*Corresponding author. Fax: #1-925-244-7129.E-mail address: yzhang@aer.com (Y. Zhang)

Atmospheric Environment 34 (2000) 117}137

A comparative review of inorganic aerosol thermodynamicequilibrium modules: similarities, di!erences, and their likely

causes

Yang Zhang!,*, Christian Seigneur!, John H. Seinfeld", Mark Jacobson#,Simon L. Clegg$, Francis S. Binkowski%

!Atmospheric & Environmental Research, Inc., 2682 Bishop Drive, Suite 120, San Ramon, CA 94583, USA"California Institute of Technology, Pasadena, CA 91125, USA

#Stanford University, Stanford, CA 94305, USA$University of East Anglia, Norwich NR4 7TJ, UK

%National Oceanic and Atmospheric Administration, On assignment to the US Environmental Protection Agency, Research Triangle Park,NC 27711, USA

Received 1 December 1998; accepted 26 April 1999

Abstract

A comprehensive comparison of "ve inorganic aerosol thermodynamic equilibrium modules, MARS-A, SEQUILIB,SCAPE2, EQUISOLV II, and AIM2, was conducted for a variety of atmospheric concentrations of particulate matter(PM) constituents, relative humidities (RHs), and temperatures. Our results show that although the PM compositionsand concentrations predicted by these modules are generally comparable under most conditions, signi"cant discrepan-cies exist under some conditions, especially at high nitrate/chloride concentrations and low/medium RHs. As a conse-quence, the absolute di!erences in total PM concentrations predicted by these modules under all simulation conditionsare 7.7}12.3% on average and as much as 68% for speci"c cases. The PM predictions are highly sensitive to changes inthe molar ratios of ammonium to sulfate, nitrate to sulfate, and sodium chloride to sulfate, relative humidity, andtemperature. The similarities and di!erences in simulation results predicted by the "ve modules are analyzed and thelikely causes for these di!erences are discussed in detail. Recommendations are provided regarding the relativeadvantages of these modules, possible improvements of their performance, and applications in three-dimensional PMmodeling studies. ( 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Inorganic particulate matter; Thermodynamic modeling; Multi-phase equilibrium; Module comparison; Sensitivity

1. Introduction

Particulate matter (PM) is an ubiquitous componentof the atmosphere and plays an important role in manyareas of atmospheric sciences including human healthe!ects of air pollution, atmospheric visibility reduction,acid deposition, and the earth's radiation budget. TheUS Environmental Protection Agency (EPA) revised the

National Ambient Air Quality Standards for PM in 1997to protect human health and has recently proposed newregulations to protect atmospheric visibility. The radi-ative forcing of aerosols is now routinely included inclimate studies. Atmospheric PM models are e!ectivetools to quantify the relationship between sources of airpollutants and their health and environmental impacts.An essential component of the PM models is the thermo-dynamic module that simulates the partitioning of chem-ical species among the gas, aqueous, and solid phasesand predicts the total mass and chemical compositionof PM.

1352-2310/99/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 1 3 5 2 - 2 3 1 0 ( 9 9 ) 0 0 2 3 6 - 8

Atmospheric PM consists of inorganic and organicspecies such as sulfate, nitrate, chloride, water content,soil dust, elemental carbon, and organic carbon. Some ofthem are emitted directly into the atmosphere (primaryPM), whereas others are formed in the atmosphere fromthe reactions of gases (secondary PM). Inorganic andorganic compounds roughly comprise 25}50% and40}65% of "ne particle mass, respectively (Gray et al.,1986). Considerable e!ort has been directed toward anunderstanding of the physical and chemical properties ofinorganic aerosols and several inorganic aerosol thermo-dynamic modules have been developed during the pasttwo decades. Such modules include EQUIL (Bassett andSeinfeld, 1983), KEQUIL (Bassett and Seinfeld, 1984),MARS (Saxena et al., 1986), SEQUILIB (Pilinis andSeinfeld, 1987), SCAPE and SCAPE2 (Kim et al., 1993a,b;Kim and Seinfeld, 1995; Meng et al., 1995), MARS-A(Binkowski and Shankar, 1995), EQUISOLV andEQUISOLV II (Jacobson et al., 1996a; Jacobson,1999a,b), AIM and AIM2 (Wexler and Seinfeld, 1990,1991;Clegg et al., 1992,1994,1995,1998a,b), ISORROPIA(Nenes et al., 1998,1999), and GFEMN (Ansari and Pan-dis, 1999a). All these modules simulate internally mixedparticles, i.e., all particles simulated in a given particle sizerange have the same composition. Most modules assumethat thermodynamic equilibrium exists between the gasand particulate phases for the volatile compounds. Non-equilibrium between the bulk gas phase and the particleshas been suggested by some observations (Allen et al.,1989) and non-equilibrium conditions involving masstransport between the bulk gas and particulate phaseshave been simulated with AIM, SCAPE2, andEQUISOLV/EQUISOLV II. Modeling of secondary or-ganic aerosol (SOA) formation and thermodynamics ismore di$cult due mainly to major uncertainties in thegas-phase chemistry of SOA formation, phase-partitioningof the condensable organic gases, and thermodynamics oforganic PM. Among these modules, only SCAPE2 andEQUISOLV/EQUISOLV II include simple thermodyn-amic treatments for a few organic compounds.

We focus here on the treatment of the thermodynamicequilibrium of inorganic species and present a quantitat-ive evaluation of "ve thermodynamic equilibrium mod-ules that are currently used in three-dimensional (3-D) airquality PM models. The comparison is performedin stand-alone modes (i.e., outside of their 3-D hostair quality models) to eliminate the in#uence of otheratmospheric processes (e.g., gas-phase chemistry andtransport) treated in these 3-D host models. Thus, thedi!erences in PM predictions among these modules aredue solely to the di!erences in the model formulationsand/or numerical algorithms. The modules selected forcomparison include MARS-A, SEQUILIB, SCAPE2,EQUISOLV II, and AIM2. We initially usedEQUISOLV for this comparison and identi"ed thatunder some conditions the numerical solution did not

converge. In conjunction with this work, an improvedversion of EQUISOLV, i.e., EQUISOLV II, was thendeveloped (Jacobson, 1999b) and used for the rest of thisstudy. MARS-A is used in EPA Models-3 (Binkowskiand Shankar, 1995) and the Denver Air Quality Model,DAQM (Middleton, 1997). SEQUILIB is used inSAQM-AERO (Dabdub et al., 1997) and UAM-AERO(Lurmann et al., 1997). SCAPE2 is used in the CIT model(Meng et al., 1998). EQUISOLV II is used in GATOR(Jacobson et al., 1996b; Jacobson, 1997). A revised ver-sion of AIM has been incorporated in UAM-IV (Sun andWexler, 1998).

Our objectives are to gain an understanding of therelative strengths and weaknesses of each thermodynamicequilibrium module by comparing the module predictionsunder a variety of thermodynamic regimes, to suggestfurther improvements of their performance, and to pro-vide recommendations for the selection of such modulesfor applications in future 3-D PM modeling studies. Theparticle size distribution and size-resolved chemical equi-librium are not taken into account in this comparison.

2. Description of thermodynamic equilibrium modules

Tables 1 and 2 summarize the major characteristics ofthe "ve thermodynamic modules and the equilibria in-cluded in these modules, respectively. All "ve modulessimulate the partitioning of chemical species among gas,aqueous, and solid phases. However, there are majordi!erences in many aspects of the module formulations.These di!erences will be described in detail along withthe discussion of results in Section 3.3. There are threeversions of AIM2. AIM2-Model I simulates theH`}SO2~

4}NO~

3}Cl~}Br~}H

2O system under strato-

spheric conditions for temperatures from less than200}328 K; AIM2-Model II simulates the H`}NH`

4}

SO2~4}NO~

3}H

2O system under tropospheric conditions

at any tropospheric temperatures; and AIM2-Model IIIsimulates the H`}NH`

4}Na`}SO2~

4}NO~

3}Cl~}H

2O

system under tropospheric conditions and is restricted to298.15 K only. AIM2-Model III is used in this study andis referred to as AIM2.

3. Comparison of simulation results

3.1. Simulation conditions and comparison procedures

The "ve modules were run for 20 di!erent sets of initialcompositions, as listed in Table 3. These compositionscover most of the expected range of thermodynamicequilibrium regimes under typical urban and coastalatmospheric conditions. For each condition, we conduc-ted 10 simulations using 10 di!erent RHs ranging from10 to 95% for 298.15 K. The simulations were repeatedfor 308.15 K (except for AIM2). Although SCAPE2 and

118 Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137

Tab

le1

Maj

orch

arac

terist

ics

ofM

AR

S-A

,SEQ

UIL

IB,SC

APE2,

EQ

UIS

OL

VII

,an

dA

IM2

MA

RS-A

SE

QU

ILIB

SC

AP

E2

EQ

UIS

OL

VII

AIM

2

Che

mic

alsp

ecie

str

eate

din

the

ther

mo-

dyna

mic

equilib

rium

calc

ulat

ions

!

