Algorithm to derive inherent optical properties from remote sensing reflectance in turbid and eutrophic lakes

Kun Xue; Emmanuel Boss; Ronghua Ma; Ming Shen

doi:10.1364/AO.58.008549

Applied Optics
Vol. 58,
Issue 31,
pp. 8549-8564
(2019)
•https://doi.org/10.1364/AO.58.008549

Algorithm to derive inherent optical properties from remote sensing reflectance in turbid and eutrophic lakes

Kun Xue, Emmanuel Boss, Ronghua Ma, and Ming Shen

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Kun Xue, Emmanuel Boss, Ronghua Ma, and Ming Shen, "Algorithm to derive inherent optical properties from remote sensing reflectance in turbid and eutrophic lakes," Appl. Opt. 58, 8549-8564 (2019)

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Abstract

Inherent optical properties play an important role in understanding the biogeochemical processes of lakes by providing proxies for a variety of biogeochemical quantities, including phytoplankton pigments. However, to date, it has been difficult to accurately derive the absorption coefficient of phytoplankton $[{a_{ph}}(\lambda )]$ in turbid and eutrophic waters from remote sensing. A large dataset of remote sensing of reflectance $[{R_{rs}}(\lambda )]$ and absorption coefficients was measured for samples collected from lakes in the middle and lower reaches of the Yangtze River and Huai River basin (MLYHR), China. In the process of scattering correction of spectrophotometric measurements, the particulate absorption coefficients $[{a_p}(\lambda )]$ were first assumed to have no absorption in the near-infrared (NIR) wavelength. This assumption was corrected by estimating the particulate absorption coefficients at 750 nm $[{a_p}({750})]$ from the concentrations of chlorophyll-a (Chla) and suspended particulate matter, which was added to the ${a_p}(\lambda )$ as a baseline. The resulting mean spectral mass-specific absorption coefficient of the nonalgal particles (NAPs) was consistent with previous work. A novel iterative IOP inversion model was then designed to retrieve the total nonwater absorption coefficients $[{a_{nw}}(\lambda )]$ and backscattering coefficients of particulates $[{b_{bp}}(\lambda )]$, ${a_{ph}}(\lambda )$, and ${a_{dg}}(\lambda )$ [absorption coefficients of NAP and colored dissolved organic matter (CDOM)] from ${R_{rs}}(\lambda )$ in turbid inland lakes. The proposed algorithm performed better than previously published models in deriving ${a_{nw}}(\lambda )$ and ${b_{bp}}(\lambda )$ in this region. The proposed algorithm performed well in estimating the ${a_{ph}}(\lambda )$ for wavelengths $ > {500}\;{\rm nm}$ for the calibration dataset [${\rm N} = {285}$, unbiased absolute percentage difference $({\rm UAPD}) = {55.22}\% $, root mean square error $({\rm RMSE}) = {0.44}\;{{\rm m}^{ - 1}}$] and for the validation dataset (${\rm N} = {57}$, ${\rm UAPD} = {56.17}\% $, ${\rm RMSE} = {0.71}\;{{\rm m}^{ - 1}}$). This algorithm was then applied to Sentinel-3A Ocean and Land Color Instrument (OLCI) satellite data, and was validated with field data. This study provides an example of how to use local data to devise an algorithm to obtain IOPs, and in particular, ${a_{ph}}(\lambda )$, using satellite ${R_{rs}}(\lambda )$ data in turbid inland waters.

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Supplementary Material (1)

Name	Description
Data File 1	Look up table of the tuned LS2 model in the manuscript. a1-a4 are parameters in Eq. C12, and bb1-bb3 are parameters in Eq. C13.

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Equations (45)

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Step	Property	Expression	Source
1	$r_{r s} (λ)$	$r_{r s} (λ) = R_{r s} (λ) / (0.52 + 1.7 R_{r s} (λ))$	literature-based [18]
2	$u (λ)$	$u (λ) = \frac{b_{b} (λ)}{a (λ) + b_{b} (λ)}$ $u (λ) = \frac{- g_{0} + {[{(g_{0})}^{2} + 4 g_{1} r_{r s} (λ)]}^{1 / 2}}{2 g_{1}}$ $g_{0} = 0.084$ , $g_{1} = 0.17$	literature-based [64]
3	$a (750)$	$a (750) = a_{w} (750) + a_{p} (750)$	--
4	$a_{p} (750)$	$a_{p} (750) = (1 - f r) \times {a_{d}}^{} (750) \times S P M$ $= (S P M - 0 .37 C h l a) \times {a_{d}}^{} (750)$ $a_{p}^{*} (750) = 0.014$ $C h l a = 22.68 [\frac{R_{r s} (709)}{R_{r s} (675)}]^{3.32}$ $S P M = 1417.6 \times R_{r s} (709)^{0.95}$	using local data and $a_{d}^{*} (750)$ from [40]
5	$b_{b p} (750)$	$b_{b p} (750) = \frac{u (750) \times a (750)}{1 - u (750)} - b_{b w} (750)$	definition of $u (λ)$
6	Y	$Y = 3.99 - 3.59 \exp [- 0.9 \frac{r_{r s} (443)}{r_{r s} (560)}]$	optimized using Ecolight simulation data
7	$b_{b} (λ)$	$b_{b} (λ) = b_{b p} (750) (\frac{750}{λ})^{Y} + b_{b w} (λ)$	assumption regarding shape of $b_{b p} (λ)$
8	$a_{n w} (λ)$	$a_{n w} (λ) = \frac{(1 - u (λ)) b_{b} (λ)}{u (λ)} - a_{w} (λ)$	definition of $u (λ)$

