P. 1



# OAR Box 1126 Prepped byOllie Stewart



### Document

Number: 

# 26 ) 11-1-14

8 Docket Number: 

# A-83-2 2

Printed 4/18/20089:58:22 AM

Sheet 26 of 182P. 2 

# USB. * tPBO ^ 

## y UNITE D STATE S ENVIRONMENTA LPROTECTIO N AGENC Y Offic e ofAi rQualityPlannin g an d Standard s Researc h Triangl e Park , Nort h Carolin a 2771 1

1 3 AP R 198 9

MEMORANDU

M SUBJECT : FROM : Alternativ e Form s o f a Revise d NAAQ S fo r Lead

Nei l Frank "/itU

" &*-'' Bo bFaor o 0f(r

<$&#*"' Dat a Analysi s Sectio n (MD-14 ) TO : John Haines , Chie f

Standard s Developmen t Sectio n B (MD-12 ) Attache d i s ou r revise d repor t "Evaluatio n o f Alternativ e Form s o f a Revise d NAAQ S fo r Lead" , whic hwa s reference d a s a Decembe r draf t i n th e OAQP S Draf t Staf f Pape r fo r Lead (March , 1989) . Ou r report , date d Apri l 1989 , doe s no t contai n an y change s t o th e conclusion s presente d earlier . However , th e bod y o f th e repor t contain s some ne wmateria l an d graphs . Specifically , i t contain s additiona l discussio n o f a monthl yfor m base d o n th e secon

d highes t monthl yaverag e pe r year . A s yo u know , thi s i s alread yreflecte d i n th e Staf f Paper . Ou r repor t als o contain s some additiona l clarifying materia l suggeste d b y yo u an d you r staff . I n particular , i t reflect s th e though t provoking comment s provide d b yGai l Bryon . Attachmen t cc : B . Laxto n (w/ o attachment ) B . Hun t T . Curra n N . Ber g G . Bryo n J . Cohe nP. 3

EVALUATIONO F ALTERNATIVE FORM S O F AREVISE D NAAQ S FOR LEA D Nei l Frank and Bo bFaor o Apri l 198 9 INTRODUCTION Whil e th e curren t Lead (Pb ) standar d i s expresse d a s a quarterl yaverage , no t t o b e exceeded , th e ne whealt hdat a supporting a shorte r equilibriu mtime betwee n th e individua l an d thei r P bcontaminate d environment , sugges t tha t sensitiv e population s shoul d b e protecte d agains t monthl yaverag e concentrations . I n thi s report , severa l alternativ e form s o f a revise d NAAQ S fo r P bar e examined , al l o f whic hemphasiz e pea k monthl yaverag e concentrations . Th e analyse s ar e conducte d independen t o f a specifi c concentratio n leve l fo r th e standard . Eac hfor

mwa s base d o n statistic s compute d during a three-yea r perio d t o b e consisten t wit hth e multi-yea r forma t adopte d fo r ozon e and particulat e matte r NAAQSs . I f attainmen t wa s onl ybase d o n a singl e year' s data , a n are a coul d alternat e betwee n attainmen t an d nonattainmen t o n a n annua l basis . Thus , a three-yea r perio d i s use d t o provid e stability , additiona l monitoring dat a an d additiona l confidenc e i n th e determinatio n o f NAAQ S attainment . Si xalternativ e monthl yaverag e NAAQ S form s ar e considered : 1 . Maximu

mmont h 2 . Expecte d maximu mcalenda r mont h 3 . Expecte d maximu mmont h 4 . Expecte d highes t thre e month s 5 . Secon

d highes t mont h 6 . Maximu

msecond highes t mont hpe r yea r Th e firs t fou r form s wer e previousl youtline d i n th e 198 5 mem o entitle d "Compariso n o f Fou r Alternativ e Lead Ai r Qualit yStandard s Using Modelle d Dat a a t a SecondaryLead Smelte r an d a Battery Plant" , (Octobe r 22 , 1985) , an d wil l no t b e describe d i n detai l here . Numbe r 1 (Maximu mmonth ) i s deterministic , an d i s simila r t o th e curren t quarterl yform . Th e nex t thre e form s ar e statistica l i n nature , tha t theydefin e expecte d value s derive d fromaverage s o f annua l values . Thes e form s ar e base d o n average s o f individua l monthl yaverages . Th e las t tw o form s ar e als o deterministic , bu t ar e base d o n a secon d highes t observe d monthl y average . Th e maximu

mmont hfor

mi s th e mos t stringen t o f al l possibl e monthl yforms . Wit hthi s form , th e standard woul d b e exceede d mor e ofte n an

d woul d requir e mor e emissio n reductio n t o achieve . I t obviousl ywoul d provid e th e greates t degre e o f healt hprotection . However , maximu

m values , no t t o b e exceeded , ar e judge d t o b e statisticall ydifficul t t o achieve ; theyd o no t allowfo r rar e condition s i n whic hhighconcentration s can b e observed . Wit hth e expecte d valu e form s an d th e secon

d maxforms , allowanc e i s mad eP. 4

fo r suc hexceedances . Wit hth e expecte d maximu mforms , th e impac t o f on e o r tw o highmonthl yaverage s ar e reduce d b yaveraging wit h othe r lowe r monthl yaverag e concentrations . Wit hth e second ma x forms , th e highes t mont hi s simpl yno t considered . Th e firs t o f thes e secon

d maxform s (numbe r 5) , terme d th e secon d highes t monthl yaverag e i n thre e years , explicitl yallow s fo r on e monthl y exceedanc e i n thre e years . Th e nex t second ma xfor m(numbe r 6) , terme d th e maximu

