p. 1



# OAR Box 1828
Prepped by Ollie Stewart



### Document

Number: 

# 298 ) IV-A-8
Docket Number: 

# A-83-2 7

Printed 11/12/200811:12:59AM Sheet 298of 325P. 2 

# A-83-2 7

IV-A- 8

DC N #85-231-372-16-7 8

DETERMINATIO N

O F MEA N S0 2 EMISSIO N

LEVEL S REQUIRE D T O MEE T A

1. 2 LB S0 2 /MILLI0 N

BT U EMISSION STANDAR D FO

RVARIOU S AVERAGING TIME S AND COMPLIANC E POLICIE S

Prepare d for : Walte r H . Stevenso n U.S . Environmenta l Protectio nAgenc y Emissio nStandard s an d Engineerin g Divisio n Durham , Nort hCarolin a 2771 1

Prepare d by : Gregor y C . Giguer e Suzann e C . Margeru

m Radia nCorporatio n Progres s Cente r 320 0 E . Chape l Hil l Road/Nelso nHighwa y Researc hTriangl e Park , Nort hCarolin a 2770 9

Marc h198 5P. 3

1. 0 INTRODUCTIO N

Th e tw o mos t commo nmethod s use d t o contro l S0 ? emission s fro m coal-fire d steam

generatin g unit s ar e flu e ga s desulfurizatio n(FGD ) system s and direc t combustio no f lo w sulfu r coal . Bot ho f thes e method s demonstrat e a natura l variabilit y wit hrespec t t o S0 2 emission s discharge dt o th e atmosphere . A

knowledg e o f th e variatio no r sprea dinS0 2 emission s wit h time an d a statistica l mode l whic hprovide s a clos e resemblanc e t o th e variabilit y

ar e require d i norde r t o understan dth e fluctuation s i nS0 2 emissio nmeasurements . Du e t o th e random fluctuatio ninemissio nlevel s bot habov e and below th e long-term

average , th e mea nemissio nrat e mus t b e maintaine d a t anemissio nleve l belo w th e emissio nstandar di norde r t o assur e compliance . Throug hanalysi s o f th e variabilit y i nemissions , a statistica l procedur e ha s bee ndevelope d whic hallow s th e projectio no f long-ter m mea n S 0 2 emissio nlevel s require d t o mee t a 1. 2 l bS0 2 /millio nBt uemissio n limit . Thi s technica l not e present s th e require dlong-term mea nS0 2 emissio nrates , projecte d a s a functio no f th e averagin g perio d(3-hou r discrete , 24-hou r discrete , 7-da y rolling , 30-da y

rolling) , enforcemen t polic y (exceedanc e frequency : 1 pe r 1 0 years , 1 pe r 1 year , 1 percen t o f time) , autocorrelatio n(dail y value s o f 0.5 , 0.7 , 0.8) , andrelativ e standar d deviatio n(dail y value s o f 5 t o 3 5 percent) . Sectio n2. 0 o f thi s technica l not e briefl y discusse s th e methodolog y use d t o determin e long-term mea nS0 2 emissio nlevels . Th e projecte dmea n emissio nlevel s t o compl y wit ha 1. 2 l bS0 2 /millio nBt uemissio nlimi t fo r variou s averagin g period s and complianc e policie s ar e summarize di ntabula r for m i nAppendi xA . Appendi xB present s a mor e detaile ddescriptio no f th e statistica l approac ht o determinin g require dmea nemissio nlevels . Appendi xC list s th e compute r program use dt o projec t th e require dmea nS0 2 emissio nlevels .P. 4

2. 0 METHODOLOG Y

Sulfu r dioxid e (S0 2 ) emission s fro m any stea m generatin g uni t wil l var y wit htime . Steam

generatin g unit s equippe dwit ha flu e ga s desulfurizatio n (FGD ) system

wil l exhibi t a certai namoun t o f variabilit y i nS0 2 emission s du e t o random

fluctuation s i noperatin g parameter s suc ha s reagen t quality , liqui d an

d ga s flo

w rates , an

dflu e ga s inle t S0 2 concentratio n(eve n ambien t temperature) . Similarly , ther e i s a certai namoun t o f natura l variabilit y

i ncoa l sulfu r conten t du e t o th e heterogeneou s natur e o f coal , difference s inminin g practices , an ddifference s inhandlin g andpreparatio n practices . Ther e ar e severa l factor s whic hdescrib e th e variabilit y characteristic s o f S0 2 dat a an d whic hinfluenc e th e projecte dmea nS0 2 emissio nlevel s require d fo r compliance :

o Standar d deviatio nan drelativ e standar ddeviation ; o Autocorrelation ; o Emission s distributio n(norma l vs . lognormal) ; o Lengt ho f th e averagin g perio dan d averagin g method ; an d

0 Complianc e polic y (exceedanc e rate )

Eac ho f thes e factor s and it s effec t onth e require dmea nemissio nleve l i s briefl y discusse d below . Th e table s i nAppendi xA presen t require dmea n emissio nlevel s a s a functio no f eac ho f thes e factors . Appendi xB contain s complet e detail s o nth e computatio no f th e value s presente di nAppendi xA . Th e standar d deviatio ni s anindicato r o f th e sprea do f value s tha t measure s th e variatio no f measurement s fro m th e average . Th e relativ e standar d deviatio n(RSD ) i s define d a s th e rati o o f th e standar ddeviatio n t o th e averag e o r mea nan d i s typicall y

use dt o describ e emission s variability . Th e greate r th e relativ e standar ddeviatio nis , th e greate r th e variabilit y

i nobserve d S0 2 emissio nwil l be . Coal s o r S0 2 emission s dat a set s whic hhav e th e sam e mea nS0 2 leve l bu t hav e differen t S0 2 variabilit y

level s (standar d deviation s o r relativ e standar ddeviations ) wil l hav e differen t level s o f difficult y i ncomplyin g wit ha 1. 2 l bP. 5

