The Influence of the Madden-Julian Oscillation on Diurnal Cycle of Rainfall over Sumatera

THE INFLUENCE OF THE MADDEN-JULIAN OSCILLATION
ON DIURNAL CYCLE OF RAINFALL OVER SUMATERA

RAHMI ARIANI

GRADUATE SCHOOL
BOGOR AGRICULTURAL UNIVERSITY
BOGOR
2014

PERNYATAAN MENGENAI THESIS DAN SUMBER
INFORMASI SERTA PELIMPAHAN HAK CIPTA
Dengan ini, saya menyatakan bahwa thesis berjudul The Influence of the
Madden-Julian Oscillation on Diurnal Cycle of Rainfall over Sumatera adalah
benar karya saya dengan arahan dari komisi pembimbing dan belum diajukan
dalam bentuk apa pun kepada perguruan tinggi mana pun. Sumber informasi
yang berasal atau dikutip dari karya yang diterbitkan maupun tidak diterbitkan
dari penulis lain telah disebutkan dalam teks dan dicantumkan dalam Daftar
Pustaka di bagian akhir Thesis ini.
Dengan ini saya melimpahkan hak cipta dari karya tulis saya kepada Institut
Pertanian Bogor.

Bogor, Juni 2014
Rahmi Ariani
NRP G251110051

RINGKASAN
RAHMI ARIANI. Pengaruh Osilasi Madden-Julian terhadap Siklus Harian Curah
Hujan di Sumatera. Dibimbing oleh TANIA JUNE, AKHMAD FAQIH dan
RAHMAT HIDAYAT.
Wilayah kepulauan Indonesia merupakan daerah yang paling intensif
untuk proses konveksi dan curah hujan. Siklus diurnal yang diakibatkan oleh
aktivitas konvektif sangat dominan di daerah daratan tropis dan menyumbang
curah hujan paling besar di Indonesia. Keragaman aktivitas konveksi yang kuat di
daerah tropis tidak hanya terjadi dalam skala waktu harian tapi juga dalam skala
waktu intra-musiman. Gangguan skala besar di daerah tropis dalam hal aktivitas
konvektif yang mempunyai peranan penting dalam mempengaruhi keragaman
curah hujan dalam skala waktu intra-musiman dikenal dengan Osilasi MaddenJulian (Madden-Julian Oscillation, MJO). Pada studi ini, data TRMM V6 3B42
yang merupakan produk estimasi curah hujan dari data satelit digunakan untuk
menganalisa pengaruh dari MJO terhadap siklus harian curah hujan di Sumatera.
Selain itu juga dilakukan uji performa dari model RegCM4 dalam melakukan
simulasi siklus harian dan kaitannya dengan MJO.

Karakteriktik siklus harian curah hujan didapatkan dengan menghitung
klimatologi dari curah hujan pada musim hujan. Sedangkan untuk mengetahui
pengaruh MJO terhadap siklus harian, dilakukan band pass filter terhadap data
curah hujan dengan menggunakan Lanczos filter weights dengan rentang frekuensi
20 sampai 90 hari. Setelah itu, data tersebut dikomposit untuk mendapatkan
anomali curah hujan pada masing-masing fase MJO. Kejadian MJO dari tahun
2000-2010 diindentifikasi dengan menggunakan kriteria, yaitu: nilai dari indeks
MJO lebih besar dari pada satu dan kejadian MJO harus terjadi berturut-turut dari
fase 1-8. Pada studi ini, analisis dibatasi pada musim hujan di Indonesia (OktoberMaret) karena MJO menunjukkan signal yang paling kuat pada periode ini.
Kejadian MJO dari tahun 2000-2010 yang bisa diidentifikasi adalah 18 kejadian.
Data ini kemudian dikomposit untuk mendapatkan anomali pada masing-masing
fase MJO.
Curah hujan di daratan mencapai puncaknya pada sore hari, sedangkan di
lautan mencapai puncaknya pada malam hari. Osilasi Madden-Julian
mempengaruhi siklus harian curah hujan di Sumatera dengan memperkuat
(melemahkan) siklus harian curah hujan pada saat fase aktif (non-aktif) dan
mengubah waktu puncak hujan di lautan. Pada saat fase aktif (non-aktif), MJO
meningkatkan (menurunkan) curah hujan di darat dan di laut berturut-turut
sebesar 33-46% (21-44%) dan 26-64% (32-54%) terhadap rata-rata klimatologi.
Puncak curah hujan di daerah lautan terjadi dua kali pada fase 2 (18 LT dan 00

LT) dan fase 3 (21 LT dan 3 LT), sedangkan pada fase non-aktif curah hujan di
lautan hampir tidak pernah terjadi atau terukur sangat kecil.
Simulasi model RegCM4 menunjukkan bahwa model mampu untuk
memperlihatkan kontras siklus harian antara darat dan lautan namun tidak mampu
menangkap waktu terjadinya puncak hujan. Pada simulasi curah hujan RegCM4,
curah hujan terjadi lebih awal dibandingkan dengan TRMM. Namun, ketika
melakukan simulasi MJO model RegCM4 mampu untuk menggambarkan
peningkatan (penurunan) curah hujan pada saat fase aktif (non-aktif) kejadian

MJO. Hal ini mengindikasikan bahwa model lebih baik dalam melakukan
simulasi variasi intra-musiman dibandingkan dengan variasi harian. Penelitian
lebih lanjut dengan konfigurasi model yang berbeda dibutuhkan karena masingmasing skema akan mempunyai performa yang berbeda pada daerah yang
berbeda.
Kata kunci: Osilasi Madden-Julian, RegCM4, Siklus harian, TRMM

