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A study of the persistencies of SO2 concentrations exceeding limit values in the ambient air of an urban area
The Science of the Total Environment, 57 (1986) 19-28 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
19
A S T U D Y OF THE P E R S I S T E N C I E S OF SO2 CONCENTRATIONS E X C E E D I N G LIMIT V A L U E S IN THE A M B I E N T AIR OF AN U R B A N AREA
SERGE HALLEZ, ALAIN DEROUANE and GEERT VERDUYN Institute for Hygiene and Epidemiology, Air Pollution Division, rue J. Wytsman, 14B 1050 Brussels (Belgium)
(Received April 13th, 1983; accepted March 20th 1986)
ABSTRACT This study of the persistencies of S O 2 concentrations takes the parameters of the SO2frequency distributions as a basis. A scheme is proposed for their calculation which allows the forecast of SO2 pollution episodes.
INTRODUCTION T h e L a r s e n h y p o t h e s i s (1969) t h a t SO2 c o n c e n t r a t i o n s in the a m b i e n t air of u r b a n a r e a s are log-normally d i s t r i b u t e d is well k n o w n . Some a u t h o r s (Benarie, 1980; G e o r g o p o u l o s and S t e i n e r 1982) h a v e s h o w n the l i m i t a t i o n s of this a p p r o a c h while emphasizing its merits and i n d i s p u t a b l e usefulness. A distribution f u n c t i o n is, h o w e v e r , u n a b l e to give a c o m p l e t e d e s c r i p t i o n of the statistical c h a r a c t e r i s t i c s of a c h r o n o l o g i c a l series. F o r example, the d i s t r i b u t i o n f u n c t i o n enables the d e t e r m i n a t i o n of the n u m b e r of days w h e n limit v a l u e s are exceeded, b u t does n o t give a n y i n f o r m a t i o n as to w h e t h e r or n o t t h e y are i n d e p e n d e n t or c o n s e c u t i v e days. Likewise, a m b i e n t air s t a n d a r d s are often assessed by two p a r a m e t e r s , the m e d i a n and a high p e r c e n t i l e (e.g. 95e p. 97e p) w i t h o u t giving a t t e n t i o n to the fact t h a t the o c c u r r e n c e s of a h i g h c o n c e n t r a tion d u r i n g a given n u m b e r of days m a y i m p a i r h e a l t h and the e n v i r o n m e n t in quite different ways a c c o r d i n g to w h e t h e r t h e days are i n d e p e n d e n t or not. This gap c a n be filled by the c a l c u l a t i o n of the persistencies. T h e first step consists of establishing a statistical r e l a t i o n s h i p b e t w e e n the c o n c e n t r a t i o n m e a s u r e d d u r i n g a given day and the c o n c e n t r a t i o n of t h e p r e c e d i n g day. The second step consists of the u t i l i z a t i o n of this r e l a t i o n s h i p in o r d e r to c a l c u l a t e the p r o b a b i l i t y of m e a s u r i n g a n e x c e e d i n g c o n c e n t r a t i o n d u r i n g a given day w h e n a n e x c e e d i n g c o n c e n t r a t i o n has been m e a s u r e d the p r e c e d i n g day. Annual p e r s i s t e n c i e s c a n t h e n be calculated.
0048-9697/86/$03.50
© 1986 Elsevier Science Publishers B.V.
20
MG=gGug/m3 DSG=2
95 %-
l
90 %-
80 ~,"
~
÷
70 %" 60 %'
/
50 % 40 %. 30 ~,!
20 %-
Ci (ug/m3 }-4~
5e
75
I00
158
20~
258
dsg-I .GO
1.54
~..49
1.4G
1,45
1.41
1.33
40
50
Fig. 1. Variation of ag(i+l) and [ln C i
75
-
100
150
200
300
CCt+l)(uglm3)
In mg(i+l)] as a function of Z i.
THE DISTRIBUTION OF DAILY AVERAGE CONCENTRATIONS AS A FUNCTION OF THE CONCENTRATION OF THE PRECEDING DAY The c a l c u l a t i o n s were made on daily average SO2 c o n c e n t r a t i o n s measured at 10 sampling sites of the B e l g i u m Sulphur-Smoke N e t w o r k located in the urban area of Brussels. A 'town daily average' was determined by c a l c u l a t i n g for e a c h day the arithmetic m e a n of the 10 daily averages. More t h a n 4,000 'town daily averages' Ci gathered during 12 years were available. The C i + l are the 'town daily averages' determined for the next day. The c u m u l a t i v e distributionoftheCi+lforsevenCiclasses(40 + 5,50 _+ 5,75 _+ 5,100 _+ 10,150 + 10, 200 + 10 and 220 + 10/xg SO2 m -a) are given in Fig. 1. These distributions are fairly log-normal and are characterized by mg(i+l) and ag(i+l). A s s u m i n g a lognormal distribution for the (7/variable, it can be transformed into a standardized variable Z i given by z,
=
In Ci - In Mg In Sg
(1)
where Zi is the number of (In Sg) b e t w e e n In (7/and In Mg, Mg is the geometric m e a n of the Q, and Sg is the standard geometric d e v i a t i o n of the Ci. Figure 1 s h o w s a regular v a r i a t i o n of ag(i+~) (slope of the line) and [ln Ci -
21 LOG(Ci/Mg(i+l)) .24
.16
t .~/~/ff''~I , ~ "/
9"
/J/
•138
/
-. BB
°J
-.16 -l.
,," _ t
' .fi
-.6
Fig. 2. Linear
regression
of [In C i
'
'
1.2
Zi 1.8
- In rag(i+1)] as a function
of Z i.
In mg(/+,)] as a f u n c t i o n of Zi. In order to find these relationships, 21 sets of data from different m o n i t o r i n g stations and corresponding to different p o l l u t i o n episodes were used to construct Fig. 2. This figure illustrates the linear regression of [ln Ci - In rag(i+1)] versus Zi. The best-fit line is given by Eqn (2) In Ci - In rag(i+1) =
0.01 + 0.13Z~
(2)
The variations of ag(i+,) are less easily expressed. The f o l l o w i n g empirical scheme was adopted: ag(i+l ) =
1.3
if ~ <
ag(i+l) =
~
if 1.3 <
0.9Sg
if0.9Sg
O'g(i+l )
=
1.3 ~ < 0.9Sg
(3)
<
w i t h ~ = 1.45 - 0.75 SgZ~. The log-normal distribution f u n c t i o n of the C~i+l) can t h e n be expressed, t h a n k s to relationships (1), (2) and (3), ifMg, Sg and C i (and thus, Zi) are k n o w n . In other words it is possible to calculate the probability of exceeding a limit v a l u e L on a given day (i + 1) w h e n the c o n c e n t r a t i o n of the preceding day (Ci) is k n o w n . R e l a t i o n s h i p s (2) and (3) give mg(i+l ) and ag(i+l). The c u m u l a t i v e probability corresponding to In L - In rag(i+1 ) Zti+l)
=
I n tYg(i+l )
is t h e n found from a u n i t normal distribution table.
