Application of the Pseudo-Deterministic Receptor Model to Resolve Power Plant Influences on Air Quality in Pittsburgh

A multivariate pseudo-deterministic receptor model was applied to determine emission and ambient source contributions rates of SO₂ and elements from four small coal-fired boilers influencing air quality at the Carnegie Mellon University (CMU) Supersite. The model was applied to ambient SO₂ and particle measurements, the latter, made every 30-min for 10 elements (Al, As, Cr, Cu, Fe, Mn, Ni, Pb, Se, and Zn) during a 12.5-h period on April 1, when winds blew from between 290–330° in which the four coal boilers are situated. Agreement between predicted and observed SO₂ concentrations was excellent (r of 0.92; and their ratio, 1.09 ± 0.22) when 4 emission sources were used in the model. Average ratios of predicted and observed concentrations for As, Cr, Cu, Ni, Pb, Se, and Zn varied from 0.97 ± 0.20 for Cr to 1.07 ± 0.44 for As. Performance indices for these elements were all well within acceptable ranges. Emission rate ratios of various metal species to Se predicted are similar for the three of the coal boilers, but differed substantially for the fourth, as expected for a boiler with minimal particle control technology. All are within the range derived from previous PDRM results and in-stack measurements (except Al) at 7 Eastern U.S. coal-fired power plants. The results suggest that the PDRM approach is applicable to a city encompassing complex topography and may successfully be applied using commonly available meteorological data.

INTRODUCTION

Source apportionment, that is quantitative determination of the contributions of pollutants from their sources to ambient atmospheric levels, is necessary for developing emission control strategies that effectively reduce exposures and health risks, and prevent degradation of air quality (Gordon 1988). Source apportionment may be accomplished with either source- or receptor-based models, however, applications of the former are often limited because of the lack of emission rate data. In the latter, source contributions are determined using observations at sampling sites. Until recently, most of the data obtained for receptor modeling has been derived from samples collected over time scales far longer than those for changes in source strengths and important meteorological parameters, e.g., wind direction and mixing height. The accompanying homogenization of source signals by this practice severely reduces the resolving power achievable with factor analytical methods (Lioy et al. 1989). Hourly resolved elemental data were used to develop a source profile for motor vehicles in the Baltimore Harbor Tunnel (Ondov et al. 1982). At 2-h resolution, Rheingrover and Gordon (1988) demonstrated that plumes of stationary sources in St. Louis are readily observed as excursions in time series profiles of the concentrations of the various marker elements and that the excursions could be correlated with wind direction to identify sources. More recently, Kidwell and Ondov (2001, 2004) developed a system for measuring elemental constituents at 30-min intervals and were able to identify influences of individual sources at this improved resolution (Ondov et al. 2003). It is now well demonstrated that wind directions corresponding to concentration peaks are consistent with the locations of known sources when wind direction is relatively constant during the time required for plume transport. Additionally, information on source distances can be inferred from the width of their plumes (US EPA 1980).

To better exploit the directionality and plume dispersion information inherent in highly time-resolved ambient data, Yamartino (1982) proposed a mass-balance model, wherein ambient concentrations were expressed as the products of source emission and plume dilution rates derived deterministically using Gaussian plume dispersion equations for individual sources of SO₂. Cooper (1982) reported a similar approach to ambient aerosol particle mass data. However, these attempts met with limited success, owing largely due to the fundamental inaccuracies in the Gaussian plume model. More recently, Park et al. (2005) devised a multivariate pseudo-deterministic receptor model (PDRM), in which a Gaussian plume model is used to constrain the solutions to the basic mass-balance model, rather than applying it in a deterministic manner. Unlike traditional receptor models, the PDRM (as well as those by Yamartino 1982 and Cooper 1982) exploits knowledge of the number and locations of major stationary sources, source and transport wind directions and distances, stack gas emission parameters, and meteorological plume dispersion during sample collections. Furthermore, emission rates are predicted for specific, individual sources, rather than generic source categories. The PDRM was applied with good success to 30-min SO₂ and aerosol metals data collected at a site in Tampa, Florida, during a period of moderate winds and good mixing, using micrometeorological parameters derived from 10-Hz u, v, w measurements made at the site. The Tampa modeling domain is relatively flat, and encompassed 6 sources, including 4 utility power plants and 2 much smaller industrial sources, lying in a 90° sector at distances ranging from 15 to 41 km from the air monitoring site. Sulfur dioxide emission rates predicted by the model were in excellent agreement with emission rates derived from continuous emission monitors (CEMs) available for the 4 power plants and ambient concentration versus time profiles were well fit for both SO₂ and the major marker species (especially Se for coal-boilers and Ni for oil).

Herein, we describe the application of the PDRM to an otherwise similar data set collected in Pittsburgh, PA, an area characterized by rough Appalachian Mountain terrain, during the Pittsburgh Air Quality Study (PAQS), and for which only standard meteorological data were available.

