Predictability of the Madden and Julian Oscillation in
JMA One-month Forecasts∗

Takuji Kubota1 , Hitoshi Mukougawa1 , Tatsuya Iwashima1(1: Disaster Prevention Research Institute, Kyoto University )* Applied Climatology, Division of Atmospheric Disaster, Disaster Prevention Research Institute,
Kyoto University, Japan, 611-0011, Gokasyo, Uji-shi, Kyoto, Japan.
e-mail: kubota@dpac.dpri.kyoto-u.ac.jp

Abstract
Predictability of the Madden and Julian Oscillation (MJO) is investigated using Japan Meteorological Agency(JMA) operational 1-month forecasts in Northern Hemisphere winter seasons during 2001-2004. The anomaly
correlations (ACs), which are utilized as a measure of forecast skill, for low-pass filtered velocity potential
on 200 hPa surface (VP200) anomalies in equatorial region are above 0.6 until 6 days lead-time. ACs tend
to become smaller than the averaged values when the MJO is quiescent. On the other hand, ACs of thestrong MJO cases tend to be above the average. In particular, relatively skillful forecasts are found for the
initial conditions with divergent anomalies over the Maritime Continent and convergent anomalies over the
Atlantic. The relationship between the forecast skill and the MJO amplitude defined by the first two principal
components at the initial condition are examined. At the 1-6 days lead-times, the variations of the forecast
skill in the equatorial regions are significantly related to those of the initial MJO amplitude. This relationship,
however, becomes insignificant after 7 days lead-time.
Keyword: Madden and Julian Oscillation, Predictability, Forecast skill.

1. Introduction
The Madden and Julian Oscillation is the dominant variability in intraseasonal time scales over the tropics (e.g.,
Madden and Julian 1994). It is characterized by eastward
propagating tropical convective anomalies and associatedcirculation anomalies, with a period between 30 and 70
days. The onset and activity of the Asian monsoon system are strongly inﬂuenced by the eastward propagationof MJO events (e.g., Yasunari 1979, Lau and Chan 1986).
The MJO is also linked to the onset and the variabilityof the Australian monsoon (e.g., Hendon and Liebmann1990) and the modulation of tropical cyclone development(Nakazawa 1986, Liebmann et al., 1994). Furthermore,some papers reported that the MJO inﬂuences weather
forecasts over the extratropical regions on medium-toextended range (Ferranti et al. 1990, Tsuyuki 1990, Lau
and Chang 1992).
However, it is well known that many atmospheric general circulation models cannot simulate the MJO realistically (e.g., Slingo et al. 1996). Jones et al.(2000) pointed
out the MJO in their model was less intense and withfaster eastward propagation. In dynamical forecasts by
National Centers for Environmental Prediction (NCEP)
medium range forecast (MRF) model, skillful forecasts arelimited to 5 to 7 days lead-time (Chen and Alpert 1990,
Lau and Chang 1992, Hendon et al. 2000, Jones et al.
2000).
Moreover, the relationship between the forecast skill
and the MJO activity has provoked a controversy. Using
the velocity potential from the NCEP MRF model, Joneset al. (2000) indicated a slight increase in the forecast
skill for periods when convective anomalies with the MJO
are intense. On the other hand, Boer (1995) showed little evidence of a dependence of forecast skill on the stateof the MJO in the European Centre for Medium-Range
Weather Forecasts (ECMWF) forecast system. Hendon

et al. (2000) and Lo and Hendon (2000) using the streamfunction from the NCEP MRF model demonstrated thatthe forecast skill was found to be better when the MJO
was quiescent than when it was active at the initial condition.
Purpose of this work is to investigate the predictabilityof the MJO using Japan Meteorological Agency (JMA)
operational 1-month forecasts during boreal winter seasons. In particular, our concern is to examine the relationship between the forecast skill in the equatorial regions and the MJO at the initial condition in terms of thestates and the amplitude.

2. Data and analysis method
Operational 1-month (34 day) forecasts of Japan Meteorological Agency (JMA) were produced every Wednesday and Thursday based upon a JMA operational model(GSM0103) with triangular 106 truncation (T106) and 40
vertical levels. The model top boundary is located at 0.4
hPa. A prognostic Arakawa-Schubert scheme by Randall
and Pan (1993) is introduced for deep convection. In the
numerical integration, sea surface temperatures are set
constant values of initial conditions. The 1-month forecasts in JMA were carried out using ensemble integrations
starting from the unperturbed initial condition (control
forecast) and twelve perturbed initial conditions. In thispaper, however, we analyzed only control forecasts from
Wednesday and Thursday. The data are stored every 24
hours and presented on a 2.5◦ × 2.5 ◦ longitude-latitude
grid at 22 levels from 1000 hPa to 1 hPa.
We used forecasts based upon the initial conditions
from the ﬁnal week of October to the second week of April
during 2001-2004, that is, from 31st October 2001 to 11th
April 2002, from 30th October 2002 to 10th April 2003,
and from 29th October 2003 to 8th April 2004. In thisperiod of 72 weeks, 144 control forecasts were performed.

