SGLI
Algorithm Theoretical Basis Document

ATMOSPHERIC CORRECTION ALGORITHM
FOR OCEAN COLOR

Version 2, Rev.4, July 15 2021

Mitsuhiro Toratani,
Kazunori Ogata* and Hajime Fukushima
Tokai University*JAXA/EORC

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

1

2. Radiative transfer model for radiance …………………………………………… 3
3. Radiative transfer model for reflectance ………………………………………… 5
3.1 Relationship between radiance and reflectance …………………………… 5
3.2 Relationship between normalized-water leaving radiance and reflectance…………

6

4. Overview of atmospheric correction for SGLI ………………………………… 10
5. Rayleigh reflectance (𝝆𝑴 ) ………………………………………………………… 12
5.1 Calculation of Rayleigh reflectance………………………………………… 12
5.2 Lookup tables for the reflectance due to Rayleigh scattering …………

13

6. Aerosol reflectance (𝝆𝑨 + 𝝆𝑴𝑨 ) …………………………………………………… 14
6.1 Overview of aerosol reflectance calculation ………………………………
6.2 Iterative procedure for aerosol reflectance determination

14…………… 14

6.3 Estimation of water-leaving reflectance at near infrared bands ……… 18
6.4 Switching between NIR-AC and SWIR-AC

7.

……………………………

23

6.5 Lookup tables for the reflectance due to aerosol scattering ……………

23

Transmittance ……………………………………………………………………… 28
7.1 Moleculer transmittance ……………………………………………………… 28
7.2 Ozone absorption correction ………………………………………………… 28
7.3 Aerosol transmittance ………………………………………………………… 29

8.

Sunglitter correction ……………………………………………………………… 31

9. Whitecap correction ………………………………………………………………

33

10. Bidirectional reflectance distribution function ………………………………… 34（𝑽𝒊𝒆𝒘)

10.1 BRDF effect of air-water interface for upward light: ℜ𝟎/ℜ（𝑽𝒊𝒆𝒘)………………………………… 34（𝑺𝒖𝒏)

10.2 BRDF effect of air-water interface for downward light: ℜ𝟎/ℜ（𝑺𝒖𝒏)………………………………… 35
10.3 BRDF effect of in-water ocean: {(𝒇/𝑸)𝑬𝒇𝒇 } ……………………………… 36
11. Ancillary data ………………………………………………………………………

37

11.1 Total ozone …………………………………………………………………… 37

11.2 Sea surface pressure ………………………………………………………… 37
11.3 Sea surface wind ……………………………………………………………… 37
Reference ………………………………………………………………………………… 38
Appendix I

Mean extraterrestrial solar irradiance ……………………………… 41

Appendix II. Ratio of aerosol Extinction Coefficient (Kext) for Aerosol Models………………………………………………………… 43
Appendix III. Single Scattering Albedo(ωA) for Aerosol Models ………………… 45
Appendix IV. QA Flags and Masks …………………………………………………… 46
Appendix V. Look-up Table for BRDF Correction function 𝑪𝒐𝒓𝒇(𝑺𝒖𝒏) …………… 47
Appendix VI. Look-Up Table for f over Q …………………………………………… 48

1. Introduction

This ATBD describes the atmospheric correction of ocean color remote sensing
for GCOM-C/SGLI.
The purpose of the atmospheric corrections is to retrieve the water-leaving
radiance spectrum from the radiance spectrum observed by the satellite. It isnecessary to correct for the effects of the atmosphere and sea surface in theradiance observed by the satellite. Atmospheric effects include scattering of gas
molecules, scattering of aerosols, absorption of gases and aerosols, as well as sea
surface effects, such as sunglint, whitecaps, and bidirectional reflectance
distribution.
Atmospheric correction methods for SGLI are based on the SeaWiFS and
MODIS atmospheric corrections (Gordon and Wang, 1994) and also the Japanese
ocean color satellite ADEOS/OCTS (Fukushima et al.,1998) and ADEOS2/GLI(Toratani et al. al.,2007).
The following items have been updated from Version 1 of the SGLI atmosphericcorrection.
(1) Updated lookup table for aerosols
The relationship between the aerosol reflectance and the optical thickness of
the aerosol was recalculated using radiative transfer simulations. In Ver.1, theupper limit of optical thickness was set at 0.3, but this was not always appropriate.
The upper limit of the aerosol optical thickness was reviewed for each aerosol
model, and the lookup tables of aerosols was updated.
(2) Change in the aerosol model selection method
In Ver.1, the inter-wavelength ratio (ε) of the single-scattering aerosol
reflectance between two wavelengths was used to select the aerosol models. In Ver.
2, the inter-wavelength ratio of aerosol-optical-thickness is used in order tosimplify and speed up the processing. The combination of wavelengths used formodel selection is twofold, that is either of "673nm & 869nm" and "869nm & 1630
nm" bands. The conditions for switching the combination were changed.
(3) Update of the in-water modelMore realistic in-water model (Ahn et al., 2015; Lee et al., 2002) is used for
calculating aerosol reflectance in the iterative aerosol correction procedure. The
convergence conditions for the iterative calculation were changed accordingly. For
the atmospheric correction with 869 nm and 1630 nm, an iterative operation is
also introduced.

1

(4) Calculation method of sunglitter
The method for calculating direct transmittance was changed.

2

2. Radiative transfer equation for radiance

The top of atmospheric radiance 𝐿∗! observed by satellite sensors is expressed
as (Gordon, 1997; Mobley et al., 2016),
𝐿∗! = 𝐿∗#$%& + 𝑇 ∗ 𝐿' + 𝑡 ∗ 𝐿() + 𝑡 ∗ 𝐿(

[𝑊 𝑚*+ 𝜇𝑚*, 𝑠𝑟 *, ],(2.1)

where 𝐿∗#$%& is the atmospheric radiation composed of the atmospheric scattered
light and the sky light specularly reflected at the ocean surface, 𝐿' is the sunglint
radiance of the direct beam reflected by sea surface, 𝐿() is the radiance reflectedby the whitecap, 𝐿( is water-leaving radiance, respectively. For simplicity, we
omit the wavelength λ. Since 𝐿' , 𝐿(* and 𝐿( are the radiance at the sea
surface, the transmittance of the atmosphere from the sea surface to the satellite
should be applied. Expressions 𝑇 ∗ and 𝑡 ∗ are used for the direct and diffuse
transmittance by the atmosphere from the sea surface to the sensor. We consider
𝑇 ∗ and 𝑡 ∗ to be composed of the following elements.
𝑇 ∗ = 𝑡 (./) 𝑇 (1) 𝑇 (2) 𝑇 (3) ,∗𝑡 =𝑡(./) (1) (2) (3)

𝑡

𝑡

𝑡

(2.2)

.

(2.3)

In the right-hand side, the superscript O3 indicates absorption of ozone, g
indicates absorption by gases other than ozone (such as O2, NO2 and H2O), M
indicates scattering of atmospheric molecules, and A indicates extinction ofaerosols. Since ozone is predominantly present in the upper atmosphere, its
interactions with other elements are negligible. The effect of ozone absorption
occurs twice, once when sunlight enters the atmosphere and once when it isemitted. The ozone transmittance is assumed to affect all components of 𝐿∗! , andhence the equation (2.1) can be transformed as follows.
#∗

!∗

$∗

$∗

()*)

!"#$
()*)
𝐿∗! = # ('()
𝑡,('() + ('() ('() 𝐿% + ('() ('() 𝐿&' + ('() ('() 𝐿& % 𝑡

$

$*

$

$*

$

$*

$

$*

(./)

𝐿∗! = .𝐿#$%& + 𝑇𝐿' + 𝑡𝐿() + 𝑡𝐿( /𝑡 (./) 𝑡4

,

,

(2.4)

𝐿 ! = 𝐿#$%& + 𝑇𝐿' + 𝑡𝐿() + 𝑡𝐿( .

In the above equation, 𝑡!(#$) is the ozone transmittance from the sun to the sea
surface, while 𝑡 (#$) is the ozone transmittance from the sea surface to the sensor.
Terms without superscript * indicate that the ozone attenuation effect has beencorrected. In the rest of this paper, we will assume that the ozone attenuation3

effect has been corrected for, unless otherwise noted.
The atmospheric contribution of 𝐿#$%& to 𝐿 ! can be decomposed as follows.
𝐿#$%& = 𝐿2 + 𝐿3 + 𝐿23 ,(2.5)

where 𝐿+ is the component due to the scattering of gas molecules only (Rayleighscattering), 𝐿, is the multiple-scattering component of the aerosol except for theinteraction with gas molecules, and 𝐿+, represents the interaction between the
scattering of gas molecules and aerosol scattering.
Substituting equation (2.5) into equation (2.4) yields the following equation.
𝐿 ! = 𝐿2 + 𝐿3 + 𝐿23 + 𝑇𝐿' + 𝑡𝐿() + 𝑡𝐿( .

(2.6)

The purpose of the atmospheric correction is to obtain the water-leaving
radiance 𝐿( from the satellite sensor observation radiance 𝐿 ! based on themodel in equation (2.6).

4

3. Radiative transfer equation for reflectance
3.1 Conversion from radiance-based to reflectance-based

In the atmospheric correction process, the calculation is done on the reflectancebasis, not on the radiance basis. The spectral radiance L [Wm-2sr-1 μm-1] of thereflected light can be converted to the spectral reflectance ρas follows.

