A TEST OF THERMODYNAMIC EQUILIBRIUM
MODELS AND 3-D AIR QUALITY MODELS FOR
PREDICTIONS OF AEROSOL N03
Shaocai Yu, Robin Dennis, Shawn Roselle, Athanasios Nenes, John
Walker, Brian Eder, Kenneth Schere, Jenise Swall, Wayne Robarge
EPA600/A-04/079
1. INTRODUCTION
The inorganic species of sulfate, nitrate and ammonium constitute a major fraction of
atmospheric aerosols. The behavior of nitrate is one of the most intriguing aspects of
inorganic atmospheric aerosols because particulate nitrate concentrations depend not only
on the amount of gas-phase nitric acid, but also on the availability of ammonia and
sulfate, together with temperature and relative humidity. Particulate nitrate is produced
mainly from the equilibrium reaction between two gas-phase species, HN03 and NH3.
It is a very challenging task to partition the semi-volatile inorganic aerosol
components between the gas and aerosol phases correctly. The normalized mean error
(NME) for predictions of nitrate is typically three times that for predictions of sulfate for
a variety of 3-D air quality models applied to sections of the U.S. (Odman, et al., 2002;
Pun, et al, 2004) For an annual average across the entire U.S. the NMEs of the
predictions of nitrate from the U.S. EPA Models-3/Community Multiscale Air Quality
Model (CMAQ) are two to three times larger than the NMEs for sulfate.
* Shaocai Yu#, Robin Dennis®, Shawn Roselle®, Athanasios Nenes*, John Walker3, Brian
Eder®, Kenneth Schere®, Jenise Swall®, Wayne Robarge+, NERL, U.S. Environmental
Protection Agency, RTP NC, 27711, USA. # On Assignment from Science and
Technology Corp., Hampton, VA 23666, USA. ®On assignment from Air Resources
Laboratory, National Oceanic and Atmospheric Administration, RTP, NC 27711, USA.
*Georgia Institute of Technology, Atlanta Georgia 30332-0340. $NRMRL, U.S. EPA,
RTP NC, 27711, USA. North Carolina State University, Raleigh, NC 27695.
1

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2.	THERMODYNAMIC MODELS AND OBSERVATIONAL DATASETS
Given total (gas + fine particulate phase) concentrations of H2S04, HN03, and NH3,
and temperature and RH as inputs, ISORROPIA and AIM (AIM model II is used in this
study) predict the partitioning of these inorganic species between the gas and fine particle
(PM2 5) phases on the basis of thermodynamic equilibrium. More detailed descriptions of
the equilibrium reactions and the solution procedures for AIM and ISORROPIA are
given by Wexler and Clegg (2002) and Nenes et al. (1999), respectively.
Three sites were chosen that had high time resolution data to test the equilibrium
models. At the Atlanta site (33.78 °N, 84.41 °W), a total of 325 observational data points
were obtained during the SOS/Atlanta '99 Supersite Experiment from August 18 to
September 1, 1999, by parsing the 9-minute HN03 and 15-minute NH3 concentrations
into 5-minute averages so as to overlap with 5-minute mean concentrations of PM25
S042", N03", and NH4+ (Weber et al., 2003) (summer case). At the Pittsburgh Supersite
(40.44 °N, 79.94 °W), Pennsylvania, a total of 313 data points for two-hourly mean
concentrations of PM25 NH4+, N03" and S042", and gas-phase HN03 were obtained
during the period of January 2 to January 31, 2002 (Wittig et al., 2004) (winter case). At
the Clinton Horticultural Crop Research Station (35°01' N, 78°16' W), North Carolina, a
total of 479 data points for 12-hour (0600-1800 h (EST) day cycle; 1800-0600 h night
cycle) mean concentrations of PM25 NH4+, N03" and S042", and gas-phase NH3 and
HN03 were obtained by an annular denuder system from January 20 to November 2,
1999 (Robarge et al., 2002).
3.	RESULTS AND DISCUSSION
3.1. TEST OF THERMODYNAMIC MODEL WITH OBSERVATIONAL DATA
Comparisons of observed aerosol N03" and NH4+, and gaseous HN03 and NH3
concentrations with those calculated by ISORROPIA and AIM at the three sites are listed
in Table 1. At the Atlanta site, 94.8% and 96.0% of the ISORROPIA and AIM
predictions of NH4+ are within a factor of 1.5 of the observations. ISORROPIA and AIM
also predict HN03 well, with 86% and 87% of the predictions within a factor of 1.5 of the
observations. However, both equilibrium models are unable to replicate a majority of the
observed N03" and NH3 concentrations, see Figure 1 and Table 1. For N03", only 32%
and 48% of the ISORROPIA and AIM predictions are within a factor of 2 of the
observations, respectively. For NH3, ISORROPIA and AIM replicate 25.2% and 51.4%
of the observations within a factor of 2, respectively. At the Pittsburgh site, both AIM
and ISORROPIA can correctly predict the N03" concentrations to within a factor 2 of the
observations for a majority of the data points (>76%) because the TN03 concentration is
constrained and the aerosol fraction is dominant. On the other hand, both models
perform much more poorly on HN03, the gas fraction, as compared to the Atlanta
situation. At the Clinton site, both models reproduce observed NH3 concentrations very
well (>95% within a factor of 1.5) and reproduce a majority of NH4+ concentration data
points within a factor of 2 (>92%). Performance of both models for aerosol N03" at the
Clinton site is better than at the Atlanta site but worse than at the Pittsburgh site.

