Open Access
Atmospheric
Chemistry
and Physics
Atmos. Chem. Phys., 14, 847–875, 2014
www.atmos-chem-phys.net/14/847/2014/
doi:10.5194/acp-14-847-2014
© Author(s) 2014. CC Attribution 3.0 License.
Sensitivity of aerosol retrieval to geometrical configuration of
ground-based sun/sky radiometer observations
B. Torres1,2 , O. Dubovik2 , C. Toledano1 , A. Berjon3 , V. E. Cachorro1 , T. Lapyonok2 , P. Litvinov2 , and P. Goloub2
1 Group
of Atmospheric Optics, Valladolid University, Valladolid, Spain
d’Optique Amosphérique, Université des Sciences et Technologies de Lille, Villeneuve d’Ascq, France
3 Izana Atmospheric Research Center, Spanish Meteorological Agency, Tenerife, Spain
2 Laboratoire
Correspondence to: B. Torres ([email protected])
Received: 13 February 2013 – Published in Atmos. Chem. Phys. Discuss.: 14 March 2013
Revised: 25 November 2013 – Accepted: 6 December 2013 – Published: 24 January 2014
Abstract. A sensitivity study of aerosol retrievals to the geometrical configuration of the ground-based sky radiometer
observations is carried out through inversion tests. Specifically, this study is focused on principal plane and almucantar observations, since these geometries are employed in
AERONET (AErosol RObotic NETwork). The following effects have been analyzed with simulated data for both geometries: sensitivity of the retrieval to variability of the observed scattering angle range, uncertainties in the assumptions of the aerosol vertical distribution, surface reflectance,
possible instrument pointing errors, and the effects of the
finite field of view. The synthetic observations of radiometer in the tests were calculated using a previous climatology
data set of retrieved aerosol properties over three AERONET
sites: Mongu (Zambia) for biomass burning aerosol, Goddard Space Flight Center (GSFC; Maryland, USA) for urban aerosol and Solar Village (Saudi Arabia) for desert dust
aerosol. The results show that almucantar retrievals, in general, are more reliable than principal plane retrievals in presence of the analyzed error sources. This fact partially can
be explained by practical advantages of the almucantar geometry: the symmetry between its left and right branches
that helps to eliminate some observational uncertainties and
the constant value of optical mass during the measurements,
that make almucantar observations nearly independent of the
vertical variability of aerosol. Nevertheless, almucantar retrievals present instabilities at high sun elevations due to the
reduction of the scattering angle range coverage, resulting in
decrease of information content. It is in such conditions that
principal plane retrievals show a better stability, as shown by
the simulation analysis of the three different aerosol models.
The last part of the study is devoted to the identification
of possible differences between the aerosol retrieval results
obtained from real AERONET data using both geometries.
In particular, we have compared AERONET retrievals at the
same sites used in the simulation analysis: Mongu (biomass
burning), GSFC (urban) and Solar Village (desert dust).
Overall, this analysis shows robust consistency between the
retrievals from simultaneous observations in principle plane
and almucantar All identified differences are within the uncertainties estimated for the AERONET operational aerosol
retrieval. The differences in the size distribution are generally under 10 % for radii between 0.1 µm and 5 µm, and outside this size range, the differences can be as large as 50 %.
For the absorption parameters, i.e., single scattering albedo
and the imaginary part of the refractive index, the differences are typically under 0.01 and 0.003, respectively. The
real part of the refractive index showed a difference of 0.01
for biomass burning and urban aerosol, and a difference of
around 0.03 for desert dust. Finally, it should be noted that
the whole data set includes only 200 pairs, which have been
taken under very stable atmospheric conditions; therefore, in
a general case, differences between principal plane (PPL) and
almucantar (ALM) are expected to be higher. Though the observed differences between ALM and PPL are rather small, it
should be noted that this analysis has been conducted using
a limited set of 200 observation pairs selected under stable
atmospheric conditions.
Published by Copernicus Publications on behalf of the European Geosciences Union.
848
1
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
Introduction
In the past decades, atmospheric aerosol has been widely recognized as an atmospheric constituent important not only for
the understanding of atmospheric processes, but also as one
of the factors impacting many different aspects of the life on
Earth (Solomon et al., 2007; IPCC, 2007). Indeed, the aerosol
directly impacts ecosystems and human health as a pollutant
(generated by industrialization and fossil fuel combustion).
It has also been recognized for its influence on the global
climate system. This effect is known as “aerosol radiative
forcing”, and includes the so-called direct effects (basically
scattering and absorption of solar radiation), as well as indirect effects, created by the modification of cloud properties
(cloud lifetime, cloud albedo, precipitation, chemistry, etc.).
The aerosol particles can be natural (sea salt, desert dust,
volcanic ash) or anthropogenic (nitrates, sulfates, organics,
carbonaceous, etc.), or a mixture of both, with particle sizes
ranging from a few nanometers to hundreds of micrometers; this leads to a complex and heterogeneous system with
different physical, chemical and optical properties (Willeke
and Baron, 1993; D’Almeida et al., 1991). This complexity makes it necessary to take a multidisciplinary approach
to studying aerosol, one which implies the integrated use of
very different methods and techniques.
In this context, this paper is focused on the analysis of the
important features of aerosol columnar properties retrieval
from radiometric observations. This approach is based on
the analysis of the light resulting from the interaction of solar radiation with the aerosol particles suspended in the atmosphere. The high spatial and temporal variability of the
aerosol properties has led to the development and establishment of measurement networks covering extensive areas.
Among all the monitoring systems, ground-based observations have been revealed as the most accurate and simplest.
The most important ground-based global remote sensing networks are AERONET (AErosol RObotic NETwork) (Holben
et al., 1998), SKYNET (Takamura and Nakajima, 2004) and
PFR-GAW (Precision Filter Radiometer-Global Atmosphere
Watch) (Wehrli, 2005).
AERONET and SKYNET networks provide aerosol information from two kinds of spectral measurements: spectral
data of direct Sun radiation attenuation by the atmosphere
and angular distribution of diffuse sky radiation, while PFRGAW only provides data of direct Sun radiation. The direct
measurements provide information about total aerosol loading, i.e. AOD (aerosol optical depth). The observations of diffuse radiation contain essential information for retrieving the
aerosol phase function and optical aerosol properties. Using
this information, important aerosol optical and microphysical
parameters, such as the particle size distribution (Nakajima
et al., 1983, 1996) and complex refractive index or single
scattering albedo (Dubovik and King, 2000; Dubovik et al.,
2006), are derived.
Atmos. Chem. Phys., 14, 847–875, 2014
The present work aims at identifying whether the retrieval
results depend on the geometry used in the sky radiance
measurements. In particular, this work has been carried out
with the inversion algorithm described in Dubovik and King
(2000) (also Dubovik et al., 2000, 2002, 2006), and using
data provided by AERONET. That is why the study will
be focused on the almucantar and principal plane geometries (hereafter, ALM and PPL respectively), that are adapted
(Holben et al., 1998; Kaufman et al., 2002; Olmo et al., 2008)
as the standard observational scenarios in operational data
acquisition of the AERONET network (Holben et al., 1998).
Also, the same observational scenarios are used by SKYNET
(Nakajima et al., 1996).
In the almucantar configuration, Fig. 1 on the left, the
sun photometers (e.g., Cimel Electronique 318, standard
in AERONET) keep the zenith angle constant (equal to
the solar zenith angle θs ). The azimuth movement is done
first towards the right (taking the Sun as reference and
up to ϕa = 180◦ ) and then is repeated towards the left.
Assuming a homogeneous atmosphere, the measurements
taken in both right and left branches are expected to be
symmetrical and the final radiance values used in the inversion algorithm for the almucantar are obtained by averaging the observations in the right and left branches.
This process allows elimination of the data contaminated
by sky inhomogeneities. In AERONET network processing, the symmetry property in almucantar has been used
for over a decade, and those measurements exhibiting radiance differences higher than 20 % between right and left
branches are eliminated (this and other quality control criteria are described in http://aeronet.gsfc.nasa.gov/new_web/
Documents/AERONETcriteria_final1_excerpt.pdf and Holben et al., 2006).
In the principal plane geometry (Fig. 1 on the right), the
azimuth angle is the one that remains constant while the
zenith angle varies. Note that this geometry does not present
any evident symmetry and, therefore, identifying and screening sky inhomogeneities in principal plane observations is
not straightforward.
Another important aspect that distinguishes ALM and
PPL geometries is the relation between the scattering angle 2, the solar zenith angle θs and the observation angles
θa and ϕp for almucantar and principal plane, respectively.
For any measurement, the scattering angle can be expressed
as cos(2) = cos2 (θs ) + sin2 (θs ) cos(ϕa − ϕs ) for the almucantar1 , and cos(2) = cos(θp ∓ θs ) for the principal plane2
(Nakajima et al., 1996). As a consequence, the maximum
scattering angle that can be reached in both geometries is
1 Normally, the azimuth origin is taken in the Sun position and
therefore ϕs = 0. Note that this assumption was made in Fig. 1.
2 The signs (−) in the case of (ϕ −ϕ = 0◦ ) and (+) for the case
p
s
of (ϕp − ϕs = 180◦ ).
www.atmos-chem-phys.net/14/847/2014/
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
849
Fig. 1. Figures describing the two geometries used within AERONET network for the measurements of the sky radiances; the almucantar is
shown on the left, the principal plane is shown on the right.
2M = 2θs in the almucantar and 2M = θs + 90◦ in the principal plane3 .
This fact plays an important role in the present study, as
the information contained in the radiance measurement critically depends on the geometry selected, especially for small
values of the solar zenith angle. Specifically, the first part
of this work contains an analysis of the consequences of having different ranges of scattering angle coverage in ALM and
PPL measurements. For that purpose, in Sect. 2 we use simulated sky radiances for different θs and aerosol types which
will be inverted afterwards to observe the differences in the
retrievals. In the same section, we include an analysis of the
effect of neglecting the vertical variability of aerosol and its
effects in both geometries. Additionally, we study the influence of some other aspects that could affect ALM and PPL
in a different way, such as an uncertainties in the surface reflectance assumption, the effect of an incorrect pointing in
both geometries and the effect of considering a finite field
of view. Finally, we examine whether or not the results obtained in the simulation are supported by real observations.
For this purpose, we analyze the differences in the retrievals
obtained from nearly simultaneous principal plane and almucantar measurements, selected under stable atmospheric conditions, at the same key sites.
2
2.1
Analysis of simulated data
Methodology and data
In the first section, we study the variability of the retrievals
for different solar zenith angles corresponding to different
3 It should be noted that operationally observations cannot be
made all the way to the horizon due to horizon obstructions and
also due to inexact optical air mass computations (refraction effects, etc.). Therefore, the maximum scattering angle in the principal plane scan is typically smaller than stated theoretically (e.g., in
AERONET, the Level 2 AOD product is limited to a maximum air
mass of 5 as the effect of atmosphere sphericity is not negligible for
larger air masses and this is not accounted in the plane-parallel radiative transfer model used for aerosol retrieval (Dubovik and King,
2000). Therefore, 2M ' θs + 80◦ ).
www.atmos-chem-phys.net/14/847/2014/
ranges of scattering angle coverage in ALM and PPL measurements. Also, in order to assure the reliability of our studies, we have conducted self-consistency tests of the inversion code. First, we simulate radiance measurements with the
forward module using the pertinent size distribution (columnar volume size distribution dV /dln(R) for radii between
0.05–15 µm) and the refractive index of the different aerosol
examples. Then these synthetic observations are inverted using the retrieval algorithm and the resulting values are compared with the assumed aerosol properties. The tests are conducted for both PPL and ALM geometries. A scheme of this
procedure is drawn in Fig. 2. The test conditions, which are
the solar zenith angles (five cases: θs =15◦ , 30◦ , 45◦ , 60◦ and
75◦ ) and the measurement geometry (almucantar or principal
plane), are also included in the diagram.
This strategy for conducting the sensitivity studies has
been adapted from a previous work by Dubovik et al. (2000).
The principal novelty here is the testing of the reliability of
principal plane retrievals and the comparison of those retrievals with retrievals from almucantar observations. In addition, for modeling the aerosol properties, we used climatology of real aerosol retrievals from AERONET observations (described in Dubovik and King, 2000; Dubovik et al.,
2006), and Dubovik et al., 2002) instead of using aerosol
models found in sparse literature. In that climatology analysis, characteristics of different aerosol types observed at several AERONET key sites are derived as a function of the
aerosol optical depth. Specifically, we have taken the information from three sites: Mongu (Zambia) for biomass burning aerosol, Goddard Space Flight Center (GSFC; Maryland,
USA) for urban aerosol and Solar Village (Saudi Arabia) for
desert dust aerosol. For these three examples, two possibilities for the aerosol load have been considered: the first one
around the averaged value of the aerosol optical depth (registered in the study Dubovik et al., 2002), and the second one
with more aerosol load so as to see if certain conditions affect
differently as the aerosol load increases.
Table 1 summarizes the aerosol properties of the all the
examples considered. We provide the full set of parameters needed to run the forward module. The first parameter is the reference value of the aerosol optical depth from
which the rest of the input parameters are derived (using the
Atmos. Chem. Phys., 14, 847–875, 2014
850
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
Fig. 1. Figures describing the two geometries used within AERONET network for the measurements of the sky radiances: the almucantar is
shown on the left, the principal plane is shown on the right.
Methodology diagram
dV
dln(R)
Aerosol models:
τa (λ)
- Biomass: Zambia
- Urban: GSFC
- Desert: Solar Vil
R(Θ,λ)
Forward Code
n(λ),k(λ)
- θs =15,30,45,60,75
COMPARISON
- ALM and PPL
dV ′
dln(R)
′
′
Backward Code
n (λ),k (λ)
Fig. 2. Methodology
diagram
followed
to carry
self-consistencytest
testof
of the
the code
used code
aerosol
types,
solarsolar
zenithzenith
anglesangles
Fig. 2. Methodology
diagram
followed
to carry
out out
the the
self-consistency
usedfor
fordifferent
different
aerosol
types,
and geometries
for measuring
theradiance.
sky radiance.
and geometries
for measuring
the sky
use simulated sky radiances for different θs and aerosol types
expressions
Dubovik
et al.,afterwards
2002). The
next parameters
in
whichinwill
be inverted
to observe
the differences
Table 1 in
arethe
used
to
describe
the
size
distribution
(modeled
as
retrievals. In the same section, we include an analysis
a bimodal
lognormal
function):the
particle
concentraof the
effect of neglecting
verticalvolume
variability
of aerosol
3 /µm2 ]), volume median radius (r
tion170(CVand
[µm
andthe 190
its
effects
in
both
geometries.
Additionally,
we study
i
V i [µm])
influence
some
other
couldThe
affect
ALM and
mode width
(σV iof
) for
fine
andaspects
coarsethat
mode.
remaining
PPLthe
in refractive
a different index
way, such
uncertainties
in the surinputs are
and astheansphericity
parameter,
reflectance
effect
an incorrect
pointwhich isface
taken
as 0 forassumption,
desert dustthe
(all
the of
particles
are coning
in
both
geometries
or
the
effect
of
considering
a
sidered to be non-spherical) and in the rest of the casesfinite
as
175
field of view. Finally, we examine if the results obtained 195
100 (considering all the particles as spheres).
in the simulation are supported by real observations. For
The simulated
aerosol
optical
and the
scatterthis purpose,
we analyze
thedepth
differences
in single
the retrievals
ob1.
It
should
ing albedo
are
shown
in
the
output
part
of
Table
tained from nearly-simultaneous principal plane and
almube notedcantar
that measurements,
the obtained spectral
aerosol
optical
depth obselected under
stable
atmospheric
contained
Dubovik
et al.key
(2002)
180 using
ditions,
at the same
sites. dynamic models is slightly
different from the entry values used for generating full opti- 200
cal properties. This can be explained by the fact that aerosol
Analysis of simulated data
models 2from
Dubovik et al. (2002) are based on the linear regression2.1
analysis,
and, therefore,
an exact match between the
Methodology
and data
entry optical thickness (τaref in Table 1) and simulated optical 205
In τthe
we Indeed,
study thethe
variability
of the retrievals
thickness
notsection,
expected.
aerosol optical
depth
a isfirst
different solar
zenithaerosol
angles parameters
corresponding
different
dependsfor
nonlinearly
on such
as toreal
and
185
range
of of
scattering
angle coverage
in ALM
and PPL
imaginary
parts
the refractive
index, and
therefore,
the mearegression analysis is just an approximation. In addition, here
the calculation for the desert dust has been made using the
spheroid package developed by Dubovik et al. (2006) while
retrieval obtained by Dubovik et al. (2002) was based on the
retrieval that used only spherical assumption. As a result, we
see a slightly higher discrepancy between entry and output
values of optical thickness, even though, generally, simulations of extinction do not almost depend on shape of large
particles. For example, if we considered the spherical model
for the desert dust type in the forward simulations, the values for the aerosol optical depth at 1020 nm for SolV1 and
SolV2 would be τa (1020) = 0.294 and τa (1020) = 0.493.
These values are in better agreement with the reference values and the differences could then be related to the mentioned
non-linear dependencies. Also note that these simulated values do not depend on the “conditions” such as the measurement geometry or the solar zenith angle. Finally, we should
remark here that larger AOD implies better retrieval accuracy; however, we have decided to maintain the typical aver-
Atmos. Chem. Phys., 14, 847–875, 2014
surements. Also, in order to assure the reliability of our stud-
age
each siteself-consistency
(even though tests
theyof
arethequite
different)
ies,values
we havefor
conducted
inversion
socode.
that our
study
is
related
to
the
average
conditions.
First, we simulate radiance measurements with the
In addition
to using
the consistency
and analysis
of depenforward
module
the pertinentcheck
size distribution
(columdence
on thesize
solardistribution
zenith angle,
the samefor
methodology
nar volume
dV /dln(R)
radii betweenis also
0.05 to
− 15µm)
index
of the different
aerosol (see
used
analyzeand
therefractive
sensitivity
to different
error sources
examples.
Then
observations
inverted
us- the
2). For example,
inare
order
to study
the
flowchart
inthese
Fig. synthetic
ing the retrieval
and they
compared
the by
influence
of the algorithm
pointing error,
we are
simulate
the with
radiances
assumed
aerosol
properties.
