Atmos. Chem. Phys., 7, 4639–4659, 2007

www.atmos-chem-phys.net/7/4639/2007/

© Author(s) 2007. This work is licensed

under a Creative Commons License.

Atmospheric

Chemistry

and Physics

ISORROPIA II: a computationally efficient thermodynamic

equilibrium model for

K+–Ca2+–Mg2+–NH+

4

–Na+–SO2−

4

–NO−

3

–Cl−–H2O aerosols

C. Fountoukis1 and A. Nenes1,2

1School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, GA

30332-0100, USA

2School of Earth and Atmospheric Sciences, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, GA 30332-0100, USA

Received: 24 January 2007 – Published in Atmos. Chem. Phys. Discuss.: 7 February 2007

Revised: 30 May 2007 – Accepted: 5 September 2007 – Published: 13 September 2007

Abstract. This study presents ISORROPIA II, a thermodynamic equilibrium model for the K+–Ca2+–Mg2+–NH+

4

–

Na+–SO2−

4

–NO−

3

–Cl−–H2O aerosol system. A comprehensive evaluation of its performance is conducted against water

uptake measurements for laboratory aerosol and predictions

of the SCAPE2 thermodynamic module over a wide range of

atmospherically relevant conditions. The two models agree

well, to within 13% for aerosol water content and total PM

mass, 16% for aerosol nitrate and 6% for aerosol chloride and

ammonium. Largest discrepancies were found under conditions of low RH, primarily from differences in the treatment

of water uptake and solid state composition. In terms of computational speed, ISORROPIA II was more than an order of

magnitude faster than SCAPE2, with robust and rapid convergence under all conditions. The addition of crustal species

does not slow down the thermodynamic calculations (compared to the older ISORROPIA code) because of optimizations in the activity coefficient calculation algorithm. Based

on its computational rigor and performance, ISORROPIA II

appears to be a highly attractive alternative for use in large

scale air quality and atmospheric transport models.

1 Introduction

Airborne particulate matter (PM), or aerosol, play a central role in atmospheric processes. They reflect a significant

amount of radiation back to space, thus enhancing the planetary albedo. Atmospheric aerosols can cause visibility impairment in highly polluted areas (Altshuller, 1984) through  ̈

Correspondence to: A. Nenes

(nenes@eas.gatech.edu)

their interactions with electromagnetic radiation. By acting as cloud condensation nuclei (CCN), they affect droplet

number concentration, effective radius, and reflectivity of

clouds. Changes in aerosol concentrations also affect droplet

size distribution, precipitation frequency and cloud lifetime.

Aerosols can also be responsible for acid rain production,

which can adversely affect soil and water quality, especially

in environments rich in SO2 and NOx. It has been established that inhaled aerosol particles are detrimental to human

health, as particles can contain toxic inorganic and organic

substances that are often correlated with asthma and chronic

obstructive pulmonary disease (Zanobetti et al., 2000; Ramachandran and Vincent, 1999; Brauer and Brook, 1997;

Schwartz, 1994). Recent studies (Kaiser, 2005) have suggested that fine particles (PM2.5) are more effective in causing respiratory illness and premature death than larger particles due to their ability to penetrate deeper into the lung.

Dockery et al. (1993), who conducted a survey on six cities

over 16 years, found that people living in areas with higher

aerosol concentrations had a lifespan two years less than

those living in cleaner areas. The knowledge of the chemical composition and physical state of atmospheric particles

may be a critical link between toxicity and particulate matter.

Atmospheric aerosols are composed of water, inorganic

salts, crustal material, organics and trace metals. A large

part of the particle (dry) mass is inorganic (25–50%) with

ammonium (NH+

4

), sodium (Na+), sulfate (SO2−

4

), bisulfate

(HSO−

4

), nitrate (NO−

3

) and chloride (Cl−) being the most

important contributors to the dry inorganic PM2.5 (Heitzenberg, 1989). Crustal species, such as Ca2+, K+, Mg2+ are

a major component of dust, hence an important constituent

of ambient particles. These inorganic species may be in the

form of aqueous ions, or in the form of precipitated solids,

Published by Copernicus Publications on behalf of the European Geosciences Union.
4640 C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model

in thermodynamic equilibrium with atmospheric gases and

humidity.

To compute the composition and phase state of aerosols,

every atmospheric gas/aerosol model requires knowledge of

the thermodynamic equilibrium state because the driving

force for mass transfer of species between gas and aerosol

phases is the departure from equilibrium. Performing thermodynamic equilibrium calculations for aerosol systems is a

demanding computational task (e.g. Nenes et al., 1999) because it involves the optimization of a nonlinear (local) convex problem, or the solution of numerous nonlinear equations. At low relative humidity, the aqueous phase is highly

concentrated (i.e. with a high ionic strength), hence strongly

non-ideal and requires the use of an activity coefficient

model. Therefore, efficient and accurate solution algorithms

are needed.

Numerous aerosol inorganic equilibrium models have

been developed, differing in the chemical species that they

can treat, the solution method used and the type of input

they can accept. Recent examples include AIM2 (Clegg

and Pitzer, 1992; Clegg et al., 1992, 1994, 1995, 1998a, b;

Wexler and Clegg, 2002), SCAPE2 (Kim et al., 1993a, b;

Kim and Seinfeld, 1995; Meng et al., 1995), EQUISOLV II

(Jacobson et al., 1996; Jacobson, 1999a, b), ISORROPIA

(Nenes et al., 1998; Nenes et al., 1999), GFEMN (Ansari

and Pandis, 1999a, b), EQSAM2 (Metzger et al., 2002a, b;

Metzger et al., 2006), HETV (Makar et al., 2003), MESA

(Zaveri et al., 2005a, b) and UHAERO (Amundson et al.,

2006). AIM2 and GFEMN use the iterative Gibbs free

energy minimization method to solve equilibrium problems

for NH+

4

/Na+/NO−

3

/SO−2

4

/Cl− systems. UHAERO uses the

Gibbs free energy minimization method (using a primaldual method, coupled to a Newton iteration method) and

offers a choice of the Pitzer, Simonson, Clegg (PSC) mole

fraction-based model (Pitzer and Simonson, 1986; Clegg

and Pitzer, 1992; Clegg et al., 1992) or the ExUNIQUAC

model (Thomsen and Rasmussen, 1999) for the activity

coefficient calculations. These models treat either the

ammonium – nitrate – sulfate system or the ammonium

– sodium – nitrate – chloride – sulfate system. MESA

simultaneously iterates for all solid-liquid equilibria using

a pseudo-transient continuation method and solves for the

NH+

4

/Na+/NO−

3

/SO−2

4

/Cl− system of species with the addition of calcium cations. EQUISOLV II sequentially solves

for the root of each equation in the system of equilibrium

reactions and then iterates over the entire domain until

convergence. This method is ideal for the incorporation of

new reactions and species with minimal programming effort,

but optimal computational performance is obtained only on

vectorized computational platforms (Zhang et al., 2000).

EQSAM2 considers activity coefficients for (semi-) volatile

compounds according to Metzger et al. (2002a) to solve the

NH+

4

/Na+/NO−

3

/SO2−

4

/Cl−/Ca2+/Mg2+/K+/RCOO− system; earlier versions of the model did not consider mineral

cations and organic acids, and used parameterizated activity

coefficients (Metzger et al., 1999). To express solution

non-idealities, Metzger and Lelieveld (2007) suggest an

approximate formulation based on osmolality and solubility

measurements (instead of the activity coefficient model);

this approach has been applied in the EQSAM3 model.

SCAPE2 divides composition space into several subdomains

based on major species that impact equilibrium partitioning

and water uptake. By always attempting to solve for a liquid

phase, SCAPE2 predicts the presence of water even at very

low ambient relative humidities (<10%), and for this reason

often does not predict the presence of a crystalline phase

(solid precipitate).

Similar to SCAPE2, ISORROPIA determines the subsystem set of equilibrium equations and solves for the equilibrium state using the chemical potential method. The code

solves analytically as many equations as possible through

successive substitutions; remaining equilibrium reactions are

solved numerically with bisection for stability. ISORROPIA

also offers the choice of using precalculated tables of binary

activity coefficients and water activities of pure salt solutions, which speeds up calculations (by ∼30%). Another

important feature of the model is the use of mutual deliquescence of multicomponent salt particle solutions, which

lowers the deliquescence point of the aerosol phase. Besides the forward problem (in which gas + aerosol concentrations of chemical species along with ambient temperature

and relative humidity are used as input), ISORROPIA also

offers the ability to solve for the “reverse problem”, in which

known quantities are the concentrations of sodium, ammonium, nitrate and sulfate in the aerosol phase together with

the ambient temperature and relative humidity. The output of

the reverse problem is (as in the forward problem) the concentration of species in solid, liquid and gas phase. Being

computationally efficient, ISORROPIA has proved to be the

model of choice for many three-dimensional air quality models (CMAQ, PMCAMx, etc.), chemical transport and general circulation models (Ansari and Pandis, 1999b; Yu et al.,

2005). HETV is based on the algorithms of ISORROPIA for

sulfate, nitrate and ammonium aerosol systems and is optimized for running on vectorized computational architectures.

An important limitation of the above codes (with the exception of SCAPE2, EQUISOLV II and EQSAM2,3) is lack

of treatment of crustal species (Ca, K, Mg). It has been

shown that the consideration of crustal material in predicting the partitioning of nitrate and ammonium, especially in

areas where dust comprises a significant portion of total PM,

is of great importance and can considerably improve model

predictions (Ansari and Pandis, 1999; Moya et al., 2002).

An attempt to treat crustal species as “equivalent sodium”

was met with modest success (Moya et al., 2001a), provided

that Ca was a relatively small fraction of aerosol dry mass.

Moya et al. (2002) showed that including crustal species is

important in determining the aerosol size distribution, while

San Martini et al. (2005) showed that treating crustal species

as “equivalent” sodium may affect the predicted response of

Atmos. Chem. Phys., 7, 4639–4659, 2007 www.atmos-chem-phys.net/7/4639/2007/
C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model 4641

inorganic PM to changes in precursor concentrations. Often, crustal species are linked with inorganic anions; organic

acids can be associated as well, especially with potassium in

biomass burning aerosol (Trebs et al., 2005; Metzger et al.,

2006). It has been shown that including both crustal species

and organic acids can be important under some conditions

(Metzger et al., 2006). The concentration of organic acids

and their impact on global aerosol thermodynamics however

still remains highly uncertain.

In the current study, we present a new model, “ISORROPIA II”, in which the thermodynamics of the crustal elements of calcium, potassium and magnesium have been

added to the preexisting suite of components of the ISORROPIA model. The new model, combining the computational advantages of ISORROPIA with the explicit thermodynamics of crustal species, is compared against the predictions of SCAPE2, both in terms of speciation and computational requirements.

2 Thermodynamic equilibrium calculations

2.1 Equilibrium constants

In a closed (aerosol-gas phase) system composed of i chemical species and j reactions at constant temperature T , and

pressure P, the Gibbs free energy of the system, G, is minimum at chemical equilibrium. This condition is equivalent

to stating that the Gibbs free energy of the reactants is equal

to that of the products, and can be written as (Nenes et al.,

1998):

Y

i

a

νij

i = Kj (T ) (1)

where aiis the activity of species i, νij is the stoichiometric

coefficient of species i participating in the reaction j , and Kj

is the equilibrium constant of the j -th reaction at temperature

T ,

Kj (T ) = exp



−

P

i

νijμ

o

i

(T )

RT



 (2)

where R is the universal gas constant and μ

o

i

(T ) is the standard chemical potential of species i at 1 atm pressure and

temperature T (in K).

