August

1986

Y.-Y.

The

30-40

Day

Oscillations

By Yoshi-Yuki

HayashiandA. SumiSimulated

451

in an "Aqua

Hayashi and Akimasa

Planet"

Model

Sumi

Geophysical Institute, University of Tokyo, Tokyo 113, Japan(Manuscript received 7 February 1986, in revised form 31 May 1986)

Abstract
Numerical experiments using a general circulation model (GCM) were performed for the purposeof investigating the possibility of the generation of a long period (30-40 days) oscillation as a collective
motion of cumulus activity (so-called wave-CISK) along the equator of an ocean covered globe ("aquaplanet"). In our model, the SST distribution was symmetric about the equator and uniform in thelongitudinal direction.
The results of a 90 day integration exhibited the spontaneous appearance of a collective motionof convective activity together with an east-west wavenumber one circulation (the "30 day oscillation"). The characteristics of this east-west circulation resemble those of the observed 30-60 day
oscillation in the actual atmosphere. The 30 day oscillation is characterized by a superposition of two
different scales: the scale of precipitation patterns ("super clusters") which is nearly equal to theequatorial radius of deformation, and the scale observed as the modulation of precipitation patterns
and the east-west circulation with a wavenumber one. The whole structure moves eastward at a slow
phase speed (15m/s).
The results also exhibited the spontaneous formation of double ITCZs around the equator.
Thus the production of the double ITCZ structure does not necessarily require a minimum SST at
the equator. In the equatorial region between the north and south ITCZs, active convection forms
super clusters, while in the regions poleward of the ITCZs, active convection forms tropical cyclones.
Another experiment without the moist processes resulted in the abrupt disintegration of the
30 day oscillation into Kelvin and Rossby waves. This indicates that strong mode coupling between
the equatorial free waves is required in order to maintain the 30 day oscillation. The slow phasespeed, the strong mode coupling and the double structure in scale indicate that the collective motionof convective activity along the equator cannot be explained simply as a Kelvin wave mode of thelinear equatorial wave-CISK theory presented so far. The 30 day oscillation should be regarded as a
new type solution of the equatorial wave-CISK problem.

1. Introduction
In recent years, the large scale variability
known as the 30-60 day oscillation has beenrecognized as a dominant component of theintraseasonal variability of the equatorial circulation (e.g., Madden and Julian, 1972; Yasunari,
1981; T. Murakami et al., 1984; Quah, 1984;
M. Murakami, 1985). It has been demonstrated
that the 30-60 day oscillation plays an important role even in the interannual variability ofthe equatorial region. For instance, the appearance of anomalous convection in the central
Pacific and drought over the maritime continent- Australia region during the ENSO (E1-Nino

Southern Oscillation) events is recognized asa shift in the distribution of the 30-60 day
oscillation (see, Fig. 15 of Lau and Chan, 1985).
The characteristics of the 30-60 day oscillation obtained from these observational studies
may be summarized as follows:(1) Zonal wavenumber one structure isdominant especially in the zonal componentof the wind field (u). (e.g., Madden and Julian,
1972; Yasunari, 1981; T. Murakami et al., 1984;
Quah,1984).
(2) The zonal wind (u) has a baroclinic
structure (opposite sign between the lower
troposphere (850mb) and the upper troposphere452

Journalof the Meteorological(200mb)), and the signal is confined to thetroposphere (T. Murakami and Nakazawa,1985).
(3) The signal propagates eastward at a
speed of about 10-15m/s,
which is muchslower than the phase speed of the equatorial
Kelvin waves with the same vertical wavelength(about 30-60m/s
with a half wavelength of
8-15km and the buoyancy frequency of N2=
10-4 s-2) (e.g., Madden and Julian, 1972; Parker,
1973; Chang, 1977). The signal sometimes also
appears to be of a standingnature over the eastern
Indian Ocean-Western Pacific region with a nodeof u-wind over Indonesia (T. Murakami et al.,
1984; Yamagata and Y. Hayashi,1985).
(4) There is a phase tilt of coherence in thenorth-south direction (Madden and Julian, 1972;
T. Murakami and Nakazawa, 1985). Both uwind (Yasunari, 1981) and outgoing long wave
radiation (OLR) (M. Murakami, 1984) seem topropagate northward.
(5) The signal in OLR is stronger over theocean than over the land (Fig. 1 of T. Murakami
et al., 1986; Fig. 1 of Knutson etal., 1986).
Compared with recent advances in observational studies as summarized above, investigations into the origin and mechanism of the 3060 day oscillation seem to be still in the preliminary stage. The efforts made so far'in theoretical and simulation studies are summarized as(1) modifying equatorial wave dynamics

Fig. 1 IR imagery taken from the GMS on May 4,
1985 (fromMonthly
Reportof Meteorological
Satellite
Center, May 1985). A super cluster (denoted by an arrow)appearsover the maritime
continent.

