Environmental

Communication

Biosci. Biotech. Res. Comm. 10(4): 662-671 (2017)

Trend step changes of seasonal and annual precipitation

over Kermanshah during a 60-year period using

non-parametric methods

Amir Hossein Hashemian,

1,3

Mansour Rezaei,

2,3

* Hajar Kashe ,

Meghdad Pirsaheb

1,4

and

Hassan Kharajpour

Research Center for Environmental Determinants of Health (RCEDH), Kermanshah University of Medical

Sciences, Kermanshah, Iran

Social Development and Health Promotion Research Centre, Kermanshah University of Medical Sciences,

Kermanshah, Iran

Department of Biostatistics, Faculty of Health, Kermanshah University of Medical Sciences, Kermanshah, Iran

Department of Environmental Health, Faculty of Health, Kermanshah University of Medical Sciences,

Kermanshah, Iran

PhD student of Meteorology, Department of Geography, University of Kharazmi, Tehran, Iran

ABSTRACT

One of the approaches usedtoinvestigate trend step changes in precipitation isstatistical techniques.The main objective ofthis paper is

toidentify and analyze thetrend ofchanges in annual and seasonalprecipitation overthe studied area.The current study employs monthly

precipitation data from 1951 to 2010 derived from a weather station in Kermanshah. Using non-parametric Mann-Kendall test and

graphic based methods depicting total annual and seasonal (cold and warm seasons) precipitation, the research analyzes trend changes

of Kermanshah over different time series. Primarily, data changes in studied seasons and years are analyzed. Then, type and time of these

changes are identi ed. Averages of monthly precipitation overKermanshah during warm and cold seasons are determined as 47.9±33.64

Mm and 169.68±54.56 Mm, respectively. There is no signi cant trend in annual precipitation over Kermanshah. Analysis of averages

precipitation of warm and cold seasons indicates no signi cant trend; however, warm season seems to follow a decreasing trend in

general. Yet, there are leaps in the average levels of both annual and seasonal precipitation. The obtained results show that general trend

of change in average precipitation during warm seasons is downward with leaps of average during the studied period. But, in general,

there is no signi cant trend of change in the averages of annual and seasonal precipitation during the studied time.

KEY WORDS: CHANGES OF PRECIPITATION, TREND ANALYSIS, ANNUAL, SEASONAL, KERMANSHAH, NON-PARAMETRIC MANN-KENDALL

TEST

662

ARTICLE INFORMATION:

*Corresponding Author: rezaei39@yahoo.com

Received 22

Oct, 2017

Accepted after revision 27

Dec, 2017

BBRC Print ISSN: 0974-6455

Online ISSN: 2321-4007 CODEN: USA BBRCBA

Thomson Reuters ISI ESC and Crossref Indexed Journal

NAAS Journal Score 2017: 4.31 Cosmos IF: 4.006

reserved.

Online Contents Available at:

http//www.bbrc.in/

DOI: 10.21786/bbrc/10.4/8

Amir Hossein Hashemian et al.

INTRODUCTION

Precipitation is the most important input data in hydro-

logical cycle which needs to be considered mostly in

runoff, drought, groundwater,  ood and sediment stud-

ies. Now a day, global warming, caused by increasing

greenhouse gases, and its effect on climate change is

a scienti c fact accepted by many researchers. Almost

all processes in the biosphere are affected by climate

change and the effect of this phenomenon on the envi-

ronment and water resources is a matter of great con-

cern. In order to be prepared against adverse effects of

climate change and to reduce its resulting damages, it is

necessary to study common trends of change in weather

variables in each area so as to adopt proper policies

and plans for development and management ofwater

resources Katirai et al., (2007) Aziz and Burn (2006) and

Chen et al., (2007).

To detect trends of weather variables in different time

intervals various test may be used which can be divided

into two groups: parametric and non-parametric tests.

Parametric tests have more trend analysis potentials than

non-parametric tests and require random (independent)

data with normal distribution. On the other side, non-

parametric tests are consistent with random data and

are not sensitive to normal distribution. Mann-Kendall

and Spearman are examples of these tests used in trend

analysis of weather variables.

