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Figure 1. The air quality monitoring network in Lisbon.

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C+"&$#5$9> 9A -$+ 49;;,5$9> ;"%";1 [(f

Figure 3. Daily mean concentration (log-transformed) of NO2 in Lisbon from 1/1/94 to 31/12/98: (a)–(h) s1 (Olivais), s2

(Entrecampos), s3 (Beato), s4 (Chelas), s5 (Rua da Prata), s6 (Casal Ribeiro), s7 (Benfica) and s8 (Av. Liberdade).

Figure 4. Daily mean concentration (log-transformed) of NO2 in Lisbon from 1/1/94 to 31/12/98 after filling in missingobservations: (a)–(h) s1 (Olivais), s2 (Entrecampos), s3 (Beato), s4 (Chelas), s5 (Rua da Prata), s6 (Casal Ribeiro), s7

(Benfica) and s8 (Av. Liberdade).

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8>#" 5@" &-5- -5 5@" "$=@5 ;9#-5$9>1 -+" &"5+">&"& ->&&"1"-19>-;$k"& *. $R"I !S ) "R"I !SI 5@"> 5@" #9%-+$->#"15+,#5,+"1 #R"S ->& !R(SR+S =$%"> $> RfS ->& RLS +"14"#5$%";.#-> *" "15$6-5"& A+96 5@" &"5+">&"& ->& &"1"-19>-;$k"&&-5-D

U<A< H")#$()#*2 *0 )1' "%()#(& .'%'2.'2-'"),/-)/,'?@" 1-64;" #9%-+$->#" *"5M""> %-;,"1 -5 15-5$9>1 "# ->& ":I

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Figure 5. (a) Spatial configuration in G-plane: s1 (Olivais), s2 (Entrecampos), s3 (Beato),s4 (Chelas), s5 (Rua da Prata), s6 (Casal Ribeiro) and s8 (Av. Liberdade). (b) Spatialdispersion versus geographical interpoint distance.

Table I. Observed spatial dispersion for the seven air qualitymonitoring stations

35-5$9> "' "( "2 "G "f "[ "F

"' l"( ([D[( l"2 'fD/J (2DJL l"G (/D[F 2(D[G (LDFf l"f 2'DJL 2FDJ( 2(D([ ([DJG l"[ (LDJJ 2'DFf (GDL2 2GDLF 2GDF' l"F 2'D(/ 2(DJL (JD'F (FD2f 2GDLL 2[DJf l

O94.+$=@5 ! (//( _9@> K$;". ` 39>1I B5&D () *+,%-%,!.#/0 (//(0 MQW [(2b[2(

C+"&$#5$9> 9A -$+ 49;;,5$9> ;"%";1 [(L

#964-+"& 59 5@" 9+$=$>-; ;9#-5$9>1 491$5$9>"& -##9+&$>= 59="9=+-4@$#-; &$15->#"D ?@$1 #-> *" -#@$"%"& *. ,1$>=6,;5$&$6">1$9>-; 1#-;$>=I M@$#@ =">"+-5"1 - 5M9:&$6">:1$9>-; #9:9+&$>-5" +"4+"1">5-5$9> 9A 5@" 1-64;$>= 15-5$9>1M$5@ $>5"+49$>5 &$15->#"1 +"4+"1">5$>= 5@" 1-64;" 14-5$-;&$14"+1$9>D 8>#" 5@" 1-64;$>= 15-5$9>1 -+" +"491$5$9>"&I -5@$> 4;-5" 14;$>" $>5"+49;-5$9> A9+ "-#@ #9:9+&$>-5" #-> *"6-&" 59 4+9%$&" - 6-44$>= *"5M""> 5@" +"4+"1">5-5$9>1 9A5@" 15-5$9>1 $> 5@" 5M9 #9:9+&$>-5" 1.15"61D 85@"+ #9:9+&$>-5"1 M@"+" 4+"&$#5$9>1 -+" >""&"& #-> "-1$;. *" 5+->1:A9+6"& A+96 9>" #9:9+&$>-5" 1.15"6 59 ->95@"+ ,1$>= 5@$1A$55"& 5@$> 4;-5" 14;$>" $>5"+49;-5$9>D 71 $> !"A"+">#" cfdI M"#-;; 5@" 9+$=$>-; #9:9+&$>-5" 1.15"6 5@" ="9=+-4@$#-; 4;->"RZ:4;->"S ->& 5@" 5+->1A9+6"& #9:9+&$>-5" 1.15"6 5@"&$14"+1$9> 4;->" RY:4;->"SD B"5 "# h R8'#I 8(#S *" - 49$>5 $>5@" Z:4;->"D ?@" #9++"149>&$>= Y:4;->" 49$>5 "!# h R;'#I ;(#S $1#-;#,;-5"& *. A$55$>= 5@" 5@$> 4;-5" 14;$>"1W