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(especially, equatorial Kelvin waves) (e.g.,
Chang,1977).
(2) considering the role of land-sea contrast
and moisture distribution (e.g., Webster, 1983),(3) looking for an oscillation of the zonallysymmetric circulation with an intraseasonal timescale by the use of a zonally symmetric generalcirculation model (Goswami and Shukla, 1984).
A difficulty in interpreting the 30-60 day
oscillation as an equatorial Kelvin wave is thelarge difference between the phase speed offree waves (30-60m/s) and the observed eastward propagation speed (10-15m/s).
Chang(1977) introduced a dissipation with a time
constant of about 5 days, and found a frictional mode with a reduced phase speed for agiven set of zonal and vertical wavelengths. He
showed that the amplitude is maximum for thelargest horizontal scale when the forcing (cumulus heating) has a fixed amplitude regardlessof wavenumber. However, it has not yet beenshown how the particular heating distribution
can be realized, and how the wave structure
could be maintained against the dissipation.
Webster (1983) considered the effect of theland-sea contrast (differential heating of landand ocean due to the surface moisture condition), and showed that the northward propagation of the signal can occur over the Indian
ocean. However, the 30-60 day signal is also
prominent over the western Pacific where nolarge land mass exists. During the 82-83 ENSO
event the oscillation was observed in the active
convection region located in the central Pacific.
On the other hand, as compared to the western
Pacific, the signal is not so apparent over the
Caribbean Sea and the Gulf of Guinea where
the land-sea contrast might be a possible mechanism. These facts suggest that the existence ofland is not an essential factor for the 30-60
day oscillation.
The model with zonally averaged variables
shows the possibility of an oscillation on theintraseasonal time scale occurring in the moist
symmetric Hadley circulation (Goswami andShukla, 1984). For the purpose of revealing themechanism of the 30-60 day oscillation, howdyer, consideration of the zonally symmetricoscillation is insufficient, since the zonallyasymmetric (wavenumber one) structure char-August

1986

Y.-Y.

Hayashiacterizes the 30-60 day oscillation.
Here, we emphasize observational fact (5):the activity of the 30-60 day oscillation is highover the ocean, especially over the oceanic
regions with high SST*. In these regions theconvective activity is also strong (low OLR)
even in the mean state. During the 82-83 ENSO
event, the warm SST region expanded eastward
and the region of the strong 30-60 day signalof OLR also expanded eastward (Lau and Chan,
1985). Sardeshmukh and Hoskins (1985) also
demonstrated that during the 82-83 event the
200mb vorticity activity of the 30-60 day
time scale is very strong over the central Pacificaround the east of the date line.
From this observational fact we can speculatethat the 30-60 day oscillation occurs as an
intrinsic property of an interactive system oflarge-scale flow and equatorial convection over
the ocean with a sufficiently large area of highSST (such as the western Pacific, the eastern
Indian Ocean, or the mid-Pacific during the
ENSO events). When the area of high-SST
ocean is large enough, an oscillation of convective activity is caused. An OLR anomaly
with a spatial extent of the order of 3000km(Lao and Chan, 1983a, b; M. Murakami, 1984;
Knutson et al., 1985) might manifest such an
oscillation. Fig. 1 (IR** imagery) shows a typicalexample of cloud activity lying over the maritime continent. The region of active convection
denoted by an arrow in Fig. 1 is composed of agroup of so-called cloud clusters, and thus it canbe referred to as a "super cluster" on a scale of
3000km. By observing sequential IR imageries,
the 30-60 day oscillation can be recognized
as a motion of these super clusters.
The behavior of these anomalies suggeststhat convective activity cannot be equally distributed over a large region exteding from theIndian Ocean to the western Pacific at one time.
When the convection is active over the Indian
Ocean, the activity over the western Pacific issuppressed, and vice versa; even if the SST is
almost equally high in both regions.
Going a step further, we expect that theidealistic 30-60 day oscillation would be real*sea

surface**infrared

temperature

andA. Sumi453

ized if the entire surface of the globe is covered
with a zonally uniform ocean. On such a uniform
boundary, cumulus convection at the equatorwould occur collectively within an areal extent
of about 3000km (super clusters) and move
eastward coherently. The idealistic form of the
30-60 day oscillation can be described mathematically as a symmetry breaking where an
asymmetric distribution of cumulus activity
takes place in spite of the symmetric (zonnaly
uniform) surface conditions.
In the following sections we present theresults of numerical experiments using a generalcirculation model (GCM). Here, our purpose is
to investigate the idealistic behavior of convective activity and associated large scale motions
over a zonally uniform area of potentially active
moist convection. The whole surface is covered
with ocean ("aqua planet"). The SST distribution is zonally uniform and symmetric about
the equator, and hence, the potential for theoccurrence of moist convection is equal in thelongitudinal direction. The main conclusion isthat, in spite of the zonally symmetric surface
conditions, small scale patterns (<3000km)
appear in the precipitation field and the wavenumber one structure appear in the circulation
field. The whole structure propagates eastward
at a phase speed of 15m/s (a period of 30 days
for wavenumber one). The simulated signal is,hereafter, referred to as the "30 day oscillation". The mechanism of the 30 day oscillation
is discussed in Section 4 as a modification of
the equatorial wave-CISK theory. Detailed
analysis to reveal the model dynamics is now
underway at the University of Tokyo.
2.

Model and experimental design

The general circulation model used here isbasically the operational weather prediction
model of the Japan Meteorological Agency,
which was originally designed by Kanamitsu
et al. (1983) and updated by N. Sato. It is a
global spectral model with a 42 wave triangulartruncation and 12 vertical levels. The performance and systematic errors of the original model
are given in Kanamitsu et al. (1983) and Sumi
and Kanamitsu (1984) for its hemispheric version.

454

Journalof the MeteorologicalSociety

2.4

Fig.

2

Zonal

in theprofileofthe SST

distribution

employedsimulation.

