SGLI

Algorithm Technical Background Document

ATMOSPHERIC CORRECTION ALGORITHM
FOR OCEAN COLOR
Version 1 Rev.1 January 17 2019

Mitsuhiro Toratani,
Kazunori Ogata and Hajime Fukushima
Tokai University

Version/Revision History:
V.1 Rev.1: January 17, 2019
Version 1

December 20, 2018

V.1 Rev.1

January 17, 2019

Several mistakes corrected
Contents page enhanced
Cover page added
Page numbers added
Introduction section added1

Table of Contents
1. Introduction ……………………………………………………………………….

3

2. Radiative transfer model ………………………………………………………..

4

3. Radiative transfer model for reflectance ………………………………………

5

4. Overview of atmospheric correction for SGLI ………………………………..

6

5. Rayleigh reflectance (𝝆𝑴 ) ………………………………………………………..

8

5.1 Lookup tables for the reflectance due to Rayleigh scattering …………

9

6. Aerosol reflectance (𝝆𝑨 + 𝝆𝑴𝑨 ) ………………………………………………….. 10
6.1. Overview ……………………………………………………………………… 10
6.2 Switching process in consideration to high turbid water ……………… 11
6.3 Determination of aerosol type from near infrared bands ……………… 12
6.4 Determination of aerosol type from shortwave infrared bands ………. 13
6.5 Liner interpolation between NIR-AC and SWIR-AC methods ……….. 13
6.6 Lookup tables for the reflectance due to aerosol scattering ………….. 14
7.

Transmittence ……………………………………………………………………. 17
7.1 Moleculer transmittance …………………………………………………… 17
7.2 Ozone absorption correction ……………………………………………….. 17
7.3 Oxygen absorption correction ……………………………………………… 17

8.

Sunglitter correction …………………………………………………………….. 19

9. Whitecap correction ……………………………………………………………… 20
10. Bidirectional reflectance distribution function ……………………………… 21
10.1 Calculation of transmittance from in-water to air for satellite view (𝒕 𝒖𝒇 )……………………………… 22
10.2 Calculation of transmittance from air to in-water for solar path (𝒕𝒅𝒇 )……………………………… 22
10.3 Calculation of Q factor …………………………………………………….. 24
11. Ancillary data …………………………………………………………………….. 25
11.1 Total ozone …………………………………………………………………..

25

11.2 Sea surface pressure ………………………………………………………. 25
11.3 Sea surface wind …………………………………………………………… 25
Appendix I Mean extratrestrial solar irradiance ……………………………… 26
Appendix II. QA Flags and Masks ………………………………………

28

Appendix III. LUT of Single Scattering Albedo(ωA) for Aerosol Models …….

29

Appendix IV. LUT of Aerosol Extinction Coefficient (Kext) for Aerosol Models . 30
Appendix V LUT of Aerosol Scattering Phase Function (PA) for Aerosol Models………………………………....

231

1. Introduction to Version 1 Revision 1 Description

This document describes the atmospheric correction algorithm (Ver.1 Rev.1) for
SGLI Level 2 standard ocean color product generation. The algorithm is to produce thenormalized water-leaving radiance, or the upwelling radiance emitted from just beneaththe sea surface (unit: W/m2/µm/sr) for each relevant observation band. As a bi-product,
the algorithm also produces aerosol optical thickness (AOT, dimensionless) for several
near infrared bands.
The algorithm inherits its basic structure from the GLI ocean color atmosphericcorrection algorithm (Fukushima et al., 1998): Toratani et al., 2007), but somemodifications and enhancements have been applied. One significant difference from thepast algorithm is the selection of NIR band pair in terms of aerosol type/optical thickness
determination: that is, lacking 750 nm band in SGLI channels, we use (673nm, 869nm)
band pair with an iterative procedure to estimate Rrs (673). Another feature of
atmospheric correction is the use of (865nm, 1630nm) band pair observation, in addition
to (673nm, 869nm), to ensure the quality of aerosol reflectance estimation over turbid
waters. The algorithm also incorporates BRDF correction.

3

2. Radiative transfer model

The satellite-observed radiance, 𝐿∗+ , is modeled as follows.
𝑳∗𝑻 = 𝑳∗𝒑𝒂𝒕𝒉 + 𝑻∗ 𝑳𝑮 + 𝒕∗ 𝑳(𝑾𝑪) + 𝒕∗ 𝑳𝑾 [𝑾 𝒎:𝟐 𝝁𝒎:𝟏 𝒔𝒓:𝟏 ](𝟐. 1)For simplicity, omit the wavelength (l). 𝐿∗CDEF is radiance that contribution of theatmosphere composed of atmospheric scattered light and sea surface specular reflectionof sky light, 𝐿G is the radiance resulting from the specular reflection by the direct sun
light, 𝐿(HI) is the radiance resulting from the whitecap, 𝐿H is water-leaving radiance.
𝑇 ∗ is the direct transmittance of the atmosphere from sea surface to satellite, 𝑡 ∗ is the

diffuse transmittance of the atmosphere from sea surface to satellite.
𝑇 ∗ and 𝑡 ∗ are component as follows,𝑻∗ = 𝑻(𝑶𝟑) 𝑻(𝒈) 𝑻(𝑴) 𝑻(𝑨)∗𝒕 =𝒕

(𝟐. 2)(𝑶𝟑) (𝒈) (𝑴) (𝑨)𝒕𝒕(𝟐. 3)𝒕𝑡 (QR) is transmittance of ozone absorption, 𝑡 (S) is transmittance of gas (O2, NO2, H2O)

absorption excluding ozone, 𝑡 (T) is transmittance of molecule, 𝑡 (U) is transmittance ofaerosol.
The satellite-observed radiance excluding the influence of ozone transmittance 𝑳𝑻 isexpressed as follows.
𝑳∗𝑻 = V𝑳∗𝒑𝒂𝒕𝒉

𝑻∗
𝒕∗
𝒕∗
(𝑶𝟑)
+
𝑳
+
𝑳
+
𝑳 X 𝒕(𝑶𝟑) 𝒕𝟎(𝑶𝟑)(𝑶𝟑) 𝑮(𝑶𝟑) 𝑾𝑪(𝑶𝟑) 𝑾
(𝑶𝟑)
(𝑶𝟑)
(𝑶𝟑)
(𝑶𝟑)
𝒕
𝒕𝟎
𝒕
𝒕𝟎
𝒕
𝒕𝟎
𝒕
𝒕𝟎
(𝑶𝟑)

𝑳∗𝑻 = Y𝑳𝒑𝒂𝒕𝒉 + 𝑻𝑳𝑮 + 𝒕𝑳𝑾𝑪 + 𝒕𝑳𝑾 Z𝒕(𝑶𝟑) 𝒕𝟎
𝑳𝑻 = 𝑳𝒑𝒂𝒕𝒉 + 𝑻𝑳𝑮 + 𝒕𝑳𝑾𝑪 + 𝒕𝑳𝑾(𝟐. 4)

where the element without superscript * has the meaning of correcting thetransmittance due to ozone. Since the ozone layer is in the upper atmosphere layer, theinfluence of ozone is corrected in advance.
𝐿CDEF is represented by the following atmospheric radiances.

