SO2 dosages in an urban area

Atmospheric hnvironme~t Vol. 14, pp. I I - 17. 8 Pergamon PressLtd. 1980. Printedin Great Britain.

C’S+-6981/80/0101-0011

W2.00/0

SO2 DOSAGES IN AN URBAN AREA G. DRUFUCA, M. GIUGLIANO* and E. TORLASCHI~ Ccntro Telecomunicazioni Spaziali de1 CNR, Polite&co di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy (First received 12 February 1979 and inJinai form 20 July 1979)

Abstract-Five winter-semesters of data of SOI concentration ai three sires in the urban area of Milan were analyzed lo generate statistics of dosage which describe the dosage distributions, the temporal structure, the dependence upon concentration thresholds and the six-month-average concentration. By considering the joint distributions of dosages and their durations it is found that the basic ambiguity between dosages and their durations can be resolved since for each dosage value only a limited range of durations is observed. It is also found that the six-month-average concentration has a dominating role on the statistics of dosages; Previous works have reported a similar intIuence on concentration statistics, durations and extreme values. For most of the statistics it has been possible to develop simple and accurate empirical models. 1. WTRODUCTION The action of pollutants is performed through doses. In toxicology the dose is defined as the mass of material introduced in the organism. For air pollutants the dose can be defined as the product of the pollutant concentration, the exposure time and the amount-per-unit-time of inhaled air. (For instance a

subject, breathing at a rate of 0.6 m3 h- ’ for 3 h in an atmosphere with 0.5 mg rnq3 of SOa, takes a dose of 0.6 x 3 x 0.5 L 0.9 mg). In practice, instead of dose, the concept of dosage, defined as: D-

J

C(t)&

(1)

At

is often used. C(t) is the pollutant concentration and At is the exposure time. In this way, the dose concept may be extended to those subjects for which the amount of inhaled air is not easily evaluated or it does not even exist, such as plants and materials. The dosage concept has been used both to study the effects of polluting atmospheres (Guderian, 1960; Thomas, 1961; McFarland, 1968, U.S. Dept of Health, 1969) and to define criteria ofair quality (Larsen, 1961; Larsen et al., 1967; Duckworth and Kupchant, 1967; Benarie, 1976). dosage-above-a-concentrationMore frequently, threshold, defined as: D=

JT

[c(t) - Cold&

(2)

is used, where Co is the concentration threshold and T is now the amount of time for which the concentration exceeds the threshold, that is the dosage duration. Usual units of D are ppm x h (part per million x hours).

* Istituto di Ingegneria Sanitaria, Poiitecnico di Milano, Piazza Leonardo da Vinci, 32,20133 Milano, Italy. t Istituto di Elettrotecnica e-d Elettronica, Politecnico di Milano, Piazza Leonardo da Vinci, 32,20133 Milano, Italy. 11

It is obvious that the above definitions of dosage are intrinsically ambiguous as identical values of D can be obtained from a multitude of combinations of Cvalues. and T-values. This ambiguity is reflected in variable dosage-responses which have been observed with plants (Haut, 1961; Larsen and Heck, 1972; Temple, 1972). Indeed, the Haber’s rule in toxicology (Haber, 1924), that foresees the same response for a given dosage C x T, is true only over limited ranges of C and T. In the ambiguous cases, it is apparent that the response is conditioned not only by the pollutant uptake, but also by the uptake rate depending upon the concentration. For this reason concentrations appear to be more relevant than the exposure time: lower concentration values with higher exposure times permit the development or the activation of mechanisms of detoxification and continuous removal of the pollutant, as has been observed for some plants under fumigation of SO, (Ziegler, 1975). Less ambiguous responses can be observed with limited ranges of C and T and for dosages of cumulative pollutants (U.S. Dept. of Health, 1969 ; Hill, 1969 ; Silverman et al., 1977). Nevertheless, in spite of the intrinsic amand complicated biguity of dosages the dosage-responses of subjects, dosage may be a useful tool in the study of air quality, in the evaluation of acute and chronic effects, and in the definition of airquality-standards. Further, the present analysis shows that the dosage ambiguity is substantially limited by the strong correlation observed between dosages and their durations. In this work we have analyzed 13 time-series of SO2 concentrations measured at 3 sites in the urban area of during 5 consecutive winter-semesters Milan, (October-March) from 1972 to 1977 (section 2). At first we have described the dosages per se, that is independently of their duration. The description is in terms of number of dosage events per semester, their intensity distribution and their temporal structure (section 3). The dependence of these quantities upon