./(1)

𝜌(𝜆, 𝜃- ) = 3 (1) 456 7 ,
-

(3.1)

-

where λ is the wavelength, 𝜃- is the solar zenith angle, and cos 𝜃- is theincident angle-dependent factor of irradiance and 𝐹- (𝜆) [Wm-2 μ m-1] is theextraterrestrial solar irradiance at wavelength λ at the time of observation. It
represents the extraterrestrial solar irradiance affected by the daily variation of the
Sun-Earth distance. Instantaneous solar irradiance for each SGLI band is
calculated from the mean solar irradiance, which is listed in Tables I.1 and I.2 inAppendix I.
The radiance of Eq. (2.6) is converted to reflectance using Eq. (3.1). The termsof radiance 𝐿 ! , 𝐿+ , 𝐿, , 𝐿+, , 𝐿' , 𝐿(* , and 𝐿( in Eq.(2.6) are converted to thesatellite observations Reflectance 𝜌! , gas molecule reflectance 𝜌+ , aerosol
reflectance 𝜌, , gas molecule and aerosol Reflectivity due to interaction 𝜌+, ,sunglitta reflectivity 𝜌' , whitecap reflectivity 𝜌(* and the water-leaving
reflectance 𝜌9 . It should be noted that the ozone-induced attenuation has alreadybeen corrected for, as explained in Chapter 2, and 𝜌& , 𝜌'( and 𝜌9 are thereflectances observed at the sea surface. The sunlight incident on the sea surface
is attenuated by the atmosphere. It is necessary to take into account thetransmittance from solar to sea surface 𝑡- on 𝜌& , 𝜌'( and 𝜌9 .
Therefore, Eq. (2.6) is transformed as follows,
𝐿 ! = 𝐿2 + 𝐿3 + 𝐿32 + 𝑇𝐿' + 𝑡𝐿() + 𝑡𝐿( ,./.

=3 456 7--.(// :/0 :/0/ )3- 456 7-+.(!/1 :%/23 :%/2 )3- 456 7- %-,𝜌! = 𝜌+ + 𝜌, + 𝜌,+ + 𝑇𝑇- 𝜌' + 𝑡𝑡- 𝜌(* + 𝑡𝑡- 𝜌( ,,(3.2)

𝜌! = 𝜌2 + 𝜌3 + 𝜌32 + 𝑇[𝜌' ]5 + 𝑡[𝜌() ]5 + 𝑡[𝜌6 ]5 .

where [𝜌' ]; is the normalized water-leaving reflectance (= 𝑡- 𝜌( ), [𝜌(* ]; is thenormalized whitecap reflectance (= 𝑡- 𝜌9* ), and [𝜌' ]; is the normalized sunglint
5reflectance (= 𝑇- 𝜌' ). 𝜌+ , 𝜌, , and 𝜌+, are the atmospheric reflectances at the
top of the atmosphere. On the other hand, [𝜌& ]) , [𝜌'( ]) , and [𝜌* ]) refer to thereflectance at sea surface. There are converted to the reflectance of the top of
the atmosphere by applying the transmittance 𝑇 and 𝑡 from the sea surface tothe top of the atmosphere. The satellite-observed reflectance 𝜌! is expressed as
the sum of these values.
The purpose of the atmospheric correction is to retrieve the water-leaving
reflectance [𝜌9 ]; . [𝜌' ]; is expressed as follows by modifying the Eq. (3.2).
𝜌! = 𝜌+ + 𝜌, + 𝜌+, + 𝑇[𝜌' ]; + 𝑡[𝜌(* ]; + 𝑡 [𝜌9 ]; ,[𝜌9 ]; =<. =(</ :<0 :</0 :![<1 ]4 :%[<23 ]4 )[𝜌9 ]; =%<3 =<0 =</0 =![<1 ]4
%

,

(3.3)

− [𝜌(* ]; ,where 𝜌* is Rayleigh-corrected reflectance which the satellite-observedreflectance 𝜌! minus the Rayleigh scattering reflectance 𝜌+ .
3.2

Relationship between normalized-water leaving radiance and reflectance

Remote sensing reflectance 𝑅@A , and normalized water-leaving radiance 𝑛𝐿9
are both mostly used physical quantities in ocean color remote sensing. In thissection, we describe the relationship between [𝜌9 ]; and each of theseparameters
The upward spectral radiance at depth 𝑧 in water is denoted by
𝐿B (𝑧, 𝜆, 𝜃- , 𝜃, ∆𝜙), where 𝜆 is the wavelength, 𝜃- is the solar zenith angle, 𝜃 isthe satellite zenith angle, and ∆𝜙 is the relative azimuth angle between thesatellite and the sun. If 𝜃 = 0, the sensor faces the nadir, i.e., it observes theradiance of the light toward the zenith. The water-leaving radiance observed justabove the sea surface is denoted as 𝐿9 (𝜆, 𝜃- , 𝜃, ∆𝜙). 𝐿B is generally obtained from
instrumental observations in the water, and 𝐿9 is obtained by atmosphericcorrection of the top of the 𝐿 ! ..
𝐿B and 𝐿9 depend on the irradiance of solar irradiance at the sea surface, 𝐸C .
Values independent of 𝐸C is desirable to evaluate the underwater conditions.
Therefore, we define the normalized water-leaving radiance 𝑛𝐿9 , which excludes
the influence of the atmosphere, assuming that the sun is at its zenith.

6𝑛𝐿6 (𝜆, 𝜃4 , 𝜃, ∆∅) ≡𝐿6 (𝜆, 𝜃4 , 𝜃, ∆∅)cos 𝜃4 𝑡(𝜃4 )[𝑊 𝑚*+ 𝜇𝑚*, 𝑠𝑟 *, ]where 𝑡(𝜃- ) is the diffuse transmittance depending on the condition of theatmosphere and the direction of the Sun. In addition, the distance between the
Sun and the Earth changes daily and has an inversely proportional effect on theirradiance to the square of the distance. Therefore, 𝑅(𝑇) is the distance between
the sun and the earth at observation time T, 𝑅- is the average distance between
the sun and the earth. Then 𝑛𝐿9 (𝜆, 𝜃- , 𝜃, ∆∅) is the following in consideration of
the correction term (𝑅/𝑅- )D (Hereinafter, time of observation T is omitted).
𝑅 + 𝐿6 (𝜆, 𝜃4 , 𝜃, ∆∅)(𝜆,𝑛𝐿6 𝜃4 , 𝜃, ∆∅) ≡ = ?
,𝑅4cos 𝜃4 𝑡(𝜃4 )(3.4)

That is, 𝑛𝐿9 is the water-leaving radiance when the distance between the sun
and the earth is equal to its mean value, the sun is at zenith, and there is no
atmospheric attenuation of the sunlight.
Next, we consider the conversion from the radiance to the reflectance.
According to the definition in Eq. (3.1), the relationship between 𝐿9 and thewater-leaving reflectance 𝜌9 is expressed by the following equation,
𝜌9 (𝜆, 𝜃- , 𝜃, ∆∅) =𝜋𝐿9 (𝜆, 𝜃- , 𝜃, ∆∅),𝐹- (𝜆) cos 𝜃-(3.5)

where cos 𝜃- is an incident angle-dependent factor of irradiance, and 𝐹- is theextraterrestrial solar irradiance, i.e., the extraterrestrial solar irradiance affectedby the daily variation in the Sun-Earth distance. Therefore, 𝐹- is related with theextraterrestrial solar irradiance >>>𝐹- at the sun-earth mean distance as following,
𝑅4 +𝐹4 = = ? AAA
𝐹4 [𝑊 𝑚*+ 𝜇𝑚*, ] .
𝑅

(3.6)

The relationship between [𝜌9 ]; and in-water parameters (𝜌9 , 𝐿9 , 𝑛𝐿9 ) is
given by Eqs. (3.4), (3.5) and (3. 6), as follow.

7

[𝜌6 (𝜆, 𝜃4 , 𝜃, ∆∅)]5 =𝜌6 (𝜆, 𝜃4 , 𝜃, ∆∅)𝜋𝐿6 (𝜆, 𝜃4 , 𝜃, ∆∅)=𝑡(𝜃4 )𝐹4 (𝜆) cos 𝜃4 𝑡(𝜃4 )𝑅 + 𝜋𝐿6 (𝜆, 𝜃4 , 𝜃, ∆∅)𝜋= = ? AAAAAAA= AAAAAAA 𝑛𝐿6 (𝜆, 𝜃4 , 𝜃, ∆∅) .
𝑅4 𝐹4 (𝜆) cos 𝜃4 𝑡(𝜃4 ) 𝐹4 (𝜆)(3.7)

The remote sensing reflectance 𝑅@A is defined by the following equation,

𝑅78 (𝜆, 𝜃4 , 𝜃, ∆∅) ≡𝐿6 (𝜆, 𝜃4 , 𝜃, ∆∅)[𝑠𝑟 *, ] .
𝐸9 (0: , 𝜆, 𝜃4 )(3.8)

In the above equation, 0: is the position just above sea surface and 𝐸C (𝑧, 𝜆, 𝜃- )is the position at altitude z. The reason for the absence of the correction term
(𝑅/𝑅- )D in Eq. (3.8) is that the mutuality of L_w and E_d to cancel each otherout.
The solar irradiance 𝐸C at 0: just above the sea surface is the solar irradianceaffected by atmospheric attenuation from the top of the atmosphere to the sea
surface, and is therefore given by the following equation.
𝐸9 (0: , 𝜆, 𝜃4 ) = 𝐹4 (𝜆) cos 𝜃4 𝑡(𝜃4 ) [𝑊 𝑚*+ 𝜇𝑚*, ](3.9)

In summary, the following relationship holds between [𝜌9 ]; , 𝜌9 , 𝑛𝐿9 , 𝐿9
and 𝑅@A .