𝑳𝒑𝒂𝒕𝒉 = 𝑳𝑴 + 𝑳𝑨 + 𝑳𝑴𝑨(𝟐. 5)

𝐿T is molecule radiance, 𝐿U is aerosol radiance, 𝐿TU is radiance due to the interaction
between molecules and aerosol particles.
The Eq.(2.5) is substituted into Eq. (2.4).
𝑳𝑻 = 𝑳𝑴 + 𝑳𝑨 + 𝑳𝑴𝑨 + 𝑻𝑳𝑮 + 𝒕𝑳𝑾𝑪 + 𝒕𝑳𝑾4(𝟐. 6)

3. Radiative transfer model for reflectanceIn atmospheric correction processing, reflectance ( 𝜌) is used. The relationshipbetween reflectance and radiance(𝐿) is as follows.,
𝝆(𝝀) =𝝅𝑳(𝝀)𝑭𝟎 (𝝀) 𝐜𝐨𝐬 𝜽𝟎(𝟑. 𝟏),

where 𝐹h is Extraterestrial solar irradiance, 𝜃h is solar zenith angle.
The extraterrestrial solar irradiance (F0) depend on the distance between the sun
jjjh ) at
and the earth. The relationship between F0 and extraterrestrial solar irradiance (𝐹mean distance between solar and the earth is as follows.
jjjh (𝜆) ∙ 𝑑𝑎𝑦𝑐𝑜𝑟 s𝐹h (𝜆) = 𝐹
𝑑𝑎𝑦𝑐𝑜𝑟 =1
1.00014 − 0.01671 ∗ cos 𝛼 − 0.00014 ∗ 𝑐𝑜𝑠 s 2𝛼

𝛼 = 0.9856002831 ∗ 𝑗𝑑𝑎𝑦 − 3.4532868(degree)jday : day of year.
For mean extraterrestrial solar irradiance, see Appendix I.
By substituting this expression, the Eq. (2.6) becomes as follows.
𝑳𝑻 = 𝑳𝑴 + 𝑳𝑨 + 𝑳𝑴𝑨 + 𝑻𝑳𝑮 + 𝒕𝑳𝑾𝑪 + 𝒕𝑳𝑾𝝅𝑳𝑻𝝅(𝑳𝑴 + 𝑳𝑨 + 𝑳𝑴𝑨 + 𝑳𝑮 + 𝒕𝑳𝑾𝑪 + 𝒕𝑳𝑾 )=𝑭𝟎 𝐜𝐨𝐬 𝜽𝟎𝑭𝟎 𝐜𝐨𝐬 𝜽𝟎𝝆𝑻 = 𝝆𝑴 + 𝝆𝑨 + 𝝆𝑴𝑨 + 𝑻𝝆𝑮 + 𝒕𝝆𝑾𝑪 + 𝒕𝝆𝒘(𝟑. 𝟐)

𝝆𝑻 − (𝝆𝑴 + 𝝆𝑨 + 𝝆𝑴𝑨 + 𝑻𝝆𝑮 + 𝒕𝝆𝑾𝑪 )𝒕(𝟑. 𝟑)

𝝆𝒘 =The 𝜌€ is calculated by subtracting 𝜌T , 𝜌U + 𝜌UT , 𝑇𝜌G , 𝑡𝜌HI and dividing by t.
The 𝜌(•‚) used for cloud detection is defined as
𝝆(𝒓𝒄) = 𝝆𝑻 − 𝝆𝑴5

4. Overview of atmospheric correction for SGLIThe flowchart of atmospheric correction for SGLI shows in fig.4.1. Processing ofeach pixel is executed in the order of Ozone transmittance, Rayleigh reflectance, Cloud
screening, Sunglitter, Whitecap, Aerosol reflectance, and bidirectinal reflectance
distribution function to estimate water-leaving radiance (nLw) from Satellite-observed
radiance (Lt).

Fig. 4.1 Flowchart of atmospheric correction for SGLICorrection of ozone transmittance is attenuation due to absorption of ozone(Chapter 7, Section 2). Rayleigh reflectance correction is correction of scattering of gas
molecules (Chapter 5). Pixels above the threshold (𝜌(•‚) (865) = 0.03) are masked as
clouds. The sunglint reflectance is corrected by the method of Cox & Munk (Chapter 8).
The white cap correction is described in Chapter 9. The most complicated part ofatmospheric correction is correction of reflectance of aerosol. In order to calculate the6aerosol reflectance, two aerosol models are selected from prepared aerosol models. In
the aerosol model selection, the near infrared region is usually used for selecting theaerosol model, but in the case of the influence of the high suspended matter
concentration, the short wavelength infrared region is used. In the case of aerosol
model selection using the near infrared region, iteration procedure is used to avoid
contribution of water-leaving reflectance at near infrared bands. Details are shown in
Chapter 6. Correction of bidirectinal reflectance distribution function described in
Chapter 10. In this chapter, the definition of normalized water-leaving radiance is also
described.

7

5. Rayleigh reflectance (𝝆𝑴 )The reflectance due to the scattering by atmospheric molecule, rM(l), is calculated
by using lookup tables. The lookup tables give rM(l) for the given q(l), q0 and Df. The
lookup tables have 24 values for satellite zenith angle in 3.5° increments (0.0° - 80.5°)
and 24 values for solar zenith angle in 3.5° increments (0.0° - 80.5°). If there is no exact
values for the target pixel in the lookup table the values needed are interpolated by twodimensional linear interpolation.
The lookup tables were constructed by solving the Radiative Transfer Model atstandard atmospheric pressure and the absorption of ozone layer was not taken into
account. At this stage, we correct the pressure impact with aid of the pressure ancillarydata.
rM(l) in consideration of pressure impact is calculated by the following equation:

𝜌T (𝜆) =1 − 𝑒𝑥𝑝Y−𝜏T (𝜆)/𝑐𝑜𝑠𝜃(𝜆)Z
𝜌Th (𝜆, 𝜃 (𝜆), 𝜃h , Δ𝜙)
1 − 𝑒𝑥𝑝Y−𝜏Th (𝜆)/𝑐𝑜𝑠𝜃(𝜆)Z

(5.1)

tM:

Rayleigh optical thickness

tM0:

Rayleigh optical thickness at standard atmospheric pressure.
tM0 at each band is shown below.

q:zenith angle of the satellite

q0:

zenith angle of the sun

rM0:

Rayleigh reflectance which are calculated from lookup tables

Df:

difference between the solar and the satellite azimuth angles

The Rayleigh optical thickness, tM, is calculated by the following equations:t M (l ) =P
t M 0 (l )
P0

(5.2)

P:

atmospheric pressure at each pixel.

