Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color

Peng Wang; Emmanuel S. Boss; Collin Roesler

doi:10.1364/AO.44.004074

Applied Optics
Vol. 44,
Issue 19,
pp. 4074-4085
(2005)
•https://doi.org/10.1364/AO.44.004074

Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color

Peng Wang, Emmanuel S. Boss, and Collin Roesler

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Peng Wang, Emmanuel S. Boss, and Collin Roesler, "Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color," Appl. Opt. 44, 4074-4085 (2005)

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Abstract

We present a method to quantify the uncertainties in the in-water constituent absorption and backscattering coefficients obtained from an inversion of remotely sensed reflectance (r_rs). We first find a set of positive inversion solutions within a given uncertainty range around the values of the inverted r_rs. The uncertainties of the solutions are then computed based on the statistics of these solutions. We demonstrate the uncertainty calculation algorithm using a specific semianalytic inversion model applied to both a field and a simulated data set. When the associated uncertainties are taken into account, the inverted parameters are generally within the uncertainties of the measured (or simulated) parameters, highlighting the success of the inversion and the method to obtain uncertainties. The specific inversion we use, however, fails to retrieve two spectral parameters within a usable range. The method presented is general and can be applied to all existing semianalytical inversion algorithms.

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Compared Quantity	Dynamic Range (m⁻¹)	Median Relative Difference (%)	95% Relative Difference (%)	Median Absolute Difference (m⁻¹)	95% Absolute Difference (m⁻¹)	R	Percentage of the Data Inside 90% Confidence Interval
a_p+CDOM(410)	0.0095 ∼ 4.53	8.95	37.9	0.0194	0.671	0.988	82.9
a_p+CDOM(440)	0.0095 ∼ 3.17	7.75	30.9	0.0138	0.438	0.989	83.1
a_p+CDOM(490)	0.0051 ∼ 1.92	6.78	21.8	0.0047	0.157	0.992	85.8
b_b_p(550)	0.00052 ∼ 0.13	7.55	15.9	0.0006	0.0082	0.993	56.8
a_ph(410)	0.0034 ∼ 0.42	20.5	63.4	0.0068	0.0977	0.911	84.8
a_ph(440)	0.0056 ∼ 0.42	19.8	61.2	0.0092	0.134	0.937	80.6
a_ph(490)	0.0031 ∼ 0.32	22.1	66.4	0.0064	0.0829	0.946	87.7
a_CDOM+NAP(410)	0.0060 ∼ 4.17	14.5	43.9	0.0218	0.628	0.988	81.8
a_CDOM+NAP(440)	0.0039 ∼ 2.75	14.4	40.1	0.0119	0.330	0.99	90.0
a_CDOM+NAP(490)	0.0012 ∼ 1.63	14.7	61.1	0.0077	0.0939	0.991	89.1

Compared Quantity Inversion/Observation	Dynamic Range (m⁻¹)	Median Relative Difference (%)	95% Relative Difference (%)	Median Absolute Difference (m⁻¹)	95% Absolute Difference (m⁻¹)	R	Percentage of the Point Inside 90% Confidence Interval
a_p+CDOM(412)	0.047 ∼ 1.01	13.3	32.8	0.0725	0.266	0.909	85
a_p+CDOM(440)	0.049 ∼ 0.83	11.7	27.9	0.0488	0.175	0.942	87.5
a_p+CDOM(488)	0.025 ∼ 0.49	13.1	27.6	0.0347	0.107	0.958	80
b_b_p(555)	0.001 ∼ 0.034	22.8	36.6	0.0026	0.0085	0.975	35.5
a_ph(676)	0.0041 ∼ 0.15	14.7	145	0.0124	0.0478	0.901	87.1
a_dg(412)/a_g(412)	0.029 ∼ 0.42	17.6	55.3	0.0573	0.208	0.934	90.3
a_dg(440)/a_g(440)	0.023 ∼ 0.42	17.8	48.2	0.0368	0.133	0.855	93.5
a_dg(488)/a_g(488)	0.0095 ∼ 0.14	27.9	63.4	0.0204	0.786	0.923	93.5