[𝜌6 (𝜃4 , 𝜃, ∆∅)]5 =𝜌6 (𝜆, 𝜃4 , 𝜃, ∆∅) 𝜋
𝜋𝐿6 (𝜃4 , 𝜃, ∆∅)= AAA 𝑛𝐿6 (𝜃4 , 𝜃, ∆∅) =𝑡(𝜃4 )𝐹4 (𝜆) cos 𝜃4 𝑡(𝜃4 )𝐹4𝜋𝐿6 (𝜃4 , 𝜃, ∆∅)== 𝜋𝑅78 (𝜆, 𝜃4 , 𝜃, ∆∅)𝐸9 (0: , 𝜆, 𝜃4 )(3.10)

Thus, 𝑅@A and 𝑛𝐿9 are expressed as follows.

𝑅78 =
𝑛𝐿6 =

1
[𝜌 ]
𝜋 6 5

𝐹4
[𝜌 ]
𝜋 6 5

[𝑠𝑟 *, ](3.11)[𝑊 𝑚*+ 𝜇𝑚*, 𝑠𝑟 *, ](3.12)The [𝜌9 (𝜃- , 𝜃, ∆∅)]; and 𝑅@A (𝜃- , 𝜃, ∆∅) given in the above equation are thus

8

normalized, or corrected for the effects of the Sun-Earth distance, atmosphericattenuation and solar zenith angle from the observed 𝐿9 . However, they stillcontain a number of direction-dependent parameters such as upward radiance 𝐿B
and surface transmittance of water light.
The directional dependency does not simply relies on the direction of thesatellite observation but also on the direction of the incident light. Hence it iscalled Bidirectional Reflectance Distribution Function (BRDF)(Morel andGentili, 1996). Our atmospheric correction process BRDF correction based onMorel and Gentilli (1996), Morel and Gentilli (2002) and Wang (2006), as
described in Chapter 10.
If 𝑅@A or 𝑛𝐿9 is BRDF-corrected, we use expression such as 𝑅𝑟𝑠 𝐸𝑋 or 𝑛𝐿𝑤 𝐸𝑋 ,respectively, and at the same time, we introduce the BRDF correction factor(𝐶𝐵𝑅𝐷𝐹 ) as follows.
,

𝑅78 ;< = 𝐶=>?@ A [𝜌6 ]5

𝑛𝐿6

;<

@*

= 𝐶=>?@ A [𝜌6 ]5[𝑠𝑟 *, ] , and

[𝑊 𝑚

*+

𝜇𝑚

*,

𝑠𝑟

(3.13)*, ].

(3.14)

The calculation of the correction factor (𝐶MNO3 ) in the above equation will be
described in Chapter 10. 𝑅@A PQ and 𝑛𝐿9 PQ are the final outputs of theatmospheric correction.

94. Overview of atmospheric correction for SGLIThe SGLI atmospheric correction method is based on the GLI atmosphericcorrection method (Toratani et al.,2007) and SeaWiFS atmospheric correction(Gordon and Wang: 1994, Siegel et al.: 2000). A schematic flow of the SGLI
atmospheric correction process is shown in Fig. 4.1. The input to the atmosphericcorrection process is the satellite-observed reflectance (ρ ! ∗ ), which is converted
from the radiance by the Eq. (3.1), The flow of the atmospheric correction process
for each pixel is as follows.
(1) Transmittance correction by ozone absorption (Section 7.2)
(2) Correction of the reflectance (𝜌+ ) of gas molecules (Chapter 5)(3) High reflectance test
If the Rayleigh-corrected reflectance (𝜌* ) of the pixel is greater than 0.07, theatmospheric correction process is skipped.
(4) Sunglitter (𝜌' ) correction (Chapter 8)(5) Whitecap (𝜌(* ) correction (Chapter 9)(6) Aerosol reflectance (𝜌, + 𝜌+, ) evaluation (Chapter 6)(7) cloud detection
Aerosol reflectance (𝜌, + 𝜌+, ) of 0.04 or more is masked as cloud.
(8) BRDF Correction (Chapter 10)
The normalized water-leaving radiance (𝑛𝐿9 ) and remote sensing reflectance(𝑅@A ) are calculated through the above process.

10

Fig. 4.1 Schematic flow of atmospheric correction for SGLI

11

5. Rayleigh reflectance (𝝆𝑴 )5.1 Calculation of Rayleigh reflectance

The Rayleigh reflectance 𝜌+ at wavelength λ is given by the following
equation (5.1) based on Gordon et al. (1998), with correction for atmosphericpressure.
)*+,-.*/ (1)/4567(1)8𝜌( (𝜆) = )*+,-.*/ . (1)/4567(1)8 𝜌(9 (𝜆, 𝜃(𝜆), 𝜃9 , Δ𝜙 ),
./

(5.1)

Where

𝜏( : Optical thickness of gas molecule,𝜏(9 : Optical thickness of gas molecule at standard atmospheric pressure,(Table 5.1)

𝜌(9 : reflectance of gas molecule at standard atmospheric pressure,𝜃 (𝜆) : Satellite zenith angle for each wavelength (λ),
𝜃9 : Solar zenith angle, andΔ𝜙 : Relative azimuth angle between sun and satellite.
The reflectance of the gas molecules at standard atmospheric pressure for all the
bands are calculated in advance by radiative transfer simulation, and prepared asa lookup table.
The optical thickness of a gas molecule (𝜏( ) is expressed as follows,𝜏+ (𝜆) =

𝑃
𝜏 (𝜆)
𝑃- +-

(5.2)

where 𝑃 is the field pressure and 𝑃- is the standard atmospheric pressure (=1013.25ℎ𝑃𝑎).
The optical thickness of the gas molecules at standard atmospheric pressure(𝜏+- ) for all the SGLI bands are shown in Table 5.1. These values were
determined by averaging the optical thickness given in the following equation(Bodhaine,1999), weighted by the sensor response function.

𝜏+- (𝜆) = 0.0021520 K

1.0455996 − 341.29061𝜆=D − 0.90230850𝜆D
Q
1 + 0.0027059889𝜆=D − 85.968563𝜆D

12

(5.3)

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

Rayleigh optical
thickness

Band

Rayleigh optical
thickness

VN1

0.4467VN90.02571

VN2

0.3189VN100.01525VN3

0.2361VN11

0.01525VN4

0.1559SW10.007107

VN5

0.1132SW20.002380

VN6

0.08714SW30.001246

VN7

0.04265SW40.0003765

VN8

0.04265

5.2 Look-up table of gas molecular scattering

The reflectance of gas molecules at standard atmospheric pressure is
calculated in advance by radiative transfer simulation and stored in a lookup
table.
The conditions for creating a lookup table are as follows
q: 0.0° - 80.5° in increments of 3.5° (24 points)
𝜃: 0.0° - 80.5° in increments of 3.5° (24 points)
Δ𝜙: 0.0° - 180° in 4.0° increments (46 points)
Atmospheric pressure: Standard atmospheric pressure (1013.25 hPa)
Consider polarization
Ignore gas absorption.
Considering multiple scattering
Assuming a plane parallel atmosphere
No sunglint (assuming sea level is flat)
Considering the sensor response function
To calculate the lookup table, we used the radiative transfer simulation code
Pstar4 (Ohta et al.,2010).

13

6. Aerosol reflectance (𝝆𝑨 + 𝝆𝑴𝑨 )6.1 Overview of aerosol reflectance calculation

As described in equation (3.2), aerosol-related top-of-atmosphere reflectanceare two-fold: 𝜌, , the reflectance that would be observed when the atmosphereconsists of aerosol particles, and 𝜌+, , the reflectance due to the interaction
between aerosol particles and gas molecules. Hereafter, we refer to the sum of𝜌, and 𝜌+, as “aerosol reflectance” and use the symbol 𝜌,:+, to represent it.
The spatio-temporal distribution of aerosol amount and types cannot be
predicted in advance. Hence, in the SGLI atmospheric correction, the pixel-wiseamount and type of aerosols are determined from the satelite-observed 𝜌,:+, atthe near-infrared and short-wave infrared bands, to estimate 𝜌,:+, at the visible
bands. For this purpose, we define ine aerosol models which have different mixing
ratios of tropospheric and oceanic type aerosols (Table 6 .6.1).
The aerosol reflectance determination process is initiated by selecting twomodels that explain best the aerosol reflectance observed in near-/shortwaveinfrared bands. To do so, we use two near-infrared/short-wavelength infrared
bands (𝜆T and 𝜆D ). There are two choices for the band pair. The one is 𝜆T =673
and 𝜆D =869 nm, while the other pair is 𝜆T =869 nm and 𝜆D =1630 nm. The
aerosol reflectance correction with the former is called NIR-AC while thecorrection with the latter is called SWIR-AC. In order to estimate the aerosol
reflectance in these bands accurately, the 𝜌9 in these bands are estimated byusing an iterative procedure. In the atmospheric correction, NIR-AC is tried first,
and then SWIR-AC is performed when iterations do not converge within thelimited number of times, or when the estimated 𝜌9 (673) is too high (usuallycaused by high turbidity waters).
6.2 Iterative procedure for aerosol reflectance determination

Schematic flow of iterative aerosol reflectance determination is illustrated in Fig.
6.2.1. The input reflectance is referred to 𝜌* , which is the satellite reflectance butwith Rayleigh, sunglint, and whitecap corrections applied beforehand. Hence, 𝜌*is understood as the sum of the aerosol reflectance (𝜌,:+, ) and the normalized
water-leaving reflectance multiplied by the transmittance (t[𝜌9 ]; ).
𝜌) (𝜆) = 𝜌3:23 (𝜆) + 𝑡(𝜆)[𝜌6 ]5 (𝜆)14(6.2.1)

Fig.6.2.1 Schematic flow of aerosol reflectance

The iterative procedure for aerosol reflectance determination is carried out asfollows.
[Step 1] Set initial value of [𝝆𝒘 ]𝑵 in the near-infrared region
The initial value of [𝜌9 ]; (869) is set to zero. The initial value of [𝜌9 ]; (673)is entered as the maximum possible value when the condition that results in thelowest 𝜌,:+, (673) assumes the oceanic aerosol (model 9) and 𝑡(673) and𝑡- (673) for 1.0.

