Evaluation of Fine Particle Number Concentrations in CMAQ

Abstract

The Community Multiscale Air Quality (CMAQ) model is widely used in air quality management and scientific investigation. Numerous studies have been conducted investigating how well CMAQ simulates fine particle mass concentrations, but relatively few studies have addressed how well CMAQ simulates fine particle number distribution. Accurate simulation of particle number concentrations is important because particle number and surface area concentrations may be directly related to human health and visibility. Simulated fine particle number concentrations derived using CMAQ are compared to measurements to identify problems and to improve model performance. Evaluation is done using measured particle number concentrations in Atlanta, Georgia, from 1/1/1999 to 8/31/2000. While homogeneous binary nucleation mechanism used in CMAQ needs to be modified for better prediction of particle number concentrations, there are also other factors that affect the predicted particle level. Assumed particle size of the primary emissions in CMAQ causes number concentrations to be significantly underestimated, while particle density has a small impact. Assuming particle size distributions by three lognormal modes cannot accurately simulate particles with size less than 0.01 μ m, particularly during nucleation events. An additional mode that accounts for particles smaller than 0.01 μ m can improve the accuracy of the number concentration simulations. Though, the use of the Expectation-Maximization (EM) algorithm to estimate size distribution parameters of measured particles suggests that assumed parameters for the lognormal modes in CMAQ are generally reasonable.

1. INTRODUCTION

Elevated levels of ambient particles have a direct influence on human health; for example, they can trigger reactions ranging from coughing and wheezing to heart attacks and premature death (Donaldson et al. 2001). Particles are also responsible for visibility reduction (Adrian and Orloff 1977; Faxvog and Roessler 1978), acid deposition, and perturbing the Earth's radiation balance. In 1997, the National Ambient Air Quality Standards (NAAQS) for fine particle mass concentrations were promulgated in response to a growing number of scientific linkages between fine particle levels and adverse health effects. In addition to studies associating particle mass concentrations with the human health (Brauer et al. 2001; Dockery and Pope 1994; Dockery et al. 1993; Ebelt et al. 2000; Gold et al. 1999; Pope et al. 1995; 1999; Saldiva et al. 1995; Vedal 1997), some studies suggest that fine particle number and surface area concentrations are more directly related to pulmonary disease than particle mass concentrations (Donaldson et al. 1998; Penttinen et al. 2001; Woo et al. 2001b). In addition, particle mass concentrations are not always correlated with particle number concentrations, for example, when very small particles are formed by nucleation, particle mass does not significantly increase (Woo et al. 2001a). Hence, if particle number or surface area concentrations are responsible for human health, strategies designed to meet the NAAQS for PM_2.5 might not be as effective for protecting human health as desired (Woo et al. 2001a). These studies also suggested that the particle number concentration itself was an important index in epidemiological analyses.

The physics, chemistry, and the response of particles to emissions have been studied using air quality models. One of the most comprehensive air quality modeling frameworks is Models-3, composed of the Community Multiscale Air Quality (CMAQ) model (Byun and Ching 1999), the Mesoscale meteorological Model version 5 (MM5) (PSU/NCAR 2003), and Sparse Matrix Operator Kernel Emissions (SMOKE) (US-EPA 2004). CMAQ predicts gas-phase species as well as particle concentrations. Particles in CMAQ are divided into two groups, fine (PM_2.5: particles with size less than 2.5 μ m) and coarse particles (PM₁₀: particles with size between 2.5 and 10 μ m).