22 CALCULATIONOF THE PERSISTENCY PROBABILITIES Let us consider a daily average C and study its persistency, i.e. the number of consecutive days this value C is reached or exceeded. It is assumed t h a t the probability density function of the concentrations is known, as well as the geometric mean Mg and the standard geometric deviation Sg. The standardized variable Zi can be related to C by
zi=
In C - In Mg In Sg
The probability of Ci reaching or exceeding C on any day is 1
f
P1 =
e-~2/2dt
(4)
Zi
and is given in a unit normal distribution table. If Ci is reached on a given day the probability of Ci+l reaching or exceeding C on the next day will depend on
c, P2(ci )
f
1
e -'2/2 dt
(5)
In C - In mai+l) in O'g(i + 1)
(6)
=
Zi+ 1
where Zi+ 1
It is thus possible to calculate Zi÷l for all the Ci using relationships (1), (2), (3) and (6) if Mg and Sg are known. However, Ci can vary from C to oc with probability density function 1 e_Z:/2
(Z/ < Z < ~ )
The average probability of exceeding concentration C on a given day when it has been exceeded the preceding day (Ci > C) is given by
S e-Z:/:P2(cl)dZ P2 = z~ S e z:/2dZ zi Taking relationship (5) into account gives e-Z:/2( ~ (1/wf~)e -':/2 dt)dZ P2 = z~ z~,~ S e -z:/2 dZ z/ Table 1 gives the values of/)2 for different values of
(7)
Zi and Sg.
23 TABLE 1 Values of P2 as a function of Z, and Sg Sg
Zi
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5
1.500
1.600
1.700
1.800
1.900
2.000
2.100
2.200
2.300
2.400
2.500
2.600
0.723 0.702 0.680 0.658 0.636 0.613 0.589 0.565 0.540 0.513 0.486 0.459 0.432 0.405 0.380 0.355 0.331 0.308 0.285 0.262 0.257 0.238 0.220 0.203 0.187 0.171
0.749 0.731 0.713 0.693 0.673 0.651 0.627 0.603 0.577 0.550 0.523 0.495 0.467 0.441 0.415 0.389 0.364 0.338 0.314 0.289 0.268 0.265 0.246 0.227 0.210 0.193
0.773 0.757 0.740 0.721 0.701 0.680 0.657 0.633 0.608 0.581 0.554 0,526 0.499 0.472 0.446 0.419 0.393 0.367 0.341 0.314 0.312 0.291 0.270 0.250 0.231 0.213
0.792 0.777 0.761 0.743 0.724 0.704 0.682 0.658 0.633 0.607 0.579 0.552 0.526 0.499 0.473 0.446 0.419 0.392 0.365 0.338 0.336 0.314 0.293 0.272 0.252 0.233
0.808 0.793 0.778 0.761 0.743 0.723 0.702 0.679 0.654 0.628 0.602 0.575 0.549 0.523 0.496 0.470 0.443 0.415 0.388 0.360 0.358 0.335 0.313 0.292 0.271 0.251
0.820 0.807 0.792 0.776 0.759 0.740 0.719 0.696 0.672 0.646 0.620 0.595 0.569 0.543 0.517 0.490 0.463 0.436 0.408 0.380 0.377 0.354 0.332 0.310 0.289 0.269
0.831 0.818 0.804 0.789 0.772 0.754 0.733 0.711 0.687 0.662 0.637 0.612 0.587 0.561 0.535 0,509 0.482 0.455 0.427 0.399 0.395 0.372 0.350 0.328 0.306 0.285
0.840 0.827 0.814 0.800 0.784 0.766 0.746 0.724 0.700 0.676 0.652 0.627 0.602 0.577 0.551 0.525 0.499 0.472 0.444 0.415 0.412 0.388 0.366 0.343 0.321 0.300
0.847 0.836 0.823 0.809 0.793 0.776 0.756 0.735 0.712 0.688 0.665 0.641 0.616 0.591 0.566 0.540 0.514 0.487 0.459 0.431 0.426 0.403 0.380 0.358 0.336 0.314
0.854 0.843 0.830 0.817 0.802 0.785 0.765 0.744 0.722 0.699 0.676 0.652 0.628 0.604 0.579 0.553 0.527 0.500 0.473 0.444 0.440 0.417 0.394 0.371 0.349 0.327
0.860 0.849 0.837 0.824 0.809 0.793 0.774 0.753 0.731 0.709 0.686 0.663 0.639 0.615 0.590 0.565 0.539 0.513 0.485 0.457 0.452 0.429 0.406 0.383 0.361 0.339
0.865 0.854 0.843 0.830 0.816 0.799 0.781 0.760 0.739 0.717 0.695 0.672 0.649 0.625 0.601 0.576 0.550 0.524 0.497 0.469 0.464 0.441 0.418 0.395 0.372 0.340
The probability P3 of exceeding C on a given day when this concentration has been exceeded during the two previous days can be calculated using the same method e-Z~/2[ S e u:/2( ~ P3
=
zi
zi÷ 1
_ (1/~/~)e-,2/2dt)du]dZ
zi÷2
(8)
e-Z2/2( S e -u2'2 du)dZ Zi
Zi + 1
where Zi+2
=
In C - In rag(i+2) In O'g(/+ 2)
(9)
Table 2 gives the values of/)3 for several values of Z i and Sg. Romanof (1982) has recently studied the dependence of the SO2 daily averages on the previous days' concentrations using a Markov chain model. The dependence of fairly high concentrations, especially those above the median, on the concentrations of the two preceding days, has been demonstrated. However, they were independent of the concentration measured 3 days before. In our case, as we are interested in concentrations exceeding the median (Zi t> 0), it implies that/)4 = P3. Thus
24 TABLE 2 Values of P3 as a function of Zi and Sg Zi