SUMMARY
RAHMI ARIANI. The Influence of the Madden-Julian Oscillation on Diurnal
Cycle of Rainfall over Sumatera. Under supervision of TANIA JUNE, AKHMAD
FAQIH and RAHMAT HIDAYAT.
The Indonesian maritime continent is the most active region for

convection process and rainfall. The references suggested that the rainfall in
maritime continent is mostly caused by the convective activity associated with a
diurnal cycle. The variability of deep convection over tropical regions operates
not only on a diurnal cycle time scale but also at intra-seasonal time scale. At
intra-seasonal time scale, the large scale disturbance in the tropical region in terms
of convective activity, which plays important role on rainfall variability, known as
Madden-Julian Oscillation (MJO). In this study, TRMM V6 3B42 satellite rainfall
estimation product was employed to analyze the influence of the Madden-Julian
Oscillation (MJO) on the diurnal cycle of rainfall over Sumatera. Moreover, we
also tested the performance of RegCM4 in simulating diurnal cycle and the
association with the MJO.
The climatology of the seasonal rainfall (rainy season) was derived to
study the characteristics of diurnal rainfall variation over Sumatera. To study the
impact of MJO on diurnal cycle of rainfall, the rainfall was band pass-filtered
using Lanczos filter weights with a cut-off frequency range from 20 to 90 days.
The composite analysis was used to obtain the anomalies of rainfall in each MJO
phase. The MJO events during 2000-2010 periods are identified using two
criteria: first, the amplitude of the MJO index must be greater than one and
second, the event of MJO need to be sequentially occurred from phase 1 to 8. The
analysis was confined to the rainy season in Indonesia (October-March) because

the MJO shows its strongest signal during this period. The MJO events identified
during the period of 2000-2010 are 18 events. The composite dataset was made
for each MJO phase.
The rainfall over land reaches a maximum in the afternoon, while over sea
maximum occurs in the night time. The MJO modulates the diurnal cycle of
rainfall around Sumatera by enhancing (reducing) the diurnal cycle of rainfall
during its active (inactive) phase and altering the time of rainfall peak over the
ocean. During its active (inactive) phase, the MJO increases (decreases) the
amplitude of rainfall over land and over ocean by 33-46% (21-44%) and 26-64%
(32-54%) to climatological mean, respectively. The rainfall peak over the ocean
occurs twice during phase 2 (18 LT and 00 LT) and phase 3 (21 LT and 3 LT),
while during inactive phase rainfall over the ocean never occurred.
The RegCM4 simulation demonstrates that the model was able to capture
the land-sea contrast of diurnal cycle but unable to capture the time of rainfall
peak. The rainfall peak comes earlier compared to TRMM. On the other hand, the
model is able to capture the increase (decrease) of rainfall during the active
(inactive) phase of MJO. This indicates that model is better in simulating the
intra-seasonal cycle variation than the diurnal cycle. Further research of different
model configuration is needed as the different schemes have different
performance over different regions.

Keywords: Diurnal cycle, Madden-Julian Oscillation, RegCM4, TRMM.

© Hak Cipta Milik IPB, Tahun 2011
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THE INFLUENCE OF THE MADDEN-JULIAN
OSCILLATION ON DIURNAL CYCLE OF RAINFALL OVER
SUMATERA

RAHMI ARIANI

Thesis
as one of the requirements to obtain a degree of

Magister Science
at
Major of Applied Climatology

GRADUATE SCHOOL
BOGOR AGRICULTURAL UNIVERSITY
BOGOR
2014

i

External examiner: Prof Dr Ir Ahmad Bey

ii

Thesis Title
Name
Student ID

: The Influence of the Madden-Julian Oscillation on Diurnal Cycle

of Rainfall over Sumatera
: Rahmi Ariani
: G251110051

Approved by
Supervisor Commission

Dr Ir Tania June, MSc
Head of Supervisor

Dr Akhmad Faqih, SSi
Co-Supervisor

Head of Major
Applied Climatology

Dr Impron, MScAgr, SSi

Date of Examination: 30th June 2014

Dr Rahmat Hidayat
Co-Supervisor

Dean of Graduate School

Dr Ir Dahrul Syah, MScAgr

Date of Passed:

iii

iv

PREFACE
The author would like to say the highest gratitude to Allah S.W.T for
giving the opportunity to accomplish the thesis entitle “The Influence of the
Madden-Julian Oscillation on Diurnal Cycle of Rainfall over Sumatera”. The
MJO impacts the rainfall variability in Indonesia, causing flood and drought that
lead to the hardship for million people, especially for those who depends their
income on agricultural sector. It has widely known that extreme rainfall and dry

event can cause crop failures. Therefore, the analysis of the influence of MJO on
diurnal cycle of rainfall could be used to help to prevent the devastating flood or
drought events that caused by MJO since it can improve the climate and weather
forecasting.
In this opportunity, many thanks are given to those who helped this study
can possibly conducted and accomplished. The Directorate General of Higher
Education, Ministry of National Education, Indonesia (DIKTI) that sponsors
author’s master degree under Beasiswa unggulan scholarship. The Supervisors
committee: Dr. Tania June, Dr. Akhmad Faqih and Dr. Rahmat Hidayat for the
constructive comments and suggestions to construct this study. Helpful
discussions and support from Sandro Wellyanto Lubis. Andrea Bache for editing
the manuscript. The Center for Climate Risk and Opportunity Management in
South East Asia and Pacific (CCROM-SEAP) for the kind permission to use
RegCM4 model and the help of their staff in installing linux. The Collaborative
Research Centre 990 (CRC990) project group A3 that support this research topic.
Friends from KLI 2011 and Summer Course 2012 for the moral supports and
various helps during this study.
This thesis is dedicated to author’s parents and family which become the
inspirations and motivation to author. Without their support in many ways, it is
impossible for author to accomplish this study and get through the difficult time in

life. Thus, author would like to say the high gratitude to them. The author realizes
that this thesis still far from perfect, therefore the comments and input will be
appreciated. Hopefully, this thesis can be useful and benefits for the readers.

