AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-11-3627-2018Cloud heterogeneity on cloud and aerosol above cloud properties retrieved
from simulated total and polarized reflectancesCloud heterogeneity on cloud and aerosol above cloud propertiesCornetCélineceline.cornet@univ-lille1.frC.-LabonnoteLaurentWaquetFabienSzczapFrédéricDeaconuLuciahttps://orcid.org/0000-0002-2919-1491ParolFrédérichttps://orcid.org/0000-0001-6470-4558VanbauceClaudineThieuleuxFrançoisRiédiJérômeUniversité Lille, CNRS, UMR8518 – LOA – Laboratoire d'Optique Atmosphérique, 59000 Lille, FranceUniversité Clermont Auvergne, CNRS, UMR6016, Laboratoire de Météorologie Physique, 63000 Clermont-Ferrand, FranceCéline Cornet (celine.cornet@univ-lille1.fr)25June20181163627364316November20174December20172June20188June2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://amt.copernicus.org/articles/11/3627/2018/amt-11-3627-2018.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/11/3627/2018/amt-11-3627-2018.pdf
Simulations of total and polarized cloud reflectance angular signatures such
as the ones measured by the multi-angular and polarized radiometer
POLDER3/PARASOL are used to evaluate cloud heterogeneity effects on cloud
parameter retrievals. Effects on optical thickness, albedo, effective radius
and variance of the cloud droplet size distribution and aerosol parameters
above cloud are analyzed. Three different clouds that have the same mean optical
thicknesses were generated: the first with a flat top, the second
with a bumpy top and the last with a fractional cloud cover. At small
scale (50 m), for oblique solar incidence, the illumination effects lead to
higher total but also polarized reflectances. The polarized reflectances even
reach values that cannot be predicted by the 1-D homogeneous cloud assumption.
At the POLDER scale (7 km × 7 km), the angular signature is modified by a
combination of the plane–parallel bias and the shadowing and illumination
effects. In order to quantify effects of cloud heterogeneity on operational
products, we ran the POLDER operational algorithms on the simulated
reflectances to retrieve the cloud optical thickness and albedo. Results show
that the cloud optical thickness is greatly affected: biases can reach up to
-70, -50 or +40 % for backward, nadir and forward viewing
directions, respectively. Concerning the albedo of the cloudy scenes, the
errors are smaller, between -4.7 % for solar incidence angle of
20∘ and up to about +8 % for solar incidence angle of
60∘. We also tested the heterogeneity effects on new algorithms
that allow retrieving cloud droplet size distribution and cloud top pressures
and also aerosol above clouds. Contrary to the bi-spectral method, the
retrieved cloud droplet size parameters are not significantly affected by the
cloud heterogeneity, which proves to be a great advantage of using polarized
measurements. However, the cloud top pressure obtained from molecular
scattering in the forward direction can be biased up to about 60 hPa (around
550 m). Concerning the aerosol optical thickness (AOT) above cloud, the
results are different depending on the available angular information. Above
the fractional cloud, when only side scattering angles between 100
and 130∘ are available, the AOT is underestimated because of the
plane–parallel bias. However, for solar zenith angle of 60∘
it is overestimated because the polarized reflectances are increased in
forward directions.
Introduction
Cloud properties such as effective radius, optical thickness and albedo are
key parameters for studies concerning cloud radiative effects and
hydrological cycle of Earth climatic system. In the context of climate
change, these properties may be modified and result in a feedback, the sign
of which remains largely uncertain. In parallel, anthropogenic activities
modify the aerosol loading in the atmosphere and consequently play an
important role on cloud through the indirect radiative effects of aerosols
(Twomey, 1977). In addition, absorbing aerosol above clouds can
generate a positive direct radiative forcing (i.e., warming), that is
currently not well quantified, and modify the properties of the underlying
cloud layer
(Chand
et al., 2008; Costantino and Bréon, 2013; Wilcox, 2010).
Currently, several satellite radiometers use solar and infrared reflectances
to infer cloud and aerosols above cloud parameters. Generally, cloud optical
thickness (COT) and albedo are obtained from visible channels. Depending on
instrument capabilities, the effective radius can be retrieved jointly with
the optical thickness from a combination of visible and near-infrared
measurements (Nakajima and King,
1990) as it is done in the operational algorithm of the Moderate Resolution
Imaging Radiometer (MODIS
Platnick et al., 2003). These parameters can also be retrieved separately
from multi-viewing total and polarized measurements
(Buriez et al., 1997;
Bréon and Goloub, 1998) as implemented for the optical thickness or
under implementation for the effective radius with the POLarization and
Directionality of the Earth's Reflectances radiometer (POLDER,
Deschamps et al., 1994).
Concerning aerosols, spaceborne active instruments, such as the lidar CALIOP
are dedicated tools to detect multi-layer situations and to retrieve Aerosol
Above Cloud (AAC) properties (Hu et al., 2007; Chand et al., 2008; Young and
Vaughan, 2009) and were used for climate studies (Zhang et al., 2016a).
Passive measurements, that provide larger global coverage, can also be used
and an operational algorithm was developed to retrieve AAC scenes from the
polarization measurements provided by the POLDER instrument onboard PARASOL
(Waquet et al., 2009, 2013a). It was used to provide global analysis of the
aerosol above clouds properties (Waquet et al., 2013b). Further, (Peers et
al., 2015) combined total and polarized radiance measurements to retrieve the
aerosol absorption above clouds. A color ratio technique was also developed
to retrieve the AAC optical thickness and the corrected cloud optical
thickness from total radiance measurements. This method was adapted for the
Ozone Monitoring Instrument (OMI) ultraviolet measurements and MODIS
multi-spectral measurements (Torres et al., 2011; Meyer et al., 2015)
For computation time and simplicity reasons, all of these operational
algorithms assume that clouds are flat, homogeneous and horizontally
infinite, which is quite far from the reality. Numerous studies presented in the review of Davis and Marshak (2005)
and
Davis and Marshak (2010) showed that this assumption can lead to large errors
on the retrieved cloud parameters. For example, the cloud optical thickness
can be affected by the so-called plane–parallel bias induced by the
sub-pixel heterogeneity and the non-linear relationship between reflectances
and optical thickness. This bias usually leads to an effective optical
thickness lower than the mean optical thickness (Cahalan, 1994; Szczap et
al., 2000a). The sub-pixel optical thickness heterogeneity can also cause a
positive bias on the mean effective radius retrieved following the
bi-spectral technique (Szczap et al., 2000b; Zhang et al., 2012), whereas the
sub-pixel microphysical heterogeneity, not studied in this paper, leads, on
the contrary, to an underestimation of the effective radius (Marshak et al.,
2006). The bias on effective radius can thus be positive or negative
depending on sub-pixel heterogeneity of the cloud optical thickness and
effective radius (Zhang et al., 2016b).
In addition to the sub-pixel heterogeneity, Loeb
and Davies (1996) detected an increase of the retrieved optical thickness
from AVHRR (Advanced Very High Resolution Radiometer) correlated with the
solar zenith angle. Indeed, for oblique solar illumination, more energy is
transmitted through the clouds along the cloud side (or bump). It leads to
an increase in upward reflectances. Consequently, the cloud optical thickness
retrieved under the homogeneous cloud assumption appears higher for tilted
Sun than for overhead Sun. This effect is combined with angular effects,
known as 3-D effects, which depend on the sensor viewing direction. Again, in
the backward scattering direction, parts of the cloud sides illuminated by
the Sun lead to a larger retrieved optical thickness value. Inversely, in
viewing directions close to the forward scattering directions, some parts of
the cloud are in the shadow resulting in smaller optical thickness or larger
effective radius. This angular signature was observed on the retrieved cloud
optical thickness by several radiometers such as AVHRR
(Loeb and Coakley, 1998), MODIS
(Varnai and Marshak, 2002) and POLDER
(Buriez
et al., 2001; Zeng et al., 2012).
Concerning aerosol above cloud (AAC), intercomparisons of passive and active
retrievals were performed for case studies (Jethva et al., 2013) and for
global and multi-year data (Deaconu et al., 2017). All the methods developed
for passive instruments are based on 1-D calculations and, so, generally
restricted to homogeneous cloudy pixels for which the 3-D effects are
minimized. In case of aerosol retrieval in partial cloudy scenes, shadowing
or enhancement of the clear areas by neighboring clouds can modify the
retrieved aerosol properties. Errors on the retrieved aerosol properties are
in general dependent of the cloud distribution, optical thickness and spatial
resolution (Stap et al., 2016a, b).
Therefore, depending on the cloud heterogeneity, solar zenith angle and
viewing geometry, cloud parameters (i.e., optical thickness and effective
radius) and AAC parameters can be either under or overestimated. Several
studies based on simulations of total reflectances were made at the scale of
1 km corresponding to a moderate resolution radiometer such as MODIS or the
GLobal Imager (GLI/ADEOS2) to assess errors for liquid water clouds on
optical thickness (Iwabuchi and Hayasaka, 2002; Zinner and Mayer, 2006) or on
effective radius (Zhang et al., 2012). Kato et al. (2006) analyzed in
addition the error on the albedo of the cloudy scenes, which is an important
parameter for cloud radiative budget studies. At 1 km pixel size, they found
significant errors ranging between -0.3 and 14 % (-5 and 30 %)
from nadir (oblique) viewing depending on the cloud heterogeneity. Some
recent studies were also made for ice clouds and found non negligible errors
on retrieved COT from infrared (IR) measurements (Fauchez et al., 2015) or
from visible and near-infrared measurements (Zhou et al., 2017). Concerning
aerosol above cloud retrieval, to our knowledge, no study has been conducted
to assess errors due to cloud heterogeneity.
