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Appendix 2: Selected Pages from the NPS-WHITEX Report Pagei CHAPTER 1 Overview (1-1) 48 Background (1-1) 48 Study Plan (1-3) 50 Interrelationships Between Aerosol, Optical, and Visibility Apportionment (1-7) 54 Measurement Program (1-7) . 54 Report Outline (1-12) 59 References- (1-13) 60 CHAPTER 9 Introduction (9-1) 63 Climatology of the Area (9-23 64 Light Extinction Budget (9-3) 65 Attribution of Regional Sulfur and Visibility Impairment (9-3) 65 Emissions Analysis (9-4) 66 Trajectory and Streakline Analysis (9-5) 67 Spatial and Temporal Trends in Ambient Concentrations (9-6) 68 Deterministic Wind Field Modeling (9-7) 69 Tracer Mass Balance Regression (TMBR) Analysis (9-7) 69 Differential Mass Balance (DMB) Analysis (9-9) 71 NP~WHITEX page numbers are shown in parentheses. 45

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46 APPENDIX 2 Attribution of Visibility Synthesis (9 9) 71 (9-10) 72 OTHER PERTINENT HPS-WHITEX REPORT PAGES CD4 Tracer Injection (3-2) 75 Sample Collection (3-2) 75 Figure 4.15: CD4 concentrations (ppt) at eight WHITED receptor sites (~20) 76 Table 4.5: Statistical summary of elemental sulfur concentrations (1lg/m5) during the WHITEX study period Table 4.6: Statistical summary of CD4 (ppt) at eight receptor sites using fully scaled CD4 at Page and Hopi Figure 5.4: Time traces of optical data and relative humidity at Hopi Point Figure 5.22: Measured and reconstructed 12-hour averaged extinction coefficients (Km~~) and the fraction due to each component at Hopi Point Table 6.1: Regional emissions in units of tons/day from coal-fired power plants, copper smelters, and large urban areas (4-29) 77 (~29) 77 (5-11) 78 (5-42) 79 (6-1) 80 - Figure 6.10: Calculated gas-phase SO2 omdation rates as a function of time of day and season (6-20) 81 Table 6.10: Estimated age of the Navajo Generating Station plume fin hours) at various locations in the WHITEX study region, January-February 1987 Table 6.43: Time history of measured total sulfur (,ug/m3), NGS total sulfur (pg/m3) and fraction of ambient total sulfur due to NGS based on DMB analysis for Hopi Point Figure 6.71: Time plot of predicted upper limit of NGS contribution to total sulfur at Hopi Point (540 x SCD4) and measured total sulfur Chemical Mass Balance with Unique Tracer (6-33) 82 (6-110) 84 (6-124) (6-124) 85 85 APPENDIX 6B Overview (6B-1) 86 Model Equations (6B-1) 86 Model Calculations and Uncertainties (6B-4) 89 ModelAssumptions (6B-6) 91

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~~ ~~ ~~ ~ ~7 Potential D^a[10= Tom ^ss~p[lons of Nonco~t~t Rc~es610n CoeGdonts e MOB Todd ~~ Gas Model Outputs ., (6B-6) (6B-6) (6B-~ (6B-8) ~1 91 ~3

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48 APPENDIX 2 Chapter 1 INTRODUCTION THE DESIGN AND IMPLEMENTATION OF THE WINTER HAZE INTENSIVE TRACER EXPERIMENT- ~THITEX 1.1 Overview Protection of vistas for certain national parks and wilderness areas as provided by the Clean Air Act Amendments of 1977~ has stimulated an interest in visibility research. Methods are being developed and used to characterize atmospheric transparency, to identify the relative importance of the various particulate and gaseous atmospheric materials and to determine the role of man- made emissions. Much of the research has been conducted in the desert Southwest, in particular in northern Arizona and southern Utah. The juxtaposition of energy resources (especially coal) and national parks (including Grand Canyon, Bryce Canyon and Canyonlands) in an area where small changes in aerosol concentration can significantly affect visibility justifies concern by government and private organizations for visibility impacts resulting from industrial emissions. Figure 1.1 is an emission density map showing locations of major SOz sources and national parks on the Colorado Plateau. Accordingly, a cooperative effort, the Subregional Cooperative Electric Utility (comprised of the Electric Power Research Institute, Southern California Edison and the Salt River Project), National Park Service (NPS), Environmental Protection Agency (EPA) and Department of Defense (DOD)) Study, SCENES, is centered in this area. It operates on a five-year plan (1984-1989) involving continual visibility and aerosol measurements at a dozen locations, plus more in-depth intensive and special studies conducted over shorter, seasonally representative periods. One of these, the Winter Haze Intensive Tracer Experiment (WHITEX) was conducted in January and February 1987 in the Colorado River area of the Colorado Plateau. 1.2 Background The Colorado Plateau, with its many associated class I national park areas, was chosen as the location to implement a scoping study designed to evaluate the ability of a variety of receptor modeling approaches to attribute visibility impairment in a number of class I areas to emissions from a single point source, the Navajo Generating Station. The area, shown in Figure 1.3, is by most standards remote, undeveloped and sparsely populated. The nearest large urban areas are over 300 km away. Only a few smaller urban areas or towns are within the area; these include Moab, Utah, Page, Arizona and at the most western end of the study area, Las Vegas, Nevada.

