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The Transport, Chemical Transformation, and Removal of SO2 and Sulfate in the Eastern United States
Atmospheric Pollution 1980,Proceedings of the 14th International Colloquium, Paris, France, May 5--8,1980, M.M. Benarie (Ed.), Studies in Environmental Science, Volume 8 0 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
31
THE TRANSPORT, CHEMICAL TRANSFORMATION, AND REMOVAL OF SO2 AND SULFATE I N THE EASTERN UNITED STATES
GREGORY R . CARMICHAEL and LEONARD K. PETERS U n i v e r s i t y o f Iowa, Iowa City, I A and U n i v e r s i t y o f Kentucky, Lexington, KY (U.S.A.)
ABSTRACT
A r e g i o n a l model o f SOE and s u l f a t e t h a t includes a d v e c t i v e and d i f f u s i v e t r a n s p o r t , homogeneous and heterogeneous o x i d a t i o n , and d r y d e p o s i t i o n o f both species i s described. and wind f i e l d .
The model i n c o r p o r a t e s t e m p o r a l l y and s p a t i a l l y v a r y i n g m i x i n g l a y e r Studies on the dynamic response o f an e l e v a t e d plume t o daytime
v a r i a t i o n s i n v e r t i c a l m i x i n g show the s h i f t toward t h e surface o f the plume c e n t e r l i n e , t h e e x i s t e n c e o f a double maxima i n ground l e v e l concentration, and the t r a p p i n g o f p o l l u t a n t s i n t h e e a r l y evening.
INTRODUCTION S u l f u r d i o x i d e has l o n g been known t o be a major p o l l u t a n t , b u t s t u d i e s now i n d i c a t e t h a t t h e o x i d a t i o n product, s u l f a t e , may present a g r e a t e r h e a l t h hazard and produce a number o f adverse e c o l o g i c a l e f f e c t s ( r e f . 1 ) .
I t i s g e n e r a l l y accepted
t h a t most s u l f a t e i s formed i n t h e atmosphere by chemical conversion from SO2. Long range t r a n s p o r t models can be used t o t r a c e the sources o f SO2 and t o t e s t t h e o r i e s o f t r a n s p o r t , t r a n s f o r m a t i o n , and removal by comparing model p r e d i c t i o n s w i t h measurements from m o n i t o r i n g networks ( r e f . 2-7). I n a p r e v i o u s paper ( r e f . 8 ) , we presented a combined transport/chemistry/surface removal model t o d e s c r i b e t h e r e g i o n a l d i s t r i b u t i o n o f s u l f u r d i o x i d e and s u l f a t e w i t h i n t h e lower troposphere.
I n t h i s paper, we w i l l summarize t h a t development and
study t h e dynamic response o f an e l e v a t e d plume t o daytime v a r i a t i o n s i n v e r t i c a l m i x i n g u s i n g a subset o f t h e model. MODEL DESCRIPTION The r e g i o n a l t r a n s p o r t o f SO2 and s u l f a t e i s modeled w i t h i n an E u l e r i a n framework. The g r i d model i n c o r p o r a t e s chemical transformation,
dry deposition, spatial varia-
t i o n o f topography, and s p a t i a l and temporal v a r i a t i o n s o f m i x i n g l a y e r h e i g h t , wind f i e l d , eddy d i f f u s i v i t y , d e p o s i t i o n v e l o c i t i e s , and temperature and water vapor concentration profiles.
A photochemical SO2 o x i d a t i o n mechanism i s i n c o r p o r a t e d i n t o
32
t h e t r a n s p o r t model w i t h t h e r a t e p a r a m e t e r i z e d u s i n g d i u r n a l l y v a r y i n g r a d i c a l s p e c i e s c o n c e n t r a t i o n s and a f i x e d heterogeneous r a t e c o n s t a n t . The matheniatical a n a l y s i s i s based on t h e coupled, t h r e e - d i m e n s i o n a l a d v e c t i ond i f f u s i o n equations f o r
ack+ at
ac
k= Lax.[ K
U J. ax.
J
(71
SO2 and s u l f a t e
j j ax.
J
+ Rk + Sk
(11,
where c k i s t h e c o n c e n t r a t i o n o f s p e c i e s k, u . i s t h e v e l o c i t y v e c t o r , K is the J jj eddy d i f f u s i v i t y t e n s o r (K. .=O f o r i f j has been assumed), Rk i s t h e r a t e o f forma1J
t i o n o r l o s s b y chemical r e a c t i o n , and Sk i s t h e e m i s s i o n r a t e . V a r i a b l e t o p o g r a p h y i s h a n d l e d by mapping t h e i r r e g u l a r v e r t i c a l r e g i o n i n t o a d i m e n s i o n l e s s r e c t a n g u l a r r e g i o n w i t h t h e t o p s e t a t 3000 m e t e r s .
There a r e t e n
v e r t i c a l g r i d s w i t h h i g h e r r e s o l u t i o n between t h e s u r f a c e and 450 meters which p e r m i t s s i m u l a t i o n o f t r a n s p o r t i n s t a b l e l a y e r s a l o f t and i t s subsequent r e - e n t r a i n ment i n t o t h e m i x i n g l a y e r . The dynamic model uses a G a l e r k i n method f o r t h e n u m e r i c a l s o l u t i o n o f t h e p a r t i a l d i f f e r e n t i a l equations ( r e f . 9).
A t t h e b o u n d a r i e s , two cases a r e i m p o r t a n t .
m a t e r i a l t r a n s p o r t i n t o t h e model r e g i o n , and t h e second i s o u t f l o w .
