minima, the specific humidity anomalies have two positive
areas. Interestingly, the one near 308E lags the OLR
minimum at 408E, while the other at 1008E leads

the OLR minimum at 908E in an eastward direction.
The spatial difference between the extremes of the
OLR and specific humidity is about 108 in longitude.
The extreme of the specific humidity in the observations
is clearly in concert with the OLR minimum (Sperber
2003; Kiladis et al. 2005). During the mature phase of the
MJO, the moisture anomalies tend to vertically tilt
westward with boundary layer moisture, leading convection eastward by about 458 in phase (Sperber 2003;
Kiladis et al. 2005). The specific humidity anomalies
in Fig. 13 do not show such an apparent westward
tilt. This quasi-barotropic structure may explain the

TABLE 2. Explaining variance of the first two leading CEOFs in the observations and the MRI-20km60L AGCM.
Observation/reanalysis

First mode
Second mode
Std dev

MRI-20km60L AGCM

Total

OLR

U850

U200

Total

OLR

U850

U200

22.2%
20.1%

13.2%
15.9%
8.4 W m22

31.7%
23.1%
1.2 m s21

21.7%
23.8%
3.3 m s21

11.9%
10.8%

3.9%
3.3%
7.1 W m22

11.9%
17.2%
0.8 m s21

19.9%
11.9%
2.5 m s21

15 APRIL 2009LIU ET AL.

FIG. 11. Phase space of the first two principal components(RMM1 and RMM2) derived by projecting the zonal wind
anomalies at 200 hPa in the MRI-20km60L AGCM onto the first
two CEOFs in the observations. Each quadrant represents one
phase of the MJO with the phase 3 on the right bottom marked by‘‘Ph3’’. Details about the phase definition can be found in WH04.

standing structure of the MJO as discussed in the lagcorrelation (Fig. 6).

4. Summary and discussions
The tropical intraseasonal variability is prominent in
the observations but is difficult to simulate realisticallyby the state-of-the-art GCMs. The difficulties are generally attributed to the quality of cumulus parameterization and model resolution, among others. The MRI20km60L AGCM has very high horizontal and verticalresolution that can resolve the mesoscale circulations associated with the cumulus convection. This model uses avariant of the Arakawa–Schubert scheme that improved
the simulated MJO in a 300-km resolution model.
Therefore, this AGCM is expected to be able to simulate the salient features of the TISV.
As reported by Rajendran et al. (2008), and further
disclosed in this study, however, the model has simulated a TISV with low variance in the 30–60-day band.
Power spectra and lag correlation show that the filteredsignals have a standing structure, particularly in theeastward-propagating mode during boreal winter. Convection and dynamical fields are coupled too weakly tosustain the TISV. Biased convection in the Indian Ocean
corresponds to the standing structure.

2019

It is interesting to note that although the simulated
TISV has low variance and standing structures, the simulated background basic states in the atmosphere arecomparable to the observations, which are particularly
realistic in zonal winds. Previous studies have shown thatthe realistic basic states are necessary for the initiationand eastward propagation of the TISV. Our results inthis model, furthermore, confirm that realistic meanstates are not sufficient for a realistic TISV. There areother vital factors that contribute greatly to the model’s
performance even when the resolution is high enough toresolve the mesoscale circulations associated with the
cumulus convection.
One probable factor can be the high ratio of convective
to total precipitation. The model convective precipitation
occupies nearly 90% of the total in the MJO active areas(Fig. 14). This ratio is much higher than that in theobservations. For example, Lin et al. (2004) disclosedthat stratiform precipitation can make up to 30%–40%of the total during an MJO event, and Haertel et al.
(2008) indicated that the radar-derived stratiform precipitation contributes to the MJO by lagging the convective component for nearly 10 days (their Fig. 18a).
Associated with the high ratio, long-term-mean moist
diabatic heating along the equator tends to be verticallyuniform particularly in the Indian Ocean with a maximum of 4 K day21 near 850 hPa at 608E, as indicated in
Rajendran et al. (2008). This nearly uniform profile isdifferent from the dipole structure as disclosed by Lin
et al. (2004), even though that structure occurred in thewest Pacific during an MJO event. The actual impact ofthe vertical heating profile on the simulated TISV,
however, will be further investigated.
The weak TISV may suggest that the Arakawa–
Schubert cumulus scheme could not be applicable to amodel at a 20-km horizontal resolution. A similarly
weak and irregular TISV was also simulated in the Soul
National University 20-km AGCM implemented with asimilar cumulus scheme (I.-S. Kang 2008, personalcommunication). The Arakawa–Schubert scheme assumes that an area for parameterization should be large
enough to host an ensemble of shallow, middle, anddeep clouds in a very small fraction with the much larger
part for the cloud-free environment. The area-wide
processes, for example, advection and surface fluxes,
destabilize the column, while the cloud ensemble releases the unstable energy through adjusting the verticalprofiles of temperature and moisture in the cloud-freeenvironment. In the MRI-20km60L AGCM, each grid
point is configured independently to its neighboring
points for the cumulus parameterization. A 20-km gridbox can be too small to satisfy the large-area assumption,in particular for the cumulus clusters in hundreds and2020