G. DRUFUCA,M. GIUGLIANOand E.

12

TORLASCHI

the concentration threshold C,, and the six-monthaverage-concentration cf is also described. Finally, information is given about the joint statistical behaviour of dosages and their durations (section 4). Luckily it appears possible to solve, at least statistically, the intrinsic ambiguity of dosage, by means of the strong relation that is observed between dosages and their durations. From this analysis it appears that the six-monthly-average-concentration is a dominating parameter for many dosage statistics as it has been observed to be for concentration distributions, duration of events of concentration and ~irn~ values. (Drufuca and Giugliano, 1977, 1978). 2. THE DATA The raw data consist in 13 time-series of SOz concentration values which were recorded every half hour at 3 stations in the urban area of Milan, during the enter-its (October-March) of 5 consecutive years from 1972 to 1977 (2 of the 15 available series have been diided because of maihtnctions in the equipment}. The representativeneas of the 3 stations has been discussed in a previous paper (Drufuca and Ciiughano, 1977). Here also the assump tion is made of statistical homogeneity for the 13 time-series although they were obtained from 3 stations in 5 different winters, as the &ism of emission and diffusion are thought to have remained the same. With this assumption, a larger sampk is available, and it is mble to consider a sufficient number of C vaIues in order to study its intluence on the statistics of dosage. This pa&u&r study is favoured by the almost uniform distribution of c values betweenaminimumvaAueof0.07ppmandamaximum value of 0.23 ppm with a mean value (c> = 0.128 ppm. ( ) indicates averaging over the 13 time series and - averaging over one semester. It may be of interest to summa&e the procedure of data reduction. At first, each time-series is time integrated in 0.5 h-steps for 6 values of the threshold Co (0.01 ppm; 0.05; 0.1; 0.3; 0.5 and l.O), thus obtaining sequences of dosage values. With each dosage is associated its duration and the time interval before the next dosage In this way one t~sfo~ the 13 concentration-time-series into 6 x 13 dosage-timeseries which still conserve the original time structure. The 6 x 13 dosage-time-series constitute the actual data base.

-.-.-.-

5

“010

t

3 2~ 1

0

01

I ! t 002 003 0.05

ttlt

01

0.2 0.3

t

0.5

CONCENTRAlK)FI THREStYXD .c,

1.0

.Ppn

1. The nuder of dosage events per semester vs the concentration thrcahoki, for repraentative vales of the sixmonth-average canantration C. The continuous line is the

average over the 13 time &es. The arrows on the abscissa indicate the actual threshold values used in the analysis. gemis strongly upon the threshold Co and the sixmonth-avera~ con~ntration C. Figure 1 shows N vetsus Co for some representative semesters: the one with the maximum c (c = 0.23 ppm), the minimum (t? = 0.07 ppm), the meanof all the 13 time-series ((C) = 0.128 ppm) and the one closest to the mean fc = 0.125 ppm). All these curves are similar with quasiparabolic shapes as would be expected intuitively and

3. D0sAGES This section describes the statisticat behaviour of dosages per se, that is independently by their duration. Dosages are considered from the point of view of their number, their intensity distribution and their temporal structure, i.e. the way in which they are distributed in time throughout the various semesters. The number-of-dosage-events-per-semester, N, de-

Fig. 2. Probability distributions of I) for representative values of the six-month average concentration C. for a threshold Co = 0.3 ppm.