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1,8 1.9 2.0 2.1 2.2 2.3 2.4 2.5
Sg 1.500
1.600
1.700
1.800
1.900
2.000
2.100
2.200
2.300
2.400
2.500
2.600
0.850 0.837 0.824 0.810 0.795 0.780 0.764 0.746 0.726 0.704 0.676 0.651 0.623 0.596 0.570 0.546 0.521 0.497 0.472 0.447 0.438 0.416 0.394 0.373 0.352 0.332
0.864 0.855 0.845 0.833 0.821 0.806 0.790 0.772 0.751 0.728 0.703 0.677 0.650 0.624 0.600 0.576 0.551 0.525 0.500 0.474 0.466 0.443 0.421 0.399 0.377 0.356
0.877 0.869 0.859 0.849 0.837 0.824 0.809 0.791 0.771 0.748 0.723 0.697 0.672 0.649 0.625 0.601 0.576 0.551 0,525 0.498 0.490 0.467 0.445 0.422 0.400 0.378
0.887 0.880 0.871 0.861 0.850 0.838 0.823 0.806 0.786 0.764 0.740 0.715 0.693 0.670 0.646 0.622 0.598 0.573 0.546 0.520 0.512 0.489 0.466 0.443 0.421 0.398
0.896 0.888 0.880 0.871 0.861 0.849 0.835 0.818 0.798 0.777 0.753 0.731 0.709 0.687 0.664 0.641 0.617 0.592 0.566 0.539 0.531 0.508 0.485 0.462 0.439 0.417
0.902 0.896 0.888 0.880 0.870 0.858 0.845 0.828 0.809 0.787 0.765 0.745 0.724 0.702 0.680 0.657 0.633 0.608 0.583 0.556 0.548 0.525 0.502 0.479 0.456 0.433
0.908 0.902 0.895 0.887 0.877 0.866 0.852 0.836 0.817 0.796 0.776 0.756 0.736 0.715 0,603 0.670 0.647 0.623 0.598 0.571 0.563 0.540 0.517 0.494 0.471 0.449
0.913 0.907 0.900 0.893 0.884 0,873 0.859 0.843 0.824 0.804 0.785 0.766 0.747 0.726 0.705 0.682 0.659 0.636 0.611 0.585 0.577 0.554 0.531 0.508 0.485 0.462
0.917 0.911 0.905 0.898 0.889 0.878 0.865 0.849 0.830 0.811 0.794 0.775 0.756 0.736 0.715 0.693 0.671 0.647 0.623 0.597 0.589 0.566 0.543 0.521 0.498 0.475
0.920 0.915 0.909 0.902 0.894 0.883 0.870 0.854 0.836 0.818 0.801 0.783 0,764 0.744 0.724 0.702 0.680 0.657 0.633 0.608 0.599 0,577 0.554 0.532 0.509 0.487
0.924 0.918 0.913 0.906 0.898 0.887 0.874 0.858 0.840 0.824 0.807 0.790 0.771 0.752 0.732 0.711 0.689 0.666 0.643 0.618 0.609 0,587 0.565 0.542 0.520 0.497
0.926 0.921 0.916 0.909 0.901 0.891 0.876 0.862 0.845 0.829 0.813 0.796 0.778 0,759 0.739 0.719 0.697 0.675 0.651 0.627 0.619 0.596 0.574 0.552 0.529 0.507
P~ =
P3
for
j
~> 3
T h e probability of r e a c h i n g or e x c e e d i n g a c o n c e n t r a t i o n C during n consec u t i v e days is g i v e n by
P(.) = Pl. P2. P~n-2)
(10)
P1 v a l u e s are listed in t h e u n i t n o r m a l d i s t r i b u t i o n table, and P2 and P3 are listed in Tables 1 and 2. T h e y c a n e a s i l y be f o u n d if t h e g e o m e t r i c m e a n and t h e s t a n d a r d g e o m e t r i c d e v i a t i o n of t h e c o n c e n t r a t i o n s are k n o w n .
PRACTICAL EXAMPLES Several 12-month periods were considered for some stations located in the urban area of Brussels. The geometric m e a n and the standard geometric deviation were derived graphically for each annual series from straight lines drawn on probability paper using the high percentiles (from 50 to 95). The occurrence of a spell exceeding a given concentration for n consecutive days is given by P(n) =
365 PI" P2" P3('-2)
(11)
K n o w i n g t h a t t h e s c h e m e b e c o m e s m o r e and m o r e a p p r o x i m a t e as n i n c r e a s e s and t a k i n g i n t o a c c o u n t t h e fact that F(.) m u s t be greater t h a n F(.+I ), w e decided
25 TABLE 3 C o m p a r i s o n b e t w e e n t h e a c t u a l (in p a r e n t h e s e s ) and c a l c u l a t e d values of F(n) Limit value C (jug m - 3): Z:
250 0.846
300 1.218
D u r a t i o n of t h e p e r s i s t e n c y (days)
N u m b e r of persistencies
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
77 (73) 47 (42) 32 (31) 23 (23) 17 (17) 12 (13) 10 (10) 9 (7) 8 (5) 7 (4) 6 (3) 5 (2) 4 (1) 3 (-) 2 1
41 25 16 10 6 2
(41) (19) (13) (8) (5) (3)
i (2)
350 1.531
400 1.80
25 13 7 4 2 1
12 3 1 1 -
(23) (9) (5) (3) (2) (1)
(13) (4) (2) (2) (1) (-)
- (-)
- (i) _ (_)
S t a t i o n RO23 (1969) (Mg = 165]~gm -3 and S~ = 1.634). TABLE 4 C o m p a r i s o n b e t w e e n t h e a c t u a l (in p a r e n t h e s e s ) and c a l c u l a t e d values of F(n) Limit value C (~g m-3): Z:
200 0.948
Duration of the p e r s i s t e n c y (days)
N u m b e r o f persistencies
1 2 3 4 5 6 7 8 9 10 11 12 13
67 37 26 19 14 12 10 8 6 4
(64) (36) (26) (19) (14) (10) (7) (5) (4) (3)
2 (2)
1 (1) - (-)
S t a t i o n RO06 (1971) (Mg = 123#gm -3 and S~ = 1.67).