S0 2 /millio nBt u emissio nlevel . A s increase d variabilit y i s observed , a lowe r mea nS0 2 emissio nleve l wil l b e necessar y t o achiev e complianc e wit h
a nS0 2 emissio nstandar d (se e Figur e 1) . Emissio nmeasurement s take na t equa l time interval s constitut e a time serie s inwhic hvalue s ar e no t necessaril y independent . Whe ndat a ar e collecte d i nsequence , ther e ca nb e a tendenc y fo r observation s mad e clos e togethe r i ntim

e t o b e mor e alik e tha nthos e take nfarthe r apart . A measur e o f thi s degre e o f associatio nbetwee nobservation s ina tim e serie s i s terme d autocorrelatio nan d ca nvar y

fro m -1. 0 fo r inversel y

relate d observation s t o 1. 0 fo r dat a whic hexhibit s a nextrem e degre e o f linea r association . S0 2 emission s value s typicall y hav e a relativel y

highamoun t o f autocorrelatio n(greate r tha n0.5) , suc htha t th e valu e o f eac h observatio ni s expecte d t o b e simila r t o tha t o f th e previou s observation . Overall , a s th e autocorrelatio nfacto r increases , a lowe r mea nS0 2 emissio n leve l wil l b e require d fo r compliance , andthi s effec t o f autocorrelatio no n complianc e determinatio ni s mor e importan t fo r longe r averagin g periods . However , autocorrelatio ni s no t a s majo r a facto r a s RS D i ndeterminin g S0 2 variabilit y

an d predictin g long-term mea nemissio nlevels . A firs t orde r autoregressiv e time serie s model , abbreviate da s AR(1) , i s use da s par t o f th e methodolog y

t o projec t th e require d long-term mea nS0 2 emission s level s show ni nAppendi xA . Thi s i s th e mos t basi c autoregressiv e mode l an dha s bee nfoun d i nman y

case s t o adequatel y fi t emission s time serie s measurement s an

d is , therefore , appropriat e fo r thi s analysis . Observe d S0 2 emission s dat a ca nb e describe db y variou s emission s distributions . Emission s dat a hav e generall y bee nfoundt o be wel l represente d b

y eithe r th e norma l o r lognorma l distributions . Th e primar y differenc e i nth e two distribution s i s tha t th e lognorma l (i nwhic hth e natura l logarithm s o f th e dat a ar e normall y distributed ) i s positivel y skewed . Th e require d mea nS0 2 emissio nlevel s necessar y fo r complianc e wit h
a standar d wil l diffe r dependin g o nwhethe r a lognorma l o r norma l distributio ni s assumed , an dth e differenc e i nth e projecte dlevel s i s primaril y

a functio no f th e lengt ho f th e averagin g perio dandth e RSD . Fo r emission s dat a wit hlowe r RSD's , th e require dmea nS0 2 level s ar e simila r fo r th e tw

o distributions ; however , i ncase s wher e hig hRSD' s ar e expected ,P. 6

th e differenc e betwee nprojecte d level s i s mor e pronounce d(se e Figure s 2
an d 3) . Similarly , fo r shor t averagin g period s th e differenc e betwee nth e projecte d level s fo r lognorma l and norma l distribution s ca nb e ^ery pronounced , bu t a s th e lengt ho f th e averagin g perio dincreases , th e difference s becom e negligible . Becaus e th e lognorma l distributio ni s skewe d t o th e right , it s us e result s i nth e projectio no f a slightl y lowe r mea n bein g necessar y

fo r complianc e tha ni f th e norma l distributio nha dbee n assumed . Th e lengt ho f th e averagin g perio d als o affect s th e require dmea n emissio nleve l necessar y fo r compliance . Longe r averagin g period s dampe n th e effect s o f variability , resultin g i nrequire dmea nS0 2 emissio nrate s close r t o th e actua l emission s limit . Th e averagin g perio di s define da s th e perio d o f time (hour s o r days ) ove r whic hemissio nmeasurement s ar e average d i norde r t o determin e complianc e wit hth e S0 2 emissio nlimit . A bloc k averag e (discret e average ) o r a rollin g averag e ma y b e use dt o determin e compliance . Discret e average s ar e compute do na separate , non-overlappin g basis ; rollin g average s ar e calculate db y addin g th e curren t valu e int o th e calculatio no f th e averag e an ddeletin g th e oldes t o r leas t curren t value . Wit hth e us e o f discret e o r bloc k averages , th e enforceabilit y

o f anemission s standar d i s directl y relate dt o th e averagin g time . Fo r example , a 24-hou r averag e woul db e enforce dfo r eac hdiscret e 24-hou r perio d an

d 36 5 suc haverage s woul db e calculate dpe r year . A 30-da y averag e woul d be enforce d fo r eac hdiscret e 30-da y perio dand1 2 suc h average s woul d b e calculate d pe r year . However , a 30-da y averag e ca nbe calculate d and enforce d o na dail y basi s throug hth e us e o f a rollin g average . Thus , rollin g averagin g period s allo w fo r stricte r enforcemen t • tha ndiscret e period s o f th e same length . Fo r a give naveragin g period , th e mea nS0 2 leve l require d fo r complianc e i s lowe r fo r a rollin g averag e tha n fo r a discret e averag e sinc e ther e i s a greate r potentia l fo r exceedin g th e emissio nlimi t whe nusin g a rollin g average . Th e fina l facto r affectin g th e require d mea nemissio nleve l i s th e complianc e polic y

(allowe d exceedanc e frequency) . Th e allowe dexceedanc e frequenc y

i s expresse d a s th e numbe r o r percentag e o f exceedance s assume dP. 7



### ove r th e specifie dtime perio dfo r a particula r emissio nlimit , an dca nb e though t o f a s anassume dviolatio nrate . O f course , a s th e allowe d exceedanc e frequenc y

increases , th e require dmea nS0 2 

### leve l als o increases . Th e probabilit y

o f violatin g th e limi t canb e calculate dfo r a specifi c averagin g perio dandexceedanc e frequency ; thi s probabilit y i s constan t fo r eac hpotentia l perio do f violatio nove r th e entir e ter m o f th e averagin g period . A s anexample , conside r a 30-da y rollin g averagin g perio dcombine d wit hanexceedanc e frequenc y o f on e pe r 1 0 years . Ther e i s a potentia l o f havin g anexceedanc e o r violatio neac hda y whe nusin g a 30-da y

rollin g averagin g period , sinc e a new 30-da y averag e emissio nleve l i s compute deac h day . Ther e ar e 3,65 0 day s ove r a 10-yea r period ; thu s assumin g on e exceedanc e divide db

y th e tota l numbe r o f potentia l exceedance s (3,650 ) yield s 0.00027 . Therefore , th e probabilit y o f violatin g th e limi t eac hda y i s a constan t o f 0.00027 , an dsummin g thes e dail y

probabilitie s ove r th e 365 0 day s result s i na probabilit y (or relativ e frequency ) o f one . Th e dail y exceedanc e probabilit y o f 0.0002 7 translate s t o a standar dnorma l distributio nZ valu e o f 3.46 . Th e implicatio no f th e abov e exampl e i s that , inorde r t o compl y wit h th e emissio nlimit , th e boile r shoul db e runa t a targe t leve l whic hi s les s tha nth e give nlimi t b y anamoun t equa l t o 3.4 6 time s th e standar ddeviatio n o f th e 30-da y

