mapping radioactivity from monitoring data - Monash University ePress

INTRODUCTION TO THE SPATIAL INTERTICLES THE DA

ARTICLES

MAPPING RADIOACTIVITY FROM MONITORING DATA AUTOMATING THE CLASSICAL GEOSTATISTICAL APPROACH

_______________________________________________________________________________________

bÇòÉê=gK=mÉÄÉëã~= aÉéí=çÑ=mÜóëáÅ~ä=dÉçÖê~éÜóI=c~Åìäíó=çÑ=dÉçëÅáÉåÅÉëI=ríêÉÅÜí=råáîÉêëáíóI== kÉíÜÉêä~åÇë= `çêêÉëéçåÇÉåÅÉ=íçW=ÉKéÉÄÉëã~]ÖÉçKììKåä=

_______________________________________________________________________________________

In the context of a comparison of spatial prediction algorithms, we applied the classical geostatistical approach to see how well it would automate, and how well it performed in case of an unexpected anomaly. In case of a test without anomaly, the method performed well. In the anomaly case, automatic variogram modelling was hindered seriously, and in terms of RMSE best results were obtained by using the variogram from the test data without the anomaly. Although the 10 days of available training data showed a strong temporally persistent spatial pattern, cokriging did not improve predictions.

1 INTRODUCTION pé~íá~ä= áåíÉêéçä~íáçå= Åçãé~êáëçå= OMMQ= Epf`OMMQF= ï~ë= ~å= çéÉå= ÅçåíÉëíI= ÜÉäÇ= çîÉê= íÜÉ= áåíÉêåÉí=EÜííéWLLïïïK~áJÖÉçëí~íëKçêÖLÉîÉåíëLëáÅOMMQLFI=Ñçê=íÜÉ=Åçãé~êáëçå=çÑ=áåíÉêéçä~íáçå= éêçÅÉÇìêÉëK=^å=É~êäáÉê=ëé~íá~ä=áåíÉêéçä~íáçå=Åçãé~êáëçå=ï~ë=ÜÉäÇ=áå=NVVTI=~ë=êÉéçêíÉÇ=Äó= aìÄçáë=EOMMPFK=qÜÉ=áëëìÉ=çÑ=pf`OMMQ=áë=~Äçìí=“~ìíçã~íáÅ=ã~ééáåÖÒW=é~êíáÅáé~åíë=Ü~Ç=íç= Éëíáã~íÉ=äÉîÉäë=çÑ=å~íìê~ä=ê~Çáç~Åíáîáíó=Äó=ãÉ~åë=çÑ=áåíÉêéçä~íáçå=~äÖçêáíÜãë=íÜ~í=~êÉ=Ñìääó= ~ìíçã~íáÅK=qÜÉ=~ìíçã~íáÅ=ã~ééáåÖ=éêçÅÉÇìêÉë=ïÉêÉ=Éî~äì~íÉÇ=Ñçê=íÜÉ=Å~ëÉ=çÑ=~åçã~äáÉë= ~åÇ=ÉãÉêÖÉåÅáÉëK= qÜÉ=î~êá~ÄäÉ=ìëÉÇ=áå=íÜáë=ÉñÉêÅáëÉ=ï~ë=å~íìê~ä=~ãÄáÉåí=ê~Çáç~Åíáîáíó=ãÉ~ëìêÉÇ=áå=dÉêJ ã~åóK=qÜÉ=Ç~í~I=éêçîáÇÉÇ=Äó=íÜÉ=dÉêã~å=cÉÇÉê~ä=lÑÑáÅÉ=Ñçê=o~Çá~íáçå=mêçíÉÅíáçå=E_ÑpFI= ~êÉ=Ö~ãã~=ÇçëÉ=ê~íÉë=êÉéçêíÉÇ=Äó=ãÉ~åë=çÑ=íÜÉ=å~íáçå~ä=~ìíçã~íáÅ=ãçåáíçêáåÖ=åÉíïçêâ= EfjfpFK= få=íÜÉ=Ñê~ãÉ=çÑ=pf`OMMQI=~=êÉÅí~åÖìä~ê=~êÉ~=ï~ë=ìëÉÇ=íç=ëÉäÉÅí=NMMU=ãçåáíçêáåÖ=ëí~J íáçåë= EÑêçã= ~= íçí~ä= çÑ= ~êçìåÇ= OMMM= ëí~íáçåëFK= cçê= íÜÉëÉ= NMMU= ëí~íáçåëI= NN= Ç~óë= çÑ= ãÉ~ëìêÉãÉåíë= ïÉêÉ= ëÉäÉÅíÉÇ= ê~åÇçãäó= ÇìêáåÖ= íÜÉ= ä~ëí= NO= ãçåíÜë= ìé= íç= íÜÉ= ëí~êí= çÑ= íÜÉ= ÉñÉêÅáëÉ=Ej~ó=NëíI=OMMQF=~åÇ=íÜÉ=~îÉê~ÖÉ=Ç~áäó=ÇçëÉ=ê~íÉë=Å~äÅìä~íÉÇ=Ñçê=É~ÅÜ=Ç~óK=eÉåÅÉI= ïÉ=ÉåÇÉÇ=ìé=Ü~îáåÖ=NN=Ç~í~=ëÉíëK= aìêáåÖ= íÜÉ= íê~áåáåÖ= éÜ~ëÉ= Ej~ó= Nëí= íç= pÉéí= NRI= OMMQFI= NM= çÑ= íÜÉ= NN= Ç~í~= ëÉíë= ïÉêÉ== êÉäÉ~ëÉÇK=aìêáåÖ=íÜÉ=íÉëí=éÜ~ëÉI=EpÉéíÉãÄÉê=Q=ìåíáä=lÅíçÄÉê=NI=OMMQF=íÜÉ=ÉäÉîÉåíÜ=Ç~í~=ëÉí= ï~ë=êÉäÉ~ëÉÇK=táíÜáå=íÜÉ=íÉëí=éÜ~ëÉI=é~êíáÅáé~åíë=ïÉêÉ=ÅÜ~ääÉåÖÉÇ=íç=Ççïåäç~Ç=íÜÉ=Ç~í~I= ~åÇ=êÉíìêå=íÜÉ=éêÉÇáÅíáçåë=Ñçê=íÜÉ=UMU=äçÅ~íáçåë=~ë=Ñ~ëí=~ë=éçëëáÄäÉ=~ÑíÉê=Ççïåäç~ÇI=ïáíÜ= íÜÉ= ÉãéÜ~ëáë= çå= ~ìíçã~íáÅ= ã~ééáåÖK= aÉí~áäë= ~Äçìí= íÜÉ= éêçÅÉÇìêÉ= íç= ÄÉ= ìëÉÇ= Ñçê= íÜÉ== ~ìíçã~íáÅ=ã~ééáåÖ=ëÜçìäÇ=Ü~îÉ=ÄÉÉå=ÖáîÉå=íç=íÜÉ=àìêó=ÄÉÑçêÉ=Ççïåäç~ÇáåÖ=íÜÉ=íÉëí=Ç~í~K=

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

11-1

^ÑíÉê=lÅíçÄÉê=NI=OMMQI=íÜÉ=Éî~äì~íáçå=éÜ~ëÉ= ëí~êíÉÇI=ÇìêáåÖ=ïÜáÅÜ=íÜÉ=çÄëÉêîÉÇ=Ç~í~=~í= íÜÉ=UMU=íÉëí=äçÅ~íáçåë=ïÉêÉ=ã~ÇÉ=~î~áä~ÄäÉ=íç=íÜÉ=é~êíáÅáé~åíëK= qÜÉ=ã~áå=çÄàÉÅíáîÉë=çÑ=íÜÉ=pf`OMMQ=~äÖçêáíÜãë=ïÉêÉW= NK íç=ÖÉåÉê~íÉ=êÉëìäíë=íÜ~í=~êÉ=êÉäá~ÄäÉI=íÜ~í=áë=íÜÉ=Éëíáã~íáçå=Éêêçêë=ëÜçìäÇ=ÄÉ=ãáåáãìãW= íÜÉ= éêáã~êó= ÅêáíÉêá~= ìëÉÇ= íç= ~ëëÉëë= íÜÉ= éÉêÑçêã~åÅÉ= çÑ= íÜÉ= ~äÖçêáíÜã= ïáää= ÄÉ= íÜÉ= jÉ~å=pèì~êÉ=bêêçêX= OK íç=ÖÉåÉê~íÉ=êÉëìäíë=áå=íÜÉ=ëÜçêíÉëí=~ãçìåí=çÑ=íáãÉ=EäÉëë=íÜ~å=OQ=ÜçìêëFX= PK íç=ÖÉåÉê~íÉ=êÉëìäíë=~ìíçã~íáÅ~ääóI=íÜ~í=áë=ïáíÜçìí=~åó=Üìã~å=áåíÉêîÉåíáçåX= QK íç= ÄÉ= ~ÄäÉ= íç= ÇÉ~ä= ïáíÜ= ~åçã~äáÉëI= íÜ~í= áë= íÜÉ= ~äÖçêáíÜã= ëÜçìäÇ= ÄÉ= ~ÄäÉ= íç= êÉëéçåÇ= éêçéÉêäó= íç= ëáíì~íáçåë= áå= ïÜáÅÜ= äÉîÉäë= êÉéçêíÉÇ= Äó= íÜÉ= ãçåáíçêáåÖ= åÉíïçêâ= ÉñÅÉÉÇ= ìëì~ä= Ä~ÅâÖêçìåÇ= äÉîÉäë= ~åÇ= éêÉëÉåí= ÇáÑÑÉêÉåí= ëé~íá~ä= é~ííÉêåë= ~ë= áí= áë= ÖÉåÉê~ääó= íÜÉ= Å~ëÉ=ïáíÜ=~ÅÅáÇÉåíëK= pÜçêíäó=ÄÉÑçêÉ=íÜÉ=íÉëí=Ç~í~=ïÉêÉ=êÉäÉ~ëÉÇI=é~êíáÅáé~åíë=ïÉêÉ=áåÑçêãÉÇ=íÜ~í=áåëíÉ~Ç=çÑ= çåÉI= íïç= íÉëí= ëÉíë= ïÉêÉ= íç= ÄÉ= êÉäÉ~ëÉÇI= çåÉ= Å~ääÉÇ= ÒáåéìíÒ= Eçê= ÑáêëíFI= íÜÉ= çíÜÉê= Å~ääÉÇ= ÒàçâÉêÒ=Eçê=ëÉÅçåÇFX=íÜÉ=ä~ííÉê=êÉÑÉêêáåÖ=íç=íÜÉ=ÑçìêíÜ=çÄàÉÅíáîÉI=éêÉëÉåÅÉ=çÑ=~åçã~äáÉëK= qÜáë=é~éÉê=íêáÉë=íç=ÑáåÇ=~=éêçÅÉÇìêÉ=íÜ~í=ãÉÉíë=íÜÉ=Ñáêëí=íÜêÉÉ=çÄàÉÅíáîÉëI=~åÇ=ïÉ=ïáää= äççâ=~í=ïÜ~í=Ü~ééÉåë=ïÜÉå=íÜÉ=éêçéçëÉÇ=éêçÅÉÇìêÉ=áë=~ééäáÉÇ=íç=íÜÉ=àçâÉê=Ç~í~I=íÉëíáåÖ= íÜÉ= ÑçìêíÜ= çÄàÉÅíáîÉK= qÜÉ= éêçÅÉÇìêÉ= íêáÉë= íç= ÄìáäÇ= çå= íÜÉ= íê~Çáíáçå~ä= ÖÉçëí~íáëíáÅ~ä= ~éJ éêç~ÅÜI= Äìí= ïáíÜçìí= Üìã~å= áåíÉêîÉåíáçåK= qÜáë= ÅÜçáÅÉ= ï~ë= ãçíáî~íÉÇ= Äó= ÉñéÉêáÉåÅÉI= ÅìêáçëáíóI=~åÇ=Äó=~å=çåÖçáåÖ=åÉÉÇ=Ñçê=ëçÑíï~êÉ=íÉëíáåÖ=~åÇ=ÇÉîÉäçéãÉåí=Eåçí~Ääó=íÜÉ=Öëí~í= éêçÖê~ãI=mÉÄÉëã~=~åÇ=tÉëëÉäáåÖI=NVVUI=ÜÉêÉ=ìëÉÇ=~ë=íÜÉ=Öëí~í=oLpJmäìë=äáÄê~êóX=mÉÄÉëã~I= OMMQFK=råäáâÉ=íÜÉ=ìëì~ä=çêÇÉêI=íÜáë=é~éÉê=áë=çêÖ~åáòÉÇ=~ë=íÜÉ=Ö~ãÉ=ï~ë=éä~óÉÇI=~äçåÖ=íÜÉ= ÅÜêçåçäçÖó=íÜÉ=êÉëÉ~êÅÜ=íççâI=~åÇ=ÑáåÇáåÖë=çÑ=íÜÉ=íê~áåáåÖI=íÉëí=~åÇ=Éî~äì~íáçå=éÜ~ëÉ=EáåJ ÅäìÇáåÖ=~=ã~àçê=ãáëí~âÉ=ïáíÜ=áåíÉêÉëíáåÖ=ÅçåëÉèìÉåÅÉë=íÜ~í=ï~ë=ã~ÇÉF=ïáää=ÄÉ=ÖáîÉåK=