PM_2.5 is treated by two interacting sub-distributions (or modes) in CMAQ. The Aitken (smaller one) mode represents fresh particles either from nucleation or from direct emissions, while the accumulation (larger one) mode represents aged particles. The production rate of new particle number, J [m^{− 3} sec^{− 1}], is calculated from the nucleation of sulfuric acid vapor, based the classical binary homogeneous nucleation theory (Wilemski 1984) incorporating the hydration effect (Kulmala et al. 1998). New particle diameter in CMAQ v4.3 is 2.0 nm. The two modes interact with each other through coagulation, and particles in the Aitken mode may grow into the accumulation mode. PM_2.5 chemical species treated in CMAQ are sulfate, nitrate, ammonium, water, anthropogenic and biogenic organic carbon, elemental carbon, and other unspecified material of anthropogenic origin. PM₁₀ is treated by the coarse mode from direct emissions by natural processes such as blowing dust or sea salt particles from waves in CMAQ. PM₁₀ includes sea salt, wind-blown dust, and other unspecified material of anthropogenic origin.

Fine particle mass concentrations simulated using CMAQ have been extensively evaluated using relatively abundant measurement data (Eder et al. 2003; Fan et al. 2005; Jun and Stein 2004; Mebust et al. 2003; Park et al. 2006; Tonnesen 2003). Initial evaluation of the aerosol species concentrations over the eastern United States in June 1995 (Mebust et al. 2003) revealed that CMAQ underestimated particle mass with the normalized mean error less than 50% for most of the species. Recently, CMAQ was used to simulate fine particle concentrations in Houston, Texas, from August 24 to August 31, 2000 (Fan et al. 2005). Daily average concentrations of PM_2.5 major species were simulated reasonably well with the normalized bias less than 25%. Those differences are likely due to the uncertainties in the calculated morning planetary boundary layer (PBL) height. Secondary organic aerosol was also underestimated. CMAQ was also used to investigate aerosol formation and transport in the Pacific Northwest during July 1–16, 1996 (O'Neill et al. 2006). The mean fractional bias and error of PM_2.5 mass were within 30% and 50%, respectively, and those of PM_2.5 species concentrations were within the acceptable bound (Boylan et al. 2006). Further, effects of spatial variability on CMAQ evaluation found that the uncertainties due to the different spatial scales between the point-observations and volume-averaged simulated concentrations did not significantly affect model errors (Park et al. 2006).

In spite of these extensive studies focusing on the evaluation of the fine particle mass concentration, CMAQ's ability to reproduce aerosol number concentrations has not been addressed in such detail. A few studies have found that CMAQ under predicts aerosol number concentrations of the Aitken mode (i.e., particles with size less than 0.1 μ m) by a factor of 10 to 100, and those of the accumulation mode (i.e., less than about 2 μ m in the diameter) by a factor of 5 to 10 in the Pacific Northwest (Elleman et al. 2004, 2005). Errors in particle number concentrations were significantly larger than those of particle mass concentrations or gas-phase constituents. Thus, the authors concluded that the modeled mean particle size in CMAQ might be significantly larger than the measured mean size due to the inadequate treatment of aerosols as three lognormal modes or inaccurate processes affecting characterization of the aerosol size distribution.

Studies also suggested that the particle numbers were underestimated because CMAQ used the binary homogeneous nucleation theory (H₂SO₄ and water), which significantly underestimate the nucleation rates (Clarke et al. 1999; Coffman and Hegg 1995; Gaydos et al. 2005; Kulmala et al. 2006; Stolzenburg et al. 2005; Weber et al. 1996; 1999). One process that could reconcile particle production is the ternary nucleation mechanism. Among several ternary systems, the H₂O-H₂SO₄-NH₃ system can produce the most realistic particle production (Coffman and Hegg 1995; Gaydos et al. 2005; Korhonen et al. 1999). The accuracy of the nucleation rates was significantly improved at higher nucleation rates when using the H₂O-H₂SO₄-NH₃ system (Napari et al. 2002). An appropriate formulation of this ternary system increased simulated nucleation rates (Gaydos et al. 2005). In addition to the ternary systems, the ion-mediated nucleation mechanism can produce new particles in a very low H₂SO₄ concentrations that are unfavorable for binary homogeneous nucleation (Katz et al. 1994; Laakso et al. 2002; Yu and Turco 2000).

