Exploring the limits for sky and sun glint correction of hyperspectral above-surface reflectance observations

Philipp M. M. Groetsch; Robert Foster; Alexander Gilerson

doi:10.1364/AO.385853

Applied Optics
Vol. 59,
Issue 9,
pp. 2942-2954
(2020)
•https://doi.org/10.1364/AO.385853

Exploring the limits for sky and sun glint correction of hyperspectral above-surface reflectance observations

Philipp M. M. Groetsch, Robert Foster, and Alexander Gilerson

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Philipp M. M. Groetsch, Robert Foster, and Alexander Gilerson, "Exploring the limits for sky and sun glint correction of hyperspectral above-surface reflectance observations," Appl. Opt. 59, 2942-2954 (2020)

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- Atmospheric and Oceanic Optics
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About this Article
History
- Original Manuscript: December 13, 2019
- Revised Manuscript: February 13, 2020
- Manuscript Accepted: February 14, 2020
- Published: March 20, 2020

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Abstract

Above-surface radiance observations of water need to be corrected for reflections on the surface to derive reflectance. The three-component glint model (3C) [Opt. Express 25, A742 (2017) [CrossRef] ] was developed to spectrally resolve contributions of sky and sun glint to the surface-reflected radiance signal $ {L_r}(\lambda ) $, and for observations recorded at high wind speed and with fixed-position measurement geometries that frequently lead to significant sun glint contributions. Performance and limitations of 3C are assessed for all relevant wind speeds, clear sky atmospheric conditions, illumination/viewing geometries, and sun glint contamination levels. For this purpose, a comprehensive set of $ {L_r}(\lambda ) $ spectra was simulated with a spectrally resolved sky radiance distribution model and Cox–Munk wave slope statistics. Reflectances were also derived from an extensive four-year data set of continuous above-surface hyperspectral observations from the Long Island Sound Coastal Observatory, allowing to corroborate 3C processing results from simulations and measurements with regard to sky and sun glint contributions. Simulation- and measurement-derived $ {L_r}(\lambda ) $ independently indicate that spectral dependencies of the sky light distribution and sun glint contributions may not be neglected for observations recorded at wind speeds exceeding $ 4\, m/s $, even for sun glint-minimizing measurement geometries (Sun-sensor azimuth angle $ \Delta \phi = 90 {-} {135° } $). These findings are in accordance with current measurement protocols for satellite calibration/validation activities. In addition, it is demonstrated that 3C is able to reliably derive water reflectance for wind speeds up to 8 m/s and $ \Delta \phi { \gt 20° } $.

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Parameter	Acronym, [unit]	Start (min/max)
Concentration of chlorophyll- $a$	Chla, $[{m g m}^{- 3}]$	7.1 (0.01/100)
Concentration of suspended particulate matter	SPM, $[{g m}^{- 3}]$	2.9 (0/100)
Colored dissolved organic matter absorption at 440 nm	CDOM, $[m^{- 1}]$	0.3 (0.1/1)
Fluorescence radiance (685 nm)	$L_{f l} (665 n m), [^{1}]$	1 (0/3)
Air–water interface reflectance factor	$ρ, [-]$	$ρ_{f}^{*}$ ( $0 / ρ_{f}$ )
Direct reflectance factor	$ρ_{d d}, [-]$	0.001 (0/4)
Diffuse reflectance factor	$ρ_{d s}, [-]$	0.01 (-0.01/1)
Ångström exponent	$α, [-]$	1 (0/5)
Aerosol optical thickness (550 nm)	$β, [-]$	0.05 (0/1)
Wavelength	$λ, [n m]$
Sun zenith angle	$θ_{s u n}$ , [ $°$ ]
Viewing zenith angle	$θ_{v}$ , [ $°$ ]
Relative azimuth angle to Sun	$Δ ϕ$ , [ $°$ ]
Wind speed	$v_{w}, [m s^{- 1}]$
Sky radiance	$L_{s} (λ), [^{1}]$
Total radiance	$L_{t} (λ), [^{1}]$
Water-leaving radiance	$L_{w} (λ), [^{1}]$
Water surface-reflected radiance	$L_{r} (λ), [^{1}]$
Downwelling vector irradiance	$E_{d} (λ), [^{2}]$
Remote-sensing reflectance $L_{w} (λ) / E_{d} (λ)$	$R_{r s} (λ), [s r^{- 1}]$
Sky reflectance $L_{s} (λ) / E_{d} (λ)$	$R_{s k y} (λ), [s r^{- 1}]$
Air–water interface reflectance $L_{r} (λ) / E_{d} (λ)$	$R_{r e f l} (λ), [s r^{- 1}]$
Fresnel reflectance factor (unpolarized)	$ρ_{f}, [-]$
Residual-sum-of-squares	$ϵ, [s r^{- 1}]$
Root-mean-square deviation	$R M S D, [s r^{- 1}]$
Normalized RMSD	$N R M S D, [%]$
Percent difference	$ψ, [%]$