2 THE TRAINING PHASE 2.1 EXPLORATORY DATA ANALYSIS

qÜÉ=íê~áåáåÖ=Ç~í~=Åçåëáëí=çÑ=íÉå=Ç~óë=çÑ=Ç~áäó=~îÉê~ÖÉÇ=å~íìê~ä=~ãÄáÉåí=ê~Çáç~Åíáîáíó= ãÉ~ëìêÉÇ= áå= dÉêã~åóI= ïÜÉêÉ= íÜÉ= íÉå= Ç~óë= ïÉêÉ= ÅÜçëÉå= ê~åÇçãäó= Ñêçã= çåÉ= óÉ~ê= Ej~ó= NëíI=OMMP=íç=j~ó=NëíI=OMMQFK=_ÉÅ~ìëÉ=~ää=ãÉ~ëìêÉÇ=Ç~óë=Ü~îÉ=ãÉ~ëìêÉãÉåíë=çå=íÜÉ=ë~ãÉ= OMM=äçÅ~íáçåëI=ïÉ=Å~å=É~ëáäó=ÑáåÇ=çìí=Üçï=ãìÅÜ=çÑ=íÜÉ=íçí~ä=î~êá~Äáäáíó=áë=ÇìÉ=íç=î~êá~íáçå= áå=íáãÉI=áå=ëé~ÅÉ=çê=íÜÉáê=áåíÉê~ÅíáçåK=cçê=íÜáëI=ïÉ=~å~äóëÉÇ=íÜÉ=Eë~íìê~íÉÇF=^kls^=ãçÇÉä= yij = µ + Ai + Bj + Cij , i = 1, ..., 10, j = 1, ..., 200

ïáíÜ=óáà=íÜÉ=çÄëÉêî~íáçå=~í=Ç~ó=á=~åÇ=äçÅ~íáçå=àI=”=íÜÉ=Öê~åÇ=ãÉ~åI=^á=íÜÉ=ëé~ÅÉJ~îÉê~ÖÉÇ= ÇÉîá~íáçå=Ñêçã=íÜÉ=ãÉ~å=äÉîÉä=~í=Ç~ó=áI=_à=íÜÉ=íáãÉJ~îÉê~ÖÉÇ=ÇÉîá~íáçå=Ñêçã=”=~í=äçÅ~íáçå= àI=~åÇ=`áà=íÜÉ=ëé~ÅÉJíáãÉ=áåíÉê~ÅíáçåI=çê=íÜÉ=ÇÉîá~íáçå=Ñêçã=íÜÉ=ëí~íáçåLÇ~ó=ÉñéÉÅíÉÇ=î~äìÉ= ïÜÉå=åç=áåíÉê~Åíáçå=áë=éêÉëÉåíI=”=H=^á=H=_à=K=qÜÉ=íçí~ä=ëìã=çÑ=ëèì~êÉë=áë=ÇáîáÇÉÇ=~ë=ÇÉãJ çåëíê~íÉÇ=áå=q~ÄäÉ=NW= Degrees of freedom day station day:station

9 199 1791

Sum of squares 16057 592787 14531

Mean squares 1784 2979 8

Table 1

eÉêÉ= Ç~óWëí~íáçå= êÉÑÉêë= íç= íÜÉ= áåíÉê~Åíáçå= íÉêãK= qÜÉ= éÉêÅÉåí~ÖÉ= î~êá~íáçå= Éñéä~áåÉÇ= Äó= O Ñ~Åíçê=ëí~íáçå=Eo =~ÇàìëíÉÇF=áë=MKVRI=Äó=Ç~ó=EíáãÉI=~ë=Ñ~ÅíçêF=áë=MKMOI=~åÇ=Äó=ÄçíÜ=áë=MKVTK=

11-2

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

tÜÉå= íÜÉ= íÉå= Ç~óë= ~êÉ= ëÉÉå= ~ë= NM= î~êá~ÄäÉëI=íÜÉ= äÉ~ÇáåÖ= éêáåÅáé~ä= ÅçãéçåÉåí= Å~äÅìä~íÉÇ= çîÉê= íÜÉã= Å~éíìêÉë= VUB= çÑ= íÜÉ= î~êá~íáçåK= cêçã= íÜáëI= ïÉ= Å~å= ÅçåÅäìÇÉ= íÜ~í= ãçëí= çÑ= íÜÉ= î~êá~íáçå= áë= EéÉêëáëíÉåíF= ëé~íá~ä= î~êá~íáçåK= qÜÉ= ëáòÉ= çÑ= íÜÉ= ëé~ÅÉJíáãÉ= áåíÉê~Åíáçå= î~êá~åÅÉ= ÅçãéçåÉåí=EÇ~óWëí~íáçåF=áë=ã~êÖáå~äI=ãÉ~åáåÖ=íÜ~í=íç=~=ä~êÖÉ=ÉñíÉåí=íÜÉ=íÉãéçê~ä=é~ííÉêå= áë=Åçåëí~åí=Eåçí=î~êóáåÖF=çîÉê=ëé~ÅÉI=çêI=Éèìáî~äÉåíäóI=íÜ~í=íÜÉ=ëé~íá~ä=é~ííÉêå=áë=íç=~=ä~êÖÉ= ÉñíÉåí=éÉêëáëíÉåí=çîÉê=íáãÉ=EdåÉáíáåÖI=OMMOFK=

15000

154,169

99,122

41,121

40,45

10000

semivariance

41,45

57,129

37,121 98,196

149,164 169,190

164,165

4,149

98,99

154,155 4,165

37,45 165,166

5000

75,134 66,67

149,163 86,90 40,42 55,56

62,67

72,73 120,121 42,43

0

30,192 154,158

2e+04

4e+04

6e+04

8e+04

1e+05

distance

Figure 1 Variogram cloud for day01, with record id (from 1 to 200) pairs denoting which records contributed to manually selected variogram cloud point; record with id 164 is present twice in point pairs with high semivariance at very short distance. Units for this and all other variograms: distance in m, semivariance in

(nSv / h) 2

cêçã= íÜáë= ïÉ= Å~å= íÉåí~íáîÉäó= ÉåíÉêí~áå= íÜÉ= ÜóéçíÜÉëáë= íÜ~í= Ñçê= ëíìÇóáåÖ= ëé~íá~ä= é~íJ íÉêåëI=~í=~å=É~êäó=ëí~ÖÉ=áí=áë=åçí=çÑ=îÉêó=ãìÅÜ=áãéçêí~åÅÉ=ïÜÉíÜÉê=ïÉ=äççâ=~í=~=ëáåÖäÉ=Ç~ó= çê=íç=äÉ~ÇáåÖ=éêáåÅáé~ä=ÅçãéçåÉåí=ëÅçêÉëI=ÄÉÅ~ìëÉ=íÜÉ=Ç~óë=~êÉ=îÉêó=ãìÅÜ=~äáâÉK= cáÖìêÉ= N= ëÜçïë= ~= î~êáçÖê~ã= ÅäçìÇ= Ñçê= Ç~óMNI= ïáíÜ= êÉÅçêÇ= áÇÉåíáÑáÉêë= ëÜçïå= Ñçê= íÜÉ= éçáåí=é~áêë=~í=ëÜçêí=Çáëí~åÅÉ=~åÇ=ä~êÖÉ=ÇáÑÑÉêÉåÅÉëK=cçê=É~ÅÜ=é~áê=çÑ=çÄëÉêî~íáçåë= y (s ) =~åÇ=

y ( s + h) I= íÜÉ= î~êáçÖê~ã= ÅäçìÇ= ëÜçïë= Ü~äÑ= íÜÉ= ëèì~êÉÇ= ÇáÑÑÉêÉåÅÉë= áå= ãÉ~ëìêÉãÉåíëI=

0.5( y ( s ) − y ( s + h)) 2 = ~ë= ~= ÑìåÅíáçå= çÑ= íÜÉáê= ëÉé~ê~íáçå= Çáëí~åÅÉ= áå= ÖÉçÖê~éÜáÅ= ëé~ÅÉI= h K= qÜÉ= ÑáÖìêÉ= ëìÖÖÉëíë= íÜ~í= Ç~í~= êçï= NSQ= EçêáÖáå~ä= êÉÅçêÇ= åìãÄÉê= UPUF= Ü~ë= ~å= ìåÉñéÉÅíÉÇ= î~äìÉW= áí= áë= ÅäçëÉ= íç= íïç= çíÜÉê= çÄëÉêî~íáçåë= ENQVI= NSRF= Äìí= ÇáÑÑÉêë= ëíêçåÖäó= Ñêçã= íÜÉãK== cáÖìêÉ= O= ëÜçïë= íÜÉ= ë~ãéäÉ= î~êáçÖê~ãë= Ñçê= ~ää= Ç~í~= EäÉÑíF= ~åÇ= Ñçê= íÜÉ= Å~ëÉ= ïÜÉêÉ= êÉÅçêÇ= åìãÄÉê= UPU= ï~ë= êÉãçîÉÇ= EêáÖÜíFK= oÉãçîáåÖ= íÜáë= êÉÅçêÇ= Ü~ë= íÜÉ= ÉÑÑÉÅí= íÜ~í= íÜÉ= Ñáêëí=

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

11-3

î~êáçÖê~ã=Éëíáã~íÉ=áë=åç=äçåÖÉê=ëíêçåÖäó=áåÑäìÉåÅÉÇ=Äó=~=ëáåÖäÉI=ìåÉñéÉÅíÉÇ=çÄëÉêî~íáçåI= ~åÇ=ïÉ=ïáää=êÉãçîÉ=íÜáë=çÄëÉêî~íáçå=áå=ÑìêíÜÉê=~å~äóëáëK= 2.2 VARIOGRAM MODEL SELECTION AND FITTING

cçê=ÑáííáåÖ=~=î~êáçÖê~ã=ãçÇÉäI=ïÉ=Ñáêëí=Ü~îÉ=íç=ÅÜççëÉ=~=ëìáí~ÄäÉ=ãçÇÉäK=qÜÉ=ãçÇÉäë=ïÉ= Éî~äì~íÉÇ= ïÉêÉ= ÉñéçåÉåíá~äI= d~ìëëá~åI= ëéÜÉêáÅ~äI= äáåÉ~êI= ~åÇ= íÜÉ= j~íÉêå= Ñ~ãáäó= çÑ= î~êáçÖê~ã= ãçÇÉäë= E`Üáä≠ë= ~åÇ= aÉäÑáåÉêI= NVVVX= píÉáåI= NVVVF= ïáíÜ= ëãççíÜáåÖ= é~ê~ãÉíÉê= î~äìÉë=áå=ôMKMRI=MKNI=MKOI=MKPI=KKK=I=NKVI=OI=RI=NMõK= 0e+00

1e+05

full data set

2e+05

3e+05

4e+05

5e+05

record 838 removed

500

semivariance

400

300

200

100

0 0e+00

1e+05

2e+05

3e+05

4e+05

5e+05

distance

Figure 2 Variograms for day01, for all data (left) and for the case where record 838 (row number 164) was left out; cut-off distance is 500,000 m, lag distance intervals are 10,000 m 0e+00

day01

2e+05

4e+05

day02

0e+00

day03

2e+05

4e+05

day04

day05 500 400 300

semivariance

200 100

day06

day07

day08

day09

0

day10

500 400 300 200 100 0 0e+00

2e+05

4e+05

0e+00

2e+05

4e+05

0e+00

2e+05

4e+05

distance

Figure 3 Variograms with fitted spherical models for each of the 10 days

jçÇÉä=ëÉäÉÅíáçå=ï~ë=ÇçåÉ=~ë=ÑçääçïëW=Ñçê=É~ÅÜ=çÑ=íÜÉ=íÉå=Ç~óëI=î~êáçÖê~ã=ãçÇÉäë=ïÉêÉ= ÑáííÉÇ=íç=ë~ãéäÉ=î~êáçÖê~ãë=EëÉÉ=ÉKÖK=ÑáÖìêÉ=PFI=~åÇ=ìëÉÇ=áå=~=äÉ~îÉJçåÉJçìí=Åêçëë=î~äáÇ~J íáçå=íç=çÄí~áå=~=Åêçëë=î~äáÇ~íáçå=êççí=ãÉ~å=ëèì~êÉ=Éêêçê=EojpbF=Äó=

11-4

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

RMSE =

^ 1 10 199 ( y ij − y [ij ] )2 ∑ ∑ 1990 i =1 j =1

^

ïáíÜ= y [ij ] íÜÉ= éêÉÇáÅíÉÇ= î~äìÉ= ìëáåÖ= ~ää= çÄëÉêî~íáçåë= çÑ= íÜ~í= Ç~óI= ÉñÅÉéí= íÜÉ= çÄëÉêî~íáçå=

y ij =áíëÉäÑ=EáKÉKI=ïÉ=äÉ~îÉ=çåÉ=çÄëÉêî~íáçå=çìíFK=qÜêÉÉ=íêÉåÇ=ãçÇÉäë=ïÉêÉ=ÅçåëáÇÉêÉÇW=~=ÅçåJ ëí~åí=íêÉåÇI=~=äáåÉ~ê=~åÇ=~=èì~Çê~íáÅ=íêÉåÇ=áå=íÜÉ=ÅççêÇáå~íÉëX=ïÜÉå=íÜÉ=íêÉåÇë=ïÉêÉ=äáåÉ~ê= çê=èì~Çê~íáÅ=íÜÉ=ë~ãéäÉ=î~êáçÖê~ã=ï~ë=Å~äÅìä~íÉÇ=Ñêçã=êÉëáÇì~äë=ïáíÜ=êÉëéÉÅí=íç=~=íêÉåÇ= Éëíáã~íÉÇ=Äó=çêÇáå~êó=äÉ~ëí=ëèì~êÉëK= no trend first order linear second order linear Nug+Sph Nug+Mat(5) Nug+Mat(2) Nug+Mat(10) Nug+Mat(1.9) Nug+Mat(1.8) Nug+Mat(1.7) Nug+Mat(1.6) Nug+Mat(1.5) Nug+Mat(1.4) Nug+Mat(1.3) Nug+Mat(1.1) Nug+Mat(1) Nug+Mat(0.9) Nug+Mat(0.8) Nug+Mat(0.7) Nug+Mat(0.6) Nug+Mat(0.5) Nug+Mat(0.2) Nug+Mat(0.1) Nug+Mat(0.05) Nug+Lin Nug+Gau Nug+Exp 10.8