msecond highes t mont hpe r year , i s les s stringen t an d allow s on e exceedanc e eac hyea r (u p t o thre e i n thre e years) . I t i s primaril yinclude d i n thi s examinatio n o f alternativ e standard s becaus e othe r shor t termstandard s (eg . TSP , S02 , CO ) hav e bee n expresse d wit hthi s form . I n orde r t o evaluat e th e statistica l characteristic s o f eac h form , tw o type s o f analyse s wer e conducted . First , a compute r simulatio n wa s performed , usin g generate d dail yP bconcentrations , ove r a three-yea r period . Thi s permitte d th e examinatio n o f a wid e rang e o f possibl e dat a set s wit hidentical , know n characteristics . Th e second typ e o f analysi s involve d th e examinatio n o f actua l P b dat a observe d a t poin t sourc e oriente d sites . Thi s second analysi s provide d additiona l perspectiv e fo r currentl ymonitore d situation s and verificatio n o f th e hypothetica l results . Al l o f th e comparison s ar e base d o n th e statisti c wit hwhic h attainmen t woul d b e judged . Thi s i s th e so-calle d desig n valu e (als o calle d th e desig n concentration) . Whe n thi s statisti c i s les s than , o r equa l to , th e concentratio n leve l o f th e NAAQS , th e dat a woul d indicat e attainmen t wit hth e NAAQ S fo r th e three-yea r perio d considered . Th e desig n valu e als o reflect s th e amoun t o f ai r pollutio n contro l necessaryt o attai n th e standard . A s use d i n thi s evaluation , a s th e design valu e increases , th e stringenc y o f th e standar d als o increase s du e t o th e nee d fo r mor e control . Mos t o f th e result s ar e presente d a s relativ e values , normalize d t o th e expecte d maximu mmonthl yaverag e concentration . B yusin g a referenc e indicato r an d presenting th e result s a s relativ e values , th e conclusion s ar e independen t o f th e concentratio n leve l selecte d fo r th e standard . DISCUSSIONAND CONCLUSION S Suggeste d Form . Amon g th e alternativ e form s examined , th e for mbase d o n th e second highes t monthl yvalu e i n thre e year s i s suggeste d fo r a revise d P bNAAQS , becaus e i t i s eas yt o comprehend an d doe s no t involve an yfancystatistica l calculations . Although thi s for

mi s les s stringen t tha n th e maximu mmonthl yvalue , i t produce s design value s comparabl e t o th e expecte d maximu mmonthl y value . Wit hthi s second ma xform , a t mos t on e monthl yvalu e i n a three-yea r perio d woul d b e permitte d t o excee d th e state d leve l o f th e NAAQS . Th e exceedance s coul d occur i n adjacen t month s o r i n separat e years . I n thi s way , i t allow s fo r explici t discounting o f on e "bad " mont hwhic hmayb e caused , fo r exampl e b yunusua lP. 5

fo r suc hexceedances . Wit hth e expecte d maximu mforms , the impac t o f on e o r tw o highmonthl yaverage s ar e reduce d b yaveraging wit h othe r lowe r monthl yaverag e concentrations . Wit hth e secon d max forms , th e highes t mont hi s simpl yno t considered . Th e firs t o f thes e secon

d maxform s (numbe r 5) , terme d th e secon d highes t monthl yaverag e i n thre e years , explicitl yallow s fo r on e monthl y exceedanc e i n thre e years . Th e nex t second maxfor m(numbe r 6) , terme d th e maximu

msecond highes t mont hpe r year , i s les s stringen t an d allow s on e exceedanc e eac hyea r (u p t o thre e i n thre e years). . I t i s primaril yinclude d i n thi s examinatio n o f alternativ e standard s becaus e othe r shor t ter mstandard s (eg . TSP , S02 , CO ) hav e bee n expresse d wit hthi s form . I n orde r t o evaluat e th e statistica l characteristic s o f eac h form , tw o type s o f analyse s wer e conducted . First , a compute r simulatio n wa s performed , using generate d dail yP bconcentrations , ove r a three-yea r period . Thi s permitte d th e examinatio n o f a wid e rang e o f possibl e dat a set s wit hidentical , know n characteristics . Th e second typ e o f analysi s involve d th e examinatio n o f actua l P b dat a observe d a t poin t sourc e oriente d sites . Thi s secon d analysi s provide d additiona l perspectiv e fo r currentl ymonitore d situation s and verificatio n o f th e hypothetica l results . Al l o f th e comparison s ar e base d o n th e statisti c wit hwhic h attainmen t woul d b e judged . Thi s i s th e so-calle d design valu e (als o calle d th e design concentration) . Whe n thi s statisti c i s les s than , o r equa l to , th e concentratio n leve l o f th e NAAQS , th e dat a woul d indicat e attainmen t wit hth e NAAQ S fo r th e three-yea r perio d considered . Th e desig n valu e als o reflect s th e amoun t o f ai r pollutio n contro l necessaryt o attai n th e standard . A s use d i n thi s evaluation , a s th e desig n valu e increases , th e stringenc y o f th e standar d als o increase s du e t o th e nee d fo r mor e control . Mos t o f th e result s ar e presente d a s relativ e values , normalize d t o th e expecte d maximu mmonthl yaverag e concentration . B yusing a referenc e indicato r an d presenting th e result s a s relativ e values , th e conclusion s ar e independen t o f th e concentratio n leve l selecte d fo r th e standard . DISCUSSIONAND CONCLUSION S Suggeste d Form . Among th e alternativ e form s examined , th e for mbase d o n th e secon d highes t monthl yvalu e i n thre e year s i s suggeste d fo r a revise d P bNAAQS , becaus e i t i s eas yt o comprehend , doe s no t involve an yfancystatistica l calculations . Althoughthi s for mi s les s stringen t than th e maximu mmonthl yvalue , i t produce s design value s comparabl e t o th e expecte d maximu m monthl yvalue . Wit hthi s second maxform , a t mos t on e monthl yvalu e i n a three