	UAPD (%)			$R M S E (m^{-} 1)$			$R^{2}$
Band (nm)	$a_{n w}$	$a_{p h}$	$a_{d g}$	$a_{n w}$	$a_{p h}$	$a_{d g}$	$a_{n w}$	$a_{p h}$	$a_{d g}$
400	31.00	81.99	41.35	3.11	3.08	3.10	0.62	0.42	0.35
412	31.39	75.92	44.25	2.88	2.83	2.96	0.58	0.42	0.31
443	33.80	72.51	51.20	2.42	2.21	2.60	0.49	0.42	0.20
490	38.19	78.87	48.93	1.83	1.49	1.68	0.40	0.42	0.20
510	39.78	76.86	47.61	1.62	1.23	1.27	0.37	0.43	0.24
560	44.46	65.89	50.04	1.15	0.64	0.76	0.27	0.45	0.27
620	36.28	44.84	46.07	0.90	0.74	0.49	0.40	0.50	0.31
665	28.31	42.16	41.66	0.78	0.77	0.38	0.48	0.50	0.37
673	27.06	45.26	40.31	0.86	0.90	0.37	0.49	0.51	0.37
681	26.91	45.03	37.41	0.84	0.88	0.34	0.49	0.50	0.42
709	34.74	54.47	34.63	0.30	0.15	0.29	0.50	0.47	0.45

Step	Property	Expression	Source
1	$r_{r s} (λ)$	$r_{r s} (λ) = R_{r s} (λ) / (0.52 + 1.7 R_{r s} (λ))$	literature-based [18]
2	$u (λ)$	$u (λ) = \frac{b_{b} (λ)}{a (λ) + b_{b} (λ)}$ $u (λ) = \frac{- g_{0} + {[{(g_{0})}^{2} + 4 g_{1} r_{r s} (λ)]}^{1 / 2}}{2 g_{1}}$ $g_{0} = 0.084$ , $g_{1} = 0.17$	literature-based [64]
3	$a (750)$	$a (750) = a_{w} (750) + a_{p} (750)$	--
4	$a_{p} (750)$	$a_{p} (750) = (1 - f r) \times {a_{d}}^{} (750) \times S P M$ $= (S P M - 0 .37 C h l a) \times {a_{d}}^{} (750)$ $a_{p}^{*} (750) = 0.014$ $C h l a = 22.68 [\frac{R_{r s} (709)}{R_{r s} (675)}]^{3.32}$ $S P M = 1417.6 \times R_{r s} (709)^{0.95}$	using local data and $a_{d}^{*} (750)$ from [40]
5	$b_{b p} (750)$	$b_{b p} (750) = \frac{u (750) \times a (750)}{1 - u (750)} - b_{b w} (750)$	definition of $u (λ)$
6	Y	$Y = 3.99 - 3.59 \exp [- 0.9 \frac{r_{r s} (443)}{r_{r s} (560)}]$	optimized using Ecolight simulation data
7	$b_{b} (λ)$	$b_{b} (λ) = b_{b p} (750) (\frac{750}{λ})^{Y} + b_{b w} (λ)$	assumption regarding shape of $b_{b p} (λ)$
8	$a_{n w} (λ)$	$a_{n w} (λ) = \frac{(1 - u (λ)) b_{b} (λ)}{u (λ)} - a_{w} (λ)$	definition of $u (λ)$

	UAPD (%)			$R M S E (m^{-} 1)$			$R^{2}$
Band (nm)	$a_{n w}$	$a_{p h}$	$a_{d g}$	$a_{n w}$	$a_{p h}$	$a_{d g}$	$a_{n w}$	$a_{p h}$	$a_{d g}$
400	31.00	81.99	41.35	3.11	3.08	3.10	0.62	0.42	0.35
412	31.39	75.92	44.25	2.88	2.83	2.96	0.58	0.42	0.31
443	33.80	72.51	51.20	2.42	2.21	2.60	0.49	0.42	0.20
490	38.19	78.87	48.93	1.83	1.49	1.68	0.40	0.42	0.20
510	39.78	76.86	47.61	1.62	1.23	1.27	0.37	0.43	0.24
560	44.46	65.89	50.04	1.15	0.64	0.76	0.27	0.45	0.27
620	36.28	44.84	46.07	0.90	0.74	0.49	0.40	0.50	0.31
665	28.31	42.16	41.66	0.78	0.77	0.38	0.48	0.50	0.37
673	27.06	45.26	40.31	0.86	0.90	0.37	0.49	0.51	0.37
681	26.91	45.03	37.41	0.84	0.88	0.34	0.49	0.50	0.42
709	34.74	54.47	34.63	0.30	0.15	0.29	0.50	0.47	0.45

Abstract

Supplementary Material (1)

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Tables (2)

Equations (45)

Applied Optics