An Air Quality Data Analysis System for Interrelating Effects, Standards, and Needed Source Reductions: Part 4. A Three-Parameter Averaging-Time Model

Long‐term probabilistic forecast of climate impact on air quality: Model development and t* distribution

“…Fortunately, most random variables derived from natural observations are either normally distributed or can be easily transformed to normal [ Box and Cox , 1964]. In air quality studies most hourly air quality data are lognormally distributed [ Larsen , 1977; Bencala and Seinfeld , 1976] which can easily be transformed to a normally distributed random variable. Longer time‐averaged data generally approach a normal distribution very quickly through averaging, as shown by the central limit theorem [ Hogg and Craig , 1978].…”

Refinements of the Lognormal Probability Model for Analysis of Aerometric Data

“…These models are based on an assumption that "pollutant concentrations are lognormally distributed for all averaging times and thus tend to plot as approximately straight lines on logprobability paper." 4 This assumption is based on an earlier report 5 in which SO2 concentrations are plotted on logarithmic probability paper giving a line which is "approximately straight" (Figure 3 in Reference 5 and reproduced here as Figure 1). Although useful as a first approximation, many important refinements can be made to this approach.…”

“…Mage and Ott have correctly noted that the arithmetic mean of the model was not calculated correctly when air quality data were censored at a true concentration of zero in Ref. 4 A number of models are available for estimating atmospheric dispersion of air pollutant emissions from area sources. 1 One of the simplest of these models is the ATDL model developed by Gifford and Hanna,…”

“…In Larsen's recent application of the three-parameter lognormal model, 4 this inconsistency is removed, because the Part 4 paper assumes that the arithmetic mean of the model is independent of averaging time and is equal to the measured arithmetic mean. Unfortunately, the paper contains an error, for the examples given do not have this property and conflict with this assumption.…”

“…For example, a series of such articles by Ralph I. Larsen, entitled "An Air Quality Data Analysis System for Interrelating Effects, Standards, and Needed Source Reductions," Parts 1, 2, 3, and 4, have proposed the two parameter x~3 and three parameter 4 lognormal models for analyzing air quality data in urban areas and near isolated point sources. These models are based on an assumption that "pollutant concentrations are lognormally distributed for all averaging times and thus tend to plot as approximately straight lines on logprobability paper."…”