10.9

11.0

11.1

11.2

11.3

RMSE of LOOCV residuals Figure 4 2 Leave-one-out cross validation (LOOCV) RMSE values ((nSv/h) ) obtained for a series of variogram models and trend functions; each time the variogram was fitted to the data from day01 and used for subsequent days

cáÖìêÉ=Q=ëÜçïë=íÜÉ=ojpb=î~äìÉë=Ñçê=É~ÅÜ=çÑ=íÜÉ=î~êáçÖê~ã=ãçÇÉäë=ÑáííÉÇI=~åÇ=Ñçê=É~ÅÜ= çÑ=íÜÉ=íêÉåÇ=ãçÇÉäëK=cêçã=íÜáë=ÑáÖìêÉ=áí=Å~å=ÄÉ=ÅçåÅäìÇÉÇ=íÜ~í=EáF=íÜÉ=áåíÉêéçä~íáçå=ïáíÜ=~= Åçåëí~åí=ãÉ~å=~ë=íêÉåÇ=ãçÇÉä=éÉêÑçêãë=ÄÉëíI=çê=Éèì~ääó=ïÉää=~ë=ÜáÖÜÉê=çêÇÉê=íêÉåÇëI=~åÇ= EááF= íÜÉ= äáåÉ~ê= H= åìÖÖÉí= ~åÇ= ëéÜÉêáÅ~ä= H= åìÖÖÉí= ãçÇÉä= éÉêÑçêã= ÄÉëíK= qÜÉëÉ= íïç= ãçÇÉäëI= ÑáííÉÇ=íç=íÜÉ=ë~ãéäÉ=î~êáçÖê~ã=çÑ=Ç~óMN=~êÉ=ëÜçïå=áå=ÑáÖìêÉ=RK=tÉ=Ñáå~ääó=ÅÜçëÉ=Ñçê=íÜÉ= ëéÜÉêáÅ~ä=H=åìÖÖÉí=ãçÇÉä=ÄÉÅ~ìëÉ=áí=áë=ãçêÉ=ÑäÉñáÄäÉ=íÜ~å=íÜÉ=äáåÉ~ê= ãçÇÉäW=áí=ÉÑÑÉÅíáîÉäó= áåÅäìÇÉë=íÜÉ=äáåÉ~ê=ãçÇÉä=~ë=~=ëéÉÅá~ä=Å~ëÉK=^ÑíÉê=ëÉäÉÅíáåÖ=~=î~êáçÖê~ã=ãçÇÉäI=ïÉ=îÉêáÑáÉÇ= Ñçê= ÇáêÉÅíáçå~ä= ÇÉéÉåÇÉåÅÉ= áå= ëÉãáî~êá~åÅÉ= E~åáëçíêçéóFK= cáÖìêÉ= S= ëÜçïë= ÇáêÉÅíáçå~ä= î~êáçÖê~ãë=Ñçê=Ç~óMNI=~äçåÖ=ïáíÜ=íÜÉ=ÑáííÉÇ=çãåáÇáêÉÅíáçå~ä=EáëçíêçéáÅF=ãçÇÉäK=qÜÉ=ÑáÖìêÉ= ÇçÉë=åçí=ÖáîÉ=êÉ~ëçå=íç=ãçÇÉä=~åáëçíêçéóK=

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

11-5

500 400 300 200 0

100

semivariance

0e+00

1e+05

2e+05

3e+05

4e+05

5e+05

distance Figure 5 The two best fitting variograms for day01, in terms of cross validation RMSE after removal of record 838: linear (straight line) and spherical; both having a RMSE of 10.82 0e+00 1e+05 2e+05 3e+05 4e+05 5e+05

90

120

150 1200 1000 800 600

semivariance

400 200

0

30

60

0

1200 1000 800 600 400 200 0 0e+00 1e+05 2e+05 3e+05 4e+05 5e+05

0e+00 1e+05 2e+05 3e+05 4e+05 5e+05

distance

Figure 6 Directional sample variograms (+) for day01: 0 refers to north-south, 90 to east-west; the fitted model (line) is the isotropic spherical variogram model fitted to the omnidirectional variogram for this day

2.3 CROSS CORRELATION AND COKRIGING

`êçëë=ÅçêêÉä~íáçå=ÄÉíïÉÉå=íÜÉ=~î~áä~ÄäÉ=Ç~óë=áë=ÉñéÉÅíÉÇ=íç=ÄÉ=ëíêçåÖI=ÄÉÅ~ìëÉ=íÜÉ=ëé~íá~ä= é~ííÉêå= ~ééÉ~êÉÇ= íç= ÄÉ= ãçëíäó= éÉêëáëíÉåí= çîÉê= íáãÉK= cáÖìêÉ= T= ëÜçïë= ÇáêÉÅí= ~åÇ= Åêçëë= î~êáçÖê~ãë=Ñçê=É~ÅÜ=çÑ=íÜÉ=NM=Ç~óë=~åÇ=íÜÉ=QR=éçëëáÄäÉ=é~áêë=çÑ=Ç~óëX=íÜÉ=ÑáííÉÇ=ãçÇÉä=áë=~= ëéÜÉêáÅ~ä= ãçÇÉä= íÜ~í= çÄÉóë= íÜÉ= äáåÉ~ê= ãçÇÉä= çÑ= ÅçêÉÖáçå~äáò~íáçå= E`Üáä≠ë= ~åÇ= aÉäÑáåÉêI= NVVVFK= `êçëë= î~äáÇ~íáçå= ìëáåÖ= NMJî~êá~ÄäÉ= ÅçâêáÖáåÖI= É~ÅÜ= íáãÉ= äÉ~îáåÖ= ~= Ñìää= äçÅ~íáçå==

11-6

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

EáKÉK=Ç~í~=Ñçê=~ää=~î~áä~ÄäÉ=Ç~óëFI=çìí=Ñçê=É~ÅÜ=ãìäíáî~êá~ÄäÉ=EÅçâêáÖáåÖF=éêÉÇáÅíáçå=ÇáÇ=åçí= äÉ~Ç=íç=áãéêçîÉãÉåíW=ojpb=î~äìÉë=ê~áëÉÇ=Ñêçã=NMKU=íç=NNKMRK=qÜáë=êÉëìäí=ã~ó=ÄÉ=ëìêéêáëJ áåÖI=~åÇ=~=éçëëáÄäÉ=Å~ìëÉ=Ñçê=áí=áë=ÖáîÉå=áå=íÜÉ=ÇáëÅìëëáçåK= day 1 +++ ++ +++ ++ +++ +++ ++++ + ++ ++

day 1.day 2 500 400 300 200 100 0

day 2

+ ++ ++ ++ ++ + + +++ +++ +++ +++ +++ +++ +++ ++++ ++++ + + ++ ++ ++ ++

day 1.day 3 day 2.day 3

day 3

++ ++ ++ ++ ++ + +++ + + ++ + ++ ++ + ++ + ++ + +++ +++ +++ +++ +++ +++ ++++ ++++ ++++ ++ + ++ + + + + ++ ++ ++

day 1.day 4 day 2.day 4 day 3.day 4

semivariance

500 400 300 200 100 0

day 4

++ ++ ++ ++ + ++ ++ +++ +++ +++ +++ + ++ ++ + + +++ +++ +++ +++ ++++ + +++ +++ +++ +++ +++ ++++ ++++ ++++ ++++ +++ +++ +++ +++ ++ ++ ++ ++

day 1.day 5 day 2.day 5 day 3.day 5 day 4.day 5

day 5

++ ++ ++ ++ + +++ +++ +++ +++ +++ +++ + +++ +++ +++++++++ ++ + +++ +++ +++ ++++ + + ++++ +++ +++ +++ +++ +++ ++++ ++++ ++++ ++++ ++++ +++ +++ +++ +++ +++ ++ ++ ++ ++ ++

day 1.day 6 day 2.day 6 day 3.day 6 day 4.day 6 day 5.day 6 500 400 300 200 100 0

day 6

+ ++ + ++ ++ +++ +++ +++ +++ +++++++ + ++ +++++++++ +++++++++ +++ +++ ++++ ++++ ++++ +++ ++++ ++++ +++ +++ +++ +++ +++ ++++ ++++ ++++ ++++ ++++ ++++ ++++ + + + + + + +++ +++ +++ +++ ++ ++ ++ ++ ++ ++

day 1.day 7 day 2.day 7 day 3.day 7 day 4.day 7 day 5.day 7 day 6.day 7

day 7

++ ++ ++ ++ + ++ ++ +++ +++ +++ +++ + +++ ++ +++++ +++ + + +++ ++ ++ +++ +++ ++++++++++ + +++ ++++ + ++ ++++ +++ +++ ++++ +++ +++ +++ +++ +++ +++ ++ +++++ ++++ ++++ ++++ ++++ ++++ ++++ + ++ +++ ++ +++ +++ +++ +++ +++ + + + ++ ++ + ++ ++ + +

day 1.day 8 day 2.day 8 day 3.day 8 day 4.day 8 day 5.day 8 day 6.day 8 day 7.day 8 500 400 300 200 100 0

day 8

++ ++ ++ ++ + ++ ++ +++ +++ +++ +++ + ++ ++ + + +++ + +++ +++ +++++ +++ +++ +++ + +++ +++ +++ +++ +++ + ++++ + +++ ++++ + + ++++ ++++ + ++++ + + +++ +++ +++ +++ +++ +++ +++ ++++ ++++ ++++ +++ ++++ ++++ ++++ ++++ ++++ +++ ++++ +++ +++ +++ +++ +++ +++ + ++ ++ ++ ++ ++ ++ ++ ++

day 1.day 9 day 2.day 9 day 3.day 9 day 4.day 9 day 5.day 9 day 6.day 9 day 7.day 9 day 8.day 9

day 9

+ ++ + ++ + ++ + ++ ++++ ++++ ++++ ++++ + ++ ++ +++ ++ ++ + ++ + + ++ ++ ++ ++ + ++ + +++ + +++ +++ +++ +++ +++ +++ +++ +++ ++ + +++ +++ +++ +++ +++ ++++ +++ +++ +++ +++ ++++ +++ +++ +++ +++ +++ +++ +++ ++ ++ ++ ++++ ++++ ++ ++ ++ ++ ++ ++ ++ ++ ++ ++ + ++ +++ ++ +++ +++ +++ +++ +++ +++ +++ ++ ++ ++ ++ ++ ++ ++ ++ ++

day 1.day 10day 2.day 10day 3.day 10day 4.day 10day 5.day 10day 6.day 10day 7.day 10day 8.day 10day 9.day 10 500 400 300 200 100 0

day 10

++ ++ ++ ++ + ++ ++ +++ + +++ +++ +++ +++ +++ + ++ ++ + ++ ++ +++ +++ + ++ ++ +++++ +++ +++ + ++ ++ +++ + ++++ +++++++++ ++++ + +++ +++ ++++ + +++ + ++++ + +++ ++++ ++++ + +++ +++ +++ ++++ +++ +++ +++ +++ +++ +++ +++ +++ ++++ ++++ ++++ ++++ ++++ ++++ ++++ ++++ ++++ + ++++ ++ ++ + + ++ ++ +++ + + + + + +++ +++ + + + + + ++ ++ ++ ++ ++ ++ ++ ++ ++ ++

0e+00

3e+05

0e+00

3e+05

0e+00

3e+05

0e+00

3e+05

0e+00

3e+05

distance

Figure 7 All direct and cross sample variograms (+) for the 10 days of data (direct variograms on the diagonal) along with a fitted linear model of coregionalization (lines); lag distance interval width is 20,000 m, cut-off 500,000 m

2.4 KRIGING NEIGHBOURHOOD SIZE

ré=íç=åçïI=Ñçê=éê~ÅíáÅ~ä=EëéÉÉÇF=êÉ~ëçåëI=äçÅ~ä=âêáÖáåÖ=åÉáÖÜÄçìêÜççÇë=ïáíÜ=ëáòÉ=QM=ïÉêÉ= ìëÉÇI= ãÉ~åáåÖ= íÜ~í= É~ÅÜ= âêáÖáåÖ= áåíÉêéçä~íáçå= ìëÉÇ= íÜÉ= åÉ~êÉëí= QM= çÄëÉêî~íáçåë= EÑçê= íÜÉ= É~ÅÜ=î~êá~ÄäÉI=ïÜÉå=áå=~=ÅçâêáÖáåÖ=ëÉííáåÖFK=qÜÉ=ÅÜçáÅÉ=çÑ=âêáÖáåÖ=åÉáÖÜÄçìêÜççÇ=ëáòÉ=ã~ó= Ü~îÉ=ëçãÉ=áåÑäìÉåÅÉ=çå=íÜÉ=ëìÅÅÉëë=çÑ=~=âêáÖáåÖ=éêçÅÉÇìêÉI=~åÇ=ïÉ=î~êáÉÇ=áí=çîÉê=íÜÉ=î~äJ ìÉë= ôNMI= OMI= PMI= QMI= RMI= TRI= NMMI= NORI= NRMI= OMMõI= íÜÉ= ä~ëí= ÉÑÑÉÅíáîÉäó= ÄÉáåÖ= ~= ÖäçÄ~ä= åÉáÖÜÄçìêÜççÇK=cáÖìêÉ=U=ëÜçïë=Üçï=ã~êÖáå~ääó=íÜÉ=äÉ~îÉJçåÉJçìí=Åêçëë=î~äáÇ~íáçå=ojpb= î~êáÉë=~ë=~=ÑìåÅíáçå=çÑ=âêáÖáåÖ=åÉáÖÜÄçìêÜççÇ=ëáòÉK=tÉ=ëÉííäÉÇ=çå=íÜÉ=“ÄÉëíÒ=î~äìÉ=çÑ=NORX= ~=Ñ~áêäó=ä~êÖÉI=Äìí=áå=íÉêãë=çÑ=Åçãéìí~íáçå=äç~Ç=Äó=Ñ~ê=åçí=éêçÜáÄáíáîÉäó=ä~êÖÉ=åÉáÖÜÄçìêJ ÜççÇK=

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

11-7

10.86 10.85

rmse

10.84 10.83 10.82 0

50

100

150

200

nmax

Figure 8 RMSE as a function of kriging neighbourhood size (nmax), leave-one-out cross validation results using the spherical variogram

Normal Q-Q Plot 1500 1000 500

Sample Quantiles

100 120 140 80 60

Sample Quantiles

Normal Q-Q Plot

-3

-2

-1

0

1

2

-3

3

-2

-1

0

1

2

3

Theoretical Quantiles

Theoretical Quantiles

Figure 9 Normal probability plots for the observations of the first test data set, input (left) and the second test data set, joker (right); Theoretical Quantiles are those of the standard normal distribution (-); Sample Quantiles are those of the measurements (nSv/h)

