E-ISSN : 2541-5794  
   P-ISSN : 2503-216X  

Journal of Geoscience,  
Engineering, Environment, and Technology 
Vol 02 No 03 2017 

 

 
Khoirunnisa. H., Wisha,  U., and Lubis M.Z.,/ JGEET Vol 02 No 03/2017  210 

 

The Coherency and Correlation between Sea Surface 
Temperature and Wind Velocity in Malacca Strait: Cross 
Wavelet Transform and Wavelet Coherency Application 

Hanah Khoirunnisa
1,
*, Ulung Jantama Wisha

2
, Muhammad Zainuddin Lubis

1
  

1
 Geomatics Engineering Department, State Polytechnics of Batam 

2
Research Institute for Coastal Resources and Vulnerability, Ministry of Marine Affairs and Fisheries 

 

 
* Corresponding author : hanah.khoirunnisa@gmail.com     
Tel.:+81-72-867-1686; fax: +81-72-867-1658  

Received: Aug  1, 2017. Revised : Aug 15, 2017, Accepted: Aug 29, 2017, Published: 1 Sept 2017  
DOI : 10.24273/jgeet.2017.2.3.590 

 
Abstract 

This study tried to observe the correlation and coherency between sea surface temperature (SST) and wind velocity in 
the Malacca Strait at the year of 2015. The SST and wind velocity data with 6 hours interval step have been used in this study. 
S-Transform, the Cross Wavelet Transform, and the Wavelet Coherency were applied to observe the influence of the variation 
of sea surface temperature to the wind velocity in Malacca Strait. These methods could produce the phase lag and the time 
of occurrence between them. S-Transform was used to show the spectrum energy of the sea surface temperature variation. 
The strongest correlation between them has the period of 32 days during July to August and October to November at each 
point with significance level of 95 %. The coherency of them has the range of 4 to 64 days at each point. The last result is the 
spectrum energy of SST variation that has the period of 5 to 50 days at each point. It was similar to the result of the correlation 
and coherence period between the wind velocity and the SST data. 
 
Keywords: Sea surface temperature, Malacca strait, Wind velocity, Coherency, Correlation. 

 

  

1. Introduction  

The Malacca Strait has been located in the 
coordinate of 96 to 106 E and 2 N to 8 S. It is directly 
connected to Andaman Sea and Indian Ocean 
(Amiruddin et al., 2011). The Indian Ocean climate 
has influence to the Malacca Strait climate. 
Monsoonal condition is the potential thing to affect 
the Northern Indian Ocean condition (Tomzcak, 
2001). Instead of that, the monsoonal condition can 
be shown by the wind reversing in two times a year, 
and also there are two conditions of monsoon 
climate, northeast monsoon (winter monsoon) and 
southwest monsoon (summer monsoon) (Wyrtki, 
1961; Rao and Sivakumar, 2000; and Susanto et al., 
2001). In the Indian Ocean, Asian monsoon intensity 
has also influenced to control the basin-margin 
instability (Lin et al., 2010). The Malacca Strait has 
been affected by the seasonal conditional. These 
were northeast monsoon and southwest monsoon 
(Hii et al., 2006). It affect to several parameters in 
the Malacca Strait. The temperature and salinity in 
the Malacca Strait have the lowest condition at the 
winter monsoon and highest condition during 
summer monsoon (Peralta and Yusoff, 2014). In 
addition, the Malacca Strait has the shallow 
bathymetry. It was an average of 53.38 m (Hii et al., 
2006). And also, the Malacca Strait water mass has 

been influenced by the rivers in the west Sumatra 
and west coast of Peninsular Malaysia (Chua et al., 
1997; Hii et al., 2006; Amiruddin et al., 2011). The 
water mass of the Malacca strait has been moving 
southwesterly towards to the Indonesian seas 
during southwest monsoon (Amiruddin et al., 2011 
and Hii et al., 2006). 

In this study, we show an analysis about the 
variation and correlation of the sea surface 
temperature (SST) and wind velocity in the year of 
2015 in the Malacca Strait. Importantly, we also 
considered the influence of monsoonal condition. 
We also quantify the phase lag between them using 
cross wavelet transform and wavelet coherency. To 
show the variation of SST in Malacca Strait we were 
using the S-Transform method. In addition, using 
these methods, we can identify the dominant period 
and its variation. 