P0:

standard atmospheric pressure ( = 1013.25hPa)

tM0(l): Rayleigh optical thickness at standard atmospheric pressure.
tM0 at each band was computed by the following equation(Bodhaine, 1999) in consideration with sensor response function.

æ 1.0455996 - 341.29061l-2 - 0.90230850l2 ö÷÷ (5.3)
t r 0 (l ) = 0.0021520çç
-22
è 1 + 0.0027059889l - 85.968563l
øl : wavelength(µm)

8Table 5.1 Rayleigh optical thickness at standard atmospheric pressure
in consideration with sensor response function
Band

Rayleigh opticalBand

thickness
VN1
VN2
VN3
VN4
VN5
VN6
VN7
VN8

Rayleigh optical
thickness

0.44670.31890.23610.15590.11320.087140.042650.04265

VN9
VN10
VN11
SW1
SW2
SW3
SW4

0.02571
0.015250.01525
0.007107
0.002380
0.001246
0.0003765

5.1 Lookup tables for the reflectance due to Rayleigh scattering
The lookup table of each band gives rM(l) for 3 parameters, i.e., q(l), q0 and Df.
(1) Calculation
The tables were calculated for the following values of the independent variables andconditions:- q : 0.0° - 80.5°(24 points)- q0 : 0.0° - 80.5° in 3.5° increments(24 points)- Δ𝜙 : 0.0° - 180° in 4.0° increments(46 points)- Atmospheric pressure : standard atmospheric pressure(1013.25hPa)- The polarization was considered.
- The absorption of ozone layer was ignored.
- The multiple scattering due to the interaction between molecules wasconsidered.
- The sea surface was assumed to be flat.
- A plane parallel atmosphere divided into several homogeneous sublayers was
assumed.
- Reflectance due to sun glint was removed.
- Response function was considered.
The lookup table are constructed by radiative transfer code (pstar4 : Ohta et al.,2008).

96. Aerosol reflectance (𝝆𝑨 + 𝝆𝑴𝑨 )6.1. Overview

The spectral variation in 𝜌+ in the near infrared is used to provide information
concerning the aerosol’s optical properties. The Rayleigh-scattering component is thenremoved, and the spectral variation of the remainder is compared with that produced
by a set of candidate aerosol models in order to determine which two models of thecandidate set are most appropriate. We implemented tables that store the relationshipbetween aerosol reflectance 𝜌U + 𝜌TU and aerosol optical thickness 𝜏U for each band.
The magnitude of 𝜌U + 𝜌TU in the shorter wavelength bands is estimated from thespectral ratio of aerosol reflectance between two near infrared bands. Since thespectral dependency of 𝜌U + 𝜌TU is dependent on aerosol type.
Generally, we use near infrared bands for aerosol model selection. If there are highsuspended matter, we use shortwave infrared bands to avoid water contribution. Justby changing the near infrared bands to shortwave infrared bands, the method ofaerosol model selection does not change without iteration.

Figure 6.1 Flowchart of aerosol reflectance correction using iteration
10

Flowchart of aerosol reflectance estimation is shown in Fig.6.1. Water-leaving
reflectance is estimated using initial values (Chlorophyll-a concentration, and CDOM).
𝜌U (𝜆‹ ) + 𝜌TU (𝜆‹ ) and 𝜌U (𝜆Œ ) + 𝜌TU (𝜆Œ ) (𝜆‹ = 670, 𝜆Œ = 865 at near infrared bands, 𝜆‹ =865, 𝜆Œ = 1630 in case of high turbid.) are converted to aerosol optical thickness (tA)using lookup tables (Section 6.4) of relationship between rA + rMA and tA for aerosol
models. Aerosol models are selected from the spectral dependency of tA. rA + rMA in thevisible bands is estimated using the selected aerosol models.
After the first atmospheric correction, the new water-leaving reflectance is estimatedfrom the obtained CHL and CDOM, with atmospheric correction repeated until thesevalues converged. We set the threshold for the convergence condition as the stage at
which the difference in CHL between, before and after processing was less than 1% andthe difference in CDOM was less than 0.001 m-1. A total of ten iterations were
performed.
The algorithm is switched in case of high turbid water or not. We use 𝜆‹ = 670, 𝜆Œ =865 at near infrared bands for Case I water, 𝜆‹ = 865, 𝜆Œ = 1630 for high turbid water.
The switching is explained in Section 6.2.
Regarding correction of absorptive aerosol, it was postponed.
6.2 Switching process in consideration to high turbid water

In considering the influence of suspended matter concentration, it is divided into
three regions, Case 1, Case 2 and its transition area. We call NIR-AC for Case 1
atmospheric correction, SWIR-AC for Case 2 atmospheric correction.
T-index was used for division.
𝑇•Ž• (869,1630) =𝜌(•‚) (673)𝜌(•‚) (869)869 − 673
exp “−𝑙𝑛 –—˜.
𝜌(•‚) (869)
1630 − 869𝜌(•‚) (1630)(6.1)

NIR-AC method is used if Tind is less than thlow, and SWIR-AC method is used if Tind isgreater than th. If Tind includes between thlow and th then 𝜌U + 𝜌TU is estimated by linerinterpolation between NIR-AC and SWIR-AC methods (Figure 6.2).

11

Figure 6.2 Method of switching Case 1, Case 2 and its transition
6.3 Determination of aerosol type from near infrared bands𝜌U (𝜆‹ ) + 𝜌TU (𝜆‹ ) and 𝜌U (𝜆Œ ) + 𝜌TU (𝜆Œ ) (𝜆‹ = 670 , 𝜆Œ = 865 at near infrared bands)
are calculated by the following equation where rW (l) is calculated by using in-watermodel.
rA(l) + rMA(l)=rT(l) - rM(l) - t(l) rG(l)-t(l) rW(l)(6.2)

Then tA(M, 𝜆‹ ) and tA(M, 𝜆Œ ) are obtained by following equation.
X = rA(M,l,q,q0,Df) + rMA(M,l,q,q0,Df)tA(M,l,q,q0,Df) = a0 + a1X + a2X2 + a3X3 + a4X4

(6.3)

