- Email: [email protected]
Statistical analysis of continuous ozone measurements
0004-6981 (> 1981
STATISTICAL ANALYSIS OF CONTINUOUS MEASUREMENTS C. S. HIRTZEL!’
81 061025-10
SO? 00 0
Perpamon Press Ltd
OZONE
and J. E. QUON
Department of Civil Engineering, Northwestern University, Evanston, Illinois 60201, U.S.A. (First received 7 April 1980 and infirm/form
23 Ocrober 1980)
Abstract-Statistical techniques for extracting information from a continuous record of air quality are presented and apphed to ozone measurements from five momtoring sites in the Chicago metropohtan area. Statistical descriptors such as the mean and variance of ozone concentration, autocorrelatlon function, and the equivalent number of independent observations m a continuous record are determined. The frequencies and durations of exceedances above selected concentration levels are developed, and models examined to describe the distribution of exceedance durations. Dally maximum hourly and hourly ozone measurements during summer months are highly autocorrelated; ttus correlation 1shighly persistent and limiting coefficients are on the order of f 0.2 to k 0.3 at time lags of 15 to 20 days or more. The equivalent number of independent observations m a continuous record of summer dally maximum hourly ozone measurements was approximately 20 to 79 ‘x of the total number of measurements; for summer hourly ozone measurements, only a few per cent of the hourly measurements were statlstlcally independent. At higher exceedance ,levels (100 ppb or greater), observed average and median exce-edance durations of summer dally maxlmum hourly ozone concentrations were, ip general, on the order of one lo two days. The observed distributions of exceedance durations were reasonably well-described by exponential and power function models. These models can be used to estimate expected frequencies and durations of exceedances and the conditional probabilities of exceedance duration. Results of the analyses of exceedance duration support the notion that episode control schemes need to include actions which can be implemented within a short time period, e.g., one day, after initiation
of an exceedance
episode m order lo be effective m protecting
the public health and air quality. INTRODUCTION Analysis of ozone measurements in urban areas is of Intrinsic interest, and also of interest in determining comphance with the recently revised ambient air quahty standards. Many of the studies on ozone in urban areas have related ozone concentrations to physical (meteorological) parameters such as wind speed, solar or ultraviolet radiation, mixing height, maximum air temperature, humidity and the presence of a particular type of pressure system using, in many cases. long term average concentrations of ozone, e.g., average weekly concentrations of hourly ozone levels or of daily peak hour ozone levels (Revlett, 1978; Wolff and L~oy. 1978). Time series techniques have been used for analyzing ozone (oxidants) data, and for developmg models to predict future ozone levels (Chock er a[., 1975; McColhster and Wilson, 1975; T~ao el al., 1976). Again, in many cases, long-term average concentrations were used. In this study, some statistical techniques for the analysis of the stochastic characteristics of ozone measurements are presented which are useful for the evaluation of the data and for developing effective episode control strategies. Prior to the passage of the revised air quality standards for ozone (January, 1979). interest centered on the total number of hourly violations (i.e., the l Present address Department of Chemical and Environmental Engmeermg. RPI, Troy, NY 12181 U.S.A.
number of hours for which ozone concentrations exceeded 80 ppb), and the total fraction of time each season for which ozone concentrations exceeded various selected levels. Since the revised standard for ozone was adopted. interest has shifted to the number of days in which the daily maximum hourly ozone concentration exceeds some preselected level (Curran and Cox. 1979; Federal Register, 1979). In this study, an exceedance (or run) is defined as an unbroken sequence of ozone concentrations at or above a preselected level. The exceedance duration (or run length) is the uninterrupted length of time that ozone concentrations contmue at or above the given level. The response time between implementation of proposed control actions and then expected impacts on air quality isan important consideration when developing regulations and episode control schemes. Control actions which require a time period longer than the ozone exceedance duration m order for beneficial effects to occur are of little value in episode control. The precision of statistical estimates such as the sample mean and variance depends on the degree of independence. or lack of independence, among the measurements in a grven sample. Consequently, statistical propertles of ozone measurements such as the frequency and duration of exceedances above selected concentration levels, the clustermg of exceedances in time, and the distribution and condltional probability function of exceedance duration; and the statistIcal dependence, or number of independent measurements in a contmuous record of an quahty, the autocorre-
1025
i
1026
S HIHTZEL dnd J E Quoh
among measurements, and the presence of cyclical patterns are important considerations m the development and evaluation of control strategies, assessment of health risk, and other issues associated with air quality management. latton
BASIC DATA
Data used in this study were continuous records of hourly ozone (0,. ,,)and daily maxtmum hourly ozone (0s. ,,)concentrations from five monitoring sites in the Chicago metropolitan area. These sites are the CAMP station (Continuous Air Monitoring Program of the U.S. Environmental Protection Agency), the Polk Street station (operated by the Illinois Environmental Protection Agency), and the Kenwood, Lindblom and Taft High Schools stations (operated by the City of Chicago). The Kenwood and Lindbiom sites are located in central residential areas. The Kenwood site is located near the shore of Lake Michigan; the Lindblom station is located inland. The CAMP station is located in the central business district, adjacent to a major expressway. The Taft and Polk Street stations are urban sites, located in residential and commercial areas, respectively. In the analysis of ozone exceedances, data for the summer months were used, e.g., May through September. These months encompass the time period during which elevated ozone concentrations occur frequently, and are referred to simply as “summer months.” A summary of the sites and time periods of the hourly ozone data records investigated is shown m Table 1. Each hourly ozone concentration is the average of four 15 min measurements taken during the hour, and is reported as the hourly concentration at the beginning of each other. The methods of analysis used to measure the ozone concentrations are instrumental chemiluminescence at the CAMP station, and instrumental ultra-violet absorption at the other four sites. Hourly ozone concentrations are recorded to the Table Site.
I. Summary
of hourly
Time pertod
ozone records Vahd hours ( “,)
Kenwood
May-Sept May-Sept May-Sept May-Sept
1975 1976 1977 1978
92.7 82.0 89.2 Xl 5
Lmdblom
May- Sept May- Sept May-Sept May-Sept
I975 1976 1977 1978
89.5 96.1 79.2 58.4
Polk Street
May-Sept May -Sept May-Sept May-Sept
1974 1975 1976 1977
91.4 87.5 96.6 95.8
Taft
May-Sept
1978
CAMP
1973 Apr-July May-Aug 1974 May- Aug I975 May-Aug 1976 June-Aug 1977 _..___~._.___
73.1 94.7 80.6 96.5 95.1 94.5
nearest ppb. The daily maximum hourly ozone concentration IS defined simply as the peak hourly ozone concentration recorded during a given 24 h day. In general, the data records (see Table 1) of hourly ozone measurements at the five sites were fairly complete for the time periods examined. With the exception of the summer of 1978 at the Lindblom and Taft sites, the hourly ozone data records were approximately 80 to 977, complete for the summers investigated. At the CAMP station, however. entire months of measurement were missmg from the data records in several cases (May 1977 and August 1973). No attempt was made to reconstruct any of the missing data from extrapolation of existing records. Ozone measurements for each siteand summer were examined as individual sets; data from different sites and/or summers were not pooled in any of the analyses due to difficulties in pooling measurements from different sites and/or time periods.
RESULTS AND DlSCUSSlON General
statistical
descriptors
Mean values of daily maximum hourly ozone, O,.,, concentrations during summer months at the five Chicago sites varied from 28 ppb (CAMP, 1974) to 69 ppb (Kenwood, 1977); and variances of summer 0, ,+ concentrations ranged from 244 ppb’ to 1740 ppbi. The general statistical characteristics of summer 05, d concentrations for each site are summarized in Table 2. Maximum ozone concentrations ranged from 85 ppb to 241 ppb. These concentrations are moderately high, and do exceed the revised ambient air quality standard of 120 ppb. For example, for the Polk site, the number of days on which ozone concentrations greater than or qua1 to 120 ppb were observed varied from approximately one to five per cent of the total days in the summer, depending on the year. The maximum observed concentration, 241 ppb, was recorded at the Kenwood station. As noted previously, the Kenwood site is located near the shore of Lake Michigan and concentrations recorded there may reflect the lake breeze effect (Lyons, 1972). As can be seen from Table 2, data recorded at the CAMP station were, in general, much less than ozone concentrations recorded at the other sites. The CAMP monitor intake was located at a height ten feet above ground, near heavy vehicular traffic. Consequently, local vehicular emissions of nitrogen oxide, a well-known ozone scavenger, are probably responsible for depressed ozone concentrations in the immediate vicinity of the monitor. It should be noted that there are many inherent inaccuracies in measurements of ambient ozone concentrations; this study did not attempt to account for these. In general, however, these inaccuracies would be expected to increase the variability of the data. The means and variances of hourly ozone. OS,hr concentrations for each summer and site were computed, and are shown in Table 2. Hourly ozone
1027
Stattstical analysis of continuous ozone measurements Table 2. Statistical charactenstics
of daily maximum hourly ozone and hourly ozone concentrations O3.h
O3.d
Site and time period*
Mean fppb)
Vanance (PPb2)
Maximum (PPb)
Mean (PPb)
Variance (Ppb’)
Kenwood 1975 1976 1977 1978
62.0 61.8 69.4 67.2
1080 1280 1740 823
233 202 241 161
29.1 28.5 32.5 33.9
683 753 1002 693
Lindblom 1975 1976 1977 1978
48.6 40.6 42.6 40.2
669 481 481 472
147 103 133 91
20.5 15.5 20.0 17.7
458 302 288 312
Polk Street 1974 1975 1976 1977
52.4 49.0 43.8 46.6
839 936 734 893
172 192 153 152
26.5 22.2 18.3 19.8
451 452 401 443
1978
65.4
828
142
34.6
593
1973 1974 1975 1976 1977
30.5 27.9 33.7 35.6 32.6
339 244 537 494 416
119 85 185 110 130
14.0 10.6 11.6 13.2 12.4
139 125 206 227 184
Taft CAMP
l
Time periods as shown in Table 1, for corresponding year.
