Atmos. Meas. Tech., 5, 1653–1665, 2012
www.atmos-meas-tech.net/5/1653/2012/
doi:10.5194/amt-5-1653-2012
© Author(s) 2012. CC Attribution 3.0 License.
Atmospheric
Measurement
Techniques
Critical surface albedo and its implications to aerosol remote sensing
F. C. Seidel1,* and C. Popp2
1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA
2 Empa, Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, Switzerland
* Invited contribution by F. C. Seidel, recipient of the EGU Outstanding Student Poster Award 2011.
Correspondence to: F. C. Seidel (felix.seidel@jpl.nasa.gov)
Received: 30 September 2011 – Published in Atmos. Meas. Tech. Discuss.: 20 December 2011
Revised: 9 June 2012 – Accepted: 15 June 2012 – Published: 17 July 2012
Abstract. We analyse the critical surface albedo (CSA)
and its implications to aerosol remote sensing. CSA is defined as the surface albedo where the reflectance at top-ofatmosphere (TOA) does not depend on aerosol optical depth
(AOD). AOD retrievals are therefore inaccurate at the CSA.
The CSA is obtained by derivatives of the TOA reflectance
with respect to AOD using a radiative transfer code. We
present the CSA and the effect of surface albedo uncertainties
on AOD retrieval and atmospheric correction as a function
of aerosol single-scattering albedo, illumination and observation geometry, wavelength and AOD. In general, increasing aerosol absorption and increasing scattering angles lead
to lower CSA. In contrast to the strict definition of the CSA,
we show that the CSA can also slightly depend on AOD and
therefore rather represent a small range of surface albedo values. This was often neglected in previous studies. The following implications to aerosol remote sensing applications
were found: (i) surface albedo uncertainties result in large
AOD retrieval errors, particularly close to the CSA; (ii) AOD
retrievals of weakly or non-absorbing aerosols require dark
surfaces, while strongly absorbing aerosols can be retrieved
more accurately over bright surfaces; (iii) the CSA may help
to estimate aerosol absorption; and (iv) the presented sensitivity of the reflectance at TOA to AOD provides error
estimations to optimise AOD retrieval algorithms.
1
Introduction
Atmospheric aerosols can affect human health (e.g.
Brunekreef and Holgate, 2002), and they have a significant influence on the Earth’s radiation budget by scattering and absorbing electromagnetic radiation (direct effect)
or by cloud formation in their role as cloud condensation nuclei (indirect effect) (e.g. Ramanathan et al., 2001;
Lohmann and Feichter, 2005; IPCC, 2007). Remote sensing
from space has made important contributions to our knowledge on the spatio-temporal distribution and optical properties of aerosols. Aerosol remote sensing has helped to reduce
large uncertainties regarding their impact on climate (IPCC,
2007). Many spaceborne sensors allow the retrieval of total
vertical columnar aerosol scattering and absorption (extinction), known as aerosol optical depth (AOD). However, the
retrieval of AOD is a challenging task and requires accurate prior knowledge of aerosol micro-physical and optical
properties, such as size distribution, single-scattering albedo
(SSA) and phase function. Further, it requires information
on the directional surface reflectance and the state of the
atmosphere (e.g. ozone and water vapour concentrations).
AOD retrieval algorithms require a correct discrimination
of the measured upwelling radiance into a part originating
from molecule and aerosol scattering and a part caused by
reflection from the Earth’s surface.
Numerous studies demonstrated that the estimations of the
surface albedo and related uncertainties are a major source of
errors in AOD retrievals (e.g. Teillet et al., 1994; Kaufman
et al., 1997; Popp et al., 2007; Kokhanovsky and Leeuw,
2009; Seidel et al., 2011). It was also shown that a certain
range of surface albedo values provides difficulties for AOD
retrievals where changes in aerosol scattering cancel out
changes in aerosol absorption. The measured radiance at topof-atmosphere (TOA) becomes therefore insensitive to AOD
changes. Fraser and Kaufman (1985) analysed and defined
this surface albedo with regard to aerosol remote sensing
applications as the critical surface reflectance. In this study,
we will use the term critical surface albedo (CSA) to avoid
Published by Copernicus Publications on behalf of the European Geosciences Union.
1654
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
possible confusions with reflectance functions (Eqs. 1, 2, and
6). Note that the CSA could represent either albedo or any reflectance factor, according to the use of term a in Eq. (6). A
few studies have taken advantage of the CSA to gain information about aerosol absorption from remote sensing measurements, which requires a good estimate as well as some
albedo variability of the underlying surface in multiple pixels
(Kaufman, 1987). For example, de Almeida Castanho et al.
(2008) improved MODIS AOD retrievals over Sao Paulo,
Brazil by estimating SSA prior to the AOD inversion using
the CSA. Recently, Zhu et al. (2011) derived the absorption
of biomass burning aerosols and Wells et al. (2012) estimated
the SSA of dust over North Africa from MODIS applying the
CSA method. The CSA is also of indirect relevance for the
Earth’s radiation budget at TOA, because it defines the surface albedo where a change in AOD has almost no influence
on the TOA reflectance and the aerosol forcing changes sign.
For example, increasing AOD over bright surfaces is usually
darkening and increasing AOD over dark surfaces is brightening the Earth from space. The darkening leads to a positive
aerosol forcing and warming, while the brightening leads to
a negative aerosol forcing and hence cooling (Seinfeld and
Pandis, 1998; Kaufman et al., 2002; Satheesh, 2002).
The objective of this study is to describe and analyse the
CSA and the related AOD retrieval sensitivity as a function
of aerosol properties under several observational conditions.
Furthermore, our study aims at contributing to a better understanding of AOD retrieval sensitivities to surface albedo
and related uncertainties. We base our theoretical study on
the Lambertian surface approximation in order to avoid inherent assumptions on specific surface types with related
bidirectional reflectance distribution function (BRDF) models. Nevertheless, the presented results are directly applicable to realistic surfaces as long as the corresponding surface
reflectance factor (e.g. hemispherical-directional reflectance
factor) is known for the solar and observational geometry.
the total spectral reflectance at TOA and wavelength λ:
RλTOA = RλATM + RλSFC .
(1)
The atmospheric intrinsic reflectance is given by the sum of
single- and multiple-scattering (MS):
ωλ Pλ (2)
−τλ [ µ1 + µ1 ]
ATM
0
1 − e
+ RλMS , (2)
Rλ
=
4 (µ0 + µ)
where
ωλ =
σλsca
σλext
(3)
is the SSA with the scattering (σλsca ) and extinction (σλext )
efficiency, τλ is the total optical depth composed of AOD
ray
(τλaer ) and Rayleigh optical depth (τλ ).
ray
ray
P aer (2) τλaer + Pλ (2) τλ
Pλ (2) = λ
τλ
(4)
is the scattering phase function (cf. Fig. 1b) for solar radiation as function of forward (+) or backward (−) scattering
angle:
q
2 = arccos ±µ0 µ + cos (φ0 − φ) 1 − µ20 1 − µ2 , (5)
with µ0 = cos θ0 and µ = cos θ, where θ is the viewing (VZA)
and θ0 the solar zenith angle (SZA), and with the solar and
viewing azimuth angle (VAA) φ0 and φ, respectively. We assume isotropically reflected light from a homogeneous surface according to Lambert’s law (Ångström, 1925; Chandrasekhar, 1960; Sobolev, 1972):
RλSFC =
aλ
Tλ ,
1 − aλ sλ
↓
↑
↓
− λ
(6)
where Tλ = Tλ Tλ is the total down- and upwelling transmit2
2.1
Method and data
Radiative transfer calculation
Remote sensing data are complex in nature and influenced
by many and often unknown parameters. We base our analysis of the CSA therefore on radiative transfer (RT) calculations to simulate different atmospheric and surface conditions for various satellite observation geometries. The RT
equation can be solved approximately by e.g. the method of
successive orders of scattering. We use here a vector version
of the Second Simulation of a Satellite Signal in the Solar
Spectrum (6S) RT model (Vermote et al., 1997; Kotchenova
et al., 2006, 2008).
The RT model calculates the atmospheric coupled
molecular-aerosol (ATM) and surface (SFC) contribution to
Atmos. Meas. Tech., 5, 1653–1665, 2012
τ
dfs↓
↑
τλ
dfs↑
tance with Tλ = e µ0 +tλ and Tλ = e− µ +tλ , where tλdfs
denotes the diffuse transmittance (Note: we neglect gaseous
absorptions for this study) and where aλ is the surface albedo
and sλ is the spherical albedo to account for multiple surface
and atmosphere scattering interactions.