EXPERIMENTAL DATA

Description of Measurement Site and Modeling Period

The sampling site (312.4 m ASL, Figure 1) was located in Schenley Park on the top of a hill adjacent to the Carnegie Mellon University campus, approximately 6 km east of downtown Pittsburgh. There are roughly two million people living in the Pittsburgh Metropolitan Statistical Area, and elderly people represent a significant fraction of the population. The area is located between the utilities and agricultural sources of the Midwest and the large urban centers of the East. The site is more than several hundred meters from any major source of air pollution, and roughly one kilometer of parkland exists between the site and the city in the predominant upwind direction (south and west). Sampling equipment was housed in a 33 m² air pollution monitoring station. Our modeling was performed on ambient data collected between 06:00 and 18:30 h on April 1, 2002, during which time wind angles (measured from true north) ranged from 290–330° and 30-min averaged wind speeds ranged from 2.5 to 5.2 m sec⁻¹ (Figure 2) with maximum ranges 5.0–8.2 m sec⁻¹. This sector contains two small-scale coal-fired boilers within 45 km from the site, which are used for supplying process steam, specifically, the Bellefield boiler plant and Pittsburgh brewing plant; and two industrial sources (Shenango coke works and Zinc Corp. Amer). Source-receptor distances and station angles (measured at Schenley Park from due North), and annual emissions data for PM_2.5 and SO₂ (NEI 1999 annual emission inventory data) are listed in Table 1. As indicated, the Bellefield boiler plant is located at an angle of 286° and 0.8 km away from the site. The Bellefield boiler plant provides steam heat to the hospital complex, museums and universities in the Oakland district of Pittsburgh, and burns bituminous/sub-bituminous coal to produce steam in an over- and under-feed stoker boiler with a cyclone separator to control particle emissions. The Pittsburgh brewing coal-fired boiler (station angle, 316°; distance, 3.4 km) uses bituminous/sub-bituminous coal in an overfeed stoker boiler to produce process steam. The Shenango coke works, located on Neville Island on the Ohio River (station angle of 297°; distance 13.0 km) operates a coke battery, a by-product facility, and a steam and power plant, and produces approximately 350,000 tons of blast furnace coke and related by-products a year. Zinc Corporation of America (ZCA) operates its multi-product zinc manufacturing plant. The ZCA is the largest zinc producer (zinc oxide, zinc metal, zinc dust) in the USA, and the plant site, powered by its own 110-MW power station, is located 41.9 km northwest of the site along the Ohio River and at an angle of 307°.

FIG. 1 Map of Pittsburg area showing CMU sampling site.

FIG. 2 Wind speed and direction during the modeling period on April 1, 2002.

TABLE 1 Emission information for stationary sources

Facility name	Control devices	Distance (km)	Station angle (deg)	PM2.5 (ton yr^−1)	SO2 (ton yr^−1)	Industry type	Category
Bellefield boiler plant	Cyclone	0.8	286	94	745	Steam supply	Coal fired steam
Pittsburgh brewing co.	—	3.4	316	9	106	Food, agricultural, and beer	Coal fired steam
Shenango Coke Works	Fabric filter	13.0	297	79	2450	Blast furnace and steel mill	Coke
Zinc Corp of America	—	41.9	307	678	8641	Coal-fired boiler/ industrial processes	Primary non-ferrous metals

Meteorological Measurements

Ten-minute averaged surface wind speed/direction, temperature, relative humidity, solar radiation, and pressure were recorded during the PAQS by Carnegie Mellon University (CMU). 30-min averages of the wind speed and direction measurements made during the study period on April 1, 2002 are shown in Figure 2. During the modeling period, the temperature and relative humidity ranged from 3.4–10.1°C and 34–93%, respectively, with moderate winds between 2.5–5.5 m/sec over a narrow range of wind directions (280–330°). On that day the mixing height remained almost constant (1960–2010 m) through the day because of the persistence of a strong inversion. Sunrise was at 6:03 eastern standard time (EST), and sunset was at 18:44 EST. Light precipitation (0.1 cm) was recorded across the study area between 02:00 and 05:00 h.

SO₂ and Elemental Measurements

SO ₂ Data

Ambient SO₂ mixing rations (ppb) were measured with a pulsed fluorescence analyzer (API 100A model) at 10-minute intervals during the study period. These were converted to μ g m⁻³ using ambient temperature and pressure data and used to construct 30-minute averages for use in the model. Examination of the SO₂ data reveals that six different excursions (04:30–06:00, 07:30, 09:00–11:00, 12:00–13:00, 14:00–15:30, and 17:00 h) were observed during the study period (see Figure 3). The highest 30-min average SO₂ concentration, 75.7 ppb (205.0 μ g m⁻³), was observed at 09:30 on April 1.

FIG. 3 Temporal profile of 30-min averaged SO₂ concentrations (a); and As and Se concentration profiles, and As/Se ratios (b).

PM_2.5 Sampling and Elemental Analyses

Approximately 800 ambient aerosol samples were collected continuously at 30-min intervals at the Pittsburgh CMU Supersite between March 31 and April 17, 2002 using the University of Maryland Semi-continuous Elements in Aerosol Sampler (SEAS). The SEAS employs a state-of-the art dynamic aerosol concentrator to extract particles as small as 80 nm after steam-injection and subsequent cooling to induce particles to grow to a size > 0.7 μ m. The resulting droplets are collected in a real impactor and then transferred to a fraction collector for storage in clean vials, every 30 min, providing 48 samples a day. Within 24 h of collection, the samples were capped and transferred to storage at CMU at −14°C. Detailed descriptions of the SEAS sampler have been presented elsewhere (Kidwell and Ondov 2001, 2004). A subset of these, including 28 of those collected for the April 1, 2002 study period were shipped to the University of Maryland at dry-ice temperature and analyzed in triplicate for 11 elements (Al, As, Cd, Cr, Cu, Fe, Mn, Ni, Pb, Se, and Zn) by simultaneous multielement Graphite Furnace Atomic Absorption Spectroscopy (GFAAS) with Zeeman background correction (SIMMA 6000, Perkin Elmar Corp., Danbury, CT) by methods developed by Pancras et al. (2005). The coefficient of variation for the three replicate measurements was < 7%, except for Ni, Al and Cr for which it was generally ≤10%. From 91 to 100% of all values measured were above their MDLs in samples comprising the study period. Except Ni (81%) and Cd (19%). Because Cd was at or below the detection limit in 81% of the samples, it could not be used in the model.