The
test
are
conducted
for
both
introducing an incorrect pointing. Subsequently, these synPPL and ALM geometries. A scheme of this procedure is
thetic data are inverted and, the obtained results compared
drawn in figure 2. The test conditions, which are the solar
with
theangles
ones (5
assumed
be◦“true”.
zenith
cases: θto=15
, 30◦ , 45◦ , 60◦ and 75◦ ) and
s
the measurement geometry (almucantar or principal plane),
are also included in the diagram.
2.2
Dependence on the solar zenith angle
This strategy for conducting the sensitivity studies have
been
adaptedoffrom
work Dubovik
al. (2000).
The 3 for
The results
theprevious
consistency
tests areetshown
in Fig.
principal novelty here is the testing the reliability of princithe three aerosol types considered: biomass burning aerosol
pal plane retrievals and its comparison with those from al(Fig.
3a), observations.
urban aerosol
(Fig. 3b)
desert
aerosol
mucantar
In addition,
for and
modeling
thedust
aerosol
(Fig.
3c). The
study
is made following
theretrievals
scheme from
presented
properties
we used
climatology
of real aerosol
inAERONET
Fig. 2. In addition
to the
size distribution
andand
theKing,
refractive
observations
(described
in (Dubovik
index
parameters
that drive
the forward
simulations),
2000;(the
Dubovik
et al., 2006)),
Dubovik
et al. (2002))
instead the
of using
aerosol models
found
in sparse
literature.due
In that
cli- great
single
scattering
albedo
is also
illustrated,
to its
significance. The results retrieved with the almucantar geometry are shown in the upper part, while results from simulations with the principal plane are placed at the bottom
of every subfigure. In all the representations, the results obtained for the case with smallest aerosol load (e.g., desert
dust: τaref (1020) = 0.3) are plotted with a solid line while
dashed line is used for the case with the largest aerosol load
(e.g., desert dust τaref (1020) = 0.5).
Size distributions are represented in the subfigures on the
left. The “true” size distribution used for producing the synthetic observations is plotted in black. The size distributions
produced from inversion of synthetic data are plotted in different colors, depending on the solar zenith angle used for
the simulations: dark blue for 15◦ , light blue for 30◦ , green
for 45◦ , orange for 60◦ , and brown for 75◦ .
The optical parameters, single scattering albedo, and the
refractive index are plotted as a function of the solar zenith
angle. Different colors have been chosen, in this case, for
different wavelengths – blue for 440 nm, green for 670 nm,
yellow for 870 nm, and red for 1020 nm. The input values
www.atmos-chem-phys.net/14/847/2014/
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
851
Table 1. Description of aerosol properties used for simulating the radiance measurements. The first row specifies the parameters describing
the size distribution which is modeled as a bimodal lognormal function: CV i [µm3 /µm2 ], rV i [µm] and σV i . Refractive index and the
sphericity parameter are also parts of the input. Single-scattering albedo and aerosol optical depth, for each wavelength, are shown as the
output after applying the forward model.
Biomass burning (Zambia)
INPUT
τaref (440)
r Vf
σ Vf
C Vf
r Vc
σVc
C Vc
Sph.
0.400
0.800
0.130
0.140
0.400
0.400
0.048
0.096
3.504
3.788
0.730
0.730
0.004
0.007
100
100
n(440)
n(670)
n(870)
n(1020)
k(440)
k(670)
k(870)
k(1020)
– Zamb1 –
– Zamb2 –
1.5100
1.5100
1.5100
1.5100
1.5100
1.5100
1.5100
1.5100
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
0.0210
OUTPUT
τa (440)
τa (670)
τa (870)
τa (1020)
ωo (440)
ωo (670)
ωo (870)
ωo (1020)
0.416
0.872
0.184
0.397
0.107
0.232
0.078
0.167
0.8778
0.8827
0.8290
0.8402
0.7811
0.7958
0.7467
0.7620
– Zamb1 –
– Zamb2 –
– Zamb1 –
– Zamb2 –
Urban (GSFC)
INPUT
τaref (440)
r Vf
σ Vf
C Vf
r Vc
σVc
C Vc
Sph.
0.200
0.500
0.142
0.175
0.380
0.380
0.030
0.075
3.128
3.275
0.790
0.790
0.018
0.030
100
100
n(440)
n(670)
n(870)
n(1020)
k(440)
k(670)
k(870)
k(1020)
– GSFC1 –
– GSFC2 –
1.4100
1.4100
1.4100
1.4100
1.4100
1.4100
1.4100
1.4100
0.0030
0.0030
0.0030
0.0030
0.0030
0.0030
0.0030
0.0030
OUTPUT
τa (440)
τa (670)
τa (870)
τa (1020)
ωo (440)
ωo (670)
ωo (870)
ωo (1020)
0.195
0.559
0.083
0.254
0.048
0.145
0.036
0.102
0.9718
0.9771
0.9588
0.9691
0.9476
0.9604
0.9404
0.9535
– GSFC1 –
– GSFC2 –
– GSFC1 –
– GSFC2 –
Desert dust (Solar Village)
INPUT
τaref (1020)
r Vf
σ Vf
C Vf
r Vc
σVc
C Vc
Sph.
0.300
0.500
0.120
0.120
0.400
0.400
0.026
0.030
2.320
2.320
0.600
0.600
0.274
0.470
0
0
n(440)
n(670)
n(870)
n(1020)
k(440)
k(670)
k(870)
k(1020)
– SolV1 –
– SolV2 –
1.5600
1.5600
1.5600
1.5600
1.5600
1.5600
1.5600
1.5600
0.0029
0.0029
0.0013
0.0013
0.0010
0.0010
0.0010
0.0010
OUTPUT
τa (440)
τa (670)
τa (870)
τa (1020)
ωo (440)
ωo (670)
ωo (870)
ωo (1020)
– SolV1 –
– SolV2 –
0.483
0.707
0.371
0.591
0.344
0.568
0.332
0.557
0.9300
0.9209
0.9664
0.9647
0.9772
0.9768
0.9794
0.9793
– SolV1 –
– SolV2 –
are not shown in order to make the interpretation of the figure
easier; they can be seen in Table 1.
The most evident tendency observed in the tests is the
instability of the optical parameters for small solar zenith
angles in the almucantar. This tendency is present in the
tests for all aerosol types. For instance, the single scattering
albedo differs on average around 0.02 at θs = 15◦ from those
obtained at larger solar zenith angle. This latter agrees with
the values given in Table 1. On the other hand, the results
obtained with the principal plane geometry do not have such
www.atmos-chem-phys.net/14/847/2014/
strong dependence on the solar zenith angle. The values are
shown in Table 1.
The instability in the retrievals obtained from almucantar
data can be explained by the fact that only aerosol scattering
in middle and large scattering angles depends on a complex
index of refraction and the forward peak of aerosol phase
function is dominated by light diffraction (Bohren and Huffman, 1983). In this regard, the maximum scattering angle
for almucantar observational geometry is 2θs , i.e., the measurements corresponding to small solar zenith angles do not
Atmos. Chem. Phys., 14, 847–875, 2014
852
6
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
0.12
1
0.03
0
PPL
0.12
Zambia: τ440 = 0.4
Zambia: τ440 = 0.8
0.09
0.06
0.9
0.8
1 15
30
45
60
75
PPL
0.9
0.8
0.03
ALM
1.55
Real Part of the Refractive Index
0.06
Single Scattering Albedo
0.09
dV/dlnR (µ m3 / µ m2)
ALM
o
SZA=15
SZA=30o
o
SZA=45
o
SZA=60
SZA=75o
1.50
0.025
1.45
0.02
1.40
0.015
15
1.55
0.1
1
3
10
15
Radius (µ m)
30
45
60
45
75
PPL
1.50
440 nm
670 nm
870 nm
1020 nm
1.45
75
15
Solar Zenith Angle [°]
0.03
0.025
1.40
0
0.03
45
75
0.02
Imag. Part of the Refractive Index
a) Mongu - Biomass burning
ALM
0.015
15
45
75
Solar Zenith Angle [°]
b) GSFC - Urban
0.03
0
0.09
PPL
GFSC: τ440 = 0.2
GSFC: τ440 = 0.5
0.06
0.96
0.94
0.92
1 15
30
45
60
75
PPL
0.98
0.96
0.94
0.03
ALM
0.1
1
3
10
15
Radius (µ m)
0.004
1.40
0.003
1.38
0.002
15
30
45
60
45
75
PPL
1.42
0.004
1.40
0.003
440 nm
670 nm
870 nm
1020 nm
1.38
0.92
0
1.42
75
15
45
75
0.002
15
45
Imag. Part of the Refractive Index
0.06
ALM
0.98
Real Part of the Refractive Index
SZA=15o
SZA=30o
SZA=45o
SZA=60o
SZA=75o
Single Scattering Albedo
0.09
dV/dlnR (µ m3 / µ m2)
1
ALM
75
Solar Zenith Angle [°]
Solar Zenith Angle [°]
0.20
0.10
0
0.30
Sol.V: τ1020 = 0.3
PPL
Sol.V: τ1020 = 0.5
0.20
ALM
0.95
0.9
1 15
30
45
60
75
PPL
0.95
0.9
0.10
0
1
ALM
0.1
1
3
10
Radius (µ m)
15
30
45
60
75
Solar Zenith Angle [°]
ALM
1.6
Real Part of the Refractive Index
SZA=15o
SZA=30o
SZA=45o
SZA=60o
SZA=75o
Single Scattering Albedo
dV/dlnR (µ m3 / µ m2)
0.30
0.004
0.002
1.5
1.6
15
45
0
75
PPL
0.002
440 nm
670 nm
870 nm
1020 nm
1.5
15
45
75
0.004
15
45
75
Imag. Part of the Refractive Index
c) Solar Village - Desert Dust
0
Solar Zenith Angle [°]
Fig. 3. Summary of the aerosol retrievals obtained in the self-consistency test using three aerosol types: biomass burning aerosol (a), urban
aerosol
(b) and desert
aerosol
(c) with
two different
AOD utilized as test
references
in each
case types:
(solid line
used burning
for the case
with(subfigure
smallest
Fig.
3. Summary
of thedust
aerosol
retrievals
obtained
in the self-consistency
using three
aerosol
biomass
aerosol
aerosol
and(subfigure
dashed line
largest).
For every
subfigure,
almucantar
resultsAOD
are shown
upper part
whereas
a),
urbanload
aerosol
b) for
andthe
desert
dust aerosol
(subfigure
c) with
two different
utilizedinasthe
reference
in each
case principal
(solid lineplane
used
results
are presented
in theaerosol
bottomload
part.and
Figures
online
the for
left the
correspond
size
distribution
results.
Figuresresults
in theare
center
illustrate
results
for
the case
with smallest
dashed
largest). to
For
every
subfigure,
almucantar
shown
in the the
upper
part
for the single
scattering
andpresented
figures oninthetheright
describe
resultson
forthe
theleft
complex
refractive
index.
whereas
principal
plane albedo,
results are
bottom
part.the
Figures
correspond
to size
distribution results. Figures in the
center illustrate the results for the single scattering albedo, and figures on the right describe the results for the complex refractive index.
Atmos. Chem. Phys., 14, 847–875, 2014
www.atmos-chem-phys.net/14/847/2014/
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
contain enough information to adequately retrieve the index
of refraction or, consequently, the single scattering albedo.
The same result was described for simulations in Dubovik
et al. (2000).
In the refractive index analysis, we observe the same result; for the principal plane, the retrievals are stable and the
values correspond to those given in Table 1 (the only exception is found for the case of the biomass burning at θs = 15◦ ).
On the other hand, the retrievals obtained for the almucantar drift further apart from their input values as the solar
zenith angle becomes smaller. The worst-case behavior can
be found with desert dust with low aerosol load, where the
real part of refractive index is 0.1 smaller than the assumed
value at θs = 15◦ (1.46 when it should be 1.56), and the
imaginary part is much higher than the inputs, especially for
long wavelengths where values are three times larger.
From the analysis of the differences in the size distribution, a dependency on the radius can be seen: the differences
observed between the retrievals and the input values do not
exceed 10 % for intermediate radii (in both retrievals ALM
and PPL) while they strongly increase in the extremes. In the
cases of urban and desert dust, these intermediate radii range
only between 0.1 µm and 5 µm, while for biomass burning
the range is smaller: between 0.3 µm and 3 µm. Moreover,
the differences between the input values and the retrievals
(and between the retrievals themselves, i.e. PPL vs. ALM)
are much higher for the case of biomass burning (which are
over 100 %) than for urban and desert dust (which are only
up to 40 %).
The analysis of the differences for the biomass burning,
illustrated in Fig. 3, shows noticeable differences in the fine
mode only when the maximum scattering angle is smaller
than 120◦ (θs = 15◦ , 30◦ , 45◦ for almucantar and θs = 15◦ for
the principal plane simulations), and especially for the case
with larger aerosol load (named Zamb2) where the values
of the size distribution become unexpectedly higher than the
original size distribution (up to 20 %). This effect is accompanied by a sharp decline in the real refractive index (from
1.51 to 1.47–1.48). Both effects compensate each other for
the calculation of optical thickness; there are more particles
but they scatter less light. There is a strong connection between the retrieved fine mode and the real part of the refractive index, as they are both more sensitive to the large angles
of the phase function. This effect has been already seen in
previous works (Dubovik et al., 2002; Sinyuk et al., 2007; Li
et al., 2009) and will be recurrent in the next sections. Nevertheless, the discrepancies are more striking in the coarse
mode. For principal plane, all the size distributions are separated from the original one when the radius is higher than
3 µm. They all have the same values and decrease faster than
the input for radii above 3 µm. For the almucantar, nonetheless, the size distributions also diverge from the original but
they do not have a defined direction.
The larger discrepancies in the extremes can be explained
by the very low sensitivity of radiometer observations to the
www.atmos-chem-phys.net/14/847/2014/
853
size distribution variation for the radius smaller than 0.1 µm
or larger than 3 µm for the wavelengths used in AERONET
(Dubovik et al., 2000). Particularly for the case of biomass
burning, this effect gets more important, since its coarse
mode is displaced towards larger radii (rVc for Mongu site is
the largest among the selected examples) while for the other
examples the volume concentration in this size region is quite
lower. Finally, we conclude that the tests did not reveal any
systematic pattern of differences between the retrievals obtained through PPL and ALM. The larger noise in the extremes compare to that for the central radii is the only effect
observed.
2.3
Dependence on the aerosol vertical distribution
Once the discrepancies obtained due to the different scattering angle coverage of both geometries are analyzed, the next
step is the study of the influence of some other aspects that
could affect ALM and PPL differently. First we analyze the
effect of the aerosol vertical distribution variability in the atmosphere. As mentioned in the introduction and illustrated in
Fig. 1, the zenith angle is kept constant during measurement
in the almucantar, and the observation in the almucantar has
a symmetry whereas principal plane does not.
The second, and less obvious, characteristic of observations in the almucantar is their low dependence on the aerosol
vertical variability, which is generally weaker than that for
observations in principle plane. This can be illustrated with
the following brief analysis of solution of radiative transfer
equation in single-scattering approximations for almucantar
and principle plane geometries.
Let us consider the solution of the radiance R for the firstorder scattering and for any observation angle θv given by
F0 −τ/µv
R=
e
×
|µv |
Z
zt
!
X
0
0
Mk e−m t (z) dz,
(1)
k
where F0 is the extraterrestrial irradiance and
Z zt X
τ=
σextk (z)dz
0
t (z) =
k
Z zX
0 k
σextk (z0 )dz0
ωok Pk σextk (z)
4π
1
1
m0 =
−
; with µs = 1/ cos θs and µv = 1/ cos θv
µs |µv |
Mk =
Observe that we have included k components at any height,
z, of the atmosphere. The parameters Pk (redefined as
Pk =Pk /4π) and σextk are, respectively, the phase function and the extinction coefficient for every single component. However, in the almucantar, observations µs = µv and
Atmos. Chem. Phys., 14, 847–875, 2014
854
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
Eq. (1) should be rewritten as
Z zt X !
F0 −τ/µs
Ra =
e
×
Mk dz.
µs
0
k
(2)
The phase function, Pk , and the single scattering albedo,
ωok (z), for every single component do not depend on the
height and can be taken out of the integral.
!
X
F0 −τ/µs
×
ωok τk Pk ,
(3)
e
Ra =
µs
k
where
Z
τk =
zt
0
σextk (z)dz.
(4)
Equation (3) is already independent from the height. Therefore, for the single-scattering approximation in the almucantar geometry, the radiance measurements do not depend on
the vertical distribution of the components in the atmosphere,
particularly not on the aerosol vertical distribution.
Note that, as is typical, we consider three main components: gaseous absorption, molecular scattering (Rayleigh),
and aerosol scattering and absorption, and Eq. (3) is rewritten as
Ra =
F0 −τ/µs
[ωo τa Pa + τR PR ] ,
e
µs
(5)
with
gas
a
a
+ τR .
τ = τabs + τscat
+ τabs
(6)
The exponential term within the integral in the general equation, Eq. (1), links the principal plane measurement to the
aerosol and gas vertical distribution. Only in the case that we
consider just one main layer in the atmosphere (without any
changes in the vertical distribution) could we deduce a similar expression for the principal plane as in Eq. (5),
τ
τ
F0 µs
ωo τa Pa + τR PR
Rp =
(7)
[e− µv − e− µs ].
µv − µs
τa + τR
Consequently, in the single-scattering approximation, a heterogeneous aerosol vertical distribution would only affect the
principal plane. Multiple scattering effects of the light in the
atmosphere add some sensitivity to vertical variability of atmosphere for both observations in the almucantar and in the
principal plane. Nonetheless, since the transmitted radiation
of aerosol is dominated by the effects of the first order of
scattering, the dependence of radiances in the almucantar on
the vertical variability of the atmosphere is generally weaker
that that for radiances measured in principal plane.
The above conclusion suggests that some differences between aerosol retrievals from simultaneous measurements in
principle plane and almucantar can appear due to their different sensitivities to the assumptions regarding aerosol vertical distribution. This aspect is of particular interest for the
Atmos. Chem. Phys., 14, 847–875, 2014
present study because generally there is no reliable information for making accurate assumptions about aerosol vertical
distribution. Only in situations when co-located data from the
lidar are available is accounting for detailed aerosol vertical
distribution possible (e.g., Lopatin et al., 2013).
To analyze the effects of the vertical distribution, we produced synthetic observations using the aerosol properties of
urban (GSFC2) and desert dust (SolV2). The forward calculations were conducted using the assumption of a multilayered plane parallel atmosphere: 30 layers, equidistant in pressure, were used. Utilizing the same idea as in Sinyuk et al.
