Methods for Quantifying Variability and Uncertainty in AP-42 Emission Factors: Case Studies for Natural Gas-Fueled Engines

Abstract

Quantitative methods for characterizing variability and uncertainty were applied to case studies of oxides of nitrogen and total organic carbon emission factors for lean-burn natural gas-fueled internal combustion engines. Parametric probability distributions were fit to represent inter-engine variability in specific emission factors. Bootstrap simulation was used to quantify uncertainty in the fitted cumulative distribution function and in the mean emission factor. Some methodological challenges were encountered in analyzing the data. For example, in one instance, five data points were available, with each data point representing a different market share. Therefore, an approach was developed in which parametric distributions were fitted to population-weighted data. The uncertainty in mean emission factors ranges from as little as ~±10% to as much as -90 to 21+180%. The wide range of uncertainty in some emission factors emphasizes the importance of recognizing and accounting for uncertainty in emissions estimates. The skewness in some uncertainty estimates illustrates the importance of using numerical simulation approaches that do not impose restrictive symmetry assumptions on the confidence interval for the mean. In this paper, the quantitative method, the analysis results, and key findings are presented.     

Quantification of variability and uncertainty in lawn and garden equipment NOx and total hydrocarbon emission factors

Variability refers to real differences in emissions among multiple emission sources at any given time or over time for any individual emission source. Variability in emissions can be attributed to variation in fuel or feedstock composition, ambient temperature, design, maintenance, or operation. Uncertainty refers to lack of knowledge regarding the true value of emissions. Sources of uncertainty include small sample sizes, bias or imprecision in measurements, nonrepresentativeness, or lack of data. Quantitative methods for characterizing both variability and uncertainty are demonstrated and applied to case studies of emission factors for lawn and garden (L&G) equipment engines. Variability was quantified using empirical and parametric distributions. Bootstrap simulation was used to characterize confidence intervals for the fitted distributions. The 95% confidence intervals for the mean grams per brake horsepower/hour (g/hp-hr) emission factors for two-stroke engine total hydrocarbon (THC) and NOx emissions were from -30 to +41% and from -45 to +75%, respectively. The confidence intervals for four-stroke engines were from -33 to +46% for THCs and from -27 to +35% for NOx. These quantitative measures of uncertainty convey information regarding the quality of the emission factors and serve as a basis for calculation of uncertainty in emission inventories (EIs).     

Quantification of Variability and Uncertainty in Lawn and Garden Equipment NOx and Total Hydrocarbon Emission Factors

Abstract

Variability refers to real differences in emissions among multiple emission sources at any given time or over time for any individual emission source. Variability in emissions can be attributed to variation in fuel or feedstock composition, ambient temperature, design, maintenance, or operation. Uncertainty refers to lack of knowledge regarding the true value of emissions. Sources of uncertainty include small sample sizes, bias or imprecision in measurements, nonrepresentativeness, or lack of data. Quantitative methods for characterizing both variability and uncertainty are demonstrated and applied to case studies of emission factors for lawn and garden (L&G) equipment engines. Variability was quantified using empirical and parametric distributions. Bootstrap simulation was used to characterize confidence intervals for the fitted distributions. The 95% confidence intervals for the mean grams per brake horsepower/hour (g/hp-hr) emission factors for two-stroke engine total hydrocarbon (THC) and NO_x emissions were from -30 to +41% and from -45 to +75%, respectively. The confidence intervals for four-stroke engines were from -33 to +46% for THCs and from -27 to +35% for NO_x. These quantitative measures of uncertainty convey information regarding the quality of the emission factors and serve as a basis for calculation of uncertainty in emission inventories (Els).     

Development of probabilistic emission inventories of air toxics for Jacksonville, Florida, USA

Probabilistic emission inventories were developed for 1,3-butadiene, mercury (Hg), arsenic (As), benzene, formaldehyde, and lead for Jacksonville, FL. To quantify inter-unit variability in empirical emission factor data, the Maximum Likelihood Estimation (MLE) method or the Method of Matching Moments was used to fit parametric distributions. For data sets that contain nondetected measurements, a method based upon MLE was used for parameter estimation. To quantify the uncertainty in urban air toxic emission factors, parametric bootstrap simulation and empirical bootstrap simulation were applied to uncensored and censored data, respectively. The probabilistic emission inventories were developed based on the product of the uncertainties in the emission factors and in the activity factors. The uncertainties in the urban air toxics emission inventories range from as small as -25 to +30% for Hg to as large as -83 to +243% for As. The key sources of uncertainty in the emission inventory for each toxic are identified based upon sensitivity analysis. Typically, uncertainty in the inventory of a given pollutant can be attributed primarily to a small number of source categories. Priorities for improving the inventories and for refining the probabilistic analysis are discussed.     