The PDRM is designed specifically to apportion contributions from stationary sources whose plumes induce excursions in concentrations above the background levels induced by dispersed and very distant sources. Therefore, background concentrations were evaluated as the concentrations of SO ₂ or metal species measured at intervals prior to the onset of an excursion and immediately after the excursion, and were subtracted prior to use in the PDRM. These were as follows: SO₂, 3.5 ppb; and metals in ng m⁻³, Al, 2.64; As, 0.66; Cr, 0.13; Cu, 2.71; Fe, 6.03; Mn, 0.52; Ni, 0.41; Pb, 1.36; Se, 0.64; and Zn, 4.24. Background-corrected concentrations for SO₂ and each of the 10 elemental particle constituents are shown in Figure 4.

FIG. 4 (a) PDRM-predicted and observed concentrations of modeled species. (b). PDRM-predicted and observed concentrations of modeled species.

Model Description

The basis of the model is a mass balance equation wherein the ambient contributions of each of the sources to each species are expressed as products of emission rates (ER _{i, j} , g s⁻¹) and meteorological dispersion factors (χ/Q _{j, t} , s m⁻³) appropriate for each sampling period, t, i.e.,

where [E _i ] _t are ambient concentrations of species of interest (i, in ng m⁻³) measured in sample, t, and ER _{i, j} s are emission rates of species, i, from j stationary sources and represent averages for the period during which the samples (time intervals) used in model were collected. To solve the model, χ/Q _{j, t} 's are calculated for each sampling interval using a simple Gaussian plume model,

where χ is the concentration (g m⁻³), Q is the continuous mass emission rate (g s⁻¹), and u is the transport speed (m s⁻¹) of the plume over its trajectory. Dispersion parameters, σ _y and σ _z , are the standard deviations of the concentration distributions in the lateral (y) and vertical (z) directions, and increase with downwind distance (x), from the source. h is the height of the plume centerline when it becomes essentially level, and is the sum of actual stack height (h _s ) and the plume rise (Δ h). The calculated plume rises for the Bellefield boiler plant, Pittsburgh brewing co., Shenango Coke Works, and Zinc Corp of America applied in the modeling study are 84, 53, 95, and 174 m, respectively. Gaussian plume models are commonly used to explain the dispersion of a species emitted from a point source and used because of their simplicity (US EPA 1980). In the plume model (Equation 2), the effects of gravitational settling and dry deposition on the ambient gases and particles are neglected, as are air pollutant removal by physical or chemical processes, and horizontal and vertical turbulence is assumed to be homogeneous. Mathematical expressions to calculate σ _y and σ _z , mean u, displacement (y) and h are described previously (Park et al. 2005; Seinfeld and Pandis 1998).

Equations (1) and (2) are solved, simultaneously, using a non-linear least squares solver (“lsqcurvefit”) in MATLAB (MathWorks, Inc., version 6.5). The MATLAB program provides a solution that minimizes an object function, FUN, which we define as follows,

to which we apply the constraint that:

where LB and UB are upper and lower bounds within which the solver is directed to find solutions. Setting up constraints is essential to the model because the number of solutions for a product of unknowns is infinite and the Gaussian plume model is inaccurate. Once configured, the constrained model was applied to estimate the emission rates of SO₂ and elemental constituents of primary particles. Solutions for (χ/Q) _{j, t} ^PDRM were constrained to the range 0.1–2.5, consistently, for all four sources. This choice was derived from information reported for an intentional tracer study (Ondov et al. 1992) conducted at a coal-fired power plant 20 km from an arc of samplers in Maryland, in which χ/Q's calculated with two different parameterizations of a Gaussian plume model differed by factors ranging from 5–10.

Input variables used in the hybrid receptor model are as follows; (1) 30-min ambient concentrations of SO₂, Al, As, Cr, Cu, Fe, Mn, Ni, Pb, Se, and Zn, (2) derived and measured meteorological parameters, as described below, (3) stack data (physical stack height, stack inside diameter, exit gas velocity, and exit gas temperature (see Table 2), and (4) station angles for the emission sources. Herein, the best fits were obtained with a four-source model.

TABLE 2 Stack information

Plant	Base Elevation (m ASL^1)	Height (m)	Inside diameter (m)	Exit temp (K)	Exit velocity (m s^−1)
Bellefield boiler plant	267.4	59.4^2	2.74	565.0	7.70
		77.7^3	3.35	426.5	5.90
Pittsburgh brewing co.	234.4	64.0	2.44	478.0	4.57
Shenango Coke Works	223.4	76.2	3.05	584.3	6.08
Zinc Corp of America	238.4	84.0^4	3.10	422.0	9.04
		121.9^5	5.40	365.0	12.00
Note: ^1 ASL means above sea level; ^2 Stack #1 spec of the Bellefield plant; ^3 stack #2 spec (used in the modeling study); ^4 stack spec of boiler plants; ^5 stack spec of primary non-ferrous metal production plant (used in the modeling study). Respective plume rises, for Bellefield, Pittsburgh Brewing Co., Shenango Coke, and Zinc Corp, were calculated to be 84, 53, 95, and 174 m during peak concentration periods.