concentrations at or above the level of the former air quality standard, 80 ppb, were relatively numerous. However, the percentage of hours during a summer that Os,h concentrations violated the former air quality standard is approximately the same as the percentage of days in the summer that 09,d concen-
trations equalled or exceeded the current standard, 120 ppb; i.e., on the order ofa few per cent. At the Polk site, for example, the percentage of hours for which 03, h concentrations equalled or exceeded 80 ppb was 2-3 7; of the total hours in the summer, for each year. The degree and persistence of correlation among successive ozone measurements may be quantified, and the presence and form of periodic components may be characterized by autocorrelation analysis (Box and Jenkins, 1976). The autocorrelation functions of 0,. *, for the sites and summers listed in Table 1, typically are of an exponential decay type pattern as illustrated by Fig. 1, although the smoothness of the pattern depends on the site. Autocorrelation coefficients at a time lag of one day are generally high, e.g., 0.38-0.67 (except at the CAMP site); and the coefficients decay to approximately f0.2 at time lags of 20 days or more. A summary of autocorrelation coefficients at selected time lags is given in Table 3. Autocorrelation functions for 03, k concentrations were computed for the sites and summers shown in Table 1, and for the CAMP station for non-summer months. Autocorrelation coefficients at a time lag of 1 h are high, ranging from 0.71 to 0.92 for summers at
all sites, and from 0.72 to 0.85 for non-summer months at the CAMP site. A regular and persistent diurnal pattern is present in the autocorrelation function of 09, ,,concentrations during summer months at all sites investigated, as illustrated by Fig. 2(a). Autocorrelation coefficients are still significant at large time lags, e.g., approximately f 0.25 at time lags of 360 h, the longest time lag examined. Other sites exhibit similar patterns; coefficients are on the order of f0.2 to f0.3 at time lags of 360 h.
\
Taft StatIon Summer 1978
1
Fig. 1. Autocorrelation function of daily maximum hourly ozone concentrattons.
(‘ S HIRTZELand J. E.
1028
Quoh
Table 3. AutocorrelatIon coefficients for daily maxtmum hourly ozone concentrauons Autocorrelatlon coef%ents Site and time penod-
Lag I
Lags 2-10 days -_Min Max
Lags 11-20 days Min
Max 0.20(12) 0.06(17) 0 31(11) -001(15)
Kenwood 1975 1976 1977 1978
0.38 0.50 0.43 043
0.09 (8)t -0.12(10) 0.17 (8) -O.lO(lO)
0.34(3) 0.32(2) 0.33(4) 0.24(2)
- 0.08(20) -0.15(11) O.oq20) -0.17(11)
Lmdblom 1975 1976 1977 1978
0.49 0.47 0.54 0.56
0.09 (8) -0.05 (8) 0.00 (9) o.Iqlo)
0.26(6) 0.22(2) 0.41(2) 0.43(2)
-0.11(20) - 0.0!&20) -0.02(12) -0.12(19)
0.12(12) 0.11(12) O.lq16) 0.09(15)
0.40
0.39 0.48 0.52
0.00 (3) 0.08 (7) -0.09(10) 0.21(10)
0.21(7) 0.30(5) 0.26(2) 0.36(7)
0.02(H) -0.02(19) - 0.13(20) - 0.03(20)
0.29(18) 0.24(17) -0.03(12) 0.2q1 I)
1978
0.67
O.ll(lO)
0.31(7)
-0.16(19)
0.04(11)
1973 1974 1975 1976 1977
0.30
-0.11 (9) 0.12(10) -0.09 (8) -0.13 (7) -0.06 (3)
0.19(6) 0.34(2) 0.20(3) 0.20(2) 0.08(4)
-0.10(15) - 0.03(20) -0.12(20) - 0.18(20) - 0.06(20)
0.13(17) 0.17(18) 0.10(12) 0.09(17) 0.17(11)
Polk Street 1974 1975 1976 1977 Taft CAMP
0.55 0.17 0.36 0.30
Time periods as shown m Table 1, for corresponding year. t Numbers in parentheses indicate time lag at which coe&ient l
For non-summer months at CAMP, autocorrelation coefbcients are also large for the 6rst few time lags; e.g, coeIIicients at time lags of 1,2 and 3 b are 0.75, 0.56 and 0.40, respectively, for 0,. Lconcentrations for November and December, 1974, as shown in Fig. 2(b). As can be seen, with the exception of a peak at a time lag of approximately 120 b, the autocorrelation function decays quickly and limiting coefficients are on the order of only f0.05, for time lags greater than about 30 b, up to 360 b. Autocorrelation functions of 0,. ,, and 0,. ,, concentrations for summer months at all sites showed a high degree of correlation persists at large time lags; in both cases, coefficients at lags up to 360 b (15 days) or 20days are still significant and on the order of f 0.2 or more. Cyclical patterns are apparently absent from the autocorrelation functions based on summer Oa,P concentrations, and from those based on 03, Lfor nonsummer months. Autocorrelation functions based on Oa,I concentrations for summer months, however, reveal the presence of a strong diurnal pattern. This pattern of summer hourly ozone concentrations is expected, of course, given the known diurnal variations of meteorological variables such as ultraviolet radiation and temperature which are important in the generation of ozone. The diRerent forms of the autocorrelation functions based on summer OJ,*
occurred.
concentrations and those based on non-summer OS*L concentrations re0ect the d&rent origins of summer ozone as opposed to non-summer ozone. The bigb degree of statistical &pe&nce among measurements must be taken into account to insure that the proper precision be ass&ated with various statistical parameters estimated from the data. One method to determine the equivalent number of independent observations within a given time period is the ratio of variances test (Benjamin and Corneil, 1970). The equivalent number of independent OS., measurements in a summer was determined for data from the Kenwood, Lindblom and Polk stations. (CAMP data were not used in this analysis since tk time intervals for different summers were not the same.) The number of equivalent independent 03,, measurements in a summer (out of a total of 153 days possible) ranged from 57 to 121 days at Ken&, from 31 to 44 daysat Lindbiom; and from 55 to Todays at Polk. Thus, only about 20-79 % of tbe total post&k OJ,d measurements during the summer could be considered statistically independent. The usual practice of treating the data as if they were imkpendent results in a significant error in estimation of the variance of the sampk mean, or any other statistical estimate which depends on the number of independent measurements. In the case of carbon monoxide, for
Statlstv2al analysis of continuous ozone measurements
1029
OZONE EXCEEDANCES (0)
Ltndblom
Stotlon
5/l - E/II/l976
iii on-
(b)
&
_’ 0::
2
-_ 0
i
I._
__-
-__-_ -.- :
CAMP Stotlon 1111 - 12/31/1974
-_. -
..-__-_-_i-
-
-02 i
Fig 2. Autocorrelatlon functions of hourly ozone concentratlons. (al Lmdblom station I May 1976-11 August 1976 tb) CAMP station, 1 November 1974-31 December 1974.
example, the number of independent hours in a year was estimated to be on the order of lOO-loo0; and it was shown that the varrance of the sample mean could be underestimated by a factor of 10 or more if the dependence among the data was ignored (Hirtzel and Quon, 1979). To insure accurate data analysis based on 03.k measurements, tt IS important to determine, for example. the number of independent hours in a day, and the number of independent hours in a summer. The equivalent number of independent hours per day vartes from 2.4 to 3.7 for different summers at the Kenwood, Lmdblom. Polk and Taft sites. Out of a possible total of 3672 hours in a summer, the number of independent hours per summer ranged as follows: from 100 to 146 at Kenwood; from 54 to 87 at Lmdblom: and from 31 to 35 at Polk. These calculations mdtcate that only about l-4 y; of the hours in a contmuous record of hourly ozone measurements for the summer are statistically independent. Smce the information about the true populatton parameters such as the mean and variance contained in a given set of observations is very much less if the ohservatrons are highly positively correlated than if they were Independent, the design of efficient sampling schemes is difficult because a long time period may be requned to accumulate a sufficiently large number of Independent observations to achieve the desired prectsion.
