Simplified Pearson distributions applied to air pollutant concentration

Determination of Pearson system of distribution is proposed by using first three moments of the data. The actual distribution of air pollutant concentration observed at two typical areas is well approximated by Type VI distribution (Beta distribution of the second kind). About half of the data observed around an isolated source show convex curve when the cumulative frequencies are drawn on the probability paper of log-normal distribution which belongs to Type VI of Pearson system. Errors of the distributions are evaluated between log-normal and Type VI of Pearson system.     

Determination of gas phase adsorption isotherms--a simple constant volume method

Single and ternary solute gas phase adsorption isotherms were conducted in this study to evaluate the effectiveness of a simple constant volume method, which was utilized by using Tedlar gas sampling bags as a constant volume batch reactor. For this purpose, gas phase adsorption of toluene, methyl ethyl ketone (MEK), and methyl isobutyl ketone (MIBK) on two types of activated carbons, BPL-bituminous base and OVC--coconut base, were investigated. For the single solute adsorption, the experimental adsorption data were found to be well correlated with Freundlich and Myers adsorption equations. The pore size distribution of adsorbents was found to affect their adsorption capacities; its effect was dependant on the solute concentration. The ternary adsorption experimental isotherms were accurately predicted by using the well-known model, i.e., ideal adsorbed solution theory (IAST).     

Multivariate stochastic modelling of grass fluoride and airborne fluorides

Stochastic modelling was used to investigate the influence of airborne fluorides (in the case of grass fluoride) and meteorological factors on both grass and airborne fluoride levels, taking into consideration lagged dependence. Using rigorous grass sampling methods, there were indications of a negative relationship between volume of rainfall and grass fluoride concentrations, but no apparent relationship between the time which the leaf was visibly wet and grass fluoride levels. No evidence was found that rainfall washed airborne fluoride from the atmosphere or that wind variables influenced grass fluoride. For one particular experimental site, a multivariate stochastic model, which accounts for 81% of the total variation of the grass fluoride series, is developed.     

Uncertainty in Nonpoint Source Pollution Models and Associated Risks

The usefulness of water quality simulation models for environmental management is explored with a focus on prediction uncertainty. The specific objective is to demonstrate how the usability of a flow and transport model (here: MACRO) can be enhanced by developing and analyzing its output probability distributions based on input variability. This infiltration-based model was designed to investigate preferential flow effects on pollutant transport. A statistical sensitivity analysis is used to identify the most uncertain input parameters based on model outputs. Probability distribution functions of input variables were determined based on field-measured data obtained under alternative tillage treatments. Uncertainty of model outputs is investigated using a Latin hypercube sampling scheme (LHS) with restricted pairing for model input sampling. Probability density functions (pdfs) are constructed for water flow rate, atrazine leaching rate, total accumulated leaching, and atrazine concentration in percolation water. Results indicate that consideration of input parameter uncertainty produces a 20% higher mean flow rate along with two to three times larger atrazine leaching rate, accumulated leachate, and concentration than that obtained using mean input parameters. Uncertainty in predicted flow rate is small but that in solute transport is an order of magnitude larger than that of corresponding input parameters. Macropore flow is observed to contribute to the variability of atrazine transport results. Overall, the analysis provides a quantification of prediction uncertainty that is found to enhance a user's ability to assess risk levels associated with model predictions.     

Uncertainty in Nonpoint Source Pollution Models and Associated Risks

The usefulness of water quality simulation models for environmental management is explored with a focus on prediction uncertainty. The specific objective is to demonstrate how the usability of a flow and transport model (here: MACRO) can be enhanced by developing and analyzing its output probability distributions based on input variability. This infiltration-based model was designed to investigate preferential flow effects on pollutant transport. A statistical sensitivity analysis is used to identify the most uncertain input parameters based on model outputs. Probability distribution functions of input variables were determined based on field-measured data obtained under alternative tillage treatments. Uncertainty of model outputs is investigated using a Latin hypercube sampling scheme (LHS) with restricted pairing for model input sampling. Probability density functions (pdfs) are constructed for water flow rate, atrazine leaching rate, total accumulated leaching, and atrazine concentration in percolation water. Results indicate that consideration of input parameter uncertainty produces a 20% higher mean flow rate along with two to three times larger atrazine leaching rate, accumulated leachate, and concentration than that obtained using mean input parameters. Uncertainty in predicted flow rate is small but that in solute transport is an order of magnitude larger than that of corresponding input parameters. Macropore flow is observed to contribute to the variability of atrazine transport results. Overall, the analysis provides a quantification of prediction uncertainty that is found to enhance a user's ability to assess risk levels associated with model predictions.     

