Algorithm Theoretical Basis Document of aerosol by
non-polarization for GCOM-C/SGLI

2018.07 JAXA/EORC

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 opticalproperties to various satellite sensors (Yoshida et al., 2018) based on themethod developed by Higurashi and Nakajima (1998) and Fukuda et al. (2013).
This approach was applied to GCOM-C/SGLI non-polarization channels. The
SGLI channels used for the retrieval are given in section 2. The details of theretrieval 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, although all
well-calibrated channels without strong gas absorption from visible tonear-infrared wavelengths are used for the algorithm over land. The optimum
channels for aerosol retrieval are automatically selected. Details of the automatic
selection of the optimum channels are given in section 3.

Table 1 Channels of SGLI for aerosol retrievalCH

spatialcenter of
resolution
wavelength[nm]
[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

SW1

1050

SW2

1380

SW3

1630

SW4

2210

x

250

x
x
x

1000
250

x
x
x

x

250

x

x

1000

x

x

1000

3. Basic principles of the aerosol retrieval algorithm
We developed a common retrieval algorithm to estimate 𝜏𝜏 , 𝜔𝜔 , and α 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 𝜌𝜌i𝑠𝑠𝑠𝑠𝑠𝑠 at a particular channel i can be approximated by:sts (θ0 )∙tv
i (θ)∙ρi (θ0 ,θ,φ)

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

where 𝜌𝜌𝑖𝑖𝑎𝑎 is the atmospheric path reflectance, and 𝑡𝑡𝑖𝑖𝑠𝑠 and 𝑡𝑡𝑖𝑖𝑣𝑣 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 𝜌𝜌𝑖𝑖𝑠𝑠

is the surface reflectance. Here, 𝜃𝜃0 is the solar zenith angle, 𝜃𝜃 is the satellite

zenith angle, and 𝜑𝜑 represents the solar/satellite relative azimuth angle.
Parameters ( 𝜌𝜌𝑖𝑖𝑎𝑎 , 𝑡𝑡𝑖𝑖𝑠𝑠 , 𝑡𝑡𝑖𝑖𝑣𝑣 𝑠𝑠𝑖𝑖 ) in eq. (1) can be precomputed as a function ofgeometries (𝜃𝜃0 , 𝜃𝜃, 𝑎𝑎𝑎𝑎𝑎𝑎 𝜑𝜑) for each candidate aerosol model that is defined by theaerosol parameters (𝜏𝜏, external mixing ratio of dry volume concentration for fineparticles 𝜂𝜂𝑓𝑓 , 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, 𝜏𝜏, 𝜂𝜂𝑓𝑓 , and mi . Finally, we calculated α and 𝜔𝜔 by applying

the three derived parameters (𝜏𝜏, 𝜂𝜂𝑓𝑓 , 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 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 and Nakajima 2009; Ishida et al. 2011). Further, we
corrected the observed TOA reflectance at a channel i (𝜌𝜌i𝑜𝑜𝑜𝑜𝑜𝑜 ) 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(𝜌𝜌i𝑜𝑜𝑜𝑜𝑜𝑜 ′) is given by:
𝑂𝑂 (𝑈𝑈𝑈𝑈𝑈𝑈)

𝑇𝑇 3

𝑇𝑇

𝐻𝐻2𝑂𝑂(𝑈𝑈𝑈𝑈𝑈𝑈)𝜌𝜌i𝑜𝑜𝑜𝑜𝑜𝑜 ′ = 𝑖𝑖𝑂𝑂3(𝑂𝑂𝑂𝑂𝑂𝑂) ∙ 𝐻𝐻𝑖𝑖2𝑂𝑂(𝐺𝐺ANAL) ∙ 𝜌𝜌i𝑜𝑜𝑜𝑜𝑜𝑜 ,
𝑇𝑇𝑖𝑖

𝑇𝑇𝑖𝑖

(2)

where TiO3 (OMI) and 𝑇𝑇𝑖𝑖𝐻𝐻2 𝑂𝑂(𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺) are the transmission factors for ozone and water

vapor at the observation points, respectively, and TiO3 (USS) and 𝑇𝑇𝑖𝑖𝐻𝐻2 𝑂𝑂(𝑈𝑈𝑈𝑈𝑈𝑈) are thetransmission factors for the US standard atmosphere, respectively. We used thetotal ozone columns from the Ozone Monitoring Instrument (OMI) on board theNASA EOS/Aura spacecraft (https://aura.gsfc.nasa.gov/omi.html) and the column
water vapor obtained from JMA global analysis (GANAL) data. Transmission
factors 𝑇𝑇𝑖𝑖𝑂𝑂3 and 𝑇𝑇𝑖𝑖𝐻𝐻2 𝑂𝑂 were pre-calculated for various total ozone columns (O)𝐻𝐻2 𝑂𝑂
𝐻𝐻 𝑂𝑂and column water vapor (w). Subsequently, coefficients 𝐾𝐾𝑖𝑖𝑂𝑂3 , 𝐾𝐾𝑖𝑖,1,𝐾𝐾𝑖𝑖,22 , and𝐻𝐻 𝑂𝑂𝐾𝐾𝑖𝑖,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):𝑂𝑂