"0# % #;'#! ;(#$ % # 4'#"#$! 4(#"#$$

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?@" 15+9>= +";-5$9> *"5M""> 5@" 14-5$-; &$14"+1$9> ->& 5@">"M T3E &$15->#" $1 >9M %"+. #;"-+ A+96 )$=,+" [R*SD 7>$195+94$# 96>$&$+"#5$9>-; "Q49>">5$-; 1"6$%-+$9=+-6 $1

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U<U< H")#$()#*2 *0 )1' )'$%*,(& -*$%*2'2)K" -11,6" 5@-5 5@" &"1"-19>-;$k"& 1"+$"1 IR"#I !S h RTR"#I!S ) "R"#I !SI ! h 'I ***I 'F([I # h 'I ***I LS A9;;9M - 15-5$9>-+.6,;5$%-+$-5" 7!R'S 4+9#"11D N9M"%"+I $> 9+&"+ 59 %-;$&-5"5@" 14-5$9:5"649+-; 4+"&$#5$9>1I M" M$;; 69&"; 9>;. 5@" A$%"15-5$9>1 -5 "( RP>5+"#-6491SI "2 RU"-59SI "G RO@";-1SI "[ RO-1-;!$*"$+9S ->& "F R7%D B$*"+&-&"SI ;"-%$>= 9,5 5@" 5$6" 1"+$"19*1"+%"& -5 ;9#-5$9>1 "' R8;$%-$1S ->& "f R!,-&- C+-5-S A9+

Figure 6. (a) Spatial configuration in D-plane: s1 (Olivais), s2 (Entrecampos), s3 (Beato),s4 (Chelas), s5 (Rua da Prata), s6 (Casal Ribeiro) and s8 (Av. Liberdade). (b) Spatialdispersion versus MSI distance. The curve represents the exponential semivariogramfitted to the MSI distance.

Table II. Estimated thin plate splines

= h ' = h (

%#=$/ /D'J /D((

%#=$' 2DGF GDJ2

%#=$( )(D/( )(DFf

&#=$' /D'/ /D'(

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&#=$2 /D/G /D(f

&#=$G )/D/( )/D/[

&#=$f /DGJ /DfG

&#=$[ /D'L /D/f

&#=$F )/Df[ )/Dff

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[(F _D TD T">&"1 ->& XD )D ?,+<6->

%-;$&-5$9>D ?@" ="9=+-4@$#-; 491$5$9>1 9A 5@"1" 15-5$9>1 -+"1@9M> $> )$=,+" LD

C9$>5 4+"&$#59+1 A9+

6#"(! ! ' +$!6#"2! ! ' +$!6#"G! ! ' +$!6#"[! ! ' +$!6#"F! ! ' +$

M$;; A9+6 5@" *-1$1 9A <+$=$>= 59 4+"&$#5 5@" %-;,"1 9A49;;,5$9> ;"%"; 9%"+ -> -+"- M$5@$> 5@" #9:9+&$>-5"1 '''Pb''[DfP ->& 'JfHb(//HI -1 M";; -1 4+"&$#5$>= 5@" 9*1"+%"&%-;,"1 -5 ;9#-5$9>1 "' R8;$%-$1S ->& "f R!,- &- C+-5-S A9+%-;$&-5$>= 5@" 69&";D ?@" =+$& ;9#-5$9>1 -1 M";; -1 5@"15-5$9>1 ,1"& A9+ %-;$&-5$9> -+" 1@9M> $> )$=,+" LD

7 6,;5$%-+$-5" 7!RGS $1 A$55"& 59 5@" &"1"-19>-;$k"& 5$6"1"+$"1 -5 5@" A$%" ;9#-5$9>1 ,1$>= 5@" 19A5M-+" C"15 c[dD ?@"->-;.1$1 9A 5@" +"1$&,-;1 1@9M"& 5@-5 5@" A$55"& 69&"; $1-&"e,-5"D

