using ordinary kriging to model radioactive contamination data

INTRODUCTION TO THE SPATIAL INTERTICLES THE DA

ARTICLES

USING ORDINARY KRIGING TO MODEL RADIOACTIVE CONTAMINATION DATA

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This paper deals with an application of ordinary kriging (OK) for spatial interpolation of data in a completely automatic (“one-click mapping”) manner. The important set of kriging parameters (semivariogram model, search strategy, etc.) were tuned based on the prior characteristics of the phenomenon considered. The prior information provided as 10 sets of monitoring observations taken at different days was used to analyse and model the spatial correlation of the phenomenon. Furthermore, the prior information was expected to be consistent within a rather long time range and therefore assumed to reflect the structure of the contamination pattern at any given day. The approach applied here gave satisfactory results for both routine and emergency data sets. The benefits and drawbacks of the kriging model were well illustrated in the study. Ordinary kriging can be considered as a real candidate for the implementation in a decision support system.

1. INTRODUCTION qÜÉ=éêÉëÉåí=é~éÉê=ÇÉëÅêáÄÉë=Å~é~ÄáäáíáÉë=çÑ=~=ïÉääJâåçïå=ÖÉçëí~íáëíáÅ~ä=áåíÉêéçä~íáçå=íÉÅÜJ åáèìÉ= Ó= çêÇáå~êó= âêáÖáåÖ= ElhF= Ó= Ñçê= Ñ~ëí= çåJäáåÉ= ~å~äóëáë= çÑ= ê~Çáç~ÅíáîÉäó= Åçåí~ãáå~íÉÇ= íÉêêáíçêáÉëK= qÜÉ= ã~áå= éêçÄäÉã= ïáíÜ= çåJäáåÉ= ~ééäáÅ~íáçå= çÑ= íÜÉ= ÖÉçëí~íáëíáÅ~ä= ~ééêç~ÅÜ= áë= íÜÉ=ÉñéÉêí=ïçêâ=ÇÉ~äí=ïáíÜ=Éëíáã~íáçå=~åÇ=ãçÇÉääáåÖ=çÑ=íÜÉ=ëé~íá~ä=ÅçêêÉä~íáçå=ëíêìÅíìêÉK= pÉîÉê~ä=~ííÉãéíëI=ãçêÉ=çê=äÉëë=ëìÅÅÉëëÑìäI=ïÉêÉ=ã~ÇÉ=íç=~ìíçã~íÉ=íÜáë=ëí~ÖÉ=E`êÉëëáÉ=NVURX= e~~ë=NVVMX=wÜ~åÖ=Éí=~äK=NVVRFK=kÉîÉêíÜÉäÉëëI=ãçëí=ÖÉçëí~íáëíáÅá~åë=~ÖêÉÉ=íÜ~í=ãçÇÉääáåÖ=~= ëé~íá~ä=ÅçêêÉä~íáçå=ëíêìÅíìêÉ=êÉèìáêÉë=ÉñéÉêí=âåçïäÉÇÖÉ=~åÇ=ÉÑÑçêí=Efë~~âë=~åÇ=pêáî~ëí~î~= NVUVX=m~åå~íáÉê=NVVSX=dççî~Éêíë=NVVTX=aÉìíëÅÜ=~åÇ=gçìêåÉä=NVVUFK= få= íÜÉ= Ñê~ãÉïçêâ= çÑ= íÜÉ= pf`OMMQ= ÉñÉêÅáëÉ= E~ééäáÅ~íáçå= çÑ= ~= “çåÉJÅäáÅâ= ã~ééáåÖÒ= ãÉíÜçÇFI=çêÇáå~êó=âêáÖáåÖ=ï~ë=éÉêÑçêãÉÇ=ïáíÜ=~=éêÉÇÉÑáåÉÇ=ëé~íá~ä=ÅçêêÉä~íáçå=ëíêìÅíìêÉ= ãçÇÉä=Ä~ëÉÇ=çå=íÜÉ=~î~áä~ÄäÉ=éêáçê=Ç~í~=ëÉíëK=qÜÉëÉ=Ç~í~=ëÉíë=~êÉ=êçìíáåÉ=ãçåáíçêáåÖ=Ç~í~= ~åÇ=íÜÉó=êÉéêÉëÉåí=ïÉää=íÜÉ=Ñáêëí=ÉñÉêÅáëÉ=Ç~í~=ëÉí=EÇ~í~=ëÉí=fFK=qÜÉ=ëÉÅçåÇ=E“àçâÉêÒF=Ç~í~= ëÉí= EffF= ëÜçïë= ~ÄëçäìíÉäó= ÇáÑÑÉêÉåí= ÄÉÜ~îáçìê= áåÅäìÇáåÖ= ëçãÉ= ~åçã~äçìë= ÑÉ~íìêÉëI= ïÜáÅÜ= ïÉêÉ= ÇáÑÑáÅìäí= íç= éêÉÇáÅíK= få= íÜÉ= ÅìêêÉåí= ïçêâ= ïÉ= ïáää= ÇáëÅìëë= ~Çî~åí~ÖÉë= çÑ= çêÇáå~êó= âêáÖáåÖI=ÉKÖK=ê~íÜÉê=Ñ~ëí=Åçãéìí~íáçåI=ÇáêÉÅí=Éëíáã~íáçå=çÑ=ìåÅÉêí~áåíóI=É~ëáåÉëë=çÑ=~å=ìåJ ÇÉêëí~åÇáåÖ=~åÇ=íêÉ~íãÉåíI=ÉíÅX=~åÇ=ëçãÉ=çÑ=áíë=Çê~ïÄ~ÅâëI=ã~áåäó=íÜÉ=ëãççíÜáåÖ=ÉÑÑÉÅíI= ïÜáÅÜ=áë=ÉëéÉÅá~ääó=ëíêçåÖ=ïÜÉå=íÜÉ=ëÉ~êÅÜ=ê~Çáìë=áë=íçç=ä~êÖÉK= qÜÉ=ã~áå=éìêéçëÉ=çÑ=íÜÉ=ïçêâ=áë=íç=Çê~ï=íÜÉ=~ííÉåíáçå=çÑ=ÇÉÅáëáçå=ã~âÉêëI=ïÜç=ïçêâ= ïáíÜ= ÉãÉêÖÉåÅó= ëáíì~íáçåë= Å~ìëÉÇ= Äó= éçääìíáçåI= íç= íÜÉ= Å~é~ÄáäáíáÉë= çÑ= ~= êÉä~íáîÉäó= ëáãéäÉ= ~åÇ= ïÉääJâåçïå= Åä~ëëáÅ~ä= ãÉíÜçÇI= ïÜáÅÜ= Å~å= ÄÉ= É~ëáäó= áãéäÉãÉåíÉÇ= áå= ~åó= ÇÉÅáëáçå== ëìééçêí=ëóëíÉã=Ñçê=Åêáëáë=ëáíì~íáçåëK=pçãÉ=áãéêçîÉãÉåíë=Å~å=ÄÉ=ÉñéÉÅíÉÇ=Äó=áåÅçêéçê~íJ