𝑇𝑇𝑖𝑖 3 = exp(−𝐺𝐺𝐾𝐾 𝑂𝑂3 𝑂𝑂),

𝐻𝐻 𝑂𝑂
𝐻𝐻 𝑂𝑂
𝐻𝐻 𝑂𝑂
𝐻𝐻 𝑂𝑂
𝑇𝑇𝑖𝑖 2 = exp�−exp�𝐾𝐾𝑖𝑖,12 + 𝐾𝐾𝑖𝑖,22 ln(𝐺𝐺𝐺𝐺) + 𝐾𝐾𝑖𝑖,22 (ln(𝐺𝐺𝐺𝐺))2��,

(3)
(4)

where the air mass factor (G) is a function of the solar (𝜃𝜃0) and the sensor zenith

angle (𝜃𝜃), such that:𝐺𝐺 =1cos(𝜃𝜃0 )+1.

cos(𝜃𝜃)(5)

Next, we derived the aerosol parameters ( 𝜏𝜏, 𝜂𝜂𝑓𝑓 , and 𝑚𝑚𝑖𝑖 ) using an optimal
estimation method (Rodgers 2000). The state vector of a set of aerosolparameters 𝒙𝒙 = �𝜏𝜏, 𝜂𝜂𝑓𝑓 , 𝑚𝑚𝑖𝑖 � was derived by minimizing the object function J (Eq.

6). It uses the measurement vector of a gas-corrected observed reflectance set
R = {𝜌𝜌i𝑜𝑜𝑜𝑜𝑜𝑜 ′,𝑖𝑖 = 1, … , N } and simulated TOA reflectance F(x) = {𝜌𝜌i𝑠𝑠𝑠𝑠𝑠𝑠 , 𝑖𝑖 = 1, … , N} thatis calculated using eq.(1), where N is the channel number.
𝑇𝑇 −1
𝐽𝐽 = [𝑹𝑹 − 𝑭𝑭(𝒙𝒙)]𝑇𝑇 𝑺𝑺−1
𝒆𝒆 [𝑹𝑹 − 𝑭𝑭(𝒙𝒙)] + [𝒙𝒙 − 𝒙𝒙𝒂𝒂 ] 𝑺𝑺𝒂𝒂 [𝒙𝒙 − 𝒙𝒙𝒂𝒂 ](6),where 𝒙𝒙𝒂𝒂 = �𝜏𝜏𝑎𝑎 , 𝜂𝜂𝑓𝑓 𝑎𝑎 , 𝑚𝑚𝑖𝑖 𝑎𝑎 � is the vector of a prior estimate of 𝒙𝒙, and Se and Sa are
the covariance matrices of R and xa, respectively, and are given as:

𝑺𝑺𝒆𝒆 = �

𝜎𝜎1 2

0

⋱

𝜎𝜎𝜏𝜏𝑎𝑎 2

𝑺𝑺𝒂𝒂 = �0

𝜎𝜎𝜂𝜂𝑓𝑓

0

𝜎𝜎𝑁𝑁
𝑎𝑎

2

2

�,

(7)
0

𝜎𝜎𝑚𝑚𝑖𝑖

𝑎𝑎

2

�,

(8)

where 𝜎𝜎𝑖𝑖 is the uncertainty in TOA reflectance, and 𝜎𝜎𝜏𝜏𝑎𝑎 , 𝜎𝜎𝜂𝜂𝑓𝑓 , and 𝜎𝜎𝑚𝑚𝑖𝑖 𝑎𝑎 are the𝑎𝑎uncertainties of 𝜏𝜏𝑎𝑎 , 𝜂𝜂𝑓𝑓 𝑎𝑎 ,and 𝑚𝑚𝑖𝑖 𝑎𝑎 , respectively. Since 𝜎𝜎𝑖𝑖 is mainly induced fromsensor noise (𝜎𝜎𝑛𝑛 ) and uncertainty in the estimated target land/ocean-surface
reflectance (∆𝜌𝜌𝑖𝑖𝑠𝑠 ), we estimate 𝜎𝜎𝑖𝑖 using eq. (9), as follows:
𝜎𝜎𝑖𝑖2 = 𝜎𝜎𝑠𝑠2 + 𝜎𝜎𝑛𝑛2 ,(9)where 𝜎𝜎𝑠𝑠 is the uncertainty in the TOA reflectance that results from ∆𝜌𝜌𝑖𝑖𝑠𝑠 . We