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EVALUATION OF REGIONAL-SCALE AIR QUALITY FORECAST MODELS	3
Table 1. Statistical summaries of the comparison of the modeled (ISORROPIA and
AIM) partitioning of total nitrate (gas + aerosol) and total ammonia (gas + aerosol)
between gas and aerosol phases with that of observations at the Atlanta Supersite, GA,
Pittsburgh Supersite, PA, and Clinton site, NC. The mean concentrations (± standard
deviation) of S042", TN03 and TNH4 (|.ig m"3), and relative humidity (RH) (%) and
temperature (T) (°C) at each site are also listed.






% within a factor


*

% within a factor of 1.5 **
of 2"

Parameters
OBS
ISORROPIA
AIM
ISORROPIA
AIM
ISORROPIA
AIM
Atlanta site (N=325)






(S042"=12.17±6.71, TNH4=4.38±2.39, TNO
3=7.57±5.27, RH=68.9±19.9, T=25.0±3.3)


Aerosol N03"
0.53±0.51
0.54±0.92
0.61 ±0.92
21.8
33.2
31.7
48.3
Gas HN03
7.15±4.84
7.13±4.94
7.06±4.92
86.2
87.1
91.7
92.9
Aerosol NH4+
3.60±1.77
4.06±2.05
3.85±1.99
94.8
96.0
98.5
98.8
Gas NH3
0.74±1.06
0.31 ±0.79
0.50±0.81
16.6
31.4
25.2
51.4
Pittsburgh site (N=313)






(S042"=2.46±1.14, TNH4=1,74±0.77, TN03=
:3.08±2.18, RH=67.1±17.6, T=3.9±5.9)


Aerosol N03"
2.09±1.51
2.04±1.74
1,98±1.79
60.8
57.4
77.0
75.7
Gas HN03
1.01 ±0.68
0.96±0.78
1.02±0.74
37.7
39.6
56.5
62.0
Clinton site (N=479)






(SO42"=3.64±4.05, TNH4=6.29±5.51, TN03=
=0.57±0.51, RH=79.9±14.2, T=19.1±7.7)


Aerosol N03"
0.30±0.26
0.28±0.28
0.24±0.27
58.0
47.2
71.8
62.0
Gas HN03
0.27±0.25
0.29±0.28
0.33±0.30
52.4
49.3
78.7
69.5
Aerosol NH4+
1 15±1.27
1,44±1.57
1,42±1.54
74.5
76.2
92.5
92.5
Gas NH3
5.13±4.73
4.86±4.62
4.88±4.63
95.4
96.5
97.5
97.9
*  is mean ± standard deviation (ug m"3)
** Percentages (%): are the percentages of the comparison points whose model results are within a factor
of 1.5 and 2.0 of the observations. N is number of samples.
There are many possible reasons for the discrepancies between the model predictions
and observations in partitioning of TN03 for aerosol N03~. To show how the
measurement errors in S042" and TNH4 can contribute to uncertainties in model
predictions of aerosol N03~, Gaussian (normally distributed) random errors are added to
the input S042" and TNH4 (base-case concentrations, Cb) to create the sensitivity-case
concentrations (<",) as follows
Cs=Cb+sp	(l)
where s represents truncated Gaussian random errors with zero mean and standard
deviation equal to 15%xCb. An error of ±15% is used to correspond with the
measurement uncertainty for both S042" and TNH4 that was estimated as part of the U.S.

