Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 540–548
Contents lists available at ScienceDirect
Journal of Quantitative Spectroscopy &
Radiative Transfer
journal homepage: www.elsevier.com/locate/jqsrt
Considering polarization in MODIS-based cloud property
retrievals by using a vector radiative transfer code
Bingqi Yi a,n, Xin Huang a, Ping Yang a, Bryan A. Baum b, George W. Kattawar c
a
b
c
Department of Atmospheric Sciences, Texas A&M University, College Station, TX 77843, USA
Space Science and Engineering Center, University of Wisconsin–Madison, Madison, WI 53706, USA
Department of Physics & Astronomy, Texas A&M University, College Station, TX 77843, USA
a r t i c l e in f o
abstract
Article history:
Received 6 November 2013
Received in revised form
13 May 2014
Accepted 15 May 2014
Available online 24 May 2014
In this study, a full-vector, adding–doubling radiative transfer model is used to investigate
the influence of the polarization state on cloud property retrievals from Moderate
Resolution Imaging Spectroradiometer (MODIS) satellite observations. Two sets of lookup
tables (LUTs) are developed for the retrieval purposes, both of which provide water cloud
and ice cloud reflectivity functions at two wavelengths in various sun-satellite viewing
geometries. However, only one of the LUTs considers polarization. The MODIS reflectivity
observations at 0.65 μm (band 1) and 2.13 μm (band 7) are used to infer the cloud optical
thickness and particle effective diameter, respectively. Results indicate that the retrievals
for both water cloud and ice cloud show considerable sensitivity to polarization.
The retrieved water and ice cloud effective diameter and optical thickness differences
can vary by as much as 7 15% due to polarization state considerations. In particular, the
polarization state has more influence on completely smooth ice particles than on severely
roughened ice particles.
& 2014 Elsevier Ltd. All rights reserved.
Keywords:
Polarization
Cloud property retrieval
MODIS
Satellite observation
Vector radiative transfer model
1. Introduction
Clouds are widely recognized as among the largest
contributors to the global radiation balance [1,2]. A better
understanding of global cloud optical and microphysical
properties is critical to an improved assessment of their
radiative impacts. Satellites provide global coverage for
cloud radiance measurements, from which cloud properties (i.e., the cloud optical thickness and effective particle
size) can be inferred using appropriate radiative transfer
models and knowledge of the atmospheric base state.
The satellite-retrieved cloud products are used increasingly, for example, in weather prediction, aviation safety,
solar energy prediction, and climate analyses. As a result,
n
Corresponding author.
E-mail address: bingqi.yi@tamu.edu (B. Yi).
http://dx.doi.org/10.1016/j.jqsrt.2014.05.020
0022-4073/& 2014 Elsevier Ltd. All rights reserved.
improving the retrieval techniques for better cloud product quality is becoming more important.
While many advances have been made in the methods
for using the radiance and reflectivity observations to solve
the inverse problem necessary for retrievals, most do not
consider the influence of polarization on the retrieval. The
polarization influence includes the cloud polarization
characteristics, the atmospheric molecular polarization
(i.e., Rayleigh scattering), and ocean/land surface polarization. These influences can potentially affect the constructed lookup tables (LUTs) that are employed for
operational retrievals and impact the cloud property
retrievals in subtle ways. For example, one of the most
widely used approaches to retrieve cloud properties is the
Nakajima–King method [3], which uses reflectivities in
several solar spectral bands to infer optical thickness and
particle effective size, which in turn are used to estimate
ice/liquid water path. Typically, LUTs constructed using
B. Yi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 540–548
reflectivities at different bands in various sun-satellite
viewing geometries are pre-calculated by “scalar” radiative
transfer models (i.e., DISORT [4] and Fast RTM [5]). Such
“scalar” models only consider the first component of the
water/ice cloud scattering phase matrix (the scattering
phase function), and ignore the influence of other phase
matrix elements (i.e., the linear and circular polarization).
Furthermore, these models fail to consider the atmospheric molecular polarization and surface polarization
(e.g., over ocean). Radiative transfer models exist in which
polarization is considered [6–8], and have been applied in
cloud retrieval processes involving polarized reflectivities
[9,10]. Ideally, conventional cloud retrievals without polarized information should consider the influence of polarization too. To our knowledge, there has been little
research to fully consider and quantify the neglected
influence of polarization. This study is intended to address
the question as to what extent polarization affects cloud
retrievals. Another open question is whether or not the
influence of polarization is sensitive to the ice particle
habits assumed in building the lookup tables used in the
satellite retrievals.