In addition to the autocorrelation coefficients, another measure of the persistence among successtve ozone m~surements is an analysis of exceedances (or runs) of ozone concentrations above preselected levels. Persistence. then, is defined to be a measure of the ability of the process, i.e.. OJ, ,, or OJ. ,,concentrations, to continue at or above a preselected exceedance level. c,. For 03. d concentrations, exceedance durations (or run lengths) were determined for nme exceedance levels: 20.40 and 60 ppb, and 70 through 120 ppb. in increments of 10 ppb; for OS-k concentratrons, seven exceedance levels were examined: 60 through 120 ppb, in increments of 10 ppb. Exceedance duration charactertstics for exceedances of summer O,,, concentrations for the Kenwood site are shown in Table 4(a); the numbers of exceedances and average exceedance durations of summer O3,6 concentrations for the other four sites are summarized in Table 4(b). Values of the average exceedance duratton,x varied from 76.0 days to 4.1 days at the lowest exceedance level, 20 ppb. for all sites and summers; and, at c, = 120 ppb, the highest level examined,rvaried from 1.6 days to 1.0 day. In generaf, the average exceedance duration deereases as the exceedance level mcreases from 20 to 120 ppb. Thts trend may partly reflect the fact that, as the exceedance level increases, the meteorological and other variables necessary to maintaining ozone concentrations at increasmgly higher levels are not as likely to persist. At the higher exceedance levels examined or as c, approaches the maximum observed concentration, the average duration 1s small and tends towards a value of 1.0 day. Based on the definition of exceedance duration. the mimmum value ofi;s one day, and corresponds to high values of c,. In some cases, however, the value oft increases slightly at high c, (e.g., 110 or 120 ppb) due to a small number of exceedances of relatively long duration. Median exceedance durations, rmcd,were 1.0 day for all exceedance levels greater than or equal to 80 ppb, for all sites and summers except summersat the Kenwood station. This result may have important implications with respect to episode control actions. Maximum exceedance durations, t,,, at the Kenwood site are shown in Table 4(a). For ail sites and summers, at an exceedance level of 80 ppb for example, tma?. ranged from 1 to 8 days. At the level of the ambient air quality standard, 120 ppb, maximum exceedance durations up to 4 days were observed. These values are an indication of the potential severity of an ozone exceedance and the need for episode control actions, since the adverse effects of a pollutant such as ozone are dependent on the concentration level, as well as the length of time that elevated concentrations persist. The total number of exceedances, N, above a selected exceedance level varied from 2 to 22 at c, = 20 ppb, and from 0 to 11 at c, = 120 ppb, for all summers and sites (see Tables 4(a) and 4(b)). In general, N decreases as c, increases from about 60 ppb
C S. HIRTZEL and J. E. QU~N
1030 Table
4(a). Exceedance
duration
characteristics
of daily maximum station) Exceedawe
20 MaySePt 1975
N F(day) LdwY)
t ,AW) s: (day*) Nt (day) MaySePt 1976
T” kai
t max
s2
h Maysept 1977
N
i tmtd
tmax sr I&-
May-
N
SePt 1978
‘i tmal s? t
rsT
40
60
70
hourly
ozone
concentrattons
(Kenwood _,-,
._
level, c, (ppb) 80
90
I10
100
120
3 50.0 7
24 5.0 3
25 2.7 2
23 1.9
20 1.7
1
11 1.9 1
8 1.6
6 1.5
5 I6
142 6357.0 1.50
22 27.7 119
I5 10.0 67
10 4.0 43
8 2.9 34
7 3.7 21
4 1.4 13
3 0.7 9
3 08 8
4 37.0 26 94 1812.7 148
21 4.6 3 16 IS.5 97
20 2.9 2 IO 7.4 59
17 2.9 2 10 7.7 49
14 2.0 1.5 5 2.0 28
12 2.0 2 5 1.5 24
IO 1.7 l 5 1.8 17
9 1.8 I 5 I.9 16
7 I.6 3 0.6 11
4 36.7 10.5 123 3346.9 147
16 7.4 3.5 24 59.6 118
17 4.3 2 23 34.2 74
18 3.1 1.5 11 9.9 56
19 2.4 2 6 2.5 45
16 2.2 2 6 1.9 35
I6 1.3
12 1.4
Ii I.5
1
1
!
2 0.2 21
2 0.3 17
_ G.3 16
2 76.0
14 9.4 7
29 3.1 2
24 2.5 2
23 1.6 1
17 1.7 1
13 1.5 1
10 1.5 1
8978.0 143 152
78.0 29 132
11 6.7 90
3.8 8 61
61.5 37
61.6 29
61.9 20
2.5 6 15
6 1.5 I 4 1.5 5
to 120 ppb (but N tends to increase with c,, for c, in the range of 20 ppb to 60 ppb). This trend is expected at higher exceedance levels since the meteorological and other conditions requisite to forming higher ozone levels will be unlikely to occur frequently. Examination of the data showed that exceedances do not occur uniformly over the summer; in some cases, most exceedances at higher levels occurred in clusters confined to a relatively short time period, e.g., one or two months, within the summer. The product NT, in the case of the OJ,r series, gives the total time in days which the process spends in exceedances at or above the selected level (see Table 4(a), for example). By definition, NTmust generally decrease (although it may remain the same) as c, increases. This product can be used to determine compliance with the air quality standards. For example, at an exceedance level of 120 ppb, NTranged from 0 to 16 days, out of a total of 153 days in a summer, depending on the site and year; thus, up to 10% of the time in a summer was in noncompliance with the ambient air quality standard for the different sites and summers investigated. For the summer O,,, series, average exceedance durations and the total numbers of exceedances above selected exceedance levels at the five sites studied are shown in Table 5. The average exceedance duration is, in general, on the order of a few hours; e.g., i ranges from 1.0 to 6.0 h at all exceedance levels for all summers and sites. Unlike the 0s. , series, there is no clear trend of decreasing T with increasing c,. In general, however, at the higher exceedance levels, Tis
1
1
I
1
i
small and approaches its minimum value of 1.0 h, the sampling interval. As was observed for the Os,, series, values of ?-for the Or,* exceedamzs at the highest excecdance levels (c, = 110 and 120 ppb) Buctuate in some casea due to a relatively small number of exceedances observed at those levels. The total number of exceedances for the Os, ,, series (Table 5) behaves similarly as for the 09,( series, i.e., N generally decreases as c, increases from 60 to 120 ppb. For the OS, ,, series, the product NTequals the total number of hours during a summer for which ozone concentrations equalled or exceeded the corresponding exceedance level.
CONTROL IMPLICATfONS
The distribution of ozone exceedance durations has important control implications since the degree and timing of episode control efforts required for an~ozone exceedance will depend on both the expected severity, i.e., c, and the exceedance duration. Here, we are referring to the short-term reeponse to ozone episodes rather than the control of average ozone levels by source reduction of precursors. A sample histogram of exceedance durations of OS,, concentrations is shown by the solid line bar graph in Fig. 3. The observed distribution is skewed to the lek towards short durations, and could be represented by an exponential or a power function model. For cases with a relatively small number of exceedances, the shape of the his-
14.2 15.2 5.6 7.9
Polk Str. 1974 1975 1976 1977
as shown
41 4.9 6.0 5.6 5.5
CAMP 1973 1974 1975 1976 1977
* Trme periods
37.5
1978
Taft
20
d:y)
12.5 10.1 19.4 9.1
t
Lindblom 1975 1976 1977 1978
Site and time period*
1.7 1.9 1.9 2.2 2.1
11.1
2.9 3.0 2.4 3.5
3.8 2.6 3.3 4.3
dk)
t
40
11 14 19 20 14
10
28 28 31 21
24 25 20 15
N
1.3 2.0 1.5 1.5 1.4
3.9
2.1 1.9 21 32
2.2 2.1 2.4 1.7
(day)
T
of exceedances
60
in Table 1, for corresponding
17 17 17 18 13
4
10 9 22 16
11 13 7 13
N
_
Table 4(b). Number
year
6 2 8 10 7
17
21 20 16 13
20 13 14 13
N
1.7 1.5 1.2 1.1 1.2
3.5
1.9 1.8 2.1 2.4
1.9 1.7 1.6 1.4
70
3 2 6 8 4
15
15 14 12 14
14 10 13 11
N
7
1.0 1.0 1.3 1.2 1.0
2.1
1.6 1.7 2.1 1.7
1.7 1.4 1.6 1.1
(day)
3 1 3 6 3
16
12 11 8 14
10 7 9 8
N
T
1.0 1.2 1.0
1.0
1.7
1.4 1.4 1.7 1.1
1.7 1.1 2.0 1.0
(day)
90
1 0 3 5 1
14
9 10 8 12
8 7 5 1
N
of dally maximum
level, c, (ppb) --.~ 80
duration
Exceedance
exceedance
(day)
T
and average
100
1.0 1,2 1.0
1.0
1.4
1.3 1.4 1.0 1.0
1.4 I.0 1.0
1 0 3 4 1
14
7 7 5 9
5 3 2 0
N
T
1.0 10 1.0
1.0
1.6
1.3 1.2 1.0 1.0
1.0
1.5
(day)
110
ozone concentratrons
(d: y)
hourly
1 0 3 3 1
7
7 6 3 7
2 0 2 0
N
1.0
1.0
1.6
1.4 1.2 1.0 I.0
1.0
1.0
(day)
T
~--
120
I
0
1
0 0
5
5 4 1 4
2 0 2 0
N
C. S. HIRTZEL and J. E. QUON
1032 Table
5. Number
of exceedances
and average
exceedance
Exceedance
durations
of hourly
ozone concentrations
level, c, (ppb)
.- ___--..-
Site and 60 time period* ?jhr) Kenwood 1975 1976 1977 1978 Lindblom 1975 1976 1977 1978 Polk Street 1974 1975 1976 1977 Taft 1978 CAMP 1973 1974 1975 1976 1977 *Time per&s
70 N
80
-ijhr)
N
T(hr)
N
Thr)
N
$hr)
N
T(hr)
,V
‘iihr,
t
11 I6 ‘0 18
4’ 31 411 2 ‘.
8 12 18 11
70
2 0 ’ n
4.4 5.1 5.0 4.2
88 73 105 108
4.7 4.0 5.0 4.0
51 60 75 78
4.1 4.8 4.3 4.2
39 32 61 47
3.4 3.5 3.7 3.0
28 29 48 42
3.7 4.3 5.3 2.5
16 16 23 28
4.0 36 4.8 2.3
3.9 3.5 2.9 3.2
53 30 33 20
3.5 3.2 2.0 1.9
31 18 21 15
3.4 2.9 2.0 14
19 10 9 8
3.0 2.1 22 I.0
14 8 5 I
2.6 1.3 2.0
8 3 3 0
2.2
4.5 4.1 4.4 3.9
57 44 41 58
3.6 3.3 3.7 3.0
43 33 30 43
4.0 4.0 3.4 3.0
24 18 20 26
3.9 3.1 3.1 2.9
14 14 14 14
4.3 2.7 3.2 2.3
9 IO 5 9
2.5 2.7 3.0 2.0
11 7 3 8
’ 8 6:o 2.0
4
4.5
86
3.7
61
3.5
39
2.8
30
2.2
25
1.9
14
I4
9
1.5 3.0 2.5 2.6 1.9
8 4 15 21 14
1.6 2.3 2.6 3.1 2.4
2.0 1.0 3.5 2.9 1.3
3
4.0
1 0 3 7 1
4.0
1 0 4 6 1
3.0
1 0 4 3 1.
as shown
in Table
1 4 7 3
1. for corresponding
4.0 1.9 2.0
f(t) = i exp( - At),
t 2 0,
(1)
f(t)=(d-l)td,-‘t-d,
dr
(2)
and 1.
