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STATISTICAL AND TREND ANALYSIS OF RAINFALL DATA
IN KUCHING, SARAWAK FROM 1968-2010
Ambun Dindang, Azlai bin Taat, Phuah Eng Beng, Atifah binti Mohd Alwi,
Alliscia Ak Mandai, Siti Fauziah binti Mat Adam, Farah Safura binti Othman,
Dayang Norazila binti Awang Bima and Delan Lah.
ABSTRACT
This study is an attempt to analyze and determine the monthly, annual and seasonal trends
of rainfall in Kuching based on the recorded rainfall data from the Kuching observation
station in 1968 to 2010. The trend is obtained using regression linear analysis while the
significance of the observed trend is calculated using Mann Kendall test. The statistical
analysis was also carried out to determine the measure of central tendency and dispersion.
The results showed an overall no statistical significant trend for annual and monthly long
term rainfall data. All monsoon seasons showed insignificant statistical trend even though
the Oct inter monsoon leans in the negative while the other monsoon favoured a positive
trend.
Keywords: Regression Linear Analysis, Mann Kendall Test, Rainfall, Trend
1. INTRODUCTION
1.1 Climate of Malaysia
Malaysia has an equatorial climate characterized by uniform temperature, high
humidity and copious rainfall. Uniform periodic changes in the wind flow patterns can be
described the four seasons, namely, the Southwest monsoon, Northeast monsoon and two
shorter periods of inter-monsoon seasons. The seasonal wind flow patterns coupled with the
local topographic features determine the rainfall distribution patterns over the country.
However, in recent years, several extreme rainfall events have been reported in
Malaysia. For example, an extreme rainfall event occurred on 9-11 December 2004 caused
severe flooding over the east coast of Peninsular Malaysia. Besides that, southern part of
peninsular Malaysia also experienced the massive floods event in the late of December
2006 and in the middle of January 2007 due to heavy rainfall. In addition, according to
previous study, 2009 was known as the extreme year for Sarawak which is two heavy rainfall
episodes occurred in Sarawak in early 2009 causing severe floods that almost covered
whole Sarawak (Hamdan, et.al, 2010). These events have raised concern promoting
research on analyzing the rainfall trend and behaviour of daily rainfall to investigate whether
these changes possibly due to climate change.
1.2 Evaluation Information and Researches on Rainfall Trend Analysis
Statistics analysis from observations data show the changes in weather pattern over
the decades can be used to identify climate change. Rainfall and temperature are often used
as important climate parameters to determine changes in global climate.
Based upon the Intergovernmental Panel on Climate Change (IPCC) Fourth
Assessment Report (AR4), global temperatures have risen by about 0.74°C since the
beginning of the 20th century. The global averaged temperature is the parameter that most
clearly defines global warming. Rising sea level and decrease in snow and ice extent during
summer are indications of global warming. There is a direct influence of global warming on
changes in precipitation and heavy rain. From the Clausius-Clapeyron relation, water-holding
capacity of atmosphere increase by about 7% per 1°C warming. This shows that the
occurrence of global warming contributed to intensify extreme rainfall as well as the rainfall
event.
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Changes in behaviour of these climate indices have attracted a lot of attention from
scientists and researchers throughout the world. Lots of studies have been conducted on the
trend of the rainfall and temperature. Reviews of relevant research included, the study about
the Turkish precipitation data trend (Partal and Kahya, 2006), investigation on the variability
and trend of Summer Monsoon Rainfall over Bangladesh (Ahasan et al. 2010), application of
Mann Kendall test to investigate rainfall trend in Orissa, India (Mondal et al. 2012), analysing
the trend of precipitation data in Pieria Region (Karpouzos et al. 2010) and a study of annual
rainfall trend for Southern Asia region (Manton et al. 2001).
In addition, a lot of researches on the rainfall trend analysis were conducted
especially in the temperate region and several in the tropic region. For the Southeast Asia
region, Manton et al. (2001) found that annual rainfall in the Southeast Asia region decrease
between 1961 and 1998. The number of rainy days is also found to decrease significantly
throughout most of the countries of Southeast Asia. In Malaysia, there are several studies in
investigate the behaviour and trend in daily rainfall data, for example, Suhaila et al. (2010)
investigate the seasonal rainfall trend in peninsula Malaysia and Hashim et al. (2010) study
the trend in rainfall data for Ipoh, Perak. However, a lot of studies on rainfall trend analysis
need to be done especially in a small scale area to find out whether there is any significant
climate change affecting that area.