Bogor, June 2014
Rahmi Ariani

v

vi

TABLE OF CONTENTS
LIST OF FIGURES

vii

LIST OF APPENDICES

viii

1

2

3

4

5

INTRODUCTION

1

Background

1

Statement of Problem

2

Objective

2

Benefit of Study

2

LITERATURE REVIEW

3

The Scale Interaction between Diurnal Cycle and Madden-Julian Oscillation

3

Regional Climate Model RegCM4

4

DATA AND METHODS

5

Research Location

5

Data

5

Analysis Procedure

5

RESULT AND DISCUSSION

13

The Characteristic of Diurnal Cycle over Sumatera

13

Modulation of Diurnal Cycle of Rainfall by the MJO

14

The Role of Topography Weakens the MJO Signal

18

RegCM4 Performance in Simulating Diurnal Cycle of Rainfall and MJO

19

CONCLUSION AND SUGGESTION

25

Conclusion

25

Suggestion

25

REFERENCES

26

APPENDICES

29

BIOGRAPHY

37

vii

LIST OF FIGURES
1

2
3
4

5
6

7

8
9
10

11
12

13
14

The Research domain with topography shaded (a) TRMM (b) RegCM4
simulation. The black dots denote the spots for analysis in figure 8. The
dashed box indicated the area used for time-longitude plot.
6
The Taylor Diagram (Taylor 2001).
11
Spatial distribution of TRMM rain rate (mm/hour) for period 2000-2010
(a)03LT (b)09LT (c)15 LT (d)21LT.
13
Time-longitude plot of diurnal variation (mm/hour) for period 2000-2010.
Averaged over region 2.5⁰S-2.5⁰N. The red dashed lines indicate the coastline
of Sumatera.
14
Composite of rain rate anomalies (mm/hour) in each MJO phase at (a) 09 LT
(b)15LT (c)21LT (d) 03 LT during boreal winter.
16
Time-longitude plot of composite diurnal variation of rainfall in each MJO
phase (a-h). Averaged over area 2.5⁰S-2.5⁰N. The red dashed lines indicate
the coastline of Sumatera. Unit is mm/hour.
17
Composite of rainfall anomalies in each MJO phase (a) over land (b) over
ocean. The fraction of decrease and increase of rainfall (c) over land (d) over
ocean to climatological mean.
18
Composite rainfall anomalies at 15 LT in each MJO phase Averaged over
area denoted in figure 1.
19
Spatial distribution of rain rate (mm/hour) simulated by RegCM4 for period
2000-2010.
20
Time-longitude plot of diurnal variation (mm/hour) simulated by RegCM4.
Averaged over region 2.5⁰S-2.5⁰N. The red dashed lines indicate the coastline
of Sumatera.
20
The diurnal variation of rainfall by TRMM and RegCM4 in four sample
points. 21
The Taylor diagram displaying the statistical comparison with TRMM of
RegCM4 rainfall estimate (mm/hour). (a) Sample over land (A dan B) (b)
sample over ocean (C and D). The number in each symbol represent the
observation time (3 LT, 9 LT, 15 LT and 21 LT).
22
Composite of rain rate anomalies (mm/hour) simulated by RegCM4 in each
MJO phase at (a) 09 LT (b)15LT (c)21LT (d) 03 LT.
23
Time-longitude plot of composite diurnal variation of rainfall in each MJO
phase (a-h) simulated by RegCM4 (mm/hour). Average over area 2.5⁰S2.5⁰N. The red dashed lines indicate the coastline of Sumatera.
24

viii

LIST OF APPENDICES
1
2
3
4
5
6
7

TRMM V6 3B42 Precipitation Product Algorithm
29
The RegCM4 configuration (the model input namelist file)
30
Roadmap of MJO
32
Research Flowchart
33
The sample of filtered data anomaly compared to daily mean anomaly
34
Location of four samples area in Figure 11
35
The Correlation, RMSE and ratio of Variance showed in Taylor Diagrams
at four sample points around Sumatera
36

1

1 INTRODUCTION
Background
The Indonesian maritime continent, which lies in the equatorial region,
receives abundant solar radiation that leads to the development of deep
convection. The complex topography of the islands and warm seawater
surrounding it are favorable for the diurnal cycle of deep convection system due to
the difference of thermal properties between land and sea surface. Hendon and
Woodberry (1993) suggested that the diurnal amplitude of deep convection is
significant over tropical landmasses, and other studies showed that rainfall in the
maritime continent is mostly caused by the convective activity associated with a
diurnal cycle (Yang and Slingo 2000, Nezbitt and Zipser 2003). The diurnal cycle
of convection is not only prominent local phenomenon, but also play important
role in maintaining planetary-scale atmospheric circulation. It is the heat engine
which provides the energy through latent heat release of condensation.
The variability of deep convection over tropical regions operates not only on
a diurnal cycle time scale but also at intra-seasonal time scale. The Madden-Julian
Oscillation (MJO) is a large scale disturbance in the tropical region in terms of
convective activity. The MJO that propagates eastward is associated with the
large-scale deep convective activity and affects rainfall variability over the
tropical region and higher latitudes (Chen and Houze 1997, Hidayat and Kizu
2009, Tian et al. 2006, Donald et al. 2006). While earlier studies have
investigated the interaction between the MJO and diurnal cycle (Sui and Lau
1992, Chen and Houze 1997, Tian et al. 2006, Fujita 2011), the impact of the
diurnal cycle in particular region with different characteristics such as Sumatera
still needs to be investigated. Nezbitt and Zipser (2003) pointed out that the
diurnal cycle varies significantly among land region depending on topography of
the region.
In this study, the analysis was conducted to investigate the characteristic of
the diurnal cycle over Sumatera and how the MJO modulates the diurnal cycle of
rainfall. Moreover, the regional climate model RegCM4 was utilized as an
example of the result’s application to model evaluation. Diro et al. (2012)
investigated the model performance by simulating the RegCM4 over Central
America and found that the model was unable to capture the peak time of diurnal
cycle of precipitation. Giorgi (2011) suggested that although the RegCM4 shows
an improvement compared to the previous version, the further testing of different
model configuration is needed since the different schemes have different
performance over different region.
Overall, understanding the impact of MJO on diurnal cycle over Sumatera is
important because the climate variability is not homogeneous at different spatial
scale especially over the region with complex topography, which leads to large
uncertainty. Therefore, the study of multi-scale interactions is important to
improve the prediction in weather and ultimately climate risk management since
the impacts of diurnal cycle and the MJO on rainfall variability can be predicted.
These small-scale processes is also important for the enhancement of modeling
capability in local climate applications since it improves regional climate
predictability

