R.W. Simpson

Modeling distributions of air pollutant concentrations—I. Identification of statistical models

Abstract In this paper the process by which a distributional model may be identified from a range of alternative models is examined. An assessment of the methods by which goodness-of-fit may be evaluated is presented. A procedure for selecting amongst the exponential, gamma, lognormal and Weibull distributions has been applied to 24-h average suspended particulates (β-scattering), ozone, carbon monoxide, sulphur dioxide, oxides of nitrogen, nitrogen dioxide and nitrogen oxide observations recorded in Melbourne, Australia. It is shown that 1. (a) lognormal distribution is appropriate for particulate data and the majority of the nitric oxide, oxides of nitrogen and sulphur dioxide data sets 2. (b) gamma distribution is best for both carbon monoxide, nitrogen dioxide and ozone 3. (c) Weibull distribution is appropriate for a significant number of carbon monoxide and ozone data sets.

Modeling distributions of air pollutant concentrations—III. The hybrid deterministic-statistical distribution approach

Abstract A general modeling approach is proposed to predict the distribution of air pollutant concentrations and in particular the upper percentiles. The approach is hybrid in that it combines features of both deterministic and statistical distribution models. These features include causality and the attempted quantification of stochastic variability and uncertainty. The properties of deterministic and statistical distribution models are discussed separately and this clarifies the contribution that can be made by hybrid modeling. In this way the underlying assumptions are clearly presented. The range of successful applications of the hybrid approach is briefly reviewed. These involve relatively inert pollutants from urban/industrial, point source, elevated point source and roadway emissions. Areas of further research are outlined which would enhance the routine use of the approach and extend its application. Sufficient development has been undertaken, however, that the present standard set of air pollutant dispersion models could be easily updated to provide hybrid models capable of predicting frequency distributions of air pollutant levels under stipulated assumptions.

Modeling distributions of air pollutant concentrations—II. Estimation of one and two parameter statistical distributions

Abstract In Part I of this series Taylor, Jakeman and Simpson (1986, Atmospheric Environment , 20 , 1781–1789) examined the problem of identifying the appropriate distributional form for air pollution concentration data. In this paper we examine the parameter estimation problem. Monte Carlo simulation is used to compare methods for fitting statistical distributions to such data where the distributional form is known. Three methods are investigated for estimating the parameters of the lognormal distribution, two methods for the exponential distribution, three methods for the γ-distribution and four methods for the Weibull distribution. For all distributions and for each method we examine the accuracy with which the upper percentiles of the distribution are evaluated as it is these percentiles which are referred to by air quality standards. For each distribution a simple empirical model, which yields approximations to the relative root mean square error of the percentile estimates against sample size and parameter values, is developed and demonstrated. Thus for each distributional model an estimate of the relative error associated with evaluating high pollutant levels may be readily determined.

The prediction of maximum air pollution concentrations for tsp and co using Larsen's model and the ATDL model

Abstract A modeling methodology is introduced to predict maximum TSP concentrations. The methodology consists of using the ATDL model of Gifford and Hanna (1971) and the Larsen model (1971) to predict the distribution of air pollution concentrations from wind speed data for the upper percentiles. The data set used is total suspended particulate (TSP) data. Since the highest TSP concentrations occur at extremely low wind speeds where the use of the ATDL model is questionable, the methodology adopted here is to use the ATDL model together with wind speed data to reproduce TSP concentrations only for the range of wind speeds where the model is applicable. Assuming these TSP concentrations are lognormally distributed, Larsens model is then used to predict the maximum TSP concentration. These results agree with the work by Daly and Steele (1976) for CO. This methodology works quite well, for time averages of 8 h or more but in its present form is questionable for shorter time averages.

An averaging time model of SO2 frequency distributions from a single point source

Abstract A model is proposed to estimate frequency distributions for SO 2 concentrations due to an isolated point source and to estimate SO 2 maxima at different averaging times, given the maximum at one averaging time. The model assumes (1) the air pollution data have an exponential distribution, (2) the maximum concentration is approximately inversely proportional to the averaging time raised to an exponent and (3) the observed arithmetic mean is the same at all averaging times. The model has been applied to the data sets from three stations monitoring SO 2 concentrations from a power station in the Upper Hunter Valley in New South Wales. Australia, it is shown that the model performs better than other statistical models, and estimates maxima quite well for the 1 2 -h , 1 -h and 3-h averaged data sets using the 8-h time averaged data set. The results using the 24-h time average values to reproduce shorter time averaged data were not satisfactory.