In this paper, we investigate the impact of cloud heterogeneities of
retrieved parameters on observations from the POLarization and Directionality
of the Earth's Reflectances radiometer, POLDER, which was on board the
platforms ADEOS1 in 1999, ADEOS2 in 2002 and PARASOL between 2005 and 2013.
POLDER/PARASOL allows to measure multi-angular total reflectances from 443 to
1020 nm and multi-angular polarized reflectances for three channels (490,
670 and 865 nm). A review of the POLDER capabilities for cloud measurements
and retrieval are presented in Parol et al. (2004). Comparisons with MODIS
cloud products were analyzed for cloud fraction in Zeng et al. (2011), for
cloud phase in Zeng et al. (2013) and cloud optical thickness in Zeng et
al. (2012). In the latter, the plane-parallel bias and 3-D cloud effects were
observed in the COT values retrieved from multi-angle measurements under
oblique solar illumination: lower COT were retrieved in the forward viewing
direction and larger COT in the backward viewing direction (Figs. 8 and 9 in
Zeng et al., 2012). Reflectance simulations from known cloud properties help
in quantitatively understanding the errors or biases on the retrieved cloud
properties. In addition, assessment of POLDER algorithms will be helpful in a
near future as the Multi-viewing, Multi-Channel, Multi-Polarization Imaging
mission (3MI), a POLDER type follow-on instrument is planned to be part of
the future generation of EUMETSAT polar satellites, EPS-SG (Marbach et al.,
2015).
Total and polarized reflectances were simulated at a small scale (50 m) from
synthetic 3-D cloud fields and averaged at the POLDER pixel size
(7 km × 7 km) to simulate POLDER measurements. The different
clouds used in our study and presented in Sect. 2 are generated using an
enhanced version of the 3DCLOUD model (Szczap et al., 2014; Alkasem et al.,
2017) and the reflectances are computed using the 3DMCPOL model (Cornet et
al., 2010). The POLDER cloud operational algorithm described in (Buriez et
al., 1997) is then used to retrieve the COT and the albedo of the cloudy
scene. Results are presented in Sect. 3.
Contrary to MODIS, POLDER does not make measurements in the near infrared to
get information on cloud particle size. The first two moments of the cloud
droplet distribution are obtained from polarized angular measurements
(Bréon and Goloub, 1998; Breon and Doutriaux-Boucher, 2005) as well as
the cloud top pressure (Goloub et al., 1994). Polarized reflectance
measurements are also used for cloud droplet retrievals by the Research
Scanning Polarimeter (Alexandrov et al., 2012). Cloud heterogeneity effects
on polarized measurements of liquid clouds have been studied for a single
flat cloud in (Cornet et al., 2013) and almost no effects were found. Here,
we go further and present in Sect. 4.1 the differences between 3-D and 1-D
polarized angular reflectances for different clouds and geometries.
Consequences for 3-D cloud radiative effects on the effective radius,
effective variance and cloud top pressure retrieval are presented in
Sect. 4.2. The impacts of the 3-D effects on the POLDER above cloud AOT
operational retrievals in case of fractional cloud were evaluated and
presented in Sect. 4.3. Conclusions are summarized in Sect. 5.
Description of the synthetically generated clouds and radiative
transfer
simulations
The clouds used in this study have been generated with the 3DCLOUD model
(Szczap et al., 2014; Alkasem et al., 2017). 3DCLOUD is a fast and flexible
algorithm designed for generating realistic 3-D extinction or 3-D optical
thickness for stratocumulus, cumulus and cirrus cloud fields. 3DCLOUD cloud
fields share some pertinent statistical properties observed in real clouds
such as a gamma distributed optical thickness and the Fourier spectral slope
β close to -5/3 between the smallest scale of the simulation to the
outer scale Lout where the spectrum becomes flat. In addition,
the user can specify the mean optical thickness COT, the heterogeneity
parameter ρ (standard deviation of COT normalized by the mean of COT)
and the cloud coverage C. In the first step, 3DCLOUD solves drastically
simplified basic atmospheric equations and integrates user's prescribed
large-scale meteorological profiles (humidity, pressure, temperature and wind
speed), in order to simulate 3-D cloud structures of liquid water content
(LWC). In the second step, the amplitude of the wavelet coefficient of the
extinctions are manipulated with a 3-D wavelet transform of the whole
3-D cloudy volume to constrain the mean COT, ρ, β and
Lout (Alkassem et al., 2017).
Here, we generated three cloud fields composed of 140 × 140 pixels with an
initial horizontal resolution of 50 m resulting to a 7 km × 7 km field,
which corresponds to a POLDER pixel size. The choice of 50 m for the pixel
scale was made considering the mean free path of the photon, (corresponding
to the inverse of the extinction coefficient so to about 70 m) but also
considering computation time and virtual memory availability.
The three generated clouds have the same mean optical thickness, close to 10,
at 865 nm. We created two stratocumulus clouds and one cumulus cloud. The
latter is the result of instabilities of the boundary layer and led to
fractional cloud cover and a larger heterogeneity parameter (Kawai and
Teixeira, 2011). The flat and bumpy clouds, representative of overcast
stratocumulus clouds, have the same heterogeneity parameter across the
140 × 140 pixels, ρ= 0.6, which is a typical value for
stratocumulus cloud. The cumulus cloud has a fractional cloud cover equal to
0.76 and a heterogeneity parameter equal to 1.12 setting clear sky pixels to
null values (0.95 if computed only with the cloudy pixels). These values are
typical values obtained from Landsat data (Barker et al., 1996) for
stratocumulus and cumulus clouds.
Figure 1 shows the vertical profiles of potential temperature and of vapor
mixing ratio prescribed in this study to generate the three cloud fields.
Globally, the vertical profiles of potential temperature and vapor mixing
ratio give the cloud position. The mean cloud top height is mainly
determined by the height where the potential temperature increases and the
vapor mixing ratio decreases. Cloud top height fluctuations (shapes of top
bumps) are mainly the result of the intensity of the vertical gradient of
the potential temperature and vapor mixing ratio.
Figure 2 shows the horizontal cloud optical thickness
fields and a vertical profile through
each cloud. In this study, we focus on the effects of the optical thickness
heterogeneity, which is supposed in real clouds to be more important than the
microphysical heterogeneity (Magaritz-Ronen et al., 2016). Consequently, the
cloud droplet size distribution is assumed to be uniform everywhere in the
cloud and follows a log-normal distribution with an effective radius of
11 µm and an effective variance of 0.02.
Vertical profiles of potential temperature and vapor mixing ratio
prescribed in this study to generate the flat stratocumulus (circle), the
bumpy stratocumulus (point) and the cumulus (star) cloud fields.
Cloud optical thickness (COT) of the three clouds used for the
study (a) the flat cloud, (c) the bumpy cloud and (e) the fractional cloud.
Extinction coefficient (km-1) along the x-z axis for y= 3.5 km for
(b) the flat cloud, (d) the bumpy cloud (f) and the fractional cloud.
From these 3-D cloud fields, we simulated the total and polarized
bidirectional reflectances function for the viewing zenith angle θ
and the viewing azimuthal angle ϕ. For
convenience, we call them total
reflectance R and polarized reflectance Rp in the following
equation:
Rθ,φ=πI(θ,φ)F0cosθ0,Rpθ,φ=πF0cosθ0Q2θ,φ+U2θ,φ+V2θ,φ,
where Iθ,φ,Qθ,φ,Uθ,φ and Vθ,φ
are the four Stokes parameters in W m-2 sr-1, F0 the solar
flux in W m-2 and θ0 the solar zenith angle.
Reflectances for three solar incidence angles 20, 40 and 60∘ are
computed with the 3-D radiative transfer model, 3DMCPOL. It is a forward
Monte-Carlo model able to compute radiative reflected or transmitted Stokes
vector as well as upwelling and downwelling fluxes in three-dimensional
atmospheres. Initially developed for solar radiation (Cornet et al., 2010),
it was next extended to thermal radiation (Fauchez et al., 2014). To save
time and for an accurate computation of reflectances, the local estimate
method (Marshak and Davis, 2005) is used. Periodic boundary conditions at the
horizontal domain limits are used. For highly peaked phase function, the
Potter truncation is implemented. Molecular scattering is computed according
to the pressure profile. A heterogeneous surface can also be specified with
Lambertian reflection, ocean or snow bidirectional function. The model
participated and was improved during the International Polarized Radiative
Transfer (IPRT) model intercomparisons on homogeneous cloud cases (Emde et
al., 2015) and on 3-D cloud cases (Emde et al., 2018).
Simulations are run with a total of 107 and 109 photons
for the homogeneous and heterogeneous clouds, respectively. The Monte-Carlo
uncertainties are estimated with the computation of the standard deviation
of 10 and 50 independent realizations of 106 and 20.106 photons
for the homogeneous and heterogeneous cloud, respectively. For the
homogeneous case, the relative standard deviation is below 0.12 % for the
total reflectances and below 1.2 % for the polarized reflectances. For the
heterogeneous clouds, at 50 m resolution, the mean relative standard
deviation is below 1.3 % for the total reflectances. For polarized
reflectances at 50 m, the mean relative standard deviation varies according
to the angular geometry and is between 2 and 107 % for very small
reflectance values with a mean value of 23 %. At 7 km resolution, as the
reflectances are averaged, relative standard deviation values are much lower
below 0.01 and 0.8 % for total and polarized reflectances,
respectively.