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EXCERPTS FROM NPS-WNITEX 49 \ 1 \ ~ U e g ~ 5 -O i 1 \ ~ e ~ ~ O J ~ v ` L o s ~ n g e I e s \ ~ " ,.~ | ~ ~ Power an~ I L g ~ s ~ _ . ~ 1 S ~ l t L ~ k e Ci tg ~P 0 ~ ~ r pl an t 14 ~ ~ a j 0 Phoen i x S ~ ~ I t e P 0 ~ e ~pl an t e. s ~ P 0 ~ e r t 1 a n t s Po ne r p I ~ n t s ~_ 1 P ~ s o Figure 1.1: Approximate SOz emissions from major point sources and urban areas in the southwest United States for 1987.

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50 APPENDIX 2 ., There are a few small industrial enterprises in the vicinity such as sawmills, mining and milling Operations and a number of large coal fired electric generating facilities, one of which is the Navajo Generating Station (NGS) located near Page, Arizona. The Navajo Generation Station is a large (2300 MWe) coal-fired power plant without sulfur dioxide control equipment; thus, it is a significant single contributor of sulfur speciessulfur dioxide (S02) and sulfate particles (5O4-)to the atmosphere of the region. With the control and shutdown of several smelters in the western U.S., NGS has become the largest single S02 emission source in the West.2 The terrain surrounding the lower Colorado River rises to about 800 meters above the water's surface. Wintertime meteorology in the area is characterized by several periods of stagnation, of about one week each. Air pollutants can be trapped by a persistent thermal inversion below the height of the surrounding terrain during the stagnation periods, resulting in a distinct visible surface haze layer. These stagnant periods are interrupted by synoptic-scale fronts with associated strong winds sweeping rapidly through the area.3 The winter haze over the Colorado Plateau area has been routinely documented with photographs since 1978 by the EPA, NPS and BLSI (Bureau of I`and Management). The haze is usually seen as a bright white layer with a distinct upper edge and it occasionally includes one or more perceptible layers.3 4 A number of earlier investigations have been prompted by the need to determine the origins of the haze. NPS sponsored several modeling efforts to evaluate the possibility that the Navajo Generating Station is partially responsible for the haze.5, 6 A wind field model was adapted for the area's terrain and winter meteorology to investigate transport and diffusion. In a separate study, ambient nitrogen chemistry was theoretically simulated to estimate the role of particulate nitrates.7 Though both efforts added to the knowledge of the source of the haze, the uncertainties in modeling this situation led to approaching the question with observational studies. A SCENES special study was previously conducted in 1986 at Glen Canyon to provide informa- tion to aid in planning subsequent observations.8 The primary objectives of this exploratory study were to determine the horizontal and vertical extent of the haze and to identify major constituents of the haze. Aircraft-based measurements confirmed the haze to be more extensive horizontally than just the Glen Canyon area (e.g., extending at least to Bryce and Grand Canyon to the west). This greater horizontal extent enlarges the number of possible emission sources to be considered. This complicates the source attribution because the contribution of any one source may vary con- sideraHy with time and location within the haze. In mapping the vertical extent of the haze with an instrumented aircraft, the air above the inversion layer was found to be essentially particle-free, while below the layer, scattering coefficients varied from two to five times clean air values. Sam- pling at the south end of the lake only, the particles were found to be composed largely of sulfates and organics. Nitrates were found to be primarily gaseous, with about a tenth of the total being particulate nitrate. 1.3 Study Plan Shortly after the completion of the winter 1986 study, the SCENES participants began planning a more comprehensive effort for the winter of 1987 to address persistent questions about the nature and sources of winter haze conditions. The overall study objective was to assess the feasibility of attributing emissions from a single point source to visibility impairment in prespecified geographic regions. Specifically, various receptor and deterministic models were to be evaluated and inter- compared as to their ability to link Navajo Generating Station emissions to visibility impairment at Grand Canyon and Canyonlands National Park and Glen Canyon National Recreation Area. Meeting this objective is a three tier process. First the relative contribution at the receptor site

