Quantification of Hourly Variability in Activity and NO x Emissions for Baseload Coal Fired Power Plants

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1 Quantification of Hourly Variability in Activity and NO x Emissions for Baseload Coal Fired Power Plants Paper No Amr Abdel-Aziz and H. Christopher Frey Department of Civil Engineering, Campus Box 789, North Carolina State University, Raleigh, NC ABSTRACT The objectives of this paper are to: () quantify variability in hourly utility NO x emission factors, activity factors, and total emissions; (2) investigate the autocorrelation structure and evaluate cyclic effects at short and long scales of the time series of total hourly emissions; (3) compare emissions for the ozone season versus the entire year to identify seasonal differences, if any; and (4) evaluate inter-annual variability. Continuous Emissions Monitoring (CEM) data were analyzed for 995 and 998 for 32 units from 9 baseload power plants in the Charlotte, NC airshed. Unit emissions have a strong 24 hour cycle attributable primarily to the capacity factor. Typical ranges of the coefficient of variation for emissions at a given hour of the day were from.2 to.45. Little difference was found when comparing weekend emissions with the entire week or when comparing the ozone season with the entire year. There were substantial differences in the mean and standard deviation of emissions when comparing 995 and 998 data, indicative of the effect of retrofits of control technology during the intervening time. The wide range of variability and its autocorrelation should be accounted for when developing probabilistic utility emission inventories for analysis of near-term future air quality episodes. INTRODUCTION Uncertainty in emission inventories pose a major concern in air quality modeling. Typically, emission inventories are estimated based on emission and activity factors of each source category. These factors are subject to both variability and uncertainty. Variability is the heterogeneity of values with respect to time, space or population. For example, NO x emission factors from coal-fired power plants vary over time due to variation in coal composition fed to the boilers, different boiler designs and different operating conditions. 2 Uncertainty is the lack of knowledge regarding the true quantity of a value. 3 There are many sources that contribute to uncertainties in inventories, including sampling error, non-representativeness of data used in developing emission and activity factors, and measurement errors. 4,5 Some studies have been conducted to propagate uncertainty in emission inventories through air quality models. 6,7,8. These studies used expert elicitation to specify probability distributions for variability in future emissions. Others have used empirical-based approaches, such as to estimate the variability in daily NO x emissions from point sources in the Atlanta metropolitan region or to evaluate the variability of NO x emission rates for coal-fired power plants of the largest electric generation owners in the U.S. 9, Other techniques for quantifying variability and uncertainty include bootstrap simulation. 2-5, For example, inter-unit variability in NO x emissions of selected types of coal fired electricity generating units was quantified for 2 month

2 averages. 2 Uncertainty in specific statistics, such as the mean emission rate, was quantified using bootstrap simulation. For air quality modeling purposes, particularly for prediction of ambient ozone levels, emission inventories must be developed on an hourly basis. Coal-fired power plants contribute substantially to the NO x emission inventory in many air quality modeling domains. Historical data regarding variability in emissions is a useful basis for estimating the possible range and relatively likelihood of emissions in the near-term future, such as would be needed when evaluating baseline emissions into the future and as a basis for developing future control strategies. Therefore, this paper aims at quantifying variability in hourly emission and activity factors for coal-fired power plants based upon continuous emissions monitoring system (CEMS) data. A hypothesis is that autocorrelation exists in the time series of the emission and activity factors. Furthermore, cyclical patterns are hypothesized in the time series that, if present, may require special attention when developing hourly probabilistic emission inventories. The objectives of this paper are to: () quantify variability in hourly NO x emission and activity factors; (2) investigate the autocorrelation structure and evaluate cyclic effects at short and long scales of the time series of total hourly emissions; (3) compare emissions for the ozone season versus the entire year to identify seasonal differences, if any; and (4) evaluate inter-annual variability. DATA USED FOR ANALYSIS The analyses were conducted for 32 units of 9 coal-fired power plants located in the Charlotte, NC air quality modeling domain. Seven of these plants are located in North Carolina while the remaining are in South Carolina. The 32 units range from 4 to 25 MW in capacity as summarized in Table. Hourly CEMS data were available from the acid rain program of the US EPA for the years 995 and 998 for the capacity factor, emission factor, heat rate and total hourly emissions. These 32 units are baseloaded. The data were screened to remove outliers or relatively rare occurrences before proceeding with analyses. Infrequent values of capacity factor below.25 were inferred to be associated with startup or shutdown of the plant. These low capacity factors were typically associated with unrealistically large values of heat rate, sometimes ranging from 2, BTU/kWh to as much as 3, BTU/kWh. A judgment was made to exclude these data from analysis. Similarly, in work by others adjusted values of heat rate above 2, BTU/kWh were excluded in data quality checks since these values are outside of expected ranges. As an example of the typical characteristics of data for a given unit, the time series of hourly capacity factor is shown in Figure for Allen unit. There is a daily cycle of capacity factor, with a minimum value of approximately.4 at night and a maximum value of approximately.9 during the day. There are comparatively abrupt transitions during which the plant ramps up or down in load. This behavior was typical of all units. During continuous operation, all units operated at capacity factors in excess of.25. Therefore, data records with capacity factors of less than.25, representing startup or shutdown, were excluded from analysis. 2