In the remainder of this paper, the model, data and
methodology used in this study are described in Section 2,
major results are presented in Section 3, and the present
work is summarized in Section 4.
2. Radiative transfer model, data, and methodology
To consider the effects of polarization, we employ a
newly developed, full vector adding–doubling radiative
transfer code developed at the Texas A&M University
(Huang et al. [11]). The “vector” version of the code can
fully consider cloud polarization, Rayleigh scattering polarization by atmospheric particles, and the ocean/land surface polarization, while the “scalar” version uses only the
first component of the cloud phase matrix (i.e., the
scattering phase function). In this study, the differences
in the LUTs and retrieved cloud properties caused by
541
whether or not the polarization state is taken into account
are defined as the polarization effects. The “vector” and
“scalar” versions of the adding–doubling code are used to
simulate the reflectivities at the 0.65 μm and 2.13 μm
wavelengths at the top of the atmosphere (TOA) for a
range of sun-satellite geometries over ocean. The solar
zenith and viewing zenith angles range from 01 to 841 in
intervals of 61, and the azimuthal angles range from 01 to
1801 in steps of 121. The US 1976 standard atmosphere
profile is used to provide the atmospheric base state.
Single layer clouds with geometrical thickness of 1 km
are assumed in a given vertical column, with a water cloud
layer located at a height of 3.5 km or an ice cloud layer at
7.5 km. The Rayleigh scattering extinction and molecular
absorption optical thickness above and below the cloud
layer are calculated with the line-by-line radiative transfer
model (LBLRTM) [12]. The ocean surface bidirectional
reflectivity diffusion property is modeled using a full
4 4 Mueller matrix assuming a Cox–Munk roughened
ocean surface [13] with the Kirchhoff approximation [14].
The ocean's surface wind is assumed to be 7 m s 1 in the
Cox–Munk rough ocean surface model.
The simulations of TOA reflectivity for the LUTs additionally need cloud single-scattering properties. For water clouds,
the single-scattering properties are calculated using the
Lorenz–Mie theory assuming spherical water particles. For
ice clouds, the single-scattering properties of two particle
habits (solid columns and aggregates of solid columns [15]),
together with two kinds of ice particle surface roughness
conditions (completely smooth and severely roughened [16])
are selected as the ice cloud particle models. The extinction
efficiency, single-scattering albedo, asymmetry factor,
absorption efficiency, and the complete scattering phase
matrix of water clouds and ice clouds are integrated over
the modified Gamma size distribution [17]:
nðDÞ ¼ n0 Dð1 3bÞ=b e ½D=ðabÞ ;
ð1Þ
where n0 is a constant, a is the effective diameter, and b is the
mean effective variance, here, equal to 0.1. Thus, following the
Fig. 1. The scattering phase matrix of a water cloud with an effective diameter of 32 μm at a wavelength of 0.65 μm: (a) P11; (b) P12.
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Fig. 2. The scattering phase matrix of an ice cloud with an effective diameter of 40 μm at a wavelength of 0.65 μm: (a) P11; (b) P12. An ice cloud model
consisting of completely smooth solid columns is used.
formulae given in Baum et al. [18] and Yi et al. [19], we can
derive the bulk scattering properties for water/ice clouds at
the 0.65 μm and 2.13 μm wavelength bands.
Note that the full phase matrix will be used in the
simulations using the “vector” version of the adding–doubling code, while the polarization is not included in the
“scalar” version. For example, Figs. 1 and 2 show the P11 and
P12 elements of the scattering phase matrix of the water and
ice clouds, both at a wavelength of 0.65 μm, and with
effective diameters of 32 μm and 40 μm, respectively. The
ice particles in Fig. 2 are assumed to be individual solid
columns (i.e., not aggregates of solid columns) with smooth
surfaces. Both the water and ice clouds clearly have distinct
polarization features. Larger polarization generally occurs at
the forward scattering angles, for example, the water clouds
have strong polarization (i.e., P12 component) at scattering
angles lower than 601. While not shown, an ice cloud
composed of severely roughened solid columns has a featureless phase function (i.e., without 221 and 461 halos and a
much reduced backward scattering peak) and fewer polarization features. The same result occurs for the completely
smooth/severely roughened column aggregate model, with
the completely smooth ice column aggregate having stronger
polarization features.
