Meteorologically adjusted ozone trends in urban areas: A probabilistic approach

Pergamon

Atmospheric Environment Vol. 27B, No. 4, pp. 425-434, 1993 Elsevier Science Ltd Printed in Great Britain. 0957 1272/93 $6.00+0.00

METEOROLOGICALLY ADJUSTED OZONE TRENDS IN URBAN AREAS: A PROBABILISTIC APPROACH WILLIAM M. C o x a n d SHAO-HANG CHU U.S. Environmental Protection Agency, Technical Support Division, MD-14, Research Triangle Park, NC 27711, U.S.A. (First received 17 November 1992 and in final form 22 July 1993) Abstract--A method has been developed that explicitly accounts for the effect of meteorological fluctuations on the annual distribution of ground-level ozone in urban areas. The model includes a trend component that adjusts the annual rate of change in ozone for concurrent impacts of meteorological conditions, including surface temperature and wind speed. The model was applied using available data from 43 urban areas throughout the U.S.A. where ozone levels frequently exceed the National Ambient Air Quality Standard. The results suggest that meteorologically adjusted upper percentiles of the distribution of daily maximum l-h ozone are decreasing in most urban areas over the period from 1981 to 1991. The median rate of change was - 1.1% per year indicating that ozone levels have decreased approximately 11% over this time period. Trends estimated by ignoring the meteorological component appear to underestimate the rate of improvement in ozone primarily because of the uneven year-to-year distribution of meteorological conditions favorable to ozone. Key word index: Ambient ozone, meteorological conditions, urban trends analysis, Weibull distribution, statistical models, bootstrap method.

1. INTRODUCTION Meteorological conditions, including daily temperature and wind speed, are known (Bruntz et at., 1974; Lamb et at., 1987; Pagnotti, 1990) to play an important role in determining the severity of ground level ozone concentrations. Because annual variations in meteorological conditions can be substantial, year-toyear fluctuations in annual ozone statistics can also be quite large. The effect of such variations is to mask any long-term trends in ozone (see U.S. EPA, 1990) that might reasonably be related to changes in precursor emissions (VOC, NO~). The National Research Council (1991) has been somewhat critical of EPA for failing to account for meteorological effects in national ozone trend assessments. The work described in this paper addresses some of these concerns. Because annual variations in meteorology have such an important effect on annual ozone behavior, researchers use various statistical techniques to remove meteorological effects on the observed ozone trend. For example, Stoeckenius and Hudischewskyj (1990) use a classification method to group days into categories according to the magnitude of ozone and similarity of meteorological conditions within each defined group. Adjusted ozone statistics for each year are computed from the meteorologically grouped data and the yearly frequency of occurrence of each group relative to its long-term frequency. Wakim (1990) uses standard regression analysis to quantify the effect of daily meteorology on ozone. Adjusted ozone statistics are calculated by adding the expected ozone statistic

for a year with typical meteorology to the average of the regression residuals obtained for the adjusted year. Shively (1991) describes a model in which the frequency of exceedance of various ozone thresholds (e.g. 120 ppb) are modeled as a non-homogeneous Poisson process where the parameter is a function of time and meteorological variables. Kolaz and Swinford (1990) categorize ozone days as "conducive" or "non-conducive" based on selected meteorological conditions within the Chicago area. Within these categories, the meteorological intensity of days conducive to daily exceedances of the National Ambient Air Quality Standard (NAAQS) for ozone (120 ppb) is calculated and used to establish long-term trends in the annual excecdance rate. The purpose of this paper is to describe a probabilistic method that may be used to obtain meteorologically adjusted trends in ground-level ozone. The method is based on the Weibull probability distribution where the scale parameter is allowed to fluctuate from day-to-day depending on meteorological conditions favorable to ozone. The advantage of this particular approach is that the annual ozone frequency distribution may be easily calculated by combining the individual daily probability distribution functions. The parameters of the distribution, including the trend component, are estimated using the method of maximum likelihood. The method has been applied to data collected in 43 urban areas throughout the U.S.A. where ozone levels have been historically high. Trends in ozone concentrations over the 11-year period from 1981 to 1991 are

