A Physical Explanation of the Lognormality of Pollutant Concentrations

Investigators In different environmental fields have reported that the concentrations of various measured substances have frequency distributions that are lognormal, or nearly so. That is, when the logarithms of the observed concentrations are plotted as a frequency distribution, the resulting distribution is approximately normal, or Gaussian, over much of the observed range. Examples include radionuclides in soil, pollutants in ambient air, Indoor air quality, trace metals In streams, metals in biological tissue, calcium In human remains. The ubiquity of the lognormal distribution in environmental processes is surprising and has not been adequately explained, since common processes in nature (for example, computation of the mean and the analysis of error) usually give rise to distributions that are normal rather than lognormal. This paper takes the first step toward explaining why lognormal distributions can arise naturally from certain physical processes that are analogous to those found in the environment. In this paper, these processes are treated mathematically, and the results are illustrated in a laboratory beaker experiment that Is simulated on the computer.     

Simplified Methods for Statistical Interpretation of Monitoring Data

Statistical techniques are useful for interpretation of monitoring data for pollutants, process variables, etc. Simplified nomographical methods are presented for relating numbers of samples to confidence intervals for their mean values, and for determining the proportion of the population exceeding a specified concentration and confidence intervals for the proportion. A chart also is given for design of a sampling program for quality control. Illustrative frequency distribution data are given for hourly-averaged methane concentrations in air over three-week periods. They show trimodal lognormal distributions. These charts are applicable to lognormal distributions, as well as to normal distributions. They are convenient for many common problems.     

On the Evaluation of Predictions from a Gaussian Plume Model

The performance of a CRSTER equivalent Gaussian plume model (CEQM) is examined using data from the EPRI Plume Model Validation study at the Klncaid, Illinois site. Four-way comparisons are made on the ordered statistics or the cumulative frequency distribution (CFD) of maximum hourly observed and predicted concentrations. Using the uniform random distribution and the lognormal random distribution as simple predictive schemes without any physical context, it Is found that the CEQM predicts a concentration CFD which matches the observed CFD significantly closer than the CFD predicted by the uniform random distribution. The two-parameter lognormal random distribution predicts the concentration CFD better than the CEQM over all concentration ranges; however, the CEQM fits the upper range of the concentration distribution better than the lognormal random distribution,, despite the fact that the predictions are generated using dispersion conditions entirely different from those of the observations. The nature of this ergodicity of distribution is probed by exercising CEQM using randomized input based on the observed frequency distributions of the Input parameters instead of feeding the hour-by-hour model input matched by time into CEQM as is customarily done. The exercise of the model by uncoupling the time linkage in model Input has no systematic effect on the predicted cumulative frequency distribution of concentrations. Only at the highest concentration range (99.5% or higher) do the two sets of predictions begin to diverge.     

Comparisons of statistical characteristic of air pollutants in Taiwan by frequency distribution

The lognormal, Weibull, and type V Pearson distributions were selected to fit the concentration frequency distributions of particulate matter with an aerodynamic diameter of < or = 10 microm (PM10) and SO2 in the Taiwan area. Air quality data from three stations, Hsin-Chu, Shalu, and Gain-Jin, were fitted with three distributions and compared with the measured data. The parameters of unimodal and bimodal fitted distributions were obtained by the methods of maximum likelihood and nonlinear least squares, respectively. Moreover, the root mean square error (RMSE), index of agreement (d), and Kolmogorov-Smirnov (K-S) test were used as criteria to judge the goodness-of-fit of these three distributions. These results show that the frequency distributions of PM10 concentration at the Hsin-Chu and Shalu stations are unimodal, but the distribution at Gain-Jin is bimodal. The distribution type of PM10 concentration varied greatly in different areas and could be influenced by local meteorological conditions. For SO2 concentration distribution, the distributions were all unimodal. The results also show that the lognormal distribution is the more appropriate to represent the PM10 distribution, while the Weibull and lognormal distributions are more suitable to represent the SO2 distribution. Moreover, the days exceeding the air quality standard (AQS) (PM10 > 125 microg/ m3) for the Hsin-Chu, Shalu, and Gain-Jin stations in the coming year are successfully predicted by the theoretic distributions.     

