3 Modeled humidification factors (*f*(RH))

20

Modeling of humidification factors (*f *(RH)) as a function of RH requires knowledge of

the changes in particle composition, size and optical properties due to changes in

aerosol water content. Thermodynamic equilibrium models require aerosol chemical

composition data and provide aerosol water content as a function of RH. Aerosol water

content is then used to calculate changes in particle size (GF), mass and composition.

25

Particle light scattering coefficients are computed by applying Mie theory to measured

4237

size distributions while incorporating variations in particle size and refractive index as

a function of RH.

We used the E-AIM inorganic thermodynamic equilibrium model III (Extended

Aerosol Inorganic Model, Clegg et al., 1998, http://www.aim.env.uea.ac.uk/aim/aim.

5

php) to calculate aerosol water content for inorganic aerosols by incorporating measured

mass concentrations of solid phase species. E-AIM models the system of ions

including hydrogen, ammonium, sodium, sulfate, nitrate and chloride as well as water.

It can be run in several configurations. Species can be partitioned into solid, liquid or

gaseous phases. Because E-AIM does not include potassium salts, we assumed all of

10

the potassium was sodium and adjusted these concentrations to achieve a charge balance

(S. L. Clegg, personal communication, 2009). We modeled both deliquescence

and metastable equilibrium. The model was run in parametric mode that allowed for

the varying of RH from 10–99% at a temperature of 298.15 K only. While E-AIM provides

an option for hygroscopic growth from organic species, we did not apply it in this

15

application.

The diameter growth factor, GF, for the inorganic aerosol mixture was computed

using Eq. (2).

GF=

h

M

RH

RH

.

M

dry

dry

i

1/3 (2)

The dry mass and density are

*M*dry and **dry, respectively. The humidified mass (*M*RH)

20

is the sum of the dry mass and the derived aerosol water content as a function of RH

from E-AIM. The humidified density (

**RH) was computed using volume-mixing rules

(Hasan and Dzubay, 1983; Ouimette and Flagan, 1982) shown in Eq. (3).

¯−1 =

X

i

X

i

*i*

(3)

The mass fraction for a given species (

*i *) is *Xi *and the density is *i *. The values of

25

*i *for each species are listed in Table 1. The POM concentrations used in this calculation

corresponded to the values derived from mass closure. In the case of dry

4238

mixture density, the mass fractions and densities were summed over each individual

dry species. In the case of the humidified density, the dry mixture density and water

density were summed. Dry mixture densities (inorganic salts

+carbon+soil) ranged

from 1.42–1.95 g cm

−3 for all of the burns with an average and one standard deviation

of 1.6

±0.2 gcm−3. 5 The dry densities for each burn are listed in Table 2. These values

are somewhat higher than the prior estimates of biomass burning aerosol densities of

1.2–1.4 gcm

−3 (Reid et al., 2005a) but are consistent with Levin et al. (2010).

The mixture GF was computed using Eq. (4) following Malm and Kreidenweis (1997)

who invoked the Zdanovskii-Stokes-Robinson (ZSR) assumption (Stokes and Robin

10

son, 1966).

GF

3 =* *

dry* *

RH

(

X

i

X

i

RH*,i *

dry*,i*

(GF

*i *)3) (4)

The growth factor for species

*i *at a given RH is GF*i *. The mixture dry density is **dry

and the humidified mixture density is

**RH. The species included were inorganic salts,

carbon (POM

+LAC) and soil. The GF values for POM, LAC and soil were set equal

15

to one and held constant with RH, and their densities were fixed at the values listed

in Table 1. GF curves were computed for both deliquescence and metastable equilibrium.

Both curves were normalized to one (GF

=1) at the RH corresponding to the dry

HTDMA measurements. This normalization resulted in suppression of the metastable

curve below the deliquescence curves at high RH. This suppression was most pro

20

nounced for cases when metastable equilibrium predicted considerable water at low

RH conditions. In the absence of the normalization the two curves agreed above the

deliquescence RH.

