Algorithm Theoretical Basis Document of aerosol
properties for GCOM-C/SGLIMayumi Yoshida (RESTEC)
Hiroshi Murakami (JAXA)
2021.11

Table of Contents

1. Introduction
2. Channels for aerosol retrieval by SGLI
3. Basic principles of the aerosol retrieval algorithm
4. Aerosol models
5. Lookup Table
6. Output
References

1. Introduction
Aerosols influence the energy budget of the earth’s climate system throughscattering and absorbing solar radiation. For a more precise estimation of the
impact of aerosols on climate systems, investigation of the behavior of aerosols
on a global scale is essential but challenging because aerosol amounts andcharacteristics vary over space and time.
The multiple uses of various imaging sensors on both geostationary andpolar-orbiting satellites are helpful to understand a complete picture of aerosol
distribution in the global scale. The common algorithm for various sensors overdifferent ground targets (ocean/land) provides more consistent aerosol retrievals
over the globe than independent algorithms. Therefore we developed a common
retrieval algorithm of the aerosol optical properties to various satellite sensors(Yoshida et al., 2018) based on the method developed by Higurashi and
Nakajima (1998) and Fukuda et al. (2013). This approach was applied to
GCOM-C/SGLI non-polarization channels.
In addition, aerosol data assimilation studies using satellite data have also
been developed to obtain better initial conditions for the aerosol transport model.
Since not all parameters can be accurately detected by satellite sensors, andunrealistic assumptions of aerosol parameters are a major cause of retrieval
errors, adding the model information is expected to improve the retrieval
accuracy.
In Version2 algorithm, we utilize the forecast of an aerosol transport model fora priori estimates of the retrieval (Yoshida et al., 2020). This allows the aerosol
information in the aerosol transport model to be used for retrieval. And by using
the assimilated forecast, information from previous satellite observations can bepropagated to future retrievals through the aerosol transport model.
In Version3 algorithm, we use polarization observations in addition to
non-polarization observations. Because the polarization reflectance has lesscontribution from land surface reflection than non-polarization reflectance, it isexpected that aerosols over land can be estimated accurately. Moreover, since
the polarization reflectance is sensitive to aerosols with small particle sizes,
improvement in the retrieval accuracy of small aerosols particles such as
anthropogenic air pollutants can be expected.
The SGLI channels used for the retrieval are given in section 2. The details of
the retrieval methodology is explained in sections 3. Details on the candidate
aerosol models and lookup table are described in sections 4 and 5, respectively.

2. Channels for aerosol retrieval by SGLIThe SGLI channels used for the aerosol retrieval are listed on Table 1. Only thechannels longer than 800 nm are used for the algorithm over ocean to avoid theinfluence of water-leaving radiance. In Version3 algorithm, we add P2 (868.5nm)
polarization channel, because the P2 channel is sensitive to small particles
shorter than about 0.4 m, which corresponds approximately to the small
particle aerosol we assume for our candidate aerosol models in section 4.

Table 1 Channels of SGLI for aerosol retrievalCH

center of
spatialwavelength[nm] resolution [m]

ocean

land

VN1

380

x

VN2

412

x

VN3

443

x

VN4

490

VN5

530

VN6

565

VN7

673.5

VN8

673.5

VN9

763

VN10

868.5

VN11

868.5

P1

673.5

P2

868.5

SW1

1050

SW2

1380

SW3

1630

250

x

SW4

2210

1000

x

250

x

x
1000
250
1000

x

x
x

1000

x

3. Basic principles of the aerosol retrieval algorithm
We developed a common retrieval algorithm to estimate 𝜏 , 𝜔 , and  fromvarious satellite imagers based on the method developed by Higurashi and
Nakajima (1999) and Fukuda et al. (2013). In case of the Lambertian target, the
TOA reflectance 𝜌i𝑠𝑖𝑚 at a particular channel i can be approximated by:ts (θ0 )∙tvi (θ)∙ρsi (θ0 ,θ,φ)

a
i
ρsim
i (θ0 , θ, φ) = ρi (θ0 , θ, φ) +1-si ∙ρsi (θ0 ,θ,φ),(1)