Kj is a function of temperature according to the Van’t Hoff

equation:

d ln K (T )

dT

=

1Ho

(T )

RT 2

(3)

where 1H

o

(T ) is the enthalpy change of the reaction at temperature T (Denbigh, 1981). For a small temperature range,

1Ho

(T ) can be approximated by:

1Ho

(T ) = 1Ho(To) + 1co

p

(T − To) (4)

where 1co

P

(T ) is the change of molar heat capacity of products minus reactants. By substituting Eq. (4) into Eq. (3)

and integrating from a reference temperature T0 (typically at

298.15 K) to T , we obtain:

K (T ) = Ko exp −

1Ho

(To)

RTo



To

T

− 1



−

1co

p

R



1 + ln

To

T



−

To

T

 (5)

where Ko is the equilibrium constant at To.

2.2 Activity of species

The activity of species i, ai, if an ideal gas, is equal to its partial pressure (ai=pi) (Seinfeld and Pandis, 1998). If ij is an

electrolyte species dissolved in water, aij=m

νi

i m

νj

j

γ

(νi+νj )

ij ,

where γij is the mean activity coefficient of an electrolyte

species ij in water, νi and νj are the moles of cations and

anions, respectively, released per mole of electrolyte and

mi, mj are their molalities, respectively. The activity of each

solid phase species is assumed to be unity.

2.3 Activity coefficients

In ISORROPIA II, the multicomponent activity coefficients,

γ 12, for each ionic pair 1–2 are computed using Bromley’s

formula (Bromley, 1973),

log γ12 = −Aγ

z1z2I

1/2

1 + I

1/2

+

z1z2

z1 + z2



F1

z1

+

F2

z2



(6)

where γ12 is the mean activity coefficient of cation 1 and

anion 2 at 298.15 K, Aγ is the Debye-Huckel constant  ̈

(0.511 kg0.5 mol−0.5at 298.15 K) and,

F1 = Y21 log γ

o

12 + Y41 log γ

o

14 + Y61 log γ

o

16 + . . .

+

Aγ I

1/2

1 + I

1/2

[z1z2Y21 + z1z4Y41 + z1z6Y61 + . . .] (7)

F2 = X12 log γ

o

12 + X32 log γ

o

32 + X52 log γ

o

52 + . . .

+

Aγ I

1/2

1 + I

1/2

[z1z2X12 + z3z2X32 + z5z2X52 + . . .] (8)

where odd subscripts refer to cations and even subscripts refer to anions, Y21=



z1+z2

2

2 m2

I

, X12=



z1+z2

2

2 m1

I

, ziis the

absolute charge of ionic species i, and γ

o

ij is the mean ionic

activity coefficient of the binary pair i−j (“binary” activity

coefficient) computed at the ionic strength of the multicomponent solution, I=

1

2

P

i

miz

2

i

.

Following the recommendations of Kim et al. (1993), binary activity coefficients, γ

o

12, are calculated using the KusikMeissner relationship (Kusik and Meissner, 1978),

log γ

o

12 = z1z2 log 0

o

(9)

www.atmos-chem-phys.net/7/4639/2007/ Atmos. Chem. Phys., 7, 4639–4659, 2007
4642 C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model

Table 1. Thermodynamic properties for all species in ISORROPIA II∗.

Species 1μ0

i

(298 K), kJ mol−1 1Ho

f

, kJ mol−1 C

o

p

, J mol−1 K

−1

Ca(NO3)

♣

2(s)

−1713.15 −2132.33 315.65

CaCl♣

2(s)

−2215.6 −2607.9 322.01

CaSO4(s) −1798.280 −2022.630 186.020

KHSO4(s) −1031.300 −1160.600 87.160

K2SO4(s) −1321.370 −1437.790 131.460

KNO3(s) −394.860 −494.630 96.400

KCl(s) −409.140 −434.750 51.300

MgSO4(s) −1170.600 −1284.900 96.480

Mg(NO3)

♣

2(s)

−2080.3 −2613.28 391.34

MgCl♣

2(s)

−2114.64 −2499.02 315.06

Ca2+

(aq)

−553.580 −542.830 –

K

+

(aq)

−283.270 −252.380 21.800

Mg2+

(aq)

−454.800 −466.850 –

NaCl(s) −384.138 −411.153 50.500

NaNO3(s) −367.000 −467.850 92.880

Na2SO4(s) −1270.160 −1387.080 128.200

NaHSO4(s) −992.800 −1125.500 85.000

NH4Cl(s) −202.870 −314.430 84.100

NH4NO3(s) −183.870 −365.560 139.300

(NH4)2SO4(s) −901.670 −1180.850 187.490

NH4HSO4(s) −823.000 −1026.960 127.500

(NH4)3H(SO4)2(s) −1730.000 −2207.000 315.000

HNO3(g) −74.720 −135.060 53.350

HCl(g) −95.299 −92.307 29.126

NH3(g) −16.450 −46.110 35.060

NH3(aq) −26.500 −80.290 79.900

H

+

(aq)

0.000 0.000 0.000

Na+

(aq)

−261.905 −240.120 46.400

NH+

4(aq)

−79.310 −132.510 79.900

HSO−

4(aq)

−755.910 −887.340 −84.000

SO2−

4(aq)

−744.530 −909.270 −293.000

NO−

3(aq)

−111.250 −207.360 −86.600

Cl−

(aq)

−131.228 −167.159 −136.400

OH−

(aq)

−157.244 −229.994 −148.500

∗ Compiled by: Kim and Seinfeld (1995) and Kim et al. (1993) unless otherwise indicated; Species in bold are new in ISORROPIA II.

♣ Compiled by: Kelly and Wexler (2005)

– Data not available

where

0

o =



1 + B(1 + 0.1I )q − B



0

∗

(10)

B = 0.75 − 0.065q (11)

log 0

∗ =

−0.5107I

1/2

1 + CI 1/2

(12)

C = 1 + 0.055q exp −0.023I

3



(13)

and q is a parameter specific for each binary pair.

The effect of temperature on multicomponent activity coefficients is described by Meissner and Peppas (1973),

log γij (T ) = [1.125 − 0.005(T − 273.15)] log γij (T0)

− [0.125 − 0.005 (T − 273.15)] A (14)

where γij (T ) is the multicomponent activity coefficient of the pair of ions i−j at temperature T , and,

A=−

0.41I

0.5

1+I

0.5 +0.039I

0.92

.

Atmos. Chem. Phys., 7, 4639–4659, 2007 www.atmos-chem-phys.net/7/4639/2007/
C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model 4643

Fig. 1. Generic solution procedure of ISORROPIA II.

2.4 Aerosol water content

During the calculation of aerosol water content, it is assumed

that aerosol curvature effects are unimportant and the ambient water vapor pressure is unaffected by the aerosol water

uptake. Therefore, if ambient relative humidity is known,

phase equilibrium between gas and aerosol-phase (Seinfeld

and Pandis, 1998) gives that the water activity, aw, is equal to

the ambient fractional relative humidity, RH, (i.e. expressed

on a 0.0 to 1.0 scale):

aw = RH (15)

Determining water content that satisfies the constraint of

Eq. (15) from explicit calculations of water activity requires an iterative hence computationally expensive procedure (Stelson and Seinfeld, 1982). Instead, water uptake of

aerosols is calculated using the ZSR correlation (Robinson

and Stokes, 1965),

W =

X

i

Mi

moi(aw)

(16)

where W is the mass concentration of aerosol water (kg m−3

air), Miis the molar concentration of species i (mol m−3air),

and moi (aw) is the molality of an aqueous binary solution of

the i-th electrolyte with the same aw (i.e. relative humidity)

as in the multicomponent solution.

2.5 Deliquescence relative humidity (DRH)

For each salt, there is a characteristic relative humidity,

known as the deliquescence relative humidity (DRH), above

which a phase transition from solid to saturated aqueous solution occurs. The DRH varies with temperature and for

small changes thereof is given by (Wexler and Seinfeld,

1991),

ln

DRH (T )

DRH (To)

= −

MwmsLs

1000 R



1

T

−

1

To



(17)

where Mw is the molar mass of water and msis the molality

of the saturated solution at temperature To. Lsis the latent

heat of fusion for the salt from a saturated solution given by

Ls=1Hcr−1Haq; 1Hcr, 1Haq are the molar enthalpies of

formation of the crystalline phase and the species in aqueous

solution, respectively.

www.atmos-chem-phys.net/7/4639/2007/ Atmos. Chem. Phys., 7, 4639–4659, 2007
4644 C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model

2.6 Mutual deliquescence relative humidity (MDRH)

In every multicomponent mixture there exists a characteristic

relative humidity, the mutual deliquescence relative humidity, MDRH (Wexler and Seinfeld, 1991), for which all salts

are simultaneously saturated with respect to all components.

The MDRH is a eutectic point so it is below the DRH of all

the pure solids composing the system and is the minimum

RH for which a stable aqueous phase exists (Wexler and Seinfeld, 1991). When MDRH <RH<RHwet (where RHwet is

the DRH of the salt with the lowest DRH in the mixture under consideration) the solution is said to be in the mutual

deliquescence region, MDR (Nenes et al., 1998). Computing

the aerosol composition in the MDR is a computationally demanding task (e.g. Potukuchi and Wexler, 1995a, b) that we

seek to avoid. Given that the MDR corresponds usually to a

narrow RH range, we use the simplified approach of Nenes

et al. (1998) to calculate composition in a MDR. This approach involves computing the weighted average of a “dry”

and “wet” solution:

W = (1 − c) Wwet (18)

G = cGdry + (1 − c) Gwet (19)

S = cSdry + (1 − c) Swet (20)

D = (1 − c) Dwet (21)

The weighting factor, c, is given by (Nenes et al., 1998):

c =

RH−RHwet

MDRH−RHwet

(22)

and G, S, D are the concentrations of gaseous, solid and

dissolved species, respectively. The subscripts “wet” and

“dry” in Eqs. (18–22) denote the two solutions which are

weighted. In the above equations, we assume that gases

and solids are linearly weighted according to their proximity

to RHwet and MDRH (as expressed by c), while dissolved

species are scaled to the amount of water. MDRH points

for the new mixtures in ISORROPIA II are shown in Table 5. Although Eqs. (18–22) are an approximation of the

thermodynamic solution, they qualitatively follow the RHdependence of speciation and conserve aerosol dry mass.

An assessment of this approximation done by comparing

predictions of ISORROPIA II with measurements by Choi

and Chan (2002) for aerosol water content of an equimolar

NaNO3:Ca(NO3)2 mixture in the mutual deliquescence region. Table 6 shows the aerosol water mass fraction for RH

ranging between 0.246 and 0.461, which is below 0.49, the

minimum DRH of Ca(NO3)2 and NaNO3 (i.e. in the mutual

deliquescence region). As shown in Table 6, ISORROPIA II

predictions agree well with measured water mass fraction ,

which suggests that Eq. (18) reasonably approximates the

aerosol water content in this region.

