20320140505008-2

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),

ISSN 0976 – 6316(Online), Volume 5, Issue 5, May (2014), pp. 76-87 © IAEME

76

TESTING THE HOMOGENEITY OF RAINFALL RECORDS FOR SOME

STATIONS IN IRAQ

Najm Obaid Salim Alghazali¹, Dhelal Adnan Hussein Alawadi²

(1)Corresponding author, Asst. Prof. Doctor, Civil Engineering Department, Babylon

University, Iraq (2)

M.Sc. Student, Civil Engineering Department, Babylon University, Iraq

ABSTRACT

In this study three homogeneity tests were used: Pettitt, Buishand and double mass curve

tests. These tests were applied to thirteen Iraqi stations of monthly rainfall observations: Mosul,

Kirkuk, Khanaqin, Ramadi, Baghdad, Karbala, Hilla, Najaf, Diwaniya, Samawa,Nasiriyah, Amara

and Basrah for the period (1970-2010) for all stations except Ramadi (1981-2010) and Hilla (1980-

2010). Pettitt test indicated that there was no break point at any station, while Buishand test indicated

that there was a break point only in Karbala station on March-1998 and double mass curve indicated

that there was a break point at Karbala on March-1998 station and Samaw station on December-1991

so, they were corrected with double mass curve and retested by each of Pettitt and Buishand tests and

they showed no break point.

Keywords: Rainfall in Iraq, Homogeneity of Time Series, Pettitt Test, Buishand Test, Double Mass

Curve Test.

1. INTRODUCTION

Homogeneous rainfall is often required in hydrologic design. However it frequently occurs

that rainfall data over different periods are not comparable since the measured amount of rainfall

depends on such factors as the type, height and exposure of the raingauge, which have not always

been the same. Therefore many meteorological institutes maintain an archive with information on the

raingauge sites and the instrument used. Unfortunately it is often not possible to specify the nature of

changes in the mean amount of rainfall from the station documentation. This is partly because it is

not always known how a change in the instrument or in the raingauge site may influence the

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING

AND TECHNOLOGY (IJCIET)

ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

Volume 5, Issue 5, May (2014), pp. 76-87

© IAEME: www.iaeme.com/ijciet.asp

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IJCIET

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77

measured amount of rainfall and partly because it is highly questionable whether the station

information gives a complete picture of raingauge site during the period that the station has been in

operation.

Because of the uncertainty about possible changes, graphical methods are often used in

climatology and hydrology to obtain some insight into the homogeneity of a record. A popular tool is

a double mass curve which is obtained by plotting the cumulative amounts of the station under

consideration against the cumulative amounts of a set of neighboring stations. The plotted points

tend to fall along a straight line under conditions of homogeneity.

Though graphs are useful for detection of shift in the mean it is usually not obvious how real

changes can be distinguished from purely random fluctuations. Therefore it is always necessary to

test the significance of departure from homogeneity by statistical methods [1].

Busuioc and Storch[2] studied the variability of winter mean precipitation at 14 Romanian

gauge stations from 1901-1988. Pettitt’s statistics was used to detect changes of regimes in the time

series. Almost all stations exhibited systemic decrease (downward shift) at about 1960. Furthermore

upward were identified for the southwestern stations at 1933, and a downward shift in the mid of

1920’s in the northwest. An upward shift at about 1919 for the Bucharest station was likely

determined by the urbanization effect. They found that Pettitt’s statistic was sensitive to the presence

of trend and serial correlation.

Tarhule and Woo [3] examined changes in several rainfall characteristics in northern Nigeria.

The records at 25 locations were analyzed for the occurrence of abrupt changes using the Pettitt

test.They concluded that changes in rainfall over the Sahel were driven by a reduction in the

frequency of rain days of high rainfall intensities during the months of August and September

Karabork et al. [4] studied the homogeneity of 212 precipitation records in Turkey for the

period 1973-2002. They were checked by Pettitt Test. Stations were considered inhomogeneous if at

least one of the tests rejects the homogeneity. He found that 43 out of 212 stations were found to be

inhomogeneous.