Accounting for averaging time in air pollution modeling

This paper examines the validity of a commonly used expression to estimate concentrations for averaging times that are much smaller than that corresponding to the model estimate. These “peak” concentrations, which can be several times larger than the model estimate, are required in applications such as odor assessment. We show that this expression cannot be justified, and that information on short-term concentrations is only contained in the probability distribution of time-averaged concentrations. The paper proposes a simple model of concentration time series to examine the effect of averaging time on concentration probability distributions. The results from the model are compared with previous theoretical and experimental studies.     

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.     

Stochastic model to forecast ground-level ozone concentration at urban and rural areas

Stochastic models that estimate the ground-level ozone concentrations in air at an urban and rural sampling points in South-eastern Spain have been developed. Studies of temporal series of data, spectral analyses of temporal series and ARIMA models have been used. The ARIMA model (1,0,0) x (1,0,1)24 satisfactorily predicts hourly ozone concentrations in the urban area. The ARIMA (2,1,1) x (0,1,1)24 has been developed for the rural area. In both sampling points, predictions of hourly ozone concentrations agree reasonably well with measured values. However, the prediction of hourly ozone concentrations in the rural point appears to be better than that of the urban point. The performance of ARIMA models suggests that this kind of modelling can be suitable for ozone concentrations forecasting.     

Technique for aerosol generation with controllable micrometer size distribution

The purpose of this study is to develop an aerosol generating system that can produce particles of micrometer size in a convenient and efficient way. This system is comprised of an ultrasonic atomizer, potassium sodium tartrate tetrahydrate (PST) as solute and a program-controlled solute feeding unit with different PST concentrations. Both the aerosol concentration and size distribution pattern can be easily controlled and reproduced in the developed system. While the initial size of droplets generated from atomizer may remain unchanged, the size of residual dry aerosols was controlled by the solute concentration adjusted by the mixing ratio of solute and water. In addition, PST concentration could be alternatively adjusted in any cyclic way to provide particles with relatively mono-disperse, bimodal, varying size as well as skew distribution to meet requirements for various applications. The main advantage of the generating system is to generate particles of specific size distribution in order to simulate aerosols in ambient air or working places.     

Use of residence time distribution for evaluation of gaseous pollutant volatilization from stored swine manure

Abstract

A quantification analysis for evaluation of gaseous pollutant volatilization as a result of mass transfer from stored swine manure is presented from the viewpoint of residence time distribution. The method is based on evaluating the moments of concentration vs. time curves of both air and gaseous pollutants. The concept of moments of concentration histories is applicable to characterize the dispersal of the supplied air or gaseous pollutant in a ventilated system. The mean age or residence time of airflow can be calculated from an inverse system state matrix [B]‐1 of a linear dynamic equation describing the dynamics of gaseous pollutant in a ventilated airspace. The sum elements in an arbitrary row i in matrix [B]‐1 is equal to the mean age of airflow in airspace i. The mean age of gaseous pollutant in airspace i can be obtained from the area under the concentration profile divided by the equilibrium concentration reading in that space caused by gaseous pollutant sources. Matrix [B]‐1 can also be represented in terms of the inverse local airflow rate matrix ([W]‐1), transition probability matrix ([P]), and air volume matrix ([V]) as, [B]‐1 =[W]‐1[P][V]. Finally the mean age of airflow in a ventilated airspace can be interpreted by the physical characteristics of matrices [W] and [P]. The practical use of the concepts is also applied in a typical pig unit.     