1.3 Purpose of the Study
This study is a preliminary attempt to observe and investigate the trend of the rainfall
in Kuching, Sarawak.
Monthly and seasonal rainfall data were analyzed to detect the
variability and changes in the trend.
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2. MATERIALS AND METHODS
2.1 Data
Long- term data records are essential for detecting trends or changes. In this study,
the observed daily and monthly rainfall data of Kuching during the period 1968-2010 (43
years) were obtained from the Climate Division of Malaysian Meteorological Department
(MMD).
Daily rainfall data has been summed into monthly and annual totals. For further
analysis, the monthly rainfall data has been categorized according to four seasons,
Northeast Monsoon (Nov-Mar), Southwest Monsoon (May-Sept), and two transition periods
(Apr and Oct).
2.2 Study area
Kuching City is located in western part of Sarawak state of Malaysia as shown in
Figure 1. This capital city of Sarawak is a fast growing city experiencing rapid urbanization
with a population of about six hundred thousand.
Figure 1: Study area – Kuching City.
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2.3 Methods
The statistical analysis is used to determine the measure of central tendency (mean and
range) and dispersion (standard deviation) for rainfall data of Kuching. For identifying the
trend in the rainfall data, the statistical analysis of linear regression method is used. The
results obtained are further verified by using a non-parametric Mann-Kendall test. Figure 2
shows the procedure of the analysis being applied in this study.
Data preparation
Linear Regression Analysis
Mann-Kendall Test Analysis
Seasonal Trend
Annual and Monthly Trend
Figure 2 : Procedure of the analysis applied in this study
2.3.1 Linear Regression
Linear regression is one of the simplest methods to calculate the trend of data in time
series. The equation of linear regression line is given by
Y=a + bX,
Where, x is the explanatory variable and Y is the dependent variable. The slope line is b,
and a is the intercept (value of y when x=0). The slope of regression describes the trend
whether positive or negative. In this study independent variable, Y is rainfall and explanatory
variable X is year.
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Linear regression requires the assumption of normal distribution. In this case, the null
hypothesis is that the slope of the line is zero or there is no trend in the data. The significant
of the slope show by the probability value (p-value) of it. In this study, Microsoft Excel was
used to calculate the trend lines and statistical values of linear regression analysis .The pvalue from the analysis is test for the significant level α=0.05.
The value of R-square (R2), or the square of the correlation coefficient from the
regression analysis is used to show how strong the correlation and relationship between the
variable X and Y. The value is a fraction between 0.0 - 1.0. A R2 value of 1.0 means that the
correlation becomes strong and all points lie on a straight line. On the other hands, when R2
value of 0.0 means that there is no any correlation and no linear relationship between X and
Y.
2.3.2 Mann-Kendall Test
The Mann-Kendall test, is a non-parametric approach, has been widely used for
detection of trend in different fields of research including hydrology and climatology
(Ampitiyawatta and Guo, 2009). It is used for identifying trends in time series data. Each
data value is compared to all subsequent data values. The initial value, S, is assumed to be
0 (no trend). If a data value from a later time period is higher than a data value from an
earlier time period, S is incremented by 1. If the data value from later time period is lower
than a data value from an earlier time period, S is decremented by 1. The net result of all
such increments and decrements yield the final value of S.