JOURNAL OF CLIMATEVOLUME 22

FIG. 12. Composited anomalies of OLR (W m22; shaded), 850-hPa velocity potential (1 3 106m2 s21; contour), and 850-hPa divergent wind vectors (m s21) in (a) the NOAA observations
and NCEP–NCAR reanalysis and (b) the MRI-20km60L AGCM during phase 3 of the MJO.
Phases are selected from the small triangle marked with Ph3 in Fig. 11.

thousands of kilometers scale associated with the TISV.
This is probably why the high-resolution version of theNavy Operational Global Atmospheric Prediction System (Peng et al. 2004) replaced the Arakawa–Schubertscheme with the Emanuel (1991) scheme that deals with
100-m scale drafts in cumulus clouds.
Because of the large number of uncertainties in the cumulus schemes, the improvement of the simulated TISV in

FIG. 13. Vertical structure of the specific humidity (g kg21) in the composited MJO phase 3.
OLR anomalies averaged in 158S–158N lats during this phase are plotted in thick lines withblack for the model and gray for the NOAA observation.

15 APRIL 2009LIU ET AL.

2021

FIG. 14. Ratio in percentile of convective-to-total precipitation during DJF (1979–2005mean) in the MRI-20km60L AGCM. Values $ 50% are contoured with a 10% interval except
the 85% (bold) and those $80% are shaded.

GCMs has depended greatly on test and trial of different schemes or different features of a specific scheme(e.g., Wang and Schlesinger 1999; Maloney and Hartmann2001). The Meteorological Research Institute (A. Kitoh
2008, personal communication) is testing the Tiedtke
scheme for the TISV simulation in this high-resolution
model. Fundamental improvement, however, will comethrough the improved cumulus schemes in representing
the cumulus–circulation interactions using expanded observations and outputs from the cloud-resolving models.
Acknowledgments. This study is supported by the Japan
Agency of Marine Science and Technology (JAMESTEC)
and NASA Grant NNX07AG53G through their sponsorship of the International Pacific Research Center(IPRC). D. Waliser was supported by the Jet Propulsion Laboratory under a contract with the National
Aeronautics and Space Administration. We thank the
U.S. CLIVAR MJO Working Group for providing thesoftware package. We also thank Diane Henderson
and three reviewers for their comments.
REFERENCES
Annamalai, H., and J. M. Slingo, 2001: Active/break cycles: Diagnosis of the intraseasonal variability of the Asian summer
monsoon. Climate Dyn., 18, 85–102.
Arakawa, O., and W. H. Schubert, 1974: Interaction of cumulus
cloud ensemble with the large-scale environment. Part I. J.
Atmos. Sci., 31, 674–701.
Emanuel, K. A., 1991: A scheme for representing cumulus convection in large-scale models. J. Atmos. Sci., 48, 2313–2335.
Gates, W. L., 1992: AMIP: The Atmospheric Model Intercomparison Project. Bull. Amer. Meteor. Soc., 73, 1962–1970.
Gualdi, S., A. Navarra, and H. von Storch, 1997: Tropical intraseasonal oscillation appearing in operational analyses and ina family of general circulation models. J. Atmos. Sci., 54,
1185–1202.
Gustafson, W. I., Jr., and B. C. Weare, 2004: MM5 modeling of the
Madden–Julian oscillation in the Indian and west Pacific
Oceans: Model description and control run results. J. Climate,17, 1320–1337.
Haertel, P. T., G. N. Kiladis, A. Denno, and T. M. Rickenbach,2008: Vertical-mode decompositions of 2-day waves and theMadden–Julian oscillation. J. Atmos. Sci., 65, 813–833.