Concentration statistics for mixing-controlled reactive transport in random heterogeneous media

Uncertainty in the distribution of hydraulic parameters leads to uncertainty in flow and reactive transport. Traditional stochastic analysis of solute transport in heterogeneous media has focused on the ensemble mean of conservative-tracer concentration. Studies in the past years have shown that the mean concentration often is associated with a high variance. Because the range of possible concentration values is bounded, a high variance implies high probability weights on the extreme values. In certain cases of mixing-controlled reactive transport, concentrations of conservative tracers, denoted mixing ratios, can be mapped to those of constituents that react with each other upon mixing. This facilitates mapping entire statistical distributions from mixing ratios to reactive-constituent concentrations. In perturbative approximations, only the mean and variance of the mixing-ratio distribution are used. We demonstrate that the second-order perturbative approximation leads to erroneous or even physically impossible estimates of mean reactive-constituent concentrations when the variance of the mixing ratio is high and the relationship between the mixing ratio and the reactive-constituent concentrations strongly deviates from a quadratic function. The latter might be the case in biokinetic reactions or in equilibrium reactions with small equilibrium constant in comparison to the range of reactive-constituent concentrations. When only the mean and variance of the mixing ratio is known, we recommend assuming a distribution that meets the known bounds of the mixing ratio, such as the beta distribution, and mapping the assumed distribution of the mixing ratio to the distributions of the reactive constituents.     

An evaluation of the methods of fractiles,moments and maximum likelihood for estimating parameters when sampling air quality data from a stationary lognormal distribution

Air pollution control officials often make the simplifying assumption that air pollutant concentrations are independent samples from a stationary probability distribution. If the parent distribution really is stationary and correctly chosen, maximum likelihood estimation almost always will provide the best possible estimate of its parameters. However, the air pollution literature makes little if any mention of this fact and often suggests using the method of moments or the method of fractiles to estimate the parameters of an assumed distribution, and using the results for computing design values to determine the control level required to meet an air quality standard. No estimate is made in the air pollution literature of the magnitude of the difference produced by these different methods.This paper investigates the effectiveness of three different approaches for estimating parameters using a lognormal distribution as an example: (a) method of fractiles; (b) method of moments and (c) method of maximum likelihood. The error associated with each approach for computing emission controls is determined by sampling from a true stationary lognormal distribution using computer simulation. These results then are compared with a fourth approach, direct empirical linear rollback, in which no model is used and design values are calculated using raw observations. The latter approach often is used in practical situations by air pollution control personnel.In 100 simulated years at a site experiencing the same lognormally distributed air pollution in the precontrol state, the correct control level was 50%. The following control levels were calculated: Empirical rollback, 22–82%; Method of fractiles, 32–64%; Method of moments, 41–59% and Method of maximum likelihood, 46–54%, with most years very close to the true value of 50%.Thus, the maximum likelihood approach effectively reduces the variance by ‘filtering out’ the effect of random phenomena occurring during the year and would be the method of choice if the observations are indeed distributed as they are assumed.     

Spatial and temporal distribution of solute leaching in heterogeneous soils: analysis and application to multisampler lysimeter data

Accurate assessment of the fate of salts, nutrients, and pollutants in natural, heterogeneous soils requires a proper quantification of both spatial and temporal solute spreading during solute movement. The number of experiments with multisampler devices that measure solute leaching as a function of space and time is increasing. The breakthrough curve (BTC) can characterize the temporal aspect of solute leaching, and recently the spatial solute distribution curve (SSDC) was introduced to describe the spatial solute distribution. We combined and extended both concepts to develop a tool for the comprehensive analysis of the full spatio-temporal behavior of solute leaching. The sampling locations are ranked in order of descending amount of total leaching (defined as the cumulative leaching from an individual compartment at the end of the experiment), thus collapsing both spatial axes of the sampling plane into one. The leaching process can then be described by a curved surface that is a function of the single spatial coordinate and time. This leaching surface is scaled to integrate to unity, and termed S can efficiently represent data from multisampler solute transport experiments or simulation results from multidimensional solute transport models. The mathematical relationships between the scaled leaching surface S, the BTC, and the SSDC are established. Any desired characteristic of the leaching process can be derived from S. The analysis was applied to a chloride leaching experiment on a lysimeter with 300 drainage compartments of 25 cm2 each. The sandy soil monolith in the lysimeter exhibited fingered flow in the water-repellent top layer. The observed S demonstrated the absence of a sharp separation between fingers and dry areas, owing to diverging flow in the wettable soil below the fingers. Times-to-peak, maximum solute fluxes, and total leaching varied more in high-leaching than in low-leaching compartments. This suggests a stochastic-convective transport process in the high-flow streamtubes, while convection dispersion is predominant in the low-flow areas. S can be viewed as a bivariate probability density function. Its marginal distributions are the BTC of all sampling locations combined, and the SSDC of cumulative solute leaching at the end of the experiment. The observed S cannot be represented by assuming complete independence between its marginal distributions, indicating that S contains information about the leaching process that cannot be derived from the combination of the BTC and the SSDC.     