APPLIED GIS, VOLUME 1, NUMBER 2, 2005 MONASH UNIVERSITY EPRESS

10-1

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2. METHODOLOGY lêÇáå~êó= âêáÖáåÖ= áë= ÉñíÉåëáîÉäó= ÇÉëÅêáÄÉÇ= áå= íÜÉ= äáíÉê~íìêÉI= Ñçê= Éñ~ãéäÉ= fë~~âë= ~åÇ= pêáî~ëí~î~= ENVUVFI= dççî~Éêíë= ENVVTFI= `ÜáäÉë= ~åÇ= aÉäÑáåÉê= ENVVVFI= ÉíÅK= _Éäçï= ïÉ= çìíäáåÉ= Üçï=ïÉ=Ü~îÉ=~Ç~éíÉÇ=íÜÉ=âêáÖáåÖ=ãÉíÜçÇ=~åÇ=Éèì~íáçåë=íç=íÜÉ=ÅìêêÉåí=ÉñÉêÅáëÉK= iÉí=ìë=ëìééçëÉ=íÜ~í=íÜÉêÉ=áë=~=ê~åÇçã=ÑáÉäÇ=wEñF=êÉéêÉëÉåíÉÇ=Äó=~=ëÉí=çÑ=ÖáîÉå=î~äìÉë= wEñiF=ãÉ~ëìêÉÇ=~í=äçÅ~íáçåë=ñiK=^ÅÅçêÇáåÖ=íç=~=äáåÉ~ê=Éëíáã~íçê=~=î~äìÉ=~í=íÜÉ=ìåãÉ~ëìêÉÇ= * äçÅ~íáçå=ñM=Ew EñMFF=áë=ÖáîÉå=Äó=íÜÉ=ÑçääçïáåÖ=Éèì~íáçåW=

Z * ( x0 ) =

N ( x0 )

∑λ Z(x ) , i =1

i

i

(1)

ïÜÉêÉ= kEñMF= áë= íÜÉ= åìãÄÉê= çÑ= ë~ãéäÉë= Ñêçã= íÜÉ= åÉáÖÜÄçìêÜççÇ= çÑ= ñM= í~âÉå= áåíç= íÜÉ== ~ÅÅçìåí=Ñçê=íÜÉ=Éëíáã~íáçåI=~åÇ= λi=~êÉ=çêÇáå~êó=âêáÖáåÖ=ïÉáÖÜíëK=qÜÉ=åÉáÖÜÄçìêÜççÇ=ÇÉJ éÉåÇë=çå=~=ìëÉêJÇÉÑáåÉÇ=ëÉ~êÅÜ=êìäÉK=fí=Å~å=ÄÉ=ÇÉÑáåÉÇ=~ë=~=ÅáêÅäÉ=ïáíÜ=~=ëÉ~êÅÜ=ê~Çáìë=çê=~ë= ~å=ÉääáéëÉ=ïáíÜ=ã~àçê=~åÇ=ãáåçê=~ñáë=~åÇ=çêáÉåí~íáçåK=qÜÉ=åÉáÖÜÄçìêÜççÇ=áë=ÉñéÉÅíÉÇ=íç= ÄÉ=ëã~ää=ÉåçìÖÜ=íç=éêÉëÉêîÉ=~=äáãáí~íáçå=çå=~=Åçåëí~åí=ãÉ~åK=cçê=~=ãÉ~åáåÖÑìä=Éëíáã~íáçå= íÜÉ=åÉáÖÜÄçìêÜççÇ=åÉÉÇë=íç=Åçåí~áå=~í=äÉ~ëí=P=ë~ãéäÉëK= qÜÉ= ëÉí=çÑ=ïÉáÖÜíë=EλF=áë=ÇÉíÉêãáåÉÇ=Äó=ãáåáãáòáåÖ=çÑ=íÜÉ=Éëíáã~íáçå=î~êá~åÅÉ=ìåÇÉê= íÜÉ=Åçåëíê~áåí=çÑ=ìåÄá~ëÉÇåÉëëW=

⎛ ⎛ N ( x0 ) ⎞ ⎞ min Var ⎜⎜ ( Z * ( x 0 ; λ ) − Z ( x 0 ) ) − µ ⎜⎜ ∑ λ i ⎟⎟ ⎟⎟ λ ⎝ i =1 ⎠ ⎠ , ⎝

(2)

Äó=ëçäîáåÖ=íÜÉ=ëçJÅ~ääÉÇ=çêÇáå~êó=âêáÖáåÖ=Éèì~íáçåëW=

⎧ N ( x0 ) ⎪⎪ ∑ λi γ ij − µ = γ j 0 , j = 1K N ( x0 ) i =1 , ⎨ N ( x0 ) ⎪ λi = 1 ∑ ⎪⎩ i =1

(3)

ïÜÉêÉ= ”= áë= íÜÉ= i~Öê~åÖá~å= ãìäíáéäáÉêK= fí= áë= ~= äáåÉ~ê= ëóëíÉã= çÑ= kEñMFHN= Éèì~íáçåë= ïáíÜ= kEñMFHN= ìåâåçïåëK= γij= ÅçêêÉëéçåÇ= íç= ~= ëé~íá~ä= ÅçêêÉä~íáçå= ëíêìÅíìêÉ= çÑ= íÜÉ= ê~åÇçã= ÑáÉäÇ= ÇÉëÅêáÄÉÇ=Äó=~=ëÉãáî~êáçÖê~ãW=

γ ij = γ (hij ) = 12 Var (Z ( x + hij ) − Z ( x ) ), r

r

(4)

r ïÜÉêÉ= hij =áë=~=îÉÅíçê=ëÉé~ê~íáåÖ=äçÅ~íáçåë=ñá=~åÇ=ñàK=qÜÉ=çêÇáå~êó=âêáÖáåÖ=Éèì~íáçåë=Ü~îÉ= ~= ìåáèìÉ= ëçäìíáçå= áÑ= íÜÉó= ~êÉ= ïÉääJÇÉÑáåÉÇ= Eåçí= ëáåÖìä~êFK= qÜÉ= âêáÖáåÖ= Éëíáã~íáçå= Éêêçê= áë= ÇÉëÅêáÄÉÇ=Äó=íÜÉ=âêáÖáåÖ=î~êá~åÅÉ=

σ2 =

N ( x0 )

