Tropical Intraseasonal Variability in 14 IPCC AR4 Climate Models. Part I:Convective Signals
JIA-LIN LIN,a GEORGE N. KILADIS,b BRIAN E. MAPES,c KLAUS M. WEICKMANN,a KENNETH R. SPERBER,d
WUYIN LIN,e MATTHEW C. WHEELER,f SIEGFRIED D. SCHUBERT,g ANTHONY DEL GENIO,h
LEO J. DONNER,i SEITA EMORI,j JEAN-FRANCOIS GUEREMY,k FREDERIC HOURDIN,l PHILIP J. RASCH,m
ERICH ROECKNER,n AND JOHN F. SCINOCCAo
a NOAA–CIRES Climate Diagnostics Center, Boulder, Coloradob NOAA/Aeronomy Laboratory, Boulder, Colorado
c Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Floridad Program for Climate Model Diagnosis and Intercomparison (PCMDI), Lawrence Livermore National Laboratory,
Livermore, Californiae State University of New York—Stony Brook, Stony Brook, New York
f Bureau of Meteorlogy Research Centre, Melbourne, Australiag Global Modeling and Assimilation Office, NASA GSFC, Greenbelt, Maryland
h NASA Goddard Institute for Space Studies, New York, New Yorki NOAA/Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey
j National Institute for Environmental Studies, Ibaraki, Japank Météo-France, CNRM, Toulouse, France
l Laboratoire de Météorologie Dynamique, Université de Paris, Paris, Francem National Center for Atmospheric Research, Boulder, Colorado
n Max Planck Institute for Meteorology, Hamburg, Germanyo Canadian Centre for Climate Modelling and Analysis, Victoria, Canada
(Manuscript received 18 May 2005, in final form 20 October 2005)
ABSTRACT
This study evaluates the tropical intraseasonal variability, especially the fidelity of Madden–Julian oscillation (MJO) simulations, in14 coupled general circulation models (GCMs) participating in the Intergovernmental Panel on Climate Change (IPCC) FourthAssessment Report (AR4). Eight years of daily precipitation from each model’s twentieth-century climate simulation are analyzed andcompared with daily satellite-retrieved precipitation. Space–time spectral analysis is used to obtain the variance and phase speed ofdominant convectively coupled equatorial waves, including the MJO, Kelvin, equatorial Rossby (ER), mixed Rossby–gravity (MRG),and eastward inertio–gravity (EIG) and westward inertio–gravity (WIG) waves. The variance and propagation of the MJO, defined asthe eastward wavenumbers 1–6, 30–70-day mode, are examined in detail.
The results show that current state-of-the-art GCMs still have significant problems and display a wide range of skill in simulating thetropical intraseasonal variability. The total intraseasonal (2–128 day) variance of precipitation is too weak in most of the models. Abouthalf of the models have signals of convectively coupled equatorial waves, with Kelvin and MRG–EIG waves especially prominent.However, the variances are generally too weak for all wave modes except the EIG wave, and the phase speeds are generally too fast,being scaled to excessively deep equivalent depths. An interesting result is that this scaling is consistent within a given model acrossmodes, in that both the symmetric and antisymmetric modes scale similarly to a certain equivalent depth. Excessively deep equivalentdepths suggest that these models may not have a large enough reduction in their “effective static stability” by diabatic heating.
The MJO variance approaches the observed value in only 2 of the 14 models, but is less than half of the observed value in the other12 models. The ratio between the eastward MJO variance and the variance of its westward counterpart is too small in most of themodels, which is consistent with the lack of highly coherent eastward propagation of the MJO in many models. Moreover, the MJOvariance in 13 of the 14 models does not come from a pronounced spectral peak, but usually comes from part of an overreddenedspectrum, which in turn is associated with too strong persistence of equatorial precipitation. The two models that arguably do best atsimulating the MJO are the only ones having convective closures/triggers linked in some way to moisture convergence.
Corresponding author address: Dr. Jia-Lin Lin, NOAA–CIRES Climate Diagnostics Center, 325 Broadway, R/CDC1, Boulder, CO80305-3328.E-mail: [email protected]
More than one-third of the earth’s precipitation fallsin the equatorial belt between 15° north and 15° south,and the released latent heat plays an important role indriving tropical circulations and in supplying energy tobalance the radiative heat losses and “fuel” the windsystems of middle and high latitudes (e.g., Simpson etal. 1988). It is well known that precipitation in the equa-torial belt does not occur randomly, but is often orga-nized by convectively coupled large-scale equatorialwaves, such as the Madden–Julian oscillation (MJO;Madden and Julian 1971), Kelvin, equatorial Rossby(ER), mixed Rossby–gravity (MRG), and eastward in-ertio–gravit (EIG) and westward inertio–gravity (WIG)waves (e.g., Takayabu 1994; Wheeler and Kiladis 1999,hereafter WK).
The MJO is the dominant tropical intraseasonalmode and a key source of untapped predictability inboth the Tropics and extratropics (e.g., WK; Wheelerand Weickmann 2001; Schubert et al. 2002; Waliser etal. 2003a; Waliser 2005; see schematic in Fig. 1). TheMJO is characterized by a convectively “forced” andhighly viscous Kelvin–Rossby wave moving eastwardfrom the western Indian Ocean to the date line with aslow phase speed of about 5 m s�1 (e.g., Knutson andWeickmann 1987; Wang and Rui 1990; Salby and Hen-don 1994; Lin et al. 2005). The MJO often excites in theeastern Pacific a fast dry Kelvin mode with a phasespeed of about 50 m s�1 (e.g., Madden and Julian 1972;Weickmann et al. 1997), and in northern summer thereis often a local amplification of the MJO over the east-ern Pacific ITCZ near Central America (Knutson andWeickmann 1987; Maloney and Hartmann 2000). TheMJO significantly affects a wide range of tropicalweather such as the onset and breaks of the Indian andAustralian summer monsoons (e.g., Yasunari 1979;Wheeler and McBride 2005), and the formation oftropical cyclones in almost all basins (e.g., Liebmann etal. 1994; Maloney and Hartmann 2001a). Being a strongtropical heating source, the MJO also drives telecon-nections to the extratropics (e.g., Weickmann et al.1985; Berbery and Nogues-Paegle 1993) and impactsprecipitation events in both the western United States(e.g., Mo and Higgins 1998; Higgins et al. 2000) andSouth America (e.g., Paegle et al. 2000; Jones andSchemm 2000). It also appears to affect both the ArcticOscillation and Antarctic Oscillation (e.g., Miller et al.2003; Carvalho et al. 2005). On a longer time scale, theMJO has been implicated in the triggering or termina-tion of some El Niño events (e.g., Kessler et al. 1995;Takayabu et al. 1999; Bergman et al. 2001). Therefore,
the MJO is important for both weather prediction andclimate prediction.
Unfortunately, poor simulation of the MJO is a fairlygeneric problem in GCMs. Typically, model MJOs aretoo weak and propagate too fast (e.g., Hayashi andSumi 1986; Hayashi and Golder 1986, 1988; Lau et al.1988; Slingo et al. 1996). The Atmospheric Model In-tercomparison Project (AMIP) study by Slingo et al.(1996) found that no model has captured the domi-nance of the MJO in space–time spectral analysis foundin observations, and nearly all have relatively morepower at higher frequencies (�30 days) than in obser-vations. Recently, several models have gotten strongerMJO variance and/or more coherent eastward propa-gation (e.g., Lee et al. 2001, 2003; Maloney and Hart-mann 2001b; Waliser et al. 2003b; Sperber et al. 2005;C. Zhang et al. 2005, manuscript submitted to ClimateDyn.; Zhang and Mu 2005). However, as pointed byWaliser et al. (2003b), when a model does exhibit arelatively good MJO, one can at best only give vague orplausible explanations for its relative success. This in-hibits the extension of current model success to futureversions.
Factors hypothesized to be important for MJO simu-lations include model physics, model resolution, andair–sea coupling. Previous modeling studies showedthat MJO simulations are quite sensitive to changes inmodel physics, especially the deep convection scheme.Slingo et al. (1996) found that schemes with convectiveavailable potential energy (CAPE) type closure tend toproduce more realistic MJO signals. Improvements ofMJO simulations were also found by adding moisturetriggers to the deep convection schemes (e.g., Tokiokaet al. 1988; Wang and Schlesinger 1999; Lee et al. 2003),or by including convective downdrafts and convectiverain evaporation (Maloney and Hartmann 2001b).Other aspects of model physics may also be importantfor the MJO simulation, such as the vertical heatingprofile (Park et al. 1990; Lin et al. 2004) and cloudradiative heating (Lee et al. 2001; Lin and Mapes 2004).
In addition to model physics, MJO simulation wasfound to be improved when using higher horizontalresolution (e.g., Kuma 1994) and/or vertical resolution(Inness et al. 2001). Coupling to the ocean has beenfound by many studies to improve the MJO signals(e.g., Flatau et al. 1997; Waliser et al. 1999; Sperber etal. 2005), although changes in a model’s mean stateneed to be taken into account (e.g., Hendon 2000; In-ness and Slingo 2003; Sperber et al. 2005). The meanstate strongly affects wave-heating � feedback in theMJO, for example, by providing the mean surface windthat determines the sign of the wind induced surface
2666 J O U R N A L O F C L I M A T E VOLUME 19
heat exchange (WISHE) feedback (Emanuel 1987;Neelin et al. 1987), or by providing strong equivalentlinear mechanical damping making the MJO a highlyviscous oscillation (Lin et al. 2005).