250 1.383
27 11 5 1 -
(30) (13) (8) (5) (3) (2) (1) (-)
300 1.739
350 2.04
16 8 3 1 -
8 2 -
(15) (5) (3) (1) (-)
(8) (2) (1) (-)
26 TABLE 5 C o m p a r i s o n b e t w e e n t h e actual (in p a r e n t h e s e s ) and c a l c u l a t e d values of F(n) Limit value C ~ugm-3): Z:
150 0.57
D u r a t i o n of t h e P e r s i s t e n c y (days)
N u m b e r o f persistencies
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
99 (104) 62 (67) 47 (54) 38 (43) 33 (34) 28 (27) 25 (22) 22 (18) 20 (14) 18 (11) 16 (9) 14 (7) 12 (6) 10 (5) 8 (4) 6 (3) 4 (2) 2 (1)
19
1()
20
- (-)
175 0.88
68 (69) 39 (39) 26 (29) 19 (21) 15 (16) 11 (12) 9 (9) 7 (6) 5 (4)
3 (3) 1 (2) (1) (-)
200 1.148
250 1.597
45 (46) 19 (23) 11 (15) 7 (10) 4 (7) 3 (5) 2 (3) 1 (2) - (1) - (-)
9 (20) 1 (S) - (4) - (2) - (1) - (-)
-
S t a t i o n R O l l (1974) (Mg = l l 3 # g m -3 and Sg = 1.644).
to assume t h a t F ( n + l ) = F ( n ) - 1 w h e n r e l a t i o n s h i p (11) gave F(n+l)= F(,). Tables 3-7 give the c o m p a r i s o n b e t w e e n the t h e o r e t i c a l F(n) c a l c u l a t e d by (11) and the a c t u a l F(n) for six series of data. T h e t h e o r e t i c a l d a t a are given in p a r e n t h e s e s . T h e s e tables show a fairly good a g r e e m e n t b e t w e e n the d a t a c o m p u t e d by the s c h e m e and the a c t u a l situation. CONCLUSIONS
T h e p r e s e n t s t u d y shows h o w it is possible to c a l c u l a t e t h e persistencies of a m b i e n t SO2 c o n c e n t r a t i o n s e x c e e d i n g a given v a l u e in an u r b a n a r e a w h e n two p a r a m e t e r s of t h e d i s t r i b u t i o n of t h e c o n c e n t r a t i o n s are k n o w n . The a p p l i c a t i o n of t h e proposed s c h e m e is easy b e c a u s e it o n l y requires the calculat i o n of t h e g e o m e t r i c mean, the s t a n d a r d g e o m e t r i c deviation, and the v a l u e of Z c o r r e s p o n d i n g to the given limit value. F o r the c a l c u l a t i o n of t h e persistencies it t h e n r e m a i n s to e x a m i n e a u n i t n o r m a l d i s t r i b u t i o n table and Tables 1 and 2 of t h e p r e s e n t paper.
27
TABLE 6 Comparison between the actual (in parentheses) and calculated values of F(,) Limit value C ~ g m - 3 ) : Z:
125 0.737
Duration of the persistency (days)
Number of persistencies
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
79 55 41 35 29 25 22 19 16 13 11 9 7 5 4 3
17 lS 19
(73) (50) (41) (34) (23) (23) (19) (15) (12) (10) (8) (7) (6) (5) (4) (3)
150 1.0
59 37 26 21 16 13 10 7 5 3 2 1 -
(58) (36) (27) (21) (16) (12) (9) (7) (5) (4) (3) (2) (1) (-)
175
200
1.222
1.415
41 26 21 17 13 10 7 5 4 3 2 1 -
29 19 14 11 9 7 5 4 3 2 1 -
(40) (23) (16) (12) (8) (6) (4) (3) (2) (1) (-) (-) (-)
(29) (15) (10) (7) (5) (3) (2) (1) (-) (-) ~) (-)
225 1.585
250 1.737
20 10 6 2 -
15 9 5 2 -
(21) (10) (6) (4) (2) (1) (-)
(15) (6) (4) (2) (1) (-)
2 (2) 1 (1) - (-)
Station RO21 (1979) (Mg = 7 5 # g m -3 and S, = 2).
The scheme can be of great use for two main purposes: to forecast the extent of expected episodes when ambient air standards given by two percentiles are exceeded; and --to assess legal standards more closely related to episodes of prolonged duration likely to induce damage to health or the environment.
--
ACKNOWLEDGEMENT
We t h a n k Dr G. Thiers, Director of the Institute for Hygiene and Epidemiology, and M.J. Bouquiaux, Head of the Department of Environmental Studies. We are indebted to Dr G. Dumont for his discerning advice, to the personnel of the Air Pollution Division for their technical assistance, and to Mrs De Gendt for the typing of the manuscript.
28
TABLE 7 Comparison between the actual (in parentheses) and calculated values of F(.) Limit value C (pg m- 3): Z:
150
175
0.896
1.092
Duration of the persistency (days)
Number of persistencies
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
71 45 31 24 19 15 12 9 6 4 2 1
(68) (46) (37) (30) (24) (19) (16) (13) (10) (8) (6) (5) (4) - (3) (2) - (1) ( )
49 30 23 19 15 12 9 7 5 3 2 1 -
(50) (32) (24) (19) (14) (11) (8) (6) (5) (4) (3) (2) (1) ~)
200 1.261
225 1.41
250 1.544
38 26 20 16 13 10 7 5 4 3 2 1 -
32 16 10 5 3 1 -
24 11 5 2 -
(38) (22) (16) (12) (9) (7) (5) (4) (3) (2) (1) (-) (-)
(29) (16) (11) (8) (9) (4) (3) (2) - (1) - (-)
(22) (12) (8) (5) (3) (2) (1) (-)
Station RO23 (1979) (M~ = 74#gm -3 and S~ = 22.2).
REFERENCES Benarie, M., 1980. U r b a n Air Pollution Modelling. MacMillan Press, London. Georgopoulos, P.G. and J.H. Steiner, 1982. Statistical distributions of air pollutant concentrations. Environ. Sci. Technol., 16: 401A-416A. Larsen, R.I., 1969. A new mathematical model of air pollutant concentrations, averaging time and frequency. J. Air Pollut. Control Assoc., 19: 24-30. Romanof, N. and A. Markov, 1982. Chain model for the mean daily SO 2 concentrations. Atmos. Environ., 16: 1895-1897.