3 Table. Summary of Database N Missing Data Points 998 Database 995 Database Total N N Data Points N N Data Points Used in Missing Data Points CF <.25 Analysis Data Points CF <.25 3 Total N Data Points Used in Analysis Capacity Unit (MW) Allen Allen Allen Allen Allen Buck Buck Buck Buck Buck Cliff Cliff Cliff Cliff Cliff Creek Creek Dan Dan Dan Lee Lee Lee Marshall Marshall Marshall Marshall Robinson River River River River * N = Number The database used for analysis is summarized in Table for both 995 and 998 CEMS data. For each unit and year, the total number of hourly data values available for analysis are given. Data were missing in some cases because data were not reported for one or more of the variables needed in order to calculate capacity factor, heat rate, emissions factor, or total emissions. The number of missing data values and the number of hours associated with operation with a capacity factor of.25 or less, are given. Typically, less than five percent of the total possible number of hourly records are associated with low capacity factors. The amount of missing data varies substantially among the units. METHODOLOGY In this section the methodology adopted to quantify the variability for heat rate, emission factor, capacity factor, and total emissions is presented. Also, the methodology to assess the autocorrelation structure and seasonality in the emission and capacity factors is discussed.

4 Hourly Capacity Factor Hour of Year Figure. Example of the Hourly Capacity Factor Time Series Pattern for Allen Unit Empirical Cumulative Distribution Functions Empirical cumulative probability distribution functions are often used to summarize data. 3 These functions provide a means for quantifying the relationship between fractiles and quantiles. A fractile is the fraction of values that are less than or equal to a specific value of a random variable while a quantile is the value of the random variable associated with a fractile. The term percentile is most commonly used instead of fractile. For empirically observed data, there are many possible methods for estimating fractiles from data. These methods are usually referred to as plotting positions. Of these, the Hazen method is commonly used: 2 Equation. i. 5 Fx ( xi ) = Pr(X < x i ) = n for i =,2,.n and x < x 2 < < x n Where: Pr(X < x i ) = probability of random variable X will have values less than that of sample x i, i = rank of each sample, n = number of data points. The 95% probability range was obtained by calculating the 2.5 th percentile and the 97.5 th percentile of the distribution. The quantiles associated with the 2.5 th and 97.5 th percentiles were used to calculate the percent difference relative to the mean. These differences were used to summarize the range of variability of each factor. Autocorrelation Structure The autocorrelation structure of data recorded in time is identified through the calculation of the autocorrelation coefficient (ρ k ). 3 The autocorrelation coefficient has a range between and and is equal to at lag. A lag refers to the value of the same variable at a specified number of previous time steps. The autocorrelation coefficient is defined as: Equation 2. ρ k = γ k / γ o 4