15

[Step2] Calculation of 𝝆𝑨:𝑴𝑨 in the near-infrared
With the preset (or later updated) values of [𝜌9 ]; in the NIR/SWIR bands,

𝜌,:+, (673) and 𝜌,:+, (869) are determined for NIR-AC. 𝜌,:+, (1630) is also
deteremined for SWIR-AC. In what follows, (𝜆T , 𝜆D ) is (673, 869) for NIR-AC, or(869, 1630) for SWIR-AC.
[Step 3] Conversion of 𝝆𝑨:𝑴𝑨 to 𝝉𝑨 in the near-infrared and short-wavelength
infrared region

To select an aerosol model, 𝜌,:+, (𝜆T ) and 𝜌,:+, (𝜆D ) is converted to 𝜏, (𝜆T )and 𝜏, (𝜆D ) . The conversion is made through reference to the aerosol LUT(section 6.5), which contains the relationship between reflectance and optical
thickness for each of the nine “aerosol models”. Hence, assuming each model, we
obtain nine pairs of model-dependent estimates, 𝜏, (𝑀, 𝜆T ) and 𝜏, (𝑀, 𝜆D ).
[Step 4] Selection of the two aerosol models

The wavelength-to-wavelength ratio of the aerosol optical thickness ( 𝛾 ) isdependent on different aerosol types. Therefore, the ratio (𝛾(𝜆T , 𝜆D )), shown
below, is used to select the two aerosol models out of the nine standard models.

𝛾(𝜆T , 𝜆2 ) =𝜏, (𝜆T )𝜏, (𝜆2 )(6.2.2)In order to estimate the aerosol optical thickness, the relationship between
reflectance and optical thickness, which is contained in the aerosol LUT, is used.
However, this "relationship" is different for each model aerosol (M). Therefore,
the ratio of aerosol optical thicknesses estimated from satellites, 𝛾P , is defined foreach model.

𝛾P (𝑀, 𝜆T , 𝜆2 ) =𝜏, (𝑀, 𝜆T )𝜏, (𝑀, 𝜆2 )(6.2.3)On the other hand, the theoretical value for the ratio of the optical thickness of
the aerosol for each aerosol model (𝛾! ) is generally different from that of 𝛾P . Since
the ratio of optical thickness 𝛾! is equal to the ratio of the extinction coefficientof the aerosol (𝑘WX% ), 𝛾! is expressed as follows.

16

𝛾! (𝑀, 𝜆T , 𝜆2 ) =𝑘WX% (𝑀, 𝜆T )𝑘WX% (𝑀, 𝜆2 )(6.2.4)In the actual implementation of the atmospheric corrections, relative value of 𝑘WX%
for each wavelength, normalized by 𝑘WX% (869), is stored in a table (Appendix II).
Aerosol model selection uses 𝛾,YP , the average of 𝛾P (𝑀, 𝜆T , 𝜆D ). After a refining
process of averaging, the final 𝛾,YP is used to determine two aerosol models 𝑀T
and 𝑀D that have closest 𝛾! values to 𝛾,YP . Detailed description of the refining
process can be found in Fukushima et a. (1998).
The interpolation ratio 𝑟 between the two selected models 𝑀T and 𝑀D , isdefined as follows.

𝑟=𝛾𝐴𝑉P − 𝛾! (𝑀T , 𝜆T , 𝜆2 )𝛾! (𝑀D , 𝜆T , 𝜆2 ) − 𝛾! (𝑀T , 𝜆T , 𝜆2 )(6.2.5)[Step 5] Estimation of 𝝉𝑨 in the visible region by two selected aerosol models.

For each of the candidate model 𝑀T and 𝑀D , the 𝜏, values at the visible bands
are calculated by the following relation.

𝜏, (𝑀, 𝜆) =𝑘WX% (𝑀, 𝜆)𝜏 (𝑀, 𝜆2 ) ,𝑘WX% (𝑀, 𝜆2 ) ,(6.2.6)

where M is either of the two selected models 𝑀T and 𝑀D , whereas λ denotes
visible band, which is either of 380, 412, 443, 490, 530, and 565 nm for NIR-AC
case. For SWIR-AC, the “visible” band set includes 673 nm.
[Step 6] Conversion from 𝝉𝑨 to 𝝆𝑨:𝑴𝑨 in the visible region.

From the 𝜏, (𝑀, 𝜆) for each wavelength in the visible region, the lookup table(see Section 6.5) is used to calculate the visible region to 𝜌,:+, (𝑀, 𝜆) in theregion, where M is one of the two selected models 𝑀T and 𝑀D .
Using 𝜌,:+, for selected 𝑀T and 𝑀D and the interpolation ratio r, we get𝜌,:+, for each visible band as follows.
𝜌3:23 (𝜆) = (1 − 𝑟)𝜌3:EF (𝑀1 , 𝜆) + 𝑟𝜌3:23 (𝑀+ , 𝜆)17(6.2.7)

We also determine 𝜏, for each wavelength in the same way.
𝜏3 (𝜆) = (1 − 𝑟)𝜏3 (𝑀1 , 𝜆) + 𝑟 ∙ 𝜏3 (𝑀1 , 𝜆)(6.2.8)This 𝜏, (𝜆) is used for the calculation of the aerosol transmittance in the following
iterative process.
[Step 7] Estimation of [𝝆𝒘 ]𝑵 in the visible region

From the obtained 𝜌,:+, in the visible region, [𝜌9 ]; in the visible region isestimated as follows,[𝜌9 ]; (𝜆) =〈𝜌C (𝜆) − 𝜌𝐴+𝑀𝐴 (𝜆)〉𝑡(𝜆)(6.2.9)[Step 8] Estimation of [𝝆𝒘 ]𝑵 in the near-infrared region
From [𝜌9 ]; (𝜆) in the visible region, [𝜌9 ]; (673) and [𝜌9 ]; (869)iscalculated, or updated, through the in-water model (see Section 6.3) in the caseof NIR-AC. For SWIR-AC, only the value [𝜌9 ]; (869) is required to be updated.
[Step 9] Check for convergence

The convergence of the iteration (step 2 through 9) is checked as follows. Let[𝜌9 ]; (𝜆T )[ be the n-th updated [𝜌9 ]; (𝜆T ) value in step 8, where n is the numberof iteration, n=0, 1, 2, … . Note that [𝜌9 ]; (𝜆T )- means the initial value definedin Step 1. Then, if the following condition,|[𝜌9 ]; (𝜆T )[:T − [𝜌9 ]; (𝜆T )[ | < 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 ,(6.2.10)does not holds, and if n is less than 10, the new iteration from Step 2 throughStep 8 is conducted. Otherwise, the iteration is terminated.
The condition of convergence (Threshold) was set to 0.00001 for both NIR-AC
and SWIR-AC.
6.3 Estimation of water-leaving reflectance at near infrared bands

The normalized water-leaving reflectance in the near-infrared does not vary
independently of the visible water-leaving reflectance, but varies in conjunction
with water conditions such as chlorophyll a concentration and suspended matter18

concentration.
An overview of the [𝜌9 ]; estimation in the near-infrared region is shown in
Fig. 6.3.1. The estimation of [𝜌9 ]; (673) is based on the Quasi Analytical
Algorithm (QAA) (Lee et al, 2002), where estimation of inherent opticalproperties (IOPs) is done by an empirical formula to simplify the calculation. The
estimation of [𝜌9 ]; (869) is also done empirically through an in-water model
based on Ahn et al. (2015).

Figure 6.3.1 Schematic flow of algorithm estimating [𝜌6 ]5 in Red-NIR

6.3.1 Estimation of [𝝆𝒘 ]𝑵 (𝟔𝟕𝟑)
The [𝜌9 ]; at wavelength λ can be expressed by the following relationship for

IOPs (Lee et al, 2002).

[𝜌6 ]5 (𝜆) = 𝜋𝑅78 (𝜆) = 𝜋

0.52𝑟78 (𝜆),1 − 1.7𝑟78 (𝜆)𝑟78 (𝜆) = [0.089 + 1.125𝑢(𝜆)]𝑢(𝜆),𝑢(𝜆) =𝑏J (𝜆),
𝑎(𝜆) + 𝑏J (𝜆)(6.3.1)(6.3.2)(6.3.3)𝑎(𝜆) = 𝑎6 (𝜆) + 𝑎KL6 (𝜆), and(6.3.4)𝑏J (𝜆) = 𝑏J6 (𝜆) + 𝑏J# (𝜆) ,(6.3.5)19

where 𝑟@A is the remote sensing reflectance just below the ocean surface, 𝑎 and𝑏\ are the total absorption and backscattering coefficients of water, 𝑎9 and 𝑏\9
are the absorption and backscattering coefficients of pure seawater, 𝑎WX9 is thesum of the absorption coefficients for all the constituents other than water(phytoplankton, CDOM, etc.), and 𝑏\# is the backscattering coefficient due tosuspended particles.
The [𝜌9 ]; (673) is estimated from the above equations, where 𝑎(673) and𝑏\ (673) in Eq. (6.3.3) are estimated using empirical formulae.
The estimation procedure is shown in Fig. 6.3.2.