425

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W.M. Cox and SHAO-HANGCHU

estimated for each city. In addition, the model is used to calculate expected annual ozone air quality statistics estimated using annual meteorological data that have been adjusted to a reference period. The bootstrap method is used to determine standard errors associated with the parameter estimates and to calculate confidence limits for the annual adjusted ozone concentration statistics.

perature and morning mixing height, respectively. Also, the 850 mb height was included for western urban areas since it appeared to be a good predictor as well. To illustrate the nature of the relationship between ozone and selected meteorological parameters, data from the Chicago MSA were examined. Figure 1 is a scatter plot of daily maximum 1-h ozone vs. daily maximum surface temperature coded by wind speed above and below 4.0 m s- 1 for Chicago. The smooth 2. DATA BASE curves through the data points were created using a smoothing spline available in SAS/GRAPH (SAS Hourly average concentrations of ozone were ob- Institute, Inc., 1990a). This figure illustrates a general tained from EPA's AIRS data base for all available relationship between temperature and wind speed that monitoring stations within each of 43 Metropolitan was found to exist in almost all of the urban areas. The Statistical Areas (MSA) where ozone levels have been data suggest that ozone has an increasing but nonhistorically high. The data were selected for the time linear relationship with temperature and that increasperiod 1981-1991 and include the months during ing wind speed tends to suppress the likelihood of which daily maximum ozone levels were likely to be higher ozone levels. For Chicago, high temperatures near or above EPA's National Ambient Air Quality (above 85°F) coupled with lower wind speeds appear Standard (120 ppb). Typically these months spanned to be associated with the highest ozone values (above from June through September in more northerly areas 160 ppb). (e.g. Chicago, New York, Boston) and April to OctoFigure 2 shows box plots of the annual distributions ber in more southerly areas (e.g. Houston, Los Angeles for each of the six meteorological parameters for and Miami). For each day, the maximum hourly Chicago. Median and upper percentiles of daily maxaverage ozone value was selected from all available imum temperatures in Chicago were higher in 1983 station hours. and 1988 than for any of the other years. Because The meteorological data base was assembled from temperature shows a strong positive association with hourly average data obtained from the National ozone, ozone levels in these 2 years were expected to Weather Service. Both surface and upper air data were be higher. Also, relative humidity and cloud cover for used to create approximately 100 daily meteorological 1988 were noticeably lower than for any other year parameters (Cox and Chu, 1991) that might be poten- during the 11-year span. Although relative humidity tially important predictors of daily ozone levels. These and cloud cover are generally negatively related to parameters encompass many of those that have been ozone, these two variables were not significant prepreviously identified with high ozone levels such as dictors of day-to-day ozone variations in Chicago. daily maximum surface temperature, relative humidFigure 3 shows a box plot of daily ozone levels for ity, mixing height and cloud cover. Daily maximum the Chicago MSA over the same l 1-year period. ozone values for each urban area were paired with Clearly 1983 and 1988 stand out as having noticeably corresponding meteorological data at the nearest sur- higher ozone levels. The relationship between daily face and upper air station. ozone and daily meteorological parameters coupled The data were screened using graphical and regres- with differences in the annual distribution of these sion methods to determine which meteorological meteorological parameters suggest that higher temparameters seemed to be most strongly associated peratures in 1983 and 1988 help explain why ozone in with day-to-day fluctuations in daily maximum 1-h these 2 years are higher than for the other 9 years. ozone. The screening process involved step-wise re- While a qualitative link appears evident between gression for each urban area coupled with inspection meteorology and daily ozone, a more quantitative of scatter plots of the residuals vs. each of the candid- association is desirable, hopefully one that can be used ate meteorological variables. Based on this process, it to accurately predict the annual distribution of daily was generally found that six meteorological para- ozone. Such a quantitative link is established by first xneters common to each urban area explained most of modeling the probability distribution of daily maxthe variability in daily ozone concentrations. These six imum ozone levels as a function of daily meteorologivariables were (1) daily maximum surface temperature cal parameters. (positive association), (2) morning average wind speed (negative), (3) afternoon average wind speed (negative), (4) relative humidity (usually negative), (5) opaque 3. PROBABILITY MODELING cloud cover (negative), and (6) morning mixing height A probability model is proposed that incorporates (negative). For urban areas located in western states (11 of the 43 areas), the 850 millibar (mb) temperature the effects of daily meteorological conditions on the at 12 Z and the afternoon mixing height were found to probability distribution of ozone concentration levels. be better predictors of daily ozone than surface tern- The probability model is based on the Weibull dis-