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EXCERPTS FROM NPS-WHITEX 51 of primary and secondary aerosols associated with the NGS must to be achieved. Secondly, the contribution of these aerosol species to atmospheric optical variables needs to be established, and finally the contribution of optical variables associated with power plant emissions to an incremental decrease in visibility below that which would have existed otherwise needs to be examined. The major focus of the WHITEX study is centered around the evaluation of receptor oriented approaches for linking NGS emissions to aerosol concentrations in Grand Canyon and Canyonlands National Parks and Glen Canyon National Recreation Area. In a receptor type model the atmo- sphere is treated as a black box through which source emissions are transferred to the receptor site. Source receptor relationships are empirically developed using statistical inference techniques. Historically, the chemical mass balance (CMB) formalism has been most often used to link source emissions to aerosol concentrations at a receptor site. The CMB approach essentially uses ratios of trace material associated with different sources in combination with trace material measured at the receptor site to apportion primary (nonconverting) aerosol species. However, CMB has serious short comings in that it is not designed to apportion secondary aerosols, such as ammonium sulfate, to its SO2 source. Other common types of receptor models include principal component analysis (PCA) and multiple linear regression (MLR). Explanations of these models are given by Watson,9 Chow,~ and Hopke.~i Furthermore, Dzubay et al., Lewis and Stevens,~3 and Stevens and Jewish have integrated a number of these approaches into a hybrid receptor model that can be used to apportion secondary aerosols. All these models can be shown to be special cases of a deterministic statement, referred to in this report as the general mass balance model (GMB), of how gases and aerosols are transported and transformed as they pass through the atmosphere. The GMB model is discussed in detail in Appendix 6A. In this report a regressional model, derivable from the GMB equations and referred to as the tracer mass balance regression (TMBR) model, will be used to apportion secondary aerosol species. A full derivation of TMBR can be found in Appendix 6B. TMBR is formulated to apportion sec- ondary aerosols if certain assumptions are met. First, a unique trace material must be associated with a source or group of sources and secondly the atmospheric transfer processes must be ap- proximated be a linear model. If a unique tracer is not available CMB can be used to apportion non-unique tracer species to source types and the analysis can still be carried out. TMBR essen- tially relies on relative changes in secondary aerosol and tracer concentrations over time to yield the desired apportionment. Finally, a differential mass balance model (DAB) having elements of both deterministic and receptor modeling approaches will be used to apportion secondary aerosols. The term differential is derived from the use of unique trace material spatial concentration gradients to calculate atmo- spheric dispersion. Atmospheric deposition, chemical conversion and transport time are calculated from first principles. A full derivation of the DMB model can be found in Appendix 6C. Table 1.1 outlines the different approaches as well as summarizes the major advantages and disadvantages of each technique. For the sake of completeness, advantages and disadvantages of deterministic modeling are also included in Table 1.1. Several less quantitative approaches are also used to gain insight into basic physio-chemical processes at work over the time period for which apportionment estimations are carried out. These include evaluation of the relative emission strengths, plume trajectory and streakline analysis, spatial and temporal trends, analysis of synoptic meteorological conditions, and deterministic wind field modeling on the mesoscale level (<200 km). The focus of attributing NGS emissions to optical variables will be directed toward the re- lationship between various attributed aerosol species and optical extinction. Since a change in atmospheric transmittance (extinction) under a variety of conditions has been shown to be a good approximation to the change in the atmospheric modulation transfer function.~5 The optical ex-

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52 APPENDIX 2 o ._ ~d o U3 ~o cd ~d .ca CO ~ C td ~ ~ ~C _, ~ ~o ~ ~o C oo o C) ._ _ ~V u, c ~ 3 ._ ~ ~ _. e ._ Z C ct: a U~ Z C ,.~,. .\ - C ;~ Ct C C~ (; C: O ~ ~ . ~ -_ E 8~ o ~ ~ I., ~ _ a' ~ C ~ rd ~ ~ O o o td ~ ~ ~ ~ ~ ~ e ~ 0 ._ ~ _ _ _ C C V Ce ~ O O O ~ ~ .0 ~ V ~ ~ ~ C, y Y. Y ~ O O ,o ~ ~ ~ ~ = = _ o _ ee ~ ed CL ~ ~. 47 ~ E. .> ~ ~ ~ ~ 8-V ~ 8~ ~ o o o ~, C C C ~ C .~ `,, ~ ~ ~ ~ ~ ,o Y _ y ~ , ~ ~ ~ ~ ~ E ~ o c _ o ~ ~ X ~ ~.= g E == o ~ ~ o _ C o c.o ~ E o C g C C ~ o ._ . 0 :~ _. ~ :- ~ _. o bO ~ C O C C ~-- 4} Lc E 13 o cE ~c ,- c ~ = E C ~ 5 46 ~ C ~ ~ E C c = _ ~ = 0 ~ a-- ~ ~ 0 ~ ~ _ `', m 0 = c~ 8 :~ _ . ~ ~ ~ .~ ~ C .o ~ 8 = ~ ~ = ~ ~ , U, o E o v -, E E .= =4 E c ~ c _ e V ~o ~ ~ _ ~o ~ ._ ._ 5 ~; . 3 5 0 E _.= ~ 0 ~ ~ ~ ._ 0 ~ ~ ~ ~ c 0 ~ ~ 0 " 00 5 ~ ~ ~ O ~ K ro 0 o. . o _ ,C ~) td 4, ~ .., . ;> Ct ~ ~ ~ O ~ C _ ._ O ~ ~ ~ O ~ a: ~ _ {c ~ O c~ E .)o = ,. C,, _ ~ 4~ u: 46 ~ ~ ~ ~ ' _ ~ E i6 . ~ ~ ~ ~c o.= 46 ~ ~ ~ ~ ^,c ._ _ O ~ ~ c ~ ~ . ~ 0 ~-. C ~ ~ ~ Cl o ~ ~ E 0=