19
A S T U D Y OF THE P E R S I S T E N C I E S OF SO2 CONCENTRATIONS E X C E E D I N G LIMIT V A L U E S IN THE A M B I E N T AIR OF AN U R B A N AREA
SERGE HALLEZ, ALAIN DEROUANE and GEERT VERDUYN Institute for Hygiene and Epidemiology, Air Pollution Division, rue J. Wytsman, 14B 1050 Brussels (Belgium)
(Received April 13th, 1983; accepted March 20th 1986)
ABSTRACT This study of the persistencies of S O 2 concentrations takes the parameters of the SO2frequency distributions as a basis. A scheme is proposed for their calculation which allows the forecast of SO2 pollution episodes.
INTRODUCTION T h e L a r s e n h y p o t h e s i s (1969) t h a t SO2 c o n c e n t r a t i o n s in the a m b i e n t air of u r b a n a r e a s are log-normally d i s t r i b u t e d is well k n o w n . Some a u t h o r s (Benarie, 1980; G e o r g o p o u l o s and S t e i n e r 1982) h a v e s h o w n the l i m i t a t i o n s of this a p p r o a c h while emphasizing its merits and i n d i s p u t a b l e usefulness. A distribution f u n c t i o n is, h o w e v e r , u n a b l e to give a c o m p l e t e d e s c r i p t i o n of the statistical c h a r a c t e r i s t i c s of a c h r o n o l o g i c a l series. F o r example, the d i s t r i b u t i o n f u n c t i o n enables the d e t e r m i n a t i o n of the n u m b e r of days w h e n limit v a l u e s are exceeded, b u t does n o t give a n y i n f o r m a t i o n as to w h e t h e r or n o t t h e y are i n d e p e n d e n t or c o n s e c u t i v e days. Likewise, a m b i e n t air s t a n d a r d s are often assessed by two p a r a m e t e r s , the m e d i a n and a high p e r c e n t i l e (e.g. 95e p. 97e p) w i t h o u t giving a t t e n t i o n to the fact t h a t the o c c u r r e n c e s of a h i g h c o n c e n t r a tion d u r i n g a given n u m b e r of days m a y i m p a i r h e a l t h and the e n v i r o n m e n t in quite different ways a c c o r d i n g to w h e t h e r t h e days are i n d e p e n d e n t or not. This gap c a n be filled by the c a l c u l a t i o n of the persistencies. T h e first step consists of establishing a statistical r e l a t i o n s h i p b e t w e e n the c o n c e n t r a t i o n m e a s u r e d d u r i n g a given day and the c o n c e n t r a t i o n of t h e p r e c e d i n g day. The second step consists of the u t i l i z a t i o n of this r e l a t i o n s h i p in o r d e r to c a l c u l a t e the p r o b a b i l i t y of m e a s u r i n g a n e x c e e d i n g c o n c e n t r a t i o n d u r i n g a given day w h e n a n e x c e e d i n g c o n c e n t r a t i o n has been m e a s u r e d the p r e c e d i n g day. Annual p e r s i s t e n c i e s c a n t h e n be calculated.
0048-9697/86/$03.50
© 1986 Elsevier Science Publishers B.V.
20
MG=gGug/m3 DSG=2
95 %-
l
90 %-
80 ~,"
~
÷
70 %" 60 %'
/
50 % 40 %. 30 ~,!
20 %-
Ci (ug/m3 }-4~
5e
75
I00
158
20~
258
dsg-I .GO
1.54
~..49
1.4G
1,45
1.41
1.33
40
50
Fig. 1. Variation of ag(i+l) and [ln C i
75
-
100
150
200
300
CCt+l)(uglm3)
In mg(i+l)] as a function of Z i.
THE DISTRIBUTION OF DAILY AVERAGE CONCENTRATIONS AS A FUNCTION OF THE CONCENTRATION OF THE PRECEDING DAY The c a l c u l a t i o n s were made on daily average SO2 c o n c e n t r a t i o n s measured at 10 sampling sites of the B e l g i u m Sulphur-Smoke N e t w o r k located in the urban area of Brussels. A 'town daily average' was determined by c a l c u l a t i n g for e a c h day the arithmetic m e a n of the 10 daily averages. More t h a n 4,000 'town daily averages' Ci gathered during 12 years were available. The C i + l are the 'town daily averages' determined for the next day. The c u m u l a t i v e distributionoftheCi+lforsevenCiclasses(40 + 5,50 _+ 5,75 _+ 5,100 _+ 10,150 + 10, 200 + 10 and 220 + 10/xg SO2 m -a) are given in Fig. 1. These distributions are fairly log-normal and are characterized by mg(i+l) and ag(i+l). A s s u m i n g a lognormal distribution for the (7/variable, it can be transformed into a standardized variable Z i given by z,
=
In Ci - In Mg In Sg
(1)
where Zi is the number of (In Sg) b e t w e e n In (7/and In Mg, Mg is the geometric m e a n of the Q, and Sg is the standard geometric d e v i a t i o n of the Ci. Figure 1 s h o w s a regular v a r i a t i o n of ag(i+~) (slope of the line) and [ln Ci -
21 LOG(Ci/Mg(i+l)) .24
.16
t .~/~/ff''~I , ~ "/
9"
/J/
•138
/
-. BB
°J
-.16 -l.
,," _ t
' .fi
-.6
Fig. 2. Linear
regression
of [In C i
'
'
1.2
Zi 1.8
- In rag(i+1)] as a function
of Z i.
In mg(/+,)] as a f u n c t i o n of Zi. In order to find these relationships, 21 sets of data from different m o n i t o r i n g stations and corresponding to different p o l l u t i o n episodes were used to construct Fig. 2. This figure illustrates the linear regression of [ln Ci - In rag(i+1)] versus Zi. The best-fit line is given by Eqn (2) In Ci - In rag(i+1) =
0.01 + 0.13Z~
(2)
The variations of ag(i+,) are less easily expressed. The f o l l o w i n g empirical scheme was adopted: ag(i+l ) =
1.3
if ~ <
ag(i+l) =
~
if 1.3 <
0.9Sg
if0.9Sg
O'g(i+l )
=
1.3 ~ < 0.9Sg
(3)
<
w i t h ~ = 1.45 - 0.75 SgZ~. The log-normal distribution f u n c t i o n of the C~i+l) can t h e n be expressed, t h a n k s to relationships (1), (2) and (3), ifMg, Sg and C i (and thus, Zi) are k n o w n . In other words it is possible to calculate the probability of exceeding a limit v a l u e L on a given day (i + 1) w h e n the c o n c e n t r a t i o n of the preceding day (Ci) is k n o w n . R e l a t i o n s h i p s (2) and (3) give mg(i+l ) and ag(i+l). The c u m u l a t i v e probability corresponding to In L - In rag(i+1 ) Zti+l)
=
I n tYg(i+l )
is t h e n found from a u n i t normal distribution table.