(2007), we used two different aerosol vertical distributions:
two Gaussian profiles with 1 km width, one with at ground
level and the other with an aerosol concentration profile median height at 3 km (Sinyuk et al., 2007, Fig. 1). To check the
possible dependency of the results on θs , we have done the
tests for θs = 45◦ and θs = 75◦ . First, the simulated radiances
for both geometries were inverted under the assumption of a
monolayered atmosphere. This assumption is used in operational AERONET (Dubovik and King, 2000) and SKYNET
processing (Nakajima et al., 1996).
Figure 4 represents the size distributions retrieved under the previously mentioned conditions for urban (left) and
desert dust (right) aerosol types. Note that in total, there are
eight size distributions for each aerosol case, corresponding
to every possible combination between the two geometries,
the two vertical aerosol profiles, and the two solar zenith angles.
The results obtained are quite similar for both aerosol
types. For almucantar geometry, the size distributions retrieved do not display any significant differences compared to
the assumed “true” values. Only small differences can be observed in the coarse mode for desert dust at θs = 75◦ , where
the effect of multiple scattering is more important. The maximum of these differences is observed for r = 3 µm with a
value around 10 %. By contrast, principal plane results show
two interesting tendencies: on the one hand, the results for
θs = 45◦ do not significantly differ from the input size distributions for both aerosol types; on the other hand, they present
important differences in the case of θs = 75◦ , especially for
the fine mode, where they reach values over 50 %.
This interesting result confirms the theoretical expectations foreseen above: the principal plane retrievals are more
likely affected by aerosol vertical distribution than almucantar inversions. The simulations reveal the larger differences
with the assumed values for the geometries with large solar zenith angles, especially for the size distribution in the
fine mode. The retrieval errors appear to be larger when the
aerosol concentration profile median height is assumed to be
at ground level than when it is at 3 km.
If the vertical structure of the aerosol is known, the accurate aerosol profile can be used in the retrieval. In such
conditions, all retrieved properties can adequately retrieved
from both geometries. Figure 5 shows the results for the retrieval using accurate vertical profile for the case of urban
www.atmos-chem-phys.net/14/847/2014/
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
855
Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
9
a) GSFC - Urban
b) Solar Village - Desert Dust
Reference Size Distribution
Reference Size Distribution
0.08
dV/dlnR (µ m3 / µ m2)
s
ALM − θ = 45° − Vert. Dist. = 3km
s
PPL − θs= 45° − Vert. Dist. = 3km
0.06
ALM − θ = 75° − Vert. Dist. = Surf.
3
s
PPL − θ = 75° − Vert. Dist. = Surf.
s
ALM − θs= 75° − Vert. Dist. = 3km
PPL − θ = 75° − Vert. Dist. = 3km
0.04
ALM − θ = 45° − Vert. Dist. = Surf.
s
PPL − θs= 45° − Vert. Dist. = Surf.
PPL − θ = 45° − Vert. Dist. = Surf.
2
dV/dlnR (µ m / µ m )
0.3
ALM − θs= 45° − Vert. Dist. = Surf.
s
0.02
0.25
ALM − θs= 45° − Vert. Dist. = 3km
PPL − θ = 45° − Vert. Dist. = 3km
s
0.2
ALM − θs= 75° − Vert. Dist. = Surf.
PPL − θs= 75° − Vert. Dist. = Surf.
ALM − θ = 75° − Vert. Dist. = 3km
s
0.15
PPL − θs= 75° − Vert. Dist. = 3km
0.1
0.05
0
0.1
1
3
0
10
Radius (µ m)
0.1
1
3
10
Radius (µ m)
Fig. 4. Aerosol size distributions retrieved in the study of the influence on the aerosol vertical profiles. Using the aerosol properties of urban
Fig. 4. Aerosol size distributions retrieved in the study of the influence on the aerosol vertical profiles. Using the aerosol properties of urban
(a) and desert (subfigure
dust (b),a)radiance
measurements have been previously simulated for the two geometries, almucantar (solid line) and principal
and desert dust (subfigure b), radiance measurements have been previously simulated for the two geometries, almucantar (solid
plane (dashed line)
line),andconsidering
30(dashed
layersline),
in the
atmosphere.
During
the retrieving
process,
only process,
one layer
used
in used
the four analyzed
principal plane
considering
30 layers
in the atmosphere.
During
the retrieving
onlyhas
onebeen
layer has
been
◦
◦ and
the four
analyzed
cases:centered
θs = 45◦ and
vertical
profile
centered
in the
earth θsurface
(red
lines),
θ
=
45
and
vertical
profile
centered
at (pink lines),
cases: θs = 45◦in and
vertical
profile
in the
Earth
surface
(red
lines),
=
45
vertical
profile
centered
at
h
=
3
km
s
s
◦
h=3 km (pink
lines),
θs = 75◦in
andthe
vertical
profile
centered
in thelines),
earth surface
lines),
θs = 75profile
and vertical
profileat
centered
h=3(blue
km lines).
θs = 75◦ and vertical
profile
centered
Earth
surface
(green
θs = (green
75◦ and
vertical
centered
h = 3atkm
(blue lines).
dV/dlnR (µ m3 / µ m2)
3
2
dV/dlnR (µ m / µ m )
a) Urban - Surface
b) Urban - 3 km
aerosol at θs = 75◦ measured in principal plane. The subfigaerosol mixed with Rayleigh scattering while the upper layer
ure on the left represents the case with aerosol Reference
concentration
contains only Rayleigh scattering.
Indeed, in the real atmoSize Distribution
Reference Size Distribution
0.08
0.08
1 Layer
profile median height
at ground level, and the1 Layer
subfigure on
sphere,
molecular scattering generally
dominates at altitudes
2 Layers
the right represents the case with the maximum25 Layers
at
3
km.
Red
above
∼
5
km
(Fig.
6
in
Elterman,
1966
and Table 4.10 in
Layers
5 Layers
and blue lines denote
the
retrievals
for
the
case
in
which
the
D’Almeida
et
al.,
1991,
and
references
therein).
In Fig. 5,
New
2
Layers
−
2km
New
2
Layers
−
2km
0.06
0.06
New 2 Layers − 4km
New 2 Layers − 4km
atmosphere is assumed to have two layers and five
layers,
regray
lines
represent
these
alternative
solutions:
solid line
New 2 Layers − 6km
New 2 Layers − 6km
spectively, defining
the
border
between
layers
as
equidistant
when
the
border
between
the
layers
is
fixed
at
2
km,
dashed
0.04
0.04
in pressure.
line when the border is at 4 km, and dash-dotted when it is at
In practice, however, accurate information about vertical
6 km.
0.02
0.02
distribution of the aerosol is rarely available, whereas the
Using the second assumption leads to generally worse revertical profile may change quite dramatically. Therefore, in
sults compared to retrievals obtained using accurate aerosol
0
0
this study we are interested
vertical
distribution.
Furthermore,
is no an optimum
0.1in finding out whether
1
3taking into
10
0.1
1
3 there 10
account at least some general features
characteristics
for the
choice of the altitude
at which
Radius
(µ m)
Radius
(µ m) to put the border between
vertical distribution of the atmosphere may reveal any advanthe two layers. Thus, in the first representation, i.e., the case
tages in comparison
to
using
the
base
assumption
of
monowithforthe
maximum
aerosol
concentrations
at atground level,
Fig. 5. Aerosol size distributions retrieved considering more than one layer
principal
plane geometry
in the
case of urban aerosol
θs = 75◦ . Subfigure-a
the results
the investigated
case with aerosol concentration
profileassumption
median height atproviding
ground level,the
and best
subfigure-b
for was the one
layered atmosphere.
With thatcontains
purpose,
we for
first
the border
results
the case with the maximum at 3 km. Red and blue lines represent the cases for 2-layers and 5-layers respectively, being this layers equidistant
the effect of in
straightforward
reduction
of
vertical
resolution
located
at
2
km,
and
the
size
distributions
retrieved
deteriopressure and adding the description of the aerosol vertical profile. Gray lines represent the alternative solutions when the vertical profile
of multilayered
atmosphere
(assuming
correct
aerosol
profile
rated iswith
increase
thetheborder
is unknown:
solid line
when the border
between
the layers
aerosol-non aerosol
fixed the
at 2 km,
dash lineof
when
border isaltitude.
at 4 km andOn the other
dash-dotted
is at 6 km. of bilayered atmosphere
in the inversion).
Thewhen
assumption
hand, the case with the maximum aerosol concentrations at
substantially improves the results compared to monolayered
3 km showed the opposite tendency, and the results improved
atmosphere (shown
retrievals (shown
figure
4), specially
the
case
the aerosol
median
height
is at thealtitude.
ground level,
atmosphere retrievals
in Fig.in4),
withwhen
increase
of the
border
of layer
especially
forforthe
the aerosol
concentration
profile
median height
height is
the Previously,
errors are around
they shown
are diminishing
as the for the case
case in whichcase
thewhen
aerosol
concentration
profile
median
we20%,
havebutonly
the results
at 3-km where the errors are practically negligible. In the
number of◦ assumed layers is increased. For instance, if the
is at 3 km (where the errors are practically negligible). In the
θs = 75 , but the addition of a second layer improves the recase when the aerosol median height is at the ground level,
sults of θs = 45◦ as well. Thus, the maximum errors found in
the errors are around 20 %, but they diminish as the number
central radii diminish from 10 % to 5 % when the border is
situated at 4 km. Note that the selection of the border altitude
of assumed layers is increased. For instance, if the retrieval
between the layers is not an easy task. Apparently, the placeis provided with five layers, the errors are under 5 % for both
cases.
ment of border layer at around 4 km is an excellent compromise for the two examples presented here. Nevertheless, this
Nevertheless, the above tests were done using the known
height could be particularly chosen for each specific site, takvertical profile of aerosol, which generally is not known.
Therefore, in the second series of tests, we have focused
ing into the account several factors, for instance, the altitude
of site, or whether or not the surrounding area is a source of
on the evaluation of the possibility to use generic assumpaerosol, etc.
tion of bilayered atmosphere where the lower layer contains
525
530
www.atmos-chem-phys.net/14/847/2014/
Atmos. Chem. Phys., 14, 847–875, 2014
Fig. 4. Aerosol size distributions retrieved in the study of the influence on the aerosol vertical profiles. Using the aerosol properties of urban
(subfigure a) and desert dust (subfigure b), radiance measurements have been previously simulated for the two geometries, almucantar (solid
line) and principal plane (dashed line), considering 30 layers in the atmosphere. During the retrieving process, only one layer has been used
in the four analyzed cases: θs = 45◦ and vertical profile centered in the earth surface (red lines), θs = 45◦ and vertical profile centered at
B.centered
Torresin et
of aerosol
retrieval
to geometrical
configuration
h=3 km (pink lines), θs = 75◦ and vertical profile
the al.:
earth Sensitivity
surface (green lines),
θs = 75◦ and
vertical profile
centered at h=3 km
(blue lines).
856
a) Urban - Surface
b) Urban - 3 km
Reference Size Distribution
Reference Size Distribution
0.08
dV/dlnR (µ m3 / µ m2)
1 Layer
2 Layers
2
dV/dlnR (µ m / µ m )
0.08
5 Layers
0.06
3
New 2 Layers − 2km
New 2 Layers − 4km
New 2 Layers − 6km
0.04
0.02
0
0.1
1
3
1 Layer
2 Layers
5 Layers
0.06
New 2 Layers − 2km
New 2 Layers − 4km
New 2 Layers − 6km
0.04
0.02
0
10
Radius (µ m)
0.1
1
3
10
Radius (µ m)
Fig. 5. Aerosol size distributions retrieved considering more than one layer for principal plane geometry in the case of urban aerosol at
Fig. 5. Aerosol size distributions retrieved considering more than one layer for principal plane geometry in the case of urban aerosol at
θs = 75◦ . (a) Contains
the resultscontains
for thethecase
with
concentration
profile profile
median
height
at at
ground
andsubfigure-b
(b) for the
θs = 75◦ . Subfigure-a
results
for aerosol
the case with
aerosol concentration
median
height
ground level,
level, and
for case with the
maximum at 3 the
km.case
Red
and
linesatrepresent
theblue
cases
for
two layers
andforfive
layers,
(the layers
being
with
the blue
maximum
3 km. Red and
lines
represent
the cases
2-layers
and respectively
5-layers respectively,
being this
layersequidistant
equidistant in pressure),
in pressure
and aerosol
adding thevertical
description
of theknown
aerosol vertical
Gray lines
representGray
the alternative
solutions the
whenalternative
the vertical profile
with the description
of the
profile
duringprofile.
the retrieval
process.
lines represent
solutions when the
solid line when the border between the layers aerosol-non aerosol is fixed at 2 km, dash line when the border is at 4 km and
vertical profileisisunknown:
unknown:
solid line when the border between the layers aerosol–non aerosol is fixed at 2 km, dashed line when the border
dash-dotted when is at 6 km.
is at 4 km and dash-dotted when is at 6 km.
525
atmosphere retrievals (shown in figure 4), specially for the
when the
aerosol concentration
profile
height is
Finally, wecase
should
mention
the discussion
ofmedian
this section
at 3-km where the errors are practically negligible. In the
was focused on the retrieval of aerosol size distribution, because the retrieval of this property showed that it was the
most sensitive to the assumption regarding the vertical structure of the atmosphere. For the other optical parameters, the
results can be summarized by two basic observations. First,
neither the retrieval of single scattering albedo nor of the
imaginary part of the refractive index showed any sensitivity to the vertical variability of aerosol. Second, the retrieval
of the real part of the refractive index for fine mode does
show some sensitivity to the vertical variability of aerosol.
However, these deviations in real part of the refractive index
strongly anti-correlate with the fine mode aerosol concentration (the smaller refractive index, the larger the concentration) and this effect disappears under the same conditions
when the retrieval errors are diminished for the size distribution retrieval.
To illustrate both tendencies, we have represented, in Table 2 the optical parameters retrieved for the case that has
shown the greatest errors in the present study: urban aerosol
at θs = 75◦ with the aerosol vertical distribution with maximum at the surface. As noted previously, there are no differences for single scattering albedo and the imaginary part
of the refractive index, while differences up to 0.12 are observed for the real part. The maximum differences are observed when monolayered atmosphere model is employed in
the retrieval. When the aerosol vertical distribution is known,
the addition of layers reduces the error. Note that for five layers the differences are already in the third decimal.
For the cases without extra information about the aerosol
vertical profile, the strategy of the two layers described here
provides the same results as for the size distribution. In this
Atmos. Chem. Phys., 14, 847–875, 2014
530
case when the aerosol median height is at the ground level,
the
errors arecase,
around
20%, the
but border
they are is
diminishing
particular
when
situated asatthe
2 km
number of assumed layers is increased. For instance, if the
there are
almost no differences, and as the border becomes higher the
differences appear. Nevertheless, the proposed intermediate
solution of settling the border at 4 km still presents acceptable differences around 0.01 in the real part of the refractive
index.
Thus, overall the tests showed that for inversions of the
radiances measured in almucantar the vertical variability of
aerosol is not an issue, and assumption of monolayered atmosphere does not result in any notable retrieval errors. This
conclusion can also be extended to the aerosol retrieval from
principle plane with a unique exception of the observations
at the large solar zenith angles. At the same time, for the last
scenario, the retrieval errors can be practically eliminated by
assuming generic bilayered aerosol + Rayleigh/Rayleigh atmosphere. These conclusions support the retrieval settings
adapted for operational retrieval in the AERONET network:
the aerosol vertical distribution is assumed homogeneous
in the almucantar inversion and bilayered for the principal plane inversion. (http://aeronet.gsfc.nasa.gov/new_web/
Documents/Inversion_products_V2.pdf).
2.4
Dependence on the surface reflectance
The second aspect under discussion will be dependence
on the surface reflectance for both geometries. With this
purpose, we will introduce a random error in the surface reflectance during the inversion procedure in order
to study the effects on the retrievals. In its current version, AERONET Version 2, the inversion algorithm (described in Dubovik and King, 2000, and Dubovik et al.,
2006) approximates the surface reflectance by a bidirectional reflectance function (BDRF). The Cox–Munk model
www.atmos-chem-phys.net/14/847/2014/
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
857
Table 2. Retrieved aerosol optical parameters considering different numbers of atmosphere layers. The aerosol type considered is the urban
aerosol at θs = 75◦ with the aerosol vertical distribution with maximum at the surface.
440 nm
Reference
1 layer
2 layers
5 layers
2 layers, 2 km
2 layers, 4 km
2 layers, 6 km
670 nm
870 nm
1020 nm
n
k
ωo
n
k
ωo
n
k
ωo
n
k
ωo
1.410
1.519
1.439
1.411
1.410
1.422
1.440
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.977
0.977
0.977
0.976
0.976
0.977
0.978
1.410
1.494
1.431
1.411
1.410
1.419
1.433
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.969
0.970
0.969
0.968
0.968
0.969
0.970
1.410
1.487
1.428
1.411
1.411
1.418
1.431
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.960
0.961
0.960
0.959
0.959
0.960
0.961
1.410
1.484
1.427
1.412
1.411
1.418
1.431
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.954
0.955
0.953
0.952
0.952
0.953
0.954
is used for retrievals over water (Cox and Munk, 1954)
and the Lie–Ross model over land (Lucht and Roujean,
2000). This surface description is also currently used
in AERONET retrievals (http://aeronet.gsfc.nasa.gov/new_
web/Documents/Inversion_products_V2.pdf).
The BDRF parameters are basically three – fiso (λ),
fvol (λ) and fgeom (λ); they characterize the isotropic, volumetric, and geometric optics surface scattering, respectively
(Roujean et al., 1992, Wanner et al., 1995 and Litvinov
et al., 2011). In AERONET version 2 retrievals (Holben
et al., 2006, Eck et al., 2008), the land BDRF parameters
are adopted from MODIS Ecotype generic BDRF models
and mixed with the ecosystem map of Moody et al. (2005):
geographically and temporally varying (16 day averages
throughout the annual cycle) surface albedos are utilized.
These spectral surface albedos are midday black sky albedos
from Moody et al. (2005), and are based on atmospherically
corrected MODIS data averaged over a 5 km radius of each
AERONET site (see Eck et al., 2008; Sect. 2.3). The BDRF
model and parameters (for each ecosystem type) are used
to compute the spectral reflectances at solar zenith angles
throughout the day over a 5 km radius of each AERONET
site (see Eck et al., 2008; Sect. 2.3). The BDRF model and
parameters (for each ecosystem type) are used to compute
the spectral reflectances at solar zenith angles throughout the
day.