Fig. 2: Anomaly correlations (ACs) in the equatorial
region (10◦ S-10◦ N) between forecast and veriﬁcation of
VP200 as a function of lead-time. The dashed black line
represents values averaged for 144 forecasts, and solidlines denote ACs in the diﬀerent phases of the MJO andthe Null case. Error bars attached in PC1+ (red), andNull (blue) cases show the standard deviations in theselected forecasts.

Fig. 1: Principal component analysis of intraseasonally bandpass ﬁltered 200hPa velocity potential (VP200)
anomalies in the tropics (30◦ S-30◦ N). a) 1st eigenvector, b) PC1 time series, c) 2nd eigenvector, d) PC2 timeseries. Red and blue solid circles represent the weeks selected for initial conditions with the strong MJO events.
Green solid circles denote the week selected for little or no
MJO activity (i.e., the Null events). Dashed lines along
the horizontal axis in b) and d) indicate 1.5 standard
deviations.

To verify model forecasts, a JMA Global Analysis(GANAL) dataset with 1.25◦ horizontal resolution wasused from June 2001 to May 2004.
The velocity potential on 200 hPa (VP200) is examined to assess the predictability of the tropical convective
circulation. As analysis procedure, the annual cycle wasremoved from the forecast and veriﬁcation ﬁelds. The annual cycle was deﬁned as the annual mean with ﬁrst two
harmonics from the climatological time series created by
the 3-year mean for each day of the GANAL. The model
systematic error was removed for the examination of theforecast skill in the intraseasonal time scales.
The prediction skill is examined for the forecast ﬁelds
applied by a 9-day moving average to remove high frequency variations (Jones et al. 2000). The beginning of
the forecasts was padded with four days of veriﬁcation
analyses. Note that this procedure can slightly inﬂate
some of the skill measures for short lead times.
In order to select initial conditions for the MJO phases,
we performed the principal component (PC) analysis of
VP200 anomalies of the GANAL in the tropics (30◦ S30◦ N) during 72 weeks in the above period. Anomalies

were averaged weekly and ﬁltered between 3 weeks (21days) and 14 weeks (98 days). The results are shown in
Fig.1. The leading two eigenvectors (VP1 and VP2) accounted for the 44.5 % and 31.0 %, respectively. The spatial structure of VP1 and VP2 shows the familiar MJO
pattern (e.g. Lorenc, 1984). We deﬁne a period of thestrong MJO activity when either of the two leading principal components exceeds 1.5 standard deviations (cf. Hendon et al., 2000). Events are selected when the magnitudes of 1st PC time series are larger than 1.5 standard
deviations (PC1+), when the magnitudes of 1st PC timeseries are less than minus 1.5 standard deviations (PC1−),
when the magnitudes of 2nd PC time series are larger than
1.5 standard deviations (PC2+), and when the magnitudes of 2nd PC time series are less than minus 1.5 standard deviations (PC2−). When the succeeding two or
more weeks exceeded 1.5 standard deviations, the weekwith the peak score was selected (see marks in Fig. 1b
and d). The cases are denoted by Null when the absolutevalues of the both ﬁrst and second PC time series are lessthan 0.5 standard deviations. In this work, 8(4), 10(5),6(3), 10(5), and 20(10) forecasts (weeks) were taken for
PC1+, PC1−, PC2+, PC2−, and Null, respectively.

3. Results in JMA 1-month forecasts
3.1. Relationship between the forecast
skill and the initial MJO states
The forecast skills of the JMA 1-month forecasts are examined for low-pass ﬁltered equatorial variations during
the boreal winter seasons. Anomaly correlation (AC) isthe commonly used measure of association that operates
on pairs of gridpoint values in the forecast and observed
ﬁelds (e.g., Wilks 1995). Here, the AC is designed to detect similarities in the patterns of departures from theclimatological ﬁelds in the equatorial (10◦ S-10◦ N) region.

Fig. 4: The amplitude of the MJO (red lines) and ACs(black lines) averaged a) between 1-5 days lead-times andb) between 6-10 days lead-times. Horizontal axis denotes
weeks. Variables are normalized by their standard deviations.

Fig. 3: Longitude-time diagrams of “unﬁltered” VP200
anomalies in the equatorial region (10◦ S-10◦ N ) for each
PC1+ event. Panels in the left column show values of
the analyses and panels in the right column show thoseof the forecasts.