where 𝜌𝑖𝑎 is the atmospheric path reflectance, and 𝑡𝑖𝑠 and 𝑡𝑖𝑣 represent totaltransmittance, from solar to surface and from surface to sensor, respectively. si
is the spherical albedo for the illumination of the atmosphere from below, and 𝜌𝑖𝑠is the surface reflectance. Here, 𝜃0 is the solar zenith angle, 𝜃 is the satellite
zenith angle, and 𝜑 represents the solar/satellite relative azimuth angle.
Parameters ( 𝜌𝑖𝑎 , 𝑡𝑖𝑠 , 𝑡𝑖𝑣 𝑠𝑖 ) in eq. (1) can be precomputed as a function ofgeometries (𝜃0 , 𝜃, 𝑎𝑛𝑑 𝜑) for each candidate aerosol model that is defined by theaerosol parameters (𝜏, external mixing ratio of dry volume concentration for fineparticles 𝜂𝑓 , and imaginary part of refractive index for fine mode mi) using aradiative transfer code called System for the Transfer of Atmospheric Radiation
whose development was initially lead by the University of Tokyo (STAR,
Nakajima and Tanaka 1986, 1988; Stamnes et al. 1988). Additionally, thecalculated values are saved as lookup tables. Details on the setting of candidate
aerosol models and lookup tables are described in section 4 and 5, respectively.
Figure 1 depicts the flowchart for our algorithm, which estimates three aerosolparameters; namely, 𝜏, 𝜂𝑓 , and mi . Finally, we calculated and 𝜔 by applying
the three derived parameters (𝜏, 𝜂𝑓 , and mi) to the aerosol model that was
described in section 4. Here, the spectral dependence of aerosol optical
thickness and single scattering albedo is assumed in the candidate aerosol
model by setting the aerosol parameters, such as size distribution and refractive
index.
In the retrieval process, we initially calibrated the observed TOA reflectance
using

the

recommended

vicarious

calibration

coefficient

in

JAXA

“kv0(MOBY+BOUSSOLE)”
SGLI

site

(https://suzaku.eorc.jaxa.jp/GCOM_C/data/prelaunch/index_cal.html). Then we
selected the clear-sky (i.e., cloud-free) pixel using a cloud detection algorithm
developed for GOSAT/CAI, GCOM-C/SGLI, and EarthCARE/MSI (Ishida andNakajima 2009; Ishida et al. 2011). Further, we corrected the observed TOA
reflectance at a channel i (𝜌i𝑜𝑏𝑠) for gas absorption at visible to near-infrared
wavelengths. Gas correction was conducted for ozone and water vapor due totheir amounts varying significantly with time and location. The corrected TOA
reflectance corresponding to the US standard atmosphere (𝜌i𝑜𝑏𝑠 ′) is given by:
𝑂 (𝑈𝑆𝑆)

𝑇 3

𝑇

𝑇𝑖

𝑇𝑖

𝐻2 𝑂(𝑈𝑆𝑆)

𝜌i𝑜𝑏𝑠 ′ = 𝑖𝑂3(𝑂𝑀𝐼) ∙ 𝐻𝑖2𝑂(𝐺ANAL) ∙ 𝜌i𝑜𝑏𝑠 ,(2)

where TiO3(OMI) and 𝑇𝑖𝐻2𝑂(𝐺𝐴𝑁𝐴𝐿) are the transmission factors for ozone and water
vapor at the observation points, respectively, and TiO3 (USS) and 𝑇𝑖𝐻2𝑂(𝑈𝑆𝑆) are thetransmission factors for the US standard atmosphere, respectively. We used thetotal ozone columns from JMA chemical transport model and the column water
vapor obtained from JMA global analysis (GANAL) data. Transmission factors
𝑂

𝐻 𝑂

𝑇𝑖 3 and 𝑇𝑖 2 were pre-calculated for various total ozone columns (O) and
𝐻2 𝑂
𝐻 𝑂
𝐻 𝑂
column water vapor (w). Subsequently, coefficients 𝐾𝑖𝑂3 , 𝐾𝑖,1
,𝐾𝑖,22 , and 𝐾𝑖,32

were derived from the fitting of eqs. (3) and (4) based on the MODIS Algorithm
Theoretical Basis Document for Collection 005 and 051 (Levy et al. 2007):
𝑂

