Clim Dyn
DOI 10.1007/s00382-011-1159-1

Bimodal representation of the tropical intraseasonal oscillation
Kazuyoshi Kikuchi • Bin Wang • Yoshiyuki Kajikawa

Received: 6 January 2011 / Accepted: 26 July 2011
Ó Springer-Verlag 2011

Abstract The tropical intraseasonal oscillation (ISO)shows distinct variability centers and propagation patterns
between boreal winter and summer. To accurately represent the state of the ISO at any particular time of a year, abimodal ISO index was developed. It consists of MaddenJulian Oscillation (MJO) mode with predominant eastward propagation along the equator and Boreal Summer
ISO (BSISO) mode with prominent northward propagation and large variability in off-equatorial monsoon troughregions. The spatial–temporal patterns of the MJO and
BSISO modes are identified with the extended empiricalorthogonal function analysis of 31 years (1979–2009)
OLR data for the December–February and June–August
period, respectively. The dominant mode of the ISO at
any given time can be judged by the proportions of the
OLR anomalies projected onto the two modes. The
bimodal ISO index provides objective and quantitative
measures on the annual and interannual variations of the

predominant ISO modes. It is shown that from December
to April the MJO mode dominates while from June to
October the BSISO mode dominates. May and November
are transitional months when the predominant modechanges from one to the other. It is also shown that thefractional variance reconstructed based on the bimodal
index is significantly higher than the counterpart reconstructed based on the Wheeler and Hendon’s index. The
bimodal ISO index provides a reliable real time monitoring skill, too. The method and results provide criticalinformation in assessing models’ performance to reproduce the ISO and developing further research on predictability of the ISO and are also useful for a variety ofscientific and practical purposes.
Keywords
Index

Tropical intraseasonal oscillation  MJO 

1 Introduction
School of Ocean and Earth Science and Technology Contribution
Number 8213 and International Pacific Research Center Contribution
Number 798.
K. Kikuchi (&)
International Pacific Research Center, School of Ocean andEarth Science and Technology, University of Hawaii, 1680 East
West Road, POST Bldg. 401, Manoa Honolulu, HI 96822, USAe-mail: kazuyosh@hawaii.edu
B. Wang
Department of Meteorology and International Pacific ResearchCenter, School of Ocean and Earth Science and Technology,
University of Hawaii, Manoa Honolulu, HI 96822, USA
Y. Kajikawa
Hydrospheric Atmospheric Research Center, Nagoya University,
Nagoya, Japan

Tropical intraseasonal oscillation (ISO) or referred to as the
Madden-Julian oscillation (MJO) in honor of the discoverers (Madden and Julian 1971), characterized by the periodof 30–90 (60) days, plays a fundamental role in regulating
weather and affecting climate both in the tropics and extra
tropics. A remarkable feature, which makes the ISO so
influential in part, is its potential interactions with a varietyof spatial and temporal scales such as diurnal cycle (Chenand Houze 1997; Ichikawa and Yasunari 2008), tropical
cyclones (Maloney and Hartmann 2000a, b; Molinari andVollaro 2000), El Niño (Kessler et al. 1995; Takayabu et al.
1999), annular modes (Miller et al. 2003), and monsoon
systems of Asia (Yasunari 1979; Kajikawa and Yasunari2005), Australia (Hendon and Liebmann 1990; McBride123

K. Kikuchi et al.: Bimodal representation

et al. 1995), and North America (Higgins and Shi 2001;
Lorenz and Hartmann 2006; Moon et al. 2010).
The fundamental feature of the ISO may be best illustrated in a longitude-height cross sections along the equator
as in the schematic summary in their pioneering work by
Madden and Julian (1972): A planetary scale convective
anomaly consisting of mesoscale convective systems coupled with large-scale circulation disturbance with thegravest baroclinic structure moves eastward at about
5 ms-1 in the eastern hemisphere. In the western hemisphere, on the other hand, upper-level circulation disturbance rarely coupled with convection moves eastward at a
speed of about 15–20 ms-1. The circulation disturbance isassociated with equatorial Kelvin and Rossby waves (Ruiand Wang 1990; Hendon and Salby 1994). More thoroughreviews can be found in some literatures (e.g., Madden andJulian 1994; Lau and Waliser 2005; Zhang 2005).
Such a simple description of the ISO which moves
exclusively eastward, although is often used to describe themajor feature of the ISO, may not necessarily be appropriate to best document the crucial aspect of the ISO
throughout the year. There is observational evidence thatthe properties of the ISO such as activity centers andpropagation patterns are strongly regulated by the annual
cycle (Madden 1986; Salby and Hendon 1994; Webster
et al. 1998; Zhang and Dong 2004). An example is given in
Fig. 1, which shows annual variation of the ISO propagation with emphasis on the eastern hemisphere where convective systems associated with the ISO rather appear
clearly. There are two distinct propagation tendencies:
during boreal winter the organized convection associatedwith the ISO shows predominantly eastward propagation
along the equator with little poleward propagation, whereas
during boreal summer it shows prominent northward
propagation over the northern Indian Ocean (and western
North Pacific, not shown) (Yasunari 1979; Knutson andWeickmann 1987; Wang and Rui 1990) with weakened
eastward propagation. The difference in propagation
characteristic can account for the difference in the ISO
activity centers (Kemball-Cook and Wang 2001; Zhang
2005). In addition, accompanied large-scale circulationshows rather symmetric about the equator during boreal
winter, whereas it shows asymmetric during boreal summer. Thus, the simplest model with only zonal propagation
component considered appears to be more relevant todocument the ISO behavior during boreal winter, and amore complex model with meridional propagation component as well as zonal propagation component consideredis more relevant to document the ISO behavior during
boreal summer.
Consideration of such annual variation of the ISO is of
critical importance for especially studies on interactions of
the ISO with a widespread variety of spatial and temporal