22 CALCULATIONOF THE PERSISTENCY PROBABILITIES Let us consider a daily average C and study its persistency, i.e. the number of consecutive days this value C is reached or exceeded. It is assumed t h a t the probability density function of the concentrations is known, as well as the geometric mean Mg and the standard geometric deviation Sg. The standardized variable Zi can be related to C by
zi=
In C - In Mg In Sg
The probability of Ci reaching or exceeding C on any day is 1
f
P1 =
e-~2/2dt
(4)
Zi
and is given in a unit normal distribution table. If Ci is reached on a given day the probability of Ci+l reaching or exceeding C on the next day will depend on
c, P2(ci )
f
1
e -'2/2 dt
(5)
In C - In mai+l) in O'g(i + 1)
(6)
=
Zi+ 1
where Zi+ 1
It is thus possible to calculate Zi÷l for all the Ci using relationships (1), (2), (3) and (6) if Mg and Sg are known. However, Ci can vary from C to oc with probability density function 1 e_Z:/2
(Z/ < Z < ~ )
The average probability of exceeding concentration C on a given day when it has been exceeded the preceding day (Ci > C) is given by
S e-Z:/:P2(cl)dZ P2 = z~ S e z:/2dZ zi Taking relationship (5) into account gives e-Z:/2( ~ (1/wf~)e -':/2 dt)dZ P2 = z~ z~,~ S e -z:/2 dZ z/ Table 1 gives the values of/)2 for different values of
(7)
Zi and Sg.
23 TABLE 1 Values of P2 as a function of Z, and Sg Sg
Zi
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5
1.500
1.600
1.700
1.800
1.900
2.000
2.100
2.200
2.300
2.400
2.500
2.600
0.723 0.702 0.680 0.658 0.636 0.613 0.589 0.565 0.540 0.513 0.486 0.459 0.432 0.405 0.380 0.355 0.331 0.308 0.285 0.262 0.257 0.238 0.220 0.203 0.187 0.171
0.749 0.731 0.713 0.693 0.673 0.651 0.627 0.603 0.577 0.550 0.523 0.495 0.467 0.441 0.415 0.389 0.364 0.338 0.314 0.289 0.268 0.265 0.246 0.227 0.210 0.193
0.773 0.757 0.740 0.721 0.701 0.680 0.657 0.633 0.608 0.581 0.554 0,526 0.499 0.472 0.446 0.419 0.393 0.367 0.341 0.314 0.312 0.291 0.270 0.250 0.231 0.213
0.792 0.777 0.761 0.743 0.724 0.704 0.682 0.658 0.633 0.607 0.579 0.552 0.526 0.499 0.473 0.446 0.419 0.392 0.365 0.338 0.336 0.314 0.293 0.272 0.252 0.233
0.808 0.793 0.778 0.761 0.743 0.723 0.702 0.679 0.654 0.628 0.602 0.575 0.549 0.523 0.496 0.470 0.443 0.415 0.388 0.360 0.358 0.335 0.313 0.292 0.271 0.251
0.820 0.807 0.792 0.776 0.759 0.740 0.719 0.696 0.672 0.646 0.620 0.595 0.569 0.543 0.517 0.490 0.463 0.436 0.408 0.380 0.377 0.354 0.332 0.310 0.289 0.269
0.831 0.818 0.804 0.789 0.772 0.754 0.733 0.711 0.687 0.662 0.637 0.612 0.587 0.561 0.535 0,509 0.482 0.455 0.427 0.399 0.395 0.372 0.350 0.328 0.306 0.285
0.840 0.827 0.814 0.800 0.784 0.766 0.746 0.724 0.700 0.676 0.652 0.627 0.602 0.577 0.551 0.525 0.499 0.472 0.444 0.415 0.412 0.388 0.366 0.343 0.321 0.300
0.847 0.836 0.823 0.809 0.793 0.776 0.756 0.735 0.712 0.688 0.665 0.641 0.616 0.591 0.566 0.540 0.514 0.487 0.459 0.431 0.426 0.403 0.380 0.358 0.336 0.314
0.854 0.843 0.830 0.817 0.802 0.785 0.765 0.744 0.722 0.699 0.676 0.652 0.628 0.604 0.579 0.553 0.527 0.500 0.473 0.444 0.440 0.417 0.394 0.371 0.349 0.327
0.860 0.849 0.837 0.824 0.809 0.793 0.774 0.753 0.731 0.709 0.686 0.663 0.639 0.615 0.590 0.565 0.539 0.513 0.485 0.457 0.452 0.429 0.406 0.383 0.361 0.339
0.865 0.854 0.843 0.830 0.816 0.799 0.781 0.760 0.739 0.717 0.695 0.672 0.649 0.625 0.601 0.576 0.550 0.524 0.497 0.469 0.464 0.441 0.418 0.395 0.372 0.340
The probability P3 of exceeding C on a given day when this concentration has been exceeded during the two previous days can be calculated using the same method e-Z~/2[ S e u:/2( ~ P3
=
zi
zi÷ 1
_ (1/~/~)e-,2/2dt)du]dZ
zi÷2
(8)
e-Z2/2( S e -u2'2 du)dZ Zi
Zi + 1
where Zi+2
=
In C - In rag(i+2) In O'g(/+ 2)
(9)
Table 2 gives the values of/)3 for several values of Z i and Sg. Romanof (1982) has recently studied the dependence of the SO2 daily averages on the previous days' concentrations using a Markov chain model. The dependence of fairly high concentrations, especially those above the median, on the concentrations of the two preceding days, has been demonstrated. However, they were independent of the concentration measured 3 days before. In our case, as we are interested in concentrations exceeding the median (Zi t> 0), it implies that/)4 = P3. Thus
24 TABLE 2 Values of P3 as a function of Zi and Sg Zi
