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Satellite characterization of urban aerosols: Importance of including
hygroscopicity and mixing state in the retrieval algorithms
Jun Wang
1
and Scot T. Martin
1
Received 27 September 2006; revised 5 April 2007; accepted 2 May 2007; published 11 September 2007.
[1]This model study examines the sensitivity of the calculated optical properties of urban
aerosols to (1) hygroscopicity and (2) internal or external mixing state, and it further
investigates the associated implications for the accuracy of satellite retrievals of aerosol
optical thickness (t) and aerosol effective radius (r
eff
). State-of-the-art retrieval algorithms
widely omit variable hygroscopicity and mixing state. For the study described herein, the
modeled urban aerosols are composed of water-soluble sulfates and water-insoluble
black carbon (BC) in the fine mode and of water-insoluble compounds in the coarse mode.
The calculations show that external compared to internal mixing of black carbon and
sulfate not only significantly affects the single-scattering albedo but also alters the
diagnostic relationship of the Angstrom exponent (a) to the aerosol effective radius. The
implication is that over a dark surface of visible reflectance less than 0.1, satellite
retrievals of urban aerosols having a BC/sulfate mass ratio of 5% can differ in tand r
eff
by
as much as 60% and 0.2 mm, respectively, depending upon the retrieval algorithm’s
assumptions regarding hygroscopicity and mixing state. For surface reflectances greater
than 0.1 or BC/sulfate mass ratios larger than 5%, the retrieval bias, including the
possibility of unphysical retrievals, increases further. The calculations also show that
hygroscopic growth at elevated relative humidity increases the single-scattering albedo of
urban aerosols, decreases their backscattering, and as a consequence reduces the influence
of mixing state on tand r
eff
. These results suggest that current operational retrieval
algorithms lead to a possibly systematic underestimate of aerosol optical thickness when
ambient BC/sulfate aerosols are internally mixed at mass ratios greater than 3%. This
study’s recommendation is that aerosol retrieval algorithms, when applied to urban
aerosols, incorporate in situ knowledge of relative humidity, mixing state, and BC/sulfate
mass ratios, either from ground-based measurements or by auxiliary use of chemical
transport models.
Citation: Wang, J., and S. T. Martin (2007), Satellite characterization of urban aerosols: Importance of including hygroscopicity and
mixing state in the retrieval algorithms, J. Geophys. Res.,112, D17203, doi:10.1029/2006JD008078.
1. Introduction
[2] Great progress has been made in recent years in the
use of satellite sensors for the quantitative characterization
of aerosol optical properties [King et al., 1999; Kaufman et
al., 2002]. Aerosol optical thickness (t) and aerosol effec-
tive radius (r
eff
) are two commonly retrieved properties.
Aerosol optical thickness in the visible spectrum has been
retrieved over the ocean by using radiance data collected
from one channel of the Advanced Very High Resolution
Radiometer (AVHRR) [Rao et al., 1989; Wagener et al.,
1997], two channels of AVHRR [Higurashi and Nakajima,
1999; Mishchenko et al., 1999], and two channels of the
Visible and Infrared Scanner (VIRS) [Ignatov and Stowe,
2000]. In an advance allowing higher temporal resolution
(e.g., hourly or half-hourly), data from geostationary satel-
lites have been used to retrieve aerosol optical thickness
over the ocean near the Saharan desert [Moulin et al., 1997],
Puerto Rico [Wang et al., 2003a], and East Asia [Wang et
al., 2003b]. Most recently, multispectral radiance data from
the Moderate Resolution Imaging Spectrometer (MODIS)
[Remer et al., 2005] and from the Multiangle Imaging
Spectro-Radiometer (MISR) [Kahn et al., 2005a], as well
as polarization data from the Polarization and Directionality
of the Earth’s Reflectances (POLDER) satellite [Deuze et
al., 1999], have been used over ocean and land to retrieve
both tand r
eff
.
[3] In the conversion of satellite-collected radiance data
to aerosol optical properties (i.e., retrieval algorithms), there
are recognized uncertainties that can affect the reported
values of tand r
eff
[Abdou et al., 2005]. The uncertainties
stem both from simplifying assumptions used in the retrieval
algorithms and from deviations of real physical processes
and properties from modeled behavior. Acknowledged
sources of uncertainty include, for example, the character-
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, D17203, doi:10.1029/2006JD008078, 2007
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1
Division of Engineering and Applied Sciences, Harvard University,
Cambridge, Massachusetts, USA.
Copyright 2007 by the American Geophysical Union.
0148-0227/07/2006JD008078$09.00
D17203 1 of 18
ization of surface reflectance [Remer et al., 2005], the
classification of aerosols and clouds [Kaufman et al.,
2005], and the calibration of satellite sensors [Wang et al.,
2003a; Kahn et al., 2005b]. Also important in the radiative
transfer model are the treatment of polarization [Levy et al.,
2004], aerosol multiple scattering [Zhang et al., 2007], and
aerosol vertical distribution [Wang et al., 2003a].
[4] There has recently been an increased use of satellite-
derived aerosol products for the study of urban particulate
matter (PM) [Wang and Christopher, 2003; Chu et al.,
2003; Liu et al., 2004; Engel-Cox et al., 2004; Al-Saadi et
al., 2005]. These studies acknowledge that the uncertainties
regarding the accuracy of the retrievals, as specifically
related to urban aerosols, are in need of systematic inves-
tigation. In particular, two factors unaddressed in the current
databases of urban-aerosol optical properties, as used in
satellite retrievals, are aerosol hygroscopicity and internal or
external mixing of the aerosol components. The present
study assesses how hygroscopicity and mixing state could
affect the accuracy of satellite retrievals of tand r
eff
of
urban aerosols.
[5] The optical properties of hygroscopic aerosols, as
implemented in many retrieval algorithms, correspond to a
fixed relative humidity (RH) (e.g., 70% RH) [Ferrare et al.,
1990; Wong and Li, 2002]. This treatment is obviously
insufficient to describe the large variation of ambient RH,
even the more so in the boundary layer where urban
aerosols are often located and relative humidity has high
spatial and temporal variability. In the case of nonurban
aerosols, the omission of RH treatment has already been
shown to have quantitatively important consequences:
Kaufman et al. [2005] showed that sea salt aerosol hygro-
scopicity could contribute an uncertainty of up to 0.02 to the
monthly averaged tretrieved from MODIS radiance data
over ocean. Wong and Li [2002] showed that the disregard
of smoke aerosol hygroscopicity results in retrieval errors of
tby up to 20% to 40% over boreal land. Compared to these
earlier studies, the sulfate particles commonly enriched in
urban aerosols imply possibly greater retrieval errors be-
cause of high sulfate hygroscopicity and great variability in
boundary layer RH.
[6] The aerosol optical property databases used in state-
of-the-art retrieval algorithms omit the possibilities of
internal compared to external mixing of the aerosols [Remer
et al., 2005; Martonchik et al., 1998]. Rather, in the
development of the databases, external mixing was assumed
[Shettle and Fenn, 1979; Hess et al., 1998]. Urban aerosol
was composed of several typical groups, such as water
soluble sulfate particles, black carbon, or water-insoluble
compounds (hereafter INSO) [Hess et al., 1998]. In con-
trast, observations have shown that sulfate is commonly
internally mixed with BC and that this fine-mode aerosol
mixture, combined with a nonhygroscopic coarse-mode
INSO particles, is typical of urban aerosols [Castanho et
al., 2005; Johnson et al., 2005; Schwarz et al., 2006].
[7] In the study results described herein, the effects of
hygroscopicity and internal or external mixing on the
optical properties of typical urban aerosols (cf. Table 1)
are investigated, and the associated implications for satellite
retrievals of tand r
eff
are considered. The study strategy is
to consider (1) an externally mixed aerosol at 0% RH as a
base case, (2) an externally mixed aerosol at 70% RH as
representative of the assumptions in retrieval algorithms
[see Ferrare et al., 1990; Wong and Li, 2002], (3) an
externally mixed aerosol at variable RH for comparison to
the results of parts 1 and 2 as an assessment of the effects of
aerosol hygroscopicity, and (4) an internally mixed aerosol
at variable RH for comparison of the results of part 3 as an
assessment of the impact of mixing. Section 2 describes the
methodologies used to compute optical properties and to
examine satellite retrievals of tand r
eff
. Results and
discussion are provided in section 3, and conclusions are
presented in section 4.