∑λ γ i =1

10-2

i

i0

+µ,

(5)

MODELLING RADIOACTIVE CONTAMINATION DATA ARTICLES

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MODELLING RADIOACTIVE CONTAMINATION DATA ARTICLES

10-3

çêáÉåíÉÇ=áå=b~ëíJtÉëí=ÇáêÉÅíáçåK=qÜÉ=çêÇáå~êó=âêáÖáåÖ=Éëíáã~íáçå=ï~ë=ÅçãéìíÉÇ=ïÜÉêÉ=íÜÉ= åÉáÖÜÄçêÜççÇ=Åçåí~áåÉÇ=~í=äÉ~ëí=P=ë~ãéäÉëI=çíÜÉêïáëÉ=íÜÉ=äçÅ~íáçå=ï~ë=äÉÑí=ìåÉëíáã~íÉÇK= qÜÉ= ã~ñáãìã= åìãÄÉê= çÑ= ë~ãéäÉë= ìëÉÇ= Ñçê= Éëíáã~íáçå= ~í= É~ÅÜ= äçÅ~íáçå= ñM= ï~ë= OM= EíÜÉ= ÅäçëÉëí=íç=ñMFK= 2.2 TUNING THE ALGORITHM

`êçëëJî~äáÇ~íáçå=äÉ~îÉJçåÉJçìí=íÉÅÜåáèìÉ=ï~ë=ìëÉÇ=íç=ÅÜÉÅâ=íÜÉ=ëìáí~Äáäáíó=çÑ=íÜÉ=ëÉäÉÅíÉÇ= é~ê~ãÉíÉêëK=`êçëëJî~äáÇ~íáçå=ï~ë=Å~êêáÉÇ=çìí=Ñçê=~ää=NM=éêáçê=Ç~í~=ëÉíëK=qÜÉ=êÉëìäíë=ïÉêÉ= Åçãé~êÉÇ= ìëáåÖ= íÜÉ= êççíJãÉ~åJëèì~êÉ= Éêêçê= EojpbF= ~åÇ= mÉ~êëçåÛë= ê= ÅçêêÉä~íáçå= ÅçJ ÉÑÑáÅáÉåí= ÄÉíïÉÉå= íÜÉ= êÉ~ä= î~äìÉë= ~åÇ= íÜÉ= çÄí~áåÉÇ= Éëíáã~íÉëK= qÜÉ= êÉëìäíë= çÑ= íÜÉ= ÅêçëëJ î~äáÇ~íáçå=ëìãã~êáëÉÇ=áå=q~ÄäÉ=N=~ééÉ~êÉÇ=íç=ÄÉ=ê~íÜÉê=ëáãáä~ê=Ñçê=~ää=NM=éêáçê=Ç~í~=ëÉíë= ~åÇ=Å~å=ÄÉ=ÅçåëáÇÉêÉÇ=~ë=ë~íáëÑ~ÅíçêóK= cáå~ääóI=~=éêÉÇáÅíáçå=ÖêáÇ=Ñçê=~ää=NM=Ç~óë=ï~ë=Éëíáã~íÉÇK=qÜÉëÉ=éêÉÇáÅíáçåë=~êÉ=ÅÜ~ê~ÅJ íÉêáëÉÇ=Äó=íÜÉ=êÉ~ëçå~ÄäÉ=ÑäìÅíì~íáçåë=ÇìÉ=íç=íÜÉ=Ç~óJíçJÇ~ó=î~êá~íáçåë=çÑ=íÜÉ=áåáíá~ä=Ç~í~K= pç= áí= ï~ë= ÇÉÅáÇÉÇ= íÜ~í= íÜÉ= ãÉíÜçÇ= ÅçìäÇ= ÄÉ= ìëÉÇ= íç= éêÉÇáÅí= ëáãáä~ê= é~ííÉêåë= ~í= ÇáÑÑÉêÉåí= íáãÉëK=^äëçI=áí=ï~ë=ÅçåëáÇÉêÉÇ=íç=ÅÜÉÅâ=Üçï=íÜÉ=ãçÇÉä=ïçìäÇ=éÉêÑçêã=Ñçê=íÜÉ=Ç~í~=ïáíÜ= ìåâåçïå= ëíêìÅíìêÉI= ïÜáÅÜ= ÅçìäÇ= ÄÉ= ~åçã~äçìë= ~åÇ= Åçåí~áå= çìíäáÉêëI= ~ë= áåÇáÅ~íÉÇ= ~Äçìí= íÜÉ=ëÉÅçåÇ=Ç~í~=ëÉí=EffF=áå=íÜÉ=pf`OMMQ=~ååçìåÅÉãÉåíK=

Figure 1 Examples of experimental semivariogram roses for prior data

Figure 2 Experimental semivariogram rose averaged over 10 days (left) and fitted semivariogram model (right)

10-4

MODELLING RADIOACTIVE CONTAMINATION DATA ARTICLES

Day 1 2 3 4 5

Pearson’s r 0.78 0.78 0.79 0.75 0.76

RMSE 17.02 16.96 15.98 15.70 15.33

Day 6 7 8 9 10

Pearson’s r 0.75 0.73 0.75 0.77 0.74

RMSE 14.90 15.63 15.41 16.34 16.27

Table 1 Cross-validation error parameters

3. RESULTS `~äÅìä~íáçåë=éÉêÑçêãÉÇ=çå=íÜÉ=íïç=Ç~í~=ëÉíë=Ef=~åÇ=ffF=áåÅäìÇáåÖ=Ççïåäç~ÇáåÖ=íÜÉã=Ñêçã= íÜÉ=áåíÉêåÉíI=ëÉííáåÖ=~=åÉï=ÅçååÉÅíáçå=ïáíÜ=íÜÉ=pf`=OMMQ=ïÉÄëáíÉ=~åÇ=ìéäç~ÇáåÖ=íÜÉ=êÉëìäí= íççâ= P= ãáåìíÉëK= `~äÅìä~íáçåë= ïÉêÉ= éÉêÑçêãÉÇ= ëÉé~ê~íÉäó= Ñçê= É~ÅÜ= Ç~í~= ëÉíI= ÉîÉêó= íáãÉ= ëçäîáåÖ=~ää=íÜÉ=çêÇáå~êó=âêáÖáåÖ=Éèì~íáçåëK=dÉåÉê~ääóI=çåÅÉ=íÜÉ=âêáÖáåÖ=ïÉáÖÜíë=Ü~Ç=ÄÉÉå= Å~äÅìä~íÉÇI=íÜÉó=ÅçìäÇ=ÄÉ=êÉìëÉÇ=Ñçê=~åçíÜÉê=Ç~í~=ëÉí=~ë=íÜÉó=ÇÉéÉåÇÉÇ=çåäó=çå=íÜÉ=ãìíì~ä= éçëáíáçå=çÑ=íÜÉ=Éëíáã~íÉÇ=äçÅ~íáçåë=~åÇ=íÜÉ=ëÉãáî~êáçÖê~ã=ãçÇÉäK= 3.1. GENERAL RESULTS