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S. YU ETAL.
EPA supersite program (Solomon et al., 2003). The errors are truncated so that only
values within 2 standard deviations (2xl5%xCj) are allowed. As shown in Figure 2, the
model with the measurement errors in both S042"and TNH4 can only reproduce 61.3 % of
the base-case aerosol N03" within a factor of 2. This indicates that random errors in
S042" and TNH4 measurements can account for most of the discrepancies between the
model predictions and observations of aerosol N03" in Figure 1 at the Atlanta site.
Similar conclusions can be obtained for the results at the Pittsburgh and Clinton sites and
for the AIM model.
3.2. EFFECTS OF 3-D MODEL PREDICTION ERRORS IN S042, TNH4,
TEMPERATURE AND RELATIVE HUMIDITY ON PREDICTING AEROSOL
no3
The 3-D CMAQ model can only reproduce 46-79% of S042" and 39-72% of aerosol
NH4+ within a factor of 1.5 (Yu et al., 2004). This means that the 3-D air quality models
are frequently making errors on the order of +50% in the simulations of S042" and NH4+.
To test how much the errors in S042" and TNH4 associated with predictions from a 3-D
air quality model such as CMAQ will affect the predictions of aerosol N03" in the
thermodynamic model, sensitivity-case concentrations (<"v) of S042" and TNH4 are
generated by adding independent Gaussian (normally distributed) random errors to their
base-case concentrations ((),) as follows:
ln(Cs) = In(Cb) + s, s ~ G(0, a - RMSE)	(2)
where s represents Gaussian random errors with zero mean and standard deviation equal
to the RMSE, the root mean square error. The RMSE used in this study is obtained from
comparisons of the paired 3-D model predictions and observations for each species (Yu
et al., 2004). The comparison of predictions of aerosol N03~ between the sensitivity-
case and the base-case is shown in Figure 3 and summarized in Table 2. The equilibrium
models with the 3-D air quality model-derived random errors in S042" and TNH4 can only
predict <50% and <62% of aerosol N03" within a factor of 1.5 and 2, respectively, as
shown in Table 2, although the modeled means are close to the observations. For
ISORROPIA in Table 2, 47% and 60% of the N03" predictions from the sensitivity cases
are within a factor of 2 of the base case for Atlanta and Pittsburgh, respectively. This
study suggests that a large source of error in predicting aerosol N03" stems from the
errors in 3-D model predictions of S042" and TNH4 for the Eastern U.S. Table 2 and
Figure 3 also indicate that errors in TNH4 are more critical than errors in S042" to
prediction of N03" and that the higher the N03" concentration, the less sensitive the
predicted N03" concentrations are to the errors in S042" and TNH4. These results indicate
that the ability of 3-D models to simulate aerosol N03" concentrations is limited by
uncertainties in predicted S042" and TNH4.
Additional studies were carried out for the comparison of sensitivity-case N03" for
single relative fixed errors of ±10% individually in temperature and RH with those of the
base-case in the summer and winter times. In contrast to large effects from the errors in
S042" and TNH4, the responses of the aerosol N03" predictions are less sensitive to errors
in temperature and RH. Generally, both models can reproduce a majority of the aerosol
N03" data points within a factor of 1.5 if there are only +10% errors in temperature and
RH, especially for the winter times, with somewhat more sensitivity to errors in RH.

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EVALUATION OF REGIONAL-SCALE AIR QUALITY FORECAST MODELS
5
However, +20% errors in both temperature and RH can result in neither model being able
to reproduce a majority of aerosol N03" data points within a factor of 1.5
(percentage<42%) (not shown) although both models can still capture 53-69% of aerosol
N03~ within a factor of 2 in the summer case. For the winter case, the predicted aerosol
N03~ is much less sensitive to errors in temperature and RH. This may be due to the fact
that temperatures in the winter times are very low (3.9+5.9 °C), and most of TN03
concentration is in the aerosol phase. This is generally in agreement with Takahama et
al. (2004), who found that errors in temperature measurements do not contribute
significantly to model errors when temperatures are low and most of the nitrate
concentration is in the aerosol phase.
Table 2. Statistical summaries of the comparisons of the modeled (ISORROPIA and
AIM) aerosol N03" for the different sensitivity cases created by the Gaussian random
errors (see text explanation) vs. those of the base cases on the basis of observational data
at the Atlanta Supersite (summer case) and Pittsburgh Supersite (winter case).
Condition
*
% within a factor of 1.5*
% within a factor of 2*
Base-case
ISORROPIA
AIM
ISORROPIA
AIM
ISORROPIA
AIM
Atlanta data







