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Statistics of extreme values of air quality—a simulation study

1985; Elsevier BV; Volume: 19; Issue: 10 Linguagem: Inglês

10.1016/0004-6981(85)90223-9

1878-2442

David P. Chock,

Atmospheric chemistry and aerosols

Some of the existing National Ambient Air Quality Standards require the use of an extreme observed concentration in a year to determine compliance. Since observed extreme values tend to be not reliable, different statistical approaches for determining the extreme values have been used or suggested. However, none of these approaches properly take into account the effects of an underlying trend and the serial correlation of the air quality time series. By means of a time series simulation, these effects can be considered concurrently in estimating the extreme values. This paper reports the results of such a simulation for determining the statistics of the seven highest values (rank m = 1–7, m = 1 representing the highest value) using actual air quality data that contain both trends and autocorrelations. The result of this simulation shows that for a high-pollution season of 122 days, the commonly used asymptotic distributions overestimate the maximum (m = 1) values and underestimate their uncertainties. As one moves from m = 1 to m = 7, the over- and underestimations by the asymptotic distributions worsen (compared to the simulation result). These findings in logarithmic space are further enhanced when they are converted back to concentration space. The simulation using the oxidant data for Azusa, California further shows that the uncertainties associated with the estimates Of the extreme values are typically 20% of the values for m = 1 and 10% of the values for m = 7. Compared to the observed data, which is a single series for each year, the result based on the popular lognormal distribution consistently overpredicts the extreme values, by about 40% for the maximum values and about 20% for the seventh highest values. Our results illustrate the difficulty of estimating the extreme values of air quality time series with accuracy and confidence. However, the accuracy and confidence of the estimates improve as the rank moves away from the extreme. This result calls for the need for using a less extreme value in setting a sensible air quality standard. Of course, such a standard can be set without sacrificing its stringency.