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.     

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.     

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.     

Comparison of six particle size distribution models on the goodness-of-fit to particulate matter sampled from animal buildings

Lognormal distribution is often used as a default model for regression analysis of particle size distribution (PSD) data; however, its goodness-of-fit to particle matter (PM) sampled from animal buildings and its comparison to other PSD models have not been well examined. This study aimed to evaluate and to compare the goodness-of-fit of six PSD models to total suspended particulate matter (TSP) samples collected from 15 animal buildings. Four particle size analyzers were used for PSD measurement. The models' goodness-of-fit was evaluated based on adjusted R2, Akaike's information criterion (AIC), and mean squared error (MSE) values. Results showed that the models' approximation of measured PSDs differed with particle size analyzer. The lognormal distribution model offered overall good approximations to measured PSD data, but was inferior to the gamma and Weibull distribution models when applied to PSD data derived from the Horiba and Malvern analyzers. Single-variable models including the exponential, Khrgian-Mazin, and Chen's empirical models provided relatively poor approximations and, thus, were not recommended for future investigations. A further examination on model-predicted PSD parameters revealed that even the best-fit model of the six could significantly misestimate mean diameter median diameter; and variance. However, compared with other models, the best-fit model still offered the relatively best estimates of mean and median diameters, whereas the best predicted variances were given by the gamma distribution model.     

Modeling solute diffusion in the presence of pore-scale heterogeneity: method development and an application to the Culebra dolomite member of the Rustler Formation, New Mexico, USA

Previous studies have revealed the presence of pore-scale variability in diffusivity in the Culebra (dolomite) member of the Rustler Formation, NM. In this study, eight laboratory-scale diffusion experiments on five Culebra samples were analyzed using a methodology for modeling solute diffusion through porous media in the presence of multiple matrix diffusivities, Dp. A lognormal distribution of Dp is assumed within each of the lab samples. The estimated standard deviation (sigma d) of ln(Dp) within each sample ranges from 0 to 1, with most values lying between 0.5 and 1. The variability over all samples leads to a combined sigma d in the range of 1.0-1.2, which is consistent with the distribution of independently determined formation factor measurements for similar Culebra samples. A comparison of our estimation results to other rock properties suggests that, at the lab-scale, the geometric mean of Dp increases with bulk porosity and the quantity of macroscopic features such as vugs and fractures. However, sigma d appears to be determined by variability within such macroscopic features and/or by micropore-scale heterogeneity. In addition, comparison of these experiments to those at larger spatial scales suggests that increasing sample volume results in an increase in sigma d.     

Estimating first-order reaction rate coefficient for transport with nonequilibrium linear mass transfer in heterogeneous media

A travel-time based approach is developed for estimating first-order reaction rate coefficients for transport with nonequilibrium linear mass transfer in heterogeneous media. Tracer transport in the mobile domain is characterized by a travel-time distribution, and mass transfer rates are described by a convolution product of concentrations in the mobile domain and a memory function rather than predefining the mass transfer model. A constant first-order reaction is assumed to occur only in the mobile domain. Analytical solutions in Laplace domain can be derived for both conservative and reactive breakthrough curves (BTCs). Temporal-moment analyses are presented by using the first and second moments of conservative and reactive BTCs and the mass consumption of the reactant for an inverse Gaussian travel-time distribution. In terms of moment matching, there is no need for one to specify the mass transfer model. With the same capacity ratio and the mean retention time, all mass transfer models will lead to the same moment-derived reaction rate coefficients. In addition, the consideration of mass transfer generally yields larger estimations of the reaction rate coefficient than models ignoring mass transfer. Furthermore, the capacity ratio and the mean retention time have opposite influences on the estimation of the reaction rate coefficient: the first-order reaction rate coefficient is positively linearly proportional to the capacity ratio, but negatively linearly proportional to the mean retention time.     

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.     

Distribution of PAHs and PCBs to dissolved organic matter: high distribution coefficients with consequences for environmental fate modeling

Dissolved organic carbon/water distribution coefficients (K(DOC)) were measured for a selection of PCBs with octanol/water partition coefficients (K(OW)) ranging from 10(5.6) to 10(7.5). A solid phase dosing and sampling technique was applied to determine K(DOC) to Aldrich humic acid. This technique is in particular suitable for determining the distribution of very hydrophobic chemicals to complex matrices like humic acids. The K(DOC) values were calculated from the experimental data using a linear model. Determined K(DOC)'s were evaluated in relation to octanol/water partition coefficients of the test compounds, and compared to literature data. Measured K(DOC) values were somewhat higher than literature data, which can probably be attributed to the overestimation of freely dissolved aqueous concentration as a result of incomplete phase separation in other studies, and to the unique character of Aldrich humic acid as a "sorbent" or co-solute or to the fact that Aldrich humic acid is not a typical DOC, and other (adsorption) processes can occur. This study reports DOC distribution coefficients that belong to the highest ones ever measured. In addition, the DOC distribution was discussed in relation to current risk assessment modeling.     

