ATBD of GCOM-C ocean color atmospheric correction
Hiroshi Murakami (JAXA/EORC), July 2020
１． Introduction
GCOM-C/SGLIoceancoloratmosphericcorrection

algorithm applicable for the global ocean is developed (Fig.
1). The method is basically same as the generalatmospheric correction algorithms developed for OCTS,
SeaWiFS, MODIS, VIIRS, and so on (Gordon and Wang,1994; Fukushima et al., 2002); normalized water-leaving
radiance nLw() or remote sensing reflectance Rrs() is
derived by using multiple channel () observations. It isdesigned as a fast and small data lack algorithm because
SGLI has 250-m spatial resolution and relatively narrowswath of 1150 km.
２． Method
Satellite observed reflectance, t(), is calculated from Lt() by the following equation (1).
t() = L t()    d2 /F0() /cos(s),(1)where F0 is solar irradiance (see Table 1), d, ratio of solar-earth distance to the yearly average distance, s,solar zenith angle.
Table 1 Center wavelengths, band weighted solar irradiance, and refractive index of SGLI channelsChannel

VN01 VN02 VN03 VN04 VN05 VN06 VN07 VN08 VN09 VN10 VN11 SW01 SW02 SW03 SW04(nm)380.03 412.51 443.24 489.85 529.64 566.15 672.00 672.10 763.07 866.76 867.12 1054.99 1385.35 1634.51 2209.48

F0(W/m2/m) 1092.14 1712.17 1898.32 1938.46 1850.96 1797.14 1502.55 1502.30 1245.45 956.34 956.62 646.54 361.24 237.58

84.25

Refractive index 1.3395 1.3383 1.3371 1.3351 1.3336 1.3327 1.3310 1.3310 1.3298 1.3287 1.3287 1.3267 1.3211 1.3168 1.2953

t() is approximated as following equation (2).
t() / tg() = r() + T()  g() + a() + w()  t() / ( 1 – sa()  w() ),(2)where r is Rayleigh scattering reflectance, a, aerosol reflectance, w, water-leaving reflectance, T, directtransmittance of sun-surface-satellite, t, direct + diffuse transmittance, sa, spherical albedo, g, sun-glint
reflectance, tg, correction factor for water vapor, ozone, and oxygen absorption (Table 2). The white cap term
is omitted in the eq. (2), because the spectral shape is similar with a and it can be corrected as a part of a().
Water-leaving reflectance w is derived by the eq. (3).
w() = aw() / (t() +aw()  sa()),(3)

Where,
aw() = t() /tg() – r() – T()  g() – a().

(4)sa  w can be omitted because w of the ocean and sa of the clear sky are generally small.
Rrs() and nLw() are derived by correcting directional dependency of in-water and sea-surface reflectance by
LUT (R) (eq. (5) and (6)) developed and distributed by Morel and Maritorena 2001.

Rrs() = (w() / )  R(=0, s=0, , W, Chl, ) / R(, s, , W, Chl, )nLw() = Rrs()  F0()

(5)

(6)

where  is solar zenith angle, s, solar zenith angle, , relative azimuth angle, W, wind speed, and Chl,chlorophyll-a concentration.
Table 2 coefficients for gas absorption correction
gas

Vapor
mm

Oxygen(sea-levelpressureratio)