Recently, in preparation for the IntergovernmentalPanel on Climate Change (IPCC) Fourth AssessmentReport (AR4), more than a dozen international climatemodeling centers conducted a comprehensive set oflong-term simulations for both the twentieth century’sclimate and different climate change scenarios in thetwenty-first century. Before conducting the extendedsimulations, many of the modeling centers applied anoverhaul to their physical schemes to incorporate state-of-the-art research results. For example, almost allmodeling centers have implemented prognostic cloudmicrophysics schemes to their models, some haveadded a moisture trigger to their deep convectionschemes, and some now take into account convectivemomentum transport. Moreover, many modeling cen-ters increased their models’ horizontal and verticalresolutions and some conducted experiments with dif-ferent resolutions. Some also did AMIP runs in addi-tion to the standard coupled runs. Therefore, it is ofinterest to assess the MJO simulations in this new gen-eration of climate models to look at the effects of theupdated physical processes, higher resolution, and air–sea coupling. Such an evaluation is also important forevaluating the general performance of the climate mod-els used for climate change projections in the IPCC AR4.
In addition to the MJO, other convectively coupledequatorial waves mentioned above also strongly affectthe tropical weather, for example, the occurrence ofwesterly wind burst events (e.g., Kiladis et al. 1994;Hartten 1996) and the formation of tropical cyclones(e.g., Dickinson and Molinari 2002; Goswami et al.2003; Bessafi and Wheeler 2006). Because changes in
tropical weather such as tropical cyclones are importantaspects of climate change, it is relevant to check wheth-er these convectively coupled equatorial waves are wellsimulated by the IPCC AR4 climate models along withthe MJO.
The purpose of this study is to evaluate the tropicalintraseasonal variability of convection in 14 IPCC AR4climate models, with an emphasis on their MJO simu-lations. The following questions are addressed below.
1) How well do the IPCC AR4 models simulate theprecipitation signals associated with convectivelycoupled equatorial waves, especially the MJO?
2) Is there any systematic dependence of model MJOsimulations on the basic characteristics of convec-tion schemes, such as closure assumption or modelresolution?
3) Is there any common bias that is important for thesimulation of the MJO?
The models and validation datasets used in this studyare described in section 2. The diagnostic methods aredescribed in section 3. Results are presented in section4. A summary and discussion are given in section 5.
2. Models and validation datasets
This analysis is based on 8 yr of the climate of thetwentieth century (20C3M) simulations from 14 coupledGCMs. Table 1 shows the model names and acronyms,their horizontal and vertical resolutions, and brief de-scriptions of their deep convection schemes. For eachmodel we use 8 yr of daily mean surface precipitation.
The model simulations are validated using multipleobservational datasets. To bracket the uncertainties as-sociated with precipitation measurements/retrievals, es-pecially the well-known difference between infrared(IR) based retrievals and microwave-based retrievals(e.g., Yuter and Houze 2000), we use two different pre-cipitation datasets: first, 8 yr (1997–2004) of daily Geosta-tionary Operational Environmental Satellite (GOES)Precipitation Index (GPI; Janowiak and Arkin 1991)precipitation with a horizontal resolution of 2.5° lati-tude by 2.5° longitude, which is retrieved based on IRmeasurements from multiple geostationary satellites;and second, 8 yr (1997–2004) of daily Global Precipita-tion Climatology Project (GPCP) 1° daily (1DD) pre-cipitation (Huffman et al. 2001) with a horizontal reso-lution of 1° latitude by 1° longitude. These are IR-basedGPI retrievals scaled by the monthly means of micro-wave-based Special Sensor Microwave Imager (SSM/I)retrievals.
FIG. 1. Schematic depiction of the MJO and its teleconnections.
15 JUNE 2006 L I N E T A L . 2667
TA
BL
E1.
Lis
tof
mod
els
that
part
icip
ated
inth
isst
udy.
Mod
elin
ggr
oups
IPC
CID
(lab
elin
figu
res)
Gri
dty
pe/r
esol
utio
n/m
odel
top
Dee
pco
nvec
tion
sche
me/
mod
ific
atio
nD
ownd
raft
s:SC
/UC
/mes
o*C
losu
re/t
rigg
er
NO
AA
/GF
DL
GF
DL
-CM
2.0
(GF
DL
2.0)
Gri
dpo
int/
144
�90
�L
24/3
mb
Moo
rthi
and
Suar
ez(1
992)
,T
okio
kaet
al.(
1988
)N
/N/N
CA
PE
/thr
esho
ld
NO
AA
/GF
DL
GF
DL
-CM
2.1
(GF
DL
2.1)
Gri
dpo
int/
144
�90
�L
24/3
mb
Moo
rthi
and
Suar
ez(1
992)
,T
okio
kaet
al.(
1988
)N
/N/N
CA
PE
/thr
esho
ld
Nat
iona
lC
ente
rfo
rA
tmos
pher
icR
esea
rch
(NC
AR
)C
CSM
3(C
CSM
3)Sp
ectr
al/T
85�
L26
/2.2
mb
Zha
ngan
dM
cFar
lane
(199
5)Y
/N/N
CA
PE
NC
AR
PC
M(P
CM
)Sp
ectr
al/T
42�
L26
/2.2
mb
Zha
ngan
dM
cFar
lane
(199
5)Y
/N/N
CA
PE
NA
SAG
odda
rdIn
stit
ute
for
Spac
eSt
udie
s(G
ISS)
GIS
S-A
OM
(GIS
S-A
OM
)G
rid
poin
t/90
�60
�L
12R
usse
llet
al.(
1995
)N
/N/N
CA
PE
NA
SAG
ISS
GIS
S-E
R(G
ISS-
ER
)G
rid
poin
t/72
�46
�L
20/0
.1m
bD
elG
enio
and
Yao
(199
3)Y
/N/N
Clo
ud-b
ase
buoy
ancy
Cen
ter
for
Clim
ate
Syst
emR
esea
rch,
Nat
iona
lIn
stit
ute
for
Env
iron
men
tal
Stud
ies
(CC
SR/N
IES)
,and
Fro
ntie
rR
esea
rch
Cen
ter
for
Glo
bal
Cha
nge
(FR
CG
C)
MIR
OC
3.2-
hire
s(M
IRO
C-h
ires
)Sp
ectr
al/T
106
�L
56P
anan
dR
anda
ll(1
998)
,E
mor
iet
al.(
2001
)Y
/N/N
CA
PE
/rel
ativ
ehu
mid
ity
CC
SR/N
IES/
FR
CG
CM
IRO
C3.
2-m
edre
s(M
IRO
C-m
edre
s)Sp
ectr
al/T
42�
L20
/30
kmP
anan
dR
anda
ll(1
998)
,E
mor
iet
al.(
2001
)Y
/N/N
CA
PE
/rel
ativ
ehu
mid
ity
Met
eoro
logi
cal
Res
earc
hIn
stit
ute
MR
I-C
GC
M2.
3.2
(MR
I)Sp
ectr
al/T
42�
L30
/0.4
mb
Pan
and
Ran
dall
(199
8)Y
/N/N
CA
PE
Can
adia
nC
ente
rfo
rC
limat
eM
odel
ing
and
Ana
lysi
sC
GC
M3.
1-T
47(C
GC
M)
Spec
tral
/T47
�L
32/1
mb
Zha
ngan
dM
cFar
lane
(199
5)Y
/N/N
CA
PE
Max
Pla
nck
Inst
itut
efo
rM
eteo
rolo
gyE
CH
AM
5/M
PI-
OM
(MP
I)Sp
ectr
al/T
63�
L31
/10
mb
Tie
dtke
(198
9),N
orde
ng(1
994)
Y/N
/NC
AP
E/m
oist
ure
conv
erge
nce
Inst
itut
Pie
rre
Sim
onL
apla
ceIP
SL-C
M4
(IP
SL)
Gri
dpo
int/
96�
72�
L19
Em
anue
l(1
991)
Y/Y
/NC
AP
EM
é téo
-Fra
nce/
Cen
tre
Nat
iona
lde
Rec
herc
hes
Mét
éoro
logi
ques
(CN
RM
)C
NR
M-C
M3
(CN
RM
)Sp
ectr
al/T
63�
L45
/0.0
5m
bB
ouge
ault
(198
5)N
/N/N
Kuo
CSI
RO
Atm
osph
eric
Res
earc
hC
SIR
OM
k3.0
(CSI
RO
)Sp
ectr
al/T
63�
L18
/4m
bG
rego
ryan
dR
ownt
ree
(199
0)Y
/N/N
Clo
ud-b
ase
buoy
ancy
*S C
�sa
tura
ted
conv
ecti
vedo
wnd
raft
s,U
C�
unsa
tura
ted
conv
ecti
vedo
wnd
raft
s,an
dm
eso
�m
esos
cale
dow
ndra
fts.
2668 J O U R N A L O F C L I M A T E VOLUME 19
3. Method
a. Identification of the dominant intraseasonalmodes
Through the space–time spectral analysis of outgoinglongwave radiation (OLR), Takayabu (1994) and WKdemonstrated that a significant portion of tropicalcloudiness is organized in waves corresponding to thenormal modes of the linear shallow water system iso-lated by Matsuno (1966). In WK, these spectra repre-sent the power remaining in the symmetric and anti-symmetric components of OLR about the equator afterdividing raw wavenumber-frequency power spectra byan estimate of the background power spectrum. Peaksstanding above the background correspond to theKelvin, n � 1 equatorial Rossby (ER), mixed Rossby–gravity (MRG), n � 0 eastward inertio–gravity (EIG),and n � 1 westward inertio–gravity (WIG) and n � 2WIG waves. It was found that the dispersion curves thatbest match the wavenumber-frequency characteristicsof these waves have surprisingly shallow equivalentdepths in the range of roughly 25 m, which is about anorder of magnitude smaller than that expected for afree wave with a similar vertical wavelength twice thedepth of the troposphere (e.g., Salby and Garcia 1987;Wheeler et al. 2000).
Using the methodology of WK, space–time spectra ofdaily tropical precipitation were obtained for the 8 yr ofmodel data used in this study and compared with theresults of 8 yr of observed precipitation estimates fromthe GPI and 1DD datasets. We will briefly outline thisprocedure here, and refer the reader to WK for furtherdetails.