Use of X-ray absorption imaging to examine heterogeneous diffusion in fractured crystalline rocks

Heterogeneous diffusion in different regions of a fractured granodiorite from Japan has been observed and measured through the use of X-ray absorption imaging. These regions include gouge-filled fractures, recrystallized fracture-filling material and hydrothermally altered matrix. With the X-ray absorption imaging technique, porosity, relative concentration, and relative mass of an iodine tracer were imaged in two dimensions with a sub-millimeter pixel size. Because portions of the samples analyzed have relatively low porosity values, imaging errors can potentially impact the results. For this reason, efforts were made to better understand and quantify this error. Based on the X-ray data, pore diffusion coefficients (Dp) for the different regions were estimated assuming a single diffusion rate and a lognormal multirate distribution of Dp. Results show Dp for the gouge-filled fractures are over an order of magnitude greater than those of the recrystallized fracture-filling material, which in turn is approximately two times greater than those for the altered matrix. The recrystallized fracture-filling material was found to exhibit the greatest degree of variability. The results of these experiments also provide evidence that diffusion from advective zones in fractures through the gouge-filled fractures and recrystallized fracture-filling material could increase the pore space available for matrix diffusion. This evidence is important for understanding the performance of potential nuclear waste repositories in crystalline rocks as diffusion is thought to be an important retardation mechanism for radionuclides.     

Sorption isotherms of brominated diphenyl ethers on natural soils with different organic carbon fractions

Sorption isotherms of BDE-28 and BDE-47 on natural soils with different contents of soil organic matter (SOM) were investigated. Due to low water solubility of BDEs and resulted narrow ranges of aqueous equilibrium concentration, the linear distribution model showed similar and good fitting efficiency to the linear portion of nonlinear Freundlich curve. For the same sample, the linear and nonlinear model fitting sorption coefficients were close. At the statistically significant level of 0.05 or 0.1, significant relationships of total organic carbon fraction (fOC) with the fitting sorption coefficients can be observed. As for BDE-28, the relationships of fOC and SOM fractions with the single point partition coefficients at different aqueous concentrations of BDEs were significant; while for BDE-47, the relationships became less significant or insignificant, especially at higher aqueous concentrations. The findings in this study may facilitate more understanding on transport and fate of studied BDEs in soil systems.     

Assessing the inhalation cancer risk of particulate matter bound polycyclic aromatic hydrocarbons (PAHs) for the elderly in a retirement community of a mega city in North China

Assessment of the health risks resulting from exposure to ambient polycyclic aromatic hydrocarbons (PAHs) is limited by the lack of environmental exposure data among different subpopulations. To assess the exposure cancer risk of particulate carcinogenic polycyclic aromatic hydrocarbon pollution for the elderly, this study conducted a personal exposure measurement campaign for particulate PAHs in a community of Tianjin, a city in northern China. Personal exposure samples were collected from the elderly in non-heating (August–September, 2009) and heating periods (November–December, 2009), and 12 PAHs individuals were analyzed for risk estimation. Questionnaire and time-activity log were also recorded for each person. The probabilistic risk assessment model was integrated with Toxic Equivalent Factors (TEFs). Considering that the estimation of the applied dose for a given air pollutant is dependent on the inhalation rate, the inhalation rate from both EPA exposure factor book was applied to calculate the carcinogenic risk in this study. Monte Carlo simulation was used as a probabilistic risk assessment model, and risk simulation results indicated that the inhalation-ILCR values for both male and female subjects followed a lognormal distribution with a mean of 4.81?×?10^?6 and 4.57?×?10^?6, respectively. Furthermore, the 95 % probability lung cancer risks were greater than the USEPA acceptable level of 10^?6 for both men and women through the inhalation route, revealing that exposure to PAHs posed an unacceptable potential cancer risk for the elderly in this study. As a result, some measures should be taken to reduce PAHs pollution and the exposure level to decrease the cancer risk for the general population, especially for the elderly.     

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.     

Analytical formulas for the below-cloud scavenging coefficient of an irreversibly soluble gas: a quantitative evaluation for HNO3

In the present paper, analytical expressions are derived for the below-cloud gas scavenging coefficient, considering various functions that can be found in the literature to describe raindrop populations and terminal velocities. Three primary cases have been identified where an analytical solution exists: (i) a raindrop size distribution described by a gamma function and raindrop terminal velocity by a power function of raindrop size; (ii) a raindrop size distribution described by a gamma function and raindrop terminal velocity by an exponential function; and (iii) a raindrop size distribution described by a log–normal function and raindrop terminal velocity by a power function. In addition, in case (i), the gas scavenging coefficient is expressed analytically as a function of rain intensity. The derived analytical expressions are subsequently used to compute the scavenging coefficients of HNO₃ for different parameterizations of the raindrop size distribution and terminal velocity functions. In order to broaden the sensitivity test of HNO3 scavenging coefficients on parameterizations, scavenging coefficients of HNO₃ are also computed numerically for the raindrop terminal velocity as a function of raindrop size and atmospheric conditions. The results show that there is a relative variation in the values of the gas scavenging coefficient up to 50% for the parameterization considered in this study, and that the overestimation given by the analytical formulas is not important for cut-off limits of raindrop spectra below 0.2 mm.     