Sulfat

e,ni

trat

e,am

moniu

m,w

ater

Sulfat

e,ni

trat

e,am

moniu

m,s

odiu

m,

chlo

ride

,w

ater

Sulfat

e,ni

trat

e,am

moni

um

,ch

loride

,so

diu

m,p

ota

ssiu

m,

calc

ium

,m

agnes

ium

,car

bon

ate,

wat

er

Sulfat

e,ni

trat

e,am

moni

um

,ch

loride

,so

diu

m,p

ota

ssiu

m,

calc

ium

,m

agnes

ium

,car

bon

ate,

wat

er

Sulfat

e,ni

trat

e,am

moni

um

,so

dium

,ch

loride

,eig

htco

mpl

exsa

lts

ofam

moniu

man

dso

dium

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ater

Act

ivity

coe$

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rm

ethod

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ethod

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Tem

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hod

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tion

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ewto

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tion

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n(M

FI)

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ytic

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rium

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imiz

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nofth

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tial

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tic

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ces$

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kow

skian

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anka

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nis

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nfel

d(1

987)

Kim

etal

.(19

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b),

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nfe

ld(1

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and

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5)

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,b)

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2,19

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ever

,they

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ract

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oth

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sin

the

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mod

ynam

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uili

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calc

ulat

ion.F

orex

ample

,sev

eral

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UIS

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.SC

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cluded

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odel

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quire

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atio

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ary

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ents

.#A

IM2-

Mod

els

Ian

dII

(for

H`

,N

O~ 3

,SO

2~ 4,C

l~,B

r~,H

2Oan

dH

`,N

H` 4

,N

O~ 3,SO

2~ 4,H

2O,re

spec

tive

ly)ac

count

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per

atur

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enden

ceof

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odel

edpr

oper

ties

incl

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geq

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rium

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,solu

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ties

,and

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zing

poin

ts.T

heve

rsio

nofA

IM2

(i.e.,A

IM2-

Model

III)

use

dfo

rth

isco

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ison

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rth

esy

stem

H`

,N

H` 4

,Na`

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~ 3,SO

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2Oan

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only

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ence

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me

mod

ules

.

Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137 119

Tab

le2

Chem

ical

equi

libr

ium

reac

tion

sin

clude

din

MA

RS-

A,SEQ

UIL

IB,S

CA

PE2,

EQ

UIS

OL

VII

,an

dA

IM2

Equili

brium

reac

tion

Equili

brium

const

ant!

,"

K(2

98.1

5)a

bM

AR

S-A

SEQ

UIL

IBSC

APE

2EQ

UIS

OLV

IIA

IM2.

E1

H2SO

4(aq)"

H`(a

q)#

HSO

~ 4(a

q)

1.0]

103$

**

@E2

HSO

~ 4(a

q)"

H`

(aq)#

SO

2~ 4(a

q)

1.01

5]10

~2%

8.85

25.1

4@

@@

@@

E3

NH

3(g)"

NH

3(aq)

5.76

39]

101

13.7

9!

5.39

3@

@@#

E4a

NH

3(aq)#

H2O

(l)"

NH

` 4(a

q)#

OH

~(a

q)

1.80

5]10

~5

!1.

5026

.92

@@

@#

E4b

NH

3(g)#

H`(a

q)"

NH

` 4(a

q)

1.06

77]

1011

$*

*@

E5

HC

l(g)"

H`(a

q)#

Cl~

(aq)

1.97

1]10

630

.20

19.9

1@

@@

@E6

HN

O3(g

)"H

`(a

q)#

NO

~ 3(a

q)

2.51

1]10

6&29

.17

16.8

3@

@@

@@

E7

H2O

(l)"

H`(a

q)#

OH

~(a

q)

1.01

0]10

~14

!22

.52

26.9

2@

@@

@E8

Na 2S

O4(s

)"2N

a`(a

q)#

SO

2~ 4(a

q)

4.79

9]10

~1

0.98

39.7

5@

@@

@E9

NH

4Cl(s)"

NH

3(g)#

HC

l(g)

1.08

6]10

~16

!71

.00

2.40

@@

@#

@E10

(NH

4) 2SO4(s

)"2N

H` 4(a

q)#

SO

2~ 4(a

q)

1.81

7'!

2.65

38.5

7@

@@

@E11

NaC

l(s)"

Na`

(aq)#

Cl~

(aq)

3.76

61]

101

!1.

5616

.90

@@

@@

E12

NaN

O3(s

)"N

a`(a

q)#

NO

~ 3(a

q)

1.19

77]

101

!8.

2216

.01

@@

@@

E13

NH

4NO

3(s)"

NH

3(g)#

HN

O3(g

)5.

746]

10~17

)!

74.3

86.

12@

@@

@#

@E14

NaH

SO

4(s)"

Na`

(aq)#

HSO

~ 4(a

q)2.

413]

104*

0.79

14.7

46@

@@

@E15

NH

4HSO

4(s)"

NH

` 4(a

q)#

HSO

~ 4(a

q)

2.55

]10

2+!

2.87

15.8

3@

@@

E16

(NH

4) 3H(S

O4) 2(s

)"3N

H` 4(a

q)#

HSO

~ 4(a

q)#

SO

2~ 4(a

q)4.

0026

]10

1,!

5.19

54.4

0@

@@

E17

NH

4Cl(s

)"N

H` 4(a

q)#

Cl~

(aq)

2.20

5]10

1$!

5.95

16.9

1@

@E18

NH

4NO

3(s)"

NH

` 4(a

q)#

NO

~ 3(a

q)1.

4863

]10

1$!

10.3

6417

.561

@@

E19

NH

3(g)#

HN

O3(g

)"N

H` 4(a

q)#

NO

~ 3(a

q)2.

587]

1017

$,-

64.0

211

.44

@@

@@

E20

NH

3(g)#

HC

l(g)"

NH

` 4(a

q)#

Cl~

(aq)

2.02

5]10

17$

65.0

514

.51

@@#

@E21

NaC

l(s)#

HN

O3(g

)"N

aNO

3(s)#

HC

l(g)

4.00

8$5.

63!

2.19

@@#

@E22

Na 3H

(SO

4) 2(s)"

3Na`

(aq)#

HSO

~ 4(a

q)#

SO2~ 4

(aq)

1.79

39]

101$

**

@E23

(NH

4) 2SO4)2

NH

4NO

3(s)"

4NH

` 4(a

q)#

SO

2~ 4(a

q)#

2NO

~ 3(a

q)

8.50

30]

101$

**

@

E24

(NH

4) 2SO4)3

NH

4NO

3(s)"

5NH

` 4(a

q)#

SO

2~ 4(a

q)#

3NO

~ 3(a

q)

8.80

20]

102$

**

@

E25

NH

4HSO

4)N

H4N

O3(s

)"2N

H` 4

(aq)#

HSO

~ 4(a

q)

#N

O~ 3(a

q)1.

2792

]10

3$*

*@

E26

Na 2S

O4)1

0H2O

(s)"

2Na`

(aq)#

SO2~ 4

(aq)#

10H

2O(l)

5.96

66]

10~2$

**

@E27

Na 2S

O4)N

aNO

3)H

2O(s)"

3Na`

(aq)#

SO2~ 4

(aq)

#N

O~ 3(a

q)#

H2O

(l)8.

0592

]10

~1$

**

@

E28

NaH

SO

4)H

2O(s)"

Na`

(aq)#

HSO

~ 4(a

q)#

H2O

(l)7.

5206

]10

1$*

*@

E29

NaH

3(SO

4) 2)H

2O(s)"

Na`

(aq)#

2HSO

~ 4(a

q)

#H

`(a

q)#

H2O

(l)5.

9121

]10

8$*

*@

E30

Na 2S

O4(N

H4) 2SO

4)4

H2(s

)"2N

a`(a

q)#

2SO

2~ 4(a

q)#

2NH

` 4(a

q)#

4H2O

(l)

2.02

84]

10~2$

**

@

E31

KC

l(s)"

K`(a

q)#

Cl~

(aq)

8.68

0!

6.90

119

.95

@#

@#

E32

K2S

O4(s

)"2K

`(a

q)#

SO

2~ 4(a

q)1.

569]

10~2

!9.

585

45.8

1@#

@#

E33

KH

SO

4(s)"

K`

(aq)#

HSO

~ 4(a

q)2.

4016

]10

1!

8.42

817

.97

@#

@#

E34

KN

O3(s

)"K

`(a

q)#

NO

~ 3(a

q)

8.72

]10

~1

!14

.07

19.3

8@#

@#

E35

CaC

l 2(s)"

Ca2

`(a

q)#

2Cl~

(aq)

7.97

4]10

11*

*@#

@#

E36

CaS

O4)2

H2O

(s)"

Ca2

`(a

q)#

SO

2~ 4(a

q)#

2H2O

(l)4.

319]

10~5

**

@#

@#

120 Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137

E37

Ca(

NO

3) 2(s)"

Ca2

`(a

q)#

2NO

~ 3(a

q)

6.60

7]10

5*

*@#

@#

E38

MgC

l 2(s)"

Mg2

`(a

q)#

2Cl~

(aq)

9.55

7]10

21*

*@#

@#

E39

MgS

O4(s

)"M

g2`(a

q)#

SO

2~ 4(a

q)1.

079]

105

**

@#

@#

E40

Mg(

NO

3) 2(s)"

Mg2

`(a

q)#

2NO

~ 3(a

q)2.

507]

1015

**

@#

@#

E41

CO

2(g)"

CO

2(aq)

3.40

4]10

~2

8.18

58!

28.9

307

@#

@#

E42

CO

2(aq)#

H2O

(l)"

HC

O~ 3

(aq)#

H`(a

q)

4.29

9]10

~7

!3.

0821

31.8

139

@#

@#

E43

HC

O~ 3(a

q)"

H`(a

q)#

CO

2~ 3(a

q)

4.67

8]10

~11

!5.

9908

38.8

440

@#

@#

E44

NH

3(aq)#

HC

O~ 3"

NH

2CO

~ 2(a

q)#

H2O

(l)3.

0424

9.71

19*

@#

E45

Na 2C

O3(s

)"2N

a`(a

q)#

CO

2~ 3(a

q)

1.81

1]10

110

.771

330

.553

3@#

@#

E46

NaH

CO

3(s)"

Na`

(aq)#

HC

O~ 3(a

q)

3.91

4]10

~1

!7.