The model and validation precipitation data werefirst interpolated to a zonal resolution of 5° longitudewith the latitudinal resolution varying from model tomodel (Table 1). As demonstrated by WK, the struc-ture of convectively coupled equatorial waves is eithersymmetric or antisymmetric about the equator, in ac-cordance with shallow water theory. A gridded field Dthat is a function of latitude, �, can be written as D(�) �DA(�) � DS(�), where DA(�) � [D(�) � D(��)]/2 isthe antisymmetric component, and DS(�) � [D(�) �D(��)]/2 is the symmetric component. We first decom-posed the precipitation into its antisymmetric and sym-metric components, averaged these from 15°N to 15°S,and computed spectra of the averaged values. Althoughthis last step is mathematically different from the pro-cedure used in WK, in which spectra of the symmetric/antisymmetric components were computed separatelyfor each latitude before being averaged together, forthe scales of interest here the results and interpretationare the same.
To reduce noise, the space–time spectra were calcu-lated as in WK for successive overlapping segments ofdata and then averaged, here 128 days long with 78 daysof overlap between each segment. Complex Fourier co-efficients are first obtained in zonal planetary wave-number space, which are then subjected to a furthercomplex FFT to obtain the wavenumber-frequencyspectrum for the symmetric and antisymmetric compo-nents of precipitation about the equator.
An estimate of the “background” space–time spec-trum is obtained for each dataset by averaging thepower of the symmetric and antisymmetric spectra andsmoothing this by successive passes of a 1–2–1 filter infrequency and wavenumber (see WK). The raw spectraare then divided by this background to obtain an esti-mate of the signal standing above the backgroundnoise. In WK, power at 1.1 times the background orgreater was deemed significant, based on a crude esti-mate of the degrees of freedom involved. In reality, atrue estimate of the degrees of freedom is difficult toobtain due to the complications of simultaneous auto-correlation in both space and time. Here, since thedatasets used are significantly shorter than those usedin WK (8 versus 18 yr), we assume the signal is signifi-cant if it stands at 1.2 times (or 20% above) the back-ground. It should be emphasized that, while this is onlya rough estimate of the true “significance” of the sig-nals, the intent is to simply identify those modes thatmight represent signals in rainfall standing above asimple red noise continuum that would presumably pre-vail if rainfall were not organized by disturbances onthe large scale.
b. Isolating the Kelvin, ER, MRG, EIG, and WIGmodes
In this paper, the definitions of Kelvin, ER, MRG,EIG, and WIG modes are as in WK (see their Fig. 6),and were isolated using the same method: each modewas isolated by filtering in the wavenumber-frequencydomain (see Fig. 6 of WK for the defined regions offiltering for each wave), and the corresponding timeseries were obtained by an inverse space–time Fouriertransform.
c. Isolating the MJO mode
The MJO is defined as significant rainfall variabilityin eastward wavenumbers 1–6 and in the period rangeof 30–70 days. To isolate the MJO mode, we first usedan inverse space–time Fourier transform to get the timeseries of the eastward wavenumber 1–6 component,which includes all available frequencies. Then these
15 JUNE 2006 L I N E T A L . 2669
time series were filtered using a 365-point 30–70-dayLanczos filter (Duchan 1979), whose response functionis shown in Fig. 2. Because the Lanczos filter is nonre-cursive, 182 days of data were lost at each end of thetime series (364 days in total). The resultant eastwardwavenumber 1–6, 30–70-day anomaly is hereafter re-ferred to as the MJO anomaly.
The variance of the MJO anomaly was also com-pared with the variance of its westward counterpart,that is, the westward wavenumber 1–6, 30–70-dayanomaly, which was isolated using the same method asabove.
It is important to note that we only focus on theMJO, which propagates eastward and amplifies to aseasonal maximum on the equator in boreal winter andspring, when climatological convection and warm SSTcross the equator (Salby and Hendon 1994; Zhang andDong 2004; Wheeler and Hendon 2004). Analysis of theboreal summer intraseasonal oscillation (BSIO; e.g.,Yasunari 1979; Knutson et al. 1986; Kemball-Cook andWang 2001; Lawrence and Webster 2002; Straub andKiladis 2003; Waliser et al. 2003c, among many others),which has a major northward propagating componentand has its maximum variance in the Asian monsoonregion, is beyond the scope of this study.
4. Results
a. Climatological precipitation in the equatorial belt
Previous observational studies indicate that the in-traseasonal variance of convection is highly correlatedwith time-mean convective intensity (e.g., WK; Hendonet al. 1999). Therefore, we first look at the 8-yr time-mean precipitation along the equatorial belt, especiallyover the Indo-Pacific warm pool region, where most ofthe convectively coupled equatorial waves have the
largest variance (WK). Figure 3a shows the annualmean precipitation versus longitude averaged between15°N and 15°S. To focus on the large-scale features, wesmoothed the data zonally to retain only zonal wave-numbers 0–6. All models reproduce the basic feature ofobserved precipitation, with the primary maximumover the Indo-Pacific warm pool region, and two sec-ondary maxima over Central/South America and Af-rica. The magnitude of the precipitation over the warmpool in all models is close to that in the observations.Within the warm pool region, several models (GFDL-CM2.0, GFDL-CM2.1, CCSM3, GISS-AOM, CNRM-CM3, MIROC3.2-medres) do not reproduce the localminimum of precipitation over the Maritime Continent,and there is a tendency for the models to produce moreprecipitation over the western Pacific than over theeastern Indian Ocean, which is a feature in 1DD databut not in GPI data. Outside the warm pool region, twonotable common biases are excessive rainfall over theeastern Pacific in most models and insufficient rainfallover Central/South America in many models.
FIG. 3. Annual mean precipitation along the equatorial beltaveraged between (a) 15°N–15°S and (b) 5°N–5°S for two obser-vational datasets and 14 models.
FIG. 2. Response function of the 365-point Lanczos filter usedin this study.
2670 J O U R N A L O F C L I M A T E VOLUME 19
Fig 3 live 4/C
When the precipitation is averaged over a narrowerbelt closer to the equator between 5°N and 5°S, modelsshow a larger scatter in their performance, especiallyover the western Pacific (Fig. 3b). Several models(CGCM3.1-T47, MIROC3.2-medres, MIROC3.2-hires,CCSM3, and GISS-ER) produce much greater precipi-tation than is found in the observations, and producemuch larger precipitation over the western Pacific thanover the eastern Indian Ocean, a feature that is notobserved. On the other hand, several other models(PCM, CNRM-CM3) show too weak precipitation overthe western Pacific, which is significantly smaller thantheir corresponding 15°N–15°S average (Fig. 3a). Thisis caused by the prominent double-ITCZ pattern intheir horizontal distributions (not shown). Outside thewarm pool region, most models (except GISS-AOM,GISS-ER, and MIROC3.2-hires) reproduce the pre-cipitation minimum over the eastern Pacific trade windcumulus region reasonably well, but there is a largescatter over Africa and the Atlantic Ocean.
In short, the climatological precipitation over theIndo-Pacific warm pool is reasonably simulated byIPCC AR4 climate models, except that several models(PCM, CNRM-CM3, and MRI-CGCM2.3.2) producetoo weak precipitation on the equator in the westernPacific due to their double-ITCZ problem.
b. Total intraseasonal (2–128 day) variance andraw space–time spectra
Figures 4a and 4b show the total variance of the2–128-day precipitation anomaly along the equator av-eraged between 15°N–15°S and 5°N–5°S, respectively.Despite their reasonable annual mean precipitationover the Indo-Pacific warm pool, the total intraseasonalvariance in most models is smaller than in the observa-tions. There is a tendency for the models to have largervariance over the western Pacific than over the IndianOcean, which is consistent with their tendency to havelarger annual mean precipitation over the western Pa-cific (Fig. 3), and agrees with the result of the atmo-spheric GCM analysis of Waliser et al. (2003d) thatmodels did a very poor job with the means and vari-ances over the Indian Ocean. The variance in severalmodels (e.g., ECHAM5/MPI-OM, MIROC3.2-medres,and CGCM3.1-T47) approaches the observed value onthe equator over the western Pacific (Fig. 4b).
The symmetric space–time spectra of the two obser-vational rainfall datasets, GPI and 1DD, are shown inFig. 5a, and Fig. 5b where, as in WK, the plotted con-tours are the logarithm of the power. These spectra arenearly identical to each other, and also very similar inshape to those obtained by WK, even though WK used
OLR instead of the blend of precipitation estimatescomposing the GPI and 1DD datasets. As in WK, thespectra are very red in time and space, with most powerat the largest spatial scales and lowest frequencies. De-spite this redness, distinct spectral peaks and gaps areevident even in these raw spectra. One obvious featureis the dominance of eastward over westward power atlow wavenumbers and frequencies, a signal correspond-ing to the MJO. Other peaks also correspond to knownequatorial wave modes, and will be discussed furtherbelow.
The remainder of Fig. 5 displays the correspondingspectra from the various models examined for thisstudy, using identical contour intervals and shading asin Figs. 5a and 5b (recall that these spectra are calcu-lated for identical daily and 5° horizontal resolutions).There are two important features in the model spectra.First, all models except the MIROC3.2-hires andMIROC3.2-medres models have much less power thanobserved at periods shorter than 6 days, while many ofthe models (e.g., CCSM3, PCM, GISS-AOM, GISS-ER, MRI-CGCM2.3.2, CGCM3.1-T47, IPSL-CM4, and
FIG. 4. Variance of the 2–128-day precipitation anomaly alongthe equator averaged between (a) 15°N–15°S and (b) 5°N–5°S.
15 JUNE 2006 L I N E T A L . 2671
Fig 4 live 4/C
FIG. 5. Space–time spectrum of 15°N–15°S symmetric component of precipitation. Frequency spectral width is1/128 cpd.
2672 J O U R N A L O F C L I M A T E VOLUME 19
Fig 5a-h live 4/C
FIG. 5. (Continued)
15 JUNE 2006 L I N E T A L . 2673
Fig 5i-p live 4/C
FIG. 6. Space–time spectrum of the 15°N–15°S symmetric component of precipitation divided by the backgroundspectrum. Superimposed are the dispersion curves of the odd meridional mode numbered equatorial waves for thefive equivalent depths of 8, 12, 25, 50, and 90 m. Frequency spectral width is 1/128 cpd.