At this stage, molecular scattering is integrated but no aerosols. To remain
consistent with assumptions made within the POLDER operational algorithm, an
oceanic surface with a wind speed of 7 m s-1 is included for total
reflectances while a black surface is included for polarized reflectances.
Indeed, for retrieval using polarized reflectances, the multi-angular
ability of POLDER provides the advantage of not using the directions close
to the sun-glint, where the polarized reflectances can be high. As POLDER
measures up to 16 directions, we simulate reflectances for 16 POLDER typical
zenith observation angles in the solar plane. Total reflectances of the
three clouds are presented in Fig. 3 (first column) with a 50 m spatial
resolution for a solar incidence angle of 60∘ in the cloudbow
direction (42∘ from the backward direction). Polarized reflectance
fields are discussed in Sect. 4.1.
Total and polarized reflectances for the flat cloud (first line),
the bumpy cloud (second line) and the fractional cloud (third line). Total
reflectances at 490 nm in the cloudbow scattering direction (first column),
polarized reflectances at 490 nm in the cloudbow direction (second column)
and polarized reflectances at 490 nm in the forward direction (third
column). The Sun illuminates the scene from the left of the figures
(SZA = 60∘). For polarized reflectances in the second column,
yellow color corresponds to polarized reflectance values higher than the
maximum value predicted with the homogeneous cloud assumption.
Impacts on total reflectances and consequences for optical thickness and
albedo retrievals
We averaged spatially the 50 m resolution reflectances fields at 7 km × 7 km
to mimic the radiometer measurements and applied the POLDER operational
algorithm on these synthetic measurements to obtain cloud optical thickness
and albedo. In order to assess the retrieval errors due to the cloud
homogeneous assumption without biases due to differences in reflectance
computations, we also computed the 1-D reflectances of the three equivalent
homogenous clouds, which are subsequently used for retrieval to act as
references for the inhomogeneous cloud retrievals. The COT of the equivalent
homogeneous clouds is the mean COT of the heterogeneous clouds, and their
cloud top and base altitudes correspond to the maximum and minimum altitudes
of the respective homogenous clouds.
Figure 4 summarizes the results obtained for the retrieved cloud optical
thickness for the three solar zenith angles and the four cases, namely the
homogeneous (1-D), the flat, the bumpy and the fractional cloud. The optical
thicknesses are plotted as a function of sensor zenith angles with negative
values corresponding to backward scattering directions and positive values
to forward scattering directions. The homogeneous cloud values (1-D) are only
plotted for control and we observe logically that the retrieved value is
almost constant and close to 10, independently of the solar incidence angle,
since the same assumption (1-D homogeneous cloud) is used in both the forward
simulation and retrieval algorithm. Slight differences appear because of
inclusion of aerosol optical thickness in the forward model used to build
the look-up table (Buriez et al.,
1997) but not in our simulations. The small angular difference in the
backward direction at 20∘ can be attributed to interpolation in
the LUT.
Looking at results concerning the heterogeneous clouds (3-D), we clearly
note, in the angular range between about -30 and +30∘, the plane-parallel bias, which leads to retrieving optical thicknesses lower
than the mean optical thickness. At nadir view, the relative error is
between -10 and -20 % both for the flat cloud and bumpy cloud and is much larger
for the fractional cloud, between -35 and -50 %. The flat and bumpy clouds
were built with the same heterogeneity parameter (ρ= 0.6), whereas
the fractional cloud has a larger heterogeneity parameter including the
zeros (ρ= 1.12) due to its fractional nature. That confirms that
heterogeneity parameters can be at first order used to characterize
plane-parallel bias (Cahalan et al., 1994; Szczap et al., 2000a).
(a) Cloud optical thickness (COT) retrieved with the POLDER
operational algorithm as function of the viewing zenith angle for the four
different simulated cloud cases (1-D, flat, bumpy and fractional clouds) and
for different solar zenith angles (20, 40 and 60∘).
(b) Relative differences
[(COT3-D - COT1-D) / COT1-D × 100] between the heterogeneous
cloud (3-D) and the homogenous cloud (1-D) COT.
For solar zenith angle (SZA) equal to 20∘, the retrieved optical
thickness is almost independent of the observation geometry whatever the
cloud type, while for SZA = 60∘, significant differences between
viewing angles are observed. We note indeed a strong decrease of the
retrieved optical thickness value in the forward scattering direction leading
to a relative bias on the retrieved optical thickness between -40 % for
the flat and bumpy cloud and -70 % for the fractional cloud. On the
contrary, we can notice an increase of the retrieved optical thickness value
in the backscatter direction (relative bias ranging from +3 % for the
flat cloud, +43 % for the bumpy cloud and +21 % for the
fractional cloud). This angular behavior was already simulated by several
authors at the resolution of 1 km (Loeb et al., 1998; Varnai, 2000; Iwabuchi
and Hayasaka, 2002; Zinner and Mayer, 2006) and agrees with POLDER
observations (Buriez et al., 2001; Zeng et al., 2012). In the backscatter
directions, the cloud sides illuminated by the Sun make the cloud brighter,
in contrast to the forward direction where cloud sides are in the shadow
(Varnai and Davies, 1999). These effects are visible for the bumpy cloud but
are much less pronounced for the flat cloud. The heterogeneity parameter thus
seems well adapted to characterize quantitatively the plane-parallel bias
(Szczap et al., 2000a) but not sufficient to characterize the amplitude of
the 3-D effects. Indeed, the flat and bumpy clouds, which are characterized
by the same heterogeneity parameter value show close plane-parallel bias
(between -10 and 20 % for nadir
view) but quite different amplitudes of the 3-D effects, especially in the
backward direction for SZA = 60∘. We note also that this error in
the backward direction is larger for the bumpy cloud (about +40 %)
compared to the fractional cloud (about +20 %) because for the latter
the plane-parallel bias is stronger (about -40 % at nadir view).
The following step in the POLDER operational algorithm consists in computing
the albedo of the cloudy scene, corresponding to the upward flux normalized
by the solar incident flux, from the retrieved cloud optical thickness using
look-up tables (Buriez et al., 1997).
The albedo is not derived from a single view, as computed in
Kato et al. (2006), at 1 km × 1 km but from all view angles. The multi-angular
capabilities of POLDER allow averaging over the different values using
a directional weighting function. The aim of this weighting function is to
limit the influence of directions for which the microphysical or 3-D effects
can be important as for example in the cloudbow, glory and forward
directions (Buriez et al., 2005).
The assessment of cloud heterogeneity effects on cloud albedo is realized by
comparing the retrieved POLDER algorithm albedos with the ones directly
computed with the 3DMCPOL radiative transfer model identified as the true
one. Direct comparisons of retrieved albedo values from homogeneous or from
heterogeneous clouds, as done for other parameters, are not suitable for
cloud albedo. Indeed, the plane-parallel bias leads to reflectances off of a
heterogeneous cloud lower than the reflectances off of an equivalent
homogenous cloud with the same (mean) COT. The retrieved optical thickness
is thus lower than the mean optical thickness of 10 (Fig. 4). Using it to
recompute the albedo in the POLDER algorithm leads to a too low value
comparing to the albedo of the equivalent homogeneous cloud. In contrast,
using 1-D cloud radiative model in the inversion and in the forward
computation as it is done in the operational algorithm is consistent and
leads to a sound cloud albedo. The plane-parallel bias is indeed almost
canceled.
For each cloud case, albedo of the cloudy scene obtained from
simulation with 3DMCPOL (first line), retrieved with the POLDER operational
algorithm (second line) and relative differences
[(Retrieval - simulation) / Simulation × 100] between the
two values (third line, in bold) for the homogeneous cloud (for control) and
for the flat, bumpy and fractional clouds for three solar zenith angles (20,
40 and 60∘). The mean optical thickness of each cloud is 10 and the
effective radius is fixed to 11 µm.
Values of the computed and retrieved albedos and their relative differences
are indicated in Table 1. The first line (homogeneous cloud) shows very good
consistency between the 3DMCPOL radiative transfer code and the retrieved
values using the POLDER operational algorithm. Relative differences between
computed and retrieved albedos remain smaller than 0.5 %.
For SZA = 20∘, the POLDER operational algorithm slightly underestimates
the albedo for the flat and bumpy cloud with relative differences
under -2.5 %. The relative error is slightly larger for the fractional
cloud (-4.7 %). The relative differences are low compared to optical
thickness errors because, as explained above, the same cloud model (i.e., the
homogeneous cloud) is used to retrieve and to compute the albedo. The slight
underestimation of the retrieved albedo comes from differences in the
non-linear relationship between reflectances and albedo as a function of the
optical thickness. It implies that effects of the plane-parallel bias are
not the same for reflectances and albedos. Inversely, for SZA = 60∘, the albedo is overestimated by 2.35 % for the flat cloud
case and 7.88 % for the fractional cloud case because illumination effects
in the backscattering direction are not completely canceled by the
weighting function.
At SZA = 40∘, negative differences due to the plane parallel
biases are on contrary almost canceled by illumination effects for bumpy and
fractional cloud leading to very small errors of -0.26 and
+0.14 %, respectively.