Development of Probabilistic Emission Inventories of Air Toxics for Jacksonville,Florida

Abstract

Probabilistic emission inventories were developed for 1,3-butadiene, mercury (Hg), arsenic (As), benzene, formaldehyde, and lead for Jacksonville, FL. To quantify inter-unit variability in empirical emission factor data, the Maximum Likelihood Estimation (MLE) method or the Method of Matching Moments was used to fit parametric distributions. For data sets that contain nondetected measurements, a method based upon MLE was used for parameter estimation. To quantify the uncertainty in urban air toxic emission factors, parametric bootstrap simulation and empirical bootstrap simulation were applied to uncensored and censored data, respectively. The probabilistic emission inventories were developed based on the product of the uncertainties in the emission factors and in the activity factors. The uncertainties in the urban air toxics emission inventories range from as small as –25 to +30% for Hg to as large as –83 to +243% for As. The key sources of uncertainty in the emission inventory for each toxic are identified based upon sensitivity analysis. Typically, uncertainty in the inventory of a given pollutant can be attributed primarily to a small number of source categories. Priorities for improving the inventories and for refining the probabilistic analysis are discussed.     

Quantification of variability and uncertainty in air pollutant emission inventories: method and case study for utility NOx emissions

The quality of stationary source emission factors is typically described using data quality ratings, which provide no quantification of the precision of the emission factor for an average source, nor of the variability from one source to another within a category. Variability refers to actual differences caused by differences in feedstock composition, design, maintenance, and operation. Uncertainty refers to lack of knowledge regarding the true emissions. A general methodology for the quantification of variability and uncertainty in emission factors, activity factors, and emission inventories (EIs) is described, featuring the use of bootstrap simulation and related techniques. The methodology is demonstrated via a case study for a selected example of NOx emissions from coal-fired power plants. A prototype software tool was developed to implement the methodology. The range of interunit variability in selected activity and emission factors was shown to be as much as a factor of 4, and the range of uncertainty in mean emissions is shown to depend on the interunit variability and sample size. The uncertainty in the total inventory of -16 to +19% was attributed primarily to one technology group, suggesting priorities for collecting data and improving the inventory. The implications for decision-making are discussed.     

Quantification of emission factor uncertainty

Emissions factors are important for estimating and characterizing emissions from sources of air pollution. There is no quantitative indication of uncertainty for these emission factors, most factors do not have an adequate data set to compute uncertainty, and it is very difficult to locate the data for those that do. The objectives are to compare the current emission factors of Electric Generating Unit NOx sources with currently available continuous emission monitoring data, develop quantitative uncertainty indicators for the Environmental Protection Agency (EPA) data quality rated emission factors, and determine the possible ranges of uncertainty associated with EPA's data quality rating of emission factors. EPA's data letter rating represents a general indication of the robustness of the emission factor and is assigned based on the estimated reliability of the tests used to develop the factor and on the quantity and representativeness of the data. Different sources and pollutants that have the same robustness in the measured emission factor and in the representativeness of the measured values are assumed to have a similar quantifiable uncertainty. For the purposes of comparison, we assume that the emission factor estimates from source categories with the same letter rating have enough robustness and consistency that we can quantify the uncertainty of these common emission factors based on the qualitative indication of data quality which is known for almost all factors. The results showed that EPA's current emission factor values for NOx emissions from combustion sources were found to be reasonably representative for some sources; however AP-42 values should be updated for over half of the sources to reflect current data. The quantified uncertainty ranges were found to be 25-62% for A rated emission factors, 45-75% for B rated emission factors, 60-82% for C rated emission factors, and 69-86% for D rated emission factors, and 82-92% for E rated emission factors.     

Sustainable Development by Design: Review of Life Cycle Design and Related Approaches

Abstract

The quality of stationary source emission factors is typically described using data quality ratings, which provide no quantification of the precision of the emission factor for an average source, nor of the variability from one source to another within a category. Variability refers to actual differences caused by differences in feedstock composition, design, maintenance, and operation. Uncertainty refers to lack of knowledge regarding the true emissions. A general methodology for the quantification of variability and uncertainty in emission factors, activity factors, and emission inventories (EIs) is described, featuring the use of bootstrap simulation and related techniques. The methodology is demonstrated via a case study for a selected example of NO_x emissions from coal-fired power plants. A prototype software tool was developed to implement the methodology. The range of interunit variability in selected activity and emission factors was shown to be as much as a factor of 4, and the range of uncertainty in mean emissions is shown to depend on the interunit variability and sample size. The uncertainty in the total inventory of ?16 to +19% was attributed primarily to one technology group, suggesting priorities for collecting data and improving the inventory. The implications for decision-making are discussed.     