𝑇𝑖 3 = exp(−𝐺𝐾 𝑂3 𝑂),
𝐻 𝑂
𝐻 𝑂
𝐻 𝑂
𝐻 𝑂
𝑇𝑖 2 = exp(−exp(𝐾𝑖,12 + 𝐾𝑖,22 ln(𝐺𝑤) + 𝐾𝑖,22 (ln(𝐺𝑤))2 )),

(3)
(4)

where the air mass factor (G) is a function of the solar (𝜃0 ) and the sensor zenith
angle (𝜃), such that:𝐺=1cos(𝜃0 )+1.

cos(𝜃)(5)

Next, we derived the aerosol parameters ( 𝜏, 𝜂𝑓 , and 𝑚𝑖 ) using an optimal
estimation method (Rodgers 2000). The state vector of a set of aerosolparameters 𝒙 = {𝜏, 𝜂𝑓 , 𝑚𝑖 } was derived by minimizing the object function J (Eq.
6). It uses the measurement vector of a gas-corrected observed reflectance set
R = {𝜌i𝑜𝑏𝑠 ′,𝑖 = 1, … , N } and simulated TOA reflectance F(x) = {𝜌i𝑠𝑖𝑚 , 𝑖 = 1, … , N}that is calculated using eq.(1), where N is the channel number.
𝑇 −1
𝐽 = [𝑹 − 𝑭(𝒙)]𝑇 𝑺−1
𝒆 [𝑹 − 𝑭(𝒙)] + [𝒙 − 𝒙𝒂 ] 𝑺𝒂 [𝒙 − 𝒙𝒂 ](6),

where 𝒙𝒂 = {𝜏𝑎 , 𝜂𝑓 𝑎 , 𝑚𝑖 𝑎 } is the vector of a prior estimate of 𝒙, and Se and Sa
are the covariance matrices of R and xa, respectively. Since the Se is mainly
induced from the uncertainty in the target land/ocean-surface reflectance, weestimate Se from the uncertainties in the land/ocean surface reflectance. The
uncertainties of the land surface reflectance is calculated from the in-situ
validation results for the land surface reflectance. The error co-variance ofchannels over land are also calculated from the validation data, and used for theoff-diagonal component of Se, while the off-diagonal component are set to 0 in
version 1 and 2 for land surface and all versions for ocean surface.
We then apply canonical correlation analysis to find the optimal coordinate
system, and converted R, 𝑭(𝒙) , and 𝑺𝒆 to the coordinate system whose
dimension is reduced to the number of retrieved parameters (three).
In the Version1 algorithm, we used spatially and temporally constant values ofxa, and Sa that are derived from climate analysis, and assumed that thenon-diagonal component of covariance matrices was set to 0 (Yoshida et al.
2018). In the Version2 algorithm, to introduce more realistic a prior estimate andcovariance into the retrieval process, we employ the forecast from aerosol
assimilation system of the Advanced Himawari Imager (AHI) onboard
Himawari-8 instead of the constants (Yoshida et al.,2020). In the Himawari-8/AHI
aerosol

assimilation

system,Level3aerosol

opticalthicknessfrom

Himawari-8/AHI (Kikuchi et al., 2018) is assimilated into a global aerosol
transport model by the 2D-Var assimilation system (Yumimoto et al. 2018). For
the aerosol transport model, we use MASINGAR (Model of Aerosol Species IN
the Global AtmospheRe; Tanaka et al. 2003; Tanaka and Chiba 2005) developed
at the Meteorological Research Institute (MRI) of the Japan Meteorological
Agency (JMA). MASINGAR covers the major tropospheric aerosol components(i.e., black and organic carbon, mineral dust (10-size bins), sea salt (10-sizebins), sulfate aerosols)) and their precursors (e.g., sulfur dioxide (SO2), dimethyl
sulfide, terpenes)), and is coupled online with an atmospheric general circulation
model (MRI-AGCM3; Yukimoto et al. 2012). The detailed method to calculate xa,
and Sa from the aerosol assimilation system are described in Yoshida el al.,2020. Finally, the optimal solution of x that minimizes J (Eq. 6) was searched byLevenberg-Marquardt Method.
In the Version3 algorithm, the observation from the polarization channel is usedin addition to the non-polarization observations in order to retrieve moreaccurate aerosol parameters. The flowchart added in Version 3 is shown inblue-box on the right side of Fig.1. The satellite-observed polarizationreflectance is calculated by Stokes parameters (Q, U) of SGLI polarization
channel as follows:𝑄

