Global and Planetary Change 75 (2011) 67–75

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Global and Planetary Change

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Statistically-based regionalization of rainfall climates of Iran

Reza Modarres a,⁎, Ali Sarhadi b

a INRS-ETE, 490 de la Couronne, Quebec, Qc, Canada, G1K 9A9b Faculty of Natural Resources, Isfahan University of Technology, Isfahan, Iran

⁎ Corresponding author.E-mail address: reza.modarres@ete.inrs.ca (R. Moda

0921-8181/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.gloplacha.2010.10.009

a b s t r a c t

a r t i c l e i n f o

Article history:Received 6 September 2009Accepted 18 October 2010Available online 28 October 2010

Keywords:spatial analysisclimate regionfrequency distributionstatistical analysiscluster analysisWard's methodL-momentsIran

Iran is a large country with diverse geophysical and climatic conditions which are influenced by both largeatmospheric circulation patterns and local effects. The density of rainfall station network of Iran is not enoughfor rainfall estimation at ungauged regions.Therefore, rainfall regionalization should be used to extend rainfall data to regions where rainfall data are notavailable. The aim of this study is to use cluster analysis and L-moment methods together to quantify regionalrainfall patterns of Iran using annual rainfall of 137 stations for the period of 1952–2003. The cluster analysisfollows “Ward's method” and shows eight regions of rainfall in Iran. The homogeneity test of L-moments showsthat most of these regions are homogeneous. Using the goodness-of-fit test, ZDist, the regional frequencydistribution functions for each group are then selected. The 3-parameter LogNormal (LN3), Generalized ExtremeValue (GEV) and generalize logistic (GLOG) distributions are selected for the first, second and the remaining 6regions of rainfall over Iran, respectively. However, because of different rainfall generating mechanisms in Iransuch as elevation, sea neighborhood and large atmospheric circulation systems, no parent distribution could befound for the entire country.

rres).

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© 2010 Elsevier B.V. All rights reserved.

1. Introduction

The identification of the spatial pattern of rainfall is usually anessential need for water resources planning and management.However, the rainfall fluctuation from year to year and from placeto place is usually difficult to be fully recognized. Therefore, manypresent-day hydrologic and climatic studies are trying to find anddevelop methods for the regionalization of hydrologic and climaticvariables. Regional classification of these variables helps scientists tosimplify the hydro-climatic convolution and therefore reduce themassive body of information, observation and variables.

Several methods are commonly used for the regionalization ofhydro-climatic variables such as rainfall, streamflow, flood, drought,evapotranspiration and other components of the water cycle.Multivariate techniques, such as a cluster analysis (CA) and principalcomponent analysis (PCA), are very common methods for classifica-tion (Romero et al., 1999; Singh, 1999; Ramos, 2001).

Since the introduction of L-moments by Hosking andWallis (1997),many studies have used L-moments for regionalization of hydro-climatic variables. For example this method is widely used for regionalflood frequency analysis. Kjeldsen et al. (2002) applied L-moments forregional frequency analysis of annual maximum series of flood flows in

KwaZulu-Natal Province of South Africa and identified homogeneousregions and a suitable regional frequency distribution for each region.Kumar and Chatterjee (2005) employed the L-moments to definehomogenous regions within 13 gauging sites of the north Brahmaputraregion of India. They found a homogenous region including 10 gaugingsites for which the Generalized Extreme Value (GEV) distribution wasidentified as a parent distribution.

Themethod of L-moments has also been used for regional low flowfrequency analysis. Zaidman et al. (2003) concluded that, for shortduration low flows such as 7-day low flows, the Pearson Type 3 (PIII)and Generalized Logistic (GLOG) distributions are favored for water-sheds with low rainfall while the GEV distribution is the bestdistribution for watersheds with high rainfall. Modarres (2008a)used low flow data from 19 stations in the north of Iran to define thehomogenous regions and the regional distribution function. The northof Iran was divided into one eastern and two western regions forwhich the Generalized Logistic distribution (GLOG) and GeneralizedExtreme Value (GEV), respectively, were found as parent distribu-tions. The regional frequency distribution function for the extremehydrologic drought periods in the southeastern arid region of Iranwasalso investigated byModarres and Sarhadi (2010) where 3-parameterLog Normal distribution (LN3) was selected as a regional distributionfunction.