2.1 The surface conditions
The whole globe is covered with an ocean
whose SST distribution is uniform in the zonal
direction and symmetrical about the equator.
The model SST (Fig. 2) was derived from averaging the April climatic temperature of all theoceans longitudinally and from taking the meanof the Northern and the Southern Hemispheredistribution. The model SST is fixed (not predicted), and affects the atmospheric temperature
and water vapor content through boundary
fluxes. The fluxes from the sea surface are
given by the bulk formula.
2.2

Radiation (shortwave)
The position of the sun (solar declination)
was fixed at equinox, but the diurnal variation
included in the original model was not changed.
The absorption of O3 is given by the two-hemispheric and zonal average of the climatologicalvalue of April. The absorption due to H2O andscattering due to clouds are calculated throughthe predicted amount of water vapor.

2.3

Cumulus parameterization

The parameterization scheme developed by
Kuo (1974) is used in the model. The criteria foradjustment are(1) conditionally unstable stratification,(2) convergence of moisture flux in thecloud layer,(3) mean relative humidity in the cloudlayer greater than the critical value (90%).
Here the cloud layer is defined as the layer be.
tween the cloud base (the first level above theplanetary boundary layer where the stratification is conditionally unstable) and the cloud
top where the moist adiabat intersects theenvironmental temperature of the model.

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4

Initial conditions and time integration

Two experiments were carried out. The "wet"experiment was started from the initial value
derived from taking the zonal and two-hemispheric average of the monthly mean grid data ofApril 1979 produced by ECMWF.The model was
integrated for 90 days and the results are shownin Figs. 3-6. The "dry" experiment was started
from t=45 days of the first experiment, butwith the water processes excluded (dry atmosphere). The model was integrated for 55 days
(Fig. 7).
3.

Results

3.1

Signal of the about 30 day period

Fig. 3a shows the time-longitude section of
the zonal wind deviation u' at the 850mb levelat the equator. (The definition of symbols issummarized in the Appendix.) Note that in thelongitudinal direction the diagram is duplicatedto clarify the periodicity of the signal. The timeinterval for data sampling is 24 hours (once aday). No time-space filtering technique was utilized in obtaining Fig. 3. It is evident from thefigure that a clear zonal wavenumber one structure (a pair of easterly and westerly) emerges
spontaneously after about 20 days. The structure
propagates eastward at a speed of about 15m/s(period of about 30 days).
It is surprising that the signal is quite regularin the zonal wind at the equator. The term, "30
day oscillation", is used here to distinguish thesignal obtained in this aqua planet model fromthe 30-60 day oscillation in the actual atmosphere. The structure of the "30 day oscillation"
resembles the observed 30-60 day oscillation as
will be presented later; the term "oscillation" isretained, even though it would seem more
appropriate to call it a wave.
The time-longitude section of the 12 hour
integrated precipitation is shown in Fig. 3b.
In contrast with the wind pattern, small scale
structures dominate the distribution of precipitation (cf. Fig. 4). The sampling rate isdoubled for Fig. 3b (twice a day) in order toresolve the motion of these small scale structures.
It should be noted that the largest scale ofprecipitation patterns is less than 3000km. As
will be explained in the next subsection, weAugust

1986

Y.-Y.

HayashiandA. SumiFig. 3 Longitude-time sections of (a) 850 mb zonal wind deviation (u') and (b) precipitation
per 12 hours. The figures are duplicated in the longitudinal direction to clarify the periodicity.
The contour intervals are 2.5m/s for u' and 2.5mm/12h for precipitation. The regions of (a)easterly (u' < 0) and (b) precipitation greater than 1mm/12h
are shaded. The line segment
AB denotes the phase line (c0=15m/s)
along which the composite structures are constructed.

455

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Journalof the Meteorologicalconsider these small patches of precipitation
pattern to correspond to the "super clusters"
often seen in the IR satellite imageriesespeciallyover the western Pacific (Fig. 1). The dominanceof small scale structures appears also in *' andthe horizontal divergence fields (not shown).
In Fig. 3b the precipitation patches move coherently along the phase line of 15m/s. A comparison between Figs. 3a and 3b indicates thatthese small structures are modulated by wavenumber one. Intense precipitation tends tooccur near the longitude where the westerly
changes to the easterly.
The successive formation of precipitation
along the phase line as shown in Fig. 3b cannot
be observed poleward of 12* (not shown). The
precipitation patches of these latitudes areusually due to disturbances which are considered
to be tropical cyclones (as will be explainedlater), and they do not move systematically inthe longitudinal direction.

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4

Horizontal structure

Snap shots of the horizontal distribution of
precipitation are shown in Fig. 4. The four
figures correspond to the time t=66, 74, 82,
90 days. There appear three types of precipitation patterns. In the mid-latitudes, band
structures oriented in the north-south direction
caused by baroclinic waves can be seen. In thelatitudes between 10* and 30*, circular areas ofintense precipitation are observed; these areassociated with vorticity and low surface pressure(not shown), and hence considered to be tropical
cyclones. Around the equator (between 10N andS), precipitation patches on the scale of about
10
3000km can be seen. These correspond to theeastward propagating precipitation areas shownin Fig. 3b. They are not associated with strong
vorticity like that of tropical cyclones. It is notdifficult to recognize in Fig. 4 that the distribution of these precipitation patches is modulated,
producing the wavenumber one structure, andFig. 4 Snapshots of precipitation per 12 hours at four different times (t=66,
interval is 2.5mm/12h and the regions of precipitation greater than 1mm/12h

74, 82, 90 days). The contour
are shaded.