The following scheme is used for the tests: first radiances
are simulated (as in Fig. 2) with the typical BDRF parameters observed in the three sites (see Table 3). Subsequently,
the data are inverted for 200 different scenarios using BDRF
parameters perturbed by Gaussian noise. Specifically, the errors in fiso will be relative errors generated randomly from
a normal distribution with mean 0 and standard deviation of
15 %, with a limit of ±30 %. The errors in fvol and fgeom will
be absolute errors generated randomly, and with values of the
standard deviations of 0.05 and 0.025 respectively; the error
limits will be established as ±0.1 for fvol (with fvol > 0) and
0.05 for fgeom (with fvol , fgeom > 0). Note that we have considered a general case with random error even though the
BDRF model based on several ecosystem types could have
www.atmos-chem-phys.net/14/847/2014/
biases for different geographical locations and therefore bias
errors are likely to be significant in some conditions.
In the illustrations of the results, we focus on the analysis
of the cases (from Table 1) with the largest aerosol load for
the three aerosol types; as in the previous section, we will
only evaluate the cases at θs = 45◦ and θs = 75◦ .
Figures 6 and 7 depict the means and the standard deviations of the differences between the 200 retrievals and the
non-error case. The results are shown for principal plane
and almucantar geometry and for each aerosol type: biomass
burning (Zamb2, at the top), urban (GSFC2, in the middle)
and desert dust (SolV2, at the bottom). Relative differences
have been used for the analyses of the size distribution (figures in the left), while the differences in the optical parameters are provided in absolute terms.
Analyzing the outcomes, there are two results that stand
out from the rest. First, there is not a clearly defined tendency in the mean of the differences, as could be expected,
because in our analysis only random errors were considered.
In the size distribution, for instance, the means rarely exceed
10 % and their signs do not follow a clear pattern. In the optical parameters the means are also very small; in this way,
the maximum mean of the absolute difference for the single
scattering albedo is 0.003. Therefore, the analysis needs to
be carried out in terms of the standard deviation, which contains, in this case, the information about the dependency of
the retrieved products on a random error in the surface reflectance. Secondly, and from this new approach, it can be
seen that the error in the surface reflectance affects more at
θs = 45◦ than at θs = 75◦ . The last result is even more evident
for the principal plane geometry, as will be further discussed.
For instance, if we start the study with the size distribution,
while in the almucantar we observe a small improvement of
the results from θs = 45◦ to θs = 75◦ , the improvement in the
principal plane is considerably more obvious.
The highest values of the means and the standard deviations are observed for the fine mode for desert dust and urban aerosols at θs = 45◦ , as commented. For both cases, all
the standard deviations for radii smaller than 0.3 µm are over
10 %, reaching the maximum of 22 % at 0.07 µm in the desert
Atmos. Chem. Phys., 14, 847–875, 2014
858
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
12 of fiso (λ), fvol (λ) and fgeom (λ) used to approximates
Torres et al.: the
Sensitivity
aerosol retrieval
to geometricalreflectance
configuration
Table 3. Values
surfaceofreflectance
by a bidirectional
function (BDRF)
in the sites used in the simulations Mongu, Goddard and Solar Village.
Table 3. Values of fiso (λ), fvol (λ) and fgeom (λ) used to approximates the surface reflectance by a Bi-directional Reflectance Function
(BDRF) in the sites used in the440
simulations:
Mongu, Goddard and670
Solar
nm
nmVillage.
870 nm
1020 nm
fvol440 nm
fgeom
fiso
fvol
fgeom
Mongu (dry
season)
0.064 0.064
0.026
Mongu
(dry season)
0.026 0.010
0.010
Goddard (winter)
0.008 0.003
0.003
Goddard (winter)
0.032 0.032
0.008
0.074 0.024
0.024
Solar Village Solar Village0.161 0.161
0.074
Size Distribution
fiso
fiso
0.147
0.147
0.092
0.092
0.405
0.405
670fnm
vol
fvol
0.076
0.076
0.035
0.035
0.217
0.217
870 nm fvol
fgeom
fiso
fgeom
fiso
fvol
fgeom
0.0240.2740.274
0.024
0.173 0.173
0.029
0.011
0.234 0.234
0.033
0.0110.2090.209
0.057
0.272 0.272
0.037
0.0570.4450.445
SSA
Real Ref. Index
0.04
0.01
10
0
0
0.002
0
0
−0.02
−0.01
20
10
0
−10
−20
20
−0.002
−0.04
0.04
0.01
0.002
0.02
0
0
0
−0.02
−0.002
−0.01
−0.04
0.04
0.01
0.002
10
0.02
0
0
0
−10
−0.02
−0.01
−20
0.1
0.3
1
3
10
Radius (µ m)
0.033
0.032
0.040
Urban
Absolute differences
−20
fgeom
Imag. Ref. Index
0.02
−10
Relative differences [%]
fvol
fiso
fvol
fgeom
0.029
0.3110.0330.196
0.311 0.196
0.232 0.227
0.033
0.2320.0320.227
0.479 0.293
0.037
0.4790.0400.293
−0.04
0
θs = 45°
−0.002
Almucantar
Desert Dust
20
fgeom 1020fnm
iso
Biomass Burning
fiso
Pr. Plane
440 670 870 1020
440 670 870 1020
440 670 870 1020
Wavelength [nm]
Wavelength [nm]
Wavelength [nm]
Fig. 6. Means
and the standard deviations of the differences between the 200 retrievals, where Gaussian errors are introduced in the BDRF
Fig. 6. Means and the standard deviations ◦of the differences between the 200 retrievals, where gaussian errors are introduced in the BDRF
◦
parameters, parameters,
and the non-error
case atcase
θs at=θ45
. Figures
at the top correspond to biomass burning aerosol, in the middle to urban aerosol,
and the non-error
s = 45 . Figures at the top correspond to biomass burning aerosol, in the middle to urban aerosol
and at the bottom
to bottom
deserttodust
aerosol.
Relative
differences
usedforfor
analyses
size distribution
(figures
in the
and at the
desert
dust aerosol.
Relative
differences are
are used
thethe
analyses
of the of
sizethe
distribution
(figures in the
left), while
the left), while the
differences
in theparameters
optical parameters
are provided
in absolute terms.
terms. Results
areare
shown
for almucantar
(gray-color)
and and
for principal
plane plane (black)
differences in
the optical
are provided
in absolute
Results
shown
for almucantar
(gray)
for principal
geometry. (black-color).
the standard deviation about 12%.
dust. For larger radii, both the means and the standard deviaAs mentioned above, the retrieval results are more accutions of720therate
differences
are reduced (the latter rarely exceeds
at θs = 75◦ . The means of the differences are smaller
5 % when the
radii
are
larger
the burning.
only exception
than 5% in the urban than
and in0.3
theµm);
biomass
For the 730
is the relative
theprincipal
principal
plane
desertlarge
dust, values
there areobserved
some valuesfor
of the
plane
rein the than
fine mode
andOn
some
of hand,
the almucantar
when radiitrievals
are larger
5 µm.
thevalues
other
the reretrievals in the coarse mode which are larger that the 5%.
sults for725 biomass
burning do not depend on the radii. In this
In fact, the results for the almucantar retrieval of the coarse
case, the maximum values of the means are around 8 % and
the standard deviation is about 12 %.
As mentioned above, the retrieval results are more accurate
at θs = 75◦ . The means of the differences are smaller than
5 % in the urban and in the biomass burning. For the desert
dust, there are some values of the principal plane retrievals
in the fine mode and some values of the almucantar retrievals
in the coarse mode which are larger that the 5 %. In fact, the
Atmos. Chem. Phys., 14, 847–875, 2014
mode are worse than at θs = 45◦.
results for the almucantar retrieval of the coarse mode are
In the single scattering albedo the means
worse
than they are at θs =
45◦ . of the differences
are smaller than 0.003 for all the
simulations. The standard
In thearesingle
albedo
means
the differences
deviations
similarscattering
for the three
aerosolthe
cases
beingofthe
◦
are smaller
0.003
all the
maximum
valuesthan
around
0.013,for
reached
at θsimulations.
s = 45 . It can The standard
bedeviations
also observed,
thatsimilar
the principal
plane
valuesaerosol
are slightly
are
for the
three
cases, being the
higher than the almucantar ones. Following the general outmaximum values around 0.013,
reached at θs = 45◦ . It can
◦
come, the results are better at θs = 75 with maximum of the
be also observed that the principal plane values are slightly
higher than the almucantar ones. Following the general outcome, the results are better at θs = 75◦ , with the maximum
of the standard deviations being 0.008. The improvement is
more notorious in the principal plane resulting in lower values of the standard deviations than almucantar at this solar
zenith angle.
A similar result is found for the refractive index; at θs =
45◦ , the results for almucantar retrieval are better, while at
www.atmos-chem-phys.net/14/847/2014/
Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
13
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
SSA
0.04
0.01
10
0.002
0.02
0
0
0
−10
0
−0.02
−0.01
20
10
0
−10
−20
20
−0.002
−0.04
0.04
0.01
0.002
0.02
0
0
Urban
Absolute differences
−20
Relative differences [%]
Imag. Ref. Index
0
−0.02
−0.002
−0.01
−0.04
0.04
0.01
0.002
10
0.02
0
0
0
−10
−0.02
−0.01
−20
0.1
0.3
1
3
10
Radius (µ m)
−0.04
0
θs = 75°
Almucantar
−0.002
Desert Dust
20
Real Ref. Index
Biomass Burning
Size Distribution
859
Pr. Plane
440 670 870 1020
440 670 870 1020
440 670 870 1020
Wavelength [nm]
Wavelength [nm]
Wavelength [nm]
Fig. 7. Means and standard deviations of the differences between the 200 retrievals, where Gaussian errors are introduced in the BDRF
Fig. 7. Means and the standard deviations of
the differences between the 200 retrievals, where gaussian errors are introduced in the BDRF
parameters, parameters,
and the non-error
case at θ = 75◦ . Figures at the top correspond to biomass burning aerosol, those in the middle to urban
and the non-error case sat θs = 75◦ . Figures at the top correspond to biomass burning aerosol, in the middle to urban aerosol
aerosol, andand
those
the bottom
desert
dust
aerosol.
Relative
differences
are used
for
the
analyses(figures
of theinsize
distribution
at theatbottom
to deserttodust
aerosol.
Relative
differences
are used
for the analyses
of the
size
distribution
the left),
while the (figures in the
differences
in the optical
are providedare
in absolute
terms.
Results areterms.
shown Results
for almucantar
(gray-color)
and for principal
plane
left), while the
differences
in the parameters
optical parameters
provided
in absolute
are shown
for almucantar
(gray)
and for principal
plane (black)(black-color).
geometry.
735
standard deviations 0.008. The improvement is more noto-
θs = 75◦ they
notprincipal
as good
asresulting
the principal
plane ofones.
riousare
in the
plane
in lower values
the
deviations
than almucantar
at this solar
zenith an-is755
For the realstandard
part, the
maximum
of the standard
deviation
gle.
around 0.03
at θs = 45◦ (reached in principal plane geomeSimilar result is found for the refractive index: at θs = 45◦ ,
try) and740around
0.02for(reached
inretrieval
almucantar
geometry).
the results
almucantar
are better,
while at θs =
◦
For the 75
imaginary
part,
the as
biomass
burning
case For
shows
they are not
as good
the principal
plane ones.
the
real part,
the maximum
the standard
deviation
larger standard
deviations
thanofthe
other two
cases,is around
due to
◦
0.03 at θs = 45The
(reached
in principal
its larger absorption.
maxima
at θs =plane
45◦ geometry)
and at θand
s=
760
around 0.02 (reached in almucantar geometry).
◦
75 are745reached
for
this
aerosol
type,
with
values
0.0028
and
For the imaginary part, the biomass burning case shows
0.0015, respectively.
Fordeviations
urban and
dust,
standard
larger standard
thandesert
the other
two the
cases,
due to
◦
its larger
absorption.
The maxima
θs = 45
and angles.
at θs =
deviations are
smaller
than 0.001
for bothat solar
zenith
75◦ arethe
reached
for this aerosol
with values
0.0028
In summary,
introduction
of type,
a random
noise
in and
the
0.0015 respectively. For urban and desert dust, the standard
BDRF 750
parameters
affects
all
the
analyzed
aerosol
properties
deviations
are smaller than 0.001 for both solar zenith angles.
◦ than at θ = 75◦ . This is more evident in the
more at θs = In
45summary,
s introduction of a random noise in the
the
case of theBDRF
principal
planeaffects
geometry,
parameters
more at which
θs = 45◦presents
than at θshigher
= 75◦ 765
◦
differences at θs = 45 than the almucantar geometry, while
at θs = 75◦ the differences are similar for both geometries
(even slightly smaller for the principal plane geometry).
2.5
Dependence on the pointing error
The pointing error is defined as the angle between the Sun
position (correct pointing) and the erroneous pointing direction. As sun photometers are moved by two motors, azimuth
and zenith axes, the value of the pointing error, 2ξ , is norwww.atmos-chem-phys.net/14/847/2014/
for all the analyzed aerosol properties. This is more evident
spherical
formally
the casegiven
of the in
principal
plane,coordinates:
which presents higher differences at θs = 45◦ than the almucantar geometry, while at
◦
θs 2
= ξ75=
the
2ξdifferences
(ξϕ , ξθ ), are similar for both geometries being even slightly smaller for the principal plane.
(8)
where ξϕ and ξθ are the error components in azimuth and
zenith angles, respectively. Assuming that the pointing errorpointing
is sufficiently
small,
it can
bebetween
expressed
as an infinitesiThe
error is defined
as the
angle
the Sun
position
(correct pointing)
the erroneous
pointing direcmal displacement
inand
spherical
coordinates
(with dr = 0) and
tion.
As sun-photometers
are in
moved
motors,
therefore
the relation
Eq. by
(8)two
takes
theazimuth
following form:
and zenith axes, the value of the pointing error, Θξ , is norq
mally given in spherical coordinates:
(9)
2ξ = ξθ θ̂ + sin θs ξϕ ϕ̂ = ξθ2 + sin θs 2 ξϕ2 .
2.5 Dependence on the pointing error
Θξ = Θξ (ξϕ ,ξθ )
(8)
The work by Torres et al. (2013) (also in Torres, 2012) dewhere
ξϕ aand
ξθ are the errorused
components
azimuth and
scribes
methodology
for theincharacterization
of these
zenith angles respectively. Considering the pointing error
magnitudes and a first evaluation of the results for several
individual instruments (all of them Cimel 318 sun photometers). One of the main outcomes of this evaluation is that the
magnitudes ξθ and sin θs ξϕ are constant for each photometer,
regardless of θs . This result indicates that the pointing error,
2ξ , can be understood as the scattering angle between the
Sun beam and the direction in which the detector (in charge
of the Sun pointing-process in the instrument) is pointing,
which is constant through the day. In the present work, the
characteristic magnitudes 2ξθ = ξθ and 2ξϕ = sin θs ξϕ , will
be called the total vertical and horizontal error, respectively,
keeping the names zenith and azimuth error for ξθ and ξϕ ,
Atmos. Chem. Phys., 14, 847–875, 2014
860
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
respectively. The first tests on this topic, done with seven
photometers in the work by Torres et al. (2013), showed that
for most of the instruments the magnitudes of ξθ and sin θs ξϕ
were smaller than 0.1◦ . The maximum values obtained for
vertical and horizontal error were 0.25◦ , while the maximum
of the total error, 2ξ , was 0.3◦ .
The scheme for this study is similar to the one presented
in Fig. 2, but introduces the pointing errors in the forward
code. The value of the simulated pointing error will be 0.4◦
(horizontal and vertical) as it is the maximum realistic error
that can be committed without affecting the aerosol optical
depth and therefore not noticeable in the data obtained from
AERONET network (the value of the field of view is around
1.2◦ in the standard sun photometers of the network). Note
that in the work by Torres (2012), the retrieval errors for 0.2◦
and 1◦ are also analyzed; one of the most important results
obtained in that study is that differences in the retrievals can
be neglected in the case of 0.2◦ , which means that the typical
pointing errors (under 0.1◦ ) do not have any significant influence in AERONET retrievals. The results obtained for the
case of 1◦ are also depicted in Torres (2012), and they were
not included in the present study as they do not represent a
realistic error. Here, the value of 0.4◦ will be considered for
positive or negative errors in the vertical component and only
positive errors in the horizontal component.
The vertical error can be committed from the Sun towards
the zenith or towards the Earth surface; these two possibilities result in different consequences in almucantar and principal plane measurements, and therefore both of them should
be considered. In this study, the sign of the error is established as positive in the case of variation towards the zenith,
and negative in the case of variation towards the Earth surface. The horizontal error can be committed either to the left
or to the right of the Sun. In the principal plane, regardless of
the error direction, the consequences are symmetric. In the
almucantar, the errors are initially not symmetric, but due to
the possibility of averaging the left and right branches (as it
is done operationally in AERONET), they become symmetric. As a consequence, for both geometries, there is no need
to consider the sign of the horizontal error and only the absolute value is relevant. Note also that the averaging process
produces that in the almucantar the horizontal error effect is
much weaker than in the principal plane.
The results of the simulations of the pointing error test
are presented in Fig. 8 for the size distribution, in Fig. 9 for
the single scattering albedo, and in Fig. 10 for the refractive
index. In each figure, the results are depicted for the three
aerosol types considered: biomass burning aerosol (subfigure a), urban aerosol (subfigure b) and desert dust aerosol
(subfigure c). For each aerosol type, results retrieved with
the almucantar geometry are shown in the upper part, while
results from simulations with the principal plane are placed
at the bottom. The subfigures on the left correspond to retrievals with vertical errors (positive and negative), and the
ones on the right to horizontal errors (only positive). Note
Atmos. Chem. Phys., 14, 847–875, 2014
that the x axis is the radius for the size distribution and different colors represent different solar zenith angle; for the
optical parameters the x axis is precisely the solar zenith angle and the colors distinguish between the wavelengths.
Analyzing Fig. 8, the first thing we observe is that there
are only remarkable differences with respect to the results
obtained in Fig. 3 for the cases involving principal plane and
vertical errors; i.e., there are no differences in the almucantar
regardless of the error pointing type, nor are there differences
in the principal plane with horizontal error.
Centering the study on the case with vertical errors in PPL,
the aerosol type showing the largest differences is desert dust,
where for the case with a positive vertical error there is a
10 % decrease in the size distributions between 1 µm and
3 µm and a little increment around 4–5 % for larger radii.