The regional frequency distribution of maximum wind speed hasalso been studied for the arid region of Iran (Modarres, 2008b) whrereGLOGdistribution functionwas selected as thebest regional distributionfunction.

68 R. Modarres, A. Sarhadi / Global and Planetary Change 75 (2011) 67–75

The L-moments are also useful tools for regional annual rainfallfrequency analysis. Guttman (1993) defined 104 homogenous regionalrainfall groups across the USA using L-moments. Gonzalez and Valdes(2008) applied L-moments for regionalization of monthly rainfall in theJucar River basin located in the eastern Iberian Peninsula.

Lee and Maeng (2003) applied L-moments for regional frequencyanalysis of extreme rainfall data across Korea. Fowler and Kilsby(2003) defined the regional distribution of United Kingdom maxi-mum rainfall and estimated maximum rainfall over different returnperiods. Trefry et al. (2005) developed intensity–duration–frequencycurves for Michigan State in the United States. Di Balldassarre et al.(2006) used the L-moment method for regionalization of annualprecipitation in northern central Italy. Casas et al. (2007) used 145pluviometric stations for regional estimation of extreme rainfall inCatalonia using L-moments. More recently, Yurekli et al. (2009) foundGEV and LN3 distributions as the regional distribution functions forthemaximumdaily rainfall of Cekerec watershed, Turkey, through theL-moment approach.

Iran lies approximately between 40°E and 64°E in longitude and25°N and 40°N in latitude. The topographic features of Iran showtwo major mountain ranges, Elburz and Zagros, in north and west ofIran which surround the arid and semi arid region of the centralpart of Iran and act as a barrier to rainfall reaching the center ofIran.

In the north and western regions, however, different rainfallgeneration mechanisms bring rainfall to Iran. Different local featuressuch as elevation and sea neighborhood may influence the fluctuationof rainfall too. Although the density of rainfall network of Iran shouldbe very high to cover the spatial variation of rainfall across Iran thepresent network is not enough to allow scientists, researchers andwater resources managers of Iran to have an accurate estimation ofrainfall for locations without rainfall stations or with short period oruncompleted rainfall data. The scope and the aim of this study are toidentify the main regional rainfall groups of Iran by coupling L-moments with cluster analysis (CA).

Fig. 1. The topographic map of Iran with location of synoptic

2. Data and scope of this study

The annual rainfall time series for 137 synoptic stations in Irancovering the period of 1952–2003 were selected for this study. Themap and spatial distribution of the selected stations are illustrated inFig. 1. The annual rainfall of Iran varies between 1800 mm in the northto less than 100 mm in the central arid regions of Iran (Fig. 2). Thecoefficient of variation (CV) varies between 20% and 75% from northto the south of Iran (Fig. 3).

This paper includes the following sections: in the next section, theL-moments and their characteristics are first defined and then appliedfor all rainfall data of Iran. In Section 3, a hierarchical cluster analysis isillustrated and applied to find initial rainfall groups. In Section 4, themethod of L-moments is used to investigate the homogeneity of theinitial groups and to identify a regional parent rainfall distribution foreach group.

3. L-moment approach

L-moments are alternative systems of describing the shape of aprobability, which is used for summarizing the theoretical distribu-tion of an observed sample of a random variable (X). Hosking andWallis (1997) defined L-moments as linear functions of probabilityweighted moments (PWM), which are robust to outliers and virtuallyunbiased for small sample. Greenwood et al. (1979) defined PWM as:

βr = E X F Xð Þ½ �r� � ð1Þ

where F(x) is the cumulative distribution function (cdf) of X, and βr isthe rth-order PWM. The first four L-moments related to the PWMs arecalculated as the following (Hosking and Wallis, 1997):

λ1 = α0 = β0 ð2Þ

λ2 = α0−2α1 = 2β1−β0 ð3Þ

stations and spatial distribution of rainfall groups of Iran.

Fig. 2. Map of mean annual rainfall of Iran.