3 ISORROPIA II: species considered and general solution procedure

The system modeled by ISORROPIA II consists of the following potential components (species in bold are new in

ISORROPIA II):

Gas phase: NH3(g), HNO3(g), HCl(g), H2O(g)

Liquid phase: NH4(aq)

+ , Na+

(aq)

, H+

(aq)

, Cl−

(aq)

, NO−

3(aq)

,

SO2−

4(aq)

, HNO3(aq), NH3(aq), HCl(aq), HSO−

4(aq)

, OH−

(aq)

,

H2O(aq), Ca2+

(aq)

, K

+

(aq)

, Mg2+

(aq)

Solid phase: (NH4)2SO4(s), NH4HSO4(s),

(NH4)3H(SO4)2(s), NH4NO3(s), NH4Cl(s), NaCl(s),

NaNO3(s), NaHSO4(s), Na2SO4(s), CaSO4(s), Ca(NO3)2(s),

CaCl2(s), K2SO4(s), KHSO4(s), KNO3(s), KCl(s),

MgSO4(s), Mg(NO3)2(s), MgCl2(s)

where the subscripts (g), (aq), (s) denote gas, aqueous and

solid, respectively. Table 1 shows thermodynamic properties for all species considered. Table 2 displays all the equilibrium reactions used in ISORROPIA II along with values

for their equilibrium constants. When the concentration of

crustal species (Ca, K, Mg) is zero, routines of ISORROPIA

are used, which since its original release (Nenes et al., 1998)

has been substantially improved for robustness, speed and

expanded to solve a wider range of problems (updates can be

obtained from http://nenes.eas.gatech.edu/ISORROPIA).

3.1 Solution procedure

The number of species and equilibrium reactions is determined by the relative abundance of each aerosol precursor

(NH3, Na, Ca, K, Mg, HNO3, HCl, H2SO4) and the ambient

relative humidity and temperature. The major species potentially present are determined from the value of the following

ratios:

R1 =



NH+

4



+



Ca2+



+



K

+



+



Mg2+



+



Na+



h

SO−2

4

i

R2 =



Ca2+



+



K

+



+



Mg2+



+



Na+



h

SO−2

4

i

R3 =



Ca2+



+



K

+



+



Mg2+



h

SO−2

4

i

where [X] denotes the concentration of an aerosol precursor

X (mol m−3 of air). R1, R2 and R3 are termed “total sulfate ratio”, “crustal species and sodium ratio” and “crustal

species ratio” respectively; based on their values, 5 aerosol

composition regimes are defined. The possible species for

each regime are listed in Table 3.

The DRH at To=298.15 K, the thermodynamic data for the

Ls (Eq. 17) as well as the Kussik-Meissner activity coefficient parameters (Eq. 13) are shown in Table 4. Table 7

Atmos. Chem. Phys., 7, 4639–4659, 2007 www.atmos-chem-phys.net/7/4639/2007/
C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model 4645

Table 2. Equilibrium relations and temperature dependence constants used in ISORROPIA II∗.

Reaction Equilibrium K0(298.15 K) 1H0

(T0)

RT0

1c0

p

R Units

Constant Expression

Ca(NO3)2(s)↔Ca2+

(aq)+2NO−

3 (aq)

h

Ca2+

i hNO−

3

i

2γCa2+ γ

2

NO−

3

6.067×105 −11.299♣ – mol3 kg−3

CaCl2(s)↔Ca2+

(aq)+2Cl−(aq)

h

Ca2+

i 

Cl−

2

γCa2+ γ

2

Cl− 7.974×1011 −14.087♣ – mol3 kg−3

CaSO4.2H2O(s)↔Ca2+

(aq)+SO2−4(aq)+2H2O

h

Ca2+

i hSO2−

4

i

γCa2+ γ

SO2−

4

a

2

w 4.319×10−5 – – mol2 kg−2

K2SO4(s)↔2K+

(aq)+SO2−

4 (aq)



K

+

2

h

SO2−

4

i

γ

2

K+ γ

SO2−

4

1.569×10−2 −9.589 45.807 mol3 kg−3

KHSO4(s)↔K

+

(aq)+HSO−

4 (aq)



K

+



h

HSO−

4

i

γK+ γHSO−

4

24.016 −8.423 17.964 mol2 kg−2

KNO3(s)↔K

+

(aq)+NO−

3 (aq)



K

+



h

NO−

3

i

γK+ γNO−

3

0.872 14.075 19.388 mol2 kg−2

KCl(s)↔K

+

(aq)+Cl−(aq)



K

+

 Cl−

γK+ γCl− 8.680 −6.167 19.953 mol2 kg−2

MgSO4(s)↔Mg2+

(aq)+SO2−

4 (aq)

h

Mg2+

i hSO2−

4

i

γMg2+ γ

SO2−

4

1.079×105 36.798 – mol2 kg−2

Mg(NO3)2(s)↔Mg2+

(aq)+2NO−

3 (aq)

h

Mg2+

i hNO−

3

i

2γMg2+ γ

2

NO−

3

2.507×1015 −8.754♣ – mol3 kg−3

MgCl2(s)↔Mg2+

(aq)+2Cl−

(aq)

h

Mg2+

i 

Cl−



2γMg2+ γ

2

Cl− 9.557×1021 −1.347♣ – mol3 kg−3

HSO−

4(aq)↔H

+

(aq)+SO2−4(aq)



H

+



h

SO2−

4

i



HSO−

4



γH+ γ

SO2−

4

γHSO−

4

1.015×10−2 8.85 25.14 mol kg−1

NH3(g)↔NH3(aq)



NH3(aq)



h

PNH3(aq)

i γNH3(aq)

5.764×101 13.79 −5.39 mol kg−1 atm−1

NH3(aq)+H2O(aq)↔NH+

4(aq)+OH−(aq)



NH+

4

OH−





NH3(aq)



aw

γNH+

4

γOH−

γNH3(aq)

1.805×10−5 −1.50 26.92 mol kg−1

HNO3(g)↔H

+

(aq)+NO−3(aq)



H

+

NO−

3



PHNO3

γH+ γNO−

3

2.511×106 29.17 16.83 mol2 kg−2 atm−1

HNO3(g)↔HNO3(aq)

♠



HNO3(aq)



h

PHNO3

i γHNO3(aq)

2.1×105 29.17 16.83 mol kg−1 atm−1

HCl(g)↔H

+

(aq)+Cl−(aq)



H

+

Cl−



PHCl

γH+ γCl− 1.971×106 30.20 19.91 mol2 kg−2 atm−1

HCl(g)↔HCl(aq)

♦



HCl(aq)



[PHCl]

γHCl(aq) 2.5×103 30.20 19.91 mol kg−1 atm−1

H2O(aq)↔H

+

(aq)+OH−(aq)



H

+

OH−



aw

γH+ γOH− 1.010×10−14 −22.52 26.92 mol2 kg−2

Na2SO4(s)↔2Na+

(aq)+SO2−4(aq)



Na+

2

h

SO2−

4

i

γ

2

Na+ γ

SO2−

4

4.799×10−1 0.98 39.75 mol3 kg−3

(NH4)2 SO4(s)↔2NH+

4(aq)+SO2−4(aq)

h

NH+

4

i2h

SO2−

4

i

γ

2

NH+

4

γ

SO2−

4

1.817×100 −2.65 38.57 mol3 kg−3

NH4(s)Cl↔NH3(g)+HCl(g) PNH3PHCl 1.086×10−16 −71.00 2.40 atm2

NaNO3(s)↔Na+

(aq)+NO−3(aq)



Na+



h

NO−

3

i

γNa+ γNO−

3

1.197×101 −8.22 16.01 mol2 kg−2

NaCl(s)↔Na+

(aq)+Cl−

(aq)



Na+

 Cl−

γNa+ γCl− 3.766×101 −1.56 16.90 mol2 kg−2

NaHSO4(s)↔Na+

(aq)+HSO−4(aq)



Na+



h

HSO−

4

i

γNa+ γHSO−

4

2.413×104 0.79 14.75 mol2 kg−2

NH4NO3(s)↔NH3(g)+HNO3(g) PNH3PHNO3

4.199×10−17 −74.735 6.025 atm2

NH4HSO4(s)↔NH+

4(aq)+HSO−4(aq)

h

NH+

4

i hHSO−

4

i

γNH+

4

γHSO−

4

1.383×100 −2.87 15.83 mol2 kg−2

(NH4)3 H (SO4)2(s) ↔

3NH+

4(aq)+HSO−4(aq)+SO2−4(aq)

h

NH+

4

i3h

SO2−

4

i hHSO−

4

i

×

γ

3

NH+

4

γ

SO2−

4

γHSO−

4

2.972×101 −5.19 54.40 mol5 kg−5

∗ Compiled by: Kim and Seinfeld (1995) and Kim et al. (1993) unless otherwise indicated; Reactions with constants in bold are new in

ISORROPIA II.

♣ Compiled by: Kelly and Wexler (2005)

♠ The equilibrium constant K1b of the reaction HNO3(aq) ←→

K1b H

+

(aq)

+NO−

3(aq)

is calculated from K1 and K1a of the reactions

HNO3(g) ←→

K1 H

+

(aq)

+NO−

3(aq)

and HNO3(g) ←→

K1a HNO3(aq)

, respectively: K1b=K1



K1a

♦ The equilibrium constant K2b of the reaction HCl(aq) ←→

K2b H

+

(aq)

+Cl−

(aq)

is calculated from K2 and K2a of the reactions

HCl(g) ←→

K2 H

+

(aq)

+Cl−

(aq)

and HCl(g) ←→

K2a HCl(aq)

, respectively: K2b=K2



K2a

− Data not available

www.atmos-chem-phys.net/7/4639/2007/ Atmos. Chem. Phys., 7, 4639–4659, 2007
4646 C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model

Table 3. Potential species for the five aerosol typesa.

R1 R2 R3 Aerosol type Major species Minor species Solid phase Aqueous phase Gas phase

R1<1 any value any value Sulfate Rich

(free acid)

NaHSO4, NH4HSO4,

KHSO4, CaSO4

Na+, NH+

4

, H+, HSO−

4

,

SO2−

4

, NO−

3

, Cl−, Ca2+,

K+, H2O

H2O NH3(g),

NO−

3(aq)

,

Cl−

(aq)

,

NH3(aq),

HNO3(aq),

HCl(aq)

1≤R1<2 any value any value Sulfate Rich NaHSO4, NH4HSO4,

Na2SO4, (NH4)2SO4,

(NH4)3H(SO4)2,

CaSO4, KHSO4,

K2SO4, MgSO4

Na+, NH+

4

, H+, HSO−

4

,

SO2−

4

, NO−

3

, Cl−, Ca2+,

K+, Mg2+, H2O

H2O NH3(g),

NO−

3(aq)

,

Cl−

(aq)

,

NH3(aq),

HNO3(aq),

HCl(aq)

R1≥2 R2<2 any value Sulfate Poor,

Crustal & Sodium

Poor

Na2SO4, (NH4)2SO4,

NH4NO3, NH4Cl,

CaSO4, K2SO4, MgSO4

Na+, NH+

4

, H+, SO2−

4

,

NO−

3

, Cl−, Ca2+, K+,

Mg2+, H2O, NH3(aq)

,

HNO3(aq), HCl(aq)

HNO3, HCl,

NH3, H2O

HSO−

4(aq)

R1≥2 R2≥2 R3<2 Sulfate Poor,

Crustal & Sodium

Rich, Crustal Poor

Na2SO4, NaNO3, NaCl,

NH4NO3, NH4Cl,

CaSO4, K2SO4, MgSO4

Na+, NH+

4

, H+, SO2−

4

,

NO−

3

, Cl−, Ca2+, K+,

Mg2+, H2O, NH3(aq),

HNO3(aq), HCl(aq)

HNO3, HCl,

NH3, H2O

HSO−

4(aq)

R1≥2 R2≥2 R3>2 Sulfate Poor,

Crustal & Sodium

Rich, Crustal Rich

NaNO3, NaCl, NH4NO3,

NH4Cl, CaSO4, K2SO4,

MgSO4, Ca(NO3)2,

CaCl2, Mg(NO3)2,

MgCl2, KNO3, KCl

Na+, NH+

4

, H+, SO2−

4

,

NO−

3

, Cl−, Ca2+, K+,

Mg2+, H2O, NH3(aq),

HNO3(aq), HCl(aq)

HNO3, HCl,

NH3, H2O

HSO−

4(aq)

a Species in bold are new in ISORROPIA II

displays the polynomial fit parameters for computing the

molalities of binary solutions as a function of water activity (obtained from Kim and Seinfeld, 1995; Ha and Chan,

1999; Kelly and Wexler, 2005, 2006) for CaSO4, Ca(NO3)2,

CaCl2, K2SO4, KHSO4, KNO3, KCl, MgSO4, Mg(NO3)2

and MgCl2. For (NH4)2SO4, NH4HSO4, (NH4)3H(SO4)2,

NH4NO3, NH4Cl, NaCl, NaNO3, NaHSO4 and Na2SO4, the

water activity database was updated since the original release of ISORROPIA, using the output from the AIM model

(http://www.hpc1.uea.ac.uk/∼e770/aim.html).