yea r perio d woul d b e permitte d t o excee d th e state d leve l o f th e NAAQS . Th e exceedance s coul d occu r i n adjacen t month s o r i n separat e years . I n thi s way , i t allow s fo r explici t discounting o f on e "bad. " mont hwhic hmayb e caused , fo r exampl e b yunusua lP. 6

meteorology . Thi s approac hi s mor e stringen t than th e alternativ e maximimu

m secon d maxfor

mi n whic hon e monthl yexceedanc e i s allowe d i n eac han

d everyyear . Th e suggeste d standar d woul d b e state d "deterministically" , i n term s o f a three-yea r perio d wit hn o mor e than on e monthl y averag e exceedance . I t i s deterministi c i n th e sens e tha t th e observe d dat a explicitl ydetermine s th e attainmen t status . Becaus e th e secon

d ma xfor

mignore s th e magnitud e o f th e highes t averag e monthl yvalu e (i n thre e years) , healt hprotectio n agains t wors t cas e exposur e woul d no t b e explicitl yincorporate d int o th e for m o f th e standard . However , additiona l protectio n fro m highaverag e concentration s coul d b e provide d b ya significan t har mlevel . Precisio n vs . Sampling Frequency . Sinc e attainmen t i s t o b e base d o n pea k monthl yaverages , th e precisio n o f th e monthl y averag e P bconcentration s i s critical . Thi s i s because , wit h imprecision , pea k value s selecte d froma se t o f dat a tend t o b e overestimated . On e sourc e o f imprecisio n i s measuremen t error . Anothe r sourc e i s incomplet e sampling . Although , average s o f measuremen t concentration s hav e les s measuremen t erro r tha n individua l 24-hou r samples , thes e error s stil l persis t wit hsmal l sampl e sizes . Wit honc e i n si xday(1/6) , o r eve n everyothe r day (1/2 ) sampling (couple d wit hth e inevitabl e missing samples) , monthl yaverage s woul d b e base d o n fewvalues . Fo r example , ther e woul d b e a t mos t 5- 6 value s wit h1/ 6 sampling . Consequentl ysuc h average s woul d b e highl yvariabl e (imprecise) , causing th e potentia l fo r highe r tha n norma l monthl yaverag e concentratio n estimates . Th e pea k value s selecte d from thes e highl yvariabl e monthl yaverage s woul d yiel d overestimate s o f th e tru e pea k averag e concentrations . Th e simulatio n analyse s confirme d this , an d showe d verylarg e overestimate s i n desig n concentration s ar e possibl e wit h 1/ 6 sampling , an

d moderat e overestimate s ar e stil l possibl e eve n wit h1/ 2 sampling . Therefore , incomplet e sampling doe s no t appea r t o b e a viabl e monitoring strateg ywit hwhic ht o judg e attainment/nonattainmen t wit ha pea k monthl yaverag e NAAQ S fo r P b fo r an ycas e clos e t o th e standard . Recommende d Sampling Frequency . Everydaysampling i s viewe d a s being highl ydesireable , an d i s generall yrecommende d i n orde r t o judg e attainmen t / nonattainmen t fo r a revise d P bNAAQS . T o reduc e imprecisio n o f th e monthl yaverag e concentrations , genera l minimu mdat a completenes s criteri a (say , 7 5 percent ) woul d als o b e neede d an

d shoul d b e explicitl ystate d i n th e NAAQS . Nevertheless , attainmen t o r nonattainmen t coul d stil l b e determine d wit hles s precis e estimate s fo r thos e case s i n whic hth e tru e pea k average s wer e sufficientl yfa r fro mth e leve l o f th e NAAQS . Thi s coul d b e handled , a s exceptions , on a case-by-cas e basis . Thes e analyse s sugges t tha t everyda ysampling an

d highes t dat a captur e woul d onl y b e neede d whe n th e tru e design valu e i s withi n a facto r o f tw o o f th e NAAQ S level ; thi s wil l maintai n error s o f attainment/nonattainmen t misclassificatio n belo w5 percent . Finally , wher e comparison s t o th e NAAQ S o n a site-by-sit e basi s ar eP. 7

no t important , incomplet e sampling coul d als o b e utilized . Fo r example , fo r thos e roadwayP bsite s no t expecte d t o violat e th e NAAQS , 1/ 6 sampling woul d b e sufficien t t o continu e th e stud yo f aggregat e nationa l trend s i n averag e concentration s a t thes e locations .