Kang and Yusof[5]used Buishand and Pettitt test in checking homogeneity of daily rainfall

series in variables for 33 stations in Damansara, Johor and Kelantan. The results were assessed by

classifying the stations into 3 categories, which are useful, doubtful and suspect. They found that are

28 stations (84.84%) are homogeneous and “useful”, 4 stations (12.12%) are inhomogeneous and

“doubtful” and 1 station is considered as “suspect”.

Arndt and Redmond [6] used the double-mass method to subjectively identify in

homogeneities in temperature and precipitation observations for modernized cooperative observer

(COOP) stations in U.S. Results showed that in most long-term records, the accumulation of values

becomes so large that a double-mass plot masks significant changes in relationship between climate

elements.

Metzger and Sohn[7] used double mass analysis as consistency tool of rainfall data in three

watersheds: Chancay Lambayeque, Chillon and Ramis in Peru from 2008-2011. This analysis was

made to the stations for the three watersheds in order to determine whether there was a need for

corrections to the data. They found that the double mass analysis that applied to all stations had

shown a good behavior in time which meant that the data collection procedures or other local

conditions did not have a significant effect on the data, therefore there was no need for correction.

In this study homogeneity of thirteen Iraqi stations is checked using Pettitt, Buishand and

double mass curve tests.

2. DESCRIPTION OF THE STUDY AREA

The climate in Iraq is mainly of the continental, subtropical semi-arid type, with the north and

north-eastern mountainous regions having a Mediterranean climate. Rainfall is very seasonal and



78

occurs in the winter from December to February, except in the north and northeast of the country,

where the rainy season is from November to April. Average annual rainfall is estimated at 216 mm,

but ranges from 1200 mm in the northeast to less than 100 mm over 60 percent of the country in the

south[8].

In this study total monthly rainfall data for thirteen meteorological stations in Iraq: Mosul,

Kirkuk, Khanaqin, Ramadi, Baghdad, Kerbala, Hilla, Najaf, Diwaniya, Samawa, Nasiriya, Amara

and Basra are used. Fig. 1 shows the stations, in orange color, that are used in this study. The

monthly rainfall of these thirteen stations is analyzed with periods (1970-2010) for all station except

(1981-2010) for Ramadi station and (1980-2010) for Hilla station [9].

Figure (1): Iraqi map showing the thirteen stations, in orange color, which are used in this

study

3. THEORY

3.1 Pettitt Test

Pettit [10] developed a nonparametric test that is capable of locating the period (month or

year) where a break is likely. The null hypothesis is that the data is independent, identically

distributed random quantities, and the alternative is that a stepwise shift in the mean is present. The

test statistic is related to the Mann–Whitney statistic [11].

To detect a break point at a continuous data [10]:

1. The observations (�) are ranked from 1 to N (i.e. ��, ��, …, ��).



79

2. Estimate the value of ��,� :

��=� 1 � 2�� 1,2,3, … , � …………….………….……...…. (1)

where�� is the rank of �� in the sample of �observations.

3. Estimate the value of �� :

�� ……………………………………………… …….. (2)

�� ………….……………………………………......……..….. (3)

4. Detecting the value of ��:

�� max�� |��| ……...…………………...……......……… ...... (4)

5. Estimate the value of �� :

6.

�� 2 �� !"#$"%&"#'( ………………….……………........…..……… (5)

If �� ) * , where * is the statistical significance of the test, then the null hypothesis is rejected.