M:

aerosol modell:wavelengthq:a zenith angle of the satellite

q0:

a zenith angle of the sunDf:

a difference between the solar and the satellite azimuth angles

a0, a1, a2, a3 and a4: These values are provided by the lookup tables.
The pixel-wise procedure for the atmospheric correction is described as follows. In
what follows, e’(M) means the estimated value of the spectral ratio of wAtAPA between
670 and 865nm bands for an assumed aerosol model M, while e(M) is the theoreticallyderived value of wAKEXTPA ratio for a model M.
(1) Get rA(l)+ rMA(l)= rT(l)-rM(l) at 670 and 865nm.
(2) Estimate tA at 670nm and 865nm bands for each assumed aerosol model(M) bysolving the biquadratic equation in reference to the aerosol LUTs (LookUp Table).
(3) Calculate e'ave and select a pair of aerosol models A and B, such that e(A) < e'ave and12e(B) > e'ave, by the iteration scheme. Define interpolation ratio r as (e'ave- e(A))/( e(B)e'(A)).
(4) For models A and B, obtain tA(l,M) for band 380nm to 565nm byt A (l, M ) =K ext (l ,M )t (865, M)
K ext (865, M ) A(6.4)
Derive rA(l)+rMA(l) for the models A and B in use of the aerosol LUT.
(5) Obtain final rA(l)+rMA(l) by interpolating the rA+rMA values for the models A and B.
6.4 Determination of aerosol type from shortwave infrared bands𝜌U (𝜆‹ ) + 𝜌TU (𝜆‹ ) and 𝜌U (𝜆Œ ) + 𝜌TU (𝜆Œ ) (𝜆‹ = 865, 𝜆Œ = 1630 in case of high turbid.)
are calculated by the same equation (6.2) as 𝜌H (1630)=0. SWIR-AC method estimatesrA(l)+ rMA(l) in the basis of the single scattering approximation using ρ(rc) (865) andρ(rc) (1630) pair. In contrast to NIR-AC, this method doesn’t use the iterative procedureusing the in-water model. The reason why is that the contribution of water-leaving
reflectance for wavelengths longer than visible can be ignored because of having strongly
light absorption on water property of these wavelengths.
The Outline of SWIR-AC method is described as follows. In what follows, e’(M)means the estimated value of the spectral ratio of wAtAPA between 865nm and 1630nm
channels for an assumed aerosol model M, while e(M) is the theoretically derived valueof wAKEXTPA ratio for a model M.
(1) Get rA(l)+ rMA(l)= rT(l)-rM(l) at 865nm and 1630nm.
(2) Estimate tA at 865nm and 1630nm bands for each assumed aerosol model(M) bysolving the biquadratic equation in reference to the aerosol LUTs.
(3) Calculate e'ave and select a pair of aerosol models A and B, such that e(A) < e'ave ande(B) > e'ave, by the iteration scheme. Define interpolation ratio r as (e'ave- e(A))/( e(B)e'(A)).
(4) For models A and B, obtain tA(l,M) for band 380nm to 670nm by𝜏U (𝜆, 𝑀) =𝐾›œE (𝜆, 𝑀)𝜏 (1630, 𝑀).
𝐾›œE (1630, 𝑀) U

(6.5)

Derive rA(l)+rMA(l) for the models A and B in use of the aerosol LUT.
(5) Obtain final rA(l)+rMA(l) by interpolating the rA+rMA values for the models A and B.
6.5 Liner interpolation between NIR-AC and SWIR-AC methodsrA(l)+ rMA(l) and tA is calculated by both of NIR-AC and SWIR-AC method if the Tind
includes between thlow and th. In this case, desiring parameters, pd, are represented byliner interpolation using weight calculated from the Tind as follows,13𝑝• = 𝑤𝑝Ž + (1 − 𝑤)𝑝ž

𝑤=

(6.6)

𝑡ℎ − 𝑇𝑖𝑛𝑑 (869,1630)𝑡ℎ − 𝑡ℎŒ¡€where pn is the parameter estimated by NIR-AC method and ps is the parameter
estimated by SWIR-AC method.
6.6 Lookup tables for the reflectance due to aerosol scattering

The lookup table of each NIR band and aerosol model contains coefficients a0, a1, a2,
a3 and a4 of the following equation.
X = rA(M,l,q,q0,Df) + rMA(M,l,q,q0,Df)tA(M,l,q,q0,Df) = a0 + a1X + a2X2 + a3X3 + a4X4

(6.7)

M:

aerosol modelq:a zenith angle of the satellite

q0:

a zenith angle of the sunDf:

a difference between the solar and the satellite azimuth angles

On the other hand, the lookup table of each visible band and aerosol model contains
coefficients b0, b1, b2, b3 and a4 of the following equation.
X = tA(M,l,q,q0,Df)rA(M,l,q,q0,Df) + rMA(M,l,q,q0,Df) = b0 + b1X + b2X2 + b3X3 + b4X4

(6.8)

M:

aerosol modelq:a zenith angle of the satellite

q0:

a zenith angle of the sunDf:

a difference between the solar and the satellite azimuth angles

6.6.1 Calculation

The tables were calculated for the following values of the independent variables andconditions:- q and q0 : 0.0° - 80.5° in 3.5° increments- DF : 0.0° - 180.0° in 4° increments- tA : 0.01, 0.02, 0.03, 0.07, 0.1, 0.2, 0.3- Atmospheric pressure : standard atmospheric pressure(1013.25hPa)- The polarization was considered.
- The absorption of ozone layer was ignored.
- The multiple scattering due to the interaction between molecules and aerosol
particles was considered.
14

- The sea surface was assumed to be flat.
- A plane parallel atmosphere divided into 50 homogeneous sublayers was
assumed.
- Reflectance due to sun glint was removed.
- Response function was considered.
- aerosol models :Table 6.1 Aerosol models
Aerosol volume ration

Relative

Tropospheric

Oceanic

Humidity (%)

Model11070Model2

1

0.32

70

Model3

1

0.64

70

Model4

1

1.28

70

Model5

1

2.56

60

Model6

1

2.56

73

Model7

1

5.14

70

Model8

1

10.39

70

Model90

1

83

The lookup table are constructed by radiative transfer code (pstar4 : Ohta et al.,2008).
6.6.2 Interpolation

It uses Lagrange's interpolation for sun and satellite zenith angles and azimuth angle
difference which are not covered in the tables.