13

SO, dosages in an urban area

as can be shown under quite general conditions (Tsukatani, 1978). The value of Co for which N is maximum increases with increasing C. For instance, for C = 0.07ppm the maximum N is for C,, = 0.05 ppm (N = 270), for (C) = 0.128 ppm the maximum is for Co = 0.1 ppm (N = 290) and for C = 0.23 ppm the maximum is for Co = 0.15 ppm (N = 330). The intensity distribution of dosages appears to belong to the exponential family, although we have not succeeded in identifying the precise form. For some of the semesters and for some thresholds the distributions could be log normal whence for the others the log normal approximation differs substantially from the observed values. The D-distribution depends on the threshold Co and the six-month-average concentration C. Figure 2 shows D-distributions for C,-, = 0.3 ppm and for representative semesters, that is for C = 0.07 ppm (the minimum C observed), C = 0.125 ppm (the closest actual C to the 13-series-average (C)), (C) = 0.128ppm and C = 0.23 ppm (the maximum C observed). For instance, the 10% quantile is 0.8 ppm x h in the average, 0.4 ppm x h for the minimum C and 2.0 ppm x h for the maximum C. A similar behaviour has been observed for other threshold values. From these plots of D-distributions one can observe that the curves for C = 0.125 ppm and for (C) = 0.128 ppm are very close together, that is the D-distribution obtained by averaging over the 13 time-series is practically coincident with the individual one with a C value that is very close to (C) ; this could be indicative that the various time-series all belong to a common family, supporting the basic assumption of statistical homogeneity of the 13 time series, although they have been observed at different sites and for different years. Further support for this assumption can be obtained from analogous considerations of the number of dosage events as shown in Fig. 1 and for the mean

0

005

01

0 15 AVERAGE

02

025

CONCENTRATION

03 E

,,,,m

Fig. 4. Six-month-standard-deviation of dosage uDvs the sixmonth-average concentration c for diRerent concentration

thresholds C,,. return period (Fig. 10). where statistics for C = 0.125 ppm coincide with those for (C) = 0.128 ppm. A synthetic description of the D-distributions and of their dependence upon C and Co can be obtained by considering the first two moments, that is the mean dosage D and the standard deviation uD. Figure 3 shows observed values of b versus C for different values of C,. For instance for Co - 0.1 ppm and C = 0.128 ppm b = 0.65 ppm x h. The lighter lines in Fig. 3 represent a simple empirical model: D

0.015 = cexp(ll.42

C).

(3)

0

Figure 4 shows the analogous representation of aD; the model being: UD

=

zexp(16.5 G’s

C).

of values

(4)

It can be observed that in a previous work about the durations of concentration events (Drufuca and Giughano, 19773,the mean duration Mu and the standard deviation of duration Sa have been described by: Ma = -&exp( -0.96

So = Lexp(

C;.*

0

0.05

01

a15 AVERAGE

0.2

0.25

CC)NCENTRAlION

0.3 E,

ppn

Fig. 3. Six-month-mean dosage b vs the six-month-average concentration c for different concentration thresholds C,.

+ 5.3 C),

(5)

- 15 + 7.5 C),

(6)

which are structurally identical to (3) and (4). This should not be surprising as dosages and their durations are strongly related as it will be shown in the next section. Some insight into the temporal structure of the

G. DRUFUCA,

14

~.GIUGLIA~~~

E. TORLA~CHI

0.07 ppm. In both Figs. 5 and 6, the light lines represent the empirical model : J&jg

Do.413 for Co I 0.2 ppm

RPZ

(7) 34.2sgO.&ZS Cl 1

for Co 2 0.2 ppm.