Mann Kendall statistic (S) is given by
n −1
S =
n
∑ ∑ sign ( x
j
− xk )
k =1 j = k +1
where:
sign ( x j − x k ) =
+ 1 jika ( x j − x k ) > 0
0 jika ( x j − x k ) = 0
− 1 jika ( x j − x k ) < 0
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The S statistic, in cases where the sample size n is larger than 10, is approximately normally
distributed with the mean equal to 0. The variance statistic is given as:
n
n ( n − 1)( 2 n + 5 ) −
∑ t ( t − 1)( 2 t + 5 )
t
Var ( S ) −
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where t is the extent of any given ties. Then the test statistic, Zc is given below:
S −1
Var ( S )
z=
0
S +1
Var ( S )
if S > 0
if S = 0
if S < 0
The presence of a statistically trend is evaluated using the Z value. A positive (negative)
value of Z indicates an upward (downward) trend. The statistic Z has a normal distribution to
test for either upward or downward trend at α level of significance (usually 5% with
Z0.025=1.96), H0 is reject if the absolute value of Z is greater than Z1-α/2 (Rejected Ho:
|Z|>Z1-α/2 ) where Z1-α/2 is the standard normal deviates and α is the significant level for the
test. Probability value (p-value) from two-tailed test using the Z value also can be used to
test the significant trend. If the p-value is greater than α, the null hypothesis (Ho: there is no
trend in data series) is failed to reject.
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3. RESULT AND DISCUSSION
3.1 Annual and Monthly Rainfall Analysis
Figure 3: An average of annual rainfall in Kuching from 1968-2010
Figure 3 shows the long-term average pattern of the annual rainfall of Kuching. The
annual mean rainfall over Kuching from 1968 to 2010 is 4214.5mm . The maximum rainfall
was recorded in 1977 (5293.4 mm) while the minimum rainfall recorded in 1997 (2822.6mm).
Figure 4: The Mean Monthly Rainfall of Kuching in 1968-2010
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Figure 4, shows the mean monthly rainfall of Kuching during the period 1968-2010
(43 years). It shows that Kuching experiences unimodal mean monthly rainfall pattern
throughout the year. The highest amount of average monthly rainfall was recorded in
January (719.0mm) and contributes to 32% of annual rainfall, followed by December
(11.48%) and February (11.35%), and the lowest was in July (201.4mm) with 4.78% of
annual total followed by June ( 5.34% ) and August (5.57%). Rainfall decrease gradually
from the month of January to July and start increases in the month of August to December.
Table 1: Kuching statistical properties of annual and monthly rainfall from 1968-2010
Month
Season
Mean
(mm)
Minimum
(mm)
Maximum
(mm)
Range
(mm)
Standard
Deviation (mm)
Coeff.
Variation
Jan
Feb
Mar
Apr
May
Jun
July
Aug
Sep
Oct
Nov
Dec
Annual
NE
NE
NE
INT
SW
SW
SW
SW
SW
INT
NE
NE
719.0
478.3
348.8
278.5
251.6
225.2
201.4
234.6
270.4
359.2
364.1
483.6
4214.5
145.8
119.5
148.7
84.6
86.7
105.2
70.1
22.2
94.8
165.6
157.4
145
2822.6
1351.2
1274.5
748.4
503.2
431.8
542.2
385.2
546.5
451.4
625.2
600.8
880.8
5293.4
1205.4
1155
599.7
418.6
345.1
437
315.1
524.3
356.6
459.6
443.4
735.8
2470.8
281.8
226.6
139.9
102.8
74.5
85.4
78.5
106.4
99.7
120.2
104.2
148.0
562.4
0.39
0.47
0.40
0.37
0.30
0.38
0.39
0.45
0.37
0.33
0.29
0.31
0.13
Table 1 shows statistical properties of monthly and annual rainfall for Kuching.
Generally, the monthly rainfall distribution in Kuching is variable. Coefficient of variation
(ratio of standard deviation and mean) is suitable measure of variability of rainfall. The
monthly coefficient of variation (CV) for this area lies between 0.29-0.47. The CV is highest
during February (0.47), followed by August (0.45) and the least during November (0.29) and
May (0.30).