2

Statement of Problem
1. How are the characteristics of the diurnal cycle of rainfall over Sumatera?
2. How does the MJO modulate the diurnal cycle of rainfall over Sumatera
during rainy season (October-March)?
3. Does regional climate model RegCM4 well simulate the diurnal cycle of
rainfall over Sumatera and the intra-seasonal cycle such as MJO using the
selected model configuration? How good the model performance compared to
observation?
Objective
1. Study the characteristics of diurnal cycle of rainfall over Sumatera.
2. Investigate the MJO influence on diurnal cycle of rainfall.
3. Simulate diurnal cycle of rainfall and its association with MJO using regional
climate model RegCM4
Benefit of Study
The MJO impacts the rainfall variability in Indonesia which can possibly
causes flood and drought and lead to the hardship for million people, especially
for those who depend their income on agricultural sector. It has widely known that
extreme rainfall and dry event can cause crop failure. Therefore, the analysis of
the influence of MJO on diurnal cycle of rainfall over the specific region with
complex topography can be used to help to prevent the devastating flood or
drought events that caused by MJO since it can improve the climate predictability.

3

2

LITERATURE REVIEW

The Scale Interaction between Diurnal Cycle and Madden-Julian Oscillation
Madden-Julian Oscillation is a planetary scale phenomenon with intraseasonal time scale whereas diurnal cycle is a local or regional scale with daily
time scale. Yet, both of them are two fundamental features of deep convection
variability in the tropics. Several studies have investigated the scale interaction
between them (Sui and Lau 1992, Chen and Houze 1997, Tian et al. 2006, Fujita
2011). Although previous studies have been conducted to understand the impact
of the MJO on the diurnal cycle their results do not agree. Moreover, the domain
of research is different for each study.
Sui and Lau (1992) investigated relationship between the diurnal cycle and
intra-seasonal over the Maritime Continent and found that during the active
periods of the MJO, the diurnal cycle was diminished by MJO and vice versa.
Contrary to Sui and Lau (1992), Chen and Houze (1997) that investigated the
diurnal cycle of tropical deep convection over the western Pacific warm pool
region during the Tropical Ocean Global Atmosphere Coupled Ocean–
Atmosphere Response Experiment (TOGA COARE) reported that cloud systems
are spatially larger and their lifetime is longer during the active phase of MJO.
They reach maximum in the night time until dawn and decay after sunrise.
Meanwhile, cloud systems are small and their lifetimes relatively short during the
inactive phase of MJO. The cloud systems reach maximum in the afternoon and
then dissipate. Tian et al. (2006) demonstrated that the diurnal cycle of tropical
deep convective cloud is enhanced (reduced) over both land and ocean during the
convectively enhanced (suppressed) phase of MJO. Fujita (2011) that investigated
the diurnal convection peak over the eastern Indian Ocean off Sumatera during
different phase of MJO suggested that while the atmosphere over the eastern
Indian Ocean contains abundant water vapor fairly well heated by solar radiation
created the favorable condition for the development of two diurnal convection
peaks, i.e. the evening convection over the land induced by solar radiative heating
and the midnight convection over the ocean triggered by convergence of the lowlevel westerly wind and the land breeze.
Sumatera is one of the largest island in Indonesia with complex
topography where the mountain range with average height of 2000 meter lies
along its southwestern coastline (Figure 1). The previous studies found the diurnal
migration of cloud over Sumatera which indicated that the rainfall system in the
island follows a clear diurnal cycle (Mori et al. 2004, Sakurai et al. 2005, Hamada
et al. 2008, Sakurai et al. 2009). Nitta and Sekine (1994) indicated that super
cloud cluster forms in the eastern Indian Ocean and blocked by the mountain that
lies from the northwestern to southeastern of the Island when it propagates
eastward, causing the western side of the Island receive larger rainfall than the
eastern side. The previous studies also reported that the topography of maritime
continents, including Sumatera weakens the signal of MJO (Hsu and Lee 2005,
Wu and Hsu 2009).