2. Methodology
2.1. Size Distribution of Dry Aerosols
[8] A lognormal number size distribution is employed for
each component jof the urban aerosol described in Table 1
[Hess et al., 1998]:
njrð Þ ¼ Nj
rln sg;jffiffiffiffiffiffi
2p
pexp $ln r$ln rg;j
" #2
2 ln2sg;j
! ð1Þ
where r
g
is the geometric mean radius, s
g
is the geometric
standard deviation of particle radii, Nis the number of
particles per unit air volume, and n(r) is the number of
particles having a radius between rand r+dr per unit air
volume. The effective radius (r
eff
) of the number size
distribution (equation (2)) is approximately predictive of the
aerosol optical properties (i.e., extinction coefficient; see
section 2.3) [Hansen and Travis, 1974]:
reff;j%Rrmax
rmin njrð Þr3dr
Rrmin
rmax njrð Þr2dr ð2Þ
In our calculation, we set r
min
to 0.001 mm and r
max
to
20 mm. The values of r
g
,s
g
, and r
eff
of BC, sulfate, and
INSO particles are given in Table 1. As an example, a
typical urban aerosol is 60% by mass sulfate, 5% black
carbon, and 35% INSO [Hess et al., 1998]. The respective
Table 1. Dry Aerosol Properties Used in This Study
a
Aerosol Component
r
g
,
mms
g
r
eff
,
mm
Density,
g cm
$3
Refractive Index
(at 0.55 mm)
Refractive Index
(at 0.67 mm)
Externally mixed black carbon (BC) 0.01 1.8 0.02 1.0 1.76 $4.6 &10
$1
i 1.76 $4.6 &10
$1
i
Externally mixed sulfate 0.07 1.8 0.17 1.7 1.54 $1.0 &10
$7
i 1.52 $1.0 &10
$7
i
Internally mixed black-carbon/sulfate 0.07g1.8 equation (12) Appendix B sulfate shell and BC core sulfate shell and BC core
Externally mixed water insoluble (INSO) 0.47 2.5 3.83 2.0 1.53 $8.0 &10
$3
i 1.53 $8.0 &10
$3
i
a
The entries are mainly based upon Hess et al. [1998]. The density of BC is from Lesins et al. [2002]. See equations (1) and (2) in the text for the
definitions of r
g
,s
g
, and r
eff
. See Appendix B for the definition of g.
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
2 of 18
D17203
corresponding fractional number concentrations are 0.021,
0.979, and 3.5 &10
$6
.
2.2. Hygroscopicity of Sulfate Aerosols
[9] As RH increases, sulfate particles take up water and
swell, affecting both particle diameter and refractive index.
The extent of growth is a function of RH, chemical
composition, and the RH history of the particles [Martin,
2000]. In the present study, the particle growth behavior is
specified by using the growth factor g(RH), which is
defined as the ratio of wet particle radius to the dry particle
radius [Tang, 1996].
[10] Our treatment computes the particle growth factor as
the volume-fraction weighted average of pure components
[Hanel, 1976]. The pure components we consider are
aqueous ammonium sulfate (fully neutralized), aqueous
ammonium bisulfate (half neutralized), and sulfuric acid
(no neutralization) [Tang and Munkelwitz, 1994; Tang,
1996]. Figure 1 shows that the growth factor used for
sulfate aerosols in the traditional aerosol optical databases
[d’Almeida et al., 1991] is not accurate between 5% and
85% RH for describing the hygroscopic growth of partially
neutralized sulfate particles. The dependence on the extent
of neutralization, however, is less than on aerosol hygro-
scopicity and on internal or external mixing: the variation of
single scattering albedo and the phase function due to
composition differences is less than 15% for a fixed RH
and mixing state [Tang, 1996]. For this reason, the results
described in this study are restricted to ammonium sulfate,
which is more representative than sulfuric acid of boundary-
layer compositions nearby to urban centers [Martin et al.,
2004]. In contrast, optical properties of sulfuric acid are
assumed in the database widely employed in satellite
retrievals, even for urban aerosols [d’Almeida et al., 1991].
[11] The function g(RH) of ammonium sulfate is poten-
tially complicated by phase transitions. Dry ammonium
sulfate particles start to grow only at 80% RH, which is
called the deliquescence RH (DRH). As RH decreases,
aqueous ammonium sulfate particles start to shrink and
become solid at 35% RH, a point referred to as the
crystallization RH (CRH). This hystersis between DRH
and CRH has important ramifications for quantifying aero-
sol radiative forcing [Martin et al., 2004]. The focus of the
present analysis, however, is restricted to the upper branch
of the hystersis loop [e.g., Nemesure et al., 1995]. This
restriction also implies that the shape of the particles is
spherical.
[12] The wet sulfate particle size distribution n
wet
(r
0
) can
be written in terms of the dry distribution n
dry
(r) as follows:
nwet r0
ð Þdr0¼ndry rð Þdr where r0¼gr ð3Þ
under the assumption that the number of particles does not
change during the hygroscopic growth (e.g., as possibly by
coagulation or deposition). Hence the wet particle size
distribution has a lognormal form similar to that of the dry
particle size distribution, although r
g
is scaled by a factor of
g(RH) [Li et al., 2001].
2.3. Optical Properties of One Aerosol Type
[13] The extinction coefficient K
j
ext
and the scattering
coefficient K
j
sca
of an aerosol of type j(i.e., sulfate, BC,
or INSO) having a size distribution n
j
(r) are computed at
wavelength las follows [Hess et al., 1998]:
Kext
jlð Þ ¼ Zrmax
rmin
Qext
jr;mj;l
" #pr2njrð Þdrð4Þ
Ksca
jlð Þ ¼ Zrmax
rmin
Qsca
jr;mj;l
" #pr2njrð Þdrð5Þ
where Q
j
ext
and Q
j
sca
are, respectively, the extinction and
scattering efficiencies of individual particles (e.g., obtained
from Lorenz-Mie theory for spherical particles) having
refractive indices m
j
(l). The single-scattering albedo w
j
and
the phase function P
j
(q) of the aerosol are computed as
follows:
wjlð Þ ¼ Ksca
jlð Þ
Kext
jlð Þ ð6Þ
Pjq;lð Þ ¼ Rrmax
rmin Qsca r;mj;l
" #pr2njrð Þpq;r;mj;l
" #dr
Ksca
jlð Þ ð7Þ
where p(q) is the single-particle phase function at scattering
angle q, which is normalized by 4pin our treatment [Hess et
al., 1998].
[14] Equations (4) to (7) show that the aerosol optical
properties depend on the number size distribution, the
shape, and the refractive index of the constituent particles.
These parameters depend on aerosol dry chemical compo-
sition and ambient meteorological conditions, such as
Figure 1. Particle growth factor gas a function of RH for
aqueous ammonium sulfate, ammonium bisulfate, and
sulfuric acid. Data are from Tang and Munkelwitz [1994].
Circles are the growth factors of sulfate aerosols (75%
H
2
SO
4
) in the Global Aerosol Data Set (GADS) [d’Almeida
et al., 1991]. Unless stated otherwise, the growth curve of
ammonium sulfate is employed in this study (i.e., Figures 2
to 10).
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
3 of 18
D17203
relative humidity [d’Almeida et al., 1991]. The absorption
of water, which is especially important for sulfate aerosols,
both increases the particle size and alters the refractive
index [Hanel, 1976]. There are two common methods to
calculate the effective refractive index of an aerosol particle
having a homogenous mixed composition. The first is based
upon the volume mixing of each component [Hanel, 1976],
and the second is based on the molar refraction of each
component [Moelwyn-Hughes, 1961]. The two methods
yield negligible differences for partially to wholly neutral-
ized sulfate (cf. Appendix A), and the molar-refraction
method is employed in the current study.
2.4. Optical Properties of Externally Mixed
Aerosol Types
[15] For externally mixed aerosols, the particles of the
different aerosol types sulfate, BC, and INSO are entirely
physically separate. The overall optical properties are then
the sum of those of the component aerosols, as follows [e.g.,
Hess et al., 1998]:
Kext lð Þ ¼ XKext
jlð Þ ð8Þ
Ksca lð Þ ¼ XKsca
jlð Þ ð9Þ
w lð Þ ¼ Ksca lð Þ
Kext lð Þ ð10Þ
Pq;lð Þ ¼ PKsca
jlð ÞPjq;lð Þ
Ksca lð Þ ð11Þ
reff ¼Pnjrð Þr3dr
Pnjr
ð Þr2dr ð12Þ
a¼ln Kext l2
ð Þ $ ln Kext l1
ð Þ
ln l1$ln l2ð13Þ
for j2{sulfate, BC, INSO}.
