Algorithm Description Ver.0 (2011.09.30)
Algorithm Description Ver.0 加筆修正

(2011.10.10)

Algorithm Description Ver.1(2014.11.12)

Algorithm Description Ver.2(2019.3.1)

PI No. 134 Takafumi Hirata (GCOM-C/SGLI Ocean Team)
Theoretical Description of the Inherent Optical Property Algorithm
1. Derivation of the inherent optical properties (IOPs)
1.1 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) 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). Morel and Gentili(2002) showed in their Eq. 9 that the Eq. (1) can be related to the absorption coefficient at and thebackscattering coefficient of the bulk water bbt byRrs(θv,φv,z=0+,θs,φs,λ)= Rg (W, z=0,θs, φs, λ) F(θv, φv,z=0-,θs,φs,λ) [bbt (z=0-,λ)/at(z=0-,λ)](2)where Rg is a transmittance term for the interface between the above and below sea surface anddepends on the wind speed, W. For convenience, all dependencies of the variables on illumination andobservation geometries, depth, and wavelength etc in Eq. 2 are omitted hereafter, unless otherwise
specified. In addition, Rg・F will be denoted by F’ so that Eq.2 is simplified by
Rrs = F’ [bbt/at].

(3)

The absorption coefficient of the bulk seawater is decomposed into the absorption coefficients of thepure seawater (aw) and any other materials (at),a=aw+at.

(4)

Similarly, the backscattering coefficient of the bulk seawater is decomposed into the backscattering
coefficients of the pure seawater (bbw) and any other particles (bbp)
bbt=bbw+bbp.

(5)

In the following sections, an algorithm to retrieve the absorption (at) and backscattering coefficients(bbp) (and their components thereafter) will be described.
2. IOP algorithm
2.1 Derivation of the at and bbp
Substitutions of Eqs. 4 and 5 into Eq. 3 give a set of equations for wavelengths λ1 and λ2:
Rrs (λ1) a0(λ1) - F’ (λ1) bbp(λ1) = F’ (λ1) bbw(λ1) - Rrs(λ1) aw(λ1)
Rrs (λ2) a0(λ2) - F’ (λ2) bbp(λ2) = F’ (λ2) bbw(λ2) - Rrs(λ2) aw(λ2),(6)

where Rrs is obtained by satellite observation and aw and bbw are assumed known for each λ (i.e. they
are given by Morel, 1974; Pope and Fry, 1997 for example, although their values of aw and bbw may
be corrected for temperature and salinity dependencies). Eq. 6 can be solved to derive at (λ1 and λ2)
and bbp (λ1 and λ2), when (1) the wavelength dependencies of the inherent optical properties (bbp andat) and (2) F’(λ) are known.
2.2 The wavelength dependencies of the inherent optical properties
The wavelength dependency of bbp (denoted by εbb) may be modeled byεbb = bbp(λ1) /bbp(λ2) = (λ1/λ2)-m(7)where m is related to the particle size distribution and is set as a pre-defined parameter value in thepresent algorithm. The wavelength dependency of a0 is expressed by
εa = at(λ1) /at(λ2),(8)

and it is another algorithm parameter value pre-defined. According to in situ observation, εa =at(λ=490nm) /at(λ=510nm) is least variable and therefore applicable for a wide range of seawaters (Fig.
1, see Smyth et al., 2006). Since SGLI does not have 510nm, it is replaced by the 530nm. Substituting
Eqs. 7 and 8 into Eq. 6, as well as a use of Rrs(λ=490) and Rrs(λ=530) observed by the satellite, givesat (490), at (530), bbp(490) and bbp(530) for a known F’ (Determination of F’ will be described in thenext subsection). Once bbp(490) (or bbp(530) ) are obtained, substituting them into Eq. 7 gives bbp at
any wavelength λ for an “m” assumed: (e.g.)bbp(λ)= bbp(490) (λ/490)m.

(9)

When F’ is known, Eq. 9 allows us to derive at at any SGLI short wavelength λ, using Eqs. 3-5:a0(λ)=F’ (λ) [ bbw(λ) + bbp(λ) ] – aw(λ).

(10)

Fig. 1 Wavelength dependencies of the absorption coefficient of optical components determined fromin situ observation (Smyth et al., 2006). εph: phytoplankton absorption, εd: non-algal particle (NAP)absorption, εy: CDOM, εdy: NAP plus CDOM, εa: total absorption without pure sea water component.
2.3 Derivation of F’
Figure 2 shows a summary of derivation of F’ (and at and bbp). F’ is initially assumed to be acertain value. Using the initial value, Equation 6 is solved to produce initial outputs of at and bbt. Theseoutputs are then used to search for the new value of F’ from a forward radiative transfer simulation.
However, to save a computation time for this simulation, the simulations for the various conditions ofobservation geometry (θv, φv), solar geometry (θs, φs) and inherent optical properties at SGLIwavelengths were conducted to generate a Look-Up Table (LUT) of F’, in prior to the algorithm
implementation. Using the new value of F’ obtained from the LUT(or the simulation), Eq. 6 is again
solved to produce another set of at (λ) and bt (λ)(i.e. second estimates), which are then used to search
for a third, forth, … nth estimation of F’ (λ) using the same LUT. This procedure is repeated until aconvergence of at(λ) and bt (λ) is reached. Also, when a pre-fixed number of iteration is implemented,
the iteration is terminated. A value of F’ (λ) at the convergence or termination is given as F’ (λ) value
to produce final outputs of at and bbp using Eq. 6. The LUT is made as a function of θv, φv, z, θs, φs, at ,bt and λ. Note that, in the LUT, φv is defined such that a direction of wind is set to φv=0, which hasπ/2 phase difference with the solar principal plane.