In general, trend analysis of climate change, changes

in precipitation trend in particular, is among issues that

have been considered by researchers of climate and

hydrology science, in recent years. Regardless of climate

status of a region (wet or dry), precipitation trend analy-

sis of a region may aid executives and managers asso-

ciated with water issue to make better decisions about

implementation of future development projects. Consid-

ering that large parts of Iran is located in belt of arid and

semi-arid regions of earth , on one hand, and impor-

tant role of precipitation in supplying water resources of

the country, on the other hand, has put more emphasis

on gaining greater awareness of trends of precipitation

over Iran. Broad investigations have been carried out

to identify the process of precipitation over the whole

world and Iran. With respect to the signi cant impact of

precipitation on climate system numerous studies have

been conducted, including the studies of Matyasovszky

et al. 1993, Angel and Huff (1997) Keily et al (1998)

Gellens (2000) Piccarreta et al. (2004) Xu et al. (2003)

Turgay and Ercan (2005).

All of these studies, trend analysis of precipitation

intervals is carried out using non-parametric tests.

Trend analysis of precipitation in different time inter-

vals using parametric and non-parametric methods has

attracted the attention of many domestic researches, as

well. Kamali (11) investigated precipitation trend of dif-

ferent stations during statistical period from 1986-1996

and found that precipitation trend was both increscent

and decrescent depending on the region. He indicated

that increscent trend has been more frequent Iran than

decrescent trend.

Javeri investigated temporal changes in temperature

and precipitation over Iran using statistical tests with

 xed and variable model and proved that the variation

is signi cant and these changes appear in the form of

random displacements, changes in trend, seasonal  uc-

tuations, and periodical changes. Accordingly, in term of

temporal changes in temperature and precipitation, Iran

is divided to  ve different zones. In this study, to meas-

ure seasonal and annual trend of precipitation data, two

non-parametric tests, Mann-Kendall test and Sen’s Esti-

mator, are used and the results are compared. Proving

the signi cance of precipitation trend in a given time

interval cannot be decisive evidence on climate changes

in a region on its own, however, it strengthens such a

hypothesis. It is caused bymultiplicity offactors control-

ling the climate system (KamaliGh 1996., Javeri 2003

Serrano et al., (1999)

Kermanshah Province, situated in western Iran,

spreads over an area of 25,000 km2 (9,560 square miles,

roughly the size of Vermont), or 1.5 percent of the total

area of the country (Fig.1). It lies between latitudinal

45.5° and 48° E, longitudinal 33.7° and 35.3° N .The

province is bound on the south by Il

¯m Province, on the

southeast by Lorest

¯n Province, on the east by Hamad

¯n Province, on the north by Kordest

¯n Province, and

on the west by Iraq, with about 250 km of international

borderline. The capital city of this province is Kerman-

shah (Ahmadi et al 2010 ).

The province is bound on the south by Il

¯m Province,

on the southeast by Lorest

¯n Province, on the east by

Hamad

¯n Province, on the north by Kordest

¯n Province,

and on the west by Iraq, with about 250 km of interna-

tional borderline. Considering the geographical location

of Kermanshah, studies of climate change during the

past decades and identifying that it follows a trend or

not, with respect to recent droughts and growing popu-

lation, may affect making proper policies to deal with

drought and proper consumption. Such a study has not

been done in this way in the metropolis of Kermanshah,

so far.

MATERIAL AND METHODS

To examine the trend of change in precipitation of Ker-

manshah and  nd a proper model for it, monthly pre-

cipitation data of synoptic meteorological station (mm)

in a 60-year period (1951-2010) are derived from Mete-

BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS TREND STEP CHANGES OF SEASONAL AND ANNUAL PRECIPITATION 663

Amir Hossein Hashemian et al.

FIGURE 1. Map of geographical location of Kermanshah

orological Organization of Iran. Seasonal precipitation is

a collection of monthly rainfall and annual precipitation

is a collection of seasonal rainfall. The obtained data are

restored using correlation method and regression model.

Data homogeneity is evaluated using Run test so as to

be sure homogeneity of data in a 60-year period. In the

 rst place, this test is employed to indicate that time

series are non-parametric. In doing so, statistical series

are arranged in ascending order. In this test, having no

de ned trend indicates that data are random. If we  nd

a trend, data are not random. To show that data are ran-

dom, the following test was carried out as per Mitchell

et al (1996):

Where T is Kendall’s statistic, n is total statistical years,

and P is total number of ratings bigger than n

placed

under it and can be determined through the following

relation:

The following equation tests the signi cance of T:

Where t

is critical value of normal standard (z) with the

test probability level which is 1.96 at the con dence

level of 95%. If -T, < T < +T, series are random with no

trend. T < - T

indicates a downtrend and if T < + T

a ris-

ing trend is governs the time series (16). If n represents

a 60-year period, the obtained values would be ± 0.089.