qÜÉ=ã~áå=ëí~íáëíáÅë=Ñçê=íÜÉ=çÄëÉêîÉÇ=~åÇ=Éëíáã~íÉÇ=Ç~í~=~êÉ=ÖáîÉå=áå=q~ÄäÉ=OK=fí=áë=ÉîáÇÉåí= íÜ~í=ãÉ~åë=~åÇ=ãÉÇá~åë=~êÉ=êÉéêçÇìÅÉÇ=ê~íÜÉê=ïÉää=Ñçê=ÄçíÜ=Ç~í~=ëÉíëK=bîáÇÉåÅÉ=Ñçê=íÜÉ= ëãççíÜáåÖ= ÉÑÑÉÅí= äáÉë= áå= íÜÉ= ìåÇÉêÉëíáã~íÉÇ= ëí~åÇ~êÇ= ÇÉîá~íáçåK= qÜÉ= ã~ñáãìã= î~äìÉ= áë= ìåÇÉêÉëíáã~íÉÇ=~ë=ïÉää=ÇìÉ=íç=íÜáë=ëãççíÜáåÖ=ÉÑÑÉÅíK=qÜÉ=ëãççíÜáåÖ=áë=ãìÅÜ=ëíêçåÖÉê=Ñçê= íÜÉ=ëÉÅçåÇ=Ç~í~=ëÉí=ffI=ïÜÉêÉ=íÜÉ=~Åíì~ä=ÅçêêÉä~íáçå=ê~åÖÉ=áë=ëã~ääÉê=íÜ~å=íÜÉ=çåÉ=ìëÉÇ=Ñçê= Éëíáã~íáçåI= ~ÅÅçêÇáåÖ= íç= íÜÉ= ëçìêÅÉ= Ç~í~= EaìÄçáë= ~åÇ= d~äã~êáåáI= OMMRFK= ^å= áåíÉêÉëíáåÖ= çÄëÉêî~íáçå=áë=íÜÉ=ìåÇÉêÉëíáã~íáçå=çÑ=íÜÉ=ãáåáãìã=î~äìÉ=áå=íÜÉ=ëÉÅçåÇ=Ç~í~=ëÉíK=lå=íÜÉ= Åçåíê~êóI=çîÉêÉëíáã~íáçå=çÑ=íÜÉ=ãáåáãìã=ï~ë=ÉñéÉÅíÉÇ=ÇìÉ=íç=íÜÉ=ëãççíÜáåÖ=ÉÑÑÉÅíK=qÜáë= ãáåáãìãI=íçÖÉíÜÉê=ïáíÜ=S=çíÜÉê=Ç~í~=éçáåíë=Éëíáã~íÉÇ=íç=ÄÉ=äçïÉê=íÜ~å=íÜÉ=ãáåáãìã=çÑ= íÜÉ=ê~ï=Ç~í~I=áë=äçÅ~íÉÇ=àìëí=kçêíÜ=çÑ=íÜÉ=Üçí=ëéçí=EïÜáíÉ=ëéçí=áå=cáÖìêÉ=PI=êáÖÜíFK=^ää=çÑ= íÜÉ=ìåÇÉêÉëíáã~íÉÇ=éçáåíë=~êÉ=äçÅ~íÉÇ=áå=íÜÉ=~êÉ~=çÑ=íÜÉ=ëíêçåÖÉëí=é~ííÉêå=Öê~ÇáÉåíI=ïÜÉêÉ= áí= áë= ÉîÉå= ÅçêêÉÅí= íç= ~ééäó= äçÅ~ä= âêáÖáåÖ= ÄÉÅ~ìëÉ= íÜÉ= ëí~íáçå~êáíó= ~ëëìãéíáçå= áë= îáçä~íÉÇ= EÅçåëí~åí=ãÉ~å=Å~åÛí=ÄÉ=ÉñéÉÅíÉÇ=ÉîÉå=ÅäçëÉ=íç=íÜÉëÉ=äçÅ~íáçåëFK=fí=äççâë=~ë=áÑ=íÜÉ=Éëíáã~íÉë= ~í=íÜÉëÉ=éçáåíë=ÅçãéÉåë~íÉ=íÜÉ=ÜáÖÜ=Üçí=ëéçí=î~äìÉë=ëç=~ë=íç=âÉÉé=íÜÉ=äçÅ~ä=ãÉ~å=Åçåëí~åíK= Min.

N = 808

Max.

Mean

Median

Std. dev.

Observed (first data set I)

57.00

180.00

98.02

98.80

20.02

Estimates (first data set II)

66.80

130.35

96.63

98.50

15.19

Observed (second data set I)

57.00

1528.20

105.42

98.95

83.71

Estimates (second data set II)

37.53

651.18

103.23

97.89

53.17

Table 2 Comparison of estimated and measured values (nSv/h)

qÜÉ=ãÉ~å=~ÄëçäìíÉ=Éêêçê=Ej^bFI=íÜÉ=Äá~ë=Eçê=ãÉ~å=ÉêêçêI=jbFI=íÜÉ=êççíJãÉ~åJëèì~êÉÇ= Éêêçê= EojpbF= ~åÇ= mÉ~êëçåÛë= ê= ÅçÉÑÑáÅáÉåí= çÑ= ÅçêêÉä~íáçå= ÄÉíïÉÉå= íÜÉ= Éëíáã~íÉÇ= ~åÇ= íêìÉ= î~äìÉë=ïÉêÉ=ÅçãéìíÉÇ=Ä~ëÉÇ=çå=íÜÉ=UMU=î~äáÇ~íáçå=äçÅ~íáçåëK=qÜÉ=êÉëìäíë=~êÉ=éêÉëÉåíÉÇ=áå= q~ÄäÉ=PK=