2.2
Synthetic data
A synthetic dataset of TOA reflectances was computed with
various single-scattering albedo, illumination and observation geometries, wavelengths and AOD values. An overview
of the different parameters and their discretisation is given in
Table 1. Besides geometrical parameters (φ, θ, φ0 , θ0 ), surface albedo values from zero to unity are integrated to represent all possible surface types and clouds. In addition, simulations are performed at the wavelength 412 nm, 550 nm, and
865 nm to investigate the spectral dependence of the CSA.
The AOD ranges from zero to unity which is representative
www.atmos-meas-tech.net/5/1653/2012/
0.1
Continental
Maritime
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
3
Urban
(a) Separated Rayleigh and aerosol phase functions
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
1655Desert
Table 2: Micro-physical and optical properties of the aerosol
Biomass
models
at 550 nm. g and α denote the asymmetry Stratospheric
paramray+mar
continental
maritime
urban
desert
biomassb.
stratosph.
ray+strato
ray+conti
ray+urb
ray+des
ray+bio
0
30
60
90
120
scattering angle, degrees
150
180
total phase function (550 nm)
total phase function (550 nm)
Rayleigh and aerosol phase function (550 nm)
eter and Ångström exponent between 412 nm and 865 nm,
respectively. The continental, urban and maritime aerosol
10.0
models are composed of a mixture of basic aerosol proper10.0
ties (water-soluble, soot, dust, and oceanic) from (d’Almeida
160
that less
et al., 1991). The background desert aerosol
model
wasthan 1
Reid
(2010) pre
adopted from d’Almeida et al. (1991), the biomass burnments
for other
Rayleigh
ing model from Dubovik et al. (2002) and the stratospheric
1.0
1.0
Micro-physic
model from Russell et al. (1996).
els used in the R
165
tinental, urban,
ω412nm ω550nm ω865nm
g fromαspecific m
0.1
0.1
soot, dust, and o
0
30
60
90
120
150
180
0
30
60
90
150
180
Continental
0.901 120 0.893
0.857
0.619 The
1.327
backgroun
scattering angle, degrees
scattering angle, degrees
Maritime
0.989
0.989
0.987
0.638 d’Almeida
1.323
et a
Urban
0.696
0.689
0.630
0.515 1.350
170
model from R
(a) Separated Rayleigh and aerosol phase functions
(b) Total phase functions
Desert(b) Total phase
0.924
0.966
0.992
0.665 1.008
(a) Separated Rayleigh and aerosol phase functions.
functions.
ing aerosol mo
Biomass
0.943
0.932
0.896
0.623 2.004
Fig. 1:ofRayleigh,
aerosol
and
total phase
functions
P
asnm, with
550nm
used
aerosol m
and
(5)
at
550
Fig. 1. Rayleigh, aerosol
and
total
phase
functions
P
as
function
scattering
angle
2
according
to
Eqs.
(4)
ray+mar
Stratospheric
1.000
1.000
1.000
0.808
0.302
nm ray+strato
ray+conti
ray+urb
ray+des 550
ray+bio
ray
aer
function
ofofscattering
angle
Θasaccording
toinEqs.
(4)2 and
(5)
atFig. 8. absorbing (e.g.
=
0.098.
The
vertical
grey
lines
indicate
the
subset
scattering
angles
represented
Figs.
τ550
=
0.2
and
τ
to
6
and
550 nm
nm
ray
aer
550 nm, with τ550nm
= 0.2 and τ550nm
= 0.098. The vertical
completely non
gray lines indicate the subset of scattering angles as repre- 175 ω550nm = 1.0).
10.0
sented Table
in Figs.
2 to 6 and Fig.and
8.
longer wavelen
Table 1. Parameters and their discretisation (in brackets) of the sim2.that
Micro-physical
the aerosol
160
less than 1 % ofoptical
AODproperties
(550 nm)ofexceed
0.8. modZhang and
in this study. T
ulated conditions.
els at 550 nm. g and α denote the asymmetry parameter and
Reid (2010) presented similar results from satellite measurewell as the cor
Ångström exponent between 412 nm and 865 nm, respectively. The
ments for other regions in the world.
continental, urban and maritime aerosol models are composedFig.
of 1 since Pλ
Viewing azimuth
0◦ , 90◦ , 180◦
1.0 angle, φ
Table 1: Parameters
and their discretisation
(in brackets)
of aerosol modoptical(water-soluble,
properties
of the
a mixture Micro-physical
of basic aerosol and
properties
soot,
Viewing zenith angle, θ
0◦ , 30◦ , 60◦
180 dust,
reflectance
(RλA
the simulated els
conditions.
the RT calculations
areThe
given
in Table desert
2. The conet al. (1991).
background
and oceanic)used
fromind’Almeida
Solar azimuth angle, φ0
180◦
165
tinental,
urban,
and from
maritime
aerosoletmodels
are composed
aerosol
model was
adopted
d’Almeida
al. (1991),
the Critical s
Solar zenith angle, θ0
0◦ , 15◦ , 30◦ , 45◦ , 60◦
2.3
specific
of
basic
components
(water-soluble,
biomassfrom
burning
modelmixtures
from
Dubovik
et
al.
(2002)
and
the
stratoSurface albedo, aλ
0.0(0.1)1.0
◦
◦
Viewing
azimuth
φ
0◦ , et
90al.
, 180
soot, angle,
dust,
oceanic)
described
by d’Almeida et al.
(1991).
Russell
spheric
model
from and
Wavelength, λ0.1
412 nm, 550 nm, 865 nm
◦
◦ (1996).
◦
The
relationsh
Viewing
zenith
angle,
θ
0
,
30
,
60
30
60
90
120
150
AOD, τ550 nm 0
0.0,scattering
0.05, angle,
0.1(0.1)0.5,
0.75,
1.0 180
The background desert
aerosol model was adopted
degrees
◦
(Eq.from
1) as funct
Solar azimuth angle, φ0
180
Sensor-, Target level
TOA, Sea level
d’Almeida et al. (1991),
the ◦stratospheric
aerosol
ω550
g volcanic
α model
◦ nm
with diff
Solar zenith angle, θ0 ω412 nm0◦ , 15
, 30◦ , 45ω
,865
60◦nm
170
model
from
Russell
et
al.
(1996)
and
the
biomass
burn- TOA
(b) Total phase functions
Surface
albedo, aλ
In general,
Continental
0.9010.0(0.1)1.0
0.893
0.857
0.619 1851.327
ing
model
from
Dubovik
et al.0.638
(2002).1.323
The
Wavelength,
λ aerosol0.989
412 nm,
550
nm, 0.987
865 nm
Maritime
0.989
forherein
darker surfa
Fig. 1: Rayleigh, aerosol and total phase functions P550nm
as
used
aerosol
models
span
a
large
range
of
SSA
from
highlysurface
AOD, Urban
τ550nm
0.1(0.1)0.5,
1.0
0.6960.0, 0.05,
0.689
0.6300.75,0.515
1.350
brighter
of a majority
of aerosol
loadings,
of extreme
aerosol
function
of scattering
angleexcept
Θ according
to Eqs.
(4) andSensor-,
(5) atDesert
absorbing
(e.g.TOA,
urban
type with
ω550nm
=nates
0.69)over
to aero
Target
level 0.924
Seaaerosol
level 0.992
0.966
0.665
1.008
aer dust outbreaksray
events such
dense
or volcanic
550as
nm,
withdesert
τ550nm
= 0.2 and τ550nm
= 0.098.smoke
The verticalBiomass
completely0.943
non-absorbing
aerosol
type
with
0.932 (stratospheric
0.896
0.623
2.004
illuminated fro
plumes close
the indicate
source. For
et al.angles
(2010)
gray to
lines
the example,
subset of Riffler
scattering
as repre-Stratospheric
1.000 Note
1.000
0.808 decreases
0.302
175
ω550nm = 1.0).
that the1.000
SSA usually
190
occursfor
where b
found, from
Aerosol
Robotic
Network
sented
in Figs.