3.2 Bushand Test This test is used to detect a change in the mean by studying the cumulative deviation from the

mean. It bases on the adjusted partial sums or cumulative deviation from the mean. According to

Buishand [1] the null hypothesis is that the data are homogenous and normally distributed and the

alternative hypothesis is that there is a date at which a change in a mean is occurred. The adjusted

partial sum is defined as:

+,-=0 ;+.- � ∑ 0�� 12.�3� , 4 � 1,2, … , � ….…...…………...…….. (6)

where:

�1 : the mean of time series observations (��, ��, … , ��)

4 : the number of the observation at which a break point is occurred

Rescaled adjusted partial sums are obtained by dividing the +.- ′s by the sample standard

deviation:

+.-- � +.-/67 , 4 � 1,2, … , � ….…………...…………......………. (7)

67 � 8∑ 0"9:; 79�712²� …………….………..……………......…….……. (8)

A statistic which can be used for testing homogeneity is:

< � max,�.��|+.--| ……………………………......……………..… (9)



80

</√�is then compared with the critical values given by Buishand [1]. If a calculated </√� is less

than a critical </√� the null hypothesis is accepted but if a calculated </√� is greater than a

critical </√� the null hypothesis should be rejected.

3.3 Double mass Curve Test The theory of double mass curve is based on the fact that a graph of the accumulation of one

quantity against the accumulation of another quantity during the same period will plot as a straight

line so long as the data are proportional; the slope of the line will represent the constant of

proportionality between the quantities. A break in the slope of the double-mass curve means that a

change in the constant of proportionality between the two variables has occurred or perhaps that the

proportionality is not a constant at all rates of accumulation. If the possibility of a variable ratio

between the two quantities can be ignored, a break in the slope indicates the time at which a change

occurs in the relation between the two quantities. The difference in the slope of the lines on either

side of the break in the slope indicates the degree of change in the relation.

The use of accumulations of two measured variables plotted as a double mass curve may give

indefinite results. To give more definite results, the accumulation of one of the variables can be

plotted against the accumulations of a pattern, which is composed of all similar records in a given

area. The pattern which is composed of the average of many records is less affected by an

inconsistency in the record of any one station[12].

The theory of the double-mass curve suggests the method of adjusting an inconsistent record:

�> � ?>/?@�@ …………………………………………………….. (10)

where:

�>: the adjusted data

�@: the observed data

?>: the slope of graph to which records are adjusted

?@: the slope of graph at time �@ was observed

Significance of an apparent break in the double-mass curve can be determined by an analysis-

of-variance test (or covariance). The statistics used in this test is F, the ratio of the among-periods

variance to the within periods variance. The larger apparent shift in the relation the larger this ratio

becomes.

The test consists of computing f,the variance ratio, from the data being tested and comparing

the computed value with the tabulated value of the F distribution for the level of significance

selected (generally 5%) [12].The null hypothesis is that the break point is not statically significant

and doesn’t need to be adjusted, while the alternative hypothesis is that the break is statistically

significant and needs to be adjusted. The steps of computing f value is are explained in Searcy and

Hardison [12].

If A is smaller than F(α,k-1,N-k), where α is a level of significance (generally 5%), then the

null hypothesis is accepted but if A is larger than F(α,k-1,N-k) then the null hypothesis must be

rejected and the break is statistically significant and it should be adjusted.

4. TESTING OF HOMOGENEITY BY PETTITT TEST

The first step in Pettitt test is ranking the data. After that, the value of each ��is calculated, by

using Equation (1). The value of each �� is calculated by using Equations (2) and (3)and then the

value of ��is detected which equals the maximum absolute value of �� as stated in Equation (4). The

value of �� B * (* � 0.052 which means that the data are homogenous.Table 1 shows the Final

calculations of Pettitt test for Iraqi stations.



81

Table (1): Final calculations of Pettitt test for Iraqi stations

Station Sample Size

(N)

Significance

Level (α) ��

Mosul 492 0.05 4568 0.700489714

Kirkuk 492 0.05 5405 0.288621138

Khanaqin 492 0.05 4366 0.76702084

Ramadi 360 0.05 3310 0.490704409

Baghdad 492 0.05 2708 1.383267725

Hilla 372 0.05 5278 0.078473797

Karbala 492 0.05 4935 0.587826385

Najaf 492 0.05 3332 1.454581077

Diwaniyah 492 0.05 3108 1.230576698

Samawa 492 0.05 5376 0.467692963

Nasiriyah 492 0.05 3834 0.955127429

Amara 492 0.05 2586 1.428923379

Basrah 492 0.05 4699 0.659013415

5. TESTING OF HOMOGENEITY BY BUISHAND TEST

As mentioned in Section (1.2) Buishandtest is used to detect a change in the mean by

studying the cumulative deviation from the mean. The null hypothesis is that the observations have

no break point, while the alternative hypothesis is that the observations have a significant break point