Figure 6.3.2 Estimation flow of [𝜌6 ]5 (673)[STEP 1] Estimation of IOPs at 565 nm:

Estimation of 𝑎(565) is done empirically form 𝑅@A (443) , 𝑅@A (490) and𝑅@A (565) (Ahn, personal comm.). The details are omitted.
𝑏\ (565) is obtained from 𝑅@A (565) and 𝑎(565) from Eq. (6.3.6), where 𝑏\ isfrom the equation (Z. P. Lee et al., 2002).

𝑏J (565) =𝑢(565) =𝑎(565) 𝑢(565),
1 − 𝑢(565)−0.0895 + T0.00801 + 0.499𝑟78 (565),0.249

𝑟78 (565) =(6.3.6)

𝑅78 (565).
0.52 + 1.7𝑅78 (565)[STEP 2] Estimation of IOPs at 673 nm:

The values for 𝑎(673) and 𝑏\ (673) are estimated from 𝑎(565) and 𝑏\ (565)through an empirical formula (Ahn, personal comm.). Details are omitted.

20

[STEP 3] The estimation of [𝝆𝒘 ]𝑵 at 673 nm:[𝜌9 ]; (673) is determined by equations (6.3.1)- (6.3.3) with 𝑎(673) and𝑏\ (673) values obtained in STEP 2.
The results of validation of the model with the MOBY and AERONET-OC
measurements are shown in Fig. 6.3.3. The validation was performed afterconverting the model to nLw.

Figure 6.3.3 Comparison between In-situ and predicted values

As is shown in the figure, when in-situ 𝑛𝐿( (673) is higher than 7 W m-2 sr-1
μm-1, it tends to be underestimate. The reason for this is that the effects ofinorganic suspended matter such as soil particles in coastal areas are not fully
considered. To deal with this problem, the following correction equation wasderived based on the comparison between in-situ and estimated data (Fig,6.3.4).
[𝜌6 ]5 (673) = 𝐶[𝜌6 ]∗5 (673),
3.7 (𝑐 > 3.7)
𝐶=V,𝑐 (𝑐 ≤ 3.7)
𝑐 = 2.3122 × 10M 𝑥 + − 5.7814 × 10𝑥 + 1.2365,
𝑥 = [𝜌6 ]∗5 (673) ,where [𝜌9 ]∗; (673) represents original estimate of [𝜌9 ]; (673).

21(6.3.7)

Figure 6.3.4 Ratio of In-situ to predicted values

Figure 6.3.5 Comparison between In-situ and corrected values
Table 6.3.1 Accuracies of nLw(673)RMSE*

RMSE/Mean

Bias*

R

Uncorrected

0.025822.4%-2.09E-2

0.87

Corrected

0.0152

13.2%

3.61E-4

0.87(b) AERONET-OC

RMSE

RMSE/Mean

Bias

R

Uncorrected

5.6663130.8%-1.79E0

0.90

Corrected

2.446656.5%-3.85E-2

0.95(a) MOBY*

Unit: W m-2 sr-1 μm-1

22

Fig. 6.3.5 shows the validation results for the estimated values with correction.
The accuracy before and after the correction is shown in Table 6.3.1, which shows
improvement by 40-60% in terms of RMSE. We apply this correction of Eq.
(6.3.7) to [𝜌9 ]; (673).
6.3.2 Estimation of [𝝆𝒘 ]𝑵 (𝟖𝟔𝟗)[𝜌9 ]; (869) is estimated by the following equation, which was derived from Eqs.

(24) and Eq. (25) in Ahn et al. (2015)[𝜌6 ]5 (869) = 2269.3𝑥 M − 326.32𝑥 + + 16.147𝑥 − 0.1592,
𝑥 = [𝜌6 ]5 (673) ,(6.3.8)where [𝜌9 ]; (673) is the result from Eq. (6.3.7).
6.4 Switching between NIR-AC and SWIR-AC

The combination of wavelengths in the aerosol model selection, for normal
atmospheric correction (NIR-AC), is 673 nm and 869 nm, as in the case of highsuspended matter concentrations, the combination switch to 869 nm and Switch
to 1630 nm (SWIR-AC).
The conditions for the switch are as follows,
Condition 1 𝑛𝐿( (673) > 10[𝑊 ∙ 𝑠𝑟 =T ∙ 𝑚=D ∙ 𝜇𝑚=T ]Condition 2 When the iterative operations do not converge
Condition 3 𝑛𝐿( (490) < 0
The only difference between NIR-AC and SWIR-AC is the combination of
wavelengths. The calculation procedure is the same. The wavelength of [𝜌9 ]; ,which is used as the convergence condition is changed from 673 to 869nm in
SWIR-AC.
6.5 Lookup tables of aerosol

There are two aerosol lookup tables used to calculate aerosol reflectance. The
first is a table that converts 𝜌,:+, to 𝜏, , while the other is a table that converts
𝜏, to 𝜌,:+, . The former is used in the selection of aerosol models in the nearinfrared and short-wavelength infrared bands. The latter is used to determine theaerosol reflectance in the visible region for the assumed aerosol model.
The first lookup table stores the following quadratic equation coefficients (𝑎- ,𝑎T , 𝑎D , 𝑎] , and 𝑎^ ) for conversion from 𝜌,:+, to 𝜏, . Note that 𝑎- is always

23

zero.
𝜏3 (𝑀, 𝜆, 𝜃, 𝜃4 , Δ𝜙) = 𝑎0 + 𝑎1 𝑋 + 𝑎2 𝑋2 + 𝑎3 𝑋3 + 𝑎4 𝑋4 ,(6.5.1)where
𝑋 = 𝜌𝐴 (𝑀, 𝜆, 𝜃, 𝜃0 , Δ𝜙) + 𝜌𝑀𝐴 (𝑀, 𝜆, 𝜃, 𝜃0 , Δ𝜙) ,𝑀 :Aerosol Models,𝜃 :Satellite zenith angle,
𝜃- :Solar zenith angle,
Δ𝜙 :Relative azimuth angle of the sun and the satellite.
The second look-up table that convert 𝜏, to 𝜌,:+, similarly stores thecoefficients 𝑎- , 𝑎T , 𝑎D , 𝑎] , and 𝑎^ of the following quadratic equation, where𝑎- is assumed to be zero.
𝜌3:23 (𝑀, 𝜆, 𝜃, 𝜃4 , Δ𝜙) = 𝑎0 + 𝑎1 𝑌 + 𝑎2 𝑌2 + 𝑎3 𝑌3 + 𝑎4 𝑌4 ,(6.5.2)where
𝑌 = 𝜏𝐴 (𝑀, 𝜆, 𝜃, 𝜃0 , Δ𝜙).

Aerosol lookup tables were prepared in advance by the radiative transfer
simulation code Pstar4 (Ohta et al.,2010). The conditions for the calculations
were as follows.
𝜃 :0.0° - 80.5° in increments of 3.5° (24 points)
𝜃- :0.0° - 80.5° in increments of 3.5° (24 points)
Δ𝜙 :0.0° - 180° in 4.0° increments (46 points)
Considering polarization
Considering multiple scattering
Assuming a plane parallel atmosphere
No sunglint (assuming sea level is flat)
Considering the sensor response function
Model-wise “optimized” maximum aerosol optical thickness settings(Table 6.5.2)
To calculate the aerosol reflectance for each aerosol model under the pixel-wisescan geometry 𝜃 , 𝜃- , and Δ𝜙 , we use three dimensional interpolation todetermine the 𝑎[ values for the pixel. The interpolation is based on a linear
Lagrange interpolation for 𝜃 ≤ 60° and 𝜃- ≤ 60°, whereas if 𝜃 > 60° or 𝜃- >24

60°, second-order Lagrange interpolation is used.
(1) Coefficient for 𝜃 ≤ 60° and 𝜃- ≤ 60°.
The coefficients in equations (6.5.1) and (6.5.2) when 𝜃 ≤ 60° and 𝜃- ≤ 60°
are calculated as follows.
B:T g:T 9:T

𝑎[ (𝜃, 𝜃- , Δ𝜙) = n n n 𝐴[,cde 𝐿c (𝜃)𝑀d (𝜃- ) 𝑁e (Δ𝜙)(6.5.3)cfB dfg ef9

The grid index triplet (u, v, w) is chosen so that it meets the following .
𝜃B < 𝜃 < 𝜃B:T
𝜃- g < 𝜃- < 𝜃- g:T
Δ𝜙9 < Δ𝜙 < Δ𝜙9:T
where
0 ≤ 𝑢 ≤ 22, 0 ≤ 𝑣 ≤ 22, 0 ≤ 𝑤 ≤ 44,
𝐴[,cde : Coefficients stored in the lookup table of grid numbers i, j and k
Since the number of divisions of θ is 24, i=0,.... ,23
Since the number of divisions of θ_0 is 24, j=0,.... ,23
The number of divisions of Δϕ is 46, k=0,.... ,45
The interpolation coefficients 𝐿B (𝜃) and 𝐿B:T (𝜃) are defined as
𝐿B (𝜃) =𝜃 − 𝜃B:T, and𝜃B − 𝜃B:T𝜃 − 𝜃B
𝐿B:T (𝜃) =.
𝜃B:T − 𝜃B(6.5.4)The interpolation coefficients 𝑀d (𝜃- ) and 𝑁e (Δ𝜙) are defined in similar way.
(2) Coefficient for 𝜃 > 60° or 𝜃- > 60°
The coefficients in equations (6.5.1) and (6.5.2) when 𝜃 > 60° or 𝜃- > 60°
are calculated as follows.
𝑢+2 𝑣+2 𝑤+2𝑎N (𝜃, 𝜃4 , Δ𝜙) = _ _ _ 𝐴𝑛,𝑖𝑗𝑘 𝐿𝑖 (𝜃)𝑀𝑗 (𝜃0 ) 𝑁𝑘 (Δ𝜙)𝑖=𝑢 𝑗=𝑣 𝑘=𝑤