rollin g averages .P. 8

APPENDI XA

Thi s Appendi xcontain s projecte d mea nS0 2 emissio nlevel s require dt o mee t a 1. 2 lb . pe r millio nBt uemissio nlimi t base dondifferen t averagin g time , complianc e policies , andstatistica l assumptions . Eac htabl e correspond s t o a distributiona l assumptio n(lognorma l o r normal ) an dan averagin g period , bot ho f whic har e specifie dinth e title . T o us e th e tables , selec t th e dail y autocorrelatio n(0.5 , 0.7 , o r 0.8 ) desired ; on e o f th e thre e row s unde r th e dail y autocorrelatio nheadin g whic hcorrespond s t o exceedanc e frequenc y (on e pe r te nyears , on e pe r year , o r on e percent) ; an d lastly , on e o f th e seve ncolumn s whic hsignif y th e dail y

relativ e standar d deviation . Th e valu e i nth e body o f th e tabl e i s th e mea nS0 ? emissio n level ) whic hth e boile r operato r mus t achiev e inorde r t o mee t th e 1. 2 lb S 0 2 pe r millio nBt u emissio nlimi t give nth e particular s o f emission s dat a variabilit y

and complianc e practices . Fo r example , i nTabl e A-4 , th e require d mea nS0 « emissio nleve l t o compl y wit ha 1. 2 l bS0 2 /millio nBt u limi t base d upo na 30-da y rollin g averag e period , a dail y autocorrelatio no f 0.7 , anexceedanc e frequenc y o f on e pe r year , anda dail y relativ e standar d deviatio no f 2 0 percent , i s 0.9 8 Ib/M M Btu .
Lognorma l Distributio nAssumptio nTabl e 3-Hou r Discret e Averagin g Perio dA- l 24-Hou r Discret e Averagin g Perio d A- 2 7-Day Rollin g Averag e Perio dA- 3 30-Da y Rollin g Averag e Perio d A- 4

Norma l Distributio nAssumptio nTabl e 3-Hou r Discret e Averagin g Perio d A- 5 24-Hou r Discret e Averagin g Perio d A- 6 7-Day Rollin g Averag e Perio d A- 7 30-Da y Rollin g Averag e Perio d A- 8



### A- lP. 9

TABL E A-6 . PROJECTE D LON GTER M MEA N S0 2 EMISSION

LEVEL S REQUIRE D T O MEE T 1. 2 L B LIMI T ASSUMIN GA 24-HOURDISCRETE AVERAGINGPERIO D AN D A NORMA L DISTRIBUTION 3, 5

Dail y Relativ e Standar d Deviatio n(Percent ) Exceedanc e Frequency

5 1 0 1 5 2 0 2 5 3 0 3 5
Dail y Autocorrelatio no f 0. 5 On e pe r 1 0 year s 1.0 5 On e pe r yea r 1.0 7 On e percen t 1.0 9 Dail y Autocorrelatio no f 0. 7 On e pe r 1 0 year s 1.0 4 On e pe r yea r 1.0 6 On e percen t 1.0 8 Dail y Autocorrelatio no f 0. 8 On e pe r 1 0 year s 1.0 3 On e pe r yea r 1.0 6 On e percen t 1.0 8 0.9 8 0.9 0 0.8 3 0.7 8 0.7 3 0.6 9

a Assume s tha t 24-hou r discret e average s ar e normall y distributed . S0 2 emission s level s expresse di nl bS0 2 /millio nBt uhea t input . 0.9 3 0.9 7 1.0 0

0.9 1 0.9 6 0.9 9

0.9 0 0.9 5 0.8 4

0.8 9 0.9 3

0.8 1 0.8 7 0.9 1

0.8 0 0.8 6 0.7 6

0.8 2 0.8 6

0.7 3 0.8 0 0.8 4

0.7 3 0.7 9 0.6 9

0.7 6 0.8 1

0.6 7 0.7 3 0.7 8

0.6 7 0.7 3 0.6 4

0.7 1 0.7 6

0.6 2 0.6 8 0.7 3

0.6 2 0.6 8 0.5 9

0.6 6 0.7 1

0.5 7 0.6 3 0.6 9

0.5 7 0.6 3



### A- 2P.1 0



### TABL E A-7 . PROJECTE D LONG-TERM MEA N S0 2 

### EMISSION

LEVEL S REQUIRE D T O MEE T 1. 2 L B LIMI T ASSUMINGA 7-DA YROLLINGAVERAGINGPERIO D AND A NORMA L DISTRIBUTION 3 

### » b

Exceedanc e Frequenc

y
Dail y Autocorrelatio

n One pe r 1 0 year s On e per yea r On e percent Dail y Autocorrelatio

n On e pe r 1 0 year s On e per yea r On e percent Daily Autocorrelatio

n
On e pe r 1 0 year s On e pe r yea r On e percen t 

### Da i 5

o f 0. 5 1.0 9 1.1 1 1.1 3

o f 0. 7 1.0 7 1.1 0 1.1 1

o f 0. 8
1.0 6 1.0 9 1.1 0 l

y Rela t 

### 10

1.0 1 1.0 4 1.0 6

0.9 7 1.0 1 1.0 4

0.9 5 0.9 9 1.0 2 iv

e Standar

d Deviatio

n 

### 1 5

0.9 3 0.9 7 1.0 1

0.8 9 0.9 4 0.9 7

0.8 6 0.9 1 0.9 5 

### 2 0

0.8 7 0.9 2 0.9 5

0.8 2 0.8 7 0.9 1

0.7 9 0.8 4 0.8 9 

### 2 5

0.8 1 0.8 7 0.9 1

0.7 6 0.8 2 0.8 6

0.7 2 0.7 9 0.8 3 (Percent )



