Algorithm Theoretical Basis Document:
Aerosol Retrieval by Polarization with GCOM-C/SGLI

Sonoyo Mukai (KCGI, Kyoto)
Itaru Sano (Kindai Univ.)
2020

Preface
GCOM-C/SGLI has multiple channels (19), including the near-UV (0.380 µm) andviolet (0.412 µm) wavelengths, and polarization channels in the red (0.670 µm) and nearIR (0.865 µm) wavelengths. This feature of SGLI is useful for the remote sensing ofaerosols. It has been demonstrated, from measurements by the Polarization andDirectionality of the Earth’s Reflectances (POLDER)-1, -2 and -3, that polarization
information is very effective for aerosol retrieval (Mukai and Sano, 2000; Deuzé et al.,2001), and also, from the Total Ozone Mapping Spectrometer (TOMS) on the Nimbus-7
satellite, that UV wavelengths are effective for aerosol remote sensing, especially for thesensing of absorbing aerosols (Torres et al., 1998). The present system utilizes not only
polarization information, but also near-UV data, in order to reproduce aerosol properties
from SGLI measurements.
Method
1. Overview
Figure 1 presents the basic block flow of the proposed aerosol retrieval method fromSGLI data.

Forward module

Inversion modulesurfacemodel

aerosol
products

aerosolmodel

radiation
simulation
vector/scalar

singlescattering"Simplification"

LUT
calculated
reflection

DBSGLI data

"Optimization"

size distribution,refractive index, etc.

Fig. 1: Basic framework for aerosol retrieval.

The system is roughly divided into two modules: the forward module and the inversion
module. The former completes numerical simulations for the Earth atmosphere-surface
system, and the latter contains the optimization process for the calculated values andsatellite observed data.
Advanced aerosol models, such as Fig. 1, play an important role in the efficiency ofaerosol retrieval because radiation simulations require long computing times in thevarious aerosol models at each pixel of the satellite data.
In practice, the module given by Fig.1 is processed in the case of polarization bands
to that of non-polarization bands in order (cf. Fig.2).

Polarization bands
Process according to Fig.1
in the vector field

Non-Polarization bands
Process according to Fig.1
in the scalar field

Fig.2: Execution process.
2. Aerosol model
The characteristics of aerosols can be represented using several parameters. The mostbasic parameter is the spectral aerosol optical thickness, AOT), at wavelength TheÅngström exponent (AE) is derived from the spectral AOT) and is closely related tothe aerosol size. Several other aerosol parameters, such as the size distribution andrefractive index, are also derived from the AOT) and radiance.
First, the size of the aerosols is discussed. The size distributions, derived from theaccumulated NASA/AERONET data, had two modes (fine and coarse) in a bimodal lognormal distribution of particle volume, with six parameters (volume concentration, mode
radius, and the standard deviation of the fine and coarse mode particles). Too many
parameters are excessive for the retrieval of the optimized size of aerosols at a global
scale. Therefore, a simplification was made for the aerosol size distribution function(Mukai et al., 2015). As a result, the size distribution function of particle volume (V) for
continental aerosols can be approximately expressed in a simpler form, defined by aunique variable of the fine particle fraction (f ) of the volume concentration: ln r  ln 0.1442 dVf~expd ln r
2 ln 2 1.533 2 ln 1.533
 ln r  ln 3.6072 (1  f )exp 
.
2 ln 2 2.104 
2 ln 2.104
(1)

The next aerosol characteristic of interest is the refractive index. It is reasonable toconsider that a mixture of various aerosol types exists in nature. Although particle mixing
is an issue to be considered, as well as understood, a simple homogeneous internal twocomponent mixing model was adopted here, using the Maxwell Garnett mixing (MGM)rule (Bohren and Wickramasinghe, 1977). The MGM rule provides a complex refractive
index, calculated as follows:  m( j  2 m )  2 g ( j   m )( j  2 m )  g ( j   m ),(2)

where  denotes the dielectric constant; the subscripts m and j represent the matrix andinclusion, respectively; g is the volume fraction of the inclusions. The present aerosol
retrieval is made using visible and near-IR band data because the refractive index can beassumed to be independent of the wavelength in these spectral regions. It was determinedthat the matrix and inclusions were 1.410–0.004i and 1.520–0.035i, respectively, forapplications using the visible and near-IR bands data. This indicated that the matrix andinclusions are weakly and strongly absorbing particles, respectively. Moreover, spectral
absorption was considered (i.e., the imaginary part of the refractive index) at near-UV
wavelengths. In short, aerosol models are more simply represented by two parameters (f,g) (Mukai et al., 2016); the size of the aerosols is represented by an approximate bimodal
log-normal distribution defined by the fine particle fraction (f), as given by Eq. (1), andthe refractive index is induced from the internal mixing of aerosol types with the volume
fraction of the inclusions (g) by Eq. (2).
3. Surface model
The polarized reflectance by the Earth surface was interpreted by POLDER'sempirical model (Nadal and Bréon, 1999). In practice, according to a simple equation
proposed by Deuze et al. (2001), the surface polarization signal was combined with theupward radiance at TOA (top of atmosphere) simulated in the complex system ofatmosphere and black & Lambert (no polarization) bottom surface.

4. Radiation simulation
Radiation simulation denotes multiple light scattering calculations in the Earthatmosphere model, which are hereinafter referred to as radiative transfer. Radiativetransfer takes Rayleigh scattering by molecules and Mie scattering by aerosols in theatmosphere, as well as reflection by the Earth’s surface, into account. The space-borne
sensors measure upwelling radiance at the top of atmosphere, and it is known that incidentsolar light multiply interacts with atmospheric particles.
Function I (, ) is defined to be the specific intensity vector at the optical depth  inthe direction of , given by  = (µ, ) and d = dµd, where µ is the cosine of the zenith
angle  between the outward normal of the plane parallel medium and the direction of thelight (i.e. µ= cos ), and  is the azimuth angle of the light measured from a fixed direction.
~Also, P (,) is the matrix of μ, μ, , and ; similarly defined quantities on incident
and scattered ray (denoted by  after the variable). Hereafter, (μ, ) is abbreviated to .
The standard problem in the functions for a given medium with constant or verticallyresolved single scattering albedo . The basic physical concept is simple. The intensity I(,) is reduced by e-d after traversing over an optical thickness dτ at wavelength . The
equation of radiative transfer describes this circumstance (Chandrasekhar 1960):
dI( , )
 ~ I( , ) P(, )  I( , )d,d4(3)~where  and P represent the albedo and phase matrix for single scattering,respectively. The integration is carried out over all solid angle. The vector I is defined
to be the four-dimensional representation of the polarized radiation field,I  ( I l , I r ,U ,V ) or ( I , Q, U ,V ) ,(4)~These four quantities represent the Stokes parameters, and the 4 × 4 matrix P
represents the phase relation in light scattering. The boundary conditions for the standard
problem are (i) at the top of the medium, τ = 0, there is no radiation falling, except indirection –0. (ii) at the bottom of the medium,  = 0, for a finite medium, radiationreflects according to the surface refection law, as mentioned in the previous section.
A more direct approach to solving the problem is by formulating a set of functional
equations for the reflection and transmission functions. The principle of invariance, statedoriginally by Ambartsumian (1958) and examined extensively by Chandrasekhar (1960),

is an elegant way to approach the problem. Suppose there is an incident radiation of flux
F in direction (μ0, 0) falling on the top of the atmosphere, and the flux is supposed to bepolarized asF  Fl , Fr , FU , FV  .

(5)Let the diffusely reflected radiation intensity vector be I( ) . The diffusely reflected
intensity denotes the emergent intensity from TOA ( = 0) and is derived using the~reflection matrix R so thatI() 1 ~R(, ' )  F(' ) ' d'4 (6)where the integration covers the inward hemisphere and the reflection matrix is expressedby the Stokes parameters:

 R ll~  R rlRR Ul
R Vl

R lr
R rr

R lU
R rU

R UrR Vr

R UU
R VU

R lV 
R rV .
R UV 
R VV (7)In a similar way, the diffusely transmitted intensity at the bottom of atmosphere (= 0) is defined by the transmission matrix T . As usual, the solar incident flux isassumed to be non-polarized, namely F = (0.5, 0.5, 0, 0), and hence computational
efforts are rather reduced. The calculation algorithm was the same as previous studies(Mukai et al. 1996, Sano, 2004).
Output and Outlook
This work proposed algorithms for aerosol retrieval from SGLI. The output of SGLIis AOT, AE and SSA (single scattering albedo) in terms of polarization data at 0.670 µm
and 0.865 µm, and radiance data at 0.38 µm and/or others. The SGLI has multiplechannels (19) including not only polarization channels in the red and near-IR wavelengths,
but also in near-UV (0.380 m) channel. The near-UV data should be utilized more, forexample in the detection of absorbing aerosols (Mukai et al. 2019). The combined use ofmulti-band data and polarization information is expected to facilitate subsequentaerosol/cloud characterization.
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