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Table 2: Regression Statistic results for annual and monthly rainfall
Month
Regression Equation
R-square
P-value
Statistical
significant
Jan
y=2.94x+654.3
0.02
0.40
No
Feb
y=0.65x+464.3
0.00
0.82
No
Mar
y=0.36x+340.8
0.00
0.84
No
April
y=0.40x+269.7
0.00
0.77
No
May
y=0.61x+238.2
0.01
0.51
No
June
y=1.44x+193.4
0.05
0.17
No
July
y=0.98x+179.9
0.02
0.32
No
Aug
y=0.26x+228.8
0.00
0.84
No
Sept
y=-0.07x+272.0
0.00
0.95
No
Oct
y=-0.63x+373.1
0.00
0.67
No
Nov
y=-1.23x+391.3
0.02
0.34
No
Dec
y=-0.30x+490.3
0.00
0.87
No
Annual
y=5.34x+4095.8
0.01
0.44
No
The result of the linear regression and Mann- Kendall trend analysis is presented in
Table 2 and Table 3 respectively. In these trend test, trend of rainfall for 43 years from
January to December has been calculated for each month individually.
The linear trend lines of the monthly rainfall shows decreasing trend in September,
October, November and December and increasing trend for other months and annual rainfall
data. Since the probability value (p-value) from regression analysis for the slopes of monthly
and annual trend lines greater than the significant level α=0.05, the null hypothesis, H0: there
is no trend in data, is fail to reject. That means, there is no statistical significant trend in the
annual and monthly rainfall data for Kuching. The R-squared statistic also indicates a very
weak relationship between the variables (rainfall) and year.
To verify the results of linear trend lines, Mann-Kendall statistic, S, is used. Table 3
below shows the result from the Mann-Kendall trend analysis. From the value of S, the
monthly rainfall trend from January to December shows the increasing trend except for
August, October and November. The positive value of S also is an indicator of an increasing
trend for annual rainfall. However, the result of annual and monthly p-value have shown that
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there is no significant trend neither at 0.1, 0.01 nor 0.05 significant level, so that we cannot
reject the null hypothesis H0 (no trend in the series). In other words, there is no significant
trend in annual and monthly rainfall data for Kuching.
Table 3: Mann-Kendall Statistic Result for annual and monthly rainfall
Month
Range (years)
Z value
p- value
Trend
43
MK
Statistic(S)
51
0.5233
0.6008
Increase
Statistically
Significant
No
Jan
Feb
43
43
0.4395
0.6603
Increase
No
Mar
43
41
0.4186
0.6755
Increase
No
Apr
43
47
0.4814
0.6302
Increase
No
May
43
113
1.1721
0.2412
Increase
No
June
43
89
0.9210
0.3571
Increase
No
July
43
70
0.7221
0.4702
Increase
No
Aug
43
-31
-0.3140
0.7535
Decrease
No
Sept
43
3
0.0209
0.9833
Increase
No
Oct
43
-53
-0.5442
0.5863
Decrease
No
Nov
43
-73
-0.7535
0.4511
Decrease
No
Dec
43
49
0.5023
0.6155
Increase
No
Annual
43
91
0.9419
0.3462
Increase
No
3.2 Seasonal Rainfall Analysis
The variability and distribution pattern of rainfall in Malaysia is much influenced by
seasonal wind flow and local topographic features. Northeast monsoon in Malaysia is
characterized by steady easterly or north easterly winds of 10-20 knots. This season is
known as the major rainy seasons which often cause the severe floods due to heavy rainfall.
The prevailing wind flow generally from southwestly of light, below 15 knots is characterized
the Southwest Monsoon. The Southwest Monsoon is comparatively drier seasons
throughout the country. During the inter monsoon seasons, the wind are generally light and
variable.
From the Figure 5, it shows that the highest amount of rainfall in Kuching is in
Northeast Monsoon (Nov- Mar) which is 2393.8mm that contributes 56.8% of the annual
rainfall. For inter-monsoon (Apr), Southwest Monsoon (May- Sept), and inter-monsoon (Oct)
to annual rainfall is 6.6%, 28.1 % and 8.5%, respectively. The result shows that Kuching
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rainfall is directly influence by the monsoon seasons, which is wet season in Northeast
Monsoon and comparatively dry season in Southwest Monsoon.
The coefficient of variation in Inter-monsoon (Apr and Oct) is higher than the
Northeast and Southwest monsoon (Table 4). It is show that the rainfall variability in the
Inter-Monsoon is larger than other seasons.