arctan(𝑈)𝜋2４ρr = √𝑄 2 + 𝑈 2 if |

|≤ ,

𝑄

ρr = −√𝑄2 + 𝑈 2

if |arctan(𝑈)

𝜋

(7)

|> .
４

2

The polarization reflectance is also simulated from the Stokes parameters (Q, U)
by radiative transfer code STAR, while the conversion of reference plane isrequired

since

it

is

different

between

SGLI

and

STAR

code

( https://suzaku.eorc.jaxa.jp/GCOM_C/instruments/files/PL_reference_plane_18
1129.pdf ). The pre-calculated Q and U using STAR code are saved aspolarization look-up-tables as well as non-polarization look-up-tables. Here, thepolarization by the ground surface cannot be ignored, while it is generally small.
We thus utilize the observed polarization reflectance on clear-sky day, when the

TOA reflectance corrected for Rayleigh scattering at channel P1 (673.5nm) is thesecond lowest within 60 days, as the polarization reflectance including surface
polarization. The degree of surface polarization is obtained as the ratio between
the polarization look-up-tables with and without the surface polarization, which
can explain the polarization reflectance on clear-sky day, and then thelook-up-tables are used according to that ratio. The satellite-observed andsimulated polarization reflectance calculated above are used as input of R andF(x) in Eq. (6), respectively. Here, the optimal channels among non-polarizationand polarization observations for aerosol retrieval is chosen automatically byapplying canonical correlation analysis as described above.
The uncertainties of the three aerosol parameters ( 𝜏, 𝜂𝑓 , and 𝑚i ) 𝐒𝐱̂ were
calculated using the law of error propagation, as follows:𝑺𝐱̂ = (𝑨𝑇 𝐒𝐞−𝟏 𝐀)−1,(8)

where A is the Jacobian matrix, and Se is same as in eq. (6). The three aerosolparameters (𝜏, 𝜂𝑓 , and 𝑚i ), for which the uncertainties exceeded a thresholdvalue, were treated as invalid values.

Fig. 1 Flowchart illustrating the retrieval algorithm for L2 aerosol opticalpropertie. The blue box is added in Version 3.

4. Aerosol models
We used common candidate aerosol models over both land and ocean toretrieve aerosols consistently over land and ocean. The candidate aerosol
models included aerosol types that were dominant over both ocean and land,
and an optimum model was automatically selected. We assumed that theaerosol model was an external mixture of fine and coarse particles ( 𝜂𝑓 is theexternal mixing ratio of the dry volume concentration of fine particles). We set
the fine aerosol model based on the average properties of the fine mode forcategory 1–6 by Omar et al. (2005), which provide the global aerosol models
using Aerosol Robotic Network (AERONET) (Holben et al. 1998) measurements.
For the coarse aerosol model, we set the external mixture of the pure marine
aerosol on the basis of the model that was illustrated by Sayer et al. (2012) anda dust model based on the coarse model of category 1 (dust) that was illustratedby Omar et al. (2005). We define 𝜂𝑐𝑑𝑠𝑡 as the external mixing ratio of the dry
volume concentration of dust particles for the coarse model. Regarding eachaerosol size of the fine and coarse models, we used a monomodal lognormal
volume size (rd) distribution, which is as follows:dV (rd )d ln rd (ln rd  ln rv ) 2 exp
,2 ln 2 
2 ln 