### 3 0

0.7 6 0.8 2 0.8 6

0.7 1 0.7 7 0.8 2

0.6 7 0.7 3 0.7 8 

### 35

0.7 2 0.7 8 0.8 3

0.6 6 0.7 2 0.7 7

0.6 2 0.6 9 0.7 4

a 

### Assume s tha t 7-day

rollin g average s ar e normall y distributed . S 0 2 

### emission s level s expresse di n l bS0 2 

### /millio nBt uhea t input .

A- 3P.1 1

TABL E A-l . PROJECTE D LONG-TER M MEA N S0 2 EMISSION

LEVEL S REQUIRE D TO MEE T 1. 2 LB LIMI T ASSUMINGA 3-HOU RDISCRET E AVERAGIN

GPERIO D AN D A LOGNORMA

L DISTRIBUTION 3, b

Dail y Relativ e Standar d Deviatio n(Percent ) Exceedanc e Frequenc y

5 1 0 1 5 2 0 2 5 3 0 3 5
Dail y Autocorrelatio no f 0. 5 On e pe r 1 0 year s 0.9 9 0.8 2 0.6 8 0.5 6 0.4 7 0.4 0 0.3 4 On e pe r yea r 1.0 2 0.8 6 0.7 4 0.6 3 0.5 4 0.4 7 0.4 1 On e percen t 1.0 7 0.9 6 0.8 6 0.7 8 0.7 0 0.6 4 0.5 8 Dail y Autocorrelatio no f 0. 7 On e pe r 1 0 year s 0.9 9 0.8 1 0.6 7 0.5 6 0.4 7 0.3 9 0.3 3 On e pe r yea r 1.0 2 0.8 6 0.7 3 0.6 3 0.5 4 0.4 7 0.4 0 On e percen t 1.0 7 0.9 6 0.8 6 0.7 7 0.7 0 0.6 4 0.5 8 Dail y Autocorrelatio no f 0. 8 On e pe r 1 0 year s 0.9 9 0.8 1 0.6 7 0.5 6 0.4 7 0.3 9 0.3 3 On e pe r yea r 1.0 1 0.8 6 0.7 3 0.6 3 0.5 4 0.4 6 0.4 0 On e percen t 1.0 7 0.9 6 0.8 6 0.7 7 0.7 0 0.6 4 0.5 8

a Assume s tha t 3-hou r discret e average s ar e lognormall y distributed . SO p emission s level s expresse d inl bS0 2 /millio nBt u hea t input .



### A- 4P.1 2



### TABL E A-5 . PROJECTE D LONG-TERM MEA N S0 2 

### EMISSION

LEVEL S REQUIRE D T O MEE T 1. 2 LB LIMI T ASSUMINGA

3-HOU RDISCRET E AVERAGINGPERIO D AN D A NORMA L DISTRIBUTION 3 

### ' 1 5



### Dail y Relativ e Standar dDeviatio n(Percent ) Exceedanc e •• Frequenc y 5 1 0 1 5 2 0 2 5 3 0 3 5 Dail y Autocorrelatio no f 0. 5 On e pe r 1 0 year s 1.0 0 On e pe r yea r 1.0 3 On e percen t 1.0 8 Dail y Autocorrelatio no f 0. 7 On e pe r 1 0 year s 1.0 0 On e pe r yea r 1.0 3 On e percen t 1.0 8 Dail y Autocorrelatio no f 0. 8 On e pe r 1 0 year s 1.0 0 On e pe r yea r 1.0 3 On e percen t 1.0 8

3 

### Assume s tha t 3-hou r discret e average s ar e normall y distributed . S 0 2 

### emission s level s expresse dinl bS0 2 

### /millio nBt uhea t input . 0.8 6 0.9 0 0.9 8

0.8 6 0.9 0 0.9 8

0.8 6 0.9 0 0.9 7 0.7 6

0.8 0 0.8 9

0.7 5 0.8 0 0.8 9

0.7 5 0.8 0 0.8 9 0.6 7

0.7 2 0.8 2

0.6 7 0.7 2 0.8 2

0.6 7 0.7 2 0.8 2 0.6 1

0.6 5 0.7 6

0.6 0 0.6 5 0.7 6

0.6 0 0.6 5 0.7 6 0.5 5

0.6 0 0.7 1

0.5 5 0.6 0 0.7 1

0.5 5 0.6 0 0.7 1 0.5 1

0.5 5 0.6 7

0.5 0 0.5 5 0.6 6

0.5 0 0.5 5 0.6 6



### A- 5P.1 3

TABL E A-2 . PROJECTE D LONG-TERM MEA N S0 2 EMISSION

LEVEL S REQUIRE D T O MEE T 1. 2 L B LIMI T ASSUMINGA 24-HOURDISCRET E AVERAGINGPERIO D AND A LOGNORMAL DISTRIBUTION 3 ' b

Dail y Relativ e Standar d Deviatio n(Percent ) Exceedanc e Frequenc y

5 1 0 1 5 2 0 2 5 3 0 3 5
Dail y Autocorrelatio no f 0. 5
On e pe r 1 0 year s 1.0 4 On e pe r yea r 1.0 7 On e percen t 1.0 9 Dail y Autocorrelatio no f 0. 7 On e pe r 1 0 year s 1.0 3 On e pe r yea r 1.0 6 On e percen t 1.0 8 Dail y Autocorrelatio no f 0. 8
On e pe r 1 0 year s 1.0 2 On e pe r yea r 1.0 5 On e percen t 1.0 8

3 Assume s tha t 24-hou r discret e average s ar e lognormall y distributed , S0 2 emission s level s expresse d inl bS0 2 /millio nBt u hea t input . 0.9 0 0.9 5 0.9 9

0.8 8 0.93 ; 0.9 7

0.8 7 0.9 3 0.9 7 0.7 8

0.8 5 0.9 0

0.7 6 0.8 3 0.8 8

0.7 4 0.8 2 0.8 7 0.6 8

0.7 7 0.8 2

0.6 5 0.7 4 0.8 0

0.6 4 0.7 3 0.7 9 0.6 0

0.6 9 0.7 6

0.5 6 0.6 6 0.7 3

0.5 5 0.6 4 0.7 2 0.5 2

0.6 2 0.6 9

0.4 9 0.5 9 0.6 6

0.4 8 0.5 8 0.6 5 0.4 6

0.5 6 0.6 4

0.4 3 0.5 3 0.6 1

0.4 1 0.5 2 0.6 0



### A- 6P.1 4



### TABL E A-3 . PROJECTE D LONG-TERM MEA N S0 2 

### EMISSIO N

LEVEL S REQUIRE D T O MEE T 1. 2 L B LIMI T ASSUMIN GA 7-DA YROLLIN GAVERAGINGPERIO D AND A LOGNORMAL DISTRIBUTION 3 

### ' 5

Exceedanc e Frequenc y Dail y Autocorrelatio n On e pe r 1 0 year s On e pe r yea r On e percen t Dail y Autocorrelatio n On e pe r 1 0 year s On e pe r yea r On e percen t Dail y Autocorrelatio n On e pe r 1 0 year s On e pe r yea r On e percen t 