4

Regional Climate Model RegCM4
The RegCM system is a community model coordinated by the Earth
System Physics section of the Abdus Salam International Centre for Theoretical
Physics (ICTP; Giorgi et al. 2006). It has been used for a wide range of studies,
from process studies to paleo-climate and future climate simulation (Qian 2010,
Gu et al. 2012, Wook and Gyu 2012, Notaro et al. 2013). It is also a tool for
downscaling, which is a method for obtaining high-resolution climate or climate
change information from coarse-resolution global climate models. RegCM4 was
released by the ICTP in April 2011 as a first complete version (RegCM4.1).
Regional climate model is receiving increased attention in diurnal cycle of
rainfall because it is not well demonstrated yet. Whereas, a good simulation of the
diurnal cycle is important to represent the mean climate and the variability on a
longer time scales (Yang & Slingo 2001). A numerous studies have studied the
diurnal cycle using the regional climate models (Yang and Slingo 2001, Dai and
Trenberth 2004, Diro et al 2012, Fuente-Franco et al 2013). The errors in the
diurnal cycle which related to the convection trigger affect the intensity and the
frequency of simulated precipitation. Many of convection schemes allow the
convection to start very early in the day (Dai and Trenberth 2004), resulting in
overestimates of light rainfall events. Dai and Trenberth (2004) suggested that
such errors can be masked in monthly mean or longer time scale rainfall statistics
though it may contributes to biases in the other fields, such as cloudiness. The
errors in simulating the diurnal cycle is caused by the model deficiencies in
physical parameterizations such as boundary layer and convective
parameterization which related to the surface heating (Diro et al. 2012). FuenteFranco et al (2013) which analyzed the diurnal cycle over Mexico using RegCM4
found that the precipitation was overestimated over the mountainous region due to
the high frequency of low-precipitation events. They also suggested that the biases
may caused by the anomalies in capturing the shift of ITCZ position along with
the shortcoming of model parameterization of convection over the mountainous
region.
The MIT scheme is the newest cumulus convection option to RegCM4 and
is the most complex of the 3 other schemes. In MIT scheme, the convection is
triggered when the level of neutral buoyancy is greater than the cloud base level.
Between these two levels, air is lifted and a fraction of the condensed moisture
forms precipitation while the remaining fraction forms the cloud. The MIT
scheme tends to produce excessive rainfall over land, especially through the
occurrence of very intense individual rainfall events. In other words, “once the
scheme is activated, it becomes difficult to decelerate” (Giorgi 2011). Diro et al.
(2012) suggested that the cumulus parameterizations tend to maximize rain in the
early afternoon in response to the surface heating which often leads to an earlier
than observed diurnal rainfall maximum over tropical regions. Giorgi et al. (2011)
pointed out that RegCM4 shows an improved performance in several respects
compared to previous versions, yet further testing is still needed to explore its
sensitivities and range of applications in different climate region.

5

3

DATA AND METHODS
Research Location

The research was carried out in the laboratory of Climatology, Department
of Geophysics and Meteorology, Bogor Agricultural University and Center for
Climate Risk and Opportunity Management in Southeast Asia and Pacific
(CCROM-SEAP) from February 2013 to March 2014. The domain of research
areas was between 8º S - 8º N and 92º E -109º E (Figure 1) from period of 20002010.
Data
The data that we employed to examine the diurnal cycle characteristic and
the influence of the MJO in this study is TRMM V6 3B42 precipitation data
product. This TRMM has 3 hourly temporal resolution and 0.25ºx0.25º spatial
resolution. It integrates three sensors (VIRS, TMI, and PR) with merged Infra-Red
rain rate data and the Global Precipitation Index (GPI) (Huffman et al. 2007;
http://www.mirador.gsfc.nasa.gov). High temporal and spatial resolution of the
data and the algorithm used to obtain the product makes the product suitable to
study the diurnal characteristic of rainfall and its association with MJO. Huffman
et al. (2007) showed that a diurnal cycle of TRMM product has a slight difference
in phase and amplitude with gauge observations (the algorithm of TRMM 3B42
V6 Product can be seen in Appendix 1). To run the RegCM4 simulation, two
observational data were used: (1) The Optimum Interpolation Weekly Sea Surface
Temperature (SST oi_wk) from NOAA’s website (http://www.esrl.noaa.gov) with
spatial resolution 1° x 1° (Reynolds et al. 2002) and NCEP/NCAR Re-analysis
Project Version 1 (NNRP 1) with spatial resolution 2.5° x 2.5° and time
resolution 8 hours (Kalnay et al. 1996; http://www.esrl. noaa.gov). In order to
identified the MJO events, we used the index so-called Real Time Multivariate
MJO (RMM1 and RMM2; http://cawcr.gov.au/staff/mwheeler/maproom/RMM/;
wheeler and Hendon 2004. The periods of all the data were from 2000 to 2010.

Analysis Procedure
1. Diurnal Cycle Characteristic Analysis
In order to investigate the daily cycle of rainfall characteristic, TRMM V6
3B42 precipitation data was employed. The climatology of the seasonal rainfall
(rainy season; October-March) per six hours from period of 2000 to 2010 was
derived from the TRMM data. The cross section analysis was also performed to
investigate the diurnal variation where the direction and speed of rainfall
migration can be seen from time-longitude plot. The speed of rainfall migration
was calculated by dividing the distance of migration (the distance of the rainfall
peaks from their start over land until they stopped or disappeared over the ocean)
with time of migration. In this cross section analysis, the rainfall was averaged
within 2.5⁰N-2.5⁰S latitudes.

6

(a)

(b)

Figure 1 The Research domain with topography shaded (a) TRMM (b)

RegCM4 simulation. The black dots denote the spots for analysis
in figure 8. The dashed box indicated the area used for timelongitude plot.
2. Band-Pass Filter and Composite Analysis
To examine the impact of MJO on diurnal cycle of rainfall, the data was
band pass-filtered using Lanczos filter. The filter is the fourier method of filtering
the digital data by the given number of weights and the value of cut-off frequency
(Duchon 1979). The purpose of this filter is to produce the new data sequence in
the frequency domain which have been modified by applying the set of weight
into the given data. In the other words, the weight will affect the amplitude of the
data in the frequency domain. The digital filtering involves transforming the input
data sequence xi, where t is time, into an output data sequence yi using the linier
relationship:
∑
In which the wk are the suitable chosen weight. The effect of filtering data is
best observed in the frequency domain. The minimum number of weight required
to achieve best response in frequency domain is determined by the equation below
(Duchon 1979):

Where the fc2 and fc1 is the frequency domain. In this study, the frequency domain
used in order to obtain the rainfall anomalies in association with the MJO is 20-90
days. To complete analysis of MJO impact, the composite analysis was applied to