[16] An avalue, representing the wavelength dependence
of K
ext
, is a good indicator of aerosol effective radius: for
typical atmospheric particles at solar wavelengths a larger
value of acorresponds to a smaller r
eff
because the
wavelength dependence of Q
ext
(l) increases for smaller size
parameter 2pr/l[Tomasi et al., 1983]. Thus for the larger
r
eff
, the relative change of Q
ext
and K
ext
(cf. equation (4)) with l
is smaller. The aerosol Angstrom exponent ain this study is
calculated for l
1
= 0.55 mm and l
2
= 0.67 mm. For typical
urban aerosols, Eck et al. [1999, Figure 8] show that an a
value calculated at 0.55 and 0.67 mm provides a good
representation of the overall wavelength dependence from
0.34 to 1.02 mm.
2.5. Optical Properties of Internally Mixed
Aerosol Types
[17] For the internally mixed treatment, BC and sulfate
occur in the same particle in the fine mode while INSO
particles remain externally mixed from them in the coarse
mode. The overall optical properties are therefore calculated
in two steps. First, Q
ext
,Q
sca
, and pof the internally mixed
BC/sulfate particles are computed (vida infra), from which
K
ext
,K
sca
,w, and Pare determined by equations (4) to (7).
Second, the overall optical properties of the externally
mixed aerosol are obtained by using equations (8) to (13)
for j2{mixed BC/sulfate, INSO}. As a caveat, although
coarse-mode INSO particles can also become coated by
sulfate during long-range transport, these coatings, unlike
their counterparts on BC particles, are not optically impor-
tant because they result in relatively small changes of
particle size and refractive index.
[18] Two approaches have been used in previous studies
to calculate the optical properties of internally mixed BC/
sulfate particles [Lesins et al., 2002]. (1) A refractive index
is calculated by assuming that sulfate and BC are homoge-
neously mixed (cf. Appendix A). The derived refractive
index and the particle size are then used in a Lorenz-Mie
calculation of Q
sca
,Q
ext
, and p. (2) A BC-core/sulfate-shell
structure is assumed, and a core/shell Mie code is employed,
which requires input of the refractive indices of BC and
sulfate as well as the core and shell particle radii [Ackerman
and Toon, 1981; Redemann et al., 2001]. The difference of
Q
sca
,Q
ext
, and ppredicted by the two methods, however, is
small [Lesins et al., 2002], and we employ the core/shell
model.
[19] In addition to these two cases, a third plausible case
is that several BC particles could be randomly imbedded
inside a sulfate particle, either centrically or eccentrically,
because BC particles have a larger number concentration
than sulfate particles in a typical urban aerosol plume. As a
statistical average of a particle ensemble, however, in which
BC particles are randomly positioned inside each sulfate
particle, the optical properties are equivalent to those of an
agglomerated BC core inside each sulfate particle [Chylek et
al., 1995], which corresponds to our case 2.
[20] In calculations comparing external and internal mix-
ing, the relative mass percentage of each aerosol component
is conserved (cf. Appendix B).
3. Results and Discussion
3.1. Optical Properties of Sulfate and Black-Carbon
Aerosols
[21] The phase functions P(q) of aqueous ammonium
sulfate aerosols are shown in Figure 2 for several RH values
and internal or external mixing with 5% by mass of BC.
Elevated RH increases forward scattering (i.e., P(q) for q!
0!) because particle growth enhances forward diffraction
[Liou, 2002]. Likewise, backscattering at 180!weakens for
elevated RH, decreasing by 45% for 90% RH compared to
0% RH (Figure 2a inset). The average decrease across all
backscattering angles (i.e., 90!<q< 180!) is 60%.
[22] The effect of hygroscopicity on sulfate aerosol back-
scattering can be compared to the effect of nonsphericity on
dust aerosol backscattering. The latter effect increases P(q)
for q< 150!but decreases it for q> 150![Wang et al.,
2003c]. In comparison, sulfate hygroscopicity decreases
P(q) for all backscattering angles (Figure 2a). The magni-
tude of the variation in P(q) is nearly the same for both
effects. Therefore in satellite retrieval algorithms for tthat
employ angular-dependant radiance observations, the pos-
sibility of aerosol hygroscopicity should be considered.
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
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D17203
[23] The effects of aerosol mixing on the phase functions
can be seen by comparing Figures 2b and 2c (internal and
external mixing, respectively) with Figure 2a (sulfate
alone). The phase functions corresponding to aqueous
sulfate particles internally mixed with 5% by mass of BC
at several RH values (Figure 2b) are broadly similar to those
of sulfate alone (Figure 2a). However, a detailed compari-
son afforded by the insets in Figures 2a and 2b shows that
above 80% RH internal mixing with BC significantly
decreases P(RH)/P(RH = 0) for 90!<q< 160!RH. The
conclusion is that the internal mixing of BC with sulfate
amplifies the decrease of backscattering caused by hygro-
scopic growth. In contrast, external mixing of sulfate and
BC aerosols (Figure 2c) leaves P(q) nearly unchanged
compared to sulfate alone, a result explained by the small
scattering coefficient of externally mixed BC particles
because of their small size. There is also an absolute
increase of P(q) for internal compared to external mixing,
which is greatest for lower RH (Figure 2d). The maximum
difference is 25% at q= 120!and 0% RH.
[24] The mixing state also has an important effect on the
single-scattering albedo (Figure 2d inset). The wvalue of
Figure 2. (a) Phase function at 0.67 mm of aqueous ammonium sulfate particles for different relative
humidities. (b, c) Same as Figure 2a except that there is 5% by mass black carbon internally and
externally mixed, respectively, with sulfate. The insets in Figures 2a, 2b, and 2c show the ratio of the
phase function at elevated RH to that at 0% RH (excluding aerosol hygroscopicity). (d) The percentage
difference of the phase function for external compared to internal mixing. The inset shows the single-
scattering albedo. Aerosol parameters are given in Table 1. INSO particles are not included in the
calculations shown for this figure.
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
5 of 18
D17203
internal mixing is 0.08 smaller than that of external mixing
at 0% RH because the BC core enhances the light absorp-
tion inside the sulfate shell [Ackerman and Toon, 1981]. The
enhancement, however, weakens as the shell radius
increases for a fixed core radius. The difference of wcaused
by the aerosol mixing state therefore decreases because of
hygroscopic growth at elevated RH, approaching zero for
RH > 95%.
[25] Isopleths of wfor variable RH and BC/sulfate mass
ratio are shown in Figure 3a for internal mixing. As
expected, higher BC/sulfate mass ratios and lower RH
values favor smaller wvalues. In addition, hygroscopic
growth (i.e., an RH dependence to the isopleths) affects w
for mass ratios greater than 0.05. The mass ratio has its most
significant effect on wfor RH < 90%. For higher RH,
increasing the mass ratio has a small effect because the
enhancement of light absorption by BC saturates for large
particles (i.e., hygroscopic growth, as described for inset of
Figure 2d). Isopleths for the difference of wbetween
internal and external mixing are shown in Figure 3b.
Internal mixing decreases wby 0.01 to 0.11, with the
greatest effect at low RH and high BC/sulfate mass ratio.
The role of INSO particles was also explored (results not
shown), but due to their smaller number concentrations, the
external mixing of INSO with sulfate and BC had a
negligible effect on the overall phase function and single-
scattering albedo.
3.2. Implications for Satellite Characterization of
Aerosols
3.2.1. Theory Regarding Satellite Retrievals of tand r
eff
[26] The theory employed in this study for the retrieval of
tand r
eff
follows that of Wang et al. [2003a, 2003b].
Briefly, the satellite measures an irradiance on a pixel of
its imaging sensor (W m
$2
) that, given the geometric and
spectral factors of the instrument and the assumption of a
point source, is converted to a radiance (L
sat
, W m
$2
sr
$1
mm
$1
) upwelling from the top of atmosphere. Satellite-
measured reflectance r
sat
is given by r
sat
=L
sat
/L
solar
=
pL
sat
/S
0
m
0
where L
solar
is the collimated solar radiance
incident at the top of atmosphere, S
0
is the solar constant,
and m
0
is the cosine of solar zenith angle [Higurashi and
Nakajima, 1999]. An expected value of the radiance at the
top of atmosphere (L
model_toa
) and hence the reflectance
(r
model_toa
=L
model_toa
/L
solar
) at a given relative sun-sensor
positioning can be calculated under cloud-free conditions by
using a radiative transfer model (RTM) that considers the
radiation source strength (i.e., the Sun), atmospheric scat-
tering and absorption by gas molecules and aerosol par-
ticles, and the Earth’s surface reflectance (r
sfc
).