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tribution (Georgopoulos and Seinfeld, 1982; Holland and Fitz-Simons, 1982) in which the scale parameter is allowed to vary from day-to-day in response to changes in meteorological conditions favorable to ozone. The Weibull model was selected since it has been widely used to describe air pollution distributions (Curran and Frank, 1975). In particular, the

Weibull distribution has been found to be particularly suitable for describing the annual distribution of daily maximum ozone (Johnson, 1979; U.S. EPA, 1979). The basic form of the probability model is: Prob [ y > Y] i = exp -

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W.M. Cox and SHAO-HANGCHU

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where = regression coefficient for parameter j; M o =meteorological parameter j on day i; (=annual trend rate; T=year (T= 1, 2 , . . . , 11). This model is designed to account for the effects of daily variations in meteorological conditions and slowly changing trends that may take place over a number of years. The advantage is that meteorological and trend effects are estimated simultaneously to minimize potential confounding between the two types of effects. In addition, annual ozone statistics may be computed by simply combining daily ozone distributions fitted from the model. Thus, it is possible to quantitatively explain how shifts in the annual distribution of temperature, for instance, affect the annual distribution of ozone. Conversely, the distribution of ozone under more typical conditions may be predicted simply by substituting meteorological conditions into the model and recomputing the distribution of ozone. This model was applied using the data base assembled for the Chicago MSA. Maximum Likelihood Estimates (Rao, 1973) of the parameters were obtained from code prepared using the SAS Interactive Matrix Language (SAS Institute, Inc., 1989). Results shown in Table 1 include the parameter estimates, standard errors and T ratio. The six meteorological parameters represent the most consistently significant predictors of ozone within the 43 urban areas. The interaction term formed between temperature and morning aver-

age wind speed was included to account for the combined effects of these parameters (Fig. 1). Because the scale parameter is expressed exponentially, the parameter estimates represent a fractional change per unit change in the independent variable. For example, the afternoon wind speed coefficient is -0.021, which means that each 1 m s-1 increase in afternoon wind speed produces a 2.1% decrease in the scale parameter. The linear trend parameter was estimated at -0.0054, which means that, on average, ozone is estimated to be decreasing at approximately 0.5% per year over the 1I-year period in Chicago. This trend statistic may be interpreted as the annual rate of change in ozone levels that would most likely have been observed had the meteorological variables been the same each year. While the estimation process makes use of all of the data, accuracy in predicting the occurrence of higher concentrations is of particular concern given that the focus of the ozone NAAQS is on ozone peaks. For this reason, the validity of the model is assessed (Fig. 4) by comparing measured and model predicted upper percentiles (e.g. 95th and 99th) of daily maximum ozone levels for each of the 11 years. The measured percentiles were determined using the SAS UNIVARIATE procedure (SAS Institute, Inc., 1990b) for each year's observed ozone data. The percentiles based on the model were obtained by substituting parameter estimates into Equation (1) and solving for the value of Y such that the sum of the probabilities is equal to the product N ~(1 - P ) , where N is the number of ozone measurements in a year and P is the percentile expressed as a fraction. In effect, this calculation establishes a composite annual distribution by averaging each of the predicted daily distributions for each year. From the composite distribution, the percentile corresponding to P is simply the concentration value which is exceeded with probability ( 1 - P).

Meteorologically adjusted ozone trends

429

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For 95th percentiles, the model fits the observed data fairly well for each of the 11 years. For 99th percentiles, the most severe discrepancy between observed and predicted values occurs for 1988 where the magnitude of the underprediction is approximately 15%. The upper and lower 95% confidence bounds on the two percentiles were obtained using the bootstrap technique as described later in Section 5. Note that each observed percentile, except the 99th percentile value for 1988, falls within the 95% confidence limits shown for the predicted value. The potential implications for this "lack-of-fit" are discussed further in Section 4. The model was expanded to determine if performance could be improved by allowing both the scale (a) and the shape parameter (2) to vary with meteorology. In the expanded model, 2 was included AE(9)

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as a simple linear function of selected meteorological parameters (e.g. temperature, wind speed) and then refit using the maximum likelihood method. The results from fitting the expanded model indicated no significant improvement over that obtained when only the scale parameter (¢) is allowed to vary from day-today.

