Optical closure in a complex coastal environment: particle effects

Grace Chang; Andrew Barnard; J. Ronald V. Zaneveld

doi:10.1364/AO.46.007679

Optical closure in a complex coastal environment: particle effects

Grace Chang, Andrew Barnard, and J. Ronald V. Zaneveld

Applied Optics
Vol. 46,
Issue 31,
pp. 7679-7692
(2007)
•https://doi.org/10.1364/AO.46.007679

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Grace Chang, Andrew Barnard, and J. Ronald V. Zaneveld, "Optical closure in a complex coastal environment: particle effects," Appl. Opt. 46, 7679-7692 (2007)

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Related Topics
Table of Contents Category
- Remote Sensing and Sensors
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Oceanic optics (010.4450)
- Remote sensing and sensors (280.0280)

About this Article
History
- Original Manuscript: April 23, 2007
- Revised Manuscript: September 5, 2007
- Manuscript Accepted: September 6, 2007
- Published: October 25, 2007
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Abstract

An optical dataset was collected on a mooring in the Santa Barbara Channel. Radiative transfer modeling and statistical analyses were employed to investigate sources of variability of in situ remote sensing reflectance $[r_{r s} (λ, 4 m)]$ and the f∕Q ratio. It was found that the variability of inherent optical properties and the slope of the particle size distribution (ξ) were strongly related to the variability of $r_{r s} (λ, 4 m)$ . The variability of f∕Q was strongly affected by particle type characteristics. A semianalytical radiative transfer model was applied and effects of variable particle characteristics on optical closure were evaluated. Closure was best achieved in waters composed of a mixture of biogenic and minerogenic particles.

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Symbol	Units	Definition
$a_{d}$ (λ)	m⁻¹	Spectral detrital absorption coefficient
a _dg(λ)	m⁻¹	Spectral detrital plus gelbstoff absorption coefficient
a _g(λ)	m⁻¹	Spectral gelbstoff absorption coefficient
a _p(λ)	m⁻¹	Spectral particulate absorption coefficient
a _ph(λ)	m⁻¹	Spectral phytoplankton absorption coefficient
a _pg(λ)	m⁻¹	Spectral particulate plus gelbstoff absorption coefficient
a _t(λ)	m⁻¹	Spectral total absorption coefficient
b _bp(λ)∕b _p(λ)		Spectral backscattering ratio
b _bp(λ)	m⁻¹	Spectral particulate backscattering coefficient
b _bt(λ)	m⁻¹	Spectral total backscattering coefficient
b _p(λ)	m⁻¹	Spectral particulate scattering coefficient
b _t(λ) or b	m⁻¹	Spectral total scattering coefficient
c _g(λ)	m⁻¹	Spectral gelbstoff attenuation coefficient
c _p(λ)	m⁻¹	Spectral particulate attenuation coefficient
c _pg(λ)	m⁻¹	Spectral particulate plus gelbstoff attenuation coefficient
c _t(λ) or c(λ)	m⁻¹	Spectral total attenuation coefficient
Chl	μg l⁻¹	Chlorophyll concentration
E _d(λ, 0⁺)	W m⁻² nm⁻¹	Spectral downwelling irradiance just above the sea surface
E _d(λ, z)	W m⁻² nm⁻¹	Spectral downwelling irradiance at a depth z
f∕Q or f(λ)∕Q(λ)	sr⁻¹	A parameter that depends on the shape of the upwelling light field and the volume scattering function where Q or Q(λ) is the ratio of irradiance to radiance at the same depth
g ₀ and g ₁	sr⁻¹	g-constants representing the angular dependency of the underwater light field empirically derived by Lee et al. [34]
K _L(λ, z) or K _L	m⁻¹	Spectral diffuse attenuation coefficient for upwelling radiance at a depth z
L _u(λ, z)	W m⁻² nm⁻¹ sr⁻¹	Spectral upwelling radiance at a depth z
L _w(λ)	W m⁻² nm⁻¹ sr⁻¹	Spectral water-leaving radiance
n		Number of data points
n _p		Real part of the index of refraction of particles
r _rs(λ, 4 m) or r _rs(λ)	sr⁻¹	Spectral remote sensing reflectance at a depth z, where z = 4 m
R _rs(λ)	sr⁻¹	Spectral remote sensing reflectance just above the sea surface
z	m	Depth below the sea surface
γ		Slope of the particulate attenuation spectrum
λ	nm	Wavelength of light
ω₀(λ) or ω₀		Ratio of particulate scattering to particulate plus gelbstoff attenuation
ξ		Slope of the particle size distribution

Statistic	Deployment	a _pg(530)	b _p(530)	c _pg(530)	b _bp(532)	$\frac{b_{b p} (532)}{b_{p} (530)}$	ξ	n _p	Chl