2. Data and Method 

This research used the gridded reanalysis ERA 
Interim daily SST and wind velocity data in the 
Malacca Strait area in the year of 2015 by six 
hourlies interval step. They have the resolution as 
big as 0.125

o
 and 0.5

o
, and it was downloaded by 

European Centre for Medium-Range Weather 
Forecasts (ECMWF) in the region of 8

o
N  2

o
S and 

96
o
E  106

o
E. It would be processed by the methods 

mailto:hanah.khoirunnisa@gmail.com


 
Khoirunnisa. H., Wisha,  U., and Lubis M.Z.,/ JGEET Vol 02 No 03/2017 211 

 

of S-Transform to observe the dominant period of 
sea surface temperature, Ocean Data View as a 
visual analytic, Cross Wavelet Transform, and 
Wavelet Coherency by Morlet Wavelet with 
significance level 95 % (Grinsted et al., 2004). 

2.1 S-transform 

The first method to observe the dominant period 
of SST is the S-Transform. It was a window variable 
from Short Time Fourier Transform (STFT) or it 
would be extension from wavelet transform (WT) 
(Wang, 2010). The time series spectrum component 
could be shown by the Fourier Transform and only 
contains the information about the time series 
spectrum 
distribution at different frequencies. Wavelet 
Transform either to extract the data information in 
time and frequency domains. However, the wavelet 
transform is sensitive to noise. Equation 1 shows 
the correlation between S-Transform and STFT. The 
STFT equation to h(t) signal is shown in the below:  

 

𝑆𝑇𝐹𝑇(𝜏, 𝑓) = ∫ ℎ(𝑡)𝑔(𝜏 − 𝑡)𝑒−𝑗2𝜋𝑓𝑡 𝑑𝑡
∞

−∞

 
(1) 

Where: 
𝜏 : Spectrum localization time  
𝑓 : Fourier frequency 
𝑔(𝑡) : Window function  
 
 Changing 𝑔(𝑡) value is the one of the way to 
determine S-transform with the Gaussian function, 
such as: 
 

𝑔(𝑡) =
|𝑓|

√2𝜋
𝑒

𝑡 2𝑓2

2  
(2) 

  
From the Equation 1 and 2, can be identified to S-
Transform and it becomes the Equation 3: 
 

𝑆(𝜏, 𝑓) = 𝑆𝑇𝐹𝑇(𝜏, 𝑓)   
 

= ∫ ℎ(𝑡)
|𝑓|

√2𝜋
𝑒

(𝜏−𝑡)2𝑓2

2 𝑒−𝑗2𝜋𝑓𝑡 𝑑𝑡
∞

−∞

 

 (3) 

   
In the other words, the S-Transform is the 

other form of STFT with Gaussian window. 

2.2 Wavelet Coherence 

 Using Wavelet coherence, the highest 
coherence between the correlated time series data 
can be observed in the time-frequency domain. 
Torrence and Webster (1998) in Grinsted et al. 
(2004) have formulated the equations for the 
wavelet coherency as follows: 
 



















2
1

2
1

2
1

2

)(.)(

))((
)(

sWsSsWsS

sWsS
sR

Y

n

X

n

XY

n

n
 

(4) 

 
Using S as a smoothing operator and its equation 
become:  

)))((()( sWSSWS
ntimescale

  (5) 

 
 The Sscale is the notation of the smoothing along 

the wavelet scale and timeS  is the   smoothing in 

time. The smoothing operator which suitable to 
Morlet wavelet as follows: 
 

S

x

t

nstime
csWWS

















2

2

2
1

*)()( , 

 
nnstime

scsWWS )6,0(*)()(
2
  

(6) 

  

Whereas 
1

c  and 
2

c are used to normalization. 