Estimation of Micrometeorological Parameters

Horizontal and vertical dispersion parameters (σ _y and σ _z ) and atmospheric turbulence components were derived from micrometeorological parameters (i.e., friction velocity, u*; Monin-Obukhov length, L; and convective velocity scale, w*) via similarity theory as described previously (Park et al. 2005). Calculation of the micrometeorological parameters is described below as are atmospheric stability Class and mixing layer heights. Also, because 3-D sonic anemometer data were not available, sensible heat fluxes (H) and friction velocities (u*) were obtained from a 3-hourly, 80 km NCEP's EDAS dataset (http://www.arl.noaa.gov/ready/ametus.html) from which hourly data were then interpolated. Kleissl (2004) observed that values of u* and H deived from the 80 km NCEP's EDAS data corresponded fairly well to those derived from 3-D sonic anemometer measurements at the Baltimore Supersite.

Atmospheric Stability

Stability class was estimated based on Turner's method (1964), which considers the effects of solar altitude (a function of time of day and time of year), total cloud cover, and ceiling height. The net radiation index is related to the solar altitude and is determined from the procedure described by the US EPA (1999). Solar altitude can be determined from the Smithsonian Meteorological Tables (ref. 17). The solar altitude angle (α) is calculated as follows:

where L is local latitude (40.44°), δ is solar declination (List 1966), and h _s is hour angle, describing the difference between local solar time and solar noon. Accordingly, the atmospheric stability was estimated to be slightly unstable or neutral during the study period.

Mixing Layer Height (z)

Hourly mixing heights were determined from (1) morning and afternoon estimates of mixing heights; (2) the local standard time of sunrise and sunset; and (3) hourly estimates of stability. Morning and afternoon mixing height estimates are based on Holzworth's method (Holzworth 1972) using radio-sonde data from the Pittsburgh airport. The morning mixing height is estimated as the height above ground at which the dry adiabatic extension of the morning minimum surface temperature (i.e., between 02:00 and 06:00 local standard time) plus 5 intersects the vertical temperature profile observed at 12:00 GMT. A similar computation for the afternoon mixing height is made using the maximum surface temperature observed from 12:00 through 16:00 LST, except that the surface temperature is not adjusted. Hourly mixing heights are interpolated from these twice per day estimates, as described in the user's guide for the ISC dispersion model (19). The procedure uses the maximum mixing height (z _max) from the previous day (i − 1; March 31), the computation day (i; April 1) and the following day (i + 1; April 2) and the minimum mixing height (z _min) for days April 1 and 2. If the boundary layer was classified as stable in the hour before sunrise, the value for the minimum mixing height is used as the mixing heights between midnight and sunrise. Between sunrise and 14:00 LST, the interpolation is between z _min,i and z _max,i . For the period 14:00 LST and sunset, the value for z _max,i is used. During the hours between sunset and midnight under stable stability, the interpolation is between z _max,i at sunset and z _{min,i + 1} at midnight.

Monin-Obukhov Length (L) and Convective Velocity Scale (w*)

The Monin-Obukhov length (L), a stability parameter relating u* and H, was computed from the equation suggested by Venkatram (1996)

where ρ is the density of dry air (1.25 kg m⁻³), C _p is the specific heat capacity of air (1004 J kg⁻¹ · K⁻¹), T is ambient temperature (K), u* is the surface friction velocity (m s⁻¹), K is the von Karman constant (0.4), g is the acceleration due to gravity (9.81 m s⁻²), and H is the surface sensible heat flux (W m⁻²); the negative sign is used by convention to distinguish stable from unstable conditions.

Convective velocity scale (w*) is computed from the following definition (Wyngaard, 1988) as:

where z _i denotes mixing layer height (m).

RESULTS AND DISCUSSION

Ambient concentrations of SO₂, As, and Se are plotted in Figure 3. Herein, the model was solved for a set of 44 emission rates and 100 dispersion factors (χ/Q)^PDRM. The χ/Q, s predicted by both the PDRM and Gaussian plume model (Equation 2) for each of the four sources are plotted as a function of time of day in Figure 5. Predicted emission rates (averages for the study period) are listed in Table 3 and emission rate ratios (to Se) predicted for the four sources are listed in Table 4. Analogous ratios derived previously from application of the PDRM as well as those derived from in-stack measurements reported for coal-fired boilers/power plants in the Eastern U.S. are listed in Table 5. Average concentrations induced by each of the sources during the study period were calculated as the product of the predicted average ER _j s and (χ/Q)^PDRMs, and are expressed as percentages of total elemental concentrations observed for the study period in Table 6. Results of a sensitivity analysis to the choice of constraints applied to solutions for (χ/Q)^PDRM are shown in Figure 6. Last, Observed and predicted concentrations are compared in Figure 4, and model performance statistics are listed in Table 7.

FIG. 5 Calculated and PDRM-derived dispersion factor (χQ)j,t for each of 4 emission sources.

FIG. 6 Normalized SO₂ emission rates predicted as a function of the value of the base upper-bound constraint.