5439

!5.

6796

@#

@#

E47

K2C

O3(s

)"2K

`(a

q)#

CO

2~ 3(a

q)2.

541]

105

12.4

575

36.7

272

@#

@#

E48

KH

CO

3(s)"

K`(a

q)#

HC

O~ 3(a

q)1.

399]

101

!7.

5964

!2.

5210

@#

@#

E49

CaC

O3(c

alci

te,s

)"C

a2`(a

q)#

CO

2~ 3(a

q)

4.95

9]10

~9

**

@#

@#

E50

MgC

O3(s

)"M

g2`(a

q)#

CO

2~ 3(a

q)6.

812]

10~6

**

@#

@#

E51

NH

2CO

ON

H4(s

)"N

H2C

O~ 2

(aq)#

NH

` 4(a

q)6.

4023

]10

1*

*@#

!The

subsc

ripts

g,aq

,l,a

nd

sin

the

equili

briu

mre

actions

repre

sent

conce

ntra

tion

sof

the

spec

iesin

the

gas,

the

aque

ous,

the

liqui

d,a

nd

the

solid

phas

es,

resp

ective

ly.Equ

ilibrium

cons

tant

sar

eex

pre

ssed

as:

K(¹

)"K

(¹0)e

xpGa A¹

0¹

!1 B#

b A1#lnA¹

0¹B!

¹0

¹BH,w

her

e¹

0"29

8.15

K

The

valu

esof

equili

brium

cons

tants

are

those

use

din

SC

APE

2ex

ceptoth

erw

ise

indic

ated

.The

equi

librium

cons

tants

used

inth

eot

her

module

sar

eth

esa

me

asor

sim

ilar

toth

ose

ofSC

AP

E2

exce

pt

oth

erw

ise

indi

cate

d."T

he

units

for

equi

librium

const

ants

are:

A(a

q)"

B(a

q)#

C(a

q)m

olk

g~1

A(g

)"xB

(aq)#

yC(a

q)m

ol(x

`y)

kg~

(x`

y)at

m~

1

A(s)"

B(g

)#C

(g)a

tm2

A(s)"

xB(a

q)#

yC(a

q)#

zD(a

q)m

ol(x

`y`

z)kg

~(x`

y`z)

A(g

)#B(g

)"C

(aq)#

D(a

q)m

ol2

kg~

2at

m~2

A(a

q)#

B(a

q)"

C(a

q)k

gm

ol~

1

#The

equili

briu

mre

actions

are

incl

ude

din

the

origi

nal

module

form

ula

tion

butnot

use

dfo

rth

eba

sesim

ula

tions

inth

isw

ork

.$The

equili

brium

const

ants

forE1

and

E17

!E

21ar

eth

ose

used

inE

QU

ISO

LV

II.T

heeq

uili

brium

const

ants

forE4b

and

E22

-E30

are

those

used

inA

IM2.

%The

valu

esof

K,a,

and

bfo

rE

2ar

e1.

031]

10~

2,7.

59,an

d18

.825

inSE

QU

ILIB

,res

pec

tive

ly.

&The

valu

esof

K,a,

and

bfo

rE

6ar

e3.

638]

106,

29.4

7,an

d16

.835

inSEQ

UIL

IB,re

spec

tive

ly.

'The

valu

esof

K,a,

and

bfo

rE

10ar

e1.

425,

!2.

65,an

d38

.55

inSE

QU

ILIB

,re

spec

tive

ly.

)T

he

valu

esof

K,a

,and

bfo

rE

13ar

e2.

986]

10~

17,!

75.1

08,a

nd13

.456

inSE

QU

ILIB

,and

4.19

94]

10~

17,!

74.7

531,

and

6.02

5in

MA

RS-A

,re

spec

tive

ly.

*The

valu

esofK

,a,an

db

for

E14

are

2.44

]10

4,0.

79,an

d4.

53in

SEQ

UIL

IB,re

spec

tive

ly.

+The

valu

esof

K,a,

and

bfo

rE

15ar

e1.

383]

102,

!2.

87,an

d15

.83

inE

QU

ISO

LV

II,r

espe

ctiv

ely.

,The

valu

esofK

,a,an

db

for

E16

are

2.92

6]10

1,!

5.19

,and

54.4

0in

EQ

UIS

OLV

II,re

spec

tive

ly.

-The

valu

esofK

,a,a

nd

bfo

rE

19ar

e2.

5865

]10

17,6

3.98

,and

11.4

4in

MA

RS-

A,a

nd3.

999]

1017

,64.

698,

and

11.5

05in

SEQ

UIL

IB,

resp

ective

ly.

.The

vers

ion

ofA

IM2

use

din

this

wor

kis

rest

rict

edto

298.

15K

onl

y.A

IM2

does

notw

ork

inte

rms

ofeq

uili

briu

mco

nsta

nts.

The

valu

esofK

(298

.15)

wer

eco

mpu

ted

base

don

the

Gib

bsen

ergi

esoffo

rmat

ion

used

inA

IM2.

Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137 121

Table 3List of conditions for thermodynamic equilibrium module simulations!

Initial compositions Total ammonium/sulfatemole ratio

Total nitrate/sulfatemole ratio

Total sodium chloride/sulfatemole ratio

1 0.5 1.0 02 1.0 1.0 03 1.5 1.0 04 2.0 1.0 05 4.0 1.0 06 1.5 0.33 07 4.0 0.33 08 1.5 3.0 09 4.0 3.0 0

10 0.5 1.0 0.511 1.0 1.0 0.512 1.5 1.0 0.513 2.0 1.0 0.514 4.0 1.0 0.515 1.5 0.33 0.516 4.0 0.33 0.517 1.5 3.0 0.518 4.0 3.0 0.519 1.5 1.0 2.020 4.0 1.0 2.0

!Particulate sulfate concentration is 20 lg m~3 for all initial compositions. Simulations under each set of initial compositions wereconducted for 10, 20, 30, 40, 50, 60, 70, 80, 90 and 95% relative humidity (RH) and temperatures of 298.15 and 308.15 K.

EQUISOLV II treat potassium, calcium, magnesium,and carbonate, these species are not included here. Thehysteresis and the Kelvin e!ects can be simulated inSCAPE2, EQUISOLV II, and AIM2, however, they arenot considered in this study.

For the 20 conditions, the concentration of total sul-fate is set to be a constant value of 20 lg m~3. H

2SO

4has

a very low vapor pressure; consequently, it is presentsolely in the particulate phase and its concentration isused as a reference for the other species. For the purposeof this analysis, we de"ne the initial atmospheric chem-ical concentrations according to the following four di-mensionless ratios: the molar ratio of total ammonium(i.e., sum of gaseous ammonia, NH

3(g), and particulate

ammonium, NH`4(p)) to total sulfate (referred to as

TNH4/TSO

4), the molar ratio of total nitrate (i.e., sum of

gaseous nitric acid, HNO3(g), and particulate nitrate,

NO~3(p)) to total sulfate (referred to as TNO

3/TSO

4), the

molar ratio of total sodium chloride to total sulfate(referred to as TNaCl/TSO

4), and the molar ratio of total

cation species (i.e., sum of total ammonium, TNH4, and

total sodium, TNa) to total sulfate (referred to asTCAT/TSO

4). The particulate phase concentrations of

ammonium, nitrate, and chloride (i.e., NH`4(p), NO~

3(p),

and Cl~(p)) include their concentrations in the solidand aqueous phases. If TCAT/TSO

4(2, the system

contains excess sulfate and is called sulfate-rich. IfTCAT/TSO

4"2, the system contains just su$cient

sulfate to neutralize the cation species and is called sul-fate-neutral. If TCAT/TSO

4'2, the system does not

contain enough sulfate to neutralize the cation speciesand is called sulfate-poor. For the 20 sets of conditions,conditions 1}3, 6, 8, 10, and 11 are sulfate-rich, condi-tions 4, 12, 15, and 17 are sulfate-neutral, and conditions5, 7, 9, 13, 14, 16, and 18}20 are sulfate-poor.

A synoptic comparison of the simulation results isprovided in Section 3.2. The similarities and di!erences inthe model predictions for di!erent thermodynamic re-gimes as well as the likely causes are presented andanalyzed in detail in Section 3.3. In our comparisons,SCAPE2 was used as the reference for MARS-A andSEQUILIB since it contains more chemical species andequilibrium reactions and o!ers more detailed aerosolthermodynamic calculations than MARS-A and SE-QUILIB. Since SCAPE2, EQUISOLV II, and AIM2contain the similar detailed level of chemistry andthermodynamics, we compare results between SCAPE2and EQUISOLV II, between SCAPE2 and AIM2, andbetween EQUISOLV II and AIM2. For each pair ofthese three modules, we use the arithmetic average valuespredicted by each pair as reference.

3.2. Synoptic comparisons

Fig. 1 shows concentrations of total particulate phaseconcentrations of nitrate, ammonium, hydrogen ion,

122 Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137

Fig. 1. A synoptic comparison of concentrations of total particulate-phase concentrations of (a) nitrate, (b) ammonium, (c) hydrogenion, (d) chloride, (e) water, and (f ) total PM predicted by the "ve chemical equilibrium modules under all simulation conditions shownin Table 2 and a temperature of 298.15 K.

Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137 123

Fig. 1. (Continued).