Variable	Units^a	Definition
a	m⁻¹	Total absorption coefficient: a_sw + a_p+CDOM
a_sw	m⁻¹	Ocean water absorption coefficient
a_p+CDOM	m⁻¹	Particulate (phytoplankton+ NAP) and CDOM absorption coefficient
a_CDOM+NAP	m⁻¹	CDOM + NAP absorption coefficient
a_ph	m⁻¹	Phytoplankton pigments absorption coefficient
b_b	m⁻¹	Total backscattering coefficient: b_b_sw + b_b_p
b_bsw	m⁻¹	Ocean water backscattering coefficient
b_b_p	m⁻¹	Particulate backscattering
S	nm⁻¹	Combined CDOM and NAP spectral slope
S_f		Phytoplankton size parameter
Y		Particulate backscattering spectral slope
a_pico	m²mg⁻¹	Phytoplankton absorption spectral shapes for the smallest cells
a_micro	m²mg⁻¹	Phytoplankton absorption spectral shapes for the largest cells
R_rs	sr⁻¹	Above-surface remote-sensing reflectance spectra
r_rs	sr⁻¹	Below-surface remote-sensing reflectance spectra
L_u(0⁻/0.66)	Wm⁻²sr⁻¹	Upwelling radiance just beneath or at 66 cm below the sea surface
E_d(0^−/+)	Wm⁻²	Downwelling irradiance just below or just above the sea surface.
t		Radiance transmittance of the surface
n		Real index of refraction of water
θ_s		Polar direction of the Sun’s refracted beam in water

Compared Quantity	Dynamic Range (m⁻¹)	Median Relative Difference (%)	95% Relative Difference (%)	Median Absolute Difference (m⁻¹)	95% Absolute Difference (m⁻¹)	R	Percentage of the Data Inside 90% Confidence Interval
a_p+CDOM(410)	0.0095 ∼ 4.53	8.95	37.9	0.0194	0.671	0.988	82.9
a_p+CDOM(440)	0.0095 ∼ 3.17	7.75	30.9	0.0138	0.438	0.989	83.1
a_p+CDOM(490)	0.0051 ∼ 1.92	6.78	21.8	0.0047	0.157	0.992	85.8
b_b_p(550)	0.00052 ∼ 0.13	7.55	15.9	0.0006	0.0082	0.993	56.8
a_ph(410)	0.0034 ∼ 0.42	20.5	63.4	0.0068	0.0977	0.911	84.8
a_ph(440)	0.0056 ∼ 0.42	19.8	61.2	0.0092	0.134	0.937	80.6
a_ph(490)	0.0031 ∼ 0.32	22.1	66.4	0.0064	0.0829	0.946	87.7
a_CDOM+NAP(410)	0.0060 ∼ 4.17	14.5	43.9	0.0218	0.628	0.988	81.8
a_CDOM+NAP(440)	0.0039 ∼ 2.75	14.4	40.1	0.0119	0.330	0.99	90.0
a_CDOM+NAP(490)	0.0012 ∼ 1.63	14.7	61.1	0.0077	0.0939	0.991	89.1

Compared Quantity Inversion/Observation	Dynamic Range (m⁻¹)	Median Relative Difference (%)	95% Relative Difference (%)	Median Absolute Difference (m⁻¹)	95% Absolute Difference (m⁻¹)	R	Percentage of the Point Inside 90% Confidence Interval
a_p+CDOM(412)	0.047 ∼ 1.01	13.3	32.8	0.0725	0.266	0.909	85
a_p+CDOM(440)	0.049 ∼ 0.83	11.7	27.9	0.0488	0.175	0.942	87.5
a_p+CDOM(488)	0.025 ∼ 0.49	13.1	27.6	0.0347	0.107	0.958	80
b_b_p(555)	0.001 ∼ 0.034	22.8	36.6	0.0026	0.0085	0.975	35.5
a_ph(676)	0.0041 ∼ 0.15	14.7	145	0.0124	0.0478	0.901	87.1
a_dg(412)/a_g(412)	0.029 ∼ 0.42	17.6	55.3	0.0573	0.208	0.934	90.3
a_dg(440)/a_g(440)	0.023 ∼ 0.42	17.8	48.2	0.0368	0.133	0.855	93.5
a_dg(488)/a_g(488)	0.0095 ∼ 0.14	27.9	63.4	0.0204	0.786	0.923	93.5

Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color

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Applied Optics