To determine the trend direction, type, and time,

graphic Kendall test has to be carried out. In calculat-

ing thestatistics using graphical sequential mann-ken-

dalltest for detection of change time, in two phases of

beginning to end, and vice versa, plotted in one graph,

change point appears well. Detailed (short term) proce-

dures, change in position, or starting point of the series

are examined using time series graphs of u(t) and u´(t).

If you graph u and u´ sequences indexed by i, when the

trend is signi cant, the two lines intersect, outside the

range of1.96, at the starting point and move in opposite

direction. This intersection point is referred to as a leap.

While, if there was no trend, the two sequences (u and u´)

would move on roughly in a parallel direction or intersect

each other in a several points in a way that result in no

change in direction. U graph is plotted based on year and

u´ is de ned to show its signi cance of leap point. Where

-1.96<u<1.96, series are random and no certain trend can

be de ned. But, u>1.96 and u<-1.96 indicate existence of

a positive and a negative trend, respectively. This study

considers a two-dimensional data matrix (12×60: 60 =

studies years, 12=number of months).

If data series indicate a certain trend, the actual slope

(change rate per unit of time), can be obtained using a

simple non-parametric methodof Sen’s slope estimator.

First, obtain slope of each pair of consecutive data series

using the following equation:

664 TREND STEP CHANGES OF SEASONAL AND ANNUAL PRECIPITATION BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS

Amir Hossein Hashemian et al.

BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS TREND STEP CHANGES OF SEASONAL AND ANNUAL PRECIPITATION 665

Where, X

and X

are data values in time j and k, respec-

tively, which differ one unit of time, Q

is the median

value, and n is slope of line estimated by Sen’s slope

estimator. Sen’s slope estimatoris obtained through the

following equation:

Where n is an even number, Sen’s slope estimatoris

achieved as:

If you measure Q

med

with mutual test at the con dence

level of 100(1-)%, it is possible to obtain the actual value

of the line slope. Considering zero between two derived

slopes, no trend can be attributed to the time series with

this con dence level. Otherwise, signi cant trend of time

series, at the considered level of con dence, is proved.

Total monthly precipitation data in 1996, from January

to May, is not available so average precipitation value of

other months are used. Months of the year are divided

into two groups, warm and cold months, and trends in

each group are examined and compared separately.

RESULTS AND DISCUSSION

Average precipitation over Kermanshah per month

(±Standard Deviation) is 36.18 mm (±42.52) and the

highest amount of precipitation per month during the

statistical period (60 years) is 494.8 mm recorded in 1974.

The least amount of precipitation is zero and recorded

during summer. Mann- Kendall test results for total

annual precipitation are calculated and drawn. During

the studied period, no trend is detected in average pre-

cipitation over Kermanshah weather station within the

signi cant levels of the test since u and u´, at no time

interval, intersect outside the meaningful range1.96

(Chart 1). From 1968 to 1975 the graph falls above 1.96;

changes which indicate leapsin total annual precipita-

tion during these years.

Distribution of annual precipitation during the stud-

ied years is drawn. The least amount of annual precipita-

tion is 215.8 recorded in 1995 and the highest amounts

of precipitation is 785.5 recorded in 1996 and 783.9

recorded in 1957 (Chart 2).

According to the results of Mann-Kendall diagram,

no signi cant trend is detected in annual precipitation

data recorded during the studied period (60 years).Sen’s

slope estimator con rms the obtained results. The value

of statistic in Z is 0.03. With respect to obtained values

for the highest (1.67) and lowest (-2.26) amount of Q,

with con dence level of 95%, it may be concluded that

null hypothesis of this test is con rmed and no trend

in detected in the precipitation data recorded during

the 60-year period. In Sen’s slope estimator test, null

hypothesis is: there is no trend is the studied period.

Considering the obtained P-value (>0.05) and available

CHART 1. Mann-Kendall graph of total annual precipitation over Kermanshah during a 60-year period

Amir Hossein Hashemian et al.

666 TREND STEP CHANGES OF SEASONAL AND ANNUAL PRECIPITATION BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS

data, the assumption of existence of a trend in the stud-

ied period is rejected. In other words, no trend can be

attributed to existing data. With regard to the highest

and lowest slope values, zero depends on the interval

between these two values. Therefore, null hypothesis of

the test is con rmed based on this con dence interval

(Table 1).

Average precipitation over Kermanshah per month (±

standard deviation) is 47.9 Mm (±33.64) and the highest

amount of precipitation per month during the statistical

period (60 years) is 297.6 mm recorded in spring of 1963.