August

1986

Y.-Y.

Hayashiare moving to the east. On the 66th day, mostof the precipitation areas are concentrated in
the region between the longitudes 270* and30*. They then move gradually eastward andare found between 0* and 120* on the 74th
day, between 90* and 210* on the 82nd day,and between 180* and 300* on the 90th day.
We emphasize here that the precipitation
patches appearing in Fig. 4 are not far from theconvection features of the real atmosphere. The
scale of these precipitation patches at the equator corresponds to that of super clusters observed in IR imageries (Fig. 1) and of OLR
anomalies in, for example, Lau and Chan (1983a,b) and Weickmann et al. (1985). The period of
intense precipitation at a fixed longitudinal point
is about 2 to 4 days (Fig. 3b) except for the dry
phase (e.g., around t=50 days at the longitude

andA. Sumi457

360*) of the 30 day oscillation. The existence ofthe time scale of 2 to 4 days in the precipitation
field was reported by M. Murakami (1972). He
showed that disturbances of this time scale move
eastward, and that they are not associated withintense vorticity. These characters resemble
those of the precipitation patches obtained in
the model. Recently, Nakazawa (1986) produced
an interesting figure on the motion of superclusters at the equator. His time-longitudesection of negative OLR anomalies is quite
similar to Fig. 3b.
Since our model cannot resolve individualcloud clusters, only the large scale structures
are reproduced as a continuous area of precipitation with the same size (<3000km). In
the model there are many (*10) super clusters
along the equator, in contrast to the real situa-Fig. 5Composite fields along the phase speed c0=15m/s
for t=
59-90 days of (a) precipitation and (b) wind deviation (u', *') andgeopotential height (Z') at 200mb. The regions of (a) precipitation
greater than 1mm/12h
and (b) Z'<0
are shaded. The contour
interval for (a) is 1mm/12h.
The unit of barbs plotted to the left
is m/s. Zonal mean values of (a) precipitation (mm/h) and (b) zonal
wind (m/s) are plotted to the right side of each figures.

458

Journalof the Meteorologicaltion where usually only one or two super clusters
are found
over the Indian Ocean or over thewestern Pacific. The cause of this discrepancy
may be attributed
to the distributionof SST.
Namely,the highest SST exists all along theSocietyof Japan

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equator in the model, while in the real situation
the highest SST region is limited to the Indian
Ocean-westernPacific region.
An important point in regard to super clusters
is that, even under zonally symmetric surface
conditions, the convective activity cannot coverregions larger than about 3000km at one time.
Note that because of the model truncation (thelargest wavenumber is 42), the smallest precipitation patches appearing in the model correspondto almost the shortest resolvable wavelength
at the equator (=1000km). Thus, their individual
character may be affected by the model truncation. Nevertheless, the model resolution seems
adequate for describing the larger scale (*3000km) convective activity.
In the near equatorial tropical region (be-Fig. 6 Vertical cross sections of composite fields on the equator along the phase speed c0=15m/s
for t=59-90
days of (a) zonal wind deviation u' (m/s), (b) temperature deviation T' (K) (c) heightdeviation Z' (m) and (d) surface pressure deviation Ps' (mb). The contour intervals are 2.0m/s for u',
0.25K for T' and 2.5m for Z'. The vectors indicate (u', *'). The unit for vectors is (m/s, mb/hour).

August1986

Y.-Y. Hayashi

tween 10N and 10S), there are bands of strong
precipitation. The zonal and time (t=59-90
days) mean value of the precipitation is plottedalong the right side of Fig. 5a which shows adouble ITCZ structure around the equator.
Corresponding to this precipitation feature, thezonal mean vertical wind (not shown) is upwardat 10N and 10S, but it is downward at the equator. To the north or south of the ITCZs, themodulation due to wavenumber one is notrecognized. Tropical cyclones seem to appear inrather a random manner, although there remains
the possibility of some modulation which can bedetected only through statistical procedure.
The interesting point of the double ITCZs isthat the aqua planet model produces double
ITCZs even when SST minimum does not exist
above the equator. Pike (1971) indicated theexistence of double ITCZs by employing azonally symmetric air-sea coupled model. But
in his study it was necessary to have low SST
at the equator caused by equatorial upwelling.
Our result (Fig. 5a), contrary to that of Pike,
seems to support the idea that double ITCZs
are caused where Ekman convergence is large
enough (Charney,1971).
To reveal the structure associated with the
30 day oscillation, composites of variables along
the phase speed c0=15m/s(along the line
A-B of Fig. 3a) are constructed for the period
of t=59-90
days. The composite precipitation is shown in Fig. 5a. The zonal mean value
is also plotted on the right side. In Fig. 5b, thecomposite structures of the 200mb wind (u',') and geopotential height deviation Z' *areshown. Over the equator the zonal wind u' atthe 200mb level is in the opposite direction
to that of the 850mb level (cf. Fig. 6). The
latitudinal extent of the signal in u' is 10001500km which is close to the equatorial radiusof deformation: *c/*=1500km
where c=50m/s is the phase speed of the internal wave modewith roughly the same vertical wavelength as
obtained in the model (see Fig. 6). The valuesof 6 m/s for u' and 13 m for Z' (cf. Fig. 5) satisfy
the geostrophic balance relationship in theneighbourhood of the equator (*u'= -dyygZ')
by assuming the characteristic latitudinal scaleof about 1000km.