2 to 6 and
Fig. 8.(AERONET, Holben
longer wavelength, except for the desert aerosol type used
et al., 1998) sun photometer measurements in Europe, that
in this study. The aerosol and Rayleigh phase functions, as
less than 1 % of AOD (550 nm) exceeds 0.8. Zhang and Reid
wellaerosol
as the corresponding
total phase
functions
are as
given in
study. The
and Rayleigh phase
functions,
as well
(2010) presented similar results from satellite measurements
Fig.
1
since
P
has
a
direct
influence
on
atmospheric
intrinsic
λ
the
corresponding
total
phase
functions,
are
given
in
Fig.
1
Table 1: Parameters and their discretisation (in brackets) of
ATM
for other regions in the world.
180
reflectance
(R
,
cf.
Eq.
2).
λ
since
P
has
a
direct
influence
on
atmospheric
intrinsic
λ
the simulated conditions.
Micro-physical and optical properties of the aerosol modreflectance (RλATM , cf. Eq. 2).
els used in the RT calculations are given in Table 2. The con2.3 Critical surface albedo
◦
tinental, urban,
andazimuth
maritime
aerosol
are◦ composed
2.3 Critical surface albedo
Viewing
angle,
φ 0models
, 90◦ , 180
◦
from specific
mixtures
ofangle,
basicθcomponents
(water-soluble,
The relationship between the modelled TOA reflectance
Viewing
zenith
0◦ , 30◦ , 60
◦
(Eq. 1) as function
surface
albedo for
a continental
soot, dust, and
oceanic)
described
by
d’Almeida
et
al.
(1991).
The
relationship
betweenof the
modelled
TOA
reflectanceaerosol
Solar azimuth angle, φ0
180
◦
◦
◦
with of
different
values
shown in Figs.
2 and 3.
Solar zenith
angle,
θ0 model
0◦ , 15
, 30adopted
, 45◦ , 60from
The background
desert
aerosol
was
(Eq. 1) model
as function
surfaceAOD
albedo
for aiscontinental
aerosol
Surface
albedo, athe
0.0(0.1)1.0
185
In general,
TOA
reflectance
λ stratospheric
d’Almeida et
al. (1991),
volcanic aerosol
2 and 3. AOD
model
with
different
AOD
values isincreases
shown inwith
Figs.increasing
412 nm,
nm, 865burnnm
for darker
surfaces and
decreases
with
increasing
AOD for
model fromWavelength,
Russell etλ al. (1996) and
the 550
biomass
In general,
TOA reflectance
increases
with
increasing
AOD
0.05, 0.1(0.1)0.5,
0.75, 1.0 for darker
brighter
surfaces.
This is because
aerosol absorption
ing aerosol AOD,
modelτ550nm
from Dubovik et 0.0,
al. (2002).
The herein
surfaces
and decreases
with increasing
AOD for domiSensor-, Target level
TOA, Sea level
over aerosol
if the atmosphere
sufficiently
used aerosol models span a large range of SSA from highly
brighternates
surfaces.
This is scattering
because aerosol
absorptionisdomiilluminated
from below
andatmosphere
vice versa. isAn
interesting case
absorbing (e.g. urban aerosol type with ω550 nm = 0.69) to
nates over
aerosol scattering
if the
sufficiently
190
occurs
where
bothand
processes
compensate
each other
completely non-absorbing (stratospheric aerosol type with
illuminated
from
below
vice versa.
An interesting
caseand the
ω550 nm = 1.0). Note that the SSA usually decreases for longer
occurs where both processes compensate each other, and the
wavelength, except for the desert aerosol type used in this
TOA reflectance remains almost constant for changing AOD.
www.atmos-meas-tech.net/5/1653/2012/
Atmos. Meas. Tech., 5, 1653–1665, 2012
TOA
reflectance
TOA TOA
reflectance
reflectance
TOA
reflectance
TOA TOA
reflectance
reflectance
TOA reflectance
TOA
reflectance
TOA TOA
reflectance
reflectance
TOA reflectance
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
C. Seidel
and Critical
C. Popp:surface
Criticalalbedo
surfaceand
albedo
AOD retrieval
1656
F. C. SeidelF.and
C. Popp:
AODand
retrieval
F. C. Seidel
and
C.
Popp:
Critical
surface
albedo
and
AOD retrieval
Finall
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
1.0
where
Finall
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
1.0
where
Finall
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
∂RλTO
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
1.0
0.8
where
240
1.0
∂RλTO
0.8
240
∂RλTO
0.8
0.6
240
The
0.8
0.6
illumi
The
0.6
AOD.
0.4
illumi
The
0.6
exami
AOD.
0.4
illumi
245
mode
exam
AOD.
0.4
0.2
0.4
values
245
mode
exam
0.2
for
ae
value
245
mode
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.2
teristi
for
ae
value
surface albedo
0.0
0.0
0.2
0.4
0.6
0.8
1.0
for
w
teristi
ae
surface albedo
0.0
0.0
0.2
0.4
0.6
0.8
1.0
250
the
di
for
w
teristi
(a)
Maritime
aerosol
model
at
550
nm
0.0
surface
albedo
0.0
0.2
0.4
0.6
0.8
1.0
surface albedo
ythe
= 0w
250
di
for
(a) Maritime aerosol model at 550 nm
cate
n
ythe
= 0di
250
(a)
Maritime
aerosol
model
at
550
nm
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
(a) Continental aerosol model at 412 nm
in
cate
1.0
y =Fig
0n
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
over
in
cateFig
no
1.0
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
255
or
pol
over
o
in
Fig
1.0
0.8
high
so
255
or
po
over
0.8
mariti
high
s
255
or
po
0.8
0.6
in
Fig
mariti
high s
0.6
and
0
in
Fig
mariti
0.6
0.4
260
with
and
0
in Fig
0.4
tering
260
with
and 0
0.4
0.2
aeroso
tering
260
with
0.2
(Fig.
aeroso
tering
0.2
AOD
(Fig.
0.0
aeroso
0.0
0.2
0.4
0.6
0.8
1.0
surface albedo
AOD
(Fig.
0.0
0.0
0.2
0.4
0.6
0.8
1.0
surface albedo
AOD
0.0
0.0
0.4
0.6
0.8
1.0
(b) 0.2
Urban aerosol
265
3 R
surfacemodel
albedo at 550 nm
(b) Urban aerosol model at 550 nm
265
3 R
(b) Continental aerosol model at 550 nm
3.1
(b)
Urban
aerosol
model
at
550
nm
265
3 R
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
1.0
3.1
1.0
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
3.1.1
1.0
3.1
AOD=0.00
AOD=0.20
AOD=0.40
AOD=0.75
AOD=1.00
3.1.1
1.0
0.8
0.8
3.1.1
0.8
The s
0.8
0.6
270
reflec
The s
0.6
0.6
faces
270
reflec
The s
0.6
TOA
0.4
R
faces
270
reflec
λ
0.4
TOA
0.4
below
R
faces
λ
0.4
0.2
ferent
below
RλTOA
0.2
0.2
275
on
the
ferent
below
depen
275
on
the
0.2
ferent
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
surface albedo
depen
Eac
275
on
the
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
surface albedo
surface albedo
two
R
Eac
depen
0.0
0.0
0.2
0.4
0.6
0.8
1.0
(c) Continental aerosol model at 865 nm
(c) Desert
aerosol
surfacemodel
albedo at 550 nm
the
inR
twoEac
(c) Desert aerosol model at 550 nm
280
fore
oR
the
two in
Fig. 2. TOA reflectance (Eq. 1) as function of surface albedo and
Fig.
Fig.3
should
beason
same
page
as Fig.2
Fig. 3:
3. TOA reflectance
(Eq.
1)
function
of
surface
albedoTOA
and 280 CSA
(c)
Desert
aerosol
model
at
550
nm
fore
o
the in
different AOD values for a continental aerosol type at 412 nm,
different
values
atfunction
550 nm
aerosol
Solar
reflectance
(Eq.
1) as
ofdifferent
surface
albedo
and differFig.
3: AOD
Fig.3
should
be for
on
same page
as types.
Fig.2
TOA
550 nm, and 865 nm. Solar zenith angle is 0◦ , viewing zenith an(ω
CSA
280
fore
o
550n
◦
◦
zenith
isFig.3
0 1)
, viewing
angle
30 aerosol
and
scattering
angle
ent
AOD
values
at
550
nmzenith
for
different
Solar
reflectance
(Eq.
as
function
of
surface
albedo
and differFig.
