ATBD of GCOM-C chlorophyll-a concentration algorithm
Hiroshi Murakami
JAXA, EORC, Oct. 2018

1.

Background and objectives

Chlorophyll-a concentration (Chl-a) algorithm has more than 20-year history, and blue-green band ratio algorithm(OCx) which calculate Chl-a by 4th order empirical equation (Eq. (1)) is curretly used as the standard (O'Reilly etal., 2000).
log10(Chla) = c0 + c1 r + c2 r2 + c3 r3 + c4 r4,... (1)where,r = log10( MAX[ Rrs(443nm, 490nm, 530nm) ] / Rrs(555nm) ).

... (2)

Rescently, NASA/OBPG cobindly uses Color Index based Algorithm (CIA; Hu et al., 2012) in the low Chl-aranges (Eq. (3)) which can reduce noise caused from satellite sensors.
Chl-a = 10(-0.4909 + 191.6590×CI) (when CI ≤ −0.0005 sr-1),... (3)where,CI = Rrs(555nm) − [ Rrs(443nm) + (555−443) / (670 − 443) × (Rrs(670nm) − Rrs(443nm)) ].

... (4)GCOM-C algorithm is developed based on the empirical algorithms for convinient use with the other sensorproducts. We derived the OCx coefficients optimalized for the SGLI spectral bands and characterized estimation
error of the SGLI Chl-a product.

2.

Data

2.1.

NOMAD data

NASA bio-Optical Marine Algorithm Data set (NOMAD) (Werdell and Bailey, 2005) have been used for OCx
coefficient of NASA standard Chl-a products (OCTS, SeaWiFS, MODIS, VIIRS, ..). NOMAD includes abovewater downward-irradiance, Es(λ), upward radiance, Lw(λ), etc., at wavelengths λ=443, 455, 465, 489, 510, 520,530, 550, 555, 560, 565, 570 590, 619, 625, 665, 670nm with 10-nm band width. Remote-sensing reflectance, Rrs,and normalised water-leaving radiance, Lwn, can be calculated from the Es(λ) and Lw(λ) by the following equation(5).
Rrs(λ) = Lw(λ) / Es(λ) × foQ(θ=0, θ0=0, ∆φ, Chla, λ)/ foQ (θ, θ0, ∆φ, Chla, λ) ... (5)Lwn(λ) = Rrs(λ) × F0(λ) ... (6)where, foQ is bi-directional reflectance factor (the look up tables of Morel and Maritorena, 2001 is used), F0,solar irradiance, θ, θ0, ∆φ are satellite zenith, solar zenith andrelative azimuth angles respectively.

2.2.

In-situ data around Japan

Around Japan, several universities (Hokkaido, Nagoya, Tokyo, Yamanashi, and Tokai Univs.) and institutes(Japan Fisheries Research and Education Agency (FRA) including National Research Institute of Fisheries Science,Seikai National Fisheries Research Institute, Tohoku National Fisheries Research Institute, Hokkaido National
Fisheries Research Institute), have provided in-situ data for the GCOM-C algorithm development and validation.
GCOM-C standard OC4 algorithm is using only NOMAD data in the pre-launch phase considering comnatibilitywith other sensor products. However their data is used for the algorithm evaluation and will be used for algorithm
improvements after the GCOM-C launch.

3.

IOP model for SGLI-bands

We made a simple inherent optical property (IOP) model based on Gordon et al., 1988, Lee et al., 2002 adjustedto NOMAD IOP and Rrs data, and interpolated NOMAD Rrs to 1-nm spectral resolution using the model.

Figure 1. The upper panels are (a) scatter diagram of aph and Chl-a and (b) ratios of aph/Chl-a which are modeled by average in thesix Chl-a ranges. The middle panels show relationship (c) between Chl-a and adg at 442 nm, (e) between Chl-a and the spectral
slope of adg (S). (d) shows the relationship between Chl-a and adg at 442 nm which is modified by adjusting to Rrs measurements
and the IOP model. The lower panels (f, g, and h) are the same as the middle panels except for bbp and the spectral slope of bbp(Y) instead of adg and S.