Hayashi, Y.-Y., and D. G. Golder, 1986: Tropical intraseasonal
oscillation appearing in a GFDL general circulation modeland FGGE data. Part I: Phase propagation. J. Atmos. Sci., 43,
3058–3067.
Hendon, H. H., and M. L. Salby, 1994: The life cycle of the
Madden–Julian oscillation. J. Atmos. Sci., 51, 2225–2237.
Inness, P. M., J. M. Slingo, S. J. Woolnough, R. B. Neale, and V. D.
Pope, 2001: Organization of tropical convection in a
GCM with varying vertical resolution: Implication for thesimulation of the Madden-Julian oscillation. Climate Dyn., 17,
777–793.
——, ——, E. Guilyardi, and J. Cole, 2003: Simulation of the MJO
in a coupled GCM. Part II: The role of the basic state.
J. Climate, 16, 365–382.
Jiang, X., T. Li, and B. Wang, 2004: Structures and mechanisms ofthe northward propagating boreal summer intraseasonal oscillation. J. Climate, 17, 1022–1039.
Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year
Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437–471.
Kiehl, J. T., J. J. Hack, G. B. Bonan, B. A. Boville, D. L.
Williamson, and P. J. Rasch, 1998: The National Center for
Atmospheric Research Community Climate Model: CCM3.
J. Climate, 11, 1131–1149.
Kiladis, G. N., K. H. Straub, and P. T. Haertel, 2005: Zonal andvertical 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., and P. H. Chan, 1985: Aspects of the 40–50 day oscillation during the northern winter as inferred from outgoing
longwave radiation. Mon. Wea. Rev., 113, 1889–1909.
Lau, N.-C., and K.-M. Lau, 1986: The structure and propagation of
intraseasonal oscillations appearing in a GFDL general circulation model. J. Atmos. Sci., 43, 2023–2047.
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.
Liess, S., and L. Bengtsson, 2004: The intraseasonal oscillation in
ECHAM4. Part II: Sensitivity studies. Climate Dyn., 22, 671–688.
Lin, J.-L., B. Mapes, M. Zhang, and M. Newman, 2004: Stratiform
precipitation, vertical heating profiles, and the Madden–
Julian oscillation. J. Atmos. Sci., 61, 296–309.
——, and Coauthors, 2006: Tropical intraseasonal variability in 14
IPCC AR4 climate models. Part I: Convective signals. J.
Climate, 19, 2665–2690.
Liu, P., B. Wang, K. R. Sperber, T. Li, and G. A. Meehl, 2005: MJO
in the NCAR CAM2 with the Tiedtke convective scheme. J.
Climate, 18, 3007–3020.

2022

JOURNAL OF CLIMATE

Madden, R. A., and P. R. Julian, 1971: Detection of a 40–50 day
oscillation in 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.
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.
——, and ——, 2001: The sensitivity of intraseasonal variability in
the NCAR CCM3 to changes in convective parameterization.
J. Climate, 14, 2015–2034.
Martin, G. M., 1999: The simulation of the Asian summer monsoon, and its sensitivity to horizontal resolution, in the UK
Meteorological Office Unified Model. Quart. J. Roy. Meteor.
Soc., 125, 1499–1525.
Miura, H., M. Satoh, T. Nasuno, A. T. Noda, and K. Oouchi, 2007:
A Madden-Julian oscillation event realistically simulated by aglobal cloud-resolving model. Science, 318, 1763–1765.
Mizuta, R., and Coauthors, 2006: 20-km-mesh global climate
simulations using JMA-GSM model–—Mean climate states.
J. Meteor. Soc. Japan, 84, 165–185.
Moorthi, S., and M. J. Suarez, 1992: Relaxed Arakawa-Schubert: A
parameterization of moist convection for general circulation
models. Mon. Wea. Rev., 120, 978–1002.
Nakagawa, M., and A. Shimpo, 2004: Development of a cumulus
parameterization scheme for the operational global model at
JMA. RSMC Tokyo-Typhoon Center Technical Review, No.
7, Japanese Meteorological Agency, 10–15.
North, G. R., T. L. Bell, R. F. Cahalan, and F. J. Moeng, 1982:
Sampling errors in the estimation of empirical orthogonal
functions. Mon. Wea. Rev., 110, 699–706.
Pan, D.-M., and D. Randall, 1998: A cumulus parameterization
with a prognostic closure. Quart. J. Roy. Meteor. Soc., 124,
949–981.
Park, C. K., D. M. Straus, and K. M. Lau, 1990: An evaluation of
the structure of tropical intraseasonal oscillation in 3 generalcirculation models. J. Meteor. Soc. Japan, 68, 403–417.
Peng, M. S., J. A. Ridout, and T. F. Hogan, 2004: Recent modifications of the Emanuel convective scheme in the Navy Operational Global Atmospheric Prediction System. Mon. Wea.
Rev., 132, 1254–1268.
Rajendran, K., A. Kitoh, R. Mizuta, S. Sajani, and T. Nakazawa,
2008: High-resolution simulation of mean convection and its
intraseasonal variability over the tropics in MRI/JMA 20-km
mesh AGCM. J. Climate, 21, 3722–3739.
Rui, H., and B. Wang, 1990: Development characteristics anddynamic structure of tropical intraseasonal convection
anomalies. J. Atmos. Sci., 47, 357–379.
Slingo, J. M., and Coauthors, 1996: Intraseasonal oscillations in 15
atmospheric general circulation models: Results from an
AMIP diagnostic subproject. Climate Dyn., 12, 325–357.
Smith, R. N. B., 1990: A scheme for predicting layer clouds andtheir water content in a general circulation model. Quart. J.
Roy. Meteor. Soc., 116, 435–460.