[27] When the other parameters are known, the essence of
the satellite aerosol retrieval algorithm is to invoke a set of
physically consistent aerosol optical properties in the model
(thereby implying values of tand r
eff
) that minimize the
difference quantity r
sat
–r
model_toa
. Consequently, the re-
trieval accuracies of tand r
eff
are susceptible to the uncer-
tainties in the selected aerosol optical properties, in addition
to other uncertainties such as in estimating r
sfc
and in
measuring r
sat
(i.e., the sensor calibration). To better identify
the effects of uncertainties in aerosol optical properties, we
assume in the following analysis that there are no errors in r
sfc
and r
sat
and that the properties of the Sun and the atmospheric
gases are accurately known.
3.2.1.1. Retrieval of t
[28] In this study, we employ the plane-parallel discrete-
ordinate scalar radiative transfer model DISORT [Stamnes
et al., 1988; Ricchiazzi et al., 1998; Wang et al., 2003a] to
compute the upwelling radiance L
model_toa
, thus inferring
Figure 3. (a) Isopleths of single-scattering albedo (w) for variable RH and BC/sulfate mass ratio for
internal mixing. (b) Isopleths for the difference in the single-scattering albedo (Dw) for external
compared to internal mixing. Aerosol properties are given in Table 1. INSO particles are not included in
the calculations shown in this figure.
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
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D17203
r
model_toa
. The calculations are systematically completed for
different surface reflectances and Sun-sensor relative posi-
tions mand 8, where mis the satellite-viewing zenith angle
of cos
$1
(m) and 8is the relative Sun-satellite azimuth angle.
Absorption and Rayleigh scattering by atmospheric gases
are considered for a tropical summer atmospheric profile
[McClatchey et al., 1971]. Aerosol optical properties K
ext
,
w, and P(q) used in the calculation are varied for the cases
described in section 2 for different BC/sulfate mixing states,
relative humidity values, and mass ratios among BC,
sulfate, and INSO. Different tvalues, calculated as K
ext
multiplied by 3 km for the assumption that aerosols are
evenly distributed in a 3-km planetary boundary layer, are
explored by increasing the total aerosol loading (i.e., adjust-
ing Nin equation (1) and thus K
ext
in equations (4) and (5)).
This set of calculations provides a set of values that can be
arranged as a function lookup table for r
model_toa
having
eight input parameters, namely t,r
sfc
,m,m
0
,8, RH, aerosol
mixing state, and dry BC/sulfate/INSO mass ratio. Provided
that the other seven input parameters are known, a retrieval
of tfrom an observation of r
sat
is accomplished by varying
tuntil r
model_t oa
matches r
sat
. A satellite observation,
however, provides only three input parameters, namely m,
m
0
, and 8. Therefore a unique retrieval of tis not possible
without assumptions for the remaining input parameters,
including r
sfc
, RH, aerosol mixing state, and dry BC/sulfate/
INSO mass ratios. We investigate in section 3.2.2 how
different assumed values of these parameters affect the
retrieval of t.
3.2.1.2. Retrieval of r
eff
[29] In regard to the retrieval of r
eff
, there are various
approaches, all based upon the use of multispectral reflec-
tance data, to infer information about the aerosol size.
Examples include the retrieval of the aerosol Angstrom
exponent a[Higurashi and Nakajima, 1999; Mishchenko
et al., 1999], the retrieval of the fine-mode fractional
contribution to t[Tanre et al., 1997], and the retrieval of
the aerosol effective radius r
eff
[Martonchik et al., 1998].
Although these methods differ in the retrieved parameters,
they have in common the use of the physical principle that
the aerosol Angstrom exponent ais sensitive to the aerosol
number size distribution [Tomasi et al., 1983; Wang et al.,
2003b]:
a¼ln t l2
ð Þ $ ln t l1
ð Þ
ln l1$ln l2¼. . . ¼ln Kext l2
ð Þ $ ln Kext l1
ð Þ
ln l1$ln l2
¼f reff
" # ð14Þ
where the quantity on the left-hand side (LHS) is calculated
based upon satellite observations (e.g., as described in
section 3.2.1.1) and the relationship on the right-hand side
(RHS) is established by the optical properties database (e.g.,
through use of equations (12) and (13)).
[30] Use of equation (14) in the interpretation of satellite
observations requires that the optical properties database of
the RHS be uniquely established so that a=f(r
eff
) can be
inverted to r
eff
=h(a). This second relationship allows
satellite measurements of the aerosol Angstrom exponent
to be used to retrieve r
eff
. For this unique inversion to be
possible, however, an important assumption imbedded in
typical retrieval algorithms is that each aerosol type has
having a known wavelength-dependent refractive index
and a known lognormal size distribution of fixed r
g
and
s
g
(cf. equation (1)), and the variation of r
eff
in the
atmosphere is primarily caused by the change of number
mixing ratio among different types of aerosols. Some
retrieval algorithms alternatively employ ground- or air-
based in situ measurements of size distributions and optical
properties of aerosols to calibrate r
eff
=h(a) for specific uses
[Wang et al., 2003a].
[31] In the current study, the implications of a nonunique
inversion for urban aerosols are assessed as follows. The
RHS of equation (14) is calculated from K
ext
values at 550
and 670 nm (equation (8)) and from r
eff
values (equation
(12)) for many aerosol cases, including external and internal
mixing, a range of RH values, and a range of mass ratios
between the fine (i.e., BC and sulfate) and coarse (i.e.,
INSO) particles. Because the LHS equals the RHS of
equation (14), the results of these forward modeling calcu-
lations serve as an inverse-modeling lookup table for the
relationship between aand r
eff
, effectively providing a
functional relationship of r
eff
=h(a; mixing state, RH,
mass ratio). This function collapses to a unique relationship
of r
eff
=h(a) only in the special case that two of three
parameters (i.e., mixing state, RH, or mass ratio) have
fixed, known values. The calculated relationships between
aand r
eff
are shown in Figures 8 to 10 and discussed in
detail in section 3.2.3.
3.2.2. Uncertainties in Aerosol Optical Thickness
[32] Figure 4 shows several cross cuts of the dependence
of r
model_toa
on t. Figures 4a– 4e show different surface
reflectances and BC/sulfate mass ratios, with the lines
showing different relative humidities. Internal mixing of
BC and sulfate is assumed. For low r
sfc
values (such as 0.06
in Figures 4a, 4b, and 4c) and small tvalues, r
model_toa
and
tare positively linearly correlated, which can be explained
by equation (15) valid for the single-scattering regime and
for low surface reflectance [Wagener et al., 1997; Higurashi
and Nakajima, 1999]:
rmodel toa ¼rsfc þrmol þwPqð Þ
4mm0
tð15Þ
where cosq=mm
0
+ (1 $m
2
)
0.5
(1 $m
0
2
)
0.5
cos8and r
mol
is
the reflectance from molecular absorption and scattering
(typically between 0.01 and 0.05) [Wagener et al., 1997]. In
the absence of BC (Figure 4a; w!1), r
model_toa
decreases
for fixed tas RH increases as a consequence of the
decreased backscattering of the larger particles present at
elevated RH (Figure 2a). As the BC/sulfate mass ratio
increases to 5%, however, r
model_toa
drops markedly at low
RH, and as a result r
model_toa
values at low and high RH are
virtually equal (Figure 4b). The explanation is a balance
between the smaller wbut greater backscattering for low RH
than for high RH (cf. Figures 2b and 2d). For even greater
BC/sulfate mass ratio (e.g., mass ratio of 18% in Figure 4c),
the balance shifts further in the favor of even smaller w, and
as a result, r
model_toa
increases for fixed tas RH increases.
Figures 4a and 4c thus represent reverse trends depending
on the BC/sulfate mass ratio.