### Da i 5

o f 0. 5 1.0 9 1.1 1 1.1 3

o f 0. 7 1.0 7 1.0 9 1.1 1

o f 0. 8 1.0 5 1.0 8 1.1 0 l y Relativ e Standar d Deviatio n 

### 1 0

0.9 9 1.0 3 1.0 6

0.9 5 1.0 0 1.0 3

0.9 3 0.9 7 1.0 1 

### 1

5

0.9 0 0.9 6 0.9 9

0.8 5 0.9 1 0.9 5

0.8 2 0.8 8 0.9 3 

### 20

0.8 2 0.8 9 0.9 3

0.7 6 0.8 3 0.8 9

0.7 2 0.8 0 0.8 5 

### 2

5

0.7 5 0.8 3 0.8 8

0.6 8 0.7 6 0.8 2

0.6 4 0.7 2 0.6 4 (Percent ) 

### 30

0.6 9 0.7 7 0.8 3

0.6 1 0.7 0 0.7 7

0.5 6 0.6 6 0.5 6 

### 3

5

0.6 3 0.7 2 0.7 8

0.5 5 0.6 4 0.7 2

0.5 0 0.6 0 0.5 0

3 

### Assume s tha t 7-day

rollin g average s ar e lognormall y distributed . S 0 2 

### emission s level s expresse di nl bSOp/millio nBt u hea t input .

A-7P.1 5



### TABL E A-8 . PROJECTE D LONG-TERM MEA N S0 2 

### EMISSIO N

LEVEL S REQUIRE D T O MEE T 1. 2 L B LIMI T ASSUMIN GA 30-DAYROLLINGAVERAGIN GPERIO D AND A NORMAL DISTRIBUTION 3 

### ' 5

Exceedanc e Frequenc y Dail y Autocorrelatio n On e pe r 1 0 year s On e pe r yea r On e percen t Dail y Autocorrelatio n On e pe r 1 0 year s On e pe r yea r On e percen t Dail y Autocorrelatio n On e pe r 1 0 year s On e pe r yea r On e percen t 

### Da i 5

o f 0. 5 1.1 4 1.1 5 1.1 6

o f 0. 7 1.1 3 1.1 4 1.1 5

o f 0. 8 1.1 1 1.1 3 1.1 4 l y Rela t 

### 1 0

1.0 9 1.1 1 1.1 3

1.0 7 1.0 9 1.1 1

1.0 4 1.0 7 1.0 9 iv

e Standar d Deviatio n 

### 1 5

1.0 5 1.0 7 1.0 9

1.0 1 1.0 4 1.0 6

0.9 8 1.0 1 1.0 4 

### 20

1.0 0 1.0 4 1.0 6

0.9 6 1.0 0 1.0 3

0.9 2 0.9 6 1.0 0 

### 2

5

0.9 6 1.0 0 1.0 3

0.9 1 0.9 6 0.9 9

0.8 7 0.9 2 0.9 5 (Percent ) 

### 30

0.9 3 0.9 7 1.1 0

0.8 7 0.9 2 0.9 6

0.8 2 0.8 8 0.9 2 

### 3

5

0.8 9 0.9 4 0.9 8

0.8 3 0.8 9 0.9 2

0.7 8 0.8 4 0.8 8

a 

### Assume s tha t 30-da y

rollin g average s ar e normall y distributed . S 0 2 

### emission s level s expresse di nl bS0 2 

### /millio nBt u hea t input .

A- 8P.1 6

TABL E A-4 . PROJECTE D LONG-TERM MEA N S0 2 EMISSIO N

LEVEL S REQUIRE D T O MEE T 1. 2 LB LIMI T ASSUMINGA 30-DA YROLLINGAVERAGINGPERIO D AND A LOGNORMAL DISTRIBUTION 3 ' 5

Dail y Relativ e Standar d Deviatio n(Percent ) Exceedanc e Frequenc y

5 1 0 1 5 2 0 2 5 3 0 3 5
Dail y Autocorrelatio no f 0. 5 On e pe r 1 0 year s 1.1 4 On e pe r yea r 1.1 5 On e percen t 1.1 6 Dail y Autocorrelatio no f 0. 7 On e pe r 1 0 year s 1.1 3 On e pe r yea r 1.1 4 On e percen t 1.1 5 Dail y Autocorrelatio no f 0. 8 On e pe r 1 0 year s 1.1 1 On e pe r yea r 1.1 3 On e percen t 1.1 4

a Assume s tha t 30-da y rollin g average s ar e lognormall y distributed . S 0 2 emission s level s expresse di nl bS0 2 /millio nBt uhea t input . 1.0 9 1.1 1 1.1 2

1.0 6 1.0 8 1.1 0

1.0 3 1.0 6 1.0 8 1.0 4

1.0 7 1.0 9

0.9 9 1.0 3 1.0 6

0.9 6 1.0 0 1.0 3 0.9 9

1.0 3 1.0 5

0.9 3 0.9 8 1.0 1

0.8 9 0.9 4 0.9 8 0.9 4

0.9 9 1.0 2

0.8 8 0.9 4 0.9 7

0.8 2 0.8 9 0.9 3 0.9 0

0.9 5 0.9 9

0.8 3 0.8 9 0.9 4

0.7 7 0.8 4 0.8 9 0.8 6

0.9 2 0.9 6

0.7 8 0.8 5 0.9 0

0.7 1 0.7 9 0.8 5



### A- 9P.1 7



### i s necessar y

t o adjus t fo r th e covarianc e structur e associate dwit ha first-orde r time serie s process . Th e standar derro r i s calculate da s



### A-loP.1 8

APPENDI XB

Thi s Appendi xi s divide d int o tw o section s correspondin g t o th e projecte d emissio nlevel s bein g calculate d base do nth e assumptio no f a norma l distributio no r a lognorma l distribution .

Norma l Distributio nfo r Emissio nAverage s Le t Xrepresen t mea nS0 2 emissio nfo r th e give naveragin g period . Assum e tha t Xi s normall y distribute dan

d le t L b e th e mea no f al l X(y_ ) o r th e projecte d long ter m mea nemissio nleve l (targe t level ) require dt o mee t a give nemission s limit . Le t C b e th e allowanc e fo r rando m variatio ni

n emission s o r th e differenc e betwee nth e targe t leve l andth e emission s limit . Thu s th e emission s limi t equal s ( L + C) . Usin g th e same exampl e discusse d earlie r i nSectio n2.0 , th e formul a fo r computin g C i s derive da s follows :

P ( X> L + C ) = 0.00027 , wher e 2 Xi s normall y

distribute d wit hmea np - andvarianc e a - .