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EXCERPTS FROM NPS-WHITEX 53 tinction associated with particles can be calculated using Mie theory if the particle characteristics are well documented. The size distribution, shape, density and refractive index of the particles are needed for such a calculation. This information is generally either unavailable or available with insufficient detail, so that Mie theory must rely upon a number of assumptions. Mass size distribu- tion data can be obtained using size segregating samplers, however, the capability of such samplers to correctly represent the particulate nitrate or the labile fraction of organic carbon is questionable. For instance, the mass of the most common labile component, water, is not accounted for. A second approach for attributing aerosol species to extinction is a statistical methodology that relies on multilinear regression (MLR) analysis where it is assumed that the relationships between atmospheric extinction, ban, and aerosol species mass concentrations, m', are represented by bar: = Hi OCR for page 45
54 APPENDIX 2 1.4 Interrelationships Between Aerosol, Optical and Visibility Apportionment The interrelationship between measurements and apportionment methodologies as designed for the WHITEX program are schematically represented in Figure 1.2. For purposes of understanding the relative accuracy of the various receptor modeling approaches, the study was designed to calculate aerosol and optical apportionment in at least two separate ways. In this way, a relative accuracy of each technique can be estimated. For instance, measurement of be:' and aerosol composition are combined in an MER model to apportion extinction to aerosol species. An independent analysis using a literature review of theoretically derived extinction efficiencies allows for an independent estimation of extinction apportionment. The two estimations can then be intercompared, and dif- ferences, if any, reconciled. Similarly, tracer (CD4) released over time can be used in a TMBR analysis to apportion sulfur and nitrate aerosols to NGS emissions, while DMB analysis will yield an independent estimation of NGS emission contribution to secondary aerosols at the receptor site. The NGS sulfate and nitrate contribution to total particulate matter at the receptor sites is then combined with the extinction apportionment analysis to yield the extinction that can be attributed to NGS. The two techniques can then be intercompared and differences, if any, reconciled. Fi- nally, the extinction apportionment data can be combined with information from radiative transfer calculations and radiance measurement program to apportion visibility impairment. 1-.5 Measurement Program The measurement program consisted of four different types of ground station configurations and one airborne platform. The configurations are classified as major receptor, satellite, gradient, and background sites. Table 1.3 summarizes the variable measured, the methodology used to collect the data and the frequency at which the measurement was made while Table 1.2 summarizes the function of each monitoring site. Figure 1.3 shows the location of each monitoring site. Major receptor (Type A) sites had all those measurements required for aerosol, extinction, and visibility impairment attribution while satellite sites consisted only of trace element, wind speed, and wind direction measurements. Satellite sites were used to characterize air masses flowing into and out!of the study region and were used to explore temporal and spatial trends. At gradient and background sites b,Ca', fine mass, ions, carbon, trace elements, and tracer concentrations and meteorological variables were measured. Gradient sites were also used to examine spatial and temporal trends while the background site helped characterize air masses on a regional scale. A full description of how each parameter was measured is discussed in chapter three. Therefor only a brief description of the measurements will be presented here. Atmospheric extinction was measured with a newly developed long path transmissometer.20 Atmospheric scattering was mea- sured with MRI 1550 integrating nephelometers which were zeroed with clean air every few hours and span calibrated twice during the course of the study.22 Haze, contrast, and Mom, can be calcu- lated from reconstructed radiance fields derived from slides taken during the course of the study.23 The color slides were taken using automatic photographic monitoring instrumentation comprised of 35 mm cameras using 135 mm lenses and loaded with Kodachrome 25 color slide film. Particulate measurements were made by the IMPROVE sampler24 at nine sites and by the stacked filter unit25 (SFU) at three additional sites. At three of the twelve sites, the size-classifying isokinetic sequential aerosol sampler26 (SCISAS) collected fine and total (smaller than 15 ,um samples on four filters. The SCISAS sampler was used primarily to establish the relative accuracy and precision of the various sampling systems.

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EXCERPTS FROM NPS-WHITEX _ BENT 1 _ ST^T~S7~C^L , EXT#`JCTlON EF~IC'El~CY 1 ILL CO - WTIaN | Ll7ER^T~L IVES | L ~ 1 11 Ll I t~^T~E EXT'NCTtON E~ IClENCY . arm tar 1 Else . -~! Inch ..- l EXT'~CT'O eL~ \ / J~ , ~ ~ ~ ~~ ~ ~ _ 1= , , ~ _~r ~ ~ ~ 1 1 SON *~0 "T - C DECO C~7~41 MTF AT RE=PTOtR 55 _ homer Figure 1.2: Flow diagram showing the relationship between measurement and apportionment of risibility impairment.