The modei and the figures show quite a regular dependence of RP upon D and c and a less regular

,;o

005

01 DOSAGE

D pprn

L

n

Fig. 5. Average-six-month-mean return period (E) vs dosage D and for different coucentration thresholds Co.

dosage process may be obtained by considering the do~~ret~-~~ RP, that is the time eiapsed between a dosage and the next one with at-feast-equal dosage value. This concept is often employed in the climatology ofextreme events and in reliabiiity studies. RP is a random variable depending upon D, Co and C. For the sake of brevity, the - description of RP is restricted to its mean value RP, where the average is performed over all the RP values observed in one semester. Figure 5 shows (E) versus D for values of Cc, averaged over all the 13 time serim i:e. for (C> = 0.128 ppm. For instance, at C,, = 0.1 ppm, dosages of f ppm x h have an average
1

b,I 002 “’

005

01 ’

0203 1”

05

’1

'0 2“1 3 5 DOSAGE D mm.h

Fig. 6. Six-month-mean return period G vs dosage D for c0 = 0.1 ppm and for representative values of the six-month average concentration cf.

dependence upon CW The observed vaiues of RP are consistently smaiier than the ones that can be computed assuming a uniform time-distribution of the dosages in the semesters. For instance, for Co = 0.1 ppm, there are on average 40 events of dosage larger than 1 ppm x h. If these events were uniformly distributed along a semester they would be 99.2 h apart, taking into account their own duration, while the observed (g) is 62 h. That is averaging over the 13 time-series i@ is about 0.6 times the uniform one. This can be interpreted as an accmmdation of dosages in p&&s of more intense activity. This lotion is independent by D and Co but it is markedly dependent on the seasonai average c: for C = 0.23 ppm RP is 0.3 time the uniform one, while for C less than 0.1 ppm the dosage events tend to be uniformly distributed in time. 4. DOSACKS AND THEIRDURATIONS

As it was pointad out in section 1, many dosageresponses are dif%cult to interpret due to an intrinsic ambiguity about the duration of the dosages and therefore about the exposure time. This ambiguity can be partially removed ifthe joint statistical behaviour of dosages iYand their duration T is considered. Luckily, the strong dependence of dosage on duration, which is implicit in (2), and the actual temporal structure of the concentration process, assist in assigning a narrow set of duration values to any particular value of dosage. This is evident in Fig. 7 which shows in a T, D plane the joint probability density p(T, D), for Co = 0.1 ppm. Figure 7 has been obtained by pooling together all the 13 time-series for a total of 3,770 dosage events. The curves are ~~pro~~~ty curves, for instance there is a pro~bi~i~ of IO-’ for an event with dosage between 2 ppm x h and 2.1 ppm x h and with duration between 8 and 10 h. The maiu feature of p(T, D) in Fig. 7 is a strong diagonal behaviour, consequent upon the mutual dependency of D and T. A similar behaviour can be observed for other values of Co. The joint density p(T, D) depends upon C and Co and so does the joint probability distribution P( T, D). One can write, by means of the Bayes rule:

W, D) = W/WV% where P(T/D) is the conditional

(8) probability

distri-

SO2 dosages

in an urban area

Fig.7. Joint probabilitydensityof dossgcD anddosageduration T, withintervalsAD= 0.1porn x h and bT = 2bforCci - 0.1ppn.i. bution of T given D and P(D) is the marginai probability ~st~bution of A As it was shown in section 2, P(D) depends upon c and C,, : a description of this dependence can be obtained by (3) and (4); it has been found that P(T/D) depends upon C, only. As an example for Co = 0.1 ppm, Fig. 8 shows the probabiity that the duration is larger than T for a given D for classes of D,e.g., for dosages between 0.8 and 1.6 ppm x h there is a 5WAprobability that their duration is larger than 11 h and there is a 10’ probability that their duration is larger than 18 h; for

dosages between 0.1 and 0.2ppm x h the same quantiks are 3.3 and 6 h. The regular behaviour of the curves in Fig. 8 and the diagonal aspect of the surfaces in Fig. 7 suggest a synthetic description of the dependence of the du-

U-ID) =

p T~TlD)dT, i0

(9)

p(T/D) is the conditional density function of T givenD,d&ncdas: where

00) where p(T, D)isthe joint density function of T and D and p(D) is the marginal density function of D. Observed values of
a mean duration of 11 h. The regular behaviour of these curves can be described ~pi~~Iy by a simple mode1 (light lines):

rations upon the dosage values. Consider the mean value of T given 0,that is

4.62 CT/o) is

($626~2/3_

(10)