P ( ^- ^ > —

) = 0.0002 7 °x " CT x

r P ( Z > —

) = 0.00027 , wher e Z i s a standar dnorma l variat e a x

P ( Z > 3.4 6 ) = 0.0002 7

— = 3.4 6 o r C = 3.4 6 a a xx

I t i s assume d tha t hourl y S0 2 emission s follo w anAR(1 ) time serie s process . Therefor e i ncomputin g th e standar ddeviatio no f th e mea n(o-) , i t



### B- 1P.1 9

i s necessar y

t o adjus t fo r th e covarianc e structur e associate dwit ha first-orde r time serie s process . Th e standar derro r i s calculate da s



### a 

# x = ( 

# V f n 

# M ) V

wher e p i s th e lag 1 o r first-orde r autocorrelatio ncoefficien t an d a. i s th e hourl y

standar d deviation . Sinc e


### VVP I 

## > 1//7T,
th e standar d erro r ha s increase d relativ e t o th e cas e wher e independenc e i s assumed . Th e equatio nfo r f.(p ) i s derive dusin g th e theoretica l autocorrelatio nfunctio no f <j > fo r a nAR(1 ) process , wher e $ i s th e autocorrelatio ncoefficien t an d k equal s th e lag . Th e covarianc e a t lag k equal s <p

multiplie d b

y th e variance . Afte r applyin g thi s resul t t o th e standar d statistica l formul a fo r th e varianc e o f a sum , extensiv e algebrai c manipulatio nlead s t o th e followin g equatio nfo r f_(p) :

f n (p ) = — nn( l 

### 1 1 + P 2 p ( 1 - p n ) n( l - P )

Th e fina l ste p i nderivin g th e formul a use dt o comput e th e targe t leve l table s i s t o develo p a nequatio nfo r a . 

## (o h 

## )Vyp )

wher e h= hourl y

emissio nvalue s n= numbe r o f hour s i naveragin g perio d



### a , = k)\/Up) ,
wher e d = dail y

emissio nmeasuremen t



### B-2P.2 0



### a h

### = (RSD d 

### nL)/-/ f 2 4 

### (p) , wher e RSD . = relativ e standar ddeviatio no na dail y basis .

Recal l tha t C = ( Z ) a- ,

a x wher e Z i s the critica l valu e correspondin g t o th e are a (e.g. , 0.0002 7 above ) fo r a give nexceedanc e frequency an daveragin g period .

C - (Z a 

### )(L)(RSD d 

### )"[/f n 

### (p)/f 24 

### ( P 

### )

L + C Targe t leve l = L = - , fo r n> 2 5

1 + (Z a 

### )(RSD d 

### )-l/ f n 

### (p)/ f 

### 24 ( p )


### L + C 1 + ( Z HRSDJ VOe ) an dL = M- £ , fo r n< 2 5

wher e ( L + C ) equal s th e give nemissio nlimi t o f 1.2 . Lognorma l Distributio nfo r Emissio nAverage s This sectio nwil l us e th e same notatio na s above . Assum e tha t Xi s a lognormall y

distribute drandom

variable . Th e valu e Xsuc htha t a 

### P ( X< X) = a

a 

### i s relate dt o th e correspondin g percentil e Z o f th e standar dnorma l distributio nb

y th e relatio n

X= exp( u+ Z a) , a r 

### a

B- 3P.2 1

I f X(mea nemissio nlevel ) i s lognormall y distributed , the nY= log(x ) i s normall y distributed .
log (L ) = U y

+ a y 2 / 2

L = exp ( U y

+ a y 2 /2 )

a y 2 = lo g [ 1 + (RSD-) 2 ]

L + C = ex p (p y

+ Z a a y )

y y = log ( L + C ) - Z a a y
Thu s give nanemission s limi t o f ( L + C) , solv e fo r u . The nusin g substitutio nan

d th e abov e equatio nfo r L , th e targe t leve l i s calculated .



### B-4P.2 2

APPENDI XC
Sampl e listing s o f th e SA S program s use dt o predic t th e long-term mea n S 0 2 emissio nlevel s require dt o mee t a 1. 2 l bSOp/millio nBt uemissio n standar dar e presente dbelow . Bot hsampl e program s show nprojec t th e mea n emissio nlevel s fo r averagin g period s (3-hou r discrete , 24-hou r discrete , 7-day rolling , an

d30-da y

rolling ) an

dthre e autocorrelatio nlevel s (0.5 , 0.7 , and0.8) . Tabl e C- 1 present s a sampl e progra m assumin g a lognorma l distributio nan

dRSD' s o f 25 , 30 , an d3 5 percent . Tabl e C- 2 present s a sampl e progra m

assumin g a norma l distributio nandRSD' s o f 10 , 15 , and2 0 percent .



### C- 1P.2 3

TABL E C-1
. SAMPL E PROGRA M — LOGNORMA

L DISTRIBTUIO N

OOOI O /. / 0002 0 / / 0003 0 //SYSI N

D D * 0004 0 HACR O O

L 0003 0 DAT

A ONE I 0004 0 * t SE T HOURL YAUTOCORR . (HACR O VALU E X ) FO

R GIVEN

DAILYAUTOCORR. I 0007 0 0«X I OOOt O NAV0«N» « * N I S HACR O VAR . FO R HOUR S I

N AV G PERIO D I 000* 0 FN»(<<l»0>/<l-0>-2*0t < l-D«*NAVO)/<NAVOt ( !-0>«t2 > >/HAVO> I 0010 0 F24»<<<1*0)/<1-D)-2«D« ( 1-D*«2 4 >/<21* < 1-D)*«3 ) )/2-l) » 0011 0 I F N>2 4 THEN SR.FN-SQRT<FN/F2«> » 0012 0 I F N<«2 4 THE N SR.FN»SQRT<FN> I 0013 0 ttRSO.XXI S RS O O F HEA N OF XFO

R GIVEN

RS D O F X

XAN D AVERAGIN

G PERIO D 0014 0 O F LENOT H N HOURS . VARIAT E XI S LOONORHALL YDISTRIBUTED ! 0013 0 RS0.23«SR.FN«0.23 I RSD.30-3R.FNtO.30 * RS0.33-SR.FNtO.33 1 0014 0 < • S2.YX

XI S THE VARIANC E O F Y t UHER E Y1 3 TH E LO Q QF TH

E MEA N 0017 0 OF X

t YI S NORNALL T DIS T WIT H VAR.S2-YX XAN O HSAN-H.f/ * UHER E 001t O X

XI S TH E GIVE N

RSO I 001* 0 32.Y23-L0Q U •RS0.23«*2> » S2.Y30«L0G ( 1 •RSD.30**2) 1 0020 0 S2-Y33«L0Q< 1 • RS0.33(t2) i 0031 0 S.Y23«SQRT(S3.Y23> « S.Y30»S0RT<S2.Y30> » 9.Y33-S0RT(S2.YJ3) > 0023 0 < t RSOX