4. ADJUSTED OZONE STATISTICS

While the meteorologically adjusted annual trend rate is estimated at approximately - 0 . 5 % per year for Chicago, it is useful to display the trend in terms of upper percentiles of each year's annual ozone distribution. Meteorologically adjusted ozone percentiles are computed by using typical meteorological data in

430

W.M. Cox and SHAO-HANGCHU Table 1. Parameter estimates and standard errors (Chicago MSA) Variables

Parameter estimates

Lambda Constant Maximum Sfc temperature Wind speed (7-10 a.m.) Temp x wind speed (a.m.) Wind speed (1-4 p.m.) Relative humidity (10 a.m.-4 p.m.) Mixing height (a.m.) Opaque cloud cover Year

4.1480 1.8200 0.0365 0.2258 -0.0033 -0.0211 0.0004 -0.0170 - 0.0004 - 0.0054

Standard errors

T Ratio

0.1400 0.4620 0.0052 0.0764 0.0009 0.0054 0.0010 0.0371 0.0003 0.0037

29.60 3.94 7.00 2.96 -3.60 - 3.88 0.40 -0.46 - 1.12 - 1.47

Note: Standard errors are based on 100 bootstrap replications. They are approximately 30-40% larger than asymptotic results.

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place of the actual meteorological conditions for each year. For convenience, a reference meteorological period is defined in terms of averages and standard deviations of meteorological parameters over the 11year period from 1981 to 1991. F o r example, the mean re.lative humidity for the reference year is computed as the mean of the daily relative humidities across the 11year period from 1981 to 1991. Similarly, the standard deviation for the reference period is computed as the average of the 11 yearly standard deviations of daily relative humidity. The method used to adjust the meteorological data involves translation of meteorological parameters such that each parameter has the same mean and standard deviation as the reference period. Effectively, data values within each year are scaled such that they become centered over the distribution of meteorological parameters corresponding to the reference

period. Notationally, the calculation of scaled meteorological data is as follows: Y = Mr + (Xb - M b ) , (Sr/Sb),

where Mb = mean value for the given year; Sb = standard deviation for the given year; Mr = mean value for the reference period; S r = standard deviation for the reference period; X b = d a i l y meteorological parameters for the given year; Y=scaled meteorological parameters for the given year. Figure 5 illustrates the meteorological adjustment process in which maximum daily temperature is plotted vs. relative humidity. The cloud of points located toward the upper ldt-hand quadrant of the figure represents the original data for 1988. The cloud of points located closer to the lower right-hand quadrant represents these same data values after they have been adjusted to have the same mean and standard devi-

Meteorologically adjusted ozone trends

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CHICAGO OZONE TRENDS 99 th PERCENTILE--DAILY MAXIMUM (JUNE-SEPT)

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YEAR Fig. 6. ation as the reference period (i.e. 1981-1991). Clearly the effect of the meteorological adjustment is to lower the distribution of 1988 temperatures and increase the distribution of relative humidities. The expected impact of such a shift in meteorological conditions would be to adjust ozone downward in 1988 because lower temperatures favor lower ozone levels. As before, model predicted values of ozone are obtained by substituting parameter estimates and solving for the value of Y such that the sum of the probabilities given in Equation (1) is equal to the product N * ( 1 - P ) , where N is the number of ozone measurements in a year and P is the percentile expressed as a fraction. The meteorology used in this calculation is the scaled meteorology, in that it has the same mean and standard deviation as the reference period. Figure 6 shows the result of this adjustment for Chicago along with the original 99th percentiles. The adjusted result for any given year may be interpreted as the expected value for the ozone statistic if the distribution of meteorology in that year had resembled the long (11-year) average. Overall, the yearto-year changes in the adjusted 99th percentiles are much less abrupt and thus convey a smoother sense of trends over the I l-year period. Some of the smoothness in the trend line can be attributed to the fact that each year is being modeled with meteorology that has the same location (mean) and spread (standard deviation). Since the 99th percentile for 1988 was underpredicted (see Fig. 4), it could be argued that the adjusted value for 1988 should include a "lack-of-fit" term to account for