VOLUME 22

Sommeria, G., and J. W. Deardorff, 1977: Subgrid-scale condensation in models of nonprecipitating clouds. J. Atmos. Sci., 34,
344–355.
Sperber, K. R., 2003: Propagation and the vertical structure of the
Madden–Julian oscillation. Mon. Wea. Rev., 131, 3018–3037.
——, and H. Annamalai, 2008: Coupled model simulations ofboreal summer intraseasonal (30–50 day) variability, Part 1:
Systematic errors and caution on use of metrics. Climate Dyn.,
31, 345–372, doi:10.1007/s00382-008-0367-9.
Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus
parameterization in large-scale models. Mon. Wea. Rev., 117,
1779–1800.
Waliser, D. E., and Coauthors, 2003: AGCM simulations of intraseasonal variability associated with the Asian summer
monsoon. Climate Dyn., 21, 423–446.
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, W. K. M. Lau and D. E. Waliser, Eds.,
Praxis, 307–360.
——, and H. Rui, 1990: Synoptic climatology of transient tropicalintraseasonal convection anomalies: 1975-1985. Meteor. Atmos. Phys., 44, 43–61.
——, and X. Xie, 1997: A model for the boreal summer intraseasonal oscillation. J. Atmos. Sci., 54, 72–86.
Wang, W. Q., and M. E. Schlesinger, 1999: The dependence on
convective parameterization of the tropical intraseasonal oscillation simulated by the UIUC 11-layer atmospheric GCM.
J. Climate, 12, 1423–1457.
Wheeler, M. C., and H. H. Hendon, 2004: An all-season real-time
multivariate MJO index: Development of an index for monitoring and prediction. Mon. Wea. Rev., 132, 1917–1932.
Wu, M. L. C., S. Schubert, I.-S. Kang, and D. Waliser, 2002: Forced
and free intraseasonal variability over the South Asianmonsoon region simulated by 10 AGCMs. J. Climate, 15,2862–2880.
Yasunari, T., 1979: Cloudiness fluctuation associated with theNorthern Hemisphere summer monsoon. J. Meteor. Soc. Japan, 57, 227–242.
Yoshimura, H., and T. Matsumura, 2003: A semi-Lagrangian advection scheme conservative in the vertical direction. Extended Abstracts, Fifth Int. Workshop on Next Generation
Climate Models for Advanced High Performance Computing
Facilities,Rome, Italy, RIST Tokyo, 3.19–3.20. [Available
online at http://www.tokyo.rist.or.jp/rist/workshop/rome/
abstract/yoshimura.pdf.]
Zhang, C., 2005: Madden-Julian oscillation. Rev. Geophys., 43,
RG2003, doi:10.1029/2004RG000158.
Zhang, G. J., and M. Mu, 2005: Simulation of the Madden–Julian
oscillation in the NCAR CCM3 using a revised Zhang–
McFarlane convection parameterization scheme. J. Climate,18, 4046–4064.
Ziemiański, M. Z., W. W. Grabowski, and M. W. Moncrieff, 2004:
Explicit convection over the western Pacific warm pool in theCommunity Atmospheric Model. J. Climate, 18, 1482–1502.