TABLE 3 Estimation of emission rates for SO₂ and metal species for each of 4 sources (units: g s⁻¹)

Species	Bellefield boiler plant	Pittsburgh brewing plant	Shenango Coke Works	Zinc Corp of America
SO2	48	176	123	176
Al	0.0336	0.0800	0.1203	0.1453
As	0.0012	0.0105	0.0046	0.0009
Cr	0.0006	0.0021	0.0017	0.0020
Cu	0.0007	0.0408	0.0402	0.0480
Fe	0.0365	0.0926	0.1610	0.1130
Mn	0.0038	0.0032	0.0038	0.0010
Ni	0.0016	0.0065	0.0062	0.0070
Pb	0.0010	0.0232	0.0236	0.0369
Se	0.0005	0.0119	0.0126	0.0184
Zn	0.0299	0.0554	0.0807	0.0633

TABLE 4 Emission rate ratios and regression statistics for ambient concentrations

			ER_ratio from modeling results^3
Species	Regression relationship CMU measurement site (ng/m^3)	r ^2	Bellefield boiler plant	Pittsburgh brew. plant	Shenango coke works	Zinc Corp America
SO2	SO2 ^1 = (11.2 ± 1.9)*** Se + (12 ± 13)	0.772	96.0^4	14.8^4	9.76^4	9.57^4
Al	Al = (3.0 ± 0.7)** Se + (23 ± 5)**	0.635	67.2	6.7	9.55	7.9
As	As = (0.99 ± 0.03)*** Se + (−1.1 ± 0.2)***	0.987	2.4	0.88	0.36	0.049
Cr	Cr = (0.14 ± 0.01)*** Se + (0.23 ± 0.07)*	0.944	1.2	0.18	0.13	0.11
Cu	Cu = (3.31 ± 0.16)*** Se + (0.35 ± 1.1)	0.973	1.4	3.4	3.2	2.6
Fe	Fe = (3.3 ± 0.8)** Se + (30 ± 5)***	0.655	73.0	7.8	12.8	6.1
Mn	Mn = (0.029 ± 0.033) Se + (1.9 ± 0.2)***	0.177	7.6	0.27	0.30	0.05
Ni	Ni = (0.48 ± 0.04)*** Se + (0.42 ± 0.26)	0.939	3.2	0.55	0.49	0.38
Pb	Pb = (2.2 ± 0.14)*** Se + (−0.8 ± 0.9)	0.956	2.0	1.95	1.87	2.00
Zn	Zn = (2.5 ± 0.5)*** Se + (15.0 ± 3.2)***	0.726	59.8	4.7	6.4	3.4
Note: * p < 0.01, ** p < 0.001; ***p < 0.0001
^1Unit is in μ g m^−3; ^2 r indicates correlation coefficient; ^3 ER_ratio means ratio of emission rate for each species to emission rate of Se; ^4indicates the ratio divided by 1000.

TABLE 5 Fine-particle metal: Se ratios reported for various Eastern coal-fired power plants with ESPs

						Ohio River Valley Power Plants (Baker et al. 1983) ^2
	Tampa Park et al. (2005) ^1	Chalk Pt, MD Gladney et al. (1976) ^2	Mt. Tom Kowalczyk et al. [1984] ^2	Dickerson, MD Small (1974) ^2	Eddystone, PA Olmez et al. (1988) ^2	“A”	“B”	“C”
SO2	79000
Al	30	970	635	147	568	726	402	2154
As	0.91	20	1.55	1.17	2.59	4.50	1.50	6.10
Cr	0.73	1.77	1.97	0.48	1.52	4.67	1.50	7.40
Cu	0.55		0.68	0.31	1.24	1.67	1.50	4.90
Fe	33	272	377	80	307	169	94	482
Mn	0.33	3.09	2.39	0.66	1.18	1.67	1.50	5.00
Ni	0.30	2.10	0.55		1.59	2.00	1.00	3.70
Pb	1.00	3.20	0.35		1.76	1.17		1.70
Zn	1.76	5.66		1.39	1.67	2.83	1.50	5.10

TABLE 6 Predicted contribution averages for the study period, % of measured concentration attributed to indicated source

Species	Bellefield boiler plant	Pittsburgh brewing plant	Shenango Coke Works	Zinc Corp of America
SO2, Zn, Cr, Ni, Al, Fe, As	6–10	70–80	11–19	0.2–3.4
Pb, Se	1.8	75	20	3.2
Cu	0.8	76	20	2.5
Mn	15	72	12	0.6

TABLE 7 Performance statistics between the observed and predicted concentrations for SO₂ (μ g m⁻³) and primary metals species