When 60°³q and 60°³q0 one degree

Lagrange’s interpolation is used to obtain an. And when q>60° or q0>60° two degree
Lagrange’s interpolation is used.
(1) Calculation formula for one degree Lagrange’s interpolation (when 60°³q and 60°³q0)
u+1 v +1 w +1

an (q ,q 0 ,Df ) = å å å An,ijk × Li (q ) × M j (q 0 ) × Nk (D f )i =u j =v k =w

The condition of the grid point numbers, u, v and w, are as follows.

u <q < u +1

v <q0 < v +1
w < Df < w + 1
where
0 £ u £ 22, 0 £ v £ 22, 0 £ w £ 44

15

(6.9)

An,ijk:values in grid points i, j, k. It’s obtained from the lookup table.

q:

the zenith angle of the satellite. 0 - 80.5°, 3.5° increments, 24 data,i = 0,....., 23

q0:

the zenith angle of the sun. 0 - 80.5°, 3.5° increments, 24 data,
j = 0,....., 23

Df:

the difference between the solar and the satellite azimuth angles.
0 - 180.0° , 4.0° increments, 46 data, k = 0,....., 45(q - qu +1 )(qu - q u+1 )(q - q u )Lu+1 (q ) =(q u+1 - q u )Lu (q ) =(6.10)The shape of equations Mj(q0) and Nk(Df) are the same as those of Li(q).
(2) Calculation formula for two degree Lagrange’s interpolation (when q>60° or q0>60°)
u+ 2 v +2 w+ 2

an (q ,q 0 ,Df ) = å å å An,ijk × Li (q ) × M j (q 0 ) × Nk (D f )i =u j =v k =w

u+1, v+1, w+1(6.11): grid points closest to q , q0 , Df

where
0 £ u £ 21, 0 £ v £ 21, 0 £ w £ 43
An,ijk:q:values at grid point i, j, k. It’s obtained from the lookup table.
the zenith angle of the satellite. 0 - 80.5°, 3.5° increments, 24 data, i =0,....., 23

q0:

the zenith angle of the sun. 0 - 80.5°, 3.5° increments, 24 data, j = 0,.....,
23

Df:

the difference between the solar and the satellite azimuth angles. 0 180.0°, 4.0° increments, 46 data, k = 0,....., 45(q - q u+1)(q - q u+ 2 )(qu - q u+1)(q u - q u+ 2 )(q - q u )(q - qu +2 )Lu+1 (q ) =(q u+1 - q u )(qu +1 - qu+ 2 )(q - q u )(q - q u+1)
Lu+ 2 (q ) =(qu+ 2 - q u )(q u+ 2 - q u+1)
Lu (q ) =(6.12)The shape of equations Mj(q0) and Nk(Df) are the same as those of Li(q).

16

7. Transmittence
7.1 Moleculer transmittance

The moleculer transmittance is obtained by following equation.

æ t (l ) öt M (l ) = expç - M÷è 2 cos x ø(7.1)

x : q (l) or q0
tM(l) : molecular optical thickness is described in section 3.
7.2 Ozone absorption correction

The ozone transmittance is obtained by following equation.

ì - t (l ) üt OZ (l ) = expí OZýî cos x þ

(7.2)

x : q (l) or q0
tOZ(l) : optical thickness of ozone

t OZ (l ) = DU × K OZ (l )(7.3)

KOZ(l) : coefficients which relate optical thickness of ozone and DU.
KOZ is calculated beforehand (Table 7.1)
DU : Total ozone. DU(Dobson Unit) means total ozone concentration at
0°C, 1hPa (above mean sea level) and one DU is equal to a hundredth ofthe ozone layer thickness. DU at each band is shown below.
Table 7.1 Coefficients which relate optical thickness of ozone and DU
in consideration with sensor response function
Band
VN1
VN2
VN3
VN4
VN5
VN6
VN7
VN8

<Koz(l)>[DU-1]
7.97e-08
4.33e-07
3.74e-06
2.25e-05
6.79e-05
1.17e-04
4.42e-05
4.42e-05

Band
VN9
VN10
VN11
SW1
SW2
SW3
SW4

<Koz(l)>[DU-1]
7.59e-06
2.10e-08
2.10e-08
0.00e+00
0.00e+00
0.00e+00
0.00e+00

7.3 Oxygen absorption correction

The O2 A-band absorption usually reduces more than 10–15% of the measured
radiance at the SGLI 763nm band. Ding and Gordon (1995) proposed a numerical17

scheme to remove the O2 A-band absorption effects on the SeaWiFS atmosphericcorrection.

tOZ (763) =1
1 + 10(3-5)

a +b×M +cM 2

where
M : airmass
a = 21.3491, b = 10.1155, and c = 27.0218 3x 10-3.

18

8. Sunglitter correction
Reflectance of sun glint is calculated by following equations.

𝝆𝒈 (𝝀) =where

PW (q ,q 0 , Df ,W )𝝅𝒇(𝝎, 𝝀)𝑷𝑾 (𝜽, 𝜽𝟎 , 𝚫𝝓, 𝑾)
𝟒 ∙ 𝒄𝒐𝒔𝜽 ∙ 𝒄𝒐𝒔𝜽𝟎 ∙ 𝒄𝒐𝒔𝟒 𝜽𝒏(𝟖. 1): probability of seeing sun

æ - tan 2 q n ö÷÷
PW (q ,q 0 , f , f 0 ,W ) =
expçç
2
ps 2
è s
ø
1

(8.2)

s 2 = 0.003 + 0.00512W .

æ cosq + cosq 0 ö
q n = cos -1 ç÷
è 2 cos w ø
cos 2w = cosq cosq 0 + sin q sin q 0 cos(f - f 0 ).
q , f : satellite zenith and azimuth angle at typical band
q 0 , f 0 : solar zenith and azimuth angle at typical bandW : wind speed (m/s)

l : wavelengthf (l ) : Fresnel reflectancef (w, l ) = 1 - (2 × n × y × z ) × coswn(l ) : refractive index
w : incident angley=z=n(l ) + cos2 w - 1 n
2

1
1
.
+
2
{cosw + y × n(l )} {y + n(l )cosw }2

When 𝜌S (𝜆) ≥ 0.02, the pixel is masked as sun glint.

19

(8.3)

9. Whitecap correction

The estimation of whitecap reflectance follows the form
𝑳(𝑾𝑪) (𝝀) = 𝒕(𝝀) ∙ 𝒕𝟎 (𝝀) ∙ 𝒄(𝝀) ∙ 𝑹𝑾𝑪 ∙ 𝑾(𝟗. 1)

where c(l) is wavelength dependent factor (Frouin et al., 1996) in table 9.1.
The Koepke effective reflectance for whitecaps (Rwc) is 0.22. W is whitecap coverage.
W depend on wind speed. It was explained by Stramska and Petelski(2003).

