Statistical distributions of particulate matter and the error associated with sampling frequency

Abstract The distribution of particulate matter (PM) concentrations has an impact on human health effects and the setting of PM regulations. Since PM is commonly sampled on less than daily schedules, the magnitude of sampling errors needs to be determined. Daily PM data from Spokane, Washington were resampled to simulate common sampling schedules and the sampling error was computed for regulatory and distribution statistics. Probability density functions (pdf's) were fit to the annual daily data to determine the shape of the PM2.5 and PM8 concentration distributions and they were also fit to the less than daily sampling to determine if pdf's could be used to predict the daily high-concentration percentiles. There is an error when using a less than daily sampling schedule for all statistics. The error expressed as a percentage difference from the everyday sampling for the PM2.5 mean was as large as 1.7, 3.4 and 7.7% and the 98th percentile error was as great as 8.8, 18 and 67% for 1-in-2 day, 1-in-3 day and 1-in-6 day sampling, respectively. For PM8 the error in the mean was 2.5, 4.7 and 8.6% for and the error in the 99th percentile was 27, 18 and 46% for 1-in-2 day, 1-in-3 day, and 1-in-6 day sampling, respectively. The PM2.5 and PM8 concentration data were best fit by a three-parameter lognormal distribution and a generalized extreme value distribution, respectively. For PM2.5 and PM8, as the annual mean increased the mode concentration increased, but for PM8 the shape of the distribution also flattened. Predicting the daily high percentiles from pdf's that were fit to the less than daily sampled data produced mixed results. For PM8, the pdf's predicted high concentrations were closer to the daily percentiles than the actual less-than-daily sampling percentile while for PM2.5 they were not.

[1]  G Kurchatova,et al.  A study of the statistical distribution of chemical pollutants in air. , 1976, Journal of the Air Pollution Control Association.

[2]  W. Ott.  A physical explanation of the lognormality of pollutant concentrations. , 1990, Journal of the Air & Waste Management Association.

[3]  P. Preuss,et al.  Czech Air Quality Monitoring and Receptor Modeling Study , 1995 .

[4]  B E Saltzman,et al.  Lognormal model for health risk assessment of fluctuating concentrations. , 1987, American Industrial Hygiene Association journal.

[5]  Nozer D. Singpurwalla,et al.  Extreme Values from a Lognormal Law With Applications to Air Pollution Problems , 1972 .

[6]  Wayne R. Ott,et al.  A general purpose univariate probability model for environmental data analysis , 1976, Comput. Oper. Res..

[7]  R. Larsen,et al.  An Air Quality Data Analysis System for Interrelating Effects, Standards, and Needed Source Reductions: Part 4. A Three-Parameter Averaging-Time Model , 1977 .

[8]  André Berger,et al.  Statistical Distributions of Daily and High Atmospheric So2-concentrations , 1982 .

[9]  P. Royston.  Estimation, reference ranges and goodness of fit for the three-parameter log-normal distribution. , 1992, Statistics in medicine.

[10]  Betty Jones Whitten,et al.  Estimation in the Three-Parameter Lognormal Distribution , 1980 .

[11]  J H Seinfeld,et al.  On frequency distributions of air pollutant concentrations. , 1976, Atmospheric environment.

[12]  C. Claiborn,et al.  Airborne Particulate Matter Size Distributions in an Arid Urban Area. , 1999, Journal of the Air & Waste Management Association.

[13]  B. Kleiner,et al.  Measurements of extreme concentrations of tropospheric hydrogen sulfide , 1974 .

[14]  Sonia Yeh,et al.  Statistical distributions for air pollution applied to the study of the particulate problem in Santiago , 1999 .

[15]  R I Larsen,et al.  A new mathematical model of air pollutant concentration averaging time and frequency. , 1969, Journal of the Air Pollution Control Association.

[16]  David M. Holland,et al.  Fitting statistical distributions to air quality data by the maximum likelihood method , 1982 .

[17]  J. R. Wallis,et al.  Probability Weighted Moments: Definition and Relation to Parameters of Several Distributions Expressable in Inverse Form , 1979 .

[18]  B. E. Saltzman.  Health risk assessment of fluctuating concentrations using lognormal models. , 1997, Journal of the Air & Waste Management Association.

[19]  D. Griffiths.  Interval Estimation for the Three‐Parameter Lognormal Distribution Via the Likelihood Function , 1980 .

[20]  Joseph M. Prospero,et al.  Aerosol concentration statistics for the Northern Tropical Atlantic , 1977 .

[21]  J. Prospero,et al.  Frequency distribution of dust concentration in Barbados as a function of averaging time , 1987 .

[22]  Panos G. Georgopoulos,et al.  Statistical distributions of air pollutant concentrations , 1982 .

[23]  J. Hosking.  Maximum‐Likelihood Estimation of the Parameters of the Generalized Extreme‐Value Distribution , 1985 .

[24]  Joel L. Horowitz,et al.  Statistical analysis of the maximum concentration of an air pollutant: Effects of autocorrelation and non-stationarity , 1979 .

[25]  G. Trenkler.  Continuous univariate distributions , 1994 .

[26]  D. Finn,et al.  Sampling artifacts from the use of denuder tubes with glycerol based coatings in the measurement of atmospheric particulate matter. , 2001, Environmental science & technology.