2674 J O U R N A L O F C L I M A T E VOLUME 19
Fig 6a-h live 4/C
FIG. 6. (Continued)
15 JUNE 2006 L I N E T A L . 2675
Fig 6i-p live 4/C
FIG. 7. As in Fig. 6 except for the 15°N–15°S antisymmetric component of precipitation.
2676 J O U R N A L O F C L I M A T E VOLUME 19
Fig 7a-h live 4/C
FIG. 7. (Continued)
15 JUNE 2006 L I N E T A L . 2677
Fig 7i-p live 4/C
CSIRO Mk3.0) also have less power than observed atperiods longer than 6 days. These are consistent withthe too weak total intraseasonal (2–128 days) variancesin these models (Fig. 4). Second, in some model spectra(e.g., GISS-ER) westward over eastward power is toostrong at MJO time scales, while in others (e.g., CCSM,PCM1, and GISS-AOM) the power is more evenly dis-tributed. If the eastward signals and the westward sig-nals are coherent with each other, they would formmore standing oscillations rather than the predomi-nance of eastward propagations seen in the observa-tions. The characteristics of the raw antisymmetricspectra, in terms of total power and redness, are gen-erally similar to Fig. 6 and so will not be shown here.
In summary, the total intraseasonal (2–128 day) vari-ance of precipitation in most models is smaller than inthe observations. The space–time spectra of most mod-els have much less power than is observed, especially atperiods shorter than 6 days. In some model spectrawestward over eastward power is too strong at MJOtime scales, while in others the power is more evenlydistributed.
c. Dominant intraseasonal modes
Figures 6 and 7 show the results of dividing the sym-metric and antisymmetric raw spectra by the estimatesof their background spectra. This normalization proce-dure removes a large portion of the systematic biaseswithin the various models and observed datasets in Fig.5, more clearly displaying the model disturbances withrespect to their own climatological variance at eachscale.
Signals of the Kelvin, ER, and WIG waves arereadily identified in the observational symmetric spec-tra (Figs. 6a and 6b), along with the MRG and EIGwaves in the antisymmetric spectra (Figs. 7a and 7b).The MJO also appears as a prominent signal, especiallyin the symmetric spectra. Dispersion curves of the shal-low water modes are also shown on all spectra, corre-sponding to equivalent depths of 8, 12, 25, 50, and 90 m.As in the OLR spectra of WK, all of the observedspectral peaks corresponding to shallow water modesbest match an equivalent depth of around 25 m in theobservational rainfall data.
About half of the models appear to have signals ofconvectively coupled equatorial waves, with Kelvin andMRG–EIG waves especially prominent. This is an ex-tremely encouraging finding, because previous versionsof some of these same models showed very little in theway of signal corresponding to these modes (Wheeler1998). Since it is thought that the interplay betweenconvectively coupled waves is important to the low-
frequency variability of the tropical atmosphere (e.g.,Majda and Biello 2004, 2005; Moncrieff 2004; Kiladis etal. 2005), the existence of a wide variety of observedequatorial waves in these models opens the possibilitythat such scale interactions could be represented withcurrent parameterization schemes. However, it turnsout that the majority of the models with good signals(e.g., GISS-ER, MIROC3.2-hires, MRI-CGCM2.3.2,and IPSL-CM4) have too fast phase speeds and scalethese disturbances to equivalent depths of around 50 m,with some scaling closer to 90 m (e.g., GISS-AOM,CCSM). Only one model, the ECHAM5/MPI-OM, hassignals that scale closely to the observed 25 m for allmodes. Interestingly, this scaling is consistent within agiven model across modes; that is, all modes scale simi-larly to a certain equivalent depth within a given pair ofsymmetric and antisymmetric spectra. This is indicativeof similar physical processes linking the convection andlarge-scale disturbances within each model.
The spectral signature of the MJO is also representedin many of the models with varying realism. In obser-vations, there is a clear distinction between eastwardpower in the MJO range and westward power associ-ated with ER waves. Some of the models (GFDL-CM2.1, GISS-AOM, MRI-CGCM2.3.2, and ECHAM5/MPI-OM) represent this distinction to some extent,with the eastward power lying at a constant frequencyacross all wavenumbers and the westward power lyingmore along the ER dispersion curves, or at least at asomewhat higher frequency. In other models (PCM,GISS-ER, and CGCM3.1-T47) the westward power isconfined more to the lower frequencies with �30 dayperiods, which would represent a standing oscillation ifcoherent with the eastward portion of the signal. This isconfirmed by further analysis below in sections 4c and4e. Still other models have eastward but little westwardpower (CCSM, CNRM-CM3), while the MIROC3.2-medres and MIROC3.2-hires models have prominentKelvin and ER signals but little in the way of power inthe MJO range.
When a model displays signals of a certain wavemode in Figs. 6 and 7, it means that the variance of thatwave mode stands out above the background spectra(i.e., a high signal-to-noise ratio), but the absolute valueof the variance of that wave mode may not be large.Therefore, it is of interest to look further at the abso-lute values of the variance of each wave mode. Figures8a–e, respectively, show the variances of the Kelvin,ER, MRG, EIG, and WIG modes along the equatoraveraged between 15°N and 15°S. For the Kelvin mode(Fig. 8a), all models show too weak variance except thatMIROC3.2-medres and MIROC3.2-hires show strong
2678 J O U R N A L O F C L I M A T E VOLUME 19
variance over the Maritime Continent, but they do notcapture the observed longitudinal distribution. For theER mode (Fig. 8b), all models produce too weak vari-ance except ECHAM5/MPI-OM, which faithfully re-produces the observed magnitude and longitudinal dis-tribution of the variance. For the MRG mode (Fig. 8c),which is important for tropical cyclone genesis, all mod-els simulate too weak variance except that MIROC3.2-medres simulates strong variance over the MaritimeContinent. For the EIG mode (Fig. 8d), unlike othermodes, many models (ECHAM5/MPI-OM, GFDL-CM2.0, GFDL-CM2.1, CGCM3.1-T47, and MRI-CGCM2.3.2) produce realistic or too strong variance.In particular, GFDL-CM2.1 reproduces quite well the
observed magnitude and longitudinal distribution. Forthe WIG mode (Fig. 8e), all models simulate too weakvariance except MIROC3.2-medres, which has toomuch variance over the Maritime Continent.
Overall, there are three important conclusions thatcan be drawn from Fig. 8. First, most models producetoo weak variances for Kelvin, ER, MRG, EIG, andWIG waves, suggesting that the models do not haveenough wave-heating feedback in those waves, which isconsistent with the too fast phase speeds of those wavesin the models. Second, there are one or two models thatproduce strikingly realistic variances for some of thewaves, for example, the ER wave in ECHAM5/MPI-OM and the EIG wave in GFDL-CM2.1. Whether this
FIG. 8. Variances of (a) Kelvin, (b) ER, (c) MRG, (d) EIG, and(e) WIG modes along the equator averaged between 15°N and15°S.
15 JUNE 2006 L I N E T A L . 2679
Fig 8a-e live 4/C
is caused by some fundamental processes in these mod-els or merely by accident needs further study. Third,many models produce very strong EIG variance, whichis in sharp contrast with their inability in simulatingother modes. This is very interesting and warrants fur-ther work.
In summary, about half of the models have signals ofconvectively coupled equatorial waves, with Kelvin andMRG-EIG waves especially prominent. However, thevariance is generally too weak for all wave modes ex-cept the EIG wave. Furthermore, the majority of themodels with wave signals show phase speeds that aretoo fast, and scale these disturbances to equivalentdepths that are larger than the observed value. Inter-estingly, this scaling is consistent within a given modelacross modes, in that both the symmetric and antisym-metric modes scale similarly to a particular equivalentdepth, which is indicative of similar physical processeslinking the convection and large-scale disturbanceswithin each model.
d. Variance of the MJO mode
Now we focus on the variance of the MJO mode, thatis, the daily variance in the MJO window of eastwardwavenumbers 1–6 and periods of 30–70 days. Figure 9ashows the variance of the MJO anomaly along theequator averaged between 15°N and 15°S. The MJOvariance approaches the observed value in 2 of the 14models, ECHAM5/MPI-OM and CNRM-CM3 (IndianOcean only), but is less than half of the observed valuein the other 12 models. The finding that two modelsproduce nearly realistic MJO precipitation variance isvery encouraging since too weak precipitation variancein the MJO wavenumber-frequency band has been along-standing problem in GCMs, in spite of the fact thatmany of these models have reasonable values of zonalwind variance. From the viewpoint of weather and cli-mate prediction, a realistic MJO precipitation signal ismore desirable because it is the latent heat released byprecipitation that drives teleconnections to the subtrop-ics and extratropics and leads to useful predictability.
The 15°N–15°S belt analyzed above is a wide belt. Asshown by Wang and Rui (1990), eastward-propagatingMJO precipitation events occur most often on theequator, with the frequency of occurrence decreasingaway from the equator. Therefore, it is of interest to seeif the models capture this equatorial maximum of MJOvariance. Figure 9b is same as Fig. 9a except for pre-cipitation averaged between 5°N and 5°S. For both ofthe two observational datasets, the variance of the 5°N–5°S average is about twice as large as that of the 15°N–15°S average. Most of the models, such as ECHAM5/MPI-OM, CNRM-CM3 (Indian Ocean only), GFDL-
CM2.0, GFDL-CM2.1, IPSL-CM4, CSIRO Mk3.0, andCGCM3.1-T47 (western Pacific only), capture this fea-ture quite well, although the models with a double-ITCZ pattern (e.g., CNRM-CM3) cannot reproducethis in the western Pacific. As in Fig. 9a, ECHAM5/MPI-OM and CNRM-CM3 (Indian Ocean only) arethe most realistic with GFDL-CM2.0, GFDL-CM2.1,IPSL-CM4, CSIRO Mk3.0, and CGCM3.1-T47 (west-ern Pacific only) showing improved MJO variance com-pared to the 15°N–15°S data.