Figure 5: Kuching Mean Seasonal Rainfall
Table 4: Kuching statistical properties of Seasonal rainfall
Season
Mean
(mm)
Minimum
(mm)
Maximum
(mm)
Range
(mm)
Standard
Deviation
(mm)
Coeff.
Variation
NE
2393.8
1614.1
3271.3
1657.2
414.3
0.17
SW
1183.1
713.3
1729.2
1015.9
216.3
0.18
INT APR
278.5
84.6
503.2
418.6
102.8
0.37
INT OCT
359.2
165.6
625.2
459.6
120.2
0.33
The linear regression analysis shows decreasing trend in Inter-monsoon (Oct)
whereas an increasing trend has been observed for other seasons (Table 5). Since the pvalue for the slope of all monsoon system is greater than 0.05, there is no statistically
significant relationship between rainfall and year at 95% confidence level. The value of Rsquare also indicates a very weak relationship between the variables and period.
11
From the Mann-Kendall analysis, the S values for each monsoon system are
presented in Table 6. The analysis found that negative trend only detected in Inter-Monsoon
(Oct), and the other monsoon shows the positive trend. This result shows the conformation
of regression analysis. However, the probability value for each monsoon is greater than the
significant level 0.1, 0.01 and 0.05. All the values of Z are also less than Z0.025. which makes
it statistically non-significant.
Table 5: Regression Statistic results for seasonal rainfall
Season
R-Square
p- value
NE Monsoon
Regression
Equation
y=2.41x+2340.8
0.01
0.82
Statistically
Significant
No
SW Monsoon
y=3.22x+1112.3
0.03
0.33
No
Inter Monsoon (Oct)
y= -0.63x+373.06
0.00
0.59
No
Inter Monsoon (Apr)
y=0.40x+269.65
0.00
0.84
No
Table 6: Mann-Kendall Statistic Result for seasonal rainfall
Season
Range
(years)
MK
Statistic(S)
Z value
p- value
Trend
Statistically
Significant
NE Monsoon
43
37
0.3768
0.7063
Increase
No
SW Monsoon
43
81
0.8372
0.4025
Increase
No
Inter Monsoon
(Oct)
Inter Monsoon
(Apr)
43
-53
-0.5651
0.572
Decrease
No
43
47
0.4814
0.6302
Increase
No
12
4. CONCLUSION AND FUTURE STUDIES
The rainfall behaviour especially the variability and trend is important for the proper
design of water related system such as drainage system and clean water supply in rapidly
growing cities like Kuching City. From the result of the linear regression and Mann- Kendall
analysis, there is insignificant increasing trend in annual mean rainfall data. The monthly
rainfall data from linear regression analysis showed an increasing trend except for
September, October, November and December. Mann-Kendall analysis results show the
decreasing trend in August, Oct and November. However, the result indicate no statistical
significant in monthly rainfall trend and very weak correlation between rainfall and period.
The results of these test analyses also indicate no significant trend in seasonal rainfall data.
All the results signify no significant detectable effect of global warming on the annual,
monthly and seasonal rainfall trend in Kuching. Air pollution and deforestations from
urbanization process are some of the factors that affecting the climate change. As the
environmental impact from urbanization process maybe quite minimal on this area, this could
lead to the least change in rainfall trend.
Further studies are needed to be conducted to consider other rainfall characteristics
such as extreme rainfall, raindays and other climate change parameter for this station and
nearby station to verify whether the significant trend have occurred. Studies also should be
carried out to find more information on the effect of climate change at this study area which
is predicted can establish a correlation between temperature and extreme rainfall. According
to Westra et al. (2013), he found that there is a statistically significant effect of the globally
averaged near-surface temperature to the extreme rainfall, which is, the median intensity of
extreme precipitation with changed in proportion with changes in global mean temperature at
rate between 5.9% and 7.7% K−1. Hence, it could be said that extreme rainfall events is
related to global warming. As there are many extreme events occurred at this study area
recently, further investigations can be a good approach to develop the current rainfall trend
and compare with data from previous analyses as well as the relationship between
environmental impact and extreme events may be determined Moreover, result from the
future studies is also useful to provide information for the drainage system planning whereby
the occurrence of floods can be expected to be more frequent with respect to the rising
intensity of extreme rainfall events.
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