Comparisons of modeled and measured GF are shown for weak to non-hygroscopic

smoke (ponderosa pine) and for a more hygroscopic smoke (sage/rabbit brush) in

25

Figs. 2 and 3, respectively. The measured GF values corresponded to 100 nm diameter

particles only, while the modeled GF were derived from IMPROVE PM

2*.*5 bulk

mass concentrations. Dry RH for the measured and modeled GF was the same. The

4239

modeled GF for smoke particles from burns of ponderosa pine (Fig. 2) were flat as a

function of RH and showed no significant di

fference between both methods (labeled

“metastable” and “deliquescence”). The measured GF fell slightly above these curves

(outside of experimental uncertainty, 0.02) but did not demonstrate any measureable

5

growth with increased RH. In contrast, the modeled GF curves for sage/rabbit brush increased

continuously with RH for the metastable curve while the deliquescence curve

showed additional water uptake around 70% RH. The di

fferences between the modeled

curves at high RH reflect the normalization discussed earlier. The measured GF

values fell between these two curves for RH

*>*85%, suggesting the modeled curves

10

were representing the hygroscopic properties of particles during this burn. We present

these comparisons to demonstrate the typical agreement observed between measured

and modeled GF for each burn; more details regarding measured GF can be found in

Carrico et al. (2010).

The GF curves were applied to the measured size distributions to compute aerosol

light scattering coe

fficients as a function of RH. Refractive indices (*n*¯ = **m *15 −*ki *) were

calculated using volume-weighted mixing rules shown in Eq. (5) (Ouimette and Flagan,

1982; Hasan and Dzubay, 1983).

n

¯ =**¯

X

j

X

jmj

*j*

−

**¯

X

j

X

jkj

j

i

(5)

Real (

*mj *) and imaginary (*kj *) parts of the refractive indices for individual species are

20

listed in Table 1. Here we sum over species *j *to avoid confusion with the imaginary

part of the refractive index. The mixture density was computed using Eq. (3). The

real part of the dry refractive indices ranged from 1.56 to 1.79 with an average and

one standard deviation of 1.63

±0.07. The imaginary part ranged from 0.012–0.39

with an average and one standard deviation of 0.13

±0.12. LAC was the only species

25

assumed to absorb light. Some organic aerosol species may also absorb light (e.g.,

Kirchstetter et al., 2004; Hand et al., 2005; Ho

ffer et al., 2006) but the effect was

not included here. Values corresponding to each fuel are listed in Table 2. These

4240

values are consistent with previous reported estimates of biomass burning refractive

indices (Reid et al., 2005b, McMeeking et al., 2005; Hungershoefer et al., 2008) and

are consistent with values reported by Levin et al. (2010) for FLAME 2006 and 2007

studies. More discussion of these values can be found in Sect. 4.

5

Equation (6) was used to compute light scattering coefficients for dry or humidified

particles (Hand et al., 2004).

b

sp =

Z

3

2

Q

sp* *

D

pm(dry)

GF

2 *dV*dry* *

d

log*D*p* *

d

log*D*p (6)

For

*b*sp(dry), the Mie scattering efficiency (*Q*sp) is computed for diameters and complex

refractive indices of dry particles. For

*b*sp(RH)*,Q*sp is computed using diameters and

10

complex refractive indices adjusted for water content. The dry volume size distribution

is given by

*dV*dry/*d*log*D*p. Calculations were performed at a wavelength of 530 nm.

GF is the growth factor derived with the thermodynamic models described above and

D

pm(dry) corresponds to the dry midpoint diameter of a size distribution bin. The humidification

factor

*f *(RH) was computed by dividing *b*sp(RH) by *b*sp(dry) where *b*sp(dry)

15

corresponds to the RH of nephelometer measurements at 20–25% RH. The modeled* *

f

(RH) curves were normalized to one at the dry nephelometer RH, similar to the GF

case.