Flag	Expression	All	L0	L1	L2	L3
Few measurements	# Measurements $< 10$	0.21	–	–	–	–
High $θ_{s u n}$	$θ_{s u n} > 80^{\circ}$	19.21	2.38	–	–	–
Low $Δ ϕ$	$Δ ϕ < 20 °$	18.24	13.13	–	–	–
Sub-optimal $Δ ϕ$	$Δ ϕ < 90 °$ or $Δ ϕ > 135 °$	82.98	78.23	72.85	70.49	–
Negative $L_{s} (λ)$	$L_{s} (λ) < 0$	7.92	–	–	–	–
Negative $L_{t} (λ)$	$L_{t} (λ) < 0$	18.82	–	–	–	–
Negative $E_{d} (λ)$	$E_{d} (λ) < 0$	6.42	–	–	–	–
Low light	$E_{d} (^{max}) < 0.1 W / m^{2} n m$	24.66	–	–	–	–
Clouds present	$R_{s k y} (750 n m) > 0.1 s r^{- 1}$	66.24	55.92	41.03	–	–
High variability $L_{s} (λ)$	$c_{v} (L_{s}) > 5 %$	35.22	30.99	21.71	–	–
High variability $E_{d} (λ)$	$c_{v} (E_{d}) > 5 %$	21.07	15.25	11.25	–	–
Sun in $L_{s} (λ)$	$R_{s k y} (750 n m) > 2 / π$	10.63	4.00	–	–	–
High variability $R_{r s} (O_{2})$	$σ (R_{r s} (O_{2})) > 0.0003 s r^{- 1}$	59.06	43.14	27.32	–	–
High variability $R_{r s} (λ)$	$c_{v} (R_{r s}) > 10 %$	28.69	14.86	–	–	–
High variability Chla	$c_{v} (C h l a) > 25 %$	42.38	28.72	–	–	–
High variability SPM	$c_{v} (S P M) > 25 %$	18.22	4.49	–	–	–
High variability CDOM	$c_{v} (C D O M) > 25 %$	26.22	12.73	–	–	–
High RMSD	$R M S D > 0.002 s r^{- 1}$ (*)	12.86	–	–	–	–
Negative $R_{r s} (λ)$	P5( $R_{r s} (< 750 n m)$ ) < 0	11.74	–	–	–	–
	Cycles passed, [#]	17294	11842	7149	3158	932
	Cycles passed, [%]	100	68.5	41.3	18.3	5.4