124 Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137

chloride, water, and total PM (labeled as [NO~3]1,

[NH`4]1, [H`]

1, [Cl~]

1, [H

2O]

1, and PM) predicted by

the "ve modules under all simulation conditions. Forcomparisons between MARS-A and SCAPE2, only 90cases were used because MARS-A does not simulatesystems containing NaCl. For comparisons betweenAIM2 and SCAPE2 or EQUISOLV II, only 150 caseswere used because 50 of 200 cases are alkaline and AIM2does not simulate such cases. [NO~

3]1, [NH`

4]1, [H

2O]

1,

and total PM concentrations predicted by these modulesare generally comparable, but there are signi"cant dis-crepancies in the predictions of [H`]

1and [Cl~]

1.

3.2.1. Particulate nitrateUnder most conditions, [NO~

3]1

predicted byMARS-A, SCAPE2, EQUISOLV II, and AIM2 are sim-ilar to each other, whereas SEQUILIB shows signi"cantdeviations from SCAPE2, as shown in Fig. 1(a). Allmodules predict either zero or negligible amountsof NO~

3(p) for RH (30}70% (except in a few cases with

high ammonium and nitrate). Under higher RH condi-tions, MARS-A predicts slightly higher [NO~

3]1

thanSCAPE2 for TNH

4/TSO

4)2 and lower [NO~

3]1

thanSCAPE2 for TNH

4/TSO

4"4. Di!erences in the

[NO~3]1predicted by MARS-A and SCAPE2 are mainly

due to simpli"ed chemistry and thermodynamic calcu-lations used in MARS-A for NO~

3(p). SEQUILIB pre-

dicts signi"cantly higher [NO~3]1than SCAPE2 for most

cases with TNH4/TSO

4"1.5 and 4, but it predicts

signi"cantly lower [NO~3]1

than SCAPE2 for TNH4/

TSO4"1, and zero [NO~

3]1

for some cases withTNH

4/TSO

4"0.5 and 2 even under high RH condi-

tions. SCAPE2 and EQUISOLV II predict similar[NO~

3]1

for all cases with TNH4/TSO

4)2 and

RH'70%. However, [NO~3]1

predicted by SCAPE2are signi"cantly higher than that predicted byEQUISOLV II for some cases with high ammonium andmedium RHs due to di!erent NH

3(g)/NH`

4equilibria

treated in the two modules (see Section 3.3.1). [NO~3]1

predicted by AIM2 are similar to that predicted bySCAPE2 and EQUISOLV II for most acidic cases. Forsome cases with low RHs and high ammonium andnitrate, however, AIM2 predicts higher [NO~

3]1

thanSCAPE2 and EQUISOLV II. This is because AIM2simulates a di!erent chemistry involving complex saltssuch as 2 NH

4NO

3) (NH

4)2SO

4and uses a di!erent

method for calculations of multi-component activitycoe$cients.

3.2.2. Particulate ammonium[NH`

4]1

predicted by MARS-A, SCAPE2,EQUISOLV II, and AIM2 are in good agreement undermost conditions, as shown in Fig. 1(b). SEQUILIB pre-dicts [NH`

4]1deviating within 14% of that predicted by

SCAPE2 for all cases without NaCl, but it predicts signif-icantly higher [NH`

4]1

(up to 37%) than SCAPE2 for

many cases with NaCl and/or TCAT/TSO4'2, due to

more formation of NH4NO

3or NH

4Cl, or both pre-

dicted by SEQUILIB under these conditions. Signi"cantdi!erences in [NH`

4]1

predicted by SCAPE2 andEQUISOLV II are found for some cases with high am-monium and low nitrate regardless of the presence ofNaCl. Out of these cases, [NH`

4]1

predicted byEQUISOLV II are lower than those predicted bySCAPE2 in the absence of NaCl and the results becomejust the opposite in the presence of NaCl due to di!erentsets of NH

3(g)/NH`

4equilibria used in both modules. For

most acidic cases, [NH`4]1

predicted by SCAPE2 andEQUISOLV II are similar to those predicted by AIM2.[NH`

4]1

predicted by AIM2 are higher than those pre-dicted by SCAPE2 and EQUISOLV II for a few caseswith high ammonium and nitrate.

3.2.3. Particulate hydrogen ionFig. 1(c) shows [H`]

1predicted by the "ve modules.

Signi"cant discrepancies exist because of either someassumptions related to H`(p) calculations used inMARS-A and SEQUILIB or the di!erent numericalmethods used to calculate H`(p). For example, MARS-Aand SEQUILIB assume [H`]

1to be zero for all cases

with TCAT/TSO4'2 and TCAT/TSO

4*2, respect-

ively, thus no H`(p) concentrations are computed forthese cases in the two modules. For some sulfate-rich andlow RH cases, MARS-A also predicts [H`]

1to be zero.

For many sulfate rich and low RH cases (i.e., TCAT/TSO

4(2 and RH(70%), [H`]

1predicted by

SCAPE2 are signi"cantly higher than those predicted byother modules because of non convergence of the solu-tions in SCAPE2. For most cases with high RHs, allmodules predict similar [H`]

1except SEQUILIB which

sometimes predicts either zero or abnormally higher[H`]

1. In most cases, the aqueous particle predicted by

SCAPE2 is more acidic than that predictedby EQUISOLV II. In most cases, [H`]

1predicted by

SCAPE2 are either higher or slightly lower than thosepredicted by AIM2, and [H`]

1predicted by

EQUISOLV II are lower than those predicted by AIM2.

3.2.4. Particulate chlorideFig. 1(d) shows that there are substantial di!erences in

[Cl~]1predicted by SEQUILIB, SCAPE2, EQUISOLV

II, and AIM2. For most cases with RH'50%, AIM2,SCAPE2, and EQUISOLV II predict similar [Cl~]

1,

whereas SEQUILIB predicts signi"cantly lower [Cl~]1

than those predicted by the other modules. For mostcases with RH(50%, SEQUILIB, SCAPE2, and AIM2predict no [Cl~]

1. On the other hand, in most of these

cases, EQUISOLV II predicts the co-existence of solidNH

4Cl(s) and NaCl(s), resulting in signi"cantly higher

[Cl~]1

than those predicted by the other three modules.SCAPE2 and AIM2 include similar sets of reactions forNH

4Cl and NH

4NO

3and predict comparable [Cl~]

1.

Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137 125

The di!erent results of SEQUILIB and EQUISOLV IIare due mainly to the fact that the two modules includedi!erent sets of equilibrium reactions for NH

4Cl and

NH4NO

3.

3.2.5. Particulate water contentFor most conditions, [H

2O]

1predicted by the "ve

modules agree well except that SEQUILIB tends to pre-dict lower [H

2O]

1under most conditions, as shown in

Fig. 1(e). This is because the binary water activity dataused in SEQUILIB are di!erent from those used in theother modules. SEQUILIB uses the older binary wateractivity data of Cohen et al. (1987a,b) for most electro-lytes (Pilinis and Seinfeld, 1987), which may be inaccuratefor some salts. Whereas SCAPE2, EQUISOLV II, andAIM2 use the most recent and critically assessed wateractivity data of Chan et al. (1992) and other researchers.The data of Chan et al. (1992) generally result in higherwater content than those of Cohen et al. (1987a,b) (Kimet al., 1993).

3.2.6. Total PM concentrationsAlthough there remain signi"cant discrepancies in the

predicted PM compositions, the total PM concentra-tions predicted by the "ve modules under all conditionsagree remarkably well, except those predicted bySEQUILIB in the high PM concentration range (totalPM'&150 lg m~3), as shown in Fig. 1(f ). Underall conditions, the absolute di!erences are 12.3, 10.8,9.3, 9.2, and 7.7% on average between MARS-A andSCAPE2, SEQUILIB and SCAPE2, EQUISOLV II andSCAPE2, AIM2 and SCAPE2, and EQUISOLV II andAIM2, respectively. The absolute di!erences range from0.1}61, 0}50, 0}67, 0}68, and 0}67% for speci"c cases foreach pair of modules, respectively. Di!erences in PM

2.5and PM

10concentrations will be less because of the

presence of primary species in PM that are not includedin the chemical systems considered here.

3.2.7. Dominant PM compoundsThe dominant PM compounds predicted by the "ve

modules are di!erent for many cases. For cases withTNO

3/TSO

4"1, TCAT/TSO

4'2, and all RHs, MARS-

A predicts (NH4)2SO

4and NH

4NO

3to be dominant;

SEQUILIB predicts either (NH4)2SO

4and NH

4NO

3or

(NH4)2SO

4, NH

4NO

3, Na

2SO

4, and NH

4Cl to be

dominant; SCAPE2 predicts either (NH4)2SO

4alone

or (NH4)2SO

4, NH

4NO

3, Na

2SO

4, and NH

4Cl to be

dominant. EQUISOLV II predicts dominant speciessimilar to those of SCAPE2 for low RHs but an additionalspecies, NH

4NO

3, to be dominant for high RHs; and

AIM2 predicts no results for most of these cases becauseit does not simulate alkaline systems. For the acidicsystems, AIM2 predicts similar dominant species to thoseof SCAPE2 for low RHs but both (NH

4)2SO

4and

Na2SO

4) (NH

4)SO

4) 4H

2O to be dominant for most of

these cases for RH *50%. For cases with TNO3/

TSO4"1, TCAT/TSO

4)2 and all RHs, MARS-A pre-

dicts (NH4)2SO

4and NH

4HSO

4to be dominant, the

other modules predict either bisulfate salts (e.g.,NH

4HSO

4, (NH

4)3H(SO

4)2, and NaHSO

4), H

2SO

4, or

sulfate salts (e.g., (NH4)2SO

4and/or Na

2SO

4) or a com-

bination of these to be dominant. A major di!erencebetween AIM2 and the other modules is that AIM2sometimes predicts more complex salts such asNa

3H(SO

4)2, NaHSO

4)H

2O, and Na

2SO

4) (NH

4)2SO

4)

4H2O to be dominant; such salts are not treated in the

other modules.