W = 8.75 ´ 10 -5 (U10 - 6.33) 3,
where U10 is 10m wind speed. Minimum wind speed is 6.33 m/s.
Table 9.1 Wavelength dependent factor
Band
VN1
VN2
VN3
VN4
VN5
VN6
VN7
VN8

c(l)
1.0
1.0
1.0
1.0
1.0
0,990367
0.884466
0.884466

Band
VN9
VN10
VN11
SW1
SW2
SW3
SW4

20

c(l)
0.762766
0.640922
0.640922
0.526908
0.319608
0.156282
0.0

10. Bidirectional reflectance distribution function

The water-leaving radiance was defined as following (Morel and Gentili1996),
𝑳𝑾 (𝜽. 𝜽𝟎 , 𝚫𝝓) = 𝑬𝒅 (𝟎® ) “(𝟏 − 𝝆¯ )[𝟏 − 𝝆(𝜽° , 𝜽)]𝑹(𝜽𝟎 )˜
𝟐
𝑸(𝜽° , 𝜽𝟎 , 𝚫𝝓)
Y𝟏 − 𝒓j𝑹(𝜽𝟎 )Z𝒏(10. 1)𝒏 : Refractive index of sea water
𝑬𝒅 (𝟎® ) : Downward irradiance just above ocean surface(𝟏 − 𝝆¯ ) : The rate at which downward irradiance passes through the sea surface andenters the water[𝟏 − 𝝆(𝜽° , 𝜽)] : The rate at which the upward light underwater passes through the sea
surface and passes through the air²²:•̅´ (µ¶ ): Multiple scattering at sea surface

Its Maclaurin's expansion is
1＋𝑟̅ 𝑅(𝜃h ) + [𝑟̅ 𝑅(𝜃h )]s + [𝑟̅ 𝑅(𝜃h )]R + [𝑟̅ 𝑅(𝜃h )]¸ + ⋯ ⋯𝑅(𝜃h ) : Correction term when assuming that the sun is zenith.
𝑄(𝜃 ° , 𝜃h , Δ𝜙) : the ratio between downward irradiance and upward radiance at just below
surface𝑸(𝜽° , 𝜽𝟎 , 𝚫𝝓)＝𝑬𝒖 (𝟎: )𝑳𝒖 (𝜽° , 𝜽𝟎 , 𝚫𝝓)(𝟏𝟎. 2)

Eq.(10.1) is deformation of formula.
𝑳𝑾 (𝜽. 𝜽𝟎 , 𝚫𝝓) = [𝑭𝟎 𝜺𝒕𝟎 (𝜽𝟎 )𝝁𝟎 ]𝕽(𝜽𝟎 )𝑹(𝜽𝟎 )
𝑸(𝜽° , 𝜽𝟎 , 𝚫𝝓)(𝟏𝟎. 3)where𝐸• (0® ) = 𝐹h 𝜀𝑡h (𝜃h )𝜇hℜ(𝜃) = “(1 − 𝜌̅ )[1 − 𝜌(𝜃 ° , 𝜃)]
Y1 − 𝑟̅ 𝑅(𝜃)Z𝑛s

˜𝐹h : mean extraterrestrial solar irradiance
𝜀 : Correction coefficient of sun-earth distance𝑡h (𝜃h ) : Defuse transmittance from space to sea surface
𝜇h ：𝑐𝑜𝑠(𝜃h )𝑛𝐿H is the water-leaving radiance in the zenith direction when the solar zenith angle is
0. 𝑛𝐿H is described using 𝔑h , 𝑄h, 𝑅h .
𝑛𝐿H =

𝐹h 𝔑h
𝑅
𝑄h h

Using 𝔑h , 𝑄h , 𝑅h , the relational expression of 𝐿H and 𝑛𝐿H is described as

21

𝑳𝑾 (𝜽. 𝜽𝟎 , 𝚫𝝓) = [𝜺𝒕𝟎 (𝜽𝟎 )𝝁𝟎 ]𝑹(𝜽𝟎 ) 𝕽(𝜽𝟎 )
𝑸𝟎
𝒏𝑳
°
𝑹𝟎
𝕹𝟎 𝑸(𝜽 , 𝜽𝟎 , 𝚫𝝓) 𝑾(10. 4)ž
There are three normalized water-leaving radiance, (𝐿H )Ã
estimated from satelliteÄobservation data, (𝐿H )Ã
by field observation, and exact normalized water-leaving

radiance (𝐿H )ÅÆ
Ã . Their relationship is as follows (Morel and Gentili, 1996; Appendix A).
(𝑳𝑾 )𝑬𝑿𝑵 =𝕹𝟎 𝑹𝟎 𝑸(𝜽° , 𝜽𝟎 , 𝚫𝝓)(𝑳𝑾 )𝒔𝑵
𝕽(𝜽) 𝑹(𝜽𝟎 )𝑸𝟎
𝑹𝟎 𝑸(𝜽𝟎 )(𝑳𝑾 )𝒇𝑵=
𝑹(𝜽𝟎 ) 𝑸𝟎(𝟏𝟎. 5)𝑅´‹ is defined𝑅´‹ =𝐿H (𝜃 = 0, 𝜃h )𝐸• (0® , 𝜃h )The relationship between 𝑅´‹ and 𝑛𝐿H s (Morel and Gentili, 1996; Appendix B) is asfollows.
𝑅´‹ =𝔑h

𝑄 Y𝜃 0 Z

𝑅´‹ = (𝐿H )ÅÆ
Ã𝑅=𝑓
Y 𝐿𝑊 Z 𝑁

𝐹h

𝑅(𝜃h ) 1
𝑄Y𝜃0Z 𝑅h 𝐹h𝑄hAs a BRDF implementation for satellite ocean color data processing, we use Eq.(10.5).
The correction factor of BRDF is calculated as the product of ratios of three coefficients.
𝕹

𝑹

𝟎
𝟎
The calculation of 𝕽(𝜽)consists of ratio of transmittance from in-water to air (𝑡 ÌÄ )𝑹(𝜽 )𝟎

and transmittance from air to in-water (𝑡•Ä ) through the sea surface.
𝕹𝟎 𝑹𝟎 𝑸(𝜽° , 𝜽𝟎 , 𝚫𝝓) 𝒕𝒖𝒇 (𝒏, 𝟎) 𝒕𝒅𝒇 (𝝀, 𝟎, 𝟎) 𝑸(𝜽° , 𝜽𝟎 , 𝚫𝝓)=𝕽(𝜽) 𝑹(𝜽𝟎 )𝑸𝟎𝒕𝒖𝒇 (𝒏, 𝜽) 𝒕𝒅𝒇 (𝝀, 𝜽𝟎 , 𝑾𝑺) 𝑸(𝟎, 𝟎)
𝑡 ÌÄ is function of reflactive index (𝑛) and satellite zenith angle (𝜃), 𝑡•Ä is function of
wavelength (𝜆), solar zenith angle (𝜃h ) and wind speed (𝑊𝑆).
10.1 Calculation of transmittance from in-water to air for satellite view (𝒕 𝒖𝒇 )𝑡 ÌÄ is the Fresnel transmittance. The Fresnel transmittance has the following
relationship with the Fresnel reflectance (𝑟ÌÄ (𝑛, 𝜃))𝑡ÌÄ (𝑛, 𝜃) = 1 − 𝑟ÌÄ (𝑛, 𝜃)
10.2 Calculation of transmittance from air to in-water for solar path (𝒕𝒅𝒇 )𝑡•Ä (𝜆, 𝜃h , 𝑊𝑆) is calculated using following equation.
𝑡•Ä (𝜆, 𝜃h , 𝑊𝑆) = 1 + 𝑐² 𝑥 + 𝑐s 𝑥 s + 𝑐R 𝑥 R + 𝑐¸ 𝑥 ¸22where𝑥 = log (cos 𝜃h )The coefficients 𝑐² , 𝑐s , 𝑐R , 𝑐¸ depend on the wavelength (𝜆) and the wind speed (𝑊𝑆) in
table 10.1.
Table 10.1 Coefficients 𝑐² , 𝑐s , 𝑐R , 𝑐¸ from Wang (2006)
Wind speed(m/s)