COMPUTE R SIMULATION S Dat a usage . P bconcentratio n distribution s derive d from actua l sourc e oriente d monitoring site s wer e use d a s th e generating model s fo r th e simulations . Dat a i n th e vicinit yo f an ASARC O refineryi n Omaha , Nebrask a an d a lead oxid e manufacture r i n Philadelphi a wer e used . I n bot hcases , everydaysampling wa s performe d a t P bmonitoring sites , permitting th e estimatio n o f th e underlying concentratio n distribution . Th e simulatio n analyse s wer e primaril yuse d t o examin e th e relativ e stringencyamong th e alternativ e forms , an d th e potentia l effect s o f incomplet e sampling . Th e simulatio n analyse s als o considere d some effect s o f th e underlying concentratio n distributio n an d seasonality . Th e simulatio n analyse s ar e base d o n 5 0 - 10 0 set s o f 108 0 values , eac h se t representing thre e year s o f simulate d P bdata . Th e smalle r simulation s wer e use d t o explor e th e mor e specialize d dat a case s an d ar e onl ybase d o n 5 0 set s i n orde r t o reduc e compute r costs . Relativ e Stringency . Th e firs t simulatio n analysi s examine d th e relativ e stringenc yo f eac hpotentia l for m i n term s o f averag e design values . Fo r thes e comparisons , th e concentratio n distributio n show

n i n Figur e 1 wa s assumed . Th e lowe r par t o f th e distributio n i s lognormal 1 an d th e uppe r tai l i s normal 2

. Th e shap e o f thi s distributio n wa s derive d fromactua l dail y198 4 P b concentration s i n th e vicinit yo f a n ASARC O lead refinery , a s reporte d b

yth e Stat e o f Nebrask a during thei r highconcentratio n month s o f Apri l t o November . Th e sit e i s locate d a t Abot t Drive . Th e 198 4 maximu

m monthl yaverag e concentration , 3.8 6 p.g/m 3 , wa s recorde d i n September . Withi n eac hmonth , th e concentration s wer e assume d t o b e independen t an

d wer e randoml ygenerate d fro m th e specifie d concentratio n distribution . Th e resulting averag e design value s fo r th e si xalternativ e form s ar e presente d i n Tabl e 1 . Ratio s t o th e referenc e indicato r o f th e expecte d annua l maximu mmont h (three-yea r average , optio n 3 ) ar e als o presented . Th e design value s fro mth e alternativ e three-yea r form s rang e fro m2.9 7 t o 3.8 9 \iq/vui i, wit hth e maximu mmont hi n thre e year s

1 m , = 0.8 ; sg

d = 4 2 | i = -2 ; a= 7. 4P. 8

yielding th e highes t valu e an d th e maximu

mthree-yea r calenda r mont hyielding th e lowes t value . Thes e ar e 1 1 percen t abov e an d 1 5 percen t belo wth e referenc e indicator , respectively . Th e maximu m annua l secon

d highmont hproduce s a relativel ylowvalu e o f 3.0 9 p.g/m 3

. Th e othe r thre e alternatives , including th e referenc e indicator , yiel d simila r value s whic har e eac hwithi n 3 percen t o f eac hother . Among thes e thre e "middle " indicators , th e simples t i s th e secon

d maximu

mmont hi n thre e years . Thi s statisti c correspond s t o a standar d whic hallow s a singl e exceedanc e o f a monthl yaverag e P bleve l i n a thre e yea r perio d an d i s a deterministi c form . Th e othe r tw o form s - averag e o f th e thre e highmonth s an

d th e averag e o f th e annua l maxmont h- ca n b e expresse d a s statistica l (ie . expecte d value ) standards . Thi s propert yi s desireabl e sinc e attainmen t can b e judged o n th e basi s o f mor e tha n thre e year s o f data , whic hi s perhap s mor e usefu l fo r modeling whic hi s typicall ybase d o n 5 year s o f data . Th e us e o f mor e tha n thre e year s o f dat a i s als o usefu l t o hel p adjus t fo r th e effec t o f a n unusua l month . Wit hth e three-yea r deterministi c form , however , th e numbe r o f monthl yaverag e value s abov e th e specifie d concentratio n leve l fo r th e standard withi n a specifie d (i.e . three-year ) time perio d i s known an d th e design concentratio n i s actuall yobserved/measured . Thi s propert yi s verydesireable , permit s th e standar d t o b e simpl e and easil yunderstood . Effec t o f Incomplet e Sampling . Th e nex t simulatio n analysi s examine d th e effec t o f incomplet e sampling o n th e estimatio n o f desig n values , agai n b yusin g th e concentratio n distributio n representing th e dat a fromth e ASARC O plant . Fo r eac hsimulatio n o f th e si xalternativ e form s o f th e NAAQS , monthl yaverag e value s wer e als o generate d fo r subsample s corresponding t o everyothe r dayan d everysixt hdaysampling . Wit hever ysixt hdaysampling , eac hmonthl yaverag e wa s base d o n 5 generate d values ; wit hevery othe r da

ysampling , eac hmonthl yaverag e wa s base d on 1 5 values . Tabl e 2 present s th e result s i n term s o f th e averag e design values . Fo r eac halternativ e form , th e averag e design valu e increase s wit hles s complet e sampling . Thi s resulting averag e design valu e "bias " i s a consequenc e o f (1 ) th e focu s o n th e pea k monthl yaverag e concentration s (i n thi s case , th e secon d highes t month) , an

d (2 ) th e large r variabilit yi n potentiall yobservabl e monthl yaverage s whic har e th e produc t o f fewe r samples . Du e t o thi s genera l effect , tru e attainmen t site s coul d appea r t o b e nonattainmen t (s o calle d fals e positive) , unles s some adjustmen t coul d b e mad e t o th e standar d level . Sinc e thi s typ e o f adjustmen t woul d depend o n a variet yo f sit e specifi c factor s including th e variabilit yo f P bconcentration s a t a P bsite , an d thes e factor s ar e differen t among sites , a universa l adjustmen t woul d no t b e possible . Althoughth e averag e design value s increas e wit hles s complet e sampling , some chanc e fo r attainmen t misclassificatio n (fals e negative ) als o exists . Th e chanc e fo r fals e negatives , however , i s i n genera l considerabl yles s than the chanc e fo r fals eP. 9