Cv

(9)

where Cv is the particle volume concentration, rv is the volume median radius,and  is the standard deviation. rv is set to 0.143, 2.59, and 2.834 (is 1.537,
2.054, and 1.908) for fine, coarse marine, and coarse dust, respectively, basedon the observations by Omar et al. (2005) and Sayer et al. (2012). Regarding theaerosol shape, we assumed a spherical model for the fine and coarse marine
model, and a non-spherical model for the coarse dust model. The dust
non-spherical parameters were based on a yellow dust model (Nakajima et al.
1989), which employed a semi-empirical theory by Pollack and Cuzzi (1980) withr = 1.1, x0 = 7, and G = 10 which are parameters of the nonspherical particle
scattering theory defined in the original paper. The aerosol vertical distribution
was set to the same distribution that was used for rural (dominant at 0–2 km),sea-spray (below 2 km), and yellow sand (4-8 km), for fine, coarse marine, andcoarse dust in the STAR code, respectively. The real part of the refractive index
was set to 1.439, 1.362, and 1.452 for fine, coarse marine, and coarse dust,
respectively, based on Omar et al. (2005) and Sayer et al. (2012). The imaginary
part of the refractive index (mi) was set to 3.0×10-9 and 0.0036 at all wavelengths
for coarse marine, and coarse dust, respectively, based on Sayer et al. (2012)
and Omar et al. (2005). However, mi for the fine aerosol model was perturbed torepresent a nonabsorbing and absorbing aerosol. To decrease the number ofderived parameters, mi varied with 𝜂𝑐𝑑𝑠𝑡 such that the fine and coarse models
exhibited the same 𝜔 at 500 nm.

5. Lookup Table
To perform model simulations, we used a radiative transfer code called STAR.
For rapid processing, we adopted the lookup table method (Higurashi and
Nakajima 1999). The parameters (𝜌𝑖𝑎 , 𝑡𝑖𝑠 , 𝑡𝑖𝑣 𝑠𝑖 ) in eq. (1) and Stokes parameters forthree surface types (without surface polarization, with land surface polarization,with ocean polarization) were precomputed for 29 𝜃0 (0.0, 2.5, 5.0…., and
70.0°), 25 𝜃 (0.0, 2.5, 5.0…., and 60.0°), 37 𝜑 (0.0, 5.0, 10.0…., and 180.0°), 2
pressures (1,013 and 616.6 hPa), 8 𝜏 (0.0, 0.1, 0.2, 0.4, 0.8, 1.2, 1.6, and 2.0),
11 mi for fine mode (𝜂𝑐𝑑𝑠𝑡 for coarse mode ), and 4 𝜂𝑓 (0.0, 0.33, 0.66, and1.0).
We calculated these parameters by the radiative transfer code for every 1 nm
from 300 nm to 2500 nm. These high-resolution spectral parameters were thenweighted using the response function for each sensor. Thus, we could apply thealgorithm to a variety of sensors without recalculation. In this manner, we
effectively applied the same algorithm and candidate aerosol models to various
satellite sensors.

6. Output
Output for SGLI is aerosol optical thickness at 500nm (𝜏), angstrom exponent
at 500nm and 380nm (, single scattering albedo at 380nm (𝜔), and QA flag. In
version 3, we integrate the scientific data over the ocean and land which was
separately stored in version 1 and 2. In addition, the uncertainties of the retrieval
parameters (𝜏,𝜔) are added to the output in version 3. The uncertainties of theretrieved parameter ( 𝜏,  𝜔 ) are calculated as the variation range ofcorresponding ( 𝜏,𝜔) when the three derived parameter (𝜏, 𝜂𝑓 , and 𝑚i ) are
perturbed between each uncertainties which are calculated by Eq. (8). When theuncertainty is larger than the maximum value which is calculated by“Maximum_valid_DN * slope + Offset”, the DN is set to Maximum_valid_DN.
Table 2 shows the descriptions of the QA flag. In version 3, a priori used for the
retrieval as well as information about whether the polarization channel is used or
not is added to QA_flag. When the Heavy aerosol (bit 9) is “Yes”, the cloud flag(bit 3) is set to “Clear”.

Table 2 SGLI QA flag, and Mask for statics

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