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Applied Radiation and Isotopes 65 (2007) 1070–1077

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Spatial dispersion modeling of 90Sr by point cumulative semivariogramat Keban Dam Lake, Turkey

Fatih Kulahcıa,b,�, Zekai S-enb

aScience & Arts Faculty, Physics Department, Fırat University, 23169 Elazıg, TurkeybCivil Engineering Faculty, Hydraulics Department, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey

Received 13 January 2007; received in revised form 6 March 2007; accepted 16 March 2007

Abstract

Spatial analysis of 90Sr artificial radionuclide in consequence of global fallout and Chernobyl nuclear accident has been carried out by

using the point cumulative semivariogram (PCSV) technique based on 40 surface water station measurements in Keban Dam Lake

during March, April, and May 2006. This technique is a convenient tool in obtaining the regional variability features around each

sampling point, which yields the structural effects also in the vicinity of the same point. It presents the regional effect of all the other sites

within the study area on the site concerned. In order to see to change of 90Sr, the five models are constituted. Additionally, it provides a

measure of cumulative similarity of the regional variable, 90Sr, around any measurement site and hence it is possible to draw regional

similarity maps at any desired distance around each station. In this paper, such similarity maps are also drawn for a set of distances. 90Sr

activities in lake that distance approximately 4.5 km from stations show the maximum similarity.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Strontium; Point cumulative semivariogram; Spatial analysis; Lake; Artificial radionuclide

1. Introduction

The total yield of atmospheric nuclear tests carried outuntil the end of 1980 has been estimated at 217.2Mt.Nearly 90% of the resulting releases occurred before 1963and only about 1% originated from tests between 1976 and1980 (UNSCEAR, 1982). Depending on the particular typeof the test, up to 50% of the radioactive debris wasdeposited in the vicinity of testing sites giving rise to localfallout. The remainders were injected into the atmosphericstrata and entered the global circulation of air masses. Theportion injected into the stratosphere (i.e., at the altitudeabove 9–17 km) represents a major reservoir of worldwide(global) fallout. It accounts for most of the worldwidecontamination of long-lived fission products (UNSCEAR,1982; BSEP, 1995).

e front matter r 2007 Elsevier Ltd. All rights reserved.

radiso.2007.03.012

ing author at: Science & Arts Faculty, Physics Depart-

versity, 23169 Elazıg, Turkey. Tel.: +90 424 2370000/3835;

30062.

ess: fatihkulahci@firat.edu.tr (F. Kulahcı).

The semivariogram (SV) (or variogram), one of thefundamental tools of geostatistical analysis, is usedcommonly to measure the spatial similarity of a regiona-lized variable. General procedures are available forobtaining experimental SVs and fitting theoretical smoothmathematical models. Considerable emphasis is placed onanisotropic models and their relation to directionalgeologic features (Clark, 1979). A variety of importanttopics related to the SV are discussed, including theproportional effect, relative SVs, nested structures, andthe geometric meaning of many SV models (Journel andHuijbregts, 1978). Complexities in the development of SVmodels include the existence and dealing with outliers,robustness of SVs, and SVs in curved coordinate space(Sinclair and Blackwell, 2002).Traditional variance techniques and classical autocorre-

lation methods are not helpful to account directly for theregional dependence or for the variability in terms ofsample positions (Luetkepohl et al., 2004). The downsidesare due to either non-normal distribution of data and/orirregularity of sampling positions. However, the SV

ARTICLE IN PRESSF. Kulahcı, Z. S- en / Applied Radiation and Isotopes 65 (2007) 1070–1077 1071

technique developed by Matheron (1963) and used bymany researchers (Bunzl et al., 1994; S-en, 1997; Golosovet al., 1999; Kumar et al., 1999; Sanchez-Vila et al., 2004)in rather different fields, such as radon risk mapping,mining, heavy metal analysis, and contaminated soil can beapplied to characterize regional structural variability. Noneof the available regional behavior measuring techniques isable to provide specific calculations at a single samplingpoint. However, S-en (1989, 1992, 1998) developed theconcept of cumulative SV (CSV) and point cumulativesemivariogram (PCSV) techniques, which is capable ofquantifying the point properties of any regionalizedvariable.