One i s
I n b o t h cases,
t h e b e s t estimate o f t h e f l u x i s obtained from t h e concentration gradient a t the previous time step. CHEMISTRY OF SO2 AND SULFATE
SO2 o x i d a t i o n mechanism i n c o r p o r a t e d i n t o t h e model i s i n s u f f i c i e n t d e t a i l t o p r e d i c t a r e a l i s t i c o x i d a t i o n r a t e o f SO2 w i t h i n an a c c e p t a b l e c o m p u t a t i o n t i m e . The
Furthermore, b o t h homogeneous and heterogeneous processes a r e i n c l u d e d i n conversion t o sulfate. Homogeneous gas phase c h e m i s t r y A homogeneous gas phase mechanism f o r
SO2 o x i d a t i o n was developed by e v a l u a t i n g
t h e r a t e s o f i n d i v i d u a l r e a c t i o n s f r o m a d e t a i l e d k i n e t i c m o d e l i n g of two smog chamb e r s t u d i e s ( r e f . 10, 1 1 ) .
The r e s u l t s from t h e d e t a i l e d model were t h e n used t o c o n -
s t r u c t a s i m p l i f i e d scheme.
T h i s d e t a i l e d mechanism i n c l u d e d 72 r e a c t i o n s , and a com-
p l e t e d e s c r i p t i o n can be f o u n d elsewhere ( r e f . 7 2 ) .
The o v e r a l l r e s u l t s o f t h a t
s t u d y showed t h a t t h e d e t a i l e d k i n e t i c mechanism s i m u l a t e d w e l l t h e
SO2 o x i d a t i o n
r a t e s o b t a i n e d i n t h e two s t u d i e s . Based on t h e r e s u l t s , t h e most i m p o r t a n t r e a c t i o n s were r e t a i n e d . degree o f accuracy, t h e
To a h i g h
SO2 r a t e e x p r e s s i o n can be s i m p l i f i e d t o
The c o n c e n t r a t i o n s o f OH and H02 show d i u r n a l v a r i a t i o n s . The r a t e e x p r e s s i o n f o r SO2 i s uncoupled f r o m t h o s e f o r
OH and H02 by u s i n g t h e
33
SO2 c o n c e n t r a t i o n a t t h e p r e v i o u s t i m e s t e p i n t h e c a l c u l a t i o n o f OH and H o p .
This
approach agrees w e l l w i t h t h e e x p e r i m e n t a l d a t a and t h e v a l u e s p r e d i c t e d b y t h e det a i l e d model.
The r e l a t i v e c o m p u t a t i o n t i m e s f o r t h e d e t a i l e d and s i m p l i f i e d m o d e l s
a r e a p p r o x i m a t e l y 40: 1. Heterogeneous c h e m i s t r y
I n t h e atmosphere, t h e heterogeneous o x i d a t i o n o f SO2 occurs v i a o x i d a t i o n by i n t h e absence o f c a t a l y s t , c a t a l y t i c o x i d a t i o n by 02, and o x i d a t i o n by 0 3 . p o r t e d r a t e c o n s t a n t s f o r t h e u n c a t a l y z e d o x i d a t i o n by d i s s o l v e d
O2
O2
The r e -
v a r y b y two o r -
d e r s o f magnitude, w i t h most r e p o r t s on t h e l o w end i n d i c a t i n g t h a t t h i s r e a c t i o n i s n o t e x t r e m e l y i m p o r t a n t i n t h e atmosphere.
The c a t a l y z e d o x i d a t i o n o f
SO2 i s most
i m p o r t a n t i n urban a r e a s and s t a c k plumes under c o n d i t i o n s of h i g h h u m i d i t y and h i g h c a t a l y s t concentrations;
i t i s u n l i k e l y t o be s i g n i f i c a n t i n r u r a l areas.
Recent
measurements o f t h e r a t e o f o x i d a t i o n o f SO2 b y d i s s o l v e d O3 a l s o d i f f e r by two o r d e r s o f magnitude.
I f t h e h i g h e r r a t e c o n s t a n t i s c o r r e c t , t h e n t h e o x i d a t i o n by
O3 i s i m p o r t a n t even a t a t m o s p h e r i c background ozone c o n c e n t r a t i o n s . Assuming o x i d a t i o n by d i s s o l v e d 0 3 ,
02,and m e t a l c a t a l y s t s o c c u r s i m u l t a n e o u s l y ,
t h e combined heterogeneous r a t e e x p r e s s i o n can be w r i t t e n as d [SO,2-]
= -1.5
dt
d[SO,] -
60 KIHv*
dt
[H'I
h K
( h K P '3 '3 '3
+ - 02
[Hf]
+
kcatK2[M+I)Cso21
(3) >
i s i n ppm min-', [SO2] i n ppm, H i s H e n r y ' s l a w c o n s t a n t , v* i s t h e 5 aqueous volume p e r volume o f a i r , ho =1x10 -3.3x105L m o l - l s - ' , K - 2 . 2 ~ 1 0 - ~ m o l L - ~ a t m - ~
where d[S04'-]/dt
O3-8 L 2mol - 2 s -1, [M+] Po3 i s t h e O3 p a r t i a l p r e s s u r e , ho =36 ~ 1 O - ~ s -fl o r 3
By c h o o s i n g t y p i c a l r u r a l v a l u e s o f [03]d0ppb 1 a pH o f 4.6 f o r m o d e r a t e l y p o l l u t e d c o n t i n e n t a l c l o u d s , [M+]=5~1O-~mol R- ,
k -2x105R m o l - l s - ' , 03-
T=300°K,
,
and v * = ~ x ~ O - ~ ,Eq. ( 3 ) reduces t o
d[S021 - -3.69~1O-~[SO~] dt
--
(4).
The c o n t r i b u t i o n b y t h e ozone r e a c t i o n i s 92%, 5% by t h e u n c a t a l y z e d r e a c t i o n , and 3% by t h e m e t a l c a t a l y z e d o x i d a t i o n . METEOROLOGICAL DATA The f o l l o w i n g i n p u t m e t e o r o l o g i c a l d a t a a r e r e q u i r e d t o s o l v e t h e atmospheric d i f f u s i o n equation:
mean w i n d v e l o c i t y , eddy d i f f u s i v i t y , temperature, s o l a r r a d i a t i o n ,
p r e c i p i t a t i o n , d r y d e p o s i t i o n v e l o c i t i e s , and w a t e r vapor c o n c e n t r a t i o n .