potential bias associated with the underprediction. While conceptually this notion has merit, there is no clearly accepted procedure for estimating and incorporating "lack-of-fit" into the adjusted percentiles. If such a term were to be included in the adjustment process, the effect would be to increment the 1988 adjusted 99th percentile by all, or some fraction of, the difference between the actual 99th percentile (215 ppb) and the adjusted 99th percentile (154 ppb). In terms of Fig. 6, this would result in a relatively smooth curve except for 1988, when the adjusted 99th percentile would be somewhat larger than for other years. In the ease of 95th percentiles, no such adjustment (for lackof-fit) would be called for because confidence limits for the adjusted 95th percentile overlap the observed value for each year.

5.

BOOTSTRAP

ESTIMATE

OF

ERRORS

One of the important assumptions associated with maximum likelihood estimation is that the individual observations (days) are independent. Because of meteorological persistence, this is usually not the case for ozone data. The effect of non-independence among the daily values is to bias the estimate of standard errors associated with the parameter estimates. Because of the positive association among daily values, the effect is to cause the asymptotic standard errors to be underestimated. A more realistic estimate of the standard error of the parameters can be obtained using a resampling scheme such as the Bootstrap or

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W.M. Cox and SHAO-HANGCHU

Jackknife (Efron, 1982; Tukey, 1987). Because of its simplicity, the blocked bootstrap is used as the procedure to estimate the sampling errors. The sampling strategy involved first partitioning the days into consecutive 3-day blocks. The 3-day block size was determined by comparing results with longer blocking periods (e.g. 5-day blocks). The results suggested that 3-day blocks are adequate for preserving the temporal dependence that usually exists among meteorological conditions and among successive days of ozone concentrations. Next, annual bootstrap samples were chosen by randomly selecting (with replacement) data in 3-day blocks until a complete annual (ozone season) sample had been formed. Using the 11 annual samples obtained in this manner (ozone and accompanying meteorological data), the parameter estimates were obtained along with the adjusted meteorological data and adjusted ozone statistics. This step was repeated until 100 replications had been constructed. The standard errors of parameter estimates (Table 1) were computed as simply the standard deviation of the bootstrap estimates of the parameters. Typically, the bootstrap estimates of the standard error were 30-40% larger than the asymptotic results.

imum temperature was used ("eastern" areas), the median of the coefficients was 0.0365 with minimum and maximum values of 0.0144 and 0.0618, respectively. The performance of the model for each of the 43 urban areas is characterized in Table 3 in the form of simple correlation coefficients between annual measured and model predicted upper percentiles (90th, 95th and 99th). Generally, there is a tendency for the lowest percentiles to exhibit the highest correlations. Medians of the 43 urban correlation coefficients were 0.78, 0.74 and 0.67 for the 90th, 95th and 99th percentiles, respectively. Also, it is clear that model performance varies somewhat among the 43 areas. For example, 15 of the 43 urban areas had correlation coefficients (r values) for the 95th percentiles above 0.8, while an additional 14 areas had r values that exceeded 0.6. Areas where r values were lowest (less than 0.6) typically were southern coastal or desert areas (e.g. Miami, Tampa, Jacksonville, Baton Rouge and E1 Paso). Frequently, areas with the lowest correlations were also characterized by small year-to-year variations in observed ozone levels and/or poor agreement among day-today observed and predicted ozone levels. For these areas, source/receptor alignment and meso-scale meteorological effects (land/sea breezes) not accoui~ted for may be related to poorer model performance. 6. URBAN AREA RESULTS Table 4 shows the estimated trend parameter for The model was applied using data for 43 urban each of the 43 urban areas. The urban areas are sorted areas (see Table 2) located throughout the U.S.A. The such that cities at the top of the list show the most same six meteorological parameters used in the marked improvements while cities near the bottom of Chicago example, including wind speed and temper- the list show the least improvements over time. The ature interaction, were included in the model for all last column (T ratio) is simply the ratio of the estim"eastern" U.S. urban areas. For the 11 "western" areas, ated trend coefficient to its standard error determined the surface maximum temperature and morning mix- from the bootstrap procedure. The table is partitioned ing height were replaced by the 850 mb temperature such that urban areas in the first tier (Bridgeport to and afternoon mixing height, respectively. In addition, Charlotte) exhibit decreasino trends significant at apthe 850 mb height was also included. Since space does proximately the 95% level (T ratios less than - 2.00). not permit showing the results for all 43 urban areas, The second tier of urban areas (Chicago to JacksonTable 2 is included to indicate the range of outcomes ville) had no significant trend, either decreasing or for each of the meteorological parameters. For ex- increasing. The last tier of urban areas (Atlanta to ample, of the 32 urban areas for which surface max- Seattle) had increasing trends that were statistically