Trends,temporal and spatial characteristics,and uncertainties in biomass burning emissions in the Pearl River Delta,China

Multi-year inventories of biomass burning emissions were established in the Pearl River Delta (PRD) region for the period 2003–2007 based on the collected activity data and emission factors. The results indicated that emissions of sulfur dioxide (SO₂), nitrogen oxide (NO_x), ammonia (NH₃), methane (CH₄), organic carbon (OC), non-methane volatile organic compounds (NMVOC), carbon monoxide (CO), and fine particulate matter (PM_2.5) presented clear declining trends. Domestic biofuel burning was the major contributor, accounting for more than 60% of the total emissions. The preliminary temporal profiles were established with MODIS fire count information, showing that higher emissions were observed in winter (from November to March) than other seasons. The emissions were spatially allocated into grid cells with a resolution of 3 km × 3  km, using GIS-based land use data as spatial surrogates. Large amount of emissions were observed mostly in the less developed areas in the PRD region. The uncertainties in biomass burning emission estimates were quantified using Monte Carlo simulation; the results showed that there were higher uncertainties in organic carbon (OC) and elemental carbon (EC) emission estimates, ranging from ?71% to 133% and ?70% to 128%, and relatively lower uncertainties in SO₂, NO_x and CO emission estimates. The key uncertainty sources of the developed inventory included emission factors and parameters used for estimating biomass burning amounts.     

Design and Verification of a Programmable Gas Dispensing System for Exposing Plants to Dynamic Concentrations of Air Pollutants

Abstract

Landfills represent a source of distributed emissions source over an irregular and heterogeneous surface. In the method termed “Other Test Method-10” (OTM-10), the U.S. Environmental Protection Agency (EPA) has proposed a method to quantify emissions from such sources by the use of vertical radial plume mapping (VRPM) techniques combined with measurement of wind speed to determine the average emission flux per unit area per time from nonpoint sources. In such application, the VRPM is used as a tool to estimate the mass of the gas of interest crossing a vertical plane. This estimation is done by fitting the field-measured concentration spatial data to a Gaussian or some other distribution to define a plume crossing the vertical plane. When this technique is applied to landfill surfaces, the VRPM plane may be within the emitting source area itself. The objective of this study was to investigate uncertainties associated with using OTM-10 for landfills. The spatial variability of emission in the emitting domain can lead to uncertainties of –34 to 190% in the measured flux value when idealistic scenarios were simulated. The level of uncertainty might be higher when the number and locations of emitting sources are not known (typical field conditions). The level of uncertainty can be reduced by improving the layout of the VRPM plane in the field in accordance with an initial survey of the emission patterns. The change in wind direction during an OTM-10 testing setup can introduce an uncertainty of 20% of the measured flux value. This study also provides estimates of the area contributing to flux (ACF) to be used in conjunction with OTM-10 procedures. The estimate of ACF is a function of the atmospheric stability class and has an uncertainty of 10–30%.     

A sensitivity analysis of adsorption and degradation parameters in the modeling of pesticide transport in soils

The increasing use of deterministic models in predicting the movement of pesticides in soils, has focused attention on the evaluation of major parameters which represent attenuation factors of organics in the subsurface. These parameters are the degradation rate constant and the adsorption constant for the pesticide. In view of the large in situ variability of these parameters and of the difficulty in obtaining accurate field data, there is a high degree of uncertainty associated with the results obtained from deterministic models. A sensitivity analysis is performed here to quantify the impact of such variation in each of these input parameters on the output results of an unsaturated zone transport model (PRZM). Results show that variations in these parameters about their respective mean values greatly affect the predicted concentration distributions, obtained after three years, of the pesticide aldicarb in all the soil profile. A 15–22% variation in the degradation constant, or a 24% variation in the adsorption constant, lead to a 100% uncertainty in the various simulation results defined as the cumulative quantity of aldicarb or the dissolved aldicarb concentration leached below the root zone (or the unsaturated zone) of the soil. Such a deterministic model presents a high degree of sensitivity to these input parameters. Accurate field data are then needed to obtain reliable model results in predicting pesticide movement inthe unsaturated zone.     

Why Industry Needs Performance Standard Zoning

The trend toward increased use of central refuse incinerators is inevitably contributing to urban air pollution. Eventually sampling ports, emission sensing and recording equipment will be required; and more detailed data will be available. But, tradilionally, discharges have been estimated by means of emission factors for nominal design loadings. Such estimates may be unreliable, especially under highly variable processing rates.