[33] For high tvalues (i.e., the single-scattering approx-
imation fails) and for high r
sfc
, the expected breakdown in
the linear relationship between r
model_toa
and t(as described
by equation (15)) is apparent in Figure 4. For example, for a
BC/sulfate mass ratio of 5%, Figure 4 shows that as r
sfc
increases from 0.06, to 0.12, to 0.18 in Figures 4b, to 4d,
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
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Figure 4. Relationship between modeled satellite reflectance at the top of the atmosphere (r
model_toa
)
and aerosol optical thickness (t), showing (a) – (e) results for variable surface reflectances and BC/sulfate
mass ratios (internally mixed). Lines show calculations at 0% (i.e., excluding aerosol hygroscopicity),
40%, 70%, and 95% RH. Aerosol properties are given in Table 1. The INSO/(BC + sulfate + INSO) ratio
is 35% for the calculations shown in this figure. The difference between r
model_toa
and r
sfc
at t= 0 arises
from Rayleigh scattering by atmospheric gases. In legend table, wis the single scattering albedo, and Pis
the phase function at q= 180!.
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
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to 4e, an increase in tleads to a decrease in r
model_toa
(i.e.,
the reverse of the typical case) for r
sfc
of 0.18 and 40%
RH and greater (Figure 4e). This negative correlation
occurs when the aerosol is more absorptive than the
surface (such as internally mixing BC with sulfate at
low RH), and it is further favored for greater tbecause
multiple scattering leads to additional absorption, both for
the downward and the upward solar radiation. These
results imply that r
sfc
should be less than 0.12 (at least
for the conditions of Figure 4) in order that the magnitude
of the slope between r
model_toa
and tis large enough that
an observation r
sat
, given its uncertainties, well constrains
tfor all RH values, which is an important criterion for
accurate retrievals.
[34] An analysis for the case of external mixing is similar
as discussed for the results shown in Figure 4 for internal
mixing except that r
model_toa
is less sensitive to the BC/
sulfate mass ratio because wis larger for external compared
to internal mixing (Figure 2d).
[35] Figure 4 also imparts an informative caution: the
omission of an RH treatment in the retrieval algorithm can
result in unphysical tvalues (i.e., negative or alternatively
unrealistically large). For instance, to match the value of
r
model_toa
to an observed r
sat
value of 0.17 for the conditions
of Figure 4d, a retrieval algorithm that is tuned to 5% RH
when the ambient RH is actually 70% will retrieve an
unphysically large tvalue (i.e., t(1 at 5% RH) instead
of the accurate value (i.e., t= 0.6 at 70% RH). Likewise, an
unphysical t< 0 will be obtained for the conditions of
Figure 4e to match r
model_toa
with r
sat
when r
sat
= 0.21 for
ambient RH of 95% in a retrieval algorithm assuming 70%
RH. These cautionary results highlight that even in cases for
which positive tis retrieved, the accuracy of tmay be in
substantial error if hygroscopicity is not considered, and,
alarmingly, no obvious hint of t< 0 may be apparent.
[36] With a view toward a focus on the satellite charac-
terization of urban aerosols over dark surfaces, the remain-
der of the analysis in this paper is for retrievals of tunder
the condition r
sfc
< 0.1. In addition to ocean, vegetation,
pasture, and forest, this restriction also encompasses urban
regions that have dominant vegetation cover. The present-
day MODIS aerosol retrieval algorithm, for example, is
operational over land for r
sfc
< 0.125 at 0.67 mm, and dark
pixels are located within urban regions [Kaufman et al.,
1997; Remer et al., 2005].
[37] Figures 5 to 7 provide cross cuts of calculated t
values with different assumption about aerosol hygroscop-
icity and mixing state. The figures have in common a
denominator of t(int, RH = var), which is taken to represent
the actual state of ambient aerosols in the column (i.e.,
internally mixed and responsive to relative humidity) and
the corresponding optical thickness. The panels in the
figures then assume several different numerators (e.g.,
t(ext, RH = var)), which are taken to represent the tthat
would be retrieved by a satellite algorithm making those
assumptions. RH = 0 indicates the omission of aerosol
hygroscopicity in the algorithm. The error in the satellite
algorithm is then the difference from unity of the ratio in the
two tvalues.
3.2.2.1. Effect of Hygroscopicity
[38] Isopleths of the ratio of the aerosol optical thickness
without and with consideration of aerosol hygroscopicity
are shown in Figure 5 for two different cross cuts of BC/
sulfate mass ratio (Figures 5a and 5b) and two different
scattering angles (Figures 5c and 5d). Internal mixing is
assumed. For a BC/sulfate ratio of 0% (Figure 5a), t(RH =
0)/t(RH) decreases from 0.85 to 0.65 as RH increases from
45% to 90%. The angular variation is less than 0.05. This
RH-qdependency is rationalized by equation (15) as a
decrease of P(q;RH)/P(q; RH = 0) for increasing RH (cf.
inset of Figure 2a), given that wremains near unity at all RH
values. As the BC/sulfate mass ratio increases, however, a
gain in w(RH)/w(RH = 0) for elevated RH (cf. inset of
Figure 2d and also Figure 3a) compensates for the decrease
in P(q; RH)/P(q; RH = 0). As a result, for a BC/sulfate mass
ratio of 5% (Figure 5b), t(RH = 0)/t(RH) is within 0.10 of
unity for RH < 90%. Further increases in the BC/sulfate
mass ratio lead to t(RH = 0)/t(RH) > 1 (Figure 5c),
indicating that a retrieval algorithm assuming optical prop-
erties at 0% RH (i.e., omitting aerosol hygroscopicity) can
overestimate the true aerosol optical thickness when the
ambient RH is elevated.
[39] The magnitude of the error in the retrieved aerosol
optical thickness caused by an omission of RH in the
algorithm depends on the ambient RH, the BC/sulfate mass
ratio, and the scattering angle of the observation. For BC/
sulfate mass ratios of less than 3%, tis underestimated by
15 to 35% depending on ambient RH, relatively indepen-
dent of q(Figure 5a). In contrast, for a BC/sulfate mass ratio
of 10% and qof 180!, the retrieved tis overestimated by
40% at an ambient RH of 70% and by 80% at an ambient
RH of 90%. For q= 120!,tcan be underestimated by up to
30% or overestimated by up to 40% for ranges of 0 to 18%
in BC/sulfate mass ratios and of 40 to 95% in ambient RH.
For the same ambient RH and BC/sulfate ratio, t(RH = 0)/
t(RH) values are generally larger at q= 180!than at q=
120!, because a gain in w(RH)/w(RH = 0) for elevated RH is
compensated more by the larger decrease of P(q;RH)/
P(q;RH = 0) at q= 180!than at q= 120!.
3.2.2.2. Effect of Aerosol Mixing State
[40] Figures 6 and 7 provide cross cuts showing the
effects of mixing state on retrieved aerosol optical thick-
ness. As implied by equation (15), mixing state affects the
magnitude of the retrieved tby increasing w(Figure 3b)
and decreasing P(q) (Figure 2d) for external compared to
internal mixing. The dependence of P(q) on mixing state is
nearly negligible for q!180!but much greater for q<
140!. As a net effect of changes in wP(q) (i.e., the pseudo
phase function), the ratio of t(external)/t(internal) for a BC/
sulfate mass ratio of 5% is 0.80 to 0.98, depending on RH
and the scattering angle (Figure 6a), showing that the
increase in wis greater than the decrease in P(q). A retrieval
algorithm assuming external mixing thus underestimates t
by 2% to 20% in the case that the ambient aerosol is
internally mixed. The underestimate of 20% corresponds
to lower RH values and higher scattering angles (Figure 6a).
The underestimate further increases at higher BC/sulfate
mass ratios. For a BC/sulfate mass ratio of 10%, for
instance, the underestimate is 40% at 50% RH.
[41] Figure 6b shows the effects of an algorithm that errs
in the mixing state and simultaneously omits aerosol
hygroscopicity. In this case, depending on RH and q,
t(ext)/t(int) varies from 0.64 to 0.80, resulting in an
underestimate of 20% to 40% compared to the above
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
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D17203
estimate of 2% to 20% for an algorithm including hygro-
scopicity. The underestimate increases because the omis-
sion of aerosol hygroscopicity in the algorithm omits the
strong decrease of P(q) for increasing RH (Figure 2b). The
study at 180!isolates the effects of changes in P(q) from
those in w(Figure 6d). The saturation effect in Figure 6d
for increasing BC/sulfate mass ratio reflects the saturation
of w(Figure 3b).