Parameter	Acronym, [unit]	Start (min/max)
Concentration of chlorophyll- $a$	Chla, $[{m g m}^{- 3}]$	7.1 (0.01/100)
Concentration of suspended particulate matter	SPM, $[{g m}^{- 3}]$	2.9 (0/100)
Colored dissolved organic matter absorption at 440 nm	CDOM, $[m^{- 1}]$	0.3 (0.1/1)
Fluorescence radiance (685 nm)	$L_{f l} (665 n m), [^{1}]$	1 (0/3)
Air–water interface reflectance factor	$ρ, [-]$	$ρ_{f}^{*}$ ( $0 / ρ_{f}$ )
Direct reflectance factor	$ρ_{d d}, [-]$	0.001 (0/4)
Diffuse reflectance factor	$ρ_{d s}, [-]$	0.01 (-0.01/1)
Ångström exponent	$α, [-]$	1 (0/5)
Aerosol optical thickness (550 nm)	$β, [-]$	0.05 (0/1)
Wavelength	$λ, [n m]$
Sun zenith angle	$θ_{s u n}$ , [ $°$ ]
Viewing zenith angle	$θ_{v}$ , [ $°$ ]
Relative azimuth angle to Sun	$Δ ϕ$ , [ $°$ ]
Wind speed	$v_{w}, [m s^{- 1}]$
Sky radiance	$L_{s} (λ), [^{1}]$
Total radiance	$L_{t} (λ), [^{1}]$
Water-leaving radiance	$L_{w} (λ), [^{1}]$
Water surface-reflected radiance	$L_{r} (λ), [^{1}]$
Downwelling vector irradiance	$E_{d} (λ), [^{2}]$
Remote-sensing reflectance $L_{w} (λ) / E_{d} (λ)$	$R_{r s} (λ), [s r^{- 1}]$
Sky reflectance $L_{s} (λ) / E_{d} (λ)$	$R_{s k y} (λ), [s r^{- 1}]$
Air–water interface reflectance $L_{r} (λ) / E_{d} (λ)$	$R_{r e f l} (λ), [s r^{- 1}]$
Fresnel reflectance factor (unpolarized)	$ρ_{f}, [-]$
Residual-sum-of-squares	$ϵ, [s r^{- 1}]$
Root-mean-square deviation	$R M S D, [s r^{- 1}]$
Normalized RMSD	$N R M S D, [%]$
Percent difference	$ψ, [%]$

Flag	Expression	All	L0	L1	L2	L3
Few measurements	# Measurements $< 10$	0.21	–	–	–	–
High $θ_{s u n}$	$θ_{s u n} > 80^{\circ}$	19.21	2.38	–	–	–
Low $Δ ϕ$	$Δ ϕ < 20 °$	18.24	13.13	–	–	–
Sub-optimal $Δ ϕ$	$Δ ϕ < 90 °$ or $Δ ϕ > 135 °$	82.98	78.23	72.85	70.49	–
Negative $L_{s} (λ)$	$L_{s} (λ) < 0$	7.92	–	–	–	–
Negative $L_{t} (λ)$	$L_{t} (λ) < 0$	18.82	–	–	–	–
Negative $E_{d} (λ)$	$E_{d} (λ) < 0$	6.42	–	–	–	–
Low light	$E_{d} (^{max}) < 0.1 W / m^{2} n m$	24.66	–	–	–	–
Clouds present	$R_{s k y} (750 n m) > 0.1 s r^{- 1}$	66.24	55.92	41.03	–	–
High variability $L_{s} (λ)$	$c_{v} (L_{s}) > 5 %$	35.22	30.99	21.71	–	–
High variability $E_{d} (λ)$	$c_{v} (E_{d}) > 5 %$	21.07	15.25	11.25	–	–
Sun in $L_{s} (λ)$	$R_{s k y} (750 n m) > 2 / π$	10.63	4.00	–	–	–
High variability $R_{r s} (O_{2})$	$σ (R_{r s} (O_{2})) > 0.0003 s r^{- 1}$	59.06	43.14	27.32	–	–
High variability $R_{r s} (λ)$	$c_{v} (R_{r s}) > 10 %$	28.69	14.86	–	–	–
High variability Chla	$c_{v} (C h l a) > 25 %$	42.38	28.72	–	–	–
High variability SPM	$c_{v} (S P M) > 25 %$	18.22	4.49	–	–	–
High variability CDOM	$c_{v} (C D O M) > 25 %$	26.22	12.73	–	–	–
High RMSD	$R M S D > 0.002 s r^{- 1}$ (*)	12.86	–	–	–	–
Negative $R_{r s} (λ)$	P5( $R_{r s} (< 750 n m)$ ) < 0	11.74	–	–	–	–
	Cycles passed, [#]	17294	11842	7149	3158	932
	Cycles passed, [%]	100	68.5	41.3	18.3	5.4

Abstract

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Tables (2)

Equations (9)

Applied Optics