25(6.5.5)

The grid index triplet (u, v, w) is determined so that 𝜃, 𝜃- and Δ𝜙 for the grid (u+1,
v+1 and w+1) has the closest values to those of the pixel. Then, the interpolation
coefficient L is given by:

𝐿B (𝜃) =𝐿B:T (𝜃) =(𝜃 − 𝜃B:T )(𝜃 − 𝜃B:D ),(𝜃B − 𝜃B:T )(𝜃B − 𝜃B:D )(𝜃 − 𝜃B )(𝜃 − 𝜃B:D ), and(𝜃B:T − 𝜃B )(𝜃B:T − 𝜃B:D )𝐿B:D (𝜃) =(6.5.6)(𝜃 − 𝜃B )(𝜃 − 𝜃B:T ),(𝜃B:D − 𝜃B )(𝜃B:D − 𝜃B:T )where 0≤u≤21, 0≤v≤21 and 0≤w≤43. The values of 𝑀d (𝜃- ) and 𝑁e (Δ𝜙) aresimilarly defined.
Table 6.5.1 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 tropospheric and oceanic model is described in Shettle and Fenn (1979).

26

Table 6.5.2 Upper limit of aerosol optical thickness for each band and aerosol
model
Band

M1

M2

M3

M4

M5

M6

M7

M8

M9

380

1.7

1.5

1.4

1.2

1.1

1.1

0.9

0.8

0.8

412

1.6

1.4

1.3

1.2

1.0

1.0

0.9

0.8

0.8

443

1.5

1.3

1.2

1.1

0.95

0.95

0.9

0.8

0.8

490

1.3

1.2

1.1

1.0

0.9

0.9

0.85

0.8

0.8

530

1.2

1.1

1.0

1.0

0.85

0.87

0.8

0.8

0.8

565

1.1

1.0

0.93

0.9

0.8

0.85

0.8

0.8

0.8

670

0.9

0.8

0.8

0.8

0.72

0.76

0.75

0.75

0.85

763

0.7

0.7

0.7

0.7

0.7

0.7

0.7

0.7

0.85

865

0.6

0.6

0.6

0.6

0.6

0.7

0.7

0.7

0.85

1050

0.4

0.5

0.5

0.5

0.52

0.6

0.6

0.7

0.85

1380

0.3

0.4

0.4

0.4

0.45

0.55

0.55

0.6

0.83

1630

0.15

0.3

0.3

0.35

0.4

0.5

0.5

0.6

0.81

2210

0.05

0.2

0.2

0.25

0.3

0.4

0.4

0.5

0.75

(nm)

27

7. Transmittance

The atmospheric correction process takes into account the transmittance, suchas attenuation due to scattering of gas molecules and absorption by gas moleculesof ozone, nitrogen dioxide, and oxygen. When we refer to the transmittance, there
are two pathways to consider. One is from the top of atmosphere (the sun) to thesea surface, whereas the other is from the sea surface to the satellite.
Transmittance t for the former is written as 𝑡- with subscript 0 while the one forthe latter is described without the subscript.
7.1 Molecule transmittanceThe diffuse transmittance of gas molecules is evaluated as half the optical
thickness of gas molecules contributes to the extinction, since the amount offorward and back scattering is the same.
h (1)/𝑡 (+) (𝜆) = 𝑒𝑥𝑝 y− D∙jkA
z ,
7

(+)

ｔ

-

(𝜆) = 𝑒𝑥𝑝 y−h/ (1)
D∙jkA 7-

(7.1)

z ,

where 𝜏+ (𝜆) is the optical thickness of the gas molecule shown in Eq. (5.2).
The direct transmittance of gas molecule is expressed by the following equation,
since any scattering is considered to contribute to the attenuation.

𝑇 (+) (𝜆) = 𝑒𝑥𝑝 K−

𝜏+ (𝜆)Q𝑐𝑜𝑠 𝜃

𝜏+ (𝜆)(+)
𝑇- (𝜆) = 𝑒𝑥𝑝 K−
Q
𝑐𝑜𝑠 𝜃-(7.2)

7.2 Ozone transmittance

The transmittance of ozone is expressed by the following equation.

𝑡 (l]) (𝜆) = 𝑒𝑥𝑝 K−

𝜏lm (𝜆)Q , and𝑐𝑜𝑠 𝜃

𝜏lm (𝜆)(l])
𝑡- (𝜆) = 𝑒𝑥𝑝 K−
Q.
𝑐𝑜𝑠 𝜃-

28(7.3)

The ozone optical thickness 𝜏lm (𝜆) is expressed as
𝜏lm (𝜆) = 𝐷𝑈 ∙ 𝑘lm (𝜆) ,(7.4)

where Dobson Unit (𝐷𝑈, Section 11.1) is the virtual thickness of the columnar
ozone, under assumed standard condition (1 atm, 0°C), while 𝑘lm (𝜆) is theextinction coefficient of ozone at wavelength λ per DU. The values of 𝑘lm (𝜆)are shown in Table 7.1. It was calculated from the ozone absorption cross-section
data (Voigt et al., 2001) in consideration with the sensor response function.
Table 7.1 Extinction coefficient of ozone for SGLI bands,
weighted by the sensor response function.
Band<𝑘lm (𝜆)>[DU-1]
Band<𝑘lm (𝜆)>[DU-1]
VN1

7.97e-08

VN9

7.59e-06

VN2

4.33e-07

VN10

2.10e-08

VN3

3.74e-06

VN11

2.10e-08

VN4

2.25e-05

SW10.00e+00

VN5

6.79e-05

SW20.00e+00

VN6

1.17e-04SW30.00e+00

VN7

4.42e-05

SW40.00e+00

VN8

4.42e-05

7.3 aerosol transmittanceThe diffuse transmittance of the aerosol is calculated using the following
formula.

𝑡 (,) (𝜆) = 𝑒𝑥𝑝 ~−(1 − 𝜔, (𝜆)𝜂)𝜏, (𝜆)• , and𝑐𝑜𝑠 𝜃(1 − 𝜔𝐴 (𝜆)𝜂)𝜏𝐴 (𝜆)(0)𝑡! (𝜆) = 𝑒𝑥𝑝 *−
+,

(7.5)

𝑐𝑜𝑠 𝜃0where 𝜔, is the single-scattering albedo of the aerosol and 𝜂 is the forward
scattering probability (η = 1). The single-scattering albedo for each aerosol
model is described in Appendix III. The aerosol optical thickness 𝜏, (𝜆) for thetarget pixel is calculated by Eq.(6.2.8).
The direct transmittance of aerosol is expressed as follows.
29𝑇 (,) (𝜆) = 𝑒𝑥𝑝 ~−𝜏, (𝜆)• , and𝑐𝑜𝑠 𝜃𝜏, (𝜆)(,)
𝑇- (𝜆) = 𝑒𝑥𝑝 ~−•.
𝑐𝑜𝑠 𝜃030(7.6)

8. Sunglitter correction

The reflectance of the sunglitter, which is defined just above the sea surface, isgiven as follows (Cox and Munk: 1954a, 1954b and 1956).

𝜌n (𝜆) = 𝑇- (𝜆)𝜋𝑓(𝜔, 𝜆)𝑃( (𝜃, 𝜃- , Δ𝜙, 𝑊),
4 ∙ 𝑐𝑜𝑠𝜃 ∙ 𝑐𝑜𝑠𝜃- ∙ 𝑐𝑜𝑠 ^ 𝜃[

(8.1)

whereas the normalized sunglitter reflectance [𝜌' ]; , defined against theextraterrestrial solar irradiance, is given byƒ𝜌n (𝜆)„; =𝜋𝑓(𝜔, 𝜆)𝑃( (𝜃, 𝜃- , Δ𝜙, 𝑊),
4 ∙ 𝑐𝑜𝑠𝜃 ∙ 𝑐𝑜𝑠𝜃- ∙ 𝑐𝑜𝑠 ^ 𝜃[

(8.2)

since ƒ𝜌n (𝜆)„; = 𝑇- (𝜆)𝜌' (𝜆) , as defined in Eq. (3.2).
In the above equations, 𝑇- is the beam transmittance for the downward solar
light, 𝑃( (𝜃, 𝜃- , Δ𝜙, 𝑊) is the probability of the facet of the sea surface generates
the sunglitter. The latter is further shown as follows.