123

TRMM 3B42 2001

(a)

(b)

mm
Fig. 1 Daily precipitation (tropical rainfall measuring mission product 3B42) associated with the ISO for the year 2001. a Latitude-timeplot over the eastern Indian Ocean averaged between 80 and 100°E
and (b) longitude-time plot along the equator between 7.5°S and
7.5°N. Each red closed circles indicates major convection associatedwith significant ISO events, determined by our analysis to be
introduced in Sect. 4 (see also Fig. 4), sitting around the central
Indian Ocean (90°E, 0°). Solid and dashed lines show reference phasespeed corresponding to (a) northward propagation at approximately
1–2 ms-1 and (b) eastward propagation at approximately 6 ms-1.
The solid lines are intended to represent rather apparent convection
existsscales. A meticulous treatment of the ISO is the basis foranalyses of those studies, because different structures of the
ISO are expected to have different roles in weather andclimate variations. In fact, for instance, Kikuchi and Wang(2010) showed that the winter type ISO and the summer
type ISO have different manners in which tropical cyclogenesis are affected over the northern Indian Ocean.
The purpose of this study is to develop an ISO index
which reflects such annual variation of the ISO. The index,
referred to as the bimodal ISO index, relies on two distinct
ISO modes, which capture the aforementioned two distinct
propagation features for the two solstice seasons. With thismethod, the state of the ISO at any particular time can befaithfully diagnosed in terms of the two ISO modes. As aresult, any ISO event can be classified into either ISO
mode, which is critical information for studies of interactions of the ISO with weather and climate variations on awide range of timescales.
A brief review of methods used to extract ISO signals ispresented in Sect. 2. Section 3 describes the dataset andintraseasonal time-filter used. The bimodal ISO index is
introduced in Sect. 4, which also includes some sensitivity
tests and a comparison with the Wheeler and Hendon(2004) index. In Sect. 5, how the ISO can be represented
with the bimodal ISO index is examined. An application of
the index to real time monitoring is discussed in Sect. 6.
Section 7 summarizes this study.

K. Kikuchi et al.: Bimodal representation

2 A review of methods used to extract ISO signals
Before introducing the bimodal ISO index, it is worth
reviewing methods that have been used to extract ISO
signals, although majority of these methods were notintended to construct an ISO index. A variety of methods
have been used with various degrees of complexity. Perhaps the simplest method is to focus on an intraseasonal
fluctuation of a single variable at a particular location, anddocument the ISO behavior based on that variability (e.g.,
Julian and Madden 1981; Hendon and Salby 1994), while
the most meticulous and comprehensive method is a
tracking method (Wang and Rui 1990; Jones et al. 2004) as
it is carefully designed to depict various types of convective behaviors associated with the ISO.
Between those extremes, Eigen techniques have been
widely used (Table 1). Eigen techniques provide a convenient method for the description of the spatial and temporalvariability associated with the ISO in terms of empiricallyderived functions (spatial patterns in general). Since theISO is characterized by organized convection coupled withlarge-scale circulation with the gravest baroclinic structure,such variables as convection, the upper- and lower-tropospheric circulation are relevant to isolating variations
associated with the ISO. In fact, composite life cycles of
the ISO based on different variables (and also different
methods) produce consistent structures in the ISO behavior
for any particular season (references are in Table 1).
Of particular importance is the study by Wheeler andHendon (2004) (refer to as WH04 hereafter), pioneering
work introducing all-season ISO index for real time monitoring and it has become the most popular ISO index. The
Table 1 Summary of Eigen techniques used to extract ISO signals inprevious studies
Method