2.5 THE AUTOMATIC MAPPING PROCEDURE

qÜáë=äÉÇ=íç=~=éêçÅÉÇìêÉ=ïÜÉêÉ=ïÉW= NK çãáí=êÉÅçêÇ=UPUX= OK Å~äÅìä~íÉ=~=çãåáÇáêÉÅíáçå~ä=ë~ãéäÉ=î~êáçÖê~ã=Ñêçã=íÜÉ=ê~ï=Ç~í~I=ìëáåÖ=~=ÅìíJçÑÑ=çÑ= RMMIMMM=~åÇ=~å=áåíÉêî~ä=Eä~ÖF=ïáÇíÜ=çÑ=OMIMMM=ãI=~ë=áå=ÑáÖìêÉ=PX= PK ÑáííÉÇ= ~= ëéÜÉêáÅ~ä= î~êáçÖê~ã= ãçÇÉä= ïáíÜ= åìÖÖÉí= íç= íÜáë= ë~ãéäÉ= î~êáçÖê~ãI= ìëáåÖ= ïÉáÖÜíÉÇ=äÉ~ëí=ëèì~êÉë=E`êÉëëáÉI=NVVPF=ÑáííáåÖ=ïáíÜ=ïÉáÖÜíë= h −1 N h I=ïáíÜ=Çáëí~åÅÉ= h = ~åÇ=åìãÄÉê=çÑ=éçáåí=é~áêë= N h X= QK ìëÉ=çêÇáå~êó=âêáÖáåÖ=Ñçê=éêÉÇáÅíáçåI=ÖáîÉå=íÜÉ=çÄëÉêîÉÇ=Ç~í~=~åÇ=íÜÉ=ÑáííÉÇ=î~êáçÖê~ã= ãçÇÉäI=ìëáåÖ=~=äçÅ~ä=âêáÖáåÖ=åÉáÖÜÄçìêÜççÇ=çÑ=NOR=çÄëÉêî~íáçåëK= qÜÉ=áãéäÉãÉåíÉÇ=o=ÅçÇÉ=áë=ëÜçïå=áå=íÜÉ=^kkbuK=aìêáåÖ=íÜÉ=íÉëí=éÜ~ëÉI=~=åìãÄÉê=çÑ= ãáëí~âÉë=ïÉêÉ=ã~ÇÉX=íÜÉëÉ=~êÉ=~äëç=éçáåíÉÇ=çìí=áå=íÜÉ=^kkbuK=

11-8

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

3 THE TEST PHASE aìêáåÖ=íÜÉ=íÉëí=éÜ~ëÉI=íïç=ÑáäÉë=ïÉêÉ=ã~ÇÉ=~î~áä~ÄäÉ=Ñçê=Ççïåäç~ÇI=áåéìí=~åÇ=àçâÉêK=qÜÉ= ë~ãéäÉ=ÇáëíêáÄìíáçåëI=ëÜçïå=áå=íÜÉ=åçêã~ä=éêçÄ~Äáäáíó=éäçíë=çÑ=ÑáÖìêÉ=V=ÅäÉ~êäó=ëÜçï=íÜ~í= íÜÉ= àçâÉê= Ç~í~= ëÉí= Åçåí~áåë= ~= ÜìÖÉ= çìíäáÉêK= få= åçêã~ä= éêçÄ~Äáäáíó= éäçíë= åçêã~ääó= ÇáëíêáÄJ ìíÉÇ=ë~ãéäÉë=éäçí=~ë=~=ëíê~áÖÜí=äáåÉK=cçê=ê~Çá~íáçå=î~äìÉë=ïáíÜçìí=~å=~åçã~äóI=íÜÉ=Ç~í~=~êÉ= ÅäçëÉ=íç=åçêã~äK=qÜáë=éäçí=íóéÉ=Å~å=íÜÉêÉÑçêÉ=ÄÉ=ÜÉäéÑìä=áå=~å=É~êäó=ëÅêÉÉåáåÖ=ëí~ÖÉ=íç=ÇÉJ íÉÅí=íÜÉ=éêÉëÉåÅÉ=çÑ=çìíäáÉêëK= oìååáåÖ= íÜÉ= EÅçêêÉÅíÉÇI= ëÉÉ= ^kkbuF= ëÅêáéíI= íÜÉ= ÑçääçïáåÖ= çìíéìí= êÉëìäíÉÇ= Ñêçã= íÜÉ= ÉëëÉåíá~ä=é~êíI=íÜÉ=íïç=Å~ääë=íç=ÇçKëáÅ=E^kkbuF=o=ëÅêáéíW= > output = do.sic(input, sic.pred) Loading required package: gstat Loading required package: lattice [using ordinary kriging] > joker.output = do.sic(joker, sic.pred) Warning: singular model in variogram fit [using ordinary kriging]=

25000

semivariance

20000

15000

10000

5000

0 0e+00

1e+05

2e+05

3e+05

4e+05

5e+05

distance

Figure 10 Sample variogram for joker, along with last fitted variogram model before the singularity warning was issued

qÜÉ=ï~êåáåÖ=ÇáÇ=åçí=ëíçé=íÜÉ=ÉñÉÅìíáçåI=~åÇ=~=åÉï=é~áê=çÑ=éêÉÇáÅíáçå=Ç~í~=ëÉíë=ïÉêÉ= ÑçêãÉÇI=~åÇ=ëìÄãáííÉÇ=~ë=íÜÉ=Ñáå~ä=éêÉÇáÅíáçåK= qÜÉ=Åêçëë=î~äáÇ~íáçå=ojpb=Ñçê=íÜáë=ëÉÅçåÇ=êìå=ï~ë=áÇÉåíáÅ~ä=Ñçê=íÜÉ=áåéìí=Ç~í~I=Äìí= ï~ë=NONKS=Ñçê=àçâÉêK=`êìÅá~ääóI=íÜÉ=“ÅçêêÉÅíÒ=êìå=áëëìÉë=~=ï~êåáåÖ=ãÉëë~ÖÉ=íÜ~í=ï~ë=åçí= éêÉëÉåí=áå=íÜÉ=çêáÖáå~ä=êìåW=t~êåáåÖW=ëáåÖìä~ê=ãçÇÉä=áå=î~êáçÖê~ã=ÑáíK=tÉ=ïáää=åçï=äççâ= áåíç=ÇÉí~áä=ïÜ~í=íÜáë=ãÉ~åëK= qÜÉ= î~êáçÖê~ã= ãçÇÉä= ÑáííÉÇ= íç= íÜÉ= ë~ãéäÉ= î~êáçÖê~ã= áå= íÜÉ= ä~ëí= áíÉê~íáçå= ÄÉÑçêÉ= íÜÉ= ï~êåáåÖ= ãÉëë~ÖÉ= EíÜÉ= ãçÇÉä= íÜ~í= ï~ë= êÉíìêåÉÇ= Äó= íÜÉ= ÑìåÅíáçåF= ï~ë= ~= ëéÜÉêáÅ~ä= ãçÇÉä= ïáíÜ=~=åìÖÖÉí=çÑ=SNUVI=~=é~êíá~ä=ëáää=çÑ=STS=~åÇ=~=ê~åÖÉ=çÑ=PMSVS=EcáÖìêÉ=NMFK= qÜÉ=Ñáêëí=íïç=ë~ãéäÉ=î~êáçÖê~ã=Éëíáã~íÉë=ïÉêÉW= > variogram(dayx˜x, ˜x+y, joker, width=2e4, cutoff=5e5)[1:2,] np dist gamma dir.hor dir.ver id 1 103 13864.26 3884.342 0 0 var1 2 274 31057.91 27845.673 0 0 var1

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

11-9

`äÉ~êäóI=íÜÉ=ê~åÖÉ=~í=íÜÉ=ä~ëí=áíÉê~íáçå=áë=ëã~ääÉê=íÜ~å=íÜÉ=Çáëí~åÅÉ=î~äìÉ=çÑ=íÜÉ=ëÉÅçåÇ= ë~ãéäÉ=î~êáçÖê~ã=Éëíáã~íÉK= qÜáë= ãÉ~åë=íÜ~í=~í=íÜÉ=åÉñí=î~êáçÖê~ã=ÑáííáåÖ=áíÉê~íáçåI=íïç= é~ê~ãÉíÉêë= Eë~ó= íÜÉ= åìÖÖÉí= ~åÇ= íÜÉ= ê~åÖÉF= Ü~Ç= íç= ÄÉ= ÑáííÉÇ= Ñêçã= çåÉ= ëáåÖäÉ= ë~ãéäÉ= î~êáçÖê~ã=Éëíáã~íÉK=gìëí=äáâÉ=ÑáííáåÖ=~=ëíê~áÖÜí=äáåÉ=íÜêçìÖÜ=~=ëáåÖäÉ=éçáåí=íÜáë=äÉ~Çë=íç=~= ëáåÖìä~êáíóI=~åÇ=íÜÉ=ï~êåáåÖ=áë=áëëìÉÇK=fí=Ä~ëáÅ~ääó=ãÉ~åë=íÜ~í=áå=íÜÉ=ÅçåíÉñí=çÑ=íÜáë=ÑáííáåÖ= éêçÅÉÇìêÉI= ~= ä~êÖÉ= åìãÄÉê= çÑ= î~êáçÖê~ã= ãçÇÉäë= ~êÉ= åçï= éçëëáÄäÉI= ~= ëáíì~íáçå= ïÜÉêÉ= ~å= ~ìíçã~íáÅ= ÑáííáåÖ= êçìíáåÉ= Å~å= ã~âÉ= åç= ëÉåëáÄäÉ= ÅÜçáÅÉK= dáîÉå= íÜ~í= íÜÉ= ÅçêêÉÅí= éêçÅÉÇìêÉ= ï~ë=ìëÉÇ=áå=íÜÉ=Ñáêëí=éä~ÅÉI=íÜÉ=ï~êåáåÖ=ãÉëë~ÖÉ=ëÜçìäÇ=ÄÉ=í~âÉå=ëç=ëÉêáçìë=~ë=íç=êÉÅ~ää=íÜÉ= êÉëìäíáåÖ=éêÉÇáÅíáçåëK=^ÑíÉê=Ü~îáåÖ=ëìÄãáííÉÇ=íÜÉ=éêÉÇáÅíáçåë=Ñêçã=íÜÉ=éêçÅÉÇìêÉ=ïáíÜ=íÜÉ= ÉêêçêI=~åÇ=~ÑíÉê=Ü~îáåÖ=ÅçêêÉÅíÉÇ=íÜÉ=ÉêêçêI=ãó=Ñáå~ä=ëìÄãáëëáçå=Ñçê=àçâÉê=ï~ëW=ãó=éêçÅÉJ ÇìêÉ=Ñ~áäë=çå=àçâÉêK= 3.1 WHAT IF’S

pç=Ñ~êI=~=åìãÄÉê=çÑ=ÇÉÅáëáçåë=áå=íÜÉ=ãçÇÉääáåÖ=éêçÅÉëë=Ü~îÉ=ÄÉÉå=Ñ~áêäó=~Ç=ÜçÅK=qÜÉ=ÅçåJ ëÉèìÉåÅÉë=çÑ=íïç=çÑ=íÜÉãI=íÜÉ=áåíÉêî~ä=ä~Ö=ïáÇíÜ=~åÇ=íÜÉ=î~êáçÖê~ã=ãçÇÉä=íóéÉI=ïáää=ÄÉ= Éñ~ãáåÉÇ=áå=ëçãÉ=ãçêÉ=ÇÉí~áäK= 50000

semivariance

40000

30000

20000

10000

0 0e+00

1e+05

2e+05

3e+05

4e+05

5e+05

4e+05

5e+05

distance

25000

semivariance

20000

15000

10000

5000

0 0e+00

1e+05

2e+05

3e+05

distance

Figure 11 Sample variogram for joker, along with fitted (a) fitted spherical variogram model when a lag interval width of 10,000 is used, instead of 20,000, (b) fitted linear variogram model

tÜ~í= ïçìäÇ= Ü~îÉ= Ü~ééÉåÉÇ= áÑ= áåëíÉ~Ç= çÑ= ~= OMIMMM= áåíÉêî~ä= ïáÇíÜ= íÜÉ= î~äìÉ= NMIMMM= ïÉêÉ= ìëÉÇ\= qÜÉ= î~êáçÖê~ã= ÑáííáåÖ= ÑìåÅíáçå= ÇçÉë= áå= íÜáë= Å~ëÉ= åçí= ÖáîÉ= ~= ï~êåáåÖI= Äìí= êÉJ íìêåë=~=ÑáííÉÇ=ëéÜÉêáÅ~ä=ãçÇÉä=ïáíÜ=~=åìÖÖÉí=çÑ=NVMTSI=~=ê~åÖÉ=çÑ=NONRQPI=~åÇ=~=åÉÖ~íáîÉ=