Differences between 3-D and 1-D polarized reflectances and consequences for
microphysical distribution, cloud pressure and aerosol above cloud
retrievalsCloud heterogeneity effects on polarized reflectances
As explained before, we simulated using 3DMCPOL, the polarized reflectances
for the three wavelengths used in the POLDER retrieval algorithms (e.g., 490,
670 and 865 nm). Total and polarized reflectances at 490 nm for 50 m
resolution are presented in Fig. 3 (second and third columns) for
SZA = 60∘. First of all, we can see that for flat cloud, the polarized
reflectance field appears smoother than the total reflectance field. As
polarized reflectances level off for optical thickness greater than about three,
all cloudy pixels with higher optical thickness provide almost the same
polarized reflectance. Therefore, cloud heterogeneity effects are visually
less discernible on polarized reflectance fields compared to the total
reflectance fields.
For the bumpy or fractional clouds, the polarized reflectance field appears
much rougher. In the cloudbow viewing directions (second column), some parts
of the cloud facing to Sun appear brighter and other parts in the shadow
darker. At this small spatial scale (50 m), a large part of the total amount
of pixels exhibits polarized reflectance higher than the maximum value
predicted by the 1-D homogeneous cloud model (yellow pixels) and thus cannot
be obtained with 1-D radiative transfer simulation: at 490 nm, their ratio
reaches 41 % of the total number of pixels for the flat cloud, 52 % for
the bumpy cloud and 38 % for the fractional cloud. This phenomenon of
illumination and shadowing was already highlighted simply with a step cloud
in Cornet et al. (2010).
In the forward direction (Θ= 60∘) at 490 nm (third
column in Fig. 3), the “shadow areas” are not dark anymore contrary to
the total reflectance images (first column in Fig. 3) and appear even
brighter than cloudy part. For short wavelength and forward scattering
angles, molecular signal is stronger than the cloud signal and thus enhances
the polarized signal in the shadow parts.
In Fig. 5, we plot the average polarized reflectances as would be measured
by POLDER at 7 km × 7 km resolution as a function of the scattering angle
Θ for a solar zenith angle SZA = 60∘, and for the three
wavelengths. As we can see in Fig. 5a, the main differences between
homogeneous and heterogeneous clouds appear in the cloudbow direction
(Θ= 140∘) and in the forward direction (Θ < 80∘). In the cloudbow direction, the 3-D polarized
reflectances are lower than the 1-D ones for the three clouds. Similar to the
total reflectances, this is mainly due to the plane-parallel bias. In these
directions, the relative differences (Fig. 5b) are about -9, -12
and -35 % for the flat, bumpy and fractional cloud, respectively. We note
that the relative difference is slightly lower for 490 nm because of the
smoothing effects by molecular scattering above the cloud.
(a) Polarized reflectance as a function of the scattering
angle for three wavelengths (490, 670 and 865 nm) for the homogeneous cloud
(1-D), the flat cloud, the bumpy cloud and the fractional cloud.
(b) Relative difference between 3-D and 1-D polarized reflectances,
[(Rp3-D - Rp1-D) / Rp1-D × 100]. The solar zenith angle is
60∘.
In the forward scattering directions, the consequences of the 3-D effects in
terms of absolute polarized reflectances appear differently depending on the
wavelength. At 490 nm, the 3-D effects enhance the absolute polarization,
while at 865 nm they reduce it. At 490 nm, atmospheric molecular scattering
is very strong. The 3-D polarized reflectances appear greater than the 1-D
ones because, as seen in Fig. 3, the polarization in the shadow parts of
the cloud is enhanced by this molecular scattering. At 865 nm, the shadow
parts appear dark with small positive values that reduce the negative
polarization of the cloud and consequently the absolute polarization. The
relative difference (Fig. 5b) is consequently positive for 490 nm (about
+55 % for the fractional cloud) and negative for 865 nm (about -75 %
for the fractional cloud). At 670 nm, the polarized reflectance in the
shadow part is only slightly enhanced by the molecular scattering but more
compared to 865 nm. Polarized reflectances thus become positive for the
fractional cloud but not for the flat and bumpy clouds. Note that in the
backward direction, the polarized reflectances are very weak thus no
heterogeneity or 3-D effects can be detected.
Figure 5 illustrates results obtained for simulations for SZA = 60∘ with a scattering angular range between 60 and
180∘. For SZA = 20 and SZA = 40∘, the plots are
similar with a reduced scattering angular range comprised between
100 and 180∘ for SZA = 20∘, and between
80 and 180∘ for SZA = 40∘. Consequently,
for SZA = 20 and SZA = 40∘ the attenuation due to
the plane-parallel bias is the main effect that impacts the polarized
reflectances.
Consequences for droplet size distribution and cloud top pressure
retrievals
The polarized signal is used as input of a POLDER retrieval algorithm
developed to retrieve effective radius, effective variance and cloud top
pressure. It uses the polarized information as presented in Bréon and
Goloub (1998). The position of the cloudbow as well as the position of the
supernumerary bows gives information on the effective radius. The amplitude
of the supernumerary bows gives information on the effective variance of the
cloud droplet size distribution. For cloud top pressure, the algorithm uses
the information given by the molecular scattering that depends, in the
forward scattering directions, on the atmospheric air mass factor (Goloub et
al., 1994). The algorithm, under implementation in the POLDER operational
algorithm, is based on an optimal estimation method (Rodgers, 2000) and
provides errors associated to each of the retrieved parameters. It is also
possible to add in the forward model variance-covariance matrix an error due
to the non-retrieved parameter. Following previous computations made in
Waquet et al. (2013a) for the misrepresentation of the cloud heterogeneity
effects, the error added in the variance-covariance matrix on the
reflectances is 7.5 % in the directions close to the cloudbow and 5 %
elsewhere.
Retrieved cloud droplet effective radius (Reff),
effective variance (Veff) and cloud top altitude (CTOP) from
polarized reflectances with an optimal estimation algorithm. First column is
the input, second column the retrieval for the homogeneous cloud (1-D), third
column for the flat cloud, fourth column for the bumpy cloud and fifth column
for the fractional cloud. The last line is the final cost function with NC
meaning no convergence. The solar zenith angle is 60∘. Note that the
cloud top altitude is different according to the heterogeneous cloud leading
to three different lines.
The retrieved values obtained with this algorithm based on the homogeneous
cloud assumption, are presented in Table 2. We again use the homogeneous
cloud (1-D) to check the consistency of our simulations. For all clouds, even
if differences in polarized reflectances are large in amplitude, the
retrieval algorithm captures the general angular features the three
wavelengths, which results of small errors on the retrieved effective radius
and effective variance. The algorithm is able to retrieve an effective
radius of 11 µm and an effective variance of 0.02 with relative error
compared to the input under 2.6 and 2.1 %, respectively (see Table 2).
Indeed, as the cloud heterogeneity effects do not modify the cloudbow
position and the number of supernumerary bows, the retrieval of the droplet
size distribution parameters is not really affected by 3-D effects. This is a
fundamental advantage of the polarized measurements compared to the
bi-spectral method
(Zhang et al.,
2012), usually used when visible and shortwave infrared wavelengths are
available. However, we note that the cost function, which is the root-mean-square-difference between the model and measurements weighted by the
respective variance–covariance matrix is larger for 3-D clouds than for the
homogeneous cloud. It means that the forward model (homogeneous model) used
for the retrieval does not allow perfectly matching the heterogeneous cloud
reflectances used as input. For the bumpy and fractional cloud, the
algorithm does not even converge meaning that the forward model is not able
to represent the signal within the allocated uncertainties. The main impact
of cloud heterogeneities appears for cloud top pressure retrieval. In Table 2, we report the mean cloud top height for each heterogeneous cloud and the
retrieved value. The 1-D homogeneous values used for control were set to the
intermediate mean cloud top altitude. We note slight differences about -4 hPa (+37 m) between input and 1-D retrieval, which reveals slight
differences between the radiative transfer codes used for the simulation and
for the retrieval. However, differences between 3-D and 1-D are much larger,
especially for the bumpy and fractional cloud with values of +62 hPa (-550 m) and +45 hPa (-390 m). As already explained, the polarized reflectance
in the shortwave wavelengths (490 nm) is very high because of molecular
scattering. The retrieval of the cloud top pressure is based on the amount
of molecular scattering occurring above the cloud when looking in forward
scattering (for scattering angle ranging between 60 and
120∘). Consequently, as shadowing effects modify the polarized
reflectances in the forward scattering directions, the cloud top pressure
retrieval is impacted, especially for the fractional and bumpy cloud.
Impacts for aerosol above cloud retrieval
Polarized reflectances of POLDER are also used to retrieve aerosol optical
thickness (AOT) of an aerosol layer above cloud (Waquet et al., 2009, 2013a).
Waquet et al. (2013a) describes two algorithms for aerosol above clouds (AAC)
retrieval using POLDER polarization measurements: (i) the research algorithm
is an optimal estimation method that retrieves a large number of aerosol and
cloud parameters and (ii) the operational algorithm is based on LUTs
calculations and allows to retrieve the AOT at 865 nm and the
Ångström exponent of aerosol above clouds. The “operational
algorithm” is the one considered in the present study. The LUT calculations
are performed with the successive order of scattering code that assumes a
plane-parallel atmosphere (Lenoble et al., 2007). It uses assumptions of
particle microphysics: six fine mode spherical aerosol models (effective
radius varying between 0.09 and 0.24 µm) are considered and a
constant complex refractive index of 1.47+0.01i is assumed. The errors due
to the assumption made for the complex refractive index were estimated at
around 20 % on average for the AOT (Peers et al., 2015) and maximal
relative error may reach 25 % in case of extreme aerosol events
(AOT > 0.6 at 550 nm). One additional non-spherical mineral
dust model is also considered in the LUTs.