The temper-
a t u r e p r o f i l e s and s o l a r r a d i a t i o n d a t a a r e used t o e s t i m a t e t h e atmospheric s t a b i l -
i t y and r e a c t i o n r a t e c o n s t a n t s .
P r e c i p i t a t i o n d a t a a r e used t o e s t i m a t e wet deposi-
t i o n processes, and t h e w a t e r vapor c o n c e n t r a t i o n i s an i n p u t t o t h e p h o t o c h e m i s t r y mechanism.
34
Wind f i e l d and eddy d i f f u s i v i t i e s
To provide a mass-consistent wind f i e l d , a v e r t i c a l v e l o c i t y component i s found by numerically solving t h e c o n t i n u i t y equation using an e x p l i c i t second-order f i n i t e d i f f e r e n c e procedure with t h e c o n s t r a i n t t h a t i = O a t p=O.Ol.
The procedure t o c a l c u l a t e eddy d i f f u s i v i t i e s c o n s i s t e n t with theory and observation i s based on the work of Myrup and Ranzieri ( r e f . 1 3 ) . This model estimates t h e Monin-Obukhov length scale based on s t a b i l i t y c l a s s , aerodynamic roughness length, and t h e evaporation r a t e a t the surface. The s t a b i l i t y c l a s s i s estimated from r o u t i n e l y measured meteorological v a r i a b l e s - s u r f a c e w i n d speed, cloud cover, and cloud c e i l i n g ( r e f . 14). The surface roughness and evaporation r a t e s a r e estimated from a map of land use, and mixing l a y e r height within the t r a n s p o r t model i s fusivity profile.
taken i n t o account via t h e eddy d i f As a r e s u l t , eddy d i f f u s i v i t i e s a r e c a l c u l a t e d a t three-hour
i n t e r v a l s t o t r e a t v a r i a t i o n s i n mixing l a y e r heights r e a l i s t i c a l l y . The horizontal d i f f u s i v i t i e s a r e c a l c u l a t e d a s multiples of t h e v e r t i c a l c o e f f i c i e n t s . Deposi t i on vel oci t i e s Dry deposition v e l o c i t i e s a r e c a l c u l a t e d a t three-hour i n t e r v a l s from estimates o f the aerodynamic and s u r f a c e r e s i s t a n c e s based on surface windspeed, surface roughness, evaporation r a t e , and s t a b i l i t y . The a v a i l a b l e data on dry deposition of SO2 t o grass indicated t h a t the s u r f a c e r e s i s t a n c e v a r i e s from 1 t o 3 s cm-l and can be correlated with s u r f a c e roughness ( r e f . 1 2 ) . Surface r e s i s t a n c e s f o r non-grass surfaces a r e estimated from a v a i l a b l e d a t a , and t h e s u l f a t e deposition v e l o c i t i e s a r e calculated a s a l i n e a r function of f r i c t i o n v e l o c i t y ( r e f . 1 6 ) . Average values of the calcul a t e d deposition v e l o c i t i e s ( a t 20-30m) throughout t h e modeling region f o r t h e period of July 4 - J u l y 10, 1974 a r e vS02=0.44cm s-l and vS04=0.26cm s-’. 9 9 MIXING LAYER DYNAMICS An important aspect of the long range t r a n s p o r t of SO2 and s u l f a t e s concerns the i n t e r a c t i o n of elevated plumes with t h e dynamics of t h e mixing l a y e r and the overall v e r t i c a l m i x i n g . These f e a t u r e s a r e included i n the long range t r a n s p o r t model and have been studied using an i s o l a t e d two-dimensional plume from an elevated source. The plume was i n f i n i t e l y wide so t h a t crosswind d i f f u s i o n could be neglected. Convection dominated in t h e d i r e c t i o n of the wind and v e r t i c a l mixing was s o l e l y due t o t u r b u l e n t d i f f u s i o n . The emissions a r e from a 500m e f f e c t i v e source height f o r the period from 8:OOAM t o 9:OOPM. The r e a c t i o n r a t e was fixed a t 3.5% h r - ’ and the depos i t i o n v e l o c i t y was lcm s-’.
The mixing l a y e r height was changed hourly. Carmichael, Yang, and Lin ( r e f . 17) have presented d e t a i l e d r e s u l t s of these calc u l a t i o n s . Concentration i s o p l e t h s f o r d i f f e r e n t times a r e shown in Figure l . Between 9:OOAM and 12:OOPM t h e mixing l a y e r was b e l w t h e source height, and ground level concentrations were correspondingly low. A t noon the mixing l a y e r height reached 600m with fumigation occurring and t h e ground level concentrations increasing. The mixing l a y e r height was maximum (1200m) a t 3:OOPM and then decreased.
M V N W l N D DISTANCE. K Y
F i g . 1. C o n c e n t r a t i o n i s o p l e t h s r e s u l t i n g f r o m e m i s s i o n s f r o m a 500m e l e v a t e d s o u r c e d u r i n g t h e growth and d i s s i p a t i o n o f t h e m i x i n g l a y e r a t t i m e s c o r r e s p o n d i n g t o a ) 9:59 AM, b ) 10:59 AM, c ) 1:59 PM, d ) 3:59 PM, e ) 5:59 PM, f ) 7:59 PM, and g ) 8:59 PM.
m
$-
m
MVNWINO OISIANCE. K Y
F i g u r e s l c and l e show t h e c o n c e n t r a t i o n f i e l d s a t 1:59 and 5:59PM,
respectively.
A t t h e s e t i m e s t h e d i f f u s i v i t y p r o f i l e s were s i m i l a r , b u t t h e c o n c e n t r a t i o n f i e l d s were q u i t e d i f f e r e n t .
When mass reached h i g h a l t i t u d e s , i t remained a l o f t u n t i l
being advected from the region.