[42] Figures 7a and 7b shows the ratio of the retrieved t
when assuming external mixing at 70% RH (as sometimes
done in retrieval algorithms) to that when assuming internal
mixing and variable RH (i.e., t(ext, RH = 70%)/t(int, RH =
var)), which in many cases is more realistic for actual
atmospheric aerosols. For a BC/sulfate mass ratio of 5%,
the ratio varies from 0.85 to 0.99 depending on RH and the
scattering angle (Figure 7a), indicating an underestimate of
up to 15%. The variation with BC/sulfate mass ratio of
t(ext, RH = 70%)/t(int, RH = var) at 180!(Figure 7b) is
similar to that of t(ext, RH = var)/t(int, RH = var)
(Figure 6c), because the difference between P(q) at 40%
RH or 90% RH and P(q) at 70% RH is relatively small at
q= 180!. Figures 7b and 6c are then related by w(ext,
RH = 70%)/w(ext, RH = var). Similar to Figure 6c,
Figure 7b showed that for a wide range of RH from
40% to 95%, t(ext, RH = 70%)/t(int, RH = var) is less
than unity when ambient BC/sulfate aerosols are greater
than 3%, suggesting that current operational retrieval
algorithms might systematically underestimate the optical
thickness of urban aerosols. The underestimate can be as
larger as 40% to 65% at conditions of low RH and high
BC/sulfate mass ratio (Figure 7b).
[43] Figures 7c and 7d explore the effect of r
sfc
on t(ext)/
t(int) at 70% RH. Increasing r
sfc
decreases t(ext)/t(int) and
thus leads to larger underestimates of retrieved t. The
explanation is that larger r
sfc
progressively increases mul-
tiple scattering, thus amplifying w(ext)/w(int) by some
Figure 5. Isopleths of the ratio of retrieved aerosol optical thickness (t) excluding aerosol
hygroscopicity (i.e., RH = 0) to that including it. (a) Variable scattering angles (q); BC/sulfate mass
ratio of 0%. (b) Variable q; BC/sulfate mass ratio of 5%. (c) q= 180!; variable BC/sulfate mass ratio.
(d) q= 120!; variable BC/sulfate mass ratio. Aerosol properties are given in Table 1. The INSO/(BC +
sulfate + INSO) ratio is 35% for the calculations shown in this figure. The calculations are for a
wavelength of 0.67 mm, a solar zenith angle (cos
$1
m
0
) of 30!, and r
sfc
of 0.06. Black carbon and
sulfate are internally mixed.
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
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D17203
exponential factor above unity and decreasing t(ext)/t(int).
In effect, the cross cut of values at 70% RH in Figure 6a are
increased for r
sfc
< 0.06 in Figure 7c and correspondingly
decreased for r
sfc
> 0.06. A second countervailing effect is
the decreasing impact for increasing r
sfc
of differences
between down- and up-scattering (i.e., the role of P(q)),
thereby increasing t(ext)/t(int) for the reasons discussed in
relation to Figure 6a. Nevertheless, the results in Figure 7c
show that this second effect is quantitatively less important
than the role of the single-scattering albedo.
[44] The dependence of t(ext)/t(int) on r
sfc
or BC/sulfate
mass ratio is shown in Figure 7d for q= 180!and 70% RH.
The retrieved tis underestimated at 70% RH throughout the
parameter range shown in the figure. Moreover, retrievals
errors of 100% are possible for BC/sulfate mass ratios
greater than 0.12 and 0.06 < r
sfc
< 0.10. In agreement with
Figure 6c at 70% RH, consideration of BC/sulfate mixing
state is progressively more important at higher mass ratios.
Surface reflectances greater than 0.1or BC/sulfate mass
ratios larger than 5% further increase the retrieval bias,
including the possibility of unphysical retrievals (Figure 7d).
Hence cautions are needed in use of current operational
retrieval algorithms in the developing countries (such in
Indian) where the single scattering albedo of urban aerosol
can be as low as 0.78 with BC mass ration larger than 10%
[Ganguly et al., 2006].
3.2.3. Uncertainties in Aerosol Effective Radius
3.2.3.1. Effect of Hygroscopicity
[45] The effects of aerosol hygroscopicity on the Ang-
strom exponent and the aerosol effective radius are shown
in Figure 8 for the cases of external and internal mixing of
BC and sulfate, in the absence of INSO particles. Sulfate
Figure 6. Isopleths of the ratio of the retrieved aerosol optical thickness (t) assuming external mixing to
that assuming internal mixing. (a) Hygroscopic growth included in the case of external mixing; variable
scattering angles (q); BC/sulfate mass ratio of 5%. (b) Hygroscopic growth excluded (i.e., RH = 0) in the
case of external mixing; variable q; BC/sulfate mass ratio of 5%. (c) Hygroscopic growth included in the
case of external mixing; q= 180!; variable BC/sulfate mass ratio. (d) Hygroscopic growth excluded (i.e.,
RH = 0) in the case of external mixing; backscattering angle of 180!; variable BC/sulfate mass ratio.
Aerosol properties are given in Table 1. The INSO/(BC + sulfate + INSO) ratio is 35% for the
calculations shown in this figure. The calculations are for a wavelength of 0.67 mm, a solar zenith angle
(cos
$1
m
0
) of 30!, and r
sfc
of 0.06.
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
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D17203
hygroscopic growth at elevated RH increases r
eff
and
decreases a. Increasing RH from 50% to 90%, for example,
increases r
eff
by 0.1 mm, regardless of the aerosol mixing
state.
[46] The effects on r
eff
and aof an increasing presence of
externally mixed coarse-mode INSO aerosol particles, as
defined by the INSO/(sulfate + BC) mass ratio, are shown in
Figure 9. A growing presence of INSO increases r
eff
and
decreases afor all RH values, irrespective of the internal or
external mixing state of BC and sulfate, and the magnitude
of this effect is greater at lower RH than at elevated RH. For
instance, increasing the INSO/(sulfate + BC) mass ratio
from 0.1 to 1.0 increases r
eff
by 0.08 mm (Figure 9a) and
decreases aby 0.1 (Figure 9b). The effects on r
eff
and a
decrease to 0.03 mm and 0.1, respectively, at 90% RH.
[47] The data in Figure 9 constitute examples of aand r
eff
calculated for specific RH values, specific internal/external
mixing states of BC and sulfate, specific BC-to-sulfate mass
ratios of 5%, and specific INSO/(sulfate + BC) mass ratios.
Therefore the functional relationship r
eff
=h(a; mixing
state, RH, INSO/(sulfate + BC) mass ratio) exists in these
data. In Figure 10a, the effect of hygroscopicity is shown by
Figure 7. Isopleths of the ratio of the retrieved aerosol optical thickness (t) assuming external mixing
with optical properties at 70% RH to that assuming internal mixing with optical properties at either 70%
RH or variable with RH. (a) Optical properties of variable RH in the case of internal mixing; variable
scattering angle q; BC/sulfate mass ratio of 5%. (b) Optical properties of variable RH in the case of
internal mixing; q= 180!; variable BC/sulfate mass ratio. (c) Optical properties at 70% RH in the case of
internal mixing; variable q; BC/sulfate mass ratio of 5%; shown for increasing surface reflectance.
(d) Optical properties at 70% RH in the case of internal mixing q= 180!; variable BC/sulfate mass ratio;
shown for increasing surface reflectance. Aerosol properties are given in Table 1. The INSO/(BC +
sulfate + INSO) ratio is 35% for the calculations shown in this figure. The calculations are for a
wavelength of 0.67 mm, a solar zenith angle (cos
$1
m
0
) of 30!, and r
sfc
of 0.06 (Figures 7a and 7b). In the
shaded region of Figure 7d, r
model_toa
associated with t(int, RH = 70%) can be matched by t(ext, RH =
70%) only for negative values of the latter, which is physically unrealistic (see further in section 3.2.2).
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
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the lines drawn for r
eff
=h(a) at several RH values (namely,
separate lines for 0%, 50%, 70%, 80%, and 90% RH) for
external mixing of BC/sulfate. The INSO/(sulfate + BC)
mass ratio runs from 1.0 at the start of each line to 0.1 at the
end of each.
[48] A satellite observation aimplies a retrieval of r
eff
.
Figure 10a for external mixing shows that a satellite
algorithm omitting aerosol hygroscopicity (i.e., r
eff
=h(a;
RH = 0%)) greatly overestimates r
eff
if the actual atmo-
spheric RH is elevated. Specifically, at 90% compared to
0% RH, r
eff
decreases by 0.1 to 0.4 mm depending on a.