3.3. Detailed comparisons

3.3.1. The H`}NH4̀ }NO~3 }SO2~4 }H2O systemSulfate-rich cases. Under sulfate-rich conditions (i.e.,

TNH4/TSO

4(2), sulfate is in excess and the solution is

highly acidic due to insu$cient neutralization by NH`4.

Sulfate may exist as H2SO

4, HSO~

4, and SO2~

4. Most

nitrate remains in the gas phase and most ammoniumresides in the particulate phase. Fig. 2 shows [NO~

3]1,

[NH`4]1, [H`]

1, and [H

2O]

1predicted by the "ve mod-

ules for TNH4/TSO

4"1.5, where sulfate is partially

neutralized mainly as (NH4)3H(SO

4)2

and someNH

4NO

3may be formed.

While [NO~3]1

are negligible for RH)60}70%, theyincrease signi"cantly with RH for higher RHs. [NO~

3]1

from all modules agree within 20% for RH'90% butdi!er notably for RH"60}90% due to di!erences inchemistry and activity calculations. Both MARS-A andSEQUILIB predict higher [NO~

3]1

than the other threemodules for RH '70% but for di!erent reasons. InSEQUILIB, the equilibrium constant for HNO

3(g)Q

H`(aq)#NO~3(aq) is 44% higher than that used in the

other four modules (see Table 2). This causes lower[HNO

3]', thus higher [NO~

3]1. The higher [NO~

3]1

predicted by MARS-A is likely caused by its simpli-"ed chemistry and/or the quadratic approximation inthe calculation of [NO~

3]1. [NH`

4]1

predicted by the"ve modules are in good agreement, with most ammon-ium residing in the particulate phase. NH`

4(p) is mainly

present as (NH4)2SO

4in MARS-A, as (NH

4)2SO

4and/or (NH

4)3H(SO

4)2

in SEQUILIB, SCAPE2,and EQUISOLV II, and as a mixture of (NH

4)3H(SO

4)2

and NH4HSO

4or a mixture of (NH

4)3H(SO

4)2

and(NH

4)2SO

4in AIM2. SCAPE2 predicts some [H`]

1for

all RHs, on the other hand, the other four modulespredict a small [H`]

1(up to 0.06 lg m~3) for

RH'70%. The high [H`]1

predicted by SCAPE2 forRH(60% result from the non-convergence of the nu-merical solution for solid calculations. The large di!er-ences in predicted [H`]

1for RH'60% are due to

di!erences in the chemical species and equilibrium reac-tions treated and the methods used to calculate [H`]

1and the activity coe$cients.

126 Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137

Fig. 2. The concentrations of (a) NO~3

(p), (b) NH`4

(p), (c) H`(p), and (d) H2O(p) as a function of RH predicted by the "ve modules at

a temperature of 298.15 K under sulfate-rich (i.e., TNH4/TSO

4"1.5) conditions.

[H2O]

1predicted by the "ve modules are in good

agreement for RH'70%, but show some di!erences formedium and low RHs. [H

2O]

1predicted by MARS-A

are signi"cantly higher than those predicted by othermodules for 30%(RH(70%. This di!erence is causedby di!erent phase partitioning of relevant species inMARS-A and the other modules. All modules exceptMARS-A predict particulate sulfate and nitrate species(e.g., (NH

4)2SO

4, (NH

4)3H(SO

4)2, and NH

4NO

3) to par-

tition between solid and aqueous phases, depending ontheir deliquescence relative humidities (DRHs) in themulticomponent system. For 30%(RH(70%, vari-ous solid species can exist alone or co-exist with liquidspecies in these modules. On the other hand, MARS-Adoes not treat mixed-phase salts, namely, it assumes thatvarious salts are present either in the solid phase or in theaqueous phase, depending on the values of TNH

4/TSO

4and the assumed crystallization relative humidities(CRHs). For TNH

4/TSO

4*1 and RH'40%, MARS-

A predicts that all salts exist in the aqueous phase even

though these salts may be present in both solid andaqueous phases. As a result of this assumption, MARS-Apredicts much higher electrolytes and water activity,thus, higher [H

2O]

1for 30%(RH(70%.

Sulfate-neutral and sulfate-poor cases. Under sulfate-neutral and sulfate-poor conditions (TNH

4/TSO

4*2),

sulfate is fully neutralized as (NH4)2SO

4and the system

may become alkaline. The excess NH3(g) drives nitrate

from the gas to the particulate phase to form NH4NO

3via the NH

3}HNO

3equilibrium, resulting in the forma-

tion of a large amount of NH4NO

3for high RHs under

both sulfate-neutral and sulfate-poor conditions and pre-cipitation of some NH

4NO

3(s) for low RHs under

sulfate-poor conditions. Fig. 3 shows [NO~3]1

predictedby the "ve modules under sulfate-neutral (i.e., TNH

4/

TSO4"2) and sulfate-poor (i.e., TNH

4/TSO

4"4)

conditions.For TNH

4/TSO

4"2, [NO~

3]1

are negligible forRH)60}70%. [NO~

3]1predicted by all modules except

SEQUILIB signi"cantly increase with RH for higher

Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137 127

Fig. 3. The concentrations of NO~3

(p) as a function of RH predicted by the "ve modules at a temperature of 298.15 K under(a) sulfate-neutral (i.e., TNH

4/TSO

4"2), and (b) sulfate-poor (i.e., TNH

4/TSO

4"4) conditions.

RHs (up to 4.5 lg m~3), as more HNO3

dissolves anddissociates in the aqueous particles. By contrast, [NO~

3]1

predicted by SEQUILIB becomes negligible (which wasnon-negligible at RH'70% for TNH

4/TSO

4"1.5).

This is due to a simpli"ed treatment used in SEQUILIB,which assumes no excess NH

3(g) exists (thus no

NH4NO

3formation) for TNH

4/TSO

4"2.

For TNH4/TSO

4"4, the system is alkaline and the

excess NH3(g) results in substantial increases in concen-

trations of NH4NO

3(up to 12 lgm~3) for high RHs in

all modules except AIM2 (AIM2 does not simulatealkaline systems). Some NH

4NO

3precipitates for low

RHs in MARS-A and SEQUILIB. For RH(70%,[NO~

3]1

predicted by the four modules show signi"cant

128 Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137

Fig. 4. The PM chemical composition at RH"70% predicted by the "ve modules at a temperature of 298.15 K under sulfate-neutral(i.e., TNH

4/TSO

4"2) conditions.

discrepancies; agreement between them improves asRH increases. The dissociation equilibrium constantfor NH

4NO

3(s)QNH

3(g)#HNO

3(g) at 298.15 K in

MARS-A and in SEQUILIB are about 27 and 48%,respectively, lower than that used in SCAPE2 andEQUISOLV II (see Table 2). These lower equilibriumconstants result in lower NH

3(g) and HNO

3(g) thus

higher [NO~3]1

in both MARS-A and SEQUILIB thanSCAPE2 and EQUISOLV II for RH(50%. There arelarge di!erences in [NO~

3]1

predicted by SCAPE2 andEQUISOLV II for 40%(RH(80%. This can be at-tributed to two major reasons. First, NH

3/NH`

4equilib-

ria treated in the two modules are di!erent. EQUISOLVII o!ers the options to include the solid-gas and/or thesolid-liquid equilibria of NH

4Cl(s) and NH

4NO

3(s)

(i.e., E9, E13, E17, and E18, Table 2). The results ofEQUISOLV II were obtained by only turning on E17and E18. On the other hand, SCAPE2 only treats thesolid-gas equilibria of NH

4Cl(s) and NH

4NO

3(s) (i.e., E9

and E13). Second, activity coe$cients for some relevantion pairs used in the two modules are di!erent. InEQUISOLV II, the binary activity coe$cients are basedon either measurement data or published parameters,whereas in SCAPE2, the binary activity coe$cients forsome ion pairs (e.g., for NH`

4/OH~ ion pair) are assumed

to be 1.The PM composition predicted by the "ve modules

under some conditions di!ers signi"cantly. Fig. 4 shows

the predicted PM composition for TNH4/TSO

4"2

and RH"70%. Under this condition, MARS-A,SEQUILIB, and SCAPE2 predict no solid formation,whereas EQUISOLV II and AIM2 predict 23}27 lg m~3

of (NH4)2SO

4(s). Since [H

2O]

1is a strong function of

electrolyte molality (i.e., the moles of cations and anionsper kg of solution) for a given RH ((100%), the di!er-ences in PM composition and molality lead to23}25 lg m~3 of H

2O(p) formed in MARS-A, SE-

QUILIB, and SCAPE2 but only 1}4 lg m~3 of H2O(p)

formed in EQUISOLV II and AIM2.