	Unit	SO2	Al	As	Cr	Cu	Fe	Mn	Ni	Pb	Se	Zn
Observed (avg)	ng m^−3	66.12	37.51	4.33	0.88	17.74	43.42	1.61	2.77	9.50	5.32	25.44
Predicted (avg)	ng m^−3	67.82	35.73	4.13	0.84	16.83	41.78	1.58	2.71	9.01	5.01	24.61
Ratio (avg ± 1 σ)	—	1.09 ± 0.22	0.96 ± 0.23	1.07 ± 0.44	0.97 ± 0.20	0.98 ± 0.18	0.98 ± 0.21	1.02 ± 0.34	1.03 ± 0.25	1.04 ± 0.40	0.97 ± 0.22	0.98 ± 0.16
MB	ng m^−3	−1.70	1.78	0.20	0.05	0.91	1.64	0.03	0.07	0.42	0.31	0.82
MNB	%	−8.8	3.8	−7.1	3.4	2.4	2.3	−1.7	−2.6	−4.3	3.3	2.2
RMSE	ng m^−3	16.6	10.3	0.9	0.2	2.9	9.2	0.5	0.5	1.6	1.0	4.5
NMSE	%	6.2	7.9	4.6	4.3	2.8	4.6	10.4	3.6	3.1	3.4	3.2
Fa2	%	100	100	90	100	100	100	100	100	95	100	100
CC	—	0.92	0.75	0.92	0.91	0.95	0.84	0.45	0.92	0.95	0.93	0.89
Note: MB: Mean bias (= ∑ i = 1 ^N(O i − P i )), MNB: Mean normalized bias (= ∑ i = 1 ^N ), RMSE: Root mean square error (= [∑ i = 1 ^N(O i − P i )^2]^1/2), NMSE: Normalized mean square error (= ), Fa2: fractions of the predictions within a factor of 2 of the observed values, and CC: Pierson's coefficient of correlation (r).

Dispersion Factors for Each of 4 Stationary Sources

As shown in Table 1, all four boilers were quite small, the largest being the 110 MW boiler at ZCA, 42 km from the site. Nevertheless, SO₂ concentrations observed at the CMU site during the study period were quite high, 20 to 80 ppb, during the periods of plume influence (see Figure 3). We attribute this to the proximity of the Bellefield and PBC boilers and the elevation of the CMU site which reduces distance between the ground and the plume centerlines. As shown in Figure 5, χ/Q maxima predicted by the Met model for these sources were large, i.e., ∼ 10⁻⁶ s m⁻³. The largest value predicted for the PBC corresponds to the study period maximum SO₂ (30-min average) of 80 ppb (205 μ g m⁻³), which occurred at 09:30 h.

As is evident from Figure 5, the χ/Q s, plumes of each of the sources are predicted to have influenced air at the site on multiple occasions, as winds shifted them towards and away from their station angles. On this basis, plumes from the Bellefield boiler plant (286°, 0.8 km distant), influenced the site between 10:30 and 13:30 h, and (χ/Q)^PDRMs for this source were in the range 0.05–0.32 × 10⁻⁶ s m⁻³. χ/Q's calculated with the meteorological model (Equation 2) were substantially less than those predicted by the PDRM, presumably due to the effects of buildings and roughness elements on the CMU campus which tend to increase dispersion, and our application of the larger of the two stack heights reported for this source, which also leads to greater dispersion estimates. Bellefield's SO₂ plume is predicted to have influenced the site between 10:30–12:00 h and again between 12:30–13:00 h and as indicated in Table 3, its average SO₂ emission rate was 48 g s⁻¹.

χ/Q's for the PBP (station angle, 316°; distance, 3.4 km) suggest that its plume was influential on five occasions (i.e., at 07:30, 09:30, 12:30, 14:30–15:30 and 17:00 h). Maximum predicted influence occurred at 09:30 h, which as mentioned above, precisely corresponds to the time at which the period maximum SO₂ concentration (195 μ g m⁻³, after background correction) was observed at the site. The predicted SO₂ emission rate average (176 g s⁻¹, Table 3) for this source is 3-fold larger than Bellefield's but its (χ/Q)^PDRMs (0.2–0.8 × 10⁻⁶ s m⁻³) were comparable to Bellefield's. Thus, its influence was greater than that of Bellefield. In contrast to the case for Bellefield, (χ/Q)^Met s for the PBP were less than those predicted by the PDRM. This is not surprising, given the uncertainties in the inputs to the plume model as well as its simplicity. This was also the case for the SCW (station angle 297°; distance 13.0 km).

The plumes from the SCW were predicted to influence the site at 07:00, 08:30, 10:30-12:00, 13:00–13:30, and 16:30 h, during which time (χ/Q)^PDRMs (0.10–0.20 × 10⁻⁶ s m⁻³) were ∼ 5-fold less than those for Bellefield and the predicted SO₂ emission rate average (123 g s⁻¹) is comparable to that predicted for the PBC. As also indicated in Figure 4, the plumes from ZCA (station angle, 307°; distance, 41.9 km), arrived at the measurement site at 07:00–08:30, 09:30, 15:30, and 16:30 h, during which time their (χ/Q)^PDRMs (0.13–0.31 × 10⁻⁷ s m⁻³ and nearly identical to their (χ/Q)^Mets were 10- to 100-fold smaller than maxima predicted for the other sources, while their average SO₂ emission rate was estimated to have been only 176 g s⁻¹, i.e., precisely that estimated for PBC. Consequently, their influence on the site during the study period was shown to be small. As indicated in Table 6, 70–80% of the ambient concentration excesses over background during the study period are predicted to have been induced the PBP, i.e., for all species listed. Despite its proximity, predicted contributions for Bellefield were < 10% for all species except Mn (15%); those for the SCW and ZCA were 11–20% and < 3.5%, respectively.