Ozone
DU

Channelbc

VN01

1.4909E-06

a0.0000E+00

0.00

VN02

9.8080E-07

0.0000E+00

0.00

VN03

3.1745E-05

0.0000E+00

0.00

VN04

1.0449E-05

0.0000E+00

0.00

VN05

1.6566E-05

0.0000E+00

0.00

VN06

1.2198E-04

0.0000E+00

0.00

VN07

5.6657E-05

0.0000E+00

0.00

VN08

5.5299E-05

0.0000E+00

0.00

VN09

1.6525E-06

0.0000E+00

0.00

VN10

8.0907E-05

0.0000E+00

0.00

VN11

7.5751E-05

0.0000E+00

0.00

SW01

4.0931E-05

0.0000E+00

0.00

SW02

-2.5585E-01

1.4719E+00

-0.32

SW03

4.3975E-03-2.8813E-03

0.06

SW04

1.7986E-02-1.1061E-02

0.08

VN01

1.6250e-03

0.0000e+00

0.00

VN02

4.2290e-05

0.0000e+00

0.00

VN03

4.7086e-04

0.0000e+00

0.00

VN04

2.0450e-04

0.0000e+00

0.00

VN05

1.1597e-03

0.0000e+00

0.00

VN06

5.5712e-03

0.0000e+00

0.00

VN07

1.9591e-03-5.1393e-04

1.00

VN08

2.0069e-03-5.2653e-04

1.00

VN09

3.1756e-02

2.8606e-01

-0.60

VN10

4.4504e-05

0.0000e+00

0.00

VN11

4.5281e-05

0.0000e+00

0.00

SW01

8.5098e-03

0.0000e+00

0.00

SW02

-7.1343E-04

9.0805e-04

1.00

SW03

4.9989e-07

0.0000e+00

0.00

SW04

6.5526e-08

0.0000e+00

0.00

VN01

8.2534e-09

0.0000e+00

0.00

VN02

2.5426e-07

0.0000e+00

0.00

VN03

3.0227e-06

0.0000e+00

0.00

VN04

2.0641e-05

0.0000e+00

0.00

VN05

6.5554e-05

0.0000e+00

0.00

VN06

1.1461e-04

0.0000e+00

0.00

VN07

4.2756e-05

0.0000e+00

0.00

VN08

4.2661e-05

0.0000e+00

0.00

VN09

6.6933e-06

0.0000e+00

0.00

VN10

1.9163e-06

0.0000e+00

0.00

VN11

1.8778e-06

0.0000e+00

0.00

SW01

8.0493e-08

0.0000e+00

0.00

SW02

3.5094e-09

0.0000e+00

0.00

SW03

0.0000e+00

0.0000e+00

0.00

SW04

0.0000e+00

0.0000e+00

0.00

Look-up tables (LUTs) of r(), T(), a(), t(), and sa() are calculated by Pstar4 (Ota et al., 2010;
Nakajima and Tanaka, 1986; 1988; Stamnes et al., 1988) for possible solar and satellite geometries (, s, ),aerosol optical thickness at 867nm (AOT), and aerosol types (M). The sea-surface Fresnel reflection isincluded in r().
Gas absorption correction, tg in eq. (2) and (4) is calculated as followings.
tg()=tvapor()  toxygen()  tozone()(7)ti() = exp(–(ai()+bi()  (xi  am)ci())  xi  am)/ exp(–(ai()+bi()  (xnormi  am)ci())  xnormi  am) (8)where, xi= vapor (H2O), oxygen (O2), and ozone(O3), normal values of the gases, xnormi=vapor =14.186 mm,
xnormi=oxygen =1.0, xnormi=ozone =343.79 DU, am=1/cos(s) + 1/cos().
Oxygen volume, xi=oxygen, is described as ratio of sea-level pressure to nominal sea-level pressure assuming
oxygen ratio to the atmosphere is constant.

３． Aerosol model
Aerosol models (size distribution and refractive index)
are designed based on AERONET climatology (Holbenet al., 2001) and calculated by Pstar4. Volume size
distribution, V, is modeled by the eq. (9).
V= exp((ln(R/RM)/ln(S))2 / 2)

(9)

R indicates particle size, (m), RM, mode radius, and S,deviation. Ninth candidate models are made by mixing
the fine mode and the coarse mode aerosols with finemode ratio = 100, 68, 45, 29, 18, 11, 6, 3, and 0 %.
Fig. 2 shows an example of a() and t() of the ninth
aerosoltypes.

Theyarenormalized

byaerosolreflectance at the aerosol correction base channel, VN11(867nm).

Table 3 size distribution parameters and refractive index
RM (m)

Skrki

Fine

0.143

1.537

1.439

1.000E-08

Figure 2 Aerosol reflectance and transmittance calculated

Coase

2.592.054

1.363

3.000E-09

by Pstar4

４． Sun-glint correction

Sun-glint reflectance, g, is calculated using objective analysis wind speed, W, by Cox and Munk (1954)(eq.10). T of AOT=0.3 is used to reduce the amount of the correction and avoid data lack by the overcorrection
g=pw (1 –2 m  y  z  cos_w),(10)pw=exp(–tan(theta)2/s)/s/(4 cth0  cth  cos(theta)4),
y= sqrt(m2 + cos_w2 –1) / m,
z=1 / (cos_w + y  m)2 +1 / (y + m  cos_w)2,cos_w = cos(acos(cth  cth0 + sth  sth0  cdp)/2),
m: refractive index of the sea water (see Table 1),
theta=acos((cth+cth0) / (2 cos_w)),s=0.003+0.00512 W,
where, sth0=sin(0), cth0=cos(0), sth =sin(), cth =cos(), cdp=cos().

５． First guess of water-leaving reflectancew at Near-infrared (VN10) and red (VN07) channels are pre-assumed for the aerosol estimation. Empirical
relation of w to Liner Combination Index (Frouin et al., 2006) (ILC in eq. (11)) is constructed by an inherent
optical property (IOP) model based on NOMAD (Werdell and Bailey 2005) (eq. 12.1-2).
ILC = w(VN04) −1.4239 w(VN06) +0.4104 w(VN10)(11)wpre = (cL0 + cL1 ILC + cL2 ILC2)  (ILC < 0.003),(12.1)

wpre = (cH0 + cH1 ILC + cH2 ILC2)  (ILC  0.003).