Here, t is the exceedance duration, in days. The estimate of 1 in Equation (1) is the inverse of the
Excursion durotlon, days Fig. 3. Frequency
functions of exceeduration for daily maximum hourly ozone concentrations
1.7 1.0 1.0
10
1.5 1.0 1.o
4 0 2 0
1.0
1.6
8 5
1
0 0 30
I 0
10
1
year
togram of exceedance durations is somewhat Irregular. The exponential (Benjamin and Cornell, 1970) and the power function (Pate1 et al., 1976) distributions are, respectively:
dance
i IU
110
100
90
average exceedance duration calculated from observed exceedance data. For the power function distribution, Equation (2), to is one-half the characteristic time associated with the data (0.5 hour and 0.5 day for the 0 3,L and the 0J,4 series, respectively1 and d is estimated based on observed exceedance durations using the method of maximum likelihood (Benjamin and Cornell, 1970). The exponential and power function distributions give a reasonable fit to observed exceedance durattons, as illustrated in Fig. 3. At short durations of one to three days, the power function model tends to provide a better fit; and for durations greater than approximately three days, the models are comparable. Since I IS the inverse of the average exceedance duration, values can be obtained from Tables 4(a) and (b); and values of d for 03,p exceedances are tabulated In Table 6. The parameter of the exponential model varies with c,; in general, as noted previously.‘&creases as c, increases and, hence, 1 increases as c, increases. The power function model parameter, d, ranges from approximately 1.2 to 2.4, for all levels c,, for all sites and summers investigated. The probability of an exceedance continumg for tz days given the excecdance has lasted t, days may be estimated using the customary procedure for evaluattng conditional probability (Benjamin and Cornell, 1970). Based on Equations (1) and (2), the conditional probabilities for the exponential and power function distributions, respectively, are developed as: P(t 2tz{t
>~tl)=exp{-~(t2-1,)),
t2 2r,,(3)
Stattsttcal Table
6. Power
function
analysts
model
of contmuous
parameter,
ozone measurements
d. for exceedances
1033
hourly ozone
of dally maximum
concentrations Exceedance
Site and time period* Kenwood 1975 1976 1977 1978 Lindblom 1975 1976 1977 1978 Polk Street 1974 1975 1976 1977 Taft 1978 CAMP 1973 1974 1975 1976 1977 l
Time periods
20
40
60
70
80
90
100
110
120
1.33 1.29 1.31
1.77 1.68 1.62 1.66
1 95 1.70 1.70 1.73
2.01 1.83 1.74 2.01
1.94 1.81 1.76 1.94
1.99 1.97 2.10 2.07
2.01
1.23
I 55 1.52 1.46 1.42
1 93 2 02 2 15
I .95 I .95 1.99 2.08
1.35 1.42 1.32 1.46
1.68 1.72 1.63 1.53
1.79 1.88 1.76 1.91
1.88 1.94 2.01 2.09
1 93 2.12 2 12 2.28
1 92 2.26 1.95
2.03 2.44 244
1.96
2.44
2.44
244
1.33 1.36 1.48 1.53
1.67
1.78
1.86
1.93 1.83 1.91
2.03 2.11 1 92 2.33
2.12 2.12 2.44 2.44
2.12 2.24 2.44 2.44
2 03 2 15
1.85 1.77
1.82 1.92 1.94 1.81
1.95
1.68 1.78 1.66
1.25
1.40
1.60
1.62
1 85
1.94
2.12
2.01
2.03
1.56 1.55 1.52 1.47 149
1.92 1.86 1.84 1.82 1.80
2.08 1.72 1.99 1.99 2.01
I.87
2.44 2.44 2.20
2.44 2.15
2.44 2.44
as shown
in Table
2.24 2.28 2.15
(3) depends
2.08 2.24 2.44
I, for corresponding
(4) that Equation
only on the difference
t2 - tl, and is independent of individual values of t, and t,. Equation (4) depends on the ratio of tz to t,. The likelihood of an exceedance continuing, based on Equations (3) and (4) agrees generally with values calculated from observed data, as illustrated by the
year.
example m Table 7. For the sttes and summers examined, the likelihood of an exceedance continuing for one more day, once it has been in existence for one day, 1s moderately high. e.g., 0.6; and the likelihood of an excursion continumg for an additional two or three days, once initiated, is relatively low. From a control point of vtew, these results imply that eptsode control actions need to be implemented within a short time from the initiation of an exceedance if these acttons are to be effective.
Table 7. Conditional probabilittes of exceedances of daily maxtmum hourly ozone concentrations (c, =80ppb. Taft statton. summer 19781
Exponential model
(d:ys, 1 1 1 1 1 1 2 2 2 2 2 3 3 3
2 3 4 5 6 7 3 4 5 6 7 5 6 7
0.616 0.379 0.234 0144 0.088 0.054 0.616 0.379 0.234 0.144 0.088 0.379 0.234 0.144
2.44
1.96
and
Note
level, c, (ppb)
Power functton model 0.556 0.395 0.309 0.256 0.220 0.193 0710 0.556 0.461 0.395 0.347 0.649 0.556 0.488
Observed 0 624 0.374 0.374 0.25 I 0.251 0.125 0.599 0.599 0.401 0401 0.201 0.670 0.670 0.335
c’. S
1034 CONCLUDING
HIRTZELand J. E. Quo~i
REMARKS
Contmuous records of ozone measurements from five monitoring sites in the Chicago metropolitan area were used to develop statistical descriptors such as the average and variance of ozone concentrations, degree of independence, and the frequency and durations of exceedances above selected ozone levels: to assess compliance with the ambient atr quahty standard; and to estimate the likelihood of an ozone exceedance continuing after a certam duration, once It has been initiated. Autocorrelation analyses of daily maxlmum hourly ozone and hourly ozone measurements showed that a high degree of correlation exists among observations in a continuous record, and perststs up to large time lags; autocorrelation coefficients are +0.2 at time lags of 15 to 20 days. The highly persistent correlation implies that there are relatively few independent observations in a continuous record. Ratio of variance test results for different sites and summers showed that the number of independent observations of daily maximum hourly ozone in a summer (May through September) varies from 31 to 121, out of a possible total of 153 days; and the number of independent hourly observations in a summer varied from 31 to 146, out of a total of 3672 h in a summer. The accurate interpretation of air quality measurements requires that dependence among the data be accounted for when making statistical inferences based on the data. For example, estimates of confidence intervals or the variance of the sample mean may be m error by order
of magnitude or more if the lack of statistical independence is ignored (Hirtzel and Quon, 1979). Analysis of exceedances of daily maxlmum hourly ozone concentration above selected levels showed that. in the majority of cases, the average exceedance duration above 100 ppb ranged from 1.0 to 1.7 days, and the median duration was 1.Oday. Effective eptsode control strategies, then, need to in&de actions-which can be implemented within a short time. e.g.. one a day. The observed frequencies of exceedance durations above selected ozone levels were reasonably well described by a power or an exponential distribution
function. The likelihood of an exceedance contmumg after It has already been in existence for a given length of time may be estimated using these models. These estimates are useful m assessmg the severity of a given episode and the necessity for implementrng episode control actlons.
Acknowledgements-The authors wish to express apprectanon to Ms. Kay Kamalick, Enforcement Divlnon, U S. Environmental Protection Agency, Chicago. and to Mr. Jerome Hope and Mr. John Evanoff, Technical Services Division, Department of Consumer Services, City of Chicago, for their assistance m Providingdata for thisstudy Computer funds were provided by Northwestern Umversity.
REFERENCES
Benjamin J. R. and Cornell C. A. (1970) Probubifiry, Sk~rtsf~cs. and Decision/or Civil Engineers, McGraw-Hill, New York. Box G. E. P. and Jenkins G. M. (1976) Time Series Analysis. Forecustlng and Control, Holden-Day, San Francisco. Chock D. P., Terre11T. R. and Levitt S. B. (1975) Time series analysis of Riverside, California air quality data. Atmospheric
Environment
9.978-989.
Curran T. C. and Cox W. M. (1979) Data analysis procedures for the ozone NAAQS statistical format. J. Air Pollut. Control Ass. 29, 532-534. Federal Register (1979) National Primary and Secondary Ambient
Air Quality
Standards.
No. 44, 8202-8237.
Hirtzel C. S. and Quon J. E. (1979) Statistical dependence of hourly carbon monoxide measurements. J Arr Pollut. Control Ass. 29, 161-163. Lyons W. A. (1972) The climatology and pm&non of the Chicago Lake breeze. .I. uppl. Mer. Il. 1259-1270. McCollister G. M. and Wilson K. R. (1975) Linear stochastic models for forecasting daily maxima and hourty concentrations of air pollutants. Atmospheric Enwonmenr 9. 417-423.
Pate1 J. K., Kapadia C. H. and Owen D. B. (1976) Handbook of Starlstical Distributions, Marcel Dekker, New York, Revlett G. H. (1978) Ozone forecasting Ilsing empirical modelinn. J. Air Pollut. Control Ass. 28. 338-343. Tiao G. Cx Phadke M. S. and Box G. E. P. (1976) Some empirical models for the Los Angeles photochemlcat smog data. J. Air Pollut. Control Ass. 26, 485-490. Wolff G. T. and Lioy P. J. (1978) An empirical model for forecasting maximum daily ozone levels in the northeastern U.S. J. Air Pollur. Control Ass. 28. 1034-1038.