Maximum likelihood values of aof urban aerosols and of
RH in urban regions are 1.3 and 70% [Dubovik et al., 2002],
respectively. These values imply a typical overestimate in
r
eff
of 0.20 mm when not accounting for aerosol hygroscop-
icity. A similar analysis for the case of internal mixing
(Figure 10b) yields an overestimate in r
eff
of 0.18 mm. These
overestimates increase for atmospheric RH above 70% and
for avalues above 1.3 and vice versa for lower values of
RH or a. Figures 10a and 10b therefore clearly show that a
retrieval algorithm that entirely omits aerosol hygroscopic-
ity results in a retrieved r
eff
systematically larger than the
true value, at least for aerosols having the properties given
in Table 1.
[49] In comparison, a retrieval algorithm that uses the
optical properties of an aerosol at 70% RH may overesti-
mate or underestimate r
eff
, depending on the actual RH of
the atmosphere. For example, for an observed aof 1.3, the
error in r
eff
may be either negative by up to 0.15 mm or
positive by up to 0.2 mm depending on whether the real
atmospheric RH is below or above 70% RH, respectively
(Figure 10a).
3.2.3.2. Effects of Aerosol Mixing State
[50] External or internal mixing has an important effect
on the calculated relationship between the aerosol effective
radius and the Angstrom exponent for fixed RH. For
example, Figure 8 shows that at 70% RH the aand r
eff
values are 1.35 and 0.17 mm, respectively, for external
Figure 9. Effect of INSO/(sulfate+BC) mass ratio on (a) the aerosol effective radius and (b) the
Angstrom exponent. Cases are shown for internal and external mixing and for 0% (i.e., disregard
hygroscopicity), 70%, and 90% RH. The avalue is calculated based upon optical properties at 0.55 and
0.67 mm. The BC/sulfate mass ratio is 5%. Aerosol properties are given in Table 1.
Figure 8. Angstrom exponent aand aerosol effective
radius r
eff
as a function of RH for the cases of internal and
external mixing. The points show the values at 0% RH (i.e.,
disregard hygroscopicity). The avalue is calculated based
upon optical properties at 0.55 and 0.67 mm. The BC/sulfate
mass ratio is 5%. Aerosol properties are given in Table 1.
INSO particles are not included in the calculations.
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
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mixing but change to 1.22 and 0.27 mm for internal mixing.
These differences associated with external and internal
mixing have two contributing factors. (1) The number
concentration of aerosol particles is greater for external
compared to internal mixing (cf. Appendix B). In particular,
the BC mode at small size is eliminated upon internal
mixing, thereby increasing r
eff
and decreasing a, (2) Com-
pared to externally mixed particles, the core-shell micro-
structure of internally mixed BC/sulfate particles enhances
absorption, thus reducing the wavelength dependence of
K
ext
and thereby decreasing a. Since this effect is purely
optical, r
eff
remains unchanged. Through a sensitivity anal-
ysis (not shown), we find that the first contribution is the
primary factor behind the dependence of the avalues on
Figure 10. (a) Lines of r
eff
=h(a; mixing: external BC/sulfate, RH:constant, INSO/(sulfate + BC) mass
ratio:variable) for several RH values. The INSO/(sulfate + BC) mass ratio decreases from 1.0 to 0.1 along
each line (see text). The dotted lines are drawn for r
eff
= 1.9 $1.2aat 0% RH and r
eff
= 2.5 $2.0aat
90% RH. (b) Same as panel aexcept that BC and sulfate are internally mixed. The dotted lines are drawn
at r
eff
= 2.5 $1.8afor 0% RH (i.e., disregard hygroscopicity) and r
eff
= 3.4 $2.9aat 90% RH.
(c) Difference plots for each pair of RH lines shown in Figures 10a and 10b, showing the effects of
external compared to internal mixing. (d) Difference plots of the 70% RH line for external mixing
compared to those of the variable RH lines for internal mixing. (The avalue is calculated based upon
optical properties at 0.55 and 0.67 mm. The BC/sulfate mass ratio is 5%. Aerosol properties are given in
Table 1.)
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
14 of 18
D17203
mixing state. An implication of this finding in regard to
satellite retrievals is that internal or external mixing assump-
tions in retrieval algorithms affect the inferred atmospheric
aerosol number concentration, which can be a relevant
quantity for follow-on applications such as predicting aero-
sol indirect effects on cloud formation [Charlson et al.,
1992].
[51] The effect of coarse-mode INSO when externally
mixed with BC/sulfate is to decrease aand increase r
eff
(Figure 9). For internally compared to externally mixed BC/
sulfate (i.e., INSO externally mixed with BC and sulfate in
both cases), internal mixing gives a larger r
eff
and a smaller
a(Figures 9a and 9b), which is consistent with the results
shown in Figure 6. At 0% RH, the difference in avalue
calculated for internal compared to external mixing is
approximately 0.2 across an INSO mass ratio range of 0.1
to 1.0 (Figure 9b). At 70% RH, across the same INSO
range, the difference caused by mixing state is approxi-
mately 0.13. The decrease of the difference in aas RH
increases occurs because the large sulfate particles at
elevated RH have a weaker wavelength dependence of K
ext
and thus there is a reduced effect of mixing.
[52] The effect of an assumed mixing state on the r
eff
value retrieved by a satellite algorithm based upon the a
value observed by the satellite sensors is shown in
Figure 10c. At 0% RH, the difference in the retrieved r
eff
for an assumption of external compared to internal mixing
ranges from 0.01 to 0.17 mm as avaries from 1.0 to 1.3. At
70% RH, the difference range decreases to 0.04 to 0.14 mm
across the same arange. For comparison, the effect of the
assumption by a satellite retrieval algorithm of external
mixing at 70% RH compared to internal mixing at variable
RH (i.e., assumed atmospheric conditions) is shown in
Figure 10d. At 0% RH, the change in r
eff
for assuming
external mixing ranges from 0.01 to 0.16 mm as avaries
from 1.0 to 1.3. At 70% RH, the difference increases to 0.05
to 0.25 mm across the same arange.
4. Conclusions
[53] Reducing uncertainties in satellite retrievals of urban
aerosols is an important goal because satellite-based aerosol
products are making valuable contributions to monitoring
and ameliorating a diverse array of problems, such as air
quality monitoring [Al-Saadi et al., 2005], initializing and
validating regional and global aerosol models [Wang et al.,
2004], and quantifying aerosol radiative forcing [Kaufman
et al., 2002]. Theoretical simulation of retrievals is a
valuable tool for assessing uncertainties [Mishchenko and
Travis, 1997; Yan et al., 2002; Masuda et al., 2002], even
the more so because of interfering uncertainties in real
applications [Wang et al., 2003a]. The goal of reaching
the same confidence level regarding aerosol forcing as
regarding greenhouse gases requires an accuracy of satel-
lite-derived tof 0.01 or less [Chylek et al., 2003]. On the
basis of our current study, this goal cannot be successfully
achieved without a proper treatment of aerosol hygroscop-
icity and aerosol mixing state in retrieval algorithms, at least
as applied to urban aerosols.
[54] The results reported herein show that the single-
scattering albedo of urban aerosols is sensitive to the BC/
sulfate mixing state, which is consistent with Ackerman and
Toon [1981]. More interestingly, we find that the assump-
tions regarding the BC/sulfate mixing state significantly
impact the r
eff
=h(a) relationship. This important finding
has been overlooked in previous studies. Although the
impact of BC/sulfate mixing state becomes less important
as RH increases, the effects of aerosol hygroscopicity on the
aerosol phase function and aerosol single-scattering albedo
correspondingly increase.
[55] The present study further evaluates the possible
uncertainties in the satellite retrieval of tand r
eff
if treat-
ments of aerosol hygroscopicity and aerosol mixing state
are omitted from the algorithm. For the most favorable case
of surface reflectance less than 0.1 and internally mixed BC/
sulfate mass ratio less than 2%, a retrieval algorithm
assuming that aerosols are externally mixed at 70% RH
lead to an uncertainty in tof as small as 10%. The
uncertainty becomes a systematic underestimate if BC/
sulfate ratio is larger than 3%. For typical cases of urban
aerosols having BC/sulfate internally mixed at mass ratios
of 5%, an algorithm that assumes aerosol optical properties
of 0% RH results in up to a 50% underestimate of tand an
uncertainty of ±0.2 mm for r
eff
depending on ambient RH. In
comparison, for the case of aerosol optical properties fixed
at 70% RH in the retrieval algorithm, the errors in tand r
eff
are 40% and ±0.1 mm, respectively. For the most unfavor-
able case of surface reflectance greater than 0.1 or BC/
sulfate mass ratio larger than 5%, the retrieval bias, includ-
ing the possibility of unphysical retrievals, increases further.
