Analysis of Atmospheric Ozone Concentration Trends as Measured by Eighth Highest Values

The ambient air quality standard for ozone in Taiwan is 0.12 ppm (hourly average). To protect human health, this standard is not to be exceeded by the observed hourly ozone concentration. To test compliance, each day’s maximum hourly ozone concentration is identified and the eighth highest value of the 365 daily hourly maxima for the entire year is calculated. To account for the uncertainty in measurement, the regulation stipulates using the three-year moving average of the eighth highest value to compare with the standard. In this study, observed ambient hourly ozone data from 1998-2002 at 9 continuous monitoring stations maintained by the government were collated and the eighth-highest concentration (MAX8) was calculated for each site by year. For the estimate of confidence interval for MAX8, a linear regression of ozone concentrations on their ranks was applied, as well as a quadratic logistic regression of odd ratios on ozone concentration. To estimate the confidence interval using the quadratic equation for inverse prediction, a Monte Carlo simulation was carried out in conjunction with the latter method. By taking into account the uncertainty expressed by the confidence interval, it was shown that MAX8 did not exhibit differences statistically for all stations in the period.


INTRODUCTION
problem for the 1-h National Ambient Air Quality Standard.Tropospheric ozone is a secondary pollutant formed through the series of reactions of nitrogen oxides and active hydrocarbons under ultraviolet solar radiation (Colls, 2002).Due to its strong oxidative reactions, ozone can cause irritating symptoms on the respiratory system, such as coughing, asthma, headache, lethargy, and even lung Ozone is designated as a criteria pollutant under the Air Pollution Control Act of Taiwan.
High ozone concentration is a pervasive damage.Children, the elderly, patients, or persons with active outdoor activities are most vulnerable to ozone damage.Ozone can also cause damage to crops, paintings, and plastic products, such as tires (Heinsohn and Kabel, 1999).The ozone production cycle is driven by sunlight.However, other meteorological parameters, such as cloud cover, air temperature, relative humidity, atmospheric pressure and wind speeds can influence the kinetics of ozone production and distribution (Aneja et al., 1994).Furthermore, this reaction is maximized during the summer time, when incoming solar radiation is greatest, together with the temperatures (Aneja et al., 1999).
The eighth highest 1-h ozone concentration is used to delineate air pollution control zones and total quality control zones in Taiwan.The arithmetic average value of the eighth highest 1-h ozone concentration for 3 consecutive years is calculated, then listed in order to for each air quality monitoring station.The average first 50% of the highest values are taken, and those stations whose average values are less than 0.12 ppm shall be in compliance with air quality standards.Some uncertainties still exist despite considering the arithmetic average values of 3 consecutive years.This suggests that an ability to model the confidence intervals of MAX 8 would be desirable.
Monte Carlo simulation is a common name for a group of iterative statistical techniques.It has been used in several studies in environmental science for quantitative uncertainty analysis (Dodge, 2000;Moore and Londergan, 2001;Hanna and Davis, 2002;Zádor et al., 2005).The advantages of the Monte Carlo method are that (1) it can be applied to a complete set of about 100 or more input parameters, (2) it allows useful estimates of the uncertainties in model outputs, (3) it allows use of standard nonparametric statistical tests concerning confidence intervals (Hanna et al., 1998).A Monte Carlo run results in a large number of estimates, which can be displayed as a probability distribution.This highlights the fact that the final estimate is uncertain.The fundamental problem is therefore selecting probability distributions for these parameters (Rabl and Spadaro, 1999;Int Panis et al., 2004).
In the literature, many researchers have investigated the ozone concentrations with different aspects.Among the papers that interest us are studies on the prediction of ozone concentration (Dodge, 2000;Koçak, 2000;Thompson et al., 2001).Linear regression is the most familiar of the methodologies employed in studies.All linear regression models are open to the criticism that underlying chemical and physical processes are unlikely to be linear and additive.Bloomfield et al. (1996) argue that statistical linear models have difficulty capturing the complex relations between the variables and ozone.Nonlinear regression models are needed to approximate the true underlying mechanisms.Even then, if the interest is in extreme values, the regression models may be not sufficient (Smith and Huang, 1993).The inherent averaging in regression analysis often makes fitted models poor predictors of extreme values (NRC, 1991).An alternative approach, particularly useful in the context of modeling threshold exceedances, is to use extreme value theory (Thompson et al., 2001).To our knowledge, no research has studied the uncertainty analysis for the prediction of ozone MAX 8 .In this study, a method was