Atmospheric lead concentration distribution in Northern Taiwan

Atmospheric lead concentrations were measured randomly, approximately once per week, at five traffic sites in northern Taiwan from September 1994 to May 1995. Three types of theoretical distributions, lognormal, Weibull and gamma were selected to fit the frequency distribution of the measured lead concentration. Four goodness-of-fit criteria were used to judge which theoretical distribution is the most appropriate to represent the frequency distributions of atmospheric lead.The results show that atmospheric lead concentrations in total suspended particulates fit the lognormal distribution reasonably well in northern Taiwan. The intervals of fitted theoretical cumulative frequency distributions (CFDs) can successfully contain the measured data when the population mean is estimated with a 95% confidence interval. In addition, atmospheric lead concentration exceeding a critical concentration is also predicted from the fitted theoretical CFDs.     

Estimating the emission source reduction of PM10 in central Taiwan

Three theoretical parent frequency distributions; lognormal, Weibull and gamma were used to fit the complete set of PM10 data in central Taiwan. The gamma distribution is the best one to represent the performance of high PM10 concentrations. However, the parent distribution sometimes diverges in predicting the high PM10 concentrations. Therefore, two predicting methods, Method I: two-parameter exponential distribution and Method II: asymptotic distribution of extreme value, were used to fit the high PM10 concentration distributions more correctly. The results fitted by the two-parameter exponential distribution are better matched with the actual high PM10 data than that by the parent distributions. Both of the predicting methods can successfully predict the return period and exceedances over a critical concentration in the future year. Moreover, the estimated emission source reductions of PM10 required to meet the air quality standard by Method I and Method II are very close. The estimated emission source reductions of PM10 range from 34% to 48% in central Taiwan.     

Estimating the frequency distributions of particulate matter and their metal elements in a temple

Air quality inside Asian temples is typically poor because of the burning of incense. This study measured and analyzed concentrations of fine (PM2.5) and coarse (PM2.5-10) particulate matter and their metal elements inside a temple in central Taiwan. Experimental results showed that the concentrations of metals Cd, Ni, Pb, and Cr inside the temple were higher than those at rural, suburban, urban, and industrial areas in other studies. Three theoretical parent distributions (lognormal, Weibull, and gamma) were used to fit the measured data. The lognormal distribution was the most appropriate distribution for representing frequency distributions of PM10, PM2.5, and their metal elements. Furthermore, the central limit theorem, H-statistic-based scheme, and parametric and nonparametric bootstrap methods were used to estimate confidence intervals for mean pollutant concentrations. The estimated upper confidence limits (UCLs) of means between different methods were very consistent, because the sample coefficient of variation (CV) was < 1. When the sample CV was > 1, the UCL based on H-statistical method tended to overestimate the UCLs when compared with other methods. Confidence intervals for pollutant concentrations at different percentiles were evaluated using parametric and nonparametric bootstrap methods. The probabilities of pollutants exceeding a critical concentration were also calculated.     

Surface Air Pollutant Concentration Frequency Distributions: Implications for Urban Modeling

With the development of ambient air quality standards (AAQS), the need arises to describe the characteristics of regional surface air-pollutant concentration frequency distributions. In the evaluation of land use plans, numerous agencies will be concerned with evaluating the effectiveness of emission zoning and/or control actions. On a regional basis, one means of performing this assessment lies in determining the changes in the pollutant frequency distributions resulting from control actions.

This study presents new data concerning the surface air-pollutant concentration frequency distributions observed for area sources and continuous point sources, and compares these distributions with those of the pertinent meteorological variables describing the transport and diffusion of the pollutant. The observed surface air pollutant frequency distributions are compared to those corresponding to simple modeling concepts from either an urban area source or a continuous point source. For an urban source and a relatively inert pollutant like CO, we found that the observed frequency distribution for CO surface air concentration parallels the approximately log-normal frequency distribution of the reciprocal of the wind speed. We show that the constant relating these two well-correlated frequency distributions can be determined either experimentally or with a numerical simulation model of air pollution. The usefulness of numerical models in air pollution is discussed.     