As in ISORROPIA, ISORROPIA II solves two classes of

problems:

1. Forward (or “closed”) problems, in which known quantities are T , RH and the total (gas + aerosol) concentrations of NH3, H2SO4, Na, HCl, HNO3, Ca, K, and

Mg.

2. Reverse (or “open”) problems, in which known quantities are T , RH and the precursor concentrations of NH3,

H2SO4, Na, HCl, HNO3, Ca, K, and Mg in the aerosol

phase.

Below the MDRH of an aerosol mixture, the particle is a

solid if the aerosol is following its deliquescence branch.

However, when the RH over a wet particle is decreasing,

the wet aerosol may not crystallize below the MDRH but

instead remain in a metastable state, where it is composed

of an aqueous supersaturated solution (e.g. Seinfeld and Pandis, 1998). ISORROPIA II can address both states (termed

“stable” where salts precipitate once the aqueous phase becomes saturated with respect to them, and, “metastable”, if

the aerosol is composed only of an aqueous phase which can

be supersaturated with respect to dissolved salts).

Depending on the three sulfate ratios, the relative humidity

and the temperature, ISORROPIA II solves the appropriate

set of equilibrium equations, and, together with mass conservation, electroneutrality, water activity equations and activity

coefficient calculations, the final concentrations at thermodynamic equilibrium are obtained. Figure 1 illustrates a general

description of the solution procedure.

3.2 Important issues

– When calculating species concentration, the stable state

solution algorithm of ISORROPIA II starts with assuming a completely dry aerosol. As the ambient relative humidity increases (or decreases), ISORROPIA II

dissolves each of the salts present (depending on their

DRH) and calculates solid and ion concentrations and

water uptake. The exact opposite methodology is

Atmos. Chem. Phys., 7, 4639–4659, 2007 www.atmos-chem-phys.net/7/4639/2007/
C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model 4647

adopted by SCAPE2, which initially assumes that all

salts present are completely dissolved; based on the ambient relative humidity and DRH of each salt calculates

solid concentration if a precipitate is assumed to form.

Differences in the “solution dynamics” may lead to differences in water content and speciation, especially at

low RH, and are further analyzed in Sect. 4.

– ISORROPIA II uses the principle of “compositional

invariance with RH cycling” to determine the aerosol

composition at low RH (i.e. when the aerosol is solid).

This is done because aerosol cycles RH many times in

nature throughout its lifetime and the invariant solution

will better represent its composition in the atmosphere.

Compositional invariance is applied when the aerosol

contains volatile anions, sulfate and non-volatile univalent cations (Na+, K+). In such cases, Na(aq) and K(aq)

preferentially associate with SO4(aq)to form Na2SO4(s)

and K2SO4(s) before they are bound with NO3(aq) and

Cl(aq)to form NaNO3(s), KNO3(s), NaCl(s), and KCl(s).

Other models may not adopt this approach and may lead

to differences in predicted water uptake, especially at

low RH. For example, in an aerosol with 2 moles of

K(aq), 0.7 moles of SO4(aq), NO3(aq) and Cl(aq), ISORROPIA II predicts that K(aq) will preferentially associate with SO4(aq)

to form K2SO4(s). The remaining

K(aq) will associate with NO3(aq) and Cl(aq)to form

KNO3 and KCl. This is because SO4 (as H2SO4) is

less volatile than NO3 (as HNO3) and Cl (as HCl) when

exposed to RH cycling, thus K2SO4(s) is more likely to

form.

3.3 Simplifications and assumptions in ISORROPIA II

Numerous simplifying assumptions are taken to increase

computational speed and numerical stability without substantially compromising rigor. These are:

– Sulfuric acid, sodium and crustal species have a very

low vapor pressure and are assumed to exclusively reside in the aerosol phase.

– The first dissociation of sulfuric acid



H2SO4(aq)→H

+ + HSO−

4



is assumed to be complete

and not considered in the equilibrium calculations.

– For a wide range of ionic strengths (0–30 M), typical of

ambient aerosols, the solubility product of magnesium

sulfate was found to be always less than its equilibrium

constant. Therefore, ISORROPIA II assumes MgSO4(s)

is always deliquesced when an aqueous phase is present,

avoiding any computations for precipitating MgSO4(s)

out of solution.

– Calcium sulfate (CaSO4) is assumed completely insoluble.

Table 4. Deliquescence relative humidity, temperature dependence

and q parameter values for all the salts modeled in ISORROPIA II1.

Salt DRH (298.15 K) −

18

1000R

Lsms q

Ca(NO3)2 0.4906∗ 509.4# 0.93∗

CaCl2 0.2830∗ 551.1# 2.40∗

CaSO4 0.9700∗ – –,

a

KHSO4 0.8600♣ – –,

b

K2SO∗

4

0.9751 35.6 −0.25

KNO∗

3

0.9248 – −2.33

KCl∗ 0.8426 158.9 0.92

MgSO4 0.8613♦ −714.5∗ 0.15∗

Mg(NO3)2 0.5400♦ 230.2# 2.32∗

MgCl2 0.3284∗ 42.23# 2.90∗

NaCl♠ 0.7528 25.0 2.23

Na2SO♠

4

0.9300 80.0 −0.19

NaNO♠

3

0.7379 304.0 −0.39

(NH4)2SO♠

4

0.7997 80.0 −0.25

NH4NO♠

3

0.6183 852.0 −1.15

NH4Cl♠ 0.7710 239.0 0.82

NH4HSO4 0.4000♠ 384.0♠ (+),c

NaHSO4 0.5200♠ −45.0♠ (+),d

(NH4)3H(SO4)2 0.6900♠ 186.0♠ (+),e

H2SO∗

4

0.000 – −0.1

H-HSO♠

4

0.000 – 8.00

HNO♠

3

N/A – 2.60

HCl♠ N/A – 6.00

1 Species in bold are new in ISORROPIA II

∗ Kim and Seinfeld (1995)

# Kelly and Wexler (2005)

♣ Pilinis and Seinfeld (1989)

♦ Ha and Chan (1999)

♠ Kim et al. (1993)

– Data not available

a γCaSO4=0

b γKHSO4=



γH−HSO4

·γKCl

γHCl 1/2

c γNH4HSO4=



γH−HSO4

·γNH4Cl

γHCl 1/2

d γNaHSO4=



γH−HSO4·γNaCl

γHCl 1/2

e γ(NH4)3H(SO4)2=



γ

3

(NH4)2SO4

·γNH4HSO4

1/5

– For sulfate rich cases (R1<2), NH3(g), NO−

3(aq)

and Cl−

(aq)

are assumed minor species that

do not significantly perturb the equilibrium

through the NH+

3(g)H2O(aq)↔NH+4(aq) + OH−(aq)

,

HNO3(g)↔H

+

(aq) + NO−

3(aq)

and HCl(g)↔H

+

(aq) + Cl−

(aq)

reactions, respectively. The code solves the appropriate

set of equilibrium reactions (for the major species)

and then the three gases NH3(g), HNO3(g), HCl(g)



www.atmos-chem-phys.net/7/4639/2007/ Atmos. Chem. Phys., 7, 4639–4659, 2007
4648 C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model

Table 5. Mutual deliquescence relative humidity, for the new salt mixtures modeled in ISORROPIA II1.

Salt Mixture MDRH∗

Ca(NO3)2, CaCl2, K2SO4, KNO3, KCl, MgSO4, Mg(NO3)2, MgCl2, NaNO3, NaCl, NH4NO3, NH4Cl 0.200

(NH4)2SO4, NH4NO3, NH4Cl, Na2SO4, K2SO4, MgSO4 0.460

Ca(NO3)2, K2SO4, KNO3, KCl, MgSO4, Mg(NO3)2, MgCl2, NaNO3, NaCl, NH4NO3, NH4Cl 0.240

(NH4)2SO4, NH4Cl, Na2SO4, K2SO4, MgSO4 0.691

Ca(NO3)2, K2SO4, KNO3, KCl, MgSO4, Mg(NO3)2, NaNO3, NaCl, NH4NO3, NH4Cl 0.240

(NH4)2SO4, Na2SO4, K2SO4, MgSO4 0.697

K2SO4, MgSO4, KHSO4, NH4HSO4, NaHSO4, (NH4)2SO4, Na2SO4, (NH4)3H(SO4)2 0.240

(NH4)2SO4, NH4NO3, Na2SO4, K2SO4, MgSO4 0.494

K2SO4, KNO3, KCl, MgSO4, Mg(NO3)2, NaNO3, NaCl, NH4NO3, NH4Cl 0.240

K2SO4, MgSO4, KHSO4, NaHSO4, (NH4)2SO4, Na2SO4, (NH4)3H(SO4)2 0.363

K2SO4, KNO3, KCl, MgSO4, NaNO3, NaCl, NH4NO3, NH4Cl 0.596

K2SO4, MgSO4, KHSO4, (NH4)2SO4, Na2SO4, (NH4)3H(SO4)2 0.610

Ca(NO3)2, K2SO4, KNO3, KCl, MgSO4, Mg(NO3)2, NaNO3, NaCl, NH4NO3, NH4Cl 0.240

K2SO4, KNO3, KCl, MgSO4, Mg(NO3)2, NaNO3, NaCl, NH4NO3, NH4Cl 0.240

1 Species in italics determine the mixture for which the MDRH value has been taken.

∗ Obtained from Potukuchi and Wexler (1995a, b) for mixtures with closest composition (T=298.15 K)

Table 6. Observed and predicted mass fraction of water in the mutual deliquscence region, for an equimolar molar mixture of NaNO3

and Ca(NO3)2 at 298.15 K. Data obained from Choi and Chan

(2002)

Water mass Water mass aw

fraction (observed) fraction (ISORROPIA II)

0.381 0.368 0.4609

0.373 0.363 0.4451

0.364 0.352 0.4258

0.356 0.342 0.4087

0.342 0.336 0.3952

0.336 0.320 0.3743

0.319 0.309 0.3511

0.299 0.291 0.3203

0.281 0.271 0.2841

0.259 0.253 0.2457

are subsequently dissolved through the equilibria

described above. The same is assumed for the dissolved

undissociated ammonia, nitric and hydrochloric acid in

the aqueous phase (NH3(aq), HNO3(aq), HCl(aq)).