69R. Modarres, A. Sarhadi / Global and Planetary Change 75 (2011) 67–75

λ3 = α0 + 6α1 + 6α2 = 6β2−6β1 + β0 ð4Þ

= 20β3−30β2 + 12β1−β0 λ4 = α0−12α1 + 30α2−20α3 ð5Þ

Fig. 3. Map of rainfall coefficien

Different L-moment ratios can then be defined. λ1, is a measure ofcentral tendency, τ=λ2/λ1 is a measure of scale and dispersion (or theL-Coefficient of variation, LCV), the ratio λ3/λ2 is referred to as τ3 or themeasure of skewness (L- Coefficient of skewness, LCS), while the ratio

t of variation (CV) of Iran.

Fig. 4. LCV–LCs moment ratio diagram for all stations.

70 R. Modarres, A. Sarhadi / Global and Planetary Change 75 (2011) 67–75

λ4/λ2 is referred to as τ4, and it is the measure of kurtosis (L-Coefficientof kurtosis, LCK).

3.1. Moment ratio diagrams (MRDs)

Moment ratio diagrams are useful tools for discriminating betweenalternative distribution functions and selecting an approximate parentdistribution. The theoretical relationships between τ3 and τ4 aresummarized by Hosking and Wallis (1997). For selection of a suitableparametric distribution, the theoretical line of the best distributionmustcross the mean of the sample points.

Figs. 4 and 5 showMRDs of all rainfall data of Iran. Fig. 4 shows theMRD, LCs versus LCk. It appears that a GEV distribution would be thebest distribution for the entire country. The MRDs can also be used forthe inspection of heterogeneity of a region (Stedinger et al., 1993) andare always preferred to product moment ratio diagrams for goodness-of-fit tests (Vogel and Fennessey, 1993; ARIDE, 1999). It is clear fromFig. 5 that the data points are widely scattered around the mean.Therefore, we can conclude that the rainfall probabilistic behaviorover the entire country is not homogeneous. Hosking and Wallis(1997) introduced two statistics to identify the homogeneity of theregion and to identify any discordant station within a region. Thesestatistics are discussed in the following sections.

Fig. 5. LCs–LCk moment ratio diagram for all stations.

3.2. Homogeneity and discordancy test

3.2.1. Discordancy testDiscordancy measure, Di, is based on the L-moments and can be

used to determine an unusual site. Di, is defined as:

Di =13

ui−uð ÞTS−1 ui−uð Þ ð6Þ

where ui is the vector of L-moments, LCv, LCs and LCk, for a site i;

S = Ns−1ð Þ−1∑Ns

i=1ui−uð Þ ui−uð ÞT ð7Þ

u = N�1s ∑

Ns

i=1ui ð8Þ

NS is the total number of sites. If the Di exceeds 3, the site is consideredas a discordant station.

The D statistic for all 137 stations was calculated. Results show thatthe critical value, Di=3 is exceeded at nine stations. Most of thesestations are located near the Persian Gulf and in the highlands ofZagros Mountains. However, only four stations are discordant withintheir groups (see Section 4.1).

3.2.2. Homogeneity measure (H)Hosking and Wallis (1997) derived heterogeneity statistics for

estimation of the degree of heterogeneity in a group of sites. Forheterogeneity test of a group, a four parameter kappa distribution isfitted to the regional data set generated from series of 500 equivalentregion data by numerical simulation. The test compares the variabilityof the L-Statistics of actual region to those of the simulated series.

There are three heterogeneity measurements (Hi), namely H1, H2

and H3, that are calculated using the following equation:

Hi = ðVi−μVÞ=σV ð9Þ

where μV and σV are the mean and standard deviation of Nsim valuesof V, Nsim is the number of simulation data; Vobs, is calculated fromthe regional data and is based on the corresponding V-statistic,defined as follows:

V1 = ∑N

i=1ni L−CVi−LCV� �2

� �= ∑

N

i=1ni ð10aÞ

V2 = ∑N

i=1ni L−CVi−LCV

� �2+ τ3i−τð Þ2

� 1=2� �= ∑

N

i=1ni ð10bÞ

V3 = ∑N

i=1ni τ3i−τ3ð Þ2 + τ4 i

−τ4� �2

� � �1=2

= ∑N

i=1ni ð10cÞ

On the basis of Homogeneity measurements, a region is declaredacceptably homogenous when Hb1, possibly heterogeneous when1≤Hb2 and definitely heterogeneous when H≥2.