OLR

u850

EOF

LC88

MH98

WH04*

WH04*

EEOF

LC85, 86

u200

WH04*

Xupperwupper

KW87

S99

vSX90
KK99

W03, 04
CsEOF

AS05

SVD

ZH97*
H96*

ZH97*
H96*

AS05 Annamalai and Sperber (2005), H96 Hsu (1996), KK99 Kayano
and Kousky (1999), KW87 Knutson and Weickmann (1987), LC85
Lau and Chan (1985), LC86 Lau and Chan (1986), LC88 Lau andChan (1988), MH98 Maloney and Hartmann (1998), S99 Slingo et al.
(1999), vSX90 von Storch and Xu (1990), W03 Waliser et al. (2003a,b), W04 Waliser et al. (2004), WH04 Wheeler and Hendon (2004),
ZH97 Zhang and Hendon (1997), EEOF extended EOF, CsEOF
cyclostationary EOF, SVD singular value decomposition
The asterisks means multivariables are used in the corresponding
eigen techniqueuniqueness of their method is to use the combined variables(OLR and zonal winds at 850 and 200 hPa) meridionallyaveraged between 15°S and 15°N in order primarily toremove higher-frequency variability by focusing on thecoherent structure of convection and large-scale circulations associated with the ISO throughout the year without
use of ordinary time filters. More detailed procedure forreal time monitoring is discussed in Sect. 6.
Another emphasis to be put is on the extended EOF(EEOF) analysis (Weare and Nasstrom 1982). The EEOF
analysis has a unique feature that it focuses on a sequential
spatial-temporal evolution by extension of the EOF analysis to a segment of consecutive times, and thereby it may
be more appropriate to document a phenomenon that
propagates. In other words, it can be thought to have thenature of a tracking method. With appropriate series ofsuccessive time points included, a pair of the first two
EEOFs can represent a half cycle of the ISO (Lau and Chan
1985, 1986), whereas, with longer series of time points
included the first EEOF alone can represent a whole cycle(Kayano and Kousky 1999) or more cycles (Waliser et al.
2003a, 2004) of the ISO.

3 Data and intraseasonal time filter
Given the data availability, our analysis is based on a 31 year
dataset from 1979 to 2009 except for real-time monitoring to
be discussed in Sect. 6. As mentioned in Sect. 2, referring to
one or some of such variables as convection, the upper- andlower-tropospheric circulation is reasonable to isolate variations associated with the ISO. Among them the OLR data, agood proxy for organized convection in the tropics, havebeen widely used. Since the planetary scale convective
anomaly is among the major characteristics of the ISO and ofprimary interest, we also used daily OLR data with 2.5°
horizontal resolution (Liebmann and Smith 1996) to identify
typical ISO modes and significant ISO events. Daily mean
horizontal winds at 850 hPa of the Modern Era Retrospective-analysis for Research and Applications (MERRA)
product (inst6_3d_ana_Np) developed by the Global Modeling and Assimilation Office (GMAO) at the NASA Goddard Space Flight Center (Bosilovich et al. 2006) were used
to document large-scale circulations associated with the ISO
convection. The dataset is among the state-of-the-art
reanalysis, which was produced in an attempt to reduce
biases stemming from observing system changes occurred
over the past three decades, notably introduction of newsatellites. The data with 2.5° horizontal resolution, which
was created by reducing the original resolution of
2/3° 9 0.5° in longitude-latitude, was used for our analysis.
To extract variations on intraseasonal timescale, Lanczos band-pass filter (Duchon 1979) with cut-off periods 25

123

K. Kikuchi et al.: Bimodal representation

and 90 days and 139 weights is applied to the daily OLR
data and the MERRA reanalysis. This filter is referred to as
the intraseasonal time-filter hereafter. Seventy points fromeither ends of the record were discarded because the fullconvolution cannot be performed. Because the ISO during
boreal summer tends to show shorter period of near
30 days (Wang et al. 2006), the bandwidth of the band-passfilter was set somewhat wider than usual (25–90 day
instead of 30–90 day). The results to be shown later are
little affected no matter which bandwidth is selected.