– For sulfate poor cases (R1>2) bisulfate ion (HSO−

4

)

is considered a minor species from the reaction

HSO−

4(aq)↔H

+

(aq) + SO2−4(aq)

(see Table 3).

– MDRH points for multicomponent mixtures containing

crustal species are not known; they are approximated

instead with data for known mixtures with as similar

as possible composition (Table 5). For example,

the MDRH point for a (NH4)2SO4(s)-NH4NO3(s)-

NH4Cl(s)-Na2SO4(s)-K2SO4(s)-MgSO4(s) mixture is

(not known and) assumed to be the same as for the

(NH4)2SO4(s)-NH4NO3(s)-NH4Cl(s)-Na2SO4(s) mixture. The absence of crustal species in the consideration

of the MDRH points of those mixtures is expected to

introduce small underprediction of water, since i) both

potassium and magnesium have similar deliquescence

properties with sodium (Moya et al., 2001a), and, ii)

highly insoluble salts (i.e., CaSO4(s)) do not significantly impact water activity, hence do not significantly

contribute to DRH depression.

– OH−

(aq)

is assumed a minor species.

– When crustal species are in excess compared to all the

anions, ISORROPIA II assumes that the solution is

close to neutral (pH≈7). This is consistent with a presence of excess carbonate in the aerosol phase, which has

a pKa of ∼6.4 (Meng et al., 1995).

– Organic anions are not considered in the thermodynamic calculations, hence their effect on water activity

and acidity is neglected. Non-volatile anions (crustal

species and sodium) that may be associated with organic acids are treated as “excess”, and not considered

in ISORROPIA II.

– The DRH of NH4NO3(s)is strongly dependent on

temperature. Under low temperature conditions

(T<270 K), this changes the order (starting from low

to high RH) with which salts deliquesce (Fig. 2).

For these cases the DRH of NH4NO3(s)in ISORROPIA II is assumed to not “cross over” the DRH

of the other salts present in the solution, especially

Atmos. Chem. Phys., 7, 4639–4659, 2007 www.atmos-chem-phys.net/7/4639/2007/
C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model 4649

Table 7. Coefficients of m(aw) from the polynomial fit m(aw)=k0+k1aw+k2a

2

w + . . . .

Species k0 k1 k2 k3 k4 k5

Ca(NO3)

♠

2

36.356 −165.66 447.46 −673.55 510.91 −155.56

CaCl∗

2

20.847 −97.599 273.220 −422.120 331.160 −105.450

CaSO4 N/A N/A N/A N/A N/A N/A

KHSO§

4

1.061 −0.101 1.579×10−2 −1.950×10−3 9.515×10−5 −1.547×10−6

K2SO♣

4

1061.51 −4748.97 8096.16 −6166.16 1757.47 0

KNO♣

3

1.2141×104 −5.1173×104 8.1252×104 −5.7527×104 1.5305×104 0

KCl♣ 179.721 −721.266 1161.03 −841.479 221.943 0

MgSO♦

4

−0.778 177.740 −719.790 1174.600 −863.440 232.310

Mg(NO3)

♦

2

12.166 −16.154 0 10.886 0 −6.815

MgCl♦

2

11.505 −26.518 34.937 −19.829 0 0

♠ source: Kelly and Wexler (2005)

∗

source: Kim and Seinfeld (1995)

♣ source: Kelly and Wexler (2006)

§ Same as NaHSO4

♦ source: Ha and Chan (1999)

since thermodynamic data for supercooled NH4NO3(s)

solutions are not known. The same is assumed for

NH4Cl(s) and NaNO3(s) which exhibit similar behavior

with NH4NO3(s) (Fig. 2).

– γOH− and γH+ are assumed equal to unity, as the activity

coefficient routines cannot explicitly calculate them.

– The temperature dependence of DRH for Ca(NO3)2(s),

CaCl2(s), Mg(NO3)2(s) and MgCl2(s) has been calculated using thermodynamic data for the most hydrated

forms of these salts (i.e. Ca(NO3)2.4H2O, CaCl2.6H2O,

Mg(NO3)2.6H2O and MgCl2.6H2O, respectively) as

suggested by Kelly and Wexler (2005). DRH values and

equilibrium constants of these salts also correspond to

their most hydrated forms.

– Double salts (except for (NH4)3H(SO4)2(s)) and multiple hydration states are not considered in ISORROPIA II for computational efficiency. While the presence of these species may affect the partitioning of

species and the aerosol water content, it is likely that

for many atmospherically relevant conditions the effect

of these species on model predictions is small (San Martini, 2004; Wexler and Clegg, 2002).

3.4 ISORROPIA II: new features

The main improvements to the original ISORROPIA release

(Nenes et al., 1998) that are included in ISORROPIA II (and

in the latest release of ISORROPIA version 1.7, http://nenes.

eas.gatech.edu/ISORROPIA) are:

Fig. 2. DRH as a function of temperature for all ISORROPIA salts.

– Gas/liquid/solid partitioning has been extended to include crustal elements that resulted in 10 more salts in

the solid phase and 3 more ions in the aqueous phase

(Table 3).

– In addition to a thermodynamically stable state the

aerosol can also be in a metastable state where no precipitate is formed (always an aqueous solution).

– The water activity database has been updated, using the

output from the AIM model (http://www.hpc1.uea.ac.

uk/∼e770/aim.html).

– Temperature dependency of the activity coefficients is

included. This has been done for both pre-calculated

tables and online calculations of activity coefficients.

www.atmos-chem-phys.net/7/4639/2007/ Atmos. Chem. Phys., 7, 4639–4659, 2007
4650 C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model

 

Fig. 3. Comparison of mass fraction of solute as predicted by ISORROPIA II (reverse mode, metastable state) and obtained from experimental measurements (Ha and Chan, 1999; Chan et al., 2000; Choi

and Chan, 2002) for a variety of equimolar mixtures of salts. RH

ranged between 0.2 and 0.8 for room temperature conditions (21 to

23◦C).

– The MDRH points for all the systems considered have

been calculated using the GFEMN model of Ansari and

Pandis (1999b).

– The activity coefficient calculation algorithm has been

optimized to increase computational speed and avoid

numerical errors.

– The tabulated Kusik-Meissner binary activity coefficient data have been recomputed through the online calculations for the midpoint of each ionic strength interval.

– A new subroutine has been added to provide the user

with the option to “force” ISORROPIA II to conserve

mass up to machine precision.

4 Evaluation of ISORROPIA II

Salts of calcium, magnesium and sodium with chlorides, nitrates and sulfates are very hygroscopic (Chan et al., 2000). It

is useful to assess the capability of ISORROPIA II to predict

water activities of various aqueous mixtures of these salts.

Water activities (aw) for such mixtures have been measured

with an electrodynamic balance (EDB) from dilute concentrations to high supersaturations (Ha and Chan, 1999; Chan

et al., 2000; Choi and Chan, 2002). EDB involves evaporating a levitated droplet through a step decrease of the RH of

the surrounding environment. In this way, the mass fraction

of as a function of RH (or aw) is obtained. Figure 3 shows

comparison of mass fraction of solute as predicted by ISORROPIA II and obtained by experimental data for a variety of

equimolar mixtures of salts. The experimental data used here

have been taken from Ha and Chan (1999), Chan et al. (2000)

and Choi and Chan (2002). RH ranged between 0.20 and

0.80, while measurements were made at room temperature

(21 to 23◦C). As seen in Fig. 3, ISORROPIA II predictions

agree well with water activity measurements with an average standard deviation (of the difference between predictions

and measurements) of ±0.018. A noticeable deviation from

the 1:1 line was found for NaCl:MgSO4 and NaCl:MgCl2

mixtures under conditions of low RH (due to partial crystallization at low RH, Chan et al., 2000). Other mixtures were

found not to crystallize even at RH=30 or 20% (Ha and Chan,

1999; Chan et al., 2000; Choi and Chan, 2002).

ISORROPIA II is also evaluated against the predictions

of SCAPE2 for a wide range of conditions characteristic of

urban, remote continental, non-urban continental and marine aerosol (Heitzenberg, 1989; Fitzgerald, 1991; Ansari

and Pandis, 1999a). For urban and non-urban continental

aerosol, sulfates, nitrates and ammonium are usually dominant inorganic species. Sodium and chloride often compose

the majority of the marine particulate matter (usually with

some crustal species and sulfates present). This classification is mainly qualitative, as mixing between aerosol types

often occurs in the atmosphere.

Table 8 lists the 16 different sets of precursor concentrations that were used in the intercomparison study. Sulfuric

acid concentrations range between 1.0–5.7μg m−3for marine and non-urban continental and 10.0–15.0μg m−3

for urban and remote continental aerosol. For the 16 cases considered, conditions 3, 4, 15 and 16 are sulfate-rich (R1<1

or 1<R1<2), conditions 1, 2, 13 and 14 represent sulfate

near-neutral (R1≈2) aerosol and cases 5–12 are sulfate-poor

(R1>2, Table 8). For each set of precursor concentrations,

composition at thermodynamic equilibrium was calculated

for 11 values of RH ranging from 10–98%; temperature was

kept fixed at 298.15 K. Both the thermodynamically stable

and metastable state solutions of ISORROPIA II are computed.

For the intercomparison study we calculate the normalized mean error (NME), defined as NME=

Pn

i

|Ii−Si

|

Pn

i

Si

, where

Ii represents predictions of ISORROPIA II for case i, Si predictions of SCAPE2 and n is the total number of cases considered.

Finally, we compare the CPU time requirements between

SCAPE2 and ISORROPIA II, stable and metastable solution

of ISORROPIA II, as well as between ISORROPIA II and

ISORROPIA for all the simulation conditions of Table 8.

Atmos. Chem. Phys., 7, 4639–4659, 2007 www.atmos-chem-phys.net/7/4639/2007/
C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model 4651

Fig. 4. Concentration of aerosol water (a), nitrate (b), chloride (c), ammonium (d), total PM (e), and hydrogen (f), as predicted by ISORROPIA II (thermodynamically stable solution) and SCAPE2 for all the conditions described in Table 8. Temperature is set to 298.15 K. All

units are in μg m−3.

4.1 Overall assessment of ISORROPIA II vs. SCAPE2

For all the simulations performed in this work, the water activity database of SCAPE2 was replaced with the one used

in ISORROPIA II (reflecting current knowledge on water

uptake). Activities of aqueous species in SCAPE2 were

computed using Bromley’s formula for multicomponent activity coefficients and the Kussik-Meissner method for binary

coefficients.

In Fig. 4 we compare predictions of aerosol water, nitrate,

chloride, ammonium, total PM and hydrogen concentrations

between ISORROPIA II (stable solution, forward problem

solved), and SCAPE2 for the conditions specified in Table 8.