positives . Wit hincomplet e sampling , th e relativ e ranking among th e si x alternative s remain s th e same . Th e following discussio n no w focuse s mor e closel yo n th e effec t o f incomplet e sampling , using th e for m base d o n th e second maximu mmonthl yvalu e i n thre e years . Fo r th e sak e o f brevity , thi s design valu e wil l simpl yb e calle d th e three-yea r design value . Wit hincomplet e sampling , th e averag e three-yea r design value s wer e 1 8 an

d 5 7 percen t highe r wit heveryothe r an d everysixt hday sampling , respectively . Th e rati o distributio n o f incomplet e t o complet e sampling desig n value s i s illustrate d i n Figur e 2 , usin g box-plots . Wit h1/ 6 sampling , th e entir e box-plo t i s greate r tha n one . I n fact , th e probabilit yi s 0.9 8 tha t th e everysixt hday desig n valu e i s greate r tha n th e complet e sampling design value . Thi s i s th e chanc e fo r nonattainmen t misclassification . Th e 95t h percentil e o f thi s rati o distributio n i s approximatel ytwo . Therefore , unti l th e 1/ 6 design valu e i s twic e th e standar d level , i t woul d no t b e a statisticall ysignifican t violatio n (a t th e 5 % significanc e level) . Anothe r interpretatio n o f thes e dat a i s tha t i f a "true " attainmen t desig n valu e wa s greate r tha n on e hal f th e leve l o f th e NAAQS , th e chanc e o f appearing t o b e nonattainmen t woul d excee d 5 percent . I n othe r words , wit hmonthl yaverage s generate d b

y1/ 6 sampling , a larg e rang e o f possibl e value s ar e statisticall yindistinguishabl e fromth e standar d level . Wit h1/ 2 sampling , th e rang e o f uncertai n value s i s muc hsmaller , bu t nevertheles s stil l exists . A s show n i n Figur e 2 , th e chanc e tha t th e 1/ 2 design valu e i s greate r tha n th e complet e sampling valu e i s 0.9 0 (chanc e fo r fals e positive) . Th e smalles t valu e tha t i s a statisticall ysignifican t violatio n o f th e NAAQ S woul d hav e t o b e 3 6 percen t highe r tha n th e standar d level . Finally , th e chanc e fo r nonattainmen t misclassificatio n wit h1/ 2 da ysampling exceed s .0 5 whe n th e tru e attainmen t design valu e i s greate r than 7 4 percen t o f th e NAAQ S level . Effec t o f underlying distributiona l model . Th e bia s cause d b yincomplet e sampling wa s studie d fo r severa l underlying distributiona l models . Th e concer n wa s tha t th e wid e rang e o f uncertaint yi n 1/ 6 an d eve n 1/ 2 sample s coul d b e a functio n o f th e withi n mont hvariabilit ycharacteristi c o f th e underlying ASARC O distribution . I n orde r t o determin e othe r appropriat e distribution s fo r furthe r study , almos t complet e everyda yP bdat a fro

ma monitoring sit e i n Philadelphi a wa s selected . Thi s sit e i s i n th e vicinit yo f a lead oxid e manufacturer . Th e concentratio n distributio n fro

mthi s sit e can b e closel yapproximate d b ya lognorma l distributio n (a ) wit hm , = 0.3 4 an d sgd = 2.3 . Tw o additiona l lognorma l distribution s wer e als o considered , wit hth e following geometri c mean s an d standar d geometri c deviations : (b ) m=.10 , sgd=2.3 ; (c ) m, = .10 , sgd=4. 0P.1 0

Thes e tw o distribution s wer e include d t o explor e the effect s o f chang e i n concentratio n (i.e . m, ) an d chang e i n variabilit y(i.e . sgd) , separately . Afourt hdistributio n t o b e considere d wa s anothe r "hybrid " distribution , whos e lowe r portio n ha s lognorma l parameter s m,=.32 , sgd=4.3 ; an d whos e uppe r tai l correspond s t o a norma l wit hp . = 7. 2 an d a= -7.2 . Thi s distributio n represent s lowconcentratio n month s observe d i n th e vicinit yo f th e ASARC O plant . Thes e distribution s wer e selecte d i n orde r t o represen t a wid e rang e o f condition s possibl e a t P bpoin t sources . Th e result s o f th e simulatio n usin g thes e distribution s ar e presente d graphicall yfo r 1/ 6 an d 1/ 2 sampling i n Figure s 3 an d 4 , respectively . Tw o statistic s o f interes t ar e summarize d i n Tabl e 3 : (1 ) th e averag e rati o o f 1/ 6 design valu e t o tha t o f complet e sampling an d (2 ) th e 95t hpercentil e "critica l value " use d t o defin e statistica l significanc e fo r nonattainmen t determination . Th e result s fo r th e fou r ne wdistribution s bracke t thos e presente d earlier . Tw o distribution s yiel d lowe r ratio s (les s bias ) an

d tw o distribution s yiel d highe r ratio s (mor e bias) . Th e leas t bia s correspond s t o th e underlying distributio n wit hth e lowes t concentration s (m,=0.10 , sgd=2.3) . Here , th e critica l valu e fo r statistica l significanc e i s 1. 7 (i.e . 17 0 percent) . Th e bia s increase s wit haverag e concentration , an d eve n mor e wit hgreate r withi n mont hvariability . Th e highes t critica l valu e fo r statistica l significanc e i s 2. 6 (i.e . 26 0 percent) . Acrud e indicato r o f th e potentia l fo r bia s i s th e rati o betwee n th e pea k monthl yvalue s an