Modeling of the big ecosystems like lakes is ratherdifficult (McEvoy, 1980; Brugmann, 1984; Benes andCernık, 1992; Choppin and Wong, 1996; Maringer et al.,2004). It is shown in this paper that the application ofPCSV helps to overcome such a difficulty and therefore thePCSV modeling technique is applied to 90Sr data obtainedfrom the analysis of Keban Dam Lake surface watersamples. The PCSV technique also provides an opportu-nity to construct regional similarity maps at fixed levels,which guide to further interpretations such as the regionalheterogeneity.

2. Mathematical theory

The mathematical definition of the variogram is given byMatheron (1963) as

gðDx;DyÞ ¼ 12� ½fZðxþ Dx; yþ DyÞ � Zðx; yÞg2�, (1)

where Z(x, y) is the regionalized value of interest atlocation point (x, y), and e[ ] is the statistical expectationoperator. Note that the variogram, g, is a function of theseparation (distance), (Dx,Dy), between two points and nota function of the specific location (x, y). This theoreticalmathematical definition is a useful abstraction, but noteasy to apply to observed values.

On the other hand, let {(x1, y1, z1), (x2, y2, z2),y, (xn, yn,zn)} be a sequence of n irregularly located point data, where(xi, yi) is the location of observation point i, and zi is theassociated measured regionalized value. Hence, there aren(n�1)/2 distinctive pairs of observations between n points.For each of these pairs, it is possible to calculate theassociated separation vector:

ðDxi;j ;Dyi;jÞ ¼ ðxi � xj ; yi � yjÞ. (2)

To infer the variogram for a particular separation vector,(Dx,Dy), it is required to use all data pairs whoseseparation vectors are almost equal to each other.

ðDxi;j ;Dyi;jÞ � ðDx;DyÞ. (3)

In general, even though there may be several points, say7, there will be (7� 6)/2 ¼ 21 such pairs, which means thatas the number of measurement sites, n, increases the

number of SV calculation pairs increases according to theaforementioned n(n�1)/2 formulation.Let S(Dx,Dy) be the set of all such pairs, then

SðDx;DyÞ ¼ fði; jÞjðDxi;j ;Dyi;jÞ � ðDx;DyÞg. (4)

Furthermore, let N(Dx,Dy) represent the number of suchpairs in S(Dx,Dy), then the experimental SV is defined as

gðDx;DyÞ ¼1

2NðDx;DyÞ

X

ði;jÞ2SðDx;DyÞ

ðzi � zjÞ2. (5)

Herein, one-half of the differenced squares of thez-values is summed over all pairs of observations separatedby approximately that vector (Matheron, 1963; Barnes,2006).The CSV is equal to the successive summation of the

SV values, which yields a non-descending scatter diagram.The CSV has all the advantages claimed for SV, and itappears to be a better tool in the identification oftheoretical models for the spatial variability. Furthermore,standardization of CSV provides an equal footing base forthe identification of regional stationary stochastic models(S-en, 1992).On the other hand, PCSV functions are presented for

the identification of the spatial behavior of any regiona-lized variable around any concerned sampling point. Inother words, it presents the regional effect of all of theother sites within the investigation area on a finite areasurrounding the sampling point location. Consequently,the number of PCSVs is equal to the number of stations.Hence, their comparisons with each other and theirrespective groupings provide valuable information aboutthe heterogeneity of the regionalized variable concerned.The following steps lead to the desired sample PCSV forthe concerned site among n observation (measurement,sampling) sites.

(i)

Calculate distance between the concerned site and theremaining sites. If there are n sites, the number ofdifferent distances is n�1, dj (j ¼ 1, 2, y, n�1).

(ii)

For each pair, find the half-squared differencesbetween data values, in this case 90Sr values. In thisway, each distance will have its half-squared value, 1/2(zi�zj)

2 where zi and zj are the regionalized 90Srvariable values at the concerned and jth sites,respectively.

(iii)

Plot distances versus corresponding successive cumu-lative sums of half-squared differences. This proceduregives a non-decreasing function, which is the samplePCSV at the concerned site. Its mathematical expres-sion is given as

gðdjÞ ¼1

2

Xn�1

j�1

ðzi � zjÞ2. (6)

(iv)

Apply previous steps by considering different con-cerned sites, to give n sample PCSVs.

ARTICLE IN PRESS

Fig. 1. The locations of sampling stations on Keban Dam Lake in Turkey.