The results of homogeneity tests, for the entire country are shownin Table 1. Based on H1 measurement which has a much betterdiscriminatory power than either H2 or H3 (Hosking and Wallis,1997), it can be seen that the entire country is not homogenousbecause the H1 is larger than the criteria value, Hb1.

Table 1Homogeneity measures for the study area.

Regions Number ofstations

Includedstations

Homogeneitymeasure (H1)

Homogeneitymeasure (H2)

Homogeneitymeasure (H3)

Iran 137 All 23.91 0.79 3.23

Table 3Descriptive statistics and L-moments of the rainfall at selected stations.

Regions Number ofstations

Mean ofprecipitation

Mean ofSTDEV

Meanof LCv

Meanof LCs

Meanof LCk

Meanof Di

G1 44 137.9 54.31 0.238 0.115 0.154 1.028G1* 42 138.5 52.6 0.232 0.112 0.150 1.0G2 21 347.5 88.39 0.161 0.066 0.119 1.0G3 17 366.2 97.6 0.162 0.112 0.180 0.99

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3.3. Goodness-of-fit measurement

The goodness-of-fit measurement is used to identify the regionalparent distribution. This measurement, ZDist, judges the differencebetween sample L-Kurtosis and population L-Kurtosis for the fitteddistribution. The Z statistic has the form of goodness of fit and hasapproximately a standard Normal distribution.

The goodness-of-fit measure is defined as:

ZDIST = τDIST4 −τ4 + β4

� �= σ4 ð11Þ

where “Dist” refers to the candidate distribution, τ4 is the averageL-Kurtosis value computed from the data of a given region, β4is thebias of the regional average sample L-Kurtosis, and τ4DIST is theaverage L-Kurtosis value computed from simulation for a fitteddistribution. A given distribution is declared a good fit if |ZDist|≤1.64.When more than one distribution qualifies for the goodness-of-fitmeasurement criteria, the preferred distributionwill be the one that hastheminimum |ZDist| value. The criterion corresponds to acceptanceof thehypothesized distribution at a confidence level of 90% (Hosking andWallis, 1997).

The goodness-of-fit value (|ZDist|) for several distributions,Generalized Extreme Value (GEV), Generalized Logistic (GLOG), 3-parameter Log Normal (LN3) and Pearson Type 3 (P III) was calculatedassuming the entire country as a single region. The goodness-of-fitvalues are given in Table 2. It is observed from this table that none ofthe |ZDist| is less than1.64. In other words, the entire country cannot beconsidered as a homogeneous region and no parent distribution canbe selected for rainfall in Iran.

It is quite clear that the country is not homogenous because oflarge geographic and climate differences within the country. So it isnot surprising that the study area must be divided into homogenousgroups by another method. For this purpose the popular clusteranalysis (CA) is used in this study.

4. Cluster analysis

The aim of using cluster analysis with hydrologic variables is togroup observations or variables into clusters based on the highsimilarity of hydrologic features, such as geographical, physical,statistical or stochastic properties. In this way, each cluster containsthe least variance of variables (smallest dissimilarity). Gottschalk(1985) applied cluster and principal component analysis to data fromSweden and found that cluster analysis is a suitable method to use ona national scale for a country with heterogeneous regions.

In this study, the hierarchical cluster technique (described byKaufman and Rousseuw, 1990) is applied in order to classify thesynoptic rainfall stations into spatial groups. Several methods havebeen proposed for hierarchical cluster analysis, including single,average and complete linkage, and Ward's minimum variancemethod. Both the last two methods are widely used for classificationof different climatic or hydrologic data (e.g. Jackson and Weinand(1995); Ramos, 2001). Nathan and McMahon (1990), Masoodian(1998) and Domroes et al. (1998) indicated that Ward's method givesbetter results than other methods of classification. Therefore, Ward'smethod is used for cluster analysis of rainfall data in Iran.