7

the filtered data. The composites are made from 18 MJO events identified during
the period of 2000-2010 to obtain the anomalies of rainfall in each MJO phase.
3. RegCM4 Simulation and Configuration
The regional climate model RegCM4 was utilized to simulate the diurnal
cycle of rainfall and its association with the MJO. It is the latest version of the
International Centre for Theoretical Physics (ICTP) regional climate model. In
order to provide the initial conditions and lateral boundary condition of the model,
the Optimum Interpolation Weekly Sea Surface Temperature (SST oi_wk) from
NOAA with spatial resolution 1° x 1° (Reynolds et al. 2002) and NCEP/NCAR
Re-analysis Project Version 1 (NNRP 1) with spatial resolution 2.5° x 2.5° and
time resolution 8 hours (Kalnay et al. 1996) was employed. RegCM4 is a
hydrostatic model with terrain following sigma coordinates and the horizontal grid
Arakawa-Lamb B. The model calculates the radiative transfer with the radiative
scheme of the global model CCM3 (Kiehl et al. 1996) and depicts the Planetary
Boundary Layer (PBL) processes using modified version of the PBL scheme of
Holtslag et al. (1990). The model employs the large-scale precipitation scheme of
Pal et al. (2000) and uses the Community Land Model (CLM; Steiner et al. 2009)
to describe the land surface processes. The convective precipitation scheme that
we used in this study was the MIT convection parameterization of Emanuel
(1991; see the details of model configuration in Appendix 2). In order to provide
the analysis of diurnal cycle and its association with MJO, the RegCM4 was
processed in a similar manner to TRMM data.
The details of RegCM4 physical parameterization can be described as
follows:
a) Radiation Scheme
Radiative transfer calculations are carried out with the radiative transfer
scheme of the global model CCM3 (Kiehl et al. 1996). The solar component
follows the d-Eddington approximation of Kiehl et al. (1996). It takes into
accounts the calculations for the short-wave and infrared parts of the
spectrum, which includes 18 spectral intervals from 0.2 to 5 μm, including
both atmospheric gases and aerosols. The scheme also includes contributions
from all main greenhouse gases such as H2O, CO2, O3, CH4, N2O, and
CFCs. The cloud scattering and absorption of solar radiation by aerosols are
also included based on the aerosol optical properties. The parameterization
follow that of Slingo (1989), whereby the optical properties of the cloud
droplets (extinction optical depth, single scattering albedo, and asymmetry
parameter) are expressed in terms of the cloud liquid water content and an
effective droplet radius. “When cumulus clouds are formed, the gridpoint
fractional cloud cover is such that the total cover for the column extending
from the model-computed cloud-base level to the cloud-top level is a function
of horizontal gridpoint spacing. The thickness of the cloud layer is assumed to
be equal to that of the model layer, and a different cloud water content is
specified for middle and low clouds” (Elguindi et al. 2010).
b) Land Surface Model
In this study we use the CLM (Steiner 2009) to describe biogeophysicallybased parameterizations to describe the land–atmosphere exchanges of

8

energy, momentum, water, and carbon. This scheme is developed by the
National Center of Atmospheric Research (NCAR) as part of the Community
Climate System Model (CCSM). The CLM divides the cell area into three
sub-grib, i.e. the first sub-grid hierarchy composed of land units such as
glacier, wetland, lake, urban, and vegetated land cover, and the second and
third sub-grid hierarchy for vegetated land units, including different snow/soil
columns for the different vegetation fractions, and plant functional types
(PFT). The vegetated fractions are further divided into 17 different plant
functional types. Biogeophysical processes are calculated for each land unit,
column, and PFT separately and then averaged. “CLM3 biogeophysical
calculations include a coupled photosynthesis–stomata conductance model,
in-canopy radiation schemes, revised multi-layer snow parameterizations, and
surface hydrology including a distributed river runoff scheme” (Oleson et al.
2008). Hydrological and energy balance equations are calculated for each
land cover type and restore to the grid cell level. Soil temperature and water
content are solved with the use of a multiple layer model.
c) Planetary Boundary Layer Scheme
The planetary boundary layer (PBL) scheme in RegCM4 is developed by
Holtslag et al. (1990). In the Holtslag scheme, a PBL height is first calculated
based on the iteration procedure of bulk critical Richardson number
formulation. The non-local vertical profile of eddy diffusivity for heat,
moisture, and momentum is specified from the surface to the PBL height, and
a counter-gradient fluxes which resulting from large-scale eddies in an
unstable atmosphere, is added for temperature and moisture. The eddy
diffusivity depends on the friction velocity, height, Monin-Obhukov length,
and PBL height. The vertical eddy flux within the PBL is given by:

(3)
where γc is a “countergradient” transport term describing nonlocal transport
due to dry deep convection. The eddy diffusivity is given by the nonlocal
formulation:
(4)
where k is the von Karman constant; wt is a turbulent convective velocity that
depends on the friction velocity, height, and the Monin–Obhukov length and
h is the PBL height. The countergradient term for temperature and water
vapor is given by:
(5)
where C is a constant equal to 8.5, and Φc0 is the surface temperature or water
vapor flux. Equation is applied between the top of the PBL and the top of the
surface layer, which is assumed to be equal to 0.1h. Outside this region and
for momentum, γc c is assumed to be equal to 0.

9

For the calculation of the eddy diffusivity and counter-gradient terms, the
PBL height is diagnostically computed from equation:

(6)
where u(h), v(h), and θv are the wind components and the virtual potential
temperature at the PBL height, g is gravity, Ricr is the critical bulk
Richardson number, and θg is an appropriate temperature of are near the
surface.
d) Convective Precipitation Schemes
In this study, the convective precipitation is computed using the
Massachusetts Institute of Technology (MIT) scheme (Emanuel 1991). In this
parameterization, cloud mixing is assumes to be episodic and inhomogenous
(as opposed to a continuousentraining plume), and convective fluxes are
based on a model of sub-cloud-scale updrafts and downdrafts. Convection is
triggered when the level of buoyancy is higher than the cloud base level.
Between these two levels, air is lifted and a fraction of the condensed
moisture forms rainfall while the remaining fraction forms the cloud. “The
cloud is considered to mix with the air from the environment according to a
uniform spectrum of mixtures to their respective levels of neutral buoyancy.
The mixing entrainment and detrainment rates are functions of the vertical
gradients of buoyancy in clouds. The fraction of the total cloud base mass
flux that mixes with its environment at each level is proportional to the
undiluted buoyancy rate of change with altitude. The cloud base upward mass
flux is relaxed towards the sub-cloud layer quasi equilibrium. Rainfall is
based on auto-conversion of cloud water into rain water and accounts for
simplified ice processes” (Elguindi et al. 2010).
e) Large-Scale Precipitation Scheme
The scheme is based on the Subgrid Explicit Moisture Scheme (SUBEX)
which used to handle non-convective clouds and rainfall resolved by the
model. The SUBEX parameterization of Pal et al. (2000) includes a
prognostic equation for cloud water. It first calculates fractional cloud cover
at a given grid point based on the local relative humidity. The fraction of the
grid cell covered by clouds (FC) is calculated by,