Both models predict similar amount of aerosol water content

(Fig. 4a) with a normalized mean error of 13.5%. Most of

this discrepancy is found in the low RH regimes (RH<60%)

where SCAPE2 predicts higher water concentration compared to ISORROPIA II. This discrepancy is attributed to

a) non-convergence of SCAPE2, which is corroborated by

the large CPU time required for obtaining a solution (see Table 10), and, b) inaccuracies in the activity coefficient model

(both binary and multicomponent). At low RH the aqueous phase is highly non-ideal (i.e., low liquid water content,

hence high ionic strength), consequently small changes in activity coefficients may result in large changes in the dissolved

species concentrations and predicted water uptake. On average, at RH<60% ISORROPIA II predicts I>40. A few cases

exist (for RH>65%) for which ISORROPIA II predicts less

aerosol water than SCAPE2 (Fig. 4a); this originates from

differences in aerosol nitrate which then affects water uptake. For a few marine cases, SCAPE2 predicts negligible

water due to non-convergence (Fig. 4a).

www.atmos-chem-phys.net/7/4639/2007/ Atmos. Chem. Phys., 7, 4639–4659, 2007
4652 C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model

Fig. 5. Same as Fig. 4 but using the metastable solution of ISORROPIA II. All units are in μg m−3.

In Fig. 4b, total aerosol nitrate concentrations are compared for all the input conditions of Table 8. Overall,

the agreement is very good with a mean error of 16.5%.

ISORROPIA II predicts non-negligible amount of nitrate

for some urban cases while SCAPE2 does not. For a few

non-urban continental cases, ISORROPIA II underpredicts

aerosol nitrate compared to SCAPE2. The sources of these

discrepancies are further investigated through specific examples in Sect. 4.2.

Aerosol chloride concentration predictions are shown

in Fig. 4c where both models show similar results

(NME=6.5%); small discrepancies are seen for a few marine cases (due to non-convergence of SCAPE2 solution) in

which chloride exists in significant amount.

For aerosol ammonium predictions (Fig. 4d), no substantial differences between the two models were found

(NME=2.1%). Discrepancies were primarily found in some

non-urban continental cases that represent a sulfate-poor,

ammonium-rich environment and are further analyzed in

Sect. 4.2. Even though a few differences exist in the

predicted concentrations of semi-volatile species, the total PM composition (Fig. 4e) shows very good agreement

(NME=13.0%). The worst agreement between the two models was seen for H+ predictions (Fig. 4f) with the normalized

mean error significantly higher than for any other component

(NME=64%). The discrepancy occurs at low RH (as it scales

with water content).

SCAPE2 predictions are also compared against the

metastable state solution of ISORROPIA II (Fig. 5). Table 9 shows normalized mean errors between ISORROPIA II

(both stable and metastable solutions) and SCAPE2 for the

simulations of Table 8. As can be seen in Figs. 4, 5 and

Table 9, the stable state predictions of ISORROPIA II are

closer to SCAPE2 predictions. This is expected since only

for low RHs (<40%) SCAPE2 solution, by always attempting to solve for a liquid phase, deviates from the stable state

behavior, moving towards the metastable state (see Sect. 3.2).

Atmos. Chem. Phys., 7, 4639–4659, 2007 www.atmos-chem-phys.net/7/4639/2007/
C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model 4653

Table 8. List of input conditions for model simulationsa.

Case Aerosol Type Na H2SO4 NH3 HNO3 HCl Ca2+ K

+ Mg2+ R1, R2, R3

1 Urban (1) 0.000 10.000 3.400 2.000 0.000 0.400 0.330 0.000 2.14, 0.18, 0.18

2 Urban (2) 0.023 10.000 3.400 2.000 0.037 0.900 1.000 0.000 2.44, 0.48, 0.47

3 Urban (3) 0.000 15.000 2.000 10.000 0.000 0.900 1.000 0.000 1.27, 0.31, 0.32

4 Urban (4) 0.000 15.000 2.000 10.000 0.000 0.400 0.330 0.000 0.89, 0.12, 0.12

5 N-u Cont.b(1) 0.200 2.000 8.000 12.000 0.200 0.120 0.180 0.000 23.9, 0.80, 0.37

6 N-u Cont. (2) 0.100 4.000 10.000 7.000 0.100 0.120 0.180 0.050 14.8, 0.34, 0.24

7 N-u Cont. (3) 0.023 5.664 12.000 2.000 0.037 0.120 0.180 0.050 12.4, 0.18, 0.17

8 N-u Cont. (4) 0.023 5.664 20.400 0.611 0.037 0.120 0.180 0.000 20.9, 0.15, 0.13

9 Marine (1) 2.000 1.000 0.010 0.300 3.121 0.100 0.100 0.070 9.36, 9.30, 0.80

10 Marine (2) 1.500 1.000 0.010 1.500 2.500 0.360 0.450 0.050 8.66, 8.60, 2.21

11 Marine (3) 2.500 3.000 0.001 3.000 2.500 0.500 1.000 0.050 4.86, 4.86, 1.31

12 Marine (4) 3.000 3.000 0.020 2.000 3.121 0.360 0.450 0.130 5.14, 5.10, 0.84

13 Rem. Cont.b(1) 0.000 10.000 4.250 0.145 0.000 0.080 0.090 0.000 2.49, 0.04, 0.04

14 Rem. Cont. (2) 0.023 10.000 3.000 1.000 0.037 0.080 0.090 0.000 1.78, 0.05, 0.04

15 Rem. Cont. (3) 0.100 15.000 3.000 4.000 0.100 0.080 0.090 0.000 1.21, 0.06, 0.03

16 Rem. Cont. (4) 0.200 15.000 3.000 8.000 0.200 0.080 0.090 0.040 1.25, 0.10, 0.04

a Simulations for each case were conducted for 10, 25, 40, 55, 65, 70, 75, 80, 85, 90 and 98% relative humidity. Temperature was set to

298.15 K. Concentration given in μg m−3.

b N-u Cont., non-urban continental; Rem. Cont., remote continental.

Fig. 6. Concentration of aerosol water (a), aqueous potassium (b), aqueous ammonium (c), and aqueous nitrate (d) as predicted by ISORROPIA II (thermodynamically stable solution) and SCAPE2 for the urban (1) case (Table 8) corresponding to a sulfate rich aerosol behavior

(1<R1<2). Temperature is set to 298.15 K.

www.atmos-chem-phys.net/7/4639/2007/ Atmos. Chem. Phys., 7, 4639–4659, 2007
4654 C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model

Fig. 7. Concentration of aerosol water (a), aqueous potassium (b), solid sodium chloride (c), and aqueous magnesium (d) as predicted by

ISORROPIA II (thermodynamically stable solution) and SCAPE2 for the marine (4) case (Table 8) corresponding to a sulfate poor, crustal

and sodium rich aerosol behavior (R1>2, R2>2). Temperature is set to 298.15 K.

Table 9. Normalized mean errors between ISORROPIA II and SCAPE2 for the simulations in Table 8.

NME (%) H2O(p) NO3(p) Cl(p) NH4(p) Total PM H+

(aq)

ISORROPIA II (Stable) 13.5 16.5 6.5 2.1 13.0 64.9

ISORROPIA II (Metastable) 14.7 23.7 6.6 6.7 14.3 68.0

4.2 Understanding the discrepancies between ISORROPIA II and SCAPE2

The previous discussion provides an overall intercomparison of the two models for a broad RH and composition domain; some cases are further examined to understand the

causes of discrepancies. In Fig. 6 we compare aerosol water content, aqueous phase potassium, aqueous phase ammonium and aqueous phase nitrate concentration predictions for

case 3 (see Table 8) which produced the largest discrepancy

in aerosol water and total PM concentrations. This case represents an urban type aerosol with the solution being highly

acidic (R1=1.27). Under such conditions, the water content

discrepancy between the models is largest for low RHs for

the reasons outlined in Sect. 3.2 (i.e., differences in solution dynamics). This is clearly shown in Fig. 5a where only

for RH>70% SCAPE2 and ISORROPIA II closely follow

each other. SCAPE2 predicts significant amount of aqueous phase potassium (Fig. 6b) and ammonium (Fig. 6c) at

low relative humidities, while ISORROPIA II predicts gradual deliquescence of K2SO4 from 65% to 85% RH. However, SCAPE2 predicts complete deliquescence of K2SO4

at RH=55% which may be due to non-convergence of its

numerical solution. Particulate phase ammonium is mainly

present as ammonium bisulfate (NH4HSO4(s)) and letovicite

((NH4)3H(SO4)2(s)) in ISORROPIA II. However, SCAPE2

predicts the formation of (NH4)3H(SO4)2 only, throughout

the whole RH regime. This can also be seen in Fig. 6c

where ISORROPIA II predicts a two-step dissolution of

ammonium; one at RH=40% from the deliquescence of

(NH4)3H(SO4)2(s) and one at RH=70% from the deliquescence of NH4HSO4(s)

. Water uptake with SCAPE2 exhibits deliquescence only of (NH4)3H(SO4)2(s) at RH=40%.

Both models predict similar amounts of aqueous phase nitrate for all RHs (Fig. 6d) which justifies the assumption of

ISORROPIA II for considering NO−

3(aq)

a minor species for

sulfate-rich cases.

Atmos. Chem. Phys., 7, 4639–4659, 2007 www.atmos-chem-phys.net/7/4639/2007/
C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model 4655

Table 10. CPU time required for the simulations in Table 8.

Aerosol case Convergence

criterion

ISORROPIA II

(stable)

CPU time (ms)

SCAPE2

CPU time (ms)

CPUSCAPE2

CPUISORROPIAII

CPUISORROPIAII(stable)

CPUISORROPIAII(metastable)

CPUISORROPIAII

CPUISORROPIA

Marine

10−3

30 50 16.7 1.16 1.0

Urban 20 210 10.5 1.09 1.0

Remote continental 20 440 22.0 1.05 1.0

Non-urban continental 20 110 5.5 1.00 1.0

Marine

10−4

30 >1000 >1000 1.16 1.0

Urban 20 280 14.0 1.09 1.0

Remote continental 20 >1000 >1000 1.05 1.0

Non-urban continental 20 420 21.0 1.00 1.0

Marine

10−5

30 >1000 >1000 1.16 1.0

Urban 20 >1000 >1000 1.09 1.0

Remote continental 20 >1000 >1000 1.05 1.0

Non-urban continental 20 1250 62.50 1.00 1.0

Figure 7 shows comparison of aerosol water, NaCl(s) and

K(aq) and Mg(aq) predictions for case 12 (see Table 8), which

is a sulfate poor, sodium and crustal species rich aerosol

(R1=5.1). The two models agree well (mean error of 5.1%)

in aerosol water content predictions (Fig. 6a). SCAPE2,

however, predicts significantly higher aqueous potassium for

RH<40% (Fig. 6b). This is mainly due to different approaches used to associate K(aq) with NO3(aq) and SO4(aq) at

low RH. ISORROPIA II uses the principle of “compositional

invariance” (Sect. 3.2), hence it preferentially associates

K(aq) with SO4(aq)to form K2SO4(s), and then KNO3(s) and

KCl(s). SCAPE2 tends to associate K(aq) with NO3(aq) as

KNO3(s), then with Cl(aq) as KCl(s) and then with SO4(aq) as

K2SO4(s). Since the DRH of KCl(s)is lower than K2SO4(s),

SCAPE2 deliquesces aerosol potassium at a lower RH than

ISORROPIA II. Unlike potassium, both models predict the

association of sodium between nitrate (NaNO3(s)) and chloride (NaCl(s)) in a similar way. This is shown in Fig. 6c

where the dissociation of NaCl(s) as a function of RH is similar between both models (NME=12.1%). Aqueous magnesium is the same in both models (Fig. 7d), which verifies the

ISORROPIA II assumption that MgSO4(s) never precipitates

out of solution (Sect. 3.3).