V< F:!O4=+OHS:=J!8 :JHK4@O4=NF

?@" 14-5$9:5"649+-; 4+"&$#5$9> $1 6-&" ,1$>= 5@" A9;;9M$>=4+9#"&,+"D

'D C+"&$#5 +:15"4:-@"-& 49;;,5$9> ;"%";1 6R"(I !' +SI 6R"2I!' +SI 6R"GI ! ' +SI 6R"[I ! ' +S ->& 6R"FI ! ' +S A9+ &$AA"+">5%-;,"1 9A + ,1$>= 5@" A$55"& 6,;5$%-+$-5" 7!RGS 69&";D

(D U-1"& 9> 5@" "15$6-5"& 1"6$%-+$9=+-6 R''S ->& ,1$>=9+&$>-+. <+$=$>=I 4+"&$#5 5@" %-;,"1 9A 6R"/I !' +S *-1"& 9>5@" 4+"&$#5"& %-;,"1 6> R"(I !' +SI 6> R"2I ! ' +SI 6> R"GI !' +SI6> R"[I ! ' +S ->& 6> R"FI !' +SD

2D ?@" %-;,"1 9A -#5,-; 49;;,5$9> ;"%"; TR"/I ! ' +S -5 "/ #->>9M *" #-;#,;-5"& A9+ 5$6" ! ' + *. -&&$>= 59 6> R"/I ! ' +S5@" 14-5$-; 6"-> A,>#5$9> 6m R"/S ->& 5@" 14-5$9:5"649+-;1"-19>-; #9649>">5 "!#"/! !' +$ =$%"> $> R'/SI ->& 5@"> ;9=:5+->1A9+6$>= *-#< 5@" 1"+$"1D

?@" 4;95 9A 9>":15"4:-@"-& 14-5$9:5"649+-; 4+"&$#5$9>1 A9+5@" M@9;" =+$& A9+ ! h L2' $1 1@9M> $> )$=,+" F0 95@"+ 9>":15"4: -1 M";; -1 +:15"4:-@"-& 4+"&$#5$9> 1,+A-#"1 A9+ &$AA"+">5%-;,"1 9A ! #-> -;19 *" #-;#,;-5"& M$5@9,5 ->. -&&$5$9>-;&$AA$#,;5.D

W< S=KH8 X!84K!O4=N

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711,645$9>1 ' ->& ( $> 3"#5$9> ( >""& 59 *" %-;$&-5"&DN9M"%"+I 5@$1 6-. >95 *" -> "-1. 5-1< 9M$>= 59 5@" A-#5 5@-55@"1" #9>&$5$9>1 +";-5" 59 5@" &"4">&">#" 15+,#5,+" 9A 5@"4+9#"11 *"5M""> 5@" 9*1"+%-5$9> 1$5"1 ->& 95@"+ 1$5"1 M@"+"5@"+" -+" >9 9*1"+%-5$9>1D 711,645$9>1 ' ->& ( #-> *"%-;$&-5"& *. ;99<$>= -5 5@" 4-+5$-; #+911:#9++";-5$9>1 ->&4-+5$-; -,59#9++";-5$9>1 9A 5@" 4+9#"11 -5 9*1"+%"& ->&,>9*1"+%"& 1$5"1D 3$>#" -> "15$6-5" 9A 5@$1 A,>#5$9> #->>95 *"9*5-$>"& 9M$>= 59 5@" ;-#< 9A 9*1"+%-5$9>1 -5 ,>9*1"+%"&

Figure 7. Selected area for modelling and prediction.

Figure 8. One-step-ahead spatio-temporal predictions for thewhole grid for t = 731.

Table III. One-step-ahead spatio-temporal predictions and actualvalues of daily mean concentration (log-transformed) of NO2 for

s1 (Olivais) and s5 (Rua da Prata)

! 6> R"'I !S 6> R"fI !S 6 R"'I !S 6 R"fI !S

L2' 2D2F 2D2F GDGF GD/JL2( 2DF2 2DFL GDL/ 2DJfL22 2DF[ 2DF( 2DG' 2DG'L2G 2D(' 2D2' 2DL/ 2DFGL2f 2DJG 2DLJ 2DFF GD//L2[ 2DJ/ 2DL/ GD[[ GD/2L2L GD2G GD/L fD/J GD2J

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Figure 9. One-step-ahead spatio-temporal predictions, confidence intervalsand actual values of daily mean concentration (log-transformed) of NO2 for s1

(Olivais) and s5 (Rua da Prata).

Table IV. Summary of prediction results for leave-two-outvalidation

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