Estimating the Frequency Distributions of Particulate Matter and Their Metal Elements in a Temple

Abstract

Air quality inside Asian temples is typically poor because of the burning of incense. This study measured and analyzed concentrations of fine (PM_2.5) and coarse (PM_2.5–10) particulate matter and their metal elements inside a temple in central Taiwan. Experimental results showed that the concentrations of metals Cd, Ni, Pb, and Cr inside the temple were higher than those at rural, suburban, urban, and industrial areas in other studies. Three theoretical parent distributions (lognormal, Weibull, and gamma) were used to fit the measured data. The lognormal distribution was the most appropriate distribution for representing frequency distributions of PM₁₀, PM_2.5, and their metal elements.

Furthermore, the central limit theorem, H-statistic-based scheme, and parametric and nonparametric bootstrap methods were used to estimate confidence intervals for mean pollutant concentrations. The estimated upper confidence limits (UCLs) of means between different methods were very consistent, because the sample coefficient of variation (CV) was <1. When the sample CV was >1, the UCL based on H-statistical method tended to overestimate the UCLs when compared with other methods. Confidence intervals for pollutant concentrations at different percentiles were evaluated using parametric and nonparametric bootstrap methods. The probabilities of pollutants exceeding a critical concentration were also calculated.     

Statistical Study of Air Pollutant Concentrations via Generalized Gamma Distributions

This paper deals with modeling observed frequency distributions of air quality data measured in the area of Venice, Italy. The paper discusses the application of the generalized gamma distribution (ggd) which has not been commonly applied to air quality data notwithstanding the fact that it embodies most distribution models used for air quality analyses. The approach yields important simplifications for statistical analyses. A comparison among the ggd and other relevant models (standard gamma, Weibull, lognormal), carried out on daily sulphur dioxide concentrations in the area of Venice underlines the efficiency of ggd models in portraying experimental data.     

Frequency distribution of dust concentration in Barbados as a function of averaging time

Two sets of daily-averaged dust concentration data from Barbados, West Indies, have been analyzed to determine the affect of averaging time, ranging from 1 to 7 days, on the dust concentration frequency distribution. On each of the time scales examined, the frequency distribution is characterized as a bimodal lognormal distribution. The major effects of increasing the averaging are a major reduction in the percentage of the samples represented by the lower of the two modes and a significant increase in the geometric mean concentration of that mode. Consequently, predictions of the distributions on a shorter time scale are likely to substantially underestimate the frequency of low concentration samples.     

Spatial variability in the chemical composition of snowcover in a small,remote, scottish catchment

Fresh snowcover in a remote upland catchment is chemically heterogeneous. Coefficients of variation (Cof) for individual major ions range from 5 to 113%, assuming a normal distribution, or 1 to 144 % assuming a lognormal distribution. Aged snowcover is slightly more chemically variable, giving rise to Cof of 19–140 %, assuming a normal distribution, or 2–200 %, assuming a lognormal distribution. In general, the distribution of the concentration of major ions in snowcover is better described by the lognormal distribution. Both vertical and horizontal variability is observed in the chemical content of within-pack snows. Such heterogeneity has important implications for snowpack sampling. We suggest that rigorous methodologies should be devised for the sampling of fresh snowcover. The sampling of within-pack snows should also be performed under tight statistical constraints if representative estimates of the solute content of snowcover are to be obtained.     

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

Urban air pollutant concentration data often tend to fit a two-parameter averaging-time model having three characteristics: (1) pollutant concentrations are (two-parameter) lognormally distributed for all averaging times; (2) median concentrations are proportional to averaging time raised to an exponent; and (3) maximum concentrations are approximately inversely proportional to averaging time raised to an exponent. Concentration data obtained near many isolated point sources and in some urban areas often do not fit a two-parameter lognormal distribution. An increment (either positive or negative) can be added to each such concentration in order to fit the data instead to a three-parameter lognormal distribution. This increment has been incorporated as the third parameter in a new three-parameter averaging-time model that can be used in both point-source and urban settings. Examples show how this new model can be used to analyze SO₂ concentration data obtained near a point source to determine the degree of emission reduction needed to achieve the national ambient air quality standards.     