Coefficents
Wavelength

412

443

490

510

555

670

𝑐²

-0.0087-0.0122-0.0156-0.0163-0.0172-0.0172𝑐s

0.0638,0.04150.01880.01330.0048-0.0003𝑐R-0.0379-0.0780-0.1156-0.1244-0.1368-0.1430𝑐¸-0.0311-0.0427-0.0511-0.0523-0.0526-0.0478𝑐²-0.0011-0.0037-0.0068-0.0077-0.0090-0.0106𝑐s

0.09260.0746

0.05340.04730.03680.0237𝑐R-5.3E-4-0.0371-0.0762-0.0869-0.1048-0.1260𝑐¸-0.0205-0.0325-0.0438-0.0465-0.0506-0.0541𝑐²

6.8E-5-0.0018-0.0011-0.0012-0.0015-0.0013𝑐s

0.11500.11150.10750.10640.10440.1029𝑐R

0.06490.03790.03420.03010.02320.0158𝑐¸

0.0065-0.0039-0.0036-0.0047-0.0062-0.0072𝑐²-0.0088-0.0097-0.0104-0.0106-0.0110-0.0111𝑐s

0.06970.06780.06570.0651

0.06400.0637𝑐R

0.04240.03280.02330.02080.01660.0125𝑐¸

0.00470.0013-0.0016-0.0022-0.0031-0.0036𝑐²-0.0081-0.0089-0.0096-0.0098-0.0101-0.0104𝑐s

0.04820.04660.04500.04440.04390.0434𝑐R

0.02900.02200.01500.01310.01030.0070𝑐¸

0.00290.0004-0.0017-0.0022-0.0029-0.0033

(nm)

0

1.9

7.5

16.9

30.0

Table 10.2 The 𝑡•Ä values when 𝜃h = 0 and 𝑊𝑆 = 0.
Wavelength(nm)

380

412

443

490

530

565

673.5

763

868.5

𝑡ÌÄ (0,0)

0.96356

0.96598

0.96832

0.97104

0.972567

0.973800.977630.98080

0.98452𝑡•Ä (𝜆, 𝜃h , 𝑊𝑆) is interpolated by internal ratio of σ at wind speed (𝑊𝑆). σ is defined by
the following equation.
23

σ＝0.0731 ∙ √𝑊𝑆
Each σ=0.0, 0.1, 0.2, 0.3, 0.4 corresponds to wind speeds WS=0,1.9,7.5,16.9,30 (m/s). 𝑡•Äis calculated at the wavelength closest to the sensor wavelength among thesewavelengths.
𝑡•Ä (𝜆, 0,0) is constant. It shows in table 10.2.
10.3 Calculation of Q factor

𝑄(𝜃 ° , 𝜃h , Δ𝜙) is expressed as a function of wavelength, chlorophyll a concentration(CHL) , solar zenith angle (𝜃h ), satellite zenith angle (𝜃 ° ), relative azimuth angle (Δφ).
For calculation of 𝑄(𝜃 ° , 𝜃h , Δ𝜙)), a lookup table (Morel et al., 2002) is used. Look-up tables(DISTRIB_FQ_with_Raman.tar.gz) were obtained over the internet, using anonymous
ftp, from oceane.obs-vlfr.fr.
-Wavelength: 412.5, 442.5, 490, 510, 560, 620, 660 nm (7 wavelengths) (MERIS
wavelength, SeaDAS uses recent wavelength data)-CHL: 0.03, 0.1, 0.3, 1.0, 3.0, 10.0 mg / m3 (6 stages)
The table is expanded on the log 10 scale of CHL (almost equally spaced on log 10)-Sun zenith angle: 0, 15, 30, 45, 60, 75 ° (6 stages)-Satellite zenith angle: 1.078, 3.411, 6.289, 9.278, 12.3, 15.33, 18.37, 21.41, 24.45,
27.5, 30.54, 33.59, 36.64, 39.69, 42.73, 45.78, 48.83 ° (17 steps)-Relative azimuth angle: 0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180 ° (13steps)°The 𝑄(𝜃 , 𝜃h , Δ𝜙) coefficient is calculated by four-dimensional linear interpolation oflog (CHL), θ 0, θ, Δφ.
𝑄(𝜃 ° , 𝜃h , Δ𝜙) is calculated at the wavelength closest to SGLI wavelength among
MERIS wavelengths.

2411. Ancillary data

Several sets of ancillary data are required for atmospheric correction of SGLI data.
We summarize each ancillary data set required below.

11.1 Total ozone
The total ozone concentration (Dobson Units, DU) is required to calculate the ozone
optical thickness, and the ozone optical thickness is needed to compute the two-way
transmittance of satellite-observed reflectance through the ozone layer. Dobson Unitsmeans total ozone concentration at 0 ﾟ C, 1hPa(above mean sea level) and 1 DU is equal
to a hundredth of the ozone layer thickness. DU is expressed in mm.
We use OMI (Ozone Monitoring Instrument) or TOVS (Advanced Tiros-N
Operational Vertical Sounder) data.
11.2 Sea surface pressure
The atmospheric pressure (hPa) is needed to compute the Rayleigh optical thickness
that is required for the computation of 𝜌T and the diffuse transmittance of theatmosphere.
We use GGLA objective analysis data. GGLA data are provided by the Japan
Meteorological Agency (JMA).

11.3 Sea surface wind
The sea surface wind speed (m/s) and vector(degree) are required for the constructionof a sun glint mask. The sea surface wind speed also will be required for estimation of
the whitecap reflectance.
We use GGLA objective analysis data. GGLA data are provided by the Japan
Meteorological Agency (JMA).