XI S TH E VALU E O

F TARGE T LEVE L FO R RS O O

F X XPERCEHT * 0033 0 OAT

A EXC.PCT1 * SE T ONE ! « t 1 PERCEN T EXCEEDANC E FREQUENCY : 0034 0 N.Y33«L00(ST > -2.324tS.Y23 > 0023 0 N_Y30«L00<ST > -2.324*3.Y30 * 0024 0 N.Y33>L00<ST ) - 2.324*S.Y33 I 0027 0 RS023«EXP<H_Y2 3 + 0.3«S2.Y23> » 002S 0 RSD30>EXP(N.Y3 0 • 0.3*32.Y30> « 0027 0 RS033«EXP<H_Y3 3 • • 0.3*S2-Y33> » 0030 0 EXC.FREO'l t 0031 0 OAT

A EXC.1YR I SE T ONE * M t II I 1 r * EXCEEDANC E FREQUENCY * 0032 0 H.Y23"L00(ST)-Z1*3.Y23 I 0033 0 H.Y30*L0G(ST ) - Z1CS.Y30 * 0034 0 H_Y33"LU0<ST ) -Z1«S.Y33 1 0033 0 R3023*EXP(N.Y2 3 * 0.3*S2-Y23> » 0034 0 RSD30»EXP<H.Y3 0 * 0.3*32.Y30) i 0037 0 RSD33*EXF(H.Y3 3 • 0.3<S2.Y33> * 0038 0 EXC-FRE0»2 I 003* 0 DAT

A EXC.IOYR I SE T ONE I * * 1 I N 1 0 r p EXCEEDANC E FREQUENCY * 0040 0 H_Y23»L00<ST > - :iO*S.Y23 l 0041 0 H.Y30«L00<ST > -Z10*S.Y30 I 0042 0 H_Y33"L00(ST > -Z10«3.Y33 » 0043 0 RSD23>EXF<N.Y2 3 > O.S«S2.Y23) i 0044 0 RSD30*SXP(N.Y3 0 * 0.5*S2-Y30> * 0043 0 RS033«EXP<N.Y3 3 • 0.3tS2-Y33) » 0044 0 EXC.FREQ»3 » 0047 0 OAT

A AVOPER I SE T EXC.tOYR EXC-1YR E^C.PCTl * 004S 0 R23>R0UN0(RSD23..01) * R30«ROUN0(RSD3O..01)IRSS'ROUNOCRSD33..01) 1 004* 0 LABE L R23-'RS D - 23 ' 0030 0 R30«'RS D • 30 ' 0031 0 R33»'RS D • 33 ' I 0032 0 PRO C FORNATIVALU E EF O 1-QN E PERCEN T 0033 0 Z'.Ht PER YEA

R 0034 0 3-QM E ?E R TE N YEARS * 0033 0 PRO C PRINT 0 LABEL * VA R R2 3 R3 0 R33 I 0034 0 t

O EXC.FREO * 0037 0 TITLE * 0038 0 TITLE S PROJECTE O S0 2 ENISSION LEVEL S REQUIRE D T O NEi " I. : L

bLIHIT * 003* 0 TITLE 4 ASSUMIN G LOONORNA

L DISTR1BUTIU

N ?J R AVERftUE * 0040 0 TITLE S FO

R DAIL YAUTOCORRELATION O F Tl * 0041 0 TITLE 4 AN

O T 2 AVERACIN

Q PERIUD I

C- 2P.2 4

TABL E C- 1 (continued )

0042 0 FORHA T EXC.FRE O EFO . 0043 0 Xt t EN

O OF HAI N

HACRO DL ) 0044 0 • * SE T HACRO VAR . VALUE S FO R X.N.Zl.ZIOfTltT 2 I 0043 0 HACR O X0.174*00* 4 XM.«CF: 0 N 72 0 X 0044 0 HACR O Z l 2.7 8 XHACRO ZI O 3.4 4 XHACRO T l 0.7 T 0047 0 HACR O T 2 3 0 OA YROLLING ! 0048 0 HACR O S T 1. 2 Xt * SE T HACRO VA R OF STtFOR EHISSION LlHIT U 004* 0 O

L ( S CAL L HAI N

HACRO T

O PRINT 3 0 OA

YAV O TABL E F

r J * 0 .. , AUT3C0RR * 0070 0 * t CHANG E HACRO S N.T 3 T O RU N 7 DA YAV G PERIOO I 0071 0 HACR O N

14 8 XHACR O T 3 7 OA YROL L INO

XD L 0072 0 HACR O N

3 4 XHACR O T 3 2 4 HOU R DISCRETE * O

L 0073 0 HACR O N

3 XHACR O Z l 3.4 0 XHACRO ZI O 3.* 3 X 0074 0 HACR O T 3 3 HOU R OISCRETC X 0073 0 DL 0074 0 t t CHANG E HACR O VALUE S T O RU N 0. 3 AUTOCORRELATION ! 0077 0 HACR O X0.9333374 7 XHACR O N 72 0 X 0078 0 HACR O Z l 2.7 8 XHACRO ZI O 3.4 4 XHACR O T l 0.3 X 0079 0 HACR O T 2 3 0 OA YROLLING ! 0080 0 O

L 0081 0 HACR O N

14 8 XHACR O T 3 7 DA YROLLINOXD

L 0083 0 MACR O N

3 4 XHACR O T 2 2 4 HOU R DISCRET E D

L 0083 0 HACR O N

3 XHACRO Z l 3.4 0 XHACRO ZI O 3.* 8 X 0084 0 HACR O T 2 3 HOU R OISCRETE XD

L 0083 0 * • CHANO E HACR O VALUE S T O RU N 0. 3 AUTOCORR . > 00*4 0 MACR O X0.98S7334 1 X HACR O N

72 0 X 0087 0 MACRO Z l 2.7 8 XHACR O ZI O 3.4 4 X HACRO T l 0.8 X 0088 0 HACR O T 2 3 0 DA YROLLINO X 008* 0 DL 00*0 0 HACR O N