In Fig. 8 we compare aerosol water, NO3(aq) and NH4(aq)

as a function of RH for case 5 (a sulfate poor, ammonium rich aerosol, R1=23.9, R2=0.80, R3=0.37). Compared

to SCAPE2, ISORROPIA II slightly underpredicts aerosol

water, aqueous nitrate and ammonium. This difference is

seen between 25 and 65% RH, because SCAPE2 predicts

total deliquescence of sulfates at RH=40% while ISORROPIA II does at RH=70%. The increase of water content

shifts the equilibrium of HNO3(g) ←→ H

+

(aq)+NO−3(aq)

and

NH3(g)+H2O(aq)↔NH+

4(aq) + OH−

(aq)

to the right predicting

more aqueous nitrate (Fig. 7b) and ammonium (Fig. 6c) for

the same RH regime.

4.3 Metastable vs. stable solutions

The differences between metastable and stable thermodynamic solutions of ISORROPIA II are illustrated in Fig. 9,

which shows aerosol water and aqueous potassium concentration as a function of relative humidity for a sulfate nearneutral aerosol (case 13 of Table 8). SCAPE2 is also included

for comparison. The thermodynamically stable solution of

ISORROPIA II predicts deliquescence of the aerosol mixture

at 60% RH (DRH of ammonium nitrate). The MDRH for this

specific aerosol mixture is 0.46, which explains the presence

of aqueous potassium (and aerosol water) in the deliquescence solution of ISORROPIA II for RH below 60%. As expected, the metastable solution predicts significant amounts

of water below the MDRH (and by definition particulate

potassium is deliquesced at all RHs). The ionic strength are

similar in both metastable and stable solutions (which for RH

between 55 and 75% ranges between 40 and 20), suggesting

that the variations in Fig. 9 are from differences in water uptake. SCAPE2 yields a solution that is between the stable and

metastable ISORROPIA II. Below 40% RH, the predicted

concentration of aerosol water by SCAPE2 is slightly larger

than the stable solution of ISORROPIA II (Fig. 9a). This results in partial dissolution of aerosol potassium (RH<40%)

predicted by SCAPE2 as opposed to the stable solution of

ISORROPIA II which does not predict deliquescence of

aerosol potassium for this RH regime (Fig. 8b). A significant difference in predicted I is also found between ISORROPIA II and SCAPE (e.g., at RH=40% SCAPE2 predicts

I=85 while ISORROPIA II (metastable) predicts I=64).

4.4 “Forward” vs. “Reverse” problem solution

ISORROPIA II is designed to solve both forward and reverse problems. It is useful to assess whether the two solution modes predict identical outputs for the same input.

For this assessment, the output from the forward problem

www.atmos-chem-phys.net/7/4639/2007/ Atmos. Chem. Phys., 7, 4639–4659, 2007
4656 C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model

Fig. 8. Concentration of aerosol water (a), aqueous nitrate (b),

and aqueous ammonium (c) as a function of relative humidity as

predicted by ISORROPIA II (thermodynamically stable solution)

and SCAPE2 for the non-urban continental (1) case (Table 8) corresponding to a sulfate poor, ammonium rich aerosol behavior (R1>2,

R2<2). Temperature is set to 298.15 K.

(particulate phase concentrations of NH4, SO4, Na, Cl, NO3,

Ca, K, and Mg) has been used as input to the reverse problem. The two solution modes are assessed by comparing

predictions of aqueous nitrate and sulfate. Since sulfate is

only found in the aerosol phase, aqueous phase sulfate calculations are used to evaluate the solid/liquid partitioning behavior between the two solution algorithms, while aqueous

nitrate is used as a proxy for gas-aerosol partitioning (for all

the conditions specified in Table 8). The agreement between

the two solutions was found to be excellent with the NME

being 3.4±1.1% for aqueous sulfate and 2.5±1.3% for aqueous nitrate concentration.

Fig. 9. Concentration of aerosol water (a), and aqueous phase potassium (b) as a function of relative humidity as predicted by ISORROPIA II (using the thermodynamically stable and metastable solutions) and SCAPE2 for the remote continental (1) case (Table 8)

corresponding to a sulfate near-neutral aerosol behavior. Temperature is set to 298.15 K.

4.5 Computational speed

The timing tests were performed on a Dell 8300 Intel Pentium 4 CPU 3.20 GHz, 512 MB of RAM workstation running

Windows XP operating system. Both codes were compiled

with Watcom FORTRAN compiler version 2.0 with full optimization options on. Table 10 shows the CPU time needed

by the two models for the aerosol types described in Table 8.

ISORROPIA II consumes much less CPU time compared to

SCAPE2 with the difference being at least an order of magnitude for all aerosol cases. The amount of time required by

ISORROPIA II for each aerosol case was found to be approximately the same even if the convergence criterion for

solids and water was decreased down to 10−6 or 10−7 which

is a proof of the rapid and robust convergence of the code.

However, larger convergence criterion was used for the intercomparison study (see Table 10), to assure a quick and

convergent solution from SCAPE2. For completeness we

also compare the CPU time required by ISORROPIA (version 1.7, 15 March 2006) for all the simulation conditions

of Table 8, but with crustal species set to zero). Although

ISORROPIA II solves for more species than ISORROPIA,

it is not slower because of optimizations in the activity coefficient calculation algorithm in ISORROPIA II. Finally, in

Table 10 we compare the CPU time required by the stable

Atmos. Chem. Phys., 7, 4639–4659, 2007 www.atmos-chem-phys.net/7/4639/2007/
C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model 4657

and metastable solutions of ISORROPIA II. As expected, the

metastable solution is slightly faster than the stable solution

since the absence of solid species requires the solution of

fewer equations.

5 Summary

A new model, ISORROPIA II, is developed that treats the

thermodynamics of K+–Ca2+–Mg2+–NH+

4

–Na+–SO2−

4

–

NO−

3

–Cl−–H2O aerosol systems. A comprehensive evaluation was conducted against the thermodynamic model

SCAPE2 (in terms of composition predicted and computational speed) for a wide variety of aerosol conditions that

cover typical urban, remote continental, marine and nonurban continental environments. Water uptake predictions

are also evaluated against published laboratory experiments

for multicomponent mixtures. The overall predictions of

aerosol water, total PM and concentration of semi-volatile

species were generally comparable between the two models

under most conditions. For aerosol water content and total

PM mass, the two models agreed within approximately 13%.

The normalized mean error for total aerosol nitrate predictions was 16%, while for aerosol chloride and ammonium

concentration the agreement was within 2–6%. Small discrepancies were found to exist between the two models under

certain conditions, primarily for relative humidities between

40 and 70%. These discrepancies are mainly attributed to the

solution dynamics treatment of water uptake in mutual deliquescence regions and the association of non-volatile cations

with sulfate, nitrate and chloride. For all cases examined,

ISORROPIA II is more than an order of magnitude faster

than SCAPE2.

Future work will focus on evaluating various aspects of

ISORROPIA-II, which include i) code performance the transition points across solution subdomains, ii) assessing the impact of using a simplified phase diagram (lack of multiple

hydration states and double salts) on thermodynamic predictions, and, iii) evaluation with in-situ data, and within a 3-D

modeling framework. Based on the initial comparison with

SCAPE2, we can say that ISORROPIA II exhibits robust and

rapid convergence, making it one of the most computationally efficient and comprehensive inorganic thermodynamic

equilibrium modules available.

Acknowledgements. This work was supported by the National Oceanic and Atmospheric Administration under contract

NMRAC000-5-04017. We would like to acknowledge the contributions and support of the whole community that lead to significant

improvements of the original ISORROPIA code. In particular we

would like to acknowledge the contributions of (in alphabetical

order): A. Ansari, V. Bouchet, P. Bhave, S. Clegg, B. Hutzel,

K. Capaldo, B. Koo, S. Kreidenweis, P. Makar, F. San Martini,

D. Mauzerall, C. Nolte, B. Pun, A. Russell, U. Shankar, D. Tong,

J. West, D. Waldron, A. Zakey, and Y. Zhang. We also thank

C. Pilinis for his comments on the manuscript.

Edited by: J.-L. Jimenez

References

Altshuller, A. P.: Atmospheric particle sulfur and sulfur dioxide  ̈

relationships at urban and nonurban locations, Atmos. Environ.,

18, 1421–1431, 1984.

Amundson, N. R., Caboussat, A., He, J. W., Martynenko, A. V.,

Savarin, V. B., Seinfeld, J. H., and Yoo, K. Y.: A new inorganic

atmospheric aerosol phase equilibrium model (UHAERO), Atmos. Chem. Phys., 6, 975–992, 2006,

http://www.atmos-chem-phys.net/6/975/2006/.

Ansari, A. S. and Pandis, S. N.: Prediction of multicomponent inorganic atmospheric aerosol behavior, Atmos. Environ., 33, 745–

757, 1999a.

Ansari, A. S. and Pandis, S. N.: An analysis of four models predicting the partitioning of semivolatile inorganic aerosol components, Aerosol Sci. Technol., 31, 129–153, 1999b.

Brauer, M. and Brook, J. R.: Ozone personal exposures and health

effects for selected groups residing in the Fraser Valley, Atmos.

Environ., 31, 2113–2122, 1997.

Bromley, L. A.: Thermodynamic properties of strong electrolytes

in aqueous solutions, AIChE J., 19, 313–320, 1973.

Chan, M. N. and Chan, C. K.: Mass transfer effects in hygroscopic measurements of aerosol particles, Atmos. Chem. Phys.,

5, 2703–2712, 2005,

http://www.atmos-chem-phys.net/5/2703/2005/.

Clegg, S. L. and Pitzer, K. S.: Thermodynamics of multicomponent,

miscible, ionic solutions: generalized equations for symmetrical

electrolytes, J. Phys. Chem., 96, 3513–3520, 1992.

Clegg, S. L., Pitzer, K. S., and Brimblecombe, P.: Thermodynamics

of multicomponent, miscible, ionic solutions. II. Mixture including unsymmetrical electrolytes, J. Phys. Chem., 96, 9470–9479,

1992.

Clegg, S. L., Pitzer, K. S., and Brimblecombe, P.: (additions and

corrections for their published papers), J. Phys. Chem., 98, 1368,

1994.

Clegg, S. L., Pitzer, K. S., and Brimblecombe, P.: (additions and

corrections for their published papers), J. Phys. Chem., 99, 6755,

1995.

Clegg, S. L., Brimblecombe, P., and Wexler, A. S.: Thermodynamic model of the system H+−NH+

4

−SO2−

4

−NO−

3

−H2O at

tropospheric temperatures, J. Phys. Chem., A, 102, 2137–2154,

1998a.

Clegg, S. L., Brimblecombe, P., and Wexler,

A. S.: Thermodynamic model of the system

H

+−NH+

4

−Na+−SO2−

4

−NO−

3

−Cl−−H2O at 298.15 K,

J. Phys. Chem., A, 102, 2155–2171, 1998b.

Denbigh, K.: The principles of chemical equilibrium, Fourth Ed.,

Cambridge University Press, Cambridge, 1981.