d th e overal l (annual ) averag e concentration . Fo r thes e las t four simulations , thi s rati o wa s 1. 4 fo r th e distribution s corresponding t o les s bia s an d th e rati o wa s 1.7-1. 8 fo r th e distribution s generating mor e bias . Fo r th e simulatio n discusse d a t th e beginning o f thi s paper , thi s rati o wa s 1.5 . Correspondingly , th e result s fo r 1/ 2 sampling showles s bia s wit hth e sam e underlying distributions . I n th e bes t case s studied , th e averag e bia s wa s reduce d t o 1.0 8 ( 8 percent) , wit ha critica l valu e o f 1.2 7 (2 7 percent) . Thu s misclassificatio n error s excee d .0 5 whe n th e sit e i s greate r tha n 8 0 percen t o f th e NAAQS . Thes e result s ar e simila r t o thos e presente d earlier. . Effec t o f Seasonality . Th e nex t simulatio n analysi s examine d th e effec t o f seasona l P bconcentration s o n th e observe d bia s i n pea k monthl ystatistics . Th e result s indicat e a reductio n i n bia s wit hseasona l difference s i n P bconcentrations , bu t th e improvemen t depend s o n th e lengt ho f season , concentratio n gradients , a s wel l a s withi n mont hconcentratio n distribution . Sinc e th e bia s i n pea k monthl ystatistic s i s cause d b yth e imprecisio n o f estimate d monthl yaverag e concentrations , seasonalit yi n P bconcentration s affect s th e numbe r o f month s wit hP.1 1

potentia l fo r observe d peak monthl yaverages . Whe n ther e ar e fewe r month s wit hpotentia l fo r highvalues , the n th e bia s introduce d b yincomplet e sampling can b e less . Tw o analyse s wer e performe d t o illustrat e thi s phenomenon . Seasona l model s wer e employe d wherei n dat a wer e generate d fro m on e concentratio n distributio n fo r par t o f th e yea r an d froma differen t distributio n fo r th e othe r part . Thes e analyse s wer e firs t performe d i n term s o f th e lognorma l distribution s (a ) an d (b) , an

d th e tw o "hybrid " distribution s describe d earlier . Th e gradient s i n averag e concentratio n betwee n th e highan

d lowseason s ar e 3.6: 1 an d 2.5:1 , respectively . Thes e tw o case s ar e use d t o mode l larg e seasonalit yan d moderat e seasonality . Th e result s o f thes e analyse s ar e presente d i n Figure s 5 and 6 , wher e statistic s describing th e ratio s o f 1/ 6 sample d design valu e t o th e complet e sample d valu e ar e presente d b yth e numbe r o f month s wit hth e highconcentratio n season . Figur e 5 display s th e 95t hpercentil e o f th e rati o distributio n (i.e . critica l valu e fo r statistica l significance) . Figur e 6 present s th e probabilit yo f exceeding , an

d no t exceeding , th e tru e design value . Th e result s fo r 1/ 2 sampling displaye d simila r pattern s an d ar e no t presented . Th e result s o f thes e seasona l analyse s fo r 1/ 6 sampling sho w that : (1 ) th e positiv e desig n valu e bia s wa s generall yobserved , although i t disappeare d fo r th e mos t extreme cas e - a singl e high concentratio n mont hcombine d wit hth e large r seasona l concentratio n gradient . (2 ) A s th e lengt ho f th e P bseaso n increases , pea k monthl yvalue s an d relativ e bia s increase , unti l approximatel y8 month s whe n a leveling of f occurs . (3 ) Th e chanc e fo r exceeding th e tru e design valu e (fals e positive ) wa s generall ylarge . Th e probabilit yfo r no t exceeding th e tru e valu e (fals e negative ) increase d wit hfewe r tru e highconcentratio n months , an

d wit hth e large r seasona l concentratio n gradient . Fo r th e hybri d distribution s representing th e moderat e seasona l concentratio n gradient , th e larges t probabilit yo f no t exceeding th e tru e design valu e wa s 0.1 4 fo r th e singl e highmont hcase . (4 ) Wit hth e large r concentratio n gradien t wit hth e tw o lognormals , th e chanc e fo r no t exceeding th e tru e design valu e wa s larger , bu t stil l les s tha n 0.1 0 wit h6 o r mor e month s wit hhigh concentrations . I t als o increase d wit hfewe r highconcentratio n months , an

d ultimatel yachieve d a fals e negativ e probabilit yvalu e o f 0.6 5 fo r th e extreme cas e wit ha singl e highconcentratio n month . Thi s wa s becaus e wit hth e highe r seasona l concentratio n gradient , th e highseaso n wa s les s likel yt o produc e a maximu m monthl yconcentratio n greate r tha n th e tru e maximu m monthl yvalue .P.1 2