With the use of the adding–doubling code and the
water/ice cloud optical properties, LUTs are developed for
a range of sun-satellite viewing geometries, cloud effective
diameters, and optical thicknesses. In combination with
reflectivities from direct satellite measurements, the LUTs
are used to infer cloud properties. In this study, we use the
level 1B (L1B) 1-km resolution reflectivity products
(“MYD021KM”) from the Moderate Resolution Imaging
Spectroradiometer (MODIS) instrument onboard the
National Aeronautics and Space Administration (NASA)
Aqua satellite. Two separate 5-min MODIS granules are
selected for the water cloud and ice cloud cases. Fig. 3
shows the MODIS RGB images for two cases of water cloud
Fig. 3. Aqua MODIS true color RGB images of two data granules: (a) 31
March 2013, 19:35 UTC for a water cloud case; (b) 18 October 2013, 08:00
UTC for an ice cloud case.
B. Yi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 540–548
Fig. 4. LUTs for the retrievals of (a) water cloud and (b) ice cloud
properties using the MODIS band 1 (0.65 μm) and band 7 (2.13 μm)
observations.
(19:35 UTC 31 March 2013) and ice cloud (08:00 UTC 18
October 2013). Almost the entire granule located off the
west coast of South America is composed of stratocumulus
(water) clouds (Fig. 3a). The other case features widespread ice clouds near the equator over the eastern Indian
Ocean (Fig. 3b). Approximately 2030 1354 pixels are
within each granule, and, for our retrieval, the pixels are
sampled at 3-km horizontal resolution. The geo-location
(longitude and latitude) and sun-satellite viewing geometry (solar zenith angle, viewing zenith angle, and relative
azimuthal angle) information is provided in the “MYD03”
products. In our study, the MODIS Collection 5 operational
level 2 product (“MYD06”) of daytime cloud phase is used
to ensure that only pixels flagged as water/ice clouds are
used; pixels flagged as uncertain are filtered from the
analyses.
3. Results
Two examples for specific geometries in the LUTs are
shown in Fig. 4. For both the water and ice cloud cases,
two analyses are conducted: one with polarization considered within the retrieval (hereafter referred to as the
“vector case”) and the other without polarization within
the retrieval (hereafter referred to as the “scalar case”).
543
Fig. 4a is for a water cloud retrieval at the solar zenith
angle of 381, viewing zenith angle of 451, and relative
azimuthal angle of 601. For water clouds, the largest
differences between the “vector case” and the “scalar case”
occur in the medium effective diameters (12–28 μm) over
the entire range of optical thicknesses. The “scalar case”
LUT tends to retrieve smaller optical thicknesses and
effective diameters compared to their “vector case” counterparts. Fig. 4b shows the LUT for ice clouds using a
completely smooth, single solid column ice cloud model at
the solar zenith angle of 481, viewing zenith angle of 661,
and relative azimuthal angle of 1441. The differences in the
LUTs due to polarization suggest that there is greater
sensitivity in the large effective diameters ( 430 μm),
and the vector–scalar differences are more evident in
optical thickness than effective diameter. Different from
the LUT results for the water cloud, the “vector case” for
ice cloud results in a lower optical thickness than the
“scalar case” counterpart.
The LUTs constructed based on either the severely roughened solid column ice particle model or on the completely
smooth/severely roughened column aggregates (figures not
shown) are found to show minimal differences between the
“vector” and the “scalar” cases. The results indicate that the
particle surface roughening and habit complexity contributes
to a decreased polarization impact on cloud property retrievals. Note that the LUT differences between the “scalar” and
“vector” cases are highly dependent on the sun-satellite
viewing geometries. The results found in these two examples
are illustrative but may not hold true for all cases. As a result,
it is more useful to quantify the vector–scalar differences in
terms of retrieved quantities.
Before we begin the discussion regarding the retrieval
of cloud properties using the satellite observations, synthetic radiative transfer calculations are carried out to
examine the accuracy of retrievals and the sensitivity of
“scalar–vector” retrieval difference to various quantities (i.
e., viewing geometries, cloud optical thickness, and effective particle diameter). The synthetic radiative transfer
calculations provide the cloud reflectivities at the TOA at
the two wavelengths with known cloud optical thickness
and effective particle diameter, and then use the LUTs to
infer the cloud properties. Due to the complexities in the
LUTs at small cloud optical thickness and effective diameter, as well as the interpolation schemes used in the
retrieval process, retrieved cloud properties are expected
to have relatively better accuracy only in certain ranges.