and

A. Sumi459

By comparing Fig. 5a with Fig. 5b, it is clearthat the most intense convection in equatorial
latitudes occurs at the boundary of the easterlies
and westerlies. Precipitation activity is spread over
the westerly region at 200mb (to the east of
the strongest convection) at the equator, whileat the ITCZ latitudes (10N and 10S) there is atendency for fairly strong convections to occur
even to the west of the strong convection.
The modulation due to the zonal wavenumber
one is very effective at the equator. At higher
latitudes, the formation of tropical cyclones
observed as intense precipitation patches in Fig.
4 seems to obscure the structure.
3.3

Vertical structure

Composite longitude-height cross sections
are presented in Fig. 6. As mentioned alreadyin relation to the horizontal structure, the zonal
wind u' (Fig. 6a) exhibits a clear baroclinic structure with different signs between the lower
troposphere and the upper troposphere. The
half wavelength is about 12km. The signal
above the tropopause (*100mb) may be affected by the top boundary and the low verticalresolution: there are only two *-levels (*=0.075, 0.0225) in the stratosphere. It might beplausible that the 30 day oscillation in the
troposphere excites wavenumber one stratospheric Kelvin waves as discovered by Wallace
and Kousky (1968). Spectral analysis methods
as used by Y. Hayashi and Golder (1979) may
be useful for detecting such waves. They reported the existence of Kelvin waves with aperiod of about 15 days in their all ocean surface model. But the relation between the Kelvinwaves in the stratosphere and the 30-60 day
oscillation in the troposphere has not been
considered yet.
In Fig. 6d, the composite profile of surfacepressure along the equator is plotted (the zonal
mean is subtracted). The relationship between
the circulation cell and the surface pressure
obtained here resembles Fig. 16A of Madden
and Julian (1972). The westward phase tilt
reported by T. Murakami and Nakazawa (1985)
also appears in Fig. 6, which makes it possiblethat the energy generated by the cumulus heatingis converted into the large scale motions of the460

JournalFig. 7
Longitude-time
sectionmoist processes are switchedof the MeteorologicalSocietyof Japanof (a) 500mb
T' and (b) 850mb u' for the dry simulation.
off at t=45 days (cf. Fig. 3) (denoted by > <).

Vol. 64, No, 4The

August

1986

Y.-Y.

Hayashiwavenumber one structure as described in thelinear wave-CISKtheory (Emanuel, 1983).
The wavenumber one structure exemplified
in the composite figures (Figs. 5 and 6) exhibits
characteristics similar to those of equatorial
Kelvin waves (Matsuno, 1966; Gill, 1980). The
upward motion (and cooling) lags behind thetemperature deviation (Fig. 6b) by */2 while
the zonal wind deviation (Fig. 6a) is geostrophically balanced with the geopotential field (Fig.
6c), which in turn is hydrostatically balancedwith the temperature deviation. Thus, the 30 day
oscillation could be explained by some modification of linear Kelvin wave dynamics (e.g., Chang,1977). However, as will be shown in the next
subsection, the Rossby wave components arealso included in the composite structure.
3.4

Dry experiment

In order to reveal the role of the moist convection in maintaining the 30 day oscillation,
an experiment where the moist processes were
switched off at a certain time was carried out(dry experiment). If the mechanism of the 30
day oscillation is explained by a slight modification of the dynamics of linear equatorial Kelvinwaves, it would be expected that after the
moist processes are removed, the structuredeveloped would move eastward at a speed offree Kelvin waves.
The dry experiment was started from t=45
days of the former run (wet experiment) but
with the moist processes excluded. The drymodel was integrated for 55 days. The results
are presented in Fig. 7a for the time-longitudesection of the 500mb temperature (T') at theequator and in Fig. 7b for the 850mb zonal
wind (u') where the sampling rate is once a day.
In Fig. 7a the time mean of T' is subtracted toeliminate the tidal signal.
The experiment resulted in an abrupt destruction of the 30 day oscillation, and thegeneration of free Kelvin waves propagating to
the east and free Rossby waves to the west. Fig.
7a exhibits a fast signal propagating eastward
at a speed of about 30-40m/s. The verticalstructure (not shown) also changes immediately:
the vertical wavelength becomes about 20km
at t=55 days which is a little shorter than thatof the 30 day oscillation. Hence, the phaseandA. Sumi461

speed of 30-40m/s
is consistent with theequatorial linear dynamics (Kelvin waves). In
Fig. 7b, on the other hand, a westward propagating signal is apparent. The phase speed of
Fig. 7b is about one third of the eastward speedof Fig. 7a, which means that the westward
disturbances are equatorial Rossby waves (Gill,
1980).
There must be vertical dispersions of Kelvinand Rossby waves. Actually, in the early period
after the switching off, eastward and westward
propagating signals with a small longitudinalscale seem to exist in Fig. 7. But they disappear
with the passage of time. According to the dispersion relation of the equatorial modes, waves
with a smaller longitudinal scale propagate upward more easily for a given vertical wavenumber. The disappearance of short waves is considered to be the result of the vertical propagation.
From Fig. 7 it can be concluded that theexistence of moist processes is essential for
maintaining the 30 day oscillation and thestructure is composed both of equatorial free
Kelvin and free Rossby waves. The moist processes cause a mode coupling between the two.
The temperature field of the coupled disturbanceis mostly the contribution of Kelvin waves, while
the wind fluctuation comes mainly from Rossby
waves.
4.