3.3.2. The H`}Na`}NH4̀ }NO~3 }SO2~4 }Cl~}H2O SystemThe presence of NaCl reduces the acidity and increases

water content in the particle, causing signi"cant changesin thermodynamic equilibria in the system. Di!erences inthe simulation results for systems containing NaClamong the four modules (MARS-A does not treat NaCl)are generally greater than those without NaCl. Mostsigni"cant changes occur in the aforementioned sulfate-rich and sulfate-neutral systems because they becomesulfate-neutral and sulfate-poor conditions, respectively.In particular, [Cl~]

1predicted by these modules exhibit

signi"cant di!erences.Fig. 5(a) shows [Cl~]

1predicted by the four modules

for TNH4/TSO

4"4. For RH(50%, no Cl~(p) is for-

med in SEQUILIB, SCAPE2, and AIM2 but NH4Cl(s)

can be formed in EQUISOLV II. No NaCl(s) can be

Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137 129

Fig. 5. The concentrations of Cl~(p) predicted by SEQUILIB, SCAPE2, EQUISOLV II, and AIM2 at a temperature of 298.15 K for thesulfate-poor system with TNH

4/TSO

4"2, TNO

3/TSO

4"1, and TNaCl/TSO

4"0.5 using (a) the original formulation, (b) a set of

reactions similar to that used in SCAPE2.

formed under these conditions in all modules. ForRH*50%, [Cl~]

1predicted by SCAPE2, EQUISOLV

II, and AIM2 are comparable but SEQUILIB predictssigni"cantly lower [Cl~]

1(by a factor of 2}5) than the

other modules. The signi"cant di!erences in total [Cl~]1

predicted by these modules can be attributed to di!erent

sets of reactions for NH4NO

3, NH

4Cl, and their disso-

ciated ions. The most important reactions a!ecting theequilibria of NH

4Cl and NH

4NO

3include E3}E6,

E9, E13, and E17}E20. NH3(g), HNO

3(g), and HCl(g)

dissolve in the solution to form ionic species throughequilibria E3}E6 and E19}E20 given su$cient liquid

130 Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137

water (e.g., for RHs greater than DRHs of NH4NO

3(s),

62%, and NH4Cl(s), 80%, or supersaturation). Under

certain conditions (e.g., when RH decreases), these ionsmay precipitate to form NH

4Cl(s) and NH

4NO

3(s) via

E17}E18. Under low RHs, E9 and E13 can also directlylead to either the formation of NH

4Cl(s) and NH

4NO

3(s)

from heterogeneous reactions of NH3(g) with HCl(g) and

HNO3(g) on the particle or the release of NH

3(g), HCl(g),

and HNO3(g) from NH

4Cl(s) and NH

4NO

3(s).

SEQUILIB includes E5, E6, E19, and E20 and thesolid}gas equilibria of NH

4Cl(s) and NH

4NO

3(s) (i.e., E9

and E13). SCAPE2 includes E3, E4a, E5, E6, E9, andE13. EQUISOLV II includes E5, E6, and E19, thesolid}liquid and the solid}gas equilibria of NH

4Cl(s) and

NH4NO

3(s) (i.e., E9, E13, E17, and E18) but o!ers the

options to turn on/o! individual reactions. The results ofEQUISOLV II shown in Fig. 5(a) were obtained byturning on E17 and E18 and turning o! E9 and E13.AIM2 simulates E4b, E5, E6, E9, E13, E17}E20 and thesolid}liquid equilibria of double salts involving am-monium and nitrate, E23}E25.

Although it is a formidable task to make chemicalspecies and equilibrium reactions identical in these mod-ules due to their di!erent formulations, we conductedadditional simulations of SEQUILIB, EQUISOLV II,and AIM2 using a set of reactions similar to that used inSCAPE2 and the results are shown in Fig. 5(b). WhenE19 is turned o! and the equilibrium constants of E6 andE13 were set to be the same values as those in SCAPE2,SEQUILIB can predict [Cl~]

1that are much closer to

those predicted by SCAPE2 under high RHs. When E9and E13 are turned on, EQUISOLV II yields resultssimilar to those of the other three modules, i.e., no pre-cipitation of NH

4Cl(s) under low RHs. AIM2 also pre-

dicts [Cl~]1

that are much closer to those predicted bythe other three modules for 60%(RH(80% when allequilibria involving complex salts such as E23}E25 areturned o!. [Cl~]

1predicted by all the four modules agree

within 36% for most RHs if a similar set of reactionsis used in these modules. In addition, results ofEQUISOLV II using both the di!erent and similar setsof reactions show that the solid}gas equilibria E9 andE13 dominate in the system. They favor the release ofNH

3(g), HNO

3(g), and HCl(g), resulting in no NH

4Cl(s)

formation under low RH conditions.It is not clear which of these reactions will likely occur

and dominate under typical atmospheric ambient PMconditions. It is likely that NH`

4and Cl~ ions can pre-

cipitate to form NH4Cl(s) through E17 under certain low

and medium RHs when present alone in the particle sincethe DRH of NH

4Cl(s) is 80%. However, it is an open

question whether NH4Cl(s) can precipitate in particles

containing multiple salts under such conditions. Labor-atory data are urgently needed to resolve this issue and toprovide guidance for improvements in the formulation ofthermodynamic equilibrium modules.

3.3.3. Sensitivity of PM predictions

3.3.3.1. Ewect of the ratio of total nitrate to total sulfate,TNO3/TSO4. In the eastern US, the total nitrate concen-trations are usually less than the total sulfate concentra-tions, while they are generally greater than the totalsulfate concentrations in the western US. TNO

3/TSO

4a!ects the thermodynamic equilibrium between the gasand particulate phases and the di!erences in the PMcomposition predicted by these modules.

For the sulfate-rich systems, the simulation resultspredicted by the "ve modules are insensitive or moder-ately sensitive to the values of TNO

3/TSO

4because the

concentrations of NH4NO

3are small and sulfate salts

are predominant. The PM predictions are generally com-parable for the sulfate-rich systems. The sensitivity ofthese modules to the values of TNO

3/TSO

4increases

signi"cantly for the sulfate-poor system, in which theexcess gaseous ammonia and nitric acid drive NH

3(g)

and HNO3(g) from the gas phase to the particulate phase

to form a large amount of NH4NO

3. Signi"cant discrep-

ancies exist and increase when the values of TNH4/TSO

4and TNO

3/TSO

4increase for the sulfate-poor condi-

tions, under which the e!ects of di!erent formulations inthese modules become much more appreciable than un-der the sulfate-rich conditions.

As a consequence of changes in PM compositions andtheir concentrations when TNO

3/TSO

4varies, the pre-

dicted total PM concentrations also increase withTNO

3/TSO

4, especially for high RHs. For the sulfate-

rich systems with TNH4/TSO

4"1.5 and RH"95%,

the total PM concentrations predicted by MARS-A areinsensitive to changes in TNO

3/TSO

4. The other four

modules predict similar moderate sensitivity to changesin TNO

3/TSO

4, i.e., the total PM concentrations in-

crease by 19}28% when TNO3/TSO

4increases from 0.33

to 3. For the sulfate-poor systems with TNH4/TSO

4"4

and RH "95%, the sensitivity of total PM concentra-tions predicted by all modules except AIM2 (AIM2 doesnot simulate alkaline systems) increases signi"cantly. Thetotal PM concentrations increase by 89}123% whenTNO

3/TSO

4varies from 0.33 to 3.

3.3.3.2. Ewect of the ratio of total sodium chloride to totalsulfate, TNaCl/TSO4. The presence of NaCl can causedramatic changes in the systems considered here. For thesulfate-rich system, the neutralization of sulfate and ni-trate can be greatly enhanced through formation ofNa

2SO

4and/or NaNO

3in the presence of Na` ion. As

a result, the acidity is reduced and the concentrationsof electrolytes and water increase signi"cantly. Forthe sulfate-poor system, the alkalinity of the systemfurther increases and the excess NH

3(g) can be neu-

tralized by Cl~ ion to form NH4Cl, resulting in

higher concentrations of electrolytes and water. Thedi!erences in predicted PM compositions and their

Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137 131

Tab

le4

Tota

lPM

conc

entr

atio

ns

pre

dict

edat

298.

15K

and

RH"

30%

unde

ral

lco

ndi

tion

s!

Con

ditio

nPM

conce

ntr

atio

ns(l

gm

~3)

Abso

lute

di!

eren

ces,

%

MA

RS-

ASE

QU

ILIB

SCA

PE2

EQ

UIS

OL

VII

AIM

2

A(M!

SC)H

100

SC

BA(S

E!

SC)H

100

SC

BA2(

E!

SC

)H10

0

(E#

SC

)BA

2(A!

SC)H

100

(A#

SC)BA

2(A!

E)H

100

(A#

E)B

134

.230

.534

.733

.033

.0!

1.5

!12

.3!

5.0

!5.

1!

0.1

228

.423

.330

.323

.323

.3!

6.1

!23

.1!

26.1

!26

.3!

0.2

325

.125

.128

.225

.125

.1!

11.1

!11

.1!

11.6

!11

.60.

04

26.9

26.9

26.9

26.8

26.9

0.0

0.0

!0.

2!

0.1

0.1

528

.431

.526

.926

.9*

5.5

16.9

0.2

**

625

.125

.128

.225

.125

.1!

11.1

!11

.1!

11.7

!11

.60.

07

26.9

26.9

26.9

26.9

*0.

00.

00.

2*

*

825

.125

.128

.225

.125

.1!

11.1

!11

.2!

11.6

!11

.60.

09

44.7

47.8

41.7

40.5

47.3

7.4

14.7

!3.

012

.615

.710

*26

.927

.521

.523

.3*

!2.

1!

24.6

!16

.78.

011

*23

.326

.723

.323

.3*

!12

.9!

13.8

!13

.80.

012

*25

.125

.125

.525

.0*

0.0

1.6

!0.

2!

1.8

13*

26.2

25.1

27.4

25.1

*4.

48.

70.

0!

8.7

14*

31.7

26.0

30.5

**

21.7

15.9

**

15*

25.1

25.1

25.6

25.0

*0.

02.

1!

0.2

!2.

316

*26

.225

.130

.6*

*4.

419

.7*

*

17*

25.1

25.1

24.9

25.0

*0.

0!

0.9

!0.

20.

718

*49

.344

.944

.149

.6*

9.8

!1.