(N=163)







Errors in S042" and







tnh4
0.99±1.12
1.11 ±1.38
1.11 ±1.34
30.1
40.5
47.2
62.6
Errors in S042"
0.99±1.12
1,03±1.26
1,05±1.22
43.6
58.9
59.5
71.2
Errors in TNH4
0.99±1.12
1 10±1.35
1.12±1.30
34.4
42.3
54.6
68.1
Pittsburgh Data







(N=312)







Errors in S042" and







tnh4
2.00±1.72
1,80±1.84
1,80±1.85
48.4
48.1
60.3
60.3
Errors in S042"
2.00±1.72
1,93±1.78
1.91 ±1.82
70.2
75.6
77.6
84.3
Errors in TNH4
2.00±1.72
1.81±1.84
1,82±1.86
48.1
46.8
61.2
61.9
* Same as Table 1
4. SUMMARY
The capability of thermodynamic models to reproduce the observed partitioning of
TN03 and TNH4 between gas and aerosol phases differed from site to site depending on
chemical and meteorological conditions at the site. For example, at the Atlanta site, for
NH4+ 94% and 96% of ISORROPIA and AIM predictions are within a factor of 1.5 of
observations, respectively. For HN03, 86 and 87% of ISORROPIA and AIM predictions
are within a factor of 1.5 of observations. However, neither model reproduced a majority
of observed aerosol N03" and gas NH3 within a factor of 2 (N03~: <48% and NH3: <51%)
at the Atlanta site. At the Pittsburgh site, both models can predict a majority of N03" data
points within a factor of 2 (>76%), especially when N03" concentrations are higher than
1.0 |-ig m"3 (>89%), whereas both models perform more poorly on HN03 than at the
Atlanta site. At the Clinton site, both models reproduce observed NH3 concentrations
very well (>95% within a factor of 1.5), and performe a little better on aerosol N03" (47-
58% within a factor of 1.5) than at the Atlanta site but worse than at the Pittsburgh site.