Discussion

In this section, we will discuss the mechanismof maintaining the "30 day oscillation" exhibitedin the aqua planet model.
4.1

The 30 day oscillation as a wave-CISK
mode

Convective activity acts as a crucial element
in maintaining the 30 day oscillation; therefore,
the structure realized in the model should berecognized as a new type solution of the equatorial wave-CISK problem. There is a possibility
that the large scale coherent circulations which
are interactively maintained by cumulus activity
exist. The meaning of "new type" is that the
30 day oscillation has the following characteristics, which are not expected by the simple
theories of wave-CISK presented so far (e.g.,
Y. Hayashi, 1970; Lindzen, 1974).

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zonally uniform precipitation pattern might(1) Super clusters with a scale of 15003000km dominate the precipitation, divergence result. However, the model produced precipitaand * fields; and they propagate coherently
tion patches which correspond to the supereastward at a phase speed of 15m/s.
clusters in the actual atmosphere (Fig. 1). Evenin the real atmosphere convection does not(2) The wavenumber one (largest longitudinal scale) structure dominates the u', T' and *'spread over the whole highest SST, but is more
fields, and they also propagate eastward at aor less concentrated in the form of super clusters.
Furthermore, it is puzzling why both in thephase speed of 15m/s. The wavenumber one
structure also appears in the precipitation,model and the real atmosphere, super clusters
divergence and * fields as a modulating patternshould move eastward.
The dominance of "small" scale structures isof super clusters.
close
to the expectation of the linear wave-CISK(3) The whole structure is composed of boththeory. In the usual framework of the theory,
equatorial free Kelvin and Rossby wave modes.
the gravity modes (including the Kelvin wave
The strong mode coupling (item (3)) is notmode) with shorter wavelengths have the larger
expected by the usual linear wave-CISK theory(Y. Hayashi, 1970; Lindzen, 1974). The strucgrowth rates, while the rotational modes havetures of the equatorial linear wave-CISKmodes moderate growth rates (e-folding time of about
15 days). Thus, the super clusters obtained in
obtained in these earlier works are almost equal
to those of the corresponding free wave modes the model seem to correspond to Kelvin or
in the dry atmosphere, and hence the phase gravity modes. Note, however, that the "small"
speed of the Kelvin wave mode which propa- scale features appearing in the model are roughly
gates eastward is two or three times as large as of the order of the equatorial radius of deformathat of the 30 day oscillation (15m/s). Wehave tion and not the shortest length resolvable in
to alter the conventional linear wave-CISK the model.
theory to give such a slow phase speed.
As the distance increases from the equator,
Items (1) and (2) indicate that the 30 day the rotational (usual) CISK mechanism which
oscillation has a double structure. There are acts through Ekman convergence becomes imtwo characteristic scales which are relevant toportant. The feedback is unstable because heatthe equatorial wave-CISK: the equatorial radius ing occurs in the low-pressure region. Since theof deformation (*1500km) and the length of
Ekman convergence is proportional to vorticity,
the equatorial circumference (*40000km). The the Rossby wave modes, which are accompanied
appearance of small scale structure is relevant with large vorticity, have the advantage over theto the classical wave-CISK theory, while the gravity wave modes. The high activity of theappearance of wavenumber one is caused by the CISK mode off the equator explains the double
ITCZ structure, and in the poleward regions offiniteness of the earth. The later scale has notbeen considered in the earlier framework of the the ITCZ, the CISK mechanism causes the occasional appearance of tropical cyclones.
wave-CISKtheory.
The scale of the precipitation areas (<3000
In the following subsections, the mechanismof the 30 day oscillation will be discussed sepa- km) can then be explained by the efficiency ofrately according to the two scales mentioned the rotational CISK mechanism. It is mostefficient for a vorticity with a scale equivalent
above.
to the radius of deformation, since there would
4.2 The existence of the super clusters
be a balance between the efficiencies of trapWith the appearance of the small scale struc- ping heat and the moisture supply through thetures (<3000km), the important point is that Ekman pumping (Emanuel, 1983). Away fromthere exists a limit to the size of precipitation the equator the rotational CISK mechanism
areas, and it is roughly of the order of the forms tropical cyclones with a scale of 500equatorial radius of deformation. If you would 1000km. The equator is a singular point for therecall the zonally uniform surface conditions of rotational CISK mechanism because the effectour aqua planet, you would then expect that a of the earth's rotation disappears there. How-August 1986