Illumination andobservation Geometries

Initial value of F’&Model parameters

Radiative Transfer
Simulations (LUT)
Ocean Colour Measurements
Eq. 6

Tentative outputof IOPs

Final outputs
Fig. 2 Flow chart of the algorithm implementation

2.1 Decomposition of the IOPs of optical components from the IOPs of bulk seawater
The total absorption coefficient without pure seawater contribution at can further be decomposed by
at=aph+ady where the absorption coefficient of phytoplankton and of NAP plus chromophoric dissolved
organic matters (CDOM) are denoted as aph and ady, respectively. The decomposition gives thesimultaneous equations for two wavelengths λ1 and λ2.

ao(λ1)=aph(λ1)+ady(λ1)
ao(λ2)=aph(λ2)+ady(λ2).

(11)

In analogy to Eq. 6, Eq. 11 can be solved to obtain aph and ady at λ1 and λ2 when wavelength
dependencies of aph and ady defined by εph = aph(λ1) /aph(λ2) and εph = ady(λ1) /ady(λ2) are known. Figure
1 shows that variations in εph and εdy are least for the wavelength pair of λ1=412nm and λ2=443nm sothat their values may be applied to a wide range of water types. Therefore, εph(412, 443) and εdy(412,443) are used in the present algorithm.
Using the modeled wavelength dependency of ady, or equivalently εdy, expressed by:ady(λ)=ady(λ1)exp[-Y(λ-λ1)],(12)

ady for any SGLI short wavelength λ can be obtained using ady (413) and ady(443) derived as solutionof Eq. 11.
Rearrangement of Eq. 11 givesaph(λ)=a0(λ) - ady(λ).

(13)

Since a0(λ) and ady(λ) can be obtained for any SGLI short wavelength, Eq. 13 completes the derivationsof a0 , aph, ady and bbp at the SGLI wavelengths. Note that at and bbt can also be derived from these IOPs
using Eqs. 4 and 5. Fig. 3 summarizes the sequence ofthe IOPs retrieval.

Eq. 6

Eq. 7Eq. 10

Eq.11

Eq. 12

Eq. 13

Eqs. 4 & 5•Derive a0(λ1) and a0(λ2)•Derive bbp(λ1) and bbp(λ2)

Simultaneousdetermination of F’(λ)•Derive bbp at other λ•Derive at at other λ•Derive ady(λ1) and ady(λ2)•Derive aph(λ1) and aph(λ2)•Derive ady at other λ•Derive aph at other λ•Derive at at all λFig. 3

Sequence of IOP retrieval.

3. Algorithm evaluation
Figs. 4-6 show examples of evaluation results of the IOP algorithm, using the NOMAD data set(Werdell and Bailey, 2005) from which simultaneous measurements of Rrs and IOPs can be obtained.
The in situ Rrs is given as an input to the present IOP algorithm, and the algorithm outputs werecompared to the in situ IOPs in the data set. Also Table 1-3 below summarizes statistical results of theevaluation.

Fig. 4 Comparison between ady (adg) measured in situ and derived from the IOP algorithm.

Fig. 5 Comparison between bb measured in situ and derived from the IOP algorithm.

Fig. 6 Comparison between bb measured in situ and derived from the IOP algorithm.
Table 1. Statistical results of algorithm evaluation for ady against in situ data
Wavelength#

slope#

intercept#

r2 #

RMSE*

412

0.939

-0.111

0.802

0.342

443

0.0.906-0.145

0.781

0.219

490

0.856

-0.258

0.741

0.118

510

0.836

-0.307

0.723

0.091

#log scale, *Liner scale

Table 2. Statistical results of algorithm evaluation for aph against in situ data
Wavelength#

slope#

intercept#

r2 #

RMSE*

412

0.815

-0.292

0.724

0.484

443

0.796

-0.2870.7610.123

490

0.820

-0.180

0.722

0.089

510

0.748

-0.209

0.732

0.076

#log scale, *Liner scale

Table 3. Statistical results of algorithm evaluation for bb against in situ data
Wavelength

slope#

intercept#

r2 #

RMSE*

412

0.811

-0.2380.411

0.0049443

0.784-0.2790.421

0.0049490

0.748-0.3480.430

0.0048510

0.729-0.3860.430

0.0047#log scale, *Liner scale

References
Model A., D. Antoine and B. Gentili, Bidirectional reflectance of oceanic waters: accounting for
Raman emission and varying particle scattering phase function, Appl. Opt., 41, 6289-6306, 2002.
Morel, A. and B. Gentili, Diffuse reflectance of oceanic waters III. Implication of bidirectionality forthe remote-sensing problem, Appl. Opt., 35, 4860-4862, 1996.
Pope R. M. and E. S. Fry, Absorption spectrum (380-700nm) of pure water. II. Integrating cavity
measurements, Appl. Opt., 36, 8710-8722, 1997.
Morel,A., Optical properties of pure seawater, in Optical Aspects of Oceanography, N. G. Jerlov andE. Steemann Nielson, ed., Academic Press, pp. 1-24, 1974.
Smyth, T.J., G. F. Moore, T. Hirata, J. Aiken, Semianalytic model for the derivation of ocean color
inherent optical properties: description, implementation, and performance assessment, Appl. Opt., 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