Algorithm Description Ver.1.1 (2016.12.19)
Algorithm Description Ver.1.2 (2019.3.31)
Algorithm Description Ver.2 (2020.3.31)
PI:Takafumi Hirata (GCOM-C/SGLI Ocean Team)
CI: Yohei Yamashita
Derivation of the absorption coefficient of Colourd Dissolved Organic Matter (CDOM)
1. Physics of the problem
The IOP algorithm assumes that the remote sensing reflectance (Rrs) just above the sea surface(denoted by z=0+, where z represents a depth), or the water-leaving reflectance (ρ), is obtained in prior
to its implementation.
The Rrs for a wavelength λ is defined byRrs(θv, φv, z=0+, θs, φs, λ) = Lw(θv, φv, z=0+, θs, φs, λ) / Ed(z=0+, θs, φs,λ)(1)where Lw and Ed are the radiance and the downward plane irradiance at the observation angle (zenithangle θv, azimuth angle, φv) and the solar angle (zenith angle θs, azimuth angle φs). The water-leaving
reflectance ρ can be obtained by ρ = π Rrs. Morel and Gentili (1993, 1996) showed that the Eq. (1) canbe related to the absorption coefficient at and the backscattering coefficient of the bulk water bbt byRrs (θv, φv, z=0+, θs, φs, λ)= R (W, θs, φs, λ) F(θv, φv, z=0-, θs, φs, λ) [bbt (z=0-, λ)/at(z=0-, λ)] (2)where R is a transmittance from water to air and W denotes the wind speed. For convenience, alldependencies of the variables on illumination and observation geometries, depth, wavelength etc in
Eq. 2 are omitted hereafter, unless otherwise specified. In addition, R x F will be denoted by F’ so that
Eq.2 is simplified byRrs = F’ [bbt/at].

(3)

The absorption coefficient of the bulk seawater is decomposed into the absorption coefficients of
optically active components. It is a common exercise to define those components as pure seawater(aw) , phytoplankton (aph), non-algal particles NAP (ad), and CDOM(ag), so that
at=aw+aph+adg(4)whereadg=ad+ag (ad>0, ag>0)(5)

Among the components, aph and ad+ag(=adg), thus not ad and ag, can be derived from the SGLI/GCOMC1 IOP algorithm (see Smyth et al., 2006 as wel as ATBD for the IOP algorithm). Hence, we assume
that adg are known in this document. A practical problem here is to decompose adg into ad and ag toretrieve ag.
2. Dataset
A global in situ dataset was used (Werdell and Bailey 2005) to derive ag from adg. Figure 1 shows thedata distribution of the dataset.

o80 N

40oN
0oo40 S

80oS
0o

60oE

120oE

180oW

120oW

60oW0oFigure 1 NOMAD data distribution
3. Algorithm
The CDOM algorithm here takes the adg as an input. Thus, the algorithm decomposes adg into ag andad in practice. Since the IOP algorithm retrieves adg relatively well at shorter wavelengths than otherlonger wavelengths (Smyth et al., 2006), the former wavelengths will be considered below to deriveag. Considering that (i) an optical separation of ag from adg is challenging as they often have a similar
spectrum (IOCCG, 2018) and (ii) adg derived from the IOP model would in practice include someuncertainty anyway so that a fuzzy algorithm which can accepts input error may be desired , our choice
is to derive ag from adg using an empirical (or statistical) relationship between ag and adg rather thanusing an optical theory: the statistical coefficients can wrap up the above-mentioned uncertainty while
bypassing the theoretical challenge. Figure 2 show the empirical relationship between ag and adg for
412nm obtained from the in situ data. While the simple statistical model of ag=s*(adg)k (i.e. a linear
regression model in log-log scale) shows a better r2, it also exceeds 1:1 line at smaller end of adg sothat ag > adg (see a circle in Figure 2). When satellite-derived adg is even smaller than the smallest adg
found in the present in situ dataset (which is likely to happen because a satellite data usually covers alarger spatial domain than in situ observation), a resultant ag derived from the fit would violate Eq. 5.
Hence, we employ the other statistical model that never exceeds 1:1 line:(∗*+, (-..)

𝑎" (411) = /01∗*+, (-..)+𝐷(6)

where A=1.5625, B=1.7647, C=0.6058 and D=-0.0007218 which are determined by the least squarefit. Although Eq. 6 reduces r2 statistics by 0.07 (i.e. data variance of 7% is less explained) whencompared to the ag=s*(adg)k , also shows a better fit at the higher end of adg than g=s*(adg)k (squared

Absorption coefficient of CDOM, ag (411) [m-1]

area in Figure 2).

(Old fit)!" = $ ∗ (!'")k(New fit)+,!" = - . /∗*+1

r2=0.98, p<0.01, N=755)∗*

r2=0.91, p<0.01, N=755+,

NASA NOMAD dataset

2.0
1.5

Liner scale

1.0

1:1

0.5

0.5

1.0 1.52.0

2.5 3.0

Absorption coefficient of CDOM+NAP, adg (411) [m-1]
Figure 2. In situ relationship between ag (412) and adg (411).

Note that Eq. 6 (with the coefficient values mentioned above) leads to ag=-0.0007218 < 0, when adg=0.
Although this also does not make sense, the value of ag(412)=-0.0007218 is either lower than detection
limit of an instrument or within an uncertainty of the measurement.
Using the actual SGLI/GCOM-C satellite data, ag was derived and matched up with ag measured insitu (Table 1). Match up was made in such a way that satellite data do not deviate more than +/- 3
hours from the in situ observation time. A 3x3 satellite pixel window is selected (Werdell and Bailey,2005) so that a pixel nearest to the exact latitude and longitude of an in situ measurement is located at
the center of the window, and an average of ag within the window is calculated to represent the satellite
ag. Then the satellite ag is compared to the ag measured in situ. Although statistical conclusion cannot
be drawn due to a lack of a sufficient number of measurements, the differences between the satelliteand in situ ag (in linear scale) are between -89.2% and +98.3%.
Table 1

Reference:
Smyth, T. J., G.F. Moore, T. Hirata, J. Aiken, Semianalytical model for the derviation of ocean colour
inherent optical properties: description, implementation, and performance assessment, Applied Optics,
45, 8116-8131, 2006.
Werdell, P. J. and S. W. Bailey, An improved in situ data set for bio-optical algorithm development
and ocean color satellite validation, Remote Sens. Environ., 98, 122-140, 2005