I n t h e r e g i o n above t h e m i x i n g l a y e r , s t a b l e atmo-
s p h e r i c c o n d i t i o n s and maximum w i n d v e l o c i t i e s o f t e n o c c u r , e s p e c i a l l y a t n i g h t . T h i s m a t e r i a l can r e m a i n a l o f t and be t r a n s p o r t e d l o n g d i s t a n c e s w i t h l i t t l e v e r t i c a l spread u n t i l f u m i g a t i o n o c c u r s t h e n e x t a f t e r n o o n .
This i s important i n the transport
o f secondary p o l 1 u t a n t s such as s u l f a t e s .
I n t h e e a r l y e v e n i n g ( s e e F i g u r e I f ) m a t e r i a l n e a r t h e s u r f a c e was t r a p p e d , and h i g h ground l e v e l c o n c e n t r a t i o n s p e r s i s t e d .
T h i s m a t e r i a l would remain u n t i l i t i s
removed by d r y d e p o s i t i o n , chemical r e a c t i o n , and/or h o r i z o n t a l c o n v e c t i o n .
The i n -
f l u e n c e o f d r y d e p o s i t i o n on plume geometry i s a p p a r e n t i n F i g u r e s l c and I d .
Mass
was t r a n s f e r r e d t o t h e s u r f a c e , w h i c h caused t h e plume c e n t e r l i n e t o s h i f t downward. C a l c u l a t e d ground l e v e l c o n c e n t r a t i o n s o f t h e p r i m a r y p o l l u t a n t a t d i f f e r e n t downw i n d l o c a t i o n s a r e shown i n F i g u r e 2 as a f u n c t i o n o f t i m e . curred a t a l l locations.
Note t h a t two maxima oc-
The f i r s t o c c u r r e d as t h e m i x i n g l a y e r h e i g h t i n c r e a s e d j u s t
above t h e s o u r c e h e i g h t , w h i l e t h e second one o c c u r r e d as t h e m i x i n g l a y e r h e i g h t r e turned t o t h a t l e v e l i n t h e l a t e afternoon.
The d e c r e a s i n g c o n c e n t r a t i o n s i n mid-
a f t e r n o o n were due t o d i l u t i o n caused b y c o n t i n u e d growth o f t h e m i x i n g l a y e r .
The
o c c u r r e n c e o f t h e second maximum was delayed, and t h e ground l e v e l c o n c e n t r a t i o n s a t 9:OOPM were h i g h e r a t t h e i n t e r m e d i a t e downwind l o c a t i o n s .
T h i s ground l e v e l concen-
t r a t i o n b e h a v i o r has been observed i n t h e f i e l d . W o l f f e t a l . ( r e f . 1 8 ) found ground l e v e l SO2 c o n c e n t r a t i o n p r o f i l e s s i m i l a r t o t h o s e i n F i g u r e 2. I n t h e i r work, a
36 E .7
-GROUND LEVEL CONCENTRATION\
1400
1300 Ix)o 1100 1000
900
z.
;
:
- 2w 700
600 -0
400 300 200
3 z
R
e 2
100 0
Fig. 2. Calculated ground level concentrations a s a function of time of day a t d i f f e r e n t downwind p o s i t i o n s r e s u l t i n g from emissions from a 500m elevated source during t h e growth and d i s s i p a t i o n of the mixing l a y e r . s i n g l e p r o f i l e ( t h e i r Figure 2b) obtained by averaging nine days of observational data showed t h e presence of t h i s double maxima. ACKNOWLEDGEMENTS Computer time has been provided by the NASA Langley Research Center. The a s s i s tance of Dr. Henry G . Reichle, J r . i n making t h i s possible i s appreciated. REFERENCES 1 U.S. Dept. Ag., Proc. 1 s t I n t . Symp. Acid Precip. and Forest Ecosystem, USOA Forest Service Gen. Tech. Rep. WE-23, 1976. 2 M.C. MacCracken, Atmos. Environ., 12(1978) 649-659. 3 W.E. Wilson, Atmos. Environ., 12(1978)537-547. 4 R . M . Perhac, 2nd Plat. Conf. on Interagency EnergylEnviron. R & D Program, Washington, D . C . , June, 1977. 5 J.P. Bromberg and T.G. Fox, Intergovernmental cooperation in "up-valley'' pollut i o n t r a n s p o r t management, Final Rep. of Ohio River Valley Assembly, 1978. 6 5. O t t a r , Atmos. Environ., 12(1978)445-454. 7 G.M. Hidy, E . Y . Tong, P.K. Mueller, S. Rao, I . Thomson, F. Berlandi, D. Muldoon, D. McNaughton and A. Majahad, Design of t h e S u l f a t e Regional Experiment, PB-251701, 1976. 8 G . R . Carmichael and L . K . P e t e r s , Proc. 4th Symp. Turbulence, Diffusion, Air P o l l u t i o n , Reno, Nevada, January, 1979, Amer. Meteor. SOC. 9 G.R. Carmichael, T. Kitada and L . K . P e t e r s , Comp. and Fluids, (1980) in press. 10 W.C. Kocmond and J.Y. Yang, S u l f u r dioxide photooxidation r a t e s and aerosol format i o n mechanisms: A smog chamber study. Calspan Corp., PB-260-910, 1976. 11 J.W. B r a d s t r e e t , 66th Ann. APCA Meeting, Chicago, IL, June, 1973. 12 G.R. Carmichael, Development of a regional transport/transformation/removal model f o r SO2 and s u l f a t e in the Eastern United S t a t e s , Ph.D. D i s s . , Univ. of K Y , 1979. 13 L.O. Myrup and A.J. Ranzieri, A c o n s i s t e n t scheme f o r estimating d i f f u s i v i t i e s t o be used i n a i r q u a l i t y models, PB-272-484, 1976. 14 D.B. Turner, J . Air P o l l u t . Control Assoc., 11(1961)483-489. 15 G . C . Holzworth, Mon. Wea. Rev., 92(1964)235-242. 16 W . G . N . S l i n n , Symp. Atmospheric-Surface Exchange of P a r t i c u l a t e and Gaseous Pollut a n t s , Richland, Washington, 1974. 17 G . R . Carmichael, D-K Yang, and C . Lin, Atmos. Environ. (1980) s u b . f o r pub. 18 G.T. Wolff, P.R. Monson and M.A. Ferman, Environ. S c i . Tech., 13(1979)1271-1276.