MODELLING RADIOACTIVE CONTAMINATION DATA ARTICLES

10-5

få=ÖÉåÉê~äI=êÉëìäíë=Ñçê=íÜÉ=Ñáêëí=Ç~í~=ëÉí=EfF=~êÉ=ÄÉííÉêI=ïÜáÅÜ=áë=åçí=ëìêéêáëáåÖ=ÄÉÅ~ìëÉ=çÑ= áíë=ëáãáä~êáíó=ïáíÜ=íÜÉ=NM=éêáçê=ëé~íá~ä=ÇáëíêáÄìíáçåëK=qÜÉ=ojpb=~åÇ=mÉ~êëçåÛë=ê=ÅçêêÉä~J íáçå= ÅçÉÑÑáÅáÉåí= Ñçê= íÜÉ= Ñáêëí= Ç~í~= ëÉí= ~êÉ= ëáãáä~ê= íç= íÜçëÉ= çÄí~áåÉÇ= íÜêçìÖÜ= íÜÉ= ÅêçëëJ î~äáÇ~íáçå= éêçÅÉÇìêÉ= Eq~ÄäÉ= NFK= qÜÉ= ë~ãÉ= é~ê~ãÉíÉêë= Ñçê= íÜÉ= ëÉÅçåÇ= Ç~í~= ëÉí= EffF= ~êÉ= ïçêëÉI=Äìí=íÜÉó=~êÉ=åçí=ãÉ~åáåÖäÉëëK=qÜÉ=ÖÉåÉê~ä=ìåÇÉêÉëíáã~íáçå=~ééÉ~êë=áå=íÜÉ=êÉëìäíë= Ñçê=ÄçíÜ=Ç~í~=ëÉíëK= Data sets: First data set I Second data set II

MAE

ME

Pearson’s r

RMSE

9.11

-1.39

0.78

12.49

19.68

-2.18

0.56

69.08

Table 3 Comparison of the validation errors

qïç=ëÉíë=çÑ=Åçåíçìê=ã~éë=ïÉêÉ=éêçÇìÅÉÇW=íÜÉ=ã~é=çÑ=íÜÉ=lh=Éëíáã~íÉë=EcáÖìêÉ=PF=~åÇ= íÜÉ=ã~é=çÑ=íÜÉ=~ëëçÅá~íÉÇ=Éëíáã~íáçå=ìåÅÉêí~áåíáÉëI=lh=î~êá~åÅÉ=EcáÖìêÉ=QFK=lh=î~êá~åÅÉ= áë= Éñ~Åíäó= íÜÉ= ë~ãÉ= Ñçê= ÄçíÜ= Å~ëÉë= EÇ~í~= ëÉíë= f= ~åÇ= ffFI= ~ë= áí= ÇÉéÉåÇë= çåäó= çå= íÜÉ= ëÉãáî~êáçÖê~ã=ãçÇÉä=~åÇ=çå=íÜÉ=ëé~íá~ä=äçÅ~íáçå=çÑ=íÜÉ=ë~ãéäÉëK=qÜ~í=áë=ïÜó=íÜÉêÉ=áë=çåäó= çåÉ=éäçí=~ëëçÅá~íÉÇ=ïáíÜ=íÜÉ=âêáÖáåÖ=ÉêêçêëK=få=~ää=çÑ=íÜÉëÉ=ÑáÖìêÉë=ÅêçëëÉë=áåÇáÅ~íÉ=íÜÉ=äçÅ~J íáçåë=çÑ=íÜÉ=Éëíáã~íÉÇ=î~äìÉë=~åÇ=ÄçñÉë=áåÇáÅ~íÉ=íÜÉ=äçÅ~íáçåë=çÑ=íÜÉ=áåéìí=Ç~í~K= qÜÉ=êÉëìäíë=çÑ=áåíÉêéçä~íáçå=Ñçê=íÜÉ=íïç=Ç~í~=ëÉíë=ÇáÑÑÉê=Ñêçã=É~ÅÜ=çíÜÉê=EcáÖìêÉ=PFI=~ë= íÜÉó=ÇÉéÉåÇ=çå=íÜÉ=áåéìí=î~äìÉëK=qÜÉ=ÇÉíÉÅíÉÇ=Üçí=ëéçí=ÅçêêÉëéçåÇë=íç=íÜÉ=Ñäìñ=áå=íÜÉ=ëÉÅJ çåÇ=Ç~í~=ëÉí=ff=~åÇ=áë=çÄëÉêîÉÇ=áå=cáÖìêÉ=P=EêáÖÜíFK=_ìí=çíÜÉê=é~êíë=çÑ=íÜÉ=êÉÖáçå=EÉëéÉÅá~ääó= íÜÉ=åçêíÜÉêå=é~êíF=äççâ=ìå~ÑÑÉÅíÉÇ=Äó=íÜÉ=éçääìíáçå=~åçã~äóI=ëç=íÜÉó=~êÉ=îÉêó=ëáãáä~ê=íç= íÜÉ=Éëíáã~íÉë=Ä~ëÉÇ=çå=ÄçíÜ=Ç~í~=ëÉíëK=

Figure 3 Levels of OK estimates (nSv/h) for the 1st (left) and the 2nd data set (right)

10-6

MODELLING RADIOACTIVE CONTAMINATION DATA ARTICLES

Figure 4 Levels of OK variance represent the uncertainty associated with the estimates obtained for the 1st and the 2nd data sets

Figure 5 3D map showing extreme values found in the 2nd data set

3.2. DETECTING ANOMALIES AND OUTLIERS

cáÖìêÉ=R=êÉéêÉëÉåíë=íÜÉ=äçÅ~íáçåë=çÑ=íÜÉ=ÉñíêÉãÉ=î~äìÉë=çÄí~áåÉÇ=Ñêçã=lh=Ñçê=íÜÉ=ëÉÅçåÇ= Ç~í~=ëÉí=ffK=^äíÜçìÖÜ=íÜÉ=ÉñíêÉãÉë=ïÉêÉ=ÇÉíÉÅíÉÇI=íÜÉ=ëáÖåáÑáÅ~åí=ëãççíÜáåÖ=ÉÑÑÉÅí=ã~âÉë= íÜÉ=Üçí=ëéçí=äçïÉê=~åÇ=ïáÇÉêK=píáää=íÜÉ=êÉëìäí=áë=åçí=Ä~Ç=ÉîÉå=ïÜÉå=ìëáåÖ=åçí=ëìáí~ÄäÉ=ëé~J íá~ä= ÅçêêÉä~íáçå= ãçÇÉä= ~åÇ= ~= ëÉ~êÅÜ= åÉáÖÜÄçêÜççÇ= ä~êÖÉê= íÜ~å= íÜÉ= ~Åíì~ä= ÅçêêÉä~íáçå= ê~ÇáìëK=