Table 2. Summary of parameter estimates for 43 urban areas Variables

N

Median

Minimum

Maximum

Lambda Constant Max Sfc temperature Wind speed (a.m.) Temp x wind speed Wind speed (p.m.) Relative humidity Mixing height (a.m.) Opaque cloud cover Year Mixing height (p.m.) Height $50 mb Temp 850 mb

43 43 32 43 43 43 43 32 43 43 11 11 11

4.4613 2.1526 0.0365 0.1735 -0.0030 -0.0262 -0.0026 -0.1154 -0.0014 -0.0113 -0.0021 0.3046 0.0216

2.6248 -0.7855 0.0144 -0.0711 -0.0159 -0.1094 -0.0145 -0.3527 -0.0038 -0.0427 -0.1557 - 1.1792 0.0092

6.0921 5.7305 0.0618 1.3333 0.0009 0.0377 0.0066 0.1151 0.0009 0.0174 0.0524 2.8109 0.0298

Meteorologically adjusted ozone trends Table 3. Correlations between modeled and observed percentiles Urban area

N

90th

Atlanta Bakersfield Baltimore Baton Rouge Beaumont/Port Art. Birmingham Boston Bridgeport Charlotte Chicago Cincinnati Cleveland Columbia Dallas Denver Detroit El Paso Fresno Hartford Houston Huntington, WV Jacksonville Kansas City Las Vegas Los Angeles Louisville Miami Milwaukee Muskegon New York Philadelphia Phoenix Pittsburgh Providence Raleigh/Durham Sacramento San Diego Seattle St Louis Stockton Tampa Tulsa Washington

11 11 11 11 11 11 11 11 11 11 11 11 l1 11 11 11 11 11 11 11 11 11 11 11 10" 11 11 11 11 11 11 11 11 11 11 11 10" 11 11 11 11 11 11

0.81 0.29 0.85 0.69 -0.03 0.53 0.84 0.96 0.78 0.92 0.94 0.92 0.83 0.53 0.81 0.76 0.49 0.74 0.90 0.84 0.64 0.76 0.72 0.85 0.92 0.88 0.26 0.72 0.86 0.86 0.90 0.42 0.91 0.60 0.59 0.54 0.60 0.43 0.79 0.45 0.51 0.87 0.91

Median values

0.78

95th

99th

0.83 0.64 0.55 0.11 0.75 0.69 0.42 0.35 -0.07 -0.07 0.61 0.65 0.66 0.83 0.92 0.77 0.79 0.65 0.91 0.89 0.95 0.80 0.89 0.71 0.64 0.76 0.41 0.47 0.76 0.76 0.77 0.75 0.33 0.12 0.32 0.56 0.84 0.78 0.75 0.66 0.69 0.68 0.44 -0.20 0.65 0.24 0.84 0.58 0.94 0.82 0.74 0.78 0.23 0.00 0.83 0.81 0.83 0.74 0.84 0.81 0.90 0.67 0.49 0.58 0.87 0.81 0.52 0.38 0.65 0.78 0.46 0.67 0.78 0.31 0.57 0.45 0.82 0.69 0.52 - 0.04 0.28 0.09 0.62 -0.18 0.82 0.79 0.74

0.67

* Data available for trends begins in 1982.