National baseline survey of soil quality in the Netherlands

To determine background values of the 252 chemical compounds listed in Dutch legislation, a survey was designed with the aim of estimating percentiles of the cumulative frequency distributions and areal fractions exceeding the former, legislative reference values. Sampling locations were selected by probability sampling, so that in estimating the target quantities no model assumptions on the spatial variation were required, and valid estimates could be obtained by design-based inference. Strata in random sampling were formed by overlaying an aggregated soil map and land use map. For most of the heavy metals the areal fraction with concentrations in the topsoil (0-10 cm) exceeding the reference value was smaller than the allowable maximum of 5%. For these compounds a background value was determined smaller than the reference value. Exceptions were V, Co, Ba and Cu, for which a background value was defined (slightly) larger than the reference value.     

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.     

Use of the terrestrial moss Pseudoscleropodium purum to detect sources of small scale contamination by PAHs

Here we present a simple, economic method of identifying sources of small scale contamination by polycyclic aromatic hydrocarbons (PAHs). The method involves determining the concentrations of the contaminants in the terrestrial moss Pseudoscleropodium purum and consists of the following steps: i) testing for the existence of gradients of decreasing concentrations of PAHs in the moss in relation to distance from different emission sources; ii) measurement of the concentration of PAHs at 35 pairs of sampling sites, each separated by a distance of 1 km; iii) study of the distribution of the differences in concentration between these pairs of sampling sites and elimination of extreme values (affected by small scale sources of contamination); iv) characterization of normal distributions to determine the probability of the data being thus distributed; and v) testing the method in the surroundings of possible sources of small scale contamination by PAHs. The decrease in concentration of all of the compounds followed a steep gradient with increasing distance from the emission source; after elimination of the outliers, the distribution of the differences in concentration between the 35 pairs of sampling sites was normal for all compounds, except benzo(a)pyrene. Application of the method to 15 different types of industries provided satisfactory results and the method proved to be a very useful tool for monitoring and evaluating air quality.     

区域农田镉含量空间变异与综合风险的不确定性评估

我国小麦镉 (Cd) 污染格局多样,从不确定性角度评估区域小麦田Cd累积风险有助于提升污染防治决策的准确性。本研究基于不确定性理论,将蒙特卡洛 (Monte-Carlo) 随机模拟方法引入到区域土壤-小麦系统Cd污染综合风险评估中,结合多元统计和空间分析开展实例研究。结果表明河南省某小麦主产区92.8%的土壤样品Cd含量超过农田土壤风险筛选值 (0.6 mg·kg⁻¹) ,84.0%的小麦籽粒样品Cd含量超过国家食品安全限量标准 (0.1 mg·kg⁻¹) 。区域土壤-小麦系统Cd累积水平整体上呈现西北高东南低的空间分布格局。区域Cd生态风险以中度污染为主。区域人群Cd摄入量超过WHO推荐安全值的风险概率为31.6%,控制土壤Cd累积趋势可将该超标风险下降至7.3%。不确定性模拟、空间分析和场景分析的综合应用可准确识别农田Cd污染风险等级和相应概率,为区域Cd污染防治提供决策建议。     

Grid lysimeter study of steady state chloride transport in two Spodosol types using TDR and wick samplers.