3: angle
should
be on
same
page
astypes.
Fig.2
TOA
gle 30◦ and scattering angle 150◦ .
absorb
(ω
◦
CSA
550
150AOD
. angle
◦
◦
zenith
is 01)
, 550
viewing
zenith
angleaerosol
30
and
scattering
ent
values
at
nm for
different
types.
Solar
reflectance
(Eq.
as
function
of surface
albedo
and
differCSA
absor
(ω550
◦
◦
angle
150
. is 0at, 550
zenith
angle
viewing
zenith
angleaerosol
30◦ and
scattering
ent
AOD
values
nm for
different
types.
Solar 285 along
CSA
absor
◦
angle 150
. is 0◦ , viewing zenith angle 30◦ and scattering 285 along
zenith
angle
CSA
angle 150◦ .
Atmos. Meas. Tech., 5, 1653–1665, 2012
www.atmos-meas-tech.net/5/1653/2012/ 285 along
6
F. C. Seidel
6
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
1657 F. C. Seidel
derivative
TOAwith
reflectance
with
respect
derivative
ofreflectance
TOAofreflectance
with respect
to AODto AOD
derivative
of TOA
respect
to
AOD
Calculation of the critical surface albedo
We search for the CSA for which two different AOD (τλaer )
values lead to the same TOA reflectance, such that
RλTOA
τλaer1 , aλ = CSA
RλTOA
τλaer2 , aλ = CSA ≡ 0.
−
(7)
The CSA retrieval is simplified by fitting a fifth-order polynomial to a TOA reflectance (Eq. 1, Figs. 2 and 3) providing
a continuous and differentiable function:
RλTOA τλaer , aλ
≈
5
X
i
ci τλaer ,
(8)
i=0
where ci denotes the polynomial coefficients of order i. The
average reflectance fitting error is less than 0.0002 absolute
reflectance values. The sensitivity of the TOA reflectance to
AOD is derived by its partial derivative with respect to AOD:
www.atmos-meas-tech.net/5/1653/2012/
continental
0.10
maritime
urban
desert
biomassb.
stratosph.
continental
0.10
maritime
urban
desert
biomassb.
stratosph.
continental
0.05
0.10
maritime
urban
desert
biomassb.
stratosph.
−0.10
−0.05
0.0
0.2
0.4
0.6
surface albedo
0.8
1.0
−0.10
0.0
0.2
0.4
0.6
surface albedo
0.8
1.0
0.8
1.0
biomassb.
stratosph.
0.05
0.00
0.05
0.00
−0.05
0.00
−0.05
(a) 0.4
AOD = 0.05
0.6
−0.10
0.0
0.2
continental
0.10
(a) AOD = 0.05
maritime
urban = 0.05
desert
(a)
(a)AOD
AOD = 0.05
Fig.
TO
R550
Fig.
acco
TO
R
550
Fig.
zeni
acco
TO
R
550
angl
zeni
acco
angl
zeni
angl
surface albedo
derivative
TOAwith
reflectance
with
respect
derivative
ofreflectance
TOAofreflectance
with respect
to AODto AOD
derivative
of TOA
respect
to
AOD
2.4
F. C. Seidel
derivative
TOAwith
reflectance
respect
derivative
ofreflectance
TOAofreflectance
with respect
to AODto AOD
derivative
of TOA
respect
towith
AOD
6
In other words, this particular surface albedo is “critical” for
AOD retrievals, because there is almost no sensitivity of TOA
reflectance to AOD. For example, the TOA reflectance in
Fig. 2a becomes almost independent of AOD at roughly 0.18
surface albedo, which we define as the CSA.
Previous studies employed the “critical reflectance” as a
method for the retrieval of SSA (e.g. Kaufman, 1987; de
Almeida Castanho et al., 2008; Zhu et al., 2011; Wells et al.,
2012). This method assumes a linear relationship between
TOA reflectance and surface albedo, as well as a singular
CSA at all AOD values. However, Figs. 2 and 3 show that
the TOA reflectance has a non-linear relationship to the surface albedo especially at shorter wavelengths and larger AOD
values (cf. Fig. 2a). Figure 2b zooms into the area of CSA
to visualise that there is no singular CSA, because the TOA
reflectance curves do not cross at exactly the same surface
albedo. In theory, 0.5n (n − 1) CSA values exist where n denotes the number of TOA reflectance curves. The CSA is
therefore also a function of AOD if we account each crossing as a separate CSA value. In reality, the CSA represents a
range of surface albedo values given by an ensemble of TOA
reflectance crossings. Nevertheless, we use the strict definition of the CSA in this theoretical study in order to enable us
to investigate its AOD dependence. Figure 2a to c show that
CSA slightly decreases with wavelength for the continental
aerosol model due to decreasing SSA with wavelength.
Additional TOA reflectance calculations are provided in
Fig. 3 at 550 nm for a maritime (Fig. 3a), urban (Fig. 3b),
and desert (Fig. 3c) aerosol model. Absorbing aerosol types
have a much lower CSA, e.g. the urban model with a very
low SSA (550 nm) of 0.69 has the CSA at 0.07, while the
desert model with an SSA (550 nm) of 0.97 has the CSA at
roughly 0.32.
continental
0.10
maritime
urban
desert
biomassb.
stratosph.
continental
0.10
0.05
maritime
urban
desert
biomassb.
stratosph.
0.05
0.05
0.00
0.00
0.00
−0.05
290
−0.05
290
−0.05
−0.10
0.0
0.2
0.4
0.6
surface albedo
0.8
1.0
−0.10
0.0
0.2
0.4
0.6
surface albedo
0.8
1.0
−0.10
0.0
0.2
0.8
1.0
biomassb.
stratosph.
(b) 0.4AOD = 0.2
0.6
surface albedo
(b)
(b)AOD
AOD= =0.2
0.2
continental
0.10
maritime
desert
(b) urban
AOD =
0.2
continental
0.10
maritime
urban
desert
biomassb.
stratosph.
continental
0.10
0.05
maritime
urban
desert
biomassb.
stratosph.
290
295
3.1.2
295
3.1.2
295
0.05
0.05
0.00
0.00
300
0.00
−0.05
300
−0.05
300
−0.05
−0.10
0.0
0.2
0.4
0.6
surface albedo
0.8
1.0
−0.10
0.0
0.2
0.4
(c) AOD
1.00.6
surface=albedo
0.8
1.0
305
305
(c) 0.4
AOD = 1.0
0.6
0.8
1.0
Fig. 4. Derivative of TOA reflectance
with respect to AOD as a func- 305
surface albedo
(c)
AOD
=
1.0
tion of
albedoof
forTOA
different
aerosol models
550 nm.to AOD
Fig.
4:surface
Derivative
reflectance
with atrespect
(c)
AOD
=
1.0
as a function of surface albedo for different aerosol models
−0.10
0.0
The
thus
The
toge
thus
The
diffe
toge
thus
rang
diffe
toge
and
rang
diffe
for t
and
rang
mea
for
andt
mea
for t
mea
3.1.2
0.2
Fig. 4: Derivative of TOA reflectance with respect to AOD 310
at
550
nm. of surface albedo for different aerosol models
as
a function
Fig.
4: Derivative
of TOA reflectance with respect to AOD 310
at
nm. of surface albedo for different aerosol models
as 550
a function
310
at 550 nm.
Atmos. Meas. Tech., 5, 1653–1665, 2012
The
cien
The
man
cien
The
SSA
man
cien
aero
SSA
man
lar a
aero
SSA
terin
lar
a
aero
an i
terin
lar
a
mosin
an
terin
sorb
mos
an
at 4in
sorb
mos
aero
at
41
sorb
cord
aero
at
4
resp
cord
aero
type
resp
cord
fore
type
resp
Zhu
fore
type
Zhu
fore
Zhu
C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
290
295
300
305
1658
continental
1.0
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
maritime
urban
desert
biomassb.
stratosph.
3
Results
3.1
TOA reflectance
0.8
3.1.1
Sensitivity analysis
Sensitivity of top-of-atmosphere reflectance to
critical surface albedo
0.6
The surface contribution RλSFC (Eq. 6) dominates the TOA reflectance (Eq. 1), except in the case of very dark surfaces and
short wavelengths (λ / 500 nm) and therefore is RλTOA ∼ aλ .