79.

911

.619

*24

.019

.631

.019

.6*

22.7

45.2

!0.

1!

45.2

20*

32.0

30.2

40.6

**

6.1

29.4

**

!Theco

nditio

nsco

rres

pond

toth

ose

inT

able

3.SC

APE2

isuse

das

are

fere

nce

forM

AR

S-A

and

SEQ

UIL

IB,t

he

per

centab

solu

tedi!

eren

cesbe

twee

nM

AR

S-A

and

SC

APE2

and

bet

wee

nSE

QU

ILIB

and

SC

AP

E2

are

((M

!SC

)H10

0/SC

)an

d((S

E!

SC)H

100/

SC),

resp

ective

ly.For

each

pai

rof

the

thre

em

odule

s:SC

APE

2,EQ

UIS

OLV

-II,

and

AIM

2,th

ear

ithm

etic

aver

ages

ofv

alue

spre

dic

ted

by

each

pai

rofm

odu

lesar

euse

das

refe

renc

e.T

heno

rmal

ized

abso

lute

per

centdi!

eren

cesar

e(2

(E!

SC

)H10

0/(E

#SC

))bet

wee

nE

QU

ISO

LV

IIan

dSC

AP

E2,

(2(A

!SC

)H10

0/(A

#SC

))be

twee

nA

IM2

and

SC

APE2,

and

(2(A

!E

)H10

0/(A

#E))

betw

een

AIM

2an

dEQ

UIS

OL

VII

.M

AR

S-A

doe

sno

tsim

ula

tesy

stem

sco

nta

inin

gso

diu

mch

loride

(i.e.,c

onditio

ns

10}20

).A

IM2

does

notsim

ulat

eal

kalin

esy

stem

s(i.

e.,co

nditio

ns5,

7,14

,16

and

20).

132 Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137

concentrations also increase signi"cantly when TNaCl/TSO

4increases.

The changes in PM compositions and concentrationscause corresponding changes in total PM concentrationswhen TNaCl/TSO

4varies. For the ammonium-poor sys-

tem with TNH4/TSO

4"1.5 and RH"95%, the PM

concentrations predicted by SEQUILIB are only slightlysensitive to changes in TNaCl/TSO

4. However, the PM

concentrations predicted by the other modules are highlysensitive to changes in TNaCl/TSO

4, especially for

TNaCl/TSO4"2. The total PM concentrations increase

by 107}120% as TNaCl/TSO4varies from 0 to 2. For the

ammonium-rich system with TNH4/TSO

4"4 and

RH"95%, the PM concentrations predicted by thethree modules (SEQUILIB, SCAPE2, and EQUISOLVII) are also highly sensitive to changes in TNaCl/TSO

4,

with an increase by 79}105% when TNaCl/TSO4

in-creases from 0 to 2.

3.3.3.3. Ewect of temperature. Temperatures a!ect thePM predictions through changing many properties of thesystem such as equilibrium constants and activity coe$-cients. For example, at high temperatures, nitrate saltsand liquid water evaporate from the particle, reducingthe total PM concentrations. While AIM2 (i.e., AIM2-Model III) is restricted to a "xed temperature of298.15 K, the temperature dependence of chemical prop-erties is taken into account in the other four modules, asshown in Table 1. The responses of various modules tochanges in temperature may be di!erent due to di!erenttemperature parameterizations. The discrepancies amongmodules in the predicted PM compositions likely in-crease under higher temperatures due to the evaporationof water and semi-volatile species (e.g., nitrate andorganic compounds).

Temperature has a signi"cant impact on PM concen-trations for the sulfate-poor system, especially for sys-tems with high ammonium and nitrate. For cases withTNH

4/TSO

4"4, TNO

3/TSO

4"3, and RH"60%,

when the temperature increases from 298.15 to 308.15 K,the total [NO~

3]1

predicted by MARS-A, SEQUILIB,SCAPE2, and EQUISOLV II decrease by 79}100%.SEQUILIB predicts zero [H

2O]

1at 298.15 and

308.15 K, and [H2O]

1predicted by MARS-A, SCAPE2,

and EQUISOLV II decrease by 26, 65, and 100%, re-spectively. The total PM concentrations predicted by thefour modules at 308.15 K decrease by 31}55%, as com-pared to those at 298.15 K. The maximum decrease intotal PM concentrations under all modeled conditions is40% in MARS-A, 56% in SEQUILIB, 63% in SCAPE2,and 78% in EQUISOLV II when the temperature in-creases from 298.15 to 308.15 K.

3.3.4. Total PM concentrationsTable 4 presents the total PM concentrations

predicted by the "ve modules under all simulation

conditions at 298.15 K. RH was assumed to be 30%,consistent with the Federal Reference Method (FRM) forPM measurements. For the ammonium/nitrate/sulfate/water system, the absolute di!erences between the valuespredicted by MARS-A and SCAPE2, and by SEQUILIBand SCAPE2 are 6 and 11.2% on average, respectively,ranging from 0 to 11.1% and 0 to 23.1% for speci"ccases, respectively. The normalized absolute di!erencesbetween SCAPE2 and EQUISOLV II, between AIM2and SCAPE2, and between AIM2 and EQUISOLV IIare 7.7, 11.3 and 2.3% on average, respectively, rang-ing from 0.2 to 26.1, 0.1 to 26.3, and 0 to 15.7% forspeci"c cases, respectively. For the sodium/ammonium/nitrate/sulfate/chloride/water system, the absolutedi!erence between the values predicted by SEQUILIBand SCAPE2 is 7.6% on average, ranging from 0to 22.7% for speci"c cases. The normalized absolutedi!erences between SCAPE2 and EQUISOLV II, be-tween AIM2 and SCAPE2, and between AIM2 andEQUISOLV II are 14.9, 5.1, and 9.8% on average,respectively, ranging from 0.9 to 45.2, 0 to 16.7, and 0 to45.2% for speci"c cases. At 308.15 K, the absolute di!er-ences between these modules are similar to those at298.15 K.

When a similar set of reactions is used in SEQUILIB,SCAPE2, EQUISOLV II, and AIM2, the agreement inthe PM concentrations predicted by these modules canbe improved, particularly for systems containing NaCl.For the ammonium/nitrate/sulfate/water system, theabsolute di!erence between the values predicted bySEQUILIB and SCAPE2 is 7.8% on average, respective-ly, ranging from 0 to 23.1% for speci"c cases. The nor-malized absolute di!erences between SCAPE2 andEQUISOLV II, between AIM2 and SCAPE2, and be-tween AIM2 and EQUISOLV II are 7.4, 10.3, and 1.0%on average, ranging from 0.2 to 26.1, 0 to 26.1, and 0 to6.7% for speci"c cases, respectively. For the sodium/ammonium/nitrate/sulfate/chloride/water system, theabsolute di!erence between the values predicted bySEQUILIB and SCAPE2 is 5.8% on average, rangingfrom 0 to 22.4% for speci"c cases. The normalized abso-lute di!erences between SCAPE2 and EQUISOLV II,between AIM2 and SCAPE2, and between AIM2 andEQUISOLV II are 14.2, 4.7, and 2.2% on average, re-spectively, ranging from 0 to 24.5, 0 to 16.5, and 0 to 8.0%for speci"c cases.

3.3.5. Timing testsThe time to solve equilibrium equations depends on

many factors including the number of equilibrium equa-tions, the method used to solve these equations, and thevalues of error tolerances. In addition, for a given aerosolmodule, the computing time varies depending on the casesimulated.

We compared the computing times required by the "vemodules for the 10 case simulations under condition

Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137 133

1 with 10 di!erent RHs here. In these simulations, thenumbers of equations that were solved by each moduleare 7 in MARS-A, 14 in SEQUILIB, 15 in SCAPE2 andEQUISOLV II, and 18 in AIM2. MARS-A uses conver-gence criteria of 10~5 and 10~3 for ammonium-rich andammonium-poor cases, respectively. SEQUILIB usesa convergence criterion of 10~2. SCAPE2 uses conver-gence criteria of 10~7 for H` ion and water contentcalculations and 10~2 for solid calculations; the defaultmaximum iteration number is 20. EQUISOLV II usesa normalized gross error in gas and liquid water concen-trations of 10~4. AIM2 determines the minimum in theGibbs energy of the system to about 1 part in 1030. ForEQUISOLV II, the same equations were solved for twoscenarios: (1) for a single grid cell and (2) for 490 gridcells (for scenario (2), the total CPU time was thendivided by 490 to obtain the time to solve in one gridcell). These two scenarios were studied becauseEQUISOLV II uses a vectorized approach for computa-tions and, therefore, becomes more computationally e$-cient when the number of grid cells increases. MARS-A,SEQUILIB, SCAPE2, and EQUISOLV II were run ona Compaq Deskpro 2000 with 64 MB RAM, and AIM2was run on a DEC Alpha 3000 model 600. Single pre-cision was used for all MARS-A, SEQUILIB, andSCAPE2 simulations, double precision was used for allEQUISOLV II simulations. In AIM2, extended (quadru-ple) precision was used in order to obtain accurate valuesof the partial pressures of the trace gases, which contrib-ute only a very small amount to the total Gibbs energy ofthe system.