(7)
where RHmin is the relative humidity threshold at which clouds begin to form,
and RHmax is the relative humidity where FC reaches unity. FC is assumed to
be zero when RH is less than RHmin and unity when RH is greater than RHmax.
Precipitation P forms when the cloud water content exceeds the autoconversion threshold Qthc according to the following relation:

10

(8)
where 1/Cppt considered the characteristic time for which cloud droplets are
converted to raindrops. The threshold is obtained by scaling the median cloud
liquid water content equation according to the following:
(9)
where T is temperature in degrees Celsius, and Cacs is the auto-conversion
scale factor. Precipitation is assumed to fall instantaneously.
SUBEX also includes simple formulations for raindrop accretion and
evaporation. The formulation for the accretion of cloud droplets by falling
rain droplets is based on the work of Beheng (1994) and is as follows:
(10)
where Pacc is the amount of accreted cloud water, Cacc is the accretion rate
coefficient, and Psum is the accumulated precipitation from above falling
through the cloud. Precipitation evaporation is based on the work of Sundqvist et
al. (1989) and is as follows:

(11)
where Pevap is the amount of evaporated precipitation, and Cevap is the rate
coefficient.
4. RegCM4 Performance Analysis
The performance of RegCM4 model was investigated by comparing the
results of RegCM4 estimation with TRMM satellite-observation. We use the
Taylor diagram to measure how well the model estimates the diurnal cycle of
rainfall. Taylor diagrams provide a visual framework of statistical summary of
correlation, root-mean-square difference and the ratio of the variance between the
model and observations (Taylor 2001). It is comparing model results to
observations and show how close the pattern of the model resembles observations.
Taylor diagram has been used as the model performance evaluation (IPCC 2001).
The formulas for calculating the correlation coefficient (R), the centered
RMS difference (E'), and the standard deviations of the model (σf) and the
observation (σr) are given below (Taylor 2001) :

(12)

(13)

(14)

11

(15)

The Taylor diagram can represent three different statistics (the centered
RMS difference, the correlation, and the standard deviation) in the twodimensional space because these statistics are related by the following formula
(Taylor 2001):
(16)

where R is the correlation coefficient between the model and observation, E' is the
centered RMS difference, and σf 2 and σr 2 are the variances of the model and
observation, respectively. The Figure 2 displaying the Taylor diagram which
shows the correlation coefficients, the standard deviation and RMS error (RMSE).
The RMSE is indicated by the dashed line and measured by the distance from the
reference point. The simulated patterns are considered agreed well with
observation if the values lie between the point “reference” on the x-axis. At this
point, the model has relatively high correlation and low RMSE. The value which
lies on the dashed arc from reference point has the correct standard deviation
(similar standard deviation as the observation).

Figure 2 The Taylor Diagram (Taylor 2001).

12

5. MJO Events Identification
The MJO events during 2000-2010 periods are identified using the criteria
made by Wheeler and Hendon (2004). Wheeler and Hendon (2004) defined the
index of MJO called as Real time Multivariate MJO (RMM) by using the first two
modes of Empirical Orthogonal Function (EOF) of daily zonal winds at 850 and
200 hPa and Outgoing Long-wave Radiation (OLR) near the equator (15⁰S15⁰N). Those first two modes of EOF are known as RMM1 and RMM2. Using
RMM1 and RMM2 index we can define the amplitude and the eight phase of
MJO. The phase indicates the active phase of MJO or where the deep convective
activity occurred. Phase 2 and 3 are located over the Indian Ocean, phase 4 and 5
over the Maritime Continent, phase 6 and 7 over the Western Pacific and phase 1
and 8 over the western hemisphere and Africa (the MJO roadmap shown in
Appendix 3). In this study, the MJO event is identified using two criteria: first, the
amplitude of the MJO index must be greater than one and second, the event of
MJO need to be sequentially occurred from phase 1 to 8. The analysis was
confined to the rainy season in Indonesia because the MJO shows its strongest
signal during this period (Gutzler and Madden 1989, Wang and Rui 1990). The
MJO events identified during the period of 2000-2010 are 18 events. (see research
flowchart in Appendix 4)

13

4

RESULT AND DISCUSSION

The Characteristic of Diurnal Cycle over Sumatera
Figure 3 shows the diurnal variation of rainfall over Sumatera Island at six
hour interval from 11 years of climatology (rainy season). The figure indicates
that there is a clear contrast of rainfall peak between the land and the ocean
around Sumatera. The terrestrial rainfall reaches its maximum intensity in the
afternoon (15 LT) and minimum in the early morning (3 LT). Meanwhile, rainfall
over the ocean reaches its maximum during the night time (21 LT) and minimum
in the afternoon (15 LT). The rainfall in the afternoon was prominent around the
mountain range of Sumatera, indicating the terrestrial rainfall was formed by the
orographic force and sea breeze induced by radiative heating that forms the
convective cloud during the day time. This is consistent with the previous studies
about the diurnal variation in the tropical region that the rainfall peaks in the
afternoon over land (Nitta and Sekine 1994, Chen and Takahashi 1995, Ohsawa et
al. 2001). Meanwhile, the maximum rainfall over the ocean occurred earlier
compared to previous studies, where it occurred in the late midnight to the early
morning. The difference of time peak of diurnal variation could be the effect of
topography of Sumatera since diurnal convection variations and rainfall strongly
depend on local topographic conditions.
The amplitude of terrestrial rainfall is larger than that of the ocean. The
previous works comparing the tropical rainfall agreed that the amplitude of the
diurnal cycle of terrestrial rainfall is larger than over oceans (Gray and Jacobson
1977, Yang and Slingo 2001). It is caused by the radiative heating during the day
that brings abundant water vapor from Indian Ocean by the sea breeze to the land
of Sumatera. Mori et al. (2004) investigated the fraction of the rainfall type in the
Sumatera. The study concluded that 70% of rainfall over the land is caused by
convective clouds, while the rainfall in the night time and early morning over
ocean is equally caused by the convective and statiform cloud. Thus the rainfall in
the night time is not as heavy as in the day time.