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84 APPENDIX 2 Table 6.43: Time history of measured total sulfur (pg/m3), NGS total sulfur (pg/m3) and fraction of ambient total sulfur due to NGS based on DMB analysis for Hopi Point. Ambient Julian S Day Concent Total Measured 5 Uncertainties NGS due to due to S K's Measmt Concent NGS Contribution to S Uncertainties due to due to K's Measmt Fraction Due to GIGS Uncertainties Ratio due to due to K's Measmt 13.8 0.25 0.04 0.04 1.40 0.47 0.18 5.63 1.90 1.28 14.3 1.50 0.11 0.11 3.31 1.12 0.31 2.21 0.75 0.24 14.8 0.71 0.05 0.05 0.66 0.38 0.11 0.93 0.53 0.17 15.3 0.38 0.05 0.05 1.39 0.44 0.13 3.65 1.16 0.66 15.8 0.33 0.04 0.04 0.76 0.38 0.28 2.34 1.18 0.93 16.2 0.59 0.04 0.04 0.77 0.42 0.11 1.30 0.71 0.20 16.7 0.78 0.05 0.05 0.57 0.37 0.04 0.72 0.47 0.06 17.2 0.57 0.04 0.04 0.57 0.47 0.17 1.01 0.83 0.32 17.7 0.34 0.04 0.04 0.40 0.37 0.14 1.20 1.11 0.47 18.2 0.20 0.04 0.04 1.23 0.42 0.24 6.19 2.12 1.90 32.2 0.08 0.03 0.03 0.06 0.10 0.01 0.78 1.26 0.76 32.7 0.07 0.03 0.03 0.22 0.17 0.09 2.90 2.23 2.52 33.2 0.09 0.03 0.03 0.05 0.10 0.01 0.57 1.10 0.38 33.7 0.12 0.03 0.03 0.15 0.16 0.10 1.24 1.36 0.89 34.2 1.01 0.06 0.06 0.09 0.11 0.02 0.09 0.11 0.02 34.7 0.50 0.04 0.04 0.12 0.06 0.09 0.24 0.11 0.19 35.2 4.42 0.33 0.33 0.59 0.29 0.10 0.13 0.06 0.03 35.7 0.61 0.05 0.05 1.24 0.39 0.29 2.05 0.64 0.53 36.2 0.91 0.07 0.07 0.16 0.23 0.01 0.17 0.26 0.02 36.7 1.33 0.10 0.10 1.66 0.57 0.46 1.25 0.43 0.36 37.2 0.75 0.06 0.06 1.08 0.37 0.11 1.43 0.49 0.19 37.7 0.71 0.06 0.06 0.72 0.24 0.13 1.02 0.35 0.22 38.2 0.55 0.05 0.05 0.24 0.31 0.02 0.43 0.56 0.06 38.7 0.24 0.03 0.03 0.26 0.24 0.07 1.10 0.98 0.35 39.2 ~ 0.34 0.04 0.04 0.11 0.11 0.07 0.31 0.31 0.22 39.7 0.55 0.04 0.04 0.19 0.07 0.24 0.35 0.12 0.43 40.2 0.79 0.06 0.06 0.10 0.07 0.04 0.13 0.09 0.06 40.7 0.65 0.05 0.05 0.10 0.06 0.08 0.16 0.08 0.13 41.2 0.49 0.04 0.04 0.20 0.06 0.14 0.42 0.13 0.30 41.7 0.27 0.04 0.04 0.69 0.21 0.41 2.60 0.78 1.67 42.2 0.54 0.04 0.04 0.93 0.39 0.14 1.71 0.71 0.29 42.7 0.46 0.04 0.04 0.98 0.29 0.33 2.12 0.63 0.79 43.2 0.40 0.04 0.04 1.22 0.38 0.12 3.05 0.96 0.41 43.7 0.25 0.04 0.04 0.46 0.27 0.21 1.79 1.06 0.90 44.2 0.16 0.03 0.03 0.02 0.01 0.03 0.12 0.09 0.21 44.7 0.15 0.03 0.03 0.17 0.10 0.05 1.14 0.70 0.50