MODELLING RADIOACTIVE CONTAMINATION DATA ARTICLES

10-7

4. DISCUSSION qÜÉ=êÉëìäíë=çå=íÜÉ=Ñáêëí=Ç~í~=ëÉí=~êÉ=Ñ~áêI=~ë=ï~ë=ÉñéÉÅíÉÇK=qÜÉ=Ç~í~=ëÉí=f=ÉñÜáÄáíë=ÑÉ~íìêÉë= ëáãáä~ê=íç=~åó=çåÉ=çÑ=NM=éêáçê=Ç~í~=ëÉíëK=pç=íÜÉ=êçìíáåÉ=ãçåáíçêáåÖ=Ç~í~=Å~å=ÄÉ=ë~íáëÑ~ÅíçJ êáäó=áåíÉêéçä~íÉÇ=ìëáåÖ=âêáÖáåÖ=ïÉáÖÜíë=Å~äÅìä~íÉÇ=çåÅÉ=~åÇ=íÜÉå=ëíçêÉÇ=ïáíÜçìí=íìåáåÖ=íÜÉ= ãçÇÉä=~ÇÇáíáçå~ääóK=mÉêÜ~éë=í~âáåÖ=áåíç=~ÅÅçìåí=ëçãÉ=ëÉ~ëçå~ä=î~êá~íáçåë=Å~å=ÖáîÉ=~ÇÇáJ íáçå~ä=áãéêçîÉãÉåíI=áÑ=íÜÉêÉ=áë=êÉ~ëçå=íç=ëìëéÉÅí=~åó=ëÉ~ëçå~ä=áåÑäìÉåÅÉ=çå=íÜÉ=ÄÉÜ~îáçìê= çÑ=íÜÉ=ãçåáíçêáåÖ=Ç~í~K= qÜÉ=çíÜÉê=ëáíì~íáçå=ï~ë=çÄëÉêîÉÇ=ïáíÜ=íÜÉ=ëÉÅçåÇ=E“àçâÉêÒF=Ç~í~=ëÉí=ffK=_ÉÅ~ìëÉ=çÑ=íÜÉ= Ñäìñ= EçìíäáÉêëF= íÜÉ= ÉñéÉêáãÉåí~ä= ëÉãáî~êáçÖê~ã= ÑÉ~íìêÉë= îÉêó= ëÜçêí= ÅçêêÉä~íáçå= ê~åÖÉ= Ó= ãçêÉ=íÜ~å=íïç=íáãÉë=ëÜçêíÉê=íÜ~å=íÜÉ=çåÉ=Ñçê=íÜÉ=êçìíáåÉ=éêáçê=Ç~í~=EcáÖìêÉ=SFK=qÜÉêÉ=áë= åç=êÉ~ä=ÅçêêÉä~íáçå=ÄÉíïÉÉå=íÜÉ=Ñäìñ=î~äìÉë=~åÇ=íÜÉ=é~êíë=çÑ=íÜÉ=êÉÖáçå=åçí=óÉí=~ÑÑÉÅíÉÇ=Äó= íÜÉ=ÑäìñK=^äëçI=ëáåÅÉ=íÜÉ=íÜÉçêÉíáÅ~ä=äáãáí~íáçåë=çÑ=íÜÉ=lh=EÅçåëí~åí=ãÉ~åF=~êÉ=îáçä~íÉÇ=áå= íÜÉ= ~êÉ~= ~êçìåÇ= íÜÉ= ÑäìñI= Éëíáã~íáçå= áå= íÜÉ= ~êÉ~= ~êçìåÇ= íÜÉ= ~åçã~äó= ÄÉÅçãÉë= Äá~ëÉÇ= EëíêçåÖ=ìåÇÉêÉëíáã~íáçåFK=qÜÉ=ìå~ÑÑÉÅíÉÇ=é~êíë=çÑ=íÜÉ=êÉÖáçå=~êÉ=éêÉÇáÅíÉÇ=ïÉää=Äó=íÜÉ=lh= ïáíÜ=íÜÉ=éêÉJëÉäÉÅíÉÇ=é~ê~ãÉíÉêëI=~ë=íÜÉó=Çáëéä~ó=é~ííÉêå=ëáãáä~ê=íç=íÜ~í=çÑ=íÜÉ=éêáçê=Ç~í~K= píáää=íÜÉ=Ñäìñ=äçÅ~íáçå=ï~ë=ÇÉíÉÅíÉÇ=ïÉääI=ÇÉëéáíÉ=íÜÉ=ëíêçåÖ=ëãççíÜáåÖ=ÉÑÑÉÅíK=