The forecast skill is generally evaluated relative to a reference values of AC= 0.6.
In Fig.2, the dashed black line represents the averaged
values of ACs for 144 control forecasts. On average, ACs
are above 0.6 until 6 days lead-time. In the next step, therelationship is examined between the forecast skills andthe states of the MJO at the initial condition. Figure 2
shows that there is a clear diﬀerence between the strong
MJO cases and the Null case. ACs of the Null case (theline with the character “N”) are always below the averaged values. ACs for the Null case were above 0.6 until 4days lead-time. This feature seems to be common to theindividual forecasts because standard deviations denotedby error bars are small. ACs for the strong MJO cases
tend to be above the average during the lead-times whenthe ACs are above 0.6. This result is consistent with Joneset al.(2000) using zonal winds on 200 hPa of the NCEP
MRF model. Figure 2 also shows that ACs for the PC1+
case (the line with the character “1+”) are the highest,
although the result is less signiﬁcant. ACs averaged for
the PC1+ case are above 0.6 until 9 days lead-time. The
PC1+ case corresponds to the initial conditions with divergent anomalies over the Maritime Continent and convergent anomalies over the Atlantic.
Figure 3 shows longitude-time diagrams of unﬁltered
VP200 anomalies in the equatorial region of the individual

PC1+ events for the forecasts with the initial condition on
Wednesday. Modest similarity until about 10 days leadtimes is seen. The forecast based upon the initial condition on 10th March 2004 (the bottom panel) demonstrates an eastward propagating disturbance clearly although magnitudes of the predicted anomalies are smaller
than those in the analysis ﬁelds.

3.2. Relationship between the forecast
skill and the initial MJO amplitude
In this subsection, the relationship is documented indetail between the forecast skill and the amplitude of
the MJO at the initial condition. Here, the amplitude
A (t) is deﬁned by the ﬁrst two PCs as shown in Fig.1;
1/2(cf. Matthews 2000).
A (t) = P C12 (t) + P C22 (t)Red lines of Fig.4 show the amplitude A (t). We examine the relationship between the amplitude and the ACs
calculated in previous subsection. ACs based upon theinitial conditions of Wednesday and Thursday are averaged in the same week, and weekly series are analyzed
here.
Figures 4a and b indicate ACs averaged between 1-5
days lead-times and between 6-10 days lead-times, respectively (black lines). In Fig.4a, the variations of the ACs
were signiﬁcantly related to those of the MJO amplitude.
A correlation coeﬃcient between the MJO amplitude andthe AC are 0.61. Here, the 1 % signiﬁcance level is 0.42,
based on the assumption that independent events occur
every 3rd-week, according to the e-folding time for the autocorrelation of the MJO amplitude. This indicates thatthe predictions of the MJO by the JMA 1-month forecasts are skillful at the early period of the forecast when
the MJO amplitudes at the initial conditions are large.
This is consistent with the results in the previous section.
On the other hand, this relationship is not found in the
6-10 days lead-times as shown in Fig.4b. The correlationcoeﬃcient is 0.26.
In order to investigate the relationship further, we cal-Acknowledgments
We would like to thank all the members in Numerical
Prediction and Climate Prediction Divisions in JMA for
providing us 1-month forecast datasets of JMA. The GFDDENNOU Library was used for drawing ﬁgures, and also
for numerical calculations.

References

Fig. 5: Correlation between the ACs and the initial
MJO amplitudes as a function of lead-time. The dashedline along the horizontal axis denotes the 1 % signiﬁcancelevel.
culate correlation coeﬃcients between the ACs and theinitial MJO amplitudes as a function of lead-time. As
shown in Fig.5, the correlations are signiﬁcant until 6 days
lead-time. The same analysis as Fig.5 except for the unﬁltered forecasts (not shown) indicates that the correlations
are signiﬁcant until 5 days lead-time. This demonstrates
that this relationship is not established by the padded veriﬁcation analyses in a 9-day moving average for the earlylead-times.

4. Summary
The predictability of the MJO was examined using Japan
Meteorological Agency (JMA) operational 1-month forecasts during boreal winter seasons of 2001-2004. The averaged values of ACs for low-pass ﬁltered velocity potential
on 200hPa (VP200) anomalies in the equatorial (10◦ S10◦ N) region were above 0.6 until 6 days lead-time.
We examined the relationship between the forecast
skills and the states of the MJO at the initial condition.
ACs tended to be lower than the averaged values when
the MJO was quiescent. On the other hand, ACs for thestrong MJO cases tended to exceed the averaged values.
In particular, relatively skillful forecasts were found forthe initial conditions with divergent anomalies over the
Maritime Continent and convergent anomalies over the
Atlantic.
The relationship between the forecast skill and the MJO
amplitude at the initial condition was also examined using the amplitude deﬁned by the ﬁrst two PCs. At the
1-6 days lead-times, the variations of the ACs were signiﬁcantly related to those of the MJO amplitude. This
indicates that the predictions of the JMA 1-month forecasts were more skillful in the equatorial region at 1-6
days lead-times when the MJO amplitudes were large at
the initial conditions. However, this relationship became
insigniﬁcant after 7 days lead-times.

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