5 Where: ρ k = autocorrelation at lag k, γ k = autocovariance at lag k, γ o = autocovariance at lag (which is equal to the variance). The autocovariance γ k is estimated as: 4 Equation 3. γ k N k [( z µ )( z µ )] = ( z z)( z z) = E t t k t t+ N + t= k Where: γ k = autocovariance between z t and z t+k, z t and z t+k = observed values of z at times t and t+k respectively, k = time lag (when k =, the autocovariance is the same as the variance), µ = mean of time series. The autocorrelation values were obtained using the ARIMA procedure in SAS software for all units in the study scope. Seasonality A goal of this work is to identify periodic or cyclic components, if any, that explain a large portion of the variance in the time series. These components are also referred to as seasonality effects. Periodogram analysis is used to identify cyclical effects in a time series. 5 This type of analysis estimates the percentage of variance accounted for by each of the different cycles. A time series of length N, in terms of the number of time periods, can be exactly reproduced by summing N/2 sinusoidal waveforms with cycle lengths of N/, N/2, N/3, and so on, to a cycle length of N/(N/2), or simply 2. The model used to fit each cyclical component is a sinusoid model of the following form: Equation 4. Z t = µ + R cos(ωt + φ) + ε t Where: Z t = the observed value of Z at time t, µ = the mean of the time series, R = the amplitude of the waveform, φ = the phase angle, ω = the frequency in radians, which is 2π/τ where τ is the period or cycle length, and ε t = the residual term. The total sum of squares for the overall time series of length N is partitioned into N/2 sums of squares components each corresponding to one of the cycles. For example if the time series is composed of 24 observations, it can be reproduced by summing sinusoids of periods 24/, 24/2, 24/3,, 24/2. The frequency is the inverse of the period; therefore, the corresponding frequencies are /24, 2/24, 3/24,, /2. The overall variance can be divided into 24/2 different portions, each corresponding to one of the cycles mentioned above. Since the frequencies are equally spaced, they are orthogonal and hence independent of one another. 5 For each of the cyclic components, the amplitude and phase are calculated to fit a sinusoid for that frequency. The periodogram ordinate for each frequency is equal to 2R 2 /N. This ordinate represents the sum of squares (SS) accounted for by each cyclic component. The sum of these SS terms is equal to the overall SS of the time series. The SS are plotted on the y-axis versus the frequency on the x-axis. Large peaks that correspond to periodic components contributing to large portion of the variance can be identified. The periodogram values for all units in the study scope were estimated using the SPECTRA procedure in SAS software. 5

6 Cumulative Probability Allen- Creek Hourly Capacity Factor Figure 2. Empirical Cumulative Distribution Functions of Hourly Capacity Factor for Allen Unit and Belews Creek Unit RESULTS Unless otherwise mentioned, the analyses of the distributions of variables presented in this section focus on the data of the year 995. Similar results were obtained for the 998 data base. The comparison of the ozone season with the whole year data and assessment of inter-annual changes in variability in emissions are presented for both years. Empirical Distributions of Hourly Variability The diurnal pattern of the capacity factor was illustrated in Figure, as previously discussed. The empirical distribution of the hourly capacity factor for the same unit is given in Figure 2, with a comparison to data for Belews Creek unit. The distribution for Allen unit is multimodal. Approximately 3 percent of the capacity factor values are close to.38, which is indicative of night time operation at nearly constant load. The upper 3 percent of the distribution has capacity factors between approximately.9 and.95, indicative of nearly full load operation during the day. Belews Creek unit has a higher average capacity factor than that of Allen unit. For example, for Allen unit there is a 5 percent frequency of capacity factors greater than approximately.5, whereas for Belews Creek unit the corresponding frequency is nearly 8 percent. These two examples are representative of the range of results observed among all of the 32 units. An example time series of emission factors are shown in Figure 3 for Allen unit. Unlike the data shown for capacity factor in Figure, there is not a strong cyclic pattern. The empirical distribution of the hourly emission factor is shown in Figure 4 for both Allen unit and Belews Creek unit 2. The range of hourly variability in both cases was approximately.4 lb/ 6 BTU. Both distributions are slightly positively skewed, with skewness coefficients of.4 and.34, respectively. These almost symmetric distributions were typical of most of the units. Although there is a hint of multimodality for Allen unit, the Belews Creek unit 2 distribution appears to be a single component. Examples of the empirical distributions of heat rate are shown in Figure 5 for Allen unit and Lee unit 3. The former is slightly positively skewed, while the latter is approximately 6