A method of assessing air toxics concentrations in urban areas using mobile platform measurements

The objective of this paper is to demonstrate an approach to characterize the spatial variability in ambient air concentrations using mobile platform measurements. This approach may be useful for air toxics assessments in Environmental Justice applications, epidemiological studies, and environmental health risk assessments. In this study, we developed and applied a method to characterize air toxics concentrations in urban areas using results of the recently conducted field study in Wilmington, DE. Mobile measurements were collected over a 4- x 4-km area of downtown Wilmington for three components: formaldehyde (representative of volatile organic compounds and also photochemically reactive pollutants), aerosol size distribution (representing fine particulate matter), and water-soluble hexavalent chromium (representative of toxic metals). These measurements were,used to construct spatial and temporal distributions of air toxics in the area that show a very strong temporal variability, both diurnally and seasonally. An analysis of spatial variability indicates that all pollutants varied significantly by location, which suggests potential impact of local sources. From the comparison with measurements at the central monitoring site, we conclude that formaldehyde and fine particulates show a positive correlation with temperature, which could also be the reason that photochemically generated formaldehyde and fine particulates over the study area correlate well with the fine particulate matter measured at the central site.     

A Comparative Validation of the RAM and PTMTP Models for Short-Term SO2 Concentrations in Two Urban Areas

A comprehensive and comparative model validation of two EPA models for short-term SO₂ concentrations was performed. The two models tested were RAM (Urban version) and PTMTP (Terrain version). Both are multiple source, multiple receptor gaussian plume models, recommended in the EPA Guideline On Air Quality Models. ¹ The principal difference between the two models is in their use of empirical dispersion coefficients. It was because of the potential for markedly different predicted maximum SO₂ concentrations, and the absence of any testing data on the RAM model, that the validation analysis was undertaken. The current study utilized a full year of air quality data from monitoring sites in two Indiana cities, Michigan City and Indianapolis. Cumulative frequency distributions for each site and model were prepared and comparisons made. The results indicate that the RAM (Urban) model was highly inaccurate in predicting maximum short-term SO₂ concentrations. The PTMTP model, although conservative in its estimates, produces results which more closely resemble the distribution of observed SO₂ concentrations. The body of information presented in this paper is directed to environmental scientists responsible for air quality modeling, and to those persons who set policy on the use of models in air quality studies.     

Wash effect of atmospheric trace metals wet deposition and its source characteristic in subtropical watershed in China

In order to better understand air pollution in deve-loping regions, such as China, it is important to investigate the wet deposition behavior of atmospheric trace metals and its sources in the subtropical watershed. This paper studies the seasonal change of trace metal concentrations in precipitation and other potential sources in a typical subtropical watershed (Jiazhuhe watershed) located in the downstream of the Yangtze River of China. The results show that typical crustal elements (Al, Fe) and trace element (Zn) have high seasonal variation patterns and these elements have higher contents in precipitation as compared to other metals in Jiazhuhe watershed. In addition, there is no observed Pb in base flow in this study, and the concentration magnitudes of Al, Ba, Fe, Mn, Sr, and Zn in base flow are significantly higher than that of other metals. During different rainfall events, the dynamic export processes are also different for trace metals. The various trace metals dynamic export processes lead to an inconsistent mass first flush and a significant accumulative variance throughout the rainfall events. It is found that in this region, most of the trace metals in precipitation are from anthropogenic emission and marine aerosols brought by typhoon and monsoon.

     

An Air Quality Data Analysis System for Interrelating Effects,Standards, and Needed Source Reductions: Part 3. Vegetation Injury

Acute leaf injury data are analyzed for 19 plant species exposed to ozone or sulfur dioxide. The data can be depicted by a new leaf injury mathematical model with two characteristics: (1) a constant percentage of leaf surface is injured by an air pollutant concentration that is inversely proportional to exposure duration raised to an exponent; (2) for a given exposure duration, the percent leaf injury as a function of pollutant concentration tends to fit a lognormal frequency distribution. Leaf injury as a function of laboratory exposure duration is modeled and compared with ambient air pollutant concentration measurements for various averaging times to determine which exposure durations are probably most important for setting ambient air quality standards to prevent or reduce visible leaf injury. The 8 hour average appears to be most important for most of the plants investigated for most sites, 1 hr concentrations are important for most plants at a few sites, and 3 hr S0₂ concentrations are important for some plants, especially those exposed to isolated point sources of the pollutant. The 1, 3, and 8 hr threshold injury concentrations are listed for each of the 19 plant species studied. To prevent or reduce acute leaf injury, fixed, nonoverlapping ambient air quality measurements and standards are recommended for averaging times of 1, 3, and 8hr.     