4 Introduction to the bimodal ISO index
The main goal of this study is to develop an ISO index thatfaithfully represents the state of the ISO over the course ofa year by taking the annual variations of the ISO behavior
into account. The horizontal distribution of the ISO variance suggests that northward propagation predominates
over the eastward propagation during boreal summer (seeFig. 9 in Zhang 2005). As such, in addition to the eastward
propagation, capturing the northward propagation is a
desirable attribute of an ideal ISO index in some seasons.
With the ability to document a detailed spatial-temporal
evolution, the EEOF analysis is probably most suitable for
capturing such detailed propagation features. Given theobservational evidence that the ISO shows contrasting
behaviors between the two solstice seasons, we construct
an index based on two typical ISO modes predominant foreach solstice season in order that the state of the ISO aremeasured in terms of the properties not only during boreal
winter but also during boreal winter.
4.1 The bimodal ISO index: the MJO modeand the BSISO modeTwo distinct typical ISO modes, predominant during boreal
winter (referred to as the MJO mode in honor of the discoverers) and during boreal summer (referred to as the
BSISO mode), are defined. To better describe the state of
the ISO, we took an analogous setting for the EEOF
analysis as Lau and Chan (1985, 1986); The EEOF analysis
with -10 and -5 day lags was applied to the intraseasonal
time-filtered OLR data in the entire tropics between 30°S
and 30°N. The time lag was chosen in this way because of
consideration of its application to real time monitoring. To
derive the MJO (BSISO) mode the data period from
December to February (June–August) was selected.
As expected from the previous studies, a pair of the firsttwo EEOFs represents a half cycle of the ISO for bothmodes (Fig. 2). The MJO mode shows a predominant
eastward propagation along the equator that is in accordance with the classical view of the MJO (Madden and123

Julian 1972). The BSISO mode shows a prominent northward propagation over the northern Indian Ocean withweaker eastward propagation along the equator, which
eventually makes an elongated convective band tilting
from northwest to southeast covering a wide range from the
Arabian Sea to the western Pacific. Another prominent
northwestward propagation is seen over the western North
Pacific. These rather complicated features of the BSISO
mode are in good agreement with a recent composite study
using TRMM satellite precipitation data (Wang et al.
2006). Evidently, the lifecycle of the MJO mode and the
BSISO mode have distinctive characteristics.
The bimodal ISO index is based on these two ISO
modes. The EEOF coefficients (principal components, PCs
hereafter) of the MJO mode and the BSISO mode at any
given time can be obtained by projecting the intraseasonal
time-filtered OLR fields onto each mode. The strength andthe phase of the MJO mode and the BSISO mode can be
described by a combination of the first two PCs for eachmode. This is the fundamental step for constructing thebimodal ISO index.
How to utilize the bimodal ISO index, however, might
depend on analysis. In the following, we provide an
example, which would be one of the most straightforward
ways. For most practical applications, one may want to
identify significant ISO events (Step 1). For that purpose, it
is usual to use the normalized amplitude (Amode ¼
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2
2
þ PC2;mode), where PC  is the normalized PC
PC1;modeby one standard deviation during the period the EEOF
analysis was performed and the subscript ‘mode’ represents
either the MJO mode or BSISO mode. A criterion thatAmode  1 is regarded as a significant event is perhaps
the most popular (e.g., Wheeler and Hendon 2004). As aresult, significant ISO events can be identified in terms of
the following ISO modes: (1) the MJO mode, (2) the
BSISO mode, and (3) both the MJO mode and the BSISO
mode.
Although, the information listed in step 1 is useful for
certain analyses, in many cases it is more practical tofurther determine the predominant mode, i.e. which mode
dominates the ISO event (Step 2). This can be accomplished by assuming that the predominant ISO mode at agiven time accounts for a larger amount of the total variance. The reconstructed OLR anomalies by each mode attime t are given by
OLRmode ðtÞ ¼ EEOF1;mode  PC1;mode ðtÞ þ EEOF2;mode PC2;mode ðtÞ

ð1Þ

where OLRðtÞ includes spatial patterns at -10 and -5 days
as well as 0 day. With the aid of the orthogonality of the
EEOF, the norm (variance) of the reconstructed pattern ofeach mode is given by

K. Kikuchi et al.: Bimodal representation

EEOF1 (10%)(a) MJOEEOF2 (9.4%)

EEOF2 (8.3%)(b) BSISO

EEOF1 (9.9%)

W/m2

Fig. 2 Spatial-temporal pattern of OLR anomaly associated with theintraseasonal oscillation during (a) boreal winter (DJF, referred to as
MJO mode) and (b) boreal summer (JJA, referred to as BSISO mode)by means of the extended EOF (EEOF) analysis. The EEOF analysis
with three different time steps with 5 day time increment was applied
to long-term OLR anomaly (1979–2009) with 25–90 day bandpass
filter applied. The numbers in the brackets shows the relative

kOLRmode ðtÞk ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2
2
PC1;modeðtÞ þ PC2;modeðtÞ

contribution of each mode to total variance. OLR values are
multiplied by one standard deviation of the corresponding principal
components during the period each EEOF analysis was performed.
Note that the EEOFs are displayed in a way that the organized
convection associated with the ISO starts to appear in the Indian
Ocean at day 0 in the left panel for convenience