.The first procedure in calculations of Buishand test is finding the mean of data of a station and

calculating +.- using Equation (6) and then calculating +.-- and 67� ,using Equations (7) and (8)

respectively, to find the value of < and comparing the value of </√�with the critical values which

are given by Buishand [1].Table 2 shows the final results of Buishand test for Iraqi stations which are

used in the study.

Table (2): Final calculations of Buishand test for Iraqi stations

Station Sample Size (N) Critical </√� < Observed </√�

Mosul 492 1.36 25.60554 1.15487

Kirkuk 492 1.36 29.04000 1.30922

Khanaqin 492 1.36 26.38292 1.18943

Ramadi 360 1.36 24.60151 1.29661

Baghdad 492 1.36 26.61862 1.20006

Hilla 372 1.36 16.65578 0.86356

Karbala 492 1.36 32.40925 1.46112

Najaf 492 1.36 28.31888 1.27671

Diwaniyah 492 1.36 21.49021 0.96885

Samawa 492 1.36 24.63553 1.11066

Nasiriyah 492 1.36 14.4932 0.65340

Amara 492 1.36 11.11098 0.50092

Basrah 492 1.36 20.56312 0.92706



82

7. DOUBLE MASS CURVE TEST

Double mass curve is used for checking the homogeneity of twelve Iraqi stations. The

procedure that used in calculations of double mass curve is explained in section 1.3. Mosul station

has been taken as a reference station for all stations because it is homogenous, as proving by Pettitt

and Buishand tests and it is also has no missing data. F-test is used for checking the significance of

an apparent break in the double mass curve. Figs 2, 3, 4,…, 13 show the double mass curve for the

Iraqi stations that used in this study. Table 3 shows Final Calculations of F-test for Iraqi stations.

Figure (2): Double mass curve for Kirkuk station

Figure (3): Double mass curve for Khanaqin station

y = 1.0077x

R=.999

y = 0.932x + 946.4

R=0.999

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2000 4000 6000 8000 10000 12000 14000 16000

Cu

mu

lati

ve

Ra

infa

ll f

or

Kir

ku

k S

tati

on

Cumulative Rainfall for Mosul Station

Apr-98

Series1

Series2

Linear (Series1)

Linear (Series2)

y = 0.8423x

R=0.997

y = 0.7713x + 705.08

R=0.997

0

2000

4000

6000

8000

10000

12000

14000

0 2000 4000 6000 8000 10000 12000 14000 16000

Cu

mu

lati

ve

Ra

infa

ll f

or

Kh

an

aq

in s

tati

on

Cumulative Rainfall for Mosul station

Apr-98

Series1

Series2

Linear (Series1)

Linear (Series2)



83

Figure (4): Double mass curve for Ramadi station

Figure (5): Double mass curve for Baghdad station

Figure (6): Double mass curve for Hilla station

y = 0.3068x

R=0.997

y = 0.2918x + 166.39

R=0.993

0

1000

2000

3000

4000

0 2000 4000 6000 8000 10000 12000

Cu

mu

lati

ve

Ra

infa

ll f

or

Ra

ma

di st

ati

on


Mar-97

Series1

Series2

Linear (Series1)

Linear (Series2)

y = 0.3768x

R=0.985

y = 0.3159x + 302.23

R=0.988

0

1000

2000

3000

4000

5000

6000

0 2000 4000 6000 8000 10000 12000 14000 16000Cu

mu

lati

ve

Ra

infa

ll f

or

Ba

gh

da

d s

tati

on


Apr-95

Series1

Series2

Linear (Series1)