Dockery, D. W., Pope, C. A., Xu, X., Spengler, J. D., Ware, J. H.,

Fay, M. E., Ferris, B. G., and Speizer, F. E.: An Association

between Air Pollution and Mortality in Six U.S. Cities, The New

England Journal of Medicine, 329, 1753–1759, 1993.

Fitzgerald, J. W.: Marine aerosols: A review, Atmos. Environ., 25A,

533–545, 1991.

www.atmos-chem-phys.net/7/4639/2007/ Atmos. Chem. Phys., 7, 4639–4659, 2007
4658 C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model

Ha, Z. and Chan, C. K.: The water activities of MgCl2, Mg(NO3)2,

MgSO4, and their mixtures, Aerosol Sci. Technol., 31, 154–169,

1999.

Heitzenberg, J.: Fine particles in the global troposphere: a review,

Tellus, 41B, 149–160, 1989.

Intergovernmental Panel on Climate Change: The scientific Basis,

Cambridge Univ. Press, New York, 2001.

Jacobson, M. Z., Tabazadeh, A., and Turco, R. P.: Simulating equilibrium within aerosols and nonequlibrium between gases and

aerosols, J. Geophys. Res., 101, 9079–9091, 1996.

Jacobson, M. Z.: Chemical Equilibrium and dissolution processes,

Fundamentals of Atmospheric Modeling, Cambridge University

Press, New York, pp. 476–510, (Chapter 18), 1999a.

Jacobson, M. Z.: Studying the effect of calcium and magnesium

on size-distributed nitrate and ammonium with EQUISOLV II,

Atmos. Environ., 33, 3635–3649, 1999b.

Ramachandran, G. and Vincent, J. H.: A Bayesian approach to retrospective exposure assessment, Applied Occupational and Environmental Hygiene, 14, 547–558, 1999.

Kaiser, J.: Mounting evidence indicts fine-particle pollution, Science, 307, 1858–1861, 2005.

Kelly, J. T. and Wexler, A. S.: Thermodynamics of carbonates and hydrates related to heterogeneous reactions involving mineral aerosol, J. Geophys. Res., 110, D11201,

doi:10.1029/2004JD005583, 2005.

Kelly, J. T. and Wexler, A. S.: Water uptake by aerosol: Water activity in supersaturated potassium solutions and deliquescence as a

function of temperature, Atmos. Environ, 40, 4450–4468, 2006.

Kim, Y. P., Seinfeld, J. H., and Saxena, P.: Atmospheric gas

– aerosol equilibrium I. Thermodynamic model, Aerosol Sci.

Technol., 19, 157–181, 1993a.

Kim, Y. P., Seinfeld, J. H., and Saxena, P.: Atmospheric gas –

aerosol equilibrium II. Analysis of common approximations and

activity coefficient calculation methods, Aerosol Sci. Technol.,

19, 182–198, 1993b.

Kim, Y. P. and Seinfeld, J. H.: Atmospheric gas – aerosol equilibrium III. Thermodynamics of crustal elements Ca2+, K+, and

Mg2+, Aerosol Sci. Technol., 22, 93–110, 1995.

Kusik, C. L. and Meissner, H. P.: Electrolyte activity coefficients in

inorganic processing, AIChE Symp. Series, 173, 14–20, 1978.

Makar, P. A., Bouchet, V. S., and Nenes, A.: Inorganic chemistry

calculations using HETV – a vectorized solver for the SO2−

4

–

NO−

3

– NH+

4

system based on the ISORROPIA algorithms, Atmos. Environ., 37, 2279–2294, 2003.

Meng, Z. Y., Seinfeld, J. H., Saxena, P., and Kim, Y. P.: Atmospheric gas – aerosol equilibrium IV. Thermodynamics of carbonates, Aerosol Sci. Technol., 23, 131–154, 1995.

Meissner, H. P., Kusik, C. L., and Tester, J. W.: Activity coefficients

of strong electrolytes in aqueous solution – effect of temperature,

AIChE Journal, 18(3), 661–662, 1972.

Meissner, H. P. and Peppas, N. A.: Activity coefficients – aqueous Solutions of polybasic acids and their salts, AIChE Journal,

19(4), 806–809, 1973.

Metzger, S. M., Dentener, F. J., and Lelieveld, J.: Aerosol multiphase chemistry – A parameterization for global modeling, Int.

Rep. 99–12, for Mar. and Atmos. Res., Utrecht, Netherlands,

1999.

Metzger, S. M., Dentener, F. J., Lelieveld, J., and Pandis, S. N.:

Gas/aerosol partitioning I: a computationally efficient model,

J. Geophys. Res., 107(D16), 4312, doi:10.1029/2001JD001102,

2002a.

Metzger, S. M., Dentener, F. J., Jeuken, A., Krol, M., and Lelieveld,

J.: Gas/aerosol partitioning II: global modeling results, J. Geophys. Res., 107(D16), 4313, doi:10.1029/2001JD001103, 2002b.

Metzger, S., Mihalopoulos, N., and Lelieveld, J.: Importance of

mineral cations and organics in gas-aerosol partitioning of reactive nitrogen compounds: case study based on MINOS results,

Atmos. Chem. Phys., 6, 2549–2567, 2006,

http://www.atmos-chem-phys.net/6/2549/2006/.

Moya, M., Pandis, S. N., and Jacobson, M. J.: Is the size distribution of urban aerosols determined by thermodynamic equilibrium? An application to Southern California, Atmos. Environ.,

36, 2349–2365, 2002.

Moya, M., Ansari, A. S., and Pandis, S. N.: Partitioning of nitrate

and ammonium between the gas and particulate phases during

the 1997 IMADA-AVER study in Mexico City, Atmos. Environ.,

35, 1791–1804, 2001a.

Moya, M., Pandis, S. N., and Jacobson, M. Z.: Is the size distribution of urban aerosols determined by thermodynamic equilibrium? An application to Southern California, Atmos. Environ.,

36, 2349–2365, 2001b.

Nenes, A., Pandis, S. N., and Pilinis, C.: ISORROPIA: A new thermodynamic equilibrium model for multiphase multicomponent

inorganic aerosols, Aquatic Geochemistry, 4, 123–152, 1998.

Nenes, A., Pilinis, C., and Pandis, S. N.: Continued development

and testing of a new thermodynamic aerosol module for urban

and regional air quality models, Atmos. Environ., 33, 1553–

1560, 1999.

Pilinis, C. and Seinfeld, J. H.: Continued development of a general

equilibrium model for inorganic multicomponent atmospheric

aerosols, Atmos. Environ, 21, 2453–2466, 1987.

Pilinis, C. and Seinfeld, J. H.: Water content of atmospheric

aerosols, Atmos. Environ., 23, 1601–1606, 1989.

Pitzer, K. S. and Simonson, J. M.: Thermodynamics of multicomponent, miscible, ionic systems: Theory and equations, J. Phys.

Chem., 90, 3005–3009, 1986.

Potukuchi, S. and Wexler, A. S.: Identifying solid-aqueous phase

transitions in atmospheric aerosols – I. Neutral-acidity solutions,

Atmos. Environ., 29, 1663–1676, 1995a.

Potukuchi, S. and Wexler, A. S.: Identifying solid-aqueous phase

transitions in atmospheric aerosols – II. Acidic solutions, Atmos.

Environ., 29, 3357–3364, 1995b.

San Martini, F. M., West, J. J., de Foy, B., Molina, L. T., Molina, M.

J., Sosa, G., and McRae, G. J.: Modeling inorganic aerosols and

their response to changes in precursor concentration in Mexico

City, J. Air Waste Manag. Assoc., 55(6), 803–815, 2005.

San Martini, F. M.: Decision Support Tools for Urban Air Quality

Management, Ph.D Thesis, Massachusetts Institute of Technology, p. 283, 2004.

Seinfeld, J. H. and Pandis, S. N.: Atmospheric Chemistry and

Physics: From Air Pollution to Climate Change, John Wiley &

Sons, Inc., 1998.

Stelson, A. W. and Seinfeld, J. H.: Relative humidity and temperature dependence of the ammonium nitrate dissociation constant,

Atmos. Environ., 16(5), 983–992, 1982.

Thomsen, K. and Rasmussen, P.: Modeling of vapor-liquid-solid

equilibrium in gas-aqueous electrolyte systems, Chem. Eng. Sci.,

54, 1787–1802, 1999.

Atmos. Chem. Phys., 7, 4639–4659, 2007 www.atmos-chem-phys.net/7/4639/2007/
C. Fountoukis and A. Nenes: ISORROPIA II: a new aerosol equilibrium model 4659

Trebs, I., Metzger, S., Meixner, F. X., Helas, G., Hoffer, A.,

Andreae, M. O., Moura, M. A. L., da Silva, R. S., Slanina, J., Rudich, Y., Falkovich, A., and Artaxo, P.: The NH+

4

–

NO−

3

−Cl−–SO2−

4

–H2O system and its gas phase precursors at

a rural site in the Amazon Basin: How relevant are crustal species

and soluble organic compounds?, J Geophys. Res.-Atmos., 110,

D07303, doi:10.1029/2004JD005478, 2005.

Wexler, A. S. and Clegg, S. L.: Atmospheric aerosol models for systems including the ions H+, NH+

4

, Na+, SO2−

4

,

NO−

3

, Cl−, Br−, and H2O, J. Geophys. Res., 107, 4207,

doi:10.1029/2001JD000451, 2002.

Wexler, A. S. and Seinfeld, J. H.: The distribution of ammonium

salts among a size and composition dispersed aerosol, Atmos.

Environ., 24A, 1231–1246, 1990.

Wexler, A. S. and Seinfeld, J. H.: Second – generation inorganic

aerosol model, Atmos. Environ., 25A, 2731–2748, 1991.

Wexler, A. S. and Clegg, S. L.: Atmospheric aerosol models for systems including the ions H+, NH+

4

, Na+, SO2−

4

,

NO−

3

, Cl−, Br−, and H2O, J. Geophys. Res., 107, 4207,

doi:10.1029/2001JD000451, 2002.

Yu, S., Dennis. R., Roselle, S., Nenes., A., Walker, J., Eder, B.,

Schere, K., Swall, J., and Robarge, W.: An assessment of the

ability of three-dimensional air quality models with current thermodynamic equilibrium models to predict aerosol NO−

3

, J. Geophys. Res., 110, D07S13, doi:10.1029/2004JD004718, 2005.

Zanobetti, A., Schwartz, J., and Dockery, D. W.: Airborne particles

are a risk factor for hospital admissions for heart and lung disease, Environmental Health Perspective, 108, 1071–1082, 2000.

Zaveri, R. A., Easter, R. C., and Peters, L. K.: A computationally efficient multicomponent equilibrium solver for aerosols (MESA),

J. Geophys. Res., 110, D24203, doi:10.1029/2004JD005618,

2005a.

Zaveri, R. A., Easter, R. C., and Wexler, A. S.: A new method

for multicomponent activity coefficients of electrolytes in aqueous atmospheric aerosols, J. Geophys. Res., 110, D02201,

doi:10.1029/2004JD004681, 2005b.

Zhang, Y., Seigneur, C., Seinfeld, J. H., Jacobson, M., Clegg, S.

L., and Binkowski, F. S.: A comparative review of inorganic

aerosol thermodynamic equilibrium models: similarities, differences, and their likely causes, Atmos. Environ., 34, 117–137,

2000.

www.atmos-chem-phys.net/7/4639/2007/ Atmos. Chem. Phys., 7, 4639–4659, 2007