Estimation of the expected MAX 8 and confidence interval by linear regression
The highest hourly ozone concentrations for ranking x is used in X-coordinate and Y x is used in Y-coordinate.Logistic regression provides the most straightforward approach to predicting episodes of poor air quality (Dorling et al., 2003).In this study, the logistic equation: is used to simulate the distribution.
Eq. ( 1) is rearranged as: where a, b and c are the parameters which are obtained by linear regression analysis.Then the simulation model of MAX 8 for the 9 air pollution monitoring stations can be gained.
The standard deviation of the expected MAX 8 can be calculated by Eq. ( 3).
where Std e : standard error Std R : standard error of estimate n: sample size x: independent variable x : mean of independent variables S xx : sum of squares between samples Then the confidence interval (CI) of the expected MAX 8 is estimated by the following formula with 95% confidence interval (Zar, 1999): where Z α/2 : Z value for normal distribution of the α/2 area.

Estimation of the expected MAX 8 and confidence interval by Monte Carlo simulation
The standard deviation of the expected MAX 8 calculated by Eq. ( 3) was used to determine the optimum number of data.The rankings of the retained numbers were transferred to the probability P x , where P 1 corresponds to the highest one concentration.
Then a quadratic logistic regression equation was setup: The propagation of errors through complex calculations was studied in this study.The crisp estimates of the above parameters are replaced by a probability distribution that describes the range of values that the parameters can take, as well as the probability that a certain value will actually occur.It is assumed that the three parameters reflect normal distribution.The procedure is then repeated 1000 times so that a large number of combinations of different input parameters occur.In this study, the parameters a', b' and c' were calculated with the commercially available SPSS software.

Statistical analysis of MAX 8
The MAX 8 values of ozone for the air quality monitoring stations during 1998-2002 are listed in Table 1.Except for Jhushan station, the mean MAX 8 values were all lower than the Ambient Air Quality Standard (120 ppb).Some local studies have suggested that the high ozone concentration in Jhushan was caused by the effect of terrain (TEPA, 2003).
The bad airflow resulted in the accumulation of air pollutants in this area.The coefficients of variation are small (2.5%−9.2%).These show that the MAX 8 values did not change significantly for these years.
We further analyzed the occurrence time of MAX 8 for these stations.The MAX 8 appeared primarily around noon (10:00 am-3:00 pm) for all 9 air quality monitoring stations (Fig. 2).
The occurrence time of MAX 8 is similar to that of the highest ozone concentration.No significant differences were found for the occurrence time of MAX 8 between these different air quality monitoring stations.

The influence of ranking number on goodness of fit
The ranking number may influence the goodness of fit of the simulation model.At Erlin station for example, the plot of ranking number vs. the inverse of MAX 8 according to Eq. ( 2) shows that the relation between ranking number and the inverse of MAX 8 is not linear (Fig. 3).There would be an error for the prediction of MAX 8 when linear regression analysis is performed.To improve the

Prediction of MAX 8 and confidence interval by linear regression
The ranking number 180 is adopted in the established using Monte Carlo simulation to predict ozone MAX 8 and the corresponding confidence interval.The trends of expected ozone MAX 8 and the confidence intervals in central Taiwan are presented and discussed here.
in 1993.This network of 71 stations continuously monitors the air quality in Taiwan.Ambient ozone concentration measurements provided by TEPA span the years 1998-2002.Ozone concentration is measured by using the chemiluminescence technique.In this study, nine routine air quality monitoring stations (Erlin, Dali, Jhushan, Situn, Shalu, Jhongming, Nantou, Changhua and Fongyuan) in central Taiwan were considered.Fig. 1 illustrates the locations and their geographical coverage.In addition to ozone concentration, temperature and rainfall were measured.The highest hourly ozone concentrations during each day for one year were sorted and the eighth value is the MAX 8 .
Fig. 1.Locations of the monitoring stations in central Taiwan.

Fig. 4 .Fig. 5 .
Fig. 4. The expected MAX 8 values and their upper and lower confidence intervals for the 9 air quality monitoring stations.

Table 2 .
The SEE of linear regression for different ranking numbers at Erlin station.

Table 3 .
SEE values by linear regression analysis.