Statistical analysis of the maximum concentration of an air pollutant: Effects of autocorrelation and non-stationarity

A procedure for using air quality data to estimate the mean value of the maximum concentration in a year-long sequence of lognormally distributed air pollutant concentrations has been described by Larsen. This procedure and analogous procedures for non-lognormal concentrations implicitly assume that air pollutant concentrations are independently and identically distributed. However, these concentrations often are highly correlated, and they exhibit systematic variations in response to seasonal and other factors. Thus, air pollutant concentrations are, in general, not independently and identically distributed but, rather, are generated by non-stationary, autocorrelated stochastic processes. In this paper it is shown that autocorrelation does not significantly affect the validity of the Larsen procedure. However, application of procedures, such as Larsen's, that assume stationarity to a non-stationary sequence of concentrations (i.e. a sequence that exhibits systematic seasonal or other variations) can produce seriously erroneous results. Two methods for using air quality data to estimate the distributional properties of maxima of non-stationary sequences of concentrations are illustrated. One method involves identifying a non-stationary stochastic process that explains the data and computing the probability distributions of maxima of sequences generated by this stochastic process. The other involves applying the Larsen procedure to a suitably selected subsequence of the data.