assume ∆𝜌𝜌𝑖𝑖𝑠𝑠 to be some percentage of the surface reflectance (𝜌𝜌𝑖𝑖𝑠𝑠 ) at eachchannel.
The optimal solution of x that minimizes J (Eq. 6) was searched iteratively. By

considering that our algorithm was applied to various satellite sensors having
different wavelengths, eqs. (6)–(9) were designed to automatically selectoptimum channels for estimating the aerosol parameters by introducing arealistic 𝜎𝜎𝑖𝑖 , which considers the effect of surface reflectance uncertainty for eachchannel.
Finally, the uncertainties of the three aerosol parameters (𝜏𝜏, 𝜂𝜂𝑓𝑓 , and 𝑚𝑚i) 𝐒𝐒𝐱𝐱� were

calculated using the law of error propagation, as follows:
𝑺𝑺𝐱𝐱� = (𝑨𝑨𝑇𝑇 𝐒𝐒𝐞𝐞−𝟏𝟏 𝐀𝐀)−1,(10)

where A is the Jacobian matrix, and Se is same as in eq. (7), whose elements

are calculated using eq. (9). The three aerosol parameters (𝜏𝜏, 𝜂𝜂𝑓𝑓 , and 𝑚𝑚i), forwhich the uncertainties exceeded a threshold value, were treated as invalid
values.

Fig. 1

Flowchart illustrating the retrieval algorithm for L2 aerosol opticalproperties.

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 (𝜂𝜂𝑓𝑓 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 forcategory 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 𝜂𝜂𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑 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 σ
2π ln σ


Cv

(11)

where Cv is the particle volume concentration, rv is the volume median radius,and σ is the standard deviation. rv is set to 0.143, 2.59, and 2.834 (σ 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) withr = 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 etal. (2012) and Omar et al. (2005). However, mi for the fine aerosol model was
perturbed to represent a nonabsorbing and absorbing aerosol. To decrease thenumber of derived parameters, mi varied with 𝜂𝜂𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑 such that the fine and coarse
models exhibited the same 𝜔𝜔 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 (𝜌𝜌𝑖𝑖𝑎𝑎 , 𝑡𝑡𝑖𝑖𝑠𝑠 , 𝑡𝑡𝑖𝑖𝑣𝑣 𝑠𝑠𝑖𝑖 ) in eq. (1) were precomputed for 29𝜃𝜃0 (0.0, 2.5, 5.0…., and 70.0°), 25 𝜃𝜃 (0.0, 2.5, 5.0…., and 60.0°), 37 𝜑𝜑 (0.0,

5.0, 10.0…., and 180.0°), 2 pressures (1,013 and 616.6 hPa), 8 𝜏𝜏 (0.0, 0.1, 0.2,

0.4, 0.8, 1.2, 1.6, and 2.0), 11 mi for fine mode (𝜂𝜂𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑 for coarse mode ), and 4𝜂𝜂𝑓𝑓 (0.0, 0.33, 0.66, and1.0). We calculated these parameters by the radiativetransfer code for every 1 nm from 300 nm to 2500 nm. These high-resolution
spectral parameters were then weighted using the response function for eachsensor. Thus, we could apply the algorithm to a variety of sensors without
recalculation. In this manner, we effectively applied the same algorithm andcandidate aerosol models to various satellite sensors.

6. Output
Output for SGLI is aerosol optical thickness, angstrom exponent, single
scattering albedo, and QA flag. Table 2 shows the descriptions of the QA flag.

Table 2 SGLI QA flag
Bit Field
0

Flag
Aerosol Property Algorithm

Result0 = Executed / 1 = Not Executed

1

Land / Water

0 = Water / 1 = Land

2

Coastal0 = No / 1 = Yes

3

Clear / Cloud

0 = Clear / 1 = Cloudy

5, 4

AOT Confidence7, 6

AE Confidence

9, 8

SSA Confidence

00 = Very Good (suitable for validation)
01 = Good (suitable for statistics)
10 = Poor
00 = No Confidence, No Retrieval or Fill