0.4
Figure 5 shows that the CSA is just slightly below the TOA
reflectance because RλATM < RλSFC . The different AOD and
0.2
aerosol models (see Table 2) have an effect on the absolute
value of RλTOA but not much on the relative dependence between RλTOA and the corresponding CSA.
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Each point in Fig. 5 corresponds to an intersection of
critical surface albedo
two R TOA curves in Figs. 2b and 3. The distribution of
TOA (τ aer
the intersections depends on aerosol absorption and thereFig. 5. TOA reflectance R550
nm 550 nm ∈ [0.0, 0.05, 0.1 (0.1) 0.5,
fore on the aerosol model. Lower SSA corresponds to lower
0.75, 1.0]) according to Eq. (1) as a function of CSA at 550 nm.
Fig. Solar zenith5:angle is 0◦ , viewing zenithTOA
reflectance
angle 30◦ and scattering
CSA and vice versa. For example, the urban aerosol model
TOA
aer◦
R550nm
(τ150
angle
. ∈ [0.0, 0.05, 0.1 (0.1) 0.5, 0.75, 1.0])
(ω550 nm = 0.69) has a CSA of about 0.05, while the non550nm
absorbing maritime and stratospheric aerosol types have a
according to Eq. (1) as a function of CSA at 550 nm. Solar
CSA higher than 0.7. The positions of the different points
zenith angle is 0◦ , viewing zenith angle 30◦ and scattering
along the bisecting line depend on AOD (see also Sect. 2.3).
angle 150◦ .
The
sensitivity to AOD is weaker for absorbing aerosols,
5
X
aer i−1
∂RλTOA τλaer , aλ
and
thus
the CSA of the urban and continental model are
≈
ici τλ
.
(9)
∂ τλaer
i=1
close together for all analysed AOD. Generally, the CSA of
the different aerosol models is well separated for the given
Finally, the CSA is derived by finding the surface albedo:
range of AOD values, except for the non-absorbing maritime
weaker for absorbing aerosols and
The sensitivity
to
AOD
is
TOA
aer
and stratospheric aerosol models. This finding is important
∂Rλ
τλ , aλ = CSA
:=
0.
(10)
for the determination of aerosol types from TOA reflectance
thus the CSA∂ of
τλaerthe urban and continental model are close
measurements.
together for all analysed AOD. Generally, the CSA of the
retrievedmodels
CSA is aare
function
the observation
and given
differentTheaerosol
well ofseparated
for the
3.1.2 Sensitivity of critical surface albedo to
illumination geometry, wavelength, aerosol properties and
rangeAOD.
of AOD
values,
except
for
the
non-absorbing
maritime
single-scattering albedo
The sensitivities of the CSA to these parameters are
and stratospheric
aerosol
models.
This
important
examined in Sect.
3. Results
from Eq.
(9) finding
using six is
aerosol
The CSA depends strongly on the aerosol absorption effimodels
at 550 nm areofplotted
in Fig.
4 forfrom
three different
valfor the
determination
aerosol
types
TOA reflectance
ciency or SSA (ωλaer ) (cf. Eq. 3 as well as Fraser and Kaufues
of
AOD.
In
general,
this
relationship
is
almost
linear
for
measurements.
man, 1985; Kaufman, 1987). The relation between CSA and
aerosol types with moderate to strong absorption characterSSA is shown in Fig. 6. Generally, lower SSA (stronger
istics (e.g. urban or continental) and becomes non-linear for
aerosol absorption) leads to lower CSA. However, the soweakly or non-absorbing aerosol models. The CSA for the
lar and observational geometry with the corresponding scatmodels can be found at the interception with y = 0
3.1.2 different
Sensitivity
of critical surface albedo to singletering angle, and therewith the aerosol phase function, has
(dotted line). Low or non-absorbing aerosol types indicate no
an influence on CSA (as shown by Fig. 6). The CSA is
scattering
albedo
CSA
for τλaer / 0.5
(e.g. maritime and stratospheric in Fig. 4a
almost spectrally invariant for absorbing aerosols. Low aband b). Smirnov et al. (2011) found that AOD over oceans
sorbing aerosols with ωλaer > 0.9 have generally higher CSA
in the absence of continental outflow with dust or pollution
at 412 nm as compared to 865 nm. In contrast, the desert
rarely exceeds 0.2, which favours the relatively high sensitivaerosol model CSA is lower at 412 nm than 865 nm. AccordThe CSA
depends
strongly
on the
absorption
ity of aerosol
retrievals
over oceans
foraerosol
typical maritime
con- effiing to these results, the CSA could be parametrised with reaer
ciencyditions.
or SSA
(ωλ ) (cf.
Eq. 3aerosol
as well
as Fraser
and
Interestingly,
the desert
model
in Fig. 4a
re- Kaufspect to SSA and used for the determination of aerosol types
two
different CSAs
(approximately
at 0.3between
and 0.9). Furman, veals
1985;
Kaufman,
1987).
The relation
CSA and
from TOA reflectance measurements as mentioned before
it is noteworthy
CSA changes
with AOD,
SSA ther,
is shown
in Fig.that
6. theGenerally,
lower
SSAespe(stronger
and demonstrated in de Almeida Castanho et al. (2008), Zhu
cially and most pronounced for the scattering aerosol types.
et al. (2011), and Wells et al. (2012).
aerosol
absorption)
leads
to
lower
CSA.
However,
the
soFor example, the CSA for the desert aerosol (ω550 nm = 0.97)
lar and
observational
geometry
the corresponding
increases
from 0.3 with
AOD = with
0.05 (Fig.
4a) to 0.35 with scatteringAOD
angle
function, has
= 0.2and
(Fig.therewith
4b) and 0.4 the
withaerosol
AOD = 1.0phase
(Fig. 4c).
an influence on CSA as shown by Fig. 6. The CSA is almost Atmos.
spectrally
for absorbing
Meas.invariant
Tech., 5, 1653–1665,
2012 aerosols. Low abaer
sorbing aerosols with ωλ > 0.9 have generally higher CSA
at 412 nm as compared to 865 nm. In contrast, the desert
www.atmos-meas-tech.net/5/1653/2012/
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
7
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
scattering angle = 90.00 degrees
scattering angle = 104.4 degrees
1.0
1.0
412 nm
550 nm
continental
maritime
urban
desert
biomassburning
stratospheric
865 nm
0.8
critical surface albedo
critical surface albedo
0.8
0.6
0.4
0.2
0.0
0.6
0.4
0.7
0.8
single scattering albedo
0.9
0.0
0.6
1.0
412 nm
550 nm
continental
maritime
urban
desert
biomassburning
stratospheric
865 nm
0.8
critical surface albedo
critical surface albedo
0.9
1.0
scattering angle = 120.0 degrees
0.4
0.2
412 nm
550 nm
continental
maritime
urban
desert
biomassburning
stratospheric
865 nm
0.6
0.4
0.2
0.7
0.8
single scattering albedo
0.9
0.0
0.6
1.0
(c) φ = 0◦ , θ0 = 0◦ , θ = 60◦ , Θ = 120◦
0.7
0.8
single scattering albedo
0.9
1.0
(d) φ = 0◦ , θ0 = 30◦ , θ = 30◦ , Θ = 120◦
scattering angle = 150.0 degrees
scattering angle = 179.9 degrees
1.0
1.0
412 nm
550 nm
continental
maritime
urban
desert
biomassburning
stratospheric
865 nm
0.8
critical surface albedo
critical surface albedo
0.8
single scattering albedo
1.0
0.6
0.6
0.4
0.2
0.0
0.6
0.7
(b) φ = 90◦ , θ0 = 60◦ , θ = 60◦ , Θ = 104◦
scattering angle = 120.0 degrees
0.8
865 nm
0.2
1.0
0.0
0.6
412 nm
550 nm
continental
maritime
urban
desert
biomassburning
stratospheric
0.6
(a) φ = 0◦ , θ0 = 30◦ , θ = 60◦ , Θ = 90◦
0.8
1659
412 nm
550 nm
continental
maritime
urban
desert
biomassburning
stratospheric
865 nm
0.6
0.4
0.2
0.7
0.8
single scattering albedo
0.9
(e) φ = 0◦ , θ0 = 0◦ , θ = 30◦ , Θ = 150◦
1.0
0.0
0.6
0.7
0.8
single scattering albedo
0.9
1.0
(f) φ = 180◦ , θ0 = 30◦ , θ = 30◦ , Θ = 179◦
CSAas
as function
function ofofSSA
forfor
AOD
= 0.2=at0.2
412atnm,
550
nm550
and 865
wellnm,
as for
types and
different
combinations
Fig.Fig.