The operational algorithm uses a specific strategy to retrieve aerosol
properties above clouds that depends on the aerosol type and also on the
available viewing geometries (see Fig. 4 in Waquet et al., 2013a). In case of
fine mode particles, the retrieval is restricted to the use of observations
acquired for scattering angles smaller than 130∘, where polarization
measurements are highly sensitive to scattering by fine mode particles (such
as biomass burning aerosol) and only weakly sensitive to cloud microphysics.
This is illustrated in Fig. 6 with the dashed lines representing polarized
reflectances for a homogeneous cloud with an aerosol layer above (dark blue
and red curves) and without aerosol above (clear blue and pink curves). The
increase of the polarized reflectances for scattering angles less than
130∘ is clearly visible when an aerosol layer is present above a
cloud. Non-spherical particles in the coarse mode, such as mineral dust
particles, cannot be handled with this method as they do not polarize light
much. When dust particles are transported above clouds, they reduce the
magnitude of the primary cloud bow. The operational algorithm then includes
the primary bow in order to retrieve the above cloud dust AOT. In this case,
as the magnitude of the primary cloud bow primarily depends on the cloud
droplet effective radius, it must be estimated or included in the retrieval
process. Collocated cloud properties from MODIS at high resolution
(1 km × 1 km) are used to characterize and to select the cloudy
scenes within a POLDER pixel (6 km × 7 km at nadir) and the MODIS
cloud products can then be used in the operational algorithm to estimate the
droplets effective radius. As the magnitude of the primary cloud bow is only
weakly impacted by the choice of the droplet effective variance, this
parameter is assumed to be constant and equal to 0.06. Several filters are
eventually applied to obtain a quality-assessed product. For instance, the
retrievals are restricted to cloudy pixels associated with cloud optical
thicknesses larger than 3.0, since the polarized radiation reflected by the
cloud layer is then saturated and does not depend anymore on the cloud
optical thickness. Criteria are also used to reject inhomogeneous and
fractional cloudy pixels and to avoid cirrus cloud contamination. We refer to
Sect. 3.4 in (Waquet et al., 2013a) for a detailed description of the
operational algorithm.
Polarized reflectances as a function of the scattering angle. Dashed
lines are for homogeneous cloud with and without a biomass burning aerosol
layer above; solid lines are for the fractional cloud with and without a
biomass burning aerosol layer above. The solar zenith angle is 60∘.
In the POLDER operational algorithm, the underneath cloud is assumed to be
homogeneous. Empirical criterions are used to reject heterogeneous and
fractional cloudy pixels but a misclassification of the cloudy scenes is
still possible. Moreover, it is also important to evaluate the AOT retrieval
errors due to 3-D effects in case of fractional cloud covers. These scenes,
for which aerosols and clouds are potentially mixed, remain untreated and
are of primarily importance for climate studies. In the following, we
investigate the possibility of using the operational algorithm to handle these
scenes and we evaluate the biases observed in the polarized reflectances and
in the AOT retrieval errors due to 3-D effects. In order to check the AOT
value retrieved for such cases, we use the 3-D polarized reflectances
generated for the fractional cloud case, with and without aerosol, and we
used these 3-D simulations as inputs for the operational algorithm. Note that
for the synthetic retrievals discussed here, we assumed that the operational
algorithm knows the effective radius and effective variance of the cloud
droplets.
3-D Polarized reflectances used as input for the aerosol above cloud
algorithm (Waquet et al., 2013a) and polarized reflectances simulated with
the algorithm after the convergence of the retrieval. Reflectances at all
angles were used (solid line) and reflectances with only scattering angles
above 120∘ (dashed line).
The 3-D polarized reflectances used as input of the algorithm and the ones
simulated after the adjustment of the aerosol model and optical thickness
are plotted in Fig. 7 (solid lines). When a large scattering angular range
is available (between 60 and 180∘), the algorithm
works in an efficient way. The lateral polarized reflectances in scattering
angular range between 80 and 120∘ exhibit low or
negative values. Consequently, no aerosol (AOT = 0) were retrieved. However, we
note that the primary cloudbow is not well reproduced by the 1-D
simulation provided by the operational algorithm. In the POLDER
measurements, the range of sampled scattering angles varies with the
geographical position. In some cases, the scattering angle range sampled by
the instrument can be quite narrow. We tested the algorithm without
observations acquired for scattering angles smaller than 120∘
(dashed lines in Fig. 7). The cloudbow signal is then better matched but
the inversion method retrieves erroneous AOT values of 0.31 at 670 nm and
0.28 at 865 nm instead of zero for both.
Retrieved aerosol properties for a biomass aerosol layer above the
fractional cloud with the operational algorithm described in Waquet et
al. (2013a). Aerosol optical thickness at 670 nm (AOT670), at 865 nm
(AOT865) and Ångström coefficient for three solar zenith angles
(SZA). Relative differences [(Fractional - Homogeneous) / Homogeneous × 100] are indicated
in bold. Last two lines, RMSE computed between the input and the recalculated
polarized reflectances for the homogenous and fractional
cloud.
A second test is made with simulated reflectances including a
biomass-burning aerosol layer lofted above the fractional cloud. For the
simulation, the AOT of the aerosol layer is fixed to 0.28 and 0.15, the
single scattering albedo to 0.93 and 0.91 at 670 and 865 nm, respectively. In
order to avoid retrieval errors related to the choice of aerosol model, we
used one of the biomass burning aerosol model included in the operational
algorithm. The particles effective radius is 0.15 µm and the single
scattering albedo is equal to 0.91 at 865 nm. The simulated 3-D angular
polarized reflectances as a function of the scattering angles are presented
in Fig. 6 (solid blue and red lines). Compared to the 1-D reflectances with
aerosols above cloud (dashed blue and red lines), the cloud heterogeneity
effects amplify the increase of the forward signal and the decrease of the
cloudbow signal. As with molecular scattering (Sect. 4.1), aerosol
scattering contributes to enhance the polarized reflectances in the shadow
and cloud-free parts leading to higher averaged polarized reflectances in
the forward direction. In the cloudbow direction (near 140∘), and
to a lesser extent, in the side scattering (between 100 and
130∘ in scattering angle), the polarized reflectances are
additionally attenuated because of the plane-parallel biases. Note that for
other solar zenith angles (not shown here), the plots are similar with a
more restricted scattering angular range (between 100 and
180∘ for SZA = 20∘ and between 80 and
180∘ for SZA = 40∘). Consequently, only the
attenuation due to the plane-parallel bias impacts the polarized
reflectances.
The results obtained with the operational algorithm are presented in Table 3.
We repeat that the same input AOT is used in the 1-D and 3-D simulations (AOT
of 0.15 at 865 nm). The Ångström exponent is related to the ratio of
two optical thicknesses at two wavelengths and corresponds in the retrieval
to the best-selected model. As expected, the AOTs retrieved by the algorithm
for homogenous clouds are close to the input one, whatever the SZA value. The
retrieved AOTs only slightly overestimate the input (0.15) and are
respectively equal to 0.180, 0.170 and 0.170 for SZA of 20, 40 and
60∘. This overestimation is likely due to the approximations used in
the retrieval algorithm (e.g. interpolation in the LUTs). Comparing with the
retrieved values from homogeneous cloud, significant departures are observed
for fractional clouds especially for SZA = 60∘. The AOTs
retrieved at 865 nm are then equal to 0.119, 0.170 and 0.280 for SZA of 20,
40 and 60∘, respectively. For a given solar zenith angle, the viewing
geometries and the angular resolution are identical for the homogeneous and
fractional clouds. The differences observed in AOT between the 1-D and 3-D
calculations are then necessarily due to cloud heterogeneity effects. For
SZA = 40∘, the best model that minimized the cost function is the
same for the homogeneous and fractional clouds. Differences for the retrieved
AOT are negligible, but we note that the RMSE between the input and
recalculated reflectances is slightly larger for the fractional cloud than
for the homogeneous one. For SZA = 20∘, the operational algorithm
also successfully retrieves the input aerosol model for the homogeneous and
fractional cloud. However, the AOT retrieved by the operational algorithm,
under the homogenous assumption, is underestimated with an error of about
-33 %. For SZA = 20∘, the range of scattering angles
effectively used for the retrieval is between 100 and 130∘. Polarized
reflectances for SZA = 20∘ are not shown but they are similar to
the ones shown in Fig. 7 between 100 and 180∘.
Between 100 and 130∘, as
shown in Fig. 7, 3-D polarized reflectances are lower than the 1-D ones
because of the plane-parallel biases, which explains why the AOT retrieved by
the algorithm is underestimated. However, as the differences are mainly due
the plane-parallel bias, which is similar for the two wavelengths, the cloud
heterogeneity effects do not affect the selection of the best aerosol model.
For SZA = 60∘, the range of scattering angles used is between 60
and 130∘. Between 60 and 90∘, there is an increase of the
forward scattering signal due to 3-D effects, which is interpreted by the
operational algorithm as an increase in the AOT. We note also that 3-D
effects bias the aerosol model for this case as a smaller value of
Ångström exponent (corresponding to a larger effective radius) is
retrieved for the fractional cloud. The retrieved AOT is thus higher (AOT of
0.28 comparing to 0.17) with a relative error up to 65 %.
Note that the operational algorithm is not applied for pixels too
heterogeneous. Those are filtered using the standard deviation of the COT
retrieved at 1 km by MODIS that should not exceed five. For the fractional
cloud of this study, we checked the standard deviation value computed from
the input cloud optical thickness (different from the retrieved one) and
found seven. It is slightly above the homogeneity limit fixed in the aerosol
above cloud algorithm developed for POLDER
(Waquet
et al., 2013a). The results presented here for aerosol above cloud retrieval
can thus be seen as an upper limit for the operational algorithm.