While uncertainties in nucleation theory will continue to impact CMAQ, other factors also affect predicted particle concentrations, and CMAQ relies on several assumptions: assumed particle density, assumed size distribution of primary emissions, and assumed distribution of particle size. The goal of this research is to analyze the influence of those assumptions on the predicted particle number concentrations. The evaluation uses hourly measured particle number concentrations of 39 size bins from 3 nm to 3 μ m for one year and eight months (1/1/1999 to 8/31/2000) at an urban area located in Atlanta, Georgia. In addition, this paper also examines the feasibility to improve the accuracy of the simulations.

2. METHODS

Fine particle number and mass levels were monitored at the Jefferson Street (JST) monitor in urban Atlanta, Georgia (Figure 1a) from 1/1/1999 to 8/31/2000 as a part of the Southeastern Aerosol Research and Characterization (SEARCH) study (Hansen et al. 2003; Woo et al. 2001a). Hourly particle number concentrations were measured for 39 size bins from 3 nm to 3 μ m in diameter using a nano-scanning mobility particle sizer (NSMPS) (3 nm–50 nm), a standard scanning mobility particle sizer (SMPS) (20 nm–250 nm), and a laser particle counter (LPC) (100 nm–2 μ m) (Van Loy et al. 2000; Woo et al. 2001a). Hourly PM_2.5 mass concentrations were measured using a Tapered Element Oscillating Microbalance (TEOM) (Patashnick and Rupprecht 1991), which measures ambient particle concentrations using the oscillation frequency of the mass transducer.

FIG. 1 (a) Location of the Jefferson Street (JST) monitoring station in Atlanta, Georgia. (b) Air quality model (CMAQ) domain.

Hourly particle number and mass concentrations were simulated using EPA's Models-3 framework: SMOKE (v1.5), MM5 (v3.5.3), and CMAQ (v4.3). CMAQ was run from 1/1/1999 to 8/31/2000 over the eastern United States with 78 × 66 grids of size 36 km (Figure 1b) for a time-series epidemiological study (Marmur et al. 2006). Evaluating simulated number concentrations based on a finer modeling grid (e.g., 12 km) would have provided more spatially detailed data, and possibly improved model performance. However, comparing model results based on 36 km and 12 km grids, these differences are negligible compared to the discrepancies between observed and simulated (based on a 36 km grid) number concentrations (see “Results” section). Detailed information of the parameters used in the modeling system is available in elsewhere (Park et al. 2006). Meteorological fields were evaluated using the TDL surface hourly data (UCAR 2003), which were not used as an input of MM5. Mean errors (MEs) in temperature, specific humidity, and wind speed were 1.5°C, 1.8 g kg⁻¹, and 0.8 m sec^{− 1}, respectively. These values are within the benchmarks for the metrological model evaluation (Emery et al. 2001).

Particle number concentrations are measured in each of 39 size bins, but CMAQ concentrations are simulated using three modes, which make a direct comparison cumbersome. The three modes, Aitken(i), accumulation(j), and coarse(c), follow a lognormal distribution. To compare the simulated concentrations with the measured concentrations, modal particle number concentrations from CMAQ were converted into size resolved particle number concentrations expressed in the aerodynamic diameter using PMx (Jiang 2005; Jiang et al. 2004; Jiang and Yin 2001). PMx estimates the parameters of the lognormal distribution in each mode using particle number, surface area, and mass concentrations. PMx calculates particle number concentrations in each size bin by the integral of the probability density function of particle number concentrations for each interval. Accuracy of the particle concentrations in each size bin is dependent on the simulated particle number, surface area, and mass concentrations.