STATISTICAL ANALYSIS OF CONTINUOUS MEASUREMENTS C. S. HIRTZEL!’
81 061025-10
SO? 00 0
Perpamon Press Ltd
OZONE
and J. E. QUON
Department of Civil Engineering, Northwestern University, Evanston, Illinois 60201, U.S.A. (First received 7 April 1980 and infirm/form
23 Ocrober 1980)
Abstract-Statistical techniques for extracting information from a continuous record of air quality are presented and apphed to ozone measurements from five momtoring sites in the Chicago metropohtan area. Statistical descriptors such as the mean and variance of ozone concentration, autocorrelatlon function, and the equivalent number of independent observations m a continuous record are determined. The frequencies and durations of exceedances above selected concentration levels are developed, and models examined to describe the distribution of exceedance durations. Dally maximum hourly and hourly ozone measurements during summer months are highly autocorrelated; ttus correlation 1shighly persistent and limiting coefficients are on the order of f 0.2 to k 0.3 at time lags of 15 to 20 days or more. The equivalent number of independent observations m a continuous record of summer dally maximum hourly ozone measurements was approximately 20 to 79 ‘x of the total number of measurements; for summer hourly ozone measurements, only a few per cent of the hourly measurements were statlstlcally independent. At higher exceedance ,levels (100 ppb or greater), observed average and median exce-edance durations of summer dally maxlmum hourly ozone concentrations were, ip general, on the order of one lo two days. The observed distributions of exceedance durations were reasonably well-described by exponential and power function models. These models can be used to estimate expected frequencies and durations of exceedances and the conditional probabilities of exceedance duration. Results of the analyses of exceedance duration support the notion that episode control schemes need to include actions which can be implemented within a short time period, e.g., one day, after initiation
of an exceedance
episode m order lo be effective m protecting
the public health and air quality. INTRODUCTION Analysis of ozone measurements in urban areas is of Intrinsic interest, and also of interest in determining comphance with the recently revised ambient air quahty standards. Many of the studies on ozone in urban areas have related ozone concentrations to physical (meteorological) parameters such as wind speed, solar or ultraviolet radiation, mixing height, maximum air temperature, humidity and the presence of a particular type of pressure system using, in many cases. long term average concentrations of ozone, e.g., average weekly concentrations of hourly ozone levels or of daily peak hour ozone levels (Revlett, 1978; Wolff and L~oy. 1978). Time series techniques have been used for analyzing ozone (oxidants) data, and for developmg models to predict future ozone levels (Chock er a[., 1975; McColhster and Wilson, 1975; T~ao el al., 1976). Again, in many cases, long-term average concentrations were used. In this study, some statistical techniques for the analysis of the stochastic characteristics of ozone measurements are presented which are useful for the evaluation of the data and for developing effective episode control strategies. Prior to the passage of the revised air quality standards for ozone (January, 1979). interest centered on the total number of hourly violations (i.e., the l Present address Department of Chemical and Environmental Engmeermg. RPI, Troy, NY 12181 U.S.A.
number of hours for which ozone concentrations exceeded 80 ppb), and the total fraction of time each season for which ozone concentrations exceeded various selected levels. Since the revised standard for ozone was adopted. interest has shifted to the number of days in which the daily maximum hourly ozone concentration exceeds some preselected level (Curran and Cox. 1979; Federal Register, 1979). In this study, an exceedance (or run) is defined as an unbroken sequence of ozone concentrations at or above a preselected level. The exceedance duration (or run length) is the uninterrupted length of time that ozone concentrations contmue at or above the given level. The response time between implementation of proposed control actions and then expected impacts on air quality isan important consideration when developing regulations and episode control schemes. Control actions which require a time period longer than the ozone exceedance duration m order for beneficial effects to occur are of little value in episode control. The precision of statistical estimates such as the sample mean and variance depends on the degree of independence. or lack of independence, among the measurements in a grven sample. Consequently, statistical propertles of ozone measurements such as the frequency and duration of exceedances above selected concentration levels, the clustermg of exceedances in time, and the distribution and condltional probability function of exceedance duration; and the statistIcal dependence, or number of independent measurements in a contmuous record of an quahty, the autocorre-
1025
i
1026
S HIHTZEL dnd J E Quoh
among measurements, and the presence of cyclical patterns are important considerations m the development and evaluation of control strategies, assessment of health risk, and other issues associated with air quality management. latton
BASIC DATA
Data used in this study were continuous records of hourly ozone (0,. ,,)and daily maxtmum hourly ozone (0s. ,,)concentrations from five monitoring sites in the Chicago metropolitan area. These sites are the CAMP station (Continuous Air Monitoring Program of the U.S. Environmental Protection Agency), the Polk Street station (operated by the Illinois Environmental Protection Agency), and the Kenwood, Lindblom and Taft High Schools stations (operated by the City of Chicago). The Kenwood and Lindbiom sites are located in central residential areas. The Kenwood site is located near the shore of Lake Michigan; the Lindblom station is located inland. The CAMP station is located in the central business district, adjacent to a major expressway. The Taft and Polk Street stations are urban sites, located in residential and commercial areas, respectively. In the analysis of ozone exceedances, data for the summer months were used, e.g., May through September. These months encompass the time period during which elevated ozone concentrations occur frequently, and are referred to simply as “summer months.” A summary of the sites and time periods of the hourly ozone data records investigated is shown m Table 1. Each hourly ozone concentration is the average of four 15 min measurements taken during the hour, and is reported as the hourly concentration at the beginning of each other. The methods of analysis used to measure the ozone concentrations are instrumental chemiluminescence at the CAMP station, and instrumental ultra-violet absorption at the other four sites. Hourly ozone concentrations are recorded to the Table Site.
I. Summary
of hourly
Time pertod
ozone records Vahd hours ( “,)
Kenwood
May-Sept May-Sept May-Sept May-Sept
1975 1976 1977 1978
92.7 82.0 89.2 Xl 5
Lmdblom
May- Sept May- Sept May-Sept May-Sept
I975 1976 1977 1978
89.5 96.1 79.2 58.4
Polk Street
May-Sept May -Sept May-Sept May-Sept
1974 1975 1976 1977
91.4 87.5 96.6 95.8
Taft
May-Sept
1978
CAMP
1973 Apr-July May-Aug 1974 May- Aug I975 May-Aug 1976 June-Aug 1977 _..___~._.___
73.1 94.7 80.6 96.5 95.1 94.5
nearest ppb. The daily maximum hourly ozone concentration IS defined simply as the peak hourly ozone concentration recorded during a given 24 h day. In general, the data records (see Table 1) of hourly ozone measurements at the five sites were fairly complete for the time periods examined. With the exception of the summer of 1978 at the Lindblom and Taft sites, the hourly ozone data records were approximately 80 to 977, complete for the summers investigated. At the CAMP station, however. entire months of measurement were missmg from the data records in several cases (May 1977 and August 1973). No attempt was made to reconstruct any of the missing data from extrapolation of existing records. Ozone measurements for each siteand summer were examined as individual sets; data from different sites and/or summers were not pooled in any of the analyses due to difficulties in pooling measurements from different sites and/or time periods.
RESULTS AND DlSCUSSlON General
statistical
descriptors
Mean values of daily maximum hourly ozone, O,.,, concentrations during summer months at the five Chicago sites varied from 28 ppb (CAMP, 1974) to 69 ppb (Kenwood, 1977); and variances of summer 0, ,+ concentrations ranged from 244 ppb’ to 1740 ppbi. The general statistical characteristics of summer 05, d concentrations for each site are summarized in Table 2. Maximum ozone concentrations ranged from 85 ppb to 241 ppb. These concentrations are moderately high, and do exceed the revised ambient air quality standard of 120 ppb. For example, for the Polk site, the number of days on which ozone concentrations greater than or qua1 to 120 ppb were observed varied from approximately one to five per cent of the total days in the summer, depending on the year. The maximum observed concentration, 241 ppb, was recorded at the Kenwood station. As noted previously, the Kenwood site is located near the shore of Lake Michigan and concentrations recorded there may reflect the lake breeze effect (Lyons, 1972). As can be seen from Table 2, data recorded at the CAMP station were, in general, much less than ozone concentrations recorded at the other sites. The CAMP monitor intake was located at a height ten feet above ground, near heavy vehicular traffic. Consequently, local vehicular emissions of nitrogen oxide, a well-known ozone scavenger, are probably responsible for depressed ozone concentrations in the immediate vicinity of the monitor. It should be noted that there are many inherent inaccuracies in measurements of ambient ozone concentrations; this study did not attempt to account for these. In general, however, these inaccuracies would be expected to increase the variability of the data. The means and variances of hourly ozone. OS,hr concentrations for each summer and site were computed, and are shown in Table 2. Hourly ozone
1027
Stattstical analysis of continuous ozone measurements Table 2. Statistical charactenstics
of daily maximum hourly ozone and hourly ozone concentrations O3.h
O3.d
Site and time period*
Mean fppb)
Vanance (PPb2)
Maximum (PPb)
Mean (PPb)
Variance (Ppb’)
Kenwood 1975 1976 1977 1978
62.0 61.8 69.4 67.2
1080 1280 1740 823
233 202 241 161
29.1 28.5 32.5 33.9
683 753 1002 693
Lindblom 1975 1976 1977 1978
48.6 40.6 42.6 40.2
669 481 481 472
147 103 133 91
20.5 15.5 20.0 17.7
458 302 288 312
Polk Street 1974 1975 1976 1977
52.4 49.0 43.8 46.6
839 936 734 893
172 192 153 152
26.5 22.2 18.3 19.8
451 452 401 443
1978
65.4
828
142
34.6
593
1973 1974 1975 1976 1977
30.5 27.9 33.7 35.6 32.6
339 244 537 494 416
119 85 185 110 130
14.0 10.6 11.6 13.2 12.4
139 125 206 227 184
Taft CAMP
l
Time periods as shown in Table 1, for corresponding year.