*
*
AMJO
≥ 1, ABSISO<1

ð2Þ

A comparison of (2) between the MJO mode and the
BSISO mode yields the predominant mode at time t. The
procedure employed in this study for identifying significant
ISO events in terms of the MJO mode and the BSISO modeis summarized in Fig. 3.
To see how the procedure works, Fig. 4 shows a scatterplot of the MJO amplitude versus the BSISO amplitude
represented by (2). Each of the reference solid lines provides a virtually criterion for significant ISO events interms of either the MJO mode or the BSISO mode; thenormalized amplitude, A , instead of the unnormalized
amplitude is used to judge the state of the ISO for practicalapplication. Note that the difference in the reference
amplitude between the two modes reflects the seasonalvariations in the ISO strength. Of particular importance isthat there are two clusters of events that can be separated
very well in the scatter plot. Most of the significant ISO
events are readily assigned to either the MJO mode (regionI) or the BSISO mode (region III). Even in the case whenboth the MJO mode and the BSISO mode have substantial

Step 1
Bimodal
ISO
index

*
MJO

A

A*
*
MJO

A

*
BSISO

,A

<1

*
BSISO

,A

≥1

*
*
AMJO
> ABSISO

Significant
MJO

A
*
*
ABSISO> AMJO

Step 2
Insignificant A* ≥ 1, A* < 1
BSISO
MJO
ISO

Significant
BSISO

Fig. 3 Flowchart summarizes the procedure for identifying significant ISO events in terms of the MJO mode and the BSISO mode

amplitude (region II), the situation in which the two modes
have almost the same amplitude rarely occurs, and hence
the prevailing mode remains to be easily determined. One
peculiar situation occurs when a significant BSISO event
regarded as an insignificant MJO event has larger variancein terms of the MJO mode than in terms of the BSISO
mode (region IV). This situation, however, is quite rare andthus how to treat it little affects the statistical analysis
results. In summary, in the bimodal ISO index the state of
the ISO can be expressed in terms of the MJO mode andthe BSISO mode; which mode better describes at any
particular time can be reasonably identified.

123

K. Kikuchi et al.: Bimodal representation

4.2 Comparison with Wheeler and Hendon’s index

I||OLRMJO||

II

IV
III

||OLRBSISO||
Fig. 4 Scatter plot of ISO amplitude in terms of the BSISO mode (xaxis) and the MJO mode (y axis) for the period 1979–2009. Solid lines
parallel to the x and y axes represent one standard deviation of eachpﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ISO mode ( PC12 þ PC22 ) during the period each EEOF analysis was
performed. Dashed line represents the situation when both the MJO
mode and the BSISO mode have the same variance. According to thelater discussion about Fig. 8, three seasons are in different colors(June–October in red, December–April in blue, otherwise in gray)

A comparison of the bimodal ISO index with WH04 index
is discussed in terms of an example shown in Fig. 5. The
amplitude of the WH04 index for this given year does notseem to vary significantly except in the beginning of theyear when the amplitude is slightly larger than the rest of
the year. The MJO mode and the BSISO mode, on the other
hand, have substantial seasonal variations in amplitude.
Naturally, the amplitude of the MJO (BSISO) mode islarger during boreal winter (summer). The time series ofthe MJO mode and the BSISO mode are smoother due tothe absence of higher-frequency component than that of theWH04 counterpart.
As shown in Table 2, the correlations of the MJO modeand the BSISO mode with the WH04 index are statisticallysignificant at the 99% level for the entire period. Of note isthat the correlations of the WH04 index with both the MJO
mode and the BSISO mode become larger during boreal
winter. As expected, the WH04 index better represents the
ISO behavior during boreal winter because of the pronounced eastward propagation and large amplitude. Significant but lower correlations during boreal summer may
be a reflection that the ISO amplitude is misrepresented by
the eastward propagating component alone because of theprominent northward propagation during that season.
Again, the bimodal ISO index gives more detailed information on which type of the ISO mode is predominant at aparticular time.
Then which ISO index better represents variations
associated with the ISO? In order to answer this question,
composite life cycles were constructed based on thebimodal ISO index and the WH04 index for the two solstice seasons. Figure 6 shows fractional variance explainedby each composite. The patterns based on the bimodal ISO
index and based on the WH04 index are in good agreement
for both seasons. However, the amplitude based on thebimodal ISO index outperforms that based on the WH04
index by at least 50% in almost all regions where fractionalvariance has some value (C0.1). This difference indicatesthat the ISO samples chosen based on the bimodal index
are more standardized. This characteristic is anotheradvantage of the bimodal ISO index.