Conclusions
This study used simulations to understand and quantify the effects of cloud
heterogeneities on POLDER total and polarized reflectances. We investigated
the consequences of heterogeneous cloud radiative effects on the retrieved
values of cloud optical thickness, droplet effective radius, effective
variance, cloud pressure and optical properties (optical thickness and
Ångström exponent) of above cloud aerosol, provided by operational
and research algorithms of the POLarization and Directionality of Earth's
Reflectances (POLDER) instrument. 3-D cloud fields were generated with the
3DCLOUD model (Szczap et al.,
2014) and the 1-D and 3-D radiative transfer simulations were done with the
Monte Carlo 3DMCPOL model (Cornet et
al., 2010). Three types of heterogeneous water cloud were studied: a flat, a
bumpy and a fractional cloud.
The reflectances simulated at small spatial scale (50 m) and averaged at the
POLDER spatial scale (7 km × 7 km) are used as realistic input of the
different cloud operational and research algorithms. For high solar
illumination (SZA = 20∘), the optical thickness retrieval
yields, as it was already shown in numerous studies, to lower optical
thickness than the averaged ones because of the plane-parallel bias. For
POLDER, the retrieved optical thicknesses are underestimated by 10 or 35 %
depending on the cloud type. For oblique solar incidence, the POLDER
algorithm yields to higher optical thickness in the backscattering
directions due to solar illumination effects and much lower optical
thickness (up to -70 % for the fractional cloud) in the forward scattering
directions due to shadowing effects. The errors on albedo are weaker with
largest bias for albedo between -5 % for high solar illumination and
+8 % for solar zenith angle of 60∘.
We next analyzed the cloud heterogeneity effects on polarized reflectances.
We showed a reduction of the cloudbow and side reflectances due to the
plane-parallel bias and the shadowing effects. In the forward scattering
direction, the effects are spectrally dependent. For the shortest wavelength
(490 nm), the molecular scattering in the shadow areas increases the
averaged polarized signal and leads to an increase of the polarized
reflectances. At 865 nm, the weak positive polarized reflectances of the
shadow areas reduce the polarization of the clouds, which is negative for
these scattering angles. However, even if the polarized angular signature is
modified, the retrieved effective radius and effective variance are hardly
affected because cloud heterogeneities do not modify the positions of the
cloudbow and supernumerary bows. The Rayleigh cloud top pressure is, in
contrast, biased for a solar zenith angle of 60∘ by about 60 hPa
corresponding to a cloud 550 m lower in the atmosphere.
We also tested the aerosol above cloud algorithm (Waquet et al., 2013a). Even
in the absence of aerosol, the algorithm retrieves non-negligible AOT values
when only larger scattering angles (between 120 and 180∘) are
available. With aerosols above a fractional cloud, the AOT can be
underestimated for a high solar elevation (SZA = 20∘) because of
the plane-parallel bias and on contrary overestimated for low solar elevation
(SZA = 60∘) because of the shadowed effects that increase
polarized reflectances. The Ångström exponent is affected by these
shadowing effects for SZA = 60∘ but not by the plane-parallel
bias since the plane-parallel biases for 490 and 865 nm is almost spectrally
neutral and since the information used to select the aerosol model is related
to the ratio of those two wavelengths.
These results mainly show that 3-D effects for fractional clouds are
primarily significant at forward scattering geometries in case of low solar
elevation (scattering angle < 80∘ and SZA = 60∘) and in the rainbow region (scattering angle of about
140∘± 5∘). The range of scattering angles sampled
between 60 and 80∘ is not necessarily useful for an accurate
retrieval of the above cloud AOT. So, reducing the range of scattering
angles to scattering angle values larger than 80∘ will help to
reduce the errors associated with the AOT retrievals. The algorithm largely
overestimates the AOT when the primary bow is included in the retrieval
process and when forward and side scattering viewing geometries are not
available. This result suggests that polarized measurements acquired for
this configuration should not be used for AAC properties retrievals, at
least with a retrieval algorithm based on 1-D calculations.
Assessment of retrieval errors due to cloud heterogeneity is challenging for
the next generation of retrieval algorithms. Indeed, in the future, it
appears crucial to have not only values of retrieved parameters but also
estimations of their uncertainties. Realistic simulations with known input
parameters are very useful tools to assess accurately theses errors
including their dependence on the available angular sampling. Such
simulations can also be used to test the next generation of operational
algorithms.
Further to those assessments of cloud
heterogeneity uncertainties, more complex methods should also be developed to
retrieve aerosol and cloud properties accounting for the cloud
heterogeneities. Several theoretical or case studies have already been
conducted. Some tends to mitigate cloud contamination for aerosol property
retrieval (Davis et al., 2013; Stap et al., 2016b). Others aim to use 3-D
radiative transfer model to retrieve 3-D cloud properties and hence account
for some cloud heterogeneity effects. It then requires more complex inversion
methods. Feasibility studies has been conducted using a neural network method
(Cornet et al., 2004, 2005), 3-D tomography with a surrogate function (Levis
et al., 2015, 2017) or adjoint method (Martin et al., 2014; Martin and
Hasekamp, 2018). The latter two methods are very promising but have been
developed in the framework of high resolution measurements (ten to hundred
meters) involving no or small plane-parallel bias. They are consequently not
directly applicable to POLDER/PARASOL measurements.
The Multi-viewing, Multi-Channel, Multi-Polarization Imaging mission (3MI)
that will fly on METOP-A SG as part of EUMETSAT Polar System after 2021,
will have a spatial resolution of 4 × 4 km. The plane-parallel bias is thus
expected to be slightly lower than for the POLDER instrument. In addition, as 3MI
will be on the same platform as the Visible Infrared Imager, a
multispectral radiometer with a resolution of 500 m, the correction of the
plane parallel biases may be possible while the multi-angular capability of
3MI would help to detect the illumination and shadowing effects.
The source code of the 3DCLOUD algorithm is available
online at http://wwwobs.univ-bpclermont.fr/atmos/fr/restricted (last
access: 21 June 2018) under restricted access. Please contact the authors for
the password. The 3DMCPOL model and the input data used as input for the
retrieval algorithms can be made available upon request to the corresponding
author.
The authors declare that they have no conflict of
interest.
Acknowledgements
This work has been supported by the French Programme National de
Télédétection Spatiale (PNTS, http://www.insu.cnrs.fr/pnts, last access: 21 June 2018),
grant no. PNTS-2014-02 and by the Centre National d'Etudes
Spatiales (CNES). The authors are very grateful for the interesting and pertinent comments made by the reviewers. They contributed to greatly improve the manuscript.
Edited by: Piet Stammes
Reviewed by: Zhibo Zhang, Feng Xu, Gerard van Harten, and one anonymous referee
ReferencesAlexandrov, M. D., Cairns, B., Emde, C., Ackerman, A. S., and van Diedenhoven, B.:
Accuracy assessments of cloud droplet size retrievals from polarized
reflectance measurements by the research scanning polarimeter, Remote Sens.
Environ., 125, 92–111, 10.1016/j.rse.2012.07.012, 2012.Alkasem, A., Szczap, F., Cornet, C., Shcherbakov, V., Gour, Y., Jourdan, O.,
Labonnote, L. C., and Mioche, G.: Effects of cirrus heterogeneity on lidar
CALIOP/CALIPSO data, J. Quant. Spectrosc. Ra., 202, 38–49,
10.1016/j.jqsrt.2017.07.005, 2017.Barker, H. W., Wiellicki, B. A., and Parker, L.: A Parameterization for
Computing Grid-Averaged Solar Fluxes for Inhomogeneous Marine Boundary Layer
Clouds. Part II: Validation Using Satellite Data, J. Atmos. Sci., 53,
2304–2316, 10.1175/1520-0469(1996)053<2304:APFCGA>2.0.CO;2, 1996.Breon, F. M. and Doutriaux-Boucher, M.: A comparison of cloud droplet
radii measured from space, IEEE T. Geosci. Remote, 43, 1796–1805,
10.1109/TGRS.2005.852838, 2005.Bréon, F.-M. and Goloub, P.: Cloud droplet effective radius from
spaceborne polarization measurements, Geophys. Res. Lett., 25, 1879–1882,
10.1029/98GL01221, 1998.Buriez, J. C., Vanbauce, C., Parol, F., Goloub, P., Herman, M., Bonnel, B.,
Fouquart, Y., Couvert, P., and Seze, G.: Cloud detection and derivation of
cloud properties from POLDER, Int. J. Remote Sens., 18, 2785–2813,
10.1080/014311697217332, 1997.Buriez, J.-C., Doutriaux-Boucher, M., Parol, F., and Loeb, N. G.: Angular
Variability of the Liquid Water Cloud Optical Thickness Retrieved from
ADEOS–POLDER, J. Atmos. Sci., 58, 3007–3018,
10.1175/1520-0469(2001)058<3007:AVOTLW>2.0.CO;2, 2001.Buriez, J.-C., Parol, F., Cornet, C., and Doutriaux-Boucher, M.: An
improved derivation of the top-of-atmosphere albedo from POLDER/ADEOS-2:
Narrowband albedos, J. Geophys. Res.-Atmos., 110, D05202,
10.1029/2004JD005243, 2005.Cahalan, R. F.: Bounded cascade clouds: albedo and effective thickness,
Nonlin. Processes Geophys., 1, 156–167, 10.5194/npg-1-156-1994, 1994.Chand, D., Anderson, T. L., Wood, R., Charlson, R. J., Hu, Y., Liu, Z., and
Vaughan, M.: Quantifying above-cloud aerosol using spaceborne lidar for
improved understanding of cloudy-sky direct climate forcing, J. Geophys.