6: 6.CSA
SSA
AOD
412
nm,
nm nm,
andas865
asdifferent
well as aerosol
for different
aerosol
types
and different
of viewing azimuth
angle φ,
solar zenith
angle
zenith
angle
and the corresponding
angle
2.
0 , viewing
combinations
of viewing
azimuth
angle
φ, θsolar
zenith
angle
θ0 ,θviewing
zenith anglescattering
θ and the
corresponding
scattering angle
Θ.
www.atmos-meas-tech.net/5/1653/2012/
Atmos. Meas. Tech., 5, 1653–1665, 2012
320
325
325
330
330
335
335
340
340
345
345
350
350
355
355
360
360
critical critical
surfacesurface
albedoalbedo
320
CSA values are given in Fig. 7 as a function of scattering
SZA
to Eq. (5). to
Some
combinations
have aVZA,
comangle,according
which corresponds
a combination
of VAA,
mon
scattering
angle,
which
leads
to
multiple
results
per
SZA according to Eq. (5). Some combinations have a comscattering
angle angle,
in Fig. which
7. Interestingly,
SSA seems
to have
mon scattering
leads to multiple
results
1660
F.per
C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
an
influence
on
the
separation
of
these
results.
Absorbing
continental
urban
biomassburning
scattering angle in Fig. 7. Interestingly, SSA seems to have
1.0
aerosols
with
ω
<
0.95
show
a
relatively
distinct
relation
bean influence
the separation
ofsurface
these results.
continental
urban
biomassburning
3.1.3 on
Sensitivity
of critical
albedo toAbsorbing
observation
tween
CSA
and
the
scattering
angle
(Fig.
7a). Low
and non1.0
aerosols with and
ω <solar
0.95 geometry
show a relatively distinct
relation
be0.8
absorbing
with ωangle
> 0.95
show
sentween CSAaerosol
and thetypes
scattering
(Fig.
7a).much
Lowmore
and nonsitivity
of aerosol
CSA
different
solar7and
asshow
aviewing
function
of scattering
CSA
valuestotypes
are
given
Fig.
0.8
absorbing
withinω
> 0.95
muchgeometries
more
senand
therefore
different
path
lengths
through
the
atmosphere
0.6
angle,
which
corresponds
to
a
combination
of
VAA, VZA,
sitivity of CSA to different solar- and viewing geometries
(Fig.
7b).
Generally,
Fig.
7
shows
that
CSA
depend
on
the
SZA
according
to
Eq.
(5).
Some
combinations
have
a
comand therefore different path lengths through the atmosphere
0.6
monphase
scattering
angle,
to multiple
results
scattering
function
Fig. 1)leads
as well
asdepend
the SSA.
0.4
(Fig. 7b).
Generally,
Fig.(cf.
7 which
shows
that
CSA
onThe
theper
scattering
angle
in Fig.values
7. Interestingly,
SSAofseems
to have
CSA
has
therefore
smaller
in
the
range
scattering
scattering phase ◦function
(cf. Fig. 1) as well as the SSA. The
0.4
◦ separation of these results. Absorbing
an
the
angles
Θ influence
∈
[110 , on
150
], which
corresponds
tooftypical
obCSA has
therefore
smaller
values
in
the range
scattering
0.2
aerosols
with
ω
<
0.95
show
a
relatively
distinct
relation
beservation
of
◦
◦ many remote sensing instruments.
angles tween
Θ ∈geometries
[110
,
150
],
which
corresponds
to
typical
ob7a).
Low
and nonCSA
scattering
angle also
(Fig.to
0.2
The
minimum
forand
the the
CSA
corresponds
the
minimum
servation
geometries
many
remote
sensing
instruments.
absorbing
aerosoloftypes
with
ω > 0.95
show
much
more
sen0.0
◦
60
80
100
120
140
160
180
in
aerosol phase
(≃ 120 ).also
Backward
scatterThethe
minimum
thefunctions
CSA
corresponds
to the minimum
scattering angle, degrees
sitivity offorCSA
to different
solar- and viewing
geometries
ing
geometries
have
significantly
larger
0.0
◦ CSA. Some aerosol
60
80
100
120
140
160
180
in the and
aerosol
phasedifferent
functions
120 ).through
Backward
scattertherefore
path(≃lengths
the atmosphere
scattering angle, degrees
types
have
no CSA
in
theFig.
forward
scattering
direction
(see
(a) Low SSA (ω < 0.95)
ing geometries
significantly
larger
CSA.
aerosol
Generally,
7 shows
that
CSASome
depends
on the
(Fig. 7b). have
Fig.
scattering
phasein function
(cf. Fig.
1) as well
as the(see
SSA.
types7).have
no CSA
the forward
scattering
direction
(a) Low
(a)
LowSSA
SSA(ω
(ω<<0.95)
0.95)
Fig. 7).The CSA has therefore smaller values in the range of scat3.1.4 tering
Sensitivity
critical
albedo
to aerosoltoopangles of
2∈
[110◦ , surface
150◦ ], which
corresponds
typitical
depth
cal
observation
geometries
of
many
remote
sensing
instru3.1.4 Sensitivity of critical surface albedo to aerosol op-
ments.
The minimum for the CSA corresponds also to the
tical depth
minimum
in the
aerosol
functions
(≃ depend
120◦ ). BackThe findings
above
show
that phase
CSA can
slightly
on
ward
scattering
geometries
have
significantly
larger
CSA.
AOD
and that,above
in fact,
CSA
a small
range
The findings
show
thatoften
CSArepresents
can slightly
depend
on
Somealbedo
aerosolvalues
types have
no
CSA insensitivity
the forwardtoscattering
of
surface
with
minimal
AOD.
AOD and
that,
in
fact,
CSA
often
represents
a
small
range
(see Fig.
Figuredirection
8 illustrates
the 7).
relation between CSA and AOD in
of surface albedo values with minimal sensitivity to AOD.
more
Figures
to 8d show distinct
increases
in
Figuredetails.
8 illustrates
the 8a
relation
AOD in
3.1.4
Sensitivity
of criticalbetween
surface CSA
albedoand
to aerosol
CSA
largeroptical
AOD,
except
aerosol
types with
more for
details.
Figures
8a tofor
8dabsorbing
show distinct
increases
in
depth
ω
≤
0.9
(i.e.
urban
and
continental).
CSA
at
larger
550nm
CSA for larger AOD, except for absorbing aerosol types scatwith
tering
angles
(Fig.
8e
to 8f)
are
found
to depend
less
on
AOD.
The
findings
above
show
that CSA
can
slightly
depend
ω
≤ 0.9
(i.e. urban
and
continental).
CSA
at
larger
scat-on
550nm
AOD and
that,
CSA
often
a small
range
tering angles
(Fig.
8e in
to fact,
8f) are
found
to represents
depend less
on AOD.
of surface albedo
values with
minimal
sensitivity to AOD.
3.2 Implications
to aerosol
remote
sensing
Figure 8 illustrates the relation between CSA and AOD in
3.2 Implications to aerosol remote sensing
more of
details.
Figurehave
8a toseveral
d showsignificant
distinct increases
in CSA
The results
this study
implications
for
larger
AOD,
except
for
absorbing
aerosol
types
with
for
remote
sensing
ofhave
aerosols
from
satellite observations.
Thethe
results
of this
study
several
significant
implications
ω550 nm ≤ 0.9 (i.e. urban and continental). CSAs at larger
for the remote sensing
aerosols
angles of
8e to from
f) are satellite
found toobservations.
depend less on
3.2.1 scattering
Implication
to (Fig.
aerosol
optical
depth
retrieval
AOD.
3.2.1 Implication to aerosol optical depth retrieval
The AOD
error as
function
of surface
albedo for an
3.2 retrieval
Implications
to aaerosol
remote
sensing
underand
overestimation
of
surface
albedo
of
0.01 for
The AOD retrieval error as a function of surface albedo
fordifan
The
results
of
this
study
have
several
significant
implications
ferent
aerosol
types
is
shown
in
Fig.
9.