In addition to the variance of the eastward MJO,another important index for evaluating the MJO simu-lation is the ratio between the variance of the eastwardMJO and that of its westward counterpart, that is, thewestward wavenumber 1–6, 30–70-day mode, which isimportant for the zonal propagation of tropical in-traseasonal oscillation. Figure 10 shows the ratio be-tween the eastward variance and the westward varianceaveraged over an Indian Ocean box between 5°N–5°Sand 70°–100°E (panel a), and a western Pacific boxbetween 5°N–5°S and 140°–170°E (panel b). Over theIndian Ocean (Fig. 10a), the eastward MJO varianceroughly triples the westward variance in observations.
FIG. 9. Variance of the MJO mode along the equator averagedbetween (a) 15°N–15°S and (b) 5°N–5°S.
2680 J O U R N A L O F C L I M A T E VOLUME 19
Fig 9 live 4/C
Of the 14 models, 2 models (CNRM-CM3 and CSIROMk3.0) simulate a realistic or too large ratio, while theother 12 models produce a too small ratio, althoughthe ratio is significantly larger than 1 (i.e., eastwardvariance dominates over westward variance) in 7 ofthe models (GFDL-CM2.0, GFDL-CM2.1, CCSM3,MIROC3.2-medres, MIROC3.2-hires, MRI-CGCM3.0,and ECHAM5/MPI-OM). Over the western Pacific(Fig. 10b), again, the eastward MJO variance nearlytriples its westward counterpart in observations. How-ever, only one model (MIROC3.2-medres) produces arealistic ratio, while all the other models produce a toosmall ratio.
The competition between the eastward MJO vari-ance and its westward counterpart largely determinesthe zonal propagation characteristics of the tropical in-traseasonal oscillation. A useful method for evaluatingthe MJO simulation is to look at the propagation of the30–70-day filtered anomaly of the raw precipitationdata, which includes all wavenumbers (zonal mean,eastward wavenumbers 1–6, westward wavenumbers
1–6, eastward wavenumbers 7 and up, westward wave-numbers 7 and up), to see if the MJO mode (the east-ward wavenumbers 1–6 mode) dominates over othermodes, as is the case in the observations (e.g., Weick-mann et al. 1985, 1997; Kiladis and Weickmann 1992;Lin and Mapes 2004). Because the tropical intrasea-sonal oscillation is dominated by zonally asymmetric,planetary-scale phenomena, the competition is mainlybetween the MJO and its westward counterpart—thewestward wavenumber 1–6 component. Figure 11shows the lag correlation of the 30–70-day precipitationanomaly averaged between 5°N and 5°S with respect toitself at 0°, 85°E. Both observational datasets showprominent eastward-propagating signals of the MJO,with a phase speed of about 7 m s�1. The models dis-play a wide range of propagation characteristics thatare consistent with the ratio between the eastward MJOvariance and its westward counterpart shown in Fig.10a. The two models with a realistic or too large ratio(CNRM-CM3 and CSIRO Mk3.0) show a highly coher-ent eastward-propagating signal. The phase speed is re-alistic in CSIRO Mk3.0, but is a little too slow inCNRM-CM3. The models with the eastward/westwardratio being smaller than in observations but still suffi-ciently larger than one (GFDL-CM2.0, GFDL-CM2.1,CCSM3, MIROC3.2-medres, MIROC3.2-hires, MRI-CGCM3.0, and ECHAM5/MPI-OM) show only dis-cernable eastward-propagating signals. Other modelswith the ratio being nearly equal to or smaller than one(PCM, GISS-AOM, GISS-ER, MRI-CGCM2.3.2, andCGCM3.1-T47) show standing oscillations or west-ward-propagating signals. The results are similar whenusing a western Pacific reference point (not shown).
Next we apply more detailed scrutiny to the MJOprecipitation variance by looking at the shape of thepower spectrum. Figure 12a shows the raw spectra ofthe eastward wavenumber 1–6 component at 0°, 85°E.Because it is difficult to see the shape of spectra forseveral models with too small variance, we also plottedtheir normalized spectra (raw spectrum divided by itstotal variance) in Fig. 12b. Both of the observationaldatasets show prominent spectral peaks between 30-and 70-days periods, with the power of 1DD lower thanthat of GPI. Most of the models with relatively largeMJO variance (ECHAM5/MPI-OM, GFDL-CM2.0,and GFDL-CM2.1) do not show a pronounced spectralpeak in the MJO frequency band, but show too red ofa spectrum; that is, the variance of the MJO band doesnot stand above but is simply embedded within a rednoise continuum. Most models with weak MJO vari-ance (e.g., CCSM3, PCM) also lack a spectral peak inthe MJO band, and show a too red spectrum. The onlymodel showing a prominent spectral peak in the MJO
FIG. 10. Ratio between the MJO variance and the variance of itswestward counterpart (westward wavenumber 1–6, 30–70-daymode). The variances are averaged over (a) an Indian Ocean boxbetween 5°N–5°S and 70°–100°E and (b) a western Pacific boxbetween 5°N–5°S and 140°–170°E.
15 JUNE 2006 L I N E T A L . 2681
Fig 10 live 4/C
FIG. 11. Lag correlation of the 30–70-day precipitation anomaly averaged along the equator between 5°N and 5°Swith respect to itself at 0°, 85°E. The three thick lines correspond to phase speed of 3, 7, and 15 m s�1, respectively.
2682 J O U R N A L O F C L I M A T E VOLUME 19
FIG. 11. (Continued)
15 JUNE 2006 L I N E T A L . 2683
band is CNRM-CM3, whose power is similar to that of1DD. Results for 0°, 155°E (western Pacific) are similar(not shown).
For the AMIP models, Slingo et al. (1996) found thatdeep convection schemes with CAPE-type closure tendto produce more realistic MJO signals than schemeswith moisture-convergence-type closure, but we find areverse dependence in the IPCC AR4 models. The twomodels that arguably do best at simulating the MJO,CNRM-CM3 and ECHAM5/MPI-OM, are the onlyones having convective closures/triggers linked in someway to moisture convergence. One possible reason isthat the moisture–convergence-type closures/triggerstie the convection more closely with large-scale wavecirculation and thus enhance the wave-heating feed-back in the MJO.
There does not appear to be a systematic dependenceof MJO variance on a model’s horizontal resolution.For example, the high-resolution version of theMIROC model produces weaker MJO variance thanthe medium-resolution version, similar to the result ofSlingo et al. (1996). Alternatively, IPSL-CM4, which
has relatively low resolution among all of the models,does produce above-average MJO variance. Therefore,it seems that a model’s horizontal resolution is less im-portant for simulating the MJO than other factors suchas model physics or air–sea coupling, which is consis-tent with the results of Duffy et al. (2003).
To summarize, the MJO variance approaches the ob-served value in 2 of the 14 models, but is less than halfof the observed value in the other 12 models. The ratiobetween the eastward MJO variance and the varianceof its westward counterpart is too small in most of themodels, which is consistent with the lack of highly co-herent eastward propagation of the MJO in many mod-els. Moreover, the MJO variance in 13 of the 14 modelsdoes not come from a pronounced spectral peak, butusually comes from part of an overreddened spectrum.We did not find a systematic dependence of MJO vari-ance on a model’s horizontal resolution. The two mod-els that arguably do best at simulating the MJO(CNRM-CM3 and ECHAM5/MPI-OM) are the onlyones having convective closures/triggers linked in someway to moisture convergence.
e. Autocorrelation of precipitation
The redness of many model spectra shown in Fig. 12brings to mind a “red noise” spectrum of a first-orderlinear Markov process (Gilman 1963; Jenkins andWatts 1968). Following Gilman (1963), the first-orderMarkov process may be expressed as
Xn � �Xn�1 � yn, �1
where [yn ], the expected value of yn, is zero and [yn2]
� 2. As derived by Gilman (1963), the autocorrelationfunction is
�Xn Xn�k� � �X2n� � �k �2
and the raw estimate of spectral density is
PSD � �1 � �� 1 � 2� cos�h��M � �2� �3
in which M is maximum lag and h is frequency. Asshown by Eq. (2), � is the lag-one autocorrelation and ishereafter referred to as the persistence of the time se-ries. Figure 13a shows the family of red noise spectraassociated with different values of �. When � increasesfrom small to large values, the spectrum changes fromnearly white noise to red noise. The corresponding au-tocorrelation functions [Eq. (2)] are shown in Fig. 13b.Because the autocorrelation function is a simple powerfunction of �, it becomes a straight line when plottedagainst a logarithmic ordinate.
For the first-order Markov process, the redness ofthe spectrum is determined by its lag-one autocorrela-
FIG. 12. Spectrum of the eastward wavenumber 1–6 componentof equatorial precipitation (5°N–5°S) at 0°, 85°E for two obser-vational datasets and 14 models: (a) raw and (b) normalized spec-trum. Frequency spectral width 1/100 cpd.
2684 J O U R N A L O F C L I M A T E VOLUME 19
Fig 12 live 4/C
tion. Therefore, we plot in Fig. 14 the autocorrelationfunction of precipitation at 0°, 85°E. Both observationaldatasets have a � of about 0.7. Most models have toolarge values of �, which is consistent with their spectrabeing too red (Fig. 12). Several models (CNRM-CM3,MRI-CGCM2.3.2, MIROC3.2-medres, and MIROC3.2-hires) have a � similar to or smaller than the observedvalue. Results for 0°, 155°E (western Pacific) are similar(not shown).
The physical meaning of � is the persistence of pre-cipitation in the region of interest. Therefore, Fig. 14indicates that most of the models have too strong per-sistence of precipitation, which is closely associatedwith their overreddened spectra. In addition to theshape of the spectrum, the precipitation persistencealso affects the modes at the high-frequency end of thespectrum, such as the WIG mode (the 2-day wave) andthe MRG-EIG modes (the 3–6-day synoptic distur-bances). A too strong persistence tends to suppress thehigh-frequency modes (see Fig. 13a) and may contrib-ute to the generally too weak variances of these modesin the IPCC models. We will discuss the factors affect-ing the persistence of precipitation in the next section.