Average monthly precipitation over Kermanshah dur-

ing cold seasons is 169.68 mm (±54.56) and the highest

amount of monthly precipitation during cold seasons is

494.8 mm recorded in winter of 1947. The least amount

of precipitation is zero and recorded mostly in summers.

Mann – Kendall test results of average monthly pre-

cipitation are analyzed and drawn for both warm and

cold seasons. During warm seasons of the study period,

the average amount of precipitation over Kermanshah

weather station indicates no statistically signi cant

trend in the signi cant range; however, from 1951 to

1968, a rising trend is detected with sharp leaps and falls

and positive phase of change is witnessed in precipita-

tion. In 1969, a leap from average is occurredand data

are considerably increased. Again, in 1977 the precipita-

tion goes back to normal phase. Since 1978 precipitation

level follows a decreasing trend which again has its own

ups and downs and does not go beyond the signi cant

level (Chart 3).

Diagram of distribution of average monthly pre-

cipitation over Kermanshah during warm seasons of a

60-year period is drawn. The lowest and highest aver-

ages of monthly precipitation during warm seasons are 0

and 148.8, respectively, recorded in 1963 (Chart 4).

According to the results of Mann-Kendall diagram

for warm seasons, no signi cant trend is detected in

monthly precipitation data recorded during the stud-

ied period (60 years).Sen’s slope estimator con rms the

obtained results. The value of statistic in Z is 0.69. With

respect to obtained values for the highest (1.11) and low-

est (-63.1) amount of Q, with con dence level of 95%,

it may be concluded that null hypothesis of this test is

con rmed and no trend in detected in the precipitation

data recorded during the 60-year period (Table 2).

Considering the obtained P-value (>0.05) and avail-

able data, the assumption of existence of a trend in the

studied period is accepted. In other words, no trend can

CHART 2. Distribution of total annual precipitation over Kermanshah

Table 1. Results of Sen’s slope estimator test for total annual precipitation over Kermanshah

variable Time interval Number of years Z statistic p-value Qmax Qmin

Amount of

precipitation

1951-2010 60 0.03 0.488 1.67 -2.26

Amir Hossein Hashemian et al.

BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS TREND STEP CHANGES OF SEASONAL AND ANNUAL PRECIPITATION 667

CHART 3. Mann – Kendall diagram of average monthly precipitation over Kermanshah during warm sea-

sons of a 60-year period

CHART 4. Distribution of average monthly precipitation over Kermanshah during warm seasons

Amir Hossein Hashemian et al.

668 TREND STEP CHANGES OF SEASONAL AND ANNUAL PRECIPITATION BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS

Table 2. Results of Sen’s slope estimator test for total monthly precipitation over Kermanshah

variable Time interval Number of years Z statistic p-value Qmax Qmin

Amount of

precipitation

1951-2010 60 1.56 0.059 0.06 -0.712

CHART 5. Mann – Kendall diagram for average precipitation over Kermanshahduring cold seasons of a

60-year period

be attributed to existing data. With regard to the highest

and lowest slope values, zero depends on the interval

between these two values. Therefore, null hypothesis of

the test is con rmed based on this con dence interval

(table 2). Although, with regard to Sen and Mann-Kend-

all statistical indicators, no signi cant trend is detected

in average monthly precipitation during warm seasons,

the general trend of time series is decrescent (Chart 4).

The linear equation of times series obtained by trend

analysis test is

= 61.78 - 0.455  t (t is the time differ-

ence since the beginning of time series). The linear equa-

tion obtained by Sen’s slope estimator is below:

Forecasts of the two employed tests for the average

precipitation in warm seasons are very close and similar.

To examine existence of trend in precipitation during

cold seasons, Mann-Kendall test and Sen’s slope estima-

tor are used, the results of which are as follows. During

cold seasons of the studied period, no trend is detected

in average precipitation over Kermanshah weather sta-

tion within the signi cant levels of the test. In 1967, a

leap from average is occurred and this sudden change

continues in an upward positive direction until 1995.

Then, until the end of the study period, precipitation fol-

lows a downward trend (Chart 5).

The lowest and highest averages of monthly precipi-

tation during cold seasons are 51.6 and 325.35, respec-

tively (Chart 6).

According to the results of Mann-Kendall diagram,

no signi cant trend is detected in annual precipitation

data recorded during the studied period (60 years).Sen’s

slope estimator con rms the obtained results. The value

of statistic in Z is 0.69. With respect to obtained values

for the highest (1.11) and lowest (-0.63) amount of Q,

with con dence level of 95%, it may be concluded that

null hypothesis of this test is con rmed and no trend in

detected in the precipitation data recorded during the

60-year period (table 3).