𝑃( (𝜃, 𝜃- , Δ𝜙, 𝑊) =1
−𝑡𝑎𝑛D 𝜃[
𝑒𝑥𝑝
K
Q.
𝝅𝜎 𝟐
𝜎𝟐

(8.3)

The term 𝜎 𝟐 is expressed as a function of the wind speed (𝑊) and is given by
the following equation.
𝜎 𝟐 = 0.003 + 0.00512𝑊
The 𝜃[ term is the zenith angle of a normal n to the sea surface facet fromwhich the sunglitter arises, and is shown as follows.
𝑐𝑜𝑠𝜃 + 𝑐𝑜𝑠𝜃𝜃[ = 𝑐𝑜𝑠 =T ‡ˆ,
2𝑐𝑜𝑠𝜔
where 𝜔 is the angle between the directions of the n and the sun or the satellite,
expressed as𝑐𝑜𝑠2𝜔 = 𝑐𝑜𝑠𝜃𝑐𝑜𝑠𝜃- + 𝑠𝑖𝑛𝜃𝑠𝑖𝑛𝜃- 𝑐𝑜𝑠Δ𝜙𝑓(𝜔, 𝜆)) is the Fresnel reflectance as follows,𝑓(𝜔, 𝜆) = 1 − (2 ∙ 𝑛(𝜆) ∙ 𝑦 ∙ 𝑧) 𝑐𝑜𝑠𝜔 ,‹𝑛(𝜆)D + 𝑐𝑜𝑠 D 𝜔 − 1
, and
𝑛(𝜆)
1
1
𝑧=
+
,
{𝑐𝑜𝑠𝜔 + 𝑦𝑛(𝜆)}D {𝑦 + 𝑛(𝜆)𝑐𝑜𝑠𝜔}D𝑦=31

where 𝑛(𝜆) is the refractive index.
Since the contribution of sunglitter reflectance to the satellite-observedreflectance 𝜌! is 𝑇 [𝜌' ]; as shown below,
𝜌! = 𝜌+ + 𝜌, + 𝜌,+ + 𝑇[𝜌' ]; + 𝑡[𝜌(* ]; + 𝑡[𝜌9 ]; ,(3.2)
we further need to determine the beam transmittance 𝑇(𝜆) between the seasurface and the satellite. As far as the sunglitter correction is concerned, we
assume constant optical thickness 𝜏, (869) of 0.1, which seems to beappropriate based on the global SeaWiFS observation over the ocean (Wang,
2001). The 𝜏, values for other wavelengths are also set to 0.1, meaning that we
anticipate the oceanic type aerosol (see models 8 and 9 in Appendix II).

32

9. Whitecap correction

The equation for the reflectance [𝜌(* ]; due to the whitecap of the sea surface
is expressed as follows.
[𝜌(* ]; (𝜆) = 𝑘(* (𝜆) ∙ 𝑅(* ∙ 𝑊Cj ,

(9.1)

where
𝑘(* (𝜆): wavelength dependence coefficient (Table 9.1; Frouin et al., 1996)
𝑅(* : Koepke's effective reflectance in white caps (=0.22)
𝑊Cj : Wind speed dependency coefficient (Stramska and Petelski,2003)
𝑊 = 8.75 × 10=p (𝑈T- − 6.33)]
𝑈T- is the wind speed at an elevation of 10 m.
The minimum wind speed is assumed to be 6.33ms-1. If 𝑈T- is below theminimum, [𝜌(* ]; (𝜆) = 0.
Table 9.1 Wavelength dependent factor
Band

𝒌𝑾𝑪 (𝝀)Band𝒌𝑾𝑪 (𝝀)

VN1

1.0

VN9

0.762766

VN2

1.0

VN10

0.640922

VN3

1.0

VN11

0.640922

VN4

1.0

SW1

0.526908

VN5

1.0

SW2

0.319608

VN6

0,990367

SW3

0.156282

VN7

0.884466

SW4

0.0

VN8

0.88446633

10. Bidirectional reflectance distribution function (BRDF)

𝑛𝐿9 (𝜆, 𝜃, 𝜃- , ∆𝜙) and 𝑅@A (𝜃- , 𝜃, ∆∅) are “normalized” quantities, in the sensethat those are derived from the observed 𝐿9 with corrections of the effects arisingfrom variability of the Sun-Earth distance, atmospheric transmittance and solar
zenith angle. However, they still contain direction-dependent factors of upward
radiance 𝐿B and water surface transmittance of light in water. The factors depend
not only on the direction of the satellite observation but also on the direction of
the incident light. This dependency is called Bidirectional ReflectanceDistribution Function (BRDF). Our atmospheric correction process also includes
BRDF correction according to Morel and Gentilli (1996), Morel and Gentilli(2002) and Wang (2006).
The BRDF correction term 𝐶MNO3 in Eq. (3.14) is described as follows.
𝑛𝐿6 ;< = 𝑛𝐿6 𝐶=>?@= 𝑛𝐿6 (𝜆, 𝜃, 𝜃4 , ∆𝜙)`(𝑓 ⁄𝑄 );PP (𝜆, 𝜃, 𝜃4 , ∆𝜙, IOPs)g(10.1)(QRS)(TUVW)(𝜆, 𝑊)ℜ4 (𝜆, 𝜏$ , 𝑊)
ℜ4h (QRS)j h (TUVW)j,(𝜆, 𝜃4 , 𝜏$ , 𝑊) ℜ
(𝜆, 𝜃, 𝑊)ℜ

where 𝜆 is wavelength, 𝜃 is the satellite zenith angle, 𝜃- is the solar zenith
angle, ∆𝜙 is the relative azimuthal angle between the satellite and the sun, 𝜏$ is
the optical thickness of the aerosol, 𝑊 is the wind speed, IOPs is the Inherent
Optical Properties, ‘(𝑓 ⁄𝑄 )Pss (𝜆, 𝜃, 𝜃- , ∆𝜙, IOPs)— is the BRDF effect of thedownward irradiance just beneath the ocean surface and the upward radiance justbeneath surface, the ratio of ℜ(6tu) is the BRDF effect of the downward
irradiance from atmosphere to in-water at the air-water interface, ℜ(gcW9) is the
BRDF effect of the upward radiance from in-water to atmosphere at the air-waterinterface,. ℜ!(123) (𝜆, 𝜏4 , 𝑊) is defined for ℜ(AB[) (𝜆, 𝜃- = 0, 𝜏$ , 𝑊) , and(5678)(𝜆, 𝑊) is defined for ℜ(vwxy) (𝜆, 𝜃 = 0, 𝑊).
ℜ!
In the following sections, we describe each BRDF effect.
(view)

10.1 BRDF effect of air-water interface for upward light: ℜ0

kℜ(view)The BRDF effect of air-water interface from beneath to above surfaceℜ(view)0l (view
)

ℜ

(𝜆,𝑊)

(𝜆,,𝜃,𝑊)m in Eq.(10.1) was investigated by Gordon (2005). He found that theeffect is negligible for satellite zenith angle 𝜃 below 70 degrees, so that it can be34easily calculated as the ratio of Fresnel reflectivity 𝑓 by the following formula,(TUVW)(𝜆, 𝑊)ℜ4
1 − 𝑓(𝜃 = 0, 𝜆).
h (TUVW)j=(𝜆, 𝜃, 𝑊)
1 − 𝑓(𝜃, 𝜆)ℜ(10.2)

See Chapter 8 for the calculation of 𝑓(𝜃, 𝜆).
(𝑠un)10.2 BRDF effect of air-water interface for downward light: ℜ0

(sun)

kℜ

The BRDF effect of air-water interface from above to beneath surface
ℜ

(HIJ)

(1,h ,()K™ℜ(HIJ)
š is calculated by Wang(2006). This effect is expressed as a(1,7 ,h ,()- Kfunction of 𝜆 , 𝜏$ and 𝜃- , and it can be approximated using the irradiancetransmittances across downward the air‒water interface (𝑡>>>>Cs ) as follows.
(8XN)

AAAA
𝑡9P (𝜆, 𝜃4 = 0, 𝜏$ , 𝑊)
ℜ4 (𝜆, 𝜏$ , 𝑊),
h (8XN)j≈(𝜆, 𝜃4 , 𝜏$ , 𝑊)
𝑡AAAAℜ
9P (𝜆, 𝜃4 , 𝜏$ , 𝑊)

(10.3)The irradiance transmittance is defined by the following equation,
(*)

𝑡AAAA
9P =

𝐸9 (𝜆, 𝜃4 , 𝜏$ , 𝑊)(:)
𝐸9 (𝜆, 𝜃4 , 𝜏$ , 𝑊),

(10.4)(=)(:)
where 𝐸C (𝜆, 𝜃- , 𝜏$ , 𝑊) and 𝐸C (𝜆, 𝜃- , 𝜏$ , 𝑊) are downward irradiance justbeneath, and just above the surface, respectively.
Wang (2006) found that ℜ(AB[) ratio in Eq. (10.3) is almost independent of the
optical properties of the aerosol, and the ratio is expressed as follows.
M(QRS)ℜ4 (𝜆, 𝜏$ , 𝑊)h (QRS)j ≈ Corf (YRS) (𝜆, 𝜃4 , 𝑊) = 1 + _ 𝑐Z (𝜆, σ)[ln cos 𝜃4 ],(𝜆, 𝜃4 , 𝜏$ , 𝑊)ℜ

(10.5)

σ＝0.0731 ∙ √𝑊,(10.6)

Z[,

where σ is re-scaled wind speed, W [m/s], and the coefficient 𝑐c (𝜆, σ) is shownin Table V.1 in Appendix V. Interpolation of these coefficients is done by bi-linear
interpolation for 𝜆 and σ.