The IOP algorithms are based on the equation of remote sensing reflectance below the surface (rrs), the totalabsorption coefficient (a) and the backscattering coefficient (bb) proposed by Gordon et al. 1988.
rrs(λ) = g1 × u(λ) + g2 × u(λ)2(7)a(λ) = aw(λ) + aph(λ) + ad(λ) + ag(λ)(8)bb(λ) = bbw(λ) + bbp(λ)(9)u(λ) = bb(λ) / ( bb(λ) + a(λ) )

(10)

with

where g1=0.0949 and g2=0.0794 [Lee et al., 2002]. aw, aph, ad, and ag are the absorption spectra of water,
phytoplankton, detritus, and CDOM respectively. bbw and bbp are backscattering coefficients of water and particles.
We used aw and bbw values from [Pop and Fry 1997; Kou et al., 1993; Lee et al., 2015].
Remote sensing reflectance above the surface, Rrs is estimated from rrs using the relation from [Gordon et al., 1988,
Lee et al., 2002] as:Rrs(λ) = 0.529 × rrs(λ) / (1− 1.7× rrs(λ)).

(14)

BRDF effect is corrected by the look-up tables developed by Morel and Maritorena (2001) by considering in-situ
observation time, i.e., the solar zenith angle.
Phytoplankton absorption per Chl-a at 442nm, aph(442)/Chl-a, is modeled by Chl-a from NOMAD data. Spectral
shape of the aph(λ)/Chl-a is modeled for six aph(442)/Chl-a levels (Fig. 1(b)).
aph(442)/Chl-a = −1.2937 −0.2522 × Chl-a + 0.0443 × Chl-a2(15)

adg and bbp were approximated as follows.
adg(λ) = adg0 × exp(−S × (λ − 442))(12)bbp(λ) = bbp0 × (λ /442)−Y(13)where adg0 is adg at 442 nm, bbp0 is bbp at 442 nm were derived from the NOMAD in situ measurements of adg andbbp respectively (Table 1). The average of S and Y were 0.0146, and 1.18 respectively.
SGLI Rrs are simulated by the IOP model and spectral response of SGLI bands, 443 (with 10-nm width), 490 (10),530 (20), 566 (20), 672 (20) nm (Uchikawa et al., 2014), and SGLI OC4 coefficients are calculated by the simulated
Rrs and the coincident Chl-a in the NOMAD.
Table 1 Coefficients for the IOP model

λ [nm]
Solar irradiance[W/m2/sr/µm]
Reflactive index
aw [m-1]
bbw [m-1]
adg0 [m-1]bbp0 [m-1]aph0 [m-1]0.01-0.025
0.025-0.04
aph0
0.04-0.06
aph/Chl
0.06-0.09
dange
0.09-0.13
0.13-0.5

VN01
380.03VN02
412.51

VN03
443.24VN04
489.85VN05
529.64VN06
566.16VN07
672.00VN08
672.10VN10
763.07VN11
866.761092.141712.15

1898.32

1938.46

1850.96

1797.131502.55

1502.30

956.34956.621.340
0.003770.00472
2.48076
1.195540.655160.67211
0.66577
0.632170.62891
0.61897
0.64207

1.338
0.003120.00333
1.54306
1.085240.841900.859960.85133
0.813850.80775
0.798370.82440

1.337
0.005100.002390.98477
0.99705
0.98772
0.987190.98769
0.99088
0.99184
0.993230.99044

1.335
0.013380.00157
0.498410.886150.617640.63009
0.63673
0.63282
0.60805
0.616630.62424

1.334
0.042130.001120.27957
0.808300.304080.29570
0.27034
0.21233
0.178120.18184
0.221101.333
0.067680.00086
0.16400
0.74718
0.14737
0.13827
0.124630.08637
0.071890.086140.09680

1.331
0.445790.000410.035010.61056
0.58058
0.45687
0.371400.24582
0.198230.223020.28495

1.331
0.446110.000410.034960.610450.58094
0.457280.371730.24605
0.198410.223250.285211.329
4.693540.000140.00204
0.45232
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000

1.329
4.70633
0.000140.002030.452100.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000

4.

Results

4.1.

Chl-a eatimation

Figure 2 OCx coefficients of SeaWiFS (NASA standard coefficients), MODIS, SGLI, and LANDSAT (upper panels),and Chl-a
derived by the coefficients (lower panels).