concentrations at or above the level of the former air quality standard, 80 ppb, were relatively numerous. However, the percentage of hours during a summer that Os,h concentrations violated the former air quality standard is approximately the same as the percentage of days in the summer that 09,d concen-
trations equalled or exceeded the current standard, 120 ppb; i.e., on the order ofa few per cent. At the Polk site, for example, the percentage of hours for which 03, h concentrations equalled or exceeded 80 ppb was 2-3 7; of the total hours in the summer, for each year. The degree and persistence of correlation among successive ozone measurements may be quantified, and the presence and form of periodic components may be characterized by autocorrelation analysis (Box and Jenkins, 1976). The autocorrelation functions of 0,. *, for the sites and summers listed in Table 1, typically are of an exponential decay type pattern as illustrated by Fig. 1, although the smoothness of the pattern depends on the site. Autocorrelation coefficients at a time lag of one day are generally high, e.g., 0.38-0.67 (except at the CAMP site); and the coefficients decay to approximately f0.2 at time lags of 20 days or more. A summary of autocorrelation coefficients at selected time lags is given in Table 3. Autocorrelation functions for 03, k concentrations were computed for the sites and summers shown in Table 1, and for the CAMP station for non-summer months. Autocorrelation coefficients at a time lag of 1 h are high, ranging from 0.71 to 0.92 for summers at
all sites, and from 0.72 to 0.85 for non-summer months at the CAMP site. A regular and persistent diurnal pattern is present in the autocorrelation function of 09, ,,concentrations during summer months at all sites investigated, as illustrated by Fig. 2(a). Autocorrelation coefficients are still significant at large time lags, e.g., approximately f 0.25 at time lags of 360 h, the longest time lag examined. Other sites exhibit similar patterns; coefficients are on the order of f0.2 to f0.3 at time lags of 360 h.
\
Taft StatIon Summer 1978
1
Fig. 1. Autocorrelation function of daily maximum hourly ozone concentrattons.
(‘ S HIRTZELand J. E.
1028
Quoh
Table 3. AutocorrelatIon coefficients for daily maxtmum hourly ozone concentrauons Autocorrelatlon coef%ents Site and time penod-
Lag I
Lags 2-10 days -_Min Max
Lags 11-20 days Min
Max 0.20(12) 0.06(17) 0 31(11) -001(15)
Kenwood 1975 1976 1977 1978
0.38 0.50 0.43 043
0.09 (8)t -0.12(10) 0.17 (8) -O.lO(lO)
0.34(3) 0.32(2) 0.33(4) 0.24(2)
- 0.08(20) -0.15(11) O.oq20) -0.17(11)
Lmdblom 1975 1976 1977 1978
0.49 0.47 0.54 0.56
0.09 (8) -0.05 (8) 0.00 (9) o.Iqlo)
0.26(6) 0.22(2) 0.41(2) 0.43(2)
-0.11(20) - 0.0!&20) -0.02(12) -0.12(19)
0.12(12) 0.11(12) O.lq16) 0.09(15)
0.40
0.39 0.48 0.52
0.00 (3) 0.08 (7) -0.09(10) 0.21(10)
0.21(7) 0.30(5) 0.26(2) 0.36(7)
0.02(H) -0.02(19) - 0.13(20) - 0.03(20)
0.29(18) 0.24(17) -0.03(12) 0.2q1 I)
1978
0.67
O.ll(lO)
0.31(7)
-0.16(19)
0.04(11)
1973 1974 1975 1976 1977
0.30
-0.11 (9) 0.12(10) -0.09 (8) -0.13 (7) -0.06 (3)
0.19(6) 0.34(2) 0.20(3) 0.20(2) 0.08(4)
-0.10(15) - 0.03(20) -0.12(20) - 0.18(20) - 0.06(20)
0.13(17) 0.17(18) 0.10(12) 0.09(17) 0.17(11)
Polk Street 1974 1975 1976 1977 Taft CAMP
0.55 0.17 0.36 0.30
Time periods as shown m Table 1, for corresponding year. t Numbers in parentheses indicate time lag at which coe&ient l
For non-summer months at CAMP, autocorrelation coefbcients are also large for the 6rst few time lags; e.g, coeIIicients at time lags of 1,2 and 3 b are 0.75, 0.56 and 0.40, respectively, for 0,. Lconcentrations for November and December, 1974, as shown in Fig. 2(b). As can be seen, with the exception of a peak at a time lag of approximately 120 b, the autocorrelation function decays quickly and limiting coefficients are on the order of only f0.05, for time lags greater than about 30 b, up to 360 b. Autocorrelation functions of 0,. ,, and 0,. ,, concentrations for summer months at all sites showed a high degree of correlation persists at large time lags; in both cases, coefficients at lags up to 360 b (15 days) or 20days are still significant and on the order of f 0.2 or more. Cyclical patterns are apparently absent from the autocorrelation functions based on summer Oa,P concentrations, and from those based on 03, Lfor nonsummer months. Autocorrelation functions based on Oa,I concentrations for summer months, however, reveal the presence of a strong diurnal pattern. This pattern of summer hourly ozone concentrations is expected, of course, given the known diurnal variations of meteorological variables such as ultraviolet radiation and temperature which are important in the generation of ozone. The diRerent forms of the autocorrelation functions based on summer OJ,*
occurred.
concentrations and those based on non-summer OS*L concentrations re0ect the d&rent origins of summer ozone as opposed to non-summer ozone. The bigb degree of statistical &pe&nce among measurements must be taken into account to insure that the proper precision be ass&ated with various statistical parameters estimated from the data. One method to determine the equivalent number of independent observations within a given time period is the ratio of variances test (Benjamin and Corneil, 1970). The equivalent number of independent OS., measurements in a summer was determined for data from the Kenwood, Lindblom and Polk stations. (CAMP data were not used in this analysis since tk time intervals for different summers were not the same.) The number of equivalent independent 03,, measurements in a summer (out of a total of 153 days possible) ranged from 57 to 121 days at Ken&, from 31 to 44 daysat Lindbiom; and from 55 to Todays at Polk. Thus, only about 20-79 % of tbe total post&k OJ,d measurements during the summer could be considered statistically independent. The usual practice of treating the data as if they were imkpendent results in a significant error in estimation of the variance of the sampk mean, or any other statistical estimate which depends on the number of independent measurements. In the case of carbon monoxide, for
Statlstv2al analysis of continuous ozone measurements
1029
OZONE EXCEEDANCES (0)
Ltndblom
Stotlon
5/l - E/II/l976
iii on-
(b)
&
_’ 0::
2
-_ 0
i
I._
__-
-__-_ -.- :
CAMP Stotlon 1111 - 12/31/1974
-_. -
..-__-_-_i-
-
-02 i
Fig 2. Autocorrelatlon functions of hourly ozone concentratlons. (al Lmdblom station I May 1976-11 August 1976 tb) CAMP station, 1 November 1974-31 December 1974.
example, the number of independent hours in a year was estimated to be on the order of lOO-loo0; and it was shown that the varrance of the sample mean could be underestimated by a factor of 10 or more if the dependence among the data was ignored (Hirtzel and Quon, 1979). To insure accurate data analysis based on 03.k measurements, tt IS important to determine, for example. the number of independent hours in a day, and the number of independent hours in a summer. The equivalent number of independent hours per day vartes from 2.4 to 3.7 for different summers at the Kenwood, Lmdblom. Polk and Taft sites. Out of a possible total of 3672 hours in a summer, the number of independent hours per summer ranged as follows: from 100 to 146 at Kenwood; from 54 to 87 at Lmdblom: and from 31 to 35 at Polk. These calculations mdtcate that only about l-4 y; of the hours in a contmuous record of hourly ozone measurements for the summer are statistically independent. Smce the information about the true populatton parameters such as the mean and variance contained in a given set of observations is very much less if the ohservatrons are highly positively correlated than if they were Independent, the design of efficient sampling schemes is difficult because a long time period may be requned to accumulate a sufficiently large number of Independent observations to achieve the desired prectsion.