Using numerical method is one of the way to 
determine the normalization coefficient. To 
determine the confident level of wavelet coherence 
can be solved by Monte Carlo method. The squared 
of coherence is used to estimate the frequency. It 
has the range between 0 and 1 to indicate the 
correspondent of 𝑥 and 𝑦 value. The squared of 
coherence can be arranged as follows: 

)()(

)(
)(

2

fPfP

fP
fC

yyxx

xy

xy
  

(7) 

 

Whereas the )( fP
xx  

and )( fP
yy

 are the power 

spectral density of x and y data, and also the )( fP
xy

 

is the cross power spectral density of x and y data. 
 

2.3 Cross Wavelet Transform 

Morlet Wavelet shows a good relation between 
time and frequency localization. Cross wavelet 
transform is the result of a band pass filter of a time 
series data (Grinsted et al., 2004). The formulation 
for cross wavelet transform can be written as 
follows: 

 

])'[(0)(
1'

'
s

t
nnx

s

t
sW

N

n

n

X

n








  
(8) 

 
 

The )(sW
X

n
 value is a local phase and 2)(sW X

n
is a 

wavelet power. Cross wavelet transform correlate 
two time series data, whereas can be defined as: 
 

*YXXY
WWW   (9) 

 
So we can define which the value of XYW  is a 

cross wavelet power and the value of XYW can be 

interpreted as a local relative phase between the 

value of nx  and ny  at time  frequency domain. 

 
To determine the influence of the wind velocity 

to SST distribution, we decided to choose 3 
sampling points, that is quite represent the research 
area, they are A, B, C point (Fig.1). Point A is located 
between Northern of Lhokseumawe and Langkawi 



 
212  Khoirunnisa. H., Wisha,  U., and Lubis M.Z.,/ JGEET Vol 02 No 03/2017  
 

Island, these point is still under the big influence 
from Andaman Sea, point B is located between 
Eastern waters of Medan and Western of Malaysia, 
and point C is located between Bagansiapiapi 
waters and Western of Kuala Lumpur, the 
coordinates of point A, B and C are shown at Table 
1. 

 

 
Fig. 1. Study area in Malacca Strait with A, B, and C point. 
 
Table 1 Sampling point coordinates 

Point Longitude Latitude 

A 6
o
  97

o
  

B 4
o
  99

o
  

C 2
o
  101

o
  

3. Result and Discussion 

3.1 The Variation of Sea Surface Temperature and 
Wind Velocity 

Fig 2. shows that the SST variation in the straits 
changed seasonally. In January, the highest 
temperature has the value of 303.36 K or 30.21

o
C, 

whereas the highest temperature value in July is 
304.28 K or 31.18

o
C. It shows the SST is lower when 

the western monsoon (December-February) than 
the eastern monsoon (June to August). 

The condition of SST is depended on monsoon 
cycles, the change of monsoon is quietly influence 
the SST condition in Malacca Strait, specifically the 
change of the wind speed and direction significantly 
affect the distribution of SST that is come from heat 
waste and solar heating intensity, SST in the 
Malacca Strait is transported by the wind, surface 
current, wave, tide and the other physical factors 
(Syamsul et al., 2012). The change of STT value in 
every monsoon condition is not too significant ± 1

o
C 

(Table 2). 
 

Table 2.  The maximum value of SST 

Monsoon Range of SST (
o
C) 

Northeast monsoon 31.18  33.06 
Northwest monsoon 31.51  34.29 
Southwest monsoon 32.20  34.14 
Southeast monsoon 30.81  33.58 

 

  

 
 

Fig 2. Spatial SST distribution in the Malacca Strait (a) northeast monsoon (b) northwest monsoon (c) southwest 
monsoon (d) southeast monsoon. 

 
 



 
Khoirunnisa. H., Wisha,  U., and Lubis M.Z.,/ JGEET Vol 02 No 03/2017 213 

 

  

  

Fig. 3. Spatial wind velocity distribution in the Malacca Strait (a) northeast monsoon (b) northwest monsoon (c) 
southwest monsoon (d) southeast monsoon 

 

 

 
 

Fig. 4. The SST energy spectrum on the A, B, C point in the Malacca Strait using S-Transform during 2015. 
 