Linear (Series2)

y = 0.2696x

R=0.997

y = 0.2929x - 158.83

R=0.999

0

1000

2000

3000

4000

0 2000 4000 6000 8000 10000 12000

Cu

mu

lati

ve

Ra

infa

ll f

or

Hil

la s

tati

on


Mar-98

Series1

Series2

Linear (Series1)

Linear (Series2)



84

Figure (7): Double mass curve for Karbala station

Figure (8): Double mass curve for Najaf station

Figure (9): Double mass curve for Diwaniyah station

y = 0.3005x

R=0.991

y = 0.2234x + 717.16

R=0.999

0

1000

2000

3000

4000

5000

0 2000 4000 6000 8000 10000 12000 14000 16000Cu

mu

lati

ve

Ra

infa

ll

for

Ka

rba

la s

tati

on

Cumulative for Mosul station

Mar-98

Series1

Series2

Linear (Series1)

Linear (Series2)

y = 0.2955x

R=0.997

y = 0.239x + 536.91

R=0.995

0

1000

2000

3000

4000

5000

0 2000 4000 6000 8000 10000 12000 14000 16000Cu

mu

lati

ve

Ra

infa

ll f

or

Na

jaf

sta

tio

n


Mar-98

Series1

Series2

Linear (Series1)

Linear (Series2)

y = 0.2977x

R=0.995

y = 0.2428x + 887.38

R=0.996

0

1000

2000

3000

4000

5000

0 2000 4000 6000 8000 10000 12000 14000 16000

Cu

mu

lati

ve

Ra

infa

llfo

r D

iwa

niy

ah

sta

tio

n


Apr-02

Series1

Series2

Linear (Series1)

Linear (Series2)



85

Figure (10): Double mass curve for Samawa station

Figure (11): Double mass curve for Nasiriya station

Figure (12): Double mass curve for Amara station

y = 0.2293x

R=0.993

y = 0.3502x - 1115.8

R=0.9887

0

1000

2000

3000

4000

5000

0 2000 4000 6000 8000 10000 12000 14000 16000

Cu

mu

lati

ve

Ra

infa

ll f

or

Sa

ma

wa

sta

tio

n

Cumulative Rainfall of Mosul station

Dec-91

Series1

Series2

Linear (Series1)

Linear (Series2)

y = 0.3308x

R=0.998

y = 0.3907x - 630.57

R=0.995

0

1000

2000

3000

4000

5000

6000

0 2000 4000 6000 8000 10000 12000 14000 16000

Cu

mu

lati

ve

Ra

infa

ll f

or

Nsi

riy

ah

sta

tio

n


Jan-97

Series1

Series2

Linear (Series1)

Linear (Series2)

y = 0.4533x

R=0.995

y = 0.5689x - 1152.5

R=0.990

0

1000

2000

3000

4000

5000

6000

7000

8000

0 2000 4000 6000 8000 10000 12000 14000 16000

Cu

mu

lati

ve

Ra

infa

ll f

or

Am

ara

sta

tio

n


Mar-96

Series1

Series2

Linear (Series1)

Linear (Series2)



86

Figure (13): Double mass curve for Basrah station

Table 3 shows the final calculations of F-test forstations that are used in this study.

Table 3: Final Calculations of F-test for Iraqi stations

Station Sample size (N) Date of

Break point

Critical

F

Observed

f

Kirkuk 492 April-1998 3.861 1.491116

Khanaqin 492 April-1998 3.861 1.07195

Ramadi 360 March-1997 3.8742 0.141963

Baghdad 492 April-1995 3.861 1.84374

Hilla 372 March-1998 3.873 0.02773

Karbala 492 March-1998 3.861 4.106744

Najaf 492 March-1998 3.861 2.101180

Diwaniyah 492 April-2002 3.861 3.028565

Samawa 492 December-1991 3.861 7.044241

Nasiriyah 492 January-1997 3.861 0.856929

Amara 492 March-1996 3.861 2.89694

Basrah 492 December-1993 3.861 0.275821

As shown in Table 3 there are two stations that have a significant break, they are Karbala and

Samawa stations. The breaks of these stations are corrected using Equation (10).The value of

correction factor for Karbala station is 1.345 and for Samawa station is 0.655. The corrected stations

are retested by Pettitt test and Buishand and it is found that they have no break. For Pettittt test the

value of �� for Karbala station is 1.287031 and for Samawa station is 1.168666. For Buishand test

the value of </√� for Karbala station is 0.9409098 and for Samawa station is 1.1719214.