With negative vertical error, the situation is the opposite;
there is a big increase (up to 15–20 %) for radii between 1 µm
and 3 µm, accompanied by a significant reduction for larger
radii.
In the other two aerosol cases, and especially for urban
aerosol, we can see the behavior of the fine mode, which is
opposite to that of the coarse mode: it grows for positive errors and decreases for negative errors. To be more precise, the
perturbations are only observed for radii smaller than 0.3 µm,
and in general, they are smaller than the ones found in the
coarse mode. Moreover, the differences between the results
found here and the ones obtained in Sect. 2.2 depend on θs
and on the aerosol load being larger as both parameters are
smaller. The values of these differences are normally under
20 %. However, the maximum values are around 50 %, and
they are found for the urban case at θs = 15◦ with the lowest
aerosol load and at radii between 0.05 and 0.2 µm.
To explain these results, we need to check the differences
in the radiance measurements that the pointing errors generate. For this purpose, radiance relative differences are represented in Fig. 11 – for vertical errors in almucantar and principal plane in the upper part, and for horizontal errors in the
subfigures at the bottom. We have only taken the differences
for GSFC aerosol not to be repetitive, as there are no relevant
differences respect to the other aerosol types. Note also that
the differences are plotted against the scattering angle and at
different θs (from left to the right at 15◦ , 45◦ and 75◦ ).
The relative differences generated by vertical errors in the
principal plane (see Fig. 11) are five times larger than the
ones originated in the almucantar and a magnitude order
larger than the differences generated by horizontal errors in
both geometries. This fact explains why the largest differences found in Fig. 8 are for vertical errors in principal plane
geometry. We also observe that the results for positive and
negative vertical errors are symmetric in the principal plane
(not in the almucantar). These differences are positive for
small scattering angles when the errors are negative, and they
are negative for positive errors. At large scattering angles the
relation is the opposite: positive for positive errors and negative for negative errors.
www.atmos-chem-phys.net/14/847/2014/
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
861
Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
15
a) Mongu - Biomass burning
ALM
Point. Err.:
Ver. = 0.4o
Hor. = 0.0 o
ALM
Point. Err.:
Ver. = −0.4 o
Hor. = 0.0 o
PPL
Point. Err.:
Ver. = 0.4o
Hor. = 0.0 o
Zambia: τ = 0.4
PPL
Point. Err.:
Ver. = −0.4 o
Hor. = 0.0 o
dV/dlnR (µ m3 / µ m2)
0.12
ALM
Point. Err.:
Ver. = 0.0o
Hor. = 0.4 o
0.08
0.04
0
0.12
0.08
o
SZA=15
o
SZA=30
SZA=45o
o
SZA=60
SZA=75o
PPL
Point. Err.:
Ver. = 0.0o
Hor. = 0.4 o
440
Zambia: τ440 = 0.8
0.04
0
0.1
1
3
10
0.1
1
3
10
0.1
1
3
10
Radius (µ m)
b) GSFC - Urban
ALM
Point. Err.:
o
Ver. = 0.4
o
Hor. = 0.0
ALM
Point. Err.:
o
Ver. = −0.4
o
Hor. = 0.0
PPL
Point. Err.:
Ver. = 0.4o
Hor. = 0.0 o
GFSC: τ440 = 0.2
PPL
Point. Err.:
Ver. = −0.4 o
Hor. = 0.0 o
dV/dlnR (µ m3 / µ m2)
0.12
0.09
ALM
Point. Err.:
o
Ver. = 0.0
o
Hor. = 0.4
0.06
0.03
0
0.12
0.09
0.06
o
SZA=15
SZA=30o
o
SZA=45
SZA=60o
o
SZA=75
PPL
Point. Err.:
Ver. = 0.0o
Hor. = 0.4 o
GSFC: τ440 = 0.5
0.03
0
0.1
1
3
10
0.1
1
3
10
0.1
1
3
10
1
3
10
Radius (µ m)
c) Solar Village - Desert Dust
dV/dlnR (µ m3 / µ m2)
0.40
0.30
ALM
Point. Err.:
o
Ver. = 0.4
o
Hor. = 0.0
ALM
Point. Err.:
o
Ver. = −0.4
o
Hor. = 0.0
ALM
Point. Err.:
o
Ver. = 0.0
o
Hor. = 0.4
PPL
Point. Err.:
o
Ver. = 0.4
o
Hor. = 0.0
Sol.V: τ1020 = 0.3
PPL
Point. Err.:
o
Ver. = −0.4
o
Hor. = 0.0
PPL
Point. Err.:
o
Ver. = 0.0
o
Hor. = 0.4
0.20
0.10
0
0.40
0.30
0.20
o
SZA=15
o
SZA=30
o
SZA=45
SZA=60o
SZA=75o
Sol.V: τ1020 = 0.5
0.10
0
0.1
1
3
10
0.1
1
3
10
0.1
Radius (µ m)
Fig. 8. Retrieved size distributions after simulating a pointing error of 0.4◦ in
three different aerosol types: biomass burning aerosol (a), urban
Fig. 8. Retrieved size distributions after simulating a pointing error of 0.4◦ in three different aerosol types: biomass burning aerosol (subfigure
aerosol (b) and desert
dustaerosol
aerosol
(c) with
twodesert
different
AODs
as references
each AOD
case as(solid
lineinused
for (solid
the case
with
aerosol
a), urban
(subfigure
b) and
dust aerosol
(subfigure
c) with twoin
different
reference
each case
line used
forsmallest
the
load and dashed line
forwith
thesmallest
largest).
In load
eachandofdashed
the figures,
the
subfigures
thefigures,
top show
results
from
and those
case
aerosol
line for the
largest).
In each at
of the
subfigures
on top
showalmucantars
results from almucantars
andat the bottom
at theSubfigures
bottom from principal
Subfigures onto
theretrievals
left correspond
to retrievals
verticaland
errors,
and on
right,
to horizontal
errors. to horizontal
from principal planes.
on the planes.
left correspond
with
verticalwith
errors,
those
onthethe
right
correspond
◦
Colors indicate the solar zenith angle: dark blue for θs = 15◦ , light
blue for θs = 30◦ , green for θ◦s = 45◦ , orange for θs = 60
and brown for
◦
◦
errors. Colors indicate
the solar zenith angle: dark blue for θs = 15 , light blue for θs = 30 , green for θs = 45 , orange for θs = 60◦ and
θs = 75◦ while black is used for the original size distributions.
◦
brown for θs = 75 , while black is used for the original size distributions.
The coarse mode of the size distribution is more connected
to small scattering angles, while the information about fine
particles is more equally distributed. An increase of radiation for small scattering angle is interpreted by the inversion
code as an increase of the coarse mode, while an increase in
the backscattered radiation is interpreted as an enlargement
of the fine mode. Therefore, when the vertical errors in principal plane geometry are positive, there is decrease in the
radiance at small scattering angles and an increase at large
scattering angles which is the cause of the observed decrease
in the coarse mode and increase in the fine mode. The negative errors generate opposite effects in the radiance, which
www.atmos-chem-phys.net/14/847/2014/
creates the contrary effect in the size distribution to the one
we observed in Fig. 8.
The next step in the study is the analysis of the differences
in the ωo and in the refractive index. As we commented in
the Sect. 2.2, the optical properties are connected to all the
scattering angles. Single scattering albedo and imaginary refractive index are closely related. Moreover, since our simulations keep the aerosol optical depth constant, an increase
of radiance will mean more scattering compared to the absorption and therefore, ωo will rise while the imaginary part
of refractive index will fall. The opposite situation will occur for less radiance: ωo will decrease due to the reduction of
Atmos. Chem. Phys., 14, 847–875, 2014
862
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
16
Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
a) Mongu - Biomass burning
Single Scatering Albedo
1
0.92
ALM − Point. Err.:
Ver. = 0.4o
Hor. = 0.0 o
ALM − Point. Err.:
Ver. = −0.4o
Hor. = 0.0 o
ALM − Point. Err.:
Ver. = 0.0o
Hor. = 0.4 o
PPL − Point. Err.:
Ver. = −0.4o
Hor. = 0.0 o
PPL − Point. Err.:
Ver. = 0.0o
Hor. = 0.4 o
0.84
0.76
1 15
30Err.: 45
PPL − Point.
0.92
Ver. = 0.4o
Hor. = 0.0 o
60 τ440 =75
Zambia:
0.4
Zambia: τ440 = 0.8
440 nm
670 nm
870 nm
1020 nm
0.84
0.76
15
30
45
60
75
15
30
45
60
75
15
30
45
60
75
Solar Zenith Angle [°]
b) GSFC - Urban
Single Scatering Albedo
1
0.95
0.9
ALM
Point. Err.:
Ver. = 0.4o
Hor. = 0.0 o
1 15
ALM
Point. Err.:
Ver. = −0.4 o
Hor. = 0.0 o
30
45
60
ALM
Point. Err.:
Ver. = 0.0o
Hor. = 0.4 o
75
0.95
0.9
PPL
Point. Err.:
o
Ver. = 0.4
o
Hor. = 0.0
15
PPL
Point. Err.:
o
Ver. = −0.4
o
Hor. = 0.0
GFSC: τ440 = 0.2
GSFC: τ440 = 0.5
30
45
60
75
15
30
440 nm
670 nm
870 nm
1020 nm
PPL
Point. Err.:
o
Ver. = 0.0
o
Hor. = 0.4
45
60
75
15
30
45
60
75
Solar Zenith Angle [°]
c) Solar Village - Desert Dust
Single Scatering Albedo
1
0.95
ALM
Point. Err.:
Ver. = 0.4o
Hor. = 0.0 o
0.9
1 15
30
45
60
ALM
Point. Err.:
Ver. = −0.4 o
Hor. = 0.0 o
ALM
Point. Err.:
Ver. = 0.0o
Hor. = 0.4 o
75
0.95
0.9
Sol.V: τ1020 = 0.3
Sol.V: τ1020 = 0.5
15
30
45
PPL
Point. Err.:
o
Ver. = 0.4
o
Hor. = 0.0
60
75
440 nm
670 nm
870 nm
1020 nm
PPL
Point. Err.:
o
Ver. = −0.4
o
Hor. = 0.0
15
30
45
60
75
15
30
PPL
Point. Err.:
o
Ver. = 0.0
o
Hor. = 0.4
45
60
75
Solar Zenith Angle [°]
Fig. 9. Retrieved single scattering albedo after simulating a pointing error of 0.4◦◦ in three different aerosol types: biomass burning aerosol
Fig. 9. Retrieved single scattering albedo after simulating a pointing error of 0.4 in three different aerosol types: biomass burning aerosol
(a), urban aerosol (b)
and desert
dust
aerosol
(c) with
AOD
as reference
each case
line inused
case
(subfigure
a), urban
aerosol
(subfigure
b) andtwo
desertdifferent
dust aerosol
(subfigure
c) with twoindifferent
AOD (solid
as reference
eachfor
casethe
(solid
linewith smallest
aerosol load and dashed
for the
In each
figures,
subfigures
from almucantars
atfrom
the bottom from
used forline
the case
with largest).
smallest aerosol
loadof
andthe
dashed
line for
the largest).onIntop
eachshow
of the results
figures, subfigures
on top show and
results
almucantars on
and the
at theleft
bottom
from principal
planes. Subfigures
on the lefterrors,
correspond
retrievals
with vertical
errors, anderrors.
on the right,
to indicate the
principal planes. Subfigures
correspond
to retrievals
with vertical
andtoon
the right,
to horizontal
Colors
horizontal errors. Colors indicate the wavelength: blue for 440 nm, green for 670 nm, yellow for 870 nm and red for 1020 nm.
wavelength: blue for 440 nm, green for 670 nm, yellow for 870 nm and red for 1020 nm.
izontal errors in the subfigures at the bottom. We have only 875
for GSFC
aerosolindex
not to be
repetitive
the scattered lighttaken
andthe
thedifferences
imaginary
refractive
will
rise as
because of a larger absorption. The real part of the refractive
index is more connected with the shape of the radiance. High
values of radiance for small scattering angles and low values
for large angles are related to low values of the real refractive index. The opposite situation will mean high values in
the real refractive index.
Referring back to Fig. 11, the radiance differences in the
principal plane produced by positive vertical pointing errors
are mostly negative, especially for small scattering angles.
Based on this, we can expect the single scattering albedo
to decrease and the imaginary part of refractive index to in-
Atmos. Chem. Phys., 14, 847–875, 2014
there are no relevant differences respect to the other aerosol
types. Note
also that the differences
are plot against the
crease.
Expectancies
for the consequences
ofscatnegative errors
are just the opposite. Taking a quick look at Figs. 9 and 10 we
see that our expectations were correct: Fig. 9 shows that ωo
drops for positive errors and grows for negative errors. Here,
it is interesting to note that these variations are greater for the
case with less aerosol load in the three examples; in the same
manner, the differences are smaller as the aerosol is more absorptive. Maximum differences of 0.02 are found for desert
dust while the minimum differences, which are smaller than
0.01, are reached in the biomass burning.
The presence of positive vertical error in the principal
plane geometry diminishes the radiance at small scattering
www.atmos-chem-phys.net/14/847/2014/
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
863
Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
17
ALM
Point. Err.:
o
Ver. = 0.0
Hor. = 0.4 o
1.55
1.50
1.45
1.40
ALM
Point. Err.:
o
Ver. = 0.4
o
Hor. = 0.0
15
75
0.015
PPL
Point. Err.:
o
Ver. = 0.4
o
Hor. = 0.0
1.55
1.50
PPL
Point. Err.:
o
Ver. = −0.4
o
Hor. = 0.0
PPL
Point. Err.:
o
Ver. = 0.0
o
Hor. = 0.4
440 nm
670 nm
870 nm
1020 nm
1.45
Zambia: τ
= 0.4
Zambia: τ
= 0.8
440
1.40
440
15
45
75
15
45
75
15
45
0.025
0.02
ALM
Point. Err.:
o
Ver. = −0.4
o
Hor. = 0.0
45
0.03
75
15
45
75
15
45
75
0.03
0.025
0.02
0.015
15
45
Imag. Part of the Refractive Index
Real Part of the Refractive Index
a) Mongu - Biomass burning
75
Solar Zenith Angle [°]
ALM
Point. Err.:
o
Ver. = 0.4
o
Hor. = 0.0
ALM
Point. Err.:
o
Ver. = −0.4
o
Hor. = 0.0
ALM
Point. Err.:
o
Ver. = 0.0
o
Hor. = 0.4
0.009
0.006
1.4
0.003
1.3
PPL 45
1.5 15
75
Point. Err.:
Ver. = 0.4o
Hor. = 0.0 o
GFSC: τ
440
0
= 0.2
PPL
Point. Err.:
Ver. = −0.4 o
Hor. = 0.0 o
GSFC: τ440 = 0.5
440 nm
670 nm
870 nm
1020 nm
PPL
Point. Err.:
Ver. = 0.0o
Hor. = 0.4 o
1.4
0.009
0.006
0.003
1.3
15
45
75
15
45
75
15
45
75
15
45
75
15
45
75
15
45
75
0
Imag. Part of the Refractive Index
Real Part of the Refractive Index
b) GSFC - Urban
1.5
Solar Zenith Angle [°]
ALM
Point. Err.:
o
Ver. = 0.4
o
Hor. = 0.0
ALM
Point. Err.:
o
Ver. = −0.4
o
Hor. = 0.0
ALM
Point. Err.:
o
Ver. = 0.0
o
Hor. = 0.4
1.5
0.009
0.006
0.003
1.4
1.6 15
1.5
45
0
75
PPL
Point. Err.:
o
Ver. = −0.4
o
Hor. = 0.0
PPL
Point. Err.:
Ver. = 0.4o
Hor. = 0.0 o
PPL
Point. Err.:
o
Ver. = 0.0
o
Hor. = 0.4
440 nm
670 nm
870 nm
1020 nm
Sol.V: τ1020 = 0.3
1.4
Sol.V: τ1020 = 0.5
15
45
75
15
45
75
15
45
75
15
45
75
15
45
0.009
0.006
0.003
75
15
45
75
0
Imag. Part of the Refractive Index
Real Part of the Refractive Index
c) Solar Village - Desert Dust
1.6
Solar Zenith Angle [°]
◦
Fig. 10. Retrieved Fig.
refractive
index
afterindex
simulating
a pointing
error
of◦ in
0.4
threeaerosol
different
aerosol
types:
biomass
10. Retrieved
refractive
after simulating
a pointing error
of 0.4
threein
different
types: biomass
burning
aerosol
(subfigureburning aerosol (a),
urban aerosol (b) and
desert
dust
aerosol
(c)desert
with
different
inaseach
case
(solid
for
a), urban
aerosol
(subfigure
b) and
dusttwo
aerosol
(subfigureAOD
c) with as
tworeference
different AOD
reference
in each
case line
(solid used
line used
forthe
the case with smallest
case with
smallest
aerosol
load and In
dashed
lineof
forthe
the largest).
In each
of the figures,
subfigures
top showfrom
results almucantars
from almucantarsand
and at the bottom from
aerosol load and dashed
line
for the
largest).
each
figures,
subfigures
on top
showonresults
at the bottom from principal planes. Subfigures on the left correspond to retrievals with vertical errors, and on the right, to horizontal errors.
principal planes. Subfigures
onthe
thewavelength:
left correspond
tonm,
retrievals
vertical
errors,
and
right,
to Y-Axes
horizontal
Colors indicate
blue for 440
green for with
670 nm,
yellow for
870 nm
andon
redthe
for 1020
nm.
expresserrors.
the real Colors indicate the
refractive
indexgreen
(on the for
left) 670
and the
imaginary
refractive
index
(onand
the right)
wavelength: blue for
440 nm,
nm,
yellow
for 870
nm
red for 1020 nm. The y axes express the real refractive index (on the
left) and the imaginary refractive index (on the right).
angles, while at the other angles, there is no variation. For
negative errors we observe the opposite result. Due to this
fact, the real part of refractive index is expected to enlarge
(or to shrink for negative) to a great extent. And this is exactly what it is found to do in the desert dust example where
the real part rises from 1.56 to the highest value (1.6) allowed
by the inversion process in all the channels. For the negative
error, it falls to values between 1.49 and 1.52, varying with
the channel and the θs .