 
214  Khoirunnisa. H., Wisha,  U., and Lubis M.Z.,/ JGEET Vol 02 No 03/2017  
 

Table 3. The maximum value of wind velocity 

 Monsoon Range of wind 
velocity (m/s) 

Northwest monsoon 0.05  10.84 
Northeast monsoon 0.03  9.22 
Southeast monsoon 0.03  10.09 
Southwest monsoon 0.05  9.15 

 
It suggests that seasonal factor affected the 

variation of SST in the Malacca Strait. The result of 
S-Transform shows the variation of 5-50 days in SST 
at points A, B, and C does exist (Fig 3). Susanto 
(2000) said that the intra-seasonal variations have 
the period of 35 to 90 days. The influence of 
seasonal factors can also be seen from the changes 
in the Malacca Strait wind speed at different 
seasons. 

During western monsoon (December to 
February), the wind velocity in the southern of 
Malacca Strait is higher than the wind velocity in 
the northern of Malacca Strait. Meanwhile, during 
the southeast monsoon, the condition of wind 
velocity in the southern of Malacca Strait is lower 
than the wind velocity in the northern Malacca 
Strait (Fig 3). It shows that the wind velocity 
condition in the Malacca Strait is affected by 

monsoon conditions. Based on Table 3, during the 
eastern monsoon, the wind velocity has the highest 
condition, such as 13 m/s. It shows that the SST has 
the correlation to the wind velocity. 

 
3.2 The correlation between the wind velocity 
and the SST 

Fig 4. indicated that the correlation between 
SST and wind velocity has a period of 4-64 days at 
the points of A, B, and C. The strongest correlation 
occurred in July-August and October-November 
with a period of 32 days. These results are 
consistent with a dominant period of SST, which is 
50 days. It proves that the variation of SST has 
influenced by wind velocity. The arrow indicates 
the phase lag between wind velocity and SST. In Fig 
5. is shown that the wind velocity and SST has a 
phase lag as long as 18 days in July-August and 
October-November at point C. While at points A and 
B, the wind velocity has a phase lag of 8 and 24 days. 
Grinsted (2004) said that the calculation of the 
correlation between wind velocity and SST using 
cross wavelet coherency has a significance level 
greater than 95%. 

 

 

 
Fig. 5. The correlation between the SST and wind velocity at the points of A, B, and C in the Malacca Strait using Cross 

wavelet transform. 



 
Khoirunnisa. H., Wisha,  U., and Lubis M.Z.,/ JGEET Vol 02 No 03/2017 215 

 

 

 
Fig 6. The coherence of SST and wind velocity at the points of A, B, and C in the Malacca Strait using the 

Wavelet coherency. 

 

3.3 The coherence between the wind velocity and 
SST in the Malacca Strait 

Fig 1. showed that the points of A, B, and C are 
the sample to observe the correlation and 
coherence of wind speed and SST. This study proves 
the coherence between the wind velocity and SST 
(Fig 6). Figure 6 provided the coherence between 
wind velocity and SST, it has the period of 4-64 days 
at the points of A, B, and C. These results illustrate 
that the SST variations with a period of 4-64 days is 
influenced by wind velocity. This proves that the 
intra-seasonal variation of the SST in the Malacca 
Strait is influenced by the local wind velocity. 

4. Conclusion 

The SST data in the Malacca Strait have a 
correlation and coherence to the wind velocity. It 
correlation has a period of 4-64 days. In addition, 
the strongest correlation occurred in July-August 
and October-November with a period of 32 days, 
and its confidence level is greater than 95%. The 
wind velocity and SST in the Malacca Strait has a 
phase lag of 8-24 days. In addition, there was a 
coherency between the wind velocity and the SST 
data with a period of 4-64 days at the points of A, B, 
and C in July-August and October-November. These 

correlation and coherence have a similar period 
with the variation of SST, i.e. 5-50 days. It should be 
the intra-seasonal variation. The strongest energy 
spectrum of SST occurred in July-August and 
October-November. It suggests that the intra-
seasonal SST variation (35-90 days) affected the 
wind velocity. 
 

5. Acknowledgment 

The authors gratefully acknowledge to the 
European Centre for Medium-Range Weather 
Forecasts (ECMWF) since provided us the research 
data. So we had finished our research. 
 

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	Amiruddin
	Chua
	50339_b
	Hii
	Lin
	Susanto
	Grinsted
	Rao
	Syamsul
	Tomczak
	Wang
	Wyrtki