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fi.800 2.900(L 5.800(T 2. 900Q 0.000a EXCERPTS FROM NPS-WHITEX 85 Hopi Point 0.000Q'' ~ ~ I I I ~ I I I t t t t I I I t I I I t I I I I I I I I t I ~ ~ t I t 1~1 1 I~ t t I I I I Meedurea Total. Sulfur . . . : ~ : : . ~ ~ _ ~ _ ~ - I t ~ ~ ~ l I I I ~ , ~ I I ~ I I I I ,, I, I `,, I',, , ~ ., . L ~ ~ t 10 13 116 ~19t 132 25 28 3~1 44 :47 40 43 46 49 TIME(JULIAN DAY) Figure 6.71: Time plot of predicted upper limit of NGS contribution to total sulfur at Hopi Point (540 x SCD4) and measured total sulfur. . When additional source profile development has been completed, the CMB analyses should be repeated at these two sites and at the remaining WHITEX core and gradient sampling sites. Chemical Mass Balance with Unique Tracer When there is a unique tracer associated with a source and when ratios of tracer to other emissions are known, Equation 6.9 can be used to estimate the upper limit of contributions to ambient aerosol species. For instance, ambient concentrations of total sulfur associated with NGS emissions can be calculated using ST,a = IST/CD4]P X CD4,a (6.9) where the subscripts a and p refer to ambient and in-plume concentrations and ST = (SO2/2 + SO4/3) is the total sulfur. For purposes of this study ambient CD4 concentrations were scaled to an equivalent ST/CD. in-plume ratio of 540 ~g/m3ppt. Thus ST'a = t540]SCD4,a (6.10) can be used to estimate the upper bounds of NGS contributions at any site for which there are ambient CD4 data. Figure 6.71 is a time plot of predicted and measured total sulfur as a function of time at Hopi Point. In almost all cases the upper limit of the NGS contribution is considerably greater than that which was measured. The average upper limit of total sulfur calculated using Equation 6.10 is 1.58 d: 0.08 ~g/m3 while the average measured total sulfur at Hopi Point is 0.61 0.01 ~g/m3. The upper limit is approximately 3 times higher than the ambient levels. A similar plot for Page is shown in Figure 6.72 where the average upper limit of the NGS contribution is 3.16 ~ 0.15 ~g/m3 while the average measured total sulfur is 1.75 :E 0.04 ~g/m3. The mean upper limit at Page is nearly 2 times higher than the mean measured total sulfur.

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86 ~ APPENDS 2 APPENDIX 6B: Tracer Mass Balance I\Iode! Regression (T>fBR) Itio(lel and Tracer Mass Balance (TAB) Lioclel Overview The Tracer Mass Balance Regression Model is a multiple regression based model which may be used to apportion an aerosol species of interest measured at a receptor site to the various contributing sources. It has been shown to be a special case of the General Mass Balance (GMB) Model. The actual regression analysis may be performed using the method of least squares. However, since the independent variables in this model are ambient concentrations of various aerosol components which are measured levity error? the method of Orthogonal Distance Regression (ODR) is expected to give better estimates of else source contributions. A detailed discussion of the method of ODR may be found in the boor; by Fuller(1987). Model Equations The basic equation for TLIBR model equation is: . where: h Cik = yo + ~ Ink u=1 (1) Cik = concentration of species i at the receptor for time period k^. In the current application i refers to Sulfate Sulfur or S02 sulfur. Ciuk = concentration of trace element iu which serves as a tracer for a group of ogle or more sources, for time period h. Aid = regression coefficient for trace element in ~vl~icl~ acts as a tracer for a group of one or more sources. Do = intercept representing the mean background concentrations of tl~e species of interest, at the receptor.

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EXCERPTS FROM NPS-WHITEX 87 = number of groups of sources, each group being represented by a particular aerosol species which acts as a tracer for that group of sources. (ok = a factor which is a function of field measurements, sampling period and possibly source type, chosen in such a way that the ~ coefficients in the model (1) are invariant with respect to the sampling period. The model is known as the tracer mass balance (TMB) model when only a single trace element is used as a tracer for a particular source and all the remaining sources are accounted for by the intercept term in the model. When several trace elements are used in addition to the tracer for the distinguished source of interest, then the model is referred to as tracer mass balance regression (TMBR) model. The simplest versions of the TMBR model and the TMB model use Wok = 1 for all time periods and source groups. In the current application we have used Wok = 1 as weD as Auk = RHk where RHk is the relative humidity at the receptor during sampling period k. The use of RlIk as a linear factor in the above model was motivated by the following consider- ations. In apportioning a secondary aerosol, the constant ,Biu~k derived from the GLIB model had the form pi jk = ~ C2 jk riUjk CiUjk with and (2) 4, ~c(i*,i'L') r,. = Y It c(i*, j, k) + K~(i*, j, k-) - Iid(i, j,k) {exp(-Xd(i, j, k)tjk) - exp(-[Ac(i*, j, k) + Ite(~*, j, ~')]tjk)} (3) riUjk = exp((Itc(iu~i, k^) + It`(it,, j, (^))tjk) (4) If the species in does not convert and its deposition rate is the same as that of the secondary aerosol species i being apportioned, then . riujk = exp(-K`(i, j,k)t't) so that the ratio r;jk/riujk reduces to KC(i*, j, k)tjk after using the approximation exp(~) ~ 1 + ~ (when x is sufficiently small). Recall that the full infinite series expansion for exp(~) is given by exp(~) = 1 + ~ + 2! + 3! (5) (6) and we have used a first order approximation in (6). It is possible to use hillier order approximations of e~p(~) in these derivations but this is not pursued here.