For instance, we find reasonably accurate ice cloud property retrievals can be derived when the ice cloud optical
thickness is larger than 8, the effective diameter is larger
than 20 μm, and the solar and viewing zenith angles are
less than 661. As an example, we quantify the relative
differences in the retrieved cloud optical thickness (Fig. 5)
and effective diameter (Fig. 6) in the “vector” and “scalar”
cases as functions of sun-satellite viewing geometries,
optical thickness, and effective diameter, assuming a
completely smooth solid column ice cloud particle model.
The relative difference is defined as
Rrelative dif f erence ¼
V scalar V vector
100%;
V vector
ð2Þ
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Fig. 5. The relative difference in the retrieved ice cloud optical thickness between the “vector” and “scalar” cases as a function of (a) solar zenith angle;
(b) relative azimuthal angle; (c) optical thickness; (d) effective diameter. An ice cloud model consisting of completely smooth solid columns is used.
where Vscalar and Vvector refer to the variables to be
compared in the “scalar” and “vector” cases, respectively.
Figs. 5 and 6 show some hints about when and where the
“scalar” retrieval best matches the “vector” counterpart.
Smaller relative differences are found when the solar
zenith angle is small, while the relative differences are
more diverse with the relative azimuthal angle. The
relative differences are high when the cloud optical thickness (effective diameter) is small, and decrease with the
increase of optical thickness (effective diameter). Comparing Figs. 5 and 6, we find that polarization has more
influence on cloud optical thickness than effective diameter retrievals.
Fig. 7 shows the retrieved water cloud optical thickness
and effective diameter, as well as the relative differences
between the “vector” and “scalar” cases in the satellite
scene. The results show reasonable correspondence with
the satellite true color RGB image (Fig. 3a) where stratocumulus clouds are found in the majority of the granule
pixels. Notice that the sun glint region is neglected to
avoid potential problems in the retrievals. The water cloud
case has optical thicknesses ranging from 5 to 40, and has
effective diameters that are generally larger than 32 μm.
However, both the optical thickness and effective diameter
retrievals could have a relative difference of up to 715%.
Positive and negative relative differences appear alternatively in the scene partially because of scattered patches of
small-scale cumulus clouds. Interestingly, the patterns of
the relative difference share close similarities between the
optical thickness and the effective diameter, and are
clearly related to the sun-satellite viewing geometries.
The retrieved ice cloud optical thickness and effective
diameter inferred using the completely smooth solid
column ice particle model are shown in Fig. 8. Again, the
sun glint region is filtered out, i.e., where specular reflection occurs when the solar zenith and viewing zenith
angles are similar. Additionally, pixels are filtered out
where extremely large optical thickness or effective diameter values occur near the boundary of the valid range of
our LUTs; extremely high values occur infrequently but
any retrieval that occurs near the boundary of the LUT is
suspect. For the bulk of the retrievals, relative differences
up to or even greater than 15% are found. The relative
difference distributions indicate that pixels having small
values of optical thickness and effective diameter are
overestimated in the “scalar” case, while larger values
are underestimated. The relative difference patterns show
a smoother transition in the ice cloud case than in the
water cloud case and display a clear indication of the
dependence of relative differences on the sun-satellite
viewing geometries.
To relate the “vector–scalar” retrieval differences to the
phase functions (Figs. 1 and 2), we show the corresponding
scattering angles of the MODIS granules for the water
cloud and ice cloud cases in Fig. 9, where scattering angles
are calculated as
ϑ ¼ cos 1 ðsinθsinθ0 cosΔϕ cosθcosθ0 Þ;
ð3Þ
B. Yi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 540–548
545
Fig. 6. The relative difference in the retrieved ice cloud effective diameter between the “vector” and “scalar” cases as a function of (a) solar zenith angle;
(b) relative azimuthal angle; (c) optical thickness; (d) effective diameter. An ice cloud model consisting of completely smooth solid columns is used.
Δϕ ¼ 1801 jϕ0 ϕj;
ð4Þ
where ϑ is the scattering angle, θ and θ0 are the solar zenith
and satellite viewing zenith angles, Δϕ is the relative
azimuthal angle, ϕ and ϕ0 are the solar azimuthal and
satellite azimuthal angles.
Fig. 10 shows histograms of the relative differences in
water and ice cloud optical thickness and effective diameter. Interestingly, the majority of the retrievals are not
affected significantly by the polarization state for either
water clouds or ice clouds (i.e., within 75% difference);
however, large polarization influences are evident under
some conditions. It would be premature to provide generalizations about where the polarization influences will
be most evident considering the limited analysis in
this study.