Considering the obtained P-value (>0.05) and avail-

able data, the assumption of existence of a trend in the

studied period is accepted. In other words, no trend can

be attributed to existing data. With regard to the highest

and lowest slope values, zero depends on the interval

between these two values. Therefore, null hypothesis of

the test is con rmed based on this con dence interval

(Table 3).

Generally, a comparison between average precipi-

tations during warm and cold seasons indicate that

Amir Hossein Hashemian et al.

BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS TREND STEP CHANGES OF SEASONAL AND ANNUAL PRECIPITATION 669

CHART 6. Distribution of average monthly precipitation over Kermanshah during cold seasons

Table 3. Results of Sen’s slope estimator test for average precipitation over Kermanshah during

cold seasons

variable Time interval Number of years Z statistic p-value Q min Q max

Average

precipitation

1951-2010 60 0.69 0.246 -0.63 1.11

changes in warm season starts a downward trend since

1970. But an upward trend of precipitation in cold sea-

sons changes to a downward direction since 1993. In the

beginning years of the study period, changes in average

monthly precipitation during warm seasons is more than

cold seasons; however, the more we approach the end

of the study period, the less evident are these ups and

downs.

1. Statistical studies of precipitation have been large-

ly considered since 1980. Statistical studies of

Kane and Trivedi (1988), Karl (1988)and Katsoulis

and Kambetzldis (1989) are among these. When

compared with Iran with annual precipitation of

about 260 mm, Kermanshah, with average annual

precipitation of 434 mm, is regarded as an area

with high rate of precipitation. Trend step changes

in precipitation are evident in different stations.

But in most stations, the trend of change seems not

be statistically signi cant. Average monthly pre-

cipitation over Kermanshah during warm and cold

seasons indicates no signi cant trend of change.

The results of this study are different from the

 ndings of the study carried out by Jahanbakhsh

et al. in which they measured changes in precipi-

tation and temperature of Karkha region. This dif-

ference may be due to differences in geographical

location of the two regions (19). But, Hejam et al.

research is consistent with the current study. They

examined trend of changes in seasonal and annual

precipitations over several meteorological stations

and because of lack of trended and un-trended

series they could not attribute a certain trend to

seasonal and annual precipitations of the studied

region, ( Jahanbakhsh et al., (2010) Negaresh et al

(2012) .

Amir Hossein Hashemian et al.

670 TREND STEP CHANGES OF SEASONAL AND ANNUAL PRECIPITATION BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS

Investigation seasonal (warm and cold) trend of pre-

cipitation indicated that average precipitation during

warm seasons of the 60-year period is generally down-

ward; however, this trend is not signi cant at 0.05.

The results of this study are consistent with the results

obtained from the study of Alijani et al. (2012). During

summer, cloud formation and precipitation is not pos-

sible over a wide range of Iran. Therefore, this season

is the driest season. In the 60-year period, because of

lack of precipitation during summer, changes in aver-

age precipitation during warm seasons was similar to

springs which was different to that of Katirai et al report.

They found a decreasing trend for spring precipitation

in Iran. Although, they examined precipitation trend of

the whole country of Iran from 1960 to 2001 but we

only studied Kermanshah with more detail and during

a longer period. Negaresh et al. (2012 ), in a statistical

investigation of changes in precipitation over Saqqez,

found similar results and decreasing trend for precipita-

tion during summer. Although we found no signi cant

trend for precipitation during warm seasons, direction of

changes in precipitation trend was downward.

The current study found no trend for precipitation

during cold seasons and in this regard our  ndings are

consistent with Alijani et al 2012 . studies of precipita-

tion during cold seasons indicated no trend, either, and

these  ndings are consistent with the study of Negaresh

et al. (2012). In case of  nding a trend, precipitation

forecast for coming years would be possible.

CONCLUSION

In general, annual precipitation over Kermanshah, dur-

ing a 60-year period, from 1951 to 2010, follows no

speci c (downward or upward) trend. General changes

in trend of precipitation during warm seasons, although

non-signi cant, follow downward directions. Also, some

leaps of change are witnessed in annual and seasonal

trend of precipitation.

ACKNOWLEDGMENT

The researchers wish to thank Deputy of research and

technology of university for their  nancial support of

this project (No.93502), and Weather Organization for

their cooperation and allowing us to use data recorded

in synoptic meteorology station.

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