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88 APPENDIX2 Assuming that KC(i*, j, k) is proportional to RHk with proportionality constant B. we obtain that the ratio r;jk/riujk is equal to BtjkRHk which gives IrkBtjkRHi j - Defining Mink = piUk/uk (a) where Ilk = RHk and assuming that disk are constant for an sampling periods rather than the quantities .uk suggests the use of RHk as a linear factor in the T)IBR model equation (1). For purposes of attributing total sulfur or sulfate sulfur to NGS, SCD4 is a unique NGS tracer. Furthermore, As was found to be below the detectible limit in samples gathered from within the NGS pluem (refer to Table ??. Therefore, As is considered to be a unique tracer for emissions other than NGS and most probably associated with copper smelter emissions. Therefore, in actual application of the TLIBR model to WHITEX data, we have grouped the sources into 3 categories: (7) NGS with CD4 serving as the tracer Sources with Arsenic (As) serving as a tracer, and, all remaining sources, if any. - In the application of the TMB model, there are only two categories, viz, NGS with CD4 as a tracer and all remaining sources. The TMBR Model equations used in the application are: h Ck = To + ~ ~i~ci~k~uk u=1 where: C,` = concentration of sulfate sulfur or total sulfur for time period k Ci,,k = concentration of trace element in for time period k yin = regression coefficient associated with trace element is (9) ,0 = intercept representing the mean background concentration of the species being apportioned, due to all sources not accounted for explicitly. Auk = RHk, the relative humidity at the receptor during sampling period k, or 1, depending on the particular application. All of the cases considered may be written in the form 2 Ck = To + ~ hijack u=1 where: (10) I

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EXCERPTS FROM NPS-WNITE:X 89 AUk = concentration of trace element in for time period k or concentration of trace element i', multiplied by RHk- The model is known as the tracer mass balance (TAB) model when the only trace element used is CD4 or scaled CD4 (SCD4). When other trace elements are used in addition to CD4 then the model is referred to as tracer mass balance regression (TAlBR) model. Multiplication by RlI, when included, is a surrogate for the RH dependent oxidation rate of S02 to S04. Model Calculations and Uncertainties The concentrations CUk of sulfate sulfur or total sulfur associated with each trace element in for each time period are calculated by multiplying the measured values of AUk for each trace element by the respective regression coefficients as follows. Cok would just be the intercept representing the contribution from all sources not explicitly accounted for by any of the reference species used in the TMBR model. CUk = Mu X Auk The uncertainties for each of these concentrations are calculated by: aCU': = N/AUkC~,u + 72'UaAUk + arid aAuk (11) ( 12) The quantities ~Au,, are part of the ~7HITEX data base. The quantities yi', are obtained as outputs from the regression packages that were used. Errors in AUk and the estimated regression coefficients have been assumed to be uncorrelated. The total calculated sulfur Ck for each time period is the sum of the CUk'S summed over all the reference aerosol species in and the intercept. h Ck = Co + it, Cuk u=1 (13) The uncertainty associated with the total calculated sulfur concentration for each time period h ACE = ~ Deco + ~ ~Cuk u=1 (14) assuming the covariance terms arising in the derivation are negligible. The sources assumed to be associated with each trace element are: CD4 or SCD4 - Navajo Generating Station (N'GS) Selenium (Se) - All power plants including NGS Arsenic (As) - Copper smelters

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90 APPENDIX 2 Intercept- Mean background concentration The estimated fraction of sulfur from each source for any given time period is equal to the sulfur associated with the trace element divided by the total calculated sulfur concentration: FUk = k ( 1 5 ) Ok The uncertainty for each of these fractions is: aFUk = i c2 ac C4 k (16) The mean fraction Fu of the sulfur attributed to each source is estimated by the mean sulfur concentration Cu for that source divided by the mean total calculated sulfur C. r ~ flu r _ an r v where l and and ( 17) 1 ~ = ~ Cork k=1 ( 18) C = ~ Ck (19) k=1 The uncertainties for Cu and C are calculated by: ecu = .. '`I ~ aC,\ ... aC = I, ~ ~ aC k=l The uncertainties associated with the mean fractions are calculated by ARC -W c2 C4 (20) (21) (22) The uncertainty formulas are all derived using propagation of error methods and assuming the covariances between various terms occurring in the derivation are negligible.