Parameters of the lognormal distributions can be obtained from CMAQ's diagnostic output variables (Bhave and Binkowski 2005). Different parameters in the lognormal distributions lead to changes in size resolved particle number concentrations (Table 1). Number concentrations for particles with sizes between 3 to 500 nm are a slightly higher when PMx is used, and concentrations for particles with size between 0.5 μ m to 2.5 μ m are somewhat higher when CMAQ's diagnostic output variables are used. However, the differences are negligible for total particle number concentrations less than 2.5 μ m, and those differences do not significantly affect the results of the analysis performed in this paper. Also, size resolved particle number concentrations are calculated from modal concentrations from CMAQ based on the aerodynamic diameter. Size resolved concentrations differ slightly when using other kinds of diameters, such as Stokes or electric mobility diameter. Differences do not significantly influence the analysis.

TABLE 1 Geometric mean (D_g) and geometric standard deviation (σ_g) of lognormal distributions obtained from PMx and CMAQ's diagnostic variables from 3/23/1999 to 3/30/1999 at the JST station in Atlanta, Georgia

	Aitken	Mode accumulation	Coarse
PMx
Dg[μ m]	0.08	0.11	0.81
σg	1.83	2.07	2.20
Diagnostic output
Dg[μ m]	0.05	0.07	0.80
σg	2.52	2.66	2.20

3. RESULTS

Simulated fine particle number concentrations were significantly lower than measured concentrations by a factor of up to 1000 (Figure 2). Note that the y-axis is logarithmic. Simulated surface area concentrations were also much lower than measured values, whereas simulated volume and mass concentrations reasonably well match the measured values. In addition, CMAQ underestimated number concentrations for size less than 1 μ m, and overestimated concentrations for size larger than 1 μ m (Figure 3). These results suggested that CMAQ overestimated average particle sizes. Note that measured surface area and volume concentrations are calculated using number concentrations by assuming that all particles are spheres. CMAQ also assumes that particles are in a spherical shape. The spherical assumption is not correct; for example, diesel chain agglomerates are not spherical, so there exist small errors in calculated surface area and volume concentrations associated with the particle shape (McMurry et al. 2002; Park et al. 2004a). These errors were not quantified in this paper as this issue is not within the scope of this study. However, note that the correct estimation of the particle surface area is needed to accurately estimate the particle number concentrations. For example, the particle deposition velocity, which is directly related with the lifetime of particles, depends on the surface area. In addition, the surface area is important for the human health study.

FIG. 2 Daily particle number, surface area, volume, and mass concentrations for particles less than 2.5 μ m from 1/1/1999 to 8/31/2000 at the JST station in Atlanta, Georgia.

FIG. 3 Median number concentrations of particles for 39 size bins (from 3 nm to 2.5 μ m) from 1/1/1999 to 8/31/2000 at the JST station in Atlanta, Georgia.

The discrepancy between measured and simulated particle number concentrations could be partly due to the different spatial scales between the observation and the model (Park et al. 2006). Measured concentrations are point values at the monitoring station, whereas CMAQ simulates volume-averaged concentrations. To analyze the effect of the different spatial scales, particle number concentrations were simulated using 12 km grids as well as 36 km grids from July 1–31, 2001 in a separate study (Park and Russell 2003). Number concentrations at the JST station from the 12 km grid were 17% higher than those from the 36 km. Thus, a fraction of the error in simulated number concentrations arises from the different spatial scales.

Temporally, measured particle concentrations with size less than 45 nm in the diameter were relatively higher in the winter and spring, but simulated concentrations did not have an apparent seasonal trend (Figure 4). Measured concentrations had a marked weekly variation, which is not strong in the simulated concentrations. Diurnal peaks coinciding with the morning and afternoon rush hours for particles from 1 μm to 2 μm were observed in measured concentrations but not in those simulated. Thus, measured number concentrations had more apparent seasonal/daily/diurnal variations than simulated concentrations. The relatively smooth temporal variation of simulated number concentrations was consistent with that of simulated mass concentrations, which is caused in part by the smooth emission profiles used in CMAQ, the spatial averaging effect, and the spatial allocation of emissions (Marmur et al. 2005; Park et al. 2005) as well as the inability of the meteorological model to simulate the very fine features (Hogrefe et al. 2004). In summary, analysis of simulated number concentrations showed that simulated number concentrations were significantly underestimated and had less temporal variation.