For the simulation of one case, MARS-A andSEQUILIB used 0.11 and 0.16 s, respectively. SCAPE2used total times ranging from 0.11 to 0.33 s. EQUISOLVII used total times ranging from 1.81 to 2.9 s for scenario(1) with a single cell and total times ranging from lessthan 0.01 to 0.17 s for scenario (2) with 490 cells. AIM2used total times ranging from 1.14 to 3.17 s. SCAPE2,EQUISOLV II, and AIM2 ran faster for high RHs thanfor low RHs because fewer iterations were needed forhigh RHs (i.e., fewer solutes and no solids). For a simula-tion in a single cell, MARS-A, SEQUILIB, and SCAPE2are generally more computationally e$cient thanEQUISOLV II and AIM2 (faster by a factor of 7}29).Note, however, that the total CPU time for the simula-tion of one case by AIM2 can be faster by a factor of 10 ifan ordinary double precision is used. As the number ofgrid cells simulated increases, EQUISOLV II is generallymore computationally e$cient than the other fourmodules, with a factor of 2}20 faster than MARS-A,SEQUILIB, and SCAPE2, and a factor of 19}243 fasterthan AIM2.

The di!erence in program speed is due to the di!er-ences in the numerical methods and calculation proced-ures in these modules. In particular, MARS-A usesan analytical method and a subdomain approach for

PM calculations in di!erent thermodynamic regimes.SEQUILIB and SCAPE2 also use the subdomainapproach. SEQUILIB uses a method combining theiterative bisectional and Newton}Raphson methods andSCAPE2 uses the iterative bisectional method. Bothmethods can rapidly converge mass and charge for mostsystems in a box model. However, they may requireextensive iterations for some systems with highly acidicparticles and may result in small negative concentrationswhen a large number of iterations are used. For example,SCAPE2 solved the equations for the simulation for RH"30% using a CPU three times longer (i.e., 0.33 s) thanthose for high RH cases, but the solution still did notconverge. A convergence solution for this case can beobtained by increasing the iteration number from 20 to100, but the CPU also increases proportionally (i.e., bya factor of 5). When a maximum number of iterations of500 was used, SCAPE2 predicted small negative concen-trations of particulate nitrate in three cases out of 200cases. EQUISOLV II solves all equations for all thermo-dynamic regimes using a hybrid MFI/AEI scheme, whichrequires relatively large CPU time to solve equations inone grid cell but speeds up signi"cantly for simulationsfor multiple grid cells. The computational speed ofEQUISOLV II improves with increasing number of gridcells because all inner loops are vectorized around thegrid cell dimension array. On a scalar machine, thisresults in a number of array references that is constant,regardless of the number of grid cells in a grid block(group of many cells). Thus, when the number of grid cellsincreases, the computer time required per grid cell de-creases. On a vector machine, additional speed increasesoccur with multiple cells due to the vectorization. AIM2solves all equations for all thermodynamic regimes usingthe sequential quadratic programming algorithm to min-imize the Gibbs free energy of the system. The computa-tional speed of AIM2 is relatively slow, due mainly to thecomputational cost for calculations of activity coe$-cients and the use of an extended precision. Although theversion of AIM2 used in this work has not been pro-grammed for the purpose of inclusion in a 3-D model, itscomputational speed can be greatly improved for sucha 3-D application.

4. Conclusions and recommendations

We have conducted a comprehensive evaluation of "veaerosol thermodynamic equilibrium modules under avariety of atmospheric PM concentrations, RHs, and temp-eratures. Although the PM predictions of these modulesare generally comparable under most conditions, signi"-cant discrepancies exist under some conditions, espe-cially under high nitrate/chloride concentrations andlow/medium RH conditions. The normalized absolutedi!erences in total PM concentrations predicted by the

134 Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137

"ve modules under all conditions and a temperature of298.15 K are 7.7}12.3%. The di!erences can be as muchas 68% for speci"c cases. For RH"30% (i.e., conditionstypical of FRM measurements) under typical ambienttemperatures (298.15}308.15 K), the PM concentrationspredicted by the "ve modules di!er by 4}13% on averageand by as much as 63% for speci"c cases. The PMcompositions and concentrations predicted by the "vemodules are highly sensitive to changes in the molarratios of ammonium to sulfate, nitrate to sulfate, andsodium chloride to sulfate, RH, and temperature. Thedi!erences in PM predictions are due mainly to di!er-ences in the chemical species and equilibrium reactionsthat are treated, the values of the equilibrium constants,the computational procedures and associated assump-tions, and the methods used to calculate binary andmulti-component activity coe$cients and water activ-ities. The di!erences in the temperature parameteriz-ations seem to have little e!ects on the di!erences in PMpredictions among these modules under most conditionsmodeled in this study.

MARS-A predicted higher [H2O]

1for medium RHs

than other modules due mainly to its assumption that nosolid exists for medium RHs. For some conditions testedhere, SEQUILIB predicts abnormal [NO~

3]1and [H`]

1due to numerical errors and lower [Cl~]

1than those

predicted by the other modules due to a di!erent set ofequilibrium reactions used in SEQUILIB. Both MARS-A and SEQUILIB predict higher NH

4NO

3for most

cases than the other modules due to di!erences in therelevant equilibrium constants used and/or di!erencesand assumptions in thermodynamic treatment. SCAPE2predicts higher [H`]

1for highly concentrated particles

(i.e., under sulfate-rich and low RH conditions) due tonumerical artifacts caused by non convergence of thesolution. EQUISOLV II predicts higher NH

4Cl for cases

with NaCl and low RHs due to di!erent equilibriumreactions used for NH

4Cl and NH

4NO

3. AIM2 predicts

results comparable to those predicted by the other mod-ules for most acidic systems but does not simulate alka-line systems. The di!erences in PM predictions betweenAIM2 and the other modules are mainly due to thetreatments of additional equilibrium reactions involvingcomplex salts and di!erent methods to calculate activitycoe$cients. Our results also show that the di!erencesamong the "ve modules can be greatly minimized byusing a similar set of equilibrium reactions in thesemodules.

Ansari and Pandis (1999b) compared four aerosolthermodynamic modules: GFEMN, ISORROPIA,SCAPE2, and SEQUILIB under marine, remote conti-nental, and non-urban continental conditions. Theyfound that the normalized mean errors between the mostaccurate module GFEMN and the other three modulesare 13}26% for [NO~

3]1and 39}256% for [H

2O]

1under

sulfate-poor conditions and 22}52% for [NH`4]1,

403}1134% for [H`]1, and 25}82% for [H

2O]

1under

sulfate-rich conditions. Among these modules, SCAPE2predicted the highest [H`]

1under sulfate-rich and low

RH conditions. Signi"cant discrepancies exist in [H2O]

1for sulfate-rich conditions and in [NH`

4]1, [H

2O]

1, and

total dry PM concentrations (i.e., excluding [H2O]

1) for

sulfate-poor conditions between SEQUILIB and theother three modules. Despite these di!erences, the totaldry PM concentrations predicted by ISORROPIA,SCAPE2, and SEQUILIB are in good agreement tothose predicted by GFEMN, with a mean normalizederror of (6%. Our comparisons were conducted fortypical urban and coastal conditions, with a broaderrange of RHs, higher concentration of sulfate, and higherconcentration ranges of total nitrate, ammonium, andsodium chloride than those of Ansari and Pandis (1999b).Only two modules, SEQUILIB and SCAPE2, are com-mon to both studies. Our results show 8}12% di!erencesamong the total PM concentrations (including [H

2O]

1)

and much larger di!erences in concentrations of partic-ulate compositions. Overall, our results and those ofAnsari and Pandis (1999b) are consistent. The version ofSEQUILIB used by Ansari and Pandis (1999b) is a mostrecent version than that used in this work. Although themost recent version predicts slightly di!erent results thanthe earlier version, the major discrepancies identi"edunder our test conditions were found to remain the same.

Our results provide useful information for the selectionof aerosol thermodynamic equilibrium modules for fu-ture PM modeling studies. The selection of a thermodyn-amic module for 3-D air quality modeling may dependon the speci"c objectives of the study and it is importantto understand the advantages and disadvantages of exist-ing modules before incorporating them into a host airquality model.

Given its simplest chemistry, MARS-A predicts resultscomparable to those predicted by the other more com-prehensive modules under high RH conditions. However,MARS-A does not simulate sodium chloride and as-sumes a metastable state for the particles. This assump-tion may not be applicable in dry areas where RH valuesare very low and the particles may not be in a metastablestate. Therefore, caution is advised when applyingMARS-A to dry areas (e.g., southwestern US) and coastalareas.

The version of SEQUILIB that is currently used inUAM-AERO and SAQM-AERO should be improvedbecause it gives unstable or even abnormal solutions forPM predictions under many conditions. An improvedversion of SEQUILIB exists, but it generally does notimprove the major discrepancies identi"ed for the urbanand coastal conditions selected in this work. Furtherimprovements of SEQUILIB appear warranted.

SCAPE2, EQUISOLV II, and AIM2 contain mostcomprehensive aerosol chemistry and thermodynamics,providing detailed PM predictions. Both SCAPE2 and

Y. Zhang et al. / Atmospheric Environment 34 (2000) 117}137 135

EQUISOLV II can be applied to simulate PM for anyconditions, whereas AIM2 can be applied only to acidicsystems. The total CPU time is likely proportional to thenumber of grid cells simulated in SCAPE2 and AIM2,posing computational constraints and challenges fortheir applications to large domains. On the other hand,the vectorization used in the numerical scheme inEQUISOLV II permits continuous solutions with rela-tively fast speed over large numbers of spatial grid cellsand particle size bins for 3-D PM modeling. However,the computer must have su$cient memory bandwidth(ability to transfer information to and from memoryquickly) because the vectorized EQUISOLV II requiresmore memory than the other non-vectorized codes.

Acknowledgements

This project was supported by the Coordinating Re-search Council under Contract A-21-2. Y.Z. and C.S.would like to thank Spyros N. Pandis for providingsimulations for a few cases using the GFEMN module tohelp clarify discrepancies between EQUISOLV and theother four modules.

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