11-10

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

é~êíá~ä= ëáää= çÑ= JNVST= EcáÖìêÉ= NN~FI= ïÜáÅÜ= áë= çÑ= ÅçìêëÉ= éÜóëáÅ~ääó= áãéçëëáÄäÉK= rëáåÖ= íÜáë= î~êáçÖê~ã=áå=íÜÉ=âêáÖáåÖ=éêÉÇáÅíáçå=äÉ~ÇëI=éÉêÜ~éë=ëìêéêáëáåÖäóI=åçí=íç=ëáåÖìä~ê=ëóëíÉãë=çÑ= âêáÖáåÖ=Éèì~íáçåëI=Äìí=ÇçÉë=äÉ~Ç=íç=êìÄÄáëÜ=éêÉÇáÅíáçåëW=NRB=çÑ=íÜÉ=éêÉÇáÅíáçåë=~êÉ=åÉÖ~J íáîÉI=ïáíÜ=~=ãáåáãìã=î~äìÉ=çÑ=JQSVI=~åÇ=íÜÉ=Åêçëë=î~äáÇ~íáçå=ojpb=áë=NVVK=^å=Éñ~ãéäÉ= çÑ=Ö~êÄ~ÖÉ=áåI=Ö~êÄ~ÖÉ=çìíI=åçí=Å~ìÖÜí=Äó=ï~êåáåÖ=çê=Éêêçê=ãÉëë~ÖÉëK=qÜÉ=êÉ~ëçå=Ñçê=íÜÉ= î~êáçÖê~ã=ÑáííáåÖ=êçìíáåÉ=êÉíìêåáåÖ=åÉÖ~íáîÉ=ëáää=î~äìÉë=áë=íÜ~í=~=ëáåÖäÉ=êçìíáåÉ=Å~å=ÄÉ=ìëÉÇ= Ñçê=ÑáííáåÖ=ÇáêÉÅí=~åÇ=Åêçëë=î~êáçÖê~ãëK=^äíÜçìÖÜ=~=ãáåáã~ä=ä~Ö=ïáÇíÜ=ÇçÉë=ÜÉäé=áå=êÉîÉ~äJ áåÖ=çìíäáÉêë=çê=~åçã~äáÉë=E~ë=íÜÉ=î~êáçÖê~ã=ÅäçìÇ=ÇçÉëFI=íçç=ëã~ää=ä~Ö=ïáÇíÜ=î~äìÉë=äÉ~Ç=íç= åçáëó=î~êáçÖê~ãëI=ïÜáÅÜ=ã~ó=ÄÉ=éêçÄäÉã~íáÅ=Ñçê=î~êáçÖê~ã=ãçÇÉä=ÑáííáåÖK= tÜÉå=ïÉ=ÅÜçëÉ=íÜÉ=ëéÜÉêáÅ~ä=ãçÇÉäI=Åêçëë=î~äáÇ~íáçå=ëí~íáëíáÅë=ëìÖÖÉëíÉÇ=íÜ~í=íÜÉ=äáåJ É~ê= ãçÇÉä= ïáíÜçìí= ê~åÖÉ= ïçìäÇ= óáÉäÇ= Éèì~ä= êÉëìäíë= EÑáÖìêÉë= Q= ~åÇ= RFK= tÜ~í= ïçìäÇ= Ü~îÉ= Ü~ééÉåÉÇ=áÑ=íÜÉ=äáåÉ~ê=ãçÇÉä=ïÉêÉ=ìëÉÇ=áåëíÉ~Ç=çÑ=íÜÉ=ëéÜÉêáÅ~ä\=qÜÉ=ÑáííÉÇ=î~êáçÖê~ã=áë= ëÜçïå=áå=ÑáÖìêÉ=NNÄX=íÜÉ=Åêçëë=î~äáÇ~íáçå=ojpb=çÄí~áåÉÇ=áë=NNUKUI=ïÜáÅÜ=áë=íÜÉ=ÄÉëí=ïÉ= Ü~îÉ=ëÉÉå=ëç=Ñ~êK=^å=Éêêçê=ÅÜÉÅâáåÖ=o=ÑìåÅíáçå=íÜ~í=ÄêÉ~âë=Eëíçéë=ÉñÉÅìíáçåF=ïÜÉå=~=ëáåJ Öìä~ê=î~êáçÖê~ã=Ñáí=áë=ÉåÅçìåíÉêÉÇ=áë=ÖáîÉå=áå=^kkbu=^KQK=

4 RESULTS: THE EVALUATION PHASE 4.1 GLOBAL STATISTICS

cçê=íÜÉ=Ñáêëí=Ç~í~=ëÉíI=çåäó=~=ëáåÖäÉ=êìå=ï~ë=éÉêÑçêãÉÇK=cçê=íÜÉ=ëÉÅçåÇ=Ç~í~=ëÉíI=íÜÉ=ÑçäJ äçïáåÖ= ëÅÉå~êáçë= ïÉêÉ= Åçãé~êÉÇW= EáF= “ëáåÖìä~ê= ÑáíÒI= ïÜáÅÜ= ìëÉë= íÜÉ= î~êáçÖê~ã= êÉëìäíáåÖ= Ñêçã=íÜÉ=ëáåÖìä~ê=Ñáí=EÑáÖìêÉ=NMFI=EááF=íÜÉ=“äáåÉ~ê=ÑáíÒ=çÑ=ÑáÖìêÉ=NNÄK=^ë=~=ëí~åÇ~êÇ=ÄÉåÅÜJ ã~êâI= áåîÉêëÉ= Çáëí~åÅÉ= ïÉáÖÜíÉÇ= áåíÉêéçä~íáçå= EáÇïFI= ìëáåÖ= Çáëí~åÅÉ= ïÉáÖÜíáåÖ= éçïÉê= O= ~åÇ= ~= NOR= åÉ~êÉëí= åÉáÖÜÄçìêÜççÇ= ï~ë= ~ÇÇÉÇ= ~ë= ~= ëÅÉå~êáç= Ñçê= ÄçíÜ= Ç~í~= ëÉíëK= q~ÄäÉ= O= ëí~íÉë=íÜÉ=ëìãã~êó=ëí~íáëíáÅë=Ñçê=çÄëÉêîÉÇ=~åÇ=éêÉÇáÅíÉÇ=î~äìÉë=Ñçê=íÜÉ=Ñáêëí=Ç~í~=ëÉíW= Min Observed Predicted Idw

Max 57 69.92 70.69

Mean 180 125.14 129.58

Median 98.02 96.8 96.93

Std.dev 98.8 99.14 99.51

20.02 14.47 12.03

Table 2

qÜÉ=ëìãã~êó=ëí~íáëíáÅë=Ñçê=íÜÉ=çÄëÉêîÉÇ=~åÇ=éêÉÇáÅíÉÇ=î~äìÉë=Ñçê=íÜÉ=ëÉÅçåÇ=Ç~í~=ëÉí= EàçâÉêFI=ìåÇÉê=ëÉîÉê~ä=ëÅÉå~êáçë=çÑ=éêÉÇáÅíáåÖ=íÜáë=ëÉÅçåÇ~êó=Ç~í~=ëÉíI=~êÉW=ãáå=ã~ñ=ãÉ~å= ãÉÇá~å=ëíÇÇÉî=ëÅÉå~êáçI=~ë=áå=q~ÄäÉ=PW= Min Observed predicted Predicted Predicted

Max 57 92.2 73.2 71.13

Mean 1528.2 178.4 255.2 497.63

105.4 117.4 109.4 110.55

Median 99 120.7 103.6 106.4

Std.dev 83.7 9.6 31.8 39.9

Scenario Singular fit Linear fit Inverse distance w.

Table 3

pìãã~êó=ëí~íáëíáÅë=Ñçê=íÜÉ=ÉêêçêëI=ÜÉêÉ=ÇÉÑáåÉÇ=~ë=éêÉÇáÅíÉÇJçÄëÉêîÉÇI=Ñçê=íÜÉ=Ñáêëí=Ç~í~= ëÉí=~åÇ=~ää=ëÅÉå~êáçë=Ñçê=íÜÉ=ëÉÅçåÇ=EàçâÉêF=Ç~í~=ëÉíI=~êÉ=áå=q~ÄäÉ=QW=

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

11-11

Data set

MAE

ME

RMSE

Corr

Scenario

1 1

9.11 9.76

-1.22 -1.09

0.788 0.778

12.44 13.10

2 2 2

28.45 23.26 21.31

12.01 4.00 5.13

0.380 0.417 0.512

81.41 76.19 72.09

inverse distance w singular fit linear fit inverse distance w.

Table 4

få=q~ÄäÉ=Q=ã~É=êÉÑÉêë=íç=ãÉ~å=~ÄëçäìíÉ=ÉêêçêI=ãÉ=íç=ãÉ~å=ÉêêçêI=Åçêê=íç=mÉ~êëçåÛë=ÅçêJ êÉä~íáçå=ÄÉíïÉÉå=çÄëÉêîÉÇ=~åÇ=éêÉÇáÅíÉÇI=~åÇ=ojpb=íç=êççí=ãÉ~å=ëèì~êÉ=ÉêêçêK= fí=áë=ëìêéêáëáåÖ=íÜ~í=íÜÉ=ojpb=Ñçê=íÜÉ=Ñáêëí=Ç~í~=ëÉí=áë=ãìÅÜ=ä~êÖÉê=íÜ~å=íÜçëÉ=çÄí~áåÉÇ= áå=ÑáÖìêÉ=QK=^=éçëëáÄäÉ=Å~ìëÉ=áë=íÜ~í=Ñçê=É~ÅÜ=Ç~ó=íÜÉ=î~êáçÖê~ã=EáåÅäìÇáåÖ=íÜÉ=åìÖÖÉí=î~êáJ ~åÅÉF=ÅÜ~åÖÉë=EÑáÖìêÉ=PFX=íÜÉ=Ñáêëí=íÉëí=Ç~í~=ëÉí=ã~ó=ÄÉ=~=Ç~ó=ïáíÜ=ä~êÖÉê=EåìÖÖÉíF=î~êá~åÅÉ= íÜ~å=íÜÉ=~îÉê~ÖÉ=çîÉê=íÜÉ=NM=íÉëí=Ç~óëK=iÉ~îÉJçåÉJçìí=Åêçëë=î~äáÇ~íáçå=ojpb=î~äìÉë=ìëáåÖ= íÜÉ=ë~ãÉ=éêçÅÉÇìêÉ=Ñçê=íÜÉ=NM=Ç~óë=ê~åÖÉ=Ñêçã=NMKP=íç=NNKTK= qÜÉ= ojpb= î~äìÉë= Ñçê= íÜÉ= Ñçìê= âêáÖáåÖ= ëÅÉå~êáçë= Ñçê= íÜÉ= ëÉÅçåÇ= EàçâÉêF= Ç~í~= ëÉí= ~êÉ= Ñ~áêäó= Çáë~ëíêçìëK= fêçåáÅ~ääóI= ÄçíÜ= áå= íÉêãë= çÑ= ojpb= ~ë= áå= íÉêãë= çÑ= ÅçêêÉä~íáçå= ÄÉíïÉÉå= éêÉÇáÅíÉÇ=~åÇ=çÄëÉêîÉÇI=áåîÉêëÉ=Çáëí~åÅÉ=ïÉáÖÜíáåÖ=áåíÉêéçä~íáçå=ëäáÖÜíäó=çìíéÉêÑçêãë=íÜÉ= âêáÖáåÖ=ëÅÉå~êáçë=Ñçê=íÜÉ=ëÉÅçåÇ=Ç~í~=ëÉíK=qÜáë=áë=åçí=íÜÉ=Å~ëÉ=Ñçê=íÜÉ=Ñáêëí=Ç~í~=ëÉíK= 4.2 INTERPOLATED MAPS AND KRIGING STANDARD ERROR

cáÖìêÉ=NO=ëÜçïë=íÜÉ=áåíÉêéçä~íÉÇ=EâêáÖÉÇF=ã~éë=Ñçê=ÄçíÜ=Ç~í~=ëÉíëI=Ä~ëÉÇ=çå=íÜÉ=íÉëí=Ç~í~= çåäóI=~åÇ=ÄçíÜ=Ä~ëÉÇ=çå=íÜÉ=î~êáçÖê~ã=Ñçê=íÜÉ=Ñáêëí=Ç~í~=ëÉíK=qÜÉ=âêáÖáåÖ=ëí~åÇ~êÇ=Éêêçêë= ~êÉ= î~äáÇ= Ñçê= íÜÉ= Ñáêëí= Ç~í~= ëÉíW= ÄçíÜ= ã~éë= ~êÉ= Ä~ëÉÇ= çå= íÜÉ= ë~ãÉ= î~êáçÖê~ã= ãçÇÉäI= Äìí= çåäó=Ñçê=íÜÉ=Ñáêëí=Ç~í~=ëÉí=áë= íÜÉ=î~êáçÖê~ã=ãçÇÉä=íÜÉ=ãçÇÉä=ÑáííÉÇ=íç=íÜÉ=Ç~í~=ìëÉÇK=cçê= íÜÉ=ëÉÅçåÇ=Ç~í~=ëÉíI=áå=íÜÉ=~êÉ~=ïáíÜ=íÜÉ=~åçã~äó=íÜÉ=âêáÖáåÖ=ëí~åÇ~êÇ=Éêêçê=ïáää=Öêçëëäó= ìåÇÉêÉëíáã~íÉ= éêÉÇáÅíáçå= ÉêêçêëK= cáÖìêÉ= NP= ëÜçïë= ~= éÉêëéÉÅíáîÉ= éäçí= EïáêÉÑê~ãÉF= çÑ= íÜÉ= éêÉÇáÅíÉÇ=ëÉÅçåÇ=Ç~í~=ëÉí=EàçâÉêFK=