Y.-Y. Hayashi

and A. Sumi

ever, through the co-existence of Ekman convergence and wave convergence, a coupling
between Kelvin and Rossby modes is created,which in turns produces a structure that propagates coherently eastward. The existence ofsuper clusters at the equator corresponds to theexistence of tropical cyclones away from theequator. The rotational CISK mechanism associated with the Rossby wave component seems
to be responsible for limiting the maximum sizeof the super clusters, while the wave-CISK(wave
convergence CISK) mechanism seems to be
responsible for eastward propagation. Evidenceof the co-existence of the equatorial Kelvin andRossby waves is seen in Fig. 7 where small scale
eastward and westward waves appear in the T'
and u' fields for a brief period just after switching off the moist processes. We shall call thisparticular mode "coupled Kelvin-Rossby mode"or simply KR mode.
The slow phase velocity (15m/s) of this KR
mode can be understood as the natural consequence of the mode coupling. Recent studies
on the eastward propagation of the ENSO
disturbances showed that the coupling between
oceanic Kelvin and Rossby waves through theexistence of wind stress causes a slow eastward
phase speed (Philander et al., 1984; Yamagata,1985; Anderson and McCreary, 1985). For the
30 day oscillation, the moist processes play thesame role as the wind stress for the ENSO
disturbances.
The slow phase speed can also be understoodwithin the linear framework by introducing a
reduced gravity effect due to convection heating(Gill, 1982). Since the intense precipitations at
the equator occur in the regions of upward
motion (Fig. 6), the cumulus heatings reduce
the adiabatic cooling, which is equivalent to
reducing the static stability of the linear wave
dynamics. Thereby, the eastward propagationis reduced to a certain extent when comparedto the phase speed of the equatorial free Kelvinwaves. It is puzzling why the linear wave-CISK
theory presented so far did not obtain a considerably reduced phase speed. There is a possibility that the heating used there is too weak
for reducing the adiabatic cooling. Note, here,that the effect of reduced gravity is not caused
symmetrically. Cumulus heating occurs mainly463

in the updraft regions and adiabatic cooling is
reduced, while in the downdraft regions only
adiabatic heating is active. In order to adjust
the adiabatic heating to the rate of slow phasepropagation, mode coupling is essential.
4.3

The effect of the finiteness of the equatorial circumference

In the previous subsection, it was emphasizedthat the small scale structure should be regarded
as a wave-CISKmode (KR mode). In this subsection, it will be shown that the appearance of thewavenumber one can be understood as themodulation of the small-scale KR mode disturbances due to the finiteness of the equatorial
circumference.
To begin with, we would like to point out
that, while moist convection is usually considered to be a small scale phenomenon, it is not
so small if considered together with the associatedcirculation. In a two-dimensional non-rotating
fluid, steady circulation caused by a *-function
heating has an infinite extent in the horizontal
direction (Emanuel, 1983). Since the u'-field isgiven as an integral quantity of the convergence,the *-function heating (convergence) causes acirculation with the shape of a step function.
At the equator, because of the equatorial-effect , the circulations excited by heating*areconfined to the equatorial radius of deformationin the latitudinal direction (the equatorial duct).
These circulations ought to have a two dimensional nature: namely, they tend to extend in
the longitudinal direction along the equator
without any difficulty (Heckley and Gill, 1984).
However, since the equatorial circulation isperiodic in the longitudinal direction, the steadycirculation of an infinite two dimensional flow
cannot be realized. Thus, it is necessary to havea downdraft at a certain longitude along theequator.
If the KR mode has exactly the same amplitude in the zonal direction, the downdraft caused
by each convective activity would have no cumulative effect. However, in the event there is aslight enhancement of convective activity somewhere along the equator, a strong downdraft
region may appear on the opposite side of theequator. The appearance of asymmetry (nonuniform convective activity) has a positive feed-464

Journalof theMeteorologicalback effect. The equatorial area is separated into a
region where convective activity is intense,
and a region where it is suppressed becauseof the downdraft caused by the convectively
active region. The intensity of the downdraft
is comparable to that of the updraft of convectively active region because the circulationis two dimensional, and hence, it is consideredlarge enough to suppress the activity of theother region. Thus, the wavenumber one modulation of cumulus activity appears to be related
to the equatorial circumference and the u'field has the wavenumber one structure because
the u'-field corresponds to the zonal averageof the vertical motion field.
Following the assumption that the wavenumber one modulation is related to the equatorial circumference, the time scale of about
a 10-20 days for the build up of the 30 day
oscillation (Fig. 3) can be understood in thefollowing way. If we adopt c=40m/s
as asignal velocity to carry the effect of enhanced
convection from one place to other place (Fig.
7), it takes about 10 days for the signal to
travel around the equatorial circumference.
The time for building up the 30 day oscillation
is given by the time needed to establish thedowndraft region on the opposite side of theequator from the convectively active region.
5.

Conclusion

A GCM simulation of an atmosphere on aplanet covered with zonally symmetric SST("aqua planet") shows that an equatorial circulation system with the character of the socalled 30-60 day oscillation appears spontaneously. The characteristics of the "30 day
oscillation" simulated in the model are summarized as follows:(1) Small scale (<3000km) structures which
are regarded as the super clusters (Fig. 1) appear
in the precipitation patterns. They propagate
coherently eastward at a phase speed of 15m/s.
(2) The wavenumber one (largest longitudinal scale) structure dominates the u'-field andpropagates eastward with a phase speed of
15m/s. In addition, the wavenumber one structure appear in the precipitation field as a modulation of the super clusters.
(3) The vertical structure at the equator isSocietyof Japan

Vol.