Figure 6 Omnidirectional experimental semivariogram of 2nddata set II

qÜÉ=ÖççÇ=ÅçêêÉëéçåÇÉåÅÉ=çÑ=íÜÉ=äçÅ~ä=ëí~íáëíáÅë=E~ë=áåÇáÅ~íÉÇ=Äó=cáÖìêÉ=TF=Å~å=ÄÉ=ÅçåJ ëáÇÉêÉÇ=~å=~Çî~åí~ÖÉ=çÑ=íÜÉ=ãÉíÜçÇK=içÅ~ä=ãÉ~åë=ïÉêÉ=Å~äÅìä~íÉÇ=ìëáåÖ=~=ãçîáåÖ=~îÉê~ÖÉ= ~äÖçêáíÜã=Ó=~îÉê~ÖáåÖ=íÜÉ=ë~ãéäÉë=çîÉê=~=ÅÉää=Ñêçã=~=êÉÖìä~ê=êÉÅí~åÖìä~ê=ÖêáÇI=ïÜáÅÜ=ÅçîJ Éêë=íÜÉ=ëíìÇó=êÉÖáçåK=qÜÉ=ÖêáÇ=áë=T=Äó=NQI=ïáíÜ=~=ÅÉää=ëáòÉ=çÑ=~ééêçñáã~íÉäó=R=âã=Äó=R=âãK= qÜÉ= ãÉ~å= åìãÄÉê= çÑ= î~äáÇ~íáçå= äçÅ~íáçåë= ïáíÜáå= ~= ÅÉää= áë= UI= ~åÇ= çåäó= íÜêÉÉ= ÄçêÇÉê= ÅÉääë= Åçåí~áå=ÑÉïÉê=íÜ~å=P=î~äáÇ~íáçå=ë~ãéäÉëK=få=cáÖìêÉ=T=É~ÅÜ=ÅÉää=áë=ÅçäçìêÉÇ=~ÅÅçêÇáåÖ=íç=íÜÉ= ÇáÑÑÉêÉåÅÉ=ÄÉíïÉÉå=íÜÉ=äçÅ~ä=ãÉ~å=Ñçê=íÜÉ=î~äáÇ~íáçå=Ç~í~=ëÉí=ff=~åÇ=íÜÉ=ÅçêêÉëéçåÇáåÖ=lh= Éëíáã~íÉëK=`êçëëÉë=ã~êâ=î~äáÇ~íáçå=äçÅ~íáçåë=áå=cáÖìêÉ=TK=dççÇ=ÅçêêÉëéçåÇÉåÅÉ=ÄÉíïÉÉå= äçÅ~ä= ãÉ~åë= áåÇáÅ~íÉë= íÜÉ= éçëëáÄáäáíó= çÑ= ìëáåÖ= lh= ïáíÜ= ~= ëáíÉJëéÉÅáÑáÅ= Eåçí= ÉîÉåíJëéÉÅáÑáÅF= ëÉãáî~êáçÖê~ãK=^äëçI=lh=Å~å=ÄÉ=ìëÉÇ=~ë=~=ãçÇÉä=Ñçê=ìåÇÉêëí~åÇáåÖ=íÜÉ=~îÉê~ÖÉ=ÉÑÑÉÅí=çÑ= ~=Åêáëáë=~ÅÅáÇÉåí~ä=éçääìíáçåK= lh=Éëíáã~íÉë=íçÖÉíÜÉê=ïáíÜ=íÜÉ=âêáÖáåÖ=î~êá~åÅÉ=~êÉ=ìëì~ääó=ÅçåëáÇÉêÉÇ=~=ãÉ~ëìêÉ=çÑ= ìåÅÉêí~áåíóK=qç=ÅÜÉÅâ=íÜÉ=ÖççÇåÉëë=çÑ=íÜáë=ãÉ~ëìêÉI=íÜÉ=ÚéêÉÇáÅíáçå=ÉêêçêëÛ=EíÜÉ=lh=ëí~åJ Ç~êÇ= ÇÉîá~íáçåëF= ~åÇ= ÚçÄëÉêîÉÇ= ÉêêçêëÛ= EÇáÑÑÉêÉåÅÉë= ÄÉíïÉÉå= íÜÉ= lh= éêÉÇáÅíáçå= ~åÇ= íÜÉ= íêìÉ=î~äìÉF=ïÉêÉ=Åçãé~êÉÇ=~í=íÜÉ=UMU=î~äáÇ~íáçå=äçÅ~íáçåëK=iÉí=íÜÉ=w=ëÅçêÉ=ÄÉ=ÇÉÑáåÉÇ=Äó= íÜÉ= ê~íáç= çÑ= íÜÉ= çÄëÉêîÉÇ= íç= íÜÉ= éêÉÇáÅíÉÇ= ÉêêçêëK= qÜÉ= ëí~åÇ~êÇ= ÇÉîá~íáçå= çÑ= íÜÉ= w= ëÅçêÉ= î~äìÉë=ï~ë=ÅçãéìíÉÇ=~ë=ïÉääK=få=íÜÉ=áÇÉ~ä=éêÉÇáÅíáçå=Å~ëÉI=íÜÉ=w=ëÅçêÉ=ëí~åÇ~êÇ=ÇÉîá~íáçå= ëÜçìäÇ=ÄÉ=Éèì~ä=íç=çåÉK=få=íÜáë=Å~ëÉI=áí=~ééÉ~êÉÇ=íç=ÄÉ=MKVS=Ñçê=íÜÉ=Ñáêëí=Ç~í~=ëÉí=f=~åÇ=TKUT= Ñçê=íÜÉ=ëÉÅçåÇ=Ç~í~=ëÉí=ffK=qÜìëI=Ñçê=íÜÉ=Ñáêëí=Ç~í~=ëÉí=f=íÜÉ=ìåÅÉêí~áåíó=áë=ÇÉëÅêáÄÉÇ=Ñ~áêäó= ïÉääK=qÜÉ=ë~ãÉ=ìåÅÉêí~áåíó=ãçÇÉä=ÇáÇ=åçí=~ééÉ~ê=íç=ÄÉ=~ÇÉèì~íÉ=Ñçê=íÜÉ=ëÉÅçåÇ=Ç~í~=ëÉí= ffI= Äìí= ëíáää= áí= áë= åçí= íçí~ääó= áêêÉäÉî~åíK= qÜÉ= ~ééäáÅ~íáçå= çÑ= íÜÉ= áêêÉäÉî~åí= ëÉãáî~êáçÖê~ã=

10-8

MODELLING RADIOACTIVE CONTAMINATION DATA ARTICLES

ãçÇÉä= ÅÉêí~áåäó= ÄêáåÖë= ëçãÉ= åÉÖ~íáîÉ= ÅçåëÉèìÉåÅÉëI= Äìí= ëíáää= íÜÉ= lh= Éëíáã~íÉë= ~êÉ= åçí= ãÉ~åáåÖäÉëëK=

Figure 7 Difference between local means of the original data and the OK prediction for the 2nddata set II