Table 2Goodness-of-fit test measures (Zdist) for the study area.

Region Regional frequency distribution

GeneralizedLogistic

GeneralizedExtreme Value

3-parameterLog Normal

PearsonType III

All stations 3.08 −3.7 −3.39 −4.35

In Ward's method, the distance between two clusters is calculatedas the sum of squares between two clusters, added up over allvariables. At each cluster generation, the sum of squares is minimized.If CK and CL are two rainfall clusters that merged to form the clusterCM, the distance between the new cluster and another cluster CJ is:

dJ:M =nJ + nK

� �� �dJk + nJ + nL

� �dJL−nJdKLÞ

nJ + nMð12Þ

where nJ, nK, nL and nM are the number of the rainfall stations inclusters J, K, L and M, respectively, and dJk, dJL and dKL represent thedistances between the rainfall observations in the clusters J and K, Jand L, and K and L, respectively. On the basis of Ward's method, theselected stations of Iran can be classified into eight groups. The spatialdistribution of these groups is illustrated in Fig. 1. The pseudo t2 andpseudo R2 statistics are the criteria for selecting 8 groups (SAS, 1999).

The largest group covers arid and semi arid central regions of Iran.The second group is located in the highlandmargins of the first group.The third group includes northwestern cold regions of Iran. The fifthand seventh groups are located in the high areas of the ZagrosMountains. The amount of precipitation in the seventh group is higherthan the fifth group. The fourth group covers the lowland area of theZagros Mountains. This region also includes stations along with thePersian Gulf in the south of Iran, while the sixth and eighth groupscover regions located along the Caspian Sea in the north of Iran. Thesetwo regions with the average of 969.3 mm annual precipitationreceive the highest amount of rainfall across the country. The maindifference between the sixth and eighth groups is that the amount ofrainfall decreases from the western region (Anzali Station) to theeastern region (Babolsar and Gorgan) of the north of Iran. In the nextsection, L-moments are applied to check the homogeneity of theseeight groups and to find the regional frequency distribution for eachgroup.

5. L-moments for rainfall groups

5.1. Homogeneity and discordancy test

Using the FORTRAN computer program developed by Hosking andWallis (1997), the homogeneity of the groups and the existence of anydiscordant station in each group are investigated at the first step.

L-moment statistics are calculated for all groups classified bycluster analysis and summarized in Table 3. The result of thediscordancy test for these eight groups indicates that there are nodiscordant stationwithin the groups except for the first and the fourthgroups (G1 and G4). Removing these discordant stations from thegroups, the discordancy measurements recalculated for G1 and G4groups do not exceed the critical value, Di=3, whichmeans that there

G4 27 272.8 106.22 0.265 0.147 0.159 1.0G4* 25 277.8 104.6 0.253 0.130 0.156 1.0G5 14 483.15 122.83 0.153 0.076 0.209 1.001G6 6 739.3 150.21 0.119 0.082 0.189 0.99G7 4 559.3 142.14 0.162 0.102 0.228 1.0G8 4 1199.3 234.5 0.136 0.156 0.218 1.0

*Shows the amount of measure after removing the discordant station.STDEV: Standard Deviation; LCv: Measure of Variation; LCs: Measure of skewness; LCk:Measure of Kurtosis; D: Discordancy measure.

Table 4Homogeneity measure (Hi) of the derived group (Hi* shows homogeneity measure after removing the discordant station).

Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group 8

H1 7.06 −1.07 −1.00 3.95 −0.45 1.15 0.04 1.37H1* 1.22 – – 1.33 – – – –

H2 −0.8 −1.83 −2.08 2.68 −2.45 −0.96 0.12 −1.47H2* −2.17 – – 2.19 – – – –

H3 −2.0 −2.58 −2.12 −0.26 −2.03 0.51 −0.38 −1.11H3* −2.85 – – −0.45 – – – –

Discordant Chahbahar Bushehr.coastalstation Kenarak Kanganjam

72 R. Modarres, A. Sarhadi / Global and Planetary Change 75 (2011) 67–75

is no discordant station. The mean values of Di for these two groupsare also given in Table 3.