However, for the other two aerosol types, the real part of
the refractive index decreases for a positive error, which is
contrary the previous argument. It should be remembered
that this idea was used successfully in the desert dust case
and, as the radiance differences in all the cases present the
www.atmos-chem-phys.net/14/847/2014/
same behavior, apparently there is no immediate explanation
for the different behavior. A possible explanation could be
obtained by analyzing the size distributions; in the desert dust
case for positive vertical errors, the retrievals from principal
planes gave a decrease of the coarse mode and no variations
in the fine mode. More light for longer scattering angle with
less particles could be only explained with a strong increase
in the real refractive index. But for urban and biomass burning examples, the fine mode increases for vertical pointing
errors. In this second scenario, if the increment of the particles is very strong, even in the case of more light, the real
refractive index can drop even more if we consider the strong
connection between real part of refractive index and the fine
Atmos. Chem. Phys., 14, 847–875, 2014
864
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
18
Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
Radiance relative differences [%/(°)]
Almucantar measurements with positive vertical error
4
2
0
−2
−4
Almucantar measurements with negative vertical error
4
2
GFSC: τ
440 nm
670 nm
870 nm
1020 nm
440
= 0.2
GSFC: τ440 = 0.5
0
−2
−4
0
SZA=15°
10
20
30
SZA=45°
0
30
60
90
SZA=75°
0
50
100
50
100
50
100
150
Scattering Angle [°]
Radiance relative differences [%/(°)]
Pr. Plane measurements with positive vertical error
−15
10
5
0
−5
−10
−15
440 nm
670 nm
870 nm
1020 nm
GFSC: τ
= 0.2
GSFC: τ
= 0.5
440
440
Pr. Plane measurements with negative vertical error
−15
10
5
0
−5
−10
−15
0
SZA=15°
30
60
90
SZA=45°
0
30
60
90
120
SZA=75°
0
150
Scattering Angle [°]
Radiance relative differences [%/(°)]
Almucantar measurements with horizontal error
5
2.5
0
−2.5
−5
Pr. Plane measurements with horizontal error
1
0.5
440 nm
670 nm
870 nm
1020 nm
GFSC: τ
= 0.2
GSFC: τ
= 0.5
440
440
0
−0.5
SZA=15°
−1
0
30
60
90
SZA=45°
0
30
60
90
120
SZA=75°
0
150
Scattering Angle [°]
Fig. 11. Radiance relative differences obtained simulating a pointing error of 0.4◦◦ . GSFC aerosol was taken as example using two different
Fig. 11. Radiance relative differences obtained simulating a pointing error of 0.4 . GSFC aerosol was taken as example using two different
AOD: τ440 = 0.2 (solid
and τ440line)
= 0.5
line). Figures in the upper part correspond to vertical errors for almucantar and principal
AOD: τline)
and τ(dashed
440 = 0.2 (solid
440 = 0.5 (dashed line). Figures in the upper part correspond to vertical errors for almucantar and principal
plane due
(4 subfigures
to double sign).
On On
the bottom,
the effects
horizontalof
errors
are represented.
to right, θs increases
plane (four subfigures
to the due
plus/minus
sign).
the bottom,
theof effects
horizontal
errorsFrom
are left
represented.
From for
left to right, θs
the different
figures.
increases for the different
figures.
mode of the size distribution, commented on in previous sections.
There are two ideas supporting this argument. First, the
variation of the real part is minor for the 1020 nm channel,
but it becomes greater as the wavelength is shortened, as
short wavelengths are more affected by the fine mode particles. Needless to say, for negative errors the explanation
above is valid, but changes the sign of the variations. The second proof is that the real part is more stable for the biomass
burning example (more absorbing than urban), for the largest
Atmos. Chem. Phys., 14, 847–875, 2014
aerosol optical depth and for the largest solar zenith angles,
which were the same conditions that we found for the smallest variations in the size distributions.
If we now analyze the effect of vertical errors on almucantar measurements, we observe that the radiance relative
differences (in Fig. 11), are positive for θs = 15◦ , negative
for θs = 75◦ and close to zero at θs = 45◦ when the pointing
error is positive. As a consequence, ωo will increase at small
scattering angles and decrease at large scattering angles. This
tendency is found in the three aerosol types presented. Note
www.atmos-chem-phys.net/14/847/2014/
B.20Torres et al.: Sensitivity of aerosol retrieval to geometrical
865
Torres et al.:configuration
Sensitivity of aerosol retrieval to geometrical configuration
995
1000
1005
1010
1015
1020
1025
1030
1035
www.atmos-chem-phys.net/14/847/2014/
78.5
79
79.5
Zenith
990
that
thatthis
thisdrift
driftisisopposite
oppositetotothe
thefictitious
fictitiousωωoo cycle
cycle presented
presented
ininSect.
2.2 2.2
for for
almucantars.
section
almucantars.
When
areare
negative,
there
areare
negative
differWhenvertical
verticalerrors
errors
negative,
there
negative
dif◦ and◦positive differences for θ = 75◦ , find◦
ences
for θfor
s = θ15
s
ferences
=
15
and
positive
differences
for
θ
=
75
,
s
s
◦
◦
ing
no differences
again at
θs =at45θs. Thus,
wouldωhave
the
finding
no differences
again
= 45 .ωoThus,
would
o
opposite
reduction reduction
for small for
θs small
and increment
for
have thebehavior:
opposite behavior:
θs and increlarge
. Therefore,
negative vertical
will
enmentθsfor
large θs . Therefore,
negativepointing
vertical errors
pointing
errors
large
fictitious
daily cycle
ofcycle
ωo inofalmucantar
retrievals.
will the
enlarge
the fictitious
daily
ωo in almucantar
reBoth
results
areresults
confirmed
in Fig. 9. in figure 9.
trievals.
Both
are confirmed
The
Theimaginary
imaginarypart
partofofthe
therefractive
refractiveindex
indexresponds
responds in
in the
the
same
sameway
wayasasthe
thesingle
singlescattering
scatteringalbedo,
albedo, but
but its
its variations
variations
have
havethe
theopposite
oppositesign.
sign.Again,
Again,both
bothparameters
parametersare
are less
less afaffected
fectedfor
forthe
thecase
caseofofbiomass
biomassburning,
burning as
as its
its absorption
absorption is
is
greater
greaterthan
thanininthe
theother
othertwo
twocases
casesand
andthe
theaerosol
aerosol load
load conconsidered
sideredisislarger.
larger.The
Thereal
realpart
partdoes
doesnot
notsuffer
sufferrelevant
relevant varivariations
ationsatatthe
thepresence
presenceofofvertical
verticalerror
errorininthe
thealmucantar
almucantar gegeometry.
ometry.
Finally,
Finally,we
wewant
wanttotoindicate
indicatethat
thatthe
theoptical
opticalparameters
parametersananalyzed
respect
to the referalyzeddodonot
notsuffer
sufferany
anyvariations
variations with
respect
to reference
cases
3 for horizontal
errors
in both1040
ence
cases in
presented
in Fig.
presented
figure 3 for
horizontal
errors in both
geometries.
geometries.
2.6 Dependence on the finite field of view
2.6 Dependence on the finite field of view
The concept of sky radiance can be defined as the radiant
The
sky radiance
defined
as theangle
radiant
flux1045
fluxconcept
per unitofprojected
areacan
andbeper
unit solid
coming
per
unitaprojected
solid angle coming
from
specified area
pointand
in per
the unit
sky (McCluney,
1994). from
That
a is
specified
point in
sky (McCluney,
That isbe
why,
why, ideally,
thethe
observational
solid 1994).
angle should
inideally,
the observational
solid
angle should
be infinitesimal.
finitesimal.
The inversion
algorithms,
which
use radiance
The
inversion algorithms,
which use
measurements
measurements
as input, assume
thisradiance
approximation
consid1050
asering
input,
also
use this approximation,
considering
also
infinitesimal
the instrument field
of view. that the
instrument
field ofthe
view
is infinitesimal.
Nevertheless,
instruments
have a finite field of view,
Nevertheless,
have a finite
field of view,
specially
in the the
caseinstruments
of the sun-photometer
CIMEL-318,
the
◦
especially
in the
case
of theissun
value of the
field
of view
1.2photometer
(Holben etCIMEL-318,
al., 1998) in the
the
◦ (Holben◦et al., 1998) in
value
the field ofand
view
is 1.2
actualofinstruments
in old
versions
2.4 (personal comthe
actual instruments
and, in old versions, 2.4◦ (CIMEL,
munication
from CIMEL).
personal
communication,
The effect
of the finite2010).
field of view on the radiance meaThe effect
the finite
field ofpoint
viewison
the radiance
surement
in of
every
observation
obtained
by themeacon-1055
surement
observation
point and
is obtained
by the
convovolutioninofevery
the viewing
geometry
the angular
values
of
lution
of the
viewingIngeometry
and theseveral
angulartest
values
the
the sky
radiance.
Torres (2012),
doneofwith
sky
In Torres
(2012), several
teststhat
done
the sun
theradiance.
sun-photometer
CIMEL-318
showed
thewith
response
of
photometer
that theasshape
of its field
of
its field ofCIMEL-318
view can beshowed
approximated
a cylinder.
Using
view
be approximated
asisa simplified
cylinder. Using
this result,
the1060
this can
result,
the convolution
as a surface
integral
convolution
is
simplified
as
a
surface
integral
of
the
radiance
of the radiance function within the field of view region. In
function
within the
of view
region. In by
ouraapproach,
the
our approach,
the field
integral
is substituted
discrete sum
integral
is
substituted
by
a
discrete
sum
considering
17
points
considering 17 points in the field of view range around the
inobservation
the field ofpoint,
view see
range
around
observation
figure
12. the
As the
areas are point,
chosensee
in
order
equal,
integral
ap-1065
Fig.
12.toAsbethe
areasthe
arefore-mentioned
chosen in ordersurface
to be equal,
the is
foreproximated
by averaging
sky radiance values
obtainedthe
in
mentioned
surface
integralthe
is approximated
by averaging
theradiance
17 selected
points.
sky
values
obtained in the 17 selected points.
The
Thetest
testare
aredone
doneconsidering
consideringvalues
valuesof
ofthe
thefield
fieldof
ofview
view of
of
◦ ◦or 2.4◦ ◦in every measurement point for the almucantar
1.2
1.2 or 2.4 in every measurement point for the almucantar
and
in previous
previousanalyanal-1070
andfor
forthe
theprincipal
principalplane
plane geometries. As in
sis, the study is
aerosol
examples
described
ysis,
is done
doneusing
usingthe
the3three
aerosol
examples
de◦
◦ , 75
and at and
5 solar
zenith
angles
(15
, 30◦(15
, 45◦◦, ,30
60◦◦, 45
and
scribed
at five
solar
zenith
angles
60◦◦).and
75◦ ).
80
80.5
81
81.5
−1.5
−1
−0.5
0
0.5
1
1.5
Azimuth
Fig. 12. Representation of the 17 point-scheme followed to simulate
Fig. 12. Representation of the 17 point-scheme followed to simulate
the effects of a finite field of view on the radiance measurements. In
the effects of a finite field of view on◦the radiance measurements.
In
the example, the field of view is 2.4◦ and θs = 80◦ ◦ .
the example the field of view is 2.4 and θs = 80 .
The results obtained simulating a field of view of
1.2◦
The results obtained simulating a field of view of 1.2◦ (non
(non-plotted) are the same that the ones obtained in Fig. 3.
plotted) are the same that the ones obtained in figure 3. It can
It can be concluded, therefore, that the actual field of view
be concluded,
therefore, that the actual field of view of 1.2◦
◦ does not
of
1.2
include any variations with respect to the
do not include any variations respect to the non-error case.
non-error case.
On the other hand, the results for a field of view of 2.4◦ inOn the other hand, the results for a field of view of 2.4◦ indicate that the variations respect to the non error data set are
dicate
that thefor
variations
respect
to refractive
the non-error
data
set are
only relevant
the real part
of the
index.
Specifionly
relevant
for
the
real
part
of
the
refractive
index.
Specifically, in the almucantar, the results obtained for θs = 15◦◦are
cally,
the lower
almucantar,
results
for of
θs =
are
aroundin3%
than inthefigure
3, obtained
for the rest
the15solar
around
3
%
lower
than
in
Fig.
3;
for
the
rest
of
the
solar
zenith
zenith angles the differences are negligible. For the principal
angles
the real
differences
aresmaller
negligible.
For the principal
plane,
plane, the
part show
oscillations,
under 3%,
but
the
real
part
show
smaller
oscillations
(under
3
%)
but
they
they appear for all the solar zenith angles.
appear for all the solar zenith angles.
3 Check of the simulations against selected stable data
3 Check of the simulations against selected stable data
In order to complete the work, we propose a parallel study
In
to complete
work, weof principal
propose plane
a parallel
withorder
real data
comparingthe
the retrievals
and
study
with
real
data
comparing
the
retrievals
of during
princialmucantar from the same three AERONET sites used
pal
plane and analysis:
almucantar
from(Zambia,
the same
three
◦ AERONET
the sensitivity
Mongu
15.25
S-23.15◦ E,
sites
used
during
the sensitivity
analysis:
Mongu (Zambia,
1107.0
msl)
is
chosen
for
the
analysis
of
biomass
burning
◦
◦ E, 1107.0 m◦s.l.) is chosen
15.25
analyaerosol;S–23.15
GSFC (USA,
38.99 N-76.84◦ W, for
87.0the
msl)
for
sis
of aerosol;
biomassand
burning
GSFCArabia,
(USA, 24.90
38.99◦◦NN–
urban
Solar aerosol;
Village (Saudi
◦
76.84
for desert
urban dust
aerosol;
and Solar
Village
46.40◦ W,
E, 87.0
790 msl)
msl) for
aerosol.
We only
se◦ N–46.40◦ E, 790 msl) for desert dust
(Saudi
Arabia,
lect data
which24.90
accomplished
the next four requirements:
aerosol.
We
only
select
datadepth
thatbelonging
meet thetonext
four re(1) Data with aerosol optical
AERONET
quirements:
(1)
data
with
aerosol
optical
depth
belonging
Level 2.0 (though we did not only use Level 2 retrievals asto
◦
AERONET
Levelalso
2.0 in
(though
we did
notwith
onlyθsuse
Level
we are interested
almucantar
data
< 50
and2
retrievals
as
we
are
interested
also
in
almucantar
data
τa (440) < 0.4); (2) Data from those days where the ratio with
be◦
θtween
τa (440)
< 0.4); and
(2) data
from those
days
where
standard
deviation
the average
of the
aerosol
s < 50theand
the
ratiodepth
between
theisstandard
and the average
optical
values
smaller deviation
than 0.1 (evaluated
for theof
the
aerosol
optical
depth
values
is
smaller
than
0.1
(evaluated
four wavelengths used by the inversion 440, 670, 870 and
for
thenm).
four This
wavelengths
usedisby
the inversion
440,to670,
870
1020
requirement
established
in order
assure
and
1020
nm).
This
requirement
is
established
in
order
to
asthat the analysis is done for stable aerosol conditions. (3)
sure
that the
analysis isand
done
for stable
aerosol
conditions.
The pairs
almucantar
principal
plane
are selected
only (3)
if
both pairs
measurements
took
withinplane
a maximum
delayonly
of
The
almucantar
andplace
principal
are selected
30both
minutes.
(4) Finally,took
onlyplace
those within
days presenting
at least
4
if
measurements
a maximum
delay
of 30 min. (4) Finally, only those days presenting at least 4
Atmos. Chem. Phys., 14, 847–875, 2014
866
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
pairs matching the previous three conditions are chosen for
the comparison.
Following these previous requirements, a total of 204 pairs
were selected for the comparison, of which 65 pairs belong
to biomass burning (top left of Table 4), 58 pairs to urban
aerosol (top right in Table 4) and 81 pairs to desert dust. The
latter set was divided into two subgroups as it will be commented later (Table 4 at the bottom, left and right).
The comparison for Mongu includes data from 2003 to
2009 for four different sun photometers. It is worth mentioning that we guaranteed that the data correspond to biomass
burning events by the application of typical thresholds for
Angstrom exponent values in biomass burning (α > 1.65,
Eck et al., 1999). As a consequence, all the days found are
contained in the period from July to October. The comparison in GSFC can be seen on the top right part of Table 4.
All the data selected belong to the months between June and
October. As for the Mongu site, we have selected data only
when α > 1.65. The data corresponding to the comparison
in Solar Village, used in order to do the analysis of desert
dust aerosol, are contained at the bottom part of Table 4. The
reason for splitting those data in two groups was established
during the evaluation of the comparisons ALM-PPL. At this
point, we observed that for some photometers (Table 4 bottom part on the left) the results presented a similar aspect to
the ones obtained for the two previous aerosol types, whereas
for some other photometers the comparison achieved was
much worse (Table 4, bottom part on the right), especially
in the size distribution (as will be shown in the next section).
Nevertheless, this case presents a higher number of days with
stable conditions, providing enough data to carry out the double analysis.
3.1
Size distribution
Figure 13 represents the mean and standard deviation (error
bars) of the relative differences obtained for the comparison
of the size distribution in the three analyzed cases: biomass
burning (upper part of the figure, data from the top-left part
of Table 4) urban (central part of the figure, data from the
top-right part of Table 4) and desert dust (lower part of the
figure, only the data from the bottom-left of Table 4).
Observing the figure, we can see how the comparisons
for the three aerosol types present similar results as those
obtained in the self-consistency analysis from the previous
section: there is a general good agreement for radii between
0.1 µm and 5 µm, with values of the average of the relative
differences under 10 % – except for the radii around 2 µm
where the difference is a bit higher, reaching maximum values up to 20 %. Thus, these differences are a bit higher than
those obtained from simulated data. At this point, the reader
may remember the possibility of several error sources, such
as the ones we have studied in the simulation analysis, which
could provoke the increase in the discrepancy between PPL
and ALM retrievals. Nevertheless, the discrepancy is still
Atmos. Chem. Phys., 14, 847–875, 2014
within the interval 15–25 % which is the expected accuracy
suggested by AERONET for almucantar retrievals. Finally, it
should be noted that observations from all solar zenith angles
have been accounted in Fig. 13; the results represent an average between retrievals with small solar zenith angles, generally with larger errors, and large solar zenith angles.
Moving to the extremes, for radii smaller than 0.1 µm or
larger than 5 µm, the comparison is much worse than in the
previous analyzed region, as was expected. The relative differences are much larger, up to 60 %, but still similar to those
obtained in the previous section and within the confidence interval given by AERONET for these radii (up to 100 %). The
unexpected result is that these differences are positive, indicating that the values in the size distribution obtained from
the almucantar are systematically lower than those obtained
using the principal plane.