FIG. 4 Temporal trends of the particle number distribution, dN/d(Dp) [μ m^{− 1}cm^{− 3}], from 1/1/1999 to 8/31/2000 at the JST station in Atlanta, Georgia. (a) monthly, (b) day of week, and (c) hourly average distributions.

4. ANALYSIS

Underestimation of particle number and surface area is due in part to the assumptions used. Here, three assumptions: particle density, size distribution of primary emissions, and the treatment of aerosols as three lognormal modes, are examined.

4.1. Particle Density

CMAQ converts particle mass concentrations into particle number concentrations using assumed particle density information (Table 2) (Binkowski et al. 2003). Assumed particle densities of organic carbon and elemental carbon in CMAQ appear larger than measured values. Hence, simulated number concentrations in CMAQ would be somewhat underestimated if simulated mass concentrations were reasonably well matched with the measured values, and the size distributions based on particle mass are correct as well.

TABLE 2 Assumed and measured particle densities (g cm^{− 3})

[g cm^− 3]	CMAQ	Literature
Sulfate, nitrate, and ammonium	1.8	1.77 ^a , 1.72∼ 1.83 ^d
Elemental carbon	2.2	1.77 ^b , 2.0 ^d
Organic carbon	2	1.2∼ 1.78 ^c , 1.2 ^d

Influence of the inaccurate density on estimating particle number concentrations was examined by comparing the difference between measurements and simulations. Average ratios of measured to simulated number concentrations were 1.15 (mass), 1.43 (volume), 3.95 (surface area), and 29.34 (number) (Table 3). Note that PM_2.5 mass measured by TEOM contains small amounts of water, although studies suggest that the amount of water would be negligible as a Nafian drier is used (Eatough et al. 2003; Gong and Demerjian 1995; Meyer et al. 2000; Schwab et al. 2004). Considering the possibility of water in the particles, the true ratio of observed mass to modeled mass would be slightly less than 1.15. The ratio increased from mass to volume concentrations, which is due to the higher particle densities (especially, OC and EC) used in CMAQ (see Table 2).

TABLE 3 Summary statistics of hourly average particle number, surface area, volume, and mass concentrations for particles less than 2.5 μ m from 1/1/1999 to 8/31/2000 at the JST station in Atlanta, Georgia

	Number [cm^− 3]		Area [μ m^2 cm^− 3]		Volume [μ m^3 cm^− 3]		Mass [μ g m^− 3] (water was excluded)
	OBS	MODEL	OBS	MODEL	OBS	MODEL	OBS	MODEL
Mean	7.5E+04	2.5E+03	663.7	168.1	22.4	15.7	21.3	18.5
STDEV	9.5E+04	1.3E+03	549.1	101.7	13.4	9.6	13.0	10.6
Minimum	2.2E+03	7.6E+01	48.4	0.9	1.5	0.1	0.9	0.0
25th percen.	3.2E+04	1.6E+03	369.9	94.7	12.8	8.9	11.9	10.9
Median	5.2E+04	2.3E+03	529.1	151.0	18.9	14.0	18.3	17.0
75th percen.	8.8E+04	3.3E+03	781.7	222.2	28.6	20.6	27.8	24.4
Maximum	1.8E+06	1.1E+04	8533.7	827.9	127.7	79.5	97.5	81.4

Particle densities in CMAQ are changed to the measured particle densities, and particle mass and number concentrations were calculated with CMAQ (Table 2). When densities of OC and EC in CMAQ are assumed as 1.2 g cm^{− 3} and 2.0 g cm^{− 3}, respectively (McMurry et al. 2002), the number concentrations increased 10.7%. When densities of OC and EC are assumed as 1.78 and 1.77, respectively (Park et al. 2004a; Park et al. 2004b; Turpin and Lim 2001), the number concentrations increased 10.9%. However, mass concentrations changed less than 1% in both cases. Thus, CMAQ underestimated particle number concentrations about 10% due to the higher particle density, but the particle density alone cannot fully explain the large difference between measured and simulated number concentrations.