5 Characteristics of the ISO behaviors in termsof the bimodal ISO index
5.1 Composite life cycle
Fig. 5 A comparison of the ISO index between the WH04 (upper),the MJO (middle) and the BSISO (lower) for the year 2001. Note thateach PC is normalized by one standard deviation of the corresponding
PCs during the period each EEOF analysis was performed to obtain
the EEOFs. Significant ISO events are shaded in the background

123

Although, many previous studies have already documented
composite life cycles of the ISO in terms of convection
coupled with large-scale circulations during boreal winterK. Kikuchi et al.: Bimodal representation
Table 2 Maximum lag correlations and the corresponding lags (in brackets) of the first two PCs of the MJO mode and the BSISO mode withthose of the WH04 index
MJO (PC1 and PC2)

BSISO (PC2 and PC1)

All

DJF

JJA

All

DJF

JJA

-RMM1

0.63 (0)0.74 (0)0.44 (-3)

0.60 (-1)

0.66 (-1)

0.61 (-3)-RMM2

0.70 (0)0.77 (-1)

0.59 (0)0.64 (0)0.71 (1)0.62 (0)Fig. 6 Fractional variance of ISO composites in terms of OLR basedon the bimodal ISO index (upper panels) and WH04 index (lower
panels) during boreal winter (left panels) and summer (right panels)
for the period 1979–2009. The fractional variance is defined as theratio of the variance of the ISO composite which undergoes throughits life cycle to the total variance of the intraseasonal (25–90 day)fluctuation. The composite lifecycle with WH04 index was constructed in the same manner as WH04. The lifecycle with the bimodal
ISO index was constructed in a similar way, which was descried in
Sect. 4.1 except that, for a fair comparison, the criterion for
determining significant ISO events based on A was adjusted so thatthe total number of days (samples) used to construct the composite are
the same between the two indices (1,726 for DJF and 1,579 for JJA)

(corresponding to the MJO mode) (e.g., Hendon and Salby
1994; Maloney and Hartmann 1998) and boreal summer(corresponding to the BSISO mode) (e.g., Kemball-Cookand Wang 2001; Wang et al. 2006), it is useful to show thecomposite life cycles based on the bimodal ISO index toconfirm the results and facilitate the following discussions.
Note again in this composite the ISO events are not distinguished by the seasons they occur. The use of the
MERRA data updates our knowledge of large-scale circulations associated with the ISO. Composite life cycles ofthe MJO mode and the BSISO mode were constructedbased on a phase space consisting of the first two PCs(Fig. 7). Significant MJO and BSISO events were identified in the way described in Sect. 4.1.

The composite life cycles of the MJO mode and the
BSISO mode (Fig. 8) are in good agreement with those inprevious studies. It is clear that the MJO mode and the
BSISO mode have different propagation tendencies, andthus life cycles. A convective anomaly associated with the
MJO mode starts to appear over Africa-western Indian
Ocean at phase 1. Then it continues to move eastward to
the date line (phase 8) all trapped near and along theequator with coupled Kelvin-Rossby wave response nearly
symmetric about the equator. Eastward propagation of theconvective anomaly in the western hemisphere is notnecessarily apparent in this composite, while a circumglobal signal in convection may appear in a composite withmore emphasis on the ISO behavior in the western hemisphere (Kikuchi and Takayabu 2003).
A convective anomaly associated with the BSISO mode
starts to appear in the equatorial central Indian Ocean atphase 1. Then northward propagation of the convection is
pronounced in the Indian Ocean with a weak eastward
propagation along the equator (phase 2–4), which makes an
elongated northwest–southeast band of convection. The
southeastern part of the convective anomaly re-intensifies
over the South China Sea and the Philippine Sea at phase 5.
Northward propagation appears to dominate over the Indian
Ocean and the western Pacific with a salient feature of OLR
seesaw between the equatorial Indian Ocean and the Philippine Sea. The accompanied circulation is characterized byasymmetric coupled Kelvin-Rossby wave response withstronger amplitude in the northern hemisphere. In addition,a weak eastward propagation of convection can be seenalong the ITCZ traveling the North Pacific.
5.2 Annual variation
How the annual variation of the ISO is represented by thebimodal ISO index is discussed. The discussion includes avalidity check of the method as well as scientific findings.
Specific questions to be considered are the following: (1)Does the bimodal ISO index choose ISO events fairly
throughout the year? (2) Does the MJO (BSISO) mode
never predominate during boreal summer (winter)? (3)When does the predominant ISO mode tend to shift one
regime to the other? Figure 9 shows the average numbersof significant ISO events assigned to the MJO mode and123