5. CONCLUSIONS qÜÉ=ÑçääçïáåÖ=ÅçåÅäìëáçåë=Å~å=ÄÉ=Çê~ïå=Ä~ëÉÇ=çå=íÜÉ=ëíìÇó=éÉêÑçêãÉÇW= •

•

•

^= ãçÇÉä= Ñçê= ëé~íá~ä= ÅçêêÉä~íáçå= ëíêìÅíìêÉ= Å~å= ÄÉ= ïçêâÉÇ= çìí= Ä~ëÉÇ= çå= íÜÉ= éêáçê= ãçåáíçêáåÖ=çÄëÉêî~íáçåë=Ñêçã=~=ëáíÉ=áÑ=íÜÉêÉ=áë=~=íÉãéçê~ä=éÉêëáëíÉåÅÉ=áå=íÜÉ=Ç~í~K= líÜÉêïáëÉ=~=ÇáÑÑÉêÉåí=ëé~íá~ä=ÅçêêÉä~íáçå=ëíêìÅíìêÉ=ãçÇÉä=Å~å=ÄÉ=Äìáäí=~åÇ=~ééäáÉÇ= ìåÇÉê=ÇáÑÑÉêÉåí=ÅçåÇáíáçåë=EëÉ~ëçåI=ïÉ~íÜÉêI=éçääìíáçå=ÅçãéçëáíáçåI=ÉíÅKFK=fí=ã~ó=ÄÉ= áåíÉêÉëíáåÖ= íç= áåîÉëíáÖ~íÉ= ïÜÉíÜÉê= ìëáåÖ= ~= ëé~íá~ä= ÅçêêÉä~íáçå= ãçÇÉä= ÑáííÉÇ= íç== ÉãÉêÖÉåÅó=Ç~í~=Ñêçã=çíÜÉê=ëáíÉë=ïáää=éêçîáÇÉ=ÖççÇ=êÉëìäíëK= lêÇáå~êó=hêáÖáåÖ=ìëáåÖ=íÜÉ=ëÉãáî~êáçÖê~ã=ãçÇÉä=ÑáííÉÇ=íç=íÜÉ=éêáçê=Ç~í~=éêçîáÇÉë= ÖççÇ=éêÉÇáÅíáçå=Ñçê=íÜÉ=êçìíáåÉ=Å~ëÉ=EÇ~í~=ëÉí=fF=~åÇ=ëçãÉ=áåÑçêã~íáçå=áå=íÜÉ=ÉãÉêJ ÖÉåÅó= Å~ëÉ= EÇ~í~= ëÉí= ffF= Ó= ëãççíÜÉÇ= Ñäìñ= éçëáíáçåK= lh= Éëíáã~íÉë= ~êÉ= ~äï~óë= ~ÅÅçãé~åáÉÇ= Äó= íÜÉ= Éëíáã~íáçå= î~êá~åÅÉ= ìëì~ääó= íêÉ~íÉÇ= ~ë= ~= ãÉ~ëìêÉ= çÑ= íÜÉ== ìåÅÉêí~áåíóI=ïÜáÅÜ=~ééÉ~êë=íç=ÄÉ=~ÇÉèì~íÉ=Ñçê=êçìíáåÉ=Å~ëÉ=EÇ~í~= ëÉí= fF= ~åÇ=ë~íáëJ Ñ~Åíçêó=Ñçê=íÜÉ=ÉãÉêÖÉåÅó=Å~ëÉ=EÇ~í~=ëÉí=ffFK= _ÉáåÖ= ~= ê~íÜÉê= Ñ~ëí= ~åÇ= ëáãéäÉ= ãÉíÜçÇI= lh= Å~å= É~ëáäó= ÄÉ= áåÅçêéçê~íÉÇ= áåíç= ~== ÇÉÅáëáçå=ëìééçêí=ëóëíÉã=ïáíÜ=ëÉãáJ~ìíçã~íáÅ=ëÉãáî~êáçÖê~ã=íìåáåÖK=^=ëáíÉJëéÉÅáÑáÅ= éêáçê=ëé~íá~ä=ÅçêêÉä~íáçå=ãçÇÉä=ã~ó=ÄÉ=éêÉé~êÉÇ=áå=~Çî~åÅÉK=jçêÉ=ÇÉí~áäÉÇ=ÉñéÉêí= ~å~äóëáë= ã~ó= ÄÉ= éÉêÑçêãÉÇ= ä~íÉêI= ïÜÉå= ãçêÉ= ÇÉí~áäÉÇ= áåÑçêã~íáçå= Ñêçã= íÜÉ== Åçåí~ãáå~íÉÇ=ëáíÉ=Ü~ë=ÄÉÉå=ÅçääÉÅíÉÇK=

SOFTWARE CODE ^ää= Å~äÅìä~íáçåë= ~åÇ= áääìëíê~íáçåë= ïÉêÉ= ã~ÇÉ= ìëáåÖ= dpl= ëçÑíï~êÉK= qÜÉ= ÉÇìÅ~íáçå~ä= EäáãJ áíÉÇF=îÉêëáçå=çÑ=dpl=áë=ÇáëíêáÄìíÉÇ=çå=`a=ïáíÜ=h~åÉîëâá=~åÇ=j~áÖå~å=OMMQK=

MODELLING RADIOACTIVE CONTAMINATION DATA ARTICLES

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REFERENCES `ÜáäÉëI=gKJmKI=aÉäÑáåÉêI=mK=dÉçëí~íáëíáÅëK=jçÇÉäáåÖ=pé~íá~ä=råÅÉêí~áåíóI=gçÜå=táäÉó=C=pçåë=fk`X= NVVVK= `êÉëëáÉI=kK=ÚcáííáåÖ=ãçÇÉäë=Äó=ïÉáÖÜíÉÇ=äÉ~ëí=ëèì~êÉëÛK=j~íÜÉã~íáÅ~ä=dÉçäçÖó=NVURX=NTERFW=ééK=RSPÓ RUSK= aÉìíëÅÜI=`KsKI=gçìêåÉäI=^KdK=dpif_W=dÉçëí~íáëíáÅ~ä=pçÑíï~êÉ=iáÄê~êó=~åÇ=rëÉêÛë=dìáÇÉK=lñÑçêÇ= råáîÉêëáíó=mêÉëëX=NVVUK= aìÄçáëI=dKI=d~äã~êáåáI=pK=ÚfåíêçÇìÅíáçå=íç=íÜÉ=pé~íá~ä=fåíÉêéçä~íáçå=`çãé~êáëçå=Epf`F=OMMQ=ÉñÉêÅáëÉ= ~åÇ=éêÉëÉåí~íáçå=çÑ=íÜÉ=Ç~í~=ëÉíëÛK=^ééäáÉÇ=dfp=OMMRX=NEOFW=ééK=VJMN=íç=VJNMK= dççî~ÉêíëI=mK=dÉçëí~íáëíáÅë=Ñçê=k~íìê~ä=oÉëçìêÅÉë=bî~äì~íáçåK=lñÑçêÇ=råáîÉêëáíó=mêÉëëX=NVVT= e~~ëI=qK`K=ÚhêáÖáåÖ=~åÇ=~ìíçã~íÉÇ=î~êáçÖê~ã=ãçÇÉääáåÖ=ïáíÜ=~=ãçîáåÖ=ïáåÇçïÛK=^íãçëéÜÉêáÅ= båîáêçåãÉåí=NVVMX=OQ^W=ééK=NTRVÓNTSVK= fë~~âëI=bK=eKI=pÜêáî~ëí~î~=oK=jK=^å=áåíêçÇìÅíáçå=íç=~ééäáÉÇ=ÖÉçëí~íáëíáÅëK=lñÑçêÇ=råáîÉêëáíó=mêÉëëX= NVUVK= h~åÉîëâáI=jKI=j~áÖå~åI=jK=^å~äóëáë=~åÇ=jçÇÉääáåÖ=çÑ=pé~íá~ä=båîáêçåãÉåí~ä=a~í~K=bmci=mêÉëëX= OMMQK= m~åå~íáÉêI=vK=s^ofltfkK=pçÑíï~êÉ=Ñçê=pé~íá~ä=a~í~=^å~äóëáë=áå=OaK=péêáåÖÉê=sÉêä~ÖX=NVVSK= wÜ~åÖI=uKcKI=s~å=báàâÉêÉåI=gK`KeKI=eÉÉãáåâI=^KtK=Úlå=íÜÉ=ïÉáÖÜíÉÇ=äÉ~ëíJëèì~êÉ=ãÉíÜçÇ=Ñçê=ÑáííáåÖ= ~=ëÉãáî~êáçÖê~ã=ãçÇÉäÛK=`çãéìíÉêë=C=dÉçëÅáÉåÅÉë=NVVRI=ONEQFW=ééK=SMRÓSMUK=

Cite this article as: Elena Savelieva. ‘Using ordinary Kriging to model radioactive contamination data’. Applied GIS, Vol 1, No 2, 2005. pp. 10-01 to 10-10. DOI: 10.2104/ag050010 Copyright © 2005 Elena Savelieva

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