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EXCERPTS FROM NPS-WHITE:X 91 Model Assumptions. The regression coefficients, including the intercept term, in the model have been assumed to be time independent. The aerosol species used in the model are assumed to be tracers for nono~erlapping groups of sources. In particular, none of the species other than the tracer associated with the source of interest can be emitted by that source unless there is an independent method such as CMB modeling to partition the ambient species concentrations into components attributable to the various groups of sources. Potential Deviations from Assumptions. It is highly unlil;ely that the regression coefficients are constant for all sampling periods. This will inflate the uncertainty in the final apportionments but the extent to which this inflation occurs will depend on how variable the regression coefficients are. eve investigate below the possible effects of nonconstant regression coefficients in the TAB model. A similar instigation may be carried out for the more general T\IBR model but the derivations are rather cumbersome and details are omitted here. For reasons of convenience, the notation in the subsequent subsection is entirely independent of the rest of the appendix but this need not cause any confusion. Effect of nonconstant regression coefficients in the TMB model. Suppose y' = pollutant concentration at the receptor at time t. z, = concentration of tracer at the receptor at time t. u'' = pollutant concentration at the receptor attributable to the source under study. z' _ pollutant concentration at the receptor attributable to other sources. Then We define so that Y' = wt + z`. me = ut`|~t y'= m`~+z~ t23) (24) (25) It may be desirable to account for the fact that the actual measurements of {y`), {x`) involve measurement errors. Suppose the observed quantities are {id), {X'] Allege Y' = y' + St Xt = =t + Et, (26) (S`), (E`) being the independent set of measurement errors with means equal to O and lanolin standard deviations equal to aS, aE, respectively. An estimate of the a`,erage contribution of the

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92 APPENDIX 2 pollutant by the source under study is given by _ NGS = ~x, (27) where l] is the slope of a structural regression line fit obtained by regressing (Y'3 on {X'}, while the estimated average fractional contribution, f, of the source to the receptor, for the duration of the study, is (28) We now investigate how the estimated average pollutant concentrations due to NGS can differ from the actual value for the time period in question. In the following discussion, a quantity such as ,6{y, x) will refer to the slope of the least squares line fitted to ((y`, z') I t = 1, ..., n), with {y`) as observations on a dependent variable and {Gil as observations on an independent variable. A quantity such as x will represent 1 Ad=' x' and ~2 will represent L ~~=~ ~2 ~ _ r )2. The true average contribution of the pollutant from NGS to the receptor site is u' = -God. The estimated average contribution is ,Bx, where l] is the slope of the regression line fitted to the data ((Y`,X`) I t _ 1,...,n). At first we will consider else situation when ,l3 is Else least squares estimate in which case we write pts. It is easily verified that = ELSE W = (z Jr Eat, 2) ~ p{Z, A} + p{S, A} + {I, E} ~ A{Z, E} + A'{S, E}) _ W 1 + 24{E, x} + ~ (29) where ~ = aE/a2 and /` is the difference between the estimated average NGS contribution and the true average FIGS contribution. It seems reasonable to assume that the quantities E, HIS, by, {w, E), (z, E), {S, E), '{E, ~) (3o) are all nearly zero because we expect measurement errors Ed averaged over n time periods to be nearly zero and because we expect measurement errors to be uncorrelated with the true values x, z and w. To this degree of approximation, ~ ~ x{, a}w + z'{z, x)tow 1 + ~ (31) If,5 is the estimate obtained using structural regression (or Orthogonal Distance Regression (ODR)), denoted by pODR, ``e ~ ould obtain /\ ~ (I, x) - w) + Waltz, x} (32) since TODD ~ pr5(1 + a), where ~ is the difference between estimated and actual average NGS contribution during the time period under study.

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EXCERPTS FROM NPS-WHITE:X 93 The quantity :z,l~{w, z} - ~ is zero if we/ is constant and will differ from zero if the least squares line fitted to the points {(u'`, at) I t = 1, ..., n} has a nonzero intercept. On the other hand, the quantity ,B{z,x) is zero or nonzero depending on whether the least squares line fitted to Else points {(z`,~) I t = 1,..., n}hasazeroslopeornot,i.e.,whetheror not zig end x' are "correlated". Ideally, if there was a constant background pollutant concentration zig _ z and if the tracer release was directly proportional to emissions, and emissions revere conservative, so that m'ale, lee would have ~ ~ O and the reported estimated average NGS contribution should be a reliable estimate of the actual value for the time period in question. Model Inputs. The model requires the following quantities as inputs: The ambient concentrations of the aerosol species being apportioned, which is S04 in our application. The ambient concentrations of the reference or tracer species, CD4 and As. Relative humidity at the receptor for each of the sampling periods, when jUk = RHk is used in the model rather than jUk = 1. The uncertainties in else above quantities, when ODR is used to estimate the ~ coefficients, rather than OLS. Model Outputs. The model outputs include: Estimates of the actual amount of the contribution and the fractional contribution of the aerosol species of interest by the source or source type of interest to the receptor, along with the associated uncertainty estimates. Estimates of the average amount and the average fractional amount of the aerosol species of interest contributed by each source or source type of interest along with the associated uncertainty estimates.

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