In addition to the autocorrelation coefficients, another measure of the persistence among successtve ozone m~surements is an analysis of exceedances (or runs) of ozone concentrations above preselected levels. Persistence. then, is defined to be a measure of the ability of the process, i.e.. OJ, ,, or OJ. ,,concentrations, to continue at or above a preselected exceedance level. c,. For 03. d concentrations, exceedance durations (or run lengths) were determined for nme exceedance levels: 20.40 and 60 ppb, and 70 through 120 ppb. in increments of 10 ppb; for OS-k concentratrons, seven exceedance levels were examined: 60 through 120 ppb, in increments of 10 ppb. Exceedance duration charactertstics for exceedances of summer O,,, concentrations for the Kenwood site are shown in Table 4(a); the numbers of exceedances and average exceedance durations of summer O3,6 concentrations for the other four sites are summarized in Table 4(b). Values of the average exceedance duratton,x varied from 76.0 days to 4.1 days at the lowest exceedance level, 20 ppb. for all sites and summers; and, at c, = 120 ppb, the highest level examined,rvaried from 1.6 days to 1.0 day. In generaf, the average exceedance duration deereases as the exceedance level mcreases from 20 to 120 ppb. Thts trend may partly reflect the fact that, as the exceedance level increases, the meteorological and other variables necessary to maintaining ozone concentrations at increasmgly higher levels are not as likely to persist. At the higher exceedance levels examined or as c, approaches the maximum observed concentration, the average duration 1s small and tends towards a value of 1.0 day. Based on the definition of exceedance duration. the mimmum value ofi;s one day, and corresponds to high values of c,. In some cases, however, the value oft increases slightly at high c, (e.g., 110 or 120 ppb) due to a small number of exceedances of relatively long duration. Median exceedance durations, rmcd,were 1.0 day for all exceedance levels greater than or equal to 80 ppb, for all sites and summers except summersat the Kenwood station. This result may have important implications with respect to episode control actions. Maximum exceedance durations, t,,, at the Kenwood site are shown in Table 4(a). For ail sites and summers, at an exceedance level of 80 ppb for example, tma?. ranged from 1 to 8 days. At the level of the ambient air quality standard, 120 ppb, maximum exceedance durations up to 4 days were observed. These values are an indication of the potential severity of an ozone exceedance and the need for episode control actions, since the adverse effects of a pollutant such as ozone are dependent on the concentration level, as well as the length of time that elevated concentrations persist. The total number of exceedances, N, above a selected exceedance level varied from 2 to 22 at c, = 20 ppb, and from 0 to 11 at c, = 120 ppb, for all summers and sites (see Tables 4(a) and 4(b)). In general, N decreases as c, increases from about 60 ppb
C S. HIRTZEL and J. E. QU~N
1030 Table
4(a). Exceedance
duration
characteristics
of daily maximum station) Exceedawe
20 MaySePt 1975
N F(day) LdwY)
t ,AW) s: (day*) Nt (day) MaySePt 1976
T” kai
t max
s2
h Maysept 1977
N
i tmtd
tmax sr I&-
May-
N
SePt 1978
‘i tmal s? t
rsT
40
60
70
hourly
ozone
concentrattons
(Kenwood _,-,
._
level, c, (ppb) 80
90
I10
100
120
3 50.0 7
24 5.0 3
25 2.7 2
23 1.9
20 1.7
1
11 1.9 1
8 1.6
6 1.5
5 I6
142 6357.0 1.50
22 27.7 119
I5 10.0 67
10 4.0 43
8 2.9 34
7 3.7 21
4 1.4 13
3 0.7 9
3 08 8
4 37.0 26 94 1812.7 148
21 4.6 3 16 IS.5 97
20 2.9 2 IO 7.4 59
17 2.9 2 10 7.7 49
14 2.0 1.5 5 2.0 28
12 2.0 2 5 1.5 24
IO 1.7 l 5 1.8 17
9 1.8 I 5 I.9 16
7 I.6 3 0.6 11
4 36.7 10.5 123 3346.9 147
16 7.4 3.5 24 59.6 118
17 4.3 2 23 34.2 74
18 3.1 1.5 11 9.9 56
19 2.4 2 6 2.5 45
16 2.2 2 6 1.9 35
I6 1.3
12 1.4
Ii I.5
1
1
!
2 0.2 21
2 0.3 17
_ G.3 16
2 76.0
14 9.4 7
29 3.1 2
24 2.5 2
23 1.6 1
17 1.7 1
13 1.5 1
10 1.5 1
8978.0 143 152
78.0 29 132
11 6.7 90
3.8 8 61
61.5 37
61.6 29
61.9 20
2.5 6 15
6 1.5 I 4 1.5 5
to 120 ppb (but N tends to increase with c,, for c, in the range of 20 ppb to 60 ppb). This trend is expected at higher exceedance levels since the meteorological and other conditions requisite to forming higher ozone levels will be unlikely to occur frequently. Examination of the data showed that exceedances do not occur uniformly over the summer; in some cases, most exceedances at higher levels occurred in clusters confined to a relatively short time period, e.g., one or two months, within the summer. The product NT, in the case of the OJ,r series, gives the total time in days which the process spends in exceedances at or above the selected level (see Table 4(a), for example). By definition, NTmust generally decrease (although it may remain the same) as c, increases. This product can be used to determine compliance with the air quality standards. For example, at an exceedance level of 120 ppb, NTranged from 0 to 16 days, out of a total of 153 days in a summer, depending on the site and year; thus, up to 10% of the time in a summer was in noncompliance with the ambient air quality standard for the different sites and summers investigated. For the summer O,,, series, average exceedance durations and the total numbers of exceedances above selected exceedance levels at the five sites studied are shown in Table 5. The average exceedance duration is, in general, on the order of a few hours; e.g., i ranges from 1.0 to 6.0 h at all exceedance levels for all summers and sites. Unlike the 0s. , series, there is no clear trend of decreasing T with increasing c,. In general, however, at the higher exceedance levels, Tis
1
1
I
1
i
small and approaches its minimum value of 1.0 h, the sampling interval. As was observed for the Os,, series, values of ?-for the Or,* exceedamzs at the highest excecdance levels (c, = 110 and 120 ppb) Buctuate in some casea due to a relatively small number of exceedances observed at those levels. The total number of exceedances for the Os, ,, series (Table 5) behaves similarly as for the 09,( series, i.e., N generally decreases as c, increases from 60 to 120 ppb. For the OS, ,, series, the product NTequals the total number of hours during a summer for which ozone concentrations equalled or exceeded the corresponding exceedance level.
CONTROL IMPLICATfONS
The distribution of ozone exceedance durations has important control implications since the degree and timing of episode control efforts required for an~ozone exceedance will depend on both the expected severity, i.e., c, and the exceedance duration. Here, we are referring to the short-term reeponse to ozone episodes rather than the control of average ozone levels by source reduction of precursors. A sample histogram of exceedance durations of OS,, concentrations is shown by the solid line bar graph in Fig. 3. The observed distribution is skewed to the lek towards short durations, and could be represented by an exponential or a power function model. For cases with a relatively small number of exceedances, the shape of the his-
14.2 15.2 5.6 7.9
Polk Str. 1974 1975 1976 1977
as shown
41 4.9 6.0 5.6 5.5
CAMP 1973 1974 1975 1976 1977
* Trme periods
37.5
1978
Taft
20
d:y)
12.5 10.1 19.4 9.1
t
Lindblom 1975 1976 1977 1978
Site and time period*
1.7 1.9 1.9 2.2 2.1
11.1
2.9 3.0 2.4 3.5
3.8 2.6 3.3 4.3
dk)
t
40
11 14 19 20 14
10
28 28 31 21
24 25 20 15
N
1.3 2.0 1.5 1.5 1.4
3.9
2.1 1.9 21 32
2.2 2.1 2.4 1.7
(day)
T
of exceedances
60
in Table 1, for corresponding
17 17 17 18 13
4
10 9 22 16
11 13 7 13
N
_
Table 4(b). Number
year
6 2 8 10 7
17
21 20 16 13
20 13 14 13
N
1.7 1.5 1.2 1.1 1.2
3.5
1.9 1.8 2.1 2.4
1.9 1.7 1.6 1.4
70
3 2 6 8 4
15
15 14 12 14
14 10 13 11
N
7
1.0 1.0 1.3 1.2 1.0
2.1
1.6 1.7 2.1 1.7
1.7 1.4 1.6 1.1
(day)
3 1 3 6 3
16
12 11 8 14
10 7 9 8
N
T
1.0 1.2 1.0
1.0
1.7
1.4 1.4 1.7 1.1
1.7 1.1 2.0 1.0
(day)
90
1 0 3 5 1
14
9 10 8 12
8 7 5 1
N
of dally maximum
level, c, (ppb) --.~ 80
duration
Exceedance
exceedance
(day)
T
and average
100
1.0 1,2 1.0
1.0
1.4
1.3 1.4 1.0 1.0
1.4 I.0 1.0
1 0 3 4 1
14
7 7 5 9
5 3 2 0
N
T
1.0 10 1.0
1.0
1.6
1.3 1.2 1.0 1.0
1.0
1.5
(day)
110
ozone concentratrons
(d: y)
hourly
1 0 3 3 1
7
7 6 3 7
2 0 2 0
N
1.0
1.0
1.6
1.4 1.2 1.0 I.0
1.0
1.0
(day)
T
~--
120
I
0
1
0 0
5
5 4 1 4
2 0 2 0
N
C. S. HIRTZEL and J. E. QUON
1032 Table
5. Number
of exceedances
and average
exceedance
Exceedance
durations
of hourly
ozone concentrations
level, c, (ppb)
.- ___--..-
Site and 60 time period* ?jhr) Kenwood 1975 1976 1977 1978 Lindblom 1975 1976 1977 1978 Polk Street 1974 1975 1976 1977 Taft 1978 CAMP 1973 1974 1975 1976 1977 *Time per&s
70 N
80
-ijhr)
N
T(hr)
N
Thr)
N
$hr)
N
T(hr)
,V
‘iihr,
t
11 I6 ‘0 18
4’ 31 411 2 ‘.
8 12 18 11
70
2 0 ’ n
4.4 5.1 5.0 4.2
88 73 105 108
4.7 4.0 5.0 4.0
51 60 75 78
4.1 4.8 4.3 4.2
39 32 61 47
3.4 3.5 3.7 3.0
28 29 48 42
3.7 4.3 5.3 2.5
16 16 23 28
4.0 36 4.8 2.3
3.9 3.5 2.9 3.2
53 30 33 20
3.5 3.2 2.0 1.9
31 18 21 15
3.4 2.9 2.0 14
19 10 9 8
3.0 2.1 22 I.0
14 8 5 I
2.6 1.3 2.0
8 3 3 0
2.2
4.5 4.1 4.4 3.9
57 44 41 58
3.6 3.3 3.7 3.0
43 33 30 43
4.0 4.0 3.4 3.0
24 18 20 26
3.9 3.1 3.1 2.9
14 14 14 14
4.3 2.7 3.2 2.3
9 IO 5 9
2.5 2.7 3.0 2.0
11 7 3 8
’ 8 6:o 2.0
4
4.5
86
3.7
61
3.5
39
2.8
30
2.2
25
1.9
14
I4
9
1.5 3.0 2.5 2.6 1.9
8 4 15 21 14
1.6 2.3 2.6 3.1 2.4
2.0 1.0 3.5 2.9 1.3
3
4.0
1 0 3 7 1
4.0
1 0 4 6 1
3.0
1 0 4 3 1.
as shown
in Table
1 4 7 3
1. for corresponding
4.0 1.9 2.0
f(t) = i exp( - At),
t 2 0,
(1)
f(t)=(d-l)td,-‘t-d,
dr
(2)
and 1.