Performance Statistics

The overall performance of the model was evaluated for the observed and predicted SO₂ and metal concentrations using the following statistical measures (Hana 1988; Kumar et al. 1993; Patel and Kumar 1998) which they applied to modeling results for ambient SO₂ concentrations: mean bias (MB), mean normalized bias (MNB), root mean square error (RMSE), normalized mean square error (NMSE), correlation coefficients (CC), and the fraction of predicted concentrations lying within a factor of 2 (Fa2) (i.e., 0.5 ≤ C _pred/C _obs ≤ 2.0) of the measured ambient concentrations; all as defined in Table 7. According to Kumar et al. (1993), model performance is deemed acceptable if NMSE ≤ 0.5 (50%) and Fa2 ≥ 0.8 (80%).

For SO₂, the average ratio of the predicted and observed concentrations (P:O) was 1.09 ± 0.22. As indicated in Figure 5, the SO₂ concentration profile predicted by the 4-source model is in excellent agreement with the observed SO₂ concentrations except at 09:30 and between 3:30–16:00 hr. Underestimates (by 26%) occurred at 09:30 hr when the highest concentration was observed, whereas overestimates ranging from 23–64% were observed between 14:30–16:00 h, i.e., when the plume from PBC is predicted to have been its main source. During this period, the maxima in (χ/Q)^PDRM exceeded (χ/Q)^Met by 2, i.e., close to, but not in excess of the limiting factor of 2.5 imposed by our constraint (which, as indicated below, was the global optimum value). Nevertheless, the average observed SO₂ concentration (66 μ g m⁻³) is nearly identical to the predicted average (68 μ g m⁻³), and the MNB, which is sensitive to small observed concentrations, is only −8.8%. Additionally, RMSE and NMSE for SO₂ are 16.6 ng m⁻³ and 6.2%, respectively, and all predictions were within a factor of 2. All are within the acceptable ranges suggested by Kumar et al. (1993).

For those metals having temporal concentration profiles similar to that of SO₂, i.e., As, Cr, Cu, Ni, Pb, Se, and Zn, agreement between observed and predicted concentrations was excellent (see Figure 5 and Table 7). The average P:O ratio was 1.07 ± 0.44 (0.64∼ 2.33) for As, 0.97 ± 0.20 (0.65∼ 1.54) for Cr, 0.98 ± 0.18 (0.65∼ 1.54) for Cu, 1.03 ± 0.25 (0.73∼ 1.65) for Ni, 1.04 ± 0.40 (0.64∼ 2.65) for Pb, 0.97 ± 0.22 (0.64∼ 1.47) for Se, and 0.98 ± 0.16 (0.58∼ 1.26) for Zn, respectively. (Values in parentheses are uncertainties in the ratio expressed as 1 standard deviation.) The largest deviations (from 1) were mostly observed at times when their concentrations were very near background levels, e.g., at 11:30, 13:00, or 16:00 hr, and therefore, have small effects on the mean contributions predicted for the various sources. Residuals ranged from -1.8 to 1.9 ng m⁻³ (mean bias: 0.20 ng m⁻³, see Table 7) for As, from −0.3 to 0.5 ng m⁻³ (mean bias: 0.05 ng m⁻³) for Cr, from −5.5 to 6.8 ng m⁻³ (mean bias: 0.91 ng m⁻³) for Cu, from –0.5 to 1.3 ng m⁻³ (mean bias: 0.07 ng m⁻³) for Ni, from −2.8 to 4.4 ng m⁻³ (mean bias: 0.42 ng m⁻³) for Pb, from −1.8 to 2.2 ng m⁻³ (mean bias: 0.31 ng m⁻³) for Se, and from −8.4 to 8.3 ng m⁻³ (mean bias: 0.82 ng m⁻³) for Zn. As indicated in the Table 7, MNB ranged from −7.1% for As to 3.4% for Cr. The performance indices, NMSE and Fa2, are also quite reasonable for these elements described above, ranging from 4.6 and 90% for As to 3.4 and 100% for Se. The RMSE ranged from 0.9 ng m⁻³ for As to 4.5 for Zn.

Quite reasonable agreement also was observed for Al and Fe, even though their concentrations might be expected to be influenced by inopportune fluctuations in local dust concentrations. Indeed, Al (but not Fe) was severely under predicted (i.e., by nearly 2-fold) in one sample, i.e., at 14:30, possibly, due to this reason. Nonetheless, the average P:Os were 0.96 ± 0.23 (0.55∼ 1.39) and 0.98 ± 0.21 (0.60∼ 1.38) for Al and Fe, respectively, and their respective MNBs were only 3.8 and 2.3%. Clearly, both errors and performance indices (NMSE and Fa2) associated with the model predictions are all within the acceptable ranges.

Sensitivity to Constraints

A sensitivity analysis was performed by varying the upper bound of α _j (UB) from 1.0 to 5.0. Results are shown in Figure 6 wherein the P:O ratio for average SO₂ emission rates are plotted against UB. In this figure, the predicted emission rates are normalized to those calculated for the base UB constraint = 2.5. As shown in the Figure 6, there is little change in ratio of the observed and predicted SO₂ emission rates for UBs exceeding 2.5. Ratios for UB < 2.5 increased gradually, varying from 0.97–1.65 depending on the source. Quite similar behavior was observed in our Tampa study (Park et al., 2005). For these reasons, results reported herein are those obtained with UB = 2.5.