31
THE TRANSPORT, CHEMICAL TRANSFORMATION, AND REMOVAL OF SO2 AND SULFATE I N THE EASTERN UNITED STATES
GREGORY R . CARMICHAEL and LEONARD K. PETERS U n i v e r s i t y o f Iowa, Iowa City, I A and U n i v e r s i t y o f Kentucky, Lexington, KY (U.S.A.)
ABSTRACT
A r e g i o n a l model o f SOE and s u l f a t e t h a t includes a d v e c t i v e and d i f f u s i v e t r a n s p o r t , homogeneous and heterogeneous o x i d a t i o n , and d r y d e p o s i t i o n o f both species i s described. and wind f i e l d .
The model i n c o r p o r a t e s t e m p o r a l l y and s p a t i a l l y v a r y i n g m i x i n g l a y e r Studies on the dynamic response o f an e l e v a t e d plume t o daytime
v a r i a t i o n s i n v e r t i c a l m i x i n g show the s h i f t toward t h e surface o f the plume c e n t e r l i n e , t h e e x i s t e n c e o f a double maxima i n ground l e v e l concentration, and the t r a p p i n g o f p o l l u t a n t s i n t h e e a r l y evening.
INTRODUCTION S u l f u r d i o x i d e has l o n g been known t o be a major p o l l u t a n t , b u t s t u d i e s now i n d i c a t e t h a t t h e o x i d a t i o n product, s u l f a t e , may present a g r e a t e r h e a l t h hazard and produce a number o f adverse e c o l o g i c a l e f f e c t s ( r e f . 1 ) .
I t i s g e n e r a l l y accepted
t h a t most s u l f a t e i s formed i n t h e atmosphere by chemical conversion from SO2. Long range t r a n s p o r t models can be used t o t r a c e the sources o f SO2 and t o t e s t t h e o r i e s o f t r a n s p o r t , t r a n s f o r m a t i o n , and removal by comparing model p r e d i c t i o n s w i t h measurements from m o n i t o r i n g networks ( r e f . 2-7). I n a p r e v i o u s paper ( r e f . 8 ) , we presented a combined transport/chemistry/surface removal model t o d e s c r i b e t h e r e g i o n a l d i s t r i b u t i o n o f s u l f u r d i o x i d e and s u l f a t e w i t h i n t h e lower troposphere.
I n t h i s paper, we w i l l summarize t h a t development and
study t h e dynamic response o f an e l e v a t e d plume t o daytime v a r i a t i o n s i n v e r t i c a l m i x i n g u s i n g a subset o f t h e model. MODEL DESCRIPTION The r e g i o n a l t r a n s p o r t o f SO2 and s u l f a t e i s modeled w i t h i n an E u l e r i a n framework. The g r i d model i n c o r p o r a t e s chemical transformation,
dry deposition, spatial varia-
t i o n o f topography, and s p a t i a l and temporal v a r i a t i o n s o f m i x i n g l a y e r h e i g h t , wind f i e l d , eddy d i f f u s i v i t y , d e p o s i t i o n v e l o c i t i e s , and temperature and water vapor concentration profiles.
A photochemical SO2 o x i d a t i o n mechanism i s i n c o r p o r a t e d i n t o
32
t h e t r a n s p o r t model w i t h t h e r a t e p a r a m e t e r i z e d u s i n g d i u r n a l l y v a r y i n g r a d i c a l s p e c i e s c o n c e n t r a t i o n s and a f i x e d heterogeneous r a t e c o n s t a n t . The matheniatical a n a l y s i s i s based on t h e coupled, t h r e e - d i m e n s i o n a l a d v e c t i ond i f f u s i o n equations f o r
ack+ at
ac
k= Lax.[ K
U J. ax.
J
(71
SO2 and s u l f a t e
j j ax.
J
+ Rk + Sk
(11,
where c k i s t h e c o n c e n t r a t i o n o f s p e c i e s k, u . i s t h e v e l o c i t y v e c t o r , K is the J jj eddy d i f f u s i v i t y t e n s o r (K. .=O f o r i f j has been assumed), Rk i s t h e r a t e o f forma1J
t i o n o r l o s s b y chemical r e a c t i o n , and Sk i s t h e e m i s s i o n r a t e . V a r i a b l e t o p o g r a p h y i s h a n d l e d by mapping t h e i r r e g u l a r v e r t i c a l r e g i o n i n t o a d i m e n s i o n l e s s r e c t a n g u l a r r e g i o n w i t h t h e t o p s e t a t 3000 m e t e r s .
There a r e t e n
v e r t i c a l g r i d s w i t h h i g h e r r e s o l u t i o n between t h e s u r f a c e and 450 meters which p e r m i t s s i m u l a t i o n o f t r a n s p o r t i n s t a b l e l a y e r s a l o f t and i t s subsequent r e - e n t r a i n ment i n t o t h e m i x i n g l a y e r . The dynamic model uses a G a l e r k i n method f o r t h e n u m e r i c a l s o l u t i o n o f t h e p a r t i a l d i f f e r e n t i a l equations ( r e f . 9).
A t t h e b o u n d a r i e s , two cases a r e i m p o r t a n t .
m a t e r i a l t r a n s p o r t i n t o t h e model r e g i o n , and t h e second i s o u t f l o w .
One i s
I n b o t h cases,
t h e b e s t estimate o f t h e f l u x i s obtained from t h e concentration gradient a t the previous time step. CHEMISTRY OF SO2 AND SULFATE
SO2 o x i d a t i o n mechanism i n c o r p o r a t e d i n t o t h e model i s i n s u f f i c i e n t d e t a i l t o p r e d i c t a r e a l i s t i c o x i d a t i o n r a t e o f SO2 w i t h i n an a c c e p t a b l e c o m p u t a t i o n t i m e . The
Furthermore, b o t h homogeneous and heterogeneous processes a r e i n c l u d e d i n conversion t o sulfate. Homogeneous gas phase c h e m i s t r y A homogeneous gas phase mechanism f o r
SO2 o x i d a t i o n was developed by e v a l u a t i n g
t h e r a t e s o f i n d i v i d u a l r e a c t i o n s f r o m a d e t a i l e d k i n e t i c m o d e l i n g of two smog chamb e r s t u d i e s ( r e f . 10, 1 1 ) .