7 Hourly Emission Factor (lb NOx / 6 BTU) Hour of Year Figure 3. Example of the Hourly Emission Factor Time Series Pattern for Allen Unit Cumulative Probability Allen- Creek Hourly Emission Factor (lb NO x / 6 BTU) Figure 4. Empirical Cumulative Distribution Functions of Hourly Emission Factor for Allen Unit and Belews Creek Unit Cumulative Probability Allen- Lee Hourly Heat Rate (BTU/kwh) Figure 5. Empirical Cumulative Distribution Functions of Hourly Heat Rate for Allen Unit and Lee Unit

8 Total Hourly Emissions (lb NOx / hr) Hour of Year Figure 6. Example of the Hourly Total Emissions Time Series Pattern for Allen Unit Cumulative Probability Marshall-4 Allen Total Hourly Emissions (lb NO x / hr) Figure 7. Empirical Cumulative Distribution Functions of Total Emissions for Marshall Unit 4 and Allen Unit symmetric. The range of values for Allen Unit is approximately 2, BTU/kWh versus more than 4, BTU/kWh for Lee unit 3. Four units had negative skewness with values between - and -3.7, 9 units had positive skewness with values between and 2.5, while all remaining units were approximately symmetric with skewness values between -.9 to +.8. Although heat rate had a weak 24 hour cycle, the cycle for heat rate was less pronounced than that of the capacity factor. Figure 6 illustrates a typical time series of total emissions for Allen unit. There is a cyclical diurnal pattern in the total hourly emissions time series. This pattern is similar to that for the capacity factor. Because only the capacity factor, and not the emissions factor or heat rate, displayed this type of strong regular pattern, the diurnal pattern in total emissions can be attributed primarily to the capacity factor. An example of the empirical distribution of hourly total emissions is given in Figure 7 for Allen unit and Marshall unit 4. The latter is a much larger unit that has a higher average emission 8

9 rate. The range of variability in hour emissions is approximately, lb/hour for Allen unit versus more than 4, lb/hr for Marshall unit 4. The shapes of the distributions are similar. For example, both distributions are approximately symmetric, and both distributions appear to have an inflection point near the 55 th percentile. Because periods of lower emissions are likely to be associated with smaller values of the capacity factor, the multimodal nature of these distributions can be attributed to differences in capacity factor representative of night versus daytime operation. The hourly variability ranges for 995 capacity factor, emission factor, heat rate and total hourly emissions are summarized in Table 2. The mean capacity factors ranged from.6 to.8 among the 32 units, which is consistent with baseload operation. Because the capacity factor has finite upper and lower bounds, the range of variability is not always symmetric with respect to the mean. For example, for units with average capacity factors of close to.8, the typical 95 percent range of variability was -6% to +25%. For units with average capacity factors of.6, the typical range of variability was approximately ±5%. The mean emission factors ranged from.44 to.32 lb NO x / 6 BTU among the 32 units, with 27 of the units having mean values between.5 and.7 lb/ 6 BTU. The 95% probability range for the hourly emission factor was as low as ±5% of the average value in some cases to as much as -36% to +65%, with a typical range of approximately ±2% to ±3% for most units. The mean hourly heat rate ranged from approximately 9, to 5,9 BTU/kWh among the units, with 2 of the units having average hourly heat rates between, and 3, BTU/kWh. The 95 percent range of variability in hourly heat rates was as low as ±5%, as high as -48% to +3%, and typically between ±5% to ±2%. The mean hourly total emissions varied from 233 to 2, lb/hour. Of course, these values depend upon the unit capacity as well as the capacity factor, emission factor, and heat rate. The relative range of variability in total emissions was as small as -42% to +3% and as large as -77% to +74% of the mean value. Temporal Patterns in Hourly Variability The temporal pattern of hourly variability in emissions was investigated with respect to the following: () is the range of variability a function of the time of day?; (2) is variability different among days of the week?; and (3) are there seasonal patterns? The variability in emissions differs among different hours of the day. To illustrate this, examples were selected for Belews Creek units and 2 and Marshall units, 2, 3, and 4. These two plants have the largest emission rates among the nine plants in the selected modeling domain. Figure 8 shows the mean emission rate versus time of day and Figure 9 shows the coefficient of variation versus time of day. The coefficient of variation is the standard deviation divided by the mean. For both Belews Creek units, the mean emissions are highest and approximately constant from 8 am to 8 pm. There is a similar pattern for the Marshall units but the relative difference in emissions between daytime and nighttime is less pronounced. All of the units have a similar pattern with regard to the coefficient of variation versus time. The largest values of the coefficient of variation are associated with the lowest emissions. However, even during the 9