8. CONCLUSIONS

Pettitt test indicates that there is no break point at any station of the studied stations.

Buishand test indicates that there is a non-homogeneity in Karbala station at March-1998 while, the

other stations are homogeneity. Double mass curve indicates that there is a break in each of Karbala

station at March-1998 and Samawa station at December-1991 and they are corrected by double mass

curve itself. Double mass curve indicates that there is no break in other stations. KarbalaSamawa

stations are retested by Buishand and Pettitt tests and it is found that they have no break.

y = 0.3853x

R=0.998

y = 0.433x - 511.54

R=0.994

0

1000

2000

3000

4000

5000

6000

7000

0 2000 4000 6000 8000 10000 12000 14000 16000Cu

mu

lati

ve

Ra

infa

ll f

or

Ba

sra

h s

tati

on


Dec-93

Series1

Series2

Linear (Series1)

Linear (Series2)



87

9. REFERENCES

1. Buishand T. A., “Some Methods for Testing the Homogeneity of Rainfall Records”, Journal of

Hydrology, Elsevier Scientific Publishing Company, Amsterdam, Netherlands, 58, 1982,

PP. (11-27).

2. Busuioc A. and Storch H. V., “Changes in the Winter Precipitation in Romania and its

Relation to the Large-Scale Circulation”, Munksgraad, Tellus, U. K., Vol. 48A, 1996,

PP. (538-552).

3. Tarhule A. and Woo M. K., “Changes in Rainfall Characteristics in Northern Nigeria”,

International Journal of Climatology, Royal Meteorological Society, 18, 1998,

PP. (1261–1271).

4. Karabork M. C., Kahya E. and Komuscu A. U., “Analysis of Turkish Precipitation Data:

Homogeneity and the Southern Oscillation Forcings on Frequency Distributions”,

Hydrological Processes, John Wiley & Sons, Ltd., 21, 2007, PP.(3203–3210).

5. Kang H. M. and Yusof F., “Homogeneity Tests on Daily Rainfall Series in Peninsular

Malaysia”, Int. J. Contemp. Math. Sciences, Department of Mathematics, Johor, Malaysia

Vol. 7, No. 1, 2012, PP. (9 – 22).

6. Arndt D. S. and Redmond K. T., “Toward an Automated Tool for Detecting Relationship

Changes within Series of Observations”, Paper, Posted at the internet website

https://ams.confex.com/ams/pdfpapers/72826. pdf, 2004.

7. Metzger L. and Sohn S. J., “Validation of APCC Precipitation Forecasts by Using Hydrologic

Models”, Report, APEC Climate Center, Busan, Korea, 2011.

8. Frenken K., Irrigation in the Middle East region in figures”, Survay, Food and Agriculture

Organization of the United Nations (FAO), Rome, Italy, ISBN 978-92-5-106316-3, 2009.

9. Iraqi Meteorological Office, Baghdad, Iraq.

10. Pettitt A. N., “A Non-Parametric Approach to the Change-Point Problem”, Applied Statistics,

Leics, England, 28, No. 2, 1979, PP. (126-135).

11. Costa A. C. M., Negreiros J. and Soares A., “Identification of Inhomogeneities in Precipitation

Time Series Using Stochastic Simulation”, Springer Science+Business Media, 2008,

PP.(275–282).

12. Searcy J. K. and Hardison C. H., “Double-Mass Curves”, Geological Water Supply Paper

1541-8, Geological Survey, Washington, U.S, 1960.

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