Res.-Atmos., 113, D13206, 10.1029/2007JD009433, 2008.Cornet, C., Isaka, H., Guillemet, B., and Szczap, F.: Neural network
retrieval of cloud parameters of inhomogeneous clouds from multispectral and
multiscale radiance data: Feasibility study, J. Geophys. Res.-Atmos.,
109, D12203, 10.1029/2003JD004186, 2004.Cornet, C., Buriez, J.-C., Riédi, J., Isaka, H., and Guillemet, B.:
Case study of inhomogeneous cloud parameter retrieval from MODIS data, Geophys. Res. Lett., 32, L13807, 10.1029/2005GL022791, 2005.Cornet, C., C.-Labonnote, L., and Szczap, F.: Three-dimensional polarized
Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3-D effects on
polarized visible reflectances of a cirrus cloud, J. Quant. Spectrosc. Ra., 111, 174–186, 10.1016/j.jqsrt.2009.06.013, 2010.Cornet, C., Szczap, F., C.-Labonnote, L., Fauchez, T., Parol, F., Thieuleux,
F., Riedi, J., Dubuisson, P., and Ferlay, N.: Evaluation of cloud
heterogeneity effects on total and polarized visible radiances as measured
by POLDER/PARASOL and consequences for retrieved cloud properties,
Proceedings of the International Radiation Symposium (IRC/IAMAS), AIP
Publishing, 99–102, 10.1063/1.4804717, 2013.Costantino, L. and Bréon, F.-M.: Aerosol indirect effect on warm clouds over South-East Atlantic, from co-located MODIS and
CALIPSO observations, Atmos. Chem. Phys., 13, 69–88, 10.5194/acp-13-69-2013, 2013.Davis, A. B. and Marshak, A.: Solar radiation transport in the cloudy
atmosphere: a 3-D perspective on observations and climate impacts, Rep. Prog. Phys., 73, 026801, 10.1088/0034-4885/73/2/026801, 2010.Davis, A. B., Garay, M. J., Xu, F., Qu, Z., and Emde, C.: 3-D radiative
transfer effects in multi-angle/multispectral radio-polarimetric signals
from a mixture of clouds and aerosols viewed by a non-imaging sensor,
Presented at the Polarization Science and Remote Sensing VI, International
Society for Optics and Photonics, p. 887309,
10.1117/12.2023733, 2013.Deaconu, L. T., Waquet, F., Josset, D., Ferlay, N., Peers, F., Thieuleux, F., Ducos, F., Pascal, N., Tanré, D., Pelon, J., and Goloub, P.:
Consistency of aerosols above clouds characterization from A-Train active and passive measurements, Atmos. Meas. Tech., 10, 3499–3523,
10.5194/amt-10-3499-2017, 2017.Deschamps, P.-Y., Breon, F.-M., Leroy, M., Podaire, A., Bricaud, A., Buriez,
J.-C., and Seze, G.: The POLDER mission: instrument characteristics and
scientific objectives, IEEE T. Geosci. Remote, 32, 598–615,
10.1109/36.297978, 1994.Emde, C., Barlakas, V., Cornet, C., Evans, F., Korkin, S., Ota, Y.,
Labonnote, L. C., Lyapustin, A., Macke, A., Mayer, B., and Wendisch, M.:
IPRT polarized radiative transfer model intercomparison project – Phase A, J. Quant. Spectrosc. Ra., 164,
8–36,
10.1016/j.jqsrt.2015.05.007, 2015.Emde, C., Barkalas, V., Cornet, C., Evans, F., Wang, Z., Labonnote, L.C.,
Macke, A., Mayer, B., and Wendisch, M.: IPRT polarized radiative transfer
model intercomparison project – Three-dimensional test cases (phase B), J. Quant. Spectrosc. Ra., 209,
19–44,
10.1016/j.jqsrt.2018.01.024, 2018.Fauchez, T., Cornet, C., Szczap, F., Dubuisson, P., and Rosambert, T.: Impact of cirrus clouds heterogeneities on top-of-atmosphere thermal
infrared radiation, Atmos. Chem. Phys., 14, 5599–5615, 10.5194/acp-14-5599-2014, 2014.Fauchez, T., Dubuisson, P., Cornet, C., Szczap, F., Garnier, A., Pelon, J., and Meyer, K.:
Impacts of cloud heterogeneities on cirrus optical properties retrieved from space-based thermal infrared
radiometry, Atmos. Meas. Tech., 8, 633–647, 10.5194/amt-8-633-2015, 2015.Goloub, P., Deuze, J. L., Herman, M., and Fouquart, Y.: Analysis of the
POLDER polarization measurements performed over cloud covers, IEEE T. Geosci. Remote, 32, 78–88, 10.1109/36.285191, 1994.Hu, Y., Vaughan, M., Liu, Z., Powell, K., and Rodier, S.: Retrieving
Optical Depths and Lidar Ratios for Transparent Layers Above Opaque Water
Clouds From CALIPSO Lidar Measurements, IEEE Geosci. Remote S., 4,
523–526, 10.1109/LGRS.2007.901085, 2007.Iwabuchi, H. and Hayasaka, T.: Effects of Cloud Horizontal Inhomogeneity
on the Optical Thickness Retrieved from Moderate-Resolution Satellite Data, J. Atmos. Sci., 59,
2227–2242,
10.1175/1520-0469(2002)059<2227:EOCHIO>2.0.CO;2, 2002.Jethva, H., Torres, O., Waquet, F., Chand, D., and Hu, Y.: How do A-train
sensors intercompare in the retrieval of above-cloud aerosol optical depth?
A case study-based assessment, Geophys. Res. Lett., 41, 186–192,
10.1002/2013GL058405, 2013.Kato, S., Hinkelman, L. M., and Cheng, A.: Estimate of satellite-derived
cloud optical thickness and effective radius errors and their effect on
computed domain-averaged irradiances, J. Geophys. Res.-Atmos., 111,
D17201, 10.1029/2005JD006668, 2006.Kawai, H. and Teixeira, J.: Probability Density Functions of Liquid Water
Path and Total Water Content of Marine Boundary Layer Clouds: Implications
for Cloud Parameterization., J. Climate, 25, 2162–2177,
10.1175/JCLI-D-11-00117.1, 2011.Lenoble, J., Herman, M., Deuzé, J.L., Lafrance, B., Santer, R.,
and Tanré, D.: A successive order of scattering code for solving the
vector equation of transfer in the earth's atmosphere with aerosols, J. Quant. Spectrosc. Ra., 107,
479–507,
10.1016/j.jqsrt.2007.03.010, 2007.Levis, A., Schechner, Y. Y., Aides, A., and Davis, A. B.: Airborne
Three-Dimensional Cloud Tomography, in: 2015 IEEE International Conference
on Computer Vision (ICCV), Presented at the 2015 IEEE International
Conference on Computer Vision (ICCV), 3379–3387,
10.1109/ICCV.2015.386, 2015.Levis, A., Schechner, Y. Y., and Davis, A. B.: Multiple-Scattering
Microphysics Tomography, IEEE, 5797–5806,
10.1109/CVPR.2017.614, 2017.Loeb, N. G. and Coakley, J. A.: Inference of Marine Stratus Cloud Optical
Depths from Satellite Measurements: Does 1-D Theory Apply?, J. Climate, 11,
215–233, 10.1175/1520-0442(1998)011<0215:IOMSCO>2.0.CO;2, 1998.Loeb, N. G. and Davies, R.: Observational evidence of plane parallel model
biases: Apparent dependence of cloud optical depth on solar zenith angle, J. Geophys. Res.-Atmos., 101, 1621–1634, 10.1029/95JD03298, 1996.Magaritz-Ronen L., Khain A., and Pinsky M.: About the horizontal
variability of effective radius in stratocumulus clouds, J. Geophys. Res.-Atmos., 121, 9640–9660, 10.1002/2016JD024977, 2016.Marbach, T., Riedi, J., Lacan, A., and Schlüssel, P.: The 3MI mission:
multi-viewing-channel-polarisation imager of the EUMETSAT polar system:
second generation (EPS-SG) dedicated to aerosol and cloud monitoring, Proc.
SPIE 9613, Polarization Science and Remote Sensing VII, 961310,
10.1117/12.2186978, 2015.
Marshak, A. and Davis, A. (Eds.): 3-D Radiative Transfer in Cloudy
Atmospheres, Physics of Earth and Space Environments, Springer-Verlag,
Berlin/Heidelberg, 2005.Marshak, A., Platnick, S., Várnai, T., Wen, G., and Cahalan, R. F.:
Impact of three-dimensional radiative effects on satellite retrievals of
cloud droplet sizes, J. Geophys. Res.-Atmos., 111, D09207,
10.1029/2005JD006686, 2006.Martin, W. and Hasekamp, O. P.: A demonstration of adjoint methods for
multi-dimensional remote sensing of the atmosphere and surface, J. Quant. Spectrosc. Ra., 204,
215–231,
10.1016/j.jqsrt.2017.09.031, 2018.Martin, W., Cairns, B., and Bal, G.: Adjoint methods for adjusting
three-dimensional atmosphere and surface properties to fit
multi-angle/multi-pixel polarimetric measurements, J. Quant. Spectrosc. Ra., 144, 68–85, 10.1016/j.jqsrt.2014.03.030, 2014.Meyer, K., Platnick, S., and Zhang, Z.: Simultaneously inferring
above-cloud absorbing aerosol optical thickness and underlying liquid phase
cloud optical and microphysical properties using MODIS, J. Geophys. Res.-Atmos., 2015, JD023128, 10.1002/2015JD023128, 2015.Nakajima, T. and King, M. D.: Determination of the Optical Thickness and
Effective Particle Radius of Clouds from Reflected Solar Radiation
Measurements. Part I: Theory, J. Atmos. Sci., 47, 1878–1893,
10.1175/1520-0469(1990)047<1878:DOTOTA>2.0.CO;2, 1990.Parol, F., Buriez, J. C., Vanbauce, C., Riedi, J., C.-Labonnote, L.,
Doutriaux-Boucher, M., Vesperini, M., Sèze, G., Couvert, P., Viollier,
M., and Bréon, F. M.: Review of capabilities of multi-angle and
polarization cloud measurements from POLDER. Adv. Space Res., Climate Change
Processes in the Stratosphere, Earth-Atmosphere-Ocean Systems, and
Oceanographic Processes from Satellite Data 33, 1080–1088.