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S. YU ETAL.
The different chemical and meteorological conditions at the three sites can explain why
both models perform differently in partitioning of TN03 and TNH4. There are many
different possible reasons for the discrepancies between the models and observations in
partitioning of TN03. The sensitivity test indicates that in many cases measurement
uncertainties in S042" and TNH4 can explain a major fraction of the discrepancies
between the model predictions and observations in partitioning of TN03. Sensitivity tests
show that random errors associated with S042" and TNH4 predictions of the 3-D model
can result in the thermodynamic model calculation replicating only 47% and 60% of the
base case N03" within a factor of 2 for summer and winter cases, respectively. This
suggests that a large source of error in predicting aerosol N03" stems from the errors in 3-
D model predictions of S042" and TNH4 for the Eastern U.S. It was found that errors in
TNH4 are more critical than errors in S042" to prediction of N03" and that the responses of
the aerosol N03" predictions are not very sensitive to the errors in temperature and RH
under the tested conditions. The ability of 3-D models to simulate aerosol N03"
concentrations is limited by uncertainties in predicted S042" and TNH4. While there is
feedback between partitioning and the levels of predicted TN03, errors in TN03 are much
less sensitive to these uncertainties and 3-D models are capable of predicting TN03 with
accuracy comparable to that of S042" or TNH4.
5. REFERENCES
Byun, D.W. and J.K.S. Ching, Eds.,: Science algorithms of the EPA Models-3 Community Multi-scale Air
Quality (CMAQ) modeling system, EPA/600/R-99/030, Office of Research and Development, U.S.
Environmental Protection Agency, 1999.
Clegg, S.L., P. Brimblecombe, and A.S. Wexler, A thermodynamic model of the system H+-NH4+-S042—NC>3—
H20 at tropospheric temperatures. J. Phys. Chem., A, 102, 2155-2171, 1998.
Nenes, A., C. Pilinis, and S.N. Pandis, Continued development and testing of a new thermodynamic aerosol
module for urban and regional air quality models. Atmos. Environ., 33, 1553-1560, 1999.
Odman, M.T., J.W. Boylan, J.G. Wilkinson, A.G. Russell, S.F. Mueller, R.E. Imhoff, K.G. Doty, W.B. Norris,
and R.T. McNider, SAMI Air Quality Modeling, Final Report, Southern Appalachian Mountains
Initiative, Asheville, NC, 2002.
Pun, B., C. Seigneur, S-.Y. Wu, E. Knipping, and N. Kumar, Modeling Analysis of the Big Bend Regional
Aerosol Visibility Observational (BRAVO) Study, Final Report 1009283, EPRI, Palo Alto, CA, 2004.
Robarge, W.P., J.T. Walker, R.B. McCulloch, and G. Murray, Atmospheric concentrations of ammonia and
ammonium at an agricultural site in the southeast United Sates. Atmos. Environ., 36, 1661-1674, 2002.
Solomon, P.A., K. Baumann, E. Edgerton, R. Tanner, D. Eatough, W. Modey, H. Marin, D. Savoie, S.
Natarajan, M.B. Meyer, and G. Norris. Comparison of Integrated Samplers for Mass and Composition
During the 1999 Atlanta Supersites Project. J. Geophys. Res., 108(D7), 8423,
doi: 10.1029/2001JD001218, 2003.
Takahama, S., B. Wittig, D.V. Vayenas, C.I. Davidson, and S.N. Pandis, Modeling the diurnal variation of
nitrate during the Pittsburgh Air Quality Study, J. Geophys. Res., 109, D16S06,
doi:10.1029/2003JD004149, 2004
Wittig, B., S. Takahama, A. Khlystov, S.N. Pandis, S. Hering, B. Kirby, and C. Davidson, Semi-continuous
PM2.5 inorganic composition measurements during the Pittsburgh Air Quality Study. Atmos. Environ., 38,
3201-3213,2004.
Weber, R. J., et al., Intercomparison of near real-time monitors of PM2.5 nitrate and sulfate at the Environmental
Protection Agency Atlanta Supersite. J. Geophys. Res., 108, 8421, doi:10.1029/2001JD001220, 2003.
Wexler, A.S., and S.L. Clegg, Atmospheric aerosol models for systems including the ions H+, NH/, Na+, SO42",
NO3-, CI", Br", and H20, J. Geophys. Res., 107 (D14), doi: 10.1029/2001JD000451, 2002.
Yu, S.C., R. Dennis, S. Roselle, A. Nenes, J. Walker, B. Eder, K. Schere, J. Swall, W. Robarge, An assessment
of the ability of 3-D air quality models with current thermodynamic equilibrium models to predict aerosol
N03". J. Geophys. Res., 2004 (in press).

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EVALUATION OF REGIONAL-SCALE AIR QUALITY FORECAST MODELS
N0i (ISORRoblA)
N03 (AIM)
HN03 (ISORROPIA)
HN03 (AIM)
HNO (figm )
NO (fi g m )	a a
NH3 (ISORROPIA)	/ /•
NH3 (AIM)
(ISORROPIA)
NH^gm )
10' 10	10"	10"	10u	10'
Observation
Fig 1. Comparison of the modeled (ISORROPIA and AIM) partitioning of total nitrate
(gas + aerosol) and total ammonia (gas + aerosol) between gas and aerosol phases with
that of observations for aerosol N03~, HN03, aerosol NH4+ and NH3 at the Atlanta
supersite in summer of 1999. The 1:1,2:1, and 1:2 lines are shown for reference.
I 		 		
- Errors in SO
i 		
- Errors in TNH
"l 		 		
- Errors in SO 2~ and TNH
101 10
10° -lo'icr3 icr2 icr1 10° 101
Base-case aerosol N03~ (|ag m" )
Figure 2. Sensitivity-case N03~ with assumed Gaussian random errors in observed S042
TNH4 vs. the base-case N03" for the ISORROPIA model at the Atlanta site

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S. YU ETAL.
Summer, 1999 (Atlanta site)
Winter, 2002 (Pittsburgh site)
rq 		 		
Errors in SO 2~ and TNH
: o ISORROPIA
AIM
Errors in SO
and TNH
gi ifilqa iA iqt)	a Wdatoiiooft
rq 	I 		
Errors in SO
Errors in SO
kjj)' pi	
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