We
define
the
AOD
under- and overestimation
of surface albedo
of 0.01 for difaer
aer
aer
forerror
the remote
sensing
of aerosols
from
satellite
retrieval
as
τtrue
−
τretrieved
with
τWe
= 0.3 observations.
inthe
this
extrue define
ferent aerosol
types
is
shown
in
Fig.
9.
AOD
aer
ample.
We
extract
τ
from
the
lookup
table
(LUT)
(c.f.
aer
aer
aer
retrieved
retrieval
errorImplication
as τtrue
− τto
with τtrue
= 0.3retrieval
in this exretrieved
3.2.1
aerosol
depth
Sec.
2.2
andextract
Tab. 1)τ aer
by searching
foroptical
the AOD
corresponding
ample.
We
from
the
lookup
table
(LUT)
(c.f.
retrieved
to
the2.2
varying
surface
(ofa function
±0.01)
while
keeping
other
The
AOD
retrieval
error as
of surface
albedo
for an
Sec.
and
Tab.
1) byalbedo
searching
for the AOD
corresponding
model
parameters
constant.
underand
overestimation
of
surface
albedo
of
0.01
for
difto the varying surface albedo (of ±0.01) while keeping other
Seidel
et
al.
(2011),
Sect.
2.3
and
Sect.
2.4
have
shown
that
ferent
aerosol
types
is
shown
in
Fig.
9.
We
define
the
AOD
remodel parameters constant.
aer
aer
aer = at
theSeidel
TOA
reflectance
is
insensitive
to
AOD
the
CSA
and
trieval
error
as
τ
−
τ
with
τ
0.3
in
this
example.
true
et al. (2011),
Sect. retrieved
2.3 and Sect.true
2.4 have shown that
aer
We
extract
τ
from
the
lookup
table
(LUT)
Sect.
that
it
is
therefore
not
possible
to
retrieve
AOD
from(cf.
a single
retrieved
the TOA reflectance is insensitive to AOD
at the
CSA
and2.2
and Table 1) by searching for the AOD corresponding to the
varying surface albedo (of ±0.01) while keeping other model
parameters constant.
Seidel et al. (2011), Sects. 2.3 and 2.4 have shown that
the TOA reflectance is insensitive to AOD at the CSA and
that it is therefore not possible to retrieve AOD from a single
that it is therefore not possible to retrieve AOD from a single
Atmos. Meas. Tech., 5, 1653–1665, 2012
maritimee
1.0
desert
stratospheric
maritimee
1.0
desert
stratospheric
0.8
critical critical
surfacesurface
albedoalbedo
315
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
60
80
60
80
100
120
140
scattering angle, degrees
160
180
100
120
140
scattering angle, degrees
160
180
(b) High
(b)
HighSSA
SSA(ω(ω>>0.95)
0.95)
(b) High SSA (ω > 0.95)
Fig.7:7. CSA
CSA as a function
function ofofscattering
angle
for for
AODAOD
= 0.2 =at0.2
Fig.
scattering
angle
550
nm.
Certain
combinations
of solarofand
observing
geometriesgeat
550
nm.
Certain
combinations
solar
and
observing
Fig.
CSA
a function
ofwhich
scattering
forresults
AOD = 0.2
have7:the
sameasscattering
angle,
leads toangle
multiple
ometries
have
the same
scattering
angle,
which
leads toper
mulat
550
nm.
Certain
combinations
of
solar
and
observing
aerosol model, especially for less absorbing aerosol types. The solidgetiple
results
per
model,
especially
for less
absorbing
ometries
have
theaerosol
same scattering
angle,CSA.
which
leads
to mullines provide
a polynomial
fit to the retrieved
aerosol
types.
The
solid
lines
provide
a
polynomial
fit to the
tiple results per aerosol model, especially for less absorbing
retrievd types.
CSA. The solid lines provide a polynomial fit to the
aerosol
retrievd
optical CSA.
measurement at this surface albedo. This is demonstrated in Fig. 9 with AOD retrieval errors rising towards the
CSA (indicated by the vertical red line). AOD retrieval errors
close the the CSA are exceptionally high and usually exceeding 100 %, although the simulated error of the surface albedo
is small with 0.01.
In general, for surface albedo values smaller than the CSA,
an overestimation of the surface albedo leads to an underestimation of AOD and therefore a positive retrieval error in
our examples. The opposite is the case for surface albedo
values higher than the CSA, where the overestimation of the
surface albedo leads to an overestimation of AOD and thus
a negative retrieval error. The latter is due to the decrease
in TOA reflectance by increasing AOD over bright surfaces.
www.atmos-meas-tech.net/5/1653/2012/
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
9
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
continental
1.0
maritime
urban
desert
biomassb.
stratosph.
continental
1.0
0.6
0.4
0.2
0.0
0.2
0.4
0.6
aerosol optical depth
0.8
stratosph.
maritime
urban
desert
biomassb.
0.0
0.2
0.4
0.6
aerosol optical depth
0.8
1.0
(b) φ = 90°, θ0 = 60°, θ = 60°, Θ = 104°
stratosph.
continental
1.0
maritime
urban
desert
biomassb.
stratosph.
0.8
1.0
0.8
critical surface albedo
critical surface albedo
biomassb.
0.4
0.0
1.0
0.8
0.6
0.4
0.2
0.6
0.4
0.2
0.0
0.2
0.4
0.6
aerosol optical depth
0.8
0.0
1.0
0.0
(c) φ = 0°, θ0 = 0°, θ = 60°, Θ = 120°
continental
1.0
maritime
urban
desert
biomassb.
0.2
0.4
0.6
aerosol optical depth
(d) φ = 0°, θ0 = 30°, θ = 30°, Θ = 120°
stratosph.
continental
1.0
maritime
urban
desert
biomassb.
stratosph.
0.8
1.0
0.8
critical surface albedo
0.8
critical surface albedo
desert
0.2
continental
1.0
0.6
0.4
0.2
0.0
urban
0.6
(a) φ = 0°, θ0 = 30°, θ = 60°, Θ = 90°
0.0
maritime
0.8
critical surface albedo
critical surface albedo
0.8
0.0
1661
0.6
0.4
0.2
0.0
0.2
0.4
0.6
aerosol optical depth
0.8
(e) φ = 0°, θ0 = 0°, θ = 30°, Θ = 150°
1.0
0.0
0.0
0.2
0.4
0.6
aerosol optical depth
(f) φ = 180°, θ0 = 30°, θ = 30°, Θ = 179°
Criticalsurface
surface albedo
albedo asasfunction
of AOD
at 550
different
aerosol types
andtypes
different
of viewing azimuth
φ,
Fig.Fig.
8: 8.
Critical
function
of AOD
at nm
550fornm
for different
aerosol
andcombinations
different combinations
of viewing
solar
zenith
θ
and
viewing
zenith
angles
θ
,
as
well
as
the
corresponding
scattering
angle
2.
0
azimuth φ, solar zenith θ0 and viewing zenith angles θ, as well as the corresponding scattering angle Θ.
www.atmos-meas-tech.net/5/1653/2012/
Atmos. Meas. Tech., 5, 1653–1665, 2012
1662
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
Especially for aerosol models with high and moderate absorption characteristics (Fig. 9a, c, and e), the AOD retrieval
errors over bright surfaces are surprisingly low (<0.05 or
∼15 %). This suggests that bright surfaces, such as snow and
ice or clouds, are ideal to retrieve AOD of absorbing aerosols
with ωλaer < 0.9, e.g. black carbon. Bright desert regions, a
major natural source of atmospheric aerosols, have often a
surface albedo close to the CSA, which turns out to be very
challenging for spaceborne AOD retrievals or the derivation
of albedo products in deserted areas of the world (e.g. Popp et
al., 2011). Knowledge about the CSA might help to improve
both AOD and SSA retrievals in arid regions and might indirectly (e.g. through atmospheric correction) lead to better
albedo products in arid regions derived from remote sensing data. Our results show also that the AOD of less absorbing aerosols with ωλaer > 0.9 can be retrieved over dark surfaces with aλ ≤ 0.2 because their CSA is far from the surface albedo of many surfaces, such as water, vegetation, soil,
asphalt and others.
However, the observation and solar geometry must be
taken into account to avoid the CSA in AOD retrievals.