(T/D)is a useful quantity because it represents the expected value of the duration of a particular event of dosage D. Its usefulness is enhanced by the small variance of the duration values arotmd the expected value. Figure 10 shows the txeflkient of variation of the duration conditioned to the dosage vs dosage, dcfkcd as: C.O.V. = gg

x 100,

where cf D is the standard deviation of

(11)

T given D

defined bb @2/D=

OURATlON.T h

Fig. 8. Conditionalprobabilitydistributionof the doss& duration T giventhe dosageD for cIsssssof D and for C, = 0.1 ppzn.

m T'p(T/D)dT
Figure 10 shows the mean C.O.V. obtained avcraging over the various thresholds C, as the behaviour of C.O.V. vs D has been observed to be substantially the same for the different thresholds. For dosages larger than 0.2 ppm x h, C.O.V. is practically constant with a

G. DRUFUCA. M. GIUGLIANO and E.

16

TORLASCHI

10

0 Ool 0.w.

om

01

0203

03

1

2

3

5 OOSAQE.O.~~h

Fig.9.

The mean value of the dosage duration T given the dosage D, (T/D) vs the dosage D for different values of the concentration threshold Co.

value of .., uto/, thus implying that (T/D) is a reliable estimate of the duration of a dosage event. In concltion, dosage appears to behave in a well de&ted manner with respect to the duration T and to the six-month-average concentration if. As it was pointed out in section 2, C determines the number of dosageevents and their intensity distribution as shown in Figs. 1 and 2 and as described by (3) and (4); the duration of the dosages is not affocuxiby c but only by the dosage intensity. Appendix I contains an exampk of how, from the knowledge oft? alone, it is possibk to obtain a s&n&~, though synthetic, image of the dosaeepraxrn I CONCLUSIONS

The results of this study may be summarized by the

following conciusions : (1) These are indications of statistical homogeneity

in SOz concent&oh time suks observed at diff-t sites and for diffbrent years. (2) Dosages events am not uniformiy distributed along a winter-s but dosage-retum periods huiicate that dosage events tend to be concentrated in shorter pub&, depading upon the six-month-average concentration C.

(3) The intrinsk ambiguity between dosages and their duration is reaolvabk, at kast statistically. The prorzassis such that to each domgc vatue thae co-&

a liied

range ofdurations;

the standard deviation of durations is - 30% of the expected duruion for a given dosag& Further, the rdation botwocn dosages and their expected duration can be described by a simpk

Fig. 10. The cocffkieat of variation of the dourge duration T given the dosage I) vs D. The curve has been obtained by averaging over the differant tbrcsbolds Co and over all the 13 time series.

SO2 dosages in an urban area

empirical model. (4) The six-month-average

concentration C has a dominating role on the statistics of dosages ; the number of dosage events per semester N, the dosage distribution P(D) and the dosage return period RP are strongly affected by C. (5) From the knowledge of c alone it is possible to build a schematic but significant image of the dosage process, at least for the Milan area, where, as in many urban areas, there are a large number of sources which are contributing to the dosage, and where the winter climate is characterized by frequent long periods with low or zero wind speeds, and by frequent subsidence inversions. REFERENCES Benaric M. M. (1976) Empirical dosage-distance relationships around a point source at ground level. Atmospheric Environment10, 163-166. Drufuca G. and Giugiiano M. (1977) The duration of bigb SO1 concentration in an urban atmosphere. Atmospheric Environmenr 11, 729-735. Drufuca G. and Giugliano M. (1978) Rtlationsbip between maximum SO2 concentration, averaging time and average concentration in an urban area. AtmosphericEnvironment 12,1901-1905. Duckwortb S. and Kupchanko E. (1967) Air analysis: the standard dosagaarea product. J. Air Pollut. Control Ass. 17,379-383. G&erian R, van Haut H. and Stratmamt (1960) Probleme der Erfasstmg tmd Ikurteihmg von Wirktmgen gasfoermigcrLuftv e&r&ingtmgen aufdie Vegetation. 2. Plansenkraukh. P&nsenshutz

67.257-265.