Preliminary evidence suggests lhat actual emission factors are higher when the incinerator is charged at greater rates, and vice versa. Observations at the Boston municipal incinerator indicate considerable day-to-day variability in refuse loading. No measurements of emissions are made, but daily input loading records for several years are available.

This study focuses upon the variability in daily loadings. Several functions relating emission factors to charging rates are assumed in order to estimate variability in discharges to the atmosphere. Four years of daily records were analyzed for day-of-week and seasonal components, as well as secular trends. Further analysis suggested that some of the remaining variation in observations could be explained in connection with holidays and precipitation.

The implications of conventionally designed holding pits and charging policies on air pollution problems are discussed in view of such variability, and alternatives are suggested.     

Health risk analysis of PCDD/F emissions from MSW incineration: comparison of probabilistic and deterministic approaches

Incremental lifetime health risks due to polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/F) emitted from municipal waste incineration (MSWI) facilities were evaluated for resident population in the area of the plant. Risk assessment was performed through a multipathway combined probabilistic/deterministic approach for analyzing the effects of uncertainty and intrinsic variability of the main PCDD/F emission related parameters on final predicted values. Exposure through direct inhalation of contaminated air, soil ingestion, soil dermal contact and diet were considered, with the propagation of the variability of input parameters throughout the evaluation performed with Monte Carlo simulation techniques. The application to a case study representative of two different technological scenarios (modern facilities equipped with BAT - Best Available Technology - and older incinerators) in a location site typical of Northern Italy situation results in median values of the maximum individual excess risk on the order of 10(-9) and 10(-7) for most recent and older plant configurations, respectively. Corresponding ratios for the 90th and 10th percentile values are around 7 and 9. Individual risk estimates derived for the same scenarios from conventional deterministic approaches, where large conservative assumptions are normally adopted for compensating the lack of knowledge about uncertainty, are essentially comparable with maximum values resulting from the probabilistic approach, thus leading to situations with extreme and very low probabilities of occurrence. PCDD/F health risks from MSWI emissions might thus result largely overestimated if real emission characteristics are not properly considered in the assessment procedure. Sensitivity analysis for identifying the contribution of different input parameters on final predicted risk variance indicates, for the area considered in the simulation, a prevailing influence of PCDD/F stack concentration, with exposures arising from soil deposition phenomena substantially negligible: this latter result further points out the requirements for a very careful identification of base input data values for PCDD/F stack concentrations, at least for those situations where plants are located nearby urban areas.     

Emission factors for high-emitting vehicles based on on-road measurements of individual vehicle exhaust with a mobile measurement platform

Fuel-based emission factors for 143 light-duty gasoline vehicles (LDGVs) and 93 heavy-duty diesel trucks (HDDTs) were measured in Wilmington, CA using a zero-emission mobile measurement platform (MMP). The frequency distributions of emission factors of carbon monoxide (CO), nitrogen oxides (NO(x)), and particle mass with aerodynamic diameter below 2.5 microm (PM2.5) varied widely, whereas the average of the individual vehicle emission factors were comparable to those reported in previous tunnel and remote sensing studies as well as the predictions by Emission Factors (EMFAC) 2007 mobile source emission model for Los Angeles County. Variation in emissions due to different driving modes (idle, low- and high-speed acceleration, low- and high-speed cruise) was found to be relatively small in comparison to intervehicle variability and did not appear to interfere with the identification of high emitters, defined as the vehicles whose emissions were more than 5 times the fleet-average values. Using this definition, approximately 5% of the LDGVs and HDDTs measured were high emitters. Among the 143 LDGVs, the average emission factors of NO(x), black carbon (BC), PM2.5, and ultrafine particle (UFP) would be reduced by 34%, 39%, 44%, and 31%, respectively, by removing the highest 5% of emitting vehicles, whereas CO emission factor would be reduced by 50%. The emission distributions of the 93 HDDTs measured were even more skewed: approximately half of the NO(x) and CO fleet-average emission factors and more than 60% of PM2.5, UFP, and BC fleet-average emission factors would be reduced by eliminating the highest-emitting 5% HDDTs. Furthermore, high emissions of BC, PM2.5, and NO(x) tended to cluster among the same vehicles.     