Figure 3 Spatial distribution of TRMM rain rate (mm/hour) for period 2000-

2010 (a)03LT (b)09LT (c)15 LT (d)21LT.

14

Figure 4 shows the diurnal variation of rainfall at time coverage 3 hour
(climatology of rainy season). The rainfall with intensity above 0.4 mm/hour is
first observed over land in the morning (09 LT) and reaches its peak in the
afternoon (15 LT) around the mountainous region of Sumatera. In the early
evening, the rainfall begins to migrate toward the western coastline and offshore
region of the Indian Ocean. Meanwhile, the eastward migration begins in the late
night (after 21 LT). The westward migration reaches rainfall peak in the offshore
region at 21 LT while the eastward migration reach the peak after midnight (00
LT-03LT). Over both west and east offshore region of Sumatera, the rainfall
occurred until 06 LT in the morning. The speed of westward migration is
approximately 9 m/s and the eastward migration is approximately 17 m/s.

Figure 4 Time-longitude plot of diurnal variation (mm/hour) for period 2000-

2010. Averaged over region 2.5⁰S-2.5⁰N. The red dashed lines
indicate the coastline of Sumatera.
Modulation of Diurnal Cycle of Rainfall by the MJO
In this section, we discuss how MJO modulates the diurnal cycle of
rainfall over Sumatera. The rainfall anomalies in respective MJO phases, made by
composite 18 events during 11 years period (2000-2010) are depicted in Figure 5.
The anomalies shown in Figure 4 were band-pass filtered (20-90 days cut off).
Thus, the rainfall anomalies were only caused by the MJO since other frequencies
that also influence rainfall variability over Sumatera, such as Indian Ocean dipole
and El-Nino Southern oscillation were eliminated. The example of filtered data
anomalies compared to daily mean anomalies can be seen in Appendix 5. Figure 5
shows that the impact of the MJO on rainfall variability is different in each MJO
phase due to its effect on enhancing and suppressing the convective activity
during its eastward propagation. When the convective area begins to appear near
Africa during phase 1, the positive anomalies of rainfall observed in the west
coast of Sumatera appear in the afternoon (15 LT). During phase 2 and 3, when
the high convective activity is activated over Indian Ocean and moderate lowlevel westerly winds are dominant, the largest positive anomalies during an MJO
event were observed. During phase 4, when the convective activity begins to
propagate toward Indonesian maritime continents, the diurnal variation of rainfall
is small, yet the rainfall anomalies still remain positive. The amplitude of rainfall

15

anomalies is larger when the rainfall generally peaked over both land (15 LT) and
ocean (21 LT). This indicates that MJO enhances the amplitude of diurnal cycle
during its active convection activity (phase 1 to 4)
On the other hand, the diurnal cycle of rainfall tends to be weakened by
the MJO from phase 5 to phase 7. During this phase the Indian Ocean is covered
by the convectively suppressed area. The negative anomalies are larger over land
and ocean when the rainfall generally peaks, indicating that MJO weakens the
diurnal cycle of rainfall during convectively suppressed phase (phase 5 to 8).
During phase 8, although the negative anomalies of rainfall become smaller, there
is no diurnal variation observed. The influence of the MJO on the diurnal cycle of
rainfall over Sumatera is consistent with the results of few previous studies. Fujita
(2011) suggested that during phase 2 and 3 the amplitude of diurnal cycle of
convection were large and there was a clear contrast between the diurnal peaks of
convective over land and ocean. Tian et al. (2006) examined the impact of MJO to
diurnal cycle during seven winter seasons over maritime continents and found that
the diurnal cycle of tropical deep cloud convection was enhanced during the
active phase of the MJO, while it was reduced during the inactive phase of the
MJO.
The time-longitude plot of diurnal variation of rainfall over the area 2.5⁰S2.5⁰N is depicted in Figure 6. The diurnal cycle of rainfall was clearly different at
each of MJO phase (Figure 5). The most prominent diurnal cycle and largest
amplitude of rainfall was observed during phase 2 and 3. The rainfall over land
appears after 09LT, reaches its peak in the afternoon and begins to migrate to the
west offshore the island soon after the peak. Chen and Houze (1997) investigated
the diurnal cycle of tropical deep convection over the western pacific region
during Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response
Experiment (TOGA-COARE). They found that the cloud systems are larger
during the active phase of MJO and their lifetime is longer; they extend until
dawn and decay after sunrise. We can conclude that the peak of rainfall over the
ocean changes during this phase. The ocean rainfall reaches the peak twice (21 LT
and 3 LT). It is contrary with Tian et al. (2006) which examined that the diurnal
phase of deep convective cloud was not affected by the MJO over both land and
ocean.
During phase 1 and 4, although the amplitude of rainfall over both land
and ocean are small, the distinct contrast of rainfall peak between land and ocean
has a clear diurnal cycle. The west migration only exists during phase 1 to 4 and
the average speed of the migration is roughly 15 m/s. During phase 5 to 8, the
amplitude of diurnal cycle are small corresponding to the MJO suppressed
convective area and dry atmosphere. During phase 5 and 6 the rainfall only
migrates toward the east side of the isl