4.2. Size Distribution of Primary PM Emissions

Measured and simulated particle concentrations for different particle sizes also can be compared. CMAQ overestimated particle number concentrations for large particles (larger than 1.0 μ m), but significantly underestimated particle number concentrations for small particles (less than 1.0 μ m) (Figure 3 and Figure 4). This result was expected because simulated number concentrations were significantly lower than the measured although simulated volume concentrations were predicted reasonably well (Figure 2). To investigate why this might be, the influence of the size distribution of initial emissions on particle size distributions was analyzed.

The EPA emission inventory for particulate matter does not contain information about source size distributions. In CMAQ, the default assumption is that the major fraction of PM_2.5 emissions are in the accumulation mode with a small fraction in the Aitken mode; i.e., 99.9% of the fine primary organic aerosol (POA) and primary elemental carbon (PEC) emissions are assumed to be in the accumulation mode, and the remaining fraction, 0.1%, are assigned to the Aitken mode (Binkowski et al. 2003), and 100% of primary sulfate (PSO4), primary nitrate (PNO3), and unspecified fine PM (PMFINE) emissions are assigned to the accumulation mode. However, studies show that around 85% of primary organic carbon (POA) and elemental carbon (PEC) emissions should be assigned to the accumulation mode, and the remaining 15% of POA and PEC to the Aitken mode (Venkataraman et al. 1994). If so, the assumption that 99.9% of POA and PEC emissions would be in the accumulation mode needs modification. Currently, other air quality models, for example, the European Monitoring and Evaluation Program (EMEP) unified aerosol model version, assume that 85% of POA and PEC are in the accumulation mode, and 100% of PMFINE is in the accumulation mode (Tsyro 2002). The size distribution of particle emissions is a hot topic of the current issue (McMurry and Woo 2002).

Sensitivity analysis of how simulated particle number concentrations respond to the ratio of the primary PM emissions in the accumulation to Aitken mode for PM_2.5 emissions was performed for a limited period (3/23/1999 to 3/30/1999), which includes both regular (3/23∼ 3/28) and nucleation (3/29∼ 3/30) days, the latter being characterized by exceptionally high concentrations of particles with size less than 45 nm due to nucleation (Figure 5) (Woo et al. 2001a). The model was run with the ratio of 0.85/0.15 (accumulation/Aitken), 0.9/0.1, and 0.99/0.01, in addition to the default ratio of 0.999/0.001 for PEC and POA emissions. When the ratio changed from 0.999/0.001 to 0.85/0.15, simulated particle number concentrations increased by a factor of 6 (Table 4), but simulated particle mass concentrations remained virtually the same (less than 1% change). Thus, as the ratio changes from 0.999/0.001 to 0.85/0.15, the simulated number concentrations approached measured concentrations for typical days, but continued to be low on days experiencing nucleation events (Woo et al. 2001a). Nucleation can occur by rapid cooling of hot exhaust gases (Tobias et al. 2001), or oxidation of gas phase species followed by condensation (Woo et al. 2001a). However, the exact physics and chemistry leading to such phenomena is still uncertain (Gaydos et al. 2005; Kulmala et al. 2004).

FIG. 5 Daily average measured particle number concentrations in JST from 3/23/1999 to 3/30/1999 at the JST station in Atlanta, Georgia.