10 Table 2. Hourly Capacity Factor, Emission Factor, Heat Rate and Total Emissions Variability for the Year 995 Capacity Factor 2.5 % Diff 97.5 % Diff Emission Factor Heat Rate Total Emissions % % Mean % % Mean % Diff Diff HR Diff Diff TE Diff Unit Mean CF Mean EF Allen Allen Allen Allen Allen Buck Buck Buck Buck Buck Cliff Cliff Cliff Cliff Cliff Creek Creek Dan Dan Dan Lee Lee Lee Marshall Marshall Marshall Marshall Robinson River River River River * CF = hourly capacity factor, EF = hourly emission factor in lb NO x / 6 BTU, HR = heat rate in BTU/kwh, TE = total hourly emissions in lb/hr, 2.5 pr. = 2.5 percentile, 97.5 per. = 97.5 percentile, %Diff = relative percent difference from mean. daytime period of highest emissions, the coefficients of variation range from approximately.2 to.3. Thus, the range in emissions for a given hour of the day is substantial when comparing different days. The means and standard deviations of total hourly emissions were compared for all days of the year versus weekdays only for all units for the year 998. The means and standard deviations differed by only ±3.5% and ±2.5%, respectively, for most units. This indicates that data for weekends are not substantially different from other days of the week. This is expected since these units are baseloaded and therefore are dispatched similarly all days of the week, unlike peaking units % Diff

11 6 Mean Emissions (lb NOx / hr) Creek- Creek-2 Marshall- Marshall-2 Marshall-3 Marshall Hour of Day Figure 8. Diurnal Variation in Mean Emissions for Belews Creek and Marshall Plants Coeff. of Variation Hour of Day Creek- Creek-2 Marshall- Marshall-2 Marshall-3 Marshall-4 Figure 9. Coefficient of Variation for Hours of the Day for Belews Creek and Marshall Plants In order to evaluate whether emissions are different for the ozone season, which is inclusive of summer months, versus the entire year, data recorded for the hourly total emissions were compared for these two time periods for years 995 and 998. The results are given in Table 3. For 995, the difference in the mean unit emissions between the two time periods was less than ±5% difference for 26 units and was within ±% for the other 6 units. For 998, the mean emissions of 28 units were within ±5% for the two time periods and 4 units had differences of less than ±%. Thus, the mean emissions for the ozone season are judged to be similar to that for the entire year. For 995, the coefficients of variation of hour total emissions for the two time periods were within ±5% for 25 of the units and within ±% for 5 of the units. Two units had a difference of -7% and -25%. For 998 the coefficients of variation of the two time periods agreed to within ±6% for 26 units and within ±5% for 5 units. One unit had values that differed by -9%. Thus, for the majority of units, there was strong or good agreement in the variability of emissions when comparing the two time periods. Therefore, a judgment was made that there is not a substantial difference in emissions for the ozone season compared to an annual basis for these baseloaded units.