14 8 XHACR O T 2 7 DA YROLLINGXD

L 00*1 0 HACR O N

3 4 XHACR O T 3 2 4 HOU R OISCRETE XD

L 00*3 0 HACRO N

3 XHACRO Z l 3.4 0 XHACRO ZI O 3.* 3 X 00*3 0 HACR O T 2 3 HOU R OISCRETE XOL 00*4 0 / « 0093 0 / / EN O O F DAT

A

C-3P.2 5

TABL E C-2
. SAMPL

E PROGRA

M —NORMA

L DISTRIBUTIO N

OOOI O / / 0002 0 / / 0003 0 //SYSI N

D O * 0004 0 HACR O DO

A 0003 0 DAT

A ONE ) 0004 0 * * SE T HOURL YAUTOCORR . (HACR O VALU E X ) FO

R GIVEN

DAILYAUTOCORR. ) 0007 0 D'X ! 0008 0 F24-Y I * * SE T F UIT H N OF 2 4 AV

G FUNCTION

FO R AUTOCORR . (HACR O Y> ) 000* 0 N'NAVG I * * NAV O I S HACRO VALUE FO R HOUR S I

N AV G PERIOD * 0010 0 FN>(((1+D)/(1-D>-2*D*<1-D«*N>/<N«(1-D>**2>>/N> * 0011 0 I F N<2 3 THE N AR«SQRT(FN> ) • • - ' 0012 0 I F N>2 4 THE N AR«SQRT(FN/F24) I 0013 0 t * RSOX

XI S TH E VALU E U

F TARGE T LEVE L FO R RS D OF X

XPERCENT ) 0014 0 DAT

A EXC.PCT1 I SE T ONE * * t 1 PERCEN T EXCEEDANC E FREOUENCY * 0013 0 RS023>1.2/( 1 • 2.324t.25tAR) ) 0014 0 RSD30*1.2/( 1 • 2.324*.30*AR) » 0017 0 RSD33"1.2/( 1 + 2 . 324 * . 33*AR) * 0018 0 EXC.FRE0*1 I 0019 0 DAT

A EXC.1YR * SE T ONE * I t 1 I N I Y R EXCEEDANC E FREQUENCY * 0020 0 RSD23»l.2/( l t Z1«.23«AR> ) 0021 0 RSD30«1.2/< 1 + Zlt.30«AR> ! 0033 0 RSD33»1.3/< 1 + Zlt.33tAR) l 0033 0 EXC.FREG-2 ) 0024 0 DAT

A EXC.10YR * SE T ONE I « * 1 I N 1 0 Y R EXCEEDANC E FREQUENCY * 0023 0 R9D23»1.2/( 1 r Z10*.23*AR> ) 0024 0 RSD30»1.2/( 1 • Z10*.30tAR) l 0027 0 RSD33M.2/ U r Z10*.33*AR> * 0028 0 EXC.FREQ'3 ! 0029 0 DAT

A AVOPER * SE T EXC.PCT 1 EXC.1YR EXC.IOYR I J 0030 0 R23»R0UND(RSD23..01 ) * R30*R0UND(RSD30t.01) I R3I-ROUND(RSD33 . .01 > > 0031 0 LABE L R23»'RS D - J3 ' 0032 0 R30»'RS D » 30 ' 0033 0 R35*'RS D * 3 3 * 0034 0 PRO C FORHAT*VALU E EF O 1-ON E PERCEN T 0033 0 2-ON E PE R YEA R 0034 0 3»0NE PE R TE N YEARS ) 0037 0 PRO C PRIN T 0 LABEL ) VA R R2 3 R3 0 R3S ) 0038 0 I D EXC.FREO ) 0039 0 TITLE ) 0040 0 TITLE S PROJECTE D S0 2 EHISSIO N LEVEL S REQUIRE D T O rIEE T 1. 2 L

bLIMIT ; 0041 0 TITLE 4 ASSURIN G NORHAL DISTRIBUTION l-'O R (V.'tR.IO

F = 0042 0 TITLE S FO

R DAILYAUTOCORRELATION O F Tl ) 0043 0 TITLE 4 AN

D T 2 AVERAGIN

G PERIOD * 0044 0 FORHA T EXC.FRE O EFO . I 0043 0 X* t EN

D OF HAI N

HACRO DOA * 0044 0 * * SE T HACR O VAR . VALUE S FO R X> Y.NAVGtZl»ZtOfTliT 2 ' 0047 0 HACR O X0.974V009 4 X HACRO Y0.9343531 9 XHACR O NA1. G 7ZQ

~ 0048 0 HACR O Z l 2.7 8 XHACR O ZI O 3.1 4 X rlACR O T l 0.7" ? HACRO XZ 3 0 SAY X 0049 0 DO

A * * CAL L HAI N

HACRO T

O PRINT 3 0 DA

YAV G T.'.SL E .-O S 0. 7 AUTOCORR i 0030 0 * * CHANG E HACRO S NAV0.T 2 T O RU N 7 DA YAV G PERIOD * 0031 0 HACR O NAV

O 14 8 XHACRO T 2 7 DAY XDO A 0032 0 HACRO NAV

G 3 4 XHACRO T 2 2 4 HOUR XDO A 0033 0 HACR O NAV

G 3 X HACR O Z l 3.4 0 X

HACR O ZI O 3.7 3 X HACRO T 2 3 HOUR

X 0034 0 OO

A 0033 0 * « CHANG E HACRO VALUE S T O RU N 0. 3 AUTOCORRELATION * 0034 0 HACR O X0.9332274 7 X HACR O Y0.7042897 4 XHACR O M.U' G 72 0 X 0037 0 HACR O Z l 2.7 8 XHACRO ZI O 3.4 4 XHACRO T l 0.5 X Mfilfi O T 2 3 0 CAY * 0038 0 DO

A 0039 0 HACRO NAV

G 14 8 XHACR O T 2 7 DAY XDO A 0040 0 HACRO NAV

G 2 4 7. HACR O T 2 2 4 HOUR XDO A 0041 0 HACR O NAV

G 3 XHACR O Z l 3.4 0 XHACRO ZI O 3.7 8 " 0042 0 HACRO T 2 3 HOUR XDO A 0043 0 * * CHANG E HACRO VALUE S T O RU N 0. 9 AUTOCORR . * 0044 0 HACR O X0.9937334 1 XHACRO Y0.8944441 1 XHACR O NAV O 7J 0 : : 0043 0 HACRO Z l 2.7 8 XHACRO ZI O 3.4 4 XHACRO T l 0.8 XHACRO T 2 3 0 DAY X 0044 0 DO

A 0047 0 HACRO NAV

G 14 8 XHACR O T 2 7 DAY XOO A 0048 0 HACRO NAV

G 2 4 XHACRO T 2 2 4 HOUR XDO A 0049 0 HACRO NAV

G 3 XHACR O Z l 3.4 0 XHACRO ZI O 3.9 8 X 0070 0 HACRO T 2 3 HOUR XDO A 0071 0 / * 0072 0 / / EN O O F DAT A
J..-A.