Mean	2	0.0732	1.5147	1.5879	0.0141	0.0102	2.4924	1.1157	1.4963
	3	0.1129	0.8313	0.9443	0.0160	0.0191	2.4954	1.1742	2.8725
	4	0.1914	1.7909	1.9824	0.0334	0.0168	2.4986	1.1601	1.4307
	5	0.1247	1.2261	1.3508	0.0209	0.0166	2.4965	1.1607	4.1408
Median	2	0.0695	1.4811	1.5483	0.0093	0.0069	2.4924	1.1013	1.3885
	3	0.1110	0.8150	0.9304	0.0149	0.0184	2.4954	1.1713	2.7237
	4	0.1705	1.0784	1.2463	0.0172	0.0177	2.4986	1.1676	1.1773
	5	0.1243	1.1936	1.3158	0.0192	0.0166	2.4966	1.1621	3.2670
Minimum	2	0.0412	0.3617	0.4127	0.0027	0.0016	2.4732	1.0464	0.2334
	3	0.0653	0.4306	0.5101	0.0079	0.0121	2.4928	1.1366	0.7055
	4	0.0116	0.2140	0.2314	0.0022	0.0027	2.4690	1.0611	0.2093
	5	0.0257	0.2623	0.3075	0.0039	0.0076	2.4884	1.1064	0.5113
Maximum	2	0.2114	4.4790	4.6614	0.0972	0.0624	2.4993	1.3301	4.8419
	3	0.2397	1.5559	1.7449	0.0437	0.0295	2.4970	1.2208	8.7254
	4	0.8708	16.4447	17.1821	0.2052	0.0381	2.5171	1.2533	7.4860
	5	0.3938	2.8819	3.1019	0.0653	0.0476	2.5011	1.2855	27.451
Standard	2	0.0195	0.6393	0.6407	0.0135	0.0090	0.0033	0.0505	0.6491
Deviation	3	0.0243	0.1526	0.1683	0.0048	0.0032	0.0007	0.0154	1.3058
	4	0.1460	2.0650	2.1842	0.0423	0.0059	0.0043	0.0332	1.0832
	5	0.0425	0.3938	0.4278	0.0098	0.0040	0.0018	0.0205	2.9201

IOP	Water Type	412 nm	440 nm	488 nm^b	510 nm	532 nm	555 nm
a _l(λ)	Deployment 2	0.12	0.14	0.23	0.25	0.26	0.22
		−5%	−5%	6%	7%	11%	5%
	Deployment 3	0.32	0.48	0.63	0.61	0.56	0.41
		+18%	+13%	+20%	+19%	+16%	+8%
	Deployment 4	0.69	0.72	0.73	0.74	0.75	0.77
		+3%	+4%	+1%	−9%	−9%	−11%
	Deployment 5	0.05	0.01	0.00	0.00	0.00	0.00
		−0.1%	−10%	−7%	−6%	−4%	−0.1%
	Turbid inorganic	0.10	0.26	0.20	0.23	0.30	0.36
		−39%	−33%	−31%	−29%	−25%	−19%
		40%	35%	34%	32%	28%	23%
	Turbid organic	0.41	0.31	0.29	0.31	0.35	0.31
		+14%	+21%	+26%	+20%	+18%	+12%
		28%	33%	36%	30%	26%	19%
	Turbid mixture	0.78	0.75	0.80	0.75	0.73	0.77
		+0.5%	−1%	+1%	−0.1%	−0.1%	−6%
		17%	20%	22%	21%	21%	14%
	Clear mixture	0.54	0.64	0.70	0.69	0.72	0.73
		+30%	+29%	+28%	+20%	+16%	+7%
		35%	33%	31%	24%	19%	12%
b _bt(λ)	Deployment 2			0.20		0.19
				17%		−3%
	Deployment 3			0.28		0.28
				18%		−13%
	Deployment 4			0.84		0.84
				−31%		−52%
	Deployment 5			0.37		0.12
				−41%		−61%
	Turbid inorganic			0.58		0.50
				+13%		−18%
				29%		32%
	Turbid organic			0.45		0.43
				+40%		+19%
				50%		40%
	Turbid mixture			0.85		0.88
				+37%		+19%
				46%		33%
	Clear mixture			0.61		0.65
				+57%		+31%
				61%		40%