25

Appendix I Mean extratrestrial solar irradiance (Thuillier et al.,2003) inconsideration with sensor response function.
Table I.1 Mean solar irradiance of GCOM-C/SGLI on Visible and Near-Infrared (VNR)
Center wavelength: 𝜆‚ [nm]Solar irradiance: 𝐹h [W/m2/µm]

VNR01

379.853

1093.5379

VNR02

412.306

1711.2835

VNR03

443.443

1903.2471

VNR04

489.686

1937.9540

VNR05

529.638

1850.9682

565.926

1797.4827

VNR07

672.0021502.5522

VNR08

672.1481502.1799

VNR09

762.9171245.8937

VNR10

866.023956.2896

VNR11

867.023956.5311

VNR01

380.030

1092.1436

VNR02

412.5141712.1531

VNR03

443.240

1898.3185

VNR04

489.849

1938.4602

VNR05

529.640

1850.9604

566.155

1797.1344

VNR07

671.9961502.5667

VNR08

672.0981502.3177

VNR09

763.0741245.3663

VNR10

866.765956.2323

VNR11

867.120956.5352

VNR01

380.2121090.5931

VNR02

412.589

1712.4760

VNR03

443.051

1893.5879

VNR04

490.311

1941.0715

529.664

1851.0657

VNR06

566.377

1796.8275

VNR07

671.9501502.6962

VNR08

672.1201502.2582

VNR09

763.234

1244.8290

Band

VNR06

VNR06

VNR05

Telescope

Left

Nadir

Right

26

VNR10866.713956.2577

VNR11

867.086956.5735

Table I.2 Solar Irradiance of GCOM-C/SGLI on Short Wave Infrared (SWI)
Band

Center wavelength: 𝜆‚ [nm]Solar irradiance: 𝐹h [W/m2/µm]

SWI011054.994

646.5213

SWI02

1385.351

361.2250

SWI03

1634.506

237.5784

SWI04

2209.481

84.2413SGLI has three telescopes (Left, Nadir and Right).

27

Appendix II. QA Flags and Masks
Table II.1 QA flag and masks
Bit

Name

Description

Criterion

0

DATAMISSNo observation data in one or more band[s]

L3

1

LAND

Land pixel

L2

2

ATMFAIL

Atmospheric correction failure

L2

3

CLDICE

Apparent cloud/ice (high reflectance)

4

CLDAFFCTD

5STRAYLIGHT

6

HIGLITN

7

MODGLINT

8

HIOSOLZ

9

HITAUA10

EPSOUT

11

OVERITER12NEGNLW

Negative nLw in one or more bands

13

HIGHWS

Surface wind speed higher than threshold

14

TURBIDW

Turbid Case 2 water

15

SPARE

Cloud-affected (near-cloud or thin/sub-pixel
cloud)Mask

ρA>0.04

L2

ρA>0.03

L3[ρG]N > 0.02

L2

[ρG]N > 0.005

L3

θ0 > 70°

L3

τA > 0.5

L3

Stray light anticipated (ref. L1B stray lightflags & image)High sun glint predicted (atmospheric corr.
abandoned)
High sun glint predicted (atmospheric corr.
abandoned)
Solar zenith larger than threshold
Aerosol

opticalthicknesslargerthan

threshold
Atmospheric correction warning: Epsilon
out-of-bounds
Maximum

iterations

reachedfor

NIR

correction

Spare

ÔÕÖ
*1) 𝑇•Ž• (869,1630) > 𝑡ℎŒ¡€ + EF:EF, where 𝑡ℎŒ¡€ is 1.4 and 𝑡ℎ is 1.5.
s

28

L3
W/S > 12m/s*1Appendix III. LUT of Single Scattering Albedo(ωA) for Aerosol Models

Figure III.1. SSA for each assumed aerosol model. Solid lines represent LUT values
which is band weighted averaged. Dash lines represent raw values calculated by
Pstar4.
Table III.1.ωA LUT
Model

VN1

VN2

VN3

VN4

VN5

VN6

VN7

VN9

VN10

SW1

SW2

SW3

SW4

1

0.96720.96700.96700.96790.96650.96340.9616

0.95110.93570.91030.86440.82210.804920.96940.96940.96960.97070.96980.96720.9666

0.9586

0.94750.93130.91070.89800.92773

0.97130.97150.97190.9731

0.97240.97030.97050.96420.95570.94420.93290.92750.9521

4

0.97450.97490.9754

0.97680.9766

0.97510.97600.97180.96620.9592

0.9546

0.95300.9684

5

0.9763

0.97690.9776

0.97920.97920.97810.9796

0.9766

0.97280.96750.96490.96400.9727

6

0.98170.98230.98300.98440.98450.98390.98530.98350.98120.9784

0.97730.97750.98237

0.98470.98540.98610.98740.98770.98730.98870.9876

0.9861

0.98370.9826

0.98220.98318

0.99010.9907

0.99130.9922

0.99250.9924

0.99350.99300.99230.99040.98900.98840.985980.98591.00001.00001.00001.00001.00000.98591.00001.00000.99930.9971

0.99680.985929

Appendix IV. LUT of Aerosol Extinction Coefficient (Kext) for Aerosol Models

Figure IV.1. Kext values normalized by Kext at VN10 for each assumed aerosol model.
Solid lines represent LUT values which is band weighted averaged.
Table IV.1. Kext LUT
Model

VN1

VN2

VN3

VN4

VN5

VN6

VN7

VN9

VN10

SW1

SW2

SW3

SW4

1

2.976

2.750

2.554

2.285

2.081

1.914

1.514

1.240

1.000

0.714

0.393

0.260

0.085

2

2.599

2.417

2.259

2.042

1.877

1.742

1.418

1.196

1.000

0.764

0.494

0.376

0.209

3

2.340

2.188

2.056

1.874

1.737

1.624

1.352

1.166

1.000

0.799

0.563

0.455

0.294

4

2.007

1.893

1.795

1.659

1.556

1.472

1.268

1.126

1.000

0.843

0.652

0.558

0.403

5

1.758

1.674

1.600

1.499

1.422

1.359

1.205

1.098

1.000

0.870

0.710

0.624

0.475

6

1.548

1.487

1.434

1.361

1.306

1.260

1.149

1.071

1.000

0.908

0.785

0.713

0.575

7

1.379

1.338

1.303

1.253

1.216

1.185

1.108

1.053

1.000

0.927

0.821

0.751

0.610

8

1.184

1.166

1.150

1.128

1.111

1.096

1.059

1.030

1.000

0.953

0.873

0.811

0.674

8

0.914

0.923

0.932

0.944

0.953

0.961

0.979

0.991

1.000

1.007

0.997

0.974

0.889

30

Appendix V LUT of Aerosol Scattering Phase Function (PA) for Assumed Aerosol Models

Figure V.1. PA values for each assumed aerosol model.

31

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33