Algorithms to retrieve Inherent Optical Properties

R_rs(&lambda), &rho_w(&lambda) &asymp b_b(&lambda) / [a(&lambda) + b_b(&lambda)], where

a(&lambda) = a_w(&lambda) + a_dg(&lambda) + a_ph(&lambda), and

b_b(&lambda) = b_bw(&lambda) +b_bp(&lambda)

coefficients often defined as product of dimensionless basis vector (spectral shape) and magnitude (M), e.g., a_dg(&lambda) = M_dg a_dg^*(&lambda)
basis vectors used in the following algorithms are graphically presented below

reference	inversion	form	b_bp	a_dg	a_ph
Maritorena et al. 2002 (GSM)	L-M	G88	b_bp(&lambda_r) [&lambda/&lambda_r]^-n n = 1.0337	a_dg(&lambda_r) exp(-S [&lambda - &lambda_r]) S = 0.0206	chl aph* optimized aph* (SA)
Hoge et al. 1996 (LMI)	matrix	G88	b_bp(&lambda_r) [&lambda/&lambda_r]^-n n = 0.8 R_rs(490)/R_rs(555) + 0.2	a_dg(&lambda_r) exp(-S [&lambda - &lambda_r]) S = 0.018	Gaussian @ 443 fwhm (&sigma) = 70 nm a_ph(&lambda) = a_ph(&lambda_r) exp(u) u = [&lambda_r²+886(&lambda - &lambda_r)-&lambda²] / 2 &sigma²
Boss and Roesler 2006 Wang et al. 2005	matrix	G88	b_bp(&lambda_r) [&lambda/&lambda_r]^-n 0 < n < 2	a_dg(&lambda_r) exp(-S [&lambda - &lambda_r]) 0.01 < S < 0.02	Ciotti et al. 2002 0 < S_f < 1
Lee et al. 2002 (QAA)	algebraic	G88	b_bp(&lambda_r) [&lambda/&lambda_r]^-n n = 2.2 (1 - 1.2 exp[-0.9 R_rs(443)/R_rs(555)])	a_dg(&lambda_r) exp(-S [&lambda - &lambda_r]) S = 0.015	a - a_dg - a_w
Smyth et al. 2006 (PML)	spectral slope algebraic	&pi &real f/Q b_b/a	b_bp(&lambda_r) [&lambda/&lambda_r]^-n n = 0.5	a_dg(&lambda_r) exp(-S [&lambda - &lambda_r]) S = 0.014	a - a_dg - a_w
Pinkerton et al. 2006 (NIWA)	spectral slope algebraic	&pi &real f/Q b_b/a	b_{b~ b(490) n n = 0.841 X² - 2.806 X + 2.965 X = (&lambda / 490) b_{b~ = 0.01756}}	NA	NA
Loisel and Stramski 2000	algebraic	&pi &real f/Q b_b/a	fcn[&rho_w(&lambda), K_d(&lambda), solz, &eta(&lambda)]	NA	NA

GSM

n, S, and a_ph* predefined; optimized (simulated annealing) to in situ data
solution via Levenberg-Marquardt nonlinear inversion

LMI

n, S, and a_ph* predefined
only 412, 490, and 555-nm considered
solution via 3 x 3 matrix inversion

Boss and Roesler 2006

n, S, and a_ph* (through S_f) ranges predefined
412 through 555-nm considered
solution via 3 x 5 matrix inversion
multiple solutions achieved using ranges of n, S, and a_ph*
median of viable solutions retained and uncertainties reported

QAA

a(555) from R_rs(443,490,555,640)
b_bp(555) from a(555) and R_rs(555)
n estimated using R_rs(443,555)
b_bp(&lambda) from n and b_bp(555)
a(&lambda) from b_bp(&lambda) and R_rs(&lambda)
a_ph(412) / a_ph(443) [ &zeta ] from R_rs(443,555)
a_dg(412) / a_dg(443) [ &xi ] from S
a_dg(443) from a(412,443), &zeta and &xi (algebraic)
a_dg(&lambda) from a_dg(443) and S
a_ph(&lambda) = a(&lambda) - a_dg(&lambda) - a_w(&lambda)

PML

n, S, and, &epsilon predefined
F (= &pi &real f/Q) defined via a, b, and viewing geometry in HydroLight LUT
F(&lambda) initialized using guess of a(&lambda) and b(&lambda)
b_b(510) from &epsilon_a(490,510), &epsilon_bb(490,510), F(490,510), and &rho_w(490,510)
b_b(&lambda) from b_b(510) and n
a(&lambda) from b_b(&lambda), F(&lambda), and &rho_w(&lambda)
updated F(&lambda) from a(&lambda) and b(&lambda) (= b_b(&lambda) / 0.01756)
iterate until F(&lambda) remains stable
a_dg(412) from &epsilon_dg(412,443), &epsilon_ph(412,443), and a(412,443)
a_dg(&lambda) from a_dg(412) and S
a_ph(&lambda) = a(&lambda) - a_dg(&lambda) - a_w(&lambda)

NIWA

a(&lambda) and b_b(&lambda) only (natively)
n and b_b^~ (= 0.01756) predefined
F (= &real f/Q) defined via a, b, and viewing geometry in HydroLight LUT
iterate on F(&lambda) and b(&lambda) until F(&lambda) stabilizes, with initial guess for b(&lambda), b_b^~, a_w(&lambda), and &rho_w(&lambda)
"lowest" b(490) defined as greatest of b(443) > b(490) > b(510)
define 15-element array of b(490) from "lowest" value to upper limit 60 ...
for each element: iterate on a(&lambda) and F(&lambda) until a(&lambda) stabilizes, with F(&lambda) initialized as 0.02, n, b_b^~, and &rho_w(&lambda)
for each element: retain all b(490) that yield a(&lambda) that satisfy 1.32 < &epsilon_a(490,510) < 1.58
final b(490) is geometric mean of highest and lowest retained values
final b(&lambda) and b_b(&lambda) from n and b_b^~
iterate on F(&lambda) and a(&lambda) until a(&lambda) stabilizes, with F(&lambda) initialized as last calculated value, final b_b(&lambda), and &rho_w(&lambda)

Loisel and Stramski 2000

a(&lambda) and b_b(&lambda) only (natively)
developed via radiative transfer simulation using infinitely deep ocean, optically homogeneous water column, and flat sea surface
does not assume spectral shapes for a(&lambda) or b_b(&lambda)
&rho(&lambda) from R_rs(&lambda,solz) LUT
K_d(&lambda) from R_rs(443,555,solz) LUT
b_b(&lambda) from K_d(&lambda), &eta (= b_w/b), and &mu_w (via solz)
&eta initialized as 0.05, then iterated upon using b(&lambda) = b_b(&lambda) / 0.0183
a(&lambda) from K_d(&lambda), &rho(&lambda), and solz
can adjust for Raman scattering

IOP spectral shapes

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Curator: OceanColor Webmaster

Authorized by: gene carl feldman

Updated: 14 November 2008