Among the three aerosol types, the urban aerosol shows
the smallest discrepancies for fine mode; for this aerosol
type, even for radii smaller than 0.1 µm the differences are
under 10 %. In the coarse mode, the smallest differences are
obtained for the case of biomass burning; for this case, differences are under 22 % except for the last bin (at 15 µm) where
the relative difference is 44 %. Desert dust case presents the
worst-case behavior, especially in the coarse mode, where
for several bins the relative differences exceed 40 %, reaching the maximum of 60 % at 11.4 µm.
3.2
Optical parameters
Table 5 contains the mean values and the standard deviations
obtained for the single scattering albedo and the refractive
index in the analyzed days using only almucantar geometry.
The values obtained for the three aerosol cases are similar to
those presented in Table 1 (Table 1 in Dubovik et al., 2002).
For instance, ω(440) = 0.85, corresponding to the analysis
of the biomass burning, is comparable to the one used in the
simulation analysis, ω(440) = 0.88 (Table 1).
Returning to the comparison between the principal plane
and almucantar retrievals, the results for the single scattering albedo are shown in Fig. 14. The mean of the differences
between both inversions are plotted against the wavelength
for the three aerosol cases analyzed: biomass burning (gray),
urban (blue) and desert dust (orange). The standard deviation of the differences is represented using the error bar. As
it can be seen in the plot, the average of the differences is under 0.01 for the three analyzed cases and for the four wavelengths, reaching the highest value (0.007) at 440 nm for the
desert dust. On the other hand, the standard deviation is under
0.01 for all the wavelengths in the biomass burning, between
0.01–0.015 for urban aerosol, and slightly higher for the
desert dust aerosol (where values around 0.02 are obtained).
Nevertheless, this result is due to the effect of the problem
regarding the almucantar angle coverage: if we reduce the
analyses to those cases in which θs > 50◦ , the standard deviation reduces it values considerably, especially for the desert
www.atmos-chem-phys.net/14/847/2014/
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
867
Table 4. Description of the data used for the comparison between almucantar and principal plane retrievals for the different sites.
Biomass burning (Mongu)
Photo.
#36
#65
#11
#152
Urban (GSFC)
Date
No. pairs
< τa (440) >
<α>
09-08-2009
12-08-2009
16-07-2009
01-10-2004
25-07-2004
17-09-2004
30-07-2003
18-08-2003
14-08-2003
02-08-2006
25-07-2006
18-08-2006
4
7
5
4
6
6
5
6
6
6
4
6
0.34
0.63
0.71
0.37
0.61
0.78
0.45
0.68
0.72
0.42
0.53
0.73
2.00
1.89
1.85
1.72
1.75
1.83
1.92
1.79
1.66
1.71
1.79
1.80
Photo.
#101(1)
#101(2)
#89(1)
#94(1)
#89(2)
#94(2)
Date
No. pairs
< τa (440) >
<α>
21-10-2001
24-10-2001
17-07-2002
13-08-2002
23-06-2003
29-06-2003
24-06-2005
02-08-2005
08-09-2007
26-09-2007
13-10-2007
17-10-2007
6
5
6
4
4
4
6
4
5
4
5
5
0.14
0.24
0.44
1.15
0.33
0.71
0.48
0.38
0.49
0.59
0.14
0.40
1.76
1.90
1.88
1.80
1.75
1.65
1.66
1.89
1.83
1.89
1.67
1.88
Desert dust 1 (Solar Village)
Photo.
#65
#185
#95
Desert dust 2 (Solar Village)
Date
No. pairs
< τa (440) >
<α>
05-03-2003
02-04-2003
11-09-2002
20-10-2005
19-10-2005
19-06-2006
07-03-2011
09-10-2010
26-08-2010
7
5
5
5
6
4
5
5
6
0.33
0.48
0.64
0.32
0.41
0.54
0.38
0.48
0.73
0.25
0.20
0.55
0.49
0.46
0.44
0.30
0.59
0.73
Photo.
#233
#33
Date
No. pairs
< τa (440) >
<α>
25-04-2008
26-04-2008
28-05-2008
04-06-2004
22-05-2004
18-05-2004
7
4
6
7
4
5
0.36
0.43
0.51
0.33
0.46
0.71
0.25
0.28
0.25
0.55
0.16
0.11
Table 5. Mean values and standard deviations obtained for the single scattering albedo and the refractive index in the analyzed days using
only almucantar geometry.
ω(λ)
n(λ)
k(λ)
Wavelength [nm]
440
670
870
1020
440
670
870
1020
440
670
870
1020
Bio. burn.
(Mongu)
mean
std
0.85
0.03
0.81
0.05
0.78
0.05
0.76
0.05
1.53
0.04
1.53
0.03
1.54
0.03
1.54
0.03
0.032
0.012
0.032
0.013
0.030
0.012
0.027
0.011
Urban
(GSFC)
mean
std
0.96
0.02
0.94
0.03
0.93
0.04
0.93
0.04
1.40
0.05
1.41
0.05
1.41
0.05
1.42
0.05
0.005
0.003
0.005
0.003
0.005
0.003
0.005
0.003
Desert dust
(Solar Vil.)
mean
std
0.90
0.02
0.92
0.03
0.94
0.03
0.94
0.03
1.51
0.05
1.54
0.03
1.54
0.03
1.54
0.03
0.006
0.003
0.004
0.003
0.004
0.002
0.004
0.002
www.atmos-chem-phys.net/14/847/2014/
Atmos. Chem. Phys., 14, 847–875, 2014
868
Torres et configuration
al.: Sensitivity of aerosol retrieval to geometrical configuration
Torres et al.: Sensitivity of aerosol retrieval B.
to geometrical
23
100
Biomass Burn. (Mongu)
N = 65 cases
50
0
−50
Relative differences [%]
−100
100
Urban (GSFC)
N = 58 cases
50
0
−50
−100
100
Desert Dust (Solar V.)
N = 48 cases
50
0
Mean of the Relat. Differen.
−50
PPL>ALM
PPL<ALM
−100
Standard deviation
0.1
0.3
1
3
10
Radius (µ m)
Fig. 13. Relative differences found in the size distribution between the inversion obtained by almucantar and principal planes for the three
analyzed cases
description
infound
Tablein4):
burning
(upper
of the
figure),
(central
part of the
figure),
Fig. 13.(data
Relative
differences
the biomass
size distribution
between
thepart
inversion
obtained
by urban
almucantar
and principal
planes
for theand
threedesert dust
(lower partanalyzed
of the cases
figure,
only
data from
the first
set (called
desert
dust
(data
description
in table
4): biomass
burning
(upper
part1)).
of the figure) urban(central part of the figure) and desert dust (lower
part of the figure, only data from the first set (called Desert dust I)).
dust where
σ = 0.01. It should be mentioned that the uncertion reduces it values considerably, specially for the desert
tainty
given
AERONET
ωo isbe
0.03
(http://aeronet.gsfc.
1180
dustby
where
σ = 0.01. for
It should
commented
that the uncernasa.gov/new_web/Documents/inversions.pdf),
which hightainty given by AERONET for ωo is 0.03 (http://aeronet.gsfc.
web/Documents/inversions.pdf)
lights thenasa.gov/new
extraordinary
agreement obtained herewhich
whenhighthe1195
lights
extraordinary
agreement obtained here when the
atmosphere
is the
stable
and homogeneous.
stable
and homogeneous.
Figureatmosphere
15 shows isthe
results
for the real part of the refractive index.
The
averaged
values
of the
biomass
1185
Figure 15 shows the results
for difference
the real part for
of the
refracburning and
urban
aerosol
are
lower
than
0.01,
indicating
that
tive index. The averaged values of the difference for biomass
burning
andtendency
urban aerosol
are lower than
0.01and
indicating
that1200
there is no
shared
for principal
plane
almucanthere is no
between
principal
plane for
and the
almucantar
tar differences;
ontendency
the contrary,
the
difference
desert
differences;
the difference
for theofdesert
dust
dust is about
0.03, on
or the
in contrary,
other words,
the values
the real
1190
is about 0.03, or in other words, the values of the real part
part of the
refractive index retrieved using principal plane
of the refractive index retrieved using principal plane are on
are, on average, significantly higher than those obtained using almucantar for the desert dust. The standard deviation,
with a value about 0.03 for the three cases, does not depend
on the aerosol type. These results are not improved when the
study is limited to θs > 50◦ . Nonetheless, the accuracy given
for this parameter is 0.03 for biomass burning and urban and
slightly higher, 0.05, for desert dust; therefore, the results are
within this interval.
Atmos. Chem. Phys., 14, 847–875, 2014
Figure 16 depicts the averages and the standard deviations
average significantly higher than the ones obtained using alof the absolute
differences
the imaginary
part
mucantar
for the desert
dust. The for
standard
deviation does
notof the refractive
index.
Contrary
to
the
previous
cases,
the highest
depend on the aerosol type, with a value about 0.03 for the
three
cases. deviations
These resultsof
arethe
not absolute
improved when
limiting the
standard
differences
are reached
study
to θsbiomass
> 50◦ . Nonetheless,
the accuracy
given for
this around
for the
burning aerosol
presenting
values
parameter
is
0.03other
for biomass
burning
andfor
urban
anddust
a bitand urban
0.003. On the
hand, the
values
desert
higher, 0.05, for desert dust; therefore the results are within
aerosol are enclosed between 0.0015 and 0.0023. It should be
this interval.
remembered (Table 5), that the absolute values of the imagiFigure
16of
depicts
the averagesindex
and the
deviations
nary
part
the refractive
forstandard
the biomass
burning are
of
theorder
absolute
the imaginary
partfor
of the
one
of differences
magnitudefor
higher
than those
theredesert dust
fractive
index.
Contrary
to the previous
cases,terms,
the highest
and urban
aerosol.
Therefore,
in relative
the best comstandard deviations of the absolute differences are reached
parison is again obtained for biomass burning case. It can be
for the biomass burning aerosol presenting values around
noted the opposite sign for the differences of imaginary part
of the refractive index and the single scattering albedo. This
fact is justified by the strong anticorrelation between both
magnitudes. Using Table 5, we observe that the average of
the differences (principal plane vs. almucantar) of the imaginary part of the refractive index have a maximum of 13 % for
the urban aerosol, 9 % for the desert dust aerosol, and 4 % for
biomass burning.
www.atmos-chem-phys.net/14/847/2014/
Absolutedifferences
differences(PPL−ALM)
(PPL−ALM)
Absolute
Torres
Sensitivity
configuration
B. Torres24
et al.: Sensitivity of aerosol retrieval to geometrical
24
Torres et
et al.:
al.: configuration
Sensitivity of
of aerosol
aerosol retrieval
retrieval to
to geometrical
geometrical configuration
869
Single Scattering Albedo
Single Scattering Albedo
0.04
0.04
0.02
0.02
0
0
−0.02
−0.02
Biomass Burning
Biomass Burning
Urban
Urban
Desert dust
Desert dust
Standard deviation
Standard deviation
−0.04
−0.04
440
440
670
670
870
870
1020
1020
Wavelength
Wavelength [nm]
[nm]
Fig. 14. Absolute differences (with sign) found in the single scattering albedo between the inversion obtained by almucantar and principal
Fig.
14.
differences
(with
found
the
scattering
albedo
between
the inversion
obtained by
almucantar
and principal
principal
Fig.three
14. Absolute
Absolute
differences
(with sign)
sign)biomass
found in
in burning
the single
single(gray),
scattering
albedo
between
inversion
byonly
almucantar
and
planes for the
analyzed
cases (Table
4):
urban
(blue)
andthe
desert
dustobtained
(orange,
data
first set (called
planes
the from
first set
setthe
(called
planes for
for the
the three
three analyzed
analyzed cases
cases (table
(table 4):
4): biomass
biomass burning
burning (gray),
(gray), urban(blue)
urban(blue) and
and desert
desert dust
dust (orange,
(orange, only
only data
data from
from the
first
(called
desert dust Desert
1)). Bars
the standard
deviation
of the
differences.
dust indicate
I)). Bars indicate
the standard
deviation
of the
differences
Absolutedifferences
differences(PPL−ALM)
(PPL−ALM)
Absolute
Desert dust I)). Bars indicate the standard deviation of the differences
Real Refractive Index
Real Refractive Index
0.06
0.06
0.04
0.04
0.02
0.02
00
−0.02
−0.02
−0.04
−0.04
Biomass Burning
Biomass Burning
Urban
Urban
Desert dust
Desert dust
Standard deviation
Standard deviation
−0.06
−0.06
440
440
670
670
870
870
1020
1020
Wavelength
Wavelength [nm]
[nm]
Fig. 15. Absolute differences (with sign) found in the real part of the refractive index between the inversion obtained by almucantar and that
15.
differences
(with
sign)
in
real
of
the
index
between
the
by almucantar
almucantar
and only data
Fig.
15. Absolute
Absolute
differences
(with analyzed
sign) found
foundcases
in the
the(Table
real part
part4):
of biomass
the refractive
refractive
index (gray),
between urban
the inversion
inversion
obtained
by
and
obtained byFig.
principal
planes
for the three
burning
(blue)obtained
and desert
dust (orange,
principal
planes
for
three
analyzed
cases
(table
4):
(gray),
urban(blue)
and
only data
data from
from the
the first
first
principal
planesdesert
for the
the dust
three 1)).
analyzed
cases
(tablethe
4): biomass
biomass burning
burning
(gray),
urban(blue)
and desert
desert dust
dust (orange,
(orange, only
from the first
set
(called
Bars
indicate
standard
deviation
of
the
differences.
set (called Desert dust I)). Bars indicate the standard deviation of the differences.
set (called Desert dust I)). Bars indicate the standard deviation of the differences.
0.003.
other
hand,
the
for
exchanged
for
four
wavelengths.
Us-very simiDesert
dustOn
2:the
data
subset
larger
for both desert
dust cases
sets. and
Thethe
values
observed are
0.003.
On
the
other
hand,with
the values
values
for desert
desert dust
dust and
and1215
1215
exchanged
for the
the three
three
cases
and
the
four wavelengths.
Usurban
ing
5,
observe
that
of the
the differences,
differences,
urban aerosol
aerosol are
are enclosed
enclosed between
between 0.0015
0.0015 and
and 0.0023.
0.0023. It
It
ing
table
5, we
we
observeshowing
that the
the average
average
of
discrepancies
lar table
for both
groups,
that, apparently,
the higher alpha
should
principal
plane
the
part of
of the
the
should be
be remembered
remembered (table
(table 5),
5), that
that the
the absolute
absolute values
values of
of
principal
plane vs
vs almucantar,
almucantar,
of
the 1imaginary
imaginary
values observed
in desert of
dust
does notpart
seem
to have any
the
imaginary
part
of
index
the
refractive
the urban
urban aerosol,
aerosol,
the shown,
imaginarythe
partcomparisons
of the
the refractive
refractive
index for
for
the biomass
biomass
refractive index
index are
are at
at maximum
maximum 13%
13% for
for the
As was just
obtained
from
desert
consequences
in
the
retrieved
aerosol
size
distribution.
Note
burning
9%
biomass burning.
burning.
burning are
are one
one order
order of
of magnitude
magnitude higher
higher than
than those
those for
for the
the
9% for
for the
the desert
desert dust
dust aerosol
aerosol and
and 4%
4% for
for biomass
dust aerosol
have
a
larger
error
than
the
error
comparisons
here
as
well,
that
the
values
of
the
median
radius
and
the
1210
desert
dust
and
urban
aerosol.
Therefore,
in
relative
terms,
1210
desert dust and urban aerosol. Therefore, in relative terms,
obtained from
thecomparison
other aerosol
types.again
Moreover,
forburning
some
the
is
for
standard deviation for the coarse mode (rVc and σVc ) shown
the best
best
comparison
is obtained
obtained
again
for biomass
biomass
burning
case.
The
strong
the
of
photometers
these
werebetween
substantially
larger.part
This
case.
Thedifferences
strong correlation
correlation
between
the imaginary
imaginary
part
of
in Table 1 were 2.32 and 0.6, which are in a perfect agreethe
index
single
albedo
makes
the refractive
refractive
index and
and the
the
single
scattering
albedodesert
makes
was the case
for photometers
#233
andscattering
#33 (called
ment with the ones obtained in the two subgroups here.
that
mean
values
the
present their
that the
the the
meanresults
values of
of
the two
two magnitudes
magnitudes
their sign
sign
dust 2 subset);
obtained
for thesepresent
photometers
The upper chart in Fig. 17 contains the average of the relawere systematically worse for every single pair of data comtive differences and the standard deviation obtained from the
pared.
comparison between the retrievals using principal plane and
Looking at Table 4, it can be seen that the mean Angstrom
almucantar in the subset desert dust 2. The most outstandexponent of desert dust 1 spans from 0.20 to 0.73, while for
ing result is the strong increase of the values in the extremes
desert dust 2 it ranges from 0.11 to 0.55. On the other hand,
(r < 0.1 µm and r > 5 µm) compared to the previously anain Table 6, for each mode of the volume particle size dislyzed cases. For the coarse mode, the average differences extribution [dV (r)/dlnr], mean values of the particle volume
ceed 100 %. However, the averaged values for the mid-range
concentration, the median radius, and the standard deviation
are similar to the previous cases, being under 20 %. We find
(obtained only using almucantar inversions) are represented
3.3
1205
1205
www.atmos-chem-phys.net/14/847/2014/
Atmos. Chem. Phys., 14, 847–875, 2014
Torres et configuration
al.: Sensitivity of aerosol retrieval to geometrical configuration
Torres et al.: Sensitivity of aerosol retrieval B.
to geometrical
25
Absolute differences (PPL−ALM)
870
Imaginary Refractive Index
0.004
0.002
0
−0.002
Biomass Burning
Urban
Desert dust
−0.004
Standard deviation
440
670
870
1020
Wavelength [nm]
Fig. 16. Absolute differences (with sign) found in the imaginary part of the refractive index between the inversion obtained by almucantar
Fig.planes
16. Absolute
(with sign)
found
in the4):
imaginary
of the refractive
index
between
inversion
obtained
almucantar
and principal
for thedifferences
three analyzed
cases
(Table
biomasspart
burning
(gray bar)
urban
(bluethe
bar)
and desert
dustby(orange
bar, only data
and principal planes for the three analyzed cases (table 4): biomass burning (gray bar) urban(blue bar) and desert dust (orange bar, only data
from the first
set (called desert dust 1)).
26
Torres
et
al.:
Sensitivity
of
aerosol
retrieval
to
geometrical
configuration
from the first set (called Desert dust I)).