K. Kikuchi et al.: Bimodal representation(a) MJO(b) BSISO
western North Pacificphase 1phase 4phase 2

Indiia& Mariitime Contiinent

phase 5eaasternn Nortth Paccificquatorrial Inndian Oceaan& eqphase 8C1PC

phase 6phase 7

M
ContinMaritiime C
nent

P
cen
ntral Pacificc& Afriica-w
westenn Indiaan Occean

Western PacificPC
C2Fig. 7 Phase space
representation of the state of(a) the MJO mode (PC2, PC1)and (b) the BSISO mode (PC1,
PC2) for the period 1979–2009.
The state of the ISO categorized
as eight phases are used for thefollowing discussion. The
approximate positions of the
major convective area at somephases are also denoted. Notethat each PC is normalized by
one standard deviation of thecorresponding PCs during theperiod each EEOF analysis was
performed to obtain the EEOFs

phase 3eastern Indian Ocean

Bay
Bengall
B off B

PC1

PC2

Fig. 8 Composite life cycle of(a) the MJO mode and (b) the
BSISO mode. OLR anomalies(shades and contours of
5 Wm-2) and 850 hPa
horizontal winds (vectors).
Significant values at the 99%
level according to the t test with
degree of freedom being one
sixth of the number ofcomposite samples (taking into
account of persistence) are only
drawn. The number ofcomposite samples are denotedin the upper right corner of eachpanel(a) MJO composite(b) BSISO composite

W/m2

the BSISO mode, which were used to construct the composite (Fig. 8), as a function of calendar month. The total
number of significant ISO days (MJO plus BSISO) varies
little throughout the year. A clear transition of the annual
cycle of the ISO type is found: from December to Aprilalmost all ISO events are assigned to the MJO mode, whilefrom June to October almost all ISO events are assigned to
the BSISO mode. May and November appear to be123

transitional months. Of course, the feature addressed above
is consistent with Fig. 4.

6 Real time monitoring
Since the ISO has considerable effect on other phenomena
such as tropical cyclogenesis and active-break cycles of

K. Kikuchi et al.: Bimodal representation

mber of days
Aveeragee num
da pper mmonthhSignificant ISO events
MJO

BSISO

month

Fig. 9 Average number of days during which significant ISO ispresent in a month. The days are normalized such that they are theratio of the number of days classified as the significant MJO mode
(upper) or significant BSISO mode (lower) to the available number ofdays during 1979–2009 times the number of days in the month ofcommon year

monsoon systems, monitoring the state of the real-time ISO
is of great practical importance. In real time monitoring,extraction of variability associated with the ISO is the
crucial and challenging process to accomplish; ordinary
time filters are impractical because they require future
values. Alternatively, in essence, processes are required toremove higher- and lower-frequency variability. In thepioneering work, WH04 used multivariables (OLR andzonal winds at 200 and 850 hPa) meridionally averaged
over 15°S–15°N to remove higher-frequency variability;
fewer higher-frequency variations have a structure similar
to the ISO in the averaged multivariables. In addition, theysubtracted the climatological mean and annual cycle toremove the influence of the seasonal cycle, interannual
variability linearly correlated with a measure of El Niño in
SST to remove the influence of El Niño, and a 120 day
mean of the previous 120 days to remove any further
aspects of interannual variability and decadal variability
and trend.
The bimodal ISO index, on the other hand, was notintended to be developed for real time monitoring, however, we found that it can be easily applied for that purpose.
The use of the EEOF analysis with the current setting
provides a strong constraint on the spatial-temporal evolution of organized convection which is unique to the ISO
and thereby is little shared with other phenomena on
shorter and longer timescales such as El Niño. In the end,
the OLR anomaly field used for real time monitoring canbe obtained by somewhat simpler processes as follows:
subtraction of climatological mean and three harmonics ofthe climatological annual cycle based on the period ofrecord 1979–2009, and a 40 day mean of the previous

40 days to remove lower frequency variability, andapplying 5 day tapered running mean to remove higher
frequency variability. The number of days of the mean
subtraction (40) was determined based on a statisticalanalysis of the relationship between the intraseasonal timefiltered field and the anomaly field for real time monitoring.
Real time PCs of the MJO mode and the BSISO mode canbe obtained by projecting the OLR anomaly fields consisting of 3 time steps with -10, -5, and 0 day lags onto
each mode derived from the intraseasonal time-filteredhistorical data (Sect. 4.1). An example of real time monitoring is shown in Fig. 10.1 It is evident that the real time
monitoring time series of both modes primarily capture
intraseasonal variations and are well correlated withintraseasonal time-filtered (final) products.
That notion is supported by a statistical analysis of
30 year data during 1979–2009 (Table 3). The correlations
between the real time monitoring and the final products aresubstantially high (*0.9), especially in the target season ofeach mode (e.g., DJF for the MJO mode). Thus the bimodal
ISO index provides a reliable objective measure for realtime monitoring. A further careful treatment to remove
higher- and lower-frequency component based on a
sophisticated technique such as the one developed by
Arguez et al. (2008) may even improve the performance inreal time monitoring.