Seasonal and spatial distribution of metals in surface sediment of an urban estuary

Aquatic pollution by metals is of concern because of various toxic effects to marine life. The Tolka Estuary, Co. Dublin, Ireland, is a typical Irish urban estuary. It has a significant metal loading originating from the urban environment. Results of a 25month analysis of cadmium, copper, lead and zinc spatial and temporal distribution over 10 sample locations in this estuary are presented in this paper. Metal concentrations were analysed using differential pulse polarography. Significant seasonal and spatial trends in metal distribution were observed over the 25months. Sediment metal concentrations gradually increased (30-120%) in spring to a maximum at the end of summer which was followed by a decrease in winter months (30-60%). Sediment organic matter (OM) concentrations exhibited similar seasonal trends and a positive correlation between OM and metal distributions was observed, implying OM had an influence on metal distributions over time.     

An exposure assessment for selected pharmaceuticals within a watershed in Southern Ontario

Recent studies from a number of countries have shown that measurable concentrations of both human and veterinary pharmaceuticals can be found in a variety of environmental matrices such as surface and ground water, soils, and sediments. Few data are available that characterize the sources, exposure and effects of pharmaceuticals in the environment and there is clearly a need to define these parameters within a Canadian context. We present in this paper the first report in southern Ontario, Canada on the geographic and temporal distribution of pharmaceuticals detected within seven tributaries receiving primarily agricultural inputs in a typical watershed. Of the 28 pharmaceuticals surveyed, 14 were detected in the streams sampled (n=125). Temporal trends in concentration for five frequently detected pharmaceuticals show pulses occurring between May and November of 2003 at similar but varying times over the seasons, depending on the pharmaceuticals, flow rate, and precipitation. Fluctuations in concentration of ions indicative of agricultural run off, such as nitrate and phosphate, were not found to be useful predictors of changes in pharmaceutical concentration (P>0.4), however a significant correlation between dissolved organic carbon and monensin and carbamazepine concentrations were observed (P<0.013). Exposure profiles illustrating concentration distributions for three of the more prevalent pharmaceuticals detected, including lincomycin, monensin and carbamazepine, showed a log normal distribution, useful for calculating centiles of environmental concentrations. While distributions of estimated total potency of pharmaceuticals detected in the surface waters suggested small risks of environmental effects of mixtures to daphnia, green algae, Lemna gibba, and fish, the significance of non-target effects and impacts due to chronic low level exposures to chemical mixtures remains unclear.     

Atmospheric Factors Influencing Daily Sulfate Concentrations in Chicago Air

Abstract

Confidence interval construction for central tendency is a problem of practical consequence for those who must analyze air contaminant data. Determination of compliance with relevant ambient air quality criteria and assessment of associated health risks depend upon quantifying the uncertainty of estimated mean pollutant concentrations. The bootstrap is a resampling technique that has been steadily gaining popularity and acceptance during the past several years. A potentially powerful application of the bootstrap is the construction of confidence intervals for any parameter of any underlying distribution. Properties of bootstrap confidence intervals were determined for samples generated from lognormal, gamma, and Weibull distributions. Bootstrap t intervals, while having smaller coverage errors than Student's t or other bootstrap methods, under-cover for small samples from skewed distributions. Therefore, we caution against using the bootstrap to construct confidence intervals for the mean without first considering the effects of sample size and skew. When sample sizes are small, one might consider using the median as an estimate of central tendency. Confidence intervals for the median are easy to construct and do not under-cover. Data collected by the Northeast States for Coordinated Air Use Management (NESCAUM) are used to illustrate application of the methods discussed.