EXAMINATIONO F ACTUAL P B DAT A Al l poin t sourc e oriente d lead monitoring sites , whic hhad violation s o f th e presen t lead standar d i n mor e tha n on e calenda r yea r i n th e 1985-198 7 time period , wer e selecte d fo r comparison s t o th e si xalternativ e form s o f th e revise d P bNAAQS . Te n site s fromseve n differen t State s wer e selecte d fo r thes e comparisons . Thes e site s includ e th e ASARC O an d lead oxid e manufacture r discusse d earlier . I n orde r t o comput e th e design valu e statistic s fromavailabl e data , tw o ou t o f th e thre e year s ha d t o b e available . Th e result s ar e presente d i n Tabl e 4 an d Figure s 7 , an

d confirmth e relativ e stringenc yfinding s develope d fromth e compute r simulation . Figur e 7 show s th e averag e design value s fo r eac halternativ e for mexpresse d a s a rati o t o th e expecte d maximu mmonth . Th e result s sho wtha t th e mos t stringen t i s th e maximu mmont hform , whic hi s als o th e mos t sensitiv e t o a singl e "atypical " month . Th e rati o show

n i s 1.3 1 fo r thi s for mo f th e standard . Th e nex t mos t stringen t i s th e expecte d maximu mthre e months , whos e rati o i s 1.0 7 o r 7 percen t highe r tha n th e expecte d maximu m month . Th e averag e design valu e fo r th e second highes t mont hi n thre e year s i s onl y slightl yhighe r tha n th e expecte d maximu mmont h- th e rati o i s 1.01 . Th e maximu

msecond highes t mont hpe r yea r an d th e expecte d maximu mcalenda r mont hwer e th e leas t stringent , wit hratio s o f 0.8 6 an d 0.73 , respectively .P.1 3

Tabl e 1 . Relativ e stringenc yo f alternat e form s o f a monthl yNAAQ S fo r Pb , base d or

i a simulatio n o f P bdat a i n th e vicinit yo f ASARC O P brefiner y(annua l averag e = 2.3 6 ng/m 3 ) .

OPTIO N Averag e Desig n Valu e ((ig/m 3 ) Rati o t o

Referenc e Indicato r 1 ) Ma xMont h 3.8 9 1.1 1 2 ) Expecte d Ma x Calenda r Mont h 2.9 7 0.8 5 3 ) Expecte d Ma x Month * 3.5 1 1. 0 4 ) Expecte d Hig h Thre e Month s 3.6 0 1.0 3 5 ) Secon d Highes t Mont h 3.5 4 1.0 1 6 ) Ma x2n d Hig h Mont hPe r Yea r 3.0 9 0.8 8

"Referenc e indicato r

1 0Tabl e 2 . Effec t o f incomplet e sampling o n estimate d design value s

fo r alternativ e form s o f a monthl yNAAQ S fo r P bbase d on a simulatio n o f ASARC O P brefinerydata .

I DESIG

NVALU E CONCENTRATION(ng/m3 ) i P.1 4

Sampling Frequenc y 1/ 1 1/ 2 1/ 6

1/ 1 1/ 2 1/ 6 1 3.8 9 4.6 4 6.4 6

1 1.1 1 1.3 2 1.8 4 2

2.9 7 3.2 6 3.9 5

2 0.8 5 0.9 3 1.1 3 O P T

3 * 3.5 1 4.0 3 5.3 2

3 * 1 . 0 1.1 5 1.5 1 I O N

4 3.6 0 4.1 6 5.5 9

4 1.0 3 1.1 9 1.5 9 5 3.5 4 4.0 9 5.4 4

5 1.0 1 1.1 7 1.5 5 6

3.0 9 3.4 2 4.1 7

6 0.8 8 0.9 7 1.1 9 t RATI O T O REFERENC E INDICATOR O F 3.5 1 ng/m3 t

*Referenc e Indicato r (Option 3 )

1 1P.1 5

Tabl e 3 . Selecte d statistic s associate d wit hth e rati o o f incomplet e t o complet e sampling design value s fo r variou s underlying concentratio n distributions .

Rati o o f 1/ 6 t o 1/ 1 desig

nvals . Rati o o f

1/ 2 t o 1/ 1 desig n vals . Distri

bution * lognorma l a b c hybri d 1 hybri d 2 averag e

1.4 1 1.3 6 1.6 5 1.5 2 1.7 1 critica l

valu e 1.8 3 1.7 0 2.6 0 1.9 5 2.3 8 averag e

1.1 2 1.0 8 1.2 1 1.1 5 1.1 9 critica l

valu e 1.3 0 1.2 7 1.6 4 1.3 6 1.4 3

'See tex t fo r descriptio n o f distribution s

1 2Tabl e 4 . Compariso n o f Alternativ e Lead Standard s Applie d t o Poin t

Sourc e Oriente d Monitoring Dat a (1985-1987) . DESIG NVALUE S FROMOBSERVE D DAT A(ng/m3 )

AIR S SIT E OPTIO N 1 2 3 4 5 6 Ma xE xMa xExMaxExMax2ndM xMx2nd Mont hCa l Mnt hMont h3 Mo n Mont hMxMt h 01073200 4 01109000 3 18089201 3 29099000 5 29099001 1 30049071 4 30049071 9 31055004 2 42101002 8 48141003 1 Leeds , AL 1

Troy , AL 1 Hammond,IN 2 Jeff.Co.MO 3 Jeff.Co.MO 3 Lewi s & Clr k Lewi s & Clr k Omaha , NE * Phil. , PA 2 E l Paso , TX 3 MT 3

MT 3

Averag e 2. 6

7. 6 4. 1 7. 4 5. 7 7. 2 5. 2 5. 0 4. 3 4. 3 5.3 4 1.6(Nov ) 3.8(Mar ) 2.4(Jul ) 3.5(Sep ) 2.2(Jan ) 5.1(Oct ) 3.4(Oct ) 2.3(Dec ) 2.5(Jan ) 2.8(Apr ) 2.9 6 2. 0

4. 0 3. 8 5. 5 4. 7 6. 3 4. 8 3. 7 3. 1 2. 8 4.0 8 2. 2 4. 7 3. 8 5. 5 5. 1 6. 4 4. 8 3. 9 3. 4 3. 8 4.3 6 2. 1 3. 9 3. 5 4. 8 5. 3 6. 1 4. 8 3. 9 3. 3 3. 7 4.1 3 1. 8 3. 8 2. 6 3. 6 4. 2 6. 0 3. 6 2. 9 2. 6 3. 7 3.4 9

1 SecondaryLea d Smelte r 2 Lea d Oxid e Manufacture r 3 PrimaryLead Smelte r * Lead Refinery

1 3P.1 7



# FIGUR E 1 LEA

D CONCENTRATIO

N DISTRIBUTIO NFRO

MASARCO REFINER

YDAT A



# I

Z O

U J 

### o o ffi C L 

### to

10

5 4 

### 2 2 

### 1

0 5 0. 4 0. 3 0-2 .