Here, t is the exceedance duration, in days. The estimate of 1 in Equation (1) is the inverse of the
Excursion durotlon, days Fig. 3. Frequency
functions of exceeduration for daily maximum hourly ozone concentrations
1.7 1.0 1.0
10
1.5 1.0 1.o
4 0 2 0
1.0
1.6
8 5
1
0 0 30
I 0
10
1
year
togram of exceedance durations is somewhat Irregular. The exponential (Benjamin and Cornell, 1970) and the power function (Pate1 et al., 1976) distributions are, respectively:
dance
i IU
110
100
90
average exceedance duration calculated from observed exceedance data. For the power function distribution, Equation (2), to is one-half the characteristic time associated with the data (0.5 hour and 0.5 day for the 0 3,L and the 0J,4 series, respectively1 and d is estimated based on observed exceedance durations using the method of maximum likelihood (Benjamin and Cornell, 1970). The exponential and power function distributions give a reasonable fit to observed exceedance durattons, as illustrated in Fig. 3. At short durations of one to three days, the power function model tends to provide a better fit; and for durations greater than approximately three days, the models are comparable. Since I IS the inverse of the average exceedance duration, values can be obtained from Tables 4(a) and (b); and values of d for 03,p exceedances are tabulated In Table 6. The parameter of the exponential model varies with c,; in general, as noted previously.‘&creases as c, increases and, hence, 1 increases as c, increases. The power function model parameter, d, ranges from approximately 1.2 to 2.4, for all levels c,, for all sites and summers investigated. The probability of an exceedance continumg for tz days given the excecdance has lasted t, days may be estimated using the customary procedure for evaluattng conditional probability (Benjamin and Cornell, 1970). Based on Equations (1) and (2), the conditional probabilities for the exponential and power function distributions, respectively, are developed as: P(t 2tz{t
>~tl)=exp{-~(t2-1,)),
t2 2r,,(3)
Stattsttcal Table
6. Power
function
analysts
model
of contmuous
parameter,
ozone measurements
d. for exceedances
1033
hourly ozone
of dally maximum
concentrations Exceedance
Site and time period* Kenwood 1975 1976 1977 1978 Lindblom 1975 1976 1977 1978 Polk Street 1974 1975 1976 1977 Taft 1978 CAMP 1973 1974 1975 1976 1977 l
Time periods
20
40
60
70
80
90
100
110
120
1.33 1.29 1.31
1.77 1.68 1.62 1.66
1 95 1.70 1.70 1.73
2.01 1.83 1.74 2.01
1.94 1.81 1.76 1.94
1.99 1.97 2.10 2.07
2.01
1.23
I 55 1.52 1.46 1.42
1 93 2 02 2 15
I .95 I .95 1.99 2.08
1.35 1.42 1.32 1.46
1.68 1.72 1.63 1.53
1.79 1.88 1.76 1.91
1.88 1.94 2.01 2.09
1 93 2.12 2 12 2.28
1 92 2.26 1.95
2.03 2.44 244
1.96
2.44
2.44
244
1.33 1.36 1.48 1.53
1.67
1.78
1.86
1.93 1.83 1.91
2.03 2.11 1 92 2.33
2.12 2.12 2.44 2.44
2.12 2.24 2.44 2.44
2 03 2 15
1.85 1.77
1.82 1.92 1.94 1.81
1.95
1.68 1.78 1.66
1.25
1.40
1.60
1.62
1 85
1.94
2.12
2.01
2.03
1.56 1.55 1.52 1.47 149
1.92 1.86 1.84 1.82 1.80
2.08 1.72 1.99 1.99 2.01
I.87
2.44 2.44 2.20
2.44 2.15
2.44 2.44
as shown
in Table
2.24 2.28 2.15
(3) depends
2.08 2.24 2.44
I, for corresponding
(4) that Equation
only on the difference
t2 - tl, and is independent of individual values of t, and t,. Equation (4) depends on the ratio of tz to t,. The likelihood of an exceedance continuing, based on Equations (3) and (4) agrees generally with values calculated from observed data, as illustrated by the
year.
example m Table 7. For the sttes and summers examined, the likelihood of an exceedance continuing for one more day, once it has been in existence for one day, 1s moderately high. e.g., 0.6; and the likelihood of an excursion continumg for an additional two or three days, once initiated, is relatively low. From a control point of vtew, these results imply that eptsode control actions need to be implemented within a short time from the initiation of an exceedance if these acttons are to be effective.
Table 7. Conditional probabilittes of exceedances of daily maxtmum hourly ozone concentrations (c, =80ppb. Taft statton. summer 19781
Exponential model
(d:ys, 1 1 1 1 1 1 2 2 2 2 2 3 3 3
2 3 4 5 6 7 3 4 5 6 7 5 6 7
0.616 0.379 0.234 0144 0.088 0.054 0.616 0.379 0.234 0.144 0.088 0.379 0.234 0.144
2.44
1.96
and
Note
level, c, (ppb)
Power functton model 0.556 0.395 0.309 0.256 0.220 0.193 0710 0.556 0.461 0.395 0.347 0.649 0.556 0.488
Observed 0 624 0.374 0.374 0.25 I 0.251 0.125 0.599 0.599 0.401 0401 0.201 0.670 0.670 0.335
c’. S
1034 CONCLUDING
HIRTZELand J. E. Quo~i
REMARKS
Contmuous records of ozone measurements from five monitoring sites in the Chicago metropolitan area were used to develop statistical descriptors such as the average and variance of ozone concentrations, degree of independence, and the frequency and durations of exceedances above selected ozone levels: to assess compliance with the ambient atr quahty standard; and to estimate the likelihood of an ozone exceedance continuing after a certam duration, once It has been initiated. Autocorrelation analyses of daily maxlmum hourly ozone and hourly ozone measurements showed that a high degree of correlation exists among observations in a continuous record, and perststs up to large time lags; autocorrelation coefficients are +0.2 at time lags of 15 to 20 days. The highly persistent correlation implies that there are relatively few independent observations in a continuous record. Ratio of variance test results for different sites and summers showed that the number of independent observations of daily maximum hourly ozone in a summer (May through September) varies from 31 to 121, out of a possible total of 153 days; and the number of independent hourly observations in a summer varied from 31 to 146, out of a total of 3672 h in a summer. The accurate interpretation of air quality measurements requires that dependence among the data be accounted for when making statistical inferences based on the data. For example, estimates of confidence intervals or the variance of the sample mean may be m error by order
of magnitude or more if the lack of statistical independence is ignored (Hirtzel and Quon, 1979). Analysis of exceedances of daily maxlmum hourly ozone concentration above selected levels showed that. in the majority of cases, the average exceedance duration above 100 ppb ranged from 1.0 to 1.7 days, and the median duration was 1.Oday. Effective eptsode control strategies, then, need to in&de actions-which can be implemented within a short time. e.g.. one a day. The observed frequencies of exceedance durations above selected ozone levels were reasonably well described by a power or an exponential distribution
function. The likelihood of an exceedance contmumg after It has already been in existence for a given length of time may be estimated using these models. These estimates are useful m assessmg the severity of a given episode and the necessity for implementrng episode control actlons.
Acknowledgements-The authors wish to express apprectanon to Ms. Kay Kamalick, Enforcement Divlnon, U S. Environmental Protection Agency, Chicago. and to Mr. Jerome Hope and Mr. John Evanoff, Technical Services Division, Department of Consumer Services, City of Chicago, for their assistance m Providingdata for thisstudy Computer funds were provided by Northwestern Umversity.
REFERENCES
Benjamin J. R. and Cornell C. A. (1970) Probubifiry, Sk~rtsf~cs. and Decision/or Civil Engineers, McGraw-Hill, New York. Box G. E. P. and Jenkins G. M. (1976) Time Series Analysis. Forecustlng and Control, Holden-Day, San Francisco. Chock D. P., Terre11T. R. and Levitt S. B. (1975) Time series analysis of Riverside, California air quality data. Atmospheric
Environment
9.978-989.
Curran T. C. and Cox W. M. (1979) Data analysis procedures for the ozone NAAQS statistical format. J. Air Pollut. Control Ass. 29, 532-534. Federal Register (1979) National Primary and Secondary Ambient
Air Quality
Standards.
No. 44, 8202-8237.
Hirtzel C. S. and Quon J. E. (1979) Statistical dependence of hourly carbon monoxide measurements. J Arr Pollut. Control Ass. 29, 161-163. Lyons W. A. (1972) The climatology and pm&non of the Chicago Lake breeze. .I. uppl. Mer. Il. 1259-1270. McCollister G. M. and Wilson K. R. (1975) Linear stochastic models for forecasting daily maxima and hourty concentrations of air pollutants. Atmospheric Enwonmenr 9. 417-423.
Pate1 J. K., Kapadia C. H. and Owen D. B. (1976) Handbook of Starlstical Distributions, Marcel Dekker, New York, Revlett G. H. (1978) Ozone forecasting Ilsing empirical modelinn. J. Air Pollut. Control Ass. 28. 338-343. Tiao G. Cx Phadke M. S. and Box G. E. P. (1976) Some empirical models for the Los Angeles photochemlcat smog data. J. Air Pollut. Control Ass. 26, 485-490. Wolff G. T. and Lioy P. J. (1978) An empirical model for forecasting maximum daily ozone levels in the northeastern U.S. J. Air Pollur. Control Ass. 28. 1034-1038.