35

10.3 BRDF effect of in-water ocean: ‘(𝑓 ⁄𝑄 )Pss —BRDF effect of in-water ocean ‘(𝑓 ⁄𝑄)Pss (𝜆, 𝜃, 𝜃- , ∆𝜙, 𝐶)— is expressed byMorel and Gentili (2002) as follows.
`(𝑓 ⁄𝑄 );PP (𝜆, 𝜃, 𝜃4 , ∆𝜙, IOPs)g𝑓(𝜆, 𝜃4 = 0, IOPs)lm
𝑄(𝜆, 𝜃4 = 0, 𝜃 \ = 0, ∆𝜙 = 0, IOP𝑠)=,w 𝑓(𝜆, 𝜃 , IOPs)
4lm\
𝑄(𝜆, 𝜃4 , 𝜃 , ∆𝜙, IOPs)
𝜃 \ = sin*,

sin 𝜃
,
𝑛(𝜆)

(10.7)(10.8)

where 𝜃′ is the refractive angle in water corresponding to 𝜃, 𝑛 is the refractive
index of seawater with respect to the wavelength 𝜆, 𝑄 is the ratio of the upward
irradiance to the downward radiance just beneath ocean surface, and 𝑓 is theratio of the upward irradiance to the downward radiance just beneath ocean
surface.
The ratio 𝑓(𝜆, 𝜃- , IOPs)/𝑄(𝜆, 𝜃- , 𝜃 … , ∆𝜙, IOPs) is then expressed as,z𝑓(𝜆, 𝜃4 , IOPs){ = 𝑔(𝜆, 𝜃4 , 𝜃 \ , ∆𝜙, Chl),
𝑄(𝜆, 𝜃4 , 𝜃 \ , ∆𝜙, IOPs)(10.9)

where Chl is chlorophyll-a concentration [mg/m3]. The function 𝑔 is given as a𝑓⁄𝑄 lookup table, where we calculate the pixel-wise value with linear
interpolation over 𝜃- , 𝜃 … , ∆𝜙 and Chl. See Appendix VI for details of the lookup
table.

36

11. Ancillary data

As ancillary data set, the atmospheric correction refers to the columnar ozone
amount, sea surface pressure, and sea surface wind speed data during the
pixel-wise processing.
11.1 Ozone content

The amount of ozone is used to evaluate the ozone transmittance. The amountof ozone is expressed in terms of Dobson unit (DU), which is virtual/physicalthickness of the columnar ozone under assumed standard condition (1 atm, 0°C)
such that 100 DU corresponds to 1 mm of the ozone layer thickness.
The data set comes from the OMI (Ozone Monitoring Instrument)
measurement, or TOVS (Advanced Tiros-N Operational Vertical Sounder)
measurement.

11.2 Sea Surface Pressure

Sea surface pressure is used to calculate the reflectance and transmission of gas
molecules. The data used is the objective analysis data (GGLA) provided by theJapan Meteorological Agency.
11.3 Sea Surface Wind Speed

Sea surface wind speeds are used for correcting sunglitter reflectance, whitecaps,
and BRDF. We use the objective analysis data (GGLA) provided by the theJapan Meteorological Agency.

37

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40

Appendix I Mean extraterrestrial solar irradiance

Table I.1 and Table I.2 show the solar irradiance for the GCOM-C/SGLI bands(JAXA/EORC, 2010), The SGLI ocean color atmospheric correction process
refers to the solar irradiance at center wavelength for each channel of the nadir>>>- ) .
looking instrument, to take the irradiance as the mean solar irradiance (𝐹Table I.1 Solar Irradiance of GCOM-C/SGLI on Visible and Near-Infrared (VNR)
Center wavelength: 𝜆] [nm]Solar irradiance: 𝐹4 [Wm-2μm-1]

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

412.589

1712.4760

443.051

1893.5879

490.311

1941.0715

Band

VNR06

VNR06

VNR02
VNR03
VNR04

Telescope

Left

Nadir

Right

41

VNR05529.664

1851.0657

VNR06

566.377

1796.8275

VNR07

671.9501502.6962

VNR08

672.1201502.2582

VNR09

763.234

1244.8290

VNR10

866.713956.2577

VNR11

867.086956.5735

SGLI/VNR has three telescopes (Left, Nadir and Right).
Table I.2 Solar Irradiance of GCOM-C/SGLI on Short Wave Infrared (SWI)
Band

Center wavelength: 𝜆] [nm]Solar irradiance: 𝐹4 [Wm-2μm-1]

SWI01

1054.994

646.5213

SWI02

1385.351

361.2250

SWI03

1634.506

237.5784

SWI04

2209.481

84.241342

Appendix II. Ratio of aerosol Extinction Coefficient (Kext) for Aerosol Models

The spectral dependency of the aerosol extinction coefficient 𝐾WX% is an
important characteristics of different aerosol type. The atmospheric correctionuses the spectral ratio of 𝐾WX% to determine the most likely aerosol model pair.
The spectral ratio is also used to determine the AOT and aerosol reflectance ateach visible band. The model-specific spectral ratio of 𝐾WX% is tabulated as a lookup table, which is referenced during the atmospheric correction process. The
contents of the LUT is showin in Table II.1. Note that 𝐾WX% values are normalizedwith 𝐾WX% at VN10 band because we only need their “relative” value. Fig. II.1
shows the spectral dependency for all the nine aerosol models.
Table II.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

43

Figure II.1. Kext values normalized by Kext at VN10 for each assumed aerosol model. Solidlines represent LUT values which is band weighted averaged.

44

Appendix III. 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

0.99680.985945

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

Name

Description

Criterion

Mask

0

DATAMISSNo observation data in one or more band[s]

L2

1

LAND

Land pixel

L2

2

ATMFAIL

Atmospheric correction failure

L2

3

CLDICE

Apparent cloud/ice (high reflectance)

4

CLDAFFCTD

ρA>0.04

L2

ρA>0.03

L3[ρG]N > 0.02

L2

[ρG]N > 0.005

L3
L3

Cloud-affected (near-cloud or thin/sub-pixel
cloud)
Stray light anticipated (ref. L1B stray light flags
5

STRAYLIGHT

6

HIGLITN& image)High sun glint predicted (atmospheric corr.
abandoned)
High sun glint predicted (atmospheric corr.

7

MODGLINT
abandoned)

8

HIOSOLZ

Solar zenith larger than threshold

θ0 > 70°

9HITAUA

Aerosol optical thickness larger than threshold

τA > 0.5

10GAMMA-OUT

Atmospheric correction warning: Gamma outof-bounds
Maximum

11

iterations

reachedfor

NIR

OVERITER
correction

12

NEGNLW

Negative nLw in one or more bands

13

HIGHWS

Surface wind speed higher than threshold

14

ATM-METHODNIR atmospheric correction: 0,
SWIR atmospheric correction: 1

15

SPARE

Spare

46

W/S > 12m/s

Look-up Table for BRDF Correction function 𝐂𝐨𝐫𝐟 (𝐒𝐮𝐧)Appendix V.

Table V.1 Coefficients 𝒄𝟏 , 𝒄𝟐 , 𝒄𝟑 , 𝒄𝟒 from Wang (2006)
Wind
speed:

Wavelengths: λ(nm)
σ

ci

412

𝟒𝟒𝟑

𝟒𝟗𝟎

510

555

670

𝑐,

-0.0087-0.0122-0.0156-0.0163-0.0172-0.0172𝑐+

0.0638,0.04150.01880.01330.0048-0.0003𝑐/-0.0379-0.0780-0.1156-0.1244-0.1368-0.1430𝑐M-0.0311-0.0427-0.0511-0.0523-0.0526-0.0478𝑐,-0.0011-0.0037-0.0068-0.0077-0.0090-0.0106𝑐+

0.09260.0746

0.05340.04730.03680.0237𝑐/-5.3E-4-0.0371-0.0762-0.0869-0.1048-0.1260𝑐M-0.0205-0.0325-0.0438-0.0465-0.0506-0.0541𝑐,

6.8E-5-0.0018-0.0011-0.0012-0.0015-0.0013𝑐+0.11500.11150.10750.10640.10440.1029𝑐/

0.06490.03790.03420.03010.02320.0158𝑐M

0.0065-0.0039-0.0036-0.0047-0.0062-0.0072𝑐,-0.0088-0.0097-0.0104-0.0106-0.0110-0.0111𝑐+

0.06970.06780.06570.0651

0.06400.0637𝑐/0.04240.03280.02330.02080.01660.0125𝑐M

0.00470.0013-0.0016-0.0022-0.0031-0.0036𝑐,-0.0081-0.0089-0.0096-0.0098-0.0101-0.0104𝑐+

0.04820.04660.04500.04440.04390.0434𝑐/0.02900.02200.01500.01310.01030.0070𝑐M

0.00290.0004-0.0017-0.0022-0.0029-0.0033

W (m/s)

0

1.9

7.5

16.9

30.0

0.000

0.100

0.200

0.300

0.400

47

Appendix VI. Look-Up Table of f over Q

The table “morel_fq.nc” is available in DISTRIB_fQ_with_Raman.tar.gz which
can be downloaded from the Web site ftp://oceane.obsvlfr.fr/pub/gentili/AppliedOptics2002/.
The structure of table (morel_fq.nc) is as follows.
Wavelengths: 412.5, 442.5, 490, 510, 560, 620, and 660 nm (7wavelengths) (MERIS wavelengths)
CHL: 0.03, 0.1, 0.3, 1.0, 3.0, 10.0 mg/m3 (6 levels)(approximately equally spaced on log-scale)
Solar zenith angle: 0, 15, 30, 45, 60, 75 degrees (6 levels)
Satellite zenith angles: 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° (17steps)
Relative azimuth: 0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180°
(13 levels)
This table was created for MERIS. For SGLI atmospheric correction, the closest
wavelength is chosen for lookup.

48