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1,8 1.9 2.0 2.1 2.2 2.3 2.4 2.5
Sg 1.500
1.600
1.700
1.800
1.900
2.000
2.100
2.200
2.300
2.400
2.500
2.600
0.850 0.837 0.824 0.810 0.795 0.780 0.764 0.746 0.726 0.704 0.676 0.651 0.623 0.596 0.570 0.546 0.521 0.497 0.472 0.447 0.438 0.416 0.394 0.373 0.352 0.332
0.864 0.855 0.845 0.833 0.821 0.806 0.790 0.772 0.751 0.728 0.703 0.677 0.650 0.624 0.600 0.576 0.551 0.525 0.500 0.474 0.466 0.443 0.421 0.399 0.377 0.356
0.877 0.869 0.859 0.849 0.837 0.824 0.809 0.791 0.771 0.748 0.723 0.697 0.672 0.649 0.625 0.601 0.576 0.551 0,525 0.498 0.490 0.467 0.445 0.422 0.400 0.378
0.887 0.880 0.871 0.861 0.850 0.838 0.823 0.806 0.786 0.764 0.740 0.715 0.693 0.670 0.646 0.622 0.598 0.573 0.546 0.520 0.512 0.489 0.466 0.443 0.421 0.398
0.896 0.888 0.880 0.871 0.861 0.849 0.835 0.818 0.798 0.777 0.753 0.731 0.709 0.687 0.664 0.641 0.617 0.592 0.566 0.539 0.531 0.508 0.485 0.462 0.439 0.417
0.902 0.896 0.888 0.880 0.870 0.858 0.845 0.828 0.809 0.787 0.765 0.745 0.724 0.702 0.680 0.657 0.633 0.608 0.583 0.556 0.548 0.525 0.502 0.479 0.456 0.433
0.908 0.902 0.895 0.887 0.877 0.866 0.852 0.836 0.817 0.796 0.776 0.756 0.736 0.715 0,603 0.670 0.647 0.623 0.598 0.571 0.563 0.540 0.517 0.494 0.471 0.449
0.913 0.907 0.900 0.893 0.884 0,873 0.859 0.843 0.824 0.804 0.785 0.766 0.747 0.726 0.705 0.682 0.659 0.636 0.611 0.585 0.577 0.554 0.531 0.508 0.485 0.462
0.917 0.911 0.905 0.898 0.889 0.878 0.865 0.849 0.830 0.811 0.794 0.775 0.756 0.736 0.715 0.693 0.671 0.647 0.623 0.597 0.589 0.566 0.543 0.521 0.498 0.475
0.920 0.915 0.909 0.902 0.894 0.883 0.870 0.854 0.836 0.818 0.801 0.783 0,764 0.744 0.724 0.702 0.680 0.657 0.633 0.608 0.599 0,577 0.554 0.532 0.509 0.487
0.924 0.918 0.913 0.906 0.898 0.887 0.874 0.858 0.840 0.824 0.807 0.790 0.771 0.752 0.732 0.711 0.689 0.666 0.643 0.618 0.609 0,587 0.565 0.542 0.520 0.497
0.926 0.921 0.916 0.909 0.901 0.891 0.876 0.862 0.845 0.829 0.813 0.796 0.778 0,759 0.739 0.719 0.697 0.675 0.651 0.627 0.619 0.596 0.574 0.552 0.529 0.507
P~ =
P3
for
j
~> 3
T h e probability of r e a c h i n g or e x c e e d i n g a c o n c e n t r a t i o n C during n consec u t i v e days is g i v e n by
P(.) = Pl. P2. P~n-2)
(10)
P1 v a l u e s are listed in t h e u n i t n o r m a l d i s t r i b u t i o n table, and P2 and P3 are listed in Tables 1 and 2. T h e y c a n e a s i l y be f o u n d if t h e g e o m e t r i c m e a n and t h e s t a n d a r d g e o m e t r i c d e v i a t i o n of t h e c o n c e n t r a t i o n s are k n o w n .
PRACTICAL EXAMPLES Several 12-month periods were considered for some stations located in the urban area of Brussels. The geometric m e a n and the standard geometric deviation were derived graphically for each annual series from straight lines drawn on probability paper using the high percentiles (from 50 to 95). The occurrence of a spell exceeding a given concentration for n consecutive days is given by P(n) =
365 PI" P2" P3('-2)
(11)
K n o w i n g t h a t t h e s c h e m e b e c o m e s m o r e and m o r e a p p r o x i m a t e as n i n c r e a s e s and t a k i n g i n t o a c c o u n t t h e fact that F(.) m u s t be greater t h a n F(.+I ), w e decided
25 TABLE 3 C o m p a r i s o n b e t w e e n t h e a c t u a l (in p a r e n t h e s e s ) and c a l c u l a t e d values of F(n) Limit value C (jug m - 3): Z:
250 0.846
300 1.218
D u r a t i o n of t h e p e r s i s t e n c y (days)
N u m b e r of persistencies
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
77 (73) 47 (42) 32 (31) 23 (23) 17 (17) 12 (13) 10 (10) 9 (7) 8 (5) 7 (4) 6 (3) 5 (2) 4 (1) 3 (-) 2 1
41 25 16 10 6 2
(41) (19) (13) (8) (5) (3)
i (2)
350 1.531
400 1.80
25 13 7 4 2 1
12 3 1 1 -
(23) (9) (5) (3) (2) (1)
(13) (4) (2) (2) (1) (-)
- (-)
- (i) _ (_)
S t a t i o n RO23 (1969) (Mg = 165]~gm -3 and S~ = 1.634). TABLE 4 C o m p a r i s o n b e t w e e n t h e a c t u a l (in p a r e n t h e s e s ) and c a l c u l a t e d values of F(n) Limit value C (~g m-3): Z:
200 0.948
Duration of the p e r s i s t e n c y (days)
N u m b e r o f persistencies
1 2 3 4 5 6 7 8 9 10 11 12 13
67 37 26 19 14 12 10 8 6 4
(64) (36) (26) (19) (14) (10) (7) (5) (4) (3)
2 (2)
1 (1) - (-)
S t a t i o n RO06 (1971) (Mg = 123#gm -3 and S~ = 1.67).