In practice, scattering angles of less than 110◦ should be
favoured in AOD retrievals over dark targets and scattering
angles around 120◦ are ideal for retrievals over surfaces with
an albedo of more than 0.5. Small scattering angles are given
for nadir observation geometries at sunrise and sunset.
Finally, the AOD retrieval accuracy depends also on
additional parameters not considered in the modelling
study, such as gaseous absorption, accuracy of auxiliary
data, or the sensor performance and measuring accuracy
(Seidel et al., 2008).
3.2.2
Implication to single-scattering albedo retrieval
Figure 6 shows the non-linear spectral dependence of SSA,
such that ω412 nm ≈ ω550 nm > ω865 nm for absorbing aerosol
types (ω < 0.93) and ω412 nm ≈ ω550 nm ≈ ω865 nm for weakly
absorbing aerosols (ω > 0.93). An initial retrieval of CSA or
its estimation from a LUT potentially provides a good strategy to determine the SSA, which allows to estimate a corresponding aerosol model.
According to the findings in Sect. 3.1.2, a polynomial fit
to the CSA as a function of SSA could be used to identify
the SSA corresponding to a retrieved CSA (see Fig. 6). Our
results could potentially help to improve existing methods to
estimate SSA using critical reflectance methods (Kaufman,
1987; de Almeida Castanho et al., 2008; Zhu et al., 2011).
The difference of our analysis to the studies mentioned above
is that we do not assume a linear relationship between TOA
reflectance and AOD or between surface albedo and TOA
reflectance. As a consequence, we calculate the CSA by determining the derivative of TOA reflectance with respect to
AOD. This might allow to expand the derivation of SSA to
cases where a linear fit fails or is prone to fitting errors. Nevertheless, an accurate determination of SSA using remote
Atmos. Meas. Tech., 5, 1653–1665, 2012
sensing is still a difficult task but promises to distinguish
between absorbing and less or non-absorbing aerosol types.
3.2.3
Implication to atmospheric correction
Atmospheric correction of satellite images is an important
prerequisite to obtain surface properties for many remote
sensing applications. Often, aerosol micro-physical and optical properties are unknown and therefore assumed prior
to the atmospheric correction. The presented results show
clearly that uncertainties in surface albedo estimations have
a strong impact on AOD retrievals. On the other hand, an
inaccurate estimate of the AOD will have a much smaller effect on the accuracy of atmospherically corrected reflectance
if the surface albedo is around the CSA than if the surface
albedo is much lower or higher than the CSA because of
the weak sensitivity of the TOA reflectance to AOD around
the CSA.
4
Summary and conclusions
With this work, we provide a sensitivity analysis of the reflectance at TOA as function of surface albedo to AOD, as
well as of the resulting CSA to various parameters. We determine the CSA with partial derivatives of the reflectance
at TOA with respect to AOD, whereas most previous studies (Fraser and Kaufman, 1985; Kaufman, 1987; de Almeida
Castanho et al., 2008; Zhu et al., 2011) assumed linear relations between these two quantities. This allows us to conclude that the CSA depends mainly on SSA, scattering angle
and wavelength. It depends to a minor degree also on AOD,
except for strong absorbing aerosol types and for scattering
angles larger than 150◦ . We therefore propose to extend the
definition of CSA to the more general case where the CSA
represents a small surface albedo range with minimal AOD
sensitivity.
AOD retrievals over surfaces with a reflectance factor or
albedo close to the CSA will result in large errors due to
the low sensitivity of the observed quantity (radiance or intensity at TOA) to the retrieved quantity. Thus, small inaccuracies of the estimated surface albedo lead to large AOD
retrieval errors. For example, soil and desert surfaces often
have albedo values close to the CSA of moderately absorbing aerosols, where 0.01 albedo uncertainty leads to at least
0.1 AOD retrieval error. On the other side, we showed that
the retrieval error is rather small for absorbing aerosols over
bright surfaces. This offers interesting opportunities for deriving AOD over snow or clouds. The CSA may be even used
in theory to determine the aerosol type from TOA reflectance
measurements, because the CSA values depend strongly on
SSA, which are well separated for different aerosol models,
except for the non-absorbing particles. Furthermore, conditions close and at the CSA reduce the impact of AOD uncertainties in atmospherically corrected remote sensing data.
www.atmos-meas-tech.net/5/1653/2012/
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
11
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
surface albedo − 0.01
critical surface albedo
surface albedo + 0.01
0.4
0.4
0.2
0.2
AOD retrieval error
AOD retrieval error
surface albedo + 0.01
0.0
−0.2
−0.4
−0.4
0.2
0.4
0.6
surface albedo
0.8
1.0
0.0
(a) Continental aerosol model
surface albedo − 0.01
critical surface albedo
0.4
0.2
0.2
0.0
−0.2
−0.4
−0.4
0.4
0.6
surface albedo
0.8
1.0
0.0
(c) Urban aerosol model
surface albedo − 0.01
critical surface albedo
0.4
0.2
0.2
0.0
−0.2
−0.4
−0.4
0.4
0.6
surface albedo
1.0
surface albedo − 0.01
critical surface albedo
0.4
0.6
surface albedo
0.8
1.0
0.8
(e) Biomass burning aerosol model
1.0
surface albedo − 0.01
critical surface albedo
0.0
−0.2
0.2
0.2
surface albedo + 0.01
0.4
0.0
0.8
(d) Desert aerosol model
AOD retrieval error
AOD retrieval error
surface albedo + 0.01
0.4
0.6
surface albedo
0.0
−0.2
0.2
0.2
surface albedo + 0.01
0.4
0.0
critical surface albedo
(b) Maritime aerosol model
AOD retrieval error
AOD retrieval error
surface albedo + 0.01
surface albedo − 0.01
0.0
−0.2
0.0
1663
0.0
0.2
0.4
0.6
surface albedo
0.8
1.0
(f) Stratospheric aerosol model
aer −aer
aer
aer = 0.3 at φ = 0◦ ,
aer
Fig.9:9. AOD
error
(τtrue
τretrieved
) as a function
surface albedo
at 550 nm
for different
with τtrue
Fig.
AODretrieval
retrieval
error
(τtrue
− τretrieved
) as a offunction
of surface
albedo
at 550 aerosol
nm fortypes
different
aerosol types with
◦
◦
aer
◦
◦
◦
θ0 ==300.3, and
= 30
plus
signs
denote
an
overestimation
of
surface
albedo
by
+0.01
and
the
minus
signs
an
underestimation
of the
surface
τtrue
at φθ =
0 ,. θThe
=
30
,
and
θ
=
30
.
The
plus
signs
denote
an
overestimation
of
surface
albedo
by
+0.01
and
minus
0
albedo
−0.01. The CSAof
is provided
by the red
signs
an by
underestimation
surface albedo
byline.
−0.01. The CSA is provided by the red line.
www.atmos-meas-tech.net/5/1653/2012/
Atmos. Meas. Tech., 5, 1653–1665, 2012
1664
F. C. Seidel and C. Popp: Critical surface albedo and AOD retrieval
The results in this paper suggest that AOD retrievals close
to the CSA will be prone to large errors for single-view and
intensity-only observations. Such retrievals could be problematic in terms of fast convergence and finding the global
minima with the correct solution. We recommend to include
a priori information on the sensitivity of the measured radiance to AOD in retrieval algorithms similar to the retrieval
schemes outlined in Govaerts et al. (2010) and Sayer et al.
(2012). It could help to avoid unnecessary computation time
and would allow to include error estimations in the final
product. Finally, the presented findings allow to investigate
AOD retrieval sensitivities for single-view, intensity-only
spaceborne instruments with given solar and observation
geometries, as well as surface and aerosol climatologies.
Acknowledgements. The work of F. C. Seidel for the AMTD
version of this study was performed at the Remote Sensing Laboratories, University of Zurich, Switzerland, and for AMT at the Jet
Propulsion Laboratory, California Institute of Technology, under a
contract with the National Aeronautics and Space Administration.
The author’s copyright for this publication is transferred to the
California Institute of Technology. Government Sponsorship
acknowledged. C. Popp acknowledges Hyper-Swiss-Net which is
jointly funded by the Swiss University Conference and the ETH
Board as an Innovation/Cooperation project (Reference number C-19). We are very grateful for the thoughtful comments and
suggestions by Alexander A. Kokhanovsky and two anonymous
reviewers, which helped to considerably improve our manuscript.
Edited by: J. Cermak
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