The followings are SGLI Chl-a eatimation.
Chl-a =chle1 wci +chle2 (1-wci)
wci=((-0.0002)-ci)/((-0.0002)-(-0.0006))
wci=1 (wci>1)
wci=0 (wci<0)
ci=Rrs(λ6) - (Rrs(λ3) × (λ7 - λ6)+Rrs(λ7) × (λ6 - λ3)) / (λ7 - λ3);log10(chle1)= -0.38006 +238.05110 ×ci
log10(chle2) = 0.40451 -3.42411× x +5.29717× x2 -5.33247× x3 +1.68959× x4
x=log10(max(Rrs(λ3, λ4, λ5))/Rrs(λ6))

Derived OC4 coefficients and regression errors are listed in Tables 2 and 3 respectively. RMSD of SGLI Chl-aseems smaller than other sensors (Fig. 2) in Chl-a>3mg/m3. That is because SGLI has longer wavelengths at 530
nm and 565 nm which has higher sensitivity for the high Chl-a ranges.

Table 2 OCx coefficients derived in this study
SGLI
SeaWiFSMODISLANDSAT

c00.40451
0.315440.22490.2722c1-3.42411-2.95833-2.6008-2.1652

c25.29717
2.653121.38110.8958c3-5.33247-0.76475
0.83560.4047c4
1.68959-1.07165-1.7722-0.9157

Table 3 Chl-a regression error by the OCx coefficients

SGLI
SeaWiFS
MODISLANDSAT

4.2.

0.02< Chla <60
N=27310.245632.36
0.252632.97
0.262833.59
0.2557
33.25

RMSD (log10(mg/m3))
MAPD(%)RMSD (log10(mg/m3))
MAPD(%)RMSD (log10(mg/m3))
MAPD(%)RMSD (log10(mg/m3))
MAPD(%)

Chla <0.1
N=3560.1995
27.34
0.192226.360.1977
27.59
0.198926.10

0.1< Chla <3
N=18960.230131.86
0.235132.41
0.235831.96
0.233131.95

Chla >3N=479
0.323639.49
0.343042.71
0.380344.62
0.358044.06

Error evaluation

Erros were estimated by add the regression errors (RMS of the regressions in Fig. 1) to the IOP model. (a)+(b)+(c)in Table 4 show errors from the in-water model, and (d), errors from the sensor noise plus the atmospheric correction.
Table 4 SGLI Chl-a estimation error estimated by the IOP model
Input random
error (RMS)(a-1) aph/Chla[m-1/(mg/m3)]

0.1723 (log10)(b-1) adg [m-1]0.3978 (log10)(b-2) S [µm-1]

0.0029(c-1) bbp [m-1]0.1924 (log10)(c-2) Y

0.4724(a)+(b)+(c)-(d-1) NEdL (VIS)[W/m2/sr/µm]

0.03-0.06(d-2) NEdL (NIR)[W/m2/sr/µm]

0.02(d-3) NEdL
+Atmcorr*

10%(Rrs 443nm)

log10%
RMS
MAPD
RMS
MAPD
RMS
MAPD
RMS
MAPD
RMSMAPD
RMS
MAPD
RMS
MAPD
RMS
MAPD
RMS
MAPD

* N of (d-3) are 4734, 972, 2140, 1622.
MAPD means median absolute percent difference.

0.02< Chla <60
N=50000.116616.30
0.179421.31
0.03242.69
0.05457.90
0.04966.42
0.227930.30
0.03974.19
0.04465.39
0.376131.35

Chla <0.1
N=991
0.067910.48
0.229826.29
0.00641.04
0.06319.28
0.02503.86
0.245630.61
0.01902.80
0.03605.15
0.660049.77

0.1< Chla <3
N=21510.119719.76
0.208229.86
0.02552.55
0.06189.99
0.04546.18
0.253136.74
0.02983.30
0.03204.08
0.139621.98

Chla >3
N=18580.132516.79
0.091010.08
0.04524.68
0.03795.75
0.06269.34
0.183025.14
0.05517.41
0.05897.86
0.355047.10

5.

Summary and discussion

SGLI Chl-a algorithm was developed based on O'Reilly et al., 2000 and Hu et al., 2012 and optimized by an IOP
model adjusted to the NOMOAD data. The OC4 and OCI coefficients are follows.
OC4: 0.40451, -3.42411, 5.29717, -5.33247, 1.68959
OCI: -0.38006, 238.05110

The coefficients will be evaluated when the standard in-situ data set is revised in the future. The IOP model
constructed in this study can be used to estimate IOPs, aph, adg, and bbp.

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Acknowledgement

NOMAD data were constructed and provided by participants in the NASA SIMBIOS Program (NRA-96-MTPE04 and NRA-99-OES-09) and by voluntary contributors.