7 Summary
To accurately reflect the annual variation of the tropicalintraseasonal oscillation (ISO), a bimodal ISO index is
proposed, which relies on two modes with distinct life
cycles of the ISO convection. Each mode was identified
with the extended empirical orthogonal function (EEOF)
analysis for 31 years (1979–2009) OLR data. The MJO
mode represents the typical ISO behavior during boreal
winter, when eastward propagation is predominant. The
BSISO (boreal summer ISO) mode represents the typicalISO behavior during boreal summer, when northward
propagation is prominent over the northern Indian Ocean
and western North Pacific. The state of the ISO at any
given time of the year, therefore, can be expressed in termsof both the MJO mode and the BSISO mode, which provides essential information for the bimodal ISO index.
Based on that information, we further demonstrate how
the dominant ISO mode at any given time can be objectively determined. The bimodal ISO index well correlateswith the Wheeler and Hendon’s (2004) all season ISO
index, and in addition succeeds in highlighting the annual
1

Historical and real time bimodal ISO index is available from theauthor at URL: http://www.iprc.soest.hawaii.edu/*kazuyosh.

123

K. Kikuchi et al.: Bimodal representation
Fig. 10 Real time monitoringof ISO in terms of (upper) the
MJO mode and (lower) the
BSISO mode. Green lines
represent time series of real time
PCs at each time and black lines
represent time series of PCs of acomplete bandpass filtered field.
Bandpass filtered fields within
70 days of the end point are notavailable

Table 3 Serial correlations of
the MJO mode and the BSISO
mode between real time
monitoring and bandpass
filtered time series for
1979–2009

MJO
All

DJF

JJA

All

DJF

JJA

PC1

0.89

0.90

0.87

0.91

0.87

0.92

PC2

0.90

0.91

0.86

0.90

0.85

0.92

variation of the ISO characteristics. It is shown that the
MJO (BSISO) mode exists almost exclusively from
December to April (June–October). May and November
are climatological transitional months when the predominant mode changes from one to the other. The ability of thebimodal index to identify the dominant ISO patterns at agiven time can be of great importance on understanding
interaction processes of the ISO with other phenomena. For
instance, a consideration of how and why such seasonaltransition of the dominant mode occurs may lead to a better
understanding of the interaction between the ISO and the
Asian-Australian monsoon systems (e.g., Waliser et al.
2009). It is also suggested that when discussing an interaction process with the ISO in spring and fall, a careful
treatment of the ISO is required.
The use of the EEOF analysis, which relies on thespatial-temporal patterns of the ISO, appears to add someadvantages. The bimodal ISO index tends to chose welldefined ISO events. Consequently, the composite life
cycles of the ISO based on the bimodal ISO index canaccount for more variances than those based on the WH04
index by at least 50% for the two solstice seasons. Also by
the same nature, the bimodal ISO index has reliable performance in real time monitoring.
In conclusion, the bimodal ISO index is useful not
only for further studies on historical data analyses but

123

BSISO

also for practical purposes (e.g., real time monitoring).
The careful treatment of the ISO over the course of ayear provides the basis for assessing models’ reproductionof the ISO and advancing our understanding of predictability of the ISO, because the characteristics of the ISO,
which are critical information, undergo the strong seasonal variations.
Acknowledgments This research was supported by NSF Grant
AGS-1005599 and NOAA Grant NA10OAR4310247. Additional
support was provided by the Japan Agency for Marine-Earth Scienceand Technology (JAMSTEC), by NASA through grant
NNX07AG53G, and by NOAA through grant NA17RJ1230 throughtheir sponsorship of research activities at the IPRC. The interpolated
OLR data are provided by the NOAA/OAR/ESRL PSD. The MERRA
data are provided by the Global Modeling and Assimilation Office(GMAO) and the GES DISC. We also thank two anonymous
reviewers for their constructive comments. Thanks also go to Dr. Nat
Johnson for his editorial assistance and members of MJO working
group, especially Dr. Matthew Wheeler, for invaluable feedback on
the part of real time monitoring.

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