Haber F. (1924; Fiw lectures& the years 1920-1923. Berlin, Springer-Verlag. Haut H. van (1961) Die Analyse von Scwefeldioxidwirktmgen auf Pflanzen in Laboratoriumsversuch. Staub-Reinh. kcft 21,52-56. Hill A. C. (1969) Air quality standards for fluoride vegetation effect J. Air Polluf. Control Ass. 19, 331-336. Larsen R. I. (l%l) Parameters of aerometric measurements for air pollution research. Am. lad. Hyg. Ass. 2.97-101. Larsen R. I., Zimmer C. E., Lynn D. A. and Bkmel K. G. (1967) Analyzing air pollutant concentration and dosage data. J. Air Poliut. Control Ass. 17, 85-93.

17

Larsen R. I. and Heck W. W. (1976) An air quality data analysis system for interrelating effects, standards and needed source reductions : part. 3. Vegetation injury. J. Air Pollut. Control Ass. 26, 325-333. McFarland H. N. (1968) Exposure chambers-design and operation, Proc. 7th Annual Technical Meeting of tk An&can Association of Contamination Control, 19-25, Chicago. Silverman F, Shephard R. 1. and Folinsbee L. (1977) Effect of physical activity on long respon.ws to acute ozone cxposure. Proc. Fourth International Clean Air Congress, p. 10 Tokyo. Temple P. J. (1972) Dose-response of urban tree to sulfur dioxide. J. Air PO&U. Control Ass. 22, 271-274. Thomas M. D. (1961) Elkcts of air pollution on plants. Air Pollut 238, WHO Monograph Series N. 46, Geneve. Tsukatani T. (1978) Discussion on tbe duration of high SO1 concentrations in an urban atmosphere. Atmospkric Environment 12, 1242-1243. U.S. Department of Health, Education and Welfare (1969) Air quality criteria for sulfur oxides, Washington D.C., January 1969. Ziegler I. (1975) The effect of SO1 pollution on plant metabolism. Residue Rev. 56, 79-105.

APPFNDlX I Throu& the results presented in this work, knowledge of the six-month-average concentration c enables some significant statistics of the dosage process to be determined. As an example, consider a six-month timaseries with c = 0.125 ppm. This value is close to tbe average situation in the Milan~oldithasactuallybeenobserved~awofthe13 time series availabk. For this se&a some sign&ant statistics are computed and compared with those observed. Tabk 1 shows this comparison for a high threshold value of Co 0.3 ppm. The total number of events N is computed from Fig 1 obtaining N = 119 which agrees well with 109 observed events. The probability density P(D) for various classes of D may be obtained from Fig. 2. Densities for diRerent vale of c may be obtained by interpolation. The number of events in the classes of D is obtained as Np(D). The average duration (T/D) for the classes of D may be computed using Equation (10). The computed values agree very well with the average durations actually observed. Finally the average return periods RP may be calculated from Equation (7). The comparison with observation is good, except for the higher class of D, where the limited number of observed events gives an unrealistic estimate of tbe mean return period (16.5 h).

Table 1. Dosage statistics for c = 0.125 ppm and Co = 0.3 ppm

D(ppm x b)

P(D)

D D D D D D

0.62 0.06 0.12 0.07 0.10 0.03

0.1 < 0.2 5 0.4 5 0.8 5 1.6 5

LE. 14/1--R

< c < < < <

0.1 0.2 0.4 0.8 1.6 3.2

N” of events computed observed 74 7 14. 8 12 4

68 6 13 8 11 3

(h) computed Observed 0.6 2.1 3.3 5.3 8.4 13.3

0.8 2.1 3.0 5.2 6.4 9.9

E(h) computed

observed

37.7 86.1 115.5 154.8 207.6 278.3

53.6 62.2 93.2 153.0 251.4 16.5