A model for estimating the effects of fluctuations in long term meteorology on observed maximum acid gas levels

Abstract A model is proposed to estimate the effect of long term meteorology on maximum daily acid gas levels for each year of 10 years of data for Newcastle, New South Wales, Australia. The model assumes that (1) the probability density functions of both air pollution data and wind speed are lognormally distributed and (2), on average, an inverse relationship exists between air pollution levels and wind speed. Two acid gas monitoring stations in Newcastle and a nearby wind speed station have data which satisfy both these requirements. The maximum acid levels at both stations vary by a factor of about 3–4 over a ten-year period and the model shows that about half of this variation is directly related to fluctuations in the wind speed distribution, leaving the rest of the variation to be explained either by changes in emissions or more meteorological change. It is clear that, if the two prerequisite conditions hold, a significant proportion of the effect of long-term meteorological fluctions on maximum air pollutant levels may be explained by the model to within a reasonable accuracy.

Predicting frequency distributions for ozone, NO2 and TSP from restricted data sets

Abstract The results of Ott and Mage (1981) for CO indicate that random sampling yields accurate estimates of the mean and standard deviation. This paper examines the estimates for a cumulative frequency distribution using four different types of data set: (1) continuous monitoring throughout the year, (2) continuous monitoring one week out of every four, (3) random sampling at any time and (4) random sampling only on weekdays between 9.00 a.m. and 5.00 p.m. Data sets for O 3 , NO 2 and TSP are used. The results show that random sampling should only be used when there is no restriction on the time of sampling and that option (2) yields very good results indicating a cost-effective way of recording results.

The relationship between the ATDL model and the statistical distributions of wind speed and pollution data

Abstract By examining the statistical distributions for TSP and acid gas data together with wind speed data, it is shown here that the ATDL model of Gifford and Hanna (1973) predicts certain statistics of these data sets well, especially for daily average data, but not the average relationship between air pollution and wind speed data monitored at the same time. Specifically, the model performs well in the 30- to 70-percentile range of the statistical distributions. The results demonstrate why the ATDL model often works between air pollution data and wind speed data collected at different sites. They also explain the weak dependence of the ATDL model parameters on atmospheric stability found by Hanna (1971). Finally, it is shown that the medians and not the means should be used when estimating the ATDL model parameters.

Statistical modeling of restricted pollutant data sets to assess compliance with air quality criteria.

Three statistical models are used to predict the upper percentiles of the distribution of air pollutant concentrations from restricted data sets recorded over yearly time intervals. The first is an empirical quantile-quantile model. It requires firstly that a more complete date set be available from a base site within the same airshed, and secondly that the base and restricted data sets are drawn from the same distributional form. A two-sided Kolmogorov-Smirnov two-sample test is applied to test the validity of the latter assumption, a test not requiring the assumption of a particular distributional form. The second model represents the a priori selection of a distributional model for the air quality data. To demonstrate this approach the two-parameter lognormal, gamma and Weibull models and the one-parameter exponential model were separately applied to all the restricted data sets. A third model employs a model identification procedure on each data set. It selects the ‘best fit’ model.

A hybrid model for predicting the distribution of sulphur dioxide concentrations observed near elevated point sources

Abstract A hybrid model, combining a deterministic model with a distributional model, is developed for predicting the distribution of ambient sulphur dioxide concentrations recorded near point sources. The deterministic component of the hybrid model is based upon the Gaussian plume model, while the distributional models are identified from amongst the two-parameter lognormal, Weibull and gamma, and the one-parameter exponential distribution models. Using the deterministic model component output calibrated about the 50–90 percentile concentrations, the hybrid model produces estimates of 24-, 8-, 3-, 1-, 0.5-h average sulphur dioxide data to an accuracy of a factor of 2 for the 98-percentile, second-highest and maximum concentrations. The effect of the method of calibration of the deterministic component upon the statistical component of the hybrid model is examined in detail.