250 1.383
27 11 5 1 -
(30) (13) (8) (5) (3) (2) (1) (-)
300 1.739
350 2.04
16 8 3 1 -
8 2 -
(15) (5) (3) (1) (-)
(8) (2) (1) (-)
26 TABLE 5 C o m p a r i s o n b e t w e e n t h e actual (in p a r e n t h e s e s ) and c a l c u l a t e d values of F(n) Limit value C ~ugm-3): Z:
150 0.57
D u r a t i o n of t h e P e r s i s t e n c y (days)
N u m b e r o f persistencies
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
99 (104) 62 (67) 47 (54) 38 (43) 33 (34) 28 (27) 25 (22) 22 (18) 20 (14) 18 (11) 16 (9) 14 (7) 12 (6) 10 (5) 8 (4) 6 (3) 4 (2) 2 (1)
19
1()
20
- (-)
175 0.88
68 (69) 39 (39) 26 (29) 19 (21) 15 (16) 11 (12) 9 (9) 7 (6) 5 (4)
3 (3) 1 (2) (1) (-)
200 1.148
250 1.597
45 (46) 19 (23) 11 (15) 7 (10) 4 (7) 3 (5) 2 (3) 1 (2) - (1) - (-)
9 (20) 1 (S) - (4) - (2) - (1) - (-)
-
S t a t i o n R O l l (1974) (Mg = l l 3 # g m -3 and Sg = 1.644).
to assume t h a t F ( n + l ) = F ( n ) - 1 w h e n r e l a t i o n s h i p (11) gave F(n+l)= F(,). Tables 3-7 give the c o m p a r i s o n b e t w e e n the t h e o r e t i c a l F(n) c a l c u l a t e d by (11) and the a c t u a l F(n) for six series of data. T h e t h e o r e t i c a l d a t a are given in p a r e n t h e s e s . T h e s e tables show a fairly good a g r e e m e n t b e t w e e n the d a t a c o m p u t e d by the s c h e m e and the a c t u a l situation. CONCLUSIONS
T h e p r e s e n t s t u d y shows h o w it is possible to c a l c u l a t e t h e persistencies of a m b i e n t SO2 c o n c e n t r a t i o n s e x c e e d i n g a given v a l u e in an u r b a n a r e a w h e n two p a r a m e t e r s of t h e d i s t r i b u t i o n of t h e c o n c e n t r a t i o n s are k n o w n . The a p p l i c a t i o n of t h e proposed s c h e m e is easy b e c a u s e it o n l y requires the calculat i o n of t h e g e o m e t r i c mean, the s t a n d a r d g e o m e t r i c deviation, and the v a l u e of Z c o r r e s p o n d i n g to the given limit value. F o r the c a l c u l a t i o n of t h e persistencies it t h e n r e m a i n s to e x a m i n e a u n i t n o r m a l d i s t r i b u t i o n table and Tables 1 and 2 of t h e p r e s e n t paper.
27
TABLE 6 Comparison between the actual (in parentheses) and calculated values of F(,) Limit value C ~ g m - 3 ) : Z:
125 0.737
Duration of the persistency (days)
Number of persistencies
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
79 55 41 35 29 25 22 19 16 13 11 9 7 5 4 3
17 lS 19
(73) (50) (41) (34) (23) (23) (19) (15) (12) (10) (8) (7) (6) (5) (4) (3)
150 1.0
59 37 26 21 16 13 10 7 5 3 2 1 -
(58) (36) (27) (21) (16) (12) (9) (7) (5) (4) (3) (2) (1) (-)
175
200
1.222
1.415
41 26 21 17 13 10 7 5 4 3 2 1 -
29 19 14 11 9 7 5 4 3 2 1 -
(40) (23) (16) (12) (8) (6) (4) (3) (2) (1) (-) (-) (-)
(29) (15) (10) (7) (5) (3) (2) (1) (-) (-) ~) (-)
225 1.585
250 1.737
20 10 6 2 -
15 9 5 2 -
(21) (10) (6) (4) (2) (1) (-)
(15) (6) (4) (2) (1) (-)
2 (2) 1 (1) - (-)
Station RO21 (1979) (Mg = 7 5 # g m -3 and S, = 2).
The scheme can be of great use for two main purposes: to forecast the extent of expected episodes when ambient air standards given by two percentiles are exceeded; and --to assess legal standards more closely related to episodes of prolonged duration likely to induce damage to health or the environment.
--
ACKNOWLEDGEMENT
We t h a n k Dr G. Thiers, Director of the Institute for Hygiene and Epidemiology, and M.J. Bouquiaux, Head of the Department of Environmental Studies. We are indebted to Dr G. Dumont for his discerning advice, to the personnel of the Air Pollution Division for their technical assistance, and to Mrs De Gendt for the typing of the manuscript.
28
TABLE 7 Comparison between the actual (in parentheses) and calculated values of F(.) Limit value C (pg m- 3): Z:
150
175
0.896
1.092
Duration of the persistency (days)
Number of persistencies
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
71 45 31 24 19 15 12 9 6 4 2 1
(68) (46) (37) (30) (24) (19) (16) (13) (10) (8) (6) (5) (4) - (3) (2) - (1) ( )
49 30 23 19 15 12 9 7 5 3 2 1 -
(50) (32) (24) (19) (14) (11) (8) (6) (5) (4) (3) (2) (1) ~)
200 1.261
225 1.41
250 1.544
38 26 20 16 13 10 7 5 4 3 2 1 -
32 16 10 5 3 1 -
24 11 5 2 -
(38) (22) (16) (12) (9) (7) (5) (4) (3) (2) (1) (-) (-)
(29) (16) (11) (8) (9) (4) (3) (2) - (1) - (-)
(22) (12) (8) (5) (3) (2) (1) (-)
Station RO23 (1979) (M~ = 74#gm -3 and S~ = 22.2).
REFERENCES Benarie, M., 1980. U r b a n Air Pollution Modelling. MacMillan Press, London. Georgopoulos, P.G. and J.H. Steiner, 1982. Statistical distributions of air pollutant concentrations. Environ. Sci. Technol., 16: 401A-416A. Larsen, R.I., 1969. A new mathematical model of air pollutant concentrations, averaging time and frequency. J. Air Pollut. Control Assoc., 19: 24-30. Romanof, N. and A. Markov, 1982. Chain model for the mean daily SO 2 concentrations. Atmos. Environ., 16: 1895-1897.