10

Sun Glint Impact

0 = No / 1 = Yes

11

Stray-light Corrected

0 = No / 1 = Yes

12

Cloud Shadow Possibility

0 = No / 1 = Yes

13

obs < rayleigh0 = No / 1 = Yes

15, 14

Aerosol Type

TBD

References
Cox, C., and W. Munk, 1954: Statistics of the sea surface derived from sun glitter,
J. Mar. Res., 13, 198–227.
Deepak, A., and H. E. Gerber 1983: Report of the experts meeting on aerosols
and their climate effects, WCP-55, World Meteorological Organization,
Geneva, 107 pp.
Fukuda, S., Nakajima, T., Takenaka, H., Higurashi, A., Kikuchi, N., Nakajima, T.
Y., & Ishida, H.,2013: New approaches to removing cloud shadows andevaluating the 380 nm surface reflectance for improved aerosol optical
thickness retrievals from the GOSAT/TANSO‐Cloud and Aerosol Imager.
Journal of Geophysical Research: Atmospheres, 118(24), 13-520.

Higurashi, A., and T. Nakajima, 1999: Development of a two-channel aerosol
retrieval algorithm on a global scale using NOAA AVHRR, J. Atmos. Sci., 56,
924-941.
Holben, B. N., T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J.
A. Reagan, Y. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, and A. Smirnov,
1998: A federated instrument network and data archive for aerosol
characterization.

Remote Sens. Environ., 66, 1–16.

Ishida, H., and T. Y. Nakajima, 2009: Development of an unbiased clouddetection algorithm for a spaceborne multispectral imager, J. Geophys. Res.,
114, D07206, doi:10.1029/2008JD010710.
Ishida, H., T. Y. Nakajima, T. Yokota, N. Kikuchi, and H. Watanabe, 2011:
Investigation of GOSAT TANSO-CAI cloud screening ability through aninter-satellite comparison, J. Appl. Meteor. Climatol., 50, 1571–1586.
doi:10.1175/2011JAMC2672.1.
Levy, R. C., L. A. Remer, S. Mattoo, E. F. Vermote, and Y. J. Kaufman 2007:
Second-generation operational algorithm: Retrieval of aerosol properties overland from inversion of Moderate Resolution Imaging Spectroradiometer
spectralreflectance.

J.

Geophys.

Res.,

112,

D13211,

doi:10.1029/2006JD007811.
MODIS Algorithm Theoretical Basis Document for Collection 005 and 051:
https://modis-atmos.gsfc.nasa.gov/_docs/ATBD_MOD04_C005_rev2.pdf
Nakajima, T., and M. Tanaka, 1986: Matrix formulation for the transfer of solar
radiation in a plane-parallel scattering atmosphere, J. Quant. Spectrosc.
Radiat. Transfer 35, 13–21.
Nakajima, T., and M. Tanaka, 1988: Algorithms for radiative intensity calculations
in moderately thick atmospheres using a truncation approximation, J. Quant.
Spectrosc. Radiat. Transfer 40, 51–69.
Nakajima, T., M. Tanaka, M. Yamano, M. Shiobara, K. Arao, and Y. Nakanishi,
1989: Aerosol optical characteristics in the yellow sand events observed inMay, 1982 in Nagasaki—part II model, J. Meteorol. Soc. Jpn. 67, 279–291.
Omar, A. H., J.-G. Won, D. M. Winker, S.-C. Yoon, O. Dubovik, and M. P.
McCormick, 2005: Development of global aerosol models using cluster
analysis of Aerosol Robotic Network (AERONET) measurements. J. Geophys.
Res., 110, D10S14, doi:10.1029/2004JD004874.
Pollack, J. B. and J. N. Cuzzi, 1980: Scattering by non-spherical particles of size
comparable to a wavelength: A new semi-empirical theory and its application

to tropospheric aerosols.

J. Atmos. Sci., 37, 868–881.

Rodgers, C. D. (2000), Inverse Method for Atmospheric Sounding, World Sci.,
Singapore, 240 pp.
Sayer, A. M., A. Smirnov, N. C. Hsu, and B. N. Holben, 2012: A pure marine
aerosol model, for use in remote sensing applications. J. Geophys. Res., 117,
D05213, doi:10.1029/2011JD016689.
Stamnes,K., S. C. Tsay, W. Wiscombe, and K. Jayaweera, 1988: Numericallystable algorithm for discrete-ordinate-method radiative transfer in multiple
scattering and emitting layered media, Appl. Opt. 27, 2502–2509.
Yoshida, M, M. Kikuchi, T. M. Nagao, H. Murakami, T. Nomaki, A. Higurashi,Common retrieval of atmospheric aerosol properties for imaging satellite
sensors,

Journalof

thedoi:10.2151/jmsj. 2018-039.

MeteorologicalSocietyofJapan,

2018,