Comparison of emission profiles

Emission rates predicted for 9 elements from each of the 4 sources are also listed in Table 3. Unfortunately, neither SO₂ nor particle-borne elements measurements, against which these results could be substantiated, were available. Nevertheless, a test of “reasonableness” can be made by comparing the ratios of predicted concentrations (i.e., source profiles) with those reported for other coal-burning plants. Coal combustion is the largest source of SO₂ emissions in the Pittsburgh area. While there are numerous coal boilers and coking plants, there are no primary metal smelters in the modeling domain. Consequently, SO₂ and Se (a sulfur analog) are themselves, good indicators of coal or coke emissions. Moreover, ambient concentrations (uncorrected) of As and Se were highly correlated (r = 0.987, see Table 4), as were those of Pb, Ni, Cr, and Cu; and their regression equation intercepts were generally small or insignificant with respect to ambient concentrations, suggesting (1) great similarity in the sources of particles affecting air quality at different times of the day and (2) little influence from non-modeled sources.

Moreover, the As/Se ratio is reported to be approximately 1 in air sheds influenced by coal combustion and has been used to distinguish between the influences of coal combustion and other anthropogenic sources (Olmez et al., 1998). Six SO₂ excursions are evident in Figure 3 (i.e., at 04:30–05:30, 07:30, 09:30, 12:30, 14:30–15:30, and 17:00 h) and each corresponds to excursions in Se and As. As shown in Figure 3(b), Se (As) concentrations ranged from 4.4–11.4 ng m⁻³ (3.4–9.7 ng m⁻³) between 04:30-10:00 h and from 2.4–8.9 ng m⁻³ (1.5–8.3 ng m⁻³) between 14:30–17:30 h, and were substantially elevated over their regional background concentrations. During these periods, As/Se ratios were between 0.8–0.9 (04:30–10:00 h), and 0.63–0.94 (14:30–17:30 h), i.e., in reasonable agreement with a coal combustion source. For periods when impacts of As, Se, and SO₂ were minimal, the As/Se ratio was < 0.4, i.e., substantially different, as could be expected during times when air was more affected by a more diverse mixture of sources.

Comparison of entries in Table 4 and Table 5 shows that our PDRM-derived ratios are well within the ranges reported for other Eastern U.S. coal-fired boilers (Gladney 1974; Gladney et al. 1976; Baker et al. 1983; Kowalczyk 1984; Olmez et al. 1988; Park et al. 2005), especially PDRM-derived ratios for a coal-fired power plant in Tampa. Such ratios depend on the composition of coal, boiler and exhaust gas residence times and temperatures, and on the type and efficiency of emission control devices (Ondov et al. 1979). Relative to bulk ash composition and its major/minor constituents (Si, Al, and Fe), concentrations of Se, As, Ni, Pb, and Zn become enriched in submicrometer coal-combustion particles as a result of differences in volatility and the physics of nucleated condensation (Ondov and Biermann 1980) and these tend to be less efficiently removed by electrostatic precipitators (ESP), further contributing to the “enrichments” observed for emitted particles. Lower enrichments are observed for boilers with inefficient particle control devices, as a greater proportion of larger, less-enriched, particles are emitted. Thus, it is not surprising that Fe/Se and Al/Se ratios attributed to Bellefield, a plant equipped only with a cyclone, are ∼ 10 times those attributed to the other Pittsburgh boilers. Such differences are emphasized by normalizing to Se. This is because substantial fractions of Se are present in the gas phase at flue gas temperatures (typically these are in excess of 100°C). The gaseous Se is not removed by ESPs, but condenses on particles upon cooling after release into the atmosphere (Ondov et al., 1989), and thus leading to smaller element:Se ratios for boilers with highly efficient ESPs. Despite the potential for much variability, some ratios are remarkably consistent in emitted fine particles (see Table 5 footnotes), most notably those for Pb, Zn, Cu, and As. The good agreement for this substantial number of components of the PDRM-derived profiles is reassuring.

CONCLUDING REMARKS

Unlike factor analysis and chemical mass balance models, the hybrid multivariate receptor model used in this study, directly utilizes the numbers and locations of known sources, their geographic relation to the receptor site, and wind direction during sampling, in a Gaussian filter to reduce unwanted contributions. Furthermore, results for individual sources are obtained. These encompass emission rates of primary pollutants from specific sources, meteorological dispersion factors (χ/Q s) for each source, and the ambient concentrations induced at the receptor site by the modeled sources. Emission rates determined for individual sources the can be readily tested against in-stack measurements. In this study we have obtained highly credible results using ambient concentration data for only 25–30-min measurement periods and commonly available meteorological data, for a modeling domain encompassing complex terrain. The performance measures reported suggest that the PDRM, coupled with highly time-resolved ambient measurements, might be used as a tool to monitor emission rates of SO₂ and estimate emission rates of toxic and other non-criteria pollutants without expensive in-stack monitoring.

This work was funded in part by United States Environmental Protection Agency under contract R82806101 as part of the Pittsburgh Air Quality Study (PAQS), and in part by the United States Environmental Protection Agency through grant/cooperative agreement (BSS R82806301) to the University of Maryland, College Park (UMCP). Nevertheless it has not been subjected to the Agency's required peer and policy review and therefore does not necessarily reflect the views of the Agency and no official endorsement should be inferred.

Notes

¹Derived from deconvolution of ambient concentration measurements near Tampa, FL, using the Pseudo-Deterministic Receptor Model.

²Derived from analysis of in-stack sampling of fine “fine” particles, except Mt. Tom ratios, which were drived from analyses of all in-stack particles.

³Electrostatic Precipitator.