12 Unit Abdel-Aziz, A. and H.C. Frey, Quantification of Hourly Variability in Hourly Activity and NO x Emissions for Baseload Coal- Table 3. Comparison of Whole Year Data Versus Ozone Season Data for Total Emissions Mean Ann. TE (lb/hr) 995 Mean O.S. TE (lb/hr) 995 %Diff Mean Ann. Vs. O.S %Diff Coef. %Diff Var. Mean Coef. Coef. Ann. Mean Mean Ann. Var. Var. Vs. Ann. O.S. Vs. Ann. O.S. O.S. TE TE. O.S Coef. Var. Ann. 998 Coef. Var. O.S. 998 %Diff Ceof. Var. Ann. Vs. O.S. 998 Mean Ratio S.D. Ratio Allen Allen Allen Allen Allen Buck Buck Buck Buck Buck Cliff Cliff Cliff Cliff Cliff Creek Creek Dan Dan Dan Lee Lee Lee Marshall Marshall Marshall Marshall Robinson River River River River *Ann. = Annual, TE=Total Hourly Emissions, Coef. Var. = coefficient of variation, O.S. = Ozone Season, %Diff = Percent difference. Inter-Annual Variability In order to assess changes in the mean and variability of hourly emissions over time, a comparison was done for the means and standard deviations for 998 versus 995. The ratio of the 998 mean to that of the 995 mean was calculated for each unit. The same was done for the standard deviations. These results are presented in Table 2. The ratio of mean emissions for 998 versus 995 ranged from.53 to.2. Nine units had ratios of less than.7, had ratios between.7 and.8, 5 had ratios between.8 and.9, and the remaining 8 had ratios between.9 and.2. These latter units most likely had little or no 2

13 retrofitting of emissions controls, while the former units likely had varying degrees of retrofitted controls such as overfire air and low NO x burners. The ratios of the 998 to 995 standard deviations ranged from.3 to.46. For 6 of the units, the ratios of the standard deviations were between.75 and.25. Fourteen units had ratios less than this, and only two had ratios greater than this. While there is a weak linear relationship between the ratios of the standard deviations with respect to the ratios of the means, the R 2 of the linear relationship is only.9. Therefore, it is not clearly the case that a reduction in mean emissions is associated with a reduction in the range of variability in emissions. For example, for units with mean ratios of less than.8, the standard deviation ratios ranged from.3 to.4. For units with mean ratios greater than.8, the standard deviation ratios ranged from.58 to.46. The average mean ratio was.8 and the average standard deviation ratio was.82. This implies that the overall change in variability is comparable to the overall change in means, even though there is a considerable range of results among the units. Autocorrelation and Seasonality A check was done for autocorrelation as shown in Figure for 24 time lags. The highest autocorrelation value was.9 for lag. Autocorrelations of less than approximately ±.5 are deemed not to be statistically significant. The 95% confidence interval for zero autocorrelation is shown in figure. Thus, statistically significant autocorrelations were identified especially for lags to 8 and 7 to 24. However, it is also the case that the highest autocorrelations are for lags to 3 and 23 to 24. The fact that emissions in the current hour depend on emissions not only in recent hours but also emissions from approximately one day earlier are suggestive of a daily cycle. The daily cycle was confirmed by peridogram analysis as given in Figure. The results imply that the 24 hour cycle contributes most to the variance of the time series. The autocorrelation and cyclical pattern shown here were typical for all units. CONCLUSIONS Hourly variability in heat rate, emission factor, capacity factor, and total emissions was quantified for each of 32 units of 9 coal-fired power plants in the Charlotte, NC airshed. The range of variability was substantial, most notably for total emissions, with typical 95 percent ranges of hourly variability over all hours of the year in excess of ±4%. The total emissions has a strong 24 hour cycle, as is expected for baseloaded units. The daily cycle in total emissions is attributed primarily to the similar pattern observed for the capacity factor. The emission factor does not have a substantial cyclic effect in comparison to that of the capacity factor. The mean emissions and the coefficient of variation for different hours of the day were found to be a function of time of day. Typical ranges of the coefficient of variation for hourly emissions were from.2 to.3 during the daytime and as much as.45 during the night. A coefficient of variation of.3 implies that the 95 percent range of emissions value is approximately ±6 percent of the mean value. This is a substantial range of uncertainty when making estimates of future emissions under similar operating conditions as represented by the historical data. 3