5 DISCUSSION få= íÜáë= é~éÉê= ~= Åä~ëëáÅ~ä= ÖÉçëí~íáëíáÅ~ä= “~äÖçêáíÜãÒ= ï~ë= ÇÉëáÖåÉÇ= Ñçê= ~ìíçã~íáÅ= ã~ééáåÖ= Ä~ÅâÖêçìåÇ=ê~Çáç~Åíáîáíó=äÉîÉäëK=qÜÉ=éêçÅÉÇìêÉ=~ÇÇêÉëëÉÇ=íÜÉ=ÑçääçïáåÖ=ãçÇÉä=ÇÉÅáëáçåëW= EáF=çìíäáÉê=ÇÉíÉÅíáçåI=EááF=ÅÜçáÅÉ=çÑ=~å=áëçíêçéáÅ=î~êáçÖê~ã=ãçÇÉäI=EáááF=ÅÜçáÅÉ=çÑ=î~êáçÖê~ã= ÅìíJçÑÑ=Çáëí~åÅÉ=~åÇ=ä~Ö=ïáÇíÜI=EáîF=îÉêáÑáÅ~íáçå=çÑ=ÇáêÉÅíáçå~ä=ÇÉéÉåÇÉåÅÉI=EîF=îÉêáÑáÅ~íáçå= ïÜÉíÜÉê= ÅçâêáÖáåÖ= áãéêçîÉÇ= éêÉÇáÅíáçåëI= EîáF= çéíáãáòÉ= âêáÖáåÖ= åÉáÖÜÄçìêÜççÇK= `ÜçáÅÉë= ïÉêÉ=Ä~ëÉÇ=çå=îáëì~ä=áåëéÉÅíáçå=EáI=áááI=áîF=~åÇ=äÉ~îÉJçåÉJçìí=Åêçëë=î~äáÇ~íáçå=ojpb=î~äìÉë= EááI=îI=îáFK=qÜÉ=áëëìÉë=ïÉêÉ=Éî~äì~íÉÇ=áå=íÜáë=é~êíáÅìä~ê=çêÇÉêX=íÜÉ=áÇÉ~=ÄÉÜáåÇ=áí=áë=íÜ~í=éêáçê= íç=íÜÉ=~å~äóëáë=ïÉ=ÉñéÉÅíÉÇ=íÜáë=íç=ÄÉ=íÜÉ=çêÇÉê=çÑ=áãéçêí~åÅÉK=cáÖìêÉ=U=ÉKÖK=ÅçåÑáêãë=íÜ~í= íÜÉ=åÉáÖÜÄçìêÜççÇ=ëáòÉ=Ü~ë=~=îÉêó=ëã~ää=áåÑäìÉåÅÉ=çå=íÜÉ=Åêçëë=î~äáÇ~íáçå=ÉêêçêëK=tÉ=Çç= åçí= Åä~áã= íÜ~í= ÅÜççëáåÖ= ~åçíÜÉê= çêÇÉê= íÜêçìÖÜ= EáFÓEîáF= ïáää= äÉ~Ç= íç= íÜÉ= ë~ãÉ= ~ìíçã~íáÅ= ã~ééáåÖ=ëíê~íÉÖóK=fí=áë=áåíÉêÉëíáåÖ=íç=ëéÉÅìä~íÉ=ïÜ~í=ïçìäÇ=Ü~ééÉå=áÑ=íÜÉ=çìíäáÉê=ÇÉíÉÅíáçå= ïÉêÉ= ~ìíçã~íÉÇW= ëÜçìäÇ= íÜÉ= ~ìíçã~íáÅ= ã~ééáåÖ= ëÅêáéí= ÄÉ= ãçÇáÑáÉÇ= íç= ÑáäíÉê= çìíäáÉêë\= pÜçìäÇ=íÜÉó=ÄÉ=áÖåçêÉÇ=Ñçê=ë~ãéäÉ=î~êáçÖê~ã=Éëíáã~íáçå=çê=ÉîÉå=Ñçê=âêáÖáåÖ=~ë=ïÉää\=qÜÉ= ÅìêêÉåí= ëíìÇó= ëìÖÖÉëíë= íÜ~í= Ñçê= íÜÉ= ~åçã~äóI= Ñêçã= ~ää= ~ééêç~ÅÜÉë= íêáÉÇI= íÜ~í= Ä~ëÉÇ= çå= ~= î~êáçÖê~ã= ÑáííÉÇ= íç= íÜÉ= Ç~í~= ïáíÜçìí= ~åçã~äó= ÖáîÉë= íÜÉ= ÄÉëí= éêÉÇáÅíáçåëI= ÉñéêÉëëÉÇ= áå==

11-12

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

~îÉê~ÖÉ= ÉêêçêëK= lÄîáçìëäóI= íÜáë= ~ééêç~ÅÜ= ÇçÉë= åçí= ÖáîÉ= î~äì~ÄäÉ= ìåÅÉêí~áåíó= ãÉ~ëìêÉë= EâêáÖáåÖ=éêÉÇáÅíáçå=ëí~åÇ~êÇ=ÉêêçêëF=Ñçê=íÜÉ=éêÉÇáÅíáçåë=çÑ=íÜÉ=~åçã~äóK= data set 1

data set 2

+++ + ++ ++ + + + + + + + ++ + + + ++ + + + + + + + + + ++ + + ++ + + + + + + + ++ + + + + + + ++ + + + + ++ ++ +++ + + +++ + + + + + + +++ +++++ + + ++ + + + + +++ +++++ + + ++ + + +++ + + + + +++ + + + + ++ + + + + ++ + + + + ++ + +++ + + + + + + ++ + + +++ + + + + + + + + + ++ + + + + + + + + + + + ++ + + + + + ++ +++ ++ ++ + +++ + ++ + ++ + + + + + ++ +++ ++ ++ + +++ + ++ + + + + + + + + + + + + + + + ++ + ++ + + + + + + ++ + ++ + + + ++ ++ + +++ + +++ + + ++ ++ + + + ++ +++ ++ + + + + + ++ +++ ++ + + ++ ++ + + + + ++ + + + + ++ + + + + + + + + + + + + + + + ++ + ++ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + ++ + ++++ ++++ + + + + ++ ++ + +++ + +++ ++ + + + + + + ++ + + + ++ ++ + + + + + + ++ + + + + ++ + + + + + + ++ + + +++ + + + ++ + + + + + + + + + + ++ ++ + + + ++ + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + + + ++ + + + + + + + + + + ++ + + + + + + ++ + ++ + + + + + + ++ + + ++ + + ++ + + ++ + + + ++ + + ++ + + + +++ +++ + + +++ +++ + + + + + + + + + + + + + + + + + + + + + + +++ + + + + + ++ + + + + + + + + + + + + + + + + +++ ++ + + + + + ++ + + + + + + + +++ ++ + + + + + ++ +++ + + + +++ ++ + + +++ + + + +++ ++ + + ++ + ++ + + + + ++++ + + + + + + +++ + + + + + + ++ + + + ++ + + + + + + ++ + + + + +++ + ++ + + + ++ + + + + +++ + ++ + + + + + ++ + + ++ + + + + ++ + + + + ++ + + + + + + + + + ++ + + + ++ + + + ++ + + + ++ + + + ++ + + + ++ + + + + + + + ++ + ++ + + + ++ + + + ++ + ++ + ++ + + + + ++ + +++ + + + ++ + +++ + + + + + ++ + + + + + + ++ + + + ++ + + ++ + + + + + ++++ + + + +++ + + + + ++ + + ++ + + + + + ++++ + + + +++ + + + + + + + + + + + + + + + + + + + + + + + + + ++ + + + ++ + + +++ +++ + +++ + ++ + +++ + ++ ++ + ++ + + + + ++++ + + ++++ + + + + + ++ + + ++ ++ ++ + + + ++ + ++ + + + + ++ ++ + + + ++ ++ + + + + + + + ++ + + + ++ ++ + + + + + + + ++ + + + + + + ++ + + + + + + ++ + + + ++ + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + ++ ++ +++ + + ++++ + + ++ ++ + ++ + +++ + + + + + ++ + ++ + + + ++++ +++ + + + ++ + + ++ + + + + + + + + + + + + + + + ++ + ++ +++ ++ + +++ + + ++ +++ ++ + + ++ + + + ++ + + + + +++++ + + +++ + + + + + + ++ ++ + + + + ++++ + + ++++ + + + + + ++ + ++ + +++ + + + + +++ + + + + + + + + + ++ + + ++ ++ + + ++ + ++ + + + + + +++ + +++ ++++ + ++ + ++ + ++ + + + + +++ ++++ + ++ + + + ++ + + ++ + + + + + + ++++ ++++ + ++ ++ ++ ++ ++ + ++ + + ++++ + + ++ + + ++++ + ++ ++ + + + + + + + + ++ + + + + ++ + ++ + + + + + + + + + + +++ + + + + + ++ + + + + + + + + + + +++ + + + + + + + + + + + + + + + +++ + + + +++++ + + + ++ + + + + + + +++ + + + +++++ + + + + + + + + + + + + + +++ + + ++ + + + + +++ + + ++ + ++ ++ + + + ++ ++ + + + + + ++ + + + + + + + ++ + + +++ + + ++ + + ++++ + + + + ++ + + + + + + ++ +++ ++ + + +++++ + ++ ++ +++++ + + ++ + + + + + + + + ++ + ++ + + + + +

standard error 1 200

180

160

140

120

100

80

60

+++ ++ + + + + + + + + + + + ++ + + + + + ++ + + + + ++ +++ + + + + + + +++ +++++ + + ++ + + + + + + + + + + + + + + + + + +++ + + + + + + + + + + + + + + + ++ + + + + + ++ +++ ++ +++ +++ + ++ + + + + + + + + + ++ + ++ + + + ++ + +++ + ++ + + + ++ ++ + ++ + + ++ + + + + ++ + + + + + + + ++ + + + + + + + + + + + + + + + ++ + + ++++ ++ + + +++ + +++ ++ + + + + ++ + + + + + + ++ + + + + + + + + ++ ++ + + + + + ++ + + + + + + + + + + + ++ + + + + + + + ++ ++ ++ + + ++ + + ++ + + + + + ++ + ++ ++ ++ + + + + + + + + ++ + + + + + + + + ++ + + + + + + ++ + + + + ++ + ++ + ++ +++ + + + +++ ++ + + ++++ + + + + + + + + + + + ++ + + + ++ + + + + +++ + ++ + + + ++ + ++ + + + + + + ++ + + ++ + ++ + + + ++ + + + + + ++ + + + ++ + + ++ + + + + + + + +++ + + + + + ++ + + + ++ + + ++ + + + + + ++++ + + + +++ + + + + + + + + + + + + + + +++ ++ + +++ + ++ + ++++ +++ + + ++ + + + ++ ++ + + + ++ + ++ + ++ ++ + + + + + ++ + + + ++ + + ++ + + + ++ + + + ++ + + + + + + + + + + + + ++ +++ + + + ++ + ++ + + + ++++ +++ + + + ++ + ++ + + + + + + + ++ ++ + + + + ++ + + + ++ + + + + + ++ + + + + ++++ + + ++++ + + + + + + + + + + ++ + + ++ ++ + + + +++ + + + +++ ++++ + ++ + + + ++ + + + + ++++ + ++ ++ + ++ + + ++++ + ++ + + + + + + ++ + ++ + + + + + + + + + + +++ + + + + + + + + + + + + + +++ + + + +++++ + + + + + + + + + + +++ + + ++ + ++ + + + ++ ++ + + + + + ++ + + +++ + + ++ + + +++++ + ++ ++ + ++ + + + ++ + + + + +

13.5

13.0

12.5

12.0

11.5

11.0

10.5

10.0

9.5

9.0

Figure 12 Left: predictions for day 11 and joker; prediction standard errors; perspective plot of joker predictions; Right: prediction standard errors (nSv/h)

500

400

z

300

200

y

x 100

Figure 13 Perspective plot with wire frame for predictions on second (joker) data set, using the test data (nSv/h)

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

11-13

qÜÉ=èìÉëíáçå=êÉã~áåë=ïÜó=ÅçâêáÖáåÖ=ÇáÇ=åçí=äÉ~Ç=íç=áãéêçîÉãÉåí=áå=íÜÉ=Åêçëë=î~äáÇ~J íáçå= ëÉííáåÖK= ^= éçëëáÄäÉ= Å~ìëÉ= áë= áëçíçéóW= ~ää= íÉå= Ç~óë= Ü~îÉ= Ç~í~= çå= ~= íÜÉ= ë~ãÉ= ëÉí= çÑ= äçÅ~íáçåëX=íÜÉ=î~êáçÖê~éÜó=ã~ó=ÄÉ=ÅäçëÉ=íç=íÜÉ=áåíêáåëáÅ=ÅçêêÉä~íáçå=ãçÇÉä=áå=ïÜáÅÜ=Å~ëÉ= ÅçâêáÖáåÖ= áë= Éèìáî~äÉåí= íç= çêÇáå~êó= âêáÖáåÖ= Et~ÅâÉêå~ÖÉäI= NVVUFK= cìêíÜÉêãçêÉI= ÑáííáåÖ= ~= äáåÉ~ê=ãçÇÉä=çÑ=ÅçêÉÖáçå~äáò~íáçå=áãéçëÉë= èìáíÉ=ëíêáÅí=äáãáíëI= ÉëéÉÅá~ääó=íç=íÜÉ=î~êáçÖê~ã= ê~åÖÉ= é~ê~ãÉíÉêK= fëçíçéáÅ= ÅçâêáÖáåÖ= ïçìäÇ= áãéêçîÉ= çîÉê= âêáÖáåÖ= çåäó= áÑ= íÜÉ= ëÉÅçåÇ~êó= î~êá~ÄäÉ= ï~ë= ãìÅÜ= ÄÉííÉê= ÅçêêÉä~íÉÇ= áå= ëé~ÅÉ= íÜ~å= íÜÉ= éêáã~êó= î~êá~ÄäÉ= Edççî~ÉêíëI= NVVTFK= låÉ= áëëìÉ= åçí= ~ÇÇêÉëëÉÇ= áå= íÜáë= ëíìÇó= áë= íÜÉ= ïÉáÖÜíáåÖ= ëÅÜÉãÉ= ïÜÉå= ìëáåÖ= ïÉáÖÜíÉÇ= äÉ~ëí= ëèì~êÉë= íç= Ñáí= î~êáçÖê~ã= ãçÇÉäë= íç= ë~ãéäÉ= î~êáçÖê~ãëK= tÉ= ìëÉÇ= ÜÉêÉ= ïÉáÖÜíë= éêçJ éçêíáçå~ä= íç= h −1 N h I= ÖáîáåÖ= ä~êÖÉê= ïÉáÖÜíë= íç= ëã~ääÉê= Çáëí~åÅÉë= E h F= ~åÇ= íç= î~êáçÖê~ã= Éëíáã~íÉë=Ä~ëÉÇ=çå=íÜÉ=ä~êÖÉê=åìãÄÉê=çÑ=éçáåí=é~áêë=E N h =FK=líÜÉê=ïÉáÖÜíáåÖ=ëÅÜÉãÉë=áåJ Åçêéçê~íÉ=íÜÉ=ëÉãáî~êá~åÅÉ=î~äìÉI=çê=~ÇÇêÉëë=ÅçêêÉä~íáçå=~ãçåÖ=î~êáçÖê~ã=Éëíáã~íÉëK=cçê= ÉñíêÉãÉ= ë~ãéäÉ= î~êáçÖê~ãë= ëìÅÜ= ~ë= ëÜçïå= áå= ÑáÖìêÉ= NM= ~åÇ= NNI= íÜÉ= ïÉáÖÜíáåÖ= ëÅÜÉãÉ= ÅÜçëÉå=ã~ó=éä~ó=~=ÅçåëáÇÉê~ÄäÉ=êçäÉK= 5.1 AUTOMATION AND ANOMALIES