5. Summary and discussion
This study evaluates the tropical intraseasonal vari-ability, and especially the fidelity of MJO simulations,in 14 IPCC AR4 coupled GCMs. Eight years of dailyprecipitation data from each model’s twentieth-centuryclimate simulation are analyzed and compared withdaily satellite-retrieved precipitation. Space–time spec-tral analysis is used to obtain the variance and phasespeed of dominant convectively coupled equatorialwaves, including the MJO, Kelvin, ER, MRG, EIG, andWIG waves. The variance and propagation of the MJO,defined as the eastward wavenumber 1–6, 30–70-daymode, are examined in detail.
The results show that current state-of-the-art GCMsstill have significant problems and display a wide rangeof skill in simulating the tropical intraseasonal variabil-ity. The total intraseasonal (2–128 day) variance of pre-cipitation is too weak in most of the models. About halfof the models have signals of convectively coupledequatorial waves, with Kelvin and MRG–EIG wavesespecially prominent. However, the variances are gen-erally too weak for all wave modes except the EIG
FIG. 13. (a) Spectrum and (b) autocorrelation of theoreticalMarkov process.
FIG. 14. Autocorrelation of precipitation at 0°, 85°E.
15 JUNE 2006 L I N E T A L . 2685
Fig 14 live 4/C
wave, and the phase speeds are generally too fast, beingscaled to excessively deep equivalent depths. An inter-esting result is that this scaling is consistent within agiven model across modes, in that both the symmetricand antisymmetric modes scale similarly to a particularequivalent depth. Excessively deep equivalent depthssuggest that these models may not have a large enoughreduction in their “effective static stability” by diabaticheating.
The MJO variance approaches the observed value in2 of the 14 models, but is less than half of the observedvalue in the other 12 models. The ratio between theeastward MJO variance and the variance of its west-ward counterpart is too small in most of the models,which is consistent with the lack of highly coherenteastward propagation of the MJO in many models.Moreover, the MJO variance in 13 of the 14 modelsdoes not come from a pronounced spectral peak, butusually comes from part of an overreddened spectrum,which in turn is associated with a too strong persistenceof equatorial precipitation. The two models that argu-ably do best at simulating the MJO are the only oneshaving convective closures/triggers linked in some wayto moisture convergence.
Our results reveal two common biases in many cli-mate models, namely, too large equivalent depths forequatorial waves and too strong persistence of equato-rial precipitation. Equivalent depths that are too deepfor equatorial modes in many models suggest that theymay have a too large “effective static stability.” Theeffective static stability is due to the partial cancellationbetween diabatic heating and adiabatic cooling associ-ated with vertical motion (Gill 1982; Neelin and Held1987; Emanuel et al. 1994), which would lead to a re-duction of the implied equivalent depth of a convectingdisturbance (WK; Haertel and Kiladis 2004). The effec-tive static stability is thus affected by the vertical struc-ture of moist static energy, the vertical profile of up-ward motion associated with diabatic heating profile,the surface latent and sensible heat flux, and the col-umn-integrated radiative heating (e.g., Neelin and Held1987; Yu et al. 1998). Therefore, in future studies, itwould be interesting to directly evaluate the effectivestatic stability in the models, and if it is indeed toolarge, examine which of the above factors are at thecause.
The persistence of equatorial precipitation is stronglyaffected by subgrid-scale processes, and may be im-proved by refining a model’s moist physics. Since ourresults indicate that precipitation persistence is closelytied to the redness of the background spectrum, if wecan make the persistence more realistic through im-proving model physics, we may be able to get a more
realistic background spectrum. The observed weak per-sistence of precipitation may be associated with thewell-known self-suppression processes in deep convec-tion, which can be summarized as follows. Deep con-vective updrafts are usually associated with saturatedand unsaturated convective downdrafts penetratinginto the boundary layer and mesoscale downdrafts pen-etrating to the lower troposphere above the boundarylayer (e.g., Zipser 1969, 1977; Houze 1977, 1982; Mapesand Houze 1995; Mapes and Lin 2005). Convectivedowndrafts, especially the unsaturated convectivedowndrafts, significantly dry and cool the boundarylayer (e.g., Zipser 1969; Houze 1977; Barnes andGarstang 1982) and, therefore, decrease the initial en-tropy of future convective updrafts. Mesoscale down-drafts dry the lower troposphere above the boundarylayer, leading to the famous “onion” sounding (e.g.,Zipser 1977), and a too dry lower troposphere maydecrease the buoyancy of the future convective up-drafts through entrainment (e.g., Brown and Zhang1997). Therefore, in the wake of a deep convectionevent, both of the above processes suppress the devel-opment of new deep convection and, thus, decrease thepersistence of precipitation.
The current GCMs have not included all of the aboveself-suppression processes in deep convection (Table1). Although many of the models have saturated con-vective downdrafts, only a few of them have unsaturat-ed convective downdrafts (e.g., Emanuel 1991), andnone of the models have mesoscale downdrafts. More-over, the sensitivity of deep convection to moisture inthe lower troposphere above the boundary layer hasnot been well represented in many models, especiallybecause they include undiluted or weakly diluted mem-bers in the ensemble of convective updrafts. However,this sensitivity is enhanced in some models, for ex-ample, by including only the significantly diluted con-vective updrafts (e.g., Tokioka et al. 1988; Tiedtke 1989;Bougeault 1985), or by adding explicit trigger functions(e.g., Emori et al. 2001). Our results suggest that it isimportant to incorporate these self-suppression pro-cesses in deep convection in order to get realistic per-sistence of precipitation.
When models improve the representation of self-suppression processes in deep convection, the persis-tence of precipitation may decrease and approach theobserved value. As suggested by the spectrum of thetheoretical Markov process (Fig. 13a), decreasing per-sistence may have different effects on the MJO vari-ance in different models. For models now having a verystrong persistence (e.g., � � 0.9), decreasing persistencemay decrease the variance for periods longer than70 days but increase the variance in the 30–70-day MJO
2686 J O U R N A L O F C L I M A T E VOLUME 19
band. However, for models now having medium persis-tence (e.g., 0.75 � � � 0.9), decreasing persistence maydecrease the variances for both periods longer than 70days and periods of 30–70 days, although it is also pos-sible that spectral peaks previously embedded withinthe red noise spectra will be unveiled. Nevertheless, thepoint is that most of the models have a positive bias intheir persistence of precipitation, which may need to bealleviated.
It is important to note that even a realistic persis-tence can by itself only create a red noise spectrum, butnot a spectral peak. To generate a spectral peak, con-vectively coupled large-scale waves and wave-heatingfeedback must be involved. This leads us to the follow-ing questions:
1) Are the MJO precipitation anomalies in the modelsassociated with realistic MJO wave structure?
2) Are the wave-heating feedbacks well simulated inthe models?
3) What causes the spectral peak in the CNRM-CM3model?
Fortunately, 10 of the 14 models have 3D upper-airdata available, which makes it possible to analyze boththe wave structure and wave-heating feedback. We arecurrently analyzing these structures and will report theresults in separate studies.
Acknowledgments. This study benefited much fromdiscussions with Dave Randall, Sumant Nigam, ShuntaiZhou, Isaac Held, Steve Klein, Eric Maloney, NormMcFarlane, Gavin Schmidt, and Yogesh Sud. The care-ful and insightful reviews by Duane Waliser and ananonymous reviewer helped significantly to improvingthe manuscript. Gary Russell kindly provided a de-tailed description of the GISS-AOM model. We ac-knowledge the international modeling groups for pro-viding their data for analysis, the Program for ClimateModel Diagnosis and Intercomparison (PCMDI) forcollecting and archiving the model data, the JSC/CLIVAR Working Group on Coupled Modeling(WGCM) and their Coupled Model IntercomparisonProject (CMIP) and Climate Simulation Panel for or-ganizing the model data analysis activity, and the IPCCWG1 TSU for technical support. The IPCC Data Ar-chive at Lawrence Livermore National Laboratory issupported by the Office of Science, U.S. Department ofEnergy. J. L. Lin was supported by the U.S. ClimateVariability and Predictability Program (CLIVAR) Cli-mate Model Evaluation Project (CMEP; informationavailable online at http://www.usclivar.org/); theNOAA OGP CLIVAR-Pacific Program; NOAA OGPCDEP Program; the NASA Modeling, Analysis and
Prediction (MAP) Program; and the NOAA Geophysi-cal Fluid Dynamics Laboratory. B. E. Mapes was sup-ported by NSF ATM-0336790K and the NOAA OGPCLIVAR-Pacific Program. K. R. Sperber was sup-ported under the auspices of the U.S. Department ofEnergy Office of Science, Climate Change PredictionProgram by the University of California Lawrence Liv-ermore National Laboratory under Contract W-7405-Eng-48. A. Del Genio was supported by the NASAPrecipitation Measurement Missions Program.
REFERENCES
Barnes, G. M., and M. Garstang, 1982: Subcloud layer energeticsof precipitating convection. Mon. Wea. Rev., 110, 102–117.
Berbery, E. H., and J. Nogues-Paegle, 1993: Intraseasonal inter-actions between the Tropics and extratropics in the SouthernHemisphere. J. Atmos. Sci., 50, 1950–1965.
Bergman, J. W., H. H. Hendon, and K. M. Weickmann, 2001: In-traseasonal air–sea interactions at the onset of El Niño. J.Climate, 14, 1702–1719.
Bessafi, M., and M. C. Wheeler, 2006: Modulation of south IndianOcean tropical cyclones by the Madden–Julian oscillationand convectively coupled equatorial waves. Mon. Wea. Rev.,134, 638–656.
Bougeault, P., 1985: A simple parameterization of the large-scaleeffects of cumulus convection. Mon. Wea. Rev., 113, 2108–2121.