Quantitative assessment of variability and uncertainty of hazardous trace element (Cd, Cr, and Pb) contents in Chinese coals by using bootstrap simulation

The quantitative measurements of uncertainties regarding the contents of hazardous trace elements (HTEs) serve as a basis for better assessment of the geochemistry and mineralogical characteristics of coals and their environmental impacts. In this paper, by using bootstrap simulation methodology, a quantitative procedure was demonstrated to characterize the variability and uncertainty of HTE (Cd, Cr, and Pb) contents in Chinese coals, which were specified by 27 different provinces and mining areas. Original data samples for Cd, Cr, and Pb contents in Chinese coals were compiled and summarized from the results reported in published literature. Sampling distributions for uncertainties in statistics such as the mean, median, and confidence interval were calculated. The national average contents were estimated at approximately 0.61 microg/g for Cd, 30.37 microg/g for Cr, and 23.04 microg/g for Pb. The ranges of uncertainties for bootstrap samples of national HTE contents were nearly symmetrical, and the ranges of the 95% confidence interval for the arithmetic mean were relatively small, with relative uncertainties of -16.39% to +21.31% for Cd, -10.11% to +11.72% for Cr, and -8.55% to +8.64% for Pb. This shows that the arithmetic mean contents f HHTEs in Chinese coals are higher in southern provinces than those in northern provinces, obviously differing because of different coal basins. The high values of HTE contents occur in provinces such as Sichuan, Chongqing, Yunnan, Hubei, and Guangxi. Provinces with low contents are located in northwestern China and include Xinjiang, Qinghai, Gansu, and Inner Mongolia; this can be mainly attributed to the medium moisture content, low ash, and low sulfur content in coals. Several provinces with high HTE contents such as Ningxia for Cd, Guangdong for Cr, and Shaanxi for Pb may be associated with the representativeness of the original data samples.     

Uncertainty analysis on simple mass balance model to calculate critical loads for soil acidity

Simple mass balance equations (SMBE) of critical acid loads (CAL) in forest soil were developed to assess potential risks of air pollutants to ecosystems. However, to apply SMBE reliably at large scales, SMBE must be tested for adequacy and uncertainty. Our goal was to provide a detailed analysis of uncertainty in SMBE so that sound strategies for scaling up CAL estimates to the national scale could be developed. Specifically, we wanted to quantify CAL uncertainty under natural variability in 17 model parameters, and determine their relative contributions in predicting CAL. Results indicated that uncertainty in CAL came primarily from components of base cation weathering (BC(w); 49%) and acid neutralizing capacity (46%), whereas the most critical parameters were BC(w) base rate (62%), soil depth (20%), and soil temperature (11%). Thus, improvements in estimates of these factors are crucial to reducing uncertainty and successfully scaling up SMBE for national assessments of CAL.     

Statistical distributions of uncertainty and variability in activated sludge model parameters.

All models used in activated sludge design and analysis use parameters to characterize process performance. The values of these parameters are often assumed based on default values recommended in the literature, but to date, no quantitative estimates of the parameter uncertainties have been published. Similarly, little attention has been given to quantifying site-specific parameter variability, even though its occurrence has been observed several times in the literature. In this paper, universal uncertainty distributions of the model parameters from Activated Sludge Model No. 1 are developed from a database of parameter values reported in the literature using Bayesian statistics. Site-specific distributions of parameter variability were developed using the same techniques. All parameter distributions developed demonstrated that significant uncertainty and variability exist, which could lead to overdesign or plant failure if not considered during the design process.     

DNAPL distribution in the source zone: effect of soil structure and uncertainty reduction with increased sampling density

This paper focuses on parameters describing the distribution of dense nonaqueous phase liquid (DNAPL) contaminants and investigates the variability of these parameters that results from soil heterogeneity. In addition, it quantifies the uncertainty reduction that can be achieved with increased density of soil sampling. Numerical simulations of DNAPL releases were performed using stochastic realizations of hydraulic conductivity fields generated with the same geostatistical parameters and conditioning data at two sampling densities, thus generating two simulation ensembles of low and high density (three-fold increase) of soil sampling. The results showed that DNAPL plumes in aquifers identical in a statistical sense exhibit qualitatively different patterns, ranging from compact to finger-like. The corresponding quantitative differences were expressed by defining several alternative measures that describe the DNAPL plume and computing these measures for each simulation of the two ensembles. The uncertainty in the plume features under study was affected to different degrees by the variability of the soil, with coefficients of variation ranging from about 20% to 90%, for the low-density sampling. Meanwhile, the increased soil sampling frequency resulted in reductions of uncertainty varying from 7% to 69%, for low- and high-uncertainty variables, respectively. In view of the varying uncertainty in the characteristics of a DNAPL plume, remedial designs that require estimates of the less uncertain features of the plume may be preferred over others that need a more detailed characterization of the source zone architecture.     

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.