få= éêáåÅáéäÉI= ïÉ= ÄÉäáÉîÉ= íÜ~í= âêáÖáåÖ= áåíÉêéçä~íáçå= áë= ~= ëìáí~ÄäÉ= ãÉíÜçÇ= Ñçê= ~ìíçã~íáÅ== áåíÉêéçä~íáçåK= ^ìíçã~íáçå= çÑ= íÜÉ= ã~åì~ä= ëíÉéë= Å~êêáÉÇ= çìí= áå= íÜáë= ëíìÇóI= åçí~Ääó= çìíäáÉê= êÉàÉÅíáçåI=î~êáçÖê~ã=ãçÇÉä=ÅÜçáÅÉ=~åÇ=î~êáçÖê~ã=é~ê~ãÉíÉê=Éëíáã~íáçå=E“ãçÇÉä=ÑáííáåÖÒF= ã~ó=åçí=ÄÉ=~Çîáë~ÄäÉ=áå=Å~ëÉë=ïÜÉêÉ=~åçã~äáÉë=Å~å=ÄÉ=ÉñéÉÅíÉÇ=çê=ëÜçìäÇ=ÄÉ=ÇÉíÉÅíÉÇK= qÜÉ= ~ìíçã~íáÅ= ã~ééáåÖ= ~äÖçêáíÜã= ÇÉîáëÉÇ= áå= íÜáë= ëíìÇó= Ñ~áäÉÇ= íêÉãÉåÇçìëäó= ïÜÉå= ÅçåÑêçåíÉÇ= ïáíÜ= ~å= ~åçã~äó= EàçâÉêI= çê= ëÉÅçåÇ= íÉëí= ëÉíFK= ^äíÜçìÖÜ= ~í= íÜ~í= ãçãÉåí= íÜáë= Å~ãÉ=ê~íÜÉê=~ë=~=ëÜçÅâI=áå=ÜáåÇëáÖÜí=áí=áë=åç=ëìêéêáëÉ=~í=~ääW=Ñáêëí=çÑ=~ää=íÜÉ=~äÖçêáíÜã=Ü~Ç= åçí=ÄÉÉå=ëìÄàÉÅí=íç=ëíêçåÖ=íÉëíáåÖI=~åÇ=ëÉÅçåÇ=åç=íÉëíáåÖ=~í=~ää=Ü~Ç=ÄÉÉå=ÇçåÉ=ïáíÜ=Ç~í~= Åçåí~áåáåÖ= ~å= ~åçã~äóK= få= íÜáë= äáÖÜíI= íÜÉ= ÅìêêÉåí= éêçÅÉÇìêÉ= ëÜçìäÇ= ÄÉ= ëÉÉå= ~ë= ~= Ñáêëí= ~íJ íÉãéíI=Åçåí~áåáåÖ=ã~åó=~ëéÉÅíë=íÜ~í=Å~å=ÄÉ=áãéêçîÉÇK=rëáåÖ=~=ëÅêáéíáåÖ=ä~åÖì~ÖÉ=EëìÅÜ=~ë= oF=áë=áå=ëç=Ñ~ê=~å=~Çî~åí~ÖÉ=íÜ~í=Éêêçêë= Å~å=ÄÉ=Å~ìÖÜí=~ÑíÉêï~êÇëÔáí=áë=ãìÅÜ=Ü~êÇÉê= íç= ÇÉíÉÅí= Éêêçêë= áÑ= íÜÉ= éêçÅÉÇìêÉ= áåîçäîÉÇ= åìãÉêçìë= áåíÉê~ÅíáîÉ= ÅäáÅâë= ïáíÜ= ~= ãçìëÉK= fí= ëÜçìäÇ=ÄÉ=åçíÉÇ=íÜ~í=íÜÉ=ãáëí~âÉë=ÑçìåÇ=êÉÑÉê=íç=Éêêçêë=áå=íÜÉ=ëÅêáéíë=ïêáííÉå=Ñçê=íÜáë=é~êJ íáÅìä~ê=~ìíçã~íáçå=éêçàÉÅíI=åçí=íç=Éêêçêë=áå=íÜÉ=Öëí~í=ëçÑíï~êÉ=EmÉÄÉëã~I=OMMQFK= få=ÖÉåÉê~äI=íê~áåáåÖ=~äÖçêáíÜãë=ïáíÜ=Ç~í~=íÜ~í=Åçåí~áå=åç=~åçã~äáÉë=áå=çêÇÉê=íç=çÄí~áå= ~å=~äÖçêáíÜã=íÜ~í=Å~å=Ü~åÇäÉ=~å=~åçã~äó=ïÜÉå=áí=çÅÅìêë=ëÉÉãë=íç=ÄÉ=~=ëáääó=ìåÇÉêí~âáåÖK= fí=áë=ãçêÉ=~Çîáë~ÄäÉ=íç=~ÇÇ=~åçã~äáÉë=ëìÅÜ=~ë=íÜÉ=ëÉÅçåÇ=EàçâÉêF=Ç~í~=ëÉí=íç=íÜÉ=íê~áåáåÖ= Ç~í~=áå=çêÇÉê=íç=ÇÉîÉäçé=êçÄìëí=éêçÅÉÇìêÉëK=cçê=Éñ~ãéäÉI=çåÉ=ÅçìäÇ=äççâ=Ñçê=EãçêÉF=êçJ Äìëí=Éëíáã~íçêë=çÑ=î~êáçÖê~ãëI=~åÇ=çåÉ=ÅçìäÇ=Åçåëíê~áå=íÜÉ=ÑáííáåÖ=çÑ=~=î~êáçÖê~ã=ãçÇÉä= Äó=ÑáñáåÖ=íÜÉ=åìÖÖÉí=î~êá~åÅÉK=tÉ=ÜçäÇ=áí=äáâÉäó=íÜ~í=íÜÉ=ëÉÅçåÇ=íÉëí=Ç~í~=Åçåí~áåë=íçç=äáíJ íäÉ=áåÑçêã~íáçå=~Äçìí=íÜÉ=~åçã~äó=íç=êÉäá~Ääó=éêÉÇáÅí=áíë=ëé~íá~ä=ÉñíÉåíK= 5.2 LESSONS LEARNED AND SOFTWARE DESIGN

få= íÜáë= ëíìÇóI= ïÉ= ÉåÅçìåíÉêÉÇ= ~= ëáåÖìä~êáíó= ÇìêáåÖ= íÜÉ= ~ìíçã~íáÅ= ÑáííáåÖ= çÑ= ~= î~êáçÖê~ã= ãçÇÉä=íç=íÜÉ= ë~ãéäÉ=î~êáçÖê~ãK=tÜ~í= ëÜçìäÇ=íÜÉ=ëçÑíï~êÉ=Çç=ïÜÉå=íÜáë=Ü~ééÉåë\=`ìêJ êÉåíäóI= Öëí~í= áëëìÉë= ~= ï~êåáåÖ= ãÉëë~ÖÉX= áí= áë= ëÜçïå= Üçï= ëÅêáéíë= Å~å= ÄÉ= Äìáäí= íç= íìêå= íÜáë= áåíç=~å=Éêêçê=ãÉëë~ÖÉX=~å=Éêêçê=ãÉëë~ÖÉ=ëíçéë=íÜÉ=ëÅêáéí=~åÇ=åç=E~ìíçã~íáÅF=ã~é=ïáää=ÄÉ= éêçÇìÅÉÇK=^=ëáåÖìä~êáíó=~ë=ÑçìåÇ=ÜÉêÉ=áë=åçí=ëéÉÅáÑáÅ=íç=íÜÉ=Öëí~í=ëçÑíï~êÉI=~åÇ=~åó=~ìíçJ ã~íáÅ=ã~ééáåÖ=ëçÑíï~êÉ=ëÜçìäÇ=Å~íÅÜ=áíI=~åÇ=ÇÉ~ä=ïáíÜ=áíK=

11-14

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

fí=ëÜçìäÇ=ÄÉ=åçíÉÇ=íÜ~í=ëáåÖìä~êáíó=ÇìêáåÖ= î~êáçÖê~ã=ãçÇÉä=Ñáí=áë=åçí= ~äï~óë=~=éêçÄJ äÉãW= áå= ëçãÉ= Å~ëÉë= ëéÜÉêáÅ~ä= çê= ÉñéçåÉåíá~ä= ãçÇÉäë= ÅçåîÉêÖÉ= íç= ~å= ÉÑÑÉÅíáîÉäó= äáåÉ~ê= ãçÇÉäI= áå= ïÜáÅÜ= Å~ëÉ= ÑáííáåÖ= íÜêÉÉ= é~ê~ãÉíÉêë= áë= ~= ëáåÖìä~ê= éêçÄäÉã= Äìí= íÜÉ= êÉëìäíáåÖ= î~êáçÖê~ã=ÄÉÅçãÉë=ìëÉÑìäI=áKÉK=áí=Ñáíë=íÜÉ=êÉäÉî~åí=é~êí=çÑ=íÜÉ=ë~ãéäÉ=î~êáçÖê~ãK= ^=äÉëëçå=äÉ~êåÉÇ=áå=íÜáë=ëíìÇó=áë=íÜ~í=åÉÖ~íáîÉ=é~êíá~ä=ëáääë=áå=ÇáêÉÅí=î~êáçÖê~ãë=ëÜçìäÇ= äÉ~Ç=íç=~å=Éêêçê=ãÉëë~ÖÉK=qÜáë=áë=~åÇ=åçï=áãéäÉãÉåíÉÇ=áå=íÜÉ=Öëí~í=oLpJmäìë=äáÄê~êóK=^åJ çíÜÉê= ãÉëë~ÖÉ= áë= íÜÉ= Ç~åÖÉê= íÜ~í= äáÉë= áå= p= ëÅçéáåÖ= êìäÉëW= çÄàÉÅíë= éêÉëÉåí= áå= íçé= äÉîÉä= ÉåîáêçåãÉåíë=Eçê=ëóëíÉã=ÉåîáêçåãÉåíë=áå=íÜÉ=ëÉ~êÅÜ=é~íÜF=~êÉ=îáëáÄäÉ=~ë=ÖäçÄ~ä=î~êá~ÄäÉëK= 5.3 COMPUTING TIME

qÜÉ= ~îÉê~ÖÉ= ÅçãéìíáåÖ= íáãÉ= Ñçê= î~êáçÖê~ã= Åçãéìí~íáçåI= î~êáçÖê~ã= ãçÇÉääáåÖ= ~åÇ= âêáÖáåÖ=éêÉÇáÅíáçå=çÑ=~=ëáåÖäÉ=î~êá~ÄäÉ=çå=UMU=äçÅ~íáçåë=ï~ë=~êçìåÇ=P=ëÉÅçåÇë=çå=~=Odeò= ëí~åÇ~êÇ=ä~éíçéK= CODES

^ää= Åçãéìí~íáçåë= ïÉêÉ= ÇçåÉ= áå= o= EfÜ~â~= ~åÇ= dÉåíäÉã~åI= NVVSX= a~äÖ~~êÇI= NVVUFI= ìëáåÖ= íÜÉ=Öëí~í=é~Åâ~ÖÉ=Ñçê=ÖÉçëí~íáëíáÅ~ä=Åçãéìí~íáçåë=EmÉÄÉëã~I=OMMQFX=íÜáë=é~Åâ~ÖÉ=~äëç=éêçJ îáÇÉë=íÜÉ=pf`OMMQ=Ç~í~K=qç=êÉJêìå=é~êí=çÑ=íÜÉ=~å~äóëáë=~åÇ=êÉéêçÇìÅÉ=ÑáÖìêÉ=NOI=éêçÅÉÉÇ= ~ë= ÑçääçïëW= EáF= Ççïåäç~Ç= oI= EááF= ëí~êí= oI= EáááF= áåëí~ää= é~Åâ~ÖÉ= Öëí~í= Ñêçã= `o^kI= ~åÇ= EáîF= íóéÉ=çå=íÜÉ=o=éêçãéíW= > demo(sic2004)

ANNEX A.1 R SCRIPT

qÜÉ= ÅçãéäÉíÉ= o= ëÅêáéí= Ñçê= íÜÉ= ~ìíçã~íáÅ= ã~ééáåÖX= íÜÉ= íïç= Å~ääë= íç= ÇçKëáÅ= éêçÅÉëë= áåéìí= ~åÇ= àçâÉêK= kçíÉ= íÜ~í= íÜÉ= ÑìåÅíáçå= Åçåí~áåë= íïç= ìåÅçêêÉÅíÉÇ= ÉêêçêëI= åçíÉÇ= Äó= ÄçäÇ= Ñçåí= EëÉÉ=íÉñíFK= # everything after a # sign denotes comments # read input: sic.pred = read.csv("sic2004_out.csv", header=f) names(sic.pred) = c("record", "x", "y") input = read.csv("sic2004_input.csv", header=f) names(input) = c("record", "x", "y", "dayx") joker = read.csv("sic2004_joker.csv", header=f) names(joker) = c("record", "x", "y", "dayx") # define the working function: do.sic = function(sic.input, sic.output) { require(gstat) # remove the unexpected observation: sic.input = sic.input[sic.input$record != 838, ] trend = dayx˜ x # i.e., the model has a constant mean # (error: x should be 1) locations = ˜x+y # names of x and y coordinates width = 2e4 # interval lag width cutoff = 5e5 # cutoff v.sample = variogram(trend, locations, input, width = width, cutoff = cutoff) # (error: input should be sic.input) # initial spherical model for fit: nug=100, p.sill=400,range=4.5e5 initial.model = vgm(psill = 400, mod = "sph", ran = 450000, nug = 100) # fit the nugget, sill and range to the sample variogram: v.fitted = fit.variogram(v.sample, initial.model, fit.method = 2) # the function returns the output from the call to krige():