Brown, R. G., and C. Zhang, 1997: Variability of midtropospherichumidity and its effect on cloud-top height distribution dur-ing TOGA COARE. J. Atmos. Sci., 54, 2760–2774.
Carvalho, L. M. V., C. Jones, and T. Ambrizzi, 2005: Oppositephases of the Antarctic Oscillation and relationships withintraseasonal to interannual activity in the Tropics during theaustral summer. J. Climate, 18, 702–718.
Del Genio, A. D., and M.-S. Yao, 1993: Efficient cumulus param-eterization for long-term climate studies: The GISS scheme.The Representation of Cumulus Convection in NumericalModels, Meteor. Monogr., No. 46, Amer. Meteor. Soc., 181–184.
Dickinson, M., and J. Molinari, 2002: Mixed Rossby–gravitywaves and western Pacific tropical cyclogenesis. Part I: Syn-optic evolution. J. Atmos. Sci., 59, 2183–2196.
Duchan, C. E., 1979: Lanczos filtering in one and two dimensions.J. Appl. Meteor., 18, 1016–1022.
Duffy, P. B., B. Govindasamy, J. P. Iorio, J. Milovich, K. R. Sper-ber, K. E. Taylor, M. F. Wehner, and S. L. Thompson, 2003:High-resolution simulation of global climate. Part I: Presentclimate. Climate Dyn., 21, 371–390.
Emanuel, K. A., 1987: An air–sea interaction model of intrasea-sonal oscillation in the tropics. J. Atmos. Sci., 44, 2324–2340.
——, 1991: A scheme for representing cumulus convection inlarge-scale models. J. Atmos. Sci., 48, 2313–2329.
——, J. D. Neelin, and C. S. Bretherton, 1994: On large-scale cir-culations in convecting atmospheres. Quart. J. Roy. Meteor.Soc., 120, 1111–1143.
Emori, S., T. Nozawa, A. Numaguti, and I. Uno, 2001: Importanceof cumulus parameterization for precipitation simulationover East Asia in June. J. Meteor. Soc. Japan, 79, 939–947.
Flatau, M., P. J. Flatau, P. Phoebus, and P. P. Niiler, 1997: Thefeedback between equatorial convection and local radiative
15 JUNE 2006 L I N E T A L . 2687
and evaporative processes: The implications for intraseasonaloscillations. J. Atmos. Sci., 54, 2373–2386.
Gill, A. E., 1982: Studies of moisture effects in simple atmosphericmodels: The stable case. Geophys. Astrophys. Fluid Dyn., 19,119–152.
Gilman, D. L., F. J. Fuglister, and J. M. Mitchell Jr., 1963: On thepower spectrum of “red noise. J. Atmos. Sci., 20, 182–184.
Goswami, B. N., R. S. Ajayamohan, P. K. Xavier, and D. Sen-gupta, 2003: Clustering of synoptic activity by Indian summermonsoon intraseasonal oscillations. Geophys. Res. Lett., 30,1431–1434.
Gregory, D., and P. R. Rowntree, 1990: A mass flux convectionscheme with representation of cloud ensemble characteristicsand stability-dependent closure. Mon. Wea. Rev., 118, 1483–1506.
Haertel, P. T., and G. N. Kiladis, 2004: Dynamics of 2-day equa-torial waves. J. Atmos. Sci., 61, 2707–2721.
Hartten, L. M., 1996: Synoptic settings of westerly wind bursts. J.Geophys. Res., 101 (D12), 16 997–17 019.
Hayashi, Y., and D. G. Golder, 1986: Tropical intraseasonal os-cillations appearing in a GFDL general circulation model andFGGE data. Part I: Phase propagation. J. Atmos. Sci., 43,3058–3067.
——, and A. Sumi, 1986: The 30–40 day oscillation simulated in an“aquaplanet” model. J. Meteor. Soc. Japan, 64, 451–466.
——, and D. G. Golder, 1988: Tropical intraseasonal oscillationsappearing in a GFDL general circulation model and FGGEdata. Part II: Structure. J. Atmos. Sci., 45, 3017–3033.
Hendon, H. H., 2000: Impact of air–sea coupling on the Madden–Julian oscillation in a general circulation model. J. Atmos.Sci., 57, 3939–3952.
——, C. Zhang, and J. D. Glick, 1999: Interannual variation of theMJO during austral summer. J. Climate, 12, 2538–2550.
Higgins, R. W., J.-K. E. Schemm, W. Shi, and A. Leetmaa, 2000:Extreme precipitation events in the western United Statesrelated to tropical forcing. J. Climate, 13, 793–820.
Houze, R. A., 1977: Structure and dynamics of a tropical squall–line system. Mon. Wea. Rev., 105, 1540–1567.
——, 1982: Cloud clusters and large-scale vertical motions in theTropics. J. Meteor. Soc. Japan, 60, 396–410.
Huffman, G. J., R. F. Adler, M. M. Morrissey, S. Curtis, R. Joyce,B. McGavock, and J. Susskind, 2001: Global precipitation at1° daily resolution from multisatellite observations. J. Hy-drometeor., 2, 36–50.
Inness, P. M., and J. M. Slingo, 2003: Simulation of the Madden–Julian oscillation in a coupled general circulation model. PartI: Comparisons with observations and an atmosphere-onlyGCM. J. Climate, 16, 345–364.
——, ——, S. J. Woolnough, R. B. Neale, and V. D. Pope, 2001:Organization of tropical convection in a GCM with varyingvertical resolution: Implications for the simulation of theMadden–Julian oscillation. Climate Dyn., 17, 777–793.
Janowiak, J. E., and P. A. Arkin, 1991: Rainfall variations in theTropics during 1986–1989, as estimated from observations ofcloud-top temperatures. J. Geophys. Res., 96 (Suppl.), 3359–3373.
Jenkins, G. M., and D. G. Watts, 1968: Spectral Analysis and ItsApplications. Holden Day, 525 pp.
Jones, C., and J.-K. E. Schemm, 2000: The influence of intrasea-sonal variations on medium-range weather forecasts overSouth America. Mon. Wea. Rev., 128, 486–494.
Kemball-Cook, S., and B. Wang, 2001: Equatorial waves and air–
sea interaction in the boreal summer intraseasonal oscilla-tion. J. Climate, 14, 2923–2942.
Kessler, W. S., M. J. McPhaden, and K. M. Weickmann, 1995:Forcing of intraseasonal Kelvin waves in the equatorial Pa-cific. J. Geophys. Res., 100, 10 613–10 631.
Kiladis, G. N., and K. M. Weickmann, 1992: Circulation anoma-lies associated with tropical convection during northern win-ter. Mon. Wea. Rev., 120, 1900–1923.
——, G. A. Meehl, and K. M. Weickmann, 1994: Large-scale cir-culation associated with westerly wind bursts and deep con-vection over the western equatorial Pacific. J. Geophys. Res.,99, 18 527–18 544.
——, K. H. Straub, and P. T. Haertel, 2005: Zonal and verticalstructure of the Madden–Julian oscillation. J. Atmos. Sci., 62,2790–2809.
Knutson, T. R., and K. M. Weickmann, 1987: 30–60 day atmo-spheric oscillations: Composite life cycles of convection andcirculation anomalies. Mon. Wea. Rev., 115, 1407–1436.
——, ——, and J. E. Kutzbach, 1986: Global-scale intraseasonaloscillations of outgoing longwave radiation and 250 mb zonalwind during Northern Hemisphere summer. Mon. Wea. Rev.,114, 605–623.
Kuma, K. I., 1994: The Madden and Julian and tropical distur-bances in an aqua-planet version of JMA global model withT63 and T159 resolution. J. Meteor. Soc. Japan, 72, 147–172.
Lau, N. C., I. M. Held, and J. D. Neelin, 1988: The Madden–Julianoscillations in an idealized general circulation model. J. At-mos. Sci., 45, 3810–3831.
Lawrence, D. M., and P. J. Webster, 2002: The boreal summerintraseasonal oscillation: Relationship between northwardand eastward movement of convection. J. Atmos. Sci., 59,1593–1606.
Lee, M.-I., I.-S. Kang, J.-K. Kim, and B. E. Mapes, 2001: Influenceof cloud-radiation interaction on simulating tropical intrasea-sonal oscillation with an atmospheric general circulationmodel. J. Geophys. Res., 106, 14 219–14 233.
——, ——, and ——, 2003: Impacts of cumulus convection pa-rameterization on aqua-planet AGCM simulations of tropicalintraseasonal variability. J. Meteor. Soc. Japan, 81, 963–992.
Liebmann, B., H. H. Hendon, and J. D. Glick, 1994: The relation-ship between tropical cyclones of the western Pacific andIndian Oceans and the Madden–Julian oscillation. J. Meteor.Soc. Japan, 72, 401–411.
Lin, J. L., and B. E. Mapes, 2004: Radiation budget of the tropicalintraseasonal oscillation. J. Atmos. Sci., 61, 2050–2062.
——, ——, M. H. Zhang, and M. Newman, 2004: Stratiform pre-cipitation, vertical heating profiles, and the Madden–Julianoscillation. J. Atmos. Sci., 61, 296–309.
——, ——, and ——, 2005: Zonal momentum budget of the Mad-den–Julian oscillation: The source and strength of equivalentlinear damping. J. Atmos. Sci., 62, 2172–2188.
Madden, R. A., and P. R. Julian, 1971: Detection of a 40–50 dayoscillation in the zonal wind in the tropical Pacific. J. Atmos.Sci., 28, 702–708.
——, and ——, 1972: Description of global-scale circulation cellsin the tropics with a 40–50 day period. J. Atmos. Sci., 29,1109–1123.
Majda, A. J., and J. A. Biello, 2004: A multi-scale model for tropi-cal intraseasonal oscillations. Proc. Natl. Acad. Sci., 101,4736–4741.
——, and ——, 2005: A new multiscale model for the Madden–Julian oscillation. J. Atmos. Sci., 62, 1694–1721.