The r e s u l t s from t h e d e t a i l e d model were t h e n used t o c o n -
s t r u c t a s i m p l i f i e d scheme.
T h i s d e t a i l e d mechanism i n c l u d e d 72 r e a c t i o n s , and a com-
p l e t e d e s c r i p t i o n can be f o u n d elsewhere ( r e f . 7 2 ) .
The o v e r a l l r e s u l t s o f t h a t
s t u d y showed t h a t t h e d e t a i l e d k i n e t i c mechanism s i m u l a t e d w e l l t h e
SO2 o x i d a t i o n
r a t e s o b t a i n e d i n t h e two s t u d i e s . Based on t h e r e s u l t s , t h e most i m p o r t a n t r e a c t i o n s were r e t a i n e d . degree o f accuracy, t h e
To a h i g h
SO2 r a t e e x p r e s s i o n can be s i m p l i f i e d t o
The c o n c e n t r a t i o n s o f OH and H02 show d i u r n a l v a r i a t i o n s . The r a t e e x p r e s s i o n f o r SO2 i s uncoupled f r o m t h o s e f o r
OH and H02 by u s i n g t h e
33
SO2 c o n c e n t r a t i o n a t t h e p r e v i o u s t i m e s t e p i n t h e c a l c u l a t i o n o f OH and H o p .
This
approach agrees w e l l w i t h t h e e x p e r i m e n t a l d a t a and t h e v a l u e s p r e d i c t e d b y t h e det a i l e d model.
The r e l a t i v e c o m p u t a t i o n t i m e s f o r t h e d e t a i l e d and s i m p l i f i e d m o d e l s
a r e a p p r o x i m a t e l y 40: 1. Heterogeneous c h e m i s t r y
I n t h e atmosphere, t h e heterogeneous o x i d a t i o n o f SO2 occurs v i a o x i d a t i o n by i n t h e absence o f c a t a l y s t , c a t a l y t i c o x i d a t i o n by 02, and o x i d a t i o n by 0 3 . p o r t e d r a t e c o n s t a n t s f o r t h e u n c a t a l y z e d o x i d a t i o n by d i s s o l v e d
O2
O2
The r e -
v a r y b y two o r -
d e r s o f magnitude, w i t h most r e p o r t s on t h e l o w end i n d i c a t i n g t h a t t h i s r e a c t i o n i s n o t e x t r e m e l y i m p o r t a n t i n t h e atmosphere.
The c a t a l y z e d o x i d a t i o n o f
SO2 i s most
i m p o r t a n t i n urban a r e a s and s t a c k plumes under c o n d i t i o n s of h i g h h u m i d i t y and h i g h c a t a l y s t concentrations;
i t i s u n l i k e l y t o be s i g n i f i c a n t i n r u r a l areas.
Recent
measurements o f t h e r a t e o f o x i d a t i o n o f SO2 b y d i s s o l v e d O3 a l s o d i f f e r by two o r d e r s o f magnitude.
I f t h e h i g h e r r a t e c o n s t a n t i s c o r r e c t , t h e n t h e o x i d a t i o n by
O3 i s i m p o r t a n t even a t a t m o s p h e r i c background ozone c o n c e n t r a t i o n s . Assuming o x i d a t i o n by d i s s o l v e d 0 3 ,
02,and m e t a l c a t a l y s t s o c c u r s i m u l t a n e o u s l y ,
t h e combined heterogeneous r a t e e x p r e s s i o n can be w r i t t e n as d [SO,2-]
= -1.5
dt
d[SO,] -
60 KIHv*
dt
[H'I
h K
( h K P '3 '3 '3
+ - 02
[Hf]
+
kcatK2[M+I)Cso21
(3) >
i s i n ppm min-', [SO2] i n ppm, H i s H e n r y ' s l a w c o n s t a n t , v* i s t h e 5 aqueous volume p e r volume o f a i r , ho =1x10 -3.3x105L m o l - l s - ' , K - 2 . 2 ~ 1 0 - ~ m o l L - ~ a t m - ~
where d[S04'-]/dt
O3-8 L 2mol - 2 s -1, [M+] Po3 i s t h e O3 p a r t i a l p r e s s u r e , ho =36 ~ 1 O - ~ s -fl o r 3
By c h o o s i n g t y p i c a l r u r a l v a l u e s o f [03]d0ppb 1 a pH o f 4.6 f o r m o d e r a t e l y p o l l u t e d c o n t i n e n t a l c l o u d s , [M+]=5~1O-~mol R- ,
k -2x105R m o l - l s - ' , 03-
T=300°K,
,
and v * = ~ x ~ O - ~ ,Eq. ( 3 ) reduces t o
d[S021 - -3.69~1O-~[SO~] dt
--
(4).
The c o n t r i b u t i o n b y t h e ozone r e a c t i o n i s 92%, 5% by t h e u n c a t a l y z e d r e a c t i o n , and 3% by t h e m e t a l c a t a l y z e d o x i d a t i o n . METEOROLOGICAL DATA The f o l l o w i n g i n p u t m e t e o r o l o g i c a l d a t a a r e r e q u i r e d t o s o l v e t h e atmospheric d i f f u s i o n equation:
mean w i n d v e l o c i t y , eddy d i f f u s i v i t y , temperature, s o l a r r a d i a t i o n ,
p r e c i p i t a t i o n , d r y d e p o s i t i o n v e l o c i t i e s , and w a t e r vapor c o n c e n t r a t i o n .
The temper-
a t u r e p r o f i l e s and s o l a r r a d i a t i o n d a t a a r e used t o e s t i m a t e t h e atmospheric s t a b i l -
i t y and r e a c t i o n r a t e c o n s t a n t s .