F. Kulahcı, Z. S- en / Applied Radiation and Isotopes 65 (2007) 1070–10771072

3. Experimental

3.1. Research area

Uluova Region at Keban Dam Lake has almost 35 kmlength and approximately 10–12 km width, with a surface

area of 360–370 km2. However, the area of the researchfield is approximately 250 km2 and lies at the latitude38150N and 38140E longitude in Eastern Turkey. Thealtitude of the lake plain changes between 845 and1000m. One-third of this plain, i.e., about 110 km2, iscovered by the Keban Dam reservoir lake. This region is

ARTICLE IN PRESSF. Kulahcı, Z. S- en / Applied Radiation and Isotopes 65 (2007) 1070–1077 1073

encircled by high mountains such as Mastar Mountain(2171m), C- elemlik (1658m), and Sivrice (1908m) in thesouth; Hasret Mountain (1621m) in the north; andMeryem Mountain (1471m) in the west. Hasret Mountainlimits Uluova in the west. The altitude is 1621m in thewestern part of Hasret Mountain. It reaches 1724m in theKartal Hill in the eastern part. The evaluation decreaseseastwards so that it reaches 1200m in Murat Valley. Theslope values change between 15% and 45% in thismountainous area.

The surface water samples taken from approximately20 cm depth have been collected from 40 stations, in orderto characterize the lake during March, April, and May2006 (Fig. 1).

3.2. Determination of 90Sr

A known amount of stable Sr, in the form of strontiumnitrate Sr(NO3)2, is added as a carrier. The alkaline earthsand rare-earths carrier is precipitated as the carbonate toconcentrate the radio-strontium. Along with the radio-nuclides of Sr, it is separated from other radioactiveelements and inactive sample solids by precipitation asSr(NO3)2 from fuming nitric acid solution. The Sr carrier,together with the radionuclides of Sr, is precipitated finallyas SrCO3, which is dried, weighed to determine recovery ofcarrier, and immediately measured for radioactivity. Theactivity in the final precipitate is due to radioactive Sr only,because all other radioactive elements have been removed.

Due to the impossibility to separate the 89Sr and 90Srisotopes by any chemical procedure, the 90Sr amount isdetermined by separating the measurement of its daughteractivity, 90Y. After the equilibrium is reached, the 90Yactivity is exactly equal to the activity of 90Sr. Two

Table 1

Locations and 90Sr radioactivity measurements

Station Latitude (North) Longitude (East) 90Sr (Bq/l) (� 10�2)

1 38.37 39.24 0.10

2 38.37 39.25 0.09

3 38.36 39.25 0.11

4 38.37 39.26 2.02

5 38.36 39.27 0.89

6 38.37 39.27 0.97

7 38.37 39.29 0.10

8 38.38 39.30 0.09

9 38.38 39.31 0.10

10 38.39 39.33 0.28

11 38.39 39.34 0.28

12 38.40 39.35 0.38

13 38.40 39.34 1.22

14 38.40 39.33 1.18

15 38.40 39.32 1.17

16 38.39 39.31 1.84

17 38.39 39.30 1.78

18 38.38 39.29 2.23

19 38.38 39.28 1.35

20 38.38 39.27 1.45

alternate procedures are given for the separation of 90Y. Inthe first method, 90Y is separated by extraction into tributylphosphate from concentrated nitric acid solution. Thesecond method consists of an addition of yttrium carrier,separation by precipitation as yttrium hydroxide, Y(OH)3,and finally precipitation of yttrium oxalate for counting. Inorder to determine 90Sr activity was used the secondmethod and the activity of 90Sr was calculated as follows(Clescerl et al., 1989):

90Sr ðBq=lÞ ¼net cpm� 0:0166

abcdf e�lt, (7)

where a is the counting efficiency for 90Y, b is the chemicalyield of extracting or precipitating 90Y, c is the ingrowthcorrection factor if not in secular equilibrium, d is thechemical yield of Sr gravimetrically, f is the volumeof sample, liters, and e�lt is the 90Y decay factor(t1/2 ¼ 2.671d). In order to determine 90Sr radioactivity,beta spectroscopy is used which has been performed by alow background plastic b-scintillation system supported bya plastic b-scintillator (2059) and a photomultiplier tubethrough a SR8 dual radiation counter from NE Technol-ogy Inc. Lead shielding was used for both systems for theprotection against external radiation. The precision (ran-dom error) at the 95% confidence level was 10% and 12%for the two sets of paired samples.