Symbol	Units	Definition
$a_{d}$ (λ)	m⁻¹	Spectral detrital absorption coefficient
a _dg(λ)	m⁻¹	Spectral detrital plus gelbstoff absorption coefficient
a _g(λ)	m⁻¹	Spectral gelbstoff absorption coefficient
a _p(λ)	m⁻¹	Spectral particulate absorption coefficient
a _ph(λ)	m⁻¹	Spectral phytoplankton absorption coefficient
a _pg(λ)	m⁻¹	Spectral particulate plus gelbstoff absorption coefficient
a _t(λ)	m⁻¹	Spectral total absorption coefficient
b _bp(λ)∕b _p(λ)		Spectral backscattering ratio
b _bp(λ)	m⁻¹	Spectral particulate backscattering coefficient
b _bt(λ)	m⁻¹	Spectral total backscattering coefficient
b _p(λ)	m⁻¹	Spectral particulate scattering coefficient
b _t(λ) or b	m⁻¹	Spectral total scattering coefficient
c _g(λ)	m⁻¹	Spectral gelbstoff attenuation coefficient
c _p(λ)	m⁻¹	Spectral particulate attenuation coefficient
c _pg(λ)	m⁻¹	Spectral particulate plus gelbstoff attenuation coefficient
c _t(λ) or c(λ)	m⁻¹	Spectral total attenuation coefficient
Chl	μg l⁻¹	Chlorophyll concentration
E _d(λ, 0⁺)	W m⁻² nm⁻¹	Spectral downwelling irradiance just above the sea surface
E _d(λ, z)	W m⁻² nm⁻¹	Spectral downwelling irradiance at a depth z
f∕Q or f(λ)∕Q(λ)	sr⁻¹	A parameter that depends on the shape of the upwelling light field and the volume scattering function where Q or Q(λ) is the ratio of irradiance to radiance at the same depth
g ₀ and g ₁	sr⁻¹	g-constants representing the angular dependency of the underwater light field empirically derived by Lee et al. [34]
K _L(λ, z) or K _L	m⁻¹	Spectral diffuse attenuation coefficient for upwelling radiance at a depth z
L _u(λ, z)	W m⁻² nm⁻¹ sr⁻¹	Spectral upwelling radiance at a depth z
L _w(λ)	W m⁻² nm⁻¹ sr⁻¹	Spectral water-leaving radiance
n		Number of data points
n _p		Real part of the index of refraction of particles
r _rs(λ, 4 m) or r _rs(λ)	sr⁻¹	Spectral remote sensing reflectance at a depth z, where z = 4 m
R _rs(λ)	sr⁻¹	Spectral remote sensing reflectance just above the sea surface
z	m	Depth below the sea surface
γ		Slope of the particulate attenuation spectrum
λ	nm	Wavelength of light
ω₀(λ) or ω₀		Ratio of particulate scattering to particulate plus gelbstoff attenuation
ξ		Slope of the particle size distribution

Statistic	Deployment	a _pg(530)	b _p(530)	c _pg(530)	b _bp(532)	$\frac{b_{b p} (532)}{b_{p} (530)}$	ξ	n _p	Chl

Mean	2	0.0732	1.5147	1.5879	0.0141	0.0102	2.4924	1.1157	1.4963
	3	0.1129	0.8313	0.9443	0.0160	0.0191	2.4954	1.1742	2.8725
	4	0.1914	1.7909	1.9824	0.0334	0.0168	2.4986	1.1601	1.4307
	5	0.1247	1.2261	1.3508	0.0209	0.0166	2.4965	1.1607	4.1408
Median	2	0.0695	1.4811	1.5483	0.0093	0.0069	2.4924	1.1013	1.3885
	3	0.1110	0.8150	0.9304	0.0149	0.0184	2.4954	1.1713	2.7237
	4	0.1705	1.0784	1.2463	0.0172	0.0177	2.4986	1.1676	1.1773
	5	0.1243	1.1936	1.3158	0.0192	0.0166	2.4966	1.1621	3.2670
Minimum	2	0.0412	0.3617	0.4127	0.0027	0.0016	2.4732	1.0464	0.2334
	3	0.0653	0.4306	0.5101	0.0079	0.0121	2.4928	1.1366	0.7055
	4	0.0116	0.2140	0.2314	0.0022	0.0027	2.4690	1.0611	0.2093
	5	0.0257	0.2623	0.3075	0.0039	0.0076	2.4884	1.1064	0.5113
Maximum	2	0.2114	4.4790	4.6614	0.0972	0.0624	2.4993	1.3301	4.8419
	3	0.2397	1.5559	1.7449	0.0437	0.0295	2.4970	1.2208	8.7254
	4	0.8708	16.4447	17.1821	0.2052	0.0381	2.5171	1.2533	7.4860
	5	0.3938	2.8819	3.1019	0.0653	0.0476	2.5011	1.2855	27.451
Standard	2	0.0195	0.6393	0.6407	0.0135	0.0090	0.0033	0.0505	0.6491
Deviation	3	0.0243	0.1526	0.1683	0.0048	0.0032	0.0007	0.0154	1.3058
	4	0.1460	2.0650	2.1842	0.0423	0.0059	0.0043	0.0332	1.0832
	5	0.0425	0.3938	0.4278	0.0098	0.0040	0.0018	0.0205	2.9201

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