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Table 4. Adjusted ozone trends (1981-1991) Trend rate (% per year)

T ratio

Significant decreasing trends Bridgeport Los Angeles* Hartford Houston Louisville New York Dallas Birmingham Pittsburgh Tampa Providence St Louis Cleveland Denver* Kansas City Philadelphia Beaumont/Port Arthur Las Vegas* San Diego* Cincinnati Detroit Baltimore Phoenix* Boston Charlotte

-4.3 - 2.8 - 2.8 -2.8 -2.7 -2.5 -2.4 - 1.8 - 1.8 - 1.7 - 1.7 - 1.7 - 1.6 - 1.5 - 1.4 - 1.4 - 1.4 - 1.4 - 1.4 - 1.3 - 1.3 - 1.1 - 1.0 - 1.0 -0.6

- 14.10 - 14.73 - 8.55 -9.28 -5.53 -8.52 -8.13 - 8.63 - 6.31 - 6.78 - 5.21 -6.86 - 8.10 - 6.93 - 5.54 - 5.71 - 3.51 - 5.66 - 5.65 -4.32 - 5.08 - 4.31 -4.96 - 3.01 -2.99

No significant trend Chicago Milwaukee Huntington, WV Miami Fresno* Columbia Baton Rouge Tulsa Sacramento* Muskegon Jacksonville

- 0.5 -0.5 -0.5 -0.3 - 0.3 - 0.2 -0.1 - 0.1 - 0.1 0.0 0.1

- 1.47 - 1.57 - 2.00 -0.84 - 1.16 - 1.35 -0.38 - 0.42 - 0.37 0.02 0.47

0.7 1.0 1.0 1.2 1.6 1.7

3.35 6.22 4.33 4.05 6.39 3.48

Urban area

Significant increasing trends Atlanta Bakersfield* Raleigh/Durham El Paso* Stockton* Seattle*

* Temperature at 850 mb and p.m. mixing height used in place of surface temperature and a.m. mixing height. In addition, the model also includes 850 mb height. significant at approximately the 95% level (T ratios greater than 2.00). Seven of the urban areas displayed improvements that exceeded 2 % per year (Bridgeport, Los Angeles, Hartford, H o u s t o n , Louisville, N e w York and Dallas) while a n o t h e r 15 u r b a n areas had rates of improvement better than 1% per year. Several cities appearing near the b o t t o m of the list actually showed slight increases in ozone over the l 1-year period. The median rate of change a m o n g the 43 urban areas indicates a 1.1% per year decrease in ozone which is equivalent to an i m p r o v e m e n t of approximately 11% over the 11-year period. F o r c o m p a r i s o n purposes, ozone trends in the 43 u r b a n areas were r e c o m p u t e d using the Weibull p r o b -

ability model with only the linear trend c o m p o n e n t included in the scale parameter. The purpose for this calculation is to illustrate the potential bias that results by failing to explicitly consider meteorological variations. For 32 of the 43 urban areas, the adjusted trend rate is numerically lower than the unadjusted rate. The median rate of change for the unadjusted trends was a 0.5% decrease per year, indicating that improvements after adjustment (i.e. 1.1% decrease per year) are substantially greater t h a n before adjustment. Clearly, the adjusted ozone trends provide an indication that national efforts to reduce the severity of the

434

W.M. Cox and SHAO-HANt3CHU

urban ozone problem have been more productive than would otherwise be suggested from the data.

7. SUMMARY AND CONCLUSIONS

A statistical model has been developed for describing day-to-day changes in the probability distribution of ground level ozone as a function of meteorological conditions. The model includes a long-term trend component such that meteorological effects are accounted for directly in the estimation procedure. The model was applied to data available from 43 urban areas for the summer periods of 1981 to 1991. The performance of the model was evaluated by comparing measured and model predicted 90th, 95th and 99th percentiles. Overall, the measured and model predicted percentiles tracked closely in the northern latitudes but performed less well in southern coastal and desert areas where meso-scale meteorological conditions are suspected to dominate. Generally, the adjusted 99th percentiles have considerably less year-to-ycar variability than do the unadjusted 99th percentiles. The median rate of change in daily maximum l-h ozone levels among the 43 U.S. urban areas reflected a 1.1% per year decrease over the period from 1981 to 1991. Because annual changes in meteorological conditions are directly considered, the method produces adjusted trend rates that have less bias than those produced without consideration of meteorological fluctuations. Acknowledoements--The authors would like to acknowledge the efforts of Phil Gibbs, SAS Institute, Cary, NC. While Phil was with the Computer SciencesCorporation, he directed the preparation of the ozone and meteorological data base and prepared the computer code for calculating bootstrap standard errors of the parameters estimates and the adjusted ozone statistics. REFERENCES

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