TABLE 4 Simulated fine particle number concentrations by CMAQ, as initial ratio of particle emissions in the Aitken (E_i) and accumulation (E_j) modes change from 3/23/1999 to 3/30/1999 at the JST station in Atlanta, Georgia

Ei:Ej	Number [cm^− 3]
CMAQ
0.001:0.999 (default)	4.2E+03
0.01:0.99	5.9E+03
0.10:0.90	1.8E+04
0.15:0.85	2.5E+04
OBS
Regular days	4.5E+04
Nucleation event days	1.8E+05

4.3. Treatment of Aerosol as Three Lognormal Modes

CMAQ simulates particles assuming that the particle size distribution follows three lognormal distributions: Aitken, accumulation, and coarse modes (Binkowski et al. 2003; Whitby 1978). Distribution parameters in CMAQ are summarized in Table 5. To evaluate the distribution parameters used, measured data were fit to lognormal distributions (Figure 6) using an Expectation-Maximization (EM) algorithm (see Appendix). Coarse mode parameters could not be evaluated because size measurements were not made above 3 μ m.

FIG. 6 (a) Measured median particle number, (b) surface area, and (c) volume concentrations from 1/1/1999 to 8/31/1999 at the JST station in Atlanta, Georgia, and the fitted distributions using parameters from the EM algorithm along with the number (N), surface area (S), and volume (V) concentrations, and the geometric mean (D_g), and geometric standard deviation (σ g) for the Aitken (i), and accumulation (j) modes.

TABLE 5 Parameters of the lognormal distribution for the particle number, surface area, and volume concentrations used in CMAQ, and those based on the measurements at the JST station in Atlanta, Georgia

		CMAQ*		OBS**
Variable	Mode	Geometric mean (μ m)	Geometric standard deviation	Geometric mean (μ m)	Geometric standard deviation
Number (n)	Aitken accumulation coarse	0.01	1.7	0.017	2.34
		0.07	2.0	0.07	1.88
		1.00	2.2	NA	NA
Surface area (s)	Aitken accumulation coarse	0.02	1.7	0.043	2.03
		0.18	2.0	0.18	1.81
		3.47	2.2	NA	NA
Volume (mass) (v)	Aitken accumulation coarse	0.02	1.7	0.045	2.03
		0.30	2.0	0.28	2.03
		6.46	2.2	NA	NA
• Surface area: Dgs = ln Dgn+ 2 (lnσgn)^2, σgs = σgn
• Volume (mass): Dgv = ln Dgn+ 3 (ln σgn)^2, σgs = σgn
.

The distribution using the lognormal parameters from the EM algorithm fit well the measured number concentrations for particles larger than 0.01 μ m (Figure 6). Parameters estimated using the measured data were similar to those assumed in CMAQ (Table 5), and also to those of typical urban aerosols (Whitby 1978). However, the measured number concentrations did not fit well for particles with size less than 0.01 μ m (Figure 6). This result shows that an additional mode, the geometric mean diameter of which is smaller than that of the Aitken mode, i.e., a nucleation mode, should be considered in order to better predict particles with sizes less than 0.01 mm. The appropriate shape of the new mode should be selected, and the proper treatment of the nucleation process is needed. In summary, the treatment of aerosols as three lognormal modes should simulate particles larger than 0.01 μ m reasonably well, but does not accurately simulate particles smaller than 0.01 μ m. Currently, the EMEP aerosol model version includes a nucleation mode, in addition to the Aitken, accumulation, and coarse modes (Tsyro 2002). EMEP aerosol model version uses MM32 as aerosol dynamic module (Pirjola et al. 2003; Tsyro et al. 2002). MM32 is another version of the multicomponent monodisperse model (MULTIMONO), which uses monodisperse approach to represent particle size distribution (Pirjola and Kulmala 2000). Performance of predicting particle number concentrations of the four-distribution model was significantly better than that of the mono-distribution model.

Note that the improvement in the particle prediction cannot be truly achieved without modifying the binary homogeneous nucleation mechanism used in the CMAQ. Studies suggest that the absolute rate of the particle formation used in CMAQ is also uncertain, so using relative rates of new particle formation and condensation on existing particles is less uncertain than the absolute rates. Experimental study shows that the growth of nucleated particles to a detectable size involves a competition between the coagulation loss of nucleated clusters to preexisting particles and their growth to larger sizes. This result also suggests that using the rate of formation on existing particles is reasonable (McMurry et al. 2005). Recently, a new ternary homogeneous nucleation parameterization was implemented and tested using CMAQ. The results showed that the ternary nucleation parameterization gave better performance in predicting particle number and size distributions compared with the binary nucleation parameterization (Zhang, Liu et al. 2005).