0. 1

0.05 -

-

-

1 O

» P B CONCENTRATIO N DISTRIBUTIO N

OBSERVE D FRO M MONITORIN G DAT A

HYBRI D DISTRIBUTIO N LOWE R TAI L LOGNORMA L UPPE R TAI L NORMA L

/ 0 1 / / / / / / 0 / / / 1 0 ' 1 t 1 1 1 0 1

1 1 1 1 Yl 1 1 . 1 1 1 . / 7 - " 0''' r • 

# ?' 0' 1 1 1 0' 1 t 1 Of 1 d / / / / / / /

, 0

lllllll , 1 IZ 5 1

0 30SO 7 0 l o<? S .1 8 < H <tt<\ PERCENTIL EP.1 8

-WhPEKXNT

U -OO.POOW U -90n>PO«3NIl£

-ratiroicom r -COUFOSI C JNCTAG C nthPOKDms.

Figur e Z Rati o Distributio n o fincomplet e t o complet e samplin g

desig n vdue s fb rth e 2n d highes tmcrithS yvalu e I n 3 year s base d o n a simulatio n o fASARC O P b Refiner y

y/2 DAY SAMPLIN G O -m. Lm O 

### 2 - 1.5 - 

### 1 - 0.5 -

n RATI O

X



## rffell V < HSiP ii d X

• 

### xin^iiiiii w 

# M • X

1/ 6 DAY SAMPLIN GP.1 9



# ¥ -9msKKOiat

-aahFoxxxi u

-7smfOKiNn £ -awosi c«owx

-ShHHXNI U —KkfOBOaU | Illiwtntla oo f

plottin gooni—tirai oto ebaKpioto . Figur e 3 . Variabilit

yI n secon d highes

tirrcn ^ crverage I n three years Ratio s ofIncomplet

e (y &t o complet

e samplin g desig n values base d o n a smiatto n o fvariou s lea d ccricentratio n dstributfons . 3 . 5 tjM&vakM

A B C

Lognorma l Distribution s 1 2 Hybri d Distribution sP.2 0

«t>KKCD« U ntiFCKZMI U 90lt i PWCtXI U

-7SllifOICO(ll £ -COW09I E UOtACL -r»«pconi x -nhKKXMI U

Xllaotntia o o f

plottin gUUIIIMILII Wfa rbtnvlots . Rgur e 4 . VariabflH

yI n secon d highes

tmonthlyaverag e tn three years Ratio s ofincomplet

e (1/2 ) to complet

e samplin g desig n value s base d o n a simulatio n o fvariou s lead concentratio n distributions . O R - 

### z . o 2 - 1.5 - 

### 1 - 0.5 -

n WteofVSte V cWBtvak w 1

X —X — X X

X

' X

.X..

_ 

# i X X

- X• X X 

# ft _x _

X

A B C Lognorma l Distribution s 1 2 Hybri d Distribution s

# FIGUR

E5 EFFEC SECON D HIGHES T YEAR S WIT HINCO CRITICALRATI O FOR NONATTAINMENT

2. 4 

# O

FSEASONALIT

YO NVARIABIL 1 ONTHL YAVERAG

EOBSERVE

D I NTHREE PLETE(t/(8 ) SAMPLIN

G

2. 2

2 -

1. 8

1. 6

1. 4 \/

J I I L

. * RATI O O F OBERVE D T O TRU E DESIG N VALUE S FO R STATISTICAL SIGNIFICANC E

J L J I I L 1 2 3 4 5 6 7 8 •9 1 0 1 1 1 2 NUMBE R O F MONTH S WITH HIG H LEAD SEASO N SEASONA LCONCENTRATION S GRADIENT « o

MODERATE LARG E

oo SE E TEX

T

T J h o

# 6 EFFEC TQF.S E EXCEEDIN

GTRU ESECON

D PROBABILIT

YO F EXCEEDIN G TRU E DESIG N VALU E (1/ 6 SAMPLING ) 

# ONAL1T YO NPROBABILIT

YO F HMONT HI NTHRE EYEAR S

0. 2 0. 1 0 I L ml. Ii - J L . J l

_ -i—. J SEASONA LCONCENTRATION S GRADIENT o «

MODERATE LARG E

oo SE E TEX

T

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 NUMBE R O F MONTH S WITH HIG H P B SEASO N

# RATI O OFALTERNATIV

EFORM S ONT HBASE D O NDAT AFRO M TENPOINT MONITORINGSITE S TO THEEXPMA X SOURCELEA

D

ALTERNATIV E FORM S O F LEAD STANDAR D

MA XMONTH EX P MA XCA LMONT H EX P MA XMONTH EX P MA X3 MONTH S 2N D MA XMONTH MA X2N D MA

XMONT H

0. 2 0. 4 0. 6 0. 8 1 1. 2 1. 4 1. 6 1. 8 AVERAG E RATI O O F ALTERNATIV E FORM S T O TH E EX P MA

XMONTH