Solute transport in soils is affected by soil layering and soil-specific morphological properties. We studied solute transport in two sandy Spodosols: a dry Spodosol developed under oxidizing conditions of relatively deep groundwater and a wet Spodosol under periodically reducing conditions above a shallow groundwater table. The wet Spodosol is characterized by a diffuse and heterogeneous humus-B-horizon (i.e., Spodic horizon), whereas the dry Spodosol has a sharp Spodic horizon. Drainage fluxes were moderately variable with a coefficient of variation (CV) of 25% in the wet Spodosol and 17% in the dry Spodosol. Solute transport in 1-m-long and 0.8-m-diameter soil columns was investigated using spatial averages of solute concentrations measured by a network of 36 Time Domain Reflectometry (TDR) probes. In the dry Spodosol, solute transport evolves from stochastic-convective to convective-dispersive at a depth of 0.25 m, coinciding with the depth of the Spodic horizon. Chloride breakthrough at the bottom of the soil columns was adequately well predicted by a convection-dispersion model. In the wet Spodosol, solute transport was heterogeneous over the entire depth of the column. Chloride breakthrough at 1 m depth was predicted best using a stochastic-convective transport model. The TDR sampling volume of 36 probes was too small to capture the heterogeneous flow and concomitant transport in the wet Spodosol.     

Analysis of the long-term behavior of solute transport with nonlinear equilibrium sorption using breakthrough curves and temporal moments

We analyzed the long-term behavior of breakthrough curves (BTCs) and temporal moments of a solute subjected to Freundlich equilibrium sorption (s = kc(n)). For one-dimensional transport in a homogeneous porous medium, we derived a power-law relation between travel time, tau, and solute displacement, chi, with the exponent being equal to the Freundlich n exponent. The mean solute velocity, derived from the first time moment, was found to change as tau(n-1). For n values larger than 0.66, the second time moment could be related to c chi(2/n), where c is a constant. An approach based on the use of a critical concentration was developed to estimate the presence of the asymptotic regime in the tail of the BTC. This approach was tested successfully using numerical case studies. One-dimensional numerical simulations with varying values of k, n and initial mass were run to verify the closed form analytical expressions for the large time behavior of temporal moments and the tailing part of breakthrough curves. Good agreement between the slope of the tailing part of log-log transformed BTCs and the predicted slope using asymptotic theory was found. Asymptotic theory in general underestimated the magnitude of the concentration in the tail. The quality of the estimated concentrations in the tail improved for small values of the dispersivity. Experimental BTCs of uranin and benazolin were analyzed in combination with sorption/desorption batch experiments using asymptotic theory. A good agreement between the value of n parameter derived from desorption experiment with benazolin and the value of the n parameter derived from the tail of the BTC was found.     

Analyses of locally measured bromide breakthrough curves from a natural gradient tracer experiment at Krauthausen

Solute travel time distributions were derived from breakthrough curves (BTCs) of bromide concentrations, which were measured during a large-scale tracer experiment in a quaternary fluviatile aquifer at Krauthausen. Travel time distributions to a specific point in the aquifer were derived from locally measured BTCs, using averaged absolute concentrations ?abs(x1,t), normalized concentrations ?norm(x1,t), and velocity-weighted normalized concentrations ?vw(x1,t). The travel time distributions were characterized in terms of equivalent convective-dispersive transport parameters: the equivalent solute velocity and equivalent dispersivity. Parameters were derived from BTCs using moment analyses and least-squares fits of the 1-D convection-dispersion equation (CDE). Both local and averaged BTCs showed pronounced tailing which was not well described by the 1-D CDE and which indicates the presence of macroscopic regions with low velocities in the aquifer. Therefore, dispersivities derived from CDE fits were significantly smaller than those derived from time moments. The BTCs of ?abs(x1,t) were dominated by only a few local BTCs with high concentrations and were less representative for the travel time distribution than BTCs of averaged normalized concentrations. Dispersivities derived from ?norm(x1,t) and ?vw(x1,t) were very similar. Finally, estimates of dispersivities and vertical correlation length of lnK, gamma 3, from BTCs were in agreement with a first-order estimate of the dispersivity and gamma 3 based on grain size data and flow meter measurements.