14 Autocorrelation Autocorrelation 95% C.I. 3 Time Lag Figure. Autocorrelation of Total Emissions for Unit of Allen Power Plant 995 Periodogram. (lb/hr) 2.E+7.E+7 8.E+6 6.E+6 4.E+6 2.E+6.E Period Figure. Periodogram of Total Emissions for Unit of Allen Power Plant 999. Although there is clearly a 24 hour cycle, little difference was found when comparing weekend emissions with the entire week or when comparing the ozone season with the entire year. While such differences are hypothesized to be more substantial for peaking units, it is not surprising that no substantial differences were found for these baseload units. There were substantial differences in the mean and standard deviation of emissions when comparing 995 and 998 data, which is indicative of the effect of retrofits of control technology during the intervening time. On average a reduction in mean emissions is weakly associated with a reduction in the standard deviation in emissions; however, there is substantial inter-unit variability regarding how the standard deviation changes from one year to another as a result of control measures. The implication of these results for air quality modeling is substantial. Although it is increasingly possible to simply look up CEMS data for use when estimating emissions for recent past air quality episodes, a key challenge remains regarding how to estimate emissions for future episodes, whether for next week or several years from now. The historical record of CEMS data provides information regarding the possible range of values that might be encountered for a similar time of day, day of the week, and time of year in the future. The statistical analysis here

15 reveals that there is substantial variability regarding what emissions are for a given unit at a given hour of the day, and that for these units there is no substantial effect of day of week or time of year. The latter also implies that ambient temperature, which does vary during the year, has a negligible effect regarding total emissions for the units included in the database. Furthermore, there is a strong autocorrelation effect that should be accounted for in estimating uncertainty in emissions for the multiple hourly time steps that are needed to model an air quality episode. Based upon the findings of this work, we recommend more detailed development of time series models for quantification of variability in hourly emissions, taking into account intra-unit dependence in terms of autocorrelations. The possibility of inter-unit dependence and methods for addressing it should also be explored. Furthermore, the implications of uncertainty in the utility NO x inventory for near term future episodes should be explored based upon uncertainty analysis with an air quality model. These areas are the subject of ongoing research. ACKNOWLEDGMENTS Although the research described in this paper has been funded wholly or in part by the U.S. Environmental Protection Agency under Science to Achieve Results (STAR) Grant No. R826766, this paper has not been subject to any EPA review. Therefore, this paper does not necessarily reflect the views of the Agency, and no official endorsement should be inferred. ABOUT THE AUTHORS Amr Abdel-Aziz conducted this work while a Ph.D. student and graduate research assistant in the Department of Civil Engineering at North Carolina State University. H. Christopher Frey is an associate professor of civil engineering at NCSU, Campus Box 798, Raleigh, NC Dr. Frey is the corresponding author. KEY WORDS Variability, Uncertainty, Emissions, Emission Inventories, Emission Factors, Activity Factors, Monte Carlo simulation, Time Series, Nitrogen Oxides REFERENCES. Placet, M., Mann, C.O., Gilbert, R.O. and Niefer, M.J. (999). Emissions of Ozone Precursors from Stationary Sources: A Critical Review, Atmospheric Environment, 34: Frey, H. C., Zheng, J. (22), Quantification of Variability and Uncertainty in Air Pollutant Emission Inventories: Method and Case Study for Utility NO x Emissions, Journal of Air and Waste Management Association, 52: Cullen, A.C., and Frey, H.C. (999). Probabilistic Techniques in Exposure Assessment: A Handbook for Dealing with Variability and Uncertainty in Models and Inputs. Plenum Press: New York. 4. Frey, H.C., and Bammi, S. (22), "Quantification of Variability and Uncertainty in Lawn and Garden Equipment NO x and Total Hydrocarbon Emission Factors," Journal of the Air & Waste Management Association, 52(4):

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