5. CONCLUSIONS

Fine particle mass concentrations simulated using CMAQ have been extensively evaluated, but CMAQ's ability to reproduce aerosol number concentrations is not as thoroughly demonstrated. Particle number concentrations simulated by CMAQ from 1/1/1999 to 8/31/2000 were evaluated. Simulated number concentrations were significantly underestimated up to a factor of 1000. While the nucleation mechanism, which remains an active area of research, is one uncertainty likely leading to the underestimation of particle number concentrations, other model specification affects predicted particle levels. Influences of assumptions used in CMAQ on the predicted particle number concentrations were investigated, including impacts of particle density, size distribution of the initial emissions, and the treatment of aerosols as three lognormal modes.

One cause of underestimating particle number concentrations was that the assumed particle density in CMAQ is higher than the observed values, though this had a small impact as did using larger grid sizes. Another cause of the underestimation was that the assumed size distribution of initial particle emissions in CMAQ was larger particles than observed. Currently, CMAQ assigns only 0.1% of fine particle emissions to the Aitken mode, and the remaining 99.9% of POA and PEC emissions to the accumulation mode. Measurements show that around 15% of POA and PEC emissions should be treated as being in the Aitken mode, and the remaining 85% as the accumulation mode. Sensitivity test results showed that when the fraction of initial particle emissions in the Aitken mode increased, particle number concentrations increased and approached measured values. Another cause of the underestimation was the treatment of aerosols using three lognormal distributions. The size distribution of the measured concentrations showed that three lognormal distributions could not accurately capture particles with size less than 0.01 μ m. An additional mode that accounts for the nucleated particles can improve the accuracy of the number concentration simulations.

APPENDIX

An Expectation-Maximization (EM) algorithm was employed to estimate the parameters of a mixture of lognormal distributions. The EM algorithm is based on the concept of incomplete data for optimizing likelihood functions (Demster et al. 1977; Redner and Walker 1984). When estimating the parameters of mixture distributions, we posit that the observed data X are incomplete and consider the existence of unobserved data, Y. This significantly facilitates optimizing the likelihood function since the optimizing process is analytically intractable in many cases without assuming Y. More precisely, let's assume the following mixture lognormal distributions.

where

and Φ = {α _i , θ _i }, θ _i = {μ _i , σ _i ²} for i = 1, …, K such that ∑_{i = 1} ^K α _i = 1.

Parameters of mixture lognormal distributions include the number of components in the mixtures, their coefficients, means, and variances denoted K, α _i μ _i , and σ _i ², respectively. K is usually obtained by prior knowledge. Here, we set K = 2 as the number of particles that are typically divided into two modes for size less than 2.5 μ m (Whitby 1978). The EM algorithm is performed by repeating between the so-called the E-step and the M-step. In the E-step, we compute the expectation of complete log-likelihood function conditional on the initial guess of parameters and the observed data called the Q function.

In the M-step, we update the estimate of parameters to maximize the function computed in E-step.

We then obtain a set of updated parameters by iterating between the E-step and the M-step. Final parameters are determined when the difference between Φ⁽ⁱ⁾ and Φ^{(i + 1)}is less than the specified threshold or satisfied with the specified number of iterations. More details of the EM algorithm is available elsewhere (Hogg et al. 2005).

Acknowledgments

This research was supported by the U.S. Environmental Protection Agency under Agreements RD82897602, RD83107601, and RD83096001.

Notes

^a Zhang, Canagaratna et al. 2005

^b Park et al. 2004a; Park et al. 2004b;

^c Turpin and Lim 2001;

^d McMurry et al. 2002.

*Parameters for the surface area and mass (volume) concentrations are calculated as follows.

^a **Refer to Figure 6