10.1016/S0273-1177(03)00734-8, 2004.Peers, F., Waquet, F., Cornet, C., Dubuisson, P., Ducos, F., Goloub, P., Szczap, F., Tanré, D., and Thieuleux, F.: Absorption of
aerosols above clouds from POLDER/PARASOL measurements and estimation of their direct radiative effect,
Atmos. Chem. Phys., 15, 4179–4196, 10.5194/acp-15-4179-2015, 2015.Platnick, S., King, M. D., Ackerman, S. A., Menzel, W. P., Baum, B. A., Riedi,
J. C., and Frey, R. A.: The MODIS cloud products: algorithms and examples
from Terra, IEEE T. Geosci. Remote, 41, 459–473,
10.1109/TGRS.2002.808301, 2003.
Rodgers, C. D.: Inverse methods for atmospheric sounding: theory and
practice, World Scientific Publishing Co. Ltd, London, UK, p. 238, 2000.Stap, F. A., Hasekamp, O. P., Emde, C., and Röckmann, T.: Influence of
3-D effects on 1-D aerosol retrievals in synthetic, partially clouded scenes, J. Quant. Spectrosc. Ra., 170,
54–68,
10.1016/j.jqsrt.2015.10.008, 2016a.Stap, F. A., Hasekamp, O. P., Emde, C., and Röckmann, T.: Multiangle
photopolarimetric aerosol retrievals in the vicinity of clouds: Synthetic
study based on a large eddy simulation, J. Geophys. Res.-Atmos., 121,
12914–12935, 10.1002/2016JD024787, 2016b.Szczap, F., Isaka, H., Saute, M., Guillemet, B., and Ioltukhovski, A.:
Effective radiative properties of bounded cascade nonabsorbing clouds:
Definition of the equivalent homogeneous cloud approximation, J. Geophys. Res.-Atmos., 105, 20617–20633, 10.1029/2000JD900146, 2000a.Szczap, F., Isaka, H., Saute, M., Guillemet, B., and Ioltukhovski, A.:
Effective radiative properties of bounded cascade absorbing clouds:
Definition of an effective single-scattering albedo, J. Geophys. Res.-Atmos., 105, 20635–20648, 10.1029/2000JD900145, 2000b.Szczap, F., Gour, Y., Fauchez, T., Cornet, C., Faure, T., Jourdan, O., Penide, G., and Dubuisson, P.: A flexible three-dimensional
stratocumulus, cumulus and cirrus cloud generator (3DCLOUD) based on drastically simplified atmospheric equations and the Fourier
transform framework, Geosci. Model Dev., 7, 1779–1801, 10.5194/gmd-7-1779-2014, 2014.Torres, O., Jethva, H., and Bhartia, P. K.: Retrieval of Aerosol Optical
Depth above Clouds from OMI Observations: Sensitivity Analysis and Case
Studies, J. Atmos. Sci., 69, 1037–1053,
10.1175/JAS-D-11-0130.1, 2011.Twomey, S.: The Influence of Pollution on the Shortwave Albedo of Clouds, J.
Atmos. Sci., 34, 1149–1152,
10.1175/1520-0469(1977)034<1149:TIOPOT>2.0.CO;2, 1977.Varnai, T.: Influence of Three-Dimensional Radiative Effects on the
Spatial Distribution of Shortwave Cloud Reflection, J. Atmos. Sci., 57,
216–229, 10.1175/1520-0469(2000)057<0216:IOTDRE>2.0.CO;2, 2000.Varnai, T. and Davies, R.: Effects of Cloud Heterogeneities on Shortwave
Radiation: Comparison of Cloud-Top Variability and Internal Heterogeneity, J. Atmos. Sci., 56,
4206–4224,
10.1175/1520-0469(1999)056<4206:EOCHOS>2.0.CO;2, 1999.Varnai, T. and Marshak, A.: Observations of Three-Dimensional Radiative
Effects that Influence MODIS Cloud Optical Thickness Retrievals, J. Atmos. Sci., 59,
1607–1618,
10.1175/1520-0469(2002)059<1607:OOTDRE>2.0.CO;2, 2002.Waquet, F., Riedi, J., Labonnote, L.C., Goloub, P., Cairns, B., Deuzé,
J.-L., and Tanré, D.: Aerosol Remote Sensing over Clouds Using A-Train
Observations, J. Atmos. Sci., 66, 2468–2480,
10.1175/2009JAS3026.1, 2009.Waquet, F., Cornet, C., Deuzé, J.-L., Dubovik, O., Ducos, F., Goloub, P., Herman, M., Lapyonok, T., Labonnote, L. C., Riedi, J., Tanré, D.,
Thieuleux, F., and Vanbauce, C.: Retrieval of aerosol microphysical and optical properties above liquid clouds from POLDER/PARASOL polarization
measurements, Atmos. Meas. Tech., 6, 991–1016, 10.5194/amt-6-991-2013, 2013a.Waquet, F., Peers, F., Ducos, F., Goloub, P., Platnick, S., Riedi, J.,
Tanré, D., and Thieuleux, F.: Global analysis of aerosol properties
above clouds, Geophys. Res. Lett., 40, 5809–5814,
10.1002/2013GL057482, 2013b.Wilcox, E. M.: Stratocumulus cloud thickening beneath layers of absorbing smoke aerosol, Atmos. Chem. Phys.,
10, 11769–11777, 10.5194/acp-10-11769-2010, 2010.Young, S. A. and Vaughan, M. A.: The Retrieval of Profiles of Particulate
Extinction from Cloud-Aerosol Lidar Infrared Pathfinder Satellite
Observations (CALIPSO) Data: Algorithm Description, J. Atmos. Ocean.,
Tech., 26, 1105–1119, 10.1175/2008JTECHA1221.1, 2009.Zeng, S., Parol, F., Riedi, J., Cornet, C., and Thieuleux, F.: Examination
of POLDER/PARASOL and MODIS/Aqua Cloud Fractions and Properties
Representativeness, J. Climate, 24, 4435–4450,
10.1175/2011JCLI3857.1, 2011.Zeng, S., Cornet, C., Parol, F., Riedi, J., and Thieuleux, F.: A better understanding of cloud optical thickness derived
from the passive sensors MODIS/AQUA and POLDER/PARASOL in the A-Train constellation, Atmos. Chem. Phys., 12, 11245–11259, 10.5194/acp-12-11245-2012, 2012.Zeng, S., Riedi, J., Parol, F., Cornet, C., and Thieuleux, F.: An assessment
of cloud top thermodynamic phase products obtained from A-Train passive and
active sensors, Atmos. Meas. Tech. Discuss., 6, 8371–8411,
10.5194/amtd-6-8371-2013, 2013.Zhang, Z., Ackerman, A. S., Feingold, G., Platnick, S., Pincus, R., and Xue, H.: Effects of cloud horizontal inhomogeneity and drizzle on remote
sensing of cloud droplet effective radius: Case studies based on large-eddy
simulations, J. Geophys. Res.-Atmos., 117, D19208,
10.1029/2012JD017655, 2012.Zhang, Z., Meyer, K., Yu, H., Platnick, S., Colarco, P., Liu, Z., and Oreopoulos, L.: Shortwave direct radiative effects
of above-cloud aerosols over global oceans derived from 8 years of CALIOP and MODIS observations,
Atmos. Chem. Phys., 16, 2877–2900, 10.5194/acp-16-2877-2016, 2016a.Zhang, Z., Werner, F., Cho, H.-M., Wind, G., Platnick, S., Ackerman, A. S.,
Di Girolamo, L., Marshak, A., and Meyer, K.: A framework based on 2-D
Taylor expansion for quantifying the impacts of subpixel reflectance
variance and covariance on cloud optical thickness and effective radius
retrievals based on the bispectral method, J. Geophys. Res.-Atmos., 121,
2016JD024837, 10.1002/2016JD024837, 2016b.
Zhou, Y., Sun, X., Zhang, R., Zhang, C., Li, H., Zhou, J., and Li, S.:
Influences of cloud heterogeneity on cirrus optical properties retrieved
from the visible and near-infrared channels of MODIS/SEVIRI for flat and
optically thick cirrus clouds, J. Quant. Spectrosc. Ra., 187,
232–246, 10.1016/j.jqsrt.2016.09.020, 2017.Zinner, T. and Mayer, B.: Remote sensing of stratocumulus clouds:
Uncertainties and biases due to inhomogeneity, J. Geophys. Res.-Atmos.,
111, D14209, 10.1029/2005JD006955, 2006.