1225
1230
1235
1240
1245
1250
3.3 Desert dust II: data150
sub-set with larger discrepanDesertexceed
Dust II100%. However, the averaged values for the central
cies.
similar to the previous cases being under 20%. We find
N = 33are
cases
100
an exception for the radii between 3µm and 5µm, where the
50
differences, affected by the strong increase in the extremes,
As it was just shown, the comparisons
obtained from desert
dust aerosol have larger error than
0 for the other aerosol types.1255 present values up to 60%. In the same way, the standard deviation shows a similar behavior, doubling its value in the
Moreover, for some photometers these differences were sub−50
extremes (from 30%-40% it increases to 60%) but keeping
stantially larger. This was the
case of photometers #233 and
around 20% in the central part.
#33 (called Desert dust −100
II subset); the results obtained for
these photometers were systematically worse for every sinThe central and the bottom chart of figure 17 correspond
−150
gle pair of data compared.
1260
to the same analysis (photometers #233 and #33) but limiting the study to those cases where the solar zenith angle is
Looking at table 4 it can be seen that the mean Angstrom
Desert Dust II (θs > 30°) ◦
150
larger than 30 and 50◦ respectively. As it can be seen, both
exponent of Desert dust I spans from 0.20 to 0.73 while for
improve the comparison considerably. The comcases
Desert dust II it ranges from100
0.11 to 0.55. On the other hand, N = 22limitations
parison for solar zenith angles larger than 30◦ eliminates 11
in table 6, for each mode of
50the volume particle size distribution [dV(r)/d lnr], mean values of the particle volume1265 pairs of data (from 33 to 22) and the results, especially the av0 and the standard deviation
erage value of the relative differences are diminished reachconcentration, the median radius,
ing similar values as the ones obtained for the photometers
(obtained only using almucantar
inversions)
are
represented
−50
classed in the sub-set Desert Dust I. Again, another 11 pairs
for both desert dust sets. The values observed are very simi−100
of data disappear when the limitation is extended to θs > 50◦;
lar for both groups showing
that, apparently, the higher alpha
values observed in Desert−150
dust I does not seem to have any1270 under this criterion, the average values do not suffer any improvements but the standard deviations are appreciably lower
consequences in the retrieved aerosol size distribution. Note
for r > 3µm.
here as well, that the values
the Dustspecially
Desert
II (θs > 50°)
150of the median radius and
standard deviation for the coarse mode (rV c and σV c ) shown
Continuing with the analysis of the data set Desert dust II,
cases
in table 1 were 2.32 and 0.6100
which are in a perfect agreement N = 11the
results for the optical parameters are shown in table 7.
with the ones obtained in the50
two subgroups here.
1275
Averaged values and the standard deviations of the differences between the retrievals of principal plane and almucanThe upper chart in figure 17
0 contains the average of the
tar are presented for all data (upper part of the table 7), those
relative differences and the standard deviation obtained from
◦ of the Relat. Differen.
Mean
−50
data with θs > 30
(central part of the table 7) and only for
the comparison between the
retrievals using principal plane
those
cases
where
θs >PPL>ALM
50◦ (bottom part of the table 7).
and almucantar in the sub-set
−100Desert dust II. The most outPPL<ALM
The means of the differences observed for the whole data
standing result is the strong increase of the values in the ex-1280
Standard deviation
−150
set are, in general, considerably larger than the values obtremes (r < 0.1µm and r >
5µm) compared to the previously
served
in
the
data
set
Desert dust
analyzed cases. For the coarse mode, the 0.1
average differences
0.3
1
3
10 I (Figures 14 - 16). Thus,
Relative differences [%]
1220
Radius (µ m)
Fig. 17. Relative differences found in the size distribution between the inversion obtained by almucantar and principal planes for the phodesertobtained
dust 2).byThe
upper chart
containsplanes
a comparison
for the
tometers #233
andRelative
#33 in differences
Solar Village
site
description
Table 4thecase
Fig. 17.
found
in (data
the size
distributioninbetween
inversion
almucantar
and principal
for the
and #33
Solar
Villagechart
site (data
description
in table only
4 casefor
Desert
dust
II).with
The upper
chartzenith
contains
the comparison
whole dataphotometers
set, while#233
the central
andinthe
bottom
contain
comparisons
those
data
the solar
angle
larger than 30◦ and
for the whole data set while the central and the bottom chart only for those data with the solar zenith angle larger than 30◦ and 50◦
50◦ , respectively.
respectively.
Table 6. Mean values of the particle volume concentration CV i , the median radius rV i , and the standard deviation σV i for each mode of the
volume particle size distribution for the defined groups Desert dust I and Desert dust II
CV f
Atmos. Chem. Phys., 14, 847–875, 2014
Desert dust I
Desert dust II
0.03 ± 0.02
0.03 ± 0.01
rV f
0.14 ± 0.02
0.17 ± 0.04
σV f
0.51 ± 0.07
0.61 ± 0.07
CV c
0.25 ± 0.07
0.23 ± 0.09
rV c
σV c
www.atmos-chem-phys.net/14/847/2014/
2.33 ± 0.24
1.95 ± 0.33
0.62 ± 0.03
0.57 ± 0.06
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
871
Table 6. Mean values of the particle volume concentration CV i , the median radius rV i , and the standard deviation σV i for each mode of the
volume particle size distribution for the defined groups desert dust 1 and desert dust 2.
Desert dust 1
Desert dust 2
CVf
rVf
σVf
CVc
rVc
σVc
0.03 ± 0.02
0.03 ± 0.01
0.14 ± 0.02
0.17 ± 0.04
0.51 ± 0.07
0.61 ± 0.07
0.25 ± 0.07
0.23 ± 0.09
2.33 ± 0.24
1.95 ± 0.33
0.62 ± 0.03
0.57 ± 0.06
Table 7. Mean values and the standard deviations of the absolute differences (with sign principal plane minus almucantar) for the optical
parameters found for the data set desert dust 2.
Total differences
ω(λ)
n(λ)
k(λ)
Wavelength [nm]
440
670
870
1020
440
670
870
1020
440
670
870
1020
All data
mean
std
0.03
0.05
0.03
0.05
0.03
0.04
0.02
0.03
0.03
0.06
0.03
0.05
0.03
0.05
0.03
0.06
−0.004
0.006
−0.003
0.005
−0.003
0.004
−0.002
0.004
θs >
30◦
mean
std
0.01
0.02
0.00
0.02
0.00
0.02
0.00
0.01
0.01
0.02
0.01
0.02
0.01
0.02
0.01
0.02
−0.001
0.003
−0.000
0.002
−0.000
0.002
−0.000
0.002
θs >
50◦
mean
std
−0.00
0.01
−0.01
0.01
-0.00
0.01
−0.00
0.01
0.01
0.02
0.01
0.02
0.01
0.02
0.01
0.02
0.001
0.001
0.000
0.001
0.000
0.001
0.000
0.001
an exception for the radii between 3 µm and 5 µm, where the
differences, affected by the strong increase in the extremes,
present values up to 60 %. In the same way, the standard deviation shows a similar behavior, doubling its value in the
extremes (from 30–40 % it increases to 60 %) but keeping
around 20 % in the central part.
The central and the bottom chart of Fig. 17 correspond to
the same analysis (photometers #233 and #33) but are limited to those cases where the solar zenith angle is larger than
30◦ and 50◦ , respectively. As can be seen, both limitations
improve the comparison considerably. The comparison for
solar zenith angles larger than 30◦ eliminates 11 pairs of data
(from 33 to 22) and the results, especially the average value
of the relative differences, are diminished, reaching similar
values to the ones obtained for the photometers classed in the
subset Desert Dust I. Again, another 11 pairs of data disappear when the limitation is extended to θs > 50◦ ; under this
criterion, the average values do not suffer any improvements,
but the standard deviations are appreciably lower, especially
for r > 3 µm.
Continuing with the analysis of the data set desert dust 2,
the results for the optical parameters are shown in Table 7.
Averaged values and the standard deviations of the differences between the retrievals of principal plane and almucantar are presented for all data (upper part of the Table 7), those
data with θs > 30◦ (central part of the Table 7) and only for
those cases where θs > 50◦ (bottom part of the Table 7).
The means of the differences observed for the whole data
set are, in general, considerably larger than the values observed in the data set desert dust 1 (Figs. 14–16). Thus, averaged differences are about three times larger for the single
www.atmos-chem-phys.net/14/847/2014/
scattering albedo and for the imaginary part of the refractive
index in this data set than those obtained for the desert dust 1.
In the same manner, the values of the standard deviation are
typically twice as large.
On the other hand, the real part of the refractive index
presents similar means of the differences as those obtained
for the data set desert dust 1. Nevertheless, the values of the
standard deviation for this parameter are again twice as large
as the ones shown in Fig. 15.
Once we limit the study to those data with θs > 30◦ and
θs > 50◦ , the differences descend for the three parameters analyzed. The values of the differences for both restricted data
sets (presented in the central and bottom part of Table 7) are
similar to the ones obtained in the study for desert dust 1.
It should be noted here that, apart from the error sources
considered throughout the study, the AOD errors are of importance in the retrieving process (Dubovik et al., 2000). We
have not focused on them in the present study, since in principle the AOD measurements are equivalent to the PPL or
ALM geometries. However, if AOD errors are significant,
they may have different effects on aerosol retrievals using
PPL and ALM observations, especially in those cases with
larger differences in the information content, i.e., for small
solar zenith angles where the scattering angle coverage in the
almucantar is significantly smaller. Furthermore, the error in
AOD due to calibration is proportional to 1/m (m = optical
air mass; m ∼ 1/cos(SZA); see Hamonou et al., 1999) which
particularly enlarges the AOD errors for short solar zenith angles. The combination of both factors can explain the better
agreement between the two geometries at larger SZA, where
the AOD is more accurate. In fact, some uncertainties in the
Atmos. Chem. Phys., 14, 847–875, 2014
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B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
AOD calibration have been found in the set desert dust 2 data
(e.g., spectral crossovers of 440 and 500 nm).
4
Discussion
PPL retrievals are not available for the use of the wider scientific community and most of the studies presented in the literature where aerosol microphysical properties are retrieved
using Sun and sky radiance measurements have been done
exclusively using almucantar measurements (Holben et al.,
2001; Smirnov et al., 2002; Dubovik et al., 2002; Eck et al.,
2010; Giles et al., 2012, to cite some). One of the reasons
for such situation is that aerosol community generally has
higher confidence in the almucantar retrievals. Significant efforts have been undertaken in order to understand the potential of PPL retrievals and compare them with ALM data – for
instance, in the AERONET project, internal research activities have been developed (Alexander Sinyuk and Brent Holben, personal communication). However, no comprehensive
analysis of the expected differences of almucantar retrievals
with respect to principal planes is available in open-access
literature. As a result, for the wider scientific community, the
positive potential and shortcomings of using PPL aerosol remains unclear, in particular since the inversion strategy does
not reveal any clear preference in the geometry of the radiance measurement. Therefore, the purpose of this study is to
summarize and document the sensitivity of aerosol retrievals
to geometrical configurations of observations with a focus on
detailed comparative analysis of PPL and ALM retrievals.
One of the main practical reasons for preferring the aerosol
retrieval from almucantar observations is the great advantage
provided by the symmetry existing in the almucantar measurements. First, taking the average of left and right branches
results in more stable measurements and helps to reduce the
error effects. In addition, the averaging process also provides
a more representative spatial (angular) distribution of sky radiances, diminishing the effect of the aerosol inhomogeneity. Moreover, the symmetry allows one to perform a cloud
screening that can not be automatically assessed from principal plane data. These facts and others potentially compromise the accuracy of PPL retrievals (Holben et al., 1998,
2006; Dubovik et al., 2000), and consequentially prevented
the AERONET project from releasing PPL retrieval for public use since the reliability of the data is one of the primary
objectives of the AERONET network.
Indeed, during the present analysis, both the sensitivity
tests with the introduced modeled errors and the analysis of
data acquired under stable conditions confirmed the greater
reliability that is generally assumed regarding almucantar retrievals. It has been shown that the average between the left
and right branches in the almucantar largely diminishes the
consequences of possible pointing offsets in the instruments,
while for the principal plane the consequences of such errors
are more significant. Furthermore, almucantar retrievals have
Atmos. Chem. Phys., 14, 847–875, 2014
shown less dependency on the aerosol vertical distribution, as
generally expected from theoretical considerations.
On the other hand, the retrievals from almucantars taken
at high solar elevation show significant decreases in accuracy
for most of the retrieved aerosol parameters (Fig. 3). This result was already well discussed in Dubovik et al. (2000) and
is accounted for in the quality selection criteria (summarized
in Dubovik et al., 2002) and adapted for Level 2 retrieval
in AERONET version 2, where only retrievals with θs > 50◦
are accepted. Therefore, one of the immediate consequences
of using exclusively almucantar geometry is the lack of high
accuracy aerosol retrievals during the middle of the day (except at high latitudes and in wintertime at subtropical to midlatitudes), which are highly desirable for the various aerosol
studies. However, in the same simulation analysis (Fig. 3) the
principal plane retrievals remain stable over the course of the
day due to their larger angular scattering coverage.
The sensitivity tests and the real data analysis conducted in
this study show sufficiently high consistency between principal plane and almucantar retrievals, and this fact supports
the idea of using principal plane inversions to complement
almucantar retrievals in some specific cases, such as groundbased campaigns or the study of aerosol events. Nevertheless,
we should note that in both tests we have used quite selective data: in the first analysis, the data have been synthetically generated and in the real data analysis we have manually inspected the radiance data and maintained quite restrictive conditions low AOD daily variation, etc.; see Sect. 3).
Therefore, the use of principal plane data can only be recommended if a reliable cloud-screening procedure is developed
for PPL observations or for those cases when the manual inspection of the data is possible.
5
Conclusions
The simulated studies carried out using synthetic data from
a climatology analyses of the sites Solar Village, GSFC,
and Mongu have confirmed that the symmetry existing for
the almucantar geometry confers a greater robustness of the
aerosol retrievals in presence of various systematic uncertainties. In fact, the straightforward symmetry check used
in aerosol quality screening seemed to be a very efficient
and practical procedure to eliminate sky inhomogeneities
and reduce some of possible instrumental biases. For example, the present study has showed that if pointing errors are
present, the consequences for principal plane retrievals are
much larger than for almucantar retrievals. Only in an ideal
situation of homogeneous atmosphere when no extra errors
were introduced, would data from the principal plane geometry provide more reliable results than those from almucantar
for high Sun observation due to lower information content in
the almucantar radiances, where the range of observed scattering angles is substantially reduced.
www.atmos-chem-phys.net/14/847/2014/
B. Torres et al.: Sensitivity of aerosol retrieval to geometrical configuration
An analysis of data during stable atmospheric conditions
has been developed for the same three sites using a set of selection criteria (see Sect. 3). The comparison between principal plane and almucantar retrievals obtained in this analysis
has shown that the differences in the products are, in general,
within AERONET-estimated uncertainties for almucantar retrievals. The differences between the retrievals of the size distribution are generally under 10 % for radii between 0.1 µm
and 5 µm. Outside this size range, the differences can be as
large as 50 % and mostly positive (i.e., principal plane inversion results in larger volume concentrations than the almucantar). This result was expected due to the loss of sensitivity
of the retrievals to particles of those sizes for the wavelengths
used in AERONET and it was previously obtained with simulated data (similar result also in Dubovik et al., 2000).
These high differences in the extremes have almost no impact on other aerosol properties retrieved, such as the aerosol
optical depth or the optical parameters. Indeed, even though
there are differences over 50 % in the edge bins of the size
distribution, the subsequent differences in the optical parameters are almost negligible (e.g., absolute differences in the
single scattering albedo under 0.01 for all cases).
On the other hand, the comparison between the almucantar and principal plane retrievals in the subset desert dust 2
are systematically worse than those obtained in the other analyzed cases, in particular the subset desert dust 1. The cause
of these higher discrepancies has not been fully identified,
however, it is reasonable to expect different tendencies in the
results of PPL-ALM retrieval comparisons in the two subsets
desert dust 1 and 2 because of the different instrument performance (in this case photometers #233 and #33). Indeed,
instrumental issues related to AOD accuracy may cause discrepancies at low solar zenith angles. Another possible explanation is the different aerosol average conditions. In particular, the mean Angstrom exponent in subset desert dust 1
(about 0.6) is higher than for pure desert dust and indicates
the presence of a significant fine mode fraction. Alternatively, the subset desert dust 2 (with mean Angstrom exponent of 0.3) is representative of nearly pure dust.
Finally, this last group has been reanalyzed, limiting the
data set to large θs > 50◦ , which is in agreement with the
well-known AERONET level 2.0 criterion about SZA. This
threshold significantly reduces the AOD uncertainty related
to calibration (e.g., due to filter degradation) and therefore
improves the retrieval accuracy. In addition, the analysis for
different errors in Sect. 2 also indicates that the differences
between almucantar and principal plane are smaller for larger
θs . Thus, the differences in the scattering angle range in the
two geometries could amplify the discrepancies obtained between the retrievals if they are associated with instrumental
problems. As a result, significant improvements have been
observed in the retrieval comparison of PPL vs. ALM when
limiting the data set to large θs (> 50◦ ); one observes the
same typical differences as in the other data subset, desert
dust 1.
www.atmos-chem-phys.net/14/847/2014/
873
Acknowledgements. We thank the AERONET principal investigators and site managers at sites Solar Village (Naif Al-Abbadi,
Steve Wilcox), GSFC (Mikhail Sorokin, Brent Holben) and Mongu
(Mukufute Mukulabai, Brent Holben) We thank the AERONET,
PHOTONS, RIMA and WRC staff for their scientific and technical support. We acknowledge AERONET team members for
calibrating and maintaining instrumentation and processing data.
We especially thank I. Slutsker for providing us with useful tools
for data treatment and Brent Holben for his scientific support. The
authors also thank T. Eck and the anonymous reviewer for comments that led to a significant improvement to the paper. Financial
support was provided by the Spanish CICYT (CGL2009-09740
and CGL2011-23413, CGL2011-13085-E). The research leading
to these results was supported by funding from the European
Union Seventh Framework Programme (FP7/2007-2013) under
grant agreement no. 262254 [ACTRIS]. We also thank the Environmental Council of the CyL Regional Government (Consejería
de Medio Ambiente, Junta de Castilla y León) for supporting this
research. The publication of this article is financed by CNRS-INSU.
Edited by: D. Tanre
The publication of this article is
financed by CNRS-INSU.
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