[56] The practical retrieval of tand r
eff
can be affected by
many factors in addition to those analyzed in this paper,
such as the characterization of surface reflectance, the
sensor calibration, and the vertical distribution of aerosols.
The impact of the first two factors on retrieval accuracy is
analyzed by Wang et al. [2003a]; in the present study, we
further show that r
sfc
values exceeding the dark-surface
condition can result in an underestimate of the aerosol
optical thickness of absorbing urban aerosols. The retrieval
uncertainties caused by the multilayer aerosol distribution,
possibly due to long-range aerosol transport and causing
vertical variation of aerosol optical properties, are not
assessed in the present study because our treatment assumes
that aerosols are well mixed in the boundary layer. We make
this assumption because turbulent mixing in cloud-free days
is usually strong for the observation schedule of polar-
orbiting satellites, i.e., from local late morning (e.g., 10:30
for Terra) to local early afternoon (e.g., 13:30 for Aqua
[Wang and Christopher, 2003]). Hence the results of this
study should be further tested by using actual retrieval
algorithms and satellite data in conjunction with simulta-
neous and accurate ground-based measurements of surface
reflectance, ambient relative humidity, particle composition
and microstructure, and aerosol optical properties.
[57] Compared to other aerosol types, the heterogeneity
in urban-aerosol optical properties is large and therefore
poses a challenge for successful satellite applications. The
heterogeneity of urban aerosols arises from the different
industrial and seasonal patterns of aerosols around the
world. Therefore although detailed information of aerosol
chemical composition cannot realistically be available for
routine retrievals, we suggest that, as a step forward, the
relative mass ratios of sulfate particles, soot, and INSO
should be included in the retrieval algorithm for the correct
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
15 of 18
D17203
selection of aerosol optical model. In this regard, we
recommend the use of chemical transport models (CTMs)
to provide such information for the satellite retrieval of
aerosols. CTM simulations, even with their uncertainties,
are able to capture the large scale features of aerosol
composition, distribution, and to a limited extent the aerosol
phase and aerosol mixing state [Jacobson, 2001; Park et al.,
2004; Martin et al., 2004], thus providing valuable infor-
mation for selection of the proper aerosol optical models in
the retrievals. This approach is similar to the currently
implemented retrieval algorithms for trace gases from
satellite observations, such as CO retrievals from the
MOPITT satellite for which CTM-based trace gas profiles
are used as a first guess in the retrieval algorithm [Pan et al.,
1998]. Therefore in addition to the needs for improvements
in sensor calibration, surface reflectance characterization,
and cloud screening, incorporation of aerosol information
from CTMs is recommended for a better consideration of
aerosol hygroscopicity and aerosol mixing state and, there-
by, for improvements in the accuracies of satellite retrievals
of tand r
eff
for urban aerosols.
Appendix A: Refractive Index: Volume-Mixing
and Molar Refraction Rules
[58] The volume-mixing rule calculates the effective
refractive index (m) of a mixture as the sum of the refractive
in dex (m
j
) of e ach co m pone nt jwei g hted b y its
corresponding volume fraction (V
j
), i.e., m=PV
j
m
j
[Heller,
1945]. This mixing rule is used in the several widely
employed databases of aerosol optical properties [Shettle
and Fenn, 1979; d’Almeida et al., 1991; Hess et al., 1998].
The molar-refraction rule infers the effective refractive
index from the molar refractions (R), which is calculated
as the sum of the component molar refractions (R
j
) weighted
by the corresponding mole fractions (x
j
), i.e., R=Px
j
R
j
[Moelwyn-Hughes, 1961; Stelson and Seinfeld, 1982; Tang,
1996]. The molar refraction is then as follows: R=V
m
(m
2
$
1)/(m
2
+ 1), where V
m
is the molar volume. Figure A1
shows that these two mixing rules yield similar results for
the effective refractive index of aqueous aerosols of ammo-
nium sulfate, ammonium hydrate sulfate, and sulfuric acid.
Appendix B: Internal or External Mixing: Mass
Conservation and the Calculation of Core-to-Shell
Radius Ratio
[59] An explanation of how the internal and external
mixing calculations are performed is necessary to completely
understand the effects of mixing on the aerosol optical
properties shown in Figures 2 through 10. The mass mixing
ratio M
j
of each aerosol type is conserved. An associated
implication is that the volume mixing ratio V
j
of each aerosol
type is also conserved because the chemical species jare
immiscible with one another. A further implication is that
total aerosol number concentration decreases from (N
BC
+
N
sulf
+N
INSO
) for external mixing to (N
BC/sulf
+N
INSO
) for
internal mixing because N
BC/sulf
is set equal to N
sulf
. As a
result, even before consideration of any other factors, K
ext
and K
sca
decrease in the calculations for internal compared to
external mixing because of the lower number concentration
of the former, even though the sulfate particle size increases
slightly.
[60] The number size distributions for external mixing are
defined by the r
g
and s
g
parameters given in Table 1,
equation (1) in the main text, and N
j
values for prescribed
mass ratios. In further regard to N
j
, the mass mixing ratio is
given by the Hatch-Choate relations for a log-normal size
distribution as follows:
Mj¼4p
3hjZr3njrð Þdr ¼4p
3Njhjr3
g;jexp 4:5 ln2sg;j
" # ðB1Þ
where his the particle density. Equation (B1) combined
with the parameters in Table 1 is sufficient to define the
number size distribution of an externally mixed aerosol
having, for example, 5% by mass BC and 95% by sulfate
(e.g., Figure 2c). Similarly, the running axis of Figure 9 of
the mass ratio of INSO/(sulfate + BC) is defined by
equation (B1) and Table 1 for an externally mixed aerosol.
[61] For internal mixing, the BC particles are modeled as
imbedded in the sulfate particles, thereby increasing r
g,sulf
of
external mixing by some multiplicative factor gto a value
r
g,BC/sulf
of internal mixing, namely r
g,BC/sulf
%gr
g,sulf
.
Given that the integrated particle volume is conserved
regardless of internal or external mixing (i.e., V
internal
=
V
external
), setting s
g,BC/sulf
=s
g,sulf
and using V
j
=M
j
/r
j
, we
derive the value of the factor g, as follows:
VBC=sulf ¼Nsulf g3r3
g;sulf exp 4:5 ln2sg;sulf
" #¼g3Vsulf ðB2Þ
VBC=sulf ¼Vinternal ¼Vexternal ¼VBC þVsulf ðB3Þ
Figure A1. Real part of refractive index for aqueous
solutions of ammonium sulfate, ammonium bisulfate, and
sulfuric acid at different relative humidities. Values are
calculated by using a volume-mixing rule (dotted line) and a
molar-refraction rule (solid line). The refractive indices at
0% RH (dry conditions) are from Tang and Munkelwitz
[1994] and Tang [1996]. The line for aqueous ammonium
sulfate begins at the CRH value of 35%.
D17203 WANG AND MARTIN: AEROSOL HYGROSCOPICITY AND MIXING STATE
16 of 18
D17203
Combining equations (B2) and (B3) yields:
g¼1þVBC
Vsulf
$ %1
=3
ðB4Þ
where V
BC
and V
sulf
are defined by the parameters of
external mixing (e.g., 5% BC/sulfate mass) and used in the
calculation of gfor internal mixing. Figure 2b compared to
Figure 2c provides an example of this approach in use.
[62] The gvalue is an important input to the shell/core
optical model used to calculate the effects of BC/sulfate
internal mixing on the aerosol optical properties. For V
BC
and V
sulf
defined by the parameters r
g
and s
g
of Table 1, the
gvalue at low RH does not exceed 1.007 for many cases in
this study, namely those having BC compared to sulfate of
20% or less by mass. The corresponding upper limit of the
core-to-shell ratio is 0.27. The gvalue and the corresponding
core-to-shell ratio decrease further at elevated RH because of
hygroscopic growth by sulfate.
[63]Acknowledgments. We are grateful for support received from
the NSF Atmospheric Chemistry Program (ATM-0317583). J. Wang is
supported by a NOAA Climate & Global Change Postdoctoral Fellowship
under the administration of the UCAR visiting scientist program. The
authors thank D. J. Jacob for insightful discussion and W. Wiscombe for
computer codes.
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S. T. Martin and J. Wang, Division of Engineering and Applied Science,
Harvard University, 29 Oxford Street, Cambridge, MA 02138, USA.
(scot_martin@harvard.edu; junwang@fas.harvard.edu)
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