We also examine the retrievals derived using the LUTs
generated using column aggregates, with completely
smooth and severely roughened surfaces, and the severely
roughened single solid column ice cloud models. None of
the cases show significant differences (less than 5%) in the
retrieved ice cloud properties whether or not polarization
is considered. Both particle surface roughening and particle aggregation have the similar effect of decreasing the
degree of polarization due to an increase in multiple
scattering.
Based on the above results, we conclude that the
conventional scalar radiative transfer model without
polarization can capture the majority of cloud features in
retrievals; however, under certain circumstances, the
influence of polarization is non-negligible. More work
need to be done to understand the conditions for which
the inclusion of polarization is important.
4. Conclusions
In this study, we investigate the importance of considering polarization in the process of satellite remote
sensing retrievals of cloud properties, specifically optical
thickness and effective diameter. A vector radiative transfer code based on the adding–doubling method is used,
which permits the use of the “vector version”, where the
polarization state is fully considered, and the “scalar
version”, where polarization is neglected. The polarization
state includes the contributions from Rayleigh scattering
by atmospheric molecules, land/ocean surface, and cloud
polarization. The Rayleigh scattering optical thickness is
calculated using the LBLRTM with the US 1976 standard
atmospheric profile. A Cox–Munk rough ocean surface is
assumed using the Kirchhoff approximation. Water clouds
are assumed to have spherical water particles with the
optical properties calculated by the Lorenz–Mie theory.
The ice cloud particle models used are the completely
smooth/severely roughened single solid column and the
complex aggregate of solid columns. Both water and ice
clouds are assumed to be composed of particles that follow
modified Gamma size distributions with an effective
variance of 0.1. Bulk scattering properties of water clouds
and ice clouds at various effective diameters are calculated
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Fig. 7. Retrieved water cloud optical thickness (a) and effective diameter (μm) (b) and the relative differences (c, d) between the “vector case” and
“scalar case”.
Fig. 8. Retrieved ice cloud optical thickness (a) and effective diameter (μm) (b) and the relative differences (c, d) between the “vector case” and “scalar
case”. An ice cloud model consisting of completely smooth solid columns is used.
for two solar MODIS bands at 0.65 μm and 2.13 μm (bands
1 and 7, respectively).
Pre-calculated reflectivities for the two MODIS bands
over a range of cloud effective diameters, optical thicknesses, and viewing geometries are used to construct
lookup tables. The LUTs are used to infer the cloud properties from the MODIS satellite reflectivity measurements.
Synthetic radiative transfer calculations are employed to
find the conditions where the polarization has an impact.
Case studies are presented for two Aqua MODIS granules
B. Yi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 540–548
547
Fig. 9. The scattering angles of the MODIS granules for the water cloud (a) and ice cloud (b) cases.
Fig. 10. Histograms of the relative difference in the retrieved (a) water cloud optical thickness; (b) water cloud effective diameter; (c) ice cloud optical
thickness; (d) ice cloud effective diameter.
over ocean with predominant coverage of either water
clouds or ice clouds. Our analyses are limited to those
pixels identified to be water/ice clouds in the MODIS
daytime cloud phase product, and the areas affected by
sun glint are ignored.
The retrieved cloud properties in the water cloud and
ice cloud cases share some similarities, as well as discrepancies. The ice cloud case retrieved much larger optical
thicknesses and effective diameters than the water cloud
case. However, a similar magnitude of relative differences
between the “vector case” and “scalar case” retrievals is
apparent. Although the relative differences vary dramatically with the sun-satellite viewing geometries (i.e., different combinations of solar zenith angle, satellite viewing
zenith angle, and the relative azimuthal angle), the
maximum variation can be as large as 715%. Comparatively, such differences decrease to within 75% for LUTs
generated assuming a severely roughened single solid
column or when completely smooth/severely roughened
complex hexagonal column aggregate ice cloud particle
models are used. Results from this study suggest that it
might be important to extend this study to global analyses
to better gain an understanding of where polarization is
important. Such analyses would help to better characterize
the uncertainties in global cloud retrievals of optical
thickness and particle size, as well as the resulting ice/
liquid water paths.
Acknowledgments
This study is supported by NASA Grants NNX11AF40G and
NNX11AR06G and the associated subcontracts to Texas A&M
University through the University of Wisconsin–Madison
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B. Yi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 146 (2014) 540–548
(301K630). Bryan Baum and Ping Yang thank Drs. Ramesh
Kakar and Hal Maring for their encouragement and support
over the years. George Kattawar acknowledges the support of
the Office of Naval Research under contracts N00014-09-11054 and N00014-11-1-0154 and also the National Science
Foundation Grant OCE-1130906.
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