P r e c i p i t a t i o n d a t a a r e used t o e s t i m a t e wet deposi-
t i o n processes, and t h e w a t e r vapor c o n c e n t r a t i o n i s an i n p u t t o t h e p h o t o c h e m i s t r y mechanism.
34
Wind f i e l d and eddy d i f f u s i v i t i e s
To provide a mass-consistent wind f i e l d , a v e r t i c a l v e l o c i t y component i s found by numerically solving t h e c o n t i n u i t y equation using an e x p l i c i t second-order f i n i t e d i f f e r e n c e procedure with t h e c o n s t r a i n t t h a t i = O a t p=O.Ol.
The procedure t o c a l c u l a t e eddy d i f f u s i v i t i e s c o n s i s t e n t with theory and observation i s based on the work of Myrup and Ranzieri ( r e f . 1 3 ) . This model estimates t h e Monin-Obukhov length scale based on s t a b i l i t y c l a s s , aerodynamic roughness length, and t h e evaporation r a t e a t the surface. The s t a b i l i t y c l a s s i s estimated from r o u t i n e l y measured meteorological v a r i a b l e s - s u r f a c e w i n d speed, cloud cover, and cloud c e i l i n g ( r e f . 14). The surface roughness and evaporation r a t e s a r e estimated from a map of land use, and mixing l a y e r height within the t r a n s p o r t model i s fusivity profile.
taken i n t o account via t h e eddy d i f As a r e s u l t , eddy d i f f u s i v i t i e s a r e c a l c u l a t e d a t three-hour
i n t e r v a l s t o t r e a t v a r i a t i o n s i n mixing l a y e r heights r e a l i s t i c a l l y . The horizontal d i f f u s i v i t i e s a r e c a l c u l a t e d a s multiples of t h e v e r t i c a l c o e f f i c i e n t s . Deposi t i on vel oci t i e s Dry deposition v e l o c i t i e s a r e c a l c u l a t e d a t three-hour i n t e r v a l s from estimates o f the aerodynamic and s u r f a c e r e s i s t a n c e s based on surface windspeed, surface roughness, evaporation r a t e , and s t a b i l i t y . The a v a i l a b l e data on dry deposition of SO2 t o grass indicated t h a t the s u r f a c e r e s i s t a n c e v a r i e s from 1 t o 3 s cm-l and can be correlated with s u r f a c e roughness ( r e f . 1 2 ) . Surface r e s i s t a n c e s f o r non-grass surfaces a r e estimated from a v a i l a b l e d a t a , and t h e s u l f a t e deposition v e l o c i t i e s a r e calculated a s a l i n e a r function of f r i c t i o n v e l o c i t y ( r e f . 1 6 ) . Average values of the calcul a t e d deposition v e l o c i t i e s ( a t 20-30m) throughout t h e modeling region f o r t h e period of July 4 - J u l y 10, 1974 a r e vS02=0.44cm s-l and vS04=0.26cm s-’. 9 9 MIXING LAYER DYNAMICS An important aspect of the long range t r a n s p o r t of SO2 and s u l f a t e s concerns the i n t e r a c t i o n of elevated plumes with t h e dynamics of t h e mixing l a y e r and the overall v e r t i c a l m i x i n g . These f e a t u r e s a r e included i n the long range t r a n s p o r t model and have been studied using an i s o l a t e d two-dimensional plume from an elevated source. The plume was i n f i n i t e l y wide so t h a t crosswind d i f f u s i o n could be neglected. Convection dominated in t h e d i r e c t i o n of the wind and v e r t i c a l mixing was s o l e l y due t o t u r b u l e n t d i f f u s i o n . The emissions a r e from a 500m e f f e c t i v e source height f o r the period from 8:OOAM t o 9:OOPM. The r e a c t i o n r a t e was fixed a t 3.5% h r - ’ and the depos i t i o n v e l o c i t y was lcm s-’.
The mixing l a y e r height was changed hourly. Carmichael, Yang, and Lin ( r e f . 17) have presented d e t a i l e d r e s u l t s of these calc u l a t i o n s . Concentration i s o p l e t h s f o r d i f f e r e n t times a r e shown in Figure l . Between 9:OOAM and 12:OOPM t h e mixing l a y e r was b e l w t h e source height, and ground level concentrations were correspondingly low. A t noon the mixing l a y e r height reached 600m with fumigation occurring and t h e ground level concentrations increasing. The mixing l a y e r height was maximum (1200m) a t 3:OOPM and then decreased.
M V N W l N D DISTANCE. K Y
F i g . 1. C o n c e n t r a t i o n i s o p l e t h s r e s u l t i n g f r o m e m i s s i o n s f r o m a 500m e l e v a t e d s o u r c e d u r i n g t h e growth and d i s s i p a t i o n o f t h e m i x i n g l a y e r a t t i m e s c o r r e s p o n d i n g t o a ) 9:59 AM, b ) 10:59 AM, c ) 1:59 PM, d ) 3:59 PM, e ) 5:59 PM, f ) 7:59 PM, and g ) 8:59 PM.
m
$-
m
MVNWINO OISIANCE. K Y
F i g u r e s l c and l e show t h e c o n c e n t r a t i o n f i e l d s a t 1:59 and 5:59PM,
respectively.
A t t h e s e t i m e s t h e d i f f u s i v i t y p r o f i l e s were s i m i l a r , b u t t h e c o n c e n t r a t i o n f i e l d s were q u i t e d i f f e r e n t .
When mass reached h i g h a l t i t u d e s , i t remained a l o f t u n t i l
being advected from the region.
I n t h e r e g i o n above t h e m i x i n g l a y e r , s t a b l e atmo-
s p h e r i c c o n d i t i o n s and maximum w i n d v e l o c i t i e s o f t e n o c c u r , e s p e c i a l l y a t n i g h t . T h i s m a t e r i a l can r e m a i n a l o f t and be t r a n s p o r t e d l o n g d i s t a n c e s w i t h l i t t l e v e r t i c a l spread u n t i l f u m i g a t i o n o c c u r s t h e n e x t a f t e r n o o n .
