Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering

Hubert Loisel; Dariusz Stramski

doi:10.1364/AO.39.003001

Applied Optics
Vol. 39,
Issue 18,
pp. 3001-3011
(2000)
•https://doi.org/10.1364/AO.39.003001

Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering

Hubert Loisel and Dariusz Stramski

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Hubert Loisel and Dariusz Stramski, "Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering," Appl. Opt. 39, 3001-3011 (2000)

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Abstract

By means of radiative transfer simulations we developed a model for estimating the absorption a, the scattering b, and the backscattering b _b coefficients in the upper ocean from irradiance reflectance just beneath the sea surface, R(0^-), and the average attenuation coefficient for downwelling irradiance, 〈K _d〉₁, between the surface and the first attenuation depth. The model accounts for Raman scattering by water, and it does not require any assumption about the spectral shapes of a, b, and b _b. The best estimations are obtained for a and b _b in the blue and green spectral regions, where errors of a few percent to <10% are expected over a broad range of chlorophyll concentration in water. The model is useful for satellite ocean color applications because the model input, R(0^-) and 〈K _d〉₁, can be retrieved from remote sensing and the model output, a and b _b, is the major determinant of remote-sensing reflectance.

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Equations (23)

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Symbol	Definition	Unit
a	Absorption coefficient	m^-1
β(ψ)	Volume scattering function	m^-1 sr^-1
$\bar{β (ψ)}$	Scattering phase function [=β(ψ)/b]	sr^-1
$\bar{β_{w} (ψ)}$	Molecular-scattering phase function [=β_w(ψ)/b _w]	sr^-1
$\bar{β_{p} (ψ)}$	Particle-scattering phase function [=β_p(ψ)/b _p]	sr^-1
b	Scattering coefficient	m^-1
b _w	Molecular-scattering coefficient	m^-1
b _p	Particle-scattering coefficient	m^-1
c	Beam attenuation coefficient (=a + b)	m^-1
b _b	Backscattering coefficient	m^-1
η	Ratio of molecular scattering to total scattering (=b _w/b)
ω₀	Single-scattering albedo (=b/c)
θ₀	Solar zenith angle in air
μ_w	Cosine of solar zenith angle in water
λ	Wavelength of light in vacuum	nm
τ_a(550)	Aerosol optical thickness at 550 nm
Chl	Chlorophyll concentration	mg m^-3
z	Geometrical depth	m
z ₁	First attenuation depth	m
E _u	Upwelling irradiance on a horizontal surface	W m^-2
E _d	Downwelling irradiance on a horizontal surface	W m^-2
K _d	Vertical attenuation coefficient for E _d (=-d ln E _d/dz)	m^-1
〈K _d〉₁	Average K _d within the layer between the surface and z ₁	m^-1
R	Irradiance reflectance (=E _u/E _d)
ΔR	Contribution to irradiance reflectance associated with Raman scattering
R ^e	Irradiance reflectance in the absence of Raman scattering

IOP	Eqs.	Average Error, 0° < θ₀ < 75°	Maximum Error, 0° < θ₀ < 75°	Average Error, 0° < θ₀ < 60°	Maximum Error, 0° < θ₀ < 60°
a	(11)	3.3	15	2.4	6.5
b	(13)	11	30	8.5	23
b	(14)	16	35	12	26
b _b ^d	(17) and (13)	7.6	26	5.9	20
b _b	(17) and (14)	8.5	27	6.1	20

Symbol	Definition	Unit
a	Absorption coefficient	m^-1
β(ψ)	Volume scattering function	m^-1 sr^-1
$\bar{β (ψ)}$	Scattering phase function [=β(ψ)/b]	sr^-1
$\bar{β_{w} (ψ)}$	Molecular-scattering phase function [=β_w(ψ)/b _w]	sr^-1
$\bar{β_{p} (ψ)}$	Particle-scattering phase function [=β_p(ψ)/b _p]	sr^-1
b	Scattering coefficient	m^-1
b _w	Molecular-scattering coefficient	m^-1
b _p	Particle-scattering coefficient	m^-1
c	Beam attenuation coefficient (=a + b)	m^-1
b _b	Backscattering coefficient	m^-1
η	Ratio of molecular scattering to total scattering (=b _w/b)
ω₀	Single-scattering albedo (=b/c)
θ₀	Solar zenith angle in air
μ_w	Cosine of solar zenith angle in water
λ	Wavelength of light in vacuum	nm
τ_a(550)	Aerosol optical thickness at 550 nm
Chl	Chlorophyll concentration	mg m^-3
z	Geometrical depth	m
z ₁	First attenuation depth	m
E _u	Upwelling irradiance on a horizontal surface	W m^-2
E _d	Downwelling irradiance on a horizontal surface	W m^-2
K _d	Vertical attenuation coefficient for E _d (=-d ln E _d/dz)	m^-1
〈K _d〉₁	Average K _d within the layer between the surface and z ₁	m^-1
R	Irradiance reflectance (=E _u/E _d)
ΔR	Contribution to irradiance reflectance associated with Raman scattering
R ^e	Irradiance reflectance in the absence of Raman scattering

IOP	Eqs.	Average Error, 0° < θ₀ < 75°	Maximum Error, 0° < θ₀ < 75°	Average Error, 0° < θ₀ < 60°	Maximum Error, 0° < θ₀ < 60°
a	(11)	3.3	15	2.4	6.5
b	(13)	11	30	8.5	23
b	(14)	16	35	12	26
b _b ^d	(17) and (13)	7.6	26	5.9	20
b _b	(17) and (14)	8.5	27	6.1	20

Estimation of the inherent optical properties of natural waters from the irradiance attenuation coefficient and reflectance in the presence of Raman scattering

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Tables (2)

Equations (23)

Applied Optics

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