4. Results and discussion

The PCSV technique is applied to 90Sr radioactivityconcentrations measured at 40 irregularly distributed sitesin the Keban Dam Lake as shown in Table 1.The PCSV versus distance plots obtained from 90Sr

radioactivity analyses at 40 sampling stations are drawn

Station Latitude (North) Longitude (East) 90Sr (Bq/l) (� 10�2)

21 38.38 39.26 1.35

22 38.37 39.24 0.09

23 38.38 39.25 0.11

24 38.38 39.26 0.12

25 38.39 39.28 0.08

26 38.40 39.29 0.09

27 38.40 39.30 0.10

28 38.40 39.31 1.33

29 38.40 39.32 1.40

30 38.41 39.34 1.33

31 38.41 39.33 1.80

32 38.41 39.32 1.88

33 38.41 39.30 1.80

34 38.42 39.30 2.30

35 38.41 39.29 0.23

36 38.40 39.29 0.24

37 38.40 39.28 0.23

38 38.39 39.27 1.55

39 38.38 39.25 1.50

40 38.38 39.23 1.55

ARTICLE IN PRESSF. Kulahcı, Z. S- en / Applied Radiation and Isotopes 65 (2007) 1070–10771074

and then their similarity groups yielded five PCSV modelsas shown in Fig. 2, where each group is labeled as A, B, C,D, E model. For the sake of brevity, only one sample PCSVis presented in the same figure and the five PCSV modelsare plotted in idealized form in Fig. 2 from A to E. Each

No.1, modelA

No.22, model C

No.14, model E

0.00 4.00 8.00 12.00 16.00

Distance (km)

2.84x10-2

2.88x10-2

2.92x10-2

2.96x10-2

3.00x10-2

Poin

t C

SV

0.00 4.00 8.00 12.00 16.00 20.00

Distance (km)

3.50x10-3

4.00x10-3

4.50x10-3

5.00x10-3

5.50x10-3

6.00x10-3

6.50x10-3

Poin

t C

SV

0.00 4.00 8.00 12.00

Distance (km)

16.004.48x10-2

4.52x10-2

4.56x10-2

4.60x10-2

4.64x10-2

4.68x10-2

Poin

t C

SV

1CCo

C1

{

{

Co

a

a

C

C

Fig. 2. The examples of point cumulative semi

one can be described according to its characteristic shape.For instance, the first four models are bounded becausethey reach maximum PCSV values, which are known as thesill in the geostatistical literature (Matheron, 1963). For thetheoretical exponential and Gaussian model, the sill is

No.25,model B

No.35, model D

0.00 4.00 8.00 12.00 16.00

Distance(km)

5.10x10-2

5.15x10-2

5.20x10-2

5.25x10-2

5.30x10-2

5.35x10-2

Poin

t C

SV

0.00 4.00 8.00 12.00

Distance(km)

7.32x10-2

7.36x10-2

7.40x10-2

7.44x10-2

7.48x10-2

7.52x10-2

Poin

t C

SV

{Co

C1

a

a

C

C

variograms (PCSV) of 90Sr concentrations.

ARTICLE IN PRESS

Table 2

The PCSV models assigned to stations

PCSV

models

Stations

Model A 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 21, 23, 24,

26, 29, 30, 31, 32, 33, 34, 37, 38, 39

Model B 20, 25, 27, 28

Model C 22, 40

Model D 35, 36

Model E 14, 15

F. Kulahcı, Z. S- en / Applied Radiation and Isotopes 65 (2007) 1070–1077 1075

approached asymptotically and these models never reachthe sill (Journel and Huijbregts, 1978).

None of the PCSVs modeling passes through the origin,which means that all the sampling stations are under theinfluence of some regional control structure (geology, deepcurrents, etc.). This study is adopted as a pilot regionalstudy due to its interesting geological and geographiccharacteristics. The lake basin is completely covered withthe clay minerals (Gunek and Tonbul, 1995).

The PCSV categories at Keban Dam Lake stations aregiven in Table 2.

Models A, B, and C in Fig. 2 show a discontinuity(Co) at the origin, followed by a gradual increase in g(h) asthe lag increases to h ¼ a (the range); for lags beyondthe range (h4a), the experimental values of g(h) areroughly constant (C). These models have an intercept onthe y-axis except D model, which intersects the horizontalx-axis. However, all the PCSV models have a gradualincrease in g(h) up to sample spacing a at which g(h)becomes uniform.