Maloney, E. D., and D. L. Hartmann, 2000: Modulation of eastern
2688 J O U R N A L O F C L I M A T E VOLUME 19
North Pacific hurricanes by the Madden–Julian oscillation. J.Climate, 13, 1451–1460.
——, and ——, 2001a: The Madden–Julian oscillation, barotropicdynamics, and North Pacific tropical cyclone formation. PartI: Observations. J. Atmos. Sci., 58, 2545–2558.
——, and ——, 2001b: The sensitivity of intraseasonal variabilityin the NCAR CCM3 to changes in convective parameteriza-tion. J. Climate, 14, 2015–2034.
Mapes, B. E., and R. A. Houze, 1995: Diabatic divergence profilesin western Pacific mesoscale convective systems. J. Atmos.Sci., 52, 1807–1828.
——, and J. L. Lin, 2005: Doppler radar observations of mesoscalewind divergence in regions of tropical convection. Mon. Wea.Rev., 133, 1808–1824.
Matsuno, T., 1966: Quasi-geostrophic motions in the equatorialarea. J. Meteor. Soc. Japan, 44, 25–43.
Miller, A. J., S. Zhou, and S.-K. Yang, 2003: Relationship of theArctic and Antarctic Oscillation to outgoing longwave radia-tion. J. Climate, 16, 1583–1592.
Mo, K. C., and R. W. Higgins, 1998: Tropical influences on Cali-fornia precipitation. J. Climate, 11, 412–430.
Moncrieff, M. W., 2004: Analytic representation of the large-scaleorganization of tropical convection. J. Atmos. Sci., 61, 1521–1538.
Moorthi, S., and M. J. Suarez, 1992: Relaxed Arakawa–Schubert:A parameterization of moist convection for general circula-tion models. Mon. Wea. Rev., 120, 978–1002.
Neelin, J. D., and I. M. Held, 1987: Modeling tropical convergencebased on the moist static energy budget. Mon. Wea. Rev., 115,3–12.
Nordeng, T. E., 1994: Extended versions of the convective param-eterization scheme at ECMWF and their impact on the meanand transient activity of the model in the tropics. ECMWFTech. Memo. 206, European Centre for Medium-RangeWeather Forecasts, Reading, United Kingdom, 41 pp.
Paegle, J. N., L. A. Byerle, and K. C. Mo, 2000: Intraseasonalmodulation of South American summer precipitation. Mon.Wea. Rev., 128, 837–850.
Pan, D.-M., and D. A. Randall, 1998: A cumulus parameterizationwith a prognostic closure. Quart. J. Roy. Meteor. Soc., 124,949–981.
Park, C. K., D. M. Straus, and K.-M. Lau, 1990: An evaluation ofthe structure of tropical intraseasonal oscillations in threegeneral circulation models. J. Meteor. Soc. Japan, 68, 403–417.
Russell, G. L., J. R. Miller, and D. Rind, 1995: A coupled atmo-sphere–ocean model for transient climate change studies. At-mos.–Ocean, 33, 683–730.
Salby, M., and R. R. Garcia, 1987: Transient response to localizedepisodic heating in the Tropics. Part I: Excitation and short-time near-field behavior. J. Atmos. Sci., 44, 458–498.
——, and H. H. Hendon, 1994: Intraseasonal behavior of clouds,temperature, and motion in the Tropics. J. Atmos. Sci., 51,2207–2224.
Schubert, S., R. Dole, H. Van den Dool, M. Suarez, and D. Wa-liser, 2002: Proceedings from a workshop on “Prospects forimproved forecasts of weather and short-term climate vari-ability on subseasonal (2 week to 2 month) time scales.”NASA/TM 2002-104606, Vol. 23, 171 pp.
Simpson, J., R. F. Adler, and G. R. North, 1988: A proposedTropical Rainfall Measuring Mission (TRMM) satellite. Bull.Amer. Meteor. Soc., 69, 278–295.
Slingo, J. M., and Coauthors, 1996: Intraseasonal oscillations in 15atmospheric general circulation models: Results from anAMIP diagnostic subproject. Climate Dyn., 12, 325–357.
Sperber, K. R., S. Gualdi, S. Legutke, and V. Gayler, 2005: TheMadden–Julian oscillation in ECHAM4 coupled and un-coupled general circulation models. Climate Dyn., 25, 117–140.
Straub, K. H., and G. N. Kiladis, 2003: Interactions between theboreal summer intraseasonal oscillation and higher-frequency tropical wave activity. Mon. Wea. Rev., 131, 945–960.
Takayabu, Y. N., 1994: Large-scale cloud disturbances associatedwith equatorial waves. Part I: Spectral features of the clouddisturbances. J. Meteor. Soc. Japan, 72, 433–448.
——, T. Iguchi, M. Kachi, A. Shibata, and H. Kanzawa, 1999:Abrupt termination of the 1997–98 El Niño in response to aMadden–Julian oscillation. Nature, 402, 279–282.
Tiedtke, M., 1989: A comprehensive mass flux scheme for cumu-lus parameterization in large-scale models. Mon. Wea. Rev.,117, 1779–1800.
Tokioka, T., K. Yamazaki, A. Kitoh, and T. Ose, 1988: The equa-torial 30–60-day oscillation and the Arakawa–Schubert pen-etrative cumulus parameterization. J. Meteor. Soc. Japan, 66,883–901.
Waliser, D. E., 2005: Predictability and forecasting. IntraseasonalVariability of the Atmosphere–Ocean Climate System, W. K.M. Lau and D. E. Waliser, Eds., Springer, 389–418.
——, K. M. Lau, and J. H. Kim, 1999: The influence of coupledsea surface temperatures on the Madden–Julian oscillation:A model perturbation experiment. J. Atmos. Sci., 56, 333–358.
——, ——, W. Stern, and C. Jones, 2003a: Potential predictabilityof the Madden–Julian oscillation. Bull. Amer. Meteor. Soc.,84, 33–50.
——, S. Schubert, A. Kumar, K. Weickmann, and R. Dole, 2003b:Proceedings from a workshop on “Modeling, Simulation andForecasting of Subseasonal Variability.” NASA/CP 2003-104606, Vol. 25, 62 pp.
——, W. Stern, S. Schubert, and K. M. Lau, 2003c: Dynamicpredicatability of intraseasonl variability associated with theAsian summer monsoon. Quart. J. Roy. Meteor. Soc., 129,2897–2925.
——, and Coauthors, 2003d: AGCM simulations of intraseasonalvariability associated with the Asian summer monsoon. Cli-mate Dyn., 21, 423–446.
Wang, B., and H. L. Rui, 1990: Synoptic climatology of transienttropical intraseasonal convective anomalies: 1975–1985. Me-teor. Atmos. Phys., 44, 43–61.
Wang, W., and M. E. Schlesinger, 1999: The dependence on con-vective parameterization of the tropical intraseasonal oscil-lation simulated by the UIUC 11-layer atmospheric GCM. J.Climate, 12, 1423–1457.
Weickmann, K. M., G. R. Lussky, and J. E. Kutzbach, 1985: In-traseasonal (30–60 day) fluctuations of outgoing longwaveradiation and 250 mb streamfunction during northern winter.Mon. Wea. Rev., 113, 941–961.
——, G. Kiladis, and P. Sardeshmukh, 1997: The dynamics ofintraseasonal atmospheric angular momentum oscillations. J.Atmos. Sci., 54, 1445–1461.
Wheeler, M., 1998: Convectively coupled equatorial waves. Ph.D.thesis, University of Colorado, Boulder, CO, 164 pp.
——, and G. N. Kiladis, 1999: Convectively coupled equatorial
15 JUNE 2006 L I N E T A L . 2689
waves: Analysis of clouds and temperature in the wavenum-ber-frequency domain. J. Atmos. Sci., 56, 374–399.
——, and K. M. Weickmann, 2001: Real-time monitoring and pre-diction of modes of coherent synoptic to intraseasonal tropi-cal variability. Mon. Wea. Rev., 129, 2677–2694.
——, and H. H. Hendon, 2004: An all-season real-time multivari-ate MJO index: Development of an index for monitoring andprediction. Mon. Wea. Rev., 132, 1917–1932.
——, and J. L. McBride, 2005: Australian–Indonesian monsoon.Intraseasonal Variability in the Atmosphere–Ocean ClimateSystem, W. K. M. Lau and D. E. Waliser, Eds., SpringerPraxis, 125–173.
——, G. N. Kiladis, and P. J. Webster, 2000: Large-scale dynami-cal fields associated with convectively coupled equatorialwaves. J. Atmos. Sci., 57, 613–640.
Yasunari, T., 1979: Cloudiness fluctuations associated with theNorthern Hemisphere summer monsoon. J. Meteor. Soc. Ja-pan, 57, 227–242.
Yu, J.-Y., C. Chou, and J. D. Neelin, 1998: Estimating the gross
moist stability of the tropical atmosphere. J. Atmos. Sci., 55,1354–1372.
Yuter, S. E., and R. A. Houze Jr., 2000: The 1997 Pan AmericanClimate Studies Tropical Eastern Pacific Process Study. PartI: ITCZ region. Bull. Amer. Meteor. Soc., 81, 451–481.
Zhang, C., and M. Dong, 2004: Seasonality in the Madden–Julianoscillation. J. Climate, 17, 3169–3180.
Zhang, G. J., and N. A. McFarlane, 1995: Sensitivity of climatesimulations to the parameterization of cumulus convection inthe CCC-GCM. Atmos.–Ocean, 3, 407–446.
——, and M. Mu, 2005: Simulation of the Madden–Julian Oscil-lation in the NCAR CCM3 using a revised Zhang–McFarlaneconvection parameterization scheme. J. Climate, 18, 4046–4064.
Zipser, E. J., 1969: The role of organized unsaturated convectivedowndrafts in the structure and rapid decay of an equatorialdisturbance. J. Appl. Meteor., 8, 799–814.
——, 1977: Mesoscale and convective–scale downdrafts as distinctcomponents of squall-line structure. Mon. Wea. Rev., 105,1568–1589.