64,

No. 4

baroclinic and extends over the whole troposphere.
(4) The latitudinal extent is about theequatorial radius of deformation.
(5) The structure is composed of both
equatorial free Kelvin and Rossby wave modes.
The northward propagation of the 30-60 day
oscillation is not recognized.
The dry experiment verifies that moist processes are essential for maintaining the 30 day
oscillation, and hence it is regarded as a waveCISK mode of its non-linear version. It has adouble structure: the existence of small scale(<3000km)
structures (super clusters) andthe largest scale (wavenumber one) structure.
The appearance of super clusters should be
regarded as a new type solution (KR mode)of the equatorial wave-CISK problem, because
the slow phase speed (items (1), (2)) and thestrong mode coupling (item (5)) are not expectedfrom the linear wave-CISK theory presented sofar.
The modulation due to the wavenumber
one can be understood as the result of the twodimensional nature of the circulation along
the equatorial circumference. The downdraft
which compensates the updraft must be locatedopposite the convectively active region along theequator, and suppress the precipitation there.
The model also shows that a double ITCZ
structure appears even when SST minimum does
not exist along the equator. The eastward motionof super clusters associated with the 30 day
oscillation can be seen with the equatorial belt
bounded by the north and south ITCZs.
The 30 day oscillation can be described asa symmetry breaking of the zonally symmetricHadley circulation. A circulation with zonallysymmetric upward motion at the equator anddownward motion over the subtropics is notrealized, even if the boundary condition iszonally symmetric. The cumulus activity at theequator forms super clusters which move coherently to the east. The 30 day oscillation is
intrinsically associated with the equatorial circulation of its idealistic form. The simulation
presented here suggests that the 30-60 day
oscillation in the actual atmosphere is the resultof this intrinsic nature of the equatorial circulation, although it is modified by the effect ofAugust

1986

Y.-Y.

Hayashiandnon-zonal distribution of SST and the land-sea
contrast of the real surface.
Recently, the 30-60 day oscillation is reported to appear in GCMs with realistic surface
boundary conditions (Chiba, 1986; Y. Hayashi
and Golder, 1986). The predominant periods
simulated in these models differ from one modelto another, although they are within the rangeof 30 to 60 days. An interesting problem placedby these model studies is to search for the conditions additional to our aqua planet model
which causes the change in period and structure.
Dependency of model oscillations on cumulus
parameterization schemes is also a matter of consideration. Through the study of the wave-CISK
problem, Lau and Peng (1986) shows the existence of 30 day oscillation by using a simple
CISK feedback model. But they do not have anumber of super clusters: only wavenumber one
structure appears.
Further study is now being made to confirm
the discussion presented in section 4 and toreveal the effects of asymmetric surface boundary conditions.

A. Sumi465

Ppressure* Angular
frequency of earth's rotationRradius of the earth
2*/R
**
N
buoyancy (Brunt-Vaisala)frequencycphase speed of gravity waves
c0 the phase speed of the "30 day oscillation"(=15m/s)( ) longitudinal mean of ( )( )'*( )-( )References
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Y.-Y. Hayashi

and A. Sumi

467

『水 惑 星 』 モ デ ル で シ ミ ュ レ ー ト され た30‑40日
林

祥 介 ・住周期振動

明正

東 京大学 理学 部地 球物理 学 教室
積 雲 対 流 活 動 の 集 団 的 運 動(い わ ゆ るwave‑CISK)に起 因 す る長 周 期(30‑40日
程 度)変 動 の 可 能 性
を議 論 す る た め に,南 北 対 称 ・東 西 一 様 な る 仮 想 的 海 洋 に お お わ れ た『 水 惑 星 』 上 で の 大 気 の ふ る ま いを 大 気 大 循 環 モ デ ル を 用 い た 数 値 実 験 に よ り調 べ た 。
90日 間 の 積 分 結 果 は 対 流 活 動 の 集 団 的 運 動 が 自発 的 に 出 現 す る こ と を 示 した 。 そ れ に と も な う東 西 循
環 は,現 実 大 気 で 知 られ て い る30‑60日
周 期 振 動 に 類 似 した 特 徴 を 持 つ 。 こ の 循 環(『30日 周 期 振 動 』)は,
赤 道 変 形 半 径 に 特 徴 づ け ら れ る 『ス ー パ ー ク ラ ス タ ー 』 とそ の 変 調 と して 現 れ る 『波 数1』
空 間 的 二 重 構 造 を持 っ て お り,全 体 と して ゆ っ く り(15m/s)東向きに 伝 わ る。

とか ら な る

モ デ ル は ま た,二 重 赤 道 収 束 帯 を も再 現 し た 。 赤 道 上 に 低 海 水 面 温 度 域 が 存 在 し な く と も 赤 道 収 束 帯
は 赤 道 を ま た い で 南 北 二 本 存 在 す る 。 こ の 両 収 束 帯 に か こ ま れ た 領 域 で は 積 雲 活動 は,ス ー パ ー ク ラ ス
タ ー と し て 組 織 さ れ る が,一方 そ の 外 側 で は 熱帯 低 気 圧(台風)とし て 組 織 され る。

湿 潤 過 程 の 除 去 は30日 周 期 振 動 の 赤 道 ケ ル ビ ン 波 ・ロ ス ビー 波 へ の 崩 壊 を も た ら した 。 こ の こ とは30
日周 期 振 動 の 構 造 が,赤 道 波 間 の 強 い モ ー ド結 合 に よ り維 持 さ れ て い る こ と を示 す 。 対 流 活 動 の 集 団 的
運 動 の こ れ ら の 特 徴(遅 い 位 相 速 度 ・モ ー ド結 合 ・空 間 的 二 重 構 造)は こ れ ま で の 線 形wave‑CISK理論 の ケ ル ビ ン 波 モ ー ドで は 説 明 で き な い 。 『30日周 期 振 動 』 は 赤 道wave‑CISK問
題 に対 す る新種 の解とみ な す こ と が で き よ う 。