In the first group, Chahbahar and Kenarak Stations are discordant.These two stations which are located near Oman Sea in thesoutheastern corner of Iran may be discordant due to the effects ofa monsoon rainfall regime coming from the east. In the fouth group,Kanganjam and Bushehr, both coastal stations, are discordant. Itseems that their locations at the margin of Persian Gulf and the effectof sea moisture may be the main reasons of discordancy comparedwith other inland stations of the group.

The homogeneity statistics for each of these eight regions revealthat the homogeneous regions are limited to G3, G5 and G7 regionswhich are acceptably homogenous (Table 4). On the basis of H1

measurement, which is reported to be discriminatory and morepowerful than H2 or H3 measurements (Hosking and Wallis, 1997),G2, G6 and G8 groups are possibly heterogeneous regions while G1and G4 are definitely heterogeneous. If the two discordant stations areremoved from G1 and G4 regions, H1 reduces to 1.22 and 1.33,respectively, which implies that the regions can still be considered aspossibly heterogeneous.

These four stations in groups G1 and G4 are located near the coast ofPersian Gulf. One, high, unusual rainfall event due to the effect of seamoisture may have influenced the statistical characteristics of annualrainfall such as the coefficients of variation and skewness andmay haveresulted in discordancy of the above stations. However, as the H1

measurements of the groups are very close to H1=1, we can considerthe region homogeneous. These results indicate that the cluster analysisis not enough to accept homogeneity of a region. In other words, the

Table 5The goodness-of-fit test measure (Zdist) for homogeneous rainfall groups within Iran.

Distributions Iran Group1 Group2 G

Generalized Logistic (GLOG) 3.08 2.43 4.68Generalized Extreme Value (GEV) −3.7 −1.05 0.71 −3-parameter Log Normal (LogN3) −3.39 −1.0 1.36 −Pearson Type III (PIII) −4.35 −1.6 1.18 −

Table 6Regional rainfall estimations for rainfall groups of Iran.

Groups Group 1 Group 2 Group 3 Gro

Return period(year)

Best distribution

LogN3 GEV GLOG GLO

2 147.3 330.7 281.3 1455 203.6 410.7 350.1 20610 237.2 453.5 397.1 24820 267.3 488.3 445.7 29250 304.1 525.7 515.3 356100 330.4 549.1 573.5 410200 355.7 568.9 637.5 470

basic assumption of homogeneity in cluster analysis is different fromthose in frequency analysis. Therefore, it would be usefull to test thehomogeneity of each cluster by homogeneity measurement, Hi.

Fig. 1 reveals that twopossibly homogenous climate groups (G6, G8)are located in the north of Iran. The G1 group, or the arid and semi aridregion of Iran, covers nearly 2/3 of the country. The other groups, G2, G5and G7, cover high mountainous areas of Zagros Mountains whichreceive rainfall from Mediterranean rainfall system while G3 includesnorth western Iran which may be influenced by Mediterraneanprecipitation systems and Black Sea moisture (Masoodian, 1998).

5.2. Regional distribution function

In this section, the regional rainfall frequency distribution functionfor each rainfall group is identified by the use of goodness-of-fit |ZDist|statistics. The results of the goodness-of-fit test for common 3-parameter distributions, GLOG, GEV, LN3 and PIII distributions areshown in Table 5. Except for G1 and G2 groups for which the LN3 andGEV distributions are the best parent distributions, the GLOGdistribution is the best distribution for other groups. However, it isclear that for the entire country, none of the distributions could beselected as a parent distribution. It is an expectable result because ofthe complexity of rainfall generatingmechanisms of Iran. The regionalannual rainfall for each group at different return periods have beengiven in Table 6, using the regional distribution function. At-site andregional cumulative distribution functions (CDFs) for one represen-tative station at each group are also shown in Fig. 6 using plottingposition formula Pi:n=(i−0.35)/n, where n is the sample size and i is