This i s important i n the transport
o f secondary p o l 1 u t a n t s such as s u l f a t e s .
I n t h e e a r l y e v e n i n g ( s e e F i g u r e I f ) m a t e r i a l n e a r t h e s u r f a c e was t r a p p e d , and h i g h ground l e v e l c o n c e n t r a t i o n s p e r s i s t e d .
T h i s m a t e r i a l would remain u n t i l i t i s
removed by d r y d e p o s i t i o n , chemical r e a c t i o n , and/or h o r i z o n t a l c o n v e c t i o n .
The i n -
f l u e n c e o f d r y d e p o s i t i o n on plume geometry i s a p p a r e n t i n F i g u r e s l c and I d .
Mass
was t r a n s f e r r e d t o t h e s u r f a c e , w h i c h caused t h e plume c e n t e r l i n e t o s h i f t downward. C a l c u l a t e d ground l e v e l c o n c e n t r a t i o n s o f t h e p r i m a r y p o l l u t a n t a t d i f f e r e n t downw i n d l o c a t i o n s a r e shown i n F i g u r e 2 as a f u n c t i o n o f t i m e . curred a t a l l locations.
Note t h a t two maxima oc-
The f i r s t o c c u r r e d as t h e m i x i n g l a y e r h e i g h t i n c r e a s e d j u s t
above t h e s o u r c e h e i g h t , w h i l e t h e second one o c c u r r e d as t h e m i x i n g l a y e r h e i g h t r e turned t o t h a t l e v e l i n t h e l a t e afternoon.
The d e c r e a s i n g c o n c e n t r a t i o n s i n mid-
a f t e r n o o n were due t o d i l u t i o n caused b y c o n t i n u e d growth o f t h e m i x i n g l a y e r .
The
o c c u r r e n c e o f t h e second maximum was delayed, and t h e ground l e v e l c o n c e n t r a t i o n s a t 9:OOPM were h i g h e r a t t h e i n t e r m e d i a t e downwind l o c a t i o n s .
T h i s ground l e v e l concen-
t r a t i o n b e h a v i o r has been observed i n t h e f i e l d . W o l f f e t a l . ( r e f . 1 8 ) found ground l e v e l SO2 c o n c e n t r a t i o n p r o f i l e s s i m i l a r t o t h o s e i n F i g u r e 2. I n t h e i r work, a
36 E .7
-GROUND LEVEL CONCENTRATION\
1400
1300 Ix)o 1100 1000
900
z.
;
:
- 2w 700
600 -0
400 300 200
3 z
R
e 2
100 0
Fig. 2. Calculated ground level concentrations a s a function of time of day a t d i f f e r e n t downwind p o s i t i o n s r e s u l t i n g from emissions from a 500m elevated source during t h e growth and d i s s i p a t i o n of the mixing l a y e r . s i n g l e p r o f i l e ( t h e i r Figure 2b) obtained by averaging nine days of observational data showed t h e presence of t h i s double maxima. ACKNOWLEDGEMENTS Computer time has been provided by the NASA Langley Research Center. The a s s i s tance of Dr. Henry G . Reichle, J r . i n making t h i s possible i s appreciated. REFERENCES 1 U.S. Dept. Ag., Proc. 1 s t I n t . Symp. Acid Precip. and Forest Ecosystem, USOA Forest Service Gen. Tech. Rep. WE-23, 1976. 2 M.C. MacCracken, Atmos. Environ., 12(1978) 649-659. 3 W.E. Wilson, Atmos. Environ., 12(1978)537-547. 4 R . M . Perhac, 2nd Plat. Conf. on Interagency EnergylEnviron. R & D Program, Washington, D . C . , June, 1977. 5 J.P. Bromberg and T.G. Fox, Intergovernmental cooperation in "up-valley'' pollut i o n t r a n s p o r t management, Final Rep. of Ohio River Valley Assembly, 1978. 6 5. O t t a r , Atmos. Environ., 12(1978)445-454. 7 G.M. Hidy, E . Y . Tong, P.K. Mueller, S. Rao, I . Thomson, F. Berlandi, D. Muldoon, D. McNaughton and A. Majahad, Design of t h e S u l f a t e Regional Experiment, PB-251701, 1976. 8 G . R . Carmichael and L . K . P e t e r s , Proc. 4th Symp. Turbulence, Diffusion, Air P o l l u t i o n , Reno, Nevada, January, 1979, Amer. Meteor. SOC. 9 G.R. Carmichael, T. Kitada and L . K . P e t e r s , Comp. and Fluids, (1980) in press. 10 W.C. Kocmond and J.Y. Yang, S u l f u r dioxide photooxidation r a t e s and aerosol format i o n mechanisms: A smog chamber study. Calspan Corp., PB-260-910, 1976. 11 J.W. B r a d s t r e e t , 66th Ann. APCA Meeting, Chicago, IL, June, 1973. 12 G.R. Carmichael, Development of a regional transport/transformation/removal model f o r SO2 and s u l f a t e in the Eastern United S t a t e s , Ph.D. D i s s . , Univ. of K Y , 1979. 13 L.O. Myrup and A.J. Ranzieri, A c o n s i s t e n t scheme f o r estimating d i f f u s i v i t i e s t o be used i n a i r q u a l i t y models, PB-272-484, 1976. 14 D.B. Turner, J . Air P o l l u t . Control Assoc., 11(1961)483-489. 15 G . C . Holzworth, Mon. Wea. Rev., 92(1964)235-242. 16 W . G . N . S l i n n , Symp. Atmospheric-Surface Exchange of P a r t i c u l a t e and Gaseous Pollut a n t s , Richland, Washington, 1974. 17 G . R . Carmichael, D-K Yang, and C . Lin, Atmos. Environ. (1980) s u b . f o r pub. 18 G.T. Wolff, P.R. Monson and M.A. Ferman, Environ. S c i . Tech., 13(1979)1271-1276.