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

11-15

krige(trend, locations, sic.input, sic.output, model = v.fitted, nmax = 125) } # do the spatial interpolations: output = do.sic(input, sic.pred) joker.output = do.sic(joker, sic.pred) # write output to .csv write.table(output, "sic2004_output.csv", sep=",", col.names=FALSE, row.names=FALSE) write.table(joker.output, "sic2004_joker_output.csv", sep=",", col.names=FALSE, row.names=FALSE)= A.2 INITIAL SUBMISSION

aìêáåÖ=íÜÉ=íÉëí=éÜ~ëÉI=íïç=ÑáäÉë=ïÉêÉ=ã~ÇÉ=~î~áä~ÄäÉ=Ñçê=Ççïåäç~ÇI=áåéìí=~åÇ=àçâÉêK=qç= íÉëí= íÜÉ= ÑìåÅíáçå= ÇçKëáÅEFI= ïÉ= ê~å= íÜÉ= ~î~áä~ÄäÉ= Ç~í~= ~= ÑÉï= íáãÉëI= êÉå~ãáåÖ= íÜÉã= íç= íÜÉ= áåéìí= ~åÇ= àçâÉêK= qÜÉ= êÉëìäíë= ïÉêÉ= ÅÜÉÅâÉÇ= Äó= Åêçëë= î~äáÇ~íáåÖ= íÜÉãI= ìëáåÖ= ~= Å~ää= íç= âêáÖÉKÅî= áåëíÉ~Ç= çÑ= âêáÖÉ= áå= íÜÉ= ÑìåÅíáçå= ÄçÇóI= ~åÇ= íÜÉå= Å~äÅìä~íáåÖ= íÜÉ= ojpbK= ojpb= î~äìÉë=ÑçìåÇ=ïÉêÉ=îÉêó=ÅäçëÉ=íç=íÜÉ=ëã~ääÉëí=î~äìÉë=ÑçìåÇ=áå=ÑáÖìêÉ=U=~åÇ=QI=~åÇ=Ñêçã=íÜáë= áí=ï~ë=ÅçåÅäìÇÉÇ=íÜ~í=íÜÉ=éêçÅÉÇìêÉ=ïçêâÉÇK= kÉñíI= íÜÉ= ÑáäÉë= ïÉêÉ= Ççïåäç~ÇÉÇI= êìå= íÜêçìÖÜ= íÜÉ= ÑìåÅíáçå= ÇÉëáÖåÉÇI= ~åÇ= íÜÉ= êÉëìäíë= ïÉêÉ=ìéäç~ÇÉÇ=Eçê=ê~íÜÉê=Éã~áäÉÇI=ÄÉÅ~ìëÉ=íÜÉ=ìéäç~Ç=ÑìåÅíáçå=ï~ë=åçí=ÑìåÅíáçåáåÖ=óÉíFK= bñÉÅìíáçå=íáãÉ=ï~ë=~Äçìí=T=ëÉÅçåÇëI=~åÇ=åç=Üìã~å=áåíÉêîÉåíáçå=íççâ=éä~ÅÉ=~é~êí=Ñêçã= íÜÉ=Ççïåäç~Ç=Ó=êìå=Ó=êÉíìêå=ÅóÅäÉK= A.3 A MISTAKE

^ÑíÉê= íÜ~íI= çåÉ= ÅçìäÇ= ~êÖìÉ= íÜ~í= íÜÉ= Üìã~å= áåíÉêîÉåíáçå= é~êí= ëí~êíÉÇI= ~åÇ= Äó= íÜ~í= íÜÉ= Éî~äì~íáçå=éÜ~ëÉ=ëí~êíÉÇX=áå=ëçãÉ=ëÉåëÉ=íÜÉ=íÉëí=éÜ~ëÉ=Ü~ë=ÉåÇÉÇK=tÉ=ïáää=ÜçïÉîÉê=åçí=ÄÉ= äççâáåÖ= ~í= íÜÉ= êÉ~ä= Éî~äì~íáçå= éÜ~ëÉ= ÄÉÑçêÉ= íÜÉ= çÄëÉêî~íáçåë= ~í= íÜÉ= UMU= äçÅ~íáçåë= Ü~îÉ= ÄÉÅçãÉ=~î~áä~ÄäÉK=iççâáåÖ=~í=íÜÉ=äÉ~îÉJçåÉJçìí=Åêçëë=î~äáÇ~íáçå=ojpbI=íÜÉ=áåéìí=Ç~í~=ëÉí= Ö~îÉ= ~= î~äìÉ= çÑ= NMKTQI= íÜÉ= àçâÉê= ëÉí= çÑ= NOMI= ãçêÉ= íÜÉå= NM= íáãÉë= ~ë= ÜáÖÜK= `äÉ~êäóI= àçâÉê= Åçåí~áåë=~å=~åçã~äóI=~ë=Å~å=ÄÉ=ëÉÉå=Ñêçã=ÑáÖìêÉ=VK= iççâáåÖ= ~í= íÜÉ= ëìãã~êáÉë= çÑ= éêÉÇáÅíÉÇ= î~äìÉë= ~åÇ= éêÉÇáÅíÉÇ= î~êá~åÅÉëI= áí= íìêåÉÇ= çìí= íÜ~í=íÜÉ=éêÉÇáÅíáçå=î~êá~åÅÉë=ïÉêÉ=Éèì~ä=Ñçê=ÄçíÜ=ëÉíëK=qÜáë=ÅçìäÇ=çåäó=ÄÉ=Å~ìëÉÇ=Äó=íÜÉ= Ñ~Åí=íÜ~í=ÄçíÜ=ïÉêÉ=Ä~ëÉÇ=çå=Éñ~Åíäó=íÜÉ=ë~ãÉ=ÑáííÉÇ=î~êáçÖê~ã=ãçÇÉä=EÄÉÅ~ìëÉ=íÜÉó=Ü~îÉ= íÜÉ=ë~ãÉ=íçéçäçÖóFI=~åÇ=äÉÇ=íç=íÜÉ=ÇáëÅçîÉêó=çÑ=~=ÄìÖ=áå=íÜÉ=ëÅêáéí=ÖáîÉå=íÜÉ=^kkbuW=áå= íÜÉ=ÑìåÅíáçå=ìëÉÇI=áåéìí=ï~ë=é~ëëÉÇ=íç=íÜÉ=î~êáçÖê~ãEF=ÑìåÅíáçåI=áåëíÉ~Ç=çÑ=ëáÅKáåéìíK=qÜÉ= Ç~í~=ëÉí=áåéìí=áë=ÖäçÄ~ääó=îáëáÄäÉ=ÄÉÅ~ìëÉ=áí=ï~ë=~ëëáÖåÉÇ=ÄÉÑçêÉ=íÜÉ=ÑìåÅíáçå=Å~ääK= ^ÑíÉê=ÅçêêÉÅíáåÖ=íÜáë=EÅÜ~åÖáåÖ=áåéìí=áåíç=ëáÅKáåéìí=áå=íÜÉ=Å~ää=íç=î~êáçÖê~ãFI=íÜÉ=ëáåÖìJ ä~ê=î~êáçÖê~ã=Ñáí=ï~ë=çÄí~áåÉÇK= A.4 ERROR CHECKING

^=ÇçKëáÅ=ÑìåÅíáçå=ÇÉÑáåáíáçå=íÜ~í=ïçìäÇ=Ü~îÉ=ÖáîÉå=íÜÉ=êÉëìäíë=ï~åíÉÇI=ëç=Ñ~ê=Ü~ë=íÜÉ=íïç= Éêêçê= ÅÜÉÅâëI= Ñçê= ëáåÖìä~êáíó= ÇìêáåÖ= Ñáí= ~åÇ= Ñçê= åÉÖ~íáîÉ= é~êíá~ä= ëáääëK= få= Å~ëÉ= çÑ= Éêêçê= áí= éêáåíë=~=ÜÉäéÑìä=Éêêçê=ãÉëë~ÖÉI=áåÇáÅ~íáåÖ=ïÜáÅÜ=éêçÄäÉã=çÅÅìêÉÇW=ëáåÖìä~êáíó=çê=åÉÖ~íáîÉ= é~êíá~ä= ëáääI= áí= ëÜçïë= íÜÉ= î~êáçÖê~ã= ÑáííÉÇ= Äó= íÜÉåI= ~åÇ= íÜÉåI= ãçëí= áãéçêí~åíäóI= áí= ëíçéë= ÉñÉÅìíáçåK= do.sic = function(sic.input, sic.output) { require(gstat) sic.input = sic.input[sic.input$record != 838, ] v.sample = variogram(dayx˜1, ˜x+y, sic.input, width = 2e4, cutoff = 5e5)

11-16

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

initial.model = vgm(psill = 400, mod = "Sph", range = 450000, nug = 100) v.fitted = fit.variogram(v.sample, initial.model, fit.method = 2) if (attr(v.fitted, "singular") || any(v.fitted$psill < 0)) { print(plot(v.sample, v.fitted)) stop(paste("could not fit sensible model:", ifelse(attr(v.fitted, "singular"), "singular variogram fit", "negative sills"))) } else krige(dayx˜1, ˜x+y, sic.input, sic.output, model = v.fitted, nmax = 125) }

REFERENCES `Üáä≠ëI=gJmK=~åÇ=aÉäÑáåÉêI=mK=dÉçëí~íáëíáÅëI=ãçÇÉäáåÖ=ëé~íá~ä=ìåÅÉêí~áåíóK=táäÉóI=kÉï=vçêâX=NVVV= a~äÖ~~êÇI=mK=fåíêçÇìÅíçêó=ëí~íáëíáÅë=ïáíÜ=oK=péêáåÖÉêI=_ÉêäáåX=OMMOK= aìÄçáëI=dK=pé~íá~ä=fåíÉêéçä~íáçå=`çãé~êáëçå=VTK=fåíêçÇìÅíáçå=~åÇ=ÇÉëÅêáéíáçå=çÑ=íÜÉ=Ç~í~ëÉíK=fåW= “j~ééáåÖ=o~Çáç~Åíáîáíó=áå=íÜÉ=ÉåîáêçåãÉåíK=pé~íá~ä=fåíÉêéçä~íáçå=`çãé~êáëçåK=NVVTÒK== aìÄçáëI=dKI=j~äÅòÉïëâáI=gKI=aÉ=`çêíI=jK=EbÇëFI=ééK=PVJQQK=bro=OMSST=bkI=lÑÑáÅÉ=Ñçê== lÑÑáÅá~ä=mìÄäáÅ~íáçåë=çÑ=íÜÉ=bìêçéÉ~å=`çããìåáíáÉëI=iìñÉãÄçìêÖX=OMMPK= aìÄçáëI=dKI=d~äã~êáåáI=pK=“fåíêçÇìÅíáçå=íç=íÜÉ=pé~íá~ä=fåíÉêéçä~íáçå=`çãé~êáëçå=Epf`FOMMQ== ÉñÉêÅáëÉ=~åÇ=éêÉëÉåí~íáçå=çÑ=íÜÉ=Ç~í~=ëÉíëÒK=^ééäáÉÇ=dfpX=N=EOFW=MVJMN=íç=MVJNNK= dåÉáíáåÖI=qK=kçåëÉé~ê~ÄäÉI=ëí~íáçå~êó=Åçî~êá~åÅÉ=ÑìåÅíáçåë=Ñçê=ëé~ÅÉJíáãÉ=Ç~í~K=gçìêå~ä=çÑ=íÜÉ= ^ãÉêáÅ~å=pí~íáëíáÅ~ä=^ëëçÅá~íáçåI=VTI=RVMJSMMX=OMMOK= dççî~ÉêíëI=mK=dÉçëí~íáëíáÅë=Ñçê=k~íìê~ä=oÉëçìêÅÉë=bî~äì~íáçåK=lñÑçêÇ=råáîÉêëáíó=mêÉëëX=NVVTK= fÜ~â~I=oKI=dÉåíäÉã~åI=oK=oW=^=i~åÖì~ÖÉ=Ñçê=a~í~=^å~äóëáë=~åÇ=dê~éÜáÅëK=gçìêå~ä=çÑ=`çãéìí~íáçå~ä= ~åÇ=dê~éÜáÅ~ä=pí~íáëíáÅë=REPF=OVVÓPNQX=NVVSK= mÉÄÉëã~I=bKgK=jìäíáî~êá~ÄäÉ=ÖÉçëí~íáëíáÅë=áå=pW=íÜÉ=Öëí~í=é~Åâ~ÖÉK=`çãéìíÉêë=C=dÉçJëÅáÉåÅÉëI=PMW= SUPJSVNX=OMMQK= mÉÄÉëã~I=bKgKI=tÉëëÉäáåÖI=`KdK=dëí~íI=~=éêçÖê~ã=Ñçê=ÖÉçëí~íáëíáÅ~ä=ãçÇÉääáåÖI=éêÉÇáÅíáçå=~åÇ== ëáãìä~íáçåK=`çãéìíÉêë=C=dÉçëÅáÉåÅÉëI=OQ=ENFI=ééK=NTÓPNX=NVVUK= píÉáåI=jKiK=fåíÉêéçä~íáçå=çÑ=ëé~íá~ä=Ç~í~W=ëçãÉ=íÜÉçêó=Ñçê=âêáÖáåÖK=péêáåÖÉêI=kÉï=vçêâX=NVVVK= t~ÅâÉêå~ÖÉäI=eK=jìäíáî~êá~íÉ=dÉçëí~íáëíáÅëI=^å=fåíêçÇìÅíáçå=ïáíÜ=^ééäáÅ~íáçåëK=pÉÅçåÇ=ÉÇáíáçåK= péêáåÖÉêJsÉêä~ÖI=_ÉêäáåX=NVVUK=

Cite this article as: Pebesma, Edzer J. ‘Mapping radioactivity from monitoring data: automating the classical geostatistical approach’. Applied GIS, Vol 1, No 2, 2005. pp. 11-01 to 11-17. DOI: 10.2104/ag050011

Copyright © 2005 G. Edzer J. Pebesma

MAPPING RADIOACTIVITY FROM MONITORING DATA ARTICLES

11-17