roup3 Group4 Group5 Group6 Groug7 Group8

0.3 1.48 −1.58 0.9 −1.62 −0.522.03 −1.16 −3.79 −2.56 −2.83 −1.521.92 −1.35 −3.52 −2.46 −2.74 −1.612.25 −2.08 −3.68 −2.66 −2.82 −1.89

up 4 Group 5 Group 6 Group 7 Group 8

G GLOG GLOG GLOG GLOG

.3 503.4 876.2 633.3 1809.7

.1 613.3 1024.7 805.8 2134.9

.5 683.8 1119.1 924.3 2358.4

.6 753.2 1211.4 1046.3 25,589.2

.6 847.7 1336.1 1222 2920.4

.8 922.9 1434.7 1368.9 3198.5

.9 1002.3 1537.9 1530.5 3504.2

73R. Modarres, A. Sarhadi / Global and Planetary Change 75 (2011) 67–75

the ith observation of ordered random variable (X). The 95%confidence interval (CI) or the uncertainty bands for the functionshave also been calculated for each function according to Rao andHamed (2000).

6. Summary and conclusion

A set of rainfall time series for 137 synoptic stations across Iran isapplied in this study to investigate the spatial pattern of rainfallfrequency functions over Iran. The cluster and L-moment methods areused together in order to find the spatial rainfall regions and theregional rainfall frequency for each region, respectively.

The hierarchical Ward's method identifies eight rainfall regionsover Iran. The spatial pattern of these regions indicates the effects ofelevation, sea neighborhood and large atmospheric systems onrainfall spatial pattern in Iran. However, this paper suggests the useof the cluster analysis with L-moments to find the regional frequencydistribution of rainfall in each region classified by cluster analysis.

As for the regional analysis the region should be homogeneous interms of both rainfall amount (investigated by cluster analysis) andfrequency distribution, the homogeneity measurement based on L-momentswas used to find that these rainfall groups are homogeneousregions. Although most of the regions classified by cluster analysis

Fig. 6. At-site cumulative distribution functions for one selected station in each rainfall grouuncertainty bands. a. Abadan station, GLOG distribution. b. Anazali station, GLOG distribe. Kerman station, LN3 distribution. f. Khoramabad station, GLOG distribution. g. Tabriz stat

were considered as homogeneous or possibly homogenous regions,some regions have discordant stations, the stations that arestatistically different from other stations in a region. The differencemay come from special effects of atmospheric circulation pattern orsome rare events that may affect the statistical properties of rainfallduring the record of data. Removing these stations may reduce thenon-homogeneity of the region. Therefore at-site frequency analysis isrequired for rainfall frequency at these stations and it is necessary toinvestigate the reasons for their discordancy.

The best regional distribution function for each group is alsoidentified using the goodness-of-fit test measurement. This statisticsreveals that the Generalized Logistic distribution, GLOG, is thedominant distribution function for most of the rainfall regions exceptfor the central arid zone of Iran, (G1) and the margins of Persian Gulfin south and southwestern regions of Iran (G4) where LN3 and GEVdistributions can be selected as the parent distributions, respectively.Although, the results give a parent distribution for each rainfall group,they do not support any parent frequency distribution function for theentire country. This is the consequence of the combination of localrainfall factors such as elevation and topography with large differentatmospheric systems.

In general, the climate regions of Iran are influenced by threemajor factors of sea neighborhood, elevation and large atmospheric

p of Iran. The solid line shows theoretical distribution and the dashed lines show 95%ution. 6c. Babolsar station, GLOG distribution. d. Hamedan station, GEV distribution.ion, GLOG distribution. h. Yasuj station, GLOG distribution.

Fig. 6 (continued).

74 R. Modarres, A. Sarhadi / Global and Planetary Change 75 (2011) 67–75

systems. The cluster analysis may be a useful tool to find and classifythe regions influenced by different atmospheric phenomenon and canshow their effects on the amount of rainfall. However, the frequencydistribution type of rainfall in these regions is not unique. In other words,the type of climate could not be represented by a unique distribution, atleast for Iran. The application of cluster analysis together with L-momentmethod is highly recommended in different geographical and climateregions to prove the relationship between rainfall regimes and rainfalldistribution functions.

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