Solute transport properties of compacted Ca-bentonite used in FEBEX project

The present Spanish concept of a deep geological high level waste repository includes an engineered clay barrier around the canister. The clay presents a very high sorption capability for radionuclides and a very small hydraulic conductivity, so that the migration process of solutes is limited by sorption and diffusion processes. Therefore, diffusion and distribution coefficients in compacted bentonite (i.e. in "realistic" liquid to solid ratio conditions) are the main parameters that have to be obtained in order to characterise solute transport that could be produced after the canister breakdown. Through-Diffusion (TD) and In-Diffusion (ID) experiments with HTO, Sr, Cs and Se were carried out using compacted FEBEX bentonite, which is the reference material for the Spanish concept of radioactive waste disposal. Experiments were interpreted by means of available analytical solutions that allow the estimation of diffusion coefficients and, in some cases, distribution coefficients. Analytical solutions are simple to use, but rely on hypotheses that do not hold in all the experiments. These experiments were interpreted also using an automatic parameter estimation code that overcomes the limitations of analytical solutions. Numerical interpretation allows the simultaneous estimation of porosity, diffusion and distribution coefficients, accounts for the role of porous sinters and time-varying boundary concentrations, and can use different types of raw concentration data.     

Evaluating factors that influence microbial phenanthrene biodegradation rates by regression with categorical variables

To advance the accuracy of bioremediation measurements, it is useful before specific experiments to attribute or estimate the influence of both experimental as well as field conditions on the expected magnitudes of microbial degradation rate coefficients. This paper analyzes the numerical contribution, or influence, of categories of conditions, such as bacterial adaptive state, electron acceptor type, mixing, generalized sorption conditions, and biodegradation temperature, on published phenanthrene biodegradation rates as an example of our regression approach. A fundamental microbial degradation rate equation is transformed to an additive model, then using multiple linear regression on published data, coefficients (of categorical variables) and a linear model are presented that estimate first-order biodegradation rate coefficients to within a factor of 3. Numerical estimates of how much bacterial adaptive state and presence of a sorption phase, the two most statistically significant factors, alter the phenanthrene biodegradation rate are presented. The influence of some measurement or field conditions, for example, the influence of oxygen reduction versus optimal nitrate reduction, cannot be distinguished statistically given the available data and range. The regression model is tested using conditions from newly published papers to estimate a priori the expected rate, which compares very favorably to measurements reported in the papers. Due to limited published data and range for extreme cases, the current coefficients do not apply to degradation of very aged phenanthrene nor very low concentrations of electron acceptors. As estimating tools, however, the coefficients themselves and the regression approach have very beneficial roles in design of experiments for both laboratory and field settings. Our method can be applied to other PAHs as sufficient data become available.     

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.     

Nonequilibrium sorption of phenols onto geosorbents: the impact of pH on intraparticle mass transfer

While the pH effect on sorption equilibrium of weak acids on natural sorbents was investigated in a number of studies, less is known about the pH dependence of sorption kinetics. This paper investigates the impact of pH on sorption kinetics during the transport of some selected phenols through a sandy aquifer material. Breakthrough curves measured in column experiments were analyzed using a mass transfer based nonequilibrium model designated as dispersed flow, film and particle diffusion model (DF-FPDM). In this model, the rate limiting intraparticle diffusion is characterized by the mass transfer coefficient, kSaV, which can be determined from breakthrough curves by curve fitting. The experimental results indicate that the kSaV is pH-dependent and inversely correlated with the pH-dependent distribution coefficient, K(d,app). Regression equations are presented that may be used to estimate approximate values of intraparticle mass transfer coefficients on the basis of experimentally determined or LFER predicted distribution coefficients.     

Assessment of intrinsic bioremediation of a coal-tar-affected aquifer using Two-dimensional reactive transport and Biogeochemical mass balance approaches.

Expedited site characterization and groundwater monitoring using direct-push technology and conventional monitoring wells were conducted at a former manufactured gas plant site. Biogeochemical data and heterotrophic plate counts support the presence of microbially mediated remediation. By superimposing solutions of a two-dimensional reactive transport analytical model, first-order degradation rate coefficients ((day-1) ) of various compounds for the dissolved-phase plume were estimated (i.e., benzene [0.0084], naphthalene [0.0058], and acenaphthene [0.0011]). The total mass transformed by aerobic respiration, nitrate reduction, and sulfate reduction around the free-phase coal-tar dense-nonaqueous-phase-liquid region and in the plume was estimated to be approximately 4.5 kg/y using a biogeochemical mass-balance approach. The total mass transformed using the degradation rate coefficients was estimated to be approximately 3.6 kg/y. Results showed that a simple two-dimensional analytical model and a biochemical mass balance with geochemical data from expedited site characterization can be useful for rapid estimation of mass-transformation rates.     

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.