Models A, B, and C in Fig. 2 are characterized by twocomponents: (a) a purely random component referredto as the nugget effect, or Co; and (b) a structuredcomponent in which the structure is characterized by therange a of an autocorrelation function. The range is thedistance over which average variability for the structuredcomponent rises from zero to C1 (or from Co to C).Furthermore, the models A and B show Gaussian shape upto spacing a. As for model C, it appears in the form of anexponential model (model C, Fig. 2), but approaches thesill more sharply. Herein, exponential model isg(h) ¼ C[1�e�h], where g(h) is the semivariogram and C

is the scale for the structured component of the variogram(Cressie, 1991). The range, therefore, is shorter than theexponential range. Moreover, the slope decreases formodels A, B, C, and D with increasing distance graduallyreaching the saturation. The smaller the slope, the less isthe effect of the atmospheric environment as the globalfactor, and there is more effect of the geologic formation(the absorption to elements on clay minerals, etc.) as theregional factor.

Model C in Fig. 2 shows an exponential model variation,which approaches the sill asymptotically. The variance islower than the spherical variance for all distance values lessthan the range. Besides, this model applies when the spatial

dependence decreases exponentially with increasing dis-tance, which disappears completely only at infinitedistances.The PCSV in model D in Fig. 2 intersects the horizontal

axis, which indicates that 90Sr radioactivity dispersionbetween the concerned site and the remaining sites atdistances less than the distance of the intersection is almostthe same.Model E in Fig. 2 has two parameters: the slope in

addition to the intercept on the vertical axis. The linerises without limit and consequently has no sill. It applieswhen the spatial variability observed for a variableincreases linearly with distance and never levels off.Its shape near the origin comes close to that of theGaussian and exponential models. S-en (1989) has shownthat the slope of the straight line of linear model isrepresented exactly by the variance of the underlyingrandom field or the regionalized variable, which is 90Sr inthis case. Hence, the smaller the slope, the smaller is therandom fluctuation in the regionalized variable. For thisreason, in the model E, due to the sample PCSVsappearance as a single straight line, it implies the existenceof rather homogeneous areas of influence around thesestations.Finally, after the explanations of the PCSV models

earlier in the text, and in order to show the similarities ofeach station to others with respect to 90Sr radioactivitymeasurements, representative distances of Ro ¼ 1.5, 4.5,and 7.5 km are considered from which correspondingPCSV values are read for each station. The regionaldistribution of these values on the sampling points, as inFig. 1, results in a similarity map. Fig. 3 shows thesimilarity maps obtained from the PCSV graphs atRo ¼ 1.5, 4.5, and 7.5 km distances and Table 3 presentsthe PCSV values obtained for these distances.The similarity maps in Fig. 3a–c give very detailed

information about the 90Sr radioactivity dispersion in thelake. According to S-en (1998), if the two PCSVs atdifferent sites follow the same pattern within the limits ofsampling errors, then they are said to be similar. Such asimilarity implies the existence of heterogeneity betweenthe two sites.As seen in Fig. 3, there is not much variation with the

distance Ro and, especially in Fig. 3a and b, the PCSVvalues are almost at the same. However, the centralregions for all the Ro distances of the lake basin showelevated radioactivity levels. In particular, the radio-activity of lake increases gradually towards southwest. Ithas already been stated that there are substantial claylayers at the bottom of the lake (Gunek and Tonbul,1995). Clay absorbs radioactive minerals, so this area isexpected to be higher in 90Sr radioactivity than otherregions.Similarity contours (for Ro ¼ 4.5 km) in Fig. 3b are

more intensive than the others. Essentially, levels ofsimilarity for Keban Dam Lake in Fig. 3 may be arrangedas ‘‘b4a4c’’.

ARTICLE IN PRESS

39.24 39.25 39.26 39.27 39.28 39.29 39.3 39.31 39.32 39.33 39.34

Longitude

38.36

38.37

38.38

38.39

38.4

38.41

Latitu

de

Ro= 1.5 km

39.24 39.26 39.28 39.3 39.32 39.34

Longitude

38.36

38.38

38.4

38.42

Latitu

de

Ro= 4.5 km

39.24 39.26 39.28 39.3 39.32

E

N

W

S

39.34

Longitude

38.36

38.38

38.4

38.42

Latitu

de

Ro= 7.5 km

Fig. 3. Similarity maps for Ro ¼ 1.5, 4.5, and 7.5 km on the Keban Dam Lake.

F. Kulahcı, Z. S- en / Applied Radiation and Isotopes 65 (2007) 1070–10771076

5. Conclusions

Keban Dam Lake in Turkey is chosen as a pilot area tostudy the effect of the global fallout and Chernobyl nuclearaccident. The PCSV technique is employed for themodeling purpose in order to identify possible regionalfeatures and similarities of 90Sr. The following ad-

vantages make the PCSV model interesting in practicalapplications:

(i)

The PCSV model may be used for irregularly dis-tributed sample positions within the study region.

(ii)

The PCSV does not require complex mathematicaltheorems and it is fairly easy to apply in practical studies.

ARTICLE IN PRESS

Table 3

Similarity levels at different distances

Station Fixed PCSV levels

Ro ¼ 1.5 km Ro ¼ 4.5 km Ro ¼ 7.5 km

1 3.9� 10�3 4.2� 10�3 4.7� 10�3

2 6.2� 10�3 6.7� 10�3 7.4� 10�3

3 8.6� 10�3 9.0� 10�3 9.6� 10�3

4 1.0� 10�2 1.2� 10�2 1.3� 10�3

5 1.4� 10�2 1.4� 10�2 1.5� 10�3

6 1.5� 10�2 1.5� 10�2 1.6� 10�3

7 1.6� 10�2 1.6� 10�2 1.7� 10�3

8 1.8� 10�2 1.9� 10�2 2.0� 10�3

9 2.1� 10�2 2.1� 10�2 2.2� 10�2

10 2.3� 10�2 2.3� 10�2 2.4� 10�2

11 2.5� 10�2 2.5� 10�2 2.6� 10�2

12 – 2.7� 10�2 2.7� 10�2

13 2.8� 10�2 2.8� 10�2 2.9� 10�2

14 2.9� 10�2 3.0� 10�2 3.0� 10�2

15 3.1� 10�2 3.1� 10�2 3.1� 10�2

16 3.2� 10�2 3.2� 10�2 3.4� 10�2

17 3.4� 10�2 3.5� 10�2 3.6� 10�2

18 3.7� 10�2 3.9� 10�2 4.1� 10�2

19 4.2� 10�2 4.2� 10�2 4.3� 10�2

20 4.3� 10�2 4.4� 10�2 4.4� 10�2

21 4.5� 10�2 4.5� 10�2 4.6� 10�2

22 4.6� 10�2 4.7� 10�2 4.7� 10�2

23 4.9� 10�2 4.9� 10�2 5.0� 10�2

24 5.1� 10�2 5.1� 10�2 5.2� 10�2

25 5.3� 10�2 5.4� 10�2 5.5� 10�2

26 5.5� 10�2 5.6� 10�2 5.8� 10�2

27 5.8� 10�2 5.9� 10�2 6.0� 10�2

28 6.0� 10�2 6.0� 10�2 6.1� 10�2

29 6.1� 10�2 6.2� 10�2 6.2� 10�2

30 6.3� 10�2 6.3� 10�2 6.4� 10�2

31 6.4� 10�2 6.5� 10�2 6.6� 10�2

32 6.7� 10�2 6.8� 10�2 6.9� 10�2

33 7.0� 10�2 7.1� 10�2 7.1� 10�2

34 – 7.3� 10�2 7.4� 10�2

35 7.5� 10�2 7.5� 10�2 7.6� 10�2

36 7.6� 10�2 7.7� 10�2 7.8� 10�2

37 7.8� 10�2 7.9� 10�2 8.0� 10�2

38 8.0� 10�2 8.1� 10�2 8.1� 10�2

39 7.5� 10�2 8.2� 10�2 8.3� 10�2

40 – 8.4� 10�2 8.5� 10�2

F. Kulahcı, Z. S- en / Applied Radiation and Isotopes 65 (2007) 1070–1077 1077

The PCSV modeling technique is applied to 90Sr surfacewater data taken from Keban Dam Lake. After theidentification of individual PCSV at each location, theyare then grouped according to their similarity, whichled to five distinctive groups in the study area. All togetherthere were 40 locations and hence 40 PCSVs, but therepresentative number is deduced as five distinctivePCSVs. The spatial dispersion of 90Sr radionuclide is seento be heterogeneous and spatially uncorrelated at bigdistances.

It is seen that changing in the lake of the 90Sr approvesgenerally the model A. In this situation, last but not theleast, changing of the 90Sr radioactivity, nowadays, isrelated to geological structure of the study area rather thanatmospheric effects.

Acknowledgments

This work is a part of the post-doctorate research projectsupported by The Scientific and Technical Research Councilof Turkey (TUBITAK). The authors would like to thankTUBITAK for financial support and encouragement.

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