Algorithm Description Ver.1.1 (2016.12.19)
Algorithm Description Ver.1.2 (2019.3.31)
PI No. 134 Takafumi Hirata (GCOM-C/SGLI Ocean Team)
CIs: 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 inprior 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) can be related to the absorption coefficient at and the backscattering coefficient of thebulk 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’ sothat 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(5)

Among the components, aph and ad+ag(=adg), thus not ad and ag, can be derived from theSGLI/GCOM-C1 IOP algorithm (see Smyth et al., 2006 as wel as ATBD for IOPs). Hence, we
assume that adg are known in this document. A Practical problem here is to decompose adg into ad andag to retrieve 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
0o60oE

120oE

180oW

120oW

60oW

0oFigure 1 NOMAD data distribution
3. Algorithm
Since the IOP algorithm retrieves adg at 412, 443 and 490 relatively well than other longer
wavebands, the former wavelengths will be considered below. From Eq. 5, we have:ag=adg – ad(5)Considering that adg varies orders of magnitude over global scale and that adg derived from the IOP

model would include some uncertainty in practice, we assume that there is the following
relationship between adg measured in situ (adg(measured)) and adg derived from the IOP model(adg(measured)) so that
log10(ag (measured)) =g*log10(adg (derived)) + h(7)where g and h are a slope and an intercept obtained from a comparison between log10(ag (measured))and log10(adg (derived)) and depends also on instrument used to obtain log10(adg (derived)) (if it is asatellite or in situ instrument).
Figure 2 shows a comparison between ag measured in situ (ag(true)) and derived from Eq. 7(ag(reproduced)), using the adg derived from the IOP algorithm that was applied to the in situ
radiometry coincided with ag(true).

110443 (nm): log10(Y)=0.953 log10(X) −0.075 (r2=0.747)−110−210ga (443)(reprudced) [1/m]010−310−410 −31010−2−110ag(443)(true) [1/m]100101Fig. 3 Relationship between ag(443nm) measured in situ and derived(reproduced) using Eq. 7.
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