(12.2)

Eq. (11) can be applied to w derived by eqs. (3) and (4) without aerosol because ILC is not sensitive toaerosols (Frouin et al., 2006). The coefficients of eqs. (12-1,2) are shown in Table 4.
Table 4 Coefficients for pre-estimation of w
cL0

cL1

cL2

cH0

cH1

cH2

VN07

0.00057-0.04968

0.750740.00057-0.04968

0.75074VN10

0.00005-0.00935

0.368030.00005-0.00935

0.36803

６． Aerosol optical thickness and model selection
AOT and M (Mi=1~9) are selected by searching a condition that the observed left hand is agree with the Pstar
simulated right hand in eq. (13).
t() / tg() r() – T()  g() = a() + wpre()  t() / ( 1 – sa()  wpre() ),(13)Practically, AOT is selected by eq. (13) using observation and simulation at VN10 for each M firstly, and anoptimal M is selected by observation and simulation at VN07.
If w at visible channels (VN02-VN05) become negative by the selected M, it is re-selected by assuming theblue channel w is zero.

７． Vicarious calibration

The ocean color estimation requires 0.2-0.3% accuracy of the inter-band relative calibration, even though theerror of pre-launch characterization and on-orbit calibration can reach to 2-3%. The inter-band calibration(adjustment) can be conducted by using in-situ Rrs and the ocean color atmospheric correction LUTs. The
temporal change is estimated by post-launch moon calibration, and the results will be reflected in the SGLI
Ver.2 calibrated radiance data (L1B data).
LL1B() = Lorig() / (1.0 + kt() D)(14)

where D indicates days from 00:00 1st Jan 2018(=0). kt() is shown in Table 5.
Rrs of MOBY (Clark et al., 2003) and BOUSSOLE (Antoine et al., 2006) are used as the vicarious calibration
standard in multiple satellite missions. The coefficients, k0(), are derived by Murakami et al., 2005 (Table 5,Fig. 3). Lcorr() in eq. (15) is used as Lt() in eq. (1).
Lcorr() = LL1B()/ k0()(15)

The MOBY +BOUSSOLE result in Table 5 is used for the SGLI ver. 2 ocean color processing.
Table 5 SGLI Vicarious calibration coefficients
Channel VN01
kt (day-1)
k0 (MOBY +BOUSSOLE

VN08

VN09

VN10

VN11-6.20E-5 -6.06E-5 -5.79E-5 -5.05E-5 -4.20E-5 -3.06E-5 -5.04E-6 -4.34E-6

VN02

VN03

VN04

VN05

VN06

VN07

0.0

0.0

0.0

0.976

1.023

0.997

1.015

1.051

1.033

11.0020.998

1

1k0 (MOBY N=55)

0.982

1.029

1.003

1.019

1.056

1.036

11.0031.017

11k0 (BOUSSOLE N=17)

0.954

0.999

0.977

1.001

1.036

1.026

10.996

0.945

11N=72)** recommended for the ocean color processing

Figure 3 SGLI Vicarious calibration by MOBY and BOUSSOLE
Blue dots indicate MOBY samples, and red, BOUSSOLE samples

８． QA_flag
The first 0-1 bits are common for the Level-2
products, input data lack and land/water flags.

Table 6 Bit specification of QA_flagbit

Description

L3 mask L3 mask L3 mask
(NWLR) (PAR) (FAI)

Others are defined as the right table.

0 no observation data

1

1

1

Cloud masks are set by the Rayleigh corrected

1 land (0: ocean, 1: land)

1

1

1

reflectance of blue, red and near-infrared channels,

2 incomplete VNR bands

11

1and the near cloud is set by the maximum or

3 cloud or ice

101

deviation of the 5x5 pixel reflectance. Dark pixel is

4 near cloud (+-2pix)

101

set when water-leaving reflectance of VN06<0.002.

5 dark pixel000

Case-2 flag is set if water-leaving reflectance of

6 coast pixel

001

VN07>0.008 and Chl-a>60mg/m3.

7 straylight flag000

The Level-3 statistics processing will input data

8 sunglint mask>0.16000when the bits of QA_flag indicated in Table 6 are

9 sunglint flag>0.01

000not set and the product value is within the valid

10 wind speed>20m/s

